Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8018,2,Mod(1,8018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8018, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8018 = 2 \cdot 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8018.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.0240523407\) |
Analytic rank: | \(0\) |
Dimension: | \(47\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 8018.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.99735 | −1.15317 | −0.576585 | − | 0.817037i | \(-0.695615\pi\) | ||||
−0.576585 | + | 0.817037i | \(0.695615\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.291796 | −0.130495 | −0.0652475 | − | 0.997869i | \(-0.520784\pi\) | ||||
−0.0652475 | + | 0.997869i | \(0.520784\pi\) | |||||||
\(6\) | −1.99735 | −0.815415 | ||||||||
\(7\) | −0.492820 | −0.186268 | −0.0931342 | − | 0.995654i | \(-0.529689\pi\) | ||||
−0.0931342 | + | 0.995654i | \(0.529689\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0.989407 | 0.329802 | ||||||||
\(10\) | −0.291796 | −0.0922739 | ||||||||
\(11\) | −5.82808 | −1.75723 | −0.878616 | − | 0.477529i | \(-0.841532\pi\) | ||||
−0.878616 | + | 0.477529i | \(0.841532\pi\) | |||||||
\(12\) | −1.99735 | −0.576585 | ||||||||
\(13\) | −2.76888 | −0.767948 | −0.383974 | − | 0.923344i | \(-0.625445\pi\) | ||||
−0.383974 | + | 0.923344i | \(0.625445\pi\) | |||||||
\(14\) | −0.492820 | −0.131712 | ||||||||
\(15\) | 0.582818 | 0.150483 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −7.53438 | −1.82736 | −0.913678 | − | 0.406438i | \(-0.866771\pi\) | ||||
−0.913678 | + | 0.406438i | \(0.866771\pi\) | |||||||
\(18\) | 0.989407 | 0.233206 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | −0.291796 | −0.0652475 | ||||||||
\(21\) | 0.984334 | 0.214799 | ||||||||
\(22\) | −5.82808 | −1.24255 | ||||||||
\(23\) | −1.16315 | −0.242534 | −0.121267 | − | 0.992620i | \(-0.538696\pi\) | ||||
−0.121267 | + | 0.992620i | \(0.538696\pi\) | |||||||
\(24\) | −1.99735 | −0.407707 | ||||||||
\(25\) | −4.91486 | −0.982971 | ||||||||
\(26\) | −2.76888 | −0.543021 | ||||||||
\(27\) | 4.01586 | 0.772852 | ||||||||
\(28\) | −0.492820 | −0.0931342 | ||||||||
\(29\) | −5.53317 | −1.02748 | −0.513742 | − | 0.857945i | \(-0.671741\pi\) | ||||
−0.513742 | + | 0.857945i | \(0.671741\pi\) | |||||||
\(30\) | 0.582818 | 0.106408 | ||||||||
\(31\) | 0.123478 | 0.0221772 | 0.0110886 | − | 0.999939i | \(-0.496470\pi\) | ||||
0.0110886 | + | 0.999939i | \(0.496470\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 11.6407 | 2.02639 | ||||||||
\(34\) | −7.53438 | −1.29214 | ||||||||
\(35\) | 0.143803 | 0.0243071 | ||||||||
\(36\) | 0.989407 | 0.164901 | ||||||||
\(37\) | 0.138353 | 0.0227451 | 0.0113726 | − | 0.999935i | \(-0.496380\pi\) | ||||
0.0113726 | + | 0.999935i | \(0.496380\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | 5.53041 | 0.885575 | ||||||||
\(40\) | −0.291796 | −0.0461369 | ||||||||
\(41\) | −0.934090 | −0.145880 | −0.0729402 | − | 0.997336i | \(-0.523238\pi\) | ||||
−0.0729402 | + | 0.997336i | \(0.523238\pi\) | |||||||
\(42\) | 0.984334 | 0.151886 | ||||||||
\(43\) | 1.73877 | 0.265160 | 0.132580 | − | 0.991172i | \(-0.457674\pi\) | ||||
0.132580 | + | 0.991172i | \(0.457674\pi\) | |||||||
\(44\) | −5.82808 | −0.878616 | ||||||||
\(45\) | −0.288705 | −0.0430376 | ||||||||
\(46\) | −1.16315 | −0.171497 | ||||||||
\(47\) | 3.19055 | 0.465390 | 0.232695 | − | 0.972550i | \(-0.425246\pi\) | ||||
0.232695 | + | 0.972550i | \(0.425246\pi\) | |||||||
\(48\) | −1.99735 | −0.288293 | ||||||||
\(49\) | −6.75713 | −0.965304 | ||||||||
\(50\) | −4.91486 | −0.695066 | ||||||||
\(51\) | 15.0488 | 2.10725 | ||||||||
\(52\) | −2.76888 | −0.383974 | ||||||||
\(53\) | 0.526470 | 0.0723162 | 0.0361581 | − | 0.999346i | \(-0.488488\pi\) | ||||
0.0361581 | + | 0.999346i | \(0.488488\pi\) | |||||||
\(54\) | 4.01586 | 0.546489 | ||||||||
\(55\) | 1.70061 | 0.229310 | ||||||||
\(56\) | −0.492820 | −0.0658558 | ||||||||
\(57\) | 1.99735 | 0.264555 | ||||||||
\(58\) | −5.53317 | −0.726540 | ||||||||
\(59\) | −7.55977 | −0.984198 | −0.492099 | − | 0.870539i | \(-0.663770\pi\) | ||||
−0.492099 | + | 0.870539i | \(0.663770\pi\) | |||||||
\(60\) | 0.582818 | 0.0752415 | ||||||||
\(61\) | 5.41561 | 0.693398 | 0.346699 | − | 0.937976i | \(-0.387303\pi\) | ||||
0.346699 | + | 0.937976i | \(0.387303\pi\) | |||||||
\(62\) | 0.123478 | 0.0156817 | ||||||||
\(63\) | −0.487600 | −0.0614318 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.807946 | 0.100213 | ||||||||
\(66\) | 11.6407 | 1.43287 | ||||||||
\(67\) | −2.44673 | −0.298915 | −0.149458 | − | 0.988768i | \(-0.547753\pi\) | ||||
−0.149458 | + | 0.988768i | \(0.547753\pi\) | |||||||
\(68\) | −7.53438 | −0.913678 | ||||||||
\(69\) | 2.32322 | 0.279683 | ||||||||
\(70\) | 0.143803 | 0.0171877 | ||||||||
\(71\) | −5.21157 | −0.618500 | −0.309250 | − | 0.950981i | \(-0.600078\pi\) | ||||
−0.309250 | + | 0.950981i | \(0.600078\pi\) | |||||||
\(72\) | 0.989407 | 0.116603 | ||||||||
\(73\) | 10.6474 | 1.24619 | 0.623094 | − | 0.782147i | \(-0.285875\pi\) | ||||
0.623094 | + | 0.782147i | \(0.285875\pi\) | |||||||
\(74\) | 0.138353 | 0.0160832 | ||||||||
\(75\) | 9.81669 | 1.13353 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 2.87219 | 0.327317 | ||||||||
\(78\) | 5.53041 | 0.626196 | ||||||||
\(79\) | 6.09239 | 0.685448 | 0.342724 | − | 0.939436i | \(-0.388650\pi\) | ||||
0.342724 | + | 0.939436i | \(0.388650\pi\) | |||||||
\(80\) | −0.291796 | −0.0326237 | ||||||||
\(81\) | −10.9893 | −1.22103 | ||||||||
\(82\) | −0.934090 | −0.103153 | ||||||||
\(83\) | 0.696438 | 0.0764440 | 0.0382220 | − | 0.999269i | \(-0.487831\pi\) | ||||
0.0382220 | + | 0.999269i | \(0.487831\pi\) | |||||||
\(84\) | 0.984334 | 0.107400 | ||||||||
\(85\) | 2.19850 | 0.238461 | ||||||||
\(86\) | 1.73877 | 0.187496 | ||||||||
\(87\) | 11.0517 | 1.18486 | ||||||||
\(88\) | −5.82808 | −0.621275 | ||||||||
\(89\) | 15.6407 | 1.65791 | 0.828954 | − | 0.559317i | \(-0.188937\pi\) | ||||
0.828954 | + | 0.559317i | \(0.188937\pi\) | |||||||
\(90\) | −0.288705 | −0.0304321 | ||||||||
\(91\) | 1.36456 | 0.143044 | ||||||||
\(92\) | −1.16315 | −0.121267 | ||||||||
\(93\) | −0.246628 | −0.0255741 | ||||||||
\(94\) | 3.19055 | 0.329081 | ||||||||
\(95\) | 0.291796 | 0.0299376 | ||||||||
\(96\) | −1.99735 | −0.203854 | ||||||||
\(97\) | 3.77181 | 0.382969 | 0.191485 | − | 0.981496i | \(-0.438670\pi\) | ||||
0.191485 | + | 0.981496i | \(0.438670\pi\) | |||||||
\(98\) | −6.75713 | −0.682573 | ||||||||
\(99\) | −5.76634 | −0.579539 | ||||||||
\(100\) | −4.91486 | −0.491486 | ||||||||
\(101\) | −14.1513 | −1.40811 | −0.704055 | − | 0.710146i | \(-0.748629\pi\) | ||||
−0.704055 | + | 0.710146i | \(0.748629\pi\) | |||||||
\(102\) | 15.0488 | 1.49005 | ||||||||
\(103\) | 13.1376 | 1.29448 | 0.647242 | − | 0.762285i | \(-0.275922\pi\) | ||||
0.647242 | + | 0.762285i | \(0.275922\pi\) | |||||||
\(104\) | −2.76888 | −0.271511 | ||||||||
\(105\) | −0.287224 | −0.0280302 | ||||||||
\(106\) | 0.526470 | 0.0511352 | ||||||||
\(107\) | 3.34526 | 0.323398 | 0.161699 | − | 0.986840i | \(-0.448303\pi\) | ||||
0.161699 | + | 0.986840i | \(0.448303\pi\) | |||||||
\(108\) | 4.01586 | 0.386426 | ||||||||
\(109\) | 15.5871 | 1.49297 | 0.746486 | − | 0.665401i | \(-0.231739\pi\) | ||||
0.746486 | + | 0.665401i | \(0.231739\pi\) | |||||||
\(110\) | 1.70061 | 0.162147 | ||||||||
\(111\) | −0.276340 | −0.0262290 | ||||||||
\(112\) | −0.492820 | −0.0465671 | ||||||||
\(113\) | −18.5105 | −1.74132 | −0.870659 | − | 0.491887i | \(-0.836307\pi\) | ||||
−0.870659 | + | 0.491887i | \(0.836307\pi\) | |||||||
\(114\) | 1.99735 | 0.187069 | ||||||||
\(115\) | 0.339403 | 0.0316495 | ||||||||
\(116\) | −5.53317 | −0.513742 | ||||||||
\(117\) | −2.73955 | −0.253271 | ||||||||
\(118\) | −7.55977 | −0.695933 | ||||||||
\(119\) | 3.71310 | 0.340379 | ||||||||
\(120\) | 0.582818 | 0.0532038 | ||||||||
\(121\) | 22.9665 | 2.08786 | ||||||||
\(122\) | 5.41561 | 0.490306 | ||||||||
\(123\) | 1.86570 | 0.168225 | ||||||||
\(124\) | 0.123478 | 0.0110886 | ||||||||
\(125\) | 2.89311 | 0.258768 | ||||||||
\(126\) | −0.487600 | −0.0434388 | ||||||||
\(127\) | −14.9790 | −1.32918 | −0.664588 | − | 0.747210i | \(-0.731393\pi\) | ||||
−0.664588 | + | 0.747210i | \(0.731393\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −3.47293 | −0.305774 | ||||||||
\(130\) | 0.807946 | 0.0708615 | ||||||||
\(131\) | 4.23736 | 0.370220 | 0.185110 | − | 0.982718i | \(-0.440736\pi\) | ||||
0.185110 | + | 0.982718i | \(0.440736\pi\) | |||||||
\(132\) | 11.6407 | 1.01319 | ||||||||
\(133\) | 0.492820 | 0.0427329 | ||||||||
\(134\) | −2.44673 | −0.211365 | ||||||||
\(135\) | −1.17181 | −0.100853 | ||||||||
\(136\) | −7.53438 | −0.646068 | ||||||||
\(137\) | 13.9778 | 1.19420 | 0.597101 | − | 0.802166i | \(-0.296319\pi\) | ||||
0.597101 | + | 0.802166i | \(0.296319\pi\) | |||||||
\(138\) | 2.32322 | 0.197766 | ||||||||
\(139\) | 8.05368 | 0.683104 | 0.341552 | − | 0.939863i | \(-0.389047\pi\) | ||||
0.341552 | + | 0.939863i | \(0.389047\pi\) | |||||||
\(140\) | 0.143803 | 0.0121535 | ||||||||
\(141\) | −6.37265 | −0.536674 | ||||||||
\(142\) | −5.21157 | −0.437346 | ||||||||
\(143\) | 16.1372 | 1.34946 | ||||||||
\(144\) | 0.989407 | 0.0824506 | ||||||||
\(145\) | 1.61455 | 0.134081 | ||||||||
\(146\) | 10.6474 | 0.881188 | ||||||||
\(147\) | 13.4964 | 1.11316 | ||||||||
\(148\) | 0.138353 | 0.0113726 | ||||||||
\(149\) | 24.1329 | 1.97704 | 0.988520 | − | 0.151087i | \(-0.0482774\pi\) | ||||
0.988520 | + | 0.151087i | \(0.0482774\pi\) | |||||||
\(150\) | 9.81669 | 0.801529 | ||||||||
\(151\) | −11.8434 | −0.963803 | −0.481901 | − | 0.876226i | \(-0.660054\pi\) | ||||
−0.481901 | + | 0.876226i | \(0.660054\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | −7.45457 | −0.602667 | ||||||||
\(154\) | 2.87219 | 0.231448 | ||||||||
\(155\) | −0.0360302 | −0.00289402 | ||||||||
\(156\) | 5.53041 | 0.442787 | ||||||||
\(157\) | −11.3220 | −0.903594 | −0.451797 | − | 0.892121i | \(-0.649217\pi\) | ||||
−0.451797 | + | 0.892121i | \(0.649217\pi\) | |||||||
\(158\) | 6.09239 | 0.484685 | ||||||||
\(159\) | −1.05154 | −0.0833929 | ||||||||
\(160\) | −0.291796 | −0.0230685 | ||||||||
\(161\) | 0.573225 | 0.0451764 | ||||||||
\(162\) | −10.9893 | −0.863401 | ||||||||
\(163\) | −6.96207 | −0.545311 | −0.272656 | − | 0.962112i | \(-0.587902\pi\) | ||||
−0.272656 | + | 0.962112i | \(0.587902\pi\) | |||||||
\(164\) | −0.934090 | −0.0729402 | ||||||||
\(165\) | −3.39671 | −0.264433 | ||||||||
\(166\) | 0.696438 | 0.0540541 | ||||||||
\(167\) | −20.3291 | −1.57311 | −0.786557 | − | 0.617518i | \(-0.788138\pi\) | ||||
−0.786557 | + | 0.617518i | \(0.788138\pi\) | |||||||
\(168\) | 0.984334 | 0.0759430 | ||||||||
\(169\) | −5.33333 | −0.410256 | ||||||||
\(170\) | 2.19850 | 0.168617 | ||||||||
\(171\) | −0.989407 | −0.0756619 | ||||||||
\(172\) | 1.73877 | 0.132580 | ||||||||
\(173\) | −12.3099 | −0.935906 | −0.467953 | − | 0.883753i | \(-0.655008\pi\) | ||||
−0.467953 | + | 0.883753i | \(0.655008\pi\) | |||||||
\(174\) | 11.0517 | 0.837825 | ||||||||
\(175\) | 2.42214 | 0.183097 | ||||||||
\(176\) | −5.82808 | −0.439308 | ||||||||
\(177\) | 15.0995 | 1.13495 | ||||||||
\(178\) | 15.6407 | 1.17232 | ||||||||
\(179\) | −22.9118 | −1.71251 | −0.856253 | − | 0.516557i | \(-0.827213\pi\) | ||||
−0.856253 | + | 0.516557i | \(0.827213\pi\) | |||||||
\(180\) | −0.288705 | −0.0215188 | ||||||||
\(181\) | 16.3957 | 1.21868 | 0.609341 | − | 0.792908i | \(-0.291434\pi\) | ||||
0.609341 | + | 0.792908i | \(0.291434\pi\) | |||||||
\(182\) | 1.36456 | 0.101148 | ||||||||
\(183\) | −10.8169 | −0.799606 | ||||||||
\(184\) | −1.16315 | −0.0857487 | ||||||||
\(185\) | −0.0403709 | −0.00296813 | ||||||||
\(186\) | −0.246628 | −0.0180836 | ||||||||
\(187\) | 43.9110 | 3.21109 | ||||||||
\(188\) | 3.19055 | 0.232695 | ||||||||
\(189\) | −1.97910 | −0.143958 | ||||||||
\(190\) | 0.291796 | 0.0211691 | ||||||||
\(191\) | 19.1529 | 1.38586 | 0.692928 | − | 0.721007i | \(-0.256320\pi\) | ||||
0.692928 | + | 0.721007i | \(0.256320\pi\) | |||||||
\(192\) | −1.99735 | −0.144146 | ||||||||
\(193\) | −23.7671 | −1.71079 | −0.855396 | − | 0.517974i | \(-0.826686\pi\) | ||||
−0.855396 | + | 0.517974i | \(0.826686\pi\) | |||||||
\(194\) | 3.77181 | 0.270800 | ||||||||
\(195\) | −1.61375 | −0.115563 | ||||||||
\(196\) | −6.75713 | −0.482652 | ||||||||
\(197\) | −3.50954 | −0.250044 | −0.125022 | − | 0.992154i | \(-0.539900\pi\) | ||||
−0.125022 | + | 0.992154i | \(0.539900\pi\) | |||||||
\(198\) | −5.76634 | −0.409796 | ||||||||
\(199\) | −12.7834 | −0.906191 | −0.453095 | − | 0.891462i | \(-0.649680\pi\) | ||||
−0.453095 | + | 0.891462i | \(0.649680\pi\) | |||||||
\(200\) | −4.91486 | −0.347533 | ||||||||
\(201\) | 4.88697 | 0.344700 | ||||||||
\(202\) | −14.1513 | −0.995684 | ||||||||
\(203\) | 2.72686 | 0.191388 | ||||||||
\(204\) | 15.0488 | 1.05363 | ||||||||
\(205\) | 0.272563 | 0.0190366 | ||||||||
\(206\) | 13.1376 | 0.915338 | ||||||||
\(207\) | −1.15083 | −0.0799883 | ||||||||
\(208\) | −2.76888 | −0.191987 | ||||||||
\(209\) | 5.82808 | 0.403137 | ||||||||
\(210\) | −0.287224 | −0.0198204 | ||||||||
\(211\) | −1.00000 | −0.0688428 | ||||||||
\(212\) | 0.526470 | 0.0361581 | ||||||||
\(213\) | 10.4093 | 0.713236 | ||||||||
\(214\) | 3.34526 | 0.228677 | ||||||||
\(215\) | −0.507365 | −0.0346020 | ||||||||
\(216\) | 4.01586 | 0.273244 | ||||||||
\(217\) | −0.0608522 | −0.00413092 | ||||||||
\(218\) | 15.5871 | 1.05569 | ||||||||
\(219\) | −21.2666 | −1.43707 | ||||||||
\(220\) | 1.70061 | 0.114655 | ||||||||
\(221\) | 20.8618 | 1.40331 | ||||||||
\(222\) | −0.276340 | −0.0185467 | ||||||||
\(223\) | −24.5778 | −1.64585 | −0.822927 | − | 0.568148i | \(-0.807660\pi\) | ||||
−0.822927 | + | 0.568148i | \(0.807660\pi\) | |||||||
\(224\) | −0.492820 | −0.0329279 | ||||||||
\(225\) | −4.86279 | −0.324186 | ||||||||
\(226\) | −18.5105 | −1.23130 | ||||||||
\(227\) | −21.9324 | −1.45570 | −0.727852 | − | 0.685735i | \(-0.759481\pi\) | ||||
−0.727852 | + | 0.685735i | \(0.759481\pi\) | |||||||
\(228\) | 1.99735 | 0.132278 | ||||||||
\(229\) | 12.8876 | 0.851634 | 0.425817 | − | 0.904809i | \(-0.359987\pi\) | ||||
0.425817 | + | 0.904809i | \(0.359987\pi\) | |||||||
\(230\) | 0.339403 | 0.0223795 | ||||||||
\(231\) | −5.73678 | −0.377452 | ||||||||
\(232\) | −5.53317 | −0.363270 | ||||||||
\(233\) | 3.47952 | 0.227951 | 0.113975 | − | 0.993484i | \(-0.463642\pi\) | ||||
0.113975 | + | 0.993484i | \(0.463642\pi\) | |||||||
\(234\) | −2.73955 | −0.179090 | ||||||||
\(235\) | −0.930990 | −0.0607311 | ||||||||
\(236\) | −7.55977 | −0.492099 | ||||||||
\(237\) | −12.1686 | −0.790438 | ||||||||
\(238\) | 3.71310 | 0.240684 | ||||||||
\(239\) | 13.0297 | 0.842819 | 0.421410 | − | 0.906870i | \(-0.361535\pi\) | ||||
0.421410 | + | 0.906870i | \(0.361535\pi\) | |||||||
\(240\) | 0.582818 | 0.0376207 | ||||||||
\(241\) | −15.5204 | −0.999757 | −0.499878 | − | 0.866096i | \(-0.666622\pi\) | ||||
−0.499878 | + | 0.866096i | \(0.666622\pi\) | |||||||
\(242\) | 22.9665 | 1.47634 | ||||||||
\(243\) | 9.90190 | 0.635207 | ||||||||
\(244\) | 5.41561 | 0.346699 | ||||||||
\(245\) | 1.97170 | 0.125967 | ||||||||
\(246\) | 1.86570 | 0.118953 | ||||||||
\(247\) | 2.76888 | 0.176179 | ||||||||
\(248\) | 0.123478 | 0.00784083 | ||||||||
\(249\) | −1.39103 | −0.0881530 | ||||||||
\(250\) | 2.89311 | 0.182976 | ||||||||
\(251\) | −27.0675 | −1.70849 | −0.854243 | − | 0.519873i | \(-0.825979\pi\) | ||||
−0.854243 | + | 0.519873i | \(0.825979\pi\) | |||||||
\(252\) | −0.487600 | −0.0307159 | ||||||||
\(253\) | 6.77894 | 0.426188 | ||||||||
\(254\) | −14.9790 | −0.939869 | ||||||||
\(255\) | −4.39117 | −0.274986 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −15.5280 | −0.968608 | −0.484304 | − | 0.874900i | \(-0.660927\pi\) | ||||
−0.484304 | + | 0.874900i | \(0.660927\pi\) | |||||||
\(258\) | −3.47293 | −0.216215 | ||||||||
\(259\) | −0.0681833 | −0.00423670 | ||||||||
\(260\) | 0.807946 | 0.0501067 | ||||||||
\(261\) | −5.47456 | −0.338866 | ||||||||
\(262\) | 4.23736 | 0.261785 | ||||||||
\(263\) | 7.97221 | 0.491588 | 0.245794 | − | 0.969322i | \(-0.420951\pi\) | ||||
0.245794 | + | 0.969322i | \(0.420951\pi\) | |||||||
\(264\) | 11.6407 | 0.716436 | ||||||||
\(265\) | −0.153621 | −0.00943689 | ||||||||
\(266\) | 0.492820 | 0.0302167 | ||||||||
\(267\) | −31.2399 | −1.91185 | ||||||||
\(268\) | −2.44673 | −0.149458 | ||||||||
\(269\) | 18.4928 | 1.12752 | 0.563762 | − | 0.825937i | \(-0.309353\pi\) | ||||
0.563762 | + | 0.825937i | \(0.309353\pi\) | |||||||
\(270\) | −1.17181 | −0.0713141 | ||||||||
\(271\) | −28.4817 | −1.73014 | −0.865069 | − | 0.501653i | \(-0.832726\pi\) | ||||
−0.865069 | + | 0.501653i | \(0.832726\pi\) | |||||||
\(272\) | −7.53438 | −0.456839 | ||||||||
\(273\) | −2.72550 | −0.164955 | ||||||||
\(274\) | 13.9778 | 0.844429 | ||||||||
\(275\) | 28.6442 | 1.72731 | ||||||||
\(276\) | 2.32322 | 0.139842 | ||||||||
\(277\) | 31.9367 | 1.91889 | 0.959444 | − | 0.281900i | \(-0.0909646\pi\) | ||||
0.959444 | + | 0.281900i | \(0.0909646\pi\) | |||||||
\(278\) | 8.05368 | 0.483027 | ||||||||
\(279\) | 0.122170 | 0.00731410 | ||||||||
\(280\) | 0.143803 | 0.00859386 | ||||||||
\(281\) | 16.0852 | 0.959563 | 0.479781 | − | 0.877388i | \(-0.340716\pi\) | ||||
0.479781 | + | 0.877388i | \(0.340716\pi\) | |||||||
\(282\) | −6.37265 | −0.379486 | ||||||||
\(283\) | 26.7258 | 1.58868 | 0.794342 | − | 0.607471i | \(-0.207816\pi\) | ||||
0.794342 | + | 0.607471i | \(0.207816\pi\) | |||||||
\(284\) | −5.21157 | −0.309250 | ||||||||
\(285\) | −0.582818 | −0.0345232 | ||||||||
\(286\) | 16.1372 | 0.954214 | ||||||||
\(287\) | 0.460338 | 0.0271729 | ||||||||
\(288\) | 0.989407 | 0.0583014 | ||||||||
\(289\) | 39.7669 | 2.33923 | ||||||||
\(290\) | 1.61455 | 0.0948099 | ||||||||
\(291\) | −7.53363 | −0.441629 | ||||||||
\(292\) | 10.6474 | 0.623094 | ||||||||
\(293\) | −6.32828 | −0.369702 | −0.184851 | − | 0.982767i | \(-0.559180\pi\) | ||||
−0.184851 | + | 0.982767i | \(0.559180\pi\) | |||||||
\(294\) | 13.4964 | 0.787123 | ||||||||
\(295\) | 2.20591 | 0.128433 | ||||||||
\(296\) | 0.138353 | 0.00804162 | ||||||||
\(297\) | −23.4047 | −1.35808 | ||||||||
\(298\) | 24.1329 | 1.39798 | ||||||||
\(299\) | 3.22062 | 0.186253 | ||||||||
\(300\) | 9.81669 | 0.566767 | ||||||||
\(301\) | −0.856900 | −0.0493909 | ||||||||
\(302\) | −11.8434 | −0.681511 | ||||||||
\(303\) | 28.2651 | 1.62379 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | −1.58025 | −0.0904849 | ||||||||
\(306\) | −7.45457 | −0.426150 | ||||||||
\(307\) | 21.8190 | 1.24527 | 0.622637 | − | 0.782511i | \(-0.286061\pi\) | ||||
0.622637 | + | 0.782511i | \(0.286061\pi\) | |||||||
\(308\) | 2.87219 | 0.163658 | ||||||||
\(309\) | −26.2403 | −1.49276 | ||||||||
\(310\) | −0.0360302 | −0.00204638 | ||||||||
\(311\) | 0.448831 | 0.0254509 | 0.0127254 | − | 0.999919i | \(-0.495949\pi\) | ||||
0.0127254 | + | 0.999919i | \(0.495949\pi\) | |||||||
\(312\) | 5.53041 | 0.313098 | ||||||||
\(313\) | −7.58291 | −0.428611 | −0.214306 | − | 0.976767i | \(-0.568749\pi\) | ||||
−0.214306 | + | 0.976767i | \(0.568749\pi\) | |||||||
\(314\) | −11.3220 | −0.638938 | ||||||||
\(315\) | 0.142279 | 0.00801654 | ||||||||
\(316\) | 6.09239 | 0.342724 | ||||||||
\(317\) | −5.26198 | −0.295543 | −0.147771 | − | 0.989022i | \(-0.547210\pi\) | ||||
−0.147771 | + | 0.989022i | \(0.547210\pi\) | |||||||
\(318\) | −1.05154 | −0.0589677 | ||||||||
\(319\) | 32.2477 | 1.80553 | ||||||||
\(320\) | −0.291796 | −0.0163119 | ||||||||
\(321\) | −6.68165 | −0.372933 | ||||||||
\(322\) | 0.573225 | 0.0319446 | ||||||||
\(323\) | 7.53438 | 0.419224 | ||||||||
\(324\) | −10.9893 | −0.610516 | ||||||||
\(325\) | 13.6086 | 0.754870 | ||||||||
\(326\) | −6.96207 | −0.385593 | ||||||||
\(327\) | −31.1329 | −1.72165 | ||||||||
\(328\) | −0.934090 | −0.0515765 | ||||||||
\(329\) | −1.57237 | −0.0866875 | ||||||||
\(330\) | −3.39671 | −0.186983 | ||||||||
\(331\) | −6.85598 | −0.376839 | −0.188419 | − | 0.982089i | \(-0.560336\pi\) | ||||
−0.188419 | + | 0.982089i | \(0.560336\pi\) | |||||||
\(332\) | 0.696438 | 0.0382220 | ||||||||
\(333\) | 0.136888 | 0.00750140 | ||||||||
\(334\) | −20.3291 | −1.11236 | ||||||||
\(335\) | 0.713944 | 0.0390069 | ||||||||
\(336\) | 0.984334 | 0.0536998 | ||||||||
\(337\) | −25.1687 | −1.37103 | −0.685515 | − | 0.728059i | \(-0.740423\pi\) | ||||
−0.685515 | + | 0.728059i | \(0.740423\pi\) | |||||||
\(338\) | −5.33333 | −0.290095 | ||||||||
\(339\) | 36.9719 | 2.00804 | ||||||||
\(340\) | 2.19850 | 0.119230 | ||||||||
\(341\) | −0.719637 | −0.0389705 | ||||||||
\(342\) | −0.989407 | −0.0535010 | ||||||||
\(343\) | 6.77979 | 0.366074 | ||||||||
\(344\) | 1.73877 | 0.0937481 | ||||||||
\(345\) | −0.677906 | −0.0364972 | ||||||||
\(346\) | −12.3099 | −0.661785 | ||||||||
\(347\) | 12.2928 | 0.659910 | 0.329955 | − | 0.943997i | \(-0.392966\pi\) | ||||
0.329955 | + | 0.943997i | \(0.392966\pi\) | |||||||
\(348\) | 11.0517 | 0.592432 | ||||||||
\(349\) | 14.6723 | 0.785389 | 0.392694 | − | 0.919669i | \(-0.371543\pi\) | ||||
0.392694 | + | 0.919669i | \(0.371543\pi\) | |||||||
\(350\) | 2.42214 | 0.129469 | ||||||||
\(351\) | −11.1194 | −0.593510 | ||||||||
\(352\) | −5.82808 | −0.310638 | ||||||||
\(353\) | 12.8028 | 0.681422 | 0.340711 | − | 0.940168i | \(-0.389332\pi\) | ||||
0.340711 | + | 0.940168i | \(0.389332\pi\) | |||||||
\(354\) | 15.0995 | 0.802530 | ||||||||
\(355\) | 1.52071 | 0.0807111 | ||||||||
\(356\) | 15.6407 | 0.828954 | ||||||||
\(357\) | −7.41635 | −0.392515 | ||||||||
\(358\) | −22.9118 | −1.21092 | ||||||||
\(359\) | −30.8014 | −1.62564 | −0.812819 | − | 0.582516i | \(-0.802068\pi\) | ||||
−0.812819 | + | 0.582516i | \(0.802068\pi\) | |||||||
\(360\) | −0.288705 | −0.0152161 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 16.3957 | 0.861739 | ||||||||
\(363\) | −45.8721 | −2.40766 | ||||||||
\(364\) | 1.36456 | 0.0715222 | ||||||||
\(365\) | −3.10687 | −0.162621 | ||||||||
\(366\) | −10.8169 | −0.565407 | ||||||||
\(367\) | −0.442858 | −0.0231170 | −0.0115585 | − | 0.999933i | \(-0.503679\pi\) | ||||
−0.0115585 | + | 0.999933i | \(0.503679\pi\) | |||||||
\(368\) | −1.16315 | −0.0606335 | ||||||||
\(369\) | −0.924195 | −0.0481117 | ||||||||
\(370\) | −0.0403709 | −0.00209878 | ||||||||
\(371\) | −0.259455 | −0.0134702 | ||||||||
\(372\) | −0.246628 | −0.0127871 | ||||||||
\(373\) | 29.7502 | 1.54041 | 0.770204 | − | 0.637797i | \(-0.220154\pi\) | ||||
0.770204 | + | 0.637797i | \(0.220154\pi\) | |||||||
\(374\) | 43.9110 | 2.27058 | ||||||||
\(375\) | −5.77856 | −0.298403 | ||||||||
\(376\) | 3.19055 | 0.164540 | ||||||||
\(377\) | 15.3206 | 0.789054 | ||||||||
\(378\) | −1.97910 | −0.101794 | ||||||||
\(379\) | 11.9391 | 0.613271 | 0.306636 | − | 0.951827i | \(-0.400797\pi\) | ||||
0.306636 | + | 0.951827i | \(0.400797\pi\) | |||||||
\(380\) | 0.291796 | 0.0149688 | ||||||||
\(381\) | 29.9184 | 1.53277 | ||||||||
\(382\) | 19.1529 | 0.979948 | ||||||||
\(383\) | 7.06516 | 0.361013 | 0.180506 | − | 0.983574i | \(-0.442226\pi\) | ||||
0.180506 | + | 0.983574i | \(0.442226\pi\) | |||||||
\(384\) | −1.99735 | −0.101927 | ||||||||
\(385\) | −0.838093 | −0.0427132 | ||||||||
\(386\) | −23.7671 | −1.20971 | ||||||||
\(387\) | 1.72035 | 0.0874503 | ||||||||
\(388\) | 3.77181 | 0.191485 | ||||||||
\(389\) | 0.804055 | 0.0407672 | 0.0203836 | − | 0.999792i | \(-0.493511\pi\) | ||||
0.0203836 | + | 0.999792i | \(0.493511\pi\) | |||||||
\(390\) | −1.61375 | −0.0817154 | ||||||||
\(391\) | 8.76363 | 0.443196 | ||||||||
\(392\) | −6.75713 | −0.341287 | ||||||||
\(393\) | −8.46349 | −0.426927 | ||||||||
\(394\) | −3.50954 | −0.176808 | ||||||||
\(395\) | −1.77773 | −0.0894475 | ||||||||
\(396\) | −5.76634 | −0.289770 | ||||||||
\(397\) | −7.48659 | −0.375741 | −0.187870 | − | 0.982194i | \(-0.560159\pi\) | ||||
−0.187870 | + | 0.982194i | \(0.560159\pi\) | |||||||
\(398\) | −12.7834 | −0.640774 | ||||||||
\(399\) | −0.984334 | −0.0492783 | ||||||||
\(400\) | −4.91486 | −0.245743 | ||||||||
\(401\) | 30.1926 | 1.50775 | 0.753874 | − | 0.657019i | \(-0.228183\pi\) | ||||
0.753874 | + | 0.657019i | \(0.228183\pi\) | |||||||
\(402\) | 4.88697 | 0.243740 | ||||||||
\(403\) | −0.341894 | −0.0170310 | ||||||||
\(404\) | −14.1513 | −0.704055 | ||||||||
\(405\) | 3.20663 | 0.159339 | ||||||||
\(406\) | 2.72686 | 0.135332 | ||||||||
\(407\) | −0.806333 | −0.0399685 | ||||||||
\(408\) | 15.0488 | 0.745027 | ||||||||
\(409\) | 14.6143 | 0.722632 | 0.361316 | − | 0.932443i | \(-0.382328\pi\) | ||||
0.361316 | + | 0.932443i | \(0.382328\pi\) | |||||||
\(410\) | 0.272563 | 0.0134609 | ||||||||
\(411\) | −27.9185 | −1.37712 | ||||||||
\(412\) | 13.1376 | 0.647242 | ||||||||
\(413\) | 3.72561 | 0.183325 | ||||||||
\(414\) | −1.15083 | −0.0565603 | ||||||||
\(415\) | −0.203218 | −0.00997556 | ||||||||
\(416\) | −2.76888 | −0.135755 | ||||||||
\(417\) | −16.0860 | −0.787735 | ||||||||
\(418\) | 5.82808 | 0.285061 | ||||||||
\(419\) | −31.7737 | −1.55225 | −0.776123 | − | 0.630581i | \(-0.782816\pi\) | ||||
−0.776123 | + | 0.630581i | \(0.782816\pi\) | |||||||
\(420\) | −0.287224 | −0.0140151 | ||||||||
\(421\) | 35.8484 | 1.74715 | 0.873573 | − | 0.486694i | \(-0.161797\pi\) | ||||
0.873573 | + | 0.486694i | \(0.161797\pi\) | |||||||
\(422\) | −1.00000 | −0.0486792 | ||||||||
\(423\) | 3.15676 | 0.153487 | ||||||||
\(424\) | 0.526470 | 0.0255676 | ||||||||
\(425\) | 37.0304 | 1.79624 | ||||||||
\(426\) | 10.4093 | 0.504334 | ||||||||
\(427\) | −2.66892 | −0.129158 | ||||||||
\(428\) | 3.34526 | 0.161699 | ||||||||
\(429\) | −32.2317 | −1.55616 | ||||||||
\(430\) | −0.507365 | −0.0244673 | ||||||||
\(431\) | 2.41840 | 0.116490 | 0.0582450 | − | 0.998302i | \(-0.481450\pi\) | ||||
0.0582450 | + | 0.998302i | \(0.481450\pi\) | |||||||
\(432\) | 4.01586 | 0.193213 | ||||||||
\(433\) | 26.0821 | 1.25343 | 0.626713 | − | 0.779250i | \(-0.284400\pi\) | ||||
0.626713 | + | 0.779250i | \(0.284400\pi\) | |||||||
\(434\) | −0.0608522 | −0.00292100 | ||||||||
\(435\) | −3.22483 | −0.154619 | ||||||||
\(436\) | 15.5871 | 0.746486 | ||||||||
\(437\) | 1.16315 | 0.0556411 | ||||||||
\(438\) | −21.2666 | −1.01616 | ||||||||
\(439\) | 9.81398 | 0.468396 | 0.234198 | − | 0.972189i | \(-0.424754\pi\) | ||||
0.234198 | + | 0.972189i | \(0.424754\pi\) | |||||||
\(440\) | 1.70061 | 0.0810733 | ||||||||
\(441\) | −6.68555 | −0.318360 | ||||||||
\(442\) | 20.8618 | 0.992293 | ||||||||
\(443\) | −7.96518 | −0.378437 | −0.189219 | − | 0.981935i | \(-0.560595\pi\) | ||||
−0.189219 | + | 0.981935i | \(0.560595\pi\) | |||||||
\(444\) | −0.276340 | −0.0131145 | ||||||||
\(445\) | −4.56388 | −0.216349 | ||||||||
\(446\) | −24.5778 | −1.16379 | ||||||||
\(447\) | −48.2018 | −2.27987 | ||||||||
\(448\) | −0.492820 | −0.0232836 | ||||||||
\(449\) | 41.7261 | 1.96917 | 0.984587 | − | 0.174894i | \(-0.0559581\pi\) | ||||
0.984587 | + | 0.174894i | \(0.0559581\pi\) | |||||||
\(450\) | −4.86279 | −0.229234 | ||||||||
\(451\) | 5.44395 | 0.256345 | ||||||||
\(452\) | −18.5105 | −0.870659 | ||||||||
\(453\) | 23.6554 | 1.11143 | ||||||||
\(454\) | −21.9324 | −1.02934 | ||||||||
\(455\) | −0.398172 | −0.0186666 | ||||||||
\(456\) | 1.99735 | 0.0935345 | ||||||||
\(457\) | 1.15273 | 0.0539224 | 0.0269612 | − | 0.999636i | \(-0.491417\pi\) | ||||
0.0269612 | + | 0.999636i | \(0.491417\pi\) | |||||||
\(458\) | 12.8876 | 0.602196 | ||||||||
\(459\) | −30.2570 | −1.41228 | ||||||||
\(460\) | 0.339403 | 0.0158247 | ||||||||
\(461\) | 10.4866 | 0.488410 | 0.244205 | − | 0.969724i | \(-0.421473\pi\) | ||||
0.244205 | + | 0.969724i | \(0.421473\pi\) | |||||||
\(462\) | −5.73678 | −0.266899 | ||||||||
\(463\) | 12.0262 | 0.558904 | 0.279452 | − | 0.960160i | \(-0.409847\pi\) | ||||
0.279452 | + | 0.960160i | \(0.409847\pi\) | |||||||
\(464\) | −5.53317 | −0.256871 | ||||||||
\(465\) | 0.0719649 | 0.00333729 | ||||||||
\(466\) | 3.47952 | 0.161186 | ||||||||
\(467\) | 3.99432 | 0.184835 | 0.0924175 | − | 0.995720i | \(-0.470541\pi\) | ||||
0.0924175 | + | 0.995720i | \(0.470541\pi\) | |||||||
\(468\) | −2.73955 | −0.126636 | ||||||||
\(469\) | 1.20580 | 0.0556785 | ||||||||
\(470\) | −0.930990 | −0.0429433 | ||||||||
\(471\) | 22.6140 | 1.04200 | ||||||||
\(472\) | −7.55977 | −0.347967 | ||||||||
\(473\) | −10.1337 | −0.465947 | ||||||||
\(474\) | −12.1686 | −0.558924 | ||||||||
\(475\) | 4.91486 | 0.225509 | ||||||||
\(476\) | 3.71310 | 0.170189 | ||||||||
\(477\) | 0.520893 | 0.0238500 | ||||||||
\(478\) | 13.0297 | 0.595963 | ||||||||
\(479\) | −25.3246 | −1.15711 | −0.578556 | − | 0.815643i | \(-0.696383\pi\) | ||||
−0.578556 | + | 0.815643i | \(0.696383\pi\) | |||||||
\(480\) | 0.582818 | 0.0266019 | ||||||||
\(481\) | −0.383083 | −0.0174671 | ||||||||
\(482\) | −15.5204 | −0.706935 | ||||||||
\(483\) | −1.14493 | −0.0520961 | ||||||||
\(484\) | 22.9665 | 1.04393 | ||||||||
\(485\) | −1.10060 | −0.0499756 | ||||||||
\(486\) | 9.90190 | 0.449159 | ||||||||
\(487\) | 8.66907 | 0.392833 | 0.196417 | − | 0.980521i | \(-0.437070\pi\) | ||||
0.196417 | + | 0.980521i | \(0.437070\pi\) | |||||||
\(488\) | 5.41561 | 0.245153 | ||||||||
\(489\) | 13.9057 | 0.628837 | ||||||||
\(490\) | 1.97170 | 0.0890723 | ||||||||
\(491\) | −19.3277 | −0.872248 | −0.436124 | − | 0.899887i | \(-0.643649\pi\) | ||||
−0.436124 | + | 0.899887i | \(0.643649\pi\) | |||||||
\(492\) | 1.86570 | 0.0841124 | ||||||||
\(493\) | 41.6890 | 1.87758 | ||||||||
\(494\) | 2.76888 | 0.124578 | ||||||||
\(495\) | 1.68259 | 0.0756269 | ||||||||
\(496\) | 0.123478 | 0.00554431 | ||||||||
\(497\) | 2.56837 | 0.115207 | ||||||||
\(498\) | −1.39103 | −0.0623336 | ||||||||
\(499\) | −36.3023 | −1.62511 | −0.812556 | − | 0.582883i | \(-0.801925\pi\) | ||||
−0.812556 | + | 0.582883i | \(0.801925\pi\) | |||||||
\(500\) | 2.89311 | 0.129384 | ||||||||
\(501\) | 40.6043 | 1.81407 | ||||||||
\(502\) | −27.0675 | −1.20808 | ||||||||
\(503\) | 10.2155 | 0.455487 | 0.227744 | − | 0.973721i | \(-0.426865\pi\) | ||||
0.227744 | + | 0.973721i | \(0.426865\pi\) | |||||||
\(504\) | −0.487600 | −0.0217194 | ||||||||
\(505\) | 4.12929 | 0.183751 | ||||||||
\(506\) | 6.77894 | 0.301361 | ||||||||
\(507\) | 10.6525 | 0.473095 | ||||||||
\(508\) | −14.9790 | −0.664588 | ||||||||
\(509\) | −21.1152 | −0.935915 | −0.467958 | − | 0.883751i | \(-0.655010\pi\) | ||||
−0.467958 | + | 0.883751i | \(0.655010\pi\) | |||||||
\(510\) | −4.39117 | −0.194444 | ||||||||
\(511\) | −5.24727 | −0.232125 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −4.01586 | −0.177304 | ||||||||
\(514\) | −15.5280 | −0.684909 | ||||||||
\(515\) | −3.83349 | −0.168924 | ||||||||
\(516\) | −3.47293 | −0.152887 | ||||||||
\(517\) | −18.5948 | −0.817798 | ||||||||
\(518\) | −0.0681833 | −0.00299580 | ||||||||
\(519\) | 24.5872 | 1.07926 | ||||||||
\(520\) | 0.807946 | 0.0354308 | ||||||||
\(521\) | −33.4775 | −1.46668 | −0.733339 | − | 0.679863i | \(-0.762039\pi\) | ||||
−0.733339 | + | 0.679863i | \(0.762039\pi\) | |||||||
\(522\) | −5.47456 | −0.239615 | ||||||||
\(523\) | 9.79291 | 0.428214 | 0.214107 | − | 0.976810i | \(-0.431316\pi\) | ||||
0.214107 | + | 0.976810i | \(0.431316\pi\) | |||||||
\(524\) | 4.23736 | 0.185110 | ||||||||
\(525\) | −4.83786 | −0.211142 | ||||||||
\(526\) | 7.97221 | 0.347605 | ||||||||
\(527\) | −0.930327 | −0.0405257 | ||||||||
\(528\) | 11.6407 | 0.506597 | ||||||||
\(529\) | −21.6471 | −0.941177 | ||||||||
\(530\) | −0.153621 | −0.00667289 | ||||||||
\(531\) | −7.47969 | −0.324591 | ||||||||
\(532\) | 0.492820 | 0.0213665 | ||||||||
\(533\) | 2.58638 | 0.112028 | ||||||||
\(534\) | −31.2399 | −1.35188 | ||||||||
\(535\) | −0.976131 | −0.0422018 | ||||||||
\(536\) | −2.44673 | −0.105683 | ||||||||
\(537\) | 45.7628 | 1.97481 | ||||||||
\(538\) | 18.4928 | 0.797280 | ||||||||
\(539\) | 39.3811 | 1.69626 | ||||||||
\(540\) | −1.17181 | −0.0504267 | ||||||||
\(541\) | 13.5677 | 0.583322 | 0.291661 | − | 0.956522i | \(-0.405792\pi\) | ||||
0.291661 | + | 0.956522i | \(0.405792\pi\) | |||||||
\(542\) | −28.4817 | −1.22339 | ||||||||
\(543\) | −32.7479 | −1.40535 | ||||||||
\(544\) | −7.53438 | −0.323034 | ||||||||
\(545\) | −4.54824 | −0.194825 | ||||||||
\(546\) | −2.72550 | −0.116641 | ||||||||
\(547\) | 28.3311 | 1.21135 | 0.605676 | − | 0.795712i | \(-0.292903\pi\) | ||||
0.605676 | + | 0.795712i | \(0.292903\pi\) | |||||||
\(548\) | 13.9778 | 0.597101 | ||||||||
\(549\) | 5.35824 | 0.228684 | ||||||||
\(550\) | 28.6442 | 1.22139 | ||||||||
\(551\) | 5.53317 | 0.235721 | ||||||||
\(552\) | 2.32322 | 0.0988829 | ||||||||
\(553\) | −3.00245 | −0.127677 | ||||||||
\(554\) | 31.9367 | 1.35686 | ||||||||
\(555\) | 0.0806348 | 0.00342275 | ||||||||
\(556\) | 8.05368 | 0.341552 | ||||||||
\(557\) | −5.25046 | −0.222469 | −0.111235 | − | 0.993794i | \(-0.535480\pi\) | ||||
−0.111235 | + | 0.993794i | \(0.535480\pi\) | |||||||
\(558\) | 0.122170 | 0.00517185 | ||||||||
\(559\) | −4.81443 | −0.203629 | ||||||||
\(560\) | 0.143803 | 0.00607677 | ||||||||
\(561\) | −87.7056 | −3.70293 | ||||||||
\(562\) | 16.0852 | 0.678513 | ||||||||
\(563\) | −42.7066 | −1.79987 | −0.899935 | − | 0.436024i | \(-0.856386\pi\) | ||||
−0.899935 | + | 0.436024i | \(0.856386\pi\) | |||||||
\(564\) | −6.37265 | −0.268337 | ||||||||
\(565\) | 5.40127 | 0.227233 | ||||||||
\(566\) | 26.7258 | 1.12337 | ||||||||
\(567\) | 5.41574 | 0.227440 | ||||||||
\(568\) | −5.21157 | −0.218673 | ||||||||
\(569\) | 19.9747 | 0.837382 | 0.418691 | − | 0.908129i | \(-0.362489\pi\) | ||||
0.418691 | + | 0.908129i | \(0.362489\pi\) | |||||||
\(570\) | −0.582818 | −0.0244116 | ||||||||
\(571\) | −45.3844 | −1.89928 | −0.949640 | − | 0.313343i | \(-0.898551\pi\) | ||||
−0.949640 | + | 0.313343i | \(0.898551\pi\) | |||||||
\(572\) | 16.1372 | 0.674731 | ||||||||
\(573\) | −38.2551 | −1.59813 | ||||||||
\(574\) | 0.460338 | 0.0192141 | ||||||||
\(575\) | 5.71672 | 0.238404 | ||||||||
\(576\) | 0.989407 | 0.0412253 | ||||||||
\(577\) | −5.22582 | −0.217554 | −0.108777 | − | 0.994066i | \(-0.534693\pi\) | ||||
−0.108777 | + | 0.994066i | \(0.534693\pi\) | |||||||
\(578\) | 39.7669 | 1.65409 | ||||||||
\(579\) | 47.4712 | 1.97284 | ||||||||
\(580\) | 1.61455 | 0.0670407 | ||||||||
\(581\) | −0.343219 | −0.0142391 | ||||||||
\(582\) | −7.53363 | −0.312279 | ||||||||
\(583\) | −3.06831 | −0.127076 | ||||||||
\(584\) | 10.6474 | 0.440594 | ||||||||
\(585\) | 0.799387 | 0.0330506 | ||||||||
\(586\) | −6.32828 | −0.261419 | ||||||||
\(587\) | 40.9700 | 1.69101 | 0.845506 | − | 0.533966i | \(-0.179299\pi\) | ||||
0.845506 | + | 0.533966i | \(0.179299\pi\) | |||||||
\(588\) | 13.4964 | 0.556580 | ||||||||
\(589\) | −0.123478 | −0.00508780 | ||||||||
\(590\) | 2.20591 | 0.0908158 | ||||||||
\(591\) | 7.00978 | 0.288344 | ||||||||
\(592\) | 0.138353 | 0.00568628 | ||||||||
\(593\) | −11.5644 | −0.474892 | −0.237446 | − | 0.971401i | \(-0.576310\pi\) | ||||
−0.237446 | + | 0.971401i | \(0.576310\pi\) | |||||||
\(594\) | −23.4047 | −0.960308 | ||||||||
\(595\) | −1.08346 | −0.0444177 | ||||||||
\(596\) | 24.1329 | 0.988520 | ||||||||
\(597\) | 25.5329 | 1.04499 | ||||||||
\(598\) | 3.22062 | 0.131701 | ||||||||
\(599\) | 18.8113 | 0.768610 | 0.384305 | − | 0.923206i | \(-0.374441\pi\) | ||||
0.384305 | + | 0.923206i | \(0.374441\pi\) | |||||||
\(600\) | 9.81669 | 0.400765 | ||||||||
\(601\) | −9.98897 | −0.407459 | −0.203729 | − | 0.979027i | \(-0.565306\pi\) | ||||
−0.203729 | + | 0.979027i | \(0.565306\pi\) | |||||||
\(602\) | −0.856900 | −0.0349246 | ||||||||
\(603\) | −2.42081 | −0.0985830 | ||||||||
\(604\) | −11.8434 | −0.481901 | ||||||||
\(605\) | −6.70152 | −0.272456 | ||||||||
\(606\) | 28.2651 | 1.14819 | ||||||||
\(607\) | 22.6819 | 0.920631 | 0.460316 | − | 0.887755i | \(-0.347736\pi\) | ||||
0.460316 | + | 0.887755i | \(0.347736\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | −5.44649 | −0.220703 | ||||||||
\(610\) | −1.58025 | −0.0639825 | ||||||||
\(611\) | −8.83425 | −0.357395 | ||||||||
\(612\) | −7.45457 | −0.301333 | ||||||||
\(613\) | 13.6552 | 0.551527 | 0.275764 | − | 0.961225i | \(-0.411069\pi\) | ||||
0.275764 | + | 0.961225i | \(0.411069\pi\) | |||||||
\(614\) | 21.8190 | 0.880542 | ||||||||
\(615\) | −0.544404 | −0.0219525 | ||||||||
\(616\) | 2.87219 | 0.115724 | ||||||||
\(617\) | −11.4070 | −0.459230 | −0.229615 | − | 0.973282i | \(-0.573747\pi\) | ||||
−0.229615 | + | 0.973282i | \(0.573747\pi\) | |||||||
\(618\) | −26.2403 | −1.05554 | ||||||||
\(619\) | −20.2291 | −0.813078 | −0.406539 | − | 0.913633i | \(-0.633264\pi\) | ||||
−0.406539 | + | 0.913633i | \(0.633264\pi\) | |||||||
\(620\) | −0.0360302 | −0.00144701 | ||||||||
\(621\) | −4.67105 | −0.187443 | ||||||||
\(622\) | 0.448831 | 0.0179965 | ||||||||
\(623\) | −7.70804 | −0.308816 | ||||||||
\(624\) | 5.53041 | 0.221394 | ||||||||
\(625\) | 23.7301 | 0.949203 | ||||||||
\(626\) | −7.58291 | −0.303074 | ||||||||
\(627\) | −11.6407 | −0.464885 | ||||||||
\(628\) | −11.3220 | −0.451797 | ||||||||
\(629\) | −1.04241 | −0.0415635 | ||||||||
\(630\) | 0.142279 | 0.00566855 | ||||||||
\(631\) | 3.14265 | 0.125107 | 0.0625534 | − | 0.998042i | \(-0.480076\pi\) | ||||
0.0625534 | + | 0.998042i | \(0.480076\pi\) | |||||||
\(632\) | 6.09239 | 0.242342 | ||||||||
\(633\) | 1.99735 | 0.0793875 | ||||||||
\(634\) | −5.26198 | −0.208980 | ||||||||
\(635\) | 4.37082 | 0.173451 | ||||||||
\(636\) | −1.05154 | −0.0416964 | ||||||||
\(637\) | 18.7096 | 0.741303 | ||||||||
\(638\) | 32.2477 | 1.27670 | ||||||||
\(639\) | −5.15637 | −0.203983 | ||||||||
\(640\) | −0.291796 | −0.0115342 | ||||||||
\(641\) | 23.2901 | 0.919904 | 0.459952 | − | 0.887944i | \(-0.347867\pi\) | ||||
0.459952 | + | 0.887944i | \(0.347867\pi\) | |||||||
\(642\) | −6.68165 | −0.263704 | ||||||||
\(643\) | 29.5873 | 1.16681 | 0.583404 | − | 0.812182i | \(-0.301720\pi\) | ||||
0.583404 | + | 0.812182i | \(0.301720\pi\) | |||||||
\(644\) | 0.573225 | 0.0225882 | ||||||||
\(645\) | 1.01339 | 0.0399020 | ||||||||
\(646\) | 7.53438 | 0.296436 | ||||||||
\(647\) | 21.9890 | 0.864476 | 0.432238 | − | 0.901760i | \(-0.357724\pi\) | ||||
0.432238 | + | 0.901760i | \(0.357724\pi\) | |||||||
\(648\) | −10.9893 | −0.431700 | ||||||||
\(649\) | 44.0589 | 1.72946 | ||||||||
\(650\) | 13.6086 | 0.533774 | ||||||||
\(651\) | 0.121543 | 0.00476365 | ||||||||
\(652\) | −6.96207 | −0.272656 | ||||||||
\(653\) | −39.6858 | −1.55303 | −0.776513 | − | 0.630102i | \(-0.783013\pi\) | ||||
−0.776513 | + | 0.630102i | \(0.783013\pi\) | |||||||
\(654\) | −31.1329 | −1.21739 | ||||||||
\(655\) | −1.23644 | −0.0483118 | ||||||||
\(656\) | −0.934090 | −0.0364701 | ||||||||
\(657\) | 10.5346 | 0.410996 | ||||||||
\(658\) | −1.57237 | −0.0612973 | ||||||||
\(659\) | 3.50378 | 0.136488 | 0.0682440 | − | 0.997669i | \(-0.478260\pi\) | ||||
0.0682440 | + | 0.997669i | \(0.478260\pi\) | |||||||
\(660\) | −3.39671 | −0.132217 | ||||||||
\(661\) | −35.1467 | −1.36705 | −0.683524 | − | 0.729928i | \(-0.739553\pi\) | ||||
−0.683524 | + | 0.729928i | \(0.739553\pi\) | |||||||
\(662\) | −6.85598 | −0.266465 | ||||||||
\(663\) | −41.6683 | −1.61826 | ||||||||
\(664\) | 0.696438 | 0.0270270 | ||||||||
\(665\) | −0.143803 | −0.00557643 | ||||||||
\(666\) | 0.136888 | 0.00530429 | ||||||||
\(667\) | 6.43592 | 0.249200 | ||||||||
\(668\) | −20.3291 | −0.786557 | ||||||||
\(669\) | 49.0905 | 1.89795 | ||||||||
\(670\) | 0.713944 | 0.0275821 | ||||||||
\(671\) | −31.5626 | −1.21846 | ||||||||
\(672\) | 0.984334 | 0.0379715 | ||||||||
\(673\) | −9.52050 | −0.366988 | −0.183494 | − | 0.983021i | \(-0.558741\pi\) | ||||
−0.183494 | + | 0.983021i | \(0.558741\pi\) | |||||||
\(674\) | −25.1687 | −0.969464 | ||||||||
\(675\) | −19.7374 | −0.759691 | ||||||||
\(676\) | −5.33333 | −0.205128 | ||||||||
\(677\) | −25.6306 | −0.985063 | −0.492531 | − | 0.870295i | \(-0.663928\pi\) | ||||
−0.492531 | + | 0.870295i | \(0.663928\pi\) | |||||||
\(678\) | 36.9719 | 1.41990 | ||||||||
\(679\) | −1.85882 | −0.0713351 | ||||||||
\(680\) | 2.19850 | 0.0843086 | ||||||||
\(681\) | 43.8066 | 1.67867 | ||||||||
\(682\) | −0.719637 | −0.0275563 | ||||||||
\(683\) | −19.4007 | −0.742347 | −0.371174 | − | 0.928564i | \(-0.621045\pi\) | ||||
−0.371174 | + | 0.928564i | \(0.621045\pi\) | |||||||
\(684\) | −0.989407 | −0.0378309 | ||||||||
\(685\) | −4.07866 | −0.155837 | ||||||||
\(686\) | 6.77979 | 0.258854 | ||||||||
\(687\) | −25.7410 | −0.982079 | ||||||||
\(688\) | 1.73877 | 0.0662899 | ||||||||
\(689\) | −1.45773 | −0.0555350 | ||||||||
\(690\) | −0.677906 | −0.0258074 | ||||||||
\(691\) | −29.1286 | −1.10810 | −0.554052 | − | 0.832482i | \(-0.686919\pi\) | ||||
−0.554052 | + | 0.832482i | \(0.686919\pi\) | |||||||
\(692\) | −12.3099 | −0.467953 | ||||||||
\(693\) | 2.84177 | 0.107950 | ||||||||
\(694\) | 12.2928 | 0.466627 | ||||||||
\(695\) | −2.35003 | −0.0891416 | ||||||||
\(696\) | 11.0517 | 0.418913 | ||||||||
\(697\) | 7.03779 | 0.266575 | ||||||||
\(698\) | 14.6723 | 0.555354 | ||||||||
\(699\) | −6.94981 | −0.262866 | ||||||||
\(700\) | 2.42214 | 0.0915483 | ||||||||
\(701\) | 44.0043 | 1.66202 | 0.831009 | − | 0.556259i | \(-0.187764\pi\) | ||||
0.831009 | + | 0.556259i | \(0.187764\pi\) | |||||||
\(702\) | −11.1194 | −0.419675 | ||||||||
\(703\) | −0.138353 | −0.00521809 | ||||||||
\(704\) | −5.82808 | −0.219654 | ||||||||
\(705\) | 1.85951 | 0.0700333 | ||||||||
\(706\) | 12.8028 | 0.481838 | ||||||||
\(707\) | 6.97406 | 0.262286 | ||||||||
\(708\) | 15.0995 | 0.567474 | ||||||||
\(709\) | 41.3975 | 1.55472 | 0.777358 | − | 0.629058i | \(-0.216559\pi\) | ||||
0.777358 | + | 0.629058i | \(0.216559\pi\) | |||||||
\(710\) | 1.52071 | 0.0570714 | ||||||||
\(711\) | 6.02786 | 0.226062 | ||||||||
\(712\) | 15.6407 | 0.586159 | ||||||||
\(713\) | −0.143623 | −0.00537873 | ||||||||
\(714\) | −7.41635 | −0.277550 | ||||||||
\(715\) | −4.70877 | −0.176098 | ||||||||
\(716\) | −22.9118 | −0.856253 | ||||||||
\(717\) | −26.0248 | −0.971914 | ||||||||
\(718\) | −30.8014 | −1.14950 | ||||||||
\(719\) | −6.53979 | −0.243893 | −0.121947 | − | 0.992537i | \(-0.538914\pi\) | ||||
−0.121947 | + | 0.992537i | \(0.538914\pi\) | |||||||
\(720\) | −0.288705 | −0.0107594 | ||||||||
\(721\) | −6.47446 | −0.241122 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | 30.9997 | 1.15289 | ||||||||
\(724\) | 16.3957 | 0.609341 | ||||||||
\(725\) | 27.1947 | 1.00999 | ||||||||
\(726\) | −45.8721 | −1.70247 | ||||||||
\(727\) | 5.24387 | 0.194484 | 0.0972422 | − | 0.995261i | \(-0.468998\pi\) | ||||
0.0972422 | + | 0.995261i | \(0.468998\pi\) | |||||||
\(728\) | 1.36456 | 0.0505739 | ||||||||
\(729\) | 13.1903 | 0.488531 | ||||||||
\(730\) | −3.10687 | −0.114991 | ||||||||
\(731\) | −13.1005 | −0.484541 | ||||||||
\(732\) | −10.8169 | −0.399803 | ||||||||
\(733\) | 19.1105 | 0.705864 | 0.352932 | − | 0.935649i | \(-0.385185\pi\) | ||||
0.352932 | + | 0.935649i | \(0.385185\pi\) | |||||||
\(734\) | −0.442858 | −0.0163462 | ||||||||
\(735\) | −3.93818 | −0.145262 | ||||||||
\(736\) | −1.16315 | −0.0428744 | ||||||||
\(737\) | 14.2597 | 0.525263 | ||||||||
\(738\) | −0.924195 | −0.0340201 | ||||||||
\(739\) | −41.0095 | −1.50856 | −0.754280 | − | 0.656553i | \(-0.772014\pi\) | ||||
−0.754280 | + | 0.656553i | \(0.772014\pi\) | |||||||
\(740\) | −0.0403709 | −0.00148406 | ||||||||
\(741\) | −5.53041 | −0.203165 | ||||||||
\(742\) | −0.259455 | −0.00952488 | ||||||||
\(743\) | 14.9024 | 0.546714 | 0.273357 | − | 0.961913i | \(-0.411866\pi\) | ||||
0.273357 | + | 0.961913i | \(0.411866\pi\) | |||||||
\(744\) | −0.246628 | −0.00904182 | ||||||||
\(745\) | −7.04186 | −0.257994 | ||||||||
\(746\) | 29.7502 | 1.08923 | ||||||||
\(747\) | 0.689061 | 0.0252114 | ||||||||
\(748\) | 43.9110 | 1.60554 | ||||||||
\(749\) | −1.64861 | −0.0602389 | ||||||||
\(750\) | −5.77856 | −0.211003 | ||||||||
\(751\) | 32.5307 | 1.18706 | 0.593531 | − | 0.804811i | \(-0.297733\pi\) | ||||
0.593531 | + | 0.804811i | \(0.297733\pi\) | |||||||
\(752\) | 3.19055 | 0.116348 | ||||||||
\(753\) | 54.0633 | 1.97018 | ||||||||
\(754\) | 15.3206 | 0.557945 | ||||||||
\(755\) | 3.45585 | 0.125771 | ||||||||
\(756\) | −1.97910 | −0.0719790 | ||||||||
\(757\) | 20.6242 | 0.749599 | 0.374799 | − | 0.927106i | \(-0.377712\pi\) | ||||
0.374799 | + | 0.927106i | \(0.377712\pi\) | |||||||
\(758\) | 11.9391 | 0.433648 | ||||||||
\(759\) | −13.5399 | −0.491468 | ||||||||
\(760\) | 0.291796 | 0.0105845 | ||||||||
\(761\) | −47.8520 | −1.73463 | −0.867317 | − | 0.497757i | \(-0.834157\pi\) | ||||
−0.867317 | + | 0.497757i | \(0.834157\pi\) | |||||||
\(762\) | 29.9184 | 1.08383 | ||||||||
\(763\) | −7.68163 | −0.278094 | ||||||||
\(764\) | 19.1529 | 0.692928 | ||||||||
\(765\) | 2.17521 | 0.0786449 | ||||||||
\(766\) | 7.06516 | 0.255275 | ||||||||
\(767\) | 20.9321 | 0.755813 | ||||||||
\(768\) | −1.99735 | −0.0720732 | ||||||||
\(769\) | −45.9438 | −1.65677 | −0.828387 | − | 0.560156i | \(-0.810741\pi\) | ||||
−0.828387 | + | 0.560156i | \(0.810741\pi\) | |||||||
\(770\) | −0.838093 | −0.0302028 | ||||||||
\(771\) | 31.0148 | 1.11697 | ||||||||
\(772\) | −23.7671 | −0.855396 | ||||||||
\(773\) | 30.3210 | 1.09057 | 0.545285 | − | 0.838251i | \(-0.316421\pi\) | ||||
0.545285 | + | 0.838251i | \(0.316421\pi\) | |||||||
\(774\) | 1.72035 | 0.0618367 | ||||||||
\(775\) | −0.606874 | −0.0217996 | ||||||||
\(776\) | 3.77181 | 0.135400 | ||||||||
\(777\) | 0.136186 | 0.00488564 | ||||||||
\(778\) | 0.804055 | 0.0288268 | ||||||||
\(779\) | 0.934090 | 0.0334672 | ||||||||
\(780\) | −1.61375 | −0.0577815 | ||||||||
\(781\) | 30.3735 | 1.08685 | ||||||||
\(782\) | 8.76363 | 0.313387 | ||||||||
\(783\) | −22.2204 | −0.794093 | ||||||||
\(784\) | −6.75713 | −0.241326 | ||||||||
\(785\) | 3.30371 | 0.117914 | ||||||||
\(786\) | −8.46349 | −0.301883 | ||||||||
\(787\) | 43.9118 | 1.56529 | 0.782644 | − | 0.622470i | \(-0.213871\pi\) | ||||
0.782644 | + | 0.622470i | \(0.213871\pi\) | |||||||
\(788\) | −3.50954 | −0.125022 | ||||||||
\(789\) | −15.9233 | −0.566884 | ||||||||
\(790\) | −1.77773 | −0.0632489 | ||||||||
\(791\) | 9.12233 | 0.324353 | ||||||||
\(792\) | −5.76634 | −0.204898 | ||||||||
\(793\) | −14.9951 | −0.532493 | ||||||||
\(794\) | −7.48659 | −0.265689 | ||||||||
\(795\) | 0.306836 | 0.0108823 | ||||||||
\(796\) | −12.7834 | −0.453095 | ||||||||
\(797\) | −49.2267 | −1.74370 | −0.871849 | − | 0.489775i | \(-0.837079\pi\) | ||||
−0.871849 | + | 0.489775i | \(0.837079\pi\) | |||||||
\(798\) | −0.984334 | −0.0348451 | ||||||||
\(799\) | −24.0389 | −0.850434 | ||||||||
\(800\) | −4.91486 | −0.173766 | ||||||||
\(801\) | 15.4750 | 0.546782 | ||||||||
\(802\) | 30.1926 | 1.06614 | ||||||||
\(803\) | −62.0541 | −2.18984 | ||||||||
\(804\) | 4.88697 | 0.172350 | ||||||||
\(805\) | −0.167264 | −0.00589530 | ||||||||
\(806\) | −0.341894 | −0.0120427 | ||||||||
\(807\) | −36.9366 | −1.30023 | ||||||||
\(808\) | −14.1513 | −0.497842 | ||||||||
\(809\) | −11.2883 | −0.396876 | −0.198438 | − | 0.980113i | \(-0.563587\pi\) | ||||
−0.198438 | + | 0.980113i | \(0.563587\pi\) | |||||||
\(810\) | 3.20663 | 0.112669 | ||||||||
\(811\) | 35.0290 | 1.23003 | 0.615016 | − | 0.788514i | \(-0.289149\pi\) | ||||
0.615016 | + | 0.788514i | \(0.289149\pi\) | |||||||
\(812\) | 2.72686 | 0.0956939 | ||||||||
\(813\) | 56.8879 | 1.99514 | ||||||||
\(814\) | −0.806333 | −0.0282620 | ||||||||
\(815\) | 2.03150 | 0.0711603 | ||||||||
\(816\) | 15.0488 | 0.526813 | ||||||||
\(817\) | −1.73877 | −0.0608318 | ||||||||
\(818\) | 14.6143 | 0.510978 | ||||||||
\(819\) | 1.35010 | 0.0471764 | ||||||||
\(820\) | 0.272563 | 0.00951832 | ||||||||
\(821\) | 30.2946 | 1.05729 | 0.528644 | − | 0.848844i | \(-0.322701\pi\) | ||||
0.528644 | + | 0.848844i | \(0.322701\pi\) | |||||||
\(822\) | −27.9185 | −0.973770 | ||||||||
\(823\) | 40.8349 | 1.42342 | 0.711708 | − | 0.702475i | \(-0.247922\pi\) | ||||
0.711708 | + | 0.702475i | \(0.247922\pi\) | |||||||
\(824\) | 13.1376 | 0.457669 | ||||||||
\(825\) | −57.2124 | −1.99188 | ||||||||
\(826\) | 3.72561 | 0.129630 | ||||||||
\(827\) | −36.9776 | −1.28584 | −0.642918 | − | 0.765935i | \(-0.722276\pi\) | ||||
−0.642918 | + | 0.765935i | \(0.722276\pi\) | |||||||
\(828\) | −1.15083 | −0.0399941 | ||||||||
\(829\) | −32.7871 | −1.13874 | −0.569371 | − | 0.822081i | \(-0.692813\pi\) | ||||
−0.569371 | + | 0.822081i | \(0.692813\pi\) | |||||||
\(830\) | −0.203218 | −0.00705378 | ||||||||
\(831\) | −63.7887 | −2.21280 | ||||||||
\(832\) | −2.76888 | −0.0959935 | ||||||||
\(833\) | 50.9108 | 1.76395 | ||||||||
\(834\) | −16.0860 | −0.557013 | ||||||||
\(835\) | 5.93194 | 0.205283 | ||||||||
\(836\) | 5.82808 | 0.201568 | ||||||||
\(837\) | 0.495868 | 0.0171397 | ||||||||
\(838\) | −31.7737 | −1.09760 | ||||||||
\(839\) | −42.8184 | −1.47826 | −0.739128 | − | 0.673565i | \(-0.764762\pi\) | ||||
−0.739128 | + | 0.673565i | \(0.764762\pi\) | |||||||
\(840\) | −0.287224 | −0.00991018 | ||||||||
\(841\) | 1.61594 | 0.0557220 | ||||||||
\(842\) | 35.8484 | 1.23542 | ||||||||
\(843\) | −32.1278 | −1.10654 | ||||||||
\(844\) | −1.00000 | −0.0344214 | ||||||||
\(845\) | 1.55624 | 0.0535364 | ||||||||
\(846\) | 3.15676 | 0.108532 | ||||||||
\(847\) | −11.3183 | −0.388903 | ||||||||
\(848\) | 0.526470 | 0.0180790 | ||||||||
\(849\) | −53.3808 | −1.83202 | ||||||||
\(850\) | 37.0304 | 1.27013 | ||||||||
\(851\) | −0.160926 | −0.00551647 | ||||||||
\(852\) | 10.4093 | 0.356618 | ||||||||
\(853\) | −29.9914 | −1.02689 | −0.513443 | − | 0.858124i | \(-0.671630\pi\) | ||||
−0.513443 | + | 0.858124i | \(0.671630\pi\) | |||||||
\(854\) | −2.66892 | −0.0913286 | ||||||||
\(855\) | 0.288705 | 0.00987349 | ||||||||
\(856\) | 3.34526 | 0.114339 | ||||||||
\(857\) | 39.7381 | 1.35743 | 0.678714 | − | 0.734402i | \(-0.262537\pi\) | ||||
0.678714 | + | 0.734402i | \(0.262537\pi\) | |||||||
\(858\) | −32.2317 | −1.10037 | ||||||||
\(859\) | −21.3667 | −0.729021 | −0.364510 | − | 0.931199i | \(-0.618764\pi\) | ||||
−0.364510 | + | 0.931199i | \(0.618764\pi\) | |||||||
\(860\) | −0.507365 | −0.0173010 | ||||||||
\(861\) | −0.919456 | −0.0313350 | ||||||||
\(862\) | 2.41840 | 0.0823709 | ||||||||
\(863\) | 46.9898 | 1.59955 | 0.799775 | − | 0.600299i | \(-0.204952\pi\) | ||||
0.799775 | + | 0.600299i | \(0.204952\pi\) | |||||||
\(864\) | 4.01586 | 0.136622 | ||||||||
\(865\) | 3.59198 | 0.122131 | ||||||||
\(866\) | 26.0821 | 0.886306 | ||||||||
\(867\) | −79.4285 | −2.69753 | ||||||||
\(868\) | −0.0608522 | −0.00206546 | ||||||||
\(869\) | −35.5069 | −1.20449 | ||||||||
\(870\) | −3.22483 | −0.109332 | ||||||||
\(871\) | 6.77468 | 0.229551 | ||||||||
\(872\) | 15.5871 | 0.527846 | ||||||||
\(873\) | 3.73186 | 0.126304 | ||||||||
\(874\) | 1.16315 | 0.0393442 | ||||||||
\(875\) | −1.42578 | −0.0482003 | ||||||||
\(876\) | −21.2666 | −0.718533 | ||||||||
\(877\) | −22.0920 | −0.745993 | −0.372996 | − | 0.927833i | \(-0.621670\pi\) | ||||
−0.372996 | + | 0.927833i | \(0.621670\pi\) | |||||||
\(878\) | 9.81398 | 0.331206 | ||||||||
\(879\) | 12.6398 | 0.426330 | ||||||||
\(880\) | 1.70061 | 0.0573275 | ||||||||
\(881\) | −30.5795 | −1.03025 | −0.515124 | − | 0.857116i | \(-0.672254\pi\) | ||||
−0.515124 | + | 0.857116i | \(0.672254\pi\) | |||||||
\(882\) | −6.68555 | −0.225114 | ||||||||
\(883\) | −56.7209 | −1.90881 | −0.954405 | − | 0.298515i | \(-0.903509\pi\) | ||||
−0.954405 | + | 0.298515i | \(0.903509\pi\) | |||||||
\(884\) | 20.8618 | 0.701657 | ||||||||
\(885\) | −4.40597 | −0.148105 | ||||||||
\(886\) | −7.96518 | −0.267596 | ||||||||
\(887\) | −54.6134 | −1.83374 | −0.916869 | − | 0.399189i | \(-0.869292\pi\) | ||||
−0.916869 | + | 0.399189i | \(0.869292\pi\) | |||||||
\(888\) | −0.276340 | −0.00927336 | ||||||||
\(889\) | 7.38198 | 0.247584 | ||||||||
\(890\) | −4.56388 | −0.152982 | ||||||||
\(891\) | 64.0465 | 2.14564 | ||||||||
\(892\) | −24.5778 | −0.822927 | ||||||||
\(893\) | −3.19055 | −0.106768 | ||||||||
\(894\) | −48.2018 | −1.61211 | ||||||||
\(895\) | 6.68555 | 0.223473 | ||||||||
\(896\) | −0.492820 | −0.0164640 | ||||||||
\(897\) | −6.43271 | −0.214782 | ||||||||
\(898\) | 41.7261 | 1.39242 | ||||||||
\(899\) | −0.683222 | −0.0227867 | ||||||||
\(900\) | −4.86279 | −0.162093 | ||||||||
\(901\) | −3.96662 | −0.132147 | ||||||||
\(902\) | 5.44395 | 0.181264 | ||||||||
\(903\) | 1.71153 | 0.0569561 | ||||||||
\(904\) | −18.5105 | −0.615649 | ||||||||
\(905\) | −4.78419 | −0.159032 | ||||||||
\(906\) | 23.6554 | 0.785899 | ||||||||
\(907\) | 5.59601 | 0.185813 | 0.0929063 | − | 0.995675i | \(-0.470384\pi\) | ||||
0.0929063 | + | 0.995675i | \(0.470384\pi\) | |||||||
\(908\) | −21.9324 | −0.727852 | ||||||||
\(909\) | −14.0014 | −0.464398 | ||||||||
\(910\) | −0.398172 | −0.0131993 | ||||||||
\(911\) | 13.8939 | 0.460325 | 0.230162 | − | 0.973152i | \(-0.426074\pi\) | ||||
0.230162 | + | 0.973152i | \(0.426074\pi\) | |||||||
\(912\) | 1.99735 | 0.0661389 | ||||||||
\(913\) | −4.05889 | −0.134330 | ||||||||
\(914\) | 1.15273 | 0.0381289 | ||||||||
\(915\) | 3.15631 | 0.104345 | ||||||||
\(916\) | 12.8876 | 0.425817 | ||||||||
\(917\) | −2.08826 | −0.0689603 | ||||||||
\(918\) | −30.2570 | −0.998630 | ||||||||
\(919\) | −44.0034 | −1.45154 | −0.725768 | − | 0.687939i | \(-0.758516\pi\) | ||||
−0.725768 | + | 0.687939i | \(0.758516\pi\) | |||||||
\(920\) | 0.339403 | 0.0111898 | ||||||||
\(921\) | −43.5801 | −1.43601 | ||||||||
\(922\) | 10.4866 | 0.345358 | ||||||||
\(923\) | 14.4302 | 0.474976 | ||||||||
\(924\) | −5.73678 | −0.188726 | ||||||||
\(925\) | −0.679986 | −0.0223578 | ||||||||
\(926\) | 12.0262 | 0.395205 | ||||||||
\(927\) | 12.9984 | 0.426924 | ||||||||
\(928\) | −5.53317 | −0.181635 | ||||||||
\(929\) | −35.7726 | −1.17366 | −0.586830 | − | 0.809710i | \(-0.699624\pi\) | ||||
−0.586830 | + | 0.809710i | \(0.699624\pi\) | |||||||
\(930\) | 0.0719649 | 0.00235982 | ||||||||
\(931\) | 6.75713 | 0.221456 | ||||||||
\(932\) | 3.47952 | 0.113975 | ||||||||
\(933\) | −0.896473 | −0.0293492 | ||||||||
\(934\) | 3.99432 | 0.130698 | ||||||||
\(935\) | −12.8130 | −0.419031 | ||||||||
\(936\) | −2.73955 | −0.0895448 | ||||||||
\(937\) | 22.5479 | 0.736606 | 0.368303 | − | 0.929706i | \(-0.379939\pi\) | ||||
0.368303 | + | 0.929706i | \(0.379939\pi\) | |||||||
\(938\) | 1.20580 | 0.0393706 | ||||||||
\(939\) | 15.1457 | 0.494262 | ||||||||
\(940\) | −0.930990 | −0.0303655 | ||||||||
\(941\) | 34.4137 | 1.12186 | 0.560928 | − | 0.827865i | \(-0.310445\pi\) | ||||
0.560928 | + | 0.827865i | \(0.310445\pi\) | |||||||
\(942\) | 22.6140 | 0.736804 | ||||||||
\(943\) | 1.08649 | 0.0353809 | ||||||||
\(944\) | −7.55977 | −0.246050 | ||||||||
\(945\) | 0.577491 | 0.0187858 | ||||||||
\(946\) | −10.1337 | −0.329474 | ||||||||
\(947\) | 53.6411 | 1.74310 | 0.871551 | − | 0.490304i | \(-0.163114\pi\) | ||||
0.871551 | + | 0.490304i | \(0.163114\pi\) | |||||||
\(948\) | −12.1686 | −0.395219 | ||||||||
\(949\) | −29.4814 | −0.957007 | ||||||||
\(950\) | 4.91486 | 0.159459 | ||||||||
\(951\) | 10.5100 | 0.340811 | ||||||||
\(952\) | 3.71310 | 0.120342 | ||||||||
\(953\) | 8.28280 | 0.268306 | 0.134153 | − | 0.990961i | \(-0.457169\pi\) | ||||
0.134153 | + | 0.990961i | \(0.457169\pi\) | |||||||
\(954\) | 0.520893 | 0.0168645 | ||||||||
\(955\) | −5.58873 | −0.180847 | ||||||||
\(956\) | 13.0297 | 0.421410 | ||||||||
\(957\) | −64.4100 | −2.08208 | ||||||||
\(958\) | −25.3246 | −0.818201 | ||||||||
\(959\) | −6.88853 | −0.222442 | ||||||||
\(960\) | 0.582818 | 0.0188104 | ||||||||
\(961\) | −30.9848 | −0.999508 | ||||||||
\(962\) | −0.383083 | −0.0123511 | ||||||||
\(963\) | 3.30982 | 0.106658 | ||||||||
\(964\) | −15.5204 | −0.499878 | ||||||||
\(965\) | 6.93513 | 0.223250 | ||||||||
\(966\) | −1.14493 | −0.0368375 | ||||||||
\(967\) | −24.0647 | −0.773868 | −0.386934 | − | 0.922107i | \(-0.626466\pi\) | ||||
−0.386934 | + | 0.922107i | \(0.626466\pi\) | |||||||
\(968\) | 22.9665 | 0.738171 | ||||||||
\(969\) | −15.0488 | −0.483437 | ||||||||
\(970\) | −1.10060 | −0.0353381 | ||||||||
\(971\) | 25.9691 | 0.833390 | 0.416695 | − | 0.909046i | \(-0.363188\pi\) | ||||
0.416695 | + | 0.909046i | \(0.363188\pi\) | |||||||
\(972\) | 9.90190 | 0.317603 | ||||||||
\(973\) | −3.96901 | −0.127241 | ||||||||
\(974\) | 8.66907 | 0.277775 | ||||||||
\(975\) | −27.1812 | −0.870494 | ||||||||
\(976\) | 5.41561 | 0.173349 | ||||||||
\(977\) | −21.5467 | −0.689340 | −0.344670 | − | 0.938724i | \(-0.612009\pi\) | ||||
−0.344670 | + | 0.938724i | \(0.612009\pi\) | |||||||
\(978\) | 13.9057 | 0.444655 | ||||||||
\(979\) | −91.1550 | −2.91333 | ||||||||
\(980\) | 1.97170 | 0.0629837 | ||||||||
\(981\) | 15.4220 | 0.492386 | ||||||||
\(982\) | −19.3277 | −0.616772 | ||||||||
\(983\) | 24.1055 | 0.768845 | 0.384422 | − | 0.923157i | \(-0.374401\pi\) | ||||
0.384422 | + | 0.923157i | \(0.374401\pi\) | |||||||
\(984\) | 1.86570 | 0.0594765 | ||||||||
\(985\) | 1.02407 | 0.0326295 | ||||||||
\(986\) | 41.6890 | 1.32765 | ||||||||
\(987\) | 3.14057 | 0.0999655 | ||||||||
\(988\) | 2.76888 | 0.0880897 | ||||||||
\(989\) | −2.02245 | −0.0643102 | ||||||||
\(990\) | 1.68259 | 0.0534763 | ||||||||
\(991\) | −24.2137 | −0.769174 | −0.384587 | − | 0.923089i | \(-0.625656\pi\) | ||||
−0.384587 | + | 0.923089i | \(0.625656\pi\) | |||||||
\(992\) | 0.123478 | 0.00392042 | ||||||||
\(993\) | 13.6938 | 0.434559 | ||||||||
\(994\) | 2.56837 | 0.0814637 | ||||||||
\(995\) | 3.73014 | 0.118253 | ||||||||
\(996\) | −1.39103 | −0.0440765 | ||||||||
\(997\) | 45.9058 | 1.45385 | 0.726926 | − | 0.686716i | \(-0.240948\pi\) | ||||
0.726926 | + | 0.686716i | \(0.240948\pi\) | |||||||
\(998\) | −36.3023 | −1.14913 | ||||||||
\(999\) | 0.555607 | 0.0175786 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8018.2.a.j.1.11 | ✓ | 47 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8018.2.a.j.1.11 | ✓ | 47 | 1.1 | even | 1 | trivial |