Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [648,4,Mod(1,648)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(648, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("648.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 648 = 2^{3} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 648.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: | \(38.2332376837\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.29952.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 8x^{2} + 13 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3}\cdot 3^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.50597\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 648.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −17.9847 | −1.60860 | −0.804301 | − | 0.594222i | \(-0.797460\pi\) | ||||
−0.804301 | + | 0.594222i | \(0.797460\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.28309 | 0.393250 | 0.196625 | − | 0.980479i | \(-0.437002\pi\) | ||||
0.196625 | + | 0.980479i | \(0.437002\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.61468 | 0.126489 | 0.0632445 | − | 0.997998i | \(-0.479855\pi\) | ||||
0.0632445 | + | 0.997998i | \(0.479855\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 29.8602 | 0.637056 | 0.318528 | − | 0.947913i | \(-0.396811\pi\) | ||||
0.318528 | + | 0.947913i | \(0.396811\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 67.9721 | 0.969744 | 0.484872 | − | 0.874585i | \(-0.338866\pi\) | ||||
0.484872 | + | 0.874585i | \(0.338866\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 111.462 | 1.34585 | 0.672926 | − | 0.739710i | \(-0.265037\pi\) | ||||
0.672926 | + | 0.739710i | \(0.265037\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −218.506 | −1.98094 | −0.990472 | − | 0.137711i | \(-0.956025\pi\) | ||||
−0.990472 | + | 0.137711i | \(0.956025\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 198.450 | 1.58760 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 34.2713 | 0.219449 | 0.109725 | − | 0.993962i | \(-0.465003\pi\) | ||||
0.109725 | + | 0.993962i | \(0.465003\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −77.7046 | −0.450199 | −0.225099 | − | 0.974336i | \(-0.572271\pi\) | ||||
−0.225099 | + | 0.974336i | \(0.572271\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −130.984 | −0.632583 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −347.228 | −1.54281 | −0.771404 | − | 0.636346i | \(-0.780445\pi\) | ||||
−0.771404 | + | 0.636346i | \(0.780445\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 234.546 | 0.893413 | 0.446707 | − | 0.894680i | \(-0.352597\pi\) | ||||
0.446707 | + | 0.894680i | \(0.352597\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 53.3798 | 0.189310 | 0.0946552 | − | 0.995510i | \(-0.469825\pi\) | ||||
0.0946552 | + | 0.995510i | \(0.469825\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −385.402 | −1.19610 | −0.598049 | − | 0.801460i | \(-0.704057\pi\) | ||||
−0.598049 | + | 0.801460i | \(0.704057\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −289.957 | −0.845354 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −461.661 | −1.19649 | −0.598245 | − | 0.801313i | \(-0.704135\pi\) | ||||
−0.598245 | + | 0.801313i | \(0.704135\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −82.9938 | −0.203471 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.16328 | 0.0158064 | 0.00790322 | − | 0.999969i | \(-0.497484\pi\) | ||||
0.00790322 | + | 0.999969i | \(0.497484\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 416.109 | 0.873398 | 0.436699 | − | 0.899608i | \(-0.356147\pi\) | ||||
0.436699 | + | 0.899608i | \(0.356147\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −537.027 | −1.02477 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −869.274 | −1.58506 | −0.792528 | − | 0.609835i | \(-0.791236\pi\) | ||||
−0.792528 | + | 0.609835i | \(0.791236\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −585.943 | −0.979417 | −0.489709 | − | 0.871886i | \(-0.662897\pi\) | ||||
−0.489709 | + | 0.871886i | \(0.662897\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −733.324 | −1.17574 | −0.587870 | − | 0.808955i | \(-0.700034\pi\) | ||||
−0.587870 | + | 0.808955i | \(0.700034\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 33.6092 | 0.0497418 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1170.90 | 1.66754 | 0.833772 | − | 0.552108i | \(-0.186177\pi\) | ||||
0.833772 | + | 0.552108i | \(0.186177\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −67.4364 | −0.0891820 | −0.0445910 | − | 0.999005i | \(-0.514198\pi\) | ||||
−0.0445910 | + | 0.999005i | \(0.514198\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1222.46 | −1.55993 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −965.886 | −1.15038 | −0.575189 | − | 0.818020i | \(-0.695072\pi\) | ||||
−0.575189 | + | 0.818020i | \(0.695072\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 217.475 | 0.250522 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2004.62 | −2.16494 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.43299 | 0.00149998 | 0.000749988 | − | 1.00000i | \(-0.499761\pi\) | ||||
0.000749988 | 1.00000i | \(0.499761\pi\) | ||||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −896.177 | −0.882901 | −0.441450 | − | 0.897286i | \(-0.645536\pi\) | ||||
−0.441450 | + | 0.897286i | \(0.645536\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1940.81 | 1.85664 | 0.928318 | − | 0.371788i | \(-0.121255\pi\) | ||||
0.928318 | + | 0.371788i | \(0.121255\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1888.04 | 1.70583 | 0.852915 | − | 0.522050i | \(-0.174832\pi\) | ||||
0.852915 | + | 0.522050i | \(0.174832\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1201.72 | 1.05600 | 0.528001 | − | 0.849244i | \(-0.322942\pi\) | ||||
0.528001 | + | 0.849244i | \(0.322942\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1522.42 | −1.26741 | −0.633706 | − | 0.773574i | \(-0.718467\pi\) | ||||
−0.633706 | + | 0.773574i | \(0.718467\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3929.78 | 3.18655 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 495.047 | 0.381352 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1309.70 | −0.984001 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1320.98 | −0.945214 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2300.50 | −1.60738 | −0.803688 | − | 0.595051i | \(-0.797132\pi\) | ||||
−0.803688 | + | 0.595051i | \(0.797132\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1038.33 | −0.692517 | −0.346258 | − | 0.938139i | \(-0.612548\pi\) | ||||
−0.346258 | + | 0.938139i | \(0.612548\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 811.790 | 0.529256 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1089.53 | −0.679448 | −0.339724 | − | 0.940525i | \(-0.610334\pi\) | ||||
−0.339724 | + | 0.940525i | \(0.610334\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1919.33 | −1.17119 | −0.585594 | − | 0.810605i | \(-0.699139\pi\) | ||||
−0.585594 | + | 0.810605i | \(0.699139\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 137.795 | 0.0805807 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −616.360 | −0.353006 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2131.77 | 1.17209 | 0.586044 | − | 0.810279i | \(-0.300684\pi\) | ||||
0.586044 | + | 0.810279i | \(0.300684\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1165.86 | −0.628323 | −0.314161 | − | 0.949370i | \(-0.601723\pi\) | ||||
−0.314161 | + | 0.949370i | \(0.601723\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1397.50 | 0.724191 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 36.7762 | 0.0186947 | 0.00934733 | − | 0.999956i | \(-0.497025\pi\) | ||||
0.00934733 | + | 0.999956i | \(0.497025\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1591.40 | −0.779007 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3208.90 | 1.54197 | 0.770983 | − | 0.636856i | \(-0.219765\pi\) | ||||
0.770983 | + | 0.636856i | \(0.219765\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1796.09 | −0.832248 | −0.416124 | − | 0.909308i | \(-0.636612\pi\) | ||||
−0.416124 | + | 0.909308i | \(0.636612\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1305.37 | −0.594159 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1694.71 | −0.744778 | −0.372389 | − | 0.928077i | \(-0.621461\pi\) | ||||
−0.372389 | + | 0.928077i | \(0.621461\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1445.33 | 0.624324 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 327.128 | 0.136596 | 0.0682981 | − | 0.997665i | \(-0.478243\pi\) | ||||
0.0682981 | + | 0.997665i | \(0.478243\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4449.32 | −1.82716 | −0.913578 | − | 0.406663i | \(-0.866692\pi\) | ||||
−0.913578 | + | 0.406663i | \(0.866692\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6244.79 | 2.48176 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 313.670 | 0.122662 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2078.96 | −0.787583 | −0.393792 | − | 0.919200i | \(-0.628837\pi\) | ||||
−0.393792 | + | 0.919200i | \(0.628837\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2887.17 | −1.07680 | −0.538401 | − | 0.842688i | \(-0.680972\pi\) | ||||
−0.538401 | + | 0.842688i | \(0.680972\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2679.74 | −0.969154 | −0.484577 | − | 0.874749i | \(-0.661027\pi\) | ||||
−0.484577 | + | 0.874749i | \(0.661027\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 341.646 | 0.121702 | 0.0608508 | − | 0.998147i | \(-0.480619\pi\) | ||||
0.0608508 | + | 0.998147i | \(0.480619\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 249.601 | 0.0862984 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4218.25 | −1.43715 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 514.363 | 0.170236 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1575.78 | 0.514128 | 0.257064 | − | 0.966394i | \(-0.417245\pi\) | ||||
0.257064 | + | 0.966394i | \(0.417245\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −960.021 | −0.304525 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −565.930 | −0.177041 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2029.66 | 0.617782 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2982.80 | −0.895708 | −0.447854 | − | 0.894107i | \(-0.647812\pi\) | ||||
−0.447854 | + | 0.894107i | \(0.647812\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2139.81 | 0.625656 | 0.312828 | − | 0.949810i | \(-0.398724\pi\) | ||||
0.312828 | + | 0.949810i | \(0.398724\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 619.401 | 0.178739 | 0.0893694 | − | 0.995999i | \(-0.471515\pi\) | ||||
0.0893694 | + | 0.995999i | \(0.471515\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4272.01 | 1.20115 | 0.600577 | − | 0.799567i | \(-0.294938\pi\) | ||||
0.600577 | + | 0.799567i | \(0.294938\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6931.34 | 1.92405 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6252.62 | −1.69225 | −0.846126 | − | 0.532982i | \(-0.821071\pi\) | ||||
−0.846126 | + | 0.532982i | \(0.821071\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 250.780 | 0.0670296 | 0.0335148 | − | 0.999438i | \(-0.489330\pi\) | ||||
0.0335148 | + | 0.999438i | \(0.489330\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5214.79 | 1.35984 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3328.29 | 0.857384 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7146.55 | 1.79716 | 0.898579 | − | 0.438812i | \(-0.144601\pi\) | ||||
0.898579 | + | 0.438812i | \(0.144601\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1008.34 | −0.250568 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3027.64 | 0.734859 | 0.367429 | − | 0.930051i | \(-0.380238\pi\) | ||||
0.367429 | + | 0.930051i | \(0.380238\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2528.89 | −0.606709 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5218.96 | 1.22363 | 0.611816 | − | 0.791000i | \(-0.290439\pi\) | ||||
0.611816 | + | 0.791000i | \(0.290439\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8302.84 | 1.92468 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6038.18 | 1.36860 | 0.684302 | − | 0.729199i | \(-0.260107\pi\) | ||||
0.684302 | + | 0.729199i | \(0.260107\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3726.70 | 0.835354 | 0.417677 | − | 0.908596i | \(-0.362844\pi\) | ||||
0.417677 | + | 0.908596i | \(0.362844\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 915.784 | 0.200814 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −572.095 | −0.124093 | −0.0620466 | − | 0.998073i | \(-0.519763\pi\) | ||||
−0.0620466 | + | 0.998073i | \(0.519763\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2047.98 | 0.434777 | 0.217389 | − | 0.976085i | \(-0.430246\pi\) | ||||
0.217389 | + | 0.976085i | \(0.430246\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4793.97 | 1.00697 | 0.503484 | − | 0.864005i | \(-0.332051\pi\) | ||||
0.503484 | + | 0.864005i | \(0.332051\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1708.22 | 0.351335 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −292.797 | −0.0595963 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 69.4967 | 0.0138568 | 0.00692840 | − | 0.999976i | \(-0.497795\pi\) | ||||
0.00692840 | + | 0.999976i | \(0.497795\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −128.830 | −0.0254263 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6524.65 | −1.26197 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 388.770 | 0.0744463 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7483.60 | −1.40495 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 665.210 | 0.123666 | 0.0618331 | − | 0.998087i | \(-0.480305\pi\) | ||||
0.0618331 | + | 0.998087i | \(0.480305\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −252.564 | −0.0460501 | −0.0230251 | − | 0.999735i | \(-0.507330\pi\) | ||||
−0.0230251 | + | 0.999735i | \(0.507330\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8826.49 | −1.59394 | −0.796969 | − | 0.604020i | \(-0.793565\pi\) | ||||
−0.796969 | + | 0.604020i | \(0.793565\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 917.091 | 0.162489 | 0.0812444 | − | 0.996694i | \(-0.474111\pi\) | ||||
0.0812444 | + | 0.996694i | \(0.474111\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 158.151 | 0.0277579 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7576.32 | 1.30513 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5925.76 | 1.01139 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2806.92 | −0.470365 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1662.81 | −0.276122 | −0.138061 | − | 0.990424i | \(-0.544087\pi\) | ||||
−0.138061 | + | 0.990424i | \(0.544087\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 15633.7 | 2.54972 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2403.96 | −0.388582 | −0.194291 | − | 0.980944i | \(-0.562241\pi\) | ||||
−0.194291 | + | 0.980944i | \(0.562241\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −358.582 | −0.0569452 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4609.88 | −0.725686 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7871.63 | 1.21778 | 0.608892 | − | 0.793253i | \(-0.291614\pi\) | ||||
0.608892 | + | 0.793253i | \(0.291614\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11474.1 | −1.75987 | −0.879934 | − | 0.475096i | \(-0.842413\pi\) | ||||
−0.879934 | + | 0.475096i | \(0.842413\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4021.19 | −0.606306 | −0.303153 | − | 0.952942i | \(-0.598039\pi\) | ||||
−0.303153 | + | 0.952942i | \(0.598039\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10538.0 | 1.57549 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1662.93 | 0.244473 | 0.122237 | − | 0.992501i | \(-0.460993\pi\) | ||||
0.122237 | + | 0.992501i | \(0.460993\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5564.84 | 0.811319 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 13188.6 | 1.89130 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2938.64 | −0.417972 | −0.208986 | − | 0.977919i | \(-0.567016\pi\) | ||||
−0.208986 | + | 0.977919i | \(0.567016\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3362.32 | −0.470520 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7619.53 | −1.05771 | −0.528853 | − | 0.848713i | \(-0.677378\pi\) | ||||
−0.528853 | + | 0.848713i | \(0.677378\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1023.35 | 0.139802 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13118.3 | −1.77795 | −0.888975 | − | 0.457955i | \(-0.848582\pi\) | ||||
−0.888975 | + | 0.457955i | \(0.848582\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8602.70 | 1.14772 | 0.573861 | − | 0.818953i | \(-0.305445\pi\) | ||||
0.573861 | + | 0.818953i | \(0.305445\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −604.451 | −0.0800148 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −12921.6 | −1.68419 | −0.842095 | − | 0.539329i | \(-0.818678\pi\) | ||||
−0.842095 | + | 0.539329i | \(0.818678\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14852.3 | −1.92101 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −21058.2 | −2.68242 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5511.90 | 0.696812 | 0.348406 | − | 0.937344i | \(-0.386723\pi\) | ||||
0.348406 | + | 0.937344i | \(0.386723\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2233.31 | −0.278120 | −0.139060 | − | 0.990284i | \(-0.544408\pi\) | ||||
−0.139060 | + | 0.990284i | \(0.544408\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2320.28 | −0.286802 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1602.35 | −0.195148 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2225.31 | 0.269033 | 0.134517 | − | 0.990911i | \(-0.457052\pi\) | ||||
0.134517 | + | 0.990911i | \(0.457052\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 52.1708 | 0.00621588 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1212.82 | 0.143458 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5421.12 | 0.632074 | 0.316037 | − | 0.948747i | \(-0.397648\pi\) | ||||
0.316037 | + | 0.948747i | \(0.397648\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12820.4 | 1.48415 | 0.742075 | − | 0.670317i | \(-0.233842\pi\) | ||||
0.742075 | + | 0.670317i | \(0.233842\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 13489.1 | 1.53957 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3030.56 | 0.343464 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10070.7 | 1.12549 | 0.562747 | − | 0.826629i | \(-0.309745\pi\) | ||||
0.562747 | + | 0.826629i | \(0.309745\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5708.09 | −0.633518 | −0.316759 | − | 0.948506i | \(-0.602595\pi\) | ||||
−0.316759 | + | 0.948506i | \(0.602595\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −24355.2 | −2.66606 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2979.59 | −0.323936 | −0.161968 | − | 0.986796i | \(-0.551784\pi\) | ||||
−0.161968 | + | 0.986796i | \(0.551784\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10492.4 | −1.12530 | −0.562649 | − | 0.826696i | \(-0.690218\pi\) | ||||
−0.562649 | + | 0.826696i | \(0.690218\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 17371.2 | 1.85050 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4846.95 | 0.509447 | 0.254724 | − | 0.967014i | \(-0.418015\pi\) | ||||
0.254724 | + | 0.967014i | \(0.418015\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1082.36 | 0.113007 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3911.22 | −0.402991 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5141.73 | 0.526302 | 0.263151 | − | 0.964755i | \(-0.415238\pi\) | ||||
0.263151 | + | 0.964755i | \(0.415238\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3992.66 | 0.403377 | 0.201689 | − | 0.979450i | \(-0.435357\pi\) | ||||
0.201689 | + | 0.979450i | \(0.435357\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9507.06 | −0.954277 | −0.477139 | − | 0.878828i | \(-0.658326\pi\) | ||||
−0.477139 | + | 0.878828i | \(0.658326\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1373.54 | 0.136102 | 0.0680511 | − | 0.997682i | \(-0.478322\pi\) | ||||
0.0680511 | + | 0.997682i | \(0.478322\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6331.00 | −0.623323 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 246.331 | 0.0239457 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 22119.7 | 2.13668 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 17107.8 | 1.63189 | 0.815943 | − | 0.578133i | \(-0.196218\pi\) | ||||
0.815943 | + | 0.578133i | \(0.196218\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10368.3 | −0.982855 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −25.7718 | −0.00241286 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4627.18 | −0.430549 | −0.215275 | − | 0.976554i | \(-0.569065\pi\) | ||||
−0.215275 | + | 0.976554i | \(0.569065\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9161.66 | −0.842078 | −0.421039 | − | 0.907043i | \(-0.638334\pi\) | ||||
−0.421039 | + | 0.907043i | \(0.638334\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2329.49 | 0.212810 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4267.48 | −0.385156 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8299.08 | 0.744524 | 0.372262 | − | 0.928128i | \(-0.378582\pi\) | ||||
0.372262 | + | 0.928128i | \(0.378582\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9568.57 | −0.848194 | −0.424097 | − | 0.905617i | \(-0.639408\pi\) | ||||
−0.424097 | + | 0.905617i | \(0.639408\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 16117.5 | 1.42024 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8749.02 | −0.761874 | −0.380937 | − | 0.924601i | \(-0.624398\pi\) | ||||
−0.380937 | + | 0.924601i | \(0.624398\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5340.87 | −0.462360 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −34904.9 | −2.98659 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1778.51 | −0.151293 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4974.67 | 0.418319 | 0.209160 | − | 0.977882i | \(-0.432927\pi\) | ||||
0.209160 | + | 0.977882i | \(0.432927\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10144.9 | 0.848196 | 0.424098 | − | 0.905616i | \(-0.360591\pi\) | ||||
0.424098 | + | 0.905616i | \(0.360591\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5281.74 | −0.436578 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 35578.0 | 2.92414 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7003.60 | 0.569155 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −33955.9 | −2.74400 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1338.06 | −0.106928 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9130.53 | −0.725604 | −0.362802 | − | 0.931866i | \(-0.618180\pi\) | ||||
−0.362802 | + | 0.931866i | \(0.618180\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −21612.7 | −1.69869 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3754.31 | −0.293460 | −0.146730 | − | 0.989177i | \(-0.546875\pi\) | ||||
−0.146730 | + | 0.989177i | \(0.546875\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3819.96 | 0.295346 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8527.74 | 0.655762 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9750.59 | 0.741734 | 0.370867 | − | 0.928686i | \(-0.379061\pi\) | ||||
0.370867 | + | 0.928686i | \(0.379061\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1593.93 | 0.120601 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2886.34 | 0.216065 | 0.108033 | − | 0.994147i | \(-0.465545\pi\) | ||||
0.108033 | + | 0.994147i | \(0.465545\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 27380.3 | 2.03876 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7508.07 | −0.553171 | −0.276586 | − | 0.960989i | \(-0.589203\pi\) | ||||
−0.276586 | + | 0.960989i | \(0.589203\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9160.32 | 0.671361 | 0.335681 | − | 0.941976i | \(-0.391034\pi\) | ||||
0.335681 | + | 0.941976i | \(0.391034\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −43362.6 | −3.14495 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −21578.4 | −1.55688 | −0.778441 | − | 0.627718i | \(-0.783989\pi\) | ||||
−0.778441 | + | 0.627718i | \(0.783989\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −491.145 | −0.0350708 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2130.42 | −0.151343 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −22754.1 | −1.59994 | −0.799968 | − | 0.600042i | \(-0.795150\pi\) | ||||
−0.799968 | + | 0.600042i | \(0.795150\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8661.13 | −0.605901 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11462.9 | 0.793801 | 0.396901 | − | 0.917862i | \(-0.370086\pi\) | ||||
0.396901 | + | 0.917862i | \(0.370086\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8903.28 | −0.613443 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6000.18 | 0.409283 | 0.204642 | − | 0.978837i | \(-0.434397\pi\) | ||||
0.204642 | + | 0.978837i | \(0.434397\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12874.8 | −0.873835 | −0.436917 | − | 0.899502i | \(-0.643930\pi\) | ||||
−0.436917 | + | 0.899502i | \(0.643930\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 23554.7 | 1.58287 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −23646.1 | −1.58116 | −0.790580 | − | 0.612359i | \(-0.790221\pi\) | ||||
−0.790580 | + | 0.612359i | \(0.790221\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −11508.2 | −0.761982 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1047.98 | 0.0690500 | 0.0345250 | − | 0.999404i | \(-0.489008\pi\) | ||||
0.0345250 | + | 0.999404i | \(0.489008\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1998.69 | 0.130412 | 0.0652059 | − | 0.997872i | \(-0.479230\pi\) | ||||
0.0652059 | + | 0.997872i | \(0.479230\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15246.5 | −0.989997 | −0.494999 | − | 0.868894i | \(-0.664831\pi\) | ||||
−0.494999 | + | 0.868894i | \(0.664831\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7034.64 | −0.452386 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1048.85 | −0.0671267 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −23601.8 | −1.49613 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13870.7 | −0.875094 | −0.437547 | − | 0.899195i | \(-0.644153\pi\) | ||||
−0.437547 | + | 0.899195i | \(0.644153\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 41373.9 | 2.58563 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8658.17 | −0.538539 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19759.3 | −1.21755 | −0.608773 | − | 0.793345i | \(-0.708338\pi\) | ||||
−0.608773 | + | 0.793345i | \(0.708338\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11694.7 | −0.717252 | −0.358626 | − | 0.933481i | \(-0.616755\pi\) | ||||
−0.358626 | + | 0.933481i | \(0.616755\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3214.68 | −0.195335 | −0.0976676 | − | 0.995219i | \(-0.531138\pi\) | ||||
−0.0976676 | + | 0.995219i | \(0.531138\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 33.0563 | 0.00199934 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9247.49 | −0.554184 | −0.277092 | − | 0.960843i | \(-0.589371\pi\) | ||||
−0.277092 | + | 0.960843i | \(0.589371\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18674.1 | 1.11398 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7982.01 | −0.471829 | −0.235914 | − | 0.971774i | \(-0.575808\pi\) | ||||
−0.235914 | + | 0.971774i | \(0.575808\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17033.5 | −1.00231 | −0.501154 | − | 0.865358i | \(-0.667091\pi\) | ||||
−0.501154 | + | 0.865358i | \(0.667091\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −14599.8 | −0.851363 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7488.50 | −0.434717 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1920.21 | 0.110475 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18527.4 | 1.06119 | 0.530594 | − | 0.847626i | \(-0.321969\pi\) | ||||
0.530594 | + | 0.847626i | \(0.321969\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −32963.3 | −1.87132 | −0.935659 | − | 0.352905i | \(-0.885194\pi\) | ||||
−0.935659 | + | 0.352905i | \(0.885194\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.4366 | 0.000589865 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9336.54 | 0.523064 | 0.261532 | − | 0.965195i | \(-0.415772\pi\) | ||||
0.261532 | + | 0.965195i | \(0.415772\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 19594.8 | 1.09296 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −13785.3 | −0.762232 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28848.3 | 1.58819 | 0.794096 | − | 0.607793i | \(-0.207945\pi\) | ||||
0.794096 | + | 0.607793i | \(0.207945\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 34518.5 | 1.88397 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15942.6 | 0.866382 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 28870.8 | 1.55554 | 0.777772 | − | 0.628547i | \(-0.216350\pi\) | ||||
0.777772 | + | 0.628547i | \(0.216350\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −38702.8 | −2.07639 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6526.94 | −0.347201 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15233.6 | 0.806927 | 0.403463 | − | 0.914996i | \(-0.367806\pi\) | ||||
0.403463 | + | 0.914996i | \(0.367806\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 16979.0 | 0.891819 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2478.21 | −0.129622 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9946.12 | 0.515894 | 0.257947 | − | 0.966159i | \(-0.416954\pi\) | ||||
0.257947 | + | 0.966159i | \(0.416954\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14135.1 | 0.730122 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6801.14 | 0.348397 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −30407.4 | −1.55124 | −0.775619 | − | 0.631202i | \(-0.782562\pi\) | ||||
−0.775619 | + | 0.631202i | \(0.782562\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3628.34 | 0.183583 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15075.8 | 0.759670 | 0.379835 | − | 0.925054i | \(-0.375981\pi\) | ||||
0.379835 | + | 0.925054i | \(0.375981\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4011.43 | −0.200492 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19253.6 | 0.958399 | 0.479200 | − | 0.877706i | \(-0.340927\pi\) | ||||
0.479200 | + | 0.877706i | \(0.340927\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15733.0 | −0.776835 | −0.388417 | − | 0.921484i | \(-0.626978\pi\) | ||||
−0.388417 | + | 0.921484i | \(0.626978\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −38339.2 | −1.88542 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 13750.8 | 0.670818 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13538.6 | 0.657832 | 0.328916 | − | 0.944359i | \(-0.393317\pi\) | ||||
0.328916 | + | 0.944359i | \(0.393317\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 20967.7 | 1.01072 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25434.5 | 1.22118 | 0.610590 | − | 0.791947i | \(-0.290932\pi\) | ||||
0.610590 | + | 0.791947i | \(0.290932\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13679.5 | −0.651620 | −0.325810 | − | 0.945435i | \(-0.605637\pi\) | ||||
−0.325810 | + | 0.945435i | \(0.605637\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8752.26 | 0.415273 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 213.897 | 0.0100696 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9198.81 | −0.431362 | −0.215681 | − | 0.976464i | \(-0.569197\pi\) | ||||
−0.215681 | + | 0.976464i | \(0.569197\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −19726.5 | −0.917868 | −0.458934 | − | 0.888470i | \(-0.651769\pi\) | ||||
−0.458934 | + | 0.888470i | \(0.651769\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −15420.5 | −0.714735 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 26143.0 | 1.20240 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2703.94 | −0.123886 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −661.410 | −0.0300723 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15430.4 | 0.698901 | 0.349451 | − | 0.936955i | \(-0.386368\pi\) | ||||
0.349451 | + | 0.936955i | \(0.386368\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11087.9 | −0.498409 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12425.1 | 0.556404 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −15181.2 | −0.674712 | −0.337356 | − | 0.941377i | \(-0.609533\pi\) | ||||
−0.337356 | + | 0.941377i | \(0.609533\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −26196.5 | −1.15991 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3384.06 | −0.148718 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 28620.9 | 1.25311 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 38480.1 | 1.67230 | 0.836149 | − | 0.548503i | \(-0.184802\pi\) | ||||
0.836149 | + | 0.548503i | \(0.184802\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32207.1 | 1.39451 | 0.697253 | − | 0.716825i | \(-0.254405\pi\) | ||||
0.697253 | + | 0.716825i | \(0.254405\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −57711.1 | −2.48041 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5949.84 | 0.254784 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5861.45 | 0.249167 | 0.124583 | − | 0.992209i | \(-0.460241\pi\) | ||||
0.124583 | + | 0.992209i | \(0.460241\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 34051.2 | 1.44222 | 0.721112 | − | 0.692819i | \(-0.243631\pi\) | ||||
0.721112 | + | 0.692819i | \(0.243631\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17214.4 | 0.723824 | 0.361912 | − | 0.932212i | \(-0.382124\pi\) | ||||
0.361912 | + | 0.932212i | \(0.382124\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5144.24 | −0.215521 | −0.107760 | − | 0.994177i | \(-0.534368\pi\) | ||||
−0.107760 | + | 0.994177i | \(0.534368\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −19709.0 | −0.819778 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 32302.1 | 1.33876 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15437.1 | 0.635218 | 0.317609 | − | 0.948222i | \(-0.397120\pi\) | ||||
0.317609 | + | 0.948222i | \(0.397120\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23214.5 | −0.951842 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 23476.7 | 0.955765 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9538.70 | −0.386958 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 75871.5 | 3.05622 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19811.6 | −0.795234 | −0.397617 | − | 0.917551i | \(-0.630163\pi\) | ||||
−0.397617 | + | 0.917551i | \(0.630163\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 37919.6 | 1.51145 | 0.755723 | − | 0.654891i | \(-0.227286\pi\) | ||||
0.755723 | + | 0.654891i | \(0.227286\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8600.38 | 0.341608 | 0.170804 | − | 0.985305i | \(-0.445364\pi\) | ||||
0.170804 | + | 0.985305i | \(0.445364\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 16423.6 | 0.647816 | 0.323908 | − | 0.946089i | \(-0.395003\pi\) | ||||
0.323908 | + | 0.946089i | \(0.395003\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 30478.9 | 1.19805 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5403.31 | 0.210926 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −25956.7 | −1.00977 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9620.80 | −0.371705 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23079.8 | 0.888655 | 0.444328 | − | 0.895864i | \(-0.353443\pi\) | ||||
0.444328 | + | 0.895864i | \(0.353443\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −22691.9 | −0.867775 | −0.433887 | − | 0.900967i | \(-0.642858\pi\) | ||||
−0.433887 | + | 0.900967i | \(0.642858\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19739.1 | 0.752291 | 0.376146 | − | 0.926561i | \(-0.377249\pi\) | ||||
0.376146 | + | 0.926561i | \(0.377249\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7738.38 | 0.292931 | 0.146465 | − | 0.989216i | \(-0.453210\pi\) | ||||
0.146465 | + | 0.989216i | \(0.453210\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −16754.8 | −0.632100 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −42957.7 | −1.60977 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5883.31 | −0.219729 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2663.04 | −0.0987958 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −31380.1 | −1.16029 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 80019.7 | 2.93917 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19862.2 | −0.727139 | −0.363569 | − | 0.931567i | \(-0.618442\pi\) | ||||
−0.363569 | + | 0.931567i | \(0.618442\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 50188.4 | 1.82527 | 0.912633 | − | 0.408780i | \(-0.134046\pi\) | ||||
0.912633 | + | 0.408780i | \(0.134046\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −311.198 | −0.0112805 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7562.28 | −0.272332 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5586.87 | 0.200537 | 0.100269 | − | 0.994960i | \(-0.468030\pi\) | ||||
0.100269 | + | 0.994960i | \(0.468030\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −17496.4 | −0.623944 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −68907.3 | −2.44936 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −10242.2 | −0.361717 | −0.180858 | − | 0.983509i | \(-0.557888\pi\) | ||||
−0.180858 | + | 0.983509i | \(0.557888\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −32319.2 | −1.13772 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5641.26 | −0.197314 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −52148.1 | −1.81815 | −0.909074 | − | 0.416634i | \(-0.863210\pi\) | ||||
−0.909074 | + | 0.416634i | \(0.863210\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 44437.5 | 1.53945 | 0.769724 | − | 0.638377i | \(-0.220394\pi\) | ||||
0.769724 | + | 0.638377i | \(0.220394\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −51249.8 | −1.76980 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −10115.3 | −0.347100 | −0.173550 | − | 0.984825i | \(-0.555524\pi\) | ||||
−0.173550 | + | 0.984825i | \(0.555524\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −21897.2 | −0.749013 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −14693.2 | −0.499433 | −0.249716 | − | 0.968319i | \(-0.580337\pi\) | ||||
−0.249716 | + | 0.968319i | \(0.580337\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 37389.5 | 1.26691 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7935.11 | −0.267193 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23753.0 | −0.797321 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 51924.9 | 1.73215 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 55659.8 | 1.85098 | 0.925491 | − | 0.378769i | \(-0.123653\pi\) | ||||
0.925491 | + | 0.378769i | \(0.123653\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 52103.0 | 1.72200 | 0.861001 | − | 0.508604i | \(-0.169838\pi\) | ||||
0.861001 | + | 0.508604i | \(0.169838\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −13978.6 | −0.460569 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 46135.2 | 1.51074 | 0.755372 | − | 0.655296i | \(-0.227456\pi\) | ||||
0.755372 | + | 0.655296i | \(0.227456\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4457.26 | −0.145510 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1617.78 | 0.0524915 | 0.0262458 | − | 0.999656i | \(-0.491645\pi\) | ||||
0.0262458 | + | 0.999656i | \(0.491645\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 48194.3 | 1.55898 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −11663.8 | −0.375013 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6422.76 | 0.205879 | 0.102939 | − | 0.994688i | \(-0.467175\pi\) | ||||
0.102939 | + | 0.994688i | \(0.467175\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6144.40 | −0.195770 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 39064.7 | 1.24091 | 0.620457 | − | 0.784240i | \(-0.286947\pi\) | ||||
0.620457 | + | 0.784240i | \(0.286947\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 648.4.a.g.1.1 | ✓ | 4 | |
3.2 | odd | 2 | 648.4.a.j.1.4 | yes | 4 | ||
4.3 | odd | 2 | 1296.4.a.x.1.1 | 4 | |||
9.2 | odd | 6 | 648.4.i.u.433.1 | 8 | |||
9.4 | even | 3 | 648.4.i.v.217.4 | 8 | |||
9.5 | odd | 6 | 648.4.i.u.217.1 | 8 | |||
9.7 | even | 3 | 648.4.i.v.433.4 | 8 | |||
12.11 | even | 2 | 1296.4.a.bb.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
648.4.a.g.1.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
648.4.a.j.1.4 | yes | 4 | 3.2 | odd | 2 | ||
648.4.i.u.217.1 | 8 | 9.5 | odd | 6 | |||
648.4.i.u.433.1 | 8 | 9.2 | odd | 6 | |||
648.4.i.v.217.4 | 8 | 9.4 | even | 3 | |||
648.4.i.v.433.4 | 8 | 9.7 | even | 3 | |||
1296.4.a.x.1.1 | 4 | 4.3 | odd | 2 | |||
1296.4.a.bb.1.4 | 4 | 12.11 | even | 2 |