Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4024,2,Mod(1,4024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4024, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("4024.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4024 = 2^{3} \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4024.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: | \(32.1318017734\) |
Analytic rank: | \(0\) |
Dimension: | \(33\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.25 | ||
Character | \(\chi\) | \(=\) | 4024.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.03324 | 1.17389 | 0.586945 | − | 0.809627i | \(-0.300331\pi\) | ||||
0.586945 | + | 0.809627i | \(0.300331\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.46117 | 1.99510 | 0.997548 | − | 0.0699801i | \(-0.0222936\pi\) | ||||
0.997548 | + | 0.0699801i | \(0.0222936\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.828843 | 0.313273 | 0.156637 | − | 0.987656i | \(-0.449935\pi\) | ||||
0.156637 | + | 0.987656i | \(0.449935\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.13405 | 0.378017 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.0966604 | 0.0291442 | 0.0145721 | − | 0.999894i | \(-0.495361\pi\) | ||||
0.0145721 | + | 0.999894i | \(0.495361\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.53910 | 0.426870 | 0.213435 | − | 0.976957i | \(-0.431535\pi\) | ||||
0.213435 | + | 0.976957i | \(0.431535\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 9.07062 | 2.34202 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.59316 | −0.871470 | −0.435735 | − | 0.900075i | \(-0.643511\pi\) | ||||
−0.435735 | + | 0.900075i | \(0.643511\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.33503 | 1.91219 | 0.956094 | − | 0.293061i | \(-0.0946740\pi\) | ||||
0.956094 | + | 0.293061i | \(0.0946740\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.68523 | 0.367748 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.93109 | 0.611174 | 0.305587 | − | 0.952164i | \(-0.401147\pi\) | ||||
0.305587 | + | 0.952164i | \(0.401147\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 14.9021 | 2.98041 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.79392 | −0.730139 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.38083 | 0.256413 | 0.128207 | − | 0.991747i | \(-0.459078\pi\) | ||||
0.128207 | + | 0.991747i | \(0.459078\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.48771 | −0.446805 | −0.223403 | − | 0.974726i | \(-0.571717\pi\) | ||||
−0.223403 | + | 0.974726i | \(0.571717\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.196533 | 0.0342121 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.69761 | 0.625010 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.06621 | −0.504082 | −0.252041 | − | 0.967717i | \(-0.581102\pi\) | ||||
−0.252041 | + | 0.967717i | \(0.581102\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.12936 | 0.501099 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.09004 | −0.794930 | −0.397465 | − | 0.917617i | \(-0.630110\pi\) | ||||
−0.397465 | + | 0.917617i | \(0.630110\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −12.0742 | −1.84130 | −0.920648 | − | 0.390394i | \(-0.872339\pi\) | ||||
−0.920648 | + | 0.390394i | \(0.872339\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.05920 | 0.754181 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.75114 | −0.547160 | −0.273580 | − | 0.961849i | \(-0.588208\pi\) | ||||
−0.273580 | + | 0.961849i | \(0.588208\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.31302 | −0.901860 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.30575 | −1.02301 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.98285 | 0.821807 | 0.410904 | − | 0.911679i | \(-0.365213\pi\) | ||||
0.410904 | + | 0.911679i | \(0.365213\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.431219 | 0.0581455 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 16.9471 | 2.24470 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.55903 | 0.202968 | 0.101484 | − | 0.994837i | \(-0.467641\pi\) | ||||
0.101484 | + | 0.994837i | \(0.467641\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.6668 | −1.49378 | −0.746891 | − | 0.664947i | \(-0.768454\pi\) | ||||
−0.746891 | + | 0.664947i | \(0.768454\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.939950 | 0.118423 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.86620 | 0.851648 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.19054 | 0.145448 | 0.0727239 | − | 0.997352i | \(-0.476831\pi\) | ||||
0.0727239 | + | 0.997352i | \(0.476831\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.95959 | 0.717450 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.48402 | −0.650834 | −0.325417 | − | 0.945571i | \(-0.605505\pi\) | ||||
−0.325417 | + | 0.945571i | \(0.605505\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.93015 | 0.694072 | 0.347036 | − | 0.937852i | \(-0.387188\pi\) | ||||
0.347036 | + | 0.937852i | \(0.387188\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 30.2994 | 3.49867 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.0801163 | 0.00913010 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.9836 | 1.46077 | 0.730384 | − | 0.683036i | \(-0.239341\pi\) | ||||
0.730384 | + | 0.683036i | \(0.239341\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.1161 | −1.23512 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 16.7451 | 1.83801 | 0.919005 | − | 0.394245i | \(-0.128994\pi\) | ||||
0.919005 | + | 0.394245i | \(0.128994\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −16.0297 | −1.73867 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.80755 | 0.301001 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.41727 | −0.786229 | −0.393114 | − | 0.919490i | \(-0.628602\pi\) | ||||
−0.393114 | + | 0.919490i | \(0.628602\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.27567 | 0.133727 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.05810 | −0.524500 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 37.1840 | 3.81500 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.8864 | −1.51149 | −0.755744 | − | 0.654867i | \(-0.772724\pi\) | ||||
−0.755744 | + | 0.654867i | \(0.772724\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.109618 | 0.0110170 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.27897 | −0.127262 | −0.0636312 | − | 0.997973i | \(-0.520268\pi\) | ||||
−0.0636312 | + | 0.997973i | \(0.520268\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.74066 | 0.762710 | 0.381355 | − | 0.924429i | \(-0.375457\pi\) | ||||
0.381355 | + | 0.924429i | \(0.375457\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 7.51812 | 0.733693 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.14319 | −0.110517 | −0.0552583 | − | 0.998472i | \(-0.517598\pi\) | ||||
−0.0552583 | + | 0.998472i | \(0.517598\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.5095 | 1.19819 | 0.599094 | − | 0.800679i | \(-0.295527\pi\) | ||||
0.599094 | + | 0.800679i | \(0.295527\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.23434 | −0.591737 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.08097 | 0.666122 | 0.333061 | − | 0.942905i | \(-0.391919\pi\) | ||||
0.333061 | + | 0.942905i | \(0.391919\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 13.0761 | 1.21935 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.74542 | 0.161364 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.97817 | −0.273008 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9907 | −0.999151 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −10.3493 | −0.933161 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 44.1748 | 3.95111 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.72311 | −0.685315 | −0.342657 | − | 0.939460i | \(-0.611327\pi\) | ||||
−0.342657 | + | 0.939460i | \(0.611327\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −24.5497 | −2.16148 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.8006 | −0.943651 | −0.471826 | − | 0.881692i | \(-0.656405\pi\) | ||||
−0.471826 | + | 0.881692i | \(0.656405\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.90843 | 0.599037 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −16.9253 | −1.45670 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −17.6756 | −1.51012 | −0.755062 | − | 0.655653i | \(-0.772393\pi\) | ||||
−0.755062 | + | 0.655653i | \(0.772393\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.3348 | −1.30068 | −0.650341 | − | 0.759642i | \(-0.725374\pi\) | ||||
−0.650341 | + | 0.759642i | \(0.725374\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.62696 | −0.642306 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.148770 | 0.0124408 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.16011 | 0.511570 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −12.8359 | −1.05868 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.40314 | 0.360719 | 0.180360 | − | 0.983601i | \(-0.442274\pi\) | ||||
0.180360 | + | 0.983601i | \(0.442274\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.2749 | 1.40581 | 0.702904 | − | 0.711285i | \(-0.251886\pi\) | ||||
0.702904 | + | 0.711285i | \(0.251886\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.07483 | −0.329430 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −11.0981 | −0.891420 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.9732 | −0.875755 | −0.437877 | − | 0.899035i | \(-0.644270\pi\) | ||||
−0.437877 | + | 0.899035i | \(0.644270\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 12.1645 | 0.964711 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.42941 | 0.191464 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.5974 | 1.14336 | 0.571678 | − | 0.820478i | \(-0.306293\pi\) | ||||
0.571678 | + | 0.820478i | \(0.306293\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.876769 | 0.0682564 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −18.8031 | −1.45502 | −0.727512 | − | 0.686094i | \(-0.759324\pi\) | ||||
−0.727512 | + | 0.686094i | \(0.759324\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.6312 | −0.817782 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 9.45235 | 0.722839 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.93420 | 0.451169 | 0.225584 | − | 0.974224i | \(-0.427571\pi\) | ||||
0.225584 | + | 0.974224i | \(0.427571\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 12.3515 | 0.933683 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.16987 | 0.238262 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 16.2703 | 1.21610 | 0.608048 | − | 0.793900i | \(-0.291953\pi\) | ||||
0.608048 | + | 0.793900i | \(0.291953\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.76453 | 0.651463 | 0.325731 | − | 0.945462i | \(-0.394390\pi\) | ||||
0.325731 | + | 0.945462i | \(0.394390\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −23.7214 | −1.75354 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −13.6789 | −1.00569 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.347316 | −0.0253983 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.14456 | −0.228733 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 26.0947 | 1.88815 | 0.944073 | − | 0.329737i | \(-0.106960\pi\) | ||||
0.944073 | + | 0.329737i | \(0.106960\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.0816559 | 0.00587772 | 0.00293886 | − | 0.999996i | \(-0.499065\pi\) | ||||
0.00293886 | + | 0.999996i | \(0.499065\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 13.9606 | 0.999741 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −18.2323 | −1.29899 | −0.649497 | − | 0.760364i | \(-0.725021\pi\) | ||||
−0.649497 | + | 0.760364i | \(0.725021\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.13270 | −0.647400 | −0.323700 | − | 0.946160i | \(-0.604927\pi\) | ||||
−0.323700 | + | 0.946160i | \(0.604927\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.42065 | 0.170740 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.14449 | 0.0803274 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −22.7075 | −1.58596 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.32400 | 0.231034 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.805667 | 0.0557292 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.4387 | 0.718629 | 0.359315 | − | 0.933217i | \(-0.383011\pi\) | ||||
0.359315 | + | 0.933217i | \(0.383011\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −11.1503 | −0.764007 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −53.8650 | −3.67356 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.06192 | −0.139972 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 12.0574 | 0.814764 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.53025 | −0.372005 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.9343 | −1.00008 | −0.500039 | − | 0.866003i | \(-0.666681\pi\) | ||||
−0.500039 | + | 0.866003i | \(0.666681\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 16.8997 | 1.12665 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.60679 | 0.637625 | 0.318813 | − | 0.947818i | \(-0.396716\pi\) | ||||
0.318813 | + | 0.947818i | \(0.396716\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.0213 | −0.662227 | −0.331113 | − | 0.943591i | \(-0.607424\pi\) | ||||
−0.331113 | + | 0.943591i | \(0.607424\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.162895 | 0.0107177 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4.67799 | −0.306466 | −0.153233 | − | 0.988190i | \(-0.548968\pi\) | ||||
−0.153233 | + | 0.988190i | \(0.548968\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −16.7345 | −1.09164 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 26.3987 | 1.71478 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 21.0064 | 1.35879 | 0.679394 | − | 0.733773i | \(-0.262243\pi\) | ||||
0.679394 | + | 0.733773i | \(0.262243\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 28.3671 | 1.82729 | 0.913644 | − | 0.406515i | \(-0.133256\pi\) | ||||
0.913644 | + | 0.406515i | \(0.133256\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −11.2199 | −0.719755 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −28.1635 | −1.79930 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.8285 | 0.816256 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 34.0467 | 2.15762 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.90011 | −0.183053 | −0.0915267 | − | 0.995803i | \(-0.529175\pi\) | ||||
−0.0915267 | + | 0.995803i | \(0.529175\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.283320 | 0.0178122 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −32.5922 | −2.04100 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −15.5426 | −0.969522 | −0.484761 | − | 0.874647i | \(-0.661093\pi\) | ||||
−0.484761 | + | 0.874647i | \(0.661093\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.54141 | −0.157915 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.56593 | 0.0969286 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.41655 | 0.210673 | 0.105337 | − | 0.994437i | \(-0.466408\pi\) | ||||
0.105337 | + | 0.994437i | \(0.466408\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 26.6905 | 1.63959 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −15.0811 | −0.922946 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.20309 | 0.439180 | 0.219590 | − | 0.975592i | \(-0.429528\pi\) | ||||
0.219590 | + | 0.975592i | \(0.429528\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −32.2336 | −1.95805 | −0.979025 | − | 0.203739i | \(-0.934691\pi\) | ||||
−0.979025 | + | 0.203739i | \(0.934691\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.59375 | 0.156981 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.44044 | 0.0868617 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.8997 | 1.25574 | 0.627871 | − | 0.778318i | \(-0.283927\pi\) | ||||
0.627871 | + | 0.778318i | \(0.283927\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.82119 | −0.168900 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.9037 | 0.710116 | 0.355058 | − | 0.934844i | \(-0.384461\pi\) | ||||
0.355058 | + | 0.934844i | \(0.384461\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.15617 | 0.187615 | 0.0938074 | − | 0.995590i | \(-0.470096\pi\) | ||||
0.0938074 | + | 0.995590i | \(0.470096\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 75.6039 | 4.47839 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.21884 | −0.249030 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.08919 | −0.240540 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −30.2676 | −1.77432 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −20.7626 | −1.21297 | −0.606483 | − | 0.795097i | \(-0.707420\pi\) | ||||
−0.606483 | + | 0.795097i | \(0.707420\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.95510 | 0.404941 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.366721 | −0.0212793 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.51124 | 0.260892 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.0076 | −0.576829 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.60045 | −0.149392 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −52.0476 | −2.98024 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.1602 | 1.43597 | 0.717983 | − | 0.696061i | \(-0.245066\pi\) | ||||
0.717983 | + | 0.696061i | \(0.245066\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 15.7386 | 0.895338 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −24.0755 | −1.36520 | −0.682598 | − | 0.730794i | \(-0.739150\pi\) | ||||
−0.682598 | + | 0.730794i | \(0.739150\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.8139 | −1.06342 | −0.531712 | − | 0.846925i | \(-0.678451\pi\) | ||||
−0.531712 | + | 0.846925i | \(0.678451\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.19328 | 0.236265 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 20.2446 | 1.13705 | 0.568525 | − | 0.822666i | \(-0.307514\pi\) | ||||
0.568525 | + | 0.822666i | \(0.307514\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.133471 | 0.00747296 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.32438 | −0.129734 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −29.9491 | −1.66641 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 22.9358 | 1.27225 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 25.4347 | 1.40654 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.10911 | −0.171411 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 30.0247 | 1.65030 | 0.825152 | − | 0.564910i | \(-0.191089\pi\) | ||||
0.825152 | + | 0.564910i | \(0.191089\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.47724 | −0.190552 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.31121 | 0.290182 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −30.1862 | −1.64435 | −0.822174 | − | 0.569236i | \(-0.807239\pi\) | ||||
−0.822174 | + | 0.569236i | \(0.807239\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 14.3973 | 0.781953 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.240463 | −0.0130218 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −11.0344 | −0.595802 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 26.5868 | 1.43138 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 16.2121 | 0.870310 | 0.435155 | − | 0.900356i | \(-0.356694\pi\) | ||||
0.435155 | + | 0.900356i | \(0.356694\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −20.0437 | −1.07292 | −0.536458 | − | 0.843927i | \(-0.680238\pi\) | ||||
−0.536458 | + | 0.843927i | \(0.680238\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.83923 | −0.311675 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −31.0479 | −1.65251 | −0.826256 | − | 0.563294i | \(-0.809534\pi\) | ||||
−0.826256 | + | 0.563294i | \(0.809534\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −24.4652 | −1.29848 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.05532 | −0.320481 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.54542 | 0.0815642 | 0.0407821 | − | 0.999168i | \(-0.487015\pi\) | ||||
0.0407821 | + | 0.999168i | \(0.487015\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 50.4727 | 2.65646 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −22.3466 | −1.17289 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 26.4554 | 1.38474 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.9154 | −0.778578 | −0.389289 | − | 0.921116i | \(-0.627279\pi\) | ||||
−0.389289 | + | 0.921116i | \(0.627279\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.77236 | −0.300497 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.95884 | 0.257450 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.04661 | 0.105969 | 0.0529847 | − | 0.998595i | \(-0.483127\pi\) | ||||
0.0529847 | + | 0.998595i | \(0.483127\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 89.8178 | 4.63817 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.12524 | 0.109455 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 27.3417 | 1.40445 | 0.702226 | − | 0.711955i | \(-0.252190\pi\) | ||||
0.702226 | + | 0.711955i | \(0.252190\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −15.7029 | −0.804484 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −0.900506 | −0.0460137 | −0.0230068 | − | 0.999735i | \(-0.507324\pi\) | ||||
−0.0230068 | + | 0.999735i | \(0.507324\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.357412 | 0.0182154 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −13.6927 | −0.696041 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15.6230 | 0.792117 | 0.396059 | − | 0.918225i | \(-0.370378\pi\) | ||||
0.396059 | + | 0.918225i | \(0.370378\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.5319 | −0.532619 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −21.9601 | −1.10774 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 57.9220 | 2.91437 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.4493 | −0.624811 | −0.312406 | − | 0.949949i | \(-0.601135\pi\) | ||||
−0.312406 | + | 0.949949i | \(0.601135\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 14.0465 | 0.703203 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.60701 | −0.0802502 | −0.0401251 | − | 0.999195i | \(-0.512776\pi\) | ||||
−0.0401251 | + | 0.999195i | \(0.512776\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.82884 | −0.190728 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −49.5908 | −2.46418 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.296381 | −0.0146911 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 21.8170 | 1.07878 | 0.539390 | − | 0.842056i | \(-0.318655\pi\) | ||||
0.539390 | + | 0.842056i | \(0.318655\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −35.9386 | −1.77272 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.29219 | 0.0635845 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 74.7027 | 3.66701 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −31.1793 | −1.52686 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.73833 | 0.426896 | 0.213448 | − | 0.976954i | \(-0.431531\pi\) | ||||
0.213448 | + | 0.976954i | \(0.431531\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.3976 | 0.506750 | 0.253375 | − | 0.967368i | \(-0.418459\pi\) | ||||
0.253375 | + | 0.967368i | \(0.418459\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.25399 | −0.206836 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −53.5455 | −2.59734 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.66995 | −0.467962 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.302485 | 0.0146041 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14.8133 | −0.713533 | −0.356766 | − | 0.934194i | \(-0.616121\pi\) | ||||
−0.356766 | + | 0.934194i | \(0.616121\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.0096 | 1.00966 | 0.504829 | − | 0.863220i | \(-0.331556\pi\) | ||||
0.504829 | + | 0.863220i | \(0.331556\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 12.5250 | 0.600526 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 24.4307 | 1.16868 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −34.0623 | −1.62570 | −0.812852 | − | 0.582470i | \(-0.802086\pi\) | ||||
−0.812852 | + | 0.582470i | \(0.802086\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.15929 | −0.340918 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −23.8224 | −1.13184 | −0.565919 | − | 0.824461i | \(-0.691478\pi\) | ||||
−0.565919 | + | 0.824461i | \(0.691478\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −33.0897 | −1.56860 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.95262 | 0.423445 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.46319 | −0.446596 | −0.223298 | − | 0.974750i | \(-0.571682\pi\) | ||||
−0.223298 | + | 0.974750i | \(0.571682\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.492005 | −0.0231676 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 35.1239 | 1.65026 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.69100 | 0.266798 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 33.6524 | 1.57419 | 0.787097 | − | 0.616829i | \(-0.211583\pi\) | ||||
0.787097 | + | 0.616829i | \(0.211583\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 13.6322 | 0.636294 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.0943 | −0.516713 | −0.258357 | − | 0.966050i | \(-0.583181\pi\) | ||||
−0.258357 | + | 0.966050i | \(0.583181\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.6271 | 0.633304 | 0.316652 | − | 0.948542i | \(-0.397441\pi\) | ||||
0.316652 | + | 0.948542i | \(0.397441\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −22.5650 | −1.04643 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 16.8293 | 0.778766 | 0.389383 | − | 0.921076i | \(-0.372688\pi\) | ||||
0.389383 | + | 0.921076i | \(0.372688\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.986772 | 0.0455649 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −22.3111 | −1.02804 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.16710 | −0.0536631 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 124.209 | 5.69910 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.78486 | 0.310657 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −23.9636 | −1.09492 | −0.547462 | − | 0.836830i | \(-0.684406\pi\) | ||||
−0.547462 | + | 0.836830i | \(0.684406\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.71922 | −0.215178 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.93956 | 0.224758 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −66.4109 | −3.01556 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.83145 | 0.309563 | 0.154781 | − | 0.987949i | \(-0.450533\pi\) | ||||
0.154781 | + | 0.987949i | \(0.450533\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 29.6799 | 1.34217 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.8246 | 0.804413 | 0.402206 | − | 0.915549i | \(-0.368243\pi\) | ||||
0.402206 | + | 0.915549i | \(0.368243\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.96154 | −0.223457 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.489024 | 0.0219800 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.54539 | −0.203889 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.17945 | 0.0527993 | 0.0263997 | − | 0.999651i | \(-0.491596\pi\) | ||||
0.0263997 | + | 0.999651i | \(0.491596\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −38.2311 | −1.70804 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.00000 | 0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.70571 | −0.253901 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −21.6157 | −0.959985 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −22.5820 | −1.00093 | −0.500466 | − | 0.865756i | \(-0.666838\pi\) | ||||
−0.500466 | + | 0.865756i | \(0.666838\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.91517 | 0.217434 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −31.6224 | −1.39616 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 34.5324 | 1.52168 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.362587 | −0.0159465 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 12.0656 | 0.529622 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.3907 | −0.674281 | −0.337140 | − | 0.941454i | \(-0.609460\pi\) | ||||
−0.337140 | + | 0.941454i | \(0.609460\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.0581 | 0.570990 | 0.285495 | − | 0.958380i | \(-0.407842\pi\) | ||||
0.285495 | + | 0.958380i | \(0.407842\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 25.1134 | 1.09604 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.93874 | 0.389378 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.4087 | −0.626467 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.76802 | 0.0767255 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.83409 | −0.339332 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.09998 | −0.220491 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 33.0813 | 1.42756 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.610219 | −0.0262840 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.15271 | −0.178539 | −0.0892695 | − | 0.996008i | \(-0.528453\pi\) | ||||
−0.0892695 | + | 0.996008i | \(0.528453\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 17.8204 | 0.764745 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 55.8068 | 2.39050 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.91362 | −0.210091 | −0.105046 | − | 0.994467i | \(-0.533499\pi\) | ||||
−0.105046 | + | 0.994467i | \(0.533499\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −13.2308 | −0.564675 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11.5092 | 0.490310 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.7614 | 0.457620 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −27.8124 | −1.18057 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.89601 | −0.207451 | −0.103725 | − | 0.994606i | \(-0.533076\pi\) | ||||
−0.103725 | + | 0.994606i | \(0.533076\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −18.5834 | −0.785995 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.706177 | −0.0298148 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 30.4658 | 1.28398 | 0.641990 | − | 0.766713i | \(-0.278109\pi\) | ||||
0.641990 | + | 0.766713i | \(0.278109\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 31.5894 | 1.32898 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −9.21349 | −0.386930 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −16.0224 | −0.671693 | −0.335846 | − | 0.941917i | \(-0.609022\pi\) | ||||
−0.335846 | + | 0.941917i | \(0.609022\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.92027 | 0.164058 | 0.0820291 | − | 0.996630i | \(-0.473860\pi\) | ||||
0.0820291 | + | 0.996630i | \(0.473860\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 53.0567 | 2.21647 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 43.6792 | 1.82155 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.2327 | −0.759037 | −0.379519 | − | 0.925184i | \(-0.623910\pi\) | ||||
−0.379519 | + | 0.925184i | \(0.623910\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.166026 | 0.00689980 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.8790 | 0.575799 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.578304 | 0.0239509 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 7.78663 | 0.321937 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 19.7471 | 0.815048 | 0.407524 | − | 0.913194i | \(-0.366392\pi\) | ||||
0.407524 | + | 0.913194i | \(0.366392\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −20.7351 | −0.854376 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −37.0705 | −1.52488 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −26.3107 | −1.08045 | −0.540225 | − | 0.841521i | \(-0.681661\pi\) | ||||
−0.540225 | + | 0.841521i | \(0.681661\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −13.2861 | −0.544678 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −18.5689 | −0.759976 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.44856 | 0.140904 | 0.0704522 | − | 0.997515i | \(-0.477556\pi\) | ||||
0.0704522 | + | 0.997515i | \(0.477556\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −48.1876 | −1.96561 | −0.982806 | − | 0.184643i | \(-0.940887\pi\) | ||||
−0.982806 | + | 0.184643i | \(0.940887\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.35014 | 0.0549817 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −49.0312 | −1.99340 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −20.9551 | −0.850540 | −0.425270 | − | 0.905067i | \(-0.639821\pi\) | ||||
−0.425270 | + | 0.905067i | \(0.639821\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.32702 | 0.0942956 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.77339 | −0.233566 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.3527 | −0.458530 | −0.229265 | − | 0.973364i | \(-0.573632\pi\) | ||||
−0.229265 | + | 0.973364i | \(0.573632\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −46.1698 | −1.86175 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −33.6693 | −1.35548 | −0.677738 | − | 0.735303i | \(-0.737040\pi\) | ||||
−0.677738 | + | 0.735303i | \(0.737040\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −28.8179 | −1.15829 | −0.579145 | − | 0.815225i | \(-0.696613\pi\) | ||||
−0.579145 | + | 0.815225i | \(0.696613\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −11.1203 | −0.446242 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.14775 | −0.246304 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 122.561 | 4.90244 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.63811 | 0.0654199 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 11.0174 | 0.439293 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.5612 | −0.539864 | −0.269932 | − | 0.962879i | \(-0.587001\pi\) | ||||
−0.269932 | + | 0.962879i | \(0.587001\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 21.2243 | 0.843591 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −34.4541 | −1.36727 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9.71639 | −0.384977 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.21916 | −0.246026 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14.9901 | 0.592073 | 0.296036 | − | 0.955177i | \(-0.404335\pi\) | ||||
0.296036 | + | 0.955177i | \(0.404335\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.77896 | 0.109592 | 0.0547958 | − | 0.998498i | \(-0.482549\pi\) | ||||
0.0547958 | + | 0.998498i | \(0.482549\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −109.520 | −4.31236 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 34.1713 | 1.34341 | 0.671707 | − | 0.740817i | \(-0.265562\pi\) | ||||
0.671707 | + | 0.740817i | \(0.265562\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.150696 | 0.00591535 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.19237 | −0.164312 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −21.1668 | −0.828320 | −0.414160 | − | 0.910204i | \(-0.635925\pi\) | ||||
−0.414160 | + | 0.910204i | \(0.635925\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −48.1832 | −1.88268 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.72510 | 0.262371 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 30.1878 | 1.17595 | 0.587976 | − | 0.808879i | \(-0.299925\pi\) | ||||
0.587976 | + | 0.808879i | \(0.299925\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.1968 | −0.785564 | −0.392782 | − | 0.919632i | \(-0.628487\pi\) | ||||
−0.392782 | + | 0.919632i | \(0.628487\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −11.2443 | −0.436693 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 30.8197 | 1.19514 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.04733 | 0.156713 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −30.3651 | −1.17398 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.12772 | −0.0435351 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.0029 | 0.848150 | 0.424075 | − | 0.905627i | \(-0.360599\pi\) | ||||
0.424075 | + | 0.905627i | \(0.360599\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −56.5371 | −2.17612 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16.1953 | 0.622438 | 0.311219 | − | 0.950338i | \(-0.399263\pi\) | ||||
0.311219 | + | 0.950338i | \(0.399263\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.3385 | −0.473509 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 19.5329 | 0.748501 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.04086 | −0.154619 | −0.0773096 | − | 0.997007i | \(-0.524633\pi\) | ||||
−0.0773096 | + | 0.997007i | \(0.524633\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −78.8537 | −3.01284 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −20.3757 | −0.777381 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.20822 | 0.350805 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.75760 | −0.371197 | −0.185598 | − | 0.982626i | \(-0.559422\pi\) | ||||
−0.185598 | + | 0.982626i | \(0.559422\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.0908560 | 0.00345133 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −68.4112 | −2.59499 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18.2893 | 0.692758 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9.51147 | −0.359757 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19.5876 | 0.739814 | 0.369907 | − | 0.929069i | \(-0.379390\pi\) | ||||
0.369907 | + | 0.929069i | \(0.379390\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −25.5570 | −0.963900 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −34.0252 | −1.28146 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.06007 | −0.0398679 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.31630 | 0.199658 | 0.0998288 | − | 0.995005i | \(-0.468170\pi\) | ||||
0.0998288 | + | 0.995005i | \(0.468170\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 14.7241 | 0.552195 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.29169 | −0.273076 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.663690 | 0.0248206 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 42.7109 | 1.59507 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 26.8375 | 1.00087 | 0.500434 | − | 0.865775i | \(-0.333174\pi\) | ||||
0.500434 | + | 0.865775i | \(0.333174\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.41579 | 0.238937 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 57.6771 | 2.14503 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 20.5772 | 0.764217 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −23.0650 | −0.855434 | −0.427717 | − | 0.903913i | \(-0.640682\pi\) | ||||
−0.427717 | + | 0.903913i | \(0.640682\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 10.5356 | 0.390207 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 43.3845 | 1.60463 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 42.7383 | 1.57857 | 0.789287 | − | 0.614025i | \(-0.210451\pi\) | ||||
0.789287 | + | 0.614025i | \(0.210451\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −57.2630 | −2.11218 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.115078 | 0.00423896 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.649472 | −0.0238912 | −0.0119456 | − | 0.999929i | \(-0.503802\pi\) | ||||
−0.0119456 | + | 0.999929i | \(0.503802\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 26.0833 | 0.958195 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 17.6669 | 0.648137 | 0.324068 | − | 0.946034i | \(-0.394949\pi\) | ||||
0.324068 | + | 0.946034i | \(0.394949\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 19.6432 | 0.719670 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 18.9898 | 0.694799 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.947527 | −0.0346219 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.53204 | −0.274848 | −0.137424 | − | 0.990512i | \(-0.543882\pi\) | ||||
−0.137424 | + | 0.990512i | \(0.543882\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −5.89661 | −0.214885 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 77.0661 | 2.80472 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.73106 | 0.135608 | 0.0678039 | − | 0.997699i | \(-0.478401\pi\) | ||||
0.0678039 | + | 0.997699i | \(0.478401\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.576056 | 0.0209095 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.45314 | −0.0889264 | −0.0444632 | − | 0.999011i | \(-0.514158\pi\) | ||||
−0.0444632 | + | 0.999011i | \(0.514158\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.3684 | 0.375360 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −18.1785 | −0.657246 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.39951 | 0.0866412 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.2733 | 0.406526 | 0.203263 | − | 0.979124i | \(-0.434845\pi\) | ||||
0.203263 | + | 0.979124i | \(0.434845\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −31.6018 | −1.13811 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −43.0607 | −1.54879 | −0.774393 | − | 0.632705i | \(-0.781945\pi\) | ||||
−0.774393 | + | 0.632705i | \(0.781945\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −37.0720 | −1.33166 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.16729 | −0.185375 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −42.4256 | −1.52006 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.530088 | −0.0189680 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.23875 | −0.187218 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −48.9532 | −1.74722 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 36.4349 | 1.29876 | 0.649382 | − | 0.760462i | \(-0.275028\pi\) | ||||
0.649382 | + | 0.760462i | \(0.275028\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.94665 | 0.247307 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.86901 | 0.208678 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −17.9564 | −0.637651 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 54.2681 | 1.92469 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 31.1724 | 1.10418 | 0.552092 | − | 0.833783i | \(-0.313830\pi\) | ||||
0.552092 | + | 0.833783i | \(0.313830\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.4785 | 0.476834 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.41156 | −0.297208 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.573211 | 0.0202282 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10.8380 | 0.381990 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 14.6456 | 0.515549 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 26.8016 | 0.942294 | 0.471147 | − | 0.882055i | \(-0.343840\pi\) | ||||
0.471147 | + | 0.882055i | \(0.343840\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −26.5851 | −0.933527 | −0.466764 | − | 0.884382i | \(-0.654580\pi\) | ||||
−0.466764 | + | 0.884382i | \(0.654580\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −65.5385 | −2.29854 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 65.1214 | 2.28110 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −100.639 | −3.52090 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.44668 | 0.0505511 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 54.2548 | 1.89351 | 0.946754 | − | 0.321959i | \(-0.104341\pi\) | ||||
0.946754 | + | 0.321959i | \(0.104341\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −21.7378 | −0.757732 | −0.378866 | − | 0.925451i | \(-0.623686\pi\) | ||||
−0.378866 | + | 0.925451i | \(0.623686\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.92875 | 0.101966 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 23.2671 | 0.809077 | 0.404538 | − | 0.914521i | \(-0.367432\pi\) | ||||
0.404538 | + | 0.914521i | \(0.367432\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −51.9647 | −1.80481 | −0.902404 | − | 0.430891i | \(-0.858199\pi\) | ||||
−0.902404 | + | 0.430891i | \(0.858199\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 42.4940 | 1.47410 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 22.6837 | 0.785944 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −83.8837 | −2.90292 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 9.43815 | 0.326230 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −6.20131 | −0.214093 | −0.107047 | − | 0.994254i | \(-0.534139\pi\) | ||||
−0.107047 | + | 0.994254i | \(0.534139\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.0933 | −0.934252 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 24.2031 | 0.833598 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −47.4274 | −1.63155 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.10953 | −0.313007 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6.41724 | 0.220239 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.98733 | −0.308082 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9.53933 | −0.326620 | −0.163310 | − | 0.986575i | \(-0.552217\pi\) | ||||
−0.163310 | + | 0.986575i | \(0.552217\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 42.1686 | 1.44213 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.07636 | 0.139246 | 0.0696230 | − | 0.997573i | \(-0.477820\pi\) | ||||
0.0696230 | + | 0.997573i | \(0.477820\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.6251 | −0.362525 | −0.181263 | − | 0.983435i | \(-0.558018\pi\) | ||||
−0.181263 | + | 0.983435i | \(0.558018\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.57790 | −0.292334 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −18.7328 | −0.637674 | −0.318837 | − | 0.947810i | \(-0.603292\pi\) | ||||
−0.318837 | + | 0.947810i | \(0.603292\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 26.4735 | 0.900125 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8.31428 | −0.282368 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.25500 | 0.0425729 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.83237 | 0.0620874 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −16.8820 | −0.571368 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 36.6139 | 1.23778 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −45.1218 | −1.52365 | −0.761827 | − | 0.647780i | \(-0.775698\pi\) | ||||
−0.761827 | + | 0.647780i | \(0.775698\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −42.2153 | −1.42389 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.17898 | 0.275557 | 0.137778 | − | 0.990463i | \(-0.456004\pi\) | ||||
0.137778 | + | 0.990463i | \(0.456004\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 37.2673 | 1.25415 | 0.627073 | − | 0.778961i | \(-0.284253\pi\) | ||||
0.627073 | + | 0.778961i | \(0.284253\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 14.1414 | 0.475357 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.11112 | 0.104461 | 0.0522305 | − | 0.998635i | \(-0.483367\pi\) | ||||
0.0522305 | + | 0.998635i | \(0.483367\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.40124 | −0.214691 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.07448 | −0.0359966 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −31.2659 | −1.04627 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 72.5844 | 2.42623 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.17243 | 0.306258 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.43510 | −0.114567 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −21.4973 | −0.716180 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −20.3478 | −0.677133 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 39.1001 | 1.29973 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 58.6324 | 1.94686 | 0.973428 | − | 0.228994i | \(-0.0735437\pi\) | ||||
0.973428 | + | 0.228994i | \(0.0735437\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.45042 | −0.0481073 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.36194 | 0.277044 | 0.138522 | − | 0.990359i | \(-0.455765\pi\) | ||||
0.138522 | + | 0.990359i | \(0.455765\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.61859 | 0.0535674 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −105.825 | −3.49847 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8.95198 | −0.295621 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.5589 | 0.480253 | 0.240127 | − | 0.970742i | \(-0.422811\pi\) | ||||
0.240127 | + | 0.970742i | \(0.422811\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 51.1565 | 1.68567 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.44047 | −0.277822 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −45.6929 | −1.50237 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8.77831 | 0.288318 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.37351 | 0.0778723 | 0.0389361 | − | 0.999242i | \(-0.487603\pi\) | ||||
0.0389361 | + | 0.999242i | \(0.487603\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −52.6192 | −1.72453 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −48.9512 | −1.60259 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.54944 | −0.0506721 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32.0019 | 1.04546 | 0.522728 | − | 0.852500i | \(-0.324914\pi\) | ||||
0.522728 | + | 0.852500i | \(0.324914\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −38.2531 | −1.24834 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14.9262 | 0.486580 | 0.243290 | − | 0.969954i | \(-0.421773\pi\) | ||||
0.243290 | + | 0.969954i | \(0.421773\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −14.9193 | −0.485841 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −14.0284 | −0.456345 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 24.6714 | 0.801714 | 0.400857 | − | 0.916141i | \(-0.368712\pi\) | ||||
0.400857 | + | 0.916141i | \(0.368712\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.12712 | 0.296279 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 41.1621 | 1.33477 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.01906 | 0.0330106 | 0.0165053 | − | 0.999864i | \(-0.494746\pi\) | ||||
0.0165053 | + | 0.999864i | \(0.494746\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 116.413 | 3.76703 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.271379 | 0.00877244 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −14.6503 | −0.473081 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.8113 | −0.800365 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.29644 | −0.0417772 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.364281 | 0.0117266 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.525505 | −0.0168991 | −0.00844954 | − | 0.999964i | \(-0.502690\pi\) | ||||
−0.00844954 | + | 0.999964i | \(0.502690\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −60.8936 | −1.95619 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −36.8504 | −1.18258 | −0.591292 | − | 0.806457i | \(-0.701382\pi\) | ||||
−0.591292 | + | 0.806457i | \(0.701382\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.7102 | −0.407469 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 46.6339 | 1.49348 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −16.3528 | −0.523171 | −0.261586 | − | 0.965180i | \(-0.584245\pi\) | ||||
−0.261586 | + | 0.965180i | \(0.584245\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.716956 | −0.0229140 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.1864 | 0.452936 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 12.1552 | 0.387691 | 0.193846 | − | 0.981032i | \(-0.437904\pi\) | ||||
0.193846 | + | 0.981032i | \(0.437904\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −81.3372 | −2.59162 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.32155 | −0.201217 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −35.3905 | −1.12535 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.7096 | −0.435500 | −0.217750 | − | 0.976005i | \(-0.569872\pi\) | ||||
−0.217750 | + | 0.976005i | \(0.569872\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 61.0472 | 1.93728 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −40.7425 | −1.29163 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −38.5298 | −1.22025 | −0.610125 | − | 0.792305i | \(-0.708881\pi\) | ||||
−0.610125 | + | 0.792305i | \(0.708881\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 11.6330 | 0.368050 |
(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 | 4024.2.a.g.1.25 | ✓ | 33 | |
4.3 | odd | 2 | 8048.2.a.x.1.9 | 33 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4024.2.a.g.1.25 | ✓ | 33 | 1.1 | even | 1 | trivial | |
8048.2.a.x.1.9 | 33 | 4.3 | odd | 2 |