Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6003,2,Mod(1,6003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6003, 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("6003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6003 = 3^{2} \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6003.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: | \(47.9341963334\) |
Analytic rank: | \(1\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 4 x^{12} - 11 x^{11} + 58 x^{10} + 24 x^{9} - 298 x^{8} + 97 x^{7} + 641 x^{6} - 402 x^{5} + \cdots - 40 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 667) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(1.30511\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6003.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.30511 | −0.922853 | −0.461426 | − | 0.887178i | \(-0.652662\pi\) | ||||
−0.461426 | + | 0.887178i | \(0.652662\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.296685 | −0.148343 | ||||||||
\(5\) | −0.572849 | −0.256186 | −0.128093 | − | 0.991762i | \(-0.540886\pi\) | ||||
−0.128093 | + | 0.991762i | \(0.540886\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.21746 | 0.460155 | 0.230078 | − | 0.973172i | \(-0.426102\pi\) | ||||
0.230078 | + | 0.973172i | \(0.426102\pi\) | |||||||
\(8\) | 2.99743 | 1.05975 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.747631 | 0.236422 | ||||||||
\(11\) | 3.82178 | 1.15231 | 0.576155 | − | 0.817340i | \(-0.304552\pi\) | ||||
0.576155 | + | 0.817340i | \(0.304552\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.55748 | 0.431967 | 0.215984 | − | 0.976397i | \(-0.430704\pi\) | ||||
0.215984 | + | 0.976397i | \(0.430704\pi\) | |||||||
\(14\) | −1.58892 | −0.424656 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.31861 | −0.829652 | ||||||||
\(17\) | −3.24470 | −0.786954 | −0.393477 | − | 0.919334i | \(-0.628728\pi\) | ||||
−0.393477 | + | 0.919334i | \(0.628728\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.65905 | 1.75711 | 0.878553 | − | 0.477644i | \(-0.158509\pi\) | ||||
0.878553 | + | 0.477644i | \(0.158509\pi\) | |||||||
\(20\) | 0.169956 | 0.0380033 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.98785 | −1.06341 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.67184 | −0.934369 | ||||||||
\(26\) | −2.03268 | −0.398642 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.361201 | −0.0682606 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.54445 | −1.71423 | −0.857117 | − | 0.515123i | \(-0.827746\pi\) | ||||
−0.857117 | + | 0.515123i | \(0.827746\pi\) | |||||||
\(32\) | −1.66371 | −0.294105 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.23469 | 0.726243 | ||||||||
\(35\) | −0.697418 | −0.117885 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.96920 | −0.981330 | −0.490665 | − | 0.871348i | \(-0.663246\pi\) | ||||
−0.490665 | + | 0.871348i | \(0.663246\pi\) | |||||||
\(38\) | −9.99591 | −1.62155 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.71707 | −0.271493 | ||||||||
\(41\) | 2.82463 | 0.441133 | 0.220566 | − | 0.975372i | \(-0.429209\pi\) | ||||
0.220566 | + | 0.975372i | \(0.429209\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.8023 | −1.79983 | −0.899914 | − | 0.436067i | \(-0.856371\pi\) | ||||
−0.899914 | + | 0.436067i | \(0.856371\pi\) | |||||||
\(44\) | −1.13387 | −0.170937 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.30511 | −0.192428 | ||||||||
\(47\) | −0.392305 | −0.0572236 | −0.0286118 | − | 0.999591i | \(-0.509109\pi\) | ||||
−0.0286118 | + | 0.999591i | \(0.509109\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.51780 | −0.788257 | ||||||||
\(50\) | 6.09728 | 0.862285 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.462081 | −0.0640792 | ||||||||
\(53\) | −11.2317 | −1.54279 | −0.771394 | − | 0.636358i | \(-0.780440\pi\) | ||||
−0.771394 | + | 0.636358i | \(0.780440\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.18930 | −0.295205 | ||||||||
\(56\) | 3.64924 | 0.487650 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.30511 | 0.171369 | ||||||||
\(59\) | 13.0256 | 1.69579 | 0.847896 | − | 0.530162i | \(-0.177869\pi\) | ||||
0.847896 | + | 0.530162i | \(0.177869\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.25323 | 1.18475 | 0.592377 | − | 0.805661i | \(-0.298190\pi\) | ||||
0.592377 | + | 0.805661i | \(0.298190\pi\) | |||||||
\(62\) | 12.4566 | 1.58198 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.80854 | 1.10107 | ||||||||
\(65\) | −0.892200 | −0.110664 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.1462 | −1.23955 | −0.619776 | − | 0.784779i | \(-0.712777\pi\) | ||||
−0.619776 | + | 0.784779i | \(0.712777\pi\) | |||||||
\(68\) | 0.962653 | 0.116739 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.910208 | 0.108791 | ||||||||
\(71\) | −10.3791 | −1.23178 | −0.615889 | − | 0.787833i | \(-0.711203\pi\) | ||||
−0.615889 | + | 0.787833i | \(0.711203\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.55044 | −0.298506 | −0.149253 | − | 0.988799i | \(-0.547687\pi\) | ||||
−0.149253 | + | 0.988799i | \(0.547687\pi\) | |||||||
\(74\) | 7.79047 | 0.905624 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.27233 | −0.260654 | ||||||||
\(77\) | 4.65285 | 0.530241 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.852395 | 0.0959019 | 0.0479510 | − | 0.998850i | \(-0.484731\pi\) | ||||
0.0479510 | + | 0.998850i | \(0.484731\pi\) | |||||||
\(80\) | 1.90106 | 0.212545 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.68645 | −0.407101 | ||||||||
\(83\) | 0.606412 | 0.0665624 | 0.0332812 | − | 0.999446i | \(-0.489404\pi\) | ||||
0.0332812 | + | 0.999446i | \(0.489404\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.85872 | 0.201606 | ||||||||
\(86\) | 15.4033 | 1.66098 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 11.4555 | 1.22116 | ||||||||
\(89\) | −3.82257 | −0.405192 | −0.202596 | − | 0.979262i | \(-0.564938\pi\) | ||||
−0.202596 | + | 0.979262i | \(0.564938\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.89616 | 0.198772 | ||||||||
\(92\) | −0.296685 | −0.0309316 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.512002 | 0.0528090 | ||||||||
\(95\) | −4.38748 | −0.450146 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.13466 | 0.521346 | 0.260673 | − | 0.965427i | \(-0.416056\pi\) | ||||
0.260673 | + | 0.965427i | \(0.416056\pi\) | |||||||
\(98\) | 7.20134 | 0.727445 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.38607 | 0.138607 | ||||||||
\(101\) | 11.9061 | 1.18470 | 0.592349 | − | 0.805682i | \(-0.298201\pi\) | ||||
0.592349 | + | 0.805682i | \(0.298201\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.70761 | 0.365322 | 0.182661 | − | 0.983176i | \(-0.441529\pi\) | ||||
0.182661 | + | 0.983176i | \(0.441529\pi\) | |||||||
\(104\) | 4.66844 | 0.457778 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 14.6586 | 1.42377 | ||||||||
\(107\) | −9.65894 | −0.933765 | −0.466882 | − | 0.884319i | \(-0.654623\pi\) | ||||
−0.466882 | + | 0.884319i | \(0.654623\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.5404 | 1.00959 | 0.504794 | − | 0.863240i | \(-0.331568\pi\) | ||||
0.504794 | + | 0.863240i | \(0.331568\pi\) | |||||||
\(110\) | 2.85728 | 0.272431 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.04026 | −0.381769 | ||||||||
\(113\) | −17.8383 | −1.67809 | −0.839045 | − | 0.544062i | \(-0.816886\pi\) | ||||
−0.839045 | + | 0.544062i | \(0.816886\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.572849 | −0.0534184 | ||||||||
\(116\) | 0.296685 | 0.0275465 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −16.9999 | −1.56497 | ||||||||
\(119\) | −3.95028 | −0.362121 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.60600 | 0.327818 | ||||||||
\(122\) | −12.0765 | −1.09335 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.83170 | 0.254294 | ||||||||
\(125\) | 5.54050 | 0.495558 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.21224 | 0.728718 | 0.364359 | − | 0.931258i | \(-0.381288\pi\) | ||||
0.364359 | + | 0.931258i | \(0.381288\pi\) | |||||||
\(128\) | −8.16870 | −0.722018 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.16442 | 0.102126 | ||||||||
\(131\) | −20.3674 | −1.77951 | −0.889754 | − | 0.456441i | \(-0.849124\pi\) | ||||
−0.889754 | + | 0.456441i | \(0.849124\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.32456 | 0.808542 | ||||||||
\(134\) | 13.2419 | 1.14392 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −9.72575 | −0.833976 | ||||||||
\(137\) | −3.66808 | −0.313385 | −0.156693 | − | 0.987647i | \(-0.550083\pi\) | ||||
−0.156693 | + | 0.987647i | \(0.550083\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.77997 | −0.829526 | −0.414763 | − | 0.909929i | \(-0.636136\pi\) | ||||
−0.414763 | + | 0.909929i | \(0.636136\pi\) | |||||||
\(140\) | 0.206914 | 0.0174874 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 13.5459 | 1.13675 | ||||||||
\(143\) | 5.95235 | 0.497760 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.572849 | 0.0475725 | ||||||||
\(146\) | 3.32860 | 0.275477 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.77097 | 0.145573 | ||||||||
\(149\) | 14.7501 | 1.20837 | 0.604187 | − | 0.796843i | \(-0.293498\pi\) | ||||
0.604187 | + | 0.796843i | \(0.293498\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.30674 | 0.187720 | 0.0938601 | − | 0.995585i | \(-0.470079\pi\) | ||||
0.0938601 | + | 0.995585i | \(0.470079\pi\) | |||||||
\(152\) | 22.9575 | 1.86210 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −6.07249 | −0.489335 | ||||||||
\(155\) | 5.46752 | 0.439162 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.57476 | −0.684341 | −0.342170 | − | 0.939638i | \(-0.611162\pi\) | ||||
−0.342170 | + | 0.939638i | \(0.611162\pi\) | |||||||
\(158\) | −1.11247 | −0.0885034 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.953053 | 0.0753454 | ||||||||
\(161\) | 1.21746 | 0.0959490 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.09710 | 0.634214 | 0.317107 | − | 0.948390i | \(-0.397289\pi\) | ||||
0.317107 | + | 0.948390i | \(0.397289\pi\) | |||||||
\(164\) | −0.838025 | −0.0654388 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.791435 | −0.0614273 | ||||||||
\(167\) | −16.3123 | −1.26228 | −0.631141 | − | 0.775668i | \(-0.717413\pi\) | ||||
−0.631141 | + | 0.775668i | \(0.717413\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.5743 | −0.813404 | ||||||||
\(170\) | −2.42584 | −0.186053 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.50156 | 0.266991 | ||||||||
\(173\) | −8.46918 | −0.643900 | −0.321950 | − | 0.946757i | \(-0.604338\pi\) | ||||
−0.321950 | + | 0.946757i | \(0.604338\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.68777 | −0.429955 | ||||||||
\(176\) | −12.6830 | −0.956016 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 4.98888 | 0.373932 | ||||||||
\(179\) | −11.0527 | −0.826120 | −0.413060 | − | 0.910704i | \(-0.635540\pi\) | ||||
−0.413060 | + | 0.910704i | \(0.635540\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.3254 | 1.65943 | 0.829716 | − | 0.558185i | \(-0.188502\pi\) | ||||
0.829716 | + | 0.558185i | \(0.188502\pi\) | |||||||
\(182\) | −2.47470 | −0.183437 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.99743 | 0.220973 | ||||||||
\(185\) | 3.41945 | 0.251403 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.4005 | −0.906815 | ||||||||
\(188\) | 0.116391 | 0.00848870 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5.72614 | 0.415418 | ||||||||
\(191\) | 0.112731 | 0.00815694 | 0.00407847 | − | 0.999992i | \(-0.498702\pi\) | ||||
0.00407847 | + | 0.999992i | \(0.498702\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.9894 | −1.07896 | −0.539480 | − | 0.841998i | \(-0.681379\pi\) | ||||
−0.539480 | + | 0.841998i | \(0.681379\pi\) | |||||||
\(194\) | −6.70131 | −0.481126 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.63705 | 0.116932 | ||||||||
\(197\) | 14.4378 | 1.02865 | 0.514326 | − | 0.857595i | \(-0.328042\pi\) | ||||
0.514326 | + | 0.857595i | \(0.328042\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.3497 | −1.30078 | −0.650389 | − | 0.759601i | \(-0.725394\pi\) | ||||
−0.650389 | + | 0.759601i | \(0.725394\pi\) | |||||||
\(200\) | −14.0035 | −0.990199 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −15.5387 | −1.09330 | ||||||||
\(203\) | −1.21746 | −0.0854487 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.61808 | −0.113012 | ||||||||
\(206\) | −4.83884 | −0.337138 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −5.16866 | −0.358382 | ||||||||
\(209\) | 29.2712 | 2.02473 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.48555 | 0.584170 | 0.292085 | − | 0.956392i | \(-0.405651\pi\) | ||||
0.292085 | + | 0.956392i | \(0.405651\pi\) | |||||||
\(212\) | 3.33227 | 0.228861 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 12.6060 | 0.861727 | ||||||||
\(215\) | 6.76091 | 0.461090 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −11.6199 | −0.788813 | ||||||||
\(218\) | −13.7564 | −0.931701 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.649533 | 0.0437915 | ||||||||
\(221\) | −5.05355 | −0.339938 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.93065 | 0.531076 | 0.265538 | − | 0.964100i | \(-0.414450\pi\) | ||||
0.265538 | + | 0.964100i | \(0.414450\pi\) | |||||||
\(224\) | −2.02549 | −0.135334 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 23.2810 | 1.54863 | ||||||||
\(227\) | 26.6251 | 1.76717 | 0.883584 | − | 0.468273i | \(-0.155123\pi\) | ||||
0.883584 | + | 0.468273i | \(0.155123\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.1498 | 1.46370 | 0.731850 | − | 0.681465i | \(-0.238657\pi\) | ||||
0.731850 | + | 0.681465i | \(0.238657\pi\) | |||||||
\(230\) | 0.747631 | 0.0492973 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.99743 | −0.196791 | ||||||||
\(233\) | −4.06717 | −0.266449 | −0.133225 | − | 0.991086i | \(-0.542533\pi\) | ||||
−0.133225 | + | 0.991086i | \(0.542533\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.224732 | 0.0146599 | ||||||||
\(236\) | −3.86451 | −0.251558 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 5.15555 | 0.334185 | ||||||||
\(239\) | −7.55588 | −0.488749 | −0.244375 | − | 0.969681i | \(-0.578583\pi\) | ||||
−0.244375 | + | 0.969681i | \(0.578583\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.65618 | 0.428762 | 0.214381 | − | 0.976750i | \(-0.431227\pi\) | ||||
0.214381 | + | 0.976750i | \(0.431227\pi\) | |||||||
\(242\) | −4.70623 | −0.302528 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.74530 | −0.175750 | ||||||||
\(245\) | 3.16086 | 0.201940 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.9288 | 0.759012 | ||||||||
\(248\) | −28.6088 | −1.81666 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −7.23097 | −0.457327 | ||||||||
\(251\) | 3.90001 | 0.246166 | 0.123083 | − | 0.992396i | \(-0.460722\pi\) | ||||
0.123083 | + | 0.992396i | \(0.460722\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.82178 | 0.240273 | ||||||||
\(254\) | −10.7179 | −0.672500 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −6.95601 | −0.434751 | ||||||||
\(257\) | 9.77946 | 0.610026 | 0.305013 | − | 0.952348i | \(-0.401339\pi\) | ||||
0.305013 | + | 0.952348i | \(0.401339\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.26724 | −0.451564 | ||||||||
\(260\) | 0.264703 | 0.0164162 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 26.5817 | 1.64222 | ||||||||
\(263\) | −14.2353 | −0.877784 | −0.438892 | − | 0.898540i | \(-0.644629\pi\) | ||||
−0.438892 | + | 0.898540i | \(0.644629\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.43404 | 0.395240 | ||||||||
\(266\) | −12.1696 | −0.746165 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.01022 | 0.183878 | ||||||||
\(269\) | 19.0080 | 1.15894 | 0.579470 | − | 0.814993i | \(-0.303259\pi\) | ||||
0.579470 | + | 0.814993i | \(0.303259\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −26.6085 | −1.61635 | −0.808176 | − | 0.588941i | \(-0.799545\pi\) | ||||
−0.808176 | + | 0.588941i | \(0.799545\pi\) | |||||||
\(272\) | 10.7679 | 0.652898 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.78725 | 0.289208 | ||||||||
\(275\) | −17.8548 | −1.07668 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.9717 | −0.659224 | −0.329612 | − | 0.944116i | \(-0.606918\pi\) | ||||
−0.329612 | + | 0.944116i | \(0.606918\pi\) | |||||||
\(278\) | 12.7639 | 0.765530 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.09046 | −0.124929 | ||||||||
\(281\) | −28.0886 | −1.67563 | −0.837813 | − | 0.545957i | \(-0.816166\pi\) | ||||
−0.837813 | + | 0.545957i | \(0.816166\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.51705 | −0.506286 | −0.253143 | − | 0.967429i | \(-0.581464\pi\) | ||||
−0.253143 | + | 0.967429i | \(0.581464\pi\) | |||||||
\(284\) | 3.07934 | 0.182725 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7.76847 | −0.459359 | ||||||||
\(287\) | 3.43886 | 0.202989 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.47195 | −0.380703 | ||||||||
\(290\) | −0.747631 | −0.0439024 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.756677 | 0.0442812 | ||||||||
\(293\) | −25.2762 | −1.47665 | −0.738326 | − | 0.674444i | \(-0.764383\pi\) | ||||
−0.738326 | + | 0.674444i | \(0.764383\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.46171 | −0.434438 | ||||||||
\(296\) | −17.8923 | −1.03997 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −19.2505 | −1.11515 | ||||||||
\(299\) | 1.55748 | 0.0900714 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −14.3687 | −0.828200 | ||||||||
\(302\) | −3.01056 | −0.173238 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −25.4174 | −1.45779 | ||||||||
\(305\) | −5.30070 | −0.303517 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.8941 | −0.621759 | −0.310880 | − | 0.950449i | \(-0.600624\pi\) | ||||
−0.310880 | + | 0.950449i | \(0.600624\pi\) | |||||||
\(308\) | −1.38043 | −0.0786574 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −7.13572 | −0.405282 | ||||||||
\(311\) | −15.0844 | −0.855358 | −0.427679 | − | 0.903931i | \(-0.640669\pi\) | ||||
−0.427679 | + | 0.903931i | \(0.640669\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.08345 | 0.174287 | 0.0871434 | − | 0.996196i | \(-0.472226\pi\) | ||||
0.0871434 | + | 0.996196i | \(0.472226\pi\) | |||||||
\(314\) | 11.1910 | 0.631546 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.252893 | −0.0142263 | ||||||||
\(317\) | −20.7123 | −1.16332 | −0.581659 | − | 0.813433i | \(-0.697596\pi\) | ||||
−0.581659 | + | 0.813433i | \(0.697596\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.82178 | −0.213979 | ||||||||
\(320\) | −5.04596 | −0.282078 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.58892 | −0.0885468 | ||||||||
\(323\) | −24.8513 | −1.38276 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.27630 | −0.403617 | ||||||||
\(326\) | −10.5676 | −0.585286 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 8.46662 | 0.467491 | ||||||||
\(329\) | −0.477615 | −0.0263317 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 31.9172 | 1.75433 | 0.877165 | − | 0.480189i | \(-0.159432\pi\) | ||||
0.877165 | + | 0.480189i | \(0.159432\pi\) | |||||||
\(332\) | −0.179913 | −0.00987404 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 21.2893 | 1.16490 | ||||||||
\(335\) | 5.81222 | 0.317556 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.63778 | 0.416056 | 0.208028 | − | 0.978123i | \(-0.433295\pi\) | ||||
0.208028 | + | 0.978123i | \(0.433295\pi\) | |||||||
\(338\) | 13.8006 | 0.750652 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.551455 | −0.0299068 | ||||||||
\(341\) | −36.4768 | −1.97533 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.2399 | −0.822876 | ||||||||
\(344\) | −35.3764 | −1.90737 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 11.0532 | 0.594225 | ||||||||
\(347\) | 6.79169 | 0.364597 | 0.182298 | − | 0.983243i | \(-0.441646\pi\) | ||||
0.182298 | + | 0.983243i | \(0.441646\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.0456 | 0.698316 | 0.349158 | − | 0.937064i | \(-0.386468\pi\) | ||||
0.349158 | + | 0.937064i | \(0.386468\pi\) | |||||||
\(350\) | 7.42317 | 0.396785 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −6.35832 | −0.338900 | ||||||||
\(353\) | 17.8334 | 0.949176 | 0.474588 | − | 0.880208i | \(-0.342597\pi\) | ||||
0.474588 | + | 0.880208i | \(0.342597\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.94568 | 0.315564 | ||||||||
\(356\) | 1.13410 | 0.0601072 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 14.4250 | 0.762387 | ||||||||
\(359\) | 0.664618 | 0.0350772 | 0.0175386 | − | 0.999846i | \(-0.494417\pi\) | ||||
0.0175386 | + | 0.999846i | \(0.494417\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 39.6610 | 2.08742 | ||||||||
\(362\) | −29.1371 | −1.53141 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.562564 | −0.0294864 | ||||||||
\(365\) | 1.46101 | 0.0764730 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.77513 | −0.405859 | −0.202929 | − | 0.979193i | \(-0.565046\pi\) | ||||
−0.202929 | + | 0.979193i | \(0.565046\pi\) | |||||||
\(368\) | −3.31861 | −0.172994 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −4.46276 | −0.232008 | ||||||||
\(371\) | −13.6741 | −0.709922 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.25735 | −0.323993 | −0.161997 | − | 0.986791i | \(-0.551793\pi\) | ||||
−0.161997 | + | 0.986791i | \(0.551793\pi\) | |||||||
\(374\) | 16.1840 | 0.836857 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.17591 | −0.0606428 | ||||||||
\(377\) | −1.55748 | −0.0802143 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.9416 | −0.870231 | −0.435116 | − | 0.900375i | \(-0.643293\pi\) | ||||
−0.435116 | + | 0.900375i | \(0.643293\pi\) | |||||||
\(380\) | 1.30170 | 0.0667758 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −0.147127 | −0.00752765 | ||||||||
\(383\) | 8.01241 | 0.409415 | 0.204707 | − | 0.978823i | \(-0.434376\pi\) | ||||
0.204707 | + | 0.978823i | \(0.434376\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.66538 | −0.135840 | ||||||||
\(386\) | 19.5628 | 0.995722 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.52338 | −0.0773379 | ||||||||
\(389\) | −11.0961 | −0.562595 | −0.281297 | − | 0.959621i | \(-0.590765\pi\) | ||||
−0.281297 | + | 0.959621i | \(0.590765\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.24470 | −0.164091 | ||||||||
\(392\) | −16.5392 | −0.835357 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −18.8429 | −0.949294 | ||||||||
\(395\) | −0.488293 | −0.0245687 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.7848 | 0.942780 | 0.471390 | − | 0.881925i | \(-0.343752\pi\) | ||||
0.471390 | + | 0.881925i | \(0.343752\pi\) | |||||||
\(398\) | 23.9484 | 1.20043 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 15.5040 | 0.775201 | ||||||||
\(401\) | 8.32239 | 0.415600 | 0.207800 | − | 0.978171i | \(-0.433370\pi\) | ||||
0.207800 | + | 0.978171i | \(0.433370\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −14.8653 | −0.740493 | ||||||||
\(404\) | −3.53235 | −0.175741 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.58892 | 0.0788566 | ||||||||
\(407\) | −22.8130 | −1.13080 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −21.5434 | −1.06525 | −0.532627 | − | 0.846350i | \(-0.678795\pi\) | ||||
−0.532627 | + | 0.846350i | \(0.678795\pi\) | |||||||
\(410\) | 2.11178 | 0.104293 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.09999 | −0.0541928 | ||||||||
\(413\) | 15.8581 | 0.780328 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.347382 | −0.0170523 | ||||||||
\(416\) | −2.59119 | −0.127044 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −38.2022 | −1.86853 | ||||||||
\(419\) | 12.6654 | 0.618746 | 0.309373 | − | 0.950941i | \(-0.399881\pi\) | ||||
0.309373 | + | 0.950941i | \(0.399881\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.796006 | 0.0387950 | 0.0193975 | − | 0.999812i | \(-0.493825\pi\) | ||||
0.0193975 | + | 0.999812i | \(0.493825\pi\) | |||||||
\(422\) | −11.0746 | −0.539103 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −33.6661 | −1.63497 | ||||||||
\(425\) | 15.1587 | 0.735306 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.2654 | 0.545171 | ||||||||
\(428\) | 2.86566 | 0.138517 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −8.82374 | −0.425518 | ||||||||
\(431\) | −32.6597 | −1.57316 | −0.786580 | − | 0.617488i | \(-0.788151\pi\) | ||||
−0.786580 | + | 0.617488i | \(0.788151\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.5971 | 0.509266 | 0.254633 | − | 0.967038i | \(-0.418045\pi\) | ||||
0.254633 | + | 0.967038i | \(0.418045\pi\) | |||||||
\(434\) | 15.1653 | 0.727959 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.12718 | −0.149765 | ||||||||
\(437\) | 7.65905 | 0.366382 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 29.6100 | 1.41321 | 0.706604 | − | 0.707609i | \(-0.250226\pi\) | ||||
0.706604 | + | 0.707609i | \(0.250226\pi\) | |||||||
\(440\) | −6.56228 | −0.312844 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6.59544 | 0.313713 | ||||||||
\(443\) | 34.0175 | 1.61622 | 0.808111 | − | 0.589031i | \(-0.200490\pi\) | ||||
0.808111 | + | 0.589031i | \(0.200490\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.18975 | 0.103804 | ||||||||
\(446\) | −10.3504 | −0.490105 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 10.7240 | 0.506662 | ||||||||
\(449\) | −38.7800 | −1.83014 | −0.915071 | − | 0.403292i | \(-0.867866\pi\) | ||||
−0.915071 | + | 0.403292i | \(0.867866\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.7951 | 0.508322 | ||||||||
\(452\) | 5.29237 | 0.248932 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −34.7487 | −1.63084 | ||||||||
\(455\) | −1.08621 | −0.0509225 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −20.0321 | −0.937064 | −0.468532 | − | 0.883447i | \(-0.655217\pi\) | ||||
−0.468532 | + | 0.883447i | \(0.655217\pi\) | |||||||
\(458\) | −28.9080 | −1.35078 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.169956 | 0.00792423 | ||||||||
\(461\) | 12.2868 | 0.572252 | 0.286126 | − | 0.958192i | \(-0.407632\pi\) | ||||
0.286126 | + | 0.958192i | \(0.407632\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −37.8812 | −1.76049 | −0.880245 | − | 0.474520i | \(-0.842622\pi\) | ||||
−0.880245 | + | 0.474520i | \(0.842622\pi\) | |||||||
\(464\) | 3.31861 | 0.154062 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.30811 | 0.245893 | ||||||||
\(467\) | −0.782271 | −0.0361992 | −0.0180996 | − | 0.999836i | \(-0.505762\pi\) | ||||
−0.0180996 | + | 0.999836i | \(0.505762\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.3525 | −0.570386 | ||||||||
\(470\) | −0.293300 | −0.0135289 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 39.0434 | 1.79712 | ||||||||
\(473\) | −45.1057 | −2.07396 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −35.7819 | −1.64179 | ||||||||
\(476\) | 1.17199 | 0.0537180 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 9.86126 | 0.451044 | ||||||||
\(479\) | −7.13285 | −0.325908 | −0.162954 | − | 0.986634i | \(-0.552102\pi\) | ||||
−0.162954 | + | 0.986634i | \(0.552102\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.29691 | −0.423903 | ||||||||
\(482\) | −8.68705 | −0.395684 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.06985 | −0.0486294 | ||||||||
\(485\) | −2.94139 | −0.133561 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18.0659 | −0.818644 | −0.409322 | − | 0.912390i | \(-0.634235\pi\) | ||||
−0.409322 | + | 0.912390i | \(0.634235\pi\) | |||||||
\(488\) | 27.7359 | 1.25555 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −4.12528 | −0.186361 | ||||||||
\(491\) | 1.19496 | 0.0539278 | 0.0269639 | − | 0.999636i | \(-0.491416\pi\) | ||||
0.0269639 | + | 0.999636i | \(0.491416\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.24470 | 0.146134 | ||||||||
\(494\) | −15.5684 | −0.700457 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 31.6743 | 1.42222 | ||||||||
\(497\) | −12.6362 | −0.566809 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 22.2895 | 0.997815 | 0.498907 | − | 0.866655i | \(-0.333735\pi\) | ||||
0.498907 | + | 0.866655i | \(0.333735\pi\) | |||||||
\(500\) | −1.64379 | −0.0735123 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −5.08994 | −0.227175 | ||||||||
\(503\) | 13.3652 | 0.595924 | 0.297962 | − | 0.954578i | \(-0.403693\pi\) | ||||
0.297962 | + | 0.954578i | \(0.403693\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.82037 | −0.303503 | ||||||||
\(506\) | −4.98785 | −0.221737 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.43645 | −0.108100 | ||||||||
\(509\) | −1.42116 | −0.0629917 | −0.0314958 | − | 0.999504i | \(-0.510027\pi\) | ||||
−0.0314958 | + | 0.999504i | \(0.510027\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.10505 | −0.137359 | ||||||||
\(512\) | 25.4158 | 1.12323 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −12.7633 | −0.562964 | ||||||||
\(515\) | −2.12390 | −0.0935901 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.49930 | −0.0659393 | ||||||||
\(518\) | 9.48456 | 0.416727 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.67431 | −0.117276 | ||||||||
\(521\) | 0.459592 | 0.0201351 | 0.0100675 | − | 0.999949i | \(-0.496795\pi\) | ||||
0.0100675 | + | 0.999949i | \(0.496795\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −28.7937 | −1.25906 | −0.629530 | − | 0.776976i | \(-0.716753\pi\) | ||||
−0.629530 | + | 0.776976i | \(0.716753\pi\) | |||||||
\(524\) | 6.04271 | 0.263977 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 18.5786 | 0.810066 | ||||||||
\(527\) | 30.9688 | 1.34902 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −8.39714 | −0.364748 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.76646 | −0.119941 | ||||||||
\(533\) | 4.39930 | 0.190555 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.53311 | 0.239217 | ||||||||
\(536\) | −30.4124 | −1.31362 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −24.8076 | −1.06953 | ||||||||
\(539\) | −21.0878 | −0.908317 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.0629 | −0.432639 | −0.216320 | − | 0.976323i | \(-0.569405\pi\) | ||||
−0.216320 | + | 0.976323i | \(0.569405\pi\) | |||||||
\(542\) | 34.7271 | 1.49165 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5.39822 | 0.231447 | ||||||||
\(545\) | −6.03806 | −0.258642 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 37.1617 | 1.58892 | 0.794460 | − | 0.607317i | \(-0.207754\pi\) | ||||
0.794460 | + | 0.607317i | \(0.207754\pi\) | |||||||
\(548\) | 1.08827 | 0.0464884 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 23.3024 | 0.993620 | ||||||||
\(551\) | −7.65905 | −0.326287 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.03775 | 0.0441298 | ||||||||
\(554\) | 14.3193 | 0.608367 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.90157 | 0.123054 | ||||||||
\(557\) | −23.4235 | −0.992486 | −0.496243 | − | 0.868184i | \(-0.665287\pi\) | ||||
−0.496243 | + | 0.868184i | \(0.665287\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −18.3818 | −0.777467 | ||||||||
\(560\) | 2.31446 | 0.0978037 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 36.6588 | 1.54636 | ||||||||
\(563\) | −21.1477 | −0.891267 | −0.445634 | − | 0.895215i | \(-0.647022\pi\) | ||||
−0.445634 | + | 0.895215i | \(0.647022\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.2187 | 0.429903 | ||||||||
\(566\) | 11.1157 | 0.467228 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −31.1107 | −1.30538 | ||||||||
\(569\) | 7.90059 | 0.331210 | 0.165605 | − | 0.986192i | \(-0.447042\pi\) | ||||
0.165605 | + | 0.986192i | \(0.447042\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.5706 | 0.860851 | 0.430425 | − | 0.902626i | \(-0.358364\pi\) | ||||
0.430425 | + | 0.902626i | \(0.358364\pi\) | |||||||
\(572\) | −1.76597 | −0.0738391 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −4.48809 | −0.187329 | ||||||||
\(575\) | −4.67184 | −0.194829 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 34.1557 | 1.42192 | 0.710959 | − | 0.703233i | \(-0.248261\pi\) | ||||
0.710959 | + | 0.703233i | \(0.248261\pi\) | |||||||
\(578\) | 8.44661 | 0.351333 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.169956 | −0.00705703 | ||||||||
\(581\) | 0.738280 | 0.0306290 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −42.9249 | −1.77777 | ||||||||
\(584\) | −7.64476 | −0.316342 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 32.9883 | 1.36273 | ||||||||
\(587\) | 26.8588 | 1.10858 | 0.554290 | − | 0.832323i | \(-0.312990\pi\) | ||||
0.554290 | + | 0.832323i | \(0.312990\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −73.1014 | −3.01209 | ||||||||
\(590\) | 9.73837 | 0.400922 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 19.8094 | 0.814163 | ||||||||
\(593\) | 31.3103 | 1.28576 | 0.642881 | − | 0.765966i | \(-0.277739\pi\) | ||||
0.642881 | + | 0.765966i | \(0.277739\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.26291 | 0.0927703 | ||||||||
\(596\) | −4.37613 | −0.179253 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2.03268 | −0.0831226 | ||||||||
\(599\) | −36.5278 | −1.49248 | −0.746242 | − | 0.665675i | \(-0.768144\pi\) | ||||
−0.746242 | + | 0.665675i | \(0.768144\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.7339 | 0.804964 | 0.402482 | − | 0.915428i | \(-0.368148\pi\) | ||||
0.402482 | + | 0.915428i | \(0.368148\pi\) | |||||||
\(602\) | 18.7528 | 0.764307 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −0.684377 | −0.0278469 | ||||||||
\(605\) | −2.06569 | −0.0839823 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22.6610 | −0.919782 | −0.459891 | − | 0.887975i | \(-0.652112\pi\) | ||||
−0.459891 | + | 0.887975i | \(0.652112\pi\) | |||||||
\(608\) | −12.7424 | −0.516773 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6.91800 | 0.280102 | ||||||||
\(611\) | −0.611008 | −0.0247187 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.0972 | −0.407821 | −0.203911 | − | 0.978989i | \(-0.565365\pi\) | ||||
−0.203911 | + | 0.978989i | \(0.565365\pi\) | |||||||
\(614\) | 14.2180 | 0.573792 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 13.9466 | 0.561924 | ||||||||
\(617\) | 10.9420 | 0.440509 | 0.220254 | − | 0.975442i | \(-0.429311\pi\) | ||||
0.220254 | + | 0.975442i | \(0.429311\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −36.8923 | −1.48283 | −0.741413 | − | 0.671049i | \(-0.765844\pi\) | ||||
−0.741413 | + | 0.671049i | \(0.765844\pi\) | |||||||
\(620\) | −1.62213 | −0.0651464 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 19.6868 | 0.789369 | ||||||||
\(623\) | −4.65381 | −0.186451 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 20.1854 | 0.807414 | ||||||||
\(626\) | −4.02424 | −0.160841 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.54401 | 0.101517 | ||||||||
\(629\) | 19.3682 | 0.772262 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.52074 | −0.259587 | −0.129793 | − | 0.991541i | \(-0.541431\pi\) | ||||
−0.129793 | + | 0.991541i | \(0.541431\pi\) | |||||||
\(632\) | 2.55499 | 0.101632 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 27.0318 | 1.07357 | ||||||||
\(635\) | −4.70437 | −0.186687 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.59386 | −0.340501 | ||||||||
\(638\) | 4.98785 | 0.197471 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 4.67943 | 0.184971 | ||||||||
\(641\) | 27.5826 | 1.08945 | 0.544723 | − | 0.838616i | \(-0.316635\pi\) | ||||
0.544723 | + | 0.838616i | \(0.316635\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.6254 | 0.537333 | 0.268666 | − | 0.963233i | \(-0.413417\pi\) | ||||
0.268666 | + | 0.963233i | \(0.413417\pi\) | |||||||
\(644\) | −0.361201 | −0.0142333 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 32.4337 | 1.27609 | ||||||||
\(647\) | 21.2032 | 0.833583 | 0.416792 | − | 0.909002i | \(-0.363154\pi\) | ||||
0.416792 | + | 0.909002i | \(0.363154\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 49.7811 | 1.95408 | ||||||||
\(650\) | 9.49638 | 0.372479 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.40229 | −0.0940810 | ||||||||
\(653\) | −17.3572 | −0.679239 | −0.339620 | − | 0.940563i | \(-0.610298\pi\) | ||||
−0.339620 | + | 0.940563i | \(0.610298\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11.6674 | 0.455884 | ||||||||
\(656\) | −9.37383 | −0.365987 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.623340 | 0.0243003 | ||||||||
\(659\) | 19.9119 | 0.775658 | 0.387829 | − | 0.921731i | \(-0.373225\pi\) | ||||
0.387829 | + | 0.921731i | \(0.373225\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.21683 | 0.241807 | 0.120903 | − | 0.992664i | \(-0.461421\pi\) | ||||
0.120903 | + | 0.992664i | \(0.461421\pi\) | |||||||
\(662\) | −41.6555 | −1.61899 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.81768 | 0.0705395 | ||||||||
\(665\) | −5.34156 | −0.207137 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | 4.83962 | 0.187250 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −7.58559 | −0.293057 | ||||||||
\(671\) | 35.3638 | 1.36520 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −30.8251 | −1.18822 | −0.594109 | − | 0.804384i | \(-0.702495\pi\) | ||||
−0.594109 | + | 0.804384i | \(0.702495\pi\) | |||||||
\(674\) | −9.96815 | −0.383959 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.13723 | 0.120663 | ||||||||
\(677\) | −2.78347 | −0.106977 | −0.0534887 | − | 0.998568i | \(-0.517034\pi\) | ||||
−0.0534887 | + | 0.998568i | \(0.517034\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.25123 | 0.239900 | ||||||||
\(680\) | 5.57138 | 0.213653 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 47.6062 | 1.82294 | ||||||||
\(683\) | 32.3027 | 1.23603 | 0.618013 | − | 0.786168i | \(-0.287938\pi\) | ||||
0.618013 | + | 0.786168i | \(0.287938\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.10125 | 0.0802848 | ||||||||
\(686\) | 19.8897 | 0.759393 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 39.1671 | 1.49323 | ||||||||
\(689\) | −17.4931 | −0.666434 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −28.1794 | −1.07200 | −0.535998 | − | 0.844219i | \(-0.680065\pi\) | ||||
−0.535998 | + | 0.844219i | \(0.680065\pi\) | |||||||
\(692\) | 2.51268 | 0.0955179 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8.86391 | −0.336469 | ||||||||
\(695\) | 5.60244 | 0.212513 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.16506 | −0.347151 | ||||||||
\(698\) | −17.0260 | −0.644443 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.68748 | 0.0637806 | ||||||||
\(701\) | −18.3177 | −0.691850 | −0.345925 | − | 0.938262i | \(-0.612435\pi\) | ||||
−0.345925 | + | 0.938262i | \(0.612435\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −45.7184 | −1.72430 | ||||||||
\(704\) | 33.6643 | 1.26877 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −23.2746 | −0.875950 | ||||||||
\(707\) | 14.4951 | 0.545145 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −27.7519 | −1.04224 | −0.521122 | − | 0.853482i | \(-0.674486\pi\) | ||||
−0.521122 | + | 0.853482i | \(0.674486\pi\) | |||||||
\(710\) | −7.75977 | −0.291219 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −11.4579 | −0.429402 | ||||||||
\(713\) | −9.54445 | −0.357442 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.40979 | −0.127519 | ||||||||
\(716\) | 3.27918 | 0.122549 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −0.867400 | −0.0323711 | ||||||||
\(719\) | −35.7583 | −1.33356 | −0.666780 | − | 0.745255i | \(-0.732328\pi\) | ||||
−0.666780 | + | 0.745255i | \(0.732328\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.51385 | 0.168105 | ||||||||
\(722\) | −51.7621 | −1.92638 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −6.62361 | −0.246165 | ||||||||
\(725\) | 4.67184 | 0.173508 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17.5411 | −0.650564 | −0.325282 | − | 0.945617i | \(-0.605459\pi\) | ||||
−0.325282 | + | 0.945617i | \(0.605459\pi\) | |||||||
\(728\) | 5.68362 | 0.210649 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.90679 | −0.0705733 | ||||||||
\(731\) | 38.2948 | 1.41638 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.71604 | −0.100319 | −0.0501595 | − | 0.998741i | \(-0.515973\pi\) | ||||
−0.0501595 | + | 0.998741i | \(0.515973\pi\) | |||||||
\(734\) | 10.1474 | 0.374548 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.66371 | −0.0613251 | ||||||||
\(737\) | −38.7764 | −1.42835 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −50.4189 | −1.85469 | −0.927344 | − | 0.374210i | \(-0.877914\pi\) | ||||
−0.927344 | + | 0.374210i | \(0.877914\pi\) | |||||||
\(740\) | −1.01450 | −0.0372938 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 17.8462 | 0.655153 | ||||||||
\(743\) | 22.6523 | 0.831033 | 0.415517 | − | 0.909586i | \(-0.363601\pi\) | ||||
0.415517 | + | 0.909586i | \(0.363601\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.44956 | −0.309568 | ||||||||
\(746\) | 8.16654 | 0.298998 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.67905 | 0.134519 | ||||||||
\(749\) | −11.7593 | −0.429677 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.3305 | −0.449945 | −0.224972 | − | 0.974365i | \(-0.572229\pi\) | ||||
−0.224972 | + | 0.974365i | \(0.572229\pi\) | |||||||
\(752\) | 1.30191 | 0.0474757 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.03268 | 0.0740260 | ||||||||
\(755\) | −1.32141 | −0.0480912 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.85052 | −0.212641 | −0.106320 | − | 0.994332i | \(-0.533907\pi\) | ||||
−0.106320 | + | 0.994332i | \(0.533907\pi\) | |||||||
\(758\) | 22.1107 | 0.803095 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −13.1511 | −0.477042 | ||||||||
\(761\) | 15.9306 | 0.577484 | 0.288742 | − | 0.957407i | \(-0.406763\pi\) | ||||
0.288742 | + | 0.957407i | \(0.406763\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.8325 | 0.464567 | ||||||||
\(764\) | −0.0334457 | −0.00121002 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −10.4571 | −0.377830 | ||||||||
\(767\) | 20.2872 | 0.732527 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.5190 | −0.487506 | −0.243753 | − | 0.969837i | \(-0.578379\pi\) | ||||
−0.243753 | + | 0.969837i | \(0.578379\pi\) | |||||||
\(770\) | 3.47861 | 0.125361 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4.44714 | 0.160056 | ||||||||
\(773\) | −48.7672 | −1.75403 | −0.877017 | − | 0.480460i | \(-0.840470\pi\) | ||||
−0.877017 | + | 0.480460i | \(0.840470\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 44.5902 | 1.60173 | ||||||||
\(776\) | 15.3908 | 0.552497 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 14.4816 | 0.519192 | ||||||||
\(779\) | 21.6340 | 0.775117 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −39.6668 | −1.41939 | ||||||||
\(782\) | 4.23469 | 0.151432 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 18.3114 | 0.653979 | ||||||||
\(785\) | 4.91204 | 0.175318 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.25934 | 0.223122 | 0.111561 | − | 0.993758i | \(-0.464415\pi\) | ||||
0.111561 | + | 0.993758i | \(0.464415\pi\) | |||||||
\(788\) | −4.28349 | −0.152593 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0.637277 | 0.0226733 | ||||||||
\(791\) | −21.7174 | −0.772182 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14.4117 | 0.511775 | ||||||||
\(794\) | −24.5162 | −0.870047 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 5.44410 | 0.192961 | ||||||||
\(797\) | −27.7945 | −0.984530 | −0.492265 | − | 0.870445i | \(-0.663831\pi\) | ||||
−0.492265 | + | 0.870445i | \(0.663831\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.27291 | 0.0450324 | ||||||||
\(800\) | 7.77258 | 0.274802 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −10.8616 | −0.383538 | ||||||||
\(803\) | −9.74721 | −0.343972 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.697418 | −0.0245808 | ||||||||
\(806\) | 19.4008 | 0.683366 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 35.6876 | 1.25549 | ||||||||
\(809\) | −7.21091 | −0.253522 | −0.126761 | − | 0.991933i | \(-0.540458\pi\) | ||||
−0.126761 | + | 0.991933i | \(0.540458\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.68402 | 0.199593 | 0.0997964 | − | 0.995008i | \(-0.468181\pi\) | ||||
0.0997964 | + | 0.995008i | \(0.468181\pi\) | |||||||
\(812\) | 0.361201 | 0.0126757 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 29.7735 | 1.04356 | ||||||||
\(815\) | −4.63841 | −0.162477 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −90.3941 | −3.16249 | ||||||||
\(818\) | 28.1166 | 0.983073 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.480062 | 0.0167645 | ||||||||
\(821\) | −17.6765 | −0.616915 | −0.308458 | − | 0.951238i | \(-0.599813\pi\) | ||||
−0.308458 | + | 0.951238i | \(0.599813\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −48.5960 | −1.69395 | −0.846975 | − | 0.531633i | \(-0.821578\pi\) | ||||
−0.846975 | + | 0.531633i | \(0.821578\pi\) | |||||||
\(824\) | 11.1133 | 0.387150 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −20.6966 | −0.720128 | ||||||||
\(827\) | 48.9103 | 1.70078 | 0.850389 | − | 0.526154i | \(-0.176367\pi\) | ||||
0.850389 | + | 0.526154i | \(0.176367\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 38.9522 | 1.35287 | 0.676434 | − | 0.736504i | \(-0.263525\pi\) | ||||
0.676434 | + | 0.736504i | \(0.263525\pi\) | |||||||
\(830\) | 0.453372 | 0.0157368 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 13.7191 | 0.475625 | ||||||||
\(833\) | 17.9036 | 0.620322 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.34447 | 0.323379 | ||||||||
\(836\) | −8.68433 | −0.300354 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −16.5298 | −0.571012 | ||||||||
\(839\) | −27.9458 | −0.964797 | −0.482399 | − | 0.875952i | \(-0.660234\pi\) | ||||
−0.482399 | + | 0.875952i | \(0.660234\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −1.03888 | −0.0358020 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.51754 | −0.0866573 | ||||||||
\(845\) | 6.05745 | 0.208383 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.39015 | 0.150847 | ||||||||
\(848\) | 37.2735 | 1.27998 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −19.7838 | −0.678579 | ||||||||
\(851\) | −5.96920 | −0.204622 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 19.3309 | 0.661878 | 0.330939 | − | 0.943652i | \(-0.392635\pi\) | ||||
0.330939 | + | 0.943652i | \(0.392635\pi\) | |||||||
\(854\) | −14.7026 | −0.503113 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −28.9520 | −0.989558 | ||||||||
\(857\) | 42.6767 | 1.45781 | 0.728904 | − | 0.684616i | \(-0.240030\pi\) | ||||
0.728904 | + | 0.684616i | \(0.240030\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.8383 | −0.369800 | −0.184900 | − | 0.982757i | \(-0.559196\pi\) | ||||
−0.184900 | + | 0.982757i | \(0.559196\pi\) | |||||||
\(860\) | −2.00586 | −0.0683993 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 42.6245 | 1.45180 | ||||||||
\(863\) | −35.3269 | −1.20254 | −0.601271 | − | 0.799045i | \(-0.705339\pi\) | ||||
−0.601271 | + | 0.799045i | \(0.705339\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.85156 | 0.164958 | ||||||||
\(866\) | −13.8304 | −0.469977 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3.44747 | 0.117015 | ||||||||
\(869\) | 3.25767 | 0.110509 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −15.8025 | −0.535446 | ||||||||
\(872\) | 31.5941 | 1.06991 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −9.99591 | −0.338117 | ||||||||
\(875\) | 6.74532 | 0.228033 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.6037 | 0.560667 | 0.280333 | − | 0.959903i | \(-0.409555\pi\) | ||||
0.280333 | + | 0.959903i | \(0.409555\pi\) | |||||||
\(878\) | −38.6443 | −1.30418 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 7.26543 | 0.244918 | ||||||||
\(881\) | −23.2009 | −0.781659 | −0.390830 | − | 0.920463i | \(-0.627812\pi\) | ||||
−0.390830 | + | 0.920463i | \(0.627812\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 25.1560 | 0.846568 | 0.423284 | − | 0.905997i | \(-0.360877\pi\) | ||||
0.423284 | + | 0.905997i | \(0.360877\pi\) | |||||||
\(884\) | 1.49931 | 0.0504274 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −44.3966 | −1.49153 | ||||||||
\(887\) | 17.2591 | 0.579502 | 0.289751 | − | 0.957102i | \(-0.406427\pi\) | ||||
0.289751 | + | 0.957102i | \(0.406427\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.99804 | 0.335324 | ||||||||
\(890\) | −2.85787 | −0.0957961 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.35291 | −0.0787812 | ||||||||
\(893\) | −3.00469 | −0.100548 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.33154 | 0.211640 | ||||||||
\(896\) | −9.94504 | −0.332240 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 50.6122 | 1.68895 | ||||||||
\(899\) | 9.54445 | 0.318325 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 36.4433 | 1.21410 | ||||||||
\(902\) | −14.0888 | −0.469106 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −53.4692 | −1.77836 | ||||||||
\(905\) | −12.7891 | −0.425123 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −28.5679 | −0.948581 | −0.474290 | − | 0.880368i | \(-0.657295\pi\) | ||||
−0.474290 | + | 0.880368i | \(0.657295\pi\) | |||||||
\(908\) | −7.89927 | −0.262146 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.41763 | 0.0469940 | ||||||||
\(911\) | −13.1206 | −0.434705 | −0.217353 | − | 0.976093i | \(-0.569742\pi\) | ||||
−0.217353 | + | 0.976093i | \(0.569742\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.31757 | 0.0767005 | ||||||||
\(914\) | 26.1442 | 0.864772 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.57152 | −0.217129 | ||||||||
\(917\) | −24.7964 | −0.818850 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.49407 | −0.0822717 | −0.0411358 | − | 0.999154i | \(-0.513098\pi\) | ||||
−0.0411358 | + | 0.999154i | \(0.513098\pi\) | |||||||
\(920\) | −1.71707 | −0.0566102 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −16.0356 | −0.528104 | ||||||||
\(923\) | −16.1653 | −0.532088 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 27.8872 | 0.916925 | ||||||||
\(926\) | 49.4392 | 1.62467 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.66371 | 0.0546139 | ||||||||
\(929\) | 14.5108 | 0.476083 | 0.238042 | − | 0.971255i | \(-0.423495\pi\) | ||||
0.238042 | + | 0.971255i | \(0.423495\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −42.2611 | −1.38505 | ||||||||
\(932\) | 1.20667 | 0.0395258 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.02095 | 0.0334065 | ||||||||
\(935\) | 7.10362 | 0.232313 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −36.4431 | −1.19054 | −0.595271 | − | 0.803525i | \(-0.702955\pi\) | ||||
−0.595271 | + | 0.803525i | \(0.702955\pi\) | |||||||
\(938\) | 16.1214 | 0.526383 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.0666745 | −0.00217468 | ||||||||
\(941\) | 6.09402 | 0.198659 | 0.0993296 | − | 0.995055i | \(-0.468330\pi\) | ||||
0.0993296 | + | 0.995055i | \(0.468330\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.82463 | 0.0919825 | ||||||||
\(944\) | −43.2270 | −1.40692 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 58.8679 | 1.91396 | ||||||||
\(947\) | 11.8081 | 0.383711 | 0.191855 | − | 0.981423i | \(-0.438550\pi\) | ||||
0.191855 | + | 0.981423i | \(0.438550\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.97226 | −0.128945 | ||||||||
\(950\) | 46.6993 | 1.51513 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −11.8407 | −0.383758 | ||||||||
\(953\) | −28.4697 | −0.922225 | −0.461112 | − | 0.887342i | \(-0.652549\pi\) | ||||
−0.461112 | + | 0.887342i | \(0.652549\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.0645779 | −0.00208969 | ||||||||
\(956\) | 2.24172 | 0.0725023 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 9.30916 | 0.300765 | ||||||||
\(959\) | −4.46573 | −0.144206 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 60.0964 | 1.93860 | ||||||||
\(962\) | 12.1335 | 0.391200 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.97479 | −0.0636037 | ||||||||
\(965\) | 8.58666 | 0.276414 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13.8752 | 0.446196 | 0.223098 | − | 0.974796i | \(-0.428383\pi\) | ||||
0.223098 | + | 0.974796i | \(0.428383\pi\) | |||||||
\(968\) | 10.8087 | 0.347406 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3.83883 | 0.123258 | ||||||||
\(971\) | 13.7112 | 0.440013 | 0.220007 | − | 0.975498i | \(-0.429392\pi\) | ||||
0.220007 | + | 0.975498i | \(0.429392\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11.9067 | −0.381711 | ||||||||
\(974\) | 23.5780 | 0.755488 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −30.7078 | −0.982934 | ||||||||
\(977\) | −35.8383 | −1.14657 | −0.573284 | − | 0.819356i | \(-0.694331\pi\) | ||||
−0.573284 | + | 0.819356i | \(0.694331\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14.6090 | −0.466906 | ||||||||
\(980\) | −0.937782 | −0.0299563 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.55956 | −0.0497675 | ||||||||
\(983\) | −9.92432 | −0.316537 | −0.158268 | − | 0.987396i | \(-0.550591\pi\) | ||||
−0.158268 | + | 0.987396i | \(0.550591\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.27068 | −0.263526 | ||||||||
\(986\) | −4.23469 | −0.134860 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.53910 | −0.112594 | ||||||||
\(989\) | −11.8023 | −0.375290 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 52.4826 | 1.66716 | 0.833582 | − | 0.552396i | \(-0.186286\pi\) | ||||
0.833582 | + | 0.552396i | \(0.186286\pi\) | |||||||
\(992\) | 15.8792 | 0.504164 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 16.4916 | 0.523081 | ||||||||
\(995\) | 10.5116 | 0.333241 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.72613 | 0.118008 | 0.0590038 | − | 0.998258i | \(-0.481208\pi\) | ||||
0.0590038 | + | 0.998258i | \(0.481208\pi\) | |||||||
\(998\) | −29.0903 | −0.920836 | ||||||||
\(999\) | 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 | 6003.2.a.o.1.5 | 13 | ||
3.2 | odd | 2 | 667.2.a.c.1.9 | ✓ | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
667.2.a.c.1.9 | ✓ | 13 | 3.2 | odd | 2 | ||
6003.2.a.o.1.5 | 13 | 1.1 | even | 1 | trivial |