Properties

Label 252.4.x.a.41.16
Level $252$
Weight $4$
Character 252.41
Analytic conductor $14.868$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 252.x (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.8684813214\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 41.16
Character \(\chi\) \(=\) 252.41
Dual form 252.4.x.a.209.16

$q$-expansion

\(f(q)\) \(=\) \(q+(2.29905 - 4.65987i) q^{3} +(6.03570 - 10.4541i) q^{5} +(2.10370 - 18.4004i) q^{7} +(-16.4287 - 21.4265i) q^{9} +O(q^{10})\) \(q+(2.29905 - 4.65987i) q^{3} +(6.03570 - 10.4541i) q^{5} +(2.10370 - 18.4004i) q^{7} +(-16.4287 - 21.4265i) q^{9} +(0.00221312 - 0.00127775i) q^{11} +(6.06841 + 3.50360i) q^{13} +(-34.8386 - 52.1602i) q^{15} -28.3143 q^{17} +49.1973i q^{19} +(-80.9069 - 52.1064i) q^{21} +(44.4689 + 25.6741i) q^{23} +(-10.3594 - 17.9431i) q^{25} +(-137.615 + 27.2951i) q^{27} +(97.9469 - 56.5497i) q^{29} +(-28.4271 - 16.4124i) q^{31} +(-0.000866054 - 0.0132505i) q^{33} +(-179.663 - 133.052i) q^{35} -101.961 q^{37} +(30.2779 - 20.2230i) q^{39} +(-11.2449 + 19.4767i) q^{41} +(-227.203 - 393.527i) q^{43} +(-323.155 + 42.4243i) q^{45} +(231.260 + 400.554i) q^{47} +(-334.149 - 77.4179i) q^{49} +(-65.0960 + 131.941i) q^{51} -567.586i q^{53} -0.0308484i q^{55} +(229.253 + 113.107i) q^{57} +(-145.654 + 252.280i) q^{59} +(592.003 - 341.793i) q^{61} +(-428.818 + 257.220i) q^{63} +(73.2542 - 42.2933i) q^{65} +(269.780 - 467.273i) q^{67} +(221.874 - 148.193i) q^{69} +307.517i q^{71} -495.192i q^{73} +(-107.429 + 7.02162i) q^{75} +(-0.0188553 - 0.0434103i) q^{77} +(-324.865 - 562.683i) q^{79} +(-189.193 + 704.022i) q^{81} +(565.581 + 979.615i) q^{83} +(-170.897 + 296.002i) q^{85} +(-38.3293 - 586.430i) q^{87} +130.217 q^{89} +(77.2337 - 104.291i) q^{91} +(-141.835 + 94.7337i) q^{93} +(514.315 + 296.940i) q^{95} +(1260.41 - 727.696i) q^{97} +(-0.0637365 - 0.0264277i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 6q^{7} + 60q^{9} + O(q^{10}) \) \( 48q + 6q^{7} + 60q^{9} - 12q^{11} + 192q^{15} - 72q^{21} - 408q^{23} - 600q^{25} - 84q^{29} + 336q^{37} + 36q^{39} + 84q^{43} + 318q^{49} - 1812q^{51} - 852q^{57} - 564q^{63} + 2964q^{65} - 588q^{67} + 2400q^{77} + 204q^{79} + 1980q^{81} - 360q^{85} - 1080q^{91} + 2496q^{93} + 300q^{95} - 4968q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(1\)

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 0
\(3\) 2.29905 4.65987i 0.442452 0.896792i
\(4\) 0 0
\(5\) 6.03570 10.4541i 0.539850 0.935047i −0.459062 0.888404i \(-0.651814\pi\)
0.998912 0.0466430i \(-0.0148523\pi\)
\(6\) 0 0
\(7\) 2.10370 18.4004i 0.113589 0.993528i
\(8\) 0 0
\(9\) −16.4287 21.4265i −0.608472 0.793575i
\(10\) 0 0
\(11\) 0.00221312 0.00127775i 6.06619e−5 3.50232e-5i −0.499970 0.866043i \(-0.666656\pi\)
0.500030 + 0.866008i \(0.333322\pi\)
\(12\) 0 0
\(13\) 6.06841 + 3.50360i 0.129467 + 0.0747479i 0.563335 0.826229i \(-0.309518\pi\)
−0.433868 + 0.900977i \(0.642851\pi\)
\(14\) 0 0
\(15\) −34.8386 52.1602i −0.599685 0.897847i
\(16\) 0 0
\(17\) −28.3143 −0.403955 −0.201977 0.979390i \(-0.564737\pi\)
−0.201977 + 0.979390i \(0.564737\pi\)
\(18\) 0 0
\(19\) 49.1973i 0.594033i 0.954872 + 0.297016i \(0.0959916\pi\)
−0.954872 + 0.297016i \(0.904008\pi\)
\(20\) 0 0
\(21\) −80.9069 52.1064i −0.840730 0.541455i
\(22\) 0 0
\(23\) 44.4689 + 25.6741i 0.403148 + 0.232758i 0.687841 0.725861i \(-0.258558\pi\)
−0.284693 + 0.958619i \(0.591892\pi\)
\(24\) 0 0
\(25\) −10.3594 17.9431i −0.0828756 0.143545i
\(26\) 0 0
\(27\) −137.615 + 27.2951i −0.980892 + 0.194554i
\(28\) 0 0
\(29\) 97.9469 56.5497i 0.627182 0.362104i −0.152478 0.988307i \(-0.548725\pi\)
0.779660 + 0.626203i \(0.215392\pi\)
\(30\) 0 0
\(31\) −28.4271 16.4124i −0.164699 0.0950889i 0.415385 0.909646i \(-0.363647\pi\)
−0.580084 + 0.814557i \(0.696980\pi\)
\(32\) 0 0
\(33\) −0.000866054 0.0132505i −4.56850e−6 6.98972e-5i
\(34\) 0 0
\(35\) −179.663 133.052i −0.867674 0.642567i
\(36\) 0 0
\(37\) −101.961 −0.453034 −0.226517 0.974007i \(-0.572734\pi\)
−0.226517 + 0.974007i \(0.572734\pi\)
\(38\) 0 0
\(39\) 30.2779 20.2230i 0.124316 0.0830328i
\(40\) 0 0
\(41\) −11.2449 + 19.4767i −0.0428331 + 0.0741891i −0.886647 0.462447i \(-0.846972\pi\)
0.843814 + 0.536636i \(0.180305\pi\)
\(42\) 0 0
\(43\) −227.203 393.527i −0.805771 1.39564i −0.915769 0.401705i \(-0.868418\pi\)
0.109998 0.993932i \(-0.464916\pi\)
\(44\) 0 0
\(45\) −323.155 + 42.4243i −1.07051 + 0.140539i
\(46\) 0 0
\(47\) 231.260 + 400.554i 0.717717 + 1.24312i 0.961902 + 0.273394i \(0.0881464\pi\)
−0.244185 + 0.969729i \(0.578520\pi\)
\(48\) 0 0
\(49\) −334.149 77.4179i −0.974195 0.225708i
\(50\) 0 0
\(51\) −65.0960 + 131.941i −0.178731 + 0.362263i
\(52\) 0 0
\(53\) 567.586i 1.47102i −0.677515 0.735509i \(-0.736943\pi\)
0.677515 0.735509i \(-0.263057\pi\)
\(54\) 0 0
\(55\) 0.0308484i 7.56290e-5i
\(56\) 0 0
\(57\) 229.253 + 113.107i 0.532724 + 0.262831i
\(58\) 0 0
\(59\) −145.654 + 252.280i −0.321399 + 0.556680i −0.980777 0.195132i \(-0.937486\pi\)
0.659378 + 0.751812i \(0.270820\pi\)
\(60\) 0 0
\(61\) 592.003 341.793i 1.24259 0.717412i 0.272972 0.962022i \(-0.411993\pi\)
0.969621 + 0.244610i \(0.0786601\pi\)
\(62\) 0 0
\(63\) −428.818 + 257.220i −0.857555 + 0.514392i
\(64\) 0 0
\(65\) 73.2542 42.2933i 0.139786 0.0807053i
\(66\) 0 0
\(67\) 269.780 467.273i 0.491924 0.852037i −0.508033 0.861338i \(-0.669627\pi\)
0.999957 + 0.00930051i \(0.00296049\pi\)
\(68\) 0 0
\(69\) 221.874 148.193i 0.387109 0.258556i
\(70\) 0 0
\(71\) 307.517i 0.514022i 0.966408 + 0.257011i \(0.0827377\pi\)
−0.966408 + 0.257011i \(0.917262\pi\)
\(72\) 0 0
\(73\) 495.192i 0.793943i −0.917831 0.396971i \(-0.870061\pi\)
0.917831 0.396971i \(-0.129939\pi\)
\(74\) 0 0
\(75\) −107.429 + 7.02162i −0.165398 + 0.0108105i
\(76\) 0 0
\(77\) −0.0188553 0.0434103i −2.79060e−5 6.42476e-5i
\(78\) 0 0
\(79\) −324.865 562.683i −0.462661 0.801352i 0.536432 0.843944i \(-0.319772\pi\)
−0.999093 + 0.0425920i \(0.986438\pi\)
\(80\) 0 0
\(81\) −189.193 + 704.022i −0.259524 + 0.965737i
\(82\) 0 0
\(83\) 565.581 + 979.615i 0.747959 + 1.29550i 0.948800 + 0.315879i \(0.102299\pi\)
−0.200841 + 0.979624i \(0.564367\pi\)
\(84\) 0 0
\(85\) −170.897 + 296.002i −0.218075 + 0.377717i
\(86\) 0 0
\(87\) −38.3293 586.430i −0.0472336 0.722665i
\(88\) 0 0
\(89\) 130.217 0.155089 0.0775447 0.996989i \(-0.475292\pi\)
0.0775447 + 0.996989i \(0.475292\pi\)
\(90\) 0 0
\(91\) 77.2337 104.291i 0.0889702 0.120139i
\(92\) 0 0
\(93\) −141.835 + 94.7337i −0.158146 + 0.105628i
\(94\) 0 0
\(95\) 514.315 + 296.940i 0.555449 + 0.320688i
\(96\) 0 0
\(97\) 1260.41 727.696i 1.31933 0.761715i 0.335709 0.941966i \(-0.391024\pi\)
0.983621 + 0.180251i \(0.0576909\pi\)
\(98\) 0 0
\(99\) −0.0637365 0.0264277i −6.47046e−5 2.68292e-5i
\(100\) 0 0
\(101\) 197.600 + 342.254i 0.194673 + 0.337183i 0.946793 0.321842i \(-0.104302\pi\)
−0.752120 + 0.659026i \(0.770969\pi\)
\(102\) 0 0
\(103\) 545.260 + 314.806i 0.521612 + 0.301153i 0.737594 0.675244i \(-0.235962\pi\)
−0.215982 + 0.976397i \(0.569295\pi\)
\(104\) 0 0
\(105\) −1033.06 + 531.314i −0.960154 + 0.493818i
\(106\) 0 0
\(107\) 515.616i 0.465855i 0.972494 + 0.232927i \(0.0748305\pi\)
−0.972494 + 0.232927i \(0.925170\pi\)
\(108\) 0 0
\(109\) 794.011 0.697729 0.348864 0.937173i \(-0.386567\pi\)
0.348864 + 0.937173i \(0.386567\pi\)
\(110\) 0 0
\(111\) −234.413 + 475.124i −0.200446 + 0.406277i
\(112\) 0 0
\(113\) 1782.31 + 1029.02i 1.48377 + 0.856654i 0.999830 0.0184476i \(-0.00587238\pi\)
0.483939 + 0.875102i \(0.339206\pi\)
\(114\) 0 0
\(115\) 536.802 309.923i 0.435279 0.251308i
\(116\) 0 0
\(117\) −24.6264 187.585i −0.0194591 0.148224i
\(118\) 0 0
\(119\) −59.5649 + 520.994i −0.0458849 + 0.401340i
\(120\) 0 0
\(121\) −665.500 + 1152.68i −0.500000 + 0.866025i
\(122\) 0 0
\(123\) 64.9064 + 97.1776i 0.0475806 + 0.0712375i
\(124\) 0 0
\(125\) 1258.82 0.900738
\(126\) 0 0
\(127\) −2071.63 −1.44746 −0.723729 0.690084i \(-0.757573\pi\)
−0.723729 + 0.690084i \(0.757573\pi\)
\(128\) 0 0
\(129\) −2356.14 + 153.998i −1.60811 + 0.105107i
\(130\) 0 0
\(131\) −467.210 + 809.232i −0.311606 + 0.539717i −0.978710 0.205247i \(-0.934200\pi\)
0.667104 + 0.744964i \(0.267533\pi\)
\(132\) 0 0
\(133\) 905.249 + 103.496i 0.590188 + 0.0674758i
\(134\) 0 0
\(135\) −545.258 + 1603.40i −0.347617 + 1.02221i
\(136\) 0 0
\(137\) 2320.59 1339.79i 1.44716 0.835521i 0.448853 0.893606i \(-0.351833\pi\)
0.998312 + 0.0580849i \(0.0184994\pi\)
\(138\) 0 0
\(139\) 794.727 + 458.836i 0.484949 + 0.279985i 0.722476 0.691395i \(-0.243004\pi\)
−0.237528 + 0.971381i \(0.576337\pi\)
\(140\) 0 0
\(141\) 2398.21 156.748i 1.43238 0.0936207i
\(142\) 0 0
\(143\) 0.0179068 1.04716e−5
\(144\) 0 0
\(145\) 1365.27i 0.781926i
\(146\) 0 0
\(147\) −1128.98 + 1379.10i −0.633448 + 0.773785i
\(148\) 0 0
\(149\) 1187.44 + 685.572i 0.652881 + 0.376941i 0.789559 0.613674i \(-0.210309\pi\)
−0.136678 + 0.990616i \(0.543643\pi\)
\(150\) 0 0
\(151\) 127.186 + 220.292i 0.0685445 + 0.118723i 0.898261 0.439463i \(-0.144831\pi\)
−0.829716 + 0.558185i \(0.811498\pi\)
\(152\) 0 0
\(153\) 465.169 + 606.678i 0.245795 + 0.320568i
\(154\) 0 0
\(155\) −343.155 + 198.121i −0.177825 + 0.102667i
\(156\) 0 0
\(157\) 511.747 + 295.457i 0.260139 + 0.150191i 0.624398 0.781106i \(-0.285344\pi\)
−0.364259 + 0.931298i \(0.618678\pi\)
\(158\) 0 0
\(159\) −2644.87 1304.91i −1.31920 0.650855i
\(160\) 0 0
\(161\) 565.963 764.234i 0.277044 0.374100i
\(162\) 0 0
\(163\) −2197.17 −1.05580 −0.527901 0.849306i \(-0.677021\pi\)
−0.527901 + 0.849306i \(0.677021\pi\)
\(164\) 0 0
\(165\) −0.143749 0.0709220i −6.78235e−5 3.34622e-5i
\(166\) 0 0
\(167\) 210.903 365.295i 0.0977256 0.169266i −0.813017 0.582240i \(-0.802177\pi\)
0.910743 + 0.412974i \(0.135510\pi\)
\(168\) 0 0
\(169\) −1073.95 1860.14i −0.488826 0.846671i
\(170\) 0 0
\(171\) 1054.13 808.249i 0.471410 0.361452i
\(172\) 0 0
\(173\) 872.428 + 1511.09i 0.383407 + 0.664081i 0.991547 0.129749i \(-0.0414172\pi\)
−0.608139 + 0.793830i \(0.708084\pi\)
\(174\) 0 0
\(175\) −351.953 + 152.871i −0.152029 + 0.0660341i
\(176\) 0 0
\(177\) 840.727 + 1258.73i 0.357022 + 0.534532i
\(178\) 0 0
\(179\) 4311.61i 1.80036i −0.435518 0.900180i \(-0.643435\pi\)
0.435518 0.900180i \(-0.356565\pi\)
\(180\) 0 0
\(181\) 1307.99i 0.537141i −0.963260 0.268570i \(-0.913449\pi\)
0.963260 0.268570i \(-0.0865512\pi\)
\(182\) 0 0
\(183\) −231.667 3544.45i −0.0935808 1.43177i
\(184\) 0 0
\(185\) −615.405 + 1065.91i −0.244570 + 0.423608i
\(186\) 0 0
\(187\) −0.0626630 + 0.0361785i −2.45047e−5 + 1.41478e-5i
\(188\) 0 0
\(189\) 212.739 + 2589.60i 0.0818757 + 0.996643i
\(190\) 0 0
\(191\) −3495.99 + 2018.41i −1.32440 + 0.764644i −0.984428 0.175791i \(-0.943752\pi\)
−0.339975 + 0.940435i \(0.610419\pi\)
\(192\) 0 0
\(193\) 2209.64 3827.21i 0.824112 1.42740i −0.0784849 0.996915i \(-0.525008\pi\)
0.902596 0.430488i \(-0.141658\pi\)
\(194\) 0 0
\(195\) −28.6663 438.589i −0.0105274 0.161067i
\(196\) 0 0
\(197\) 151.673i 0.0548540i −0.999624 0.0274270i \(-0.991269\pi\)
0.999624 0.0274270i \(-0.00873138\pi\)
\(198\) 0 0
\(199\) 1838.65i 0.654966i −0.944857 0.327483i \(-0.893800\pi\)
0.944857 0.327483i \(-0.106200\pi\)
\(200\) 0 0
\(201\) −1557.19 2331.42i −0.546447 0.818139i
\(202\) 0 0
\(203\) −834.485 1921.22i −0.288519 0.664254i
\(204\) 0 0
\(205\) 135.742 + 235.111i 0.0462468 + 0.0801019i
\(206\) 0 0
\(207\) −180.461 1374.61i −0.0605936 0.461555i
\(208\) 0 0
\(209\) 0.0628616 + 0.108879i 2.08049e−5 + 3.60352e-5i
\(210\) 0 0
\(211\) 1229.27 2129.15i 0.401072 0.694678i −0.592783 0.805362i \(-0.701971\pi\)
0.993856 + 0.110684i \(0.0353042\pi\)
\(212\) 0 0
\(213\) 1432.99 + 706.997i 0.460971 + 0.227430i
\(214\) 0 0
\(215\) −5485.32 −1.73998
\(216\) 0 0
\(217\) −361.797 + 488.543i −0.113181 + 0.152832i
\(218\) 0 0
\(219\) −2307.53 1138.47i −0.712002 0.351282i
\(220\) 0 0
\(221\) −171.823 99.2019i −0.0522989 0.0301948i
\(222\) 0 0
\(223\) −4491.19 + 2592.99i −1.34867 + 0.778653i −0.988061 0.154066i \(-0.950763\pi\)
−0.360606 + 0.932718i \(0.617430\pi\)
\(224\) 0 0
\(225\) −214.266 + 516.750i −0.0634861 + 0.153111i
\(226\) 0 0
\(227\) 497.531 + 861.749i 0.145473 + 0.251966i 0.929549 0.368698i \(-0.120196\pi\)
−0.784077 + 0.620664i \(0.786863\pi\)
\(228\) 0 0
\(229\) 101.864 + 58.8111i 0.0293946 + 0.0169710i 0.514625 0.857415i \(-0.327931\pi\)
−0.485231 + 0.874386i \(0.661264\pi\)
\(230\) 0 0
\(231\) −0.245635 0.0119393i −6.99637e−5 3.40064e-6i
\(232\) 0 0
\(233\) 1484.08i 0.417276i −0.977993 0.208638i \(-0.933097\pi\)
0.977993 0.208638i \(-0.0669030\pi\)
\(234\) 0 0
\(235\) 5583.26 1.54984
\(236\) 0 0
\(237\) −3368.91 + 220.193i −0.923351 + 0.0603505i
\(238\) 0 0
\(239\) 2392.08 + 1381.07i 0.647409 + 0.373782i 0.787463 0.616362i \(-0.211394\pi\)
−0.140054 + 0.990144i \(0.544728\pi\)
\(240\) 0 0
\(241\) −3362.99 + 1941.62i −0.898877 + 0.518967i −0.876836 0.480790i \(-0.840350\pi\)
−0.0220413 + 0.999757i \(0.507017\pi\)
\(242\) 0 0
\(243\) 2845.69 + 2500.19i 0.751238 + 0.660031i
\(244\) 0 0
\(245\) −2826.16 + 3025.97i −0.736967 + 0.789070i
\(246\) 0 0
\(247\) −172.367 + 298.549i −0.0444027 + 0.0769078i
\(248\) 0 0
\(249\) 5865.18 383.350i 1.49273 0.0975655i
\(250\) 0 0
\(251\) −5549.57 −1.39556 −0.697780 0.716312i \(-0.745829\pi\)
−0.697780 + 0.716312i \(0.745829\pi\)
\(252\) 0 0
\(253\) 0.131220 3.26076e−5
\(254\) 0 0
\(255\) 986.430 + 1476.88i 0.242246 + 0.362689i
\(256\) 0 0
\(257\) 809.585 1402.24i 0.196500 0.340348i −0.750891 0.660426i \(-0.770376\pi\)
0.947391 + 0.320078i \(0.103709\pi\)
\(258\) 0 0
\(259\) −214.495 + 1876.12i −0.0514598 + 0.450102i
\(260\) 0 0
\(261\) −2820.81 1169.62i −0.668979 0.277386i
\(262\) 0 0
\(263\) −594.813 + 343.415i −0.139459 + 0.0805167i −0.568106 0.822955i \(-0.692324\pi\)
0.428647 + 0.903472i \(0.358990\pi\)
\(264\) 0 0
\(265\) −5933.62 3425.78i −1.37547 0.794128i
\(266\) 0 0
\(267\) 299.375 606.793i 0.0686196 0.139083i
\(268\) 0 0
\(269\) −1805.03 −0.409124 −0.204562 0.978854i \(-0.565577\pi\)
−0.204562 + 0.978854i \(0.565577\pi\)
\(270\) 0 0
\(271\) 6726.19i 1.50770i 0.657046 + 0.753851i \(0.271806\pi\)
−0.657046 + 0.753851i \(0.728194\pi\)
\(272\) 0 0
\(273\) −308.416 599.668i −0.0683743 0.132943i
\(274\) 0 0
\(275\) −0.0458534 0.0264735i −1.00548e−5 5.80513e-6i
\(276\) 0 0
\(277\) −336.124 582.184i −0.0729088 0.126282i 0.827266 0.561810i \(-0.189895\pi\)
−0.900175 + 0.435528i \(0.856562\pi\)
\(278\) 0 0
\(279\) 115.361 + 878.730i 0.0247544 + 0.188560i
\(280\) 0 0
\(281\) −2007.12 + 1158.81i −0.426102 + 0.246010i −0.697685 0.716405i \(-0.745786\pi\)
0.271583 + 0.962415i \(0.412453\pi\)
\(282\) 0 0
\(283\) 8014.87 + 4627.39i 1.68352 + 0.971978i 0.959294 + 0.282411i \(0.0911342\pi\)
0.724222 + 0.689567i \(0.242199\pi\)
\(284\) 0 0
\(285\) 2566.14 1713.96i 0.533350 0.356233i
\(286\) 0 0
\(287\) 334.723 + 247.883i 0.0688435 + 0.0509829i
\(288\) 0 0
\(289\) −4111.30 −0.836821
\(290\) 0 0
\(291\) −493.231 7546.34i −0.0993599 1.52019i
\(292\) 0 0
\(293\) 4392.72 7608.42i 0.875855 1.51703i 0.0200056 0.999800i \(-0.493632\pi\)
0.855849 0.517225i \(-0.173035\pi\)
\(294\) 0 0
\(295\) 1758.25 + 3045.38i 0.347015 + 0.601047i
\(296\) 0 0
\(297\) −0.269683 + 0.236245i −5.26889e−5 + 4.61559e-5i
\(298\) 0 0
\(299\) 179.904 + 311.602i 0.0347963 + 0.0602689i
\(300\) 0 0
\(301\) −7719.03 + 3352.76i −1.47813 + 0.642027i
\(302\) 0 0
\(303\) 2049.15 133.933i 0.388517 0.0253936i
\(304\) 0 0
\(305\) 8251.85i 1.54918i
\(306\) 0 0
\(307\) 599.516i 0.111453i −0.998446 0.0557267i \(-0.982252\pi\)
0.998446 0.0557267i \(-0.0177476\pi\)
\(308\) 0 0
\(309\) 2720.53 1817.08i 0.500860 0.334532i
\(310\) 0 0
\(311\) 4494.29 7784.34i 0.819447 1.41932i −0.0866437 0.996239i \(-0.527614\pi\)
0.906090 0.423084i \(-0.139052\pi\)
\(312\) 0 0
\(313\) 7102.69 4100.74i 1.28264 0.740535i 0.305314 0.952252i \(-0.401239\pi\)
0.977331 + 0.211717i \(0.0679054\pi\)
\(314\) 0 0
\(315\) 100.801 + 6035.43i 0.0180301 + 1.07955i
\(316\) 0 0
\(317\) −5894.42 + 3403.15i −1.04436 + 0.602964i −0.921066 0.389405i \(-0.872681\pi\)
−0.123298 + 0.992370i \(0.539347\pi\)
\(318\) 0 0
\(319\) 0.144512 0.250302i 2.53640e−5 4.39318e-5i
\(320\) 0 0
\(321\) 2402.70 + 1185.43i 0.417775 + 0.206118i
\(322\) 0 0
\(323\) 1392.99i 0.239962i
\(324\) 0 0
\(325\) 145.181i 0.0247791i
\(326\) 0 0
\(327\) 1825.47 3699.99i 0.308712 0.625718i
\(328\) 0 0
\(329\) 7856.85 3412.63i 1.31660 0.571867i
\(330\) 0 0
\(331\) 3875.41 + 6712.41i 0.643540 + 1.11464i 0.984637 + 0.174616i \(0.0558684\pi\)
−0.341097 + 0.940028i \(0.610798\pi\)
\(332\) 0 0
\(333\) 1675.09 + 2184.67i 0.275658 + 0.359517i
\(334\) 0 0
\(335\) −3256.63 5640.64i −0.531130 0.919944i
\(336\) 0 0
\(337\) −1544.24 + 2674.70i −0.249614 + 0.432344i −0.963419 0.268001i \(-0.913637\pi\)
0.713805 + 0.700345i \(0.246970\pi\)
\(338\) 0 0
\(339\) 8892.72 5939.58i 1.42474 0.951603i
\(340\) 0 0
\(341\) −0.0838835 −1.33213e−5
\(342\) 0 0
\(343\) −2127.47 + 5985.61i −0.334906 + 0.942252i
\(344\) 0 0
\(345\) −210.065 3213.95i −0.0327812 0.501546i
\(346\) 0 0
\(347\) 10112.9 + 5838.71i 1.56453 + 0.903281i 0.996789 + 0.0800721i \(0.0255151\pi\)
0.567739 + 0.823209i \(0.307818\pi\)
\(348\) 0 0
\(349\) −6683.19 + 3858.54i −1.02505 + 0.591814i −0.915563 0.402174i \(-0.868255\pi\)
−0.109489 + 0.993988i \(0.534921\pi\)
\(350\) 0 0
\(351\) −930.737 316.511i −0.141536 0.0481313i
\(352\) 0 0
\(353\) 2760.12 + 4780.66i 0.416165 + 0.720818i 0.995550 0.0942355i \(-0.0300407\pi\)
−0.579385 + 0.815054i \(0.696707\pi\)
\(354\) 0 0
\(355\) 3214.83 + 1856.08i 0.480635 + 0.277495i
\(356\) 0 0
\(357\) 2290.82 + 1475.36i 0.339617 + 0.218723i
\(358\) 0 0
\(359\) 6290.95i 0.924857i 0.886657 + 0.462429i \(0.153022\pi\)
−0.886657 + 0.462429i \(0.846978\pi\)
\(360\) 0 0
\(361\) 4438.63 0.647125
\(362\) 0 0
\(363\) 3841.32 + 5751.21i 0.555419 + 0.831571i
\(364\) 0 0
\(365\) −5176.81 2988.83i −0.742374 0.428610i
\(366\) 0 0
\(367\) −3342.42 + 1929.75i −0.475404 + 0.274474i −0.718499 0.695528i \(-0.755171\pi\)
0.243095 + 0.970002i \(0.421837\pi\)
\(368\) 0 0
\(369\) 602.058 79.0390i 0.0849373 0.0111507i
\(370\) 0 0
\(371\) −10443.8 1194.03i −1.46150 0.167092i
\(372\) 0 0
\(373\) −4308.29 + 7462.17i −0.598055 + 1.03586i 0.395052 + 0.918659i \(0.370726\pi\)
−0.993108 + 0.117204i \(0.962607\pi\)
\(374\) 0 0
\(375\) 2894.09 5865.93i 0.398534 0.807775i
\(376\) 0 0
\(377\) 792.509 0.108266
\(378\) 0 0
\(379\) 11100.5 1.50447 0.752237 0.658893i \(-0.228975\pi\)
0.752237 + 0.658893i \(0.228975\pi\)
\(380\) 0 0
\(381\) −4762.77 + 9653.51i −0.640431 + 1.29807i
\(382\) 0 0
\(383\) −3294.29 + 5705.87i −0.439505 + 0.761244i −0.997651 0.0684980i \(-0.978179\pi\)
0.558147 + 0.829742i \(0.311513\pi\)
\(384\) 0 0
\(385\) −0.567622 0.0648959i −7.51395e−5 8.59065e-6i
\(386\) 0 0
\(387\) −4699.27 + 11333.3i −0.617253 + 1.48865i
\(388\) 0 0
\(389\) −6913.20 + 3991.34i −0.901062 + 0.520228i −0.877545 0.479495i \(-0.840820\pi\)
−0.0235174 + 0.999723i \(0.507487\pi\)
\(390\) 0 0
\(391\) −1259.11 726.945i −0.162854 0.0940235i
\(392\) 0 0
\(393\) 2696.77 + 4037.60i 0.346143 + 0.518245i
\(394\) 0 0
\(395\) −7843.16 −0.999069
\(396\) 0 0
\(397\) 9040.06i 1.14284i 0.820658 + 0.571420i \(0.193607\pi\)
−0.820658 + 0.571420i \(0.806393\pi\)
\(398\) 0 0
\(399\) 2563.49 3980.40i 0.321642 0.499421i
\(400\) 0 0
\(401\) −836.173 482.765i −0.104131 0.0601200i 0.447030 0.894519i \(-0.352482\pi\)
−0.551161 + 0.834399i \(0.685815\pi\)
\(402\) 0 0
\(403\) −115.005 199.194i −0.0142154 0.0246218i
\(404\) 0 0
\(405\) 6218.04 + 6227.12i 0.762906 + 0.764020i
\(406\) 0 0
\(407\) −0.225652 + 0.130280i −2.74819e−5 + 1.58667e-5i
\(408\) 0 0
\(409\) −2868.77 1656.28i −0.346825 0.200240i 0.316461 0.948606i \(-0.397505\pi\)
−0.663286 + 0.748366i \(0.730839\pi\)
\(410\) 0 0
\(411\) −908.110 13893.9i −0.108987 1.66748i
\(412\) 0 0
\(413\) 4335.64 + 3210.82i 0.516569 + 0.382552i
\(414\) 0 0
\(415\) 13654.7 1.61514
\(416\) 0 0
\(417\) 3965.23 2648.44i 0.465655 0.311018i
\(418\) 0 0
\(419\) 4172.32 7226.67i 0.486470 0.842591i −0.513409 0.858144i \(-0.671618\pi\)
0.999879 + 0.0155530i \(0.00495087\pi\)
\(420\) 0 0
\(421\) 3350.59 + 5803.38i 0.387880 + 0.671828i 0.992164 0.124941i \(-0.0398741\pi\)
−0.604284 + 0.796769i \(0.706541\pi\)
\(422\) 0 0
\(423\) 4783.17 11535.7i 0.549801 1.32597i
\(424\) 0 0
\(425\) 293.321 + 508.046i 0.0334780 + 0.0579856i
\(426\) 0 0
\(427\) −5043.73 11612.1i −0.571623 1.31604i
\(428\) 0 0
\(429\) 0.0411687 0.0834434i 4.63320e−6 9.39088e-6i
\(430\) 0 0
\(431\) 9168.55i 1.02467i 0.858785 + 0.512336i \(0.171220\pi\)
−0.858785 + 0.512336i \(0.828780\pi\)
\(432\) 0 0
\(433\) 1346.90i 0.149487i 0.997203 + 0.0747436i \(0.0238138\pi\)
−0.997203 + 0.0747436i \(0.976186\pi\)
\(434\) 0 0
\(435\) −6361.97 3138.82i −0.701225 0.345965i
\(436\) 0 0
\(437\) −1263.10 + 2187.75i −0.138266 + 0.239483i
\(438\) 0 0
\(439\) 4892.07 2824.44i 0.531858 0.307069i −0.209914 0.977720i \(-0.567319\pi\)
0.741773 + 0.670651i \(0.233985\pi\)
\(440\) 0 0
\(441\) 3830.85 + 8431.53i 0.413654 + 0.910434i
\(442\) 0 0
\(443\) −7525.68 + 4344.95i −0.807124 + 0.465993i −0.845956 0.533253i \(-0.820970\pi\)
0.0388322 + 0.999246i \(0.487636\pi\)
\(444\) 0 0
\(445\) 785.950 1361.31i 0.0837249 0.145016i
\(446\) 0 0
\(447\) 5924.67 3957.17i 0.626906 0.418720i
\(448\) 0 0
\(449\) 14492.3i 1.52324i −0.648026 0.761618i \(-0.724405\pi\)
0.648026 0.761618i \(-0.275595\pi\)
\(450\) 0 0
\(451\) 0.0574724i 6.00060e-6i
\(452\) 0 0
\(453\) 1318.94 86.2062i 0.136797 0.00894111i
\(454\) 0 0
\(455\) −624.109 1436.88i −0.0643048 0.148048i
\(456\) 0 0
\(457\) −4131.68 7156.27i −0.422914 0.732508i 0.573309 0.819339i \(-0.305659\pi\)
−0.996223 + 0.0868308i \(0.972326\pi\)
\(458\) 0 0
\(459\) 3896.48 772.843i 0.396236 0.0785909i
\(460\) 0 0
\(461\) 4948.33 + 8570.75i 0.499928 + 0.865900i 1.00000 8.36677e-5i \(-2.66323e-5\pi\)
−0.500072 + 0.865984i \(0.666693\pi\)
\(462\) 0 0
\(463\) 1987.79 3442.95i 0.199525 0.345588i −0.748849 0.662740i \(-0.769393\pi\)
0.948375 + 0.317152i \(0.102727\pi\)
\(464\) 0 0
\(465\) 134.286 + 2054.55i 0.0133922 + 0.204898i
\(466\) 0 0
\(467\) −17044.5 −1.68892 −0.844460 0.535619i \(-0.820079\pi\)
−0.844460 + 0.535619i \(0.820079\pi\)
\(468\) 0 0
\(469\) −8030.47 5947.07i −0.790645 0.585522i
\(470\) 0 0
\(471\) 2553.32 1705.40i 0.249790 0.166838i
\(472\) 0 0
\(473\) −1.00566 0.580616i −9.77592e−5 5.64413e-5i
\(474\) 0 0
\(475\) 882.751 509.656i 0.0852703 0.0492308i
\(476\) 0 0
\(477\) −12161.4 + 9324.72i −1.16736 + 0.895073i
\(478\) 0 0
\(479\) −5364.93 9292.33i −0.511753 0.886383i −0.999907 0.0136250i \(-0.995663\pi\)
0.488154 0.872758i \(-0.337670\pi\)
\(480\) 0 0
\(481\) −618.740 357.230i −0.0586530 0.0338633i
\(482\) 0 0
\(483\) −2260.05 4394.33i −0.212911 0.413973i
\(484\) 0 0
\(485\) 17568.6i 1.64485i
\(486\) 0 0
\(487\) −12461.1 −1.15948 −0.579741 0.814801i \(-0.696846\pi\)
−0.579741 + 0.814801i \(0.696846\pi\)
\(488\) 0 0
\(489\) −5051.40 + 10238.5i −0.467142 + 0.946834i
\(490\) 0 0
\(491\) −4052.21 2339.55i −0.372452 0.215035i 0.302077 0.953283i \(-0.402320\pi\)
−0.674529 + 0.738248i \(0.735653\pi\)
\(492\) 0 0
\(493\) −2773.30 + 1601.16i −0.253353 + 0.146273i
\(494\) 0 0
\(495\) −0.660974 + 0.506800i −6.00173e−5 + 4.60181e-5i
\(496\) 0 0
\(497\) 5658.43 + 646.925i 0.510695 + 0.0583874i
\(498\) 0 0
\(499\) 2685.54 4651.49i 0.240924 0.417293i −0.720054 0.693918i \(-0.755883\pi\)
0.960978 + 0.276625i \(0.0892161\pi\)
\(500\) 0 0
\(501\) −1217.35 1822.61i −0.108557 0.162532i
\(502\) 0 0
\(503\) 22263.9 1.97355 0.986777 0.162086i \(-0.0518222\pi\)
0.986777 + 0.162086i \(0.0518222\pi\)
\(504\) 0 0
\(505\) 4770.63 0.420376
\(506\) 0 0
\(507\) −11137.0 + 727.921i −0.975569 + 0.0637635i
\(508\) 0 0
\(509\) −7249.76 + 12556.9i −0.631316 + 1.09347i 0.355967 + 0.934498i \(0.384152\pi\)
−0.987283 + 0.158973i \(0.949182\pi\)
\(510\) 0 0
\(511\) −9111.72 1041.74i −0.788804 0.0901834i
\(512\) 0 0
\(513\) −1342.85 6770.30i −0.115571 0.582682i
\(514\) 0 0
\(515\) 6582.05 3800.15i 0.563184 0.325155i
\(516\) 0 0
\(517\) 1.02361 + 0.590983i 8.70762e−5 + 5.02735e-5i
\(518\) 0 0
\(519\) 9047.24 591.330i 0.765182 0.0500126i
\(520\) 0 0
\(521\) −7009.79 −0.589452 −0.294726 0.955582i \(-0.595228\pi\)
−0.294726 + 0.955582i \(0.595228\pi\)
\(522\) 0 0
\(523\) 3631.76i 0.303644i 0.988408 + 0.151822i \(0.0485141\pi\)
−0.988408 + 0.151822i \(0.951486\pi\)
\(524\) 0 0
\(525\) −96.7990 + 1991.51i −0.00804696 + 0.165556i
\(526\) 0 0
\(527\) 804.894 + 464.706i 0.0665308 + 0.0384116i
\(528\) 0 0
\(529\) −4765.18 8253.53i −0.391648 0.678354i
\(530\) 0 0
\(531\) 7798.41 1023.79i 0.637330 0.0836696i
\(532\) 0 0
\(533\) −136.477 + 78.7951i −0.0110910 + 0.00640336i
\(534\) 0 0
\(535\) 5390.32 + 3112.10i 0.435596 + 0.251492i
\(536\) 0 0
\(537\) −20091.5 9912.59i −1.61455 0.796573i
\(538\) 0 0
\(539\) −0.838432 + 0.255622i −6.70015e−5 + 2.04275e-5i
\(540\) 0 0
\(541\) −12760.4 −1.01407 −0.507037 0.861925i \(-0.669259\pi\)
−0.507037 + 0.861925i \(0.669259\pi\)
\(542\) 0 0
\(543\) −6095.08 3007.14i −0.481704 0.237659i
\(544\) 0 0
\(545\) 4792.42 8300.71i 0.376669 0.652410i
\(546\) 0 0
\(547\) −3919.62 6788.98i −0.306382 0.530669i 0.671186 0.741289i \(-0.265785\pi\)
−0.977568 + 0.210620i \(0.932452\pi\)
\(548\) 0 0
\(549\) −17049.3 7069.34i −1.32540 0.549566i
\(550\) 0 0
\(551\) 2782.09 + 4818.72i 0.215101 + 0.372567i
\(552\) 0 0
\(553\) −11037.0 + 4793.93i −0.848718 + 0.368641i
\(554\) 0 0
\(555\) 3552.17 + 5318.29i 0.271678 + 0.406755i
\(556\) 0 0
\(557\) 9443.19i 0.718350i −0.933270 0.359175i \(-0.883058\pi\)
0.933270 0.359175i \(-0.116942\pi\)
\(558\) 0 0
\(559\) 3184.11i 0.240919i
\(560\) 0 0
\(561\) 0.0245217 + 0.375177i 1.84547e−6 + 2.82353e-5i
\(562\) 0 0
\(563\) −8022.13 + 13894.7i −0.600519 + 1.04013i 0.392223 + 0.919870i \(0.371706\pi\)
−0.992742 + 0.120260i \(0.961627\pi\)
\(564\) 0 0
\(565\) 21515.0 12421.7i 1.60202 0.924929i
\(566\) 0 0
\(567\) 12556.3 + 4962.27i 0.930007 + 0.367541i
\(568\) 0 0
\(569\) 19213.9 11093.2i 1.41562 0.817310i 0.419712 0.907657i \(-0.362131\pi\)
0.995910 + 0.0903469i \(0.0287976\pi\)
\(570\) 0 0
\(571\) −3211.11 + 5561.80i −0.235343 + 0.407625i −0.959372 0.282144i \(-0.908955\pi\)
0.724030 + 0.689769i \(0.242288\pi\)
\(572\) 0 0
\(573\) 1368.07 + 20931.3i 0.0997419 + 1.52603i
\(574\) 0 0
\(575\) 1063.88i 0.0771597i
\(576\) 0 0
\(577\) 21441.1i 1.54697i −0.633813 0.773486i \(-0.718511\pi\)
0.633813 0.773486i \(-0.281489\pi\)
\(578\) 0 0
\(579\) −12754.2 19095.6i −0.915454 1.37061i
\(580\) 0 0
\(581\) 19215.1 8346.09i 1.37208 0.595963i
\(582\) 0 0
\(583\) −0.725230 1.25614i −5.15197e−5 8.92347e-5i
\(584\) 0 0
\(585\) −2109.67 874.757i −0.149101 0.0618235i
\(586\) 0 0
\(587\) 342.762 + 593.681i 0.0241010 + 0.0417442i 0.877824 0.478983i \(-0.158994\pi\)
−0.853723 + 0.520727i \(0.825661\pi\)
\(588\) 0 0
\(589\) 807.445 1398.54i 0.0564859 0.0978365i
\(590\) 0 0
\(591\) −706.775 348.703i −0.0491926 0.0242703i
\(592\) 0 0
\(593\) −11503.8 −0.796635 −0.398317 0.917248i \(-0.630406\pi\)
−0.398317 + 0.917248i \(0.630406\pi\)
\(594\) 0 0
\(595\) 5087.04 + 3767.27i 0.350501 + 0.259568i
\(596\) 0 0
\(597\) −8567.85 4227.14i −0.587368 0.289791i
\(598\) 0 0
\(599\) 5124.45 + 2958.60i 0.349548 + 0.201812i 0.664486 0.747300i \(-0.268650\pi\)
−0.314938 + 0.949112i \(0.601984\pi\)
\(600\) 0 0
\(601\) −10168.3 + 5870.67i −0.690139 + 0.398452i −0.803664 0.595083i \(-0.797119\pi\)
0.113525 + 0.993535i \(0.463786\pi\)
\(602\) 0 0
\(603\) −14444.2 + 1896.25i −0.975478 + 0.128062i
\(604\) 0 0
\(605\) 8033.52 + 13914.5i 0.539850 + 0.935047i
\(606\) 0 0
\(607\) 24018.0 + 13866.8i 1.60603 + 0.927241i 0.990247 + 0.139325i \(0.0444933\pi\)
0.615782 + 0.787916i \(0.288840\pi\)
\(608\) 0 0
\(609\) −10871.2 528.402i −0.723353 0.0351591i
\(610\) 0 0
\(611\) 3240.96i 0.214592i
\(612\) 0 0
\(613\) −19338.2 −1.27416 −0.637081 0.770797i \(-0.719858\pi\)
−0.637081 + 0.770797i \(0.719858\pi\)
\(614\) 0 0
\(615\) 1407.66 92.0054i 0.0922968 0.00603255i
\(616\) 0 0
\(617\) 9927.33 + 5731.55i 0.647746 + 0.373976i 0.787592 0.616197i \(-0.211327\pi\)
−0.139846 + 0.990173i \(0.544661\pi\)
\(618\) 0 0
\(619\) −3429.59 + 1980.07i −0.222693 + 0.128572i −0.607196 0.794552i \(-0.707706\pi\)
0.384504 + 0.923123i \(0.374373\pi\)
\(620\) 0 0
\(621\) −6820.38 2319.37i −0.440728 0.149876i
\(622\) 0 0
\(623\) 273.937 2396.04i 0.0176165 0.154086i
\(624\) 0 0
\(625\) 8892.79 15402.8i 0.569139 0.985777i
\(626\) 0 0
\(627\) 0.651886 0.0426075i 4.15212e−5 2.71384e-6i
\(628\) 0 0
\(629\) 2886.95 0.183005
\(630\) 0 0
\(631\) −5409.20 −0.341263 −0.170631 0.985335i \(-0.554581\pi\)
−0.170631 + 0.985335i \(0.554581\pi\)
\(632\) 0 0
\(633\) −7095.43 10623.3i −0.445526 0.667040i
\(634\) 0 0
\(635\) −12503.7 + 21657.1i −0.781410 + 1.35344i
\(636\) 0 0
\(637\) −1756.51 1640.53i −0.109255 0.102041i
\(638\) 0 0
\(639\) 6589.02 5052.12i 0.407915 0.312768i
\(640\) 0 0
\(641\) −20809.6 + 12014.4i −1.28226 + 0.740313i −0.977261 0.212040i \(-0.931989\pi\)
−0.304999 + 0.952353i \(0.598656\pi\)
\(642\) 0 0
\(643\) −3581.87 2068.00i −0.219682 0.126833i 0.386121 0.922448i \(-0.373815\pi\)
−0.605803 + 0.795615i \(0.707148\pi\)
\(644\) 0 0
\(645\) −12611.0 + 25560.9i −0.769859 + 1.56040i
\(646\) 0 0
\(647\) 1393.75 0.0846895 0.0423447 0.999103i \(-0.486517\pi\)
0.0423447 + 0.999103i \(0.486517\pi\)
\(648\) 0 0
\(649\) 0.744436i 4.50257e-5i
\(650\) 0 0
\(651\) 1444.76 + 2809.11i 0.0869809 + 0.169121i
\(652\) 0 0
\(653\) 7846.10 + 4529.95i 0.470202 + 0.271471i 0.716324 0.697768i \(-0.245823\pi\)
−0.246122 + 0.969239i \(0.579157\pi\)
\(654\) 0 0
\(655\) 5639.89 + 9768.57i 0.336441 + 0.582732i
\(656\) 0 0
\(657\) −10610.2 + 8135.38i −0.630053 + 0.483092i
\(658\) 0 0
\(659\) 14018.1 8093.34i 0.828629 0.478409i −0.0247539 0.999694i \(-0.507880\pi\)
0.853383 + 0.521284i \(0.174547\pi\)
\(660\) 0 0
\(661\) 24821.5 + 14330.7i 1.46058 + 0.843269i 0.999038 0.0438473i \(-0.0139615\pi\)
0.461546 + 0.887116i \(0.347295\pi\)
\(662\) 0 0
\(663\) −857.297 + 572.601i −0.0502182 + 0.0335415i
\(664\) 0 0
\(665\) 6545.78 8838.93i 0.381706 0.515427i
\(666\) 0 0
\(667\) 5807.45 0.337130
\(668\) 0 0
\(669\) 1757.53 + 26889.8i 0.101569 + 1.55399i
\(670\) 0 0
\(671\) 0.873449 1.51286i 5.02521e−5 8.70391e-5i
\(672\) 0 0
\(673\) 3670.88 + 6358.15i 0.210255 + 0.364173i 0.951794 0.306737i \(-0.0992371\pi\)
−0.741539 + 0.670910i \(0.765904\pi\)
\(674\) 0 0
\(675\) 1915.38 + 2186.48i 0.109219 + 0.124678i
\(676\) 0 0
\(677\) 16478.4 + 28541.4i 0.935474 + 1.62029i 0.773787 + 0.633446i \(0.218360\pi\)
0.161687 + 0.986842i \(0.448307\pi\)
\(678\) 0 0
\(679\) −10738.4 24722.8i −0.606924 1.39731i
\(680\) 0 0
\(681\) 5159.48 337.226i 0.290326 0.0189758i
\(682\) 0 0
\(683\) 22213.0i 1.24444i 0.782841 + 0.622222i \(0.213770\pi\)
−0.782841 + 0.622222i \(0.786230\pi\)
\(684\) 0 0
\(685\) 32346.4i 1.80422i
\(686\) 0 0
\(687\) 508.242 339.463i 0.0282251 0.0188520i
\(688\) 0 0
\(689\) 1988.59 3444.34i 0.109955 0.190448i
\(690\) 0 0
\(691\) 22072.1 12743.3i 1.21514 0.701563i 0.251267 0.967918i \(-0.419153\pi\)
0.963875 + 0.266355i \(0.0858194\pi\)
\(692\) 0 0
\(693\) −0.620364 + 1.11718i −3.40053e−5 + 6.12383e-5i
\(694\) 0 0
\(695\) 9593.47 5538.79i 0.523599 0.302300i
\(696\) 0 0
\(697\) 318.391 551.470i 0.0173026 0.0299690i
\(698\) 0 0
\(699\) −6915.61 3411.97i −0.374209 0.184625i
\(700\) 0 0
\(701\) 22316.4i 1.20239i 0.799101 + 0.601197i \(0.205309\pi\)
−0.799101 + 0.601197i \(0.794691\pi\)
\(702\) 0 0
\(703\) 5016.19i 0.269117i
\(704\) 0 0
\(705\) 12836.2 26017.3i 0.685729 1.38988i
\(706\) 0 0
\(707\) 6713.29 2915.92i 0.357114 0.155113i
\(708\) 0 0
\(709\) −620.251 1074.31i −0.0328547 0.0569061i 0.849130 0.528183i \(-0.177127\pi\)
−0.881985 + 0.471277i \(0.843793\pi\)
\(710\) 0 0
\(711\) −6719.22 + 16204.9i −0.354417 + 0.854756i
\(712\) 0 0
\(713\) −842.748 1459.68i −0.0442653 0.0766698i
\(714\) 0 0
\(715\) 0.108080 0.187201i 5.65311e−6 9.79147e-6i
\(716\) 0 0
\(717\) 11935.1 7971.63i 0.621652 0.415211i
\(718\) 0 0
\(719\) 1718.52 0.0891374 0.0445687 0.999006i \(-0.485809\pi\)
0.0445687 + 0.999006i \(0.485809\pi\)
\(720\) 0 0
\(721\) 6939.62 9370.74i 0.358453 0.484028i
\(722\) 0 0
\(723\) 1316.03 + 20135.0i 0.0676952 + 1.03572i
\(724\) 0 0
\(725\) −2029.35 1171.65i −0.103956 0.0600191i
\(726\) 0 0
\(727\) 2204.74 1272.91i 0.112475 0.0649376i −0.442707 0.896666i \(-0.645982\pi\)
0.555182 + 0.831729i \(0.312649\pi\)
\(728\) 0 0
\(729\) 18193.0 7512.46i 0.924298 0.381672i
\(730\) 0 0
\(731\) 6433.10 + 11142.5i 0.325495 + 0.563774i
\(732\) 0 0
\(733\) 19126.0 + 11042.4i 0.963761 + 0.556427i 0.897328 0.441363i \(-0.145505\pi\)
0.0664323 + 0.997791i \(0.478838\pi\)
\(734\) 0 0
\(735\) 7603.13 + 20126.4i 0.381559 + 1.01003i
\(736\) 0 0
\(737\) 1.37884i 6.89149e-5i
\(738\) 0 0
\(739\) −5401.50 −0.268873 −0.134437 0.990922i \(-0.542922\pi\)
−0.134437 + 0.990922i \(0.542922\pi\)
\(740\) 0 0
\(741\) 994.918 + 1489.59i 0.0493242 + 0.0738480i
\(742\) 0 0
\(743\) −26971.1 15571.7i −1.33173 0.768872i −0.346161 0.938175i \(-0.612515\pi\)
−0.985564 + 0.169303i \(0.945848\pi\)
\(744\) 0 0
\(745\) 14334.1 8275.82i 0.704915 0.406983i
\(746\) 0 0
\(747\) 11698.0 28212.3i 0.572967 1.38184i
\(748\) 0 0
\(749\) 9487.53 + 1084.70i 0.462840 + 0.0529161i
\(750\) 0 0
\(751\) −2644.61 + 4580.61i −0.128500 + 0.222568i −0.923096 0.384571i \(-0.874350\pi\)
0.794596 + 0.607139i \(0.207683\pi\)
\(752\) 0 0
\(753\) −12758.7 + 25860.2i −0.617468 + 1.25153i
\(754\) 0 0
\(755\) 3070.62 0.148015
\(756\) 0 0
\(757\) −20794.2 −0.998384 −0.499192 0.866491i \(-0.666370\pi\)
−0.499192 + 0.866491i \(0.666370\pi\)
\(758\) 0 0
\(759\) 0.301681 0.611468i 1.44273e−5 2.92423e-5i
\(760\) 0 0
\(761\) −9126.94 + 15808.3i −0.434759 + 0.753024i −0.997276 0.0737616i \(-0.976500\pi\)
0.562517 + 0.826785i \(0.309833\pi\)
\(762\) 0 0
\(763\) 1670.36 14610.1i 0.0792546 0.693213i
\(764\) 0 0
\(765\) 9149.92 1201.21i 0.432439 0.0567712i
\(766\) 0 0
\(767\) −1767.78 + 1020.63i −0.0832213 + 0.0480478i
\(768\) 0 0
\(769\) −28098.3 16222.6i −1.31762 0.760730i −0.334278 0.942475i \(-0.608492\pi\)
−0.983346 + 0.181745i \(0.941826\pi\)
\(770\) 0 0
\(771\) −4672.99 6996.39i −0.218280 0.326808i
\(772\) 0 0
\(773\) 20600.1 0.958519 0.479259 0.877673i \(-0.340905\pi\)
0.479259 + 0.877673i \(0.340905\pi\)
\(774\) 0 0
\(775\) 680.094i 0.0315222i
\(776\) 0 0
\(777\) 8249.33 + 5312.81i 0.380879 + 0.245297i
\(778\) 0 0
\(779\) −958.201 553.217i −0.0440707 0.0254442i
\(780\) 0 0
\(781\) 0.392929 + 0.680572i 1.80027e−5 + 3.11816e-5i
\(782\) 0 0
\(783\) −11935.5 + 10455.6i −0.544749 + 0.477205i
\(784\) 0 0
\(785\) 6177.51 3566.59i 0.280872 0.162162i
\(786\) 0 0
\(787\) 12253.1 + 7074.35i 0.554990 + 0.320424i 0.751132 0.660152i \(-0.229508\pi\)
−0.196142 + 0.980575i \(0.562841\pi\)
\(788\) 0 0
\(789\) 232.766 + 3561.28i 0.0105028 + 0.160691i
\(790\) 0 0
\(791\) 22683.8 30630.5i 1.01965 1.37686i
\(792\) 0 0
\(793\) 4790.02 0.214500
\(794\) 0 0
\(795\) −29605.4 + 19773.9i