Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4034,2,Mod(1,4034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4034, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4034 = 2 \cdot 2017 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4034.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: | \(32.2116521754\) |
Analytic rank: | \(0\) |
Dimension: | \(52\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 4034.1 |
$q$-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 | ||||||||
\(3\) | −3.35325 | −1.93600 | −0.968000 | − | 0.250952i | \(-0.919257\pi\) | ||||
−0.968000 | + | 0.250952i | \(0.919257\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.0968667 | −0.0433201 | −0.0216600 | − | 0.999765i | \(-0.506895\pi\) | ||||
−0.0216600 | + | 0.999765i | \(0.506895\pi\) | |||||||
\(6\) | −3.35325 | −1.36896 | ||||||||
\(7\) | −2.67437 | −1.01082 | −0.505408 | − | 0.862881i | \(-0.668658\pi\) | ||||
−0.505408 | + | 0.862881i | \(0.668658\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 8.24428 | 2.74809 | ||||||||
\(10\) | −0.0968667 | −0.0306319 | ||||||||
\(11\) | −3.55769 | −1.07268 | −0.536342 | − | 0.844001i | \(-0.680194\pi\) | ||||
−0.536342 | + | 0.844001i | \(0.680194\pi\) | |||||||
\(12\) | −3.35325 | −0.968000 | ||||||||
\(13\) | −5.20042 | −1.44234 | −0.721169 | − | 0.692759i | \(-0.756395\pi\) | ||||
−0.721169 | + | 0.692759i | \(0.756395\pi\) | |||||||
\(14\) | −2.67437 | −0.714754 | ||||||||
\(15\) | 0.324818 | 0.0838677 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.84555 | 0.447612 | 0.223806 | − | 0.974634i | \(-0.428152\pi\) | ||||
0.223806 | + | 0.974634i | \(0.428152\pi\) | |||||||
\(18\) | 8.24428 | 1.94320 | ||||||||
\(19\) | −0.434911 | −0.0997754 | −0.0498877 | − | 0.998755i | \(-0.515886\pi\) | ||||
−0.0498877 | + | 0.998755i | \(0.515886\pi\) | |||||||
\(20\) | −0.0968667 | −0.0216600 | ||||||||
\(21\) | 8.96782 | 1.95694 | ||||||||
\(22\) | −3.55769 | −0.758502 | ||||||||
\(23\) | −9.44828 | −1.97010 | −0.985051 | − | 0.172262i | \(-0.944892\pi\) | ||||
−0.985051 | + | 0.172262i | \(0.944892\pi\) | |||||||
\(24\) | −3.35325 | −0.684479 | ||||||||
\(25\) | −4.99062 | −0.998123 | ||||||||
\(26\) | −5.20042 | −1.01989 | ||||||||
\(27\) | −17.5854 | −3.38431 | ||||||||
\(28\) | −2.67437 | −0.505408 | ||||||||
\(29\) | 5.88214 | 1.09229 | 0.546143 | − | 0.837692i | \(-0.316095\pi\) | ||||
0.546143 | + | 0.837692i | \(0.316095\pi\) | |||||||
\(30\) | 0.324818 | 0.0593034 | ||||||||
\(31\) | 9.65979 | 1.73495 | 0.867475 | − | 0.497481i | \(-0.165742\pi\) | ||||
0.867475 | + | 0.497481i | \(0.165742\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 11.9298 | 2.07671 | ||||||||
\(34\) | 1.84555 | 0.316509 | ||||||||
\(35\) | 0.259057 | 0.0437886 | ||||||||
\(36\) | 8.24428 | 1.37405 | ||||||||
\(37\) | 3.05031 | 0.501469 | 0.250734 | − | 0.968056i | \(-0.419328\pi\) | ||||
0.250734 | + | 0.968056i | \(0.419328\pi\) | |||||||
\(38\) | −0.434911 | −0.0705518 | ||||||||
\(39\) | 17.4383 | 2.79236 | ||||||||
\(40\) | −0.0968667 | −0.0153160 | ||||||||
\(41\) | −10.0990 | −1.57720 | −0.788602 | − | 0.614904i | \(-0.789195\pi\) | ||||
−0.788602 | + | 0.614904i | \(0.789195\pi\) | |||||||
\(42\) | 8.96782 | 1.38376 | ||||||||
\(43\) | 4.43508 | 0.676344 | 0.338172 | − | 0.941084i | \(-0.390191\pi\) | ||||
0.338172 | + | 0.941084i | \(0.390191\pi\) | |||||||
\(44\) | −3.55769 | −0.536342 | ||||||||
\(45\) | −0.798596 | −0.119048 | ||||||||
\(46\) | −9.44828 | −1.39307 | ||||||||
\(47\) | −5.75080 | −0.838841 | −0.419420 | − | 0.907792i | \(-0.637767\pi\) | ||||
−0.419420 | + | 0.907792i | \(0.637767\pi\) | |||||||
\(48\) | −3.35325 | −0.484000 | ||||||||
\(49\) | 0.152234 | 0.0217478 | ||||||||
\(50\) | −4.99062 | −0.705780 | ||||||||
\(51\) | −6.18859 | −0.866576 | ||||||||
\(52\) | −5.20042 | −0.721169 | ||||||||
\(53\) | −12.0959 | −1.66150 | −0.830750 | − | 0.556645i | \(-0.812088\pi\) | ||||
−0.830750 | + | 0.556645i | \(0.812088\pi\) | |||||||
\(54\) | −17.5854 | −2.39307 | ||||||||
\(55\) | 0.344621 | 0.0464687 | ||||||||
\(56\) | −2.67437 | −0.357377 | ||||||||
\(57\) | 1.45836 | 0.193165 | ||||||||
\(58\) | 5.88214 | 0.772363 | ||||||||
\(59\) | 7.87428 | 1.02514 | 0.512572 | − | 0.858644i | \(-0.328693\pi\) | ||||
0.512572 | + | 0.858644i | \(0.328693\pi\) | |||||||
\(60\) | 0.324818 | 0.0419338 | ||||||||
\(61\) | 6.56172 | 0.840142 | 0.420071 | − | 0.907491i | \(-0.362005\pi\) | ||||
0.420071 | + | 0.907491i | \(0.362005\pi\) | |||||||
\(62\) | 9.65979 | 1.22679 | ||||||||
\(63\) | −22.0482 | −2.77782 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.503748 | 0.0624822 | ||||||||
\(66\) | 11.9298 | 1.46846 | ||||||||
\(67\) | −9.40136 | −1.14856 | −0.574280 | − | 0.818659i | \(-0.694718\pi\) | ||||
−0.574280 | + | 0.818659i | \(0.694718\pi\) | |||||||
\(68\) | 1.84555 | 0.223806 | ||||||||
\(69\) | 31.6824 | 3.81412 | ||||||||
\(70\) | 0.259057 | 0.0309632 | ||||||||
\(71\) | −14.8968 | −1.76792 | −0.883962 | − | 0.467559i | \(-0.845134\pi\) | ||||
−0.883962 | + | 0.467559i | \(0.845134\pi\) | |||||||
\(72\) | 8.24428 | 0.971598 | ||||||||
\(73\) | 4.93530 | 0.577633 | 0.288817 | − | 0.957384i | \(-0.406738\pi\) | ||||
0.288817 | + | 0.957384i | \(0.406738\pi\) | |||||||
\(74\) | 3.05031 | 0.354592 | ||||||||
\(75\) | 16.7348 | 1.93237 | ||||||||
\(76\) | −0.434911 | −0.0498877 | ||||||||
\(77\) | 9.51456 | 1.08428 | ||||||||
\(78\) | 17.4383 | 1.97450 | ||||||||
\(79\) | 2.09798 | 0.236041 | 0.118020 | − | 0.993011i | \(-0.462345\pi\) | ||||
0.118020 | + | 0.993011i | \(0.462345\pi\) | |||||||
\(80\) | −0.0968667 | −0.0108300 | ||||||||
\(81\) | 34.2353 | 3.80392 | ||||||||
\(82\) | −10.0990 | −1.11525 | ||||||||
\(83\) | −0.871999 | −0.0957143 | −0.0478571 | − | 0.998854i | \(-0.515239\pi\) | ||||
−0.0478571 | + | 0.998854i | \(0.515239\pi\) | |||||||
\(84\) | 8.96782 | 0.978469 | ||||||||
\(85\) | −0.178772 | −0.0193906 | ||||||||
\(86\) | 4.43508 | 0.478247 | ||||||||
\(87\) | −19.7243 | −2.11467 | ||||||||
\(88\) | −3.55769 | −0.379251 | ||||||||
\(89\) | 1.39518 | 0.147888 | 0.0739441 | − | 0.997262i | \(-0.476441\pi\) | ||||
0.0739441 | + | 0.997262i | \(0.476441\pi\) | |||||||
\(90\) | −0.798596 | −0.0841794 | ||||||||
\(91\) | 13.9078 | 1.45794 | ||||||||
\(92\) | −9.44828 | −0.985051 | ||||||||
\(93\) | −32.3917 | −3.35886 | ||||||||
\(94\) | −5.75080 | −0.593150 | ||||||||
\(95\) | 0.0421284 | 0.00432228 | ||||||||
\(96\) | −3.35325 | −0.342240 | ||||||||
\(97\) | 17.0595 | 1.73213 | 0.866066 | − | 0.499930i | \(-0.166641\pi\) | ||||
0.866066 | + | 0.499930i | \(0.166641\pi\) | |||||||
\(98\) | 0.152234 | 0.0153780 | ||||||||
\(99\) | −29.3306 | −2.94783 | ||||||||
\(100\) | −4.99062 | −0.499062 | ||||||||
\(101\) | 12.3779 | 1.23165 | 0.615825 | − | 0.787883i | \(-0.288823\pi\) | ||||
0.615825 | + | 0.787883i | \(0.288823\pi\) | |||||||
\(102\) | −6.18859 | −0.612762 | ||||||||
\(103\) | −11.5723 | −1.14025 | −0.570126 | − | 0.821557i | \(-0.693106\pi\) | ||||
−0.570126 | + | 0.821557i | \(0.693106\pi\) | |||||||
\(104\) | −5.20042 | −0.509943 | ||||||||
\(105\) | −0.868683 | −0.0847747 | ||||||||
\(106\) | −12.0959 | −1.17486 | ||||||||
\(107\) | 16.6889 | 1.61338 | 0.806690 | − | 0.590975i | \(-0.201257\pi\) | ||||
0.806690 | + | 0.590975i | \(0.201257\pi\) | |||||||
\(108\) | −17.5854 | −1.69215 | ||||||||
\(109\) | 3.60668 | 0.345457 | 0.172729 | − | 0.984969i | \(-0.444742\pi\) | ||||
0.172729 | + | 0.984969i | \(0.444742\pi\) | |||||||
\(110\) | 0.344621 | 0.0328584 | ||||||||
\(111\) | −10.2285 | −0.970843 | ||||||||
\(112\) | −2.67437 | −0.252704 | ||||||||
\(113\) | −7.81554 | −0.735224 | −0.367612 | − | 0.929979i | \(-0.619825\pi\) | ||||
−0.367612 | + | 0.929979i | \(0.619825\pi\) | |||||||
\(114\) | 1.45836 | 0.136588 | ||||||||
\(115\) | 0.915223 | 0.0853450 | ||||||||
\(116\) | 5.88214 | 0.546143 | ||||||||
\(117\) | −42.8737 | −3.96368 | ||||||||
\(118\) | 7.87428 | 0.724886 | ||||||||
\(119\) | −4.93568 | −0.452453 | ||||||||
\(120\) | 0.324818 | 0.0296517 | ||||||||
\(121\) | 1.65714 | 0.150649 | ||||||||
\(122\) | 6.56172 | 0.594070 | ||||||||
\(123\) | 33.8646 | 3.05347 | ||||||||
\(124\) | 9.65979 | 0.867475 | ||||||||
\(125\) | 0.967758 | 0.0865589 | ||||||||
\(126\) | −22.0482 | −1.96421 | ||||||||
\(127\) | −5.31971 | −0.472048 | −0.236024 | − | 0.971747i | \(-0.575844\pi\) | ||||
−0.236024 | + | 0.971747i | \(0.575844\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −14.8719 | −1.30940 | ||||||||
\(130\) | 0.503748 | 0.0441816 | ||||||||
\(131\) | −0.580813 | −0.0507459 | −0.0253729 | − | 0.999678i | \(-0.508077\pi\) | ||||
−0.0253729 | + | 0.999678i | \(0.508077\pi\) | |||||||
\(132\) | 11.9298 | 1.03836 | ||||||||
\(133\) | 1.16311 | 0.100854 | ||||||||
\(134\) | −9.40136 | −0.812154 | ||||||||
\(135\) | 1.70344 | 0.146609 | ||||||||
\(136\) | 1.84555 | 0.158255 | ||||||||
\(137\) | −6.92694 | −0.591808 | −0.295904 | − | 0.955218i | \(-0.595621\pi\) | ||||
−0.295904 | + | 0.955218i | \(0.595621\pi\) | |||||||
\(138\) | 31.6824 | 2.69699 | ||||||||
\(139\) | 16.5579 | 1.40442 | 0.702210 | − | 0.711970i | \(-0.252197\pi\) | ||||
0.702210 | + | 0.711970i | \(0.252197\pi\) | |||||||
\(140\) | 0.259057 | 0.0218943 | ||||||||
\(141\) | 19.2839 | 1.62400 | ||||||||
\(142\) | −14.8968 | −1.25011 | ||||||||
\(143\) | 18.5015 | 1.54717 | ||||||||
\(144\) | 8.24428 | 0.687023 | ||||||||
\(145\) | −0.569784 | −0.0473180 | ||||||||
\(146\) | 4.93530 | 0.408448 | ||||||||
\(147\) | −0.510480 | −0.0421037 | ||||||||
\(148\) | 3.05031 | 0.250734 | ||||||||
\(149\) | 19.6408 | 1.60904 | 0.804518 | − | 0.593928i | \(-0.202424\pi\) | ||||
0.804518 | + | 0.593928i | \(0.202424\pi\) | |||||||
\(150\) | 16.7348 | 1.36639 | ||||||||
\(151\) | −20.3563 | −1.65657 | −0.828286 | − | 0.560305i | \(-0.810684\pi\) | ||||
−0.828286 | + | 0.560305i | \(0.810684\pi\) | |||||||
\(152\) | −0.434911 | −0.0352759 | ||||||||
\(153\) | 15.2152 | 1.23008 | ||||||||
\(154\) | 9.51456 | 0.766705 | ||||||||
\(155\) | −0.935712 | −0.0751582 | ||||||||
\(156\) | 17.4383 | 1.39618 | ||||||||
\(157\) | 8.99323 | 0.717738 | 0.358869 | − | 0.933388i | \(-0.383162\pi\) | ||||
0.358869 | + | 0.933388i | \(0.383162\pi\) | |||||||
\(158\) | 2.09798 | 0.166906 | ||||||||
\(159\) | 40.5606 | 3.21666 | ||||||||
\(160\) | −0.0968667 | −0.00765798 | ||||||||
\(161\) | 25.2682 | 1.99141 | ||||||||
\(162\) | 34.2353 | 2.68978 | ||||||||
\(163\) | −19.6081 | −1.53582 | −0.767912 | − | 0.640556i | \(-0.778704\pi\) | ||||
−0.767912 | + | 0.640556i | \(0.778704\pi\) | |||||||
\(164\) | −10.0990 | −0.788602 | ||||||||
\(165\) | −1.15560 | −0.0899635 | ||||||||
\(166\) | −0.871999 | −0.0676802 | ||||||||
\(167\) | 18.5732 | 1.43724 | 0.718619 | − | 0.695404i | \(-0.244775\pi\) | ||||
0.718619 | + | 0.695404i | \(0.244775\pi\) | |||||||
\(168\) | 8.96782 | 0.691882 | ||||||||
\(169\) | 14.0444 | 1.08034 | ||||||||
\(170\) | −0.178772 | −0.0137112 | ||||||||
\(171\) | −3.58553 | −0.274192 | ||||||||
\(172\) | 4.43508 | 0.338172 | ||||||||
\(173\) | 21.6896 | 1.64903 | 0.824516 | − | 0.565839i | \(-0.191448\pi\) | ||||
0.824516 | + | 0.565839i | \(0.191448\pi\) | |||||||
\(174\) | −19.7243 | −1.49530 | ||||||||
\(175\) | 13.3467 | 1.00892 | ||||||||
\(176\) | −3.55769 | −0.268171 | ||||||||
\(177\) | −26.4044 | −1.98468 | ||||||||
\(178\) | 1.39518 | 0.104573 | ||||||||
\(179\) | 5.69226 | 0.425460 | 0.212730 | − | 0.977111i | \(-0.431765\pi\) | ||||
0.212730 | + | 0.977111i | \(0.431765\pi\) | |||||||
\(180\) | −0.798596 | −0.0595238 | ||||||||
\(181\) | 13.2984 | 0.988463 | 0.494232 | − | 0.869330i | \(-0.335449\pi\) | ||||
0.494232 | + | 0.869330i | \(0.335449\pi\) | |||||||
\(182\) | 13.9078 | 1.03092 | ||||||||
\(183\) | −22.0031 | −1.62651 | ||||||||
\(184\) | −9.44828 | −0.696536 | ||||||||
\(185\) | −0.295474 | −0.0217237 | ||||||||
\(186\) | −32.3917 | −2.37507 | ||||||||
\(187\) | −6.56589 | −0.480146 | ||||||||
\(188\) | −5.75080 | −0.419420 | ||||||||
\(189\) | 47.0297 | 3.42091 | ||||||||
\(190\) | 0.0421284 | 0.00305631 | ||||||||
\(191\) | 2.77312 | 0.200656 | 0.100328 | − | 0.994954i | \(-0.468011\pi\) | ||||
0.100328 | + | 0.994954i | \(0.468011\pi\) | |||||||
\(192\) | −3.35325 | −0.242000 | ||||||||
\(193\) | 12.1561 | 0.875015 | 0.437507 | − | 0.899215i | \(-0.355861\pi\) | ||||
0.437507 | + | 0.899215i | \(0.355861\pi\) | |||||||
\(194\) | 17.0595 | 1.22480 | ||||||||
\(195\) | −1.68919 | −0.120966 | ||||||||
\(196\) | 0.152234 | 0.0108739 | ||||||||
\(197\) | 21.4380 | 1.52740 | 0.763698 | − | 0.645573i | \(-0.223382\pi\) | ||||
0.763698 | + | 0.645573i | \(0.223382\pi\) | |||||||
\(198\) | −29.3306 | −2.08443 | ||||||||
\(199\) | −10.8941 | −0.772262 | −0.386131 | − | 0.922444i | \(-0.626189\pi\) | ||||
−0.386131 | + | 0.922444i | \(0.626189\pi\) | |||||||
\(200\) | −4.99062 | −0.352890 | ||||||||
\(201\) | 31.5251 | 2.22361 | ||||||||
\(202\) | 12.3779 | 0.870908 | ||||||||
\(203\) | −15.7310 | −1.10410 | ||||||||
\(204\) | −6.18859 | −0.433288 | ||||||||
\(205\) | 0.978260 | 0.0683247 | ||||||||
\(206\) | −11.5723 | −0.806280 | ||||||||
\(207\) | −77.8943 | −5.41402 | ||||||||
\(208\) | −5.20042 | −0.360584 | ||||||||
\(209\) | 1.54728 | 0.107027 | ||||||||
\(210\) | −0.868683 | −0.0599448 | ||||||||
\(211\) | 11.3189 | 0.779228 | 0.389614 | − | 0.920978i | \(-0.372608\pi\) | ||||
0.389614 | + | 0.920978i | \(0.372608\pi\) | |||||||
\(212\) | −12.0959 | −0.830750 | ||||||||
\(213\) | 49.9526 | 3.42270 | ||||||||
\(214\) | 16.6889 | 1.14083 | ||||||||
\(215\) | −0.429612 | −0.0292993 | ||||||||
\(216\) | −17.5854 | −1.19653 | ||||||||
\(217\) | −25.8338 | −1.75371 | ||||||||
\(218\) | 3.60668 | 0.244275 | ||||||||
\(219\) | −16.5493 | −1.11830 | ||||||||
\(220\) | 0.344621 | 0.0232344 | ||||||||
\(221\) | −9.59764 | −0.645607 | ||||||||
\(222\) | −10.2285 | −0.686490 | ||||||||
\(223\) | 21.1149 | 1.41396 | 0.706978 | − | 0.707236i | \(-0.250058\pi\) | ||||
0.706978 | + | 0.707236i | \(0.250058\pi\) | |||||||
\(224\) | −2.67437 | −0.178689 | ||||||||
\(225\) | −41.1440 | −2.74294 | ||||||||
\(226\) | −7.81554 | −0.519882 | ||||||||
\(227\) | 9.39551 | 0.623602 | 0.311801 | − | 0.950147i | \(-0.399068\pi\) | ||||
0.311801 | + | 0.950147i | \(0.399068\pi\) | |||||||
\(228\) | 1.45836 | 0.0965825 | ||||||||
\(229\) | −12.9210 | −0.853842 | −0.426921 | − | 0.904289i | \(-0.640402\pi\) | ||||
−0.426921 | + | 0.904289i | \(0.640402\pi\) | |||||||
\(230\) | 0.915223 | 0.0603480 | ||||||||
\(231\) | −31.9047 | −2.09917 | ||||||||
\(232\) | 5.88214 | 0.386182 | ||||||||
\(233\) | −4.38813 | −0.287476 | −0.143738 | − | 0.989616i | \(-0.545912\pi\) | ||||
−0.143738 | + | 0.989616i | \(0.545912\pi\) | |||||||
\(234\) | −42.8737 | −2.80274 | ||||||||
\(235\) | 0.557061 | 0.0363387 | ||||||||
\(236\) | 7.87428 | 0.512572 | ||||||||
\(237\) | −7.03504 | −0.456975 | ||||||||
\(238\) | −4.93568 | −0.319933 | ||||||||
\(239\) | 18.0144 | 1.16526 | 0.582629 | − | 0.812738i | \(-0.302024\pi\) | ||||
0.582629 | + | 0.812738i | \(0.302024\pi\) | |||||||
\(240\) | 0.324818 | 0.0209669 | ||||||||
\(241\) | 19.8422 | 1.27815 | 0.639075 | − | 0.769144i | \(-0.279317\pi\) | ||||
0.639075 | + | 0.769144i | \(0.279317\pi\) | |||||||
\(242\) | 1.65714 | 0.106525 | ||||||||
\(243\) | −62.0434 | −3.98009 | ||||||||
\(244\) | 6.56172 | 0.420071 | ||||||||
\(245\) | −0.0147464 | −0.000942115 0 | ||||||||
\(246\) | 33.8646 | 2.15913 | ||||||||
\(247\) | 2.26172 | 0.143910 | ||||||||
\(248\) | 9.65979 | 0.613397 | ||||||||
\(249\) | 2.92403 | 0.185303 | ||||||||
\(250\) | 0.967758 | 0.0612064 | ||||||||
\(251\) | −15.4721 | −0.976588 | −0.488294 | − | 0.872679i | \(-0.662381\pi\) | ||||
−0.488294 | + | 0.872679i | \(0.662381\pi\) | |||||||
\(252\) | −22.0482 | −1.38891 | ||||||||
\(253\) | 33.6140 | 2.11330 | ||||||||
\(254\) | −5.31971 | −0.333788 | ||||||||
\(255\) | 0.599468 | 0.0375402 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 9.32801 | 0.581865 | 0.290933 | − | 0.956744i | \(-0.406034\pi\) | ||||
0.290933 | + | 0.956744i | \(0.406034\pi\) | |||||||
\(258\) | −14.8719 | −0.925887 | ||||||||
\(259\) | −8.15766 | −0.506892 | ||||||||
\(260\) | 0.503748 | 0.0312411 | ||||||||
\(261\) | 48.4940 | 3.00171 | ||||||||
\(262\) | −0.580813 | −0.0358828 | ||||||||
\(263\) | 18.4406 | 1.13710 | 0.568549 | − | 0.822649i | \(-0.307505\pi\) | ||||
0.568549 | + | 0.822649i | \(0.307505\pi\) | |||||||
\(264\) | 11.9298 | 0.734229 | ||||||||
\(265\) | 1.17169 | 0.0719764 | ||||||||
\(266\) | 1.16311 | 0.0713149 | ||||||||
\(267\) | −4.67837 | −0.286312 | ||||||||
\(268\) | −9.40136 | −0.574280 | ||||||||
\(269\) | 15.6567 | 0.954609 | 0.477304 | − | 0.878738i | \(-0.341614\pi\) | ||||
0.477304 | + | 0.878738i | \(0.341614\pi\) | |||||||
\(270\) | 1.70344 | 0.103668 | ||||||||
\(271\) | −7.53205 | −0.457539 | −0.228770 | − | 0.973481i | \(-0.573470\pi\) | ||||
−0.228770 | + | 0.973481i | \(0.573470\pi\) | |||||||
\(272\) | 1.84555 | 0.111903 | ||||||||
\(273\) | −46.6364 | −2.82257 | ||||||||
\(274\) | −6.92694 | −0.418472 | ||||||||
\(275\) | 17.7551 | 1.07067 | ||||||||
\(276\) | 31.6824 | 1.90706 | ||||||||
\(277\) | −1.69550 | −0.101873 | −0.0509363 | − | 0.998702i | \(-0.516221\pi\) | ||||
−0.0509363 | + | 0.998702i | \(0.516221\pi\) | |||||||
\(278\) | 16.5579 | 0.993075 | ||||||||
\(279\) | 79.6380 | 4.76780 | ||||||||
\(280\) | 0.259057 | 0.0154816 | ||||||||
\(281\) | −30.5556 | −1.82280 | −0.911399 | − | 0.411525i | \(-0.864996\pi\) | ||||
−0.911399 | + | 0.411525i | \(0.864996\pi\) | |||||||
\(282\) | 19.2839 | 1.14834 | ||||||||
\(283\) | 1.71177 | 0.101754 | 0.0508771 | − | 0.998705i | \(-0.483798\pi\) | ||||
0.0508771 | + | 0.998705i | \(0.483798\pi\) | |||||||
\(284\) | −14.8968 | −0.883962 | ||||||||
\(285\) | −0.141267 | −0.00836793 | ||||||||
\(286\) | 18.5015 | 1.09402 | ||||||||
\(287\) | 27.0085 | 1.59426 | ||||||||
\(288\) | 8.24428 | 0.485799 | ||||||||
\(289\) | −13.5939 | −0.799644 | ||||||||
\(290\) | −0.569784 | −0.0334589 | ||||||||
\(291\) | −57.2048 | −3.35341 | ||||||||
\(292\) | 4.93530 | 0.288817 | ||||||||
\(293\) | 10.3651 | 0.605537 | 0.302769 | − | 0.953064i | \(-0.402089\pi\) | ||||
0.302769 | + | 0.953064i | \(0.402089\pi\) | |||||||
\(294\) | −0.510480 | −0.0297718 | ||||||||
\(295\) | −0.762755 | −0.0444093 | ||||||||
\(296\) | 3.05031 | 0.177296 | ||||||||
\(297\) | 62.5633 | 3.63029 | ||||||||
\(298\) | 19.6408 | 1.13776 | ||||||||
\(299\) | 49.1350 | 2.84155 | ||||||||
\(300\) | 16.7348 | 0.966183 | ||||||||
\(301\) | −11.8610 | −0.683659 | ||||||||
\(302\) | −20.3563 | −1.17137 | ||||||||
\(303\) | −41.5063 | −2.38447 | ||||||||
\(304\) | −0.434911 | −0.0249438 | ||||||||
\(305\) | −0.635612 | −0.0363950 | ||||||||
\(306\) | 15.2152 | 0.869797 | ||||||||
\(307\) | −14.8531 | −0.847711 | −0.423856 | − | 0.905730i | \(-0.639324\pi\) | ||||
−0.423856 | + | 0.905730i | \(0.639324\pi\) | |||||||
\(308\) | 9.51456 | 0.542142 | ||||||||
\(309\) | 38.8048 | 2.20753 | ||||||||
\(310\) | −0.935712 | −0.0531449 | ||||||||
\(311\) | −19.6436 | −1.11389 | −0.556943 | − | 0.830551i | \(-0.688026\pi\) | ||||
−0.556943 | + | 0.830551i | \(0.688026\pi\) | |||||||
\(312\) | 17.4383 | 0.987250 | ||||||||
\(313\) | 4.73213 | 0.267476 | 0.133738 | − | 0.991017i | \(-0.457302\pi\) | ||||
0.133738 | + | 0.991017i | \(0.457302\pi\) | |||||||
\(314\) | 8.99323 | 0.507518 | ||||||||
\(315\) | 2.13574 | 0.120335 | ||||||||
\(316\) | 2.09798 | 0.118020 | ||||||||
\(317\) | −27.7729 | −1.55988 | −0.779941 | − | 0.625853i | \(-0.784751\pi\) | ||||
−0.779941 | + | 0.625853i | \(0.784751\pi\) | |||||||
\(318\) | 40.5606 | 2.27452 | ||||||||
\(319\) | −20.9268 | −1.17168 | ||||||||
\(320\) | −0.0968667 | −0.00541501 | ||||||||
\(321\) | −55.9621 | −3.12350 | ||||||||
\(322\) | 25.2682 | 1.40814 | ||||||||
\(323\) | −0.802650 | −0.0446606 | ||||||||
\(324\) | 34.2353 | 1.90196 | ||||||||
\(325\) | 25.9533 | 1.43963 | ||||||||
\(326\) | −19.6081 | −1.08599 | ||||||||
\(327\) | −12.0941 | −0.668805 | ||||||||
\(328\) | −10.0990 | −0.557626 | ||||||||
\(329\) | 15.3798 | 0.847913 | ||||||||
\(330\) | −1.15560 | −0.0636138 | ||||||||
\(331\) | −0.154355 | −0.00848413 | −0.00424206 | − | 0.999991i | \(-0.501350\pi\) | ||||
−0.00424206 | + | 0.999991i | \(0.501350\pi\) | |||||||
\(332\) | −0.871999 | −0.0478571 | ||||||||
\(333\) | 25.1476 | 1.37808 | ||||||||
\(334\) | 18.5732 | 1.01628 | ||||||||
\(335\) | 0.910679 | 0.0497557 | ||||||||
\(336\) | 8.96782 | 0.489234 | ||||||||
\(337\) | 9.01822 | 0.491254 | 0.245627 | − | 0.969364i | \(-0.421006\pi\) | ||||
0.245627 | + | 0.969364i | \(0.421006\pi\) | |||||||
\(338\) | 14.0444 | 0.763914 | ||||||||
\(339\) | 26.2075 | 1.42339 | ||||||||
\(340\) | −0.178772 | −0.00969529 | ||||||||
\(341\) | −34.3665 | −1.86105 | ||||||||
\(342\) | −3.58553 | −0.193883 | ||||||||
\(343\) | 18.3134 | 0.988832 | ||||||||
\(344\) | 4.43508 | 0.239124 | ||||||||
\(345\) | −3.06897 | −0.165228 | ||||||||
\(346\) | 21.6896 | 1.16604 | ||||||||
\(347\) | 14.4946 | 0.778108 | 0.389054 | − | 0.921215i | \(-0.372802\pi\) | ||||
0.389054 | + | 0.921215i | \(0.372802\pi\) | |||||||
\(348\) | −19.7243 | −1.05733 | ||||||||
\(349\) | 0.809288 | 0.0433202 | 0.0216601 | − | 0.999765i | \(-0.493105\pi\) | ||||
0.0216601 | + | 0.999765i | \(0.493105\pi\) | |||||||
\(350\) | 13.3467 | 0.713413 | ||||||||
\(351\) | 91.4514 | 4.88131 | ||||||||
\(352\) | −3.55769 | −0.189625 | ||||||||
\(353\) | 18.2823 | 0.973066 | 0.486533 | − | 0.873662i | \(-0.338261\pi\) | ||||
0.486533 | + | 0.873662i | \(0.338261\pi\) | |||||||
\(354\) | −26.4044 | −1.40338 | ||||||||
\(355\) | 1.44300 | 0.0765866 | ||||||||
\(356\) | 1.39518 | 0.0739441 | ||||||||
\(357\) | 16.5506 | 0.875948 | ||||||||
\(358\) | 5.69226 | 0.300846 | ||||||||
\(359\) | 1.09243 | 0.0576560 | 0.0288280 | − | 0.999584i | \(-0.490822\pi\) | ||||
0.0288280 | + | 0.999584i | \(0.490822\pi\) | |||||||
\(360\) | −0.798596 | −0.0420897 | ||||||||
\(361\) | −18.8109 | −0.990045 | ||||||||
\(362\) | 13.2984 | 0.698949 | ||||||||
\(363\) | −5.55681 | −0.291657 | ||||||||
\(364\) | 13.9078 | 0.728969 | ||||||||
\(365\) | −0.478066 | −0.0250231 | ||||||||
\(366\) | −22.0031 | −1.15012 | ||||||||
\(367\) | 18.8528 | 0.984109 | 0.492054 | − | 0.870564i | \(-0.336246\pi\) | ||||
0.492054 | + | 0.870564i | \(0.336246\pi\) | |||||||
\(368\) | −9.44828 | −0.492526 | ||||||||
\(369\) | −83.2593 | −4.33431 | ||||||||
\(370\) | −0.295474 | −0.0153610 | ||||||||
\(371\) | 32.3489 | 1.67947 | ||||||||
\(372\) | −32.3917 | −1.67943 | ||||||||
\(373\) | −22.1298 | −1.14584 | −0.572918 | − | 0.819613i | \(-0.694189\pi\) | ||||
−0.572918 | + | 0.819613i | \(0.694189\pi\) | |||||||
\(374\) | −6.56589 | −0.339514 | ||||||||
\(375\) | −3.24513 | −0.167578 | ||||||||
\(376\) | −5.75080 | −0.296575 | ||||||||
\(377\) | −30.5896 | −1.57545 | ||||||||
\(378\) | 47.0297 | 2.41895 | ||||||||
\(379\) | 30.4741 | 1.56535 | 0.782676 | − | 0.622430i | \(-0.213854\pi\) | ||||
0.782676 | + | 0.622430i | \(0.213854\pi\) | |||||||
\(380\) | 0.0421284 | 0.00216114 | ||||||||
\(381\) | 17.8383 | 0.913884 | ||||||||
\(382\) | 2.77312 | 0.141885 | ||||||||
\(383\) | −25.8440 | −1.32057 | −0.660283 | − | 0.751017i | \(-0.729564\pi\) | ||||
−0.660283 | + | 0.751017i | \(0.729564\pi\) | |||||||
\(384\) | −3.35325 | −0.171120 | ||||||||
\(385\) | −0.921644 | −0.0469713 | ||||||||
\(386\) | 12.1561 | 0.618729 | ||||||||
\(387\) | 36.5641 | 1.85866 | ||||||||
\(388\) | 17.0595 | 0.866066 | ||||||||
\(389\) | −7.87194 | −0.399123 | −0.199562 | − | 0.979885i | \(-0.563952\pi\) | ||||
−0.199562 | + | 0.979885i | \(0.563952\pi\) | |||||||
\(390\) | −1.68919 | −0.0855355 | ||||||||
\(391\) | −17.4373 | −0.881841 | ||||||||
\(392\) | 0.152234 | 0.00768900 | ||||||||
\(393\) | 1.94761 | 0.0982440 | ||||||||
\(394\) | 21.4380 | 1.08003 | ||||||||
\(395\) | −0.203224 | −0.0102253 | ||||||||
\(396\) | −29.3306 | −1.47392 | ||||||||
\(397\) | −20.4955 | −1.02864 | −0.514320 | − | 0.857598i | \(-0.671956\pi\) | ||||
−0.514320 | + | 0.857598i | \(0.671956\pi\) | |||||||
\(398\) | −10.8941 | −0.546072 | ||||||||
\(399\) | −3.90020 | −0.195254 | ||||||||
\(400\) | −4.99062 | −0.249531 | ||||||||
\(401\) | −14.0710 | −0.702673 | −0.351337 | − | 0.936249i | \(-0.614273\pi\) | ||||
−0.351337 | + | 0.936249i | \(0.614273\pi\) | |||||||
\(402\) | 31.5251 | 1.57233 | ||||||||
\(403\) | −50.2350 | −2.50238 | ||||||||
\(404\) | 12.3779 | 0.615825 | ||||||||
\(405\) | −3.31626 | −0.164786 | ||||||||
\(406\) | −15.7310 | −0.780717 | ||||||||
\(407\) | −10.8521 | −0.537917 | ||||||||
\(408\) | −6.18859 | −0.306381 | ||||||||
\(409\) | −18.4117 | −0.910401 | −0.455200 | − | 0.890389i | \(-0.650432\pi\) | ||||
−0.455200 | + | 0.890389i | \(0.650432\pi\) | |||||||
\(410\) | 0.978260 | 0.0483128 | ||||||||
\(411\) | 23.2278 | 1.14574 | ||||||||
\(412\) | −11.5723 | −0.570126 | ||||||||
\(413\) | −21.0587 | −1.03623 | ||||||||
\(414\) | −77.8943 | −3.82829 | ||||||||
\(415\) | 0.0844676 | 0.00414635 | ||||||||
\(416\) | −5.20042 | −0.254972 | ||||||||
\(417\) | −55.5227 | −2.71896 | ||||||||
\(418\) | 1.54728 | 0.0756798 | ||||||||
\(419\) | 23.7870 | 1.16207 | 0.581035 | − | 0.813879i | \(-0.302648\pi\) | ||||
0.581035 | + | 0.813879i | \(0.302648\pi\) | |||||||
\(420\) | −0.868683 | −0.0423874 | ||||||||
\(421\) | −6.87293 | −0.334966 | −0.167483 | − | 0.985875i | \(-0.553564\pi\) | ||||
−0.167483 | + | 0.985875i | \(0.553564\pi\) | |||||||
\(422\) | 11.3189 | 0.550997 | ||||||||
\(423\) | −47.4112 | −2.30521 | ||||||||
\(424\) | −12.0959 | −0.587429 | ||||||||
\(425\) | −9.21044 | −0.446772 | ||||||||
\(426\) | 49.9526 | 2.42021 | ||||||||
\(427\) | −17.5484 | −0.849228 | ||||||||
\(428\) | 16.6889 | 0.806690 | ||||||||
\(429\) | −62.0401 | −2.99532 | ||||||||
\(430\) | −0.429612 | −0.0207177 | ||||||||
\(431\) | −34.4500 | −1.65940 | −0.829700 | − | 0.558210i | \(-0.811488\pi\) | ||||
−0.829700 | + | 0.558210i | \(0.811488\pi\) | |||||||
\(432\) | −17.5854 | −0.846077 | ||||||||
\(433\) | −11.9923 | −0.576312 | −0.288156 | − | 0.957583i | \(-0.593042\pi\) | ||||
−0.288156 | + | 0.957583i | \(0.593042\pi\) | |||||||
\(434\) | −25.8338 | −1.24006 | ||||||||
\(435\) | 1.91063 | 0.0916076 | ||||||||
\(436\) | 3.60668 | 0.172729 | ||||||||
\(437\) | 4.10916 | 0.196568 | ||||||||
\(438\) | −16.5493 | −0.790756 | ||||||||
\(439\) | 0.762424 | 0.0363885 | 0.0181943 | − | 0.999834i | \(-0.494208\pi\) | ||||
0.0181943 | + | 0.999834i | \(0.494208\pi\) | |||||||
\(440\) | 0.344621 | 0.0164292 | ||||||||
\(441\) | 1.25506 | 0.0597649 | ||||||||
\(442\) | −9.59764 | −0.456513 | ||||||||
\(443\) | 4.91551 | 0.233543 | 0.116771 | − | 0.993159i | \(-0.462745\pi\) | ||||
0.116771 | + | 0.993159i | \(0.462745\pi\) | |||||||
\(444\) | −10.2285 | −0.485421 | ||||||||
\(445\) | −0.135146 | −0.00640654 | ||||||||
\(446\) | 21.1149 | 0.999817 | ||||||||
\(447\) | −65.8604 | −3.11509 | ||||||||
\(448\) | −2.67437 | −0.126352 | ||||||||
\(449\) | −7.50630 | −0.354244 | −0.177122 | − | 0.984189i | \(-0.556679\pi\) | ||||
−0.177122 | + | 0.984189i | \(0.556679\pi\) | |||||||
\(450\) | −41.1440 | −1.93955 | ||||||||
\(451\) | 35.9292 | 1.69184 | ||||||||
\(452\) | −7.81554 | −0.367612 | ||||||||
\(453\) | 68.2597 | 3.20712 | ||||||||
\(454\) | 9.39551 | 0.440953 | ||||||||
\(455\) | −1.34721 | −0.0631580 | ||||||||
\(456\) | 1.45836 | 0.0682941 | ||||||||
\(457\) | 25.1784 | 1.17780 | 0.588898 | − | 0.808207i | \(-0.299562\pi\) | ||||
0.588898 | + | 0.808207i | \(0.299562\pi\) | |||||||
\(458\) | −12.9210 | −0.603757 | ||||||||
\(459\) | −32.4547 | −1.51486 | ||||||||
\(460\) | 0.915223 | 0.0426725 | ||||||||
\(461\) | −32.8403 | −1.52952 | −0.764762 | − | 0.644313i | \(-0.777143\pi\) | ||||
−0.764762 | + | 0.644313i | \(0.777143\pi\) | |||||||
\(462\) | −31.9047 | −1.48434 | ||||||||
\(463\) | 20.3737 | 0.946848 | 0.473424 | − | 0.880835i | \(-0.343018\pi\) | ||||
0.473424 | + | 0.880835i | \(0.343018\pi\) | |||||||
\(464\) | 5.88214 | 0.273072 | ||||||||
\(465\) | 3.13768 | 0.145506 | ||||||||
\(466\) | −4.38813 | −0.203276 | ||||||||
\(467\) | −9.48846 | −0.439073 | −0.219537 | − | 0.975604i | \(-0.570455\pi\) | ||||
−0.219537 | + | 0.975604i | \(0.570455\pi\) | |||||||
\(468\) | −42.8737 | −1.98184 | ||||||||
\(469\) | 25.1427 | 1.16098 | ||||||||
\(470\) | 0.557061 | 0.0256953 | ||||||||
\(471\) | −30.1566 | −1.38954 | ||||||||
\(472\) | 7.87428 | 0.362443 | ||||||||
\(473\) | −15.7786 | −0.725503 | ||||||||
\(474\) | −7.03504 | −0.323130 | ||||||||
\(475\) | 2.17047 | 0.0995881 | ||||||||
\(476\) | −4.93568 | −0.226226 | ||||||||
\(477\) | −99.7220 | −4.56596 | ||||||||
\(478\) | 18.0144 | 0.823961 | ||||||||
\(479\) | −27.3667 | −1.25042 | −0.625208 | − | 0.780458i | \(-0.714986\pi\) | ||||
−0.625208 | + | 0.780458i | \(0.714986\pi\) | |||||||
\(480\) | 0.324818 | 0.0148259 | ||||||||
\(481\) | −15.8629 | −0.723287 | ||||||||
\(482\) | 19.8422 | 0.903789 | ||||||||
\(483\) | −84.7304 | −3.85537 | ||||||||
\(484\) | 1.65714 | 0.0753247 | ||||||||
\(485\) | −1.65250 | −0.0750361 | ||||||||
\(486\) | −62.0434 | −2.81435 | ||||||||
\(487\) | 17.4059 | 0.788735 | 0.394367 | − | 0.918953i | \(-0.370964\pi\) | ||||
0.394367 | + | 0.918953i | \(0.370964\pi\) | |||||||
\(488\) | 6.56172 | 0.297035 | ||||||||
\(489\) | 65.7508 | 2.97335 | ||||||||
\(490\) | −0.0147464 | −0.000666176 0 | ||||||||
\(491\) | 0.790617 | 0.0356801 | 0.0178400 | − | 0.999841i | \(-0.494321\pi\) | ||||
0.0178400 | + | 0.999841i | \(0.494321\pi\) | |||||||
\(492\) | 33.8646 | 1.52673 | ||||||||
\(493\) | 10.8558 | 0.488920 | ||||||||
\(494\) | 2.26172 | 0.101760 | ||||||||
\(495\) | 2.84116 | 0.127700 | ||||||||
\(496\) | 9.65979 | 0.433737 | ||||||||
\(497\) | 39.8395 | 1.78704 | ||||||||
\(498\) | 2.92403 | 0.131029 | ||||||||
\(499\) | 28.7338 | 1.28630 | 0.643150 | − | 0.765740i | \(-0.277627\pi\) | ||||
0.643150 | + | 0.765740i | \(0.277627\pi\) | |||||||
\(500\) | 0.967758 | 0.0432795 | ||||||||
\(501\) | −62.2806 | −2.78249 | ||||||||
\(502\) | −15.4721 | −0.690552 | ||||||||
\(503\) | −17.8810 | −0.797276 | −0.398638 | − | 0.917108i | \(-0.630517\pi\) | ||||
−0.398638 | + | 0.917108i | \(0.630517\pi\) | |||||||
\(504\) | −22.0482 | −0.982106 | ||||||||
\(505\) | −1.19901 | −0.0533552 | ||||||||
\(506\) | 33.6140 | 1.49433 | ||||||||
\(507\) | −47.0943 | −2.09153 | ||||||||
\(508\) | −5.31971 | −0.236024 | ||||||||
\(509\) | −36.0819 | −1.59930 | −0.799650 | − | 0.600466i | \(-0.794982\pi\) | ||||
−0.799650 | + | 0.600466i | \(0.794982\pi\) | |||||||
\(510\) | 0.599468 | 0.0265449 | ||||||||
\(511\) | −13.1988 | −0.583881 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 7.64807 | 0.337670 | ||||||||
\(514\) | 9.32801 | 0.411441 | ||||||||
\(515\) | 1.12097 | 0.0493958 | ||||||||
\(516\) | −14.8719 | −0.654701 | ||||||||
\(517\) | 20.4596 | 0.899810 | ||||||||
\(518\) | −8.15766 | −0.358427 | ||||||||
\(519\) | −72.7307 | −3.19252 | ||||||||
\(520\) | 0.503748 | 0.0220908 | ||||||||
\(521\) | 1.50359 | 0.0658736 | 0.0329368 | − | 0.999457i | \(-0.489514\pi\) | ||||
0.0329368 | + | 0.999457i | \(0.489514\pi\) | |||||||
\(522\) | 48.4940 | 2.12253 | ||||||||
\(523\) | −16.6308 | −0.727215 | −0.363608 | − | 0.931552i | \(-0.618455\pi\) | ||||
−0.363608 | + | 0.931552i | \(0.618455\pi\) | |||||||
\(524\) | −0.580813 | −0.0253729 | ||||||||
\(525\) | −44.7549 | −1.95327 | ||||||||
\(526\) | 18.4406 | 0.804050 | ||||||||
\(527\) | 17.8276 | 0.776584 | ||||||||
\(528\) | 11.9298 | 0.519179 | ||||||||
\(529\) | 66.2700 | 2.88130 | ||||||||
\(530\) | 1.17169 | 0.0508950 | ||||||||
\(531\) | 64.9178 | 2.81719 | ||||||||
\(532\) | 1.16311 | 0.0504272 | ||||||||
\(533\) | 52.5193 | 2.27486 | ||||||||
\(534\) | −4.67837 | −0.202453 | ||||||||
\(535\) | −1.61660 | −0.0698918 | ||||||||
\(536\) | −9.40136 | −0.406077 | ||||||||
\(537\) | −19.0876 | −0.823690 | ||||||||
\(538\) | 15.6567 | 0.675010 | ||||||||
\(539\) | −0.541602 | −0.0233285 | ||||||||
\(540\) | 1.70344 | 0.0733043 | ||||||||
\(541\) | 29.0539 | 1.24913 | 0.624563 | − | 0.780975i | \(-0.285277\pi\) | ||||
0.624563 | + | 0.780975i | \(0.285277\pi\) | |||||||
\(542\) | −7.53205 | −0.323529 | ||||||||
\(543\) | −44.5929 | −1.91366 | ||||||||
\(544\) | 1.84555 | 0.0791273 | ||||||||
\(545\) | −0.349367 | −0.0149652 | ||||||||
\(546\) | −46.6364 | −1.99585 | ||||||||
\(547\) | 5.65284 | 0.241698 | 0.120849 | − | 0.992671i | \(-0.461438\pi\) | ||||
0.120849 | + | 0.992671i | \(0.461438\pi\) | |||||||
\(548\) | −6.92694 | −0.295904 | ||||||||
\(549\) | 54.0966 | 2.30879 | ||||||||
\(550\) | 17.7551 | 0.757078 | ||||||||
\(551\) | −2.55821 | −0.108983 | ||||||||
\(552\) | 31.6824 | 1.34849 | ||||||||
\(553\) | −5.61076 | −0.238594 | ||||||||
\(554\) | −1.69550 | −0.0720348 | ||||||||
\(555\) | 0.990797 | 0.0420570 | ||||||||
\(556\) | 16.5579 | 0.702210 | ||||||||
\(557\) | −2.27382 | −0.0963450 | −0.0481725 | − | 0.998839i | \(-0.515340\pi\) | ||||
−0.0481725 | + | 0.998839i | \(0.515340\pi\) | |||||||
\(558\) | 79.6380 | 3.37135 | ||||||||
\(559\) | −23.0643 | −0.975516 | ||||||||
\(560\) | 0.259057 | 0.0109472 | ||||||||
\(561\) | 22.0171 | 0.929562 | ||||||||
\(562\) | −30.5556 | −1.28891 | ||||||||
\(563\) | 20.8280 | 0.877796 | 0.438898 | − | 0.898537i | \(-0.355369\pi\) | ||||
0.438898 | + | 0.898537i | \(0.355369\pi\) | |||||||
\(564\) | 19.2839 | 0.811998 | ||||||||
\(565\) | 0.757065 | 0.0318500 | ||||||||
\(566\) | 1.71177 | 0.0719511 | ||||||||
\(567\) | −91.5578 | −3.84506 | ||||||||
\(568\) | −14.8968 | −0.625055 | ||||||||
\(569\) | 10.0113 | 0.419693 | 0.209847 | − | 0.977734i | \(-0.432703\pi\) | ||||
0.209847 | + | 0.977734i | \(0.432703\pi\) | |||||||
\(570\) | −0.141267 | −0.00591702 | ||||||||
\(571\) | −2.42776 | −0.101599 | −0.0507993 | − | 0.998709i | \(-0.516177\pi\) | ||||
−0.0507993 | + | 0.998709i | \(0.516177\pi\) | |||||||
\(572\) | 18.5015 | 0.773586 | ||||||||
\(573\) | −9.29897 | −0.388470 | ||||||||
\(574\) | 27.0085 | 1.12731 | ||||||||
\(575\) | 47.1527 | 1.96641 | ||||||||
\(576\) | 8.24428 | 0.343512 | ||||||||
\(577\) | −31.5109 | −1.31181 | −0.655907 | − | 0.754842i | \(-0.727714\pi\) | ||||
−0.655907 | + | 0.754842i | \(0.727714\pi\) | |||||||
\(578\) | −13.5939 | −0.565433 | ||||||||
\(579\) | −40.7624 | −1.69403 | ||||||||
\(580\) | −0.569784 | −0.0236590 | ||||||||
\(581\) | 2.33204 | 0.0967495 | ||||||||
\(582\) | −57.2048 | −2.37122 | ||||||||
\(583\) | 43.0335 | 1.78226 | ||||||||
\(584\) | 4.93530 | 0.204224 | ||||||||
\(585\) | 4.15304 | 0.171707 | ||||||||
\(586\) | 10.3651 | 0.428179 | ||||||||
\(587\) | 2.15284 | 0.0888574 | 0.0444287 | − | 0.999013i | \(-0.485853\pi\) | ||||
0.0444287 | + | 0.999013i | \(0.485853\pi\) | |||||||
\(588\) | −0.510480 | −0.0210518 | ||||||||
\(589\) | −4.20115 | −0.173105 | ||||||||
\(590\) | −0.762755 | −0.0314021 | ||||||||
\(591\) | −71.8871 | −2.95704 | ||||||||
\(592\) | 3.05031 | 0.125367 | ||||||||
\(593\) | −4.18523 | −0.171867 | −0.0859335 | − | 0.996301i | \(-0.527387\pi\) | ||||
−0.0859335 | + | 0.996301i | \(0.527387\pi\) | |||||||
\(594\) | 62.5633 | 2.56700 | ||||||||
\(595\) | 0.478103 | 0.0196003 | ||||||||
\(596\) | 19.6408 | 0.804518 | ||||||||
\(597\) | 36.5306 | 1.49510 | ||||||||
\(598\) | 49.1350 | 2.00928 | ||||||||
\(599\) | 7.32978 | 0.299487 | 0.149743 | − | 0.988725i | \(-0.452155\pi\) | ||||
0.149743 | + | 0.988725i | \(0.452155\pi\) | |||||||
\(600\) | 16.7348 | 0.683195 | ||||||||
\(601\) | 16.0825 | 0.656019 | 0.328009 | − | 0.944674i | \(-0.393622\pi\) | ||||
0.328009 | + | 0.944674i | \(0.393622\pi\) | |||||||
\(602\) | −11.8610 | −0.483420 | ||||||||
\(603\) | −77.5075 | −3.15635 | ||||||||
\(604\) | −20.3563 | −0.828286 | ||||||||
\(605\) | −0.160522 | −0.00652615 | ||||||||
\(606\) | −41.5063 | −1.68608 | ||||||||
\(607\) | −5.63187 | −0.228590 | −0.114295 | − | 0.993447i | \(-0.536461\pi\) | ||||
−0.114295 | + | 0.993447i | \(0.536461\pi\) | |||||||
\(608\) | −0.434911 | −0.0176380 | ||||||||
\(609\) | 52.7500 | 2.13754 | ||||||||
\(610\) | −0.635612 | −0.0257352 | ||||||||
\(611\) | 29.9066 | 1.20989 | ||||||||
\(612\) | 15.2152 | 0.615039 | ||||||||
\(613\) | −36.5455 | −1.47606 | −0.738028 | − | 0.674770i | \(-0.764243\pi\) | ||||
−0.738028 | + | 0.674770i | \(0.764243\pi\) | |||||||
\(614\) | −14.8531 | −0.599423 | ||||||||
\(615\) | −3.28035 | −0.132276 | ||||||||
\(616\) | 9.51456 | 0.383353 | ||||||||
\(617\) | −13.8028 | −0.555680 | −0.277840 | − | 0.960627i | \(-0.589618\pi\) | ||||
−0.277840 | + | 0.960627i | \(0.589618\pi\) | |||||||
\(618\) | 38.8048 | 1.56096 | ||||||||
\(619\) | 26.6908 | 1.07279 | 0.536396 | − | 0.843966i | \(-0.319785\pi\) | ||||
0.536396 | + | 0.843966i | \(0.319785\pi\) | |||||||
\(620\) | −0.935712 | −0.0375791 | ||||||||
\(621\) | 166.152 | 6.66743 | ||||||||
\(622\) | −19.6436 | −0.787636 | ||||||||
\(623\) | −3.73121 | −0.149488 | ||||||||
\(624\) | 17.4383 | 0.698091 | ||||||||
\(625\) | 24.8593 | 0.994374 | ||||||||
\(626\) | 4.73213 | 0.189134 | ||||||||
\(627\) | −5.18840 | −0.207205 | ||||||||
\(628\) | 8.99323 | 0.358869 | ||||||||
\(629\) | 5.62951 | 0.224463 | ||||||||
\(630\) | 2.13574 | 0.0850898 | ||||||||
\(631\) | 41.8744 | 1.66699 | 0.833497 | − | 0.552524i | \(-0.186335\pi\) | ||||
0.833497 | + | 0.552524i | \(0.186335\pi\) | |||||||
\(632\) | 2.09798 | 0.0834531 | ||||||||
\(633\) | −37.9552 | −1.50858 | ||||||||
\(634\) | −27.7729 | −1.10300 | ||||||||
\(635\) | 0.515302 | 0.0204491 | ||||||||
\(636\) | 40.5606 | 1.60833 | ||||||||
\(637\) | −0.791683 | −0.0313676 | ||||||||
\(638\) | −20.9268 | −0.828501 | ||||||||
\(639\) | −122.813 | −4.85842 | ||||||||
\(640\) | −0.0968667 | −0.00382899 | ||||||||
\(641\) | −33.0780 | −1.30650 | −0.653251 | − | 0.757142i | \(-0.726595\pi\) | ||||
−0.653251 | + | 0.757142i | \(0.726595\pi\) | |||||||
\(642\) | −55.9621 | −2.20865 | ||||||||
\(643\) | −9.49992 | −0.374640 | −0.187320 | − | 0.982299i | \(-0.559980\pi\) | ||||
−0.187320 | + | 0.982299i | \(0.559980\pi\) | |||||||
\(644\) | 25.2682 | 0.995705 | ||||||||
\(645\) | 1.44060 | 0.0567234 | ||||||||
\(646\) | −0.802650 | −0.0315798 | ||||||||
\(647\) | 21.0399 | 0.827163 | 0.413582 | − | 0.910467i | \(-0.364278\pi\) | ||||
0.413582 | + | 0.910467i | \(0.364278\pi\) | |||||||
\(648\) | 34.2353 | 1.34489 | ||||||||
\(649\) | −28.0142 | −1.09965 | ||||||||
\(650\) | 25.9533 | 1.01797 | ||||||||
\(651\) | 86.6272 | 3.39519 | ||||||||
\(652\) | −19.6081 | −0.767912 | ||||||||
\(653\) | −39.1316 | −1.53134 | −0.765668 | − | 0.643236i | \(-0.777591\pi\) | ||||
−0.765668 | + | 0.643236i | \(0.777591\pi\) | |||||||
\(654\) | −12.0941 | −0.472916 | ||||||||
\(655\) | 0.0562614 | 0.00219832 | ||||||||
\(656\) | −10.0990 | −0.394301 | ||||||||
\(657\) | 40.6880 | 1.58739 | ||||||||
\(658\) | 15.3798 | 0.599565 | ||||||||
\(659\) | 20.2896 | 0.790371 | 0.395185 | − | 0.918601i | \(-0.370680\pi\) | ||||
0.395185 | + | 0.918601i | \(0.370680\pi\) | |||||||
\(660\) | −1.15560 | −0.0449817 | ||||||||
\(661\) | −25.0745 | −0.975285 | −0.487643 | − | 0.873043i | \(-0.662143\pi\) | ||||
−0.487643 | + | 0.873043i | \(0.662143\pi\) | |||||||
\(662\) | −0.154355 | −0.00599918 | ||||||||
\(663\) | 32.1833 | 1.24990 | ||||||||
\(664\) | −0.871999 | −0.0338401 | ||||||||
\(665\) | −0.112667 | −0.00436903 | ||||||||
\(666\) | 25.1476 | 0.974452 | ||||||||
\(667\) | −55.5761 | −2.15192 | ||||||||
\(668\) | 18.5732 | 0.718619 | ||||||||
\(669\) | −70.8034 | −2.73742 | ||||||||
\(670\) | 0.910679 | 0.0351826 | ||||||||
\(671\) | −23.3445 | −0.901206 | ||||||||
\(672\) | 8.96782 | 0.345941 | ||||||||
\(673\) | 21.6093 | 0.832977 | 0.416489 | − | 0.909141i | \(-0.363261\pi\) | ||||
0.416489 | + | 0.909141i | \(0.363261\pi\) | |||||||
\(674\) | 9.01822 | 0.347369 | ||||||||
\(675\) | 87.7619 | 3.37796 | ||||||||
\(676\) | 14.0444 | 0.540169 | ||||||||
\(677\) | 50.8691 | 1.95506 | 0.977530 | − | 0.210798i | \(-0.0676063\pi\) | ||||
0.977530 | + | 0.210798i | \(0.0676063\pi\) | |||||||
\(678\) | 26.2075 | 1.00649 | ||||||||
\(679\) | −45.6234 | −1.75087 | ||||||||
\(680\) | −0.178772 | −0.00685561 | ||||||||
\(681\) | −31.5055 | −1.20729 | ||||||||
\(682\) | −34.3665 | −1.31596 | ||||||||
\(683\) | 26.0620 | 0.997236 | 0.498618 | − | 0.866822i | \(-0.333841\pi\) | ||||
0.498618 | + | 0.866822i | \(0.333841\pi\) | |||||||
\(684\) | −3.58553 | −0.137096 | ||||||||
\(685\) | 0.670990 | 0.0256372 | ||||||||
\(686\) | 18.3134 | 0.699210 | ||||||||
\(687\) | 43.3272 | 1.65304 | ||||||||
\(688\) | 4.43508 | 0.169086 | ||||||||
\(689\) | 62.9038 | 2.39644 | ||||||||
\(690\) | −3.06897 | −0.116834 | ||||||||
\(691\) | 7.46053 | 0.283812 | 0.141906 | − | 0.989880i | \(-0.454677\pi\) | ||||
0.141906 | + | 0.989880i | \(0.454677\pi\) | |||||||
\(692\) | 21.6896 | 0.824516 | ||||||||
\(693\) | 78.4407 | 2.97972 | ||||||||
\(694\) | 14.4946 | 0.550206 | ||||||||
\(695\) | −1.60391 | −0.0608396 | ||||||||
\(696\) | −19.7243 | −0.747648 | ||||||||
\(697\) | −18.6383 | −0.705975 | ||||||||
\(698\) | 0.809288 | 0.0306320 | ||||||||
\(699\) | 14.7145 | 0.556553 | ||||||||
\(700\) | 13.3467 | 0.504459 | ||||||||
\(701\) | 42.8964 | 1.62017 | 0.810087 | − | 0.586310i | \(-0.199420\pi\) | ||||
0.810087 | + | 0.586310i | \(0.199420\pi\) | |||||||
\(702\) | 91.4514 | 3.45161 | ||||||||
\(703\) | −1.32661 | −0.0500342 | ||||||||
\(704\) | −3.55769 | −0.134085 | ||||||||
\(705\) | −1.86796 | −0.0703516 | ||||||||
\(706\) | 18.2823 | 0.688062 | ||||||||
\(707\) | −33.1031 | −1.24497 | ||||||||
\(708\) | −26.4044 | −0.992339 | ||||||||
\(709\) | −23.0580 | −0.865961 | −0.432981 | − | 0.901403i | \(-0.642538\pi\) | ||||
−0.432981 | + | 0.901403i | \(0.642538\pi\) | |||||||
\(710\) | 1.44300 | 0.0541549 | ||||||||
\(711\) | 17.2963 | 0.648663 | ||||||||
\(712\) | 1.39518 | 0.0522864 | ||||||||
\(713\) | −91.2684 | −3.41803 | ||||||||
\(714\) | 16.5506 | 0.619389 | ||||||||
\(715\) | −1.79218 | −0.0670236 | ||||||||
\(716\) | 5.69226 | 0.212730 | ||||||||
\(717\) | −60.4069 | −2.25594 | ||||||||
\(718\) | 1.09243 | 0.0407690 | ||||||||
\(719\) | −30.4340 | −1.13500 | −0.567498 | − | 0.823375i | \(-0.692089\pi\) | ||||
−0.567498 | + | 0.823375i | \(0.692089\pi\) | |||||||
\(720\) | −0.798596 | −0.0297619 | ||||||||
\(721\) | 30.9486 | 1.15258 | ||||||||
\(722\) | −18.8109 | −0.700067 | ||||||||
\(723\) | −66.5360 | −2.47450 | ||||||||
\(724\) | 13.2984 | 0.494232 | ||||||||
\(725\) | −29.3555 | −1.09024 | ||||||||
\(726\) | −5.55681 | −0.206233 | ||||||||
\(727\) | −2.93252 | −0.108761 | −0.0543806 | − | 0.998520i | \(-0.517318\pi\) | ||||
−0.0543806 | + | 0.998520i | \(0.517318\pi\) | |||||||
\(728\) | 13.9078 | 0.515459 | ||||||||
\(729\) | 105.341 | 3.90152 | ||||||||
\(730\) | −0.478066 | −0.0176940 | ||||||||
\(731\) | 8.18517 | 0.302740 | ||||||||
\(732\) | −22.0031 | −0.813257 | ||||||||
\(733\) | 33.7218 | 1.24554 | 0.622771 | − | 0.782404i | \(-0.286007\pi\) | ||||
0.622771 | + | 0.782404i | \(0.286007\pi\) | |||||||
\(734\) | 18.8528 | 0.695870 | ||||||||
\(735\) | 0.0494485 | 0.00182393 | ||||||||
\(736\) | −9.44828 | −0.348268 | ||||||||
\(737\) | 33.4471 | 1.23204 | ||||||||
\(738\) | −83.2593 | −3.06482 | ||||||||
\(739\) | −46.2631 | −1.70182 | −0.850908 | − | 0.525315i | \(-0.823947\pi\) | ||||
−0.850908 | + | 0.525315i | \(0.823947\pi\) | |||||||
\(740\) | −0.295474 | −0.0108618 | ||||||||
\(741\) | −7.58411 | −0.278609 | ||||||||
\(742\) | 32.3489 | 1.18756 | ||||||||
\(743\) | −9.50469 | −0.348693 | −0.174347 | − | 0.984684i | \(-0.555781\pi\) | ||||
−0.174347 | + | 0.984684i | \(0.555781\pi\) | |||||||
\(744\) | −32.3917 | −1.18754 | ||||||||
\(745\) | −1.90254 | −0.0697036 | ||||||||
\(746\) | −22.1298 | −0.810228 | ||||||||
\(747\) | −7.18900 | −0.263032 | ||||||||
\(748\) | −6.56589 | −0.240073 | ||||||||
\(749\) | −44.6323 | −1.63083 | ||||||||
\(750\) | −3.24513 | −0.118496 | ||||||||
\(751\) | −10.0412 | −0.366409 | −0.183205 | − | 0.983075i | \(-0.558647\pi\) | ||||
−0.183205 | + | 0.983075i | \(0.558647\pi\) | |||||||
\(752\) | −5.75080 | −0.209710 | ||||||||
\(753\) | 51.8817 | 1.89067 | ||||||||
\(754\) | −30.5896 | −1.11401 | ||||||||
\(755\) | 1.97185 | 0.0717629 | ||||||||
\(756\) | 47.0297 | 1.71046 | ||||||||
\(757\) | 0.743989 | 0.0270407 | 0.0135204 | − | 0.999909i | \(-0.495696\pi\) | ||||
0.0135204 | + | 0.999909i | \(0.495696\pi\) | |||||||
\(758\) | 30.4741 | 1.10687 | ||||||||
\(759\) | −112.716 | −4.09134 | ||||||||
\(760\) | 0.0421284 | 0.00152816 | ||||||||
\(761\) | −29.0144 | −1.05177 | −0.525885 | − | 0.850556i | \(-0.676266\pi\) | ||||
−0.525885 | + | 0.850556i | \(0.676266\pi\) | |||||||
\(762\) | 17.8383 | 0.646213 | ||||||||
\(763\) | −9.64558 | −0.349193 | ||||||||
\(764\) | 2.77312 | 0.100328 | ||||||||
\(765\) | −1.47385 | −0.0532871 | ||||||||
\(766\) | −25.8440 | −0.933781 | ||||||||
\(767\) | −40.9496 | −1.47860 | ||||||||
\(768\) | −3.35325 | −0.121000 | ||||||||
\(769\) | 43.3002 | 1.56145 | 0.780723 | − | 0.624877i | \(-0.214851\pi\) | ||||
0.780723 | + | 0.624877i | \(0.214851\pi\) | |||||||
\(770\) | −0.921644 | −0.0332137 | ||||||||
\(771\) | −31.2791 | −1.12649 | ||||||||
\(772\) | 12.1561 | 0.437507 | ||||||||
\(773\) | −29.0108 | −1.04344 | −0.521722 | − | 0.853115i | \(-0.674710\pi\) | ||||
−0.521722 | + | 0.853115i | \(0.674710\pi\) | |||||||
\(774\) | 36.5641 | 1.31427 | ||||||||
\(775\) | −48.2083 | −1.73169 | ||||||||
\(776\) | 17.0595 | 0.612401 | ||||||||
\(777\) | 27.3547 | 0.981343 | ||||||||
\(778\) | −7.87194 | −0.282223 | ||||||||
\(779\) | 4.39218 | 0.157366 | ||||||||
\(780\) | −1.68919 | −0.0604828 | ||||||||
\(781\) | 52.9981 | 1.89642 | ||||||||
\(782\) | −17.4373 | −0.623556 | ||||||||
\(783\) | −103.440 | −3.69663 | ||||||||
\(784\) | 0.152234 | 0.00543694 | ||||||||
\(785\) | −0.871145 | −0.0310925 | ||||||||
\(786\) | 1.94761 | 0.0694690 | ||||||||
\(787\) | 23.3719 | 0.833120 | 0.416560 | − | 0.909108i | \(-0.363236\pi\) | ||||
0.416560 | + | 0.909108i | \(0.363236\pi\) | |||||||
\(788\) | 21.4380 | 0.763698 | ||||||||
\(789\) | −61.8361 | −2.20142 | ||||||||
\(790\) | −0.203224 | −0.00723039 | ||||||||
\(791\) | 20.9016 | 0.743176 | ||||||||
\(792\) | −29.3306 | −1.04222 | ||||||||
\(793\) | −34.1237 | −1.21177 | ||||||||
\(794\) | −20.4955 | −0.727358 | ||||||||
\(795\) | −3.92897 | −0.139346 | ||||||||
\(796\) | −10.8941 | −0.386131 | ||||||||
\(797\) | −23.8931 | −0.846335 | −0.423168 | − | 0.906051i | \(-0.639082\pi\) | ||||
−0.423168 | + | 0.906051i | \(0.639082\pi\) | |||||||
\(798\) | −3.90020 | −0.138066 | ||||||||
\(799\) | −10.6134 | −0.375475 | ||||||||
\(800\) | −4.99062 | −0.176445 | ||||||||
\(801\) | 11.5022 | 0.406411 | ||||||||
\(802\) | −14.0710 | −0.496865 | ||||||||
\(803\) | −17.5583 | −0.619618 | ||||||||
\(804\) | 31.5251 | 1.11180 | ||||||||
\(805\) | −2.44764 | −0.0862681 | ||||||||
\(806\) | −50.2350 | −1.76945 | ||||||||
\(807\) | −52.5010 | −1.84812 | ||||||||
\(808\) | 12.3779 | 0.435454 | ||||||||
\(809\) | 9.70466 | 0.341198 | 0.170599 | − | 0.985341i | \(-0.445430\pi\) | ||||
0.170599 | + | 0.985341i | \(0.445430\pi\) | |||||||
\(810\) | −3.31626 | −0.116522 | ||||||||
\(811\) | 2.96299 | 0.104044 | 0.0520222 | − | 0.998646i | \(-0.483433\pi\) | ||||
0.0520222 | + | 0.998646i | \(0.483433\pi\) | |||||||
\(812\) | −15.7310 | −0.552050 | ||||||||
\(813\) | 25.2568 | 0.885796 | ||||||||
\(814\) | −10.8521 | −0.380365 | ||||||||
\(815\) | 1.89937 | 0.0665320 | ||||||||
\(816\) | −6.18859 | −0.216644 | ||||||||
\(817\) | −1.92887 | −0.0674825 | ||||||||
\(818\) | −18.4117 | −0.643751 | ||||||||
\(819\) | 114.660 | 4.00655 | ||||||||
\(820\) | 0.978260 | 0.0341623 | ||||||||
\(821\) | −15.2578 | −0.532501 | −0.266251 | − | 0.963904i | \(-0.585785\pi\) | ||||
−0.266251 | + | 0.963904i | \(0.585785\pi\) | |||||||
\(822\) | 23.2278 | 0.810161 | ||||||||
\(823\) | −16.6831 | −0.581536 | −0.290768 | − | 0.956794i | \(-0.593911\pi\) | ||||
−0.290768 | + | 0.956794i | \(0.593911\pi\) | |||||||
\(824\) | −11.5723 | −0.403140 | ||||||||
\(825\) | −59.5371 | −2.07282 | ||||||||
\(826\) | −21.0587 | −0.732726 | ||||||||
\(827\) | −24.1917 | −0.841229 | −0.420615 | − | 0.907239i | \(-0.638186\pi\) | ||||
−0.420615 | + | 0.907239i | \(0.638186\pi\) | |||||||
\(828\) | −77.8943 | −2.70701 | ||||||||
\(829\) | 7.12913 | 0.247605 | 0.123802 | − | 0.992307i | \(-0.460491\pi\) | ||||
0.123802 | + | 0.992307i | \(0.460491\pi\) | |||||||
\(830\) | 0.0844676 | 0.00293191 | ||||||||
\(831\) | 5.68543 | 0.197225 | ||||||||
\(832\) | −5.20042 | −0.180292 | ||||||||
\(833\) | 0.280956 | 0.00973456 | ||||||||
\(834\) | −55.5227 | −1.92259 | ||||||||
\(835\) | −1.79912 | −0.0622613 | ||||||||
\(836\) | 1.54728 | 0.0535137 | ||||||||
\(837\) | −169.871 | −5.87160 | ||||||||
\(838\) | 23.7870 | 0.821708 | ||||||||
\(839\) | −9.33970 | −0.322442 | −0.161221 | − | 0.986918i | \(-0.551543\pi\) | ||||
−0.161221 | + | 0.986918i | \(0.551543\pi\) | |||||||
\(840\) | −0.868683 | −0.0299724 | ||||||||
\(841\) | 5.59963 | 0.193091 | ||||||||
\(842\) | −6.87293 | −0.236857 | ||||||||
\(843\) | 102.461 | 3.52893 | ||||||||
\(844\) | 11.3189 | 0.389614 | ||||||||
\(845\) | −1.36043 | −0.0468003 | ||||||||
\(846\) | −47.4112 | −1.63003 | ||||||||
\(847\) | −4.43181 | −0.152279 | ||||||||
\(848\) | −12.0959 | −0.415375 | ||||||||
\(849\) | −5.74000 | −0.196996 | ||||||||
\(850\) | −9.21044 | −0.315915 | ||||||||
\(851\) | −28.8202 | −0.987944 | ||||||||
\(852\) | 49.9526 | 1.71135 | ||||||||
\(853\) | 31.6719 | 1.08443 | 0.542213 | − | 0.840241i | \(-0.317587\pi\) | ||||
0.542213 | + | 0.840241i | \(0.317587\pi\) | |||||||
\(854\) | −17.5484 | −0.600495 | ||||||||
\(855\) | 0.347318 | 0.0118780 | ||||||||
\(856\) | 16.6889 | 0.570416 | ||||||||
\(857\) | −38.6553 | −1.32044 | −0.660221 | − | 0.751072i | \(-0.729537\pi\) | ||||
−0.660221 | + | 0.751072i | \(0.729537\pi\) | |||||||
\(858\) | −62.0401 | −2.11801 | ||||||||
\(859\) | 11.3474 | 0.387169 | 0.193585 | − | 0.981084i | \(-0.437989\pi\) | ||||
0.193585 | + | 0.981084i | \(0.437989\pi\) | |||||||
\(860\) | −0.429612 | −0.0146496 | ||||||||
\(861\) | −90.5663 | −3.08649 | ||||||||
\(862\) | −34.4500 | −1.17337 | ||||||||
\(863\) | 40.0251 | 1.36247 | 0.681236 | − | 0.732064i | \(-0.261443\pi\) | ||||
0.681236 | + | 0.732064i | \(0.261443\pi\) | |||||||
\(864\) | −17.5854 | −0.598267 | ||||||||
\(865\) | −2.10100 | −0.0714362 | ||||||||
\(866\) | −11.9923 | −0.407514 | ||||||||
\(867\) | 45.5839 | 1.54811 | ||||||||
\(868\) | −25.8338 | −0.876857 | ||||||||
\(869\) | −7.46395 | −0.253197 | ||||||||
\(870\) | 1.91063 | 0.0647763 | ||||||||
\(871\) | 48.8911 | 1.65661 | ||||||||
\(872\) | 3.60668 | 0.122138 | ||||||||
\(873\) | 140.643 | 4.76006 | ||||||||
\(874\) | 4.10916 | 0.138994 | ||||||||
\(875\) | −2.58814 | −0.0874951 | ||||||||
\(876\) | −16.5493 | −0.559149 | ||||||||
\(877\) | −6.22331 | −0.210146 | −0.105073 | − | 0.994464i | \(-0.533508\pi\) | ||||
−0.105073 | + | 0.994464i | \(0.533508\pi\) | |||||||
\(878\) | 0.762424 | 0.0257306 | ||||||||
\(879\) | −34.7568 | −1.17232 | ||||||||
\(880\) | 0.344621 | 0.0116172 | ||||||||
\(881\) | −31.4408 | −1.05927 | −0.529633 | − | 0.848227i | \(-0.677670\pi\) | ||||
−0.529633 | + | 0.848227i | \(0.677670\pi\) | |||||||
\(882\) | 1.25506 | 0.0422602 | ||||||||
\(883\) | 44.1907 | 1.48713 | 0.743567 | − | 0.668661i | \(-0.233132\pi\) | ||||
0.743567 | + | 0.668661i | \(0.233132\pi\) | |||||||
\(884\) | −9.59764 | −0.322804 | ||||||||
\(885\) | 2.55771 | 0.0859764 | ||||||||
\(886\) | 4.91551 | 0.165140 | ||||||||
\(887\) | 23.4825 | 0.788466 | 0.394233 | − | 0.919010i | \(-0.371010\pi\) | ||||
0.394233 | + | 0.919010i | \(0.371010\pi\) | |||||||
\(888\) | −10.2285 | −0.343245 | ||||||||
\(889\) | 14.2268 | 0.477153 | ||||||||
\(890\) | −0.135146 | −0.00453010 | ||||||||
\(891\) | −121.799 | −4.08041 | ||||||||
\(892\) | 21.1149 | 0.706978 | ||||||||
\(893\) | 2.50109 | 0.0836956 | ||||||||
\(894\) | −65.8604 | −2.20270 | ||||||||
\(895\) | −0.551391 | −0.0184310 | ||||||||
\(896\) | −2.67437 | −0.0893443 | ||||||||
\(897\) | −164.762 | −5.50124 | ||||||||
\(898\) | −7.50630 | −0.250489 | ||||||||
\(899\) | 56.8203 | 1.89506 | ||||||||
\(900\) | −41.1440 | −1.37147 | ||||||||
\(901\) | −22.3236 | −0.743707 | ||||||||
\(902\) | 35.9292 | 1.19631 | ||||||||
\(903\) | 39.7730 | 1.32356 | ||||||||
\(904\) | −7.81554 | −0.259941 | ||||||||
\(905\) | −1.28817 | −0.0428203 | ||||||||
\(906\) | 68.2597 | 2.26778 | ||||||||
\(907\) | −38.7529 | −1.28677 | −0.643384 | − | 0.765543i | \(-0.722470\pi\) | ||||
−0.643384 | + | 0.765543i | \(0.722470\pi\) | |||||||
\(908\) | 9.39551 | 0.311801 | ||||||||
\(909\) | 102.047 | 3.38469 | ||||||||
\(910\) | −1.34721 | −0.0446594 | ||||||||
\(911\) | −14.0965 | −0.467039 | −0.233519 | − | 0.972352i | \(-0.575024\pi\) | ||||
−0.233519 | + | 0.972352i | \(0.575024\pi\) | |||||||
\(912\) | 1.45836 | 0.0482913 | ||||||||
\(913\) | 3.10230 | 0.102671 | ||||||||
\(914\) | 25.1784 | 0.832828 | ||||||||
\(915\) | 2.13136 | 0.0704607 | ||||||||
\(916\) | −12.9210 | −0.426921 | ||||||||
\(917\) | 1.55331 | 0.0512947 | ||||||||
\(918\) | −32.4547 | −1.07116 | ||||||||
\(919\) | −32.1144 | −1.05936 | −0.529679 | − | 0.848198i | \(-0.677687\pi\) | ||||
−0.529679 | + | 0.848198i | \(0.677687\pi\) | |||||||
\(920\) | 0.915223 | 0.0301740 | ||||||||
\(921\) | 49.8062 | 1.64117 | ||||||||
\(922\) | −32.8403 | −1.08154 | ||||||||
\(923\) | 77.4696 | 2.54994 | ||||||||
\(924\) | −31.9047 | −1.04959 | ||||||||
\(925\) | −15.2230 | −0.500528 | ||||||||
\(926\) | 20.3737 | 0.669523 | ||||||||
\(927\) | −95.4053 | −3.13352 | ||||||||
\(928\) | 5.88214 | 0.193091 | ||||||||
\(929\) | 19.4469 | 0.638031 | 0.319016 | − | 0.947749i | \(-0.396648\pi\) | ||||
0.319016 | + | 0.947749i | \(0.396648\pi\) | |||||||
\(930\) | 3.13768 | 0.102888 | ||||||||
\(931\) | −0.0662084 | −0.00216989 | ||||||||
\(932\) | −4.38813 | −0.143738 | ||||||||
\(933\) | 65.8699 | 2.15648 | ||||||||
\(934\) | −9.48846 | −0.310472 | ||||||||
\(935\) | 0.636016 | 0.0208000 | ||||||||
\(936\) | −42.8737 | −1.40137 | ||||||||
\(937\) | −10.4331 | −0.340833 | −0.170417 | − | 0.985372i | \(-0.554511\pi\) | ||||
−0.170417 | + | 0.985372i | \(0.554511\pi\) | |||||||
\(938\) | 25.1427 | 0.820938 | ||||||||
\(939\) | −15.8680 | −0.517833 | ||||||||
\(940\) | 0.557061 | 0.0181693 | ||||||||
\(941\) | 8.61317 | 0.280781 | 0.140391 | − | 0.990096i | \(-0.455164\pi\) | ||||
0.140391 | + | 0.990096i | \(0.455164\pi\) | |||||||
\(942\) | −30.1566 | −0.982554 | ||||||||
\(943\) | 95.4185 | 3.10725 | ||||||||
\(944\) | 7.87428 | 0.256286 | ||||||||
\(945\) | −4.55561 | −0.148194 | ||||||||
\(946\) | −15.7786 | −0.513008 | ||||||||
\(947\) | −5.20240 | −0.169055 | −0.0845277 | − | 0.996421i | \(-0.526938\pi\) | ||||
−0.0845277 | + | 0.996421i | \(0.526938\pi\) | |||||||
\(948\) | −7.03504 | −0.228488 | ||||||||
\(949\) | −25.6657 | −0.833142 | ||||||||
\(950\) | 2.17047 | 0.0704194 | ||||||||
\(951\) | 93.1294 | 3.01993 | ||||||||
\(952\) | −4.93568 | −0.159966 | ||||||||
\(953\) | 0.814097 | 0.0263712 | 0.0131856 | − | 0.999913i | \(-0.495803\pi\) | ||||
0.0131856 | + | 0.999913i | \(0.495803\pi\) | |||||||
\(954\) | −99.7220 | −3.22862 | ||||||||
\(955\) | −0.268623 | −0.00869244 | ||||||||
\(956\) | 18.0144 | 0.582629 | ||||||||
\(957\) | 70.1729 | 2.26837 | ||||||||
\(958\) | −27.3667 | −0.884177 | ||||||||
\(959\) | 18.5252 | 0.598209 | ||||||||
\(960\) | 0.324818 | 0.0104835 | ||||||||
\(961\) | 62.3116 | 2.01005 | ||||||||
\(962\) | −15.8629 | −0.511441 | ||||||||
\(963\) | 137.588 | 4.43372 | ||||||||
\(964\) | 19.8422 | 0.639075 | ||||||||
\(965\) | −1.17752 | −0.0379057 | ||||||||
\(966\) | −84.7304 | −2.72616 | ||||||||
\(967\) | 20.8772 | 0.671367 | 0.335683 | − | 0.941975i | \(-0.391033\pi\) | ||||
0.335683 | + | 0.941975i | \(0.391033\pi\) | |||||||
\(968\) | 1.65714 | 0.0532626 | ||||||||
\(969\) | 2.69148 | 0.0864629 | ||||||||
\(970\) | −1.65250 | −0.0530585 | ||||||||
\(971\) | −48.3132 | −1.55045 | −0.775223 | − | 0.631688i | \(-0.782362\pi\) | ||||
−0.775223 | + | 0.631688i | \(0.782362\pi\) | |||||||
\(972\) | −62.0434 | −1.99004 | ||||||||
\(973\) | −44.2818 | −1.41961 | ||||||||
\(974\) | 17.4059 | 0.557720 | ||||||||
\(975\) | −87.0279 | −2.78712 | ||||||||
\(976\) | 6.56172 | 0.210035 | ||||||||
\(977\) | −31.4026 | −1.00466 | −0.502329 | − | 0.864677i | \(-0.667523\pi\) | ||||
−0.502329 | + | 0.864677i | \(0.667523\pi\) | |||||||
\(978\) | 65.7508 | 2.10248 | ||||||||
\(979\) | −4.96360 | −0.158637 | ||||||||
\(980\) | −0.0147464 | −0.000471058 0 | ||||||||
\(981\) | 29.7345 | 0.949348 | ||||||||
\(982\) | 0.790617 | 0.0252296 | ||||||||
\(983\) | 12.9766 | 0.413891 | 0.206945 | − | 0.978352i | \(-0.433648\pi\) | ||||
0.206945 | + | 0.978352i | \(0.433648\pi\) | |||||||
\(984\) | 33.8646 | 1.07956 | ||||||||
\(985\) | −2.07663 | −0.0661670 | ||||||||
\(986\) | 10.8558 | 0.345719 | ||||||||
\(987\) | −51.5721 | −1.64156 | ||||||||
\(988\) | 2.26172 | 0.0719549 | ||||||||
\(989\) | −41.9039 | −1.33247 | ||||||||
\(990\) | 2.84116 | 0.0902979 | ||||||||
\(991\) | 62.3724 | 1.98132 | 0.990662 | − | 0.136340i | \(-0.0435339\pi\) | ||||
0.990662 | + | 0.136340i | \(0.0435339\pi\) | |||||||
\(992\) | 9.65979 | 0.306699 | ||||||||
\(993\) | 0.517591 | 0.0164253 | ||||||||
\(994\) | 39.8395 | 1.26363 | ||||||||
\(995\) | 1.05528 | 0.0334545 | ||||||||
\(996\) | 2.92403 | 0.0926514 | ||||||||
\(997\) | −4.81690 | −0.152553 | −0.0762763 | − | 0.997087i | \(-0.524303\pi\) | ||||
−0.0762763 | + | 0.997087i | \(0.524303\pi\) | |||||||
\(998\) | 28.7338 | 0.909552 | ||||||||
\(999\) | −53.6409 | −1.69712 |
(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 | 4034.2.a.d.1.1 | ✓ | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4034.2.a.d.1.1 | ✓ | 52 | 1.1 | even | 1 | trivial |