Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, 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("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.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: | \(63.8883066572\) |
Analytic rank: | \(1\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - 22 x^{13} + 186 x^{11} - 763 x^{9} - 7 x^{8} + 1588 x^{7} + 64 x^{6} - 1625 x^{5} - 185 x^{4} + 726 x^{3} + 145 x^{2} - 83 x - 13 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 889) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-0.601235\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.601235 | −0.425137 | −0.212569 | − | 0.977146i | \(-0.568183\pi\) | ||||
−0.212569 | + | 0.977146i | \(0.568183\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.63852 | −0.819258 | ||||||||
\(5\) | −4.40463 | −1.96981 | −0.984906 | − | 0.173088i | \(-0.944625\pi\) | ||||
−0.984906 | + | 0.173088i | \(0.944625\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 2.18760 | 0.773435 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.64822 | 0.837441 | ||||||||
\(11\) | −4.30434 | −1.29781 | −0.648904 | − | 0.760870i | \(-0.724772\pi\) | ||||
−0.648904 | + | 0.760870i | \(0.724772\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.91150 | −0.530154 | −0.265077 | − | 0.964227i | \(-0.585397\pi\) | ||||
−0.265077 | + | 0.964227i | \(0.585397\pi\) | |||||||
\(14\) | 0.601235 | 0.160687 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.96177 | 0.490442 | ||||||||
\(17\) | −7.97603 | −1.93447 | −0.967235 | − | 0.253881i | \(-0.918293\pi\) | ||||
−0.967235 | + | 0.253881i | \(0.918293\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00095 | 0.459050 | 0.229525 | − | 0.973303i | \(-0.426283\pi\) | ||||
0.229525 | + | 0.973303i | \(0.426283\pi\) | |||||||
\(20\) | 7.21707 | 1.61379 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.58792 | 0.551747 | ||||||||
\(23\) | −2.11447 | −0.440897 | −0.220448 | − | 0.975399i | \(-0.570752\pi\) | ||||
−0.220448 | + | 0.975399i | \(0.570752\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 14.4008 | 2.88016 | ||||||||
\(26\) | 1.14926 | 0.225388 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.63852 | 0.309651 | ||||||||
\(29\) | 4.21397 | 0.782514 | 0.391257 | − | 0.920281i | \(-0.372040\pi\) | ||||
0.391257 | + | 0.920281i | \(0.372040\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.87794 | −0.516894 | −0.258447 | − | 0.966025i | \(-0.583211\pi\) | ||||
−0.258447 | + | 0.966025i | \(0.583211\pi\) | |||||||
\(32\) | −5.55469 | −0.981940 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.79547 | 0.822416 | ||||||||
\(35\) | 4.40463 | 0.744519 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.54141 | −0.417805 | −0.208903 | − | 0.977936i | \(-0.566989\pi\) | ||||
−0.208903 | + | 0.977936i | \(0.566989\pi\) | |||||||
\(38\) | −1.20304 | −0.195159 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −9.63559 | −1.52352 | ||||||||
\(41\) | 6.34847 | 0.991464 | 0.495732 | − | 0.868475i | \(-0.334900\pi\) | ||||
0.495732 | + | 0.868475i | \(0.334900\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.2731 | 1.56663 | 0.783316 | − | 0.621624i | \(-0.213527\pi\) | ||||
0.783316 | + | 0.621624i | \(0.213527\pi\) | |||||||
\(44\) | 7.05274 | 1.06324 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.27129 | 0.187442 | ||||||||
\(47\) | −10.7858 | −1.57328 | −0.786638 | − | 0.617415i | \(-0.788180\pi\) | ||||
−0.786638 | + | 0.617415i | \(0.788180\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −8.65827 | −1.22446 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.13202 | 0.434333 | ||||||||
\(53\) | 4.18365 | 0.574668 | 0.287334 | − | 0.957830i | \(-0.407231\pi\) | ||||
0.287334 | + | 0.957830i | \(0.407231\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 18.9591 | 2.55644 | ||||||||
\(56\) | −2.18760 | −0.292331 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.53358 | −0.332676 | ||||||||
\(59\) | 14.3788 | 1.87196 | 0.935982 | − | 0.352049i | \(-0.114515\pi\) | ||||
0.935982 | + | 0.352049i | \(0.114515\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.44301 | −1.08102 | −0.540509 | − | 0.841338i | \(-0.681768\pi\) | ||||
−0.540509 | + | 0.841338i | \(0.681768\pi\) | |||||||
\(62\) | 1.73032 | 0.219751 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.583865 | −0.0729831 | ||||||||
\(65\) | 8.41946 | 1.04430 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.52093 | −0.918828 | −0.459414 | − | 0.888222i | \(-0.651941\pi\) | ||||
−0.459414 | + | 0.888222i | \(0.651941\pi\) | |||||||
\(68\) | 13.0689 | 1.58483 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.64822 | −0.316523 | ||||||||
\(71\) | −10.3166 | −1.22436 | −0.612179 | − | 0.790720i | \(-0.709707\pi\) | ||||
−0.612179 | + | 0.790720i | \(0.709707\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.45838 | −0.404773 | −0.202387 | − | 0.979306i | \(-0.564870\pi\) | ||||
−0.202387 | + | 0.979306i | \(0.564870\pi\) | |||||||
\(74\) | 1.52799 | 0.177625 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.27860 | −0.376081 | ||||||||
\(77\) | 4.30434 | 0.490525 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.3417 | 1.61356 | 0.806782 | − | 0.590850i | \(-0.201207\pi\) | ||||
0.806782 | + | 0.590850i | \(0.201207\pi\) | |||||||
\(80\) | −8.64088 | −0.966080 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.81692 | −0.421508 | ||||||||
\(83\) | 5.58186 | 0.612688 | 0.306344 | − | 0.951921i | \(-0.400894\pi\) | ||||
0.306344 | + | 0.951921i | \(0.400894\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 35.1315 | 3.81054 | ||||||||
\(86\) | −6.17654 | −0.666034 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −9.41619 | −1.00377 | ||||||||
\(89\) | 7.39046 | 0.783387 | 0.391693 | − | 0.920096i | \(-0.371889\pi\) | ||||
0.391693 | + | 0.920096i | \(0.371889\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.91150 | 0.200380 | ||||||||
\(92\) | 3.46459 | 0.361208 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.48482 | 0.668858 | ||||||||
\(95\) | −8.81347 | −0.904243 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.7121 | 1.39226 | 0.696128 | − | 0.717917i | \(-0.254904\pi\) | ||||
0.696128 | + | 0.717917i | \(0.254904\pi\) | |||||||
\(98\) | −0.601235 | −0.0607339 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −23.5960 | −2.35960 | ||||||||
\(101\) | −1.24756 | −0.124137 | −0.0620683 | − | 0.998072i | \(-0.519770\pi\) | ||||
−0.0620683 | + | 0.998072i | \(0.519770\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.12235 | 0.504720 | 0.252360 | − | 0.967633i | \(-0.418793\pi\) | ||||
0.252360 | + | 0.967633i | \(0.418793\pi\) | |||||||
\(104\) | −4.18160 | −0.410040 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.51536 | −0.244313 | ||||||||
\(107\) | 16.0637 | 1.55293 | 0.776467 | − | 0.630157i | \(-0.217010\pi\) | ||||
0.776467 | + | 0.630157i | \(0.217010\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.30523 | −0.795496 | −0.397748 | − | 0.917495i | \(-0.630208\pi\) | ||||
−0.397748 | + | 0.917495i | \(0.630208\pi\) | |||||||
\(110\) | −11.3988 | −1.08684 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.96177 | −0.185370 | ||||||||
\(113\) | 17.1150 | 1.61004 | 0.805020 | − | 0.593247i | \(-0.202154\pi\) | ||||
0.805020 | + | 0.593247i | \(0.202154\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.31345 | 0.868484 | ||||||||
\(116\) | −6.90466 | −0.641081 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −8.64505 | −0.795841 | ||||||||
\(119\) | 7.97603 | 0.731161 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.52736 | 0.684306 | ||||||||
\(122\) | 5.07624 | 0.459581 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.71556 | 0.423470 | ||||||||
\(125\) | −41.4071 | −3.70357 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.00000 | 0.0887357 | ||||||||
\(128\) | 11.4604 | 1.01297 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −5.06207 | −0.443973 | ||||||||
\(131\) | −4.01168 | −0.350502 | −0.175251 | − | 0.984524i | \(-0.556074\pi\) | ||||
−0.175251 | + | 0.984524i | \(0.556074\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.00095 | −0.173505 | ||||||||
\(134\) | 4.52185 | 0.390628 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −17.4484 | −1.49619 | ||||||||
\(137\) | 6.88474 | 0.588203 | 0.294102 | − | 0.955774i | \(-0.404980\pi\) | ||||
0.294102 | + | 0.955774i | \(0.404980\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.93504 | −0.588222 | −0.294111 | − | 0.955771i | \(-0.595024\pi\) | ||||
−0.294111 | + | 0.955771i | \(0.595024\pi\) | |||||||
\(140\) | −7.21707 | −0.609954 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 6.20271 | 0.520520 | ||||||||
\(143\) | 8.22775 | 0.688039 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −18.5610 | −1.54141 | ||||||||
\(146\) | 2.07930 | 0.172084 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.16414 | 0.342291 | ||||||||
\(149\) | 14.3035 | 1.17179 | 0.585896 | − | 0.810386i | \(-0.300743\pi\) | ||||
0.585896 | + | 0.810386i | \(0.300743\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.87716 | 0.315519 | 0.157760 | − | 0.987478i | \(-0.449573\pi\) | ||||
0.157760 | + | 0.987478i | \(0.449573\pi\) | |||||||
\(152\) | 4.37729 | 0.355045 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.58792 | −0.208541 | ||||||||
\(155\) | 12.6763 | 1.01818 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −20.8139 | −1.66113 | −0.830565 | − | 0.556921i | \(-0.811983\pi\) | ||||
−0.830565 | + | 0.556921i | \(0.811983\pi\) | |||||||
\(158\) | −8.62271 | −0.685986 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 24.4664 | 1.93424 | ||||||||
\(161\) | 2.11447 | 0.166643 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −24.2929 | −1.90277 | −0.951383 | − | 0.308011i | \(-0.900337\pi\) | ||||
−0.951383 | + | 0.308011i | \(0.900337\pi\) | |||||||
\(164\) | −10.4021 | −0.812265 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.35601 | −0.260477 | ||||||||
\(167\) | −4.02158 | −0.311200 | −0.155600 | − | 0.987820i | \(-0.549731\pi\) | ||||
−0.155600 | + | 0.987820i | \(0.549731\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.34617 | −0.718936 | ||||||||
\(170\) | −21.1223 | −1.62000 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −16.8326 | −1.28348 | ||||||||
\(173\) | 5.91524 | 0.449727 | 0.224864 | − | 0.974390i | \(-0.427806\pi\) | ||||
0.224864 | + | 0.974390i | \(0.427806\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −14.4008 | −1.08860 | ||||||||
\(176\) | −8.44413 | −0.636500 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −4.44340 | −0.333047 | ||||||||
\(179\) | 1.75316 | 0.131038 | 0.0655188 | − | 0.997851i | \(-0.479130\pi\) | ||||
0.0655188 | + | 0.997851i | \(0.479130\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.44921 | 0.107719 | 0.0538593 | − | 0.998549i | \(-0.482848\pi\) | ||||
0.0538593 | + | 0.998549i | \(0.482848\pi\) | |||||||
\(182\) | −1.14926 | −0.0851888 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.62561 | −0.341005 | ||||||||
\(185\) | 11.1940 | 0.822998 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 34.3316 | 2.51057 | ||||||||
\(188\) | 17.6728 | 1.28892 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5.29897 | 0.384428 | ||||||||
\(191\) | −2.95252 | −0.213637 | −0.106818 | − | 0.994279i | \(-0.534066\pi\) | ||||
−0.106818 | + | 0.994279i | \(0.534066\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.5764 | 1.40914 | 0.704570 | − | 0.709634i | \(-0.251140\pi\) | ||||
0.704570 | + | 0.709634i | \(0.251140\pi\) | |||||||
\(194\) | −8.24422 | −0.591900 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.63852 | −0.117037 | ||||||||
\(197\) | −9.65828 | −0.688124 | −0.344062 | − | 0.938947i | \(-0.611803\pi\) | ||||
−0.344062 | + | 0.938947i | \(0.611803\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17.5931 | −1.24714 | −0.623570 | − | 0.781768i | \(-0.714318\pi\) | ||||
−0.623570 | + | 0.781768i | \(0.714318\pi\) | |||||||
\(200\) | 31.5033 | 2.22762 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.750075 | 0.0527751 | ||||||||
\(203\) | −4.21397 | −0.295763 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −27.9627 | −1.95300 | ||||||||
\(206\) | −3.07973 | −0.214575 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.74992 | −0.260010 | ||||||||
\(209\) | −8.61279 | −0.595759 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.30191 | −0.227313 | −0.113656 | − | 0.993520i | \(-0.536256\pi\) | ||||
−0.113656 | + | 0.993520i | \(0.536256\pi\) | |||||||
\(212\) | −6.85498 | −0.470802 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −9.65805 | −0.660210 | ||||||||
\(215\) | −45.2492 | −3.08597 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.87794 | 0.195368 | ||||||||
\(218\) | 4.99339 | 0.338195 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −31.0647 | −2.09438 | ||||||||
\(221\) | 15.2462 | 1.02557 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.9302 | 1.13373 | 0.566866 | − | 0.823810i | \(-0.308156\pi\) | ||||
0.566866 | + | 0.823810i | \(0.308156\pi\) | |||||||
\(224\) | 5.55469 | 0.371138 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −10.2901 | −0.684488 | ||||||||
\(227\) | −6.21508 | −0.412509 | −0.206255 | − | 0.978498i | \(-0.566128\pi\) | ||||
−0.206255 | + | 0.978498i | \(0.566128\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.17160 | −0.0774215 | −0.0387108 | − | 0.999250i | \(-0.512325\pi\) | ||||
−0.0387108 | + | 0.999250i | \(0.512325\pi\) | |||||||
\(230\) | −5.59957 | −0.369225 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 9.21849 | 0.605224 | ||||||||
\(233\) | 23.8516 | 1.56257 | 0.781286 | − | 0.624173i | \(-0.214564\pi\) | ||||
0.781286 | + | 0.624173i | \(0.214564\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 47.5077 | 3.09906 | ||||||||
\(236\) | −23.5599 | −1.53362 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −4.79547 | −0.310844 | ||||||||
\(239\) | −14.9800 | −0.968977 | −0.484488 | − | 0.874798i | \(-0.660994\pi\) | ||||
−0.484488 | + | 0.874798i | \(0.660994\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.1108 | −0.651291 | −0.325646 | − | 0.945492i | \(-0.605582\pi\) | ||||
−0.325646 | + | 0.945492i | \(0.605582\pi\) | |||||||
\(242\) | −4.52571 | −0.290924 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 13.8340 | 0.885632 | ||||||||
\(245\) | −4.40463 | −0.281402 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.82482 | −0.243368 | ||||||||
\(248\) | −6.29580 | −0.399784 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 24.8954 | 1.57452 | ||||||||
\(251\) | −2.23745 | −0.141227 | −0.0706135 | − | 0.997504i | \(-0.522496\pi\) | ||||
−0.0706135 | + | 0.997504i | \(0.522496\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.10138 | 0.572199 | ||||||||
\(254\) | −0.601235 | −0.0377248 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −5.72268 | −0.357667 | ||||||||
\(257\) | −9.85947 | −0.615017 | −0.307508 | − | 0.951545i | \(-0.599495\pi\) | ||||
−0.307508 | + | 0.951545i | \(0.599495\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.54141 | 0.157916 | ||||||||
\(260\) | −13.7954 | −0.855555 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.41196 | 0.149012 | ||||||||
\(263\) | 8.92520 | 0.550352 | 0.275176 | − | 0.961394i | \(-0.411264\pi\) | ||||
0.275176 | + | 0.961394i | \(0.411264\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −18.4274 | −1.13199 | ||||||||
\(266\) | 1.20304 | 0.0737633 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 12.3232 | 0.752758 | ||||||||
\(269\) | −0.300991 | −0.0183518 | −0.00917588 | − | 0.999958i | \(-0.502921\pi\) | ||||
−0.00917588 | + | 0.999958i | \(0.502921\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.19940 | −0.255095 | −0.127548 | − | 0.991832i | \(-0.540711\pi\) | ||||
−0.127548 | + | 0.991832i | \(0.540711\pi\) | |||||||
\(272\) | −15.6471 | −0.948746 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.13935 | −0.250067 | ||||||||
\(275\) | −61.9860 | −3.73790 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.0056 | 0.901600 | 0.450800 | − | 0.892625i | \(-0.351139\pi\) | ||||
0.450800 | + | 0.892625i | \(0.351139\pi\) | |||||||
\(278\) | 4.16959 | 0.250075 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 9.63559 | 0.575837 | ||||||||
\(281\) | 5.79057 | 0.345437 | 0.172718 | − | 0.984971i | \(-0.444745\pi\) | ||||
0.172718 | + | 0.984971i | \(0.444745\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 23.2225 | 1.38043 | 0.690217 | − | 0.723603i | \(-0.257515\pi\) | ||||
0.690217 | + | 0.723603i | \(0.257515\pi\) | |||||||
\(284\) | 16.9039 | 1.00306 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.94681 | −0.292511 | ||||||||
\(287\) | −6.34847 | −0.374738 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 46.6170 | 2.74218 | ||||||||
\(290\) | 11.1595 | 0.655309 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5.66662 | 0.331614 | ||||||||
\(293\) | 20.2897 | 1.18534 | 0.592668 | − | 0.805447i | \(-0.298075\pi\) | ||||
0.592668 | + | 0.805447i | \(0.298075\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −63.3335 | −3.68742 | ||||||||
\(296\) | −5.55960 | −0.323145 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −8.59979 | −0.498173 | ||||||||
\(299\) | 4.04180 | 0.233743 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.2731 | −0.592131 | ||||||||
\(302\) | −2.33109 | −0.134139 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.92541 | 0.225138 | ||||||||
\(305\) | 37.1884 | 2.12940 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.9061 | 0.964883 | 0.482442 | − | 0.875928i | \(-0.339750\pi\) | ||||
0.482442 | + | 0.875928i | \(0.339750\pi\) | |||||||
\(308\) | −7.05274 | −0.401867 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −7.62143 | −0.432868 | ||||||||
\(311\) | −10.4239 | −0.591085 | −0.295543 | − | 0.955330i | \(-0.595500\pi\) | ||||
−0.295543 | + | 0.955330i | \(0.595500\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.5137 | −1.21603 | −0.608013 | − | 0.793927i | \(-0.708033\pi\) | ||||
−0.608013 | + | 0.793927i | \(0.708033\pi\) | |||||||
\(314\) | 12.5140 | 0.706209 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −23.4991 | −1.32193 | ||||||||
\(317\) | 4.79749 | 0.269454 | 0.134727 | − | 0.990883i | \(-0.456984\pi\) | ||||
0.134727 | + | 0.990883i | \(0.456984\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −18.1384 | −1.01555 | ||||||||
\(320\) | 2.57171 | 0.143763 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.27129 | −0.0708463 | ||||||||
\(323\) | −15.9597 | −0.888020 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −27.5271 | −1.52693 | ||||||||
\(326\) | 14.6057 | 0.808937 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 13.8879 | 0.766833 | ||||||||
\(329\) | 10.7858 | 0.594642 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.8566 | −1.14638 | −0.573190 | − | 0.819422i | \(-0.694294\pi\) | ||||
−0.573190 | + | 0.819422i | \(0.694294\pi\) | |||||||
\(332\) | −9.14596 | −0.501950 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2.41792 | 0.132303 | ||||||||
\(335\) | 33.1270 | 1.80992 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.154395 | 0.00841045 | 0.00420522 | − | 0.999991i | \(-0.498661\pi\) | ||||
0.00420522 | + | 0.999991i | \(0.498661\pi\) | |||||||
\(338\) | 5.61924 | 0.305647 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −57.5635 | −3.12182 | ||||||||
\(341\) | 12.3877 | 0.670829 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 22.4735 | 1.21169 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.55645 | −0.191196 | ||||||||
\(347\) | 17.7217 | 0.951350 | 0.475675 | − | 0.879621i | \(-0.342204\pi\) | ||||
0.475675 | + | 0.879621i | \(0.342204\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.2962 | 0.658202 | 0.329101 | − | 0.944295i | \(-0.393254\pi\) | ||||
0.329101 | + | 0.944295i | \(0.393254\pi\) | |||||||
\(350\) | 8.65827 | 0.462804 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 23.9093 | 1.27437 | ||||||||
\(353\) | −16.1440 | −0.859258 | −0.429629 | − | 0.903005i | \(-0.641356\pi\) | ||||
−0.429629 | + | 0.903005i | \(0.641356\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 45.4409 | 2.41175 | ||||||||
\(356\) | −12.1094 | −0.641796 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.05406 | −0.0557089 | ||||||||
\(359\) | −10.9875 | −0.579900 | −0.289950 | − | 0.957042i | \(-0.593639\pi\) | ||||
−0.289950 | + | 0.957042i | \(0.593639\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.9962 | −0.789273 | ||||||||
\(362\) | −0.871314 | −0.0457952 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.13202 | −0.164163 | ||||||||
\(365\) | 15.2329 | 0.797327 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.7238 | 0.820778 | 0.410389 | − | 0.911911i | \(-0.365393\pi\) | ||||
0.410389 | + | 0.911911i | \(0.365393\pi\) | |||||||
\(368\) | −4.14809 | −0.216234 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −6.73022 | −0.349887 | ||||||||
\(371\) | −4.18365 | −0.217204 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.75838 | 0.194602 | 0.0973008 | − | 0.995255i | \(-0.468979\pi\) | ||||
0.0973008 | + | 0.995255i | \(0.468979\pi\) | |||||||
\(374\) | −20.6413 | −1.06734 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −23.5951 | −1.21683 | ||||||||
\(377\) | −8.05500 | −0.414853 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.46136 | 0.485997 | 0.242999 | − | 0.970027i | \(-0.421869\pi\) | ||||
0.242999 | + | 0.970027i | \(0.421869\pi\) | |||||||
\(380\) | 14.4410 | 0.740809 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.77516 | 0.0908249 | ||||||||
\(383\) | 10.3557 | 0.529150 | 0.264575 | − | 0.964365i | \(-0.414768\pi\) | ||||
0.264575 | + | 0.964365i | \(0.414768\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −18.9591 | −0.966243 | ||||||||
\(386\) | −11.7700 | −0.599078 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −22.4676 | −1.14062 | ||||||||
\(389\) | −17.0981 | −0.866907 | −0.433453 | − | 0.901176i | \(-0.642705\pi\) | ||||
−0.433453 | + | 0.901176i | \(0.642705\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.8650 | 0.852902 | ||||||||
\(392\) | 2.18760 | 0.110491 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 5.80689 | 0.292547 | ||||||||
\(395\) | −63.1698 | −3.17842 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.1102 | −1.10968 | −0.554840 | − | 0.831957i | \(-0.687220\pi\) | ||||
−0.554840 | + | 0.831957i | \(0.687220\pi\) | |||||||
\(398\) | 10.5776 | 0.530205 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 28.2511 | 1.41255 | ||||||||
\(401\) | −38.1546 | −1.90535 | −0.952675 | − | 0.303990i | \(-0.901681\pi\) | ||||
−0.952675 | + | 0.303990i | \(0.901681\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.50119 | 0.274034 | ||||||||
\(404\) | 2.04414 | 0.101700 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.53358 | 0.125740 | ||||||||
\(407\) | 10.9391 | 0.542231 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.50413 | 0.469949 | 0.234974 | − | 0.972002i | \(-0.424499\pi\) | ||||
0.234974 | + | 0.972002i | \(0.424499\pi\) | |||||||
\(410\) | 16.8121 | 0.830293 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −8.39305 | −0.413496 | ||||||||
\(413\) | −14.3788 | −0.707536 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −24.5860 | −1.20688 | ||||||||
\(416\) | 10.6178 | 0.520580 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 5.17831 | 0.253279 | ||||||||
\(419\) | −5.66006 | −0.276512 | −0.138256 | − | 0.990397i | \(-0.544150\pi\) | ||||
−0.138256 | + | 0.990397i | \(0.544150\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.0019 | −0.487462 | −0.243731 | − | 0.969843i | \(-0.578371\pi\) | ||||
−0.243731 | + | 0.969843i | \(0.578371\pi\) | |||||||
\(422\) | 1.98522 | 0.0966391 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 9.15216 | 0.444468 | ||||||||
\(425\) | −114.861 | −5.57159 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.44301 | 0.408586 | ||||||||
\(428\) | −26.3206 | −1.27225 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 27.2054 | 1.31196 | ||||||||
\(431\) | −2.95645 | −0.142407 | −0.0712036 | − | 0.997462i | \(-0.522684\pi\) | ||||
−0.0712036 | + | 0.997462i | \(0.522684\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −38.2222 | −1.83684 | −0.918420 | − | 0.395607i | \(-0.870534\pi\) | ||||
−0.918420 | + | 0.395607i | \(0.870534\pi\) | |||||||
\(434\) | −1.73032 | −0.0830580 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 13.6083 | 0.651717 | ||||||||
\(437\) | −4.23095 | −0.202394 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.57924 | 0.170828 | 0.0854140 | − | 0.996346i | \(-0.472779\pi\) | ||||
0.0854140 | + | 0.996346i | \(0.472779\pi\) | |||||||
\(440\) | 41.4749 | 1.97724 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −9.16653 | −0.436007 | ||||||||
\(443\) | 1.21879 | 0.0579064 | 0.0289532 | − | 0.999581i | \(-0.490783\pi\) | ||||
0.0289532 | + | 0.999581i | \(0.490783\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −32.5523 | −1.54313 | ||||||||
\(446\) | −10.1790 | −0.481992 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.583865 | 0.0275850 | ||||||||
\(449\) | −36.5812 | −1.72637 | −0.863186 | − | 0.504885i | \(-0.831535\pi\) | ||||
−0.863186 | + | 0.504885i | \(0.831535\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −27.3260 | −1.28673 | ||||||||
\(452\) | −28.0432 | −1.31904 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3.73672 | 0.175373 | ||||||||
\(455\) | −8.41946 | −0.394710 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.708080 | −0.0331226 | −0.0165613 | − | 0.999863i | \(-0.505272\pi\) | ||||
−0.0165613 | + | 0.999863i | \(0.505272\pi\) | |||||||
\(458\) | 0.704407 | 0.0329148 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −15.2602 | −0.711512 | ||||||||
\(461\) | 7.44049 | 0.346538 | 0.173269 | − | 0.984875i | \(-0.444567\pi\) | ||||
0.173269 | + | 0.984875i | \(0.444567\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.9967 | 1.06875 | 0.534374 | − | 0.845248i | \(-0.320548\pi\) | ||||
0.534374 | + | 0.845248i | \(0.320548\pi\) | |||||||
\(464\) | 8.26683 | 0.383778 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −14.3404 | −0.664308 | ||||||||
\(467\) | 23.3688 | 1.08138 | 0.540691 | − | 0.841222i | \(-0.318163\pi\) | ||||
0.540691 | + | 0.841222i | \(0.318163\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.52093 | 0.347284 | ||||||||
\(470\) | −28.5633 | −1.31753 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 31.4552 | 1.44784 | ||||||||
\(473\) | −44.2189 | −2.03319 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 28.8154 | 1.32214 | ||||||||
\(476\) | −13.0689 | −0.599010 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 9.00651 | 0.411948 | ||||||||
\(479\) | −10.9284 | −0.499333 | −0.249667 | − | 0.968332i | \(-0.580321\pi\) | ||||
−0.249667 | + | 0.968332i | \(0.580321\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.85790 | 0.221501 | ||||||||
\(482\) | 6.07894 | 0.276888 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −12.3337 | −0.560623 | ||||||||
\(485\) | −60.3970 | −2.74248 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.259244 | −0.0117475 | −0.00587374 | − | 0.999983i | \(-0.501870\pi\) | ||||
−0.00587374 | + | 0.999983i | \(0.501870\pi\) | |||||||
\(488\) | −18.4700 | −0.836096 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.64822 | 0.119634 | ||||||||
\(491\) | −13.2585 | −0.598346 | −0.299173 | − | 0.954199i | \(-0.596711\pi\) | ||||
−0.299173 | + | 0.954199i | \(0.596711\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −33.6107 | −1.51375 | ||||||||
\(494\) | 2.29962 | 0.103465 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.64586 | −0.253507 | ||||||||
\(497\) | 10.3166 | 0.462763 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −32.5419 | −1.45677 | −0.728387 | − | 0.685166i | \(-0.759730\pi\) | ||||
−0.728387 | + | 0.685166i | \(0.759730\pi\) | |||||||
\(500\) | 67.8463 | 3.03418 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.34524 | 0.0600408 | ||||||||
\(503\) | −39.1034 | −1.74354 | −0.871768 | − | 0.489920i | \(-0.837026\pi\) | ||||
−0.871768 | + | 0.489920i | \(0.837026\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.49503 | 0.244526 | ||||||||
\(506\) | −5.47207 | −0.243263 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.63852 | −0.0726974 | ||||||||
\(509\) | −16.7722 | −0.743414 | −0.371707 | − | 0.928350i | \(-0.621227\pi\) | ||||
−0.371707 | + | 0.928350i | \(0.621227\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.45838 | 0.152990 | ||||||||
\(512\) | −19.4802 | −0.860910 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 5.92786 | 0.261467 | ||||||||
\(515\) | −22.5621 | −0.994203 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 46.4259 | 2.04181 | ||||||||
\(518\) | −1.52799 | −0.0671358 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 18.4184 | 0.807701 | ||||||||
\(521\) | 7.87075 | 0.344824 | 0.172412 | − | 0.985025i | \(-0.444844\pi\) | ||||
0.172412 | + | 0.985025i | \(0.444844\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.7546 | 0.688899 | 0.344450 | − | 0.938805i | \(-0.388066\pi\) | ||||
0.344450 | + | 0.938805i | \(0.388066\pi\) | |||||||
\(524\) | 6.57321 | 0.287152 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.36614 | −0.233975 | ||||||||
\(527\) | 22.9546 | 0.999916 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.5290 | −0.805610 | ||||||||
\(530\) | 11.0792 | 0.481251 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3.27860 | 0.142145 | ||||||||
\(533\) | −12.1351 | −0.525629 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −70.7547 | −3.05899 | ||||||||
\(536\) | −16.4528 | −0.710653 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0.180966 | 0.00780202 | ||||||||
\(539\) | −4.30434 | −0.185401 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 24.5723 | 1.05645 | 0.528223 | − | 0.849106i | \(-0.322858\pi\) | ||||
0.528223 | + | 0.849106i | \(0.322858\pi\) | |||||||
\(542\) | 2.52482 | 0.108451 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 44.3044 | 1.89953 | ||||||||
\(545\) | 36.5815 | 1.56698 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.1043 | 0.774083 | 0.387041 | − | 0.922062i | \(-0.373497\pi\) | ||||
0.387041 | + | 0.922062i | \(0.373497\pi\) | |||||||
\(548\) | −11.2808 | −0.481890 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 37.2682 | 1.58912 | ||||||||
\(551\) | 8.43196 | 0.359213 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −14.3417 | −0.609870 | ||||||||
\(554\) | −9.02190 | −0.383304 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 11.3632 | 0.481906 | ||||||||
\(557\) | −0.484330 | −0.0205217 | −0.0102609 | − | 0.999947i | \(-0.503266\pi\) | ||||
−0.0102609 | + | 0.999947i | \(0.503266\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −19.6370 | −0.830557 | ||||||||
\(560\) | 8.64088 | 0.365144 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3.48149 | −0.146858 | ||||||||
\(563\) | −25.0910 | −1.05746 | −0.528731 | − | 0.848790i | \(-0.677332\pi\) | ||||
−0.528731 | + | 0.848790i | \(0.677332\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −75.3852 | −3.17148 | ||||||||
\(566\) | −13.9622 | −0.586874 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −22.5687 | −0.946960 | ||||||||
\(569\) | 31.4579 | 1.31878 | 0.659392 | − | 0.751799i | \(-0.270814\pi\) | ||||
0.659392 | + | 0.751799i | \(0.270814\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.3592 | 0.852007 | 0.426004 | − | 0.904721i | \(-0.359921\pi\) | ||||
0.426004 | + | 0.904721i | \(0.359921\pi\) | |||||||
\(572\) | −13.4813 | −0.563681 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3.81692 | 0.159315 | ||||||||
\(575\) | −30.4500 | −1.26985 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.95608 | −0.0814326 | −0.0407163 | − | 0.999171i | \(-0.512964\pi\) | ||||
−0.0407163 | + | 0.999171i | \(0.512964\pi\) | |||||||
\(578\) | −28.0278 | −1.16580 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 30.4125 | 1.26281 | ||||||||
\(581\) | −5.58186 | −0.231574 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −18.0079 | −0.745809 | ||||||||
\(584\) | −7.56557 | −0.313065 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −12.1989 | −0.503930 | ||||||||
\(587\) | 17.7291 | 0.731760 | 0.365880 | − | 0.930662i | \(-0.380768\pi\) | ||||
0.365880 | + | 0.930662i | \(0.380768\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.75863 | −0.237280 | ||||||||
\(590\) | 38.0783 | 1.56766 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.98566 | −0.204909 | ||||||||
\(593\) | 42.1260 | 1.72991 | 0.864954 | − | 0.501852i | \(-0.167348\pi\) | ||||
0.864954 | + | 0.501852i | \(0.167348\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −35.1315 | −1.44025 | ||||||||
\(596\) | −23.4366 | −0.960000 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2.43007 | −0.0993730 | ||||||||
\(599\) | 8.55477 | 0.349538 | 0.174769 | − | 0.984609i | \(-0.444082\pi\) | ||||
0.174769 | + | 0.984609i | \(0.444082\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.49228 | 0.224035 | 0.112017 | − | 0.993706i | \(-0.464269\pi\) | ||||
0.112017 | + | 0.993706i | \(0.464269\pi\) | |||||||
\(602\) | 6.17654 | 0.251737 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −6.35280 | −0.258492 | ||||||||
\(605\) | −33.1553 | −1.34795 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13.0024 | −0.527749 | −0.263875 | − | 0.964557i | \(-0.585001\pi\) | ||||
−0.263875 | + | 0.964557i | \(0.585001\pi\) | |||||||
\(608\) | −11.1147 | −0.450760 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −22.3590 | −0.905288 | ||||||||
\(611\) | 20.6171 | 0.834079 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.24230 | −0.373293 | −0.186646 | − | 0.982427i | \(-0.559762\pi\) | ||||
−0.186646 | + | 0.982427i | \(0.559762\pi\) | |||||||
\(614\) | −10.1645 | −0.410208 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 9.41619 | 0.379389 | ||||||||
\(617\) | −33.9563 | −1.36703 | −0.683515 | − | 0.729936i | \(-0.739550\pi\) | ||||
−0.683515 | + | 0.729936i | \(0.739550\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22.8026 | −0.916515 | −0.458258 | − | 0.888819i | \(-0.651526\pi\) | ||||
−0.458258 | + | 0.888819i | \(0.651526\pi\) | |||||||
\(620\) | −20.7703 | −0.834156 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 6.26721 | 0.251292 | ||||||||
\(623\) | −7.39046 | −0.296092 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 110.379 | 4.41517 | ||||||||
\(626\) | 12.9348 | 0.516978 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 34.1039 | 1.36090 | ||||||||
\(629\) | 20.2704 | 0.808232 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.92274 | 0.116352 | 0.0581762 | − | 0.998306i | \(-0.481471\pi\) | ||||
0.0581762 | + | 0.998306i | \(0.481471\pi\) | |||||||
\(632\) | 31.3739 | 1.24799 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −2.88442 | −0.114555 | ||||||||
\(635\) | −4.40463 | −0.174793 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.91150 | −0.0757363 | ||||||||
\(638\) | 10.9054 | 0.431750 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −50.4790 | −1.99536 | ||||||||
\(641\) | 47.5449 | 1.87791 | 0.938955 | − | 0.344040i | \(-0.111795\pi\) | ||||
0.938955 | + | 0.344040i | \(0.111795\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.78341 | −0.188639 | −0.0943197 | − | 0.995542i | \(-0.530068\pi\) | ||||
−0.0943197 | + | 0.995542i | \(0.530068\pi\) | |||||||
\(644\) | −3.46459 | −0.136524 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9.59551 | 0.377530 | ||||||||
\(647\) | −27.4077 | −1.07751 | −0.538753 | − | 0.842464i | \(-0.681104\pi\) | ||||
−0.538753 | + | 0.842464i | \(0.681104\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −61.8914 | −2.42945 | ||||||||
\(650\) | 16.5503 | 0.649155 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 39.8043 | 1.55886 | ||||||||
\(653\) | 1.65336 | 0.0647009 | 0.0323504 | − | 0.999477i | \(-0.489701\pi\) | ||||
0.0323504 | + | 0.999477i | \(0.489701\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 17.6700 | 0.690424 | ||||||||
\(656\) | 12.4542 | 0.486256 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −6.48482 | −0.252805 | ||||||||
\(659\) | −21.2478 | −0.827697 | −0.413848 | − | 0.910346i | \(-0.635816\pi\) | ||||
−0.413848 | + | 0.910346i | \(0.635816\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 33.1581 | 1.28970 | 0.644850 | − | 0.764309i | \(-0.276920\pi\) | ||||
0.644850 | + | 0.764309i | \(0.276920\pi\) | |||||||
\(662\) | 12.5397 | 0.487369 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 12.2109 | 0.473874 | ||||||||
\(665\) | 8.81347 | 0.341772 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.91029 | −0.345008 | ||||||||
\(668\) | 6.58943 | 0.254953 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −19.9171 | −0.769464 | ||||||||
\(671\) | 36.3416 | 1.40295 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.3989 | 0.439394 | 0.219697 | − | 0.975568i | \(-0.429493\pi\) | ||||
0.219697 | + | 0.975568i | \(0.429493\pi\) | |||||||
\(674\) | −0.0928278 | −0.00357559 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 15.3139 | 0.588994 | ||||||||
\(677\) | 18.8081 | 0.722852 | 0.361426 | − | 0.932401i | \(-0.382290\pi\) | ||||
0.361426 | + | 0.932401i | \(0.382290\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −13.7121 | −0.526224 | ||||||||
\(680\) | 76.8538 | 2.94721 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −7.44789 | −0.285195 | ||||||||
\(683\) | 22.0996 | 0.845619 | 0.422810 | − | 0.906219i | \(-0.361044\pi\) | ||||
0.422810 | + | 0.906219i | \(0.361044\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −30.3248 | −1.15865 | ||||||||
\(686\) | 0.601235 | 0.0229553 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 20.1534 | 0.768343 | ||||||||
\(689\) | −7.99704 | −0.304663 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.0595 | −0.382682 | −0.191341 | − | 0.981524i | \(-0.561284\pi\) | ||||
−0.191341 | + | 0.981524i | \(0.561284\pi\) | |||||||
\(692\) | −9.69222 | −0.368443 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −10.6549 | −0.404454 | ||||||||
\(695\) | 30.5463 | 1.15869 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −50.6356 | −1.91796 | ||||||||
\(698\) | −7.39292 | −0.279826 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 23.5960 | 0.891844 | ||||||||
\(701\) | −4.48043 | −0.169224 | −0.0846118 | − | 0.996414i | \(-0.526965\pi\) | ||||
−0.0846118 | + | 0.996414i | \(0.526965\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.08525 | −0.191794 | ||||||||
\(704\) | 2.51316 | 0.0947181 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9.70633 | 0.365303 | ||||||||
\(707\) | 1.24756 | 0.0469192 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.8448 | 0.632618 | 0.316309 | − | 0.948656i | \(-0.397556\pi\) | ||||
0.316309 | + | 0.948656i | \(0.397556\pi\) | |||||||
\(710\) | −27.3207 | −1.02533 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 16.1674 | 0.605898 | ||||||||
\(713\) | 6.08531 | 0.227897 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −36.2402 | −1.35531 | ||||||||
\(716\) | −2.87259 | −0.107354 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 6.60609 | 0.246537 | ||||||||
\(719\) | −12.2620 | −0.457295 | −0.228647 | − | 0.973509i | \(-0.573430\pi\) | ||||
−0.228647 | + | 0.973509i | \(0.573430\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.12235 | −0.190766 | ||||||||
\(722\) | 9.01623 | 0.335549 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.37455 | −0.0882494 | ||||||||
\(725\) | 60.6845 | 2.25377 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 50.2692 | 1.86438 | 0.932190 | − | 0.361969i | \(-0.117895\pi\) | ||||
0.932190 | + | 0.361969i | \(0.117895\pi\) | |||||||
\(728\) | 4.18160 | 0.154980 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −9.15856 | −0.338973 | ||||||||
\(731\) | −81.9385 | −3.03060 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22.1666 | 0.818742 | 0.409371 | − | 0.912368i | \(-0.365748\pi\) | ||||
0.409371 | + | 0.912368i | \(0.365748\pi\) | |||||||
\(734\) | −9.45372 | −0.348943 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 11.7452 | 0.432934 | ||||||||
\(737\) | 32.3727 | 1.19246 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.9133 | −0.511808 | −0.255904 | − | 0.966702i | \(-0.582373\pi\) | ||||
−0.255904 | + | 0.966702i | \(0.582373\pi\) | |||||||
\(740\) | −18.3415 | −0.674248 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.51536 | 0.0923416 | ||||||||
\(743\) | 42.1511 | 1.54637 | 0.773187 | − | 0.634178i | \(-0.218661\pi\) | ||||
0.773187 | + | 0.634178i | \(0.218661\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −63.0019 | −2.30821 | ||||||||
\(746\) | −2.25967 | −0.0827324 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −56.2528 | −2.05681 | ||||||||
\(749\) | −16.0637 | −0.586954 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.52694 | −0.274662 | −0.137331 | − | 0.990525i | \(-0.543852\pi\) | ||||
−0.137331 | + | 0.990525i | \(0.543852\pi\) | |||||||
\(752\) | −21.1593 | −0.771601 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 4.84294 | 0.176370 | ||||||||
\(755\) | −17.0775 | −0.621513 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −25.7235 | −0.934936 | −0.467468 | − | 0.884010i | \(-0.654834\pi\) | ||||
−0.467468 | + | 0.884010i | \(0.654834\pi\) | |||||||
\(758\) | −5.68850 | −0.206616 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −19.2804 | −0.699373 | ||||||||
\(761\) | 10.1165 | 0.366723 | 0.183361 | − | 0.983046i | \(-0.441302\pi\) | ||||
0.183361 | + | 0.983046i | \(0.441302\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.30523 | 0.300669 | ||||||||
\(764\) | 4.83775 | 0.175023 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6.22619 | −0.224961 | ||||||||
\(767\) | −27.4851 | −0.992430 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.87069 | −0.247763 | −0.123882 | − | 0.992297i | \(-0.539534\pi\) | ||||
−0.123882 | + | 0.992297i | \(0.539534\pi\) | |||||||
\(770\) | 11.3988 | 0.410786 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −32.0763 | −1.15445 | ||||||||
\(773\) | −17.8361 | −0.641520 | −0.320760 | − | 0.947160i | \(-0.603938\pi\) | ||||
−0.320760 | + | 0.947160i | \(0.603938\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −41.4447 | −1.48874 | ||||||||
\(776\) | 29.9967 | 1.07682 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 10.2800 | 0.368554 | ||||||||
\(779\) | 12.7030 | 0.455132 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 44.4062 | 1.58898 | ||||||||
\(782\) | −10.1398 | −0.362600 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.96177 | 0.0700632 | ||||||||
\(785\) | 91.6777 | 3.27212 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15.3891 | −0.548562 | −0.274281 | − | 0.961650i | \(-0.588440\pi\) | ||||
−0.274281 | + | 0.961650i | \(0.588440\pi\) | |||||||
\(788\) | 15.8252 | 0.563751 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 37.9799 | 1.35126 | ||||||||
\(791\) | −17.1150 | −0.608538 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16.1388 | 0.573106 | ||||||||
\(794\) | 13.2934 | 0.471766 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 28.8265 | 1.02173 | ||||||||
\(797\) | 39.1163 | 1.38557 | 0.692786 | − | 0.721143i | \(-0.256383\pi\) | ||||
0.692786 | + | 0.721143i | \(0.256383\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 86.0281 | 3.04346 | ||||||||
\(800\) | −79.9920 | −2.82815 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 22.9399 | 0.810035 | ||||||||
\(803\) | 14.8861 | 0.525318 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.31345 | −0.328256 | ||||||||
\(806\) | −3.30751 | −0.116502 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −2.72916 | −0.0960115 | ||||||||
\(809\) | 6.83182 | 0.240194 | 0.120097 | − | 0.992762i | \(-0.461679\pi\) | ||||
0.120097 | + | 0.992762i | \(0.461679\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 36.2145 | 1.27166 | 0.635832 | − | 0.771828i | \(-0.280657\pi\) | ||||
0.635832 | + | 0.771828i | \(0.280657\pi\) | |||||||
\(812\) | 6.90466 | 0.242306 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −6.57697 | −0.230523 | ||||||||
\(815\) | 107.001 | 3.74809 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 20.5560 | 0.719163 | ||||||||
\(818\) | −5.71421 | −0.199793 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 45.8173 | 1.60001 | ||||||||
\(821\) | −14.8622 | −0.518693 | −0.259346 | − | 0.965784i | \(-0.583507\pi\) | ||||
−0.259346 | + | 0.965784i | \(0.583507\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.4230 | 0.537611 | 0.268805 | − | 0.963195i | \(-0.413371\pi\) | ||||
0.268805 | + | 0.963195i | \(0.413371\pi\) | |||||||
\(824\) | 11.2057 | 0.390368 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.64505 | 0.300800 | ||||||||
\(827\) | 35.9214 | 1.24911 | 0.624554 | − | 0.780981i | \(-0.285281\pi\) | ||||
0.624554 | + | 0.780981i | \(0.285281\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 31.5985 | 1.09746 | 0.548730 | − | 0.836000i | \(-0.315111\pi\) | ||||
0.548730 | + | 0.836000i | \(0.315111\pi\) | |||||||
\(830\) | 14.7820 | 0.513090 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.11606 | 0.0386923 | ||||||||
\(833\) | −7.97603 | −0.276353 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 17.7136 | 0.613005 | ||||||||
\(836\) | 14.1122 | 0.488081 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3.40302 | 0.117556 | ||||||||
\(839\) | 39.5472 | 1.36532 | 0.682660 | − | 0.730736i | \(-0.260823\pi\) | ||||
0.682660 | + | 0.730736i | \(0.260823\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.2425 | −0.387671 | ||||||||
\(842\) | 6.01349 | 0.207238 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 5.41023 | 0.186228 | ||||||||
\(845\) | 41.1665 | 1.41617 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.52736 | −0.258643 | ||||||||
\(848\) | 8.20735 | 0.281842 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 69.0586 | 2.36869 | ||||||||
\(851\) | 5.37373 | 0.184209 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5.00383 | −0.171328 | −0.0856639 | − | 0.996324i | \(-0.527301\pi\) | ||||
−0.0856639 | + | 0.996324i | \(0.527301\pi\) | |||||||
\(854\) | −5.07624 | −0.173705 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 35.1410 | 1.20109 | ||||||||
\(857\) | −41.4504 | −1.41592 | −0.707959 | − | 0.706254i | \(-0.750384\pi\) | ||||
−0.707959 | + | 0.706254i | \(0.750384\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 27.5845 | 0.941171 | 0.470585 | − | 0.882354i | \(-0.344043\pi\) | ||||
0.470585 | + | 0.882354i | \(0.344043\pi\) | |||||||
\(860\) | 74.1416 | 2.52821 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.77752 | 0.0605426 | ||||||||
\(863\) | −39.6613 | −1.35009 | −0.675043 | − | 0.737778i | \(-0.735875\pi\) | ||||
−0.675043 | + | 0.737778i | \(0.735875\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −26.0545 | −0.885879 | ||||||||
\(866\) | 22.9805 | 0.780909 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4.71556 | −0.160057 | ||||||||
\(869\) | −61.7314 | −2.09410 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14.3763 | 0.487121 | ||||||||
\(872\) | −18.1685 | −0.615264 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.54379 | 0.0860451 | ||||||||
\(875\) | 41.4071 | 1.39982 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.96526 | −0.167665 | −0.0838324 | − | 0.996480i | \(-0.526716\pi\) | ||||
−0.0838324 | + | 0.996480i | \(0.526716\pi\) | |||||||
\(878\) | −2.15197 | −0.0726253 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 37.1933 | 1.25379 | ||||||||
\(881\) | −32.2888 | −1.08784 | −0.543919 | − | 0.839138i | \(-0.683060\pi\) | ||||
−0.543919 | + | 0.839138i | \(0.683060\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19.3735 | −0.651969 | −0.325984 | − | 0.945375i | \(-0.605696\pi\) | ||||
−0.325984 | + | 0.945375i | \(0.605696\pi\) | |||||||
\(884\) | −24.9811 | −0.840205 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.732779 | −0.0246182 | ||||||||
\(887\) | 2.87426 | 0.0965082 | 0.0482541 | − | 0.998835i | \(-0.484634\pi\) | ||||
0.0482541 | + | 0.998835i | \(0.484634\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.00000 | −0.0335389 | ||||||||
\(890\) | 19.5716 | 0.656040 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −27.7405 | −0.928819 | ||||||||
\(893\) | −21.5820 | −0.722213 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.72204 | −0.258119 | ||||||||
\(896\) | −11.4604 | −0.382866 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 21.9939 | 0.733946 | ||||||||
\(899\) | −12.1276 | −0.404477 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −33.3689 | −1.11168 | ||||||||
\(902\) | 16.4293 | 0.547037 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 37.4408 | 1.24526 | ||||||||
\(905\) | −6.38323 | −0.212186 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −31.5100 | −1.04627 | −0.523137 | − | 0.852249i | \(-0.675238\pi\) | ||||
−0.523137 | + | 0.852249i | \(0.675238\pi\) | |||||||
\(908\) | 10.1835 | 0.337952 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 5.06207 | 0.167806 | ||||||||
\(911\) | −8.79160 | −0.291279 | −0.145639 | − | 0.989338i | \(-0.546524\pi\) | ||||
−0.145639 | + | 0.989338i | \(0.546524\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −24.0262 | −0.795152 | ||||||||
\(914\) | 0.425722 | 0.0140816 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.91969 | 0.0634282 | ||||||||
\(917\) | 4.01168 | 0.132477 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11.9465 | 0.394079 | 0.197040 | − | 0.980396i | \(-0.436867\pi\) | ||||
0.197040 | + | 0.980396i | \(0.436867\pi\) | |||||||
\(920\) | 20.3741 | 0.671715 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −4.47348 | −0.147326 | ||||||||
\(923\) | 19.7202 | 0.649098 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −36.5984 | −1.20335 | ||||||||
\(926\) | −13.8264 | −0.454364 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −23.4073 | −0.768382 | ||||||||
\(929\) | −14.7987 | −0.485530 | −0.242765 | − | 0.970085i | \(-0.578054\pi\) | ||||
−0.242765 | + | 0.970085i | \(0.578054\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.00095 | 0.0655786 | ||||||||
\(932\) | −39.0813 | −1.28015 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −14.0502 | −0.459736 | ||||||||
\(935\) | −151.218 | −4.94536 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30.4352 | 0.994274 | 0.497137 | − | 0.867672i | \(-0.334385\pi\) | ||||
0.497137 | + | 0.867672i | \(0.334385\pi\) | |||||||
\(938\) | −4.52185 | −0.147644 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −77.8421 | −2.53893 | ||||||||
\(941\) | −57.3813 | −1.87058 | −0.935288 | − | 0.353887i | \(-0.884860\pi\) | ||||
−0.935288 | + | 0.353887i | \(0.884860\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −13.4236 | −0.437133 | ||||||||
\(944\) | 28.2079 | 0.918090 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 26.5860 | 0.864384 | ||||||||
\(947\) | 28.7119 | 0.933012 | 0.466506 | − | 0.884518i | \(-0.345513\pi\) | ||||
0.466506 | + | 0.884518i | \(0.345513\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.61069 | 0.214592 | ||||||||
\(950\) | −17.3248 | −0.562091 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 17.4484 | 0.565505 | ||||||||
\(953\) | 33.7610 | 1.09363 | 0.546814 | − | 0.837254i | \(-0.315841\pi\) | ||||
0.546814 | + | 0.837254i | \(0.315841\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 13.0048 | 0.420824 | ||||||||
\(956\) | 24.5450 | 0.793842 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 6.57056 | 0.212285 | ||||||||
\(959\) | −6.88474 | −0.222320 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.7174 | −0.732821 | ||||||||
\(962\) | −2.92074 | −0.0941685 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 16.5666 | 0.533576 | ||||||||
\(965\) | −86.2269 | −2.77574 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 28.9226 | 0.930089 | 0.465045 | − | 0.885287i | \(-0.346038\pi\) | ||||
0.465045 | + | 0.885287i | \(0.346038\pi\) | |||||||
\(968\) | 16.4669 | 0.529266 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 36.3128 | 1.16593 | ||||||||
\(971\) | −0.773763 | −0.0248312 | −0.0124156 | − | 0.999923i | \(-0.503952\pi\) | ||||
−0.0124156 | + | 0.999923i | \(0.503952\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.93504 | 0.222327 | ||||||||
\(974\) | 0.155867 | 0.00499430 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −16.5633 | −0.530177 | ||||||||
\(977\) | 18.8567 | 0.603278 | 0.301639 | − | 0.953422i | \(-0.402466\pi\) | ||||
0.301639 | + | 0.953422i | \(0.402466\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −31.8111 | −1.01669 | ||||||||
\(980\) | 7.21707 | 0.230541 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 7.97145 | 0.254379 | ||||||||
\(983\) | −4.28493 | −0.136668 | −0.0683340 | − | 0.997663i | \(-0.521768\pi\) | ||||
−0.0683340 | + | 0.997663i | \(0.521768\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 42.5412 | 1.35547 | ||||||||
\(986\) | 20.2079 | 0.643552 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6.26703 | 0.199381 | ||||||||
\(989\) | −21.7221 | −0.690723 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.52397 | 0.0484105 | 0.0242052 | − | 0.999707i | \(-0.492294\pi\) | ||||
0.0242052 | + | 0.999707i | \(0.492294\pi\) | |||||||
\(992\) | 15.9861 | 0.507559 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −6.20271 | −0.196738 | ||||||||
\(995\) | 77.4910 | 2.45663 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −35.2873 | −1.11756 | −0.558780 | − | 0.829316i | \(-0.688730\pi\) | ||||
−0.558780 | + | 0.829316i | \(0.688730\pi\) | |||||||
\(998\) | 19.5653 | 0.619329 | ||||||||
\(999\) | 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 | 8001.2.a.q.1.7 | 15 | ||
3.2 | odd | 2 | 889.2.a.b.1.9 | ✓ | 15 | ||
21.20 | even | 2 | 6223.2.a.j.1.9 | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
889.2.a.b.1.9 | ✓ | 15 | 3.2 | odd | 2 | ||
6223.2.a.j.1.9 | 15 | 21.20 | even | 2 | |||
8001.2.a.q.1.7 | 15 | 1.1 | even | 1 | trivial |