Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2601,2,Mod(1,2601)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2601, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2601.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2601 = 3^{2} \cdot 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2601.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: | \(20.7690895657\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.45769536.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 15x^{4} + 72x^{2} - 109 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.31242\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2601.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.31242 | −1.63513 | −0.817565 | − | 0.575837i | \(-0.804676\pi\) | ||||
−0.817565 | + | 0.575837i | \(0.804676\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.34730 | 1.67365 | ||||||||
\(5\) | −0.803096 | −0.359155 | −0.179578 | − | 0.983744i | \(-0.557473\pi\) | ||||
−0.179578 | + | 0.983744i | \(0.557473\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.65270 | 1.00263 | 0.501314 | − | 0.865266i | \(-0.332850\pi\) | ||||
0.501314 | + | 0.865266i | \(0.332850\pi\) | |||||||
\(8\) | −3.11552 | −1.10150 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.85710 | 0.587265 | ||||||||
\(11\) | −5.85526 | −1.76543 | −0.882713 | − | 0.469912i | \(-0.844286\pi\) | ||||
−0.882713 | + | 0.469912i | \(0.844286\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.94356 | 1.09375 | 0.546874 | − | 0.837215i | \(-0.315818\pi\) | ||||
0.546874 | + | 0.837215i | \(0.315818\pi\) | |||||||
\(14\) | −6.13417 | −1.63943 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.509800 | 0.127450 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.10607 | −1.63024 | −0.815122 | − | 0.579290i | \(-0.803330\pi\) | ||||
−0.815122 | + | 0.579290i | \(0.803330\pi\) | |||||||
\(20\) | −2.68820 | −0.601100 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 13.5398 | 2.88670 | ||||||||
\(23\) | 6.37944 | 1.33021 | 0.665103 | − | 0.746752i | \(-0.268388\pi\) | ||||
0.665103 | + | 0.746752i | \(0.268388\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.35504 | −0.871007 | ||||||||
\(26\) | −9.11918 | −1.78842 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 8.87939 | 1.67805 | ||||||||
\(29\) | −5.14903 | −0.956150 | −0.478075 | − | 0.878319i | \(-0.658665\pi\) | ||||
−0.478075 | + | 0.878319i | \(0.658665\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.46791 | 0.802461 | 0.401230 | − | 0.915977i | \(-0.368583\pi\) | ||||
0.401230 | + | 0.915977i | \(0.368583\pi\) | |||||||
\(32\) | 5.05216 | 0.893105 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.13038 | −0.360099 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.71688 | 0.282254 | 0.141127 | − | 0.989992i | \(-0.454927\pi\) | ||||
0.141127 | + | 0.989992i | \(0.454927\pi\) | |||||||
\(38\) | 16.4322 | 2.66566 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.50206 | 0.395610 | ||||||||
\(41\) | 7.18254 | 1.12172 | 0.560862 | − | 0.827909i | \(-0.310470\pi\) | ||||
0.560862 | + | 0.827909i | \(0.310470\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.30541 | 0.199073 | 0.0995364 | − | 0.995034i | \(-0.468264\pi\) | ||||
0.0995364 | + | 0.995034i | \(0.468264\pi\) | |||||||
\(44\) | −19.5993 | −2.95470 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −14.7520 | −2.17506 | ||||||||
\(47\) | 1.08201 | 0.157827 | 0.0789135 | − | 0.996881i | \(-0.474855\pi\) | ||||
0.0789135 | + | 0.996881i | \(0.474855\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.0368366 | 0.00526238 | ||||||||
\(50\) | 10.0707 | 1.42421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 13.2003 | 1.83055 | ||||||||
\(53\) | 9.67701 | 1.32924 | 0.664620 | − | 0.747182i | \(-0.268594\pi\) | ||||
0.664620 | + | 0.747182i | \(0.268594\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.70233 | 0.634063 | ||||||||
\(56\) | −8.26455 | −1.10440 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 11.9067 | 1.56343 | ||||||||
\(59\) | −12.0863 | −1.57350 | −0.786751 | − | 0.617271i | \(-0.788238\pi\) | ||||
−0.786751 | + | 0.617271i | \(0.788238\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.18479 | 0.791882 | 0.395941 | − | 0.918276i | \(-0.370419\pi\) | ||||
0.395941 | + | 0.918276i | \(0.370419\pi\) | |||||||
\(62\) | −10.3317 | −1.31213 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −12.7023 | −1.58779 | ||||||||
\(65\) | −3.16706 | −0.392825 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.43376 | 0.663840 | 0.331920 | − | 0.943308i | \(-0.392304\pi\) | ||||
0.331920 | + | 0.943308i | \(0.392304\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 4.92633 | 0.588809 | ||||||||
\(71\) | 5.95212 | 0.706387 | 0.353194 | − | 0.935550i | \(-0.385096\pi\) | ||||
0.353194 | + | 0.935550i | \(0.385096\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.53209 | −0.296359 | −0.148179 | − | 0.988961i | \(-0.547341\pi\) | ||||
−0.148179 | + | 0.988961i | \(0.547341\pi\) | |||||||
\(74\) | −3.97015 | −0.461521 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −23.7861 | −2.72845 | ||||||||
\(77\) | −15.5323 | −1.77007 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.30541 | 0.709414 | 0.354707 | − | 0.934978i | \(-0.384581\pi\) | ||||
0.354707 | + | 0.934978i | \(0.384581\pi\) | |||||||
\(80\) | −0.409418 | −0.0457744 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −16.6091 | −1.83416 | ||||||||
\(83\) | 15.2534 | 1.67427 | 0.837137 | − | 0.546994i | \(-0.184228\pi\) | ||||
0.837137 | + | 0.546994i | \(0.184228\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −3.01865 | −0.325510 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 18.2422 | 1.94462 | ||||||||
\(89\) | 3.63970 | 0.385808 | 0.192904 | − | 0.981218i | \(-0.438209\pi\) | ||||
0.192904 | + | 0.981218i | \(0.438209\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.4611 | 1.09662 | ||||||||
\(92\) | 21.3539 | 2.22630 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.50206 | −0.258068 | ||||||||
\(95\) | 5.70685 | 0.585511 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.19253 | 0.831826 | 0.415913 | − | 0.909404i | \(-0.363462\pi\) | ||||
0.415913 | + | 0.909404i | \(0.363462\pi\) | |||||||
\(98\) | −0.0851818 | −0.00860466 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −14.5776 | −1.45776 | ||||||||
\(101\) | −17.8447 | −1.77561 | −0.887806 | − | 0.460217i | \(-0.847772\pi\) | ||||
−0.887806 | + | 0.460217i | \(0.847772\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.39693 | −0.531775 | −0.265887 | − | 0.964004i | \(-0.585665\pi\) | ||||
−0.265887 | + | 0.964004i | \(0.585665\pi\) | |||||||
\(104\) | −12.2862 | −1.20477 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −22.3773 | −2.17348 | ||||||||
\(107\) | 1.50933 | 0.145912 | 0.0729560 | − | 0.997335i | \(-0.476757\pi\) | ||||
0.0729560 | + | 0.997335i | \(0.476757\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −16.0719 | −1.53941 | −0.769705 | − | 0.638399i | \(-0.779597\pi\) | ||||
−0.769705 | + | 0.638399i | \(0.779597\pi\) | |||||||
\(110\) | −10.8738 | −1.03677 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.35235 | 0.127785 | ||||||||
\(113\) | −11.6769 | −1.09847 | −0.549234 | − | 0.835669i | \(-0.685080\pi\) | ||||
−0.549234 | + | 0.835669i | \(0.685080\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.12330 | −0.477750 | ||||||||
\(116\) | −17.2353 | −1.60026 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 27.9486 | 2.57288 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 23.2841 | 2.11673 | ||||||||
\(122\) | −14.3019 | −1.29483 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 14.9554 | 1.34304 | ||||||||
\(125\) | 7.51299 | 0.671982 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.29860 | 0.470175 | 0.235087 | − | 0.971974i | \(-0.424462\pi\) | ||||
0.235087 | + | 0.971974i | \(0.424462\pi\) | |||||||
\(128\) | 19.2688 | 1.70314 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 7.32358 | 0.642320 | ||||||||
\(131\) | 9.24969 | 0.808149 | 0.404075 | − | 0.914726i | \(-0.367594\pi\) | ||||
0.404075 | + | 0.914726i | \(0.367594\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −18.8503 | −1.63453 | ||||||||
\(134\) | −12.5652 | −1.08546 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.77325 | 0.407806 | 0.203903 | − | 0.978991i | \(-0.434637\pi\) | ||||
0.203903 | + | 0.978991i | \(0.434637\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.6382 | 1.58087 | 0.790434 | − | 0.612547i | \(-0.209855\pi\) | ||||
0.790434 | + | 0.612547i | \(0.209855\pi\) | |||||||
\(140\) | −7.13100 | −0.602679 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −13.7638 | −1.15503 | ||||||||
\(143\) | −23.0906 | −1.93093 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.13516 | 0.343407 | ||||||||
\(146\) | 5.85526 | 0.484585 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5.74691 | 0.472393 | ||||||||
\(149\) | −10.4465 | −0.855808 | −0.427904 | − | 0.903824i | \(-0.640748\pi\) | ||||
−0.427904 | + | 0.903824i | \(0.640748\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.67499 | −0.299067 | −0.149533 | − | 0.988757i | \(-0.547777\pi\) | ||||
−0.149533 | + | 0.988757i | \(0.547777\pi\) | |||||||
\(152\) | 22.1391 | 1.79572 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 35.9172 | 2.89429 | ||||||||
\(155\) | −3.58816 | −0.288208 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.07873 | 0.405326 | 0.202663 | − | 0.979248i | \(-0.435040\pi\) | ||||
0.202663 | + | 0.979248i | \(0.435040\pi\) | |||||||
\(158\) | −14.5808 | −1.15998 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −4.05737 | −0.320763 | ||||||||
\(161\) | 16.9228 | 1.33370 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.87258 | 0.538302 | 0.269151 | − | 0.963098i | \(-0.413257\pi\) | ||||
0.269151 | + | 0.963098i | \(0.413257\pi\) | |||||||
\(164\) | 24.0421 | 1.87737 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −35.2722 | −2.73765 | ||||||||
\(167\) | 13.2198 | 1.02298 | 0.511491 | − | 0.859289i | \(-0.329093\pi\) | ||||
0.511491 | + | 0.859289i | \(0.329093\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.55169 | 0.196284 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.36959 | 0.333178 | ||||||||
\(173\) | 1.36092 | 0.103469 | 0.0517344 | − | 0.998661i | \(-0.483525\pi\) | ||||
0.0517344 | + | 0.998661i | \(0.483525\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11.5526 | −0.873296 | ||||||||
\(176\) | −2.98501 | −0.225004 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −8.41653 | −0.630845 | ||||||||
\(179\) | 1.65773 | 0.123905 | 0.0619524 | − | 0.998079i | \(-0.480267\pi\) | ||||
0.0619524 | + | 0.998079i | \(0.480267\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.3259 | −0.990509 | −0.495255 | − | 0.868748i | \(-0.664925\pi\) | ||||
−0.495255 | + | 0.868748i | \(0.664925\pi\) | |||||||
\(182\) | −24.1905 | −1.79312 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −19.8753 | −1.46522 | ||||||||
\(185\) | −1.37882 | −0.101373 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 3.62180 | 0.264147 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −13.1967 | −0.957386 | ||||||||
\(191\) | 11.4316 | 0.827162 | 0.413581 | − | 0.910467i | \(-0.364278\pi\) | ||||
0.413581 | + | 0.910467i | \(0.364278\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15.5057 | −1.11612 | −0.558062 | − | 0.829799i | \(-0.688455\pi\) | ||||
−0.558062 | + | 0.829799i | \(0.688455\pi\) | |||||||
\(194\) | −18.9446 | −1.36014 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.123303 | 0.00880736 | ||||||||
\(197\) | 19.8446 | 1.41387 | 0.706933 | − | 0.707280i | \(-0.250078\pi\) | ||||
0.706933 | + | 0.707280i | \(0.250078\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.81521 | 0.199565 | 0.0997824 | − | 0.995009i | \(-0.468185\pi\) | ||||
0.0997824 | + | 0.995009i | \(0.468185\pi\) | |||||||
\(200\) | 13.5682 | 0.959416 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 41.2645 | 2.90336 | ||||||||
\(203\) | −13.6588 | −0.958663 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.76827 | −0.402873 | ||||||||
\(206\) | 12.4800 | 0.869521 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.01043 | 0.139398 | ||||||||
\(209\) | 41.6079 | 2.87808 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.2121 | 1.18493 | 0.592466 | − | 0.805595i | \(-0.298154\pi\) | ||||
0.592466 | + | 0.805595i | \(0.298154\pi\) | |||||||
\(212\) | 32.3918 | 2.22468 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.49020 | −0.238585 | ||||||||
\(215\) | −1.04837 | −0.0714980 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 11.8520 | 0.804569 | ||||||||
\(218\) | 37.1651 | 2.51714 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 15.7401 | 1.06120 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.7324 | −1.12048 | −0.560241 | − | 0.828330i | \(-0.689291\pi\) | ||||
−0.560241 | + | 0.828330i | \(0.689291\pi\) | |||||||
\(224\) | 13.4019 | 0.895451 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 27.0019 | 1.79614 | ||||||||
\(227\) | 0.706231 | 0.0468742 | 0.0234371 | − | 0.999725i | \(-0.492539\pi\) | ||||
0.0234371 | + | 0.999725i | \(0.492539\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.65270 | −0.109214 | −0.0546069 | − | 0.998508i | \(-0.517391\pi\) | ||||
−0.0546069 | + | 0.998508i | \(0.517391\pi\) | |||||||
\(230\) | 11.8472 | 0.781184 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 16.0419 | 1.05320 | ||||||||
\(233\) | 22.3844 | 1.46645 | 0.733224 | − | 0.679987i | \(-0.238015\pi\) | ||||
0.733224 | + | 0.679987i | \(0.238015\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.868956 | −0.0566844 | ||||||||
\(236\) | −40.4564 | −2.63349 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.3831 | 0.800997 | 0.400498 | − | 0.916298i | \(-0.368837\pi\) | ||||
0.400498 | + | 0.916298i | \(0.368837\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.5790 | 1.06795 | 0.533975 | − | 0.845501i | \(-0.320698\pi\) | ||||
0.533975 | + | 0.845501i | \(0.320698\pi\) | |||||||
\(242\) | −53.8426 | −3.46113 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 20.7023 | 1.32533 | ||||||||
\(245\) | −0.0295833 | −0.00189001 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −28.0232 | −1.78307 | ||||||||
\(248\) | −13.9199 | −0.883912 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −17.3732 | −1.09878 | ||||||||
\(251\) | −5.01852 | −0.316766 | −0.158383 | − | 0.987378i | \(-0.550628\pi\) | ||||
−0.158383 | + | 0.987378i | \(0.550628\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −37.3533 | −2.34838 | ||||||||
\(254\) | −12.2526 | −0.768797 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −19.1530 | −1.19706 | ||||||||
\(257\) | 19.5141 | 1.21726 | 0.608628 | − | 0.793456i | \(-0.291720\pi\) | ||||
0.608628 | + | 0.793456i | \(0.291720\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.55438 | 0.282995 | ||||||||
\(260\) | −10.6011 | −0.657451 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −21.3892 | −1.32143 | ||||||||
\(263\) | 9.28333 | 0.572435 | 0.286217 | − | 0.958165i | \(-0.407602\pi\) | ||||
0.286217 | + | 0.958165i | \(0.407602\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.77156 | −0.477403 | ||||||||
\(266\) | 43.5898 | 2.67266 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 18.1884 | 1.11103 | ||||||||
\(269\) | −0.0515409 | −0.00314250 | −0.00157125 | − | 0.999999i | \(-0.500500\pi\) | ||||
−0.00157125 | + | 0.999999i | \(0.500500\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −18.1506 | −1.10257 | −0.551287 | − | 0.834316i | \(-0.685863\pi\) | ||||
−0.551287 | + | 0.834316i | \(0.685863\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −11.0378 | −0.666816 | ||||||||
\(275\) | 25.4999 | 1.53770 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.55438 | 0.333730 | 0.166865 | − | 0.985980i | \(-0.446636\pi\) | ||||
0.166865 | + | 0.985980i | \(0.446636\pi\) | |||||||
\(278\) | −43.0993 | −2.58492 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 6.63722 | 0.396650 | ||||||||
\(281\) | 2.16402 | 0.129094 | 0.0645472 | − | 0.997915i | \(-0.479440\pi\) | ||||
0.0645472 | + | 0.997915i | \(0.479440\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 25.0401 | 1.48848 | 0.744241 | − | 0.667911i | \(-0.232812\pi\) | ||||
0.744241 | + | 0.667911i | \(0.232812\pi\) | |||||||
\(284\) | 19.9235 | 1.18224 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 53.3952 | 3.15732 | ||||||||
\(287\) | 19.0531 | 1.12467 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | −9.56224 | −0.561514 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −8.47565 | −0.496000 | ||||||||
\(293\) | −28.9005 | −1.68839 | −0.844193 | − | 0.536039i | \(-0.819920\pi\) | ||||
−0.844193 | + | 0.536039i | \(0.819920\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.70645 | 0.565132 | ||||||||
\(296\) | −5.34897 | −0.310903 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 24.1566 | 1.39936 | ||||||||
\(299\) | 25.1577 | 1.45491 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.46286 | 0.199596 | ||||||||
\(302\) | 8.49813 | 0.489013 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.62267 | −0.207775 | ||||||||
\(305\) | −4.96698 | −0.284408 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.09152 | 0.404734 | 0.202367 | − | 0.979310i | \(-0.435137\pi\) | ||||
0.202367 | + | 0.979310i | \(0.435137\pi\) | |||||||
\(308\) | −51.9911 | −2.96247 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 8.29734 | 0.471257 | ||||||||
\(311\) | 9.38019 | 0.531902 | 0.265951 | − | 0.963987i | \(-0.414314\pi\) | ||||
0.265951 | + | 0.963987i | \(0.414314\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 29.1857 | 1.64967 | 0.824837 | − | 0.565370i | \(-0.191267\pi\) | ||||
0.824837 | + | 0.565370i | \(0.191267\pi\) | |||||||
\(314\) | −11.7442 | −0.662761 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 21.1061 | 1.18731 | ||||||||
\(317\) | 15.6291 | 0.877819 | 0.438910 | − | 0.898531i | \(-0.355365\pi\) | ||||
0.438910 | + | 0.898531i | \(0.355365\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 30.1489 | 1.68801 | ||||||||
\(320\) | 10.2012 | 0.570264 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −39.1326 | −2.18077 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −17.1744 | −0.952662 | ||||||||
\(326\) | −15.8923 | −0.880193 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −22.3773 | −1.23558 | ||||||||
\(329\) | 2.87025 | 0.158242 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.08883 | 0.224742 | 0.112371 | − | 0.993666i | \(-0.464155\pi\) | ||||
0.112371 | + | 0.993666i | \(0.464155\pi\) | |||||||
\(332\) | 51.0575 | 2.80214 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −30.5699 | −1.67271 | ||||||||
\(335\) | −4.36383 | −0.238422 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.07604 | 0.222036 | 0.111018 | − | 0.993818i | \(-0.464589\pi\) | ||||
0.111018 | + | 0.993818i | \(0.464589\pi\) | |||||||
\(338\) | −5.90058 | −0.320949 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −26.1608 | −1.41669 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.4712 | −0.997352 | ||||||||
\(344\) | −4.06702 | −0.219279 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.14702 | −0.169185 | ||||||||
\(347\) | −11.2832 | −0.605714 | −0.302857 | − | 0.953036i | \(-0.597940\pi\) | ||||
−0.302857 | + | 0.953036i | \(0.597940\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 27.2814 | 1.46034 | 0.730169 | − | 0.683267i | \(-0.239441\pi\) | ||||
0.730169 | + | 0.683267i | \(0.239441\pi\) | |||||||
\(350\) | 26.7145 | 1.42795 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −29.5817 | −1.57671 | ||||||||
\(353\) | 21.0117 | 1.11834 | 0.559171 | − | 0.829052i | \(-0.311119\pi\) | ||||
0.559171 | + | 0.829052i | \(0.311119\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.78013 | −0.253703 | ||||||||
\(356\) | 12.1832 | 0.645706 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.83338 | −0.202600 | ||||||||
\(359\) | 30.8488 | 1.62814 | 0.814070 | − | 0.580767i | \(-0.197247\pi\) | ||||
0.814070 | + | 0.580767i | \(0.197247\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 31.4962 | 1.65769 | ||||||||
\(362\) | 30.8152 | 1.61961 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 35.0164 | 1.83536 | ||||||||
\(365\) | 2.03351 | 0.106439 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 26.7219 | 1.39487 | 0.697437 | − | 0.716646i | \(-0.254324\pi\) | ||||
0.697437 | + | 0.716646i | \(0.254324\pi\) | |||||||
\(368\) | 3.25224 | 0.169535 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3.18841 | 0.165758 | ||||||||
\(371\) | 25.6702 | 1.33273 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.24392 | −0.271520 | −0.135760 | − | 0.990742i | \(-0.543348\pi\) | ||||
−0.135760 | + | 0.990742i | \(0.543348\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.37102 | −0.173847 | ||||||||
\(377\) | −20.3055 | −1.04579 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.06923 | −0.414489 | −0.207244 | − | 0.978289i | \(-0.566449\pi\) | ||||
−0.207244 | + | 0.978289i | \(0.566449\pi\) | |||||||
\(380\) | 19.1025 | 0.979939 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −26.4347 | −1.35252 | ||||||||
\(383\) | 3.11552 | 0.159196 | 0.0795978 | − | 0.996827i | \(-0.474636\pi\) | ||||
0.0795978 | + | 0.996827i | \(0.474636\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 12.4739 | 0.635729 | ||||||||
\(386\) | 35.8557 | 1.82501 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 27.4228 | 1.39218 | ||||||||
\(389\) | 10.1833 | 0.516313 | 0.258157 | − | 0.966103i | \(-0.416885\pi\) | ||||
0.258157 | + | 0.966103i | \(0.416885\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −0.114765 | −0.00579652 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −45.8890 | −2.31185 | ||||||||
\(395\) | −5.06385 | −0.254790 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 26.3756 | 1.32375 | 0.661876 | − | 0.749613i | \(-0.269761\pi\) | ||||
0.661876 | + | 0.749613i | \(0.269761\pi\) | |||||||
\(398\) | −6.50995 | −0.326314 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.22020 | −0.111010 | ||||||||
\(401\) | 26.0639 | 1.30157 | 0.650785 | − | 0.759262i | \(-0.274440\pi\) | ||||
0.650785 | + | 0.759262i | \(0.274440\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 17.6195 | 0.877689 | ||||||||
\(404\) | −59.7315 | −2.97175 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 31.5850 | 1.56754 | ||||||||
\(407\) | −10.0528 | −0.498298 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −29.4097 | −1.45422 | −0.727109 | − | 0.686523i | \(-0.759136\pi\) | ||||
−0.727109 | + | 0.686523i | \(0.759136\pi\) | |||||||
\(410\) | 13.3387 | 0.658750 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −18.0651 | −0.890004 | ||||||||
\(413\) | −32.0614 | −1.57764 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.2499 | −0.601324 | ||||||||
\(416\) | 19.9235 | 0.976831 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −96.2149 | −4.70603 | ||||||||
\(419\) | −3.77021 | −0.184187 | −0.0920933 | − | 0.995750i | \(-0.529356\pi\) | ||||
−0.0920933 | + | 0.995750i | \(0.529356\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.50475 | 0.219548 | 0.109774 | − | 0.993957i | \(-0.464987\pi\) | ||||
0.109774 | + | 0.993957i | \(0.464987\pi\) | |||||||
\(422\) | −39.8017 | −1.93752 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −30.1489 | −1.46416 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 16.4064 | 0.793962 | ||||||||
\(428\) | 5.05216 | 0.244206 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.42427 | 0.116909 | ||||||||
\(431\) | 18.7625 | 0.903760 | 0.451880 | − | 0.892079i | \(-0.350753\pi\) | ||||
0.451880 | + | 0.892079i | \(0.350753\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.3455 | 0.785517 | 0.392758 | − | 0.919642i | \(-0.371521\pi\) | ||||
0.392758 | + | 0.919642i | \(0.371521\pi\) | |||||||
\(434\) | −27.4069 | −1.31557 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −53.7975 | −2.57643 | ||||||||
\(437\) | −45.3327 | −2.16856 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.3200 | 0.731182 | 0.365591 | − | 0.930776i | \(-0.380867\pi\) | ||||
0.365591 | + | 0.930776i | \(0.380867\pi\) | |||||||
\(440\) | −14.6502 | −0.698421 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.77021 | 0.179128 | 0.0895640 | − | 0.995981i | \(-0.471453\pi\) | ||||
0.0895640 | + | 0.995981i | \(0.471453\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.92303 | −0.138565 | ||||||||
\(446\) | 38.6923 | 1.83213 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −33.6955 | −1.59196 | ||||||||
\(449\) | −11.8926 | −0.561245 | −0.280622 | − | 0.959818i | \(-0.590541\pi\) | ||||
−0.280622 | + | 0.959818i | \(0.590541\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −42.0556 | −1.98032 | ||||||||
\(452\) | −39.0860 | −1.83845 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.63310 | −0.0766453 | ||||||||
\(455\) | −8.40127 | −0.393858 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.2472 | −0.619679 | −0.309839 | − | 0.950789i | \(-0.600275\pi\) | ||||
−0.309839 | + | 0.950789i | \(0.600275\pi\) | |||||||
\(458\) | 3.82175 | 0.178579 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −17.1492 | −0.799586 | ||||||||
\(461\) | −23.7632 | −1.10676 | −0.553381 | − | 0.832929i | \(-0.686662\pi\) | ||||
−0.553381 | + | 0.832929i | \(0.686662\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.576666 | 0.0268000 | 0.0134000 | − | 0.999910i | \(-0.495735\pi\) | ||||
0.0134000 | + | 0.999910i | \(0.495735\pi\) | |||||||
\(464\) | −2.62498 | −0.121861 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −51.7621 | −2.39783 | ||||||||
\(467\) | 9.67701 | 0.447798 | 0.223899 | − | 0.974612i | \(-0.428121\pi\) | ||||
0.223899 | + | 0.974612i | \(0.428121\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14.4142 | 0.665584 | ||||||||
\(470\) | 2.00939 | 0.0926864 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 37.6551 | 1.73321 | ||||||||
\(473\) | −7.64350 | −0.351448 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 30.9472 | 1.41995 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −28.6350 | −1.30973 | ||||||||
\(479\) | −10.6442 | −0.486348 | −0.243174 | − | 0.969983i | \(-0.578189\pi\) | ||||
−0.243174 | + | 0.969983i | \(0.578189\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.77063 | 0.308714 | ||||||||
\(482\) | −38.3377 | −1.74624 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 77.9386 | 3.54266 | ||||||||
\(485\) | −6.57939 | −0.298755 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.15982 | 0.0525563 | 0.0262781 | − | 0.999655i | \(-0.491634\pi\) | ||||
0.0262781 | + | 0.999655i | \(0.491634\pi\) | |||||||
\(488\) | −19.2688 | −0.872259 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.0684092 | 0.00309041 | ||||||||
\(491\) | −31.8340 | −1.43665 | −0.718324 | − | 0.695709i | \(-0.755090\pi\) | ||||
−0.718324 | + | 0.695709i | \(0.755090\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 64.8015 | 2.91556 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.27774 | 0.102274 | ||||||||
\(497\) | 15.7892 | 0.708243 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.0378 | 0.717949 | 0.358975 | − | 0.933347i | \(-0.383126\pi\) | ||||
0.358975 | + | 0.933347i | \(0.383126\pi\) | |||||||
\(500\) | 25.1482 | 1.12466 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 11.6049 | 0.517954 | ||||||||
\(503\) | −28.1091 | −1.25332 | −0.626661 | − | 0.779292i | \(-0.715579\pi\) | ||||
−0.626661 | + | 0.779292i | \(0.715579\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.3310 | 0.637721 | ||||||||
\(506\) | 86.3766 | 3.83991 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 17.7360 | 0.786907 | ||||||||
\(509\) | 7.13100 | 0.316076 | 0.158038 | − | 0.987433i | \(-0.449483\pi\) | ||||
0.158038 | + | 0.987433i | \(0.449483\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.71688 | −0.297137 | ||||||||
\(512\) | 5.75218 | 0.254213 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −45.1248 | −1.99037 | ||||||||
\(515\) | 4.33425 | 0.190990 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.33544 | −0.278632 | ||||||||
\(518\) | −10.5316 | −0.462734 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 9.86703 | 0.432698 | ||||||||
\(521\) | −37.1135 | −1.62597 | −0.812986 | − | 0.582283i | \(-0.802160\pi\) | ||||
−0.812986 | + | 0.582283i | \(0.802160\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −21.3182 | −0.932180 | −0.466090 | − | 0.884737i | \(-0.654338\pi\) | ||||
−0.466090 | + | 0.884737i | \(0.654338\pi\) | |||||||
\(524\) | 30.9614 | 1.35256 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −21.4670 | −0.936005 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.6973 | 0.769447 | ||||||||
\(530\) | 17.9711 | 0.780616 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −63.0975 | −2.73562 | ||||||||
\(533\) | 28.3248 | 1.22688 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.21213 | −0.0524051 | ||||||||
\(536\) | −16.9290 | −0.731221 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0.119184 | 0.00513840 | ||||||||
\(539\) | −0.215688 | −0.00929034 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −32.8780 | −1.41353 | −0.706767 | − | 0.707447i | \(-0.749847\pi\) | ||||
−0.706767 | + | 0.707447i | \(0.749847\pi\) | |||||||
\(542\) | 41.9720 | 1.80285 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12.9073 | 0.552888 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.8571 | 0.549730 | 0.274865 | − | 0.961483i | \(-0.411367\pi\) | ||||
0.274865 | + | 0.961483i | \(0.411367\pi\) | |||||||
\(548\) | 15.9775 | 0.682524 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −58.9665 | −2.51434 | ||||||||
\(551\) | 36.5893 | 1.55876 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 16.7264 | 0.711278 | ||||||||
\(554\) | −12.8441 | −0.545692 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 62.3874 | 2.64582 | ||||||||
\(557\) | −30.8193 | −1.30585 | −0.652927 | − | 0.757421i | \(-0.726459\pi\) | ||||
−0.652927 | + | 0.757421i | \(0.726459\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.14796 | 0.217735 | ||||||||
\(560\) | −1.08607 | −0.0458946 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5.00412 | −0.211086 | ||||||||
\(563\) | 9.88864 | 0.416756 | 0.208378 | − | 0.978048i | \(-0.433182\pi\) | ||||
0.208378 | + | 0.978048i | \(0.433182\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.37765 | 0.394521 | ||||||||
\(566\) | −57.9034 | −2.43386 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −18.5439 | −0.778087 | ||||||||
\(569\) | −41.5742 | −1.74288 | −0.871441 | − | 0.490500i | \(-0.836814\pi\) | ||||
−0.871441 | + | 0.490500i | \(0.836814\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 31.4219 | 1.31497 | 0.657483 | − | 0.753469i | \(-0.271621\pi\) | ||||
0.657483 | + | 0.753469i | \(0.271621\pi\) | |||||||
\(572\) | −77.2910 | −3.23170 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −44.0589 | −1.83898 | ||||||||
\(575\) | −27.7827 | −1.15862 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −27.9837 | −1.16498 | −0.582488 | − | 0.812839i | \(-0.697921\pi\) | ||||
−0.582488 | + | 0.812839i | \(0.697921\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 13.8416 | 0.574742 | ||||||||
\(581\) | 40.4626 | 1.67867 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −56.6614 | −2.34667 | ||||||||
\(584\) | 7.88877 | 0.326440 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 66.8302 | 2.76073 | ||||||||
\(587\) | −21.1244 | −0.871895 | −0.435948 | − | 0.899972i | \(-0.643587\pi\) | ||||
−0.435948 | + | 0.899972i | \(0.643587\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −31.7493 | −1.30821 | ||||||||
\(590\) | −22.4454 | −0.924063 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.875266 | 0.0359732 | ||||||||
\(593\) | 13.1230 | 0.538896 | 0.269448 | − | 0.963015i | \(-0.413159\pi\) | ||||
0.269448 | + | 0.963015i | \(0.413159\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −34.9674 | −1.43232 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −58.1753 | −2.37896 | ||||||||
\(599\) | 7.55832 | 0.308824 | 0.154412 | − | 0.988007i | \(-0.450652\pi\) | ||||
0.154412 | + | 0.988007i | \(0.450652\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17.7861 | −0.725511 | −0.362755 | − | 0.931884i | \(-0.618164\pi\) | ||||
−0.362755 | + | 0.931884i | \(0.618164\pi\) | |||||||
\(602\) | −8.00759 | −0.326365 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −12.3013 | −0.500532 | ||||||||
\(605\) | −18.6993 | −0.760236 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 37.8999 | 1.53831 | 0.769155 | − | 0.639062i | \(-0.220677\pi\) | ||||
0.769155 | + | 0.639062i | \(0.220677\pi\) | |||||||
\(608\) | −35.9010 | −1.45598 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 11.4858 | 0.465045 | ||||||||
\(611\) | 4.26697 | 0.172623 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16.9240 | −0.683552 | −0.341776 | − | 0.939781i | \(-0.611028\pi\) | ||||
−0.341776 | + | 0.939781i | \(0.611028\pi\) | |||||||
\(614\) | −16.3986 | −0.661793 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 48.3911 | 1.94973 | ||||||||
\(617\) | −0.375777 | −0.0151282 | −0.00756412 | − | 0.999971i | \(-0.502408\pi\) | ||||
−0.00756412 | + | 0.999971i | \(0.502408\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22.4074 | −0.900628 | −0.450314 | − | 0.892870i | \(-0.648688\pi\) | ||||
−0.450314 | + | 0.892870i | \(0.648688\pi\) | |||||||
\(620\) | −12.0106 | −0.482359 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −21.6910 | −0.869729 | ||||||||
\(623\) | 9.65505 | 0.386821 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.7415 | 0.629661 | ||||||||
\(626\) | −67.4897 | −2.69743 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 17.0000 | 0.678374 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.4929 | 0.497334 | 0.248667 | − | 0.968589i | \(-0.420008\pi\) | ||||
0.248667 | + | 0.968589i | \(0.420008\pi\) | |||||||
\(632\) | −19.6446 | −0.781421 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −36.1411 | −1.43535 | ||||||||
\(635\) | −4.25528 | −0.168866 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.145268 | 0.00575571 | ||||||||
\(638\) | −69.7170 | −2.76012 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −15.4747 | −0.611692 | ||||||||
\(641\) | 28.1943 | 1.11361 | 0.556804 | − | 0.830644i | \(-0.312028\pi\) | ||||
0.556804 | + | 0.830644i | \(0.312028\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −38.3773 | −1.51345 | −0.756727 | − | 0.653731i | \(-0.773203\pi\) | ||||
−0.756727 | + | 0.653731i | \(0.773203\pi\) | |||||||
\(644\) | 56.6455 | 2.23215 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −22.0718 | −0.867732 | −0.433866 | − | 0.900977i | \(-0.642851\pi\) | ||||
−0.433866 | + | 0.900977i | \(0.642851\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 70.7684 | 2.77790 | ||||||||
\(650\) | 39.7144 | 1.55773 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 23.0046 | 0.900928 | ||||||||
\(653\) | 9.83710 | 0.384955 | 0.192478 | − | 0.981301i | \(-0.438348\pi\) | ||||
0.192478 | + | 0.981301i | \(0.438348\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.42839 | −0.290251 | ||||||||
\(656\) | 3.66166 | 0.142964 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −6.63722 | −0.258746 | ||||||||
\(659\) | −0.0968652 | −0.00377333 | −0.00188667 | − | 0.999998i | \(-0.500601\pi\) | ||||
−0.00188667 | + | 0.999998i | \(0.500601\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.3523 | 0.636033 | 0.318016 | − | 0.948085i | \(-0.396983\pi\) | ||||
0.318016 | + | 0.948085i | \(0.396983\pi\) | |||||||
\(662\) | −9.45510 | −0.367483 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −47.5221 | −1.84422 | ||||||||
\(665\) | 15.1386 | 0.587049 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −32.8479 | −1.27188 | ||||||||
\(668\) | 44.2507 | 1.71211 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 10.0910 | 0.389850 | ||||||||
\(671\) | −36.2136 | −1.39801 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −36.6705 | −1.41355 | −0.706773 | − | 0.707441i | \(-0.749850\pi\) | ||||
−0.706773 | + | 0.707441i | \(0.749850\pi\) | |||||||
\(674\) | −9.42552 | −0.363057 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 8.54126 | 0.328510 | ||||||||
\(677\) | 18.1016 | 0.695703 | 0.347851 | − | 0.937550i | \(-0.386911\pi\) | ||||
0.347851 | + | 0.937550i | \(0.386911\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 21.7324 | 0.834012 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 60.4948 | 2.31646 | ||||||||
\(683\) | −51.1028 | −1.95540 | −0.977698 | − | 0.210018i | \(-0.932648\pi\) | ||||
−0.977698 | + | 0.210018i | \(0.932648\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.83338 | −0.146466 | ||||||||
\(686\) | 42.7132 | 1.63080 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.665497 | 0.0253718 | ||||||||
\(689\) | 38.1619 | 1.45385 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.2131 | −0.616774 | −0.308387 | − | 0.951261i | \(-0.599789\pi\) | ||||
−0.308387 | + | 0.951261i | \(0.599789\pi\) | |||||||
\(692\) | 4.55540 | 0.173170 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 26.0915 | 0.990421 | ||||||||
\(695\) | −14.9682 | −0.567777 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −63.0860 | −2.38784 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −38.6701 | −1.46159 | ||||||||
\(701\) | 32.6371 | 1.23269 | 0.616343 | − | 0.787478i | \(-0.288614\pi\) | ||||
0.616343 | + | 0.787478i | \(0.288614\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12.2003 | −0.460142 | ||||||||
\(704\) | 74.3754 | 2.80313 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −48.5880 | −1.82863 | ||||||||
\(707\) | −47.3367 | −1.78028 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −21.7014 | −0.815013 | −0.407507 | − | 0.913202i | \(-0.633602\pi\) | ||||
−0.407507 | + | 0.913202i | \(0.633602\pi\) | |||||||
\(710\) | 11.0537 | 0.414837 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −11.3396 | −0.424968 | ||||||||
\(713\) | 28.5028 | 1.06744 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 18.5439 | 0.693504 | ||||||||
\(716\) | 5.54892 | 0.207373 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −71.3355 | −2.66222 | ||||||||
\(719\) | −16.9963 | −0.633854 | −0.316927 | − | 0.948450i | \(-0.602651\pi\) | ||||
−0.316927 | + | 0.948450i | \(0.602651\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.3164 | −0.533172 | ||||||||
\(722\) | −72.8325 | −2.71054 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −44.6059 | −1.65776 | ||||||||
\(725\) | 22.4242 | 0.832814 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23.8212 | 0.883479 | 0.441740 | − | 0.897143i | \(-0.354362\pi\) | ||||
0.441740 | + | 0.897143i | \(0.354362\pi\) | |||||||
\(728\) | −32.5918 | −1.20793 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −4.70233 | −0.174041 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −44.1661 | −1.63131 | −0.815657 | − | 0.578536i | \(-0.803624\pi\) | ||||
−0.815657 | + | 0.578536i | \(0.803624\pi\) | |||||||
\(734\) | −61.7924 | −2.28080 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 32.2300 | 1.18801 | ||||||||
\(737\) | −31.8161 | −1.17196 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −27.7219 | −1.01977 | −0.509884 | − | 0.860243i | \(-0.670312\pi\) | ||||
−0.509884 | + | 0.860243i | \(0.670312\pi\) | |||||||
\(740\) | −4.61532 | −0.169663 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −59.3604 | −2.17919 | ||||||||
\(743\) | 21.4727 | 0.787757 | 0.393879 | − | 0.919162i | \(-0.371133\pi\) | ||||
0.393879 | + | 0.919162i | \(0.371133\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.38951 | 0.307368 | ||||||||
\(746\) | 12.1262 | 0.443970 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.00380 | 0.146296 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.40467 | −0.0512570 | −0.0256285 | − | 0.999672i | \(-0.508159\pi\) | ||||
−0.0256285 | + | 0.999672i | \(0.508159\pi\) | |||||||
\(752\) | 0.551608 | 0.0201151 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 46.9549 | 1.71000 | ||||||||
\(755\) | 2.95137 | 0.107411 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 30.8262 | 1.12040 | 0.560199 | − | 0.828358i | \(-0.310724\pi\) | ||||
0.560199 | + | 0.828358i | \(0.310724\pi\) | |||||||
\(758\) | 18.6595 | 0.677742 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −17.7798 | −0.644941 | ||||||||
\(761\) | 35.1432 | 1.27394 | 0.636971 | − | 0.770888i | \(-0.280187\pi\) | ||||
0.636971 | + | 0.770888i | \(0.280187\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −42.6340 | −1.54346 | ||||||||
\(764\) | 38.2650 | 1.38438 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −7.20439 | −0.260305 | ||||||||
\(767\) | −47.6631 | −1.72101 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24.5449 | 0.885111 | 0.442556 | − | 0.896741i | \(-0.354072\pi\) | ||||
0.442556 | + | 0.896741i | \(0.354072\pi\) | |||||||
\(770\) | −28.8449 | −1.03950 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −51.9021 | −1.86800 | ||||||||
\(773\) | 19.6625 | 0.707211 | 0.353606 | − | 0.935395i | \(-0.384955\pi\) | ||||
0.353606 | + | 0.935395i | \(0.384955\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −19.4579 | −0.698949 | ||||||||
\(776\) | −25.5240 | −0.916258 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −23.5481 | −0.844239 | ||||||||
\(779\) | −51.0396 | −1.82868 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −34.8512 | −1.24707 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.0187793 | 0.000670690 0 | ||||||||
\(785\) | −4.07870 | −0.145575 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −18.5354 | −0.660715 | −0.330358 | − | 0.943856i | \(-0.607169\pi\) | ||||
−0.330358 | + | 0.943856i | \(0.607169\pi\) | |||||||
\(788\) | 66.4256 | 2.36631 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 11.7098 | 0.416614 | ||||||||
\(791\) | −30.9753 | −1.10135 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 24.3901 | 0.866119 | ||||||||
\(794\) | −60.9915 | −2.16451 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 9.42333 | 0.334001 | ||||||||
\(797\) | 39.3923 | 1.39535 | 0.697673 | − | 0.716416i | \(-0.254219\pi\) | ||||
0.697673 | + | 0.716416i | \(0.254219\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −22.0024 | −0.777901 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −60.2708 | −2.12823 | ||||||||
\(803\) | 14.8260 | 0.523199 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −13.5906 | −0.479006 | ||||||||
\(806\) | −40.7437 | −1.43514 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 55.5954 | 1.95584 | ||||||||
\(809\) | −53.6426 | −1.88597 | −0.942987 | − | 0.332830i | \(-0.891997\pi\) | ||||
−0.942987 | + | 0.332830i | \(0.891997\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 42.3327 | 1.48650 | 0.743252 | − | 0.669012i | \(-0.233282\pi\) | ||||
0.743252 | + | 0.669012i | \(0.233282\pi\) | |||||||
\(812\) | −45.7202 | −1.60446 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 23.2463 | 0.814782 | ||||||||
\(815\) | −5.51934 | −0.193334 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.27631 | −0.324537 | ||||||||
\(818\) | 68.0077 | 2.37783 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −19.3081 | −0.674268 | ||||||||
\(821\) | −33.3433 | −1.16369 | −0.581845 | − | 0.813300i | \(-0.697669\pi\) | ||||
−0.581845 | + | 0.813300i | \(0.697669\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 30.9469 | 1.07874 | 0.539370 | − | 0.842069i | \(-0.318662\pi\) | ||||
0.539370 | + | 0.842069i | \(0.318662\pi\) | |||||||
\(824\) | 16.8142 | 0.585751 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 74.1394 | 2.57964 | ||||||||
\(827\) | −7.02245 | −0.244194 | −0.122097 | − | 0.992518i | \(-0.538962\pi\) | ||||
−0.122097 | + | 0.992518i | \(0.538962\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.2959 | 0.461786 | 0.230893 | − | 0.972979i | \(-0.425835\pi\) | ||||
0.230893 | + | 0.972979i | \(0.425835\pi\) | |||||||
\(830\) | 28.3269 | 0.983243 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −50.0925 | −1.73664 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10.6168 | −0.367410 | ||||||||
\(836\) | 139.274 | 4.81689 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 8.71831 | 0.301169 | ||||||||
\(839\) | −32.9613 | −1.13795 | −0.568976 | − | 0.822354i | \(-0.692660\pi\) | ||||
−0.568976 | + | 0.822354i | \(0.692660\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.48751 | −0.0857763 | ||||||||
\(842\) | −10.4169 | −0.358989 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 57.6141 | 1.98316 | ||||||||
\(845\) | −2.04925 | −0.0704964 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 61.7657 | 2.12229 | ||||||||
\(848\) | 4.93334 | 0.169412 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.9527 | 0.375455 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.33511 | −0.216910 | −0.108455 | − | 0.994101i | \(-0.534590\pi\) | ||||
−0.108455 | + | 0.994101i | \(0.534590\pi\) | |||||||
\(854\) | −37.9386 | −1.29823 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.70233 | −0.160722 | ||||||||
\(857\) | −11.4769 | −0.392044 | −0.196022 | − | 0.980599i | \(-0.562802\pi\) | ||||
−0.196022 | + | 0.980599i | \(0.562802\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.8817 | 0.473639 | 0.236820 | − | 0.971554i | \(-0.423895\pi\) | ||||
0.236820 | + | 0.971554i | \(0.423895\pi\) | |||||||
\(860\) | −3.50920 | −0.119663 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −43.3869 | −1.47776 | ||||||||
\(863\) | 14.3534 | 0.488595 | 0.244298 | − | 0.969700i | \(-0.421443\pi\) | ||||
0.244298 | + | 0.969700i | \(0.421443\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.09295 | −0.0371614 | ||||||||
\(866\) | −37.7978 | −1.28442 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 39.6723 | 1.34657 | ||||||||
\(869\) | −36.9198 | −1.25242 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 21.4284 | 0.726073 | ||||||||
\(872\) | 50.0724 | 1.69566 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 104.828 | 3.54587 | ||||||||
\(875\) | 19.9297 | 0.673748 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 49.3201 | 1.66542 | 0.832710 | − | 0.553709i | \(-0.186788\pi\) | ||||
0.832710 | + | 0.553709i | \(0.186788\pi\) | |||||||
\(878\) | −35.4262 | −1.19558 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.39725 | 0.0808113 | ||||||||
\(881\) | 16.2049 | 0.545955 | 0.272978 | − | 0.962020i | \(-0.411991\pi\) | ||||
0.272978 | + | 0.962020i | \(0.411991\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 45.1293 | 1.51872 | 0.759361 | − | 0.650670i | \(-0.225512\pi\) | ||||
0.759361 | + | 0.650670i | \(0.225512\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −8.71831 | −0.292897 | ||||||||
\(887\) | −13.9199 | −0.467383 | −0.233692 | − | 0.972311i | \(-0.575081\pi\) | ||||
−0.233692 | + | 0.972311i | \(0.575081\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 14.0556 | 0.471410 | ||||||||
\(890\) | 6.75928 | 0.226571 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −56.0082 | −1.87529 | ||||||||
\(893\) | −7.68882 | −0.257297 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.33132 | −0.0445011 | ||||||||
\(896\) | 51.1145 | 1.70762 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 27.5006 | 0.917708 | ||||||||
\(899\) | −23.0054 | −0.767273 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 97.2503 | 3.23808 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 36.3795 | 1.20996 | ||||||||
\(905\) | 10.7020 | 0.355747 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.87164 | 0.327783 | 0.163891 | − | 0.986478i | \(-0.447595\pi\) | ||||
0.163891 | + | 0.986478i | \(0.447595\pi\) | |||||||
\(908\) | 2.36396 | 0.0784509 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 19.4273 | 0.644008 | ||||||||
\(911\) | 38.5596 | 1.27754 | 0.638769 | − | 0.769399i | \(-0.279444\pi\) | ||||
0.638769 | + | 0.769399i | \(0.279444\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −89.3123 | −2.95581 | ||||||||
\(914\) | 30.6332 | 1.01325 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.53209 | −0.182785 | ||||||||
\(917\) | 24.5367 | 0.810273 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.885371 | 0.0292057 | 0.0146029 | − | 0.999893i | \(-0.495352\pi\) | ||||
0.0146029 | + | 0.999893i | \(0.495352\pi\) | |||||||
\(920\) | 15.9617 | 0.526243 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 54.9505 | 1.80970 | ||||||||
\(923\) | 23.4726 | 0.772609 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.47708 | −0.245845 | ||||||||
\(926\) | −1.33350 | −0.0438214 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −26.0137 | −0.853942 | ||||||||
\(929\) | −8.34973 | −0.273946 | −0.136973 | − | 0.990575i | \(-0.543737\pi\) | ||||
−0.136973 | + | 0.990575i | \(0.543737\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.261764 | −0.00857895 | ||||||||
\(932\) | 74.9271 | 2.45432 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −22.3773 | −0.732208 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 27.7374 | 0.906142 | 0.453071 | − | 0.891474i | \(-0.350328\pi\) | ||||
0.453071 | + | 0.891474i | \(0.350328\pi\) | |||||||
\(938\) | −33.3316 | −1.08832 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2.90865 | −0.0948698 | ||||||||
\(941\) | −40.6962 | −1.32666 | −0.663329 | − | 0.748328i | \(-0.730857\pi\) | ||||
−0.663329 | + | 0.748328i | \(0.730857\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 45.8206 | 1.49212 | ||||||||
\(944\) | −6.16160 | −0.200543 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 17.6750 | 0.574664 | ||||||||
\(947\) | −39.2775 | −1.27635 | −0.638174 | − | 0.769892i | \(-0.720310\pi\) | ||||
−0.638174 | + | 0.769892i | \(0.720310\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.98545 | −0.324141 | ||||||||
\(950\) | −71.5630 | −2.32181 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 29.7943 | 0.965131 | 0.482565 | − | 0.875860i | \(-0.339705\pi\) | ||||
0.482565 | + | 0.875860i | \(0.339705\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9.18067 | −0.297080 | ||||||||
\(956\) | 41.4499 | 1.34059 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 24.6140 | 0.795242 | ||||||||
\(959\) | 12.6620 | 0.408878 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.0378 | −0.356057 | ||||||||
\(962\) | −15.6566 | −0.504788 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 55.4949 | 1.78737 | ||||||||
\(965\) | 12.4525 | 0.400862 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.53384 | 0.0493251 | 0.0246625 | − | 0.999696i | \(-0.492149\pi\) | ||||
0.0246625 | + | 0.999696i | \(0.492149\pi\) | |||||||
\(968\) | −72.5419 | −2.33158 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 15.2143 | 0.488503 | ||||||||
\(971\) | −32.2214 | −1.03404 | −0.517018 | − | 0.855975i | \(-0.672958\pi\) | ||||
−0.517018 | + | 0.855975i | \(0.672958\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 49.4415 | 1.58502 | ||||||||
\(974\) | −2.68198 | −0.0859363 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.15301 | 0.100925 | ||||||||
\(977\) | 5.18889 | 0.166007 | 0.0830036 | − | 0.996549i | \(-0.473549\pi\) | ||||
0.0830036 | + | 0.996549i | \(0.473549\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −21.3114 | −0.681115 | ||||||||
\(980\) | −0.0990242 | −0.00316321 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 73.6136 | 2.34910 | ||||||||
\(983\) | −34.8307 | −1.11093 | −0.555463 | − | 0.831541i | \(-0.687459\pi\) | ||||
−0.555463 | + | 0.831541i | \(0.687459\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −15.9371 | −0.507798 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −93.8020 | −2.98424 | ||||||||
\(989\) | 8.32777 | 0.264808 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 48.5580 | 1.54250 | 0.771248 | − | 0.636535i | \(-0.219633\pi\) | ||||
0.771248 | + | 0.636535i | \(0.219633\pi\) | |||||||
\(992\) | 22.5726 | 0.716681 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −36.5113 | −1.15807 | ||||||||
\(995\) | −2.26088 | −0.0716748 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 56.2576 | 1.78170 | 0.890849 | − | 0.454300i | \(-0.150111\pi\) | ||||
0.890849 | + | 0.454300i | \(0.150111\pi\) | |||||||
\(998\) | −37.0861 | −1.17394 | ||||||||
\(999\) | 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 | 2601.2.a.bk.1.2 | yes | 6 | |
3.2 | odd | 2 | inner | 2601.2.a.bk.1.5 | yes | 6 | |
17.16 | even | 2 | 2601.2.a.bj.1.2 | ✓ | 6 | ||
51.50 | odd | 2 | 2601.2.a.bj.1.5 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2601.2.a.bj.1.2 | ✓ | 6 | 17.16 | even | 2 | ||
2601.2.a.bj.1.5 | yes | 6 | 51.50 | odd | 2 | ||
2601.2.a.bk.1.2 | yes | 6 | 1.1 | even | 1 | trivial | |
2601.2.a.bk.1.5 | yes | 6 | 3.2 | odd | 2 | inner |