Properties

Label 441.4.e.f.361.1
Level $441$
Weight $4$
Character 441.361
Analytic conductor $26.020$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 441.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(26.0198423125\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 147)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 441.361
Dual form 441.4.e.f.226.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(3.50000 - 6.06218i) q^{4} +(-6.00000 - 10.3923i) q^{5} -15.0000 q^{8} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(3.50000 - 6.06218i) q^{4} +(-6.00000 - 10.3923i) q^{5} -15.0000 q^{8} +(-6.00000 + 10.3923i) q^{10} +(10.0000 - 17.3205i) q^{11} +84.0000 q^{13} +(-20.5000 - 35.5070i) q^{16} +(48.0000 - 83.1384i) q^{17} +(6.00000 + 10.3923i) q^{19} -84.0000 q^{20} -20.0000 q^{22} +(-88.0000 - 152.420i) q^{23} +(-9.50000 + 16.4545i) q^{25} +(-42.0000 - 72.7461i) q^{26} -58.0000 q^{29} +(-132.000 + 228.631i) q^{31} +(-80.5000 + 139.430i) q^{32} -96.0000 q^{34} +(-129.000 - 223.435i) q^{37} +(6.00000 - 10.3923i) q^{38} +(90.0000 + 155.885i) q^{40} +156.000 q^{43} +(-70.0000 - 121.244i) q^{44} +(-88.0000 + 152.420i) q^{46} +(204.000 + 353.338i) q^{47} +19.0000 q^{50} +(294.000 - 509.223i) q^{52} +(-361.000 + 625.270i) q^{53} -240.000 q^{55} +(29.0000 + 50.2295i) q^{58} +(-246.000 + 426.084i) q^{59} +(-246.000 - 426.084i) q^{61} +264.000 q^{62} -167.000 q^{64} +(-504.000 - 872.954i) q^{65} +(-206.000 + 356.802i) q^{67} +(-336.000 - 581.969i) q^{68} -296.000 q^{71} +(120.000 - 207.846i) q^{73} +(-129.000 + 223.435i) q^{74} +84.0000 q^{76} +(-388.000 - 672.036i) q^{79} +(-246.000 + 426.084i) q^{80} +924.000 q^{83} -1152.00 q^{85} +(-78.0000 - 135.100i) q^{86} +(-150.000 + 259.808i) q^{88} +(372.000 + 644.323i) q^{89} -1232.00 q^{92} +(204.000 - 353.338i) q^{94} +(72.0000 - 124.708i) q^{95} +168.000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{2} + 7q^{4} - 12q^{5} - 30q^{8} + O(q^{10}) \) \( 2q - q^{2} + 7q^{4} - 12q^{5} - 30q^{8} - 12q^{10} + 20q^{11} + 168q^{13} - 41q^{16} + 96q^{17} + 12q^{19} - 168q^{20} - 40q^{22} - 176q^{23} - 19q^{25} - 84q^{26} - 116q^{29} - 264q^{31} - 161q^{32} - 192q^{34} - 258q^{37} + 12q^{38} + 180q^{40} + 312q^{43} - 140q^{44} - 176q^{46} + 408q^{47} + 38q^{50} + 588q^{52} - 722q^{53} - 480q^{55} + 58q^{58} - 492q^{59} - 492q^{61} + 528q^{62} - 334q^{64} - 1008q^{65} - 412q^{67} - 672q^{68} - 592q^{71} + 240q^{73} - 258q^{74} + 168q^{76} - 776q^{79} - 492q^{80} + 1848q^{83} - 2304q^{85} - 156q^{86} - 300q^{88} + 744q^{89} - 2464q^{92} + 408q^{94} + 144q^{95} + 336q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.176777 0.306186i 0.763998 0.645219i \(-0.223234\pi\)
−0.940775 + 0.339032i \(0.889900\pi\)
\(3\) 0 0
\(4\) 3.50000 6.06218i 0.437500 0.757772i
\(5\) −6.00000 10.3923i −0.536656 0.929516i −0.999081 0.0428575i \(-0.986354\pi\)
0.462425 0.886658i \(-0.346979\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −15.0000 −0.662913
\(9\) 0 0
\(10\) −6.00000 + 10.3923i −0.189737 + 0.328634i
\(11\) 10.0000 17.3205i 0.274101 0.474757i −0.695807 0.718229i \(-0.744953\pi\)
0.969908 + 0.243472i \(0.0782863\pi\)
\(12\) 0 0
\(13\) 84.0000 1.79211 0.896054 0.443945i \(-0.146421\pi\)
0.896054 + 0.443945i \(0.146421\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −20.5000 35.5070i −0.320312 0.554798i
\(17\) 48.0000 83.1384i 0.684806 1.18612i −0.288691 0.957422i \(-0.593220\pi\)
0.973498 0.228697i \(-0.0734466\pi\)
\(18\) 0 0
\(19\) 6.00000 + 10.3923i 0.0724471 + 0.125482i 0.899973 0.435945i \(-0.143586\pi\)
−0.827526 + 0.561427i \(0.810252\pi\)
\(20\) −84.0000 −0.939149
\(21\) 0 0
\(22\) −20.0000 −0.193819
\(23\) −88.0000 152.420i −0.797794 1.38182i −0.921050 0.389445i \(-0.872667\pi\)
0.123255 0.992375i \(-0.460667\pi\)
\(24\) 0 0
\(25\) −9.50000 + 16.4545i −0.0760000 + 0.131636i
\(26\) −42.0000 72.7461i −0.316803 0.548719i
\(27\) 0 0
\(28\) 0 0
\(29\) −58.0000 −0.371391 −0.185695 0.982607i \(-0.559454\pi\)
−0.185695 + 0.982607i \(0.559454\pi\)
\(30\) 0 0
\(31\) −132.000 + 228.631i −0.764771 + 1.32462i 0.175597 + 0.984462i \(0.443815\pi\)
−0.940368 + 0.340160i \(0.889519\pi\)
\(32\) −80.5000 + 139.430i −0.444704 + 0.770250i
\(33\) 0 0
\(34\) −96.0000 −0.484231
\(35\) 0 0
\(36\) 0 0
\(37\) −129.000 223.435i −0.573175 0.992768i −0.996237 0.0866674i \(-0.972378\pi\)
0.423062 0.906101i \(-0.360955\pi\)
\(38\) 6.00000 10.3923i 0.0256139 0.0443646i
\(39\) 0 0
\(40\) 90.0000 + 155.885i 0.355756 + 0.616188i
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 0 0
\(43\) 156.000 0.553251 0.276625 0.960978i \(-0.410784\pi\)
0.276625 + 0.960978i \(0.410784\pi\)
\(44\) −70.0000 121.244i −0.239839 0.415413i
\(45\) 0 0
\(46\) −88.0000 + 152.420i −0.282063 + 0.488547i
\(47\) 204.000 + 353.338i 0.633116 + 1.09659i 0.986911 + 0.161266i \(0.0515578\pi\)
−0.353795 + 0.935323i \(0.615109\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 19.0000 0.0537401
\(51\) 0 0
\(52\) 294.000 509.223i 0.784047 1.35801i
\(53\) −361.000 + 625.270i −0.935607 + 1.62052i −0.162059 + 0.986781i \(0.551813\pi\)
−0.773548 + 0.633737i \(0.781520\pi\)
\(54\) 0 0
\(55\) −240.000 −0.588393
\(56\) 0 0
\(57\) 0 0
\(58\) 29.0000 + 50.2295i 0.0656532 + 0.113715i
\(59\) −246.000 + 426.084i −0.542822 + 0.940195i 0.455919 + 0.890021i \(0.349311\pi\)
−0.998741 + 0.0501732i \(0.984023\pi\)
\(60\) 0 0
\(61\) −246.000 426.084i −0.516345 0.894337i −0.999820 0.0189781i \(-0.993959\pi\)
0.483474 0.875358i \(-0.339375\pi\)
\(62\) 264.000 0.540775
\(63\) 0 0
\(64\) −167.000 −0.326172
\(65\) −504.000 872.954i −0.961746 1.66579i
\(66\) 0 0
\(67\) −206.000 + 356.802i −0.375625 + 0.650602i −0.990420 0.138085i \(-0.955905\pi\)
0.614795 + 0.788687i \(0.289239\pi\)
\(68\) −336.000 581.969i −0.599206 1.03785i
\(69\) 0 0
\(70\) 0 0
\(71\) −296.000 −0.494771 −0.247385 0.968917i \(-0.579571\pi\)
−0.247385 + 0.968917i \(0.579571\pi\)
\(72\) 0 0
\(73\) 120.000 207.846i 0.192396 0.333240i −0.753647 0.657279i \(-0.771707\pi\)
0.946044 + 0.324038i \(0.105041\pi\)
\(74\) −129.000 + 223.435i −0.202648 + 0.350996i
\(75\) 0 0
\(76\) 84.0000 0.126782
\(77\) 0 0
\(78\) 0 0
\(79\) −388.000 672.036i −0.552575 0.957088i −0.998088 0.0618122i \(-0.980312\pi\)
0.445513 0.895275i \(-0.353021\pi\)
\(80\) −246.000 + 426.084i −0.343795 + 0.595471i
\(81\) 0 0
\(82\) 0 0
\(83\) 924.000 1.22195 0.610977 0.791648i \(-0.290777\pi\)
0.610977 + 0.791648i \(0.290777\pi\)
\(84\) 0 0
\(85\) −1152.00 −1.47002
\(86\) −78.0000 135.100i −0.0978018 0.169398i
\(87\) 0 0
\(88\) −150.000 + 259.808i −0.181705 + 0.314723i
\(89\) 372.000 + 644.323i 0.443055 + 0.767394i 0.997914 0.0645500i \(-0.0205612\pi\)
−0.554859 + 0.831944i \(0.687228\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −1232.00 −1.39614
\(93\) 0 0
\(94\) 204.000 353.338i 0.223840 0.387703i
\(95\) 72.0000 124.708i 0.0777584 0.134681i
\(96\) 0 0
\(97\) 168.000 0.175854 0.0879269 0.996127i \(-0.471976\pi\)
0.0879269 + 0.996127i \(0.471976\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 66.5000 + 115.181i 0.0665000 + 0.115181i
\(101\) 762.000 1319.82i 0.750711 1.30027i −0.196767 0.980450i \(-0.563044\pi\)
0.947478 0.319820i \(-0.103622\pi\)
\(102\) 0 0
\(103\) −204.000 353.338i −0.195153 0.338014i 0.751798 0.659394i \(-0.229187\pi\)
−0.946951 + 0.321379i \(0.895854\pi\)
\(104\) −1260.00 −1.18801
\(105\) 0 0
\(106\) 722.000 0.661574
\(107\) −410.000 710.141i −0.370432 0.641607i 0.619200 0.785233i \(-0.287457\pi\)
−0.989632 + 0.143627i \(0.954124\pi\)
\(108\) 0 0
\(109\) 459.000 795.011i 0.403342 0.698608i −0.590785 0.806829i \(-0.701182\pi\)
0.994127 + 0.108221i \(0.0345153\pi\)
\(110\) 120.000 + 207.846i 0.104014 + 0.180158i
\(111\) 0 0
\(112\) 0 0
\(113\) 110.000 0.0915746 0.0457873 0.998951i \(-0.485420\pi\)
0.0457873 + 0.998951i \(0.485420\pi\)
\(114\) 0 0
\(115\) −1056.00 + 1829.05i −0.856283 + 1.48313i
\(116\) −203.000 + 351.606i −0.162483 + 0.281430i
\(117\) 0 0
\(118\) 492.000 0.383833
\(119\) 0 0
\(120\) 0 0
\(121\) 465.500 + 806.270i 0.349737 + 0.605762i
\(122\) −246.000 + 426.084i −0.182556 + 0.316196i
\(123\) 0 0
\(124\) 924.000 + 1600.41i 0.669175 + 1.15904i
\(125\) −1272.00 −0.910169
\(126\) 0 0
\(127\) 16.0000 0.0111793 0.00558965 0.999984i \(-0.498221\pi\)
0.00558965 + 0.999984i \(0.498221\pi\)
\(128\) 727.500 + 1260.07i 0.502363 + 0.870119i
\(129\) 0 0
\(130\) −504.000 + 872.954i −0.340029 + 0.588947i
\(131\) −846.000 1465.31i −0.564239 0.977291i −0.997120 0.0758401i \(-0.975836\pi\)
0.432881 0.901451i \(-0.357497\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 412.000 0.265607
\(135\) 0 0
\(136\) −720.000 + 1247.08i −0.453967 + 0.786294i
\(137\) 563.000 975.145i 0.351097 0.608118i −0.635345 0.772229i \(-0.719142\pi\)
0.986442 + 0.164110i \(0.0524753\pi\)
\(138\) 0 0
\(139\) −1092.00 −0.666347 −0.333173 0.942866i \(-0.608119\pi\)
−0.333173 + 0.942866i \(0.608119\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 148.000 + 256.344i 0.0874640 + 0.151492i
\(143\) 840.000 1454.92i 0.491219 0.850816i
\(144\) 0 0
\(145\) 348.000 + 602.754i 0.199309 + 0.345214i
\(146\) −240.000 −0.136045
\(147\) 0 0
\(148\) −1806.00 −1.00306
\(149\) 535.000 + 926.647i 0.294154 + 0.509489i 0.974788 0.223134i \(-0.0716289\pi\)
−0.680634 + 0.732624i \(0.738296\pi\)
\(150\) 0 0
\(151\) 60.0000 103.923i 0.0323360 0.0560075i −0.849405 0.527742i \(-0.823039\pi\)
0.881741 + 0.471735i \(0.156372\pi\)
\(152\) −90.0000 155.885i −0.0480261 0.0831836i
\(153\) 0 0
\(154\) 0 0
\(155\) 3168.00 1.64168
\(156\) 0 0
\(157\) 918.000 1590.02i 0.466652 0.808265i −0.532622 0.846353i \(-0.678793\pi\)
0.999274 + 0.0380879i \(0.0121267\pi\)
\(158\) −388.000 + 672.036i −0.195365 + 0.338382i
\(159\) 0 0
\(160\) 1932.00 0.954613
\(161\) 0 0
\(162\) 0 0
\(163\) −458.000 793.279i −0.220082 0.381193i 0.734751 0.678337i \(-0.237299\pi\)
−0.954833 + 0.297144i \(0.903966\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) −462.000 800.207i −0.216013 0.374145i
\(167\) 504.000 0.233537 0.116769 0.993159i \(-0.462746\pi\)
0.116769 + 0.993159i \(0.462746\pi\)
\(168\) 0 0
\(169\) 4859.00 2.21165
\(170\) 576.000 + 997.661i 0.259866 + 0.450101i
\(171\) 0 0
\(172\) 546.000 945.700i 0.242047 0.419238i
\(173\) 918.000 + 1590.02i 0.403435 + 0.698770i 0.994138 0.108119i \(-0.0344828\pi\)
−0.590703 + 0.806889i \(0.701149\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −820.000 −0.351192
\(177\) 0 0
\(178\) 372.000 644.323i 0.156644 0.271315i
\(179\) 1186.00 2054.21i 0.495228 0.857760i −0.504757 0.863262i \(-0.668418\pi\)
0.999985 + 0.00550156i \(0.00175121\pi\)
\(180\) 0 0
\(181\) 1092.00 0.448440 0.224220 0.974539i \(-0.428017\pi\)
0.224220 + 0.974539i \(0.428017\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 1320.00 + 2286.31i 0.528868 + 0.916026i
\(185\) −1548.00 + 2681.21i −0.615196 + 1.06555i
\(186\) 0 0
\(187\) −960.000 1662.77i −0.375413 0.650234i
\(188\) 2856.00 1.10795
\(189\) 0 0
\(190\) −144.000 −0.0549835
\(191\) 1256.00 + 2175.46i 0.475817 + 0.824139i 0.999616 0.0277030i \(-0.00881927\pi\)
−0.523800 + 0.851842i \(0.675486\pi\)
\(192\) 0 0
\(193\) 1215.00 2104.44i 0.453148 0.784876i −0.545431 0.838155i \(-0.683634\pi\)
0.998580 + 0.0532797i \(0.0169675\pi\)
\(194\) −84.0000 145.492i −0.0310868 0.0538440i
\(195\) 0 0
\(196\) 0 0
\(197\) 1762.00 0.637245 0.318623 0.947882i \(-0.396780\pi\)
0.318623 + 0.947882i \(0.396780\pi\)
\(198\) 0 0
\(199\) 1548.00 2681.21i 0.551431 0.955107i −0.446740 0.894664i \(-0.647415\pi\)
0.998172 0.0604433i \(-0.0192514\pi\)
\(200\) 142.500 246.817i 0.0503814 0.0872631i
\(201\) 0 0
\(202\) −1524.00 −0.530833
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) −204.000 + 353.338i −0.0689969 + 0.119506i
\(207\) 0 0
\(208\) −1722.00 2982.59i −0.574035 0.994257i
\(209\) 240.000 0.0794313
\(210\) 0 0
\(211\) 156.000 0.0508980 0.0254490 0.999676i \(-0.491898\pi\)
0.0254490 + 0.999676i \(0.491898\pi\)
\(212\) 2527.00 + 4376.89i 0.818656 + 1.41795i
\(213\) 0 0
\(214\) −410.000 + 710.141i −0.130967 + 0.226842i
\(215\) −936.000 1621.20i −0.296905 0.514255i
\(216\) 0 0
\(217\) 0 0
\(218\) −918.000 −0.285206
\(219\) 0 0
\(220\) −840.000 + 1454.92i −0.257422 + 0.445868i
\(221\) 4032.00 6983.63i 1.22725 2.12565i
\(222\) 0 0
\(223\) −5040.00 −1.51347 −0.756734 0.653723i \(-0.773206\pi\)
−0.756734 + 0.653723i \(0.773206\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −55.0000 95.2628i −0.0161883 0.0280389i
\(227\) −1086.00 + 1881.01i −0.317535 + 0.549986i −0.979973 0.199130i \(-0.936188\pi\)
0.662438 + 0.749116i \(0.269522\pi\)
\(228\) 0 0
\(229\) 1350.00 + 2338.27i 0.389566 + 0.674747i 0.992391 0.123126i \(-0.0392918\pi\)
−0.602826 + 0.797873i \(0.705959\pi\)
\(230\) 2112.00 0.605483
\(231\) 0 0
\(232\) 870.000 0.246200
\(233\) −1901.00 3292.63i −0.534501 0.925782i −0.999187 0.0403071i \(-0.987166\pi\)
0.464687 0.885475i \(-0.346167\pi\)
\(234\) 0 0
\(235\) 2448.00 4240.06i 0.679532 1.17698i
\(236\) 1722.00 + 2982.59i 0.474969 + 0.822670i
\(237\) 0 0
\(238\) 0 0
\(239\) 4408.00 1.19301 0.596506 0.802609i \(-0.296555\pi\)
0.596506 + 0.802609i \(0.296555\pi\)
\(240\) 0 0
\(241\) 1548.00 2681.21i 0.413757 0.716648i −0.581540 0.813518i \(-0.697550\pi\)
0.995297 + 0.0968696i \(0.0308830\pi\)
\(242\) 465.500 806.270i 0.123651 0.214169i
\(243\) 0 0
\(244\) −3444.00 −0.903605
\(245\) 0 0
\(246\) 0 0
\(247\) 504.000 + 872.954i 0.129833 + 0.224877i
\(248\) 1980.00 3429.46i 0.506976 0.878109i
\(249\) 0 0
\(250\) 636.000 + 1101.58i 0.160897 + 0.278681i
\(251\) −924.000 −0.232360 −0.116180 0.993228i \(-0.537065\pi\)
−0.116180 + 0.993228i \(0.537065\pi\)
\(252\) 0 0
\(253\) −3520.00 −0.874706
\(254\) −8.00000 13.8564i −0.00197624 0.00342295i
\(255\) 0 0
\(256\) 59.5000 103.057i 0.0145264 0.0251604i
\(257\) 1380.00 + 2390.23i 0.334950 + 0.580150i 0.983475 0.181043i \(-0.0579474\pi\)
−0.648526 + 0.761193i \(0.724614\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −7056.00 −1.68306
\(261\) 0 0
\(262\) −846.000 + 1465.31i −0.199489 + 0.345525i
\(263\) −1180.00 + 2043.82i −0.276661 + 0.479191i −0.970553 0.240888i \(-0.922561\pi\)
0.693892 + 0.720079i \(0.255895\pi\)
\(264\) 0 0
\(265\) 8664.00 2.00840
\(266\) 0 0
\(267\) 0 0
\(268\) 1442.00 + 2497.62i 0.328672 + 0.569277i
\(269\) −2010.00 + 3481.42i −0.455583 + 0.789093i −0.998722 0.0505501i \(-0.983903\pi\)
0.543138 + 0.839643i \(0.317236\pi\)
\(270\) 0 0
\(271\) 2400.00 + 4156.92i 0.537969 + 0.931790i 0.999013 + 0.0444126i \(0.0141416\pi\)
−0.461044 + 0.887377i \(0.652525\pi\)
\(272\) −3936.00 −0.877408
\(273\) 0 0
\(274\) −1126.00 −0.248263
\(275\) 190.000 + 329.090i 0.0416634 + 0.0721631i
\(276\) 0 0
\(277\) −3223.00 + 5582.40i −0.699102 + 1.21088i 0.269676 + 0.962951i \(0.413083\pi\)
−0.968778 + 0.247929i \(0.920250\pi\)
\(278\) 546.000 + 945.700i 0.117795 + 0.204026i
\(279\) 0 0
\(280\) 0 0
\(281\) 2602.00 0.552393 0.276196 0.961101i \(-0.410926\pi\)
0.276196 + 0.961101i \(0.410926\pi\)
\(282\) 0 0
\(283\) −3450.00 + 5975.58i −0.724669 + 1.25516i 0.234442 + 0.972130i \(0.424674\pi\)
−0.959110 + 0.283033i \(0.908660\pi\)
\(284\) −1036.00 + 1794.40i −0.216462 + 0.374924i
\(285\) 0 0
\(286\) −1680.00 −0.347344
\(287\) 0 0
\(288\) 0 0
\(289\) −2151.50 3726.51i −0.437920 0.758499i
\(290\) 348.000 602.754i 0.0704664 0.122051i
\(291\) 0 0
\(292\) −840.000 1454.92i −0.168347 0.291585i
\(293\) −4452.00 −0.887674 −0.443837 0.896107i \(-0.646383\pi\)
−0.443837 + 0.896107i \(0.646383\pi\)
\(294\) 0 0
\(295\) 5904.00 1.16523
\(296\) 1935.00 + 3351.52i 0.379965 + 0.658118i
\(297\) 0 0
\(298\) 535.000 926.647i 0.103999 0.180132i
\(299\) −7392.00 12803.3i −1.42973 2.47637i
\(300\) 0 0
\(301\) 0 0
\(302\) −120.000 −0.0228650
\(303\) 0 0
\(304\) 246.000 426.084i 0.0464114 0.0803869i
\(305\) −2952.00 + 5113.01i −0.554200 + 0.959903i
\(306\) 0 0
\(307\) 2436.00 0.452866 0.226433 0.974027i \(-0.427294\pi\)
0.226433 + 0.974027i \(0.427294\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −1584.00 2743.57i −0.290210 0.502659i
\(311\) 3744.00 6484.80i 0.682646 1.18238i −0.291525 0.956563i \(-0.594163\pi\)
0.974171 0.225814i \(-0.0725040\pi\)
\(312\) 0 0
\(313\) −876.000 1517.28i −0.158193 0.273999i 0.776024 0.630703i \(-0.217234\pi\)
−0.934217 + 0.356705i \(0.883900\pi\)
\(314\) −1836.00 −0.329973
\(315\) 0 0
\(316\) −5432.00 −0.967006
\(317\) −781.000 1352.73i −0.138376 0.239675i 0.788506 0.615027i \(-0.210855\pi\)
−0.926882 + 0.375352i \(0.877522\pi\)
\(318\) 0 0
\(319\) −580.000 + 1004.59i −0.101799 + 0.176320i
\(320\) 1002.00 + 1735.51i 0.175042 + 0.303182i
\(321\) 0 0
\(322\) 0 0
\(323\) 1152.00 0.198449
\(324\) 0 0
\(325\) −798.000 + 1382.18i −0.136200 + 0.235906i
\(326\) −458.000 + 793.279i −0.0778107 + 0.134772i
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 3546.00 + 6141.85i 0.588839 + 1.01990i 0.994385 + 0.105825i \(0.0337482\pi\)
−0.405546 + 0.914075i \(0.632918\pi\)
\(332\) 3234.00 5601.45i 0.534605 0.925963i
\(333\) 0 0
\(334\) −252.000 436.477i −0.0412839 0.0715058i
\(335\) 4944.00 0.806327
\(336\) 0 0
\(337\) 366.000 0.0591611 0.0295805 0.999562i \(-0.490583\pi\)
0.0295805 + 0.999562i \(0.490583\pi\)
\(338\) −2429.50 4208.02i −0.390969 0.677177i
\(339\) 0 0
\(340\) −4032.00 + 6983.63i −0.643135 + 1.11394i
\(341\) 2640.00 + 4572.61i 0.419249 + 0.726161i
\(342\) 0 0
\(343\) 0 0
\(344\) −2340.00 −0.366757
\(345\) 0 0
\(346\) 918.000 1590.02i 0.142636 0.247052i
\(347\) −3182.00 + 5511.39i −0.492273 + 0.852642i −0.999960 0.00889958i \(-0.997167\pi\)
0.507687 + 0.861541i \(0.330500\pi\)
\(348\) 0 0
\(349\) 10500.0 1.61046 0.805232 0.592960i \(-0.202041\pi\)
0.805232 + 0.592960i \(0.202041\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 1610.00 + 2788.60i 0.243788 + 0.422253i
\(353\) −204.000 + 353.338i −0.0307587 + 0.0532756i −0.880995 0.473126i \(-0.843126\pi\)
0.850236 + 0.526401i \(0.176459\pi\)
\(354\) 0 0
\(355\) 1776.00 + 3076.12i 0.265522 + 0.459898i
\(356\) 5208.00 0.775347
\(357\) 0 0
\(358\) −2372.00 −0.350179
\(359\) −5968.00 10336.9i −0.877379 1.51966i −0.854207 0.519933i \(-0.825957\pi\)
−0.0231719 0.999731i \(-0.507376\pi\)
\(360\) 0 0
\(361\) 3357.50 5815.36i 0.489503 0.847844i
\(362\) −546.000 945.700i −0.0792738 0.137306i
\(363\) 0 0
\(364\) 0 0
\(365\) −2880.00 −0.413003
\(366\) 0 0
\(367\) −1224.00 + 2120.03i −0.174093 + 0.301539i −0.939847 0.341595i \(-0.889033\pi\)
0.765754 + 0.643134i \(0.222366\pi\)
\(368\) −3608.00 + 6249.24i −0.511087 + 0.885229i
\(369\) 0 0
\(370\) 3096.00 0.435009
\(371\) 0 0
\(372\) 0 0
\(373\) −5687.00 9850.17i −0.789442 1.36735i −0.926309 0.376764i \(-0.877037\pi\)
0.136868 0.990589i \(-0.456296\pi\)
\(374\) −960.000 + 1662.77i −0.132728 + 0.229892i
\(375\) 0 0
\(376\) −3060.00 5300.08i −0.419701 0.726943i
\(377\) −4872.00 −0.665572
\(378\) 0 0
\(379\) −5892.00 −0.798553 −0.399277 0.916830i \(-0.630739\pi\)
−0.399277 + 0.916830i \(0.630739\pi\)
\(380\) −504.000 872.954i −0.0680386 0.117846i
\(381\) 0 0
\(382\) 1256.00 2175.46i 0.168227 0.291377i
\(383\) 5244.00 + 9082.87i 0.699624 + 1.21178i 0.968597 + 0.248636i \(0.0799823\pi\)
−0.268973 + 0.963148i \(0.586684\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −2430.00 −0.320424
\(387\) 0 0
\(388\) 588.000 1018.45i 0.0769360 0.133257i
\(389\) 2257.00 3909.24i 0.294176 0.509528i −0.680617 0.732639i \(-0.738288\pi\)
0.974793 + 0.223112i \(0.0716215\pi\)
\(390\) 0 0
\(391\) −16896.0 −2.18534
\(392\) 0 0
\(393\) 0 0
\(394\) −881.000 1525.94i −0.112650 0.195116i
\(395\) −4656.00 + 8064.43i −0.593086 + 1.02725i
\(396\) 0 0
\(397\) −3018.00 5227.33i −0.381534 0.660837i 0.609748 0.792596i \(-0.291271\pi\)
−0.991282 + 0.131759i \(0.957937\pi\)
\(398\) −3096.00 −0.389921
\(399\) 0 0
\(400\) 779.000 0.0973750
\(401\) −3385.00 5862.99i −0.421543 0.730134i 0.574547 0.818471i \(-0.305178\pi\)
−0.996091 + 0.0883370i \(0.971845\pi\)
\(402\) 0 0
\(403\) −11088.0 + 19205.0i −1.37055 + 2.37387i
\(404\) −5334.00 9238.76i −0.656872 1.13774i
\(405\) 0 0
\(406\) 0 0
\(407\) −5160.00 −0.628432
\(408\) 0 0
\(409\) 6252.00 10828.8i 0.755847 1.30917i −0.189105 0.981957i \(-0.560559\pi\)
0.944952 0.327209i \(-0.106108\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −2856.00 −0.341517
\(413\) 0 0
\(414\) 0 0
\(415\) −5544.00 9602.49i −0.655769 1.13583i
\(416\) −6762.00 + 11712.1i −0.796958 + 1.38037i
\(417\) 0 0
\(418\) −120.000 207.846i −0.0140416 0.0243208i
\(419\) 9492.00 1.10672 0.553359 0.832943i \(-0.313346\pi\)
0.553359 + 0.832943i \(0.313346\pi\)
\(420\) 0 0
\(421\) 5182.00 0.599894 0.299947 0.953956i \(-0.403031\pi\)
0.299947 + 0.953956i \(0.403031\pi\)
\(422\) −78.0000 135.100i −0.00899758 0.0155843i
\(423\) 0 0
\(424\) 5415.00 9379.06i 0.620226 1.07426i
\(425\) 912.000 + 1579.63i 0.104091 + 0.180290i
\(426\) 0 0
\(427\) 0 0
\(428\) −5740.00 −0.648256
\(429\) 0 0
\(430\) −936.000 + 1621.20i −0.104972 + 0.181817i
\(431\) −2860.00 + 4953.67i −0.319632 + 0.553619i −0.980411 0.196962i \(-0.936893\pi\)
0.660779 + 0.750580i \(0.270226\pi\)
\(432\) 0 0
\(433\) −13608.0 −1.51030 −0.755149 0.655554i \(-0.772435\pi\)
−0.755149 + 0.655554i \(0.772435\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −3213.00 5565.08i −0.352924 0.611282i
\(437\) 1056.00 1829.05i 0.115596 0.200218i
\(438\) 0 0
\(439\) 6432.00 + 11140.6i 0.699277 + 1.21118i 0.968717 + 0.248166i \(0.0798279\pi\)
−0.269440 + 0.963017i \(0.586839\pi\)
\(440\) 3600.00 0.390053
\(441\) 0 0
\(442\) −8064.00 −0.867795
\(443\) −6626.00 11476.6i −0.710634 1.23085i −0.964620 0.263646i \(-0.915075\pi\)
0.253986 0.967208i \(-0.418258\pi\)
\(444\) 0 0
\(445\) 4464.00 7731.87i 0.475537 0.823654i
\(446\) 2520.00 + 4364.77i 0.267546 + 0.463403i
\(447\) 0 0
\(448\) 0 0
\(449\) −226.000 −0.0237541 −0.0118771 0.999929i \(-0.503781\pi\)
−0.0118771 + 0.999929i \(0.503781\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 385.000 666.840i 0.0400639 0.0693927i
\(453\) 0 0
\(454\) 2172.00 0.224531
\(455\) 0 0
\(456\) 0 0
\(457\) 5667.00 + 9815.53i 0.580068 + 1.00471i 0.995471 + 0.0950696i \(0.0303074\pi\)
−0.415403 + 0.909638i \(0.636359\pi\)
\(458\) 1350.00 2338.27i 0.137732 0.238559i
\(459\) 0 0
\(460\) 7392.00 + 12803.3i 0.749247 + 1.29773i
\(461\) −1596.00 −0.161243 −0.0806216 0.996745i \(-0.525691\pi\)
−0.0806216 + 0.996745i \(0.525691\pi\)
\(462\) 0 0
\(463\) 12728.0 1.27758 0.638791 0.769380i \(-0.279435\pi\)
0.638791 + 0.769380i \(0.279435\pi\)
\(464\) 1189.00 + 2059.41i 0.118961 + 0.206047i
\(465\) 0 0
\(466\) −1901.00 + 3292.63i −0.188975 + 0.327313i
\(467\) 1506.00 + 2608.47i 0.149228 + 0.258470i 0.930942 0.365166i \(-0.118988\pi\)
−0.781715 + 0.623636i \(0.785655\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −4896.00 −0.480501
\(471\) 0 0
\(472\) 3690.00 6391.27i 0.359843 0.623267i
\(473\) 1560.00 2702.00i 0.151647 0.262660i
\(474\) 0 0
\(475\) −228.000 −0.0220239
\(476\) 0 0
\(477\) 0 0
\(478\) −2204.00 3817.44i −0.210897 0.365284i
\(479\) 2148.00 3720.45i 0.204895 0.354888i −0.745204 0.666836i \(-0.767648\pi\)
0.950099 + 0.311948i \(0.100981\pi\)
\(480\) 0 0
\(481\) −10836.0 18768.5i −1.02719 1.77915i
\(482\) −3096.00 −0.292570
\(483\) 0 0
\(484\) 6517.00 0.612040
\(485\) −1008.00 1745.91i −0.0943730 0.163459i
\(486\) 0 0
\(487\) 4092.00 7087.55i 0.380752 0.659482i −0.610418 0.792079i \(-0.708998\pi\)
0.991170 + 0.132598i \(0.0423318\pi\)
\(488\) 3690.00 + 6391.27i 0.342292 + 0.592867i
\(489\) 0 0
\(490\) 0 0
\(491\) 12164.0 1.11803 0.559016 0.829157i \(-0.311179\pi\)
0.559016 + 0.829157i \(0.311179\pi\)
\(492\) 0 0
\(493\) −2784.00 + 4822.03i −0.254331 + 0.440514i
\(494\) 504.000 872.954i 0.0459029 0.0795062i
\(495\) 0 0
\(496\) 10824.0 0.979863
\(497\) 0 0
\(498\) 0 0
\(499\) −486.000 841.777i −0.0435999 0.0755172i 0.843402 0.537283i \(-0.180549\pi\)
−0.887002 + 0.461766i \(0.847216\pi\)
\(500\) −4452.00 + 7711.09i −0.398199 + 0.689701i
\(501\) 0 0
\(502\) 462.000 + 800.207i 0.0410758 + 0.0711454i
\(503\) 7728.00 0.685039 0.342519 0.939511i \(-0.388720\pi\)
0.342519 + 0.939511i \(0.388720\pi\)
\(504\) 0 0
\(505\) −18288.0 −1.61150
\(506\) 1760.00 + 3048.41i 0.154628 + 0.267823i
\(507\) 0 0
\(508\) 56.0000 96.9948i 0.00489094 0.00847136i
\(509\) −5802.00 10049.4i −0.505244 0.875108i −0.999982 0.00606572i \(-0.998069\pi\)
0.494738 0.869042i \(-0.335264\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 11521.0 0.994455
\(513\) 0 0
\(514\) 1380.00 2390.23i 0.118423 0.205114i
\(515\) −2448.00 + 4240.06i −0.209460 + 0.362795i
\(516\) 0 0
\(517\) 8160.00 0.694152
\(518\) 0 0
\(519\) 0 0
\(520\) 7560.00 + 13094.3i 0.637554 + 1.10428i
\(521\) 5424.00 9394.64i 0.456103 0.789994i −0.542648 0.839960i \(-0.682578\pi\)
0.998751 + 0.0499665i \(0.0159115\pi\)
\(522\) 0 0
\(523\) −9066.00 15702.8i −0.757989 1.31288i −0.943874 0.330305i \(-0.892848\pi\)
0.185885 0.982572i \(-0.440485\pi\)
\(524\) −11844.0 −0.987419
\(525\) 0 0
\(526\) 2360.00 0.195629
\(527\) 12672.0 + 21948.5i 1.04744 + 1.81422i
\(528\) 0 0
\(529\) −9404.50 + 16289.1i −0.772951 + 1.33879i
\(530\) −4332.00 7503.24i −0.355038 0.614944i
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) −4920.00 + 8521.69i −0.397589 + 0.688644i
\(536\) 3090.00 5352.04i 0.249007 0.431293i
\(537\) 0 0
\(538\) 4020.00 0.322146
\(539\) 0 0
\(540\) 0 0
\(541\) −3475.00 6018.88i −0.276159 0.478321i 0.694268 0.719717i \(-0.255728\pi\)
−0.970427 + 0.241395i \(0.922395\pi\)
\(542\) 2400.00 4156.92i 0.190201 0.329437i
\(543\) 0 0
\(544\) 7728.00 + 13385.3i 0.609072 + 1.05494i
\(545\) −11016.0 −0.865823
\(546\) 0 0
\(547\) 17012.0 1.32976 0.664882 0.746949i \(-0.268482\pi\)
0.664882 + 0.746949i \(0.268482\pi\)
\(548\) −3941.00 6826.01i −0.307210 0.532104i
\(549\) 0 0
\(550\) 190.000 329.090i 0.0147302 0.0255135i
\(551\) −348.000 602.754i −0.0269062 0.0466028i
\(552\) 0 0
\(553\) 0 0
\(554\) 6446.00 0.494340
\(555\) 0 0
\(556\) −3822.00 + 6619.90i −0.291527 + 0.504939i
\(557\) 1963.00 3400.02i 0.149327 0.258641i −0.781652 0.623715i \(-0.785623\pi\)
0.930979 + 0.365073i \(0.118956\pi\)
\(558\) 0 0
\(559\) 13104.0 0.991485
\(560\) 0 0
\(561\) 0 0
\(562\) −1301.00 2253.40i −0.0976501 0.169135i
\(563\) 9414.00 16305.5i 0.704712 1.22060i −0.262084 0.965045i \(-0.584410\pi\)
0.966795 0.255552i \(-0.0822571\pi\)
\(564\) 0 0
\(565\) −660.000 1143.15i −0.0491441 0.0851201i
\(566\) 6900.00 0.512418
\(567\) 0 0
\(568\) 4440.00 0.327990
\(569\) 5995.00 + 10383.6i 0.441693 + 0.765035i 0.997815 0.0660655i \(-0.0210446\pi\)
−0.556122 + 0.831101i \(0.687711\pi\)
\(570\) 0 0
\(571\) 7858.00 13610.5i 0.575914 0.997513i −0.420027 0.907511i \(-0.637980\pi\)
0.995942 0.0900014i \(-0.0286871\pi\)
\(572\) −5880.00 10184.5i −0.429817 0.744464i
\(573\) 0 0
\(574\) 0 0
\(575\) 3344.00 0.242529
\(576\) 0 0
\(577\) −6936.00 + 12013.5i −0.500432 + 0.866774i 0.499568 + 0.866275i \(0.333492\pi\)
−1.00000 0.000499291i \(0.999841\pi\)
\(578\) −2151.50 + 3726.51i −0.154828 + 0.268170i
\(579\) 0 0
\(580\) 4872.00 0.348791
\(581\) 0 0
\(582\) 0 0
\(583\) 7220.00 + 12505.4i 0.512902 + 0.888372i
\(584\) −1800.00 + 3117.69i −0.127542 + 0.220909i
\(585\) 0 0
\(586\) 2226.00 + 3855.55i 0.156920 + 0.271794i
\(587\) 8820.00 0.620171 0.310085 0.950709i \(-0.399642\pi\)
0.310085 + 0.950709i \(0.399642\pi\)
\(588\) 0 0
\(589\) −3168.00 −0.221622
\(590\) −2952.00 5113.01i −0.205986 0.356779i
\(591\) 0 0
\(592\) −5289.00 + 9160.82i −0.367190 + 0.635992i
\(593\) 8436.00 + 14611.6i 0.584191 + 1.01185i 0.994976 + 0.100116i \(0.0319213\pi\)
−0.410785 + 0.911732i \(0.634745\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 7490.00 0.514769
\(597\) 0 0
\(598\) −7392.00 + 12803.3i −0.505487 + 0.875530i
\(599\) −3028.00 + 5244.65i −0.206545 + 0.357747i −0.950624 0.310345i \(-0.899555\pi\)
0.744079 + 0.668092i \(0.232889\pi\)
\(600\) 0 0
\(601\) −10752.0 −0.729756 −0.364878 0.931055i \(-0.618889\pi\)
−0.364878 + 0.931055i \(0.618889\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −420.000 727.461i −0.0282940 0.0490066i
\(605\) 5586.00 9675.24i 0.375377 0.650172i
\(606\) 0 0
\(607\) 10128.0 + 17542.2i 0.677237 + 1.17301i 0.975810 + 0.218622i \(0.0701561\pi\)
−0.298573 + 0.954387i \(0.596511\pi\)
\(608\) −1932.00 −0.128870
\(609\) 0 0
\(610\) 5904.00 0.391879
\(611\) 17136.0 + 29680.4i 1.13461 + 1.96521i
\(612\) 0 0
\(613\) 14095.0 24413.3i 0.928698 1.60855i 0.143194 0.989695i \(-0.454263\pi\)
0.785504 0.618857i \(-0.212404\pi\)
\(614\) −1218.00 2109.64i −0.0800562 0.138661i
\(615\) 0 0
\(616\) 0 0
\(617\) −29318.0 −1.91296 −0.956482 0.291793i \(-0.905748\pi\)
−0.956482 + 0.291793i \(0.905748\pi\)
\(618\) 0 0
\(619\) 12174.0 21086.0i 0.790492 1.36917i −0.135171 0.990822i \(-0.543158\pi\)
0.925663 0.378350i \(-0.123508\pi\)
\(620\) 11088.0 19205.0i 0.718234 1.24402i
\(621\) 0 0
\(622\) −7488.00 −0.482703
\(623\) 0 0
\(624\) 0 0
\(625\) 8819.50 + 15275.8i 0.564448 + 0.977653i
\(626\) −876.000 + 1517.28i −0.0559297 + 0.0968731i
\(627\) 0 0
\(628\) −6426.00 11130.2i −0.408321 0.707232i
\(629\) −24768.0 −1.57006
\(630\) 0 0
\(631\) −25184.0 −1.58884 −0.794421 0.607368i \(-0.792226\pi\)
−0.794421 + 0.607368i \(0.792226\pi\)
\(632\) 5820.00 + 10080.5i 0.366309 + 0.634465i
\(633\) 0 0
\(634\) −781.000 + 1352.73i −0.0489235 + 0.0847379i
\(635\) −96.0000 166.277i −0.00599944 0.0103913i
\(636\) 0 0
\(637\) 0 0
\(638\) 1160.00 0.0719825
\(639\) 0 0
\(640\) 8730.00 15120.8i 0.539193 0.933910i
\(641\) 16159.0 27988.2i 0.995698 1.72460i 0.417600 0.908631i \(-0.362871\pi\)
0.578097 0.815968i \(-0.303795\pi\)
\(642\) 0 0
\(643\) 3948.00 0.242137 0.121068 0.992644i \(-0.461368\pi\)
0.121068 + 0.992644i \(0.461368\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −576.000 997.661i −0.0350811 0.0607623i
\(647\) −6924.00 + 11992.7i −0.420727 + 0.728721i −0.996011 0.0892331i \(-0.971558\pi\)
0.575284 + 0.817954i \(0.304892\pi\)
\(648\) 0 0
\(649\) 4920.00 + 8521.69i 0.297576 + 0.515417i
\(650\) 1596.00 0.0963081
\(651\) 0 0
\(652\) −6412.00 −0.385143
\(653\) −1579.00 2734.91i −0.0946264 0.163898i 0.814826 0.579705i \(-0.196832\pi\)
−0.909453 + 0.415808i \(0.863499\pi\)
\(654\) 0 0
\(655\) −10152.0 + 17583.8i −0.605605 + 1.04894i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 24596.0 1.45391 0.726953 0.686687i \(-0.240936\pi\)
0.726953 + 0.686687i \(0.240936\pi\)
\(660\) 0 0
\(661\) −7734.00 + 13395.7i −0.455095 + 0.788248i −0.998694 0.0510977i \(-0.983728\pi\)
0.543599 + 0.839345i \(0.317061\pi\)
\(662\) 3546.00 6141.85i 0.208186 0.360589i
\(663\) 0 0
\(664\) −13860.0 −0.810049
\(665\) 0 0
\(666\) 0 0
\(667\) 5104.00 + 8840.39i 0.296293 + 0.513195i
\(668\) 1764.00 3055.34i 0.102172 0.176968i
\(669\) 0 0
\(670\) −2472.00 4281.63i −0.142540 0.246886i
\(671\) −9840.00 −0.566124
\(672\) 0 0
\(673\) 13470.0 0.771516 0.385758 0.922600i \(-0.373940\pi\)
0.385758 + 0.922600i \(0.373940\pi\)
\(674\) −183.000 316.965i −0.0104583 0.0181143i
\(675\) 0 0
\(676\) 17006.5 29456.1i 0.967598 1.67593i
\(677\) 4782.00 + 8282.67i 0.271473 + 0.470205i 0.969239 0.246121i \(-0.0791559\pi\)
−0.697766 + 0.716326i \(0.745823\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 17280.0 0.974497
\(681\) 0 0
\(682\) 2640.00 4572.61i 0.148227 0.256737i
\(683\) 6926.00 11996.2i 0.388018 0.672066i −0.604165 0.796859i \(-0.706493\pi\)
0.992183 + 0.124793i \(0.0398266\pi\)
\(684\) 0 0
\(685\) −13512.0 −0.753674
\(686\) 0 0
\(687\) 0 0
\(688\) −3198.00 5539.10i −0.177213 0.306942i
\(689\) −30324.0 + 52522.7i −1.67671 + 2.90414i
\(690\) 0 0
\(691\) −162.000 280.592i −0.00891863 0.0154475i 0.861532 0.507704i \(-0.169506\pi\)
−0.870450 + 0.492256i \(0.836172\pi\)
\(692\) 12852.0 0.706011
\(693\) 0 0
\(694\) 6364.00 0.348090
\(695\) 6552.00 + 11348.4i 0.357599 + 0.619380i
\(696\) 0 0
\(697\) 0 0
\(698\) −5250.00 9093.27i −0.284693 0.493102i
\(699\) 0 0
\(700\) 0 0
\(701\) −24922.0 −1.34278 −0.671392 0.741103i \(-0.734303\pi\)
−0.671392 + 0.741103i \(0.734303\pi\)
\(702\) 0 0
\(703\) 1548.00 2681.21i 0.0830497 0.143846i
\(704\) −1670.00 + 2892.52i −0.0894041 + 0.154852i
\(705\) 0 0
\(706\) 408.000 0.0217497
\(707\) 0 0
\(708\) 0 0
\(709\) 8943.00 + 15489.7i 0.473711 + 0.820492i 0.999547 0.0300939i \(-0.00958064\pi\)
−0.525836 + 0.850586i \(0.676247\pi\)
\(710\) 1776.00 3076.12i 0.0938762 0.162598i
\(711\) 0 0
\(712\) −5580.00 9664.84i −0.293707 0.508715i
\(713\) 46464.0 2.44052
\(714\) 0 0
\(715\) −20160.0 −1.05446
\(716\) −8302.00 14379.5i −0.433324 0.750540i
\(717\) 0 0
\(718\) −5968.00 + 10336.9i −0.310200 + 0.537283i
\(719\) 3396.00 + 5882.04i 0.176147 + 0.305095i 0.940557 0.339635i \(-0.110303\pi\)
−0.764411 + 0.644729i \(0.776970\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −6715.00 −0.346131
\(723\) 0 0
\(724\) 3822.00 6619.90i 0.196193 0.339816i
\(725\) 551.000 954.360i 0.0282257 0.0488883i
\(726\) 0 0
\(727\) −1512.00 −0.0771348 −0.0385674 0.999256i \(-0.512279\pi\)
−0.0385674 + 0.999256i \(0.512279\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 1440.00 + 2494.15i 0.0730093 + 0.126456i
\(731\) 7488.00 12969.6i 0.378870 0.656221i
\(732\) 0 0
\(733\) −5622.00 9737.59i −0.283292 0.490677i 0.688901 0.724855i \(-0.258093\pi\)
−0.972194 + 0.234178i \(0.924760\pi\)
\(734\) 2448.00 0.123103
\(735\) 0 0
\(736\) 28336.0 1.41913
\(737\) 4120.00 + 7136.05i 0.205919 + 0.356662i
\(738\) 0 0
\(739\) 998.000 1728.59i 0.0496780 0.0860448i −0.840117 0.542405i \(-0.817514\pi\)
0.889795 + 0.456360i \(0.150847\pi\)
\(740\) 10836.0 + 18768.5i 0.538296 + 0.932357i
\(741\) 0 0
\(742\) 0 0
\(743\) 656.000 0.0323907 0.0161954 0.999869i \(-0.494845\pi\)
0.0161954 + 0.999869i \(0.494845\pi\)
\(744\) 0 0
\(745\) 6420.00 11119.8i 0.315719 0.546841i
\(746\) −5687.00 + 9850.17i −0.279110 + 0.483432i
\(747\) 0 0
\(748\) −13440.0 −0.656972
\(749\) 0 0
\(750\) 0 0
\(751\) −528.000 914.523i −0.0256551 0.0444360i 0.852913 0.522053i \(-0.174834\pi\)
−0.878568 + 0.477617i \(0.841501\pi\)
\(752\) 8364.00 14486.9i 0.405590 0.702503i
\(753\) 0 0
\(754\) 2436.00 + 4219.28i 0.117658 + 0.203789i
\(755\) −1440.00 −0.0694132
\(756\) 0 0
\(757\) −18702.0 −0.897934 −0.448967 0.893548i \(-0.648208\pi\)
−0.448967 + 0.893548i \(0.648208\pi\)
\(758\) 2946.00 + 5102.62i 0.141166 + 0.244506i
\(759\) 0 0
\(760\) −1080.00 + 1870.61i −0.0515470 + 0.0892820i
\(761\) −8952.00 15505.3i −0.426425 0.738590i 0.570127 0.821557i \(-0.306894\pi\)
−0.996552 + 0.0829661i \(0.973561\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 17584.0 0.832679
\(765\) 0 0
\(766\) 5244.00 9082.87i 0.247354 0.428430i
\(767\) −20664.0 + 35791.1i −0.972795 + 1.68493i
\(768\) 0 0
\(769\) 7560.00 0.354513 0.177257 0.984165i \(-0.443278\pi\)
0.177257 + 0.984165i \(0.443278\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −8505.00 14731.1i −0.396505 0.686766i
\(773\) 7146.00 12377.2i 0.332502 0.575910i −0.650500 0.759506i \(-0.725441\pi\)
0.983002 + 0.183596i \(0.0587740\pi\)
\(774\) 0 0
\(775\) −2508.00 4343.98i −0.116245 0.201343i
\(776\) −2520.00 −0.116576
\(777\) 0 0
\(778\) −4514.00 −0.208014
\(779\) 0 0
\(780\) 0 0
\(781\) −2960.00 + 5126.87i −0.135617 + 0.234896i
\(782\) 8448.00 + 14632.4i 0.386317 + 0.669121i
\(783\) 0 0
\(784\) 0 0
\(785\) −22032.0 −1.00173
\(786\) 0 0
\(787\) 13182.0 22831.9i 0.597062 1.03414i −0.396191 0.918168i \(-0.629668\pi\)
0.993252 0.115973i \(-0.0369986\pi\)
\(788\) 6167.00 10681.6i 0.278795 0.482887i
\(789\) 0 0
\(790\) 9312.00 0.419375