Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4023,2,Mod(1,4023)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4023, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4023.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4023 = 3^{3} \cdot 149 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4023.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: | \(32.1238167332\) |
Analytic rank: | \(1\) |
Dimension: | \(25\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 4023.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.45057 | −1.73281 | −0.866407 | − | 0.499339i | \(-0.833576\pi\) | ||||
−0.866407 | + | 0.499339i | \(0.833576\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.00528 | 2.00264 | ||||||||
\(5\) | −3.55507 | −1.58988 | −0.794938 | − | 0.606690i | \(-0.792497\pi\) | ||||
−0.794938 | + | 0.606690i | \(0.792497\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.769224 | −0.290739 | −0.145370 | − | 0.989377i | \(-0.546437\pi\) | ||||
−0.145370 | + | 0.989377i | \(0.546437\pi\) | |||||||
\(8\) | −4.91408 | −1.73739 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 8.71195 | 2.75496 | ||||||||
\(11\) | −5.40475 | −1.62959 | −0.814797 | − | 0.579746i | \(-0.803152\pi\) | ||||
−0.814797 | + | 0.579746i | \(0.803152\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.95178 | −0.818677 | −0.409338 | − | 0.912383i | \(-0.634240\pi\) | ||||
−0.409338 | + | 0.912383i | \(0.634240\pi\) | |||||||
\(14\) | 1.88504 | 0.503797 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.03173 | 1.00793 | ||||||||
\(17\) | 8.13105 | 1.97207 | 0.986034 | − | 0.166542i | \(-0.0532603\pi\) | ||||
0.986034 | + | 0.166542i | \(0.0532603\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.72141 | −0.624335 | −0.312168 | − | 0.950027i | \(-0.601055\pi\) | ||||
−0.312168 | + | 0.950027i | \(0.601055\pi\) | |||||||
\(20\) | −14.2391 | −3.18395 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 13.2447 | 2.82378 | ||||||||
\(23\) | −6.87800 | −1.43416 | −0.717081 | − | 0.696990i | \(-0.754522\pi\) | ||||
−0.717081 | + | 0.696990i | \(0.754522\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.63854 | 1.52771 | ||||||||
\(26\) | 7.23354 | 1.41861 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.08096 | −0.582247 | ||||||||
\(29\) | 1.15735 | 0.214915 | 0.107457 | − | 0.994210i | \(-0.465729\pi\) | ||||
0.107457 | + | 0.994210i | \(0.465729\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.1050 | 1.81492 | 0.907458 | − | 0.420143i | \(-0.138020\pi\) | ||||
0.907458 | + | 0.420143i | \(0.138020\pi\) | |||||||
\(32\) | −0.0518563 | −0.00916699 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −19.9257 | −3.41723 | ||||||||
\(35\) | 2.73465 | 0.462240 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.27148 | 1.35982 | 0.679911 | − | 0.733294i | \(-0.262018\pi\) | ||||
0.679911 | + | 0.733294i | \(0.262018\pi\) | |||||||
\(38\) | 6.66901 | 1.08186 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 17.4699 | 2.76224 | ||||||||
\(41\) | −3.54033 | −0.552906 | −0.276453 | − | 0.961027i | \(-0.589159\pi\) | ||||
−0.276453 | + | 0.961027i | \(0.589159\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.30894 | 0.657107 | 0.328554 | − | 0.944485i | \(-0.393439\pi\) | ||||
0.328554 | + | 0.944485i | \(0.393439\pi\) | |||||||
\(44\) | −21.6476 | −3.26349 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 16.8550 | 2.48513 | ||||||||
\(47\) | −5.42366 | −0.791122 | −0.395561 | − | 0.918440i | \(-0.629450\pi\) | ||||
−0.395561 | + | 0.918440i | \(0.629450\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.40829 | −0.915471 | ||||||||
\(50\) | −18.7188 | −2.64723 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −11.8227 | −1.63952 | ||||||||
\(53\) | 10.4404 | 1.43410 | 0.717052 | − | 0.697019i | \(-0.245491\pi\) | ||||
0.717052 | + | 0.697019i | \(0.245491\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 19.2143 | 2.59085 | ||||||||
\(56\) | 3.78003 | 0.505128 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.83617 | −0.372407 | ||||||||
\(59\) | 1.20453 | 0.156817 | 0.0784084 | − | 0.996921i | \(-0.475016\pi\) | ||||
0.0784084 | + | 0.996921i | \(0.475016\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.45572 | 1.08264 | 0.541322 | − | 0.840815i | \(-0.317924\pi\) | ||||
0.541322 | + | 0.840815i | \(0.317924\pi\) | |||||||
\(62\) | −24.7630 | −3.14491 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.93638 | −0.992047 | ||||||||
\(65\) | 10.4938 | 1.30160 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.6559 | 1.54616 | 0.773080 | − | 0.634308i | \(-0.218715\pi\) | ||||
0.773080 | + | 0.634308i | \(0.218715\pi\) | |||||||
\(68\) | 32.5671 | 3.94935 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −6.70144 | −0.800975 | ||||||||
\(71\) | 1.70667 | 0.202544 | 0.101272 | − | 0.994859i | \(-0.467709\pi\) | ||||
0.101272 | + | 0.994859i | \(0.467709\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −15.0915 | −1.76633 | −0.883165 | − | 0.469062i | \(-0.844592\pi\) | ||||
−0.883165 | + | 0.469062i | \(0.844592\pi\) | |||||||
\(74\) | −20.2698 | −2.35632 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −10.9000 | −1.25032 | ||||||||
\(77\) | 4.15746 | 0.473787 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.79249 | −0.764215 | −0.382107 | − | 0.924118i | \(-0.624802\pi\) | ||||
−0.382107 | + | 0.924118i | \(0.624802\pi\) | |||||||
\(80\) | −14.3331 | −1.60249 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 8.67581 | 0.958083 | ||||||||
\(83\) | 9.19144 | 1.00889 | 0.504446 | − | 0.863443i | \(-0.331697\pi\) | ||||
0.504446 | + | 0.863443i | \(0.331697\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −28.9065 | −3.13535 | ||||||||
\(86\) | −10.5594 | −1.13864 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 26.5594 | 2.83124 | ||||||||
\(89\) | 5.62099 | 0.595824 | 0.297912 | − | 0.954593i | \(-0.403710\pi\) | ||||
0.297912 | + | 0.954593i | \(0.403710\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.27058 | 0.238021 | ||||||||
\(92\) | −27.5483 | −2.87211 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 13.2910 | 1.37087 | ||||||||
\(95\) | 9.67482 | 0.992616 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.92333 | −0.195285 | −0.0976423 | − | 0.995222i | \(-0.531130\pi\) | ||||
−0.0976423 | + | 0.995222i | \(0.531130\pi\) | |||||||
\(98\) | 15.7040 | 1.58634 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 30.5945 | 3.05945 | ||||||||
\(101\) | 14.7860 | 1.47126 | 0.735629 | − | 0.677384i | \(-0.236887\pi\) | ||||
0.735629 | + | 0.677384i | \(0.236887\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.5561 | −1.43425 | −0.717127 | − | 0.696942i | \(-0.754543\pi\) | ||||
−0.717127 | + | 0.696942i | \(0.754543\pi\) | |||||||
\(104\) | 14.5053 | 1.42236 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −25.5850 | −2.48504 | ||||||||
\(107\) | 11.3547 | 1.09770 | 0.548849 | − | 0.835921i | \(-0.315066\pi\) | ||||
0.548849 | + | 0.835921i | \(0.315066\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −19.8487 | −1.90116 | −0.950579 | − | 0.310482i | \(-0.899509\pi\) | ||||
−0.950579 | + | 0.310482i | \(0.899509\pi\) | |||||||
\(110\) | −47.0859 | −4.48947 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.10130 | −0.293045 | ||||||||
\(113\) | −15.8171 | −1.48795 | −0.743974 | − | 0.668208i | \(-0.767062\pi\) | ||||
−0.743974 | + | 0.668208i | \(0.767062\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 24.4518 | 2.28014 | ||||||||
\(116\) | 4.63552 | 0.430397 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.95179 | −0.271734 | ||||||||
\(119\) | −6.25459 | −0.573358 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 18.2113 | 1.65558 | ||||||||
\(122\) | −20.7213 | −1.87602 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 40.4735 | 3.63463 | ||||||||
\(125\) | −9.38020 | −0.838990 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.52807 | 0.490537 | 0.245269 | − | 0.969455i | \(-0.421124\pi\) | ||||
0.245269 | + | 0.969455i | \(0.421124\pi\) | |||||||
\(128\) | 19.5523 | 1.72820 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −25.7158 | −2.25542 | ||||||||
\(131\) | 13.6262 | 1.19052 | 0.595261 | − | 0.803532i | \(-0.297049\pi\) | ||||
0.595261 | + | 0.803532i | \(0.297049\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.09338 | 0.181519 | ||||||||
\(134\) | −31.0141 | −2.67921 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −39.9566 | −3.42625 | ||||||||
\(137\) | −20.0632 | −1.71411 | −0.857056 | − | 0.515224i | \(-0.827709\pi\) | ||||
−0.857056 | + | 0.515224i | \(0.827709\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.32109 | −0.705786 | −0.352893 | − | 0.935664i | \(-0.614802\pi\) | ||||
−0.352893 | + | 0.935664i | \(0.614802\pi\) | |||||||
\(140\) | 10.9530 | 0.925700 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.18231 | −0.350972 | ||||||||
\(143\) | 15.9536 | 1.33411 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.11447 | −0.341688 | ||||||||
\(146\) | 36.9828 | 3.06072 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 33.1296 | 2.72324 | ||||||||
\(149\) | −1.00000 | −0.0819232 | ||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.7367 | 1.19926 | 0.599628 | − | 0.800279i | \(-0.295315\pi\) | ||||
0.599628 | + | 0.800279i | \(0.295315\pi\) | |||||||
\(152\) | 13.3733 | 1.08471 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −10.1881 | −0.820984 | ||||||||
\(155\) | −35.9241 | −2.88549 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.87623 | 0.149740 | 0.0748698 | − | 0.997193i | \(-0.476146\pi\) | ||||
0.0748698 | + | 0.997193i | \(0.476146\pi\) | |||||||
\(158\) | 16.6455 | 1.32424 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.184353 | 0.0145744 | ||||||||
\(161\) | 5.29072 | 0.416967 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.04253 | −0.394961 | −0.197481 | − | 0.980307i | \(-0.563276\pi\) | ||||
−0.197481 | + | 0.980307i | \(0.563276\pi\) | |||||||
\(164\) | −14.1800 | −1.10727 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −22.5243 | −1.74822 | ||||||||
\(167\) | 1.79823 | 0.139152 | 0.0695758 | − | 0.997577i | \(-0.477835\pi\) | ||||
0.0695758 | + | 0.997577i | \(0.477835\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.28699 | −0.329768 | ||||||||
\(170\) | 70.8372 | 5.43297 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 17.2585 | 1.31595 | ||||||||
\(173\) | −18.7212 | −1.42334 | −0.711672 | − | 0.702512i | \(-0.752062\pi\) | ||||
−0.711672 | + | 0.702512i | \(0.752062\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.87575 | −0.444165 | ||||||||
\(176\) | −21.7905 | −1.64252 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −13.7746 | −1.03245 | ||||||||
\(179\) | 25.1725 | 1.88148 | 0.940739 | − | 0.339132i | \(-0.110133\pi\) | ||||
0.940739 | + | 0.339132i | \(0.110133\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.30690 | −0.468788 | −0.234394 | − | 0.972142i | \(-0.575311\pi\) | ||||
−0.234394 | + | 0.972142i | \(0.575311\pi\) | |||||||
\(182\) | −5.56421 | −0.412447 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 33.7991 | 2.49170 | ||||||||
\(185\) | −29.4057 | −2.16195 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −43.9463 | −3.21367 | ||||||||
\(188\) | −21.7233 | −1.58433 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −23.7088 | −1.72002 | ||||||||
\(191\) | 14.8960 | 1.07784 | 0.538919 | − | 0.842358i | \(-0.318833\pi\) | ||||
0.538919 | + | 0.842358i | \(0.318833\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.81837 | −0.490797 | −0.245399 | − | 0.969422i | \(-0.578919\pi\) | ||||
−0.245399 | + | 0.969422i | \(0.578919\pi\) | |||||||
\(194\) | 4.71325 | 0.338392 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −25.6670 | −1.83336 | ||||||||
\(197\) | −11.7563 | −0.837602 | −0.418801 | − | 0.908078i | \(-0.637550\pi\) | ||||
−0.418801 | + | 0.908078i | \(0.637550\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.198511 | −0.0140721 | −0.00703605 | − | 0.999975i | \(-0.502240\pi\) | ||||
−0.00703605 | + | 0.999975i | \(0.502240\pi\) | |||||||
\(200\) | −37.5364 | −2.65423 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −36.2340 | −2.54942 | ||||||||
\(203\) | −0.890262 | −0.0624841 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12.5861 | 0.879053 | ||||||||
\(206\) | 35.6707 | 2.48530 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −11.9008 | −0.825171 | ||||||||
\(209\) | 14.7086 | 1.01741 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.37754 | 0.370205 | 0.185103 | − | 0.982719i | \(-0.440738\pi\) | ||||
0.185103 | + | 0.982719i | \(0.440738\pi\) | |||||||
\(212\) | 41.8169 | 2.87200 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −27.8254 | −1.90211 | ||||||||
\(215\) | −15.3186 | −1.04472 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.77302 | −0.527667 | ||||||||
\(218\) | 48.6405 | 3.29435 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 76.9587 | 5.18855 | ||||||||
\(221\) | −24.0011 | −1.61449 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.96264 | 0.265358 | 0.132679 | − | 0.991159i | \(-0.457642\pi\) | ||||
0.132679 | + | 0.991159i | \(0.457642\pi\) | |||||||
\(224\) | 0.0398891 | 0.00266520 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 38.7609 | 2.57834 | ||||||||
\(227\) | −12.0773 | −0.801601 | −0.400800 | − | 0.916165i | \(-0.631268\pi\) | ||||
−0.400800 | + | 0.916165i | \(0.631268\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.4497 | 1.15311 | 0.576553 | − | 0.817060i | \(-0.304397\pi\) | ||||
0.576553 | + | 0.817060i | \(0.304397\pi\) | |||||||
\(230\) | −59.9208 | −3.95106 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.68732 | −0.373391 | ||||||||
\(233\) | −15.6470 | −1.02507 | −0.512535 | − | 0.858666i | \(-0.671294\pi\) | ||||
−0.512535 | + | 0.858666i | \(0.671294\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 19.2815 | 1.25779 | ||||||||
\(236\) | 4.82449 | 0.314048 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 15.3273 | 0.993522 | ||||||||
\(239\) | 3.10356 | 0.200753 | 0.100376 | − | 0.994950i | \(-0.467995\pi\) | ||||
0.100376 | + | 0.994950i | \(0.467995\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.98984 | −0.192593 | −0.0962963 | − | 0.995353i | \(-0.530700\pi\) | ||||
−0.0962963 | + | 0.995353i | \(0.530700\pi\) | |||||||
\(242\) | −44.6281 | −2.86881 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 33.8676 | 2.16815 | ||||||||
\(245\) | 22.7820 | 1.45549 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.03302 | 0.511129 | ||||||||
\(248\) | −49.6569 | −3.15322 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 22.9868 | 1.45381 | ||||||||
\(251\) | 21.5048 | 1.35737 | 0.678687 | − | 0.734428i | \(-0.262549\pi\) | ||||
0.678687 | + | 0.734428i | \(0.262549\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 37.1739 | 2.33710 | ||||||||
\(254\) | −13.5469 | −0.850009 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −32.0416 | −2.00260 | ||||||||
\(257\) | −13.1601 | −0.820903 | −0.410451 | − | 0.911882i | \(-0.634629\pi\) | ||||
−0.410451 | + | 0.911882i | \(0.634629\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.36262 | −0.395354 | ||||||||
\(260\) | 42.0306 | 2.60663 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −33.3918 | −2.06295 | ||||||||
\(263\) | −0.748397 | −0.0461481 | −0.0230741 | − | 0.999734i | \(-0.507345\pi\) | ||||
−0.0230741 | + | 0.999734i | \(0.507345\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −37.1165 | −2.28005 | ||||||||
\(266\) | −5.12996 | −0.314538 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 50.6903 | 3.09641 | ||||||||
\(269\) | 6.62100 | 0.403689 | 0.201845 | − | 0.979418i | \(-0.435306\pi\) | ||||
0.201845 | + | 0.979418i | \(0.435306\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 22.1504 | 1.34554 | 0.672772 | − | 0.739850i | \(-0.265104\pi\) | ||||
0.672772 | + | 0.739850i | \(0.265104\pi\) | |||||||
\(272\) | 32.7822 | 1.98771 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 49.1661 | 2.97023 | ||||||||
\(275\) | −41.2844 | −2.48954 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.328464 | 0.0197355 | 0.00986774 | − | 0.999951i | \(-0.496859\pi\) | ||||
0.00986774 | + | 0.999951i | \(0.496859\pi\) | |||||||
\(278\) | 20.3914 | 1.22299 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −13.4383 | −0.803091 | ||||||||
\(281\) | −0.887497 | −0.0529436 | −0.0264718 | − | 0.999650i | \(-0.508427\pi\) | ||||
−0.0264718 | + | 0.999650i | \(0.508427\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.06911 | −0.241883 | −0.120942 | − | 0.992660i | \(-0.538591\pi\) | ||||
−0.120942 | + | 0.992660i | \(0.538591\pi\) | |||||||
\(284\) | 6.83569 | 0.405624 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −39.0955 | −2.31177 | ||||||||
\(287\) | 2.72330 | 0.160752 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 49.1139 | 2.88905 | ||||||||
\(290\) | 10.0828 | 0.592081 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −60.4459 | −3.53733 | ||||||||
\(293\) | 5.78935 | 0.338218 | 0.169109 | − | 0.985597i | \(-0.445911\pi\) | ||||
0.169109 | + | 0.985597i | \(0.445911\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.28220 | −0.249319 | ||||||||
\(296\) | −40.6467 | −2.36254 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.45057 | 0.141958 | ||||||||
\(299\) | 20.3023 | 1.17412 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.31454 | −0.191047 | ||||||||
\(302\) | −36.1133 | −2.07809 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −10.9720 | −0.629287 | ||||||||
\(305\) | −30.0607 | −1.72127 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.3621 | −0.648468 | −0.324234 | − | 0.945977i | \(-0.605106\pi\) | ||||
−0.324234 | + | 0.945977i | \(0.605106\pi\) | |||||||
\(308\) | 16.6518 | 0.948825 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 88.0344 | 5.00002 | ||||||||
\(311\) | 17.5258 | 0.993797 | 0.496898 | − | 0.867809i | \(-0.334472\pi\) | ||||
0.496898 | + | 0.867809i | \(0.334472\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −32.2326 | −1.82189 | −0.910947 | − | 0.412523i | \(-0.864648\pi\) | ||||
−0.910947 | + | 0.412523i | \(0.864648\pi\) | |||||||
\(314\) | −4.59783 | −0.259471 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −27.2058 | −1.53045 | ||||||||
\(317\) | −8.78252 | −0.493275 | −0.246638 | − | 0.969108i | \(-0.579326\pi\) | ||||
−0.246638 | + | 0.969108i | \(0.579326\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.25520 | −0.350224 | ||||||||
\(320\) | 28.2144 | 1.57723 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −12.9653 | −0.722526 | ||||||||
\(323\) | −22.1279 | −1.23123 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −22.5473 | −1.25070 | ||||||||
\(326\) | 12.3571 | 0.684394 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 17.3975 | 0.960614 | ||||||||
\(329\) | 4.17201 | 0.230010 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −21.0169 | −1.15519 | −0.577597 | − | 0.816322i | \(-0.696009\pi\) | ||||
−0.577597 | + | 0.816322i | \(0.696009\pi\) | |||||||
\(332\) | 36.8143 | 2.02045 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −4.40669 | −0.241124 | ||||||||
\(335\) | −44.9925 | −2.45820 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.84346 | 0.536207 | 0.268104 | − | 0.963390i | \(-0.413603\pi\) | ||||
0.268104 | + | 0.963390i | \(0.413603\pi\) | |||||||
\(338\) | 10.5056 | 0.571427 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −115.779 | −6.27897 | ||||||||
\(341\) | −54.6151 | −2.95758 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.3140 | 0.556902 | ||||||||
\(344\) | −21.1745 | −1.14165 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 45.8775 | 2.46639 | ||||||||
\(347\) | 12.0386 | 0.646264 | 0.323132 | − | 0.946354i | \(-0.395264\pi\) | ||||
0.323132 | + | 0.946354i | \(0.395264\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.84312 | −0.205717 | −0.102859 | − | 0.994696i | \(-0.532799\pi\) | ||||
−0.102859 | + | 0.994696i | \(0.532799\pi\) | |||||||
\(350\) | 14.3989 | 0.769654 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.280271 | 0.0149385 | ||||||||
\(353\) | 17.6205 | 0.937847 | 0.468924 | − | 0.883239i | \(-0.344642\pi\) | ||||
0.468924 | + | 0.883239i | \(0.344642\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.06733 | −0.322021 | ||||||||
\(356\) | 22.5137 | 1.19322 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −61.6868 | −3.26025 | ||||||||
\(359\) | 12.2734 | 0.647764 | 0.323882 | − | 0.946098i | \(-0.395012\pi\) | ||||
0.323882 | + | 0.946098i | \(0.395012\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.5939 | −0.610206 | ||||||||
\(362\) | 15.4555 | 0.812323 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 9.09432 | 0.476672 | ||||||||
\(365\) | 53.6515 | 2.80825 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.2785 | 0.640933 | 0.320467 | − | 0.947260i | \(-0.396160\pi\) | ||||
0.320467 | + | 0.947260i | \(0.396160\pi\) | |||||||
\(368\) | −27.7302 | −1.44554 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 72.0607 | 3.74626 | ||||||||
\(371\) | −8.03103 | −0.416950 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 20.6351 | 1.06845 | 0.534224 | − | 0.845343i | \(-0.320604\pi\) | ||||
0.534224 | + | 0.845343i | \(0.320604\pi\) | |||||||
\(374\) | 107.693 | 5.56869 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 26.6523 | 1.37449 | ||||||||
\(377\) | −3.41625 | −0.175946 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.8103 | −0.966218 | −0.483109 | − | 0.875560i | \(-0.660493\pi\) | ||||
−0.483109 | + | 0.875560i | \(0.660493\pi\) | |||||||
\(380\) | 38.7504 | 1.98785 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −36.5037 | −1.86769 | ||||||||
\(383\) | −13.9324 | −0.711912 | −0.355956 | − | 0.934503i | \(-0.615845\pi\) | ||||
−0.355956 | + | 0.934503i | \(0.615845\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −14.7801 | −0.753263 | ||||||||
\(386\) | 16.7089 | 0.850460 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −7.70348 | −0.391085 | ||||||||
\(389\) | −15.8509 | −0.803675 | −0.401837 | − | 0.915711i | \(-0.631628\pi\) | ||||
−0.401837 | + | 0.915711i | \(0.631628\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −55.9253 | −2.82827 | ||||||||
\(392\) | 31.4909 | 1.59053 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 28.8096 | 1.45141 | ||||||||
\(395\) | 24.1478 | 1.21501 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −21.1846 | −1.06322 | −0.531612 | − | 0.846988i | \(-0.678414\pi\) | ||||
−0.531612 | + | 0.846988i | \(0.678414\pi\) | |||||||
\(398\) | 0.486466 | 0.0243843 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 30.7965 | 1.53983 | ||||||||
\(401\) | −3.09415 | −0.154515 | −0.0772573 | − | 0.997011i | \(-0.524616\pi\) | ||||
−0.0772573 | + | 0.997011i | \(0.524616\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −29.8278 | −1.48583 | ||||||||
\(404\) | 59.2220 | 2.94640 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.18165 | 0.108273 | ||||||||
\(407\) | −44.7053 | −2.21596 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −25.6766 | −1.26963 | −0.634813 | − | 0.772666i | \(-0.718923\pi\) | ||||
−0.634813 | + | 0.772666i | \(0.718923\pi\) | |||||||
\(410\) | −30.8431 | −1.52323 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −58.3013 | −2.87230 | ||||||||
\(413\) | −0.926555 | −0.0455928 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −32.6762 | −1.60401 | ||||||||
\(416\) | 0.153069 | 0.00750481 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −36.0443 | −1.76299 | ||||||||
\(419\) | −8.28859 | −0.404924 | −0.202462 | − | 0.979290i | \(-0.564894\pi\) | ||||
−0.202462 | + | 0.979290i | \(0.564894\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.936357 | −0.0456352 | −0.0228176 | − | 0.999740i | \(-0.507264\pi\) | ||||
−0.0228176 | + | 0.999740i | \(0.507264\pi\) | |||||||
\(422\) | −13.1780 | −0.641496 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −51.3052 | −2.49160 | ||||||||
\(425\) | 62.1093 | 3.01274 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.50434 | −0.314767 | ||||||||
\(428\) | 45.4787 | 2.19830 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 37.5393 | 1.81030 | ||||||||
\(431\) | −35.1809 | −1.69460 | −0.847302 | − | 0.531111i | \(-0.821775\pi\) | ||||
−0.847302 | + | 0.531111i | \(0.821775\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.46548 | −0.454882 | −0.227441 | − | 0.973792i | \(-0.573036\pi\) | ||||
−0.227441 | + | 0.973792i | \(0.573036\pi\) | |||||||
\(434\) | 19.0483 | 0.914349 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −79.4996 | −3.80734 | ||||||||
\(437\) | 18.7179 | 0.895397 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.92330 | −0.425886 | −0.212943 | − | 0.977065i | \(-0.568305\pi\) | ||||
−0.212943 | + | 0.977065i | \(0.568305\pi\) | |||||||
\(440\) | −94.4206 | −4.50133 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 58.8163 | 2.79760 | ||||||||
\(443\) | 13.2830 | 0.631094 | 0.315547 | − | 0.948910i | \(-0.397812\pi\) | ||||
0.315547 | + | 0.948910i | \(0.397812\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −19.9830 | −0.947286 | ||||||||
\(446\) | −9.71071 | −0.459816 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 6.10485 | 0.288427 | ||||||||
\(449\) | −36.6142 | −1.72793 | −0.863967 | − | 0.503549i | \(-0.832027\pi\) | ||||
−0.863967 | + | 0.503549i | \(0.832027\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19.1346 | 0.901013 | ||||||||
\(452\) | −63.3520 | −2.97983 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 29.5963 | 1.38902 | ||||||||
\(455\) | −8.07208 | −0.378425 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −20.5846 | −0.962906 | −0.481453 | − | 0.876472i | \(-0.659891\pi\) | ||||
−0.481453 | + | 0.876472i | \(0.659891\pi\) | |||||||
\(458\) | −42.7616 | −1.99812 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 97.9363 | 4.56630 | ||||||||
\(461\) | −15.5222 | −0.722939 | −0.361470 | − | 0.932384i | \(-0.617725\pi\) | ||||
−0.361470 | + | 0.932384i | \(0.617725\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.29274 | 0.245975 | 0.122987 | − | 0.992408i | \(-0.460753\pi\) | ||||
0.122987 | + | 0.992408i | \(0.460753\pi\) | |||||||
\(464\) | 4.66612 | 0.216619 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 38.3441 | 1.77625 | ||||||||
\(467\) | −12.4477 | −0.576009 | −0.288004 | − | 0.957629i | \(-0.592992\pi\) | ||||
−0.288004 | + | 0.957629i | \(0.592992\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.73520 | −0.449530 | ||||||||
\(470\) | −47.2506 | −2.17951 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −5.91917 | −0.272452 | ||||||||
\(473\) | −23.2888 | −1.07082 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −20.7876 | −0.953802 | ||||||||
\(476\) | −25.0514 | −1.14823 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −7.60549 | −0.347867 | ||||||||
\(479\) | −20.8201 | −0.951296 | −0.475648 | − | 0.879636i | \(-0.657786\pi\) | ||||
−0.475648 | + | 0.879636i | \(0.657786\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −24.4156 | −1.11326 | ||||||||
\(482\) | 7.32681 | 0.333727 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 72.9416 | 3.31553 | ||||||||
\(485\) | 6.83758 | 0.310478 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.55472 | −0.387652 | −0.193826 | − | 0.981036i | \(-0.562090\pi\) | ||||
−0.193826 | + | 0.981036i | \(0.562090\pi\) | |||||||
\(488\) | −41.5521 | −1.88098 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −55.8287 | −2.52208 | ||||||||
\(491\) | 20.2650 | 0.914545 | 0.457273 | − | 0.889327i | \(-0.348826\pi\) | ||||
0.457273 | + | 0.889327i | \(0.348826\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.41048 | 0.423826 | ||||||||
\(494\) | −19.6855 | −0.885691 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 40.7407 | 1.82931 | ||||||||
\(497\) | −1.31281 | −0.0588876 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.4215 | 0.824659 | 0.412330 | − | 0.911035i | \(-0.364715\pi\) | ||||
0.412330 | + | 0.911035i | \(0.364715\pi\) | |||||||
\(500\) | −37.5704 | −1.68020 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −52.6991 | −2.35207 | ||||||||
\(503\) | −9.73021 | −0.433849 | −0.216924 | − | 0.976188i | \(-0.569603\pi\) | ||||
−0.216924 | + | 0.976188i | \(0.569603\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −52.5652 | −2.33912 | ||||||||
\(506\) | −91.0971 | −4.04976 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 22.1415 | 0.982370 | ||||||||
\(509\) | −29.0199 | −1.28629 | −0.643143 | − | 0.765746i | \(-0.722370\pi\) | ||||
−0.643143 | + | 0.765746i | \(0.722370\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.6088 | 0.513542 | ||||||||
\(512\) | 39.4154 | 1.74193 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 32.2497 | 1.42247 | ||||||||
\(515\) | 51.7480 | 2.28029 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 29.3135 | 1.28921 | ||||||||
\(518\) | 15.5920 | 0.685074 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −51.5674 | −2.26138 | ||||||||
\(521\) | −5.01993 | −0.219927 | −0.109964 | − | 0.993936i | \(-0.535073\pi\) | ||||
−0.109964 | + | 0.993936i | \(0.535073\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.63827 | −0.290271 | −0.145136 | − | 0.989412i | \(-0.546362\pi\) | ||||
−0.145136 | + | 0.989412i | \(0.546362\pi\) | |||||||
\(524\) | 54.5766 | 2.38419 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.83400 | 0.0799661 | ||||||||
\(527\) | 82.1644 | 3.57914 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 24.3069 | 1.05682 | ||||||||
\(530\) | 90.9565 | 3.95090 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 8.38456 | 0.363517 | ||||||||
\(533\) | 10.4503 | 0.452652 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −40.3667 | −1.74521 | ||||||||
\(536\) | −62.1920 | −2.68629 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −16.2252 | −0.699518 | ||||||||
\(539\) | 34.6352 | 1.49185 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −29.2243 | −1.25645 | −0.628225 | − | 0.778032i | \(-0.716218\pi\) | ||||
−0.628225 | + | 0.778032i | \(0.716218\pi\) | |||||||
\(542\) | −54.2812 | −2.33158 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.421646 | −0.0180779 | ||||||||
\(545\) | 70.5635 | 3.02261 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.35081 | 0.271541 | 0.135770 | − | 0.990740i | \(-0.456649\pi\) | ||||
0.135770 | + | 0.990740i | \(0.456649\pi\) | |||||||
\(548\) | −80.3586 | −3.43275 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 101.170 | 4.31391 | ||||||||
\(551\) | −3.14963 | −0.134179 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.22494 | 0.222187 | ||||||||
\(554\) | −0.804923 | −0.0341979 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −33.3283 | −1.41344 | ||||||||
\(557\) | −25.0987 | −1.06346 | −0.531732 | − | 0.846913i | \(-0.678459\pi\) | ||||
−0.531732 | + | 0.846913i | \(0.678459\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12.7191 | −0.537959 | ||||||||
\(560\) | 11.0253 | 0.465906 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.17487 | 0.0917414 | ||||||||
\(563\) | −15.2362 | −0.642130 | −0.321065 | − | 0.947057i | \(-0.604041\pi\) | ||||
−0.321065 | + | 0.947057i | \(0.604041\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 56.2310 | 2.36565 | ||||||||
\(566\) | 9.97162 | 0.419139 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −8.38671 | −0.351899 | ||||||||
\(569\) | 13.8321 | 0.579870 | 0.289935 | − | 0.957046i | \(-0.406366\pi\) | ||||
0.289935 | + | 0.957046i | \(0.406366\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.2430 | −0.930840 | −0.465420 | − | 0.885090i | \(-0.654097\pi\) | ||||
−0.465420 | + | 0.885090i | \(0.654097\pi\) | |||||||
\(572\) | 63.8989 | 2.67175 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −6.67364 | −0.278552 | ||||||||
\(575\) | −52.5379 | −2.19098 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 40.4322 | 1.68322 | 0.841608 | − | 0.540089i | \(-0.181609\pi\) | ||||
0.841608 | + | 0.540089i | \(0.181609\pi\) | |||||||
\(578\) | −120.357 | −5.00619 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −16.4796 | −0.684278 | ||||||||
\(581\) | −7.07027 | −0.293324 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −56.4280 | −2.33701 | ||||||||
\(584\) | 74.1611 | 3.06881 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −14.1872 | −0.586068 | ||||||||
\(587\) | −39.6873 | −1.63807 | −0.819036 | − | 0.573743i | \(-0.805491\pi\) | ||||
−0.819036 | + | 0.573743i | \(0.805491\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −27.4999 | −1.13312 | ||||||||
\(590\) | 10.4938 | 0.432024 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 33.3484 | 1.37061 | ||||||||
\(593\) | −38.0520 | −1.56261 | −0.781304 | − | 0.624151i | \(-0.785445\pi\) | ||||
−0.781304 | + | 0.624151i | \(0.785445\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 22.2355 | 0.911568 | ||||||||
\(596\) | −4.00528 | −0.164063 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −49.7523 | −2.03452 | ||||||||
\(599\) | −10.5177 | −0.429743 | −0.214872 | − | 0.976642i | \(-0.568933\pi\) | ||||
−0.214872 | + | 0.976642i | \(0.568933\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.9676 | 0.610540 | 0.305270 | − | 0.952266i | \(-0.401253\pi\) | ||||
0.305270 | + | 0.952266i | \(0.401253\pi\) | |||||||
\(602\) | 8.12251 | 0.331049 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 59.0247 | 2.40168 | ||||||||
\(605\) | −64.7427 | −2.63216 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 30.6282 | 1.24316 | 0.621580 | − | 0.783350i | \(-0.286491\pi\) | ||||
0.621580 | + | 0.783350i | \(0.286491\pi\) | |||||||
\(608\) | 0.141123 | 0.00572328 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 73.6658 | 2.98264 | ||||||||
\(611\) | 16.0095 | 0.647673 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21.9824 | 0.887862 | 0.443931 | − | 0.896061i | \(-0.353583\pi\) | ||||
0.443931 | + | 0.896061i | \(0.353583\pi\) | |||||||
\(614\) | 27.8435 | 1.12367 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −20.4301 | −0.823153 | ||||||||
\(617\) | 3.65187 | 0.147019 | 0.0735093 | − | 0.997295i | \(-0.476580\pi\) | ||||
0.0735093 | + | 0.997295i | \(0.476580\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15.8678 | −0.637782 | −0.318891 | − | 0.947791i | \(-0.603310\pi\) | ||||
−0.318891 | + | 0.947791i | \(0.603310\pi\) | |||||||
\(620\) | −143.886 | −5.77861 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −42.9482 | −1.72206 | ||||||||
\(623\) | −4.32380 | −0.173229 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.84541 | −0.193817 | ||||||||
\(626\) | 78.9882 | 3.15700 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7.51484 | 0.299875 | ||||||||
\(629\) | 67.2558 | 2.68166 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.03977 | −0.0812020 | −0.0406010 | − | 0.999175i | \(-0.512927\pi\) | ||||
−0.0406010 | + | 0.999175i | \(0.512927\pi\) | |||||||
\(632\) | 33.3789 | 1.32774 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 21.5222 | 0.854754 | ||||||||
\(635\) | −19.6527 | −0.779894 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 18.9159 | 0.749475 | ||||||||
\(638\) | 15.3288 | 0.606872 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −69.5100 | −2.74762 | ||||||||
\(641\) | 33.3829 | 1.31854 | 0.659272 | − | 0.751905i | \(-0.270865\pi\) | ||||
0.659272 | + | 0.751905i | \(0.270865\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.9368 | 0.431304 | 0.215652 | − | 0.976470i | \(-0.430812\pi\) | ||||
0.215652 | + | 0.976470i | \(0.430812\pi\) | |||||||
\(644\) | 21.1908 | 0.835036 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 54.2260 | 2.13349 | ||||||||
\(647\) | −9.42459 | −0.370519 | −0.185259 | − | 0.982690i | \(-0.559313\pi\) | ||||
−0.185259 | + | 0.982690i | \(0.559313\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.51020 | −0.255548 | ||||||||
\(650\) | 55.2537 | 2.16723 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −20.1967 | −0.790966 | ||||||||
\(653\) | 24.9058 | 0.974639 | 0.487319 | − | 0.873224i | \(-0.337975\pi\) | ||||
0.487319 | + | 0.873224i | \(0.337975\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −48.4420 | −1.89278 | ||||||||
\(656\) | −14.2736 | −0.557292 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −10.2238 | −0.398565 | ||||||||
\(659\) | −20.4389 | −0.796186 | −0.398093 | − | 0.917345i | \(-0.630328\pi\) | ||||
−0.398093 | + | 0.917345i | \(0.630328\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.7587 | 1.00190 | 0.500949 | − | 0.865477i | \(-0.332984\pi\) | ||||
0.500949 | + | 0.865477i | \(0.332984\pi\) | |||||||
\(662\) | 51.5034 | 2.00173 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −45.1675 | −1.75284 | ||||||||
\(665\) | −7.44210 | −0.288592 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.96026 | −0.308222 | ||||||||
\(668\) | 7.20244 | 0.278671 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 110.257 | 4.25961 | ||||||||
\(671\) | −45.7011 | −1.76427 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.9606 | −0.692331 | −0.346165 | − | 0.938174i | \(-0.612516\pi\) | ||||
−0.346165 | + | 0.938174i | \(0.612516\pi\) | |||||||
\(674\) | −24.1221 | −0.929147 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −17.1706 | −0.660408 | ||||||||
\(677\) | −38.1634 | −1.46674 | −0.733370 | − | 0.679830i | \(-0.762054\pi\) | ||||
−0.733370 | + | 0.679830i | \(0.762054\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.47947 | 0.0567769 | ||||||||
\(680\) | 142.049 | 5.44732 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 133.838 | 5.12493 | ||||||||
\(683\) | 16.8777 | 0.645809 | 0.322904 | − | 0.946432i | \(-0.395341\pi\) | ||||
0.322904 | + | 0.946432i | \(0.395341\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 71.3260 | 2.72523 | ||||||||
\(686\) | −25.2751 | −0.965008 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 17.3725 | 0.662319 | ||||||||
\(689\) | −30.8179 | −1.17407 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.0219 | 0.571460 | 0.285730 | − | 0.958310i | \(-0.407764\pi\) | ||||
0.285730 | + | 0.958310i | \(0.407764\pi\) | |||||||
\(692\) | −74.9836 | −2.85045 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −29.5013 | −1.11985 | ||||||||
\(695\) | 29.5821 | 1.12211 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −28.7866 | −1.09037 | ||||||||
\(698\) | 9.41783 | 0.356470 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −23.5340 | −0.889503 | ||||||||
\(701\) | −2.67425 | −0.101005 | −0.0505026 | − | 0.998724i | \(-0.516082\pi\) | ||||
−0.0505026 | + | 0.998724i | \(0.516082\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −22.5101 | −0.848985 | ||||||||
\(704\) | 42.8942 | 1.61663 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −43.1803 | −1.62511 | ||||||||
\(707\) | −11.3737 | −0.427753 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.79666 | −0.217698 | −0.108849 | − | 0.994058i | \(-0.534716\pi\) | ||||
−0.108849 | + | 0.994058i | \(0.534716\pi\) | |||||||
\(710\) | 14.8684 | 0.558001 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −27.6220 | −1.03518 | ||||||||
\(713\) | −69.5023 | −2.60288 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −56.7164 | −2.12107 | ||||||||
\(716\) | 100.823 | 3.76793 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −30.0767 | −1.12245 | ||||||||
\(719\) | −42.0447 | −1.56800 | −0.784001 | − | 0.620759i | \(-0.786824\pi\) | ||||
−0.784001 | + | 0.620759i | \(0.786824\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.1969 | 0.416994 | ||||||||
\(722\) | 28.4117 | 1.05737 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −25.2609 | −0.938815 | ||||||||
\(725\) | 8.84047 | 0.328327 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.698186 | −0.0258943 | −0.0129471 | − | 0.999916i | \(-0.504121\pi\) | ||||
−0.0129471 | + | 0.999916i | \(0.504121\pi\) | |||||||
\(728\) | −11.1578 | −0.413536 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −131.477 | −4.86617 | ||||||||
\(731\) | 35.0362 | 1.29586 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.02102 | 0.0377122 | 0.0188561 | − | 0.999822i | \(-0.493998\pi\) | ||||
0.0188561 | + | 0.999822i | \(0.493998\pi\) | |||||||
\(734\) | −30.0893 | −1.11062 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.356668 | 0.0131470 | ||||||||
\(737\) | −68.4018 | −2.51961 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 36.1575 | 1.33008 | 0.665038 | − | 0.746809i | \(-0.268415\pi\) | ||||
0.665038 | + | 0.746809i | \(0.268415\pi\) | |||||||
\(740\) | −117.778 | −4.32961 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 19.6806 | 0.722497 | ||||||||
\(743\) | −29.8813 | −1.09624 | −0.548119 | − | 0.836400i | \(-0.684656\pi\) | ||||
−0.548119 | + | 0.836400i | \(0.684656\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.55507 | 0.130248 | ||||||||
\(746\) | −50.5678 | −1.85142 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −176.017 | −6.43583 | ||||||||
\(749\) | −8.73429 | −0.319144 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.9178 | −0.434886 | −0.217443 | − | 0.976073i | \(-0.569772\pi\) | ||||
−0.217443 | + | 0.976073i | \(0.569772\pi\) | |||||||
\(752\) | −21.8667 | −0.797397 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 8.37175 | 0.304881 | ||||||||
\(755\) | −52.3901 | −1.90667 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29.5267 | 1.07317 | 0.536584 | − | 0.843847i | \(-0.319714\pi\) | ||||
0.536584 | + | 0.843847i | \(0.319714\pi\) | |||||||
\(758\) | 46.0958 | 1.67428 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −47.5429 | −1.72456 | ||||||||
\(761\) | 14.5195 | 0.526330 | 0.263165 | − | 0.964751i | \(-0.415234\pi\) | ||||
0.263165 | + | 0.964751i | \(0.415234\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15.2681 | 0.552741 | ||||||||
\(764\) | 59.6627 | 2.15852 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 34.1423 | 1.23361 | ||||||||
\(767\) | −3.55552 | −0.128382 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.09009 | −0.291736 | −0.145868 | − | 0.989304i | \(-0.546598\pi\) | ||||
−0.145868 | + | 0.989304i | \(0.546598\pi\) | |||||||
\(770\) | 36.2196 | 1.30526 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −27.3095 | −0.982891 | ||||||||
\(773\) | 6.22601 | 0.223934 | 0.111967 | − | 0.993712i | \(-0.464285\pi\) | ||||
0.111967 | + | 0.993712i | \(0.464285\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 77.1876 | 2.77266 | ||||||||
\(776\) | 9.45140 | 0.339286 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 38.8438 | 1.39262 | ||||||||
\(779\) | 9.63470 | 0.345199 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.22412 | −0.330065 | ||||||||
\(782\) | 137.049 | 4.90086 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −25.8365 | −0.922732 | ||||||||
\(785\) | −6.67014 | −0.238067 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −35.0116 | −1.24803 | −0.624015 | − | 0.781412i | \(-0.714500\pi\) | ||||
−0.624015 | + | 0.781412i | \(0.714500\pi\) | |||||||
\(788\) | −47.0873 | −1.67742 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −59.1758 | −2.10538 | ||||||||
\(791\) | 12.1669 | 0.432605 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −24.9594 | −0.886336 | ||||||||
\(794\) | 51.9143 | 1.84237 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.795094 | −0.0281814 | ||||||||
\(797\) | −5.85535 | −0.207407 | −0.103704 | − | 0.994608i | \(-0.533069\pi\) | ||||
−0.103704 | + | 0.994608i | \(0.533069\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −44.1000 | −1.56015 | ||||||||
\(800\) | −0.396107 | −0.0140045 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 7.58243 | 0.267745 | ||||||||
\(803\) | 81.5660 | 2.87840 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −18.8089 | −0.662926 | ||||||||
\(806\) | 73.0951 | 2.57466 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −72.6595 | −2.55615 | ||||||||
\(809\) | −0.611876 | −0.0215124 | −0.0107562 | − | 0.999942i | \(-0.503424\pi\) | ||||
−0.0107562 | + | 0.999942i | \(0.503424\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 36.9200 | 1.29644 | 0.648218 | − | 0.761455i | \(-0.275514\pi\) | ||||
0.648218 | + | 0.761455i | \(0.275514\pi\) | |||||||
\(812\) | −3.56575 | −0.125133 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 109.553 | 3.83984 | ||||||||
\(815\) | 17.9265 | 0.627940 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −11.7264 | −0.410255 | ||||||||
\(818\) | 62.9222 | 2.20002 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 50.4110 | 1.76043 | ||||||||
\(821\) | 13.9623 | 0.487287 | 0.243643 | − | 0.969865i | \(-0.421657\pi\) | ||||
0.243643 | + | 0.969865i | \(0.421657\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 28.7876 | 1.00347 | 0.501736 | − | 0.865021i | \(-0.332695\pi\) | ||||
0.501736 | + | 0.865021i | \(0.332695\pi\) | |||||||
\(824\) | 71.5299 | 2.49186 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.27059 | 0.0790038 | ||||||||
\(827\) | 2.83164 | 0.0984657 | 0.0492329 | − | 0.998787i | \(-0.484322\pi\) | ||||
0.0492329 | + | 0.998787i | \(0.484322\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 29.3145 | 1.01813 | 0.509067 | − | 0.860727i | \(-0.329990\pi\) | ||||
0.509067 | + | 0.860727i | \(0.329990\pi\) | |||||||
\(830\) | 80.0753 | 2.77946 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 23.4265 | 0.812166 | ||||||||
\(833\) | −52.1061 | −1.80537 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.39285 | −0.221234 | ||||||||
\(836\) | 58.9120 | 2.03751 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 20.3118 | 0.701658 | ||||||||
\(839\) | 32.5092 | 1.12234 | 0.561172 | − | 0.827699i | \(-0.310351\pi\) | ||||
0.561172 | + | 0.827699i | \(0.310351\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.6605 | −0.953812 | ||||||||
\(842\) | 2.29461 | 0.0790773 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 21.5386 | 0.741388 | ||||||||
\(845\) | 15.2405 | 0.524291 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −14.0086 | −0.481341 | ||||||||
\(848\) | 42.0930 | 1.44548 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −152.203 | −5.22052 | ||||||||
\(851\) | −56.8912 | −1.95021 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 46.2459 | 1.58343 | 0.791714 | − | 0.610892i | \(-0.209189\pi\) | ||||
0.791714 | + | 0.610892i | \(0.209189\pi\) | |||||||
\(854\) | 15.9393 | 0.545433 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −55.7978 | −1.90713 | ||||||||
\(857\) | −22.3375 | −0.763033 | −0.381517 | − | 0.924362i | \(-0.624598\pi\) | ||||
−0.381517 | + | 0.924362i | \(0.624598\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −35.5297 | −1.21226 | −0.606130 | − | 0.795366i | \(-0.707279\pi\) | ||||
−0.606130 | + | 0.795366i | \(0.707279\pi\) | |||||||
\(860\) | −61.3553 | −2.09220 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 86.2132 | 2.93643 | ||||||||
\(863\) | −28.6114 | −0.973942 | −0.486971 | − | 0.873418i | \(-0.661898\pi\) | ||||
−0.486971 | + | 0.873418i | \(0.661898\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 66.5551 | 2.26294 | ||||||||
\(866\) | 23.1958 | 0.788226 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −31.1332 | −1.05673 | ||||||||
\(869\) | 36.7117 | 1.24536 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −37.3574 | −1.26581 | ||||||||
\(872\) | 97.5380 | 3.30305 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −45.8694 | −1.55156 | ||||||||
\(875\) | 7.21547 | 0.243927 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19.8532 | 0.670397 | 0.335198 | − | 0.942148i | \(-0.391197\pi\) | ||||
0.335198 | + | 0.942148i | \(0.391197\pi\) | |||||||
\(878\) | 21.8672 | 0.737981 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 77.4668 | 2.61140 | ||||||||
\(881\) | 44.3326 | 1.49360 | 0.746802 | − | 0.665046i | \(-0.231588\pi\) | ||||
0.746802 | + | 0.665046i | \(0.231588\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.88079 | 0.332515 | 0.166258 | − | 0.986082i | \(-0.446832\pi\) | ||||
0.166258 | + | 0.986082i | \(0.446832\pi\) | |||||||
\(884\) | −96.1311 | −3.23324 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −32.5509 | −1.09357 | ||||||||
\(887\) | 19.3506 | 0.649731 | 0.324865 | − | 0.945760i | \(-0.394681\pi\) | ||||
0.324865 | + | 0.945760i | \(0.394681\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.25232 | −0.142618 | ||||||||
\(890\) | 48.9698 | 1.64147 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 15.8715 | 0.531417 | ||||||||
\(893\) | 14.7600 | 0.493925 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −89.4899 | −2.99132 | ||||||||
\(896\) | −15.0401 | −0.502455 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 89.7257 | 2.99419 | ||||||||
\(899\) | 11.6951 | 0.390052 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 84.8917 | 2.82815 | ||||||||
\(902\) | −46.8906 | −1.56129 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 77.7266 | 2.58515 | ||||||||
\(905\) | 22.4215 | 0.745316 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16.0706 | 0.533616 | 0.266808 | − | 0.963750i | \(-0.414031\pi\) | ||||
0.266808 | + | 0.963750i | \(0.414031\pi\) | |||||||
\(908\) | −48.3731 | −1.60532 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 19.7812 | 0.655740 | ||||||||
\(911\) | 27.6907 | 0.917435 | 0.458717 | − | 0.888582i | \(-0.348309\pi\) | ||||
0.458717 | + | 0.888582i | \(0.348309\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −49.6775 | −1.64408 | ||||||||
\(914\) | 50.4439 | 1.66854 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 69.8909 | 2.30926 | ||||||||
\(917\) | −10.4816 | −0.346132 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −42.9872 | −1.41802 | −0.709008 | − | 0.705201i | \(-0.750857\pi\) | ||||
−0.709008 | + | 0.705201i | \(0.750857\pi\) | |||||||
\(920\) | −120.158 | −3.96149 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 38.0381 | 1.25272 | ||||||||
\(923\) | −5.03771 | −0.165818 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 63.1820 | 2.07741 | ||||||||
\(926\) | −12.9702 | −0.426228 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.0600160 | −0.00197012 | ||||||||
\(929\) | 53.8096 | 1.76544 | 0.882718 | − | 0.469903i | \(-0.155711\pi\) | ||||
0.882718 | + | 0.469903i | \(0.155711\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 17.4396 | 0.571560 | ||||||||
\(932\) | −62.6707 | −2.05285 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 30.5038 | 0.998116 | ||||||||
\(935\) | 156.232 | 5.10934 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26.0611 | 0.851380 | 0.425690 | − | 0.904869i | \(-0.360031\pi\) | ||||
0.425690 | + | 0.904869i | \(0.360031\pi\) | |||||||
\(938\) | 23.8568 | 0.778951 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 77.2279 | 2.51890 | ||||||||
\(941\) | 26.0807 | 0.850206 | 0.425103 | − | 0.905145i | \(-0.360238\pi\) | ||||
0.425103 | + | 0.905145i | \(0.360238\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 24.3504 | 0.792957 | ||||||||
\(944\) | 4.85635 | 0.158061 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 57.0707 | 1.85553 | ||||||||
\(947\) | 52.1098 | 1.69334 | 0.846671 | − | 0.532117i | \(-0.178603\pi\) | ||||
0.846671 | + | 0.532117i | \(0.178603\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 44.5469 | 1.44605 | ||||||||
\(950\) | 50.9415 | 1.65276 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 30.7356 | 0.996146 | ||||||||
\(953\) | −17.8589 | −0.578506 | −0.289253 | − | 0.957253i | \(-0.593407\pi\) | ||||
−0.289253 | + | 0.957253i | \(0.593407\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −52.9564 | −1.71363 | ||||||||
\(956\) | 12.4306 | 0.402036 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 51.0211 | 1.64842 | ||||||||
\(959\) | 15.4331 | 0.498359 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 71.1115 | 2.29392 | ||||||||
\(962\) | 59.8321 | 1.92906 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −11.9752 | −0.385694 | ||||||||
\(965\) | 24.2398 | 0.780307 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.4449 | 0.496676 | 0.248338 | − | 0.968673i | \(-0.420116\pi\) | ||||
0.248338 | + | 0.968673i | \(0.420116\pi\) | |||||||
\(968\) | −89.4921 | −2.87638 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −16.7559 | −0.538001 | ||||||||
\(971\) | 7.46873 | 0.239683 | 0.119841 | − | 0.992793i | \(-0.461761\pi\) | ||||
0.119841 | + | 0.992793i | \(0.461761\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.40078 | 0.205200 | ||||||||
\(974\) | 20.9639 | 0.671728 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 34.0912 | 1.09123 | ||||||||
\(977\) | −54.8743 | −1.75558 | −0.877792 | − | 0.479042i | \(-0.840984\pi\) | ||||
−0.877792 | + | 0.479042i | \(0.840984\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −30.3801 | −0.970951 | ||||||||
\(980\) | 91.2482 | 2.91482 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −49.6607 | −1.58474 | ||||||||
\(983\) | −14.0687 | −0.448721 | −0.224361 | − | 0.974506i | \(-0.572029\pi\) | ||||
−0.224361 | + | 0.974506i | \(0.572029\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 41.7945 | 1.33168 | ||||||||
\(986\) | −23.0610 | −0.734412 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 32.1745 | 1.02361 | ||||||||
\(989\) | −29.6369 | −0.942398 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22.7375 | 0.722280 | 0.361140 | − | 0.932512i | \(-0.382388\pi\) | ||||
0.361140 | + | 0.932512i | \(0.382388\pi\) | |||||||
\(992\) | −0.524009 | −0.0166373 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 3.21713 | 0.102041 | ||||||||
\(995\) | 0.705722 | 0.0223729 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.23102 | −0.0389867 | −0.0194933 | − | 0.999810i | \(-0.506205\pi\) | ||||
−0.0194933 | + | 0.999810i | \(0.506205\pi\) | |||||||
\(998\) | −45.1431 | −1.42898 | ||||||||
\(999\) | 0 | 0 |
(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 | 4023.2.a.e.1.4 | ✓ | 25 | |
3.2 | odd | 2 | 4023.2.a.f.1.22 | yes | 25 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4023.2.a.e.1.4 | ✓ | 25 | 1.1 | even | 1 | trivial | |
4023.2.a.f.1.22 | yes | 25 | 3.2 | odd | 2 |