Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1088,4,Mod(1,1088)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1088, 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("1088.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1088 = 2^{6} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1088.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: | \(64.1940780862\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 136) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1088.1 |
$q$-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 | ||||||||
\(3\) | −1.46410 | −0.281766 | −0.140883 | − | 0.990026i | \(-0.544994\pi\) | ||||
−0.140883 | + | 0.990026i | \(0.544994\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.928203 | −0.0830210 | −0.0415105 | − | 0.999138i | \(-0.513217\pi\) | ||||
−0.0415105 | + | 0.999138i | \(0.513217\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.60770 | 0.410777 | 0.205388 | − | 0.978681i | \(-0.434154\pi\) | ||||
0.205388 | + | 0.978681i | \(0.434154\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −24.8564 | −0.920608 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 35.0333 | 0.960268 | 0.480134 | − | 0.877195i | \(-0.340588\pi\) | ||||
0.480134 | + | 0.877195i | \(0.340588\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 83.5692 | 1.78292 | 0.891459 | − | 0.453102i | \(-0.149683\pi\) | ||||
0.891459 | + | 0.453102i | \(0.149683\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.35898 | 0.0233925 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 17.0000 | 0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −115.636 | −1.39625 | −0.698123 | − | 0.715978i | \(-0.745981\pi\) | ||||
−0.698123 | + | 0.715978i | \(0.745981\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −11.1384 | −0.115743 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 64.6025 | 0.585677 | 0.292838 | − | 0.956162i | \(-0.405400\pi\) | ||||
0.292838 | + | 0.956162i | \(0.405400\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −124.138 | −0.993108 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 75.9230 | 0.541163 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 288.067 | 1.84457 | 0.922287 | − | 0.386506i | \(-0.126318\pi\) | ||||
0.922287 | + | 0.386506i | \(0.126318\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −186.172 | −1.07863 | −0.539313 | − | 0.842105i | \(-0.681316\pi\) | ||||
−0.539313 | + | 0.842105i | \(0.681316\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −51.2923 | −0.270571 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −7.06149 | −0.0341031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −241.769 | −1.07423 | −0.537116 | − | 0.843508i | \(-0.680486\pi\) | ||||
−0.537116 | + | 0.843508i | \(0.680486\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −122.354 | −0.502366 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −43.8564 | −0.167054 | −0.0835271 | − | 0.996506i | \(-0.526619\pi\) | ||||
−0.0835271 | + | 0.996506i | \(0.526619\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 257.646 | 0.913737 | 0.456868 | − | 0.889534i | \(-0.348971\pi\) | ||||
0.456868 | + | 0.889534i | \(0.348971\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 23.0718 | 0.0764298 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 40.1539 | 0.124618 | 0.0623090 | − | 0.998057i | \(-0.480154\pi\) | ||||
0.0623090 | + | 0.998057i | \(0.480154\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −285.123 | −0.831262 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −24.8897 | −0.0683384 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −214.995 | −0.557204 | −0.278602 | − | 0.960407i | \(-0.589871\pi\) | ||||
−0.278602 | + | 0.960407i | \(0.589871\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −32.5180 | −0.0797224 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 169.303 | 0.393416 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 585.913 | 1.29287 | 0.646435 | − | 0.762969i | \(-0.276259\pi\) | ||||
0.646435 | + | 0.762969i | \(0.276259\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −331.759 | −0.696350 | −0.348175 | − | 0.937430i | \(-0.613199\pi\) | ||||
−0.348175 | + | 0.937430i | \(0.613199\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −189.100 | −0.378164 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −77.5692 | −0.148020 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 819.426 | 1.49416 | 0.747080 | − | 0.664734i | \(-0.231455\pi\) | ||||
0.747080 | + | 0.664734i | \(0.231455\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −94.5847 | −0.165024 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 961.079 | 1.60647 | 0.803233 | − | 0.595665i | \(-0.203111\pi\) | ||||
0.803233 | + | 0.595665i | \(0.203111\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −342.420 | −0.549004 | −0.274502 | − | 0.961587i | \(-0.588513\pi\) | ||||
−0.274502 | + | 0.961587i | \(0.588513\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 181.751 | 0.279824 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 266.523 | 0.394456 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 513.290 | 0.731007 | 0.365504 | − | 0.930810i | \(-0.380897\pi\) | ||||
0.365504 | + | 0.930810i | \(0.380897\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 559.964 | 0.768126 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 270.887 | 0.358237 | 0.179119 | − | 0.983827i | \(-0.442675\pi\) | ||||
0.179119 | + | 0.983827i | \(0.442675\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −15.7795 | −0.0201356 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −421.759 | −0.519739 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 728.082 | 0.867152 | 0.433576 | − | 0.901117i | \(-0.357252\pi\) | ||||
0.433576 | + | 0.901117i | \(0.357252\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 635.769 | 0.732381 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 272.574 | 0.303921 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 107.334 | 0.115918 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 211.990 | 0.221900 | 0.110950 | − | 0.993826i | \(-0.464611\pi\) | ||||
0.110950 | + | 0.993826i | \(0.464611\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −870.802 | −0.884030 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 865.538 | 0.852716 | 0.426358 | − | 0.904555i | \(-0.359796\pi\) | ||||
0.426358 | + | 0.904555i | \(0.359796\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 772.246 | 0.738754 | 0.369377 | − | 0.929280i | \(-0.379571\pi\) | ||||
0.369377 | + | 0.929280i | \(0.379571\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 10.3387 | 0.00960912 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2200.23 | −1.98789 | −0.993946 | − | 0.109866i | \(-0.964958\pi\) | ||||
−0.993946 | + | 0.109866i | \(0.964958\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 39.9127 | 0.0350729 | 0.0175365 | − | 0.999846i | \(-0.494418\pi\) | ||||
0.0175365 | + | 0.999846i | \(0.494418\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 353.975 | 0.302683 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −823.723 | −0.685746 | −0.342873 | − | 0.939382i | \(-0.611400\pi\) | ||||
−0.342873 | + | 0.939382i | \(0.611400\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −59.9643 | −0.0486235 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2077.23 | −1.64137 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 129.331 | 0.0996280 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −103.666 | −0.0778861 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 64.2102 | 0.0470703 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 231.251 | 0.165470 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2112.78 | 1.47622 | 0.738108 | − | 0.674683i | \(-0.235720\pi\) | ||||
0.738108 | + | 0.674683i | \(0.235720\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −377.220 | −0.257460 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −921.310 | −0.614468 | −0.307234 | − | 0.951634i | \(-0.599403\pi\) | ||||
−0.307234 | + | 0.951634i | \(0.599403\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −879.722 | −0.573546 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −70.4720 | −0.0449279 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 688.656 | 0.429459 | 0.214729 | − | 0.976674i | \(-0.431113\pi\) | ||||
0.214729 | + | 0.976674i | \(0.431113\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2132.04 | 1.30099 | 0.650495 | − | 0.759511i | \(-0.274562\pi\) | ||||
0.650495 | + | 0.759511i | \(0.274562\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −58.7894 | −0.0351132 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2927.71 | 1.71208 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −267.384 | −0.153138 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 417.449 | 0.234222 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2505.65 | 1.37766 | 0.688829 | − | 0.724924i | \(-0.258125\pi\) | ||||
0.688829 | + | 0.724924i | \(0.258125\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1272.06 | 0.685553 | 0.342776 | − | 0.939417i | \(-0.388633\pi\) | ||||
0.342776 | + | 0.939417i | \(0.388633\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −422.559 | −0.223280 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 172.805 | 0.0895487 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −178.328 | −0.0906507 | −0.0453253 | − | 0.998972i | \(-0.514432\pi\) | ||||
−0.0453253 | + | 0.998972i | \(0.514432\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 314.774 | 0.157001 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 491.476 | 0.240582 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3511.89 | 1.68756 | 0.843782 | − | 0.536687i | \(-0.180324\pi\) | ||||
0.843782 | + | 0.536687i | \(0.180324\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 47.6097 | 0.0224631 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 432.854 | 0.200570 | 0.100285 | − | 0.994959i | \(-0.468024\pi\) | ||||
0.100285 | + | 0.994959i | \(0.468024\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4786.81 | 2.17880 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2874.29 | 1.28540 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2338.15 | −1.02755 | −0.513775 | − | 0.857925i | \(-0.671753\pi\) | ||||
−0.513775 | + | 0.857925i | \(0.671753\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −944.407 | −0.407946 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −857.836 | −0.364287 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1011.75 | −0.422467 | −0.211234 | − | 0.977436i | \(-0.567748\pi\) | ||||
−0.211234 | + | 0.977436i | \(0.567748\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1983.64 | 0.814599 | 0.407300 | − | 0.913295i | \(-0.366471\pi\) | ||||
0.407300 | + | 0.913295i | \(0.366471\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 485.729 | 0.196208 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 224.411 | 0.0891839 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 595.566 | 0.232899 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 577.599 | 0.222297 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2156.05 | −0.816787 | −0.408394 | − | 0.912806i | \(-0.633911\pi\) | ||||
−0.408394 | + | 0.912806i | \(0.633911\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1957.28 | 0.729991 | 0.364995 | − | 0.931009i | \(-0.381071\pi\) | ||||
0.364995 | + | 0.931009i | \(0.381071\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 113.569 | 0.0417070 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1822.13 | −0.658991 | −0.329496 | − | 0.944157i | \(-0.606879\pi\) | ||||
−0.329496 | + | 0.944157i | \(0.606879\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3990.55 | 1.42152 | 0.710759 | − | 0.703435i | \(-0.248351\pi\) | ||||
0.710759 | + | 0.703435i | \(0.248351\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1199.72 | −0.421004 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2191.52 | 0.757708 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 40.7077 | 0.0138690 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1605.79 | −0.539178 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4051.11 | −1.34077 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5971.53 | 1.94833 | 0.974163 | − | 0.225846i | \(-0.0725148\pi\) | ||||
0.974163 | + | 0.225846i | \(0.0725148\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1407.12 | −0.452648 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −239.148 | −0.0758593 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1416.34 | −0.443075 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 501.338 | 0.154691 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1420.68 | 0.432421 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1854.26 | −0.556819 | −0.278409 | − | 0.960463i | \(-0.589807\pi\) | ||||
−0.278409 | + | 0.960463i | \(0.589807\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3085.64 | 0.914262 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1958.41 | 0.572617 | 0.286309 | − | 0.958137i | \(-0.407572\pi\) | ||||
0.286309 | + | 0.958137i | \(0.407572\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3406.66 | 0.983049 | 0.491524 | − | 0.870864i | \(-0.336440\pi\) | ||||
0.491524 | + | 0.870864i | \(0.336440\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −390.217 | −0.111144 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1119.92 | −0.314885 | −0.157443 | − | 0.987528i | \(-0.550325\pi\) | ||||
−0.157443 | + | 0.987528i | \(0.550325\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −37.2710 | −0.0103459 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −751.508 | −0.205973 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4839.65 | 1.30984 | 0.654918 | − | 0.755700i | \(-0.272703\pi\) | ||||
0.654918 | + | 0.755700i | \(0.272703\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6067.19 | −1.62167 | −0.810834 | − | 0.585276i | \(-0.800986\pi\) | ||||
−0.810834 | + | 0.585276i | \(0.800986\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2869.77 | −0.757595 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 264.652 | 0.0690122 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9663.60 | −2.48939 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −396.606 | −0.100939 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2963.93 | −0.745345 | −0.372672 | − | 0.927963i | \(-0.621558\pi\) | ||||
−0.372672 | + | 0.927963i | \(0.621558\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2263.24 | 0.562406 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 23.1027 | 0.00567352 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3756.86 | 0.911854 | 0.455927 | − | 0.890017i | \(-0.349308\pi\) | ||||
0.455927 | + | 0.890017i | \(0.349308\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1839.31 | −0.441270 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7160.30 | −1.69813 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4883.27 | 1.14492 | 0.572462 | − | 0.819931i | \(-0.305988\pi\) | ||||
0.572462 | + | 0.819931i | \(0.305988\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 199.559 | 0.0462596 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1065.99 | −0.244334 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4279.27 | 0.969931 | 0.484966 | − | 0.874533i | \(-0.338832\pi\) | ||||
0.484966 | + | 0.874533i | \(0.338832\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6381.54 | −1.43045 | −0.715223 | − | 0.698896i | \(-0.753675\pi\) | ||||
−0.715223 | + | 0.698896i | \(0.753675\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −930.831 | −0.206361 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4348.98 | −0.953649 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7522.44 | 1.63169 | 0.815847 | − | 0.578268i | \(-0.196271\pi\) | ||||
0.815847 | + | 0.578268i | \(0.196271\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4627.56 | 0.992992 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6559.87 | −1.39263 | −0.696315 | − | 0.717737i | \(-0.745178\pi\) | ||||
−0.696315 | + | 0.717737i | \(0.745178\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1759.12 | −0.369501 | −0.184751 | − | 0.982785i | \(-0.559148\pi\) | ||||
−0.184751 | + | 0.982785i | \(0.559148\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −157.147 | −0.0326618 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −333.646 | −0.0686220 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 289.000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −310.374 | −0.0625240 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3079.42 | −0.613998 | −0.306999 | − | 0.951710i | \(-0.599325\pi\) | ||||
−0.306999 | + | 0.951710i | \(0.599325\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −543.846 | −0.107335 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2659.84 | 0.519661 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5398.78 | 1.04421 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1960.09 | 0.375342 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1267.24 | −0.240267 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 307.940 | 0.0578117 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7231.51 | 1.34438 | 0.672189 | − | 0.740380i | \(-0.265354\pi\) | ||||
0.672189 | + | 0.740380i | \(0.265354\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1130.65 | −0.208156 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8545.03 | 1.55802 | 0.779010 | − | 0.627012i | \(-0.215722\pi\) | ||||
0.779010 | + | 0.627012i | \(0.215722\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5808.14 | −1.04887 | −0.524434 | − | 0.851451i | \(-0.675723\pi\) | ||||
−0.524434 | + | 0.851451i | \(0.675723\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 175.523 | 0.0313956 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3478.13 | 0.616249 | 0.308125 | − | 0.951346i | \(-0.400299\pi\) | ||||
0.308125 | + | 0.951346i | \(0.400299\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10091.9 | 1.77128 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3221.36 | 0.560122 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1965.81 | −0.338640 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −10374.2 | −1.77063 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −58.4363 | −0.00988237 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 305.479 | 0.0511902 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2729.62 | −0.453273 | −0.226636 | − | 0.973979i | \(-0.572773\pi\) | ||||
−0.226636 | + | 0.973979i | \(0.572773\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6009.51 | 0.988947 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −760.594 | −0.124047 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3408.52 | −0.550962 | −0.275481 | − | 0.961307i | \(-0.588837\pi\) | ||||
−0.275481 | + | 0.961307i | \(0.588837\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1206.01 | 0.193220 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6522.22 | −1.03577 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4778.57 | −0.752240 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 87.7938 | 0.0137005 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1393.38 | 0.215564 | 0.107782 | − | 0.994175i | \(-0.465625\pi\) | ||||
0.107782 | + | 0.994175i | \(0.465625\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 390.298 | 0.0598630 | 0.0299315 | − | 0.999552i | \(-0.490471\pi\) | ||||
0.0299315 | + | 0.999552i | \(0.490471\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6344.83 | 0.964849 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6504.99 | −0.980810 | −0.490405 | − | 0.871495i | \(-0.663151\pi\) | ||||
−0.490405 | + | 0.871495i | \(0.663151\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −892.077 | −0.133371 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −189.353 | −0.0280718 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2604.52 | −0.382900 | −0.191450 | − | 0.981502i | \(-0.561319\pi\) | ||||
−0.191450 | + | 0.981502i | \(0.561319\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6512.65 | 0.949505 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 151.778 | 0.0219457 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 317.836 | 0.0455789 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10882.8 | −1.54790 | −0.773948 | − | 0.633249i | \(-0.781721\pi\) | ||||
−0.773948 | + | 0.633249i | \(0.781721\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1090.11 | 0.153791 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1635.62 | −0.228887 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2983.40 | 0.414141 | 0.207071 | − | 0.978326i | \(-0.433607\pi\) | ||||
0.207071 | + | 0.978326i | \(0.433607\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −338.575 | −0.0466238 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 24073.5 | 3.28872 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3227.09 | −0.437373 | −0.218686 | − | 0.975795i | \(-0.570177\pi\) | ||||
−0.218686 | + | 0.975795i | \(0.570177\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3093.33 | −0.415948 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6857.86 | −0.914936 | −0.457468 | − | 0.889226i | \(-0.651244\pi\) | ||||
−0.457468 | + | 0.889226i | \(0.651244\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −247.387 | −0.0327481 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6404.16 | −0.841193 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10890.1 | −1.41940 | −0.709702 | − | 0.704502i | \(-0.751170\pi\) | ||||
−0.709702 | + | 0.704502i | \(0.751170\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1098.24 | 0.142047 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1348.89 | 0.173136 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −476.437 | −0.0606890 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2759.86 | −0.348901 | −0.174450 | − | 0.984666i | \(-0.555815\pi\) | ||||
−0.174450 | + | 0.984666i | \(0.555815\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1288.00 | 0.161606 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1961.90 | 0.244321 | 0.122160 | − | 0.992510i | \(-0.461018\pi\) | ||||
0.122160 | + | 0.992510i | \(0.461018\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −15558.2 | −1.92310 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −519.760 | −0.0637706 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8469.98 | −1.03155 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8258.94 | 0.998480 | 0.499240 | − | 0.866464i | \(-0.333613\pi\) | ||||
0.499240 | + | 0.866464i | \(0.333613\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1008.26 | −0.121007 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4457.45 | 0.531081 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −251.438 | −0.0297412 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3121.53 | −0.366575 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6590.86 | 0.768459 | 0.384230 | − | 0.923238i | \(-0.374467\pi\) | ||||
0.384230 | + | 0.923238i | \(0.374467\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2451.24 | 0.283768 | 0.141884 | − | 0.989883i | \(-0.454684\pi\) | ||||
0.141884 | + | 0.989883i | \(0.454684\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −998.082 | −0.114724 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2110.35 | −0.240864 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2523.92 | −0.286045 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4286.46 | −0.482406 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12065.2 | −1.34840 | −0.674199 | − | 0.738550i | \(-0.735511\pi\) | ||||
−0.674199 | + | 0.738550i | \(0.735511\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7543.04 | −0.837171 | −0.418586 | − | 0.908177i | \(-0.637474\pi\) | ||||
−0.418586 | + | 0.908177i | \(0.637474\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 391.478 | 0.0431493 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7470.37 | −0.817749 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4914.93 | 0.534343 | 0.267172 | − | 0.963649i | \(-0.413911\pi\) | ||||
0.267172 | + | 0.963649i | \(0.413911\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7087.13 | 0.765266 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14440.1 | −1.54869 | −0.774346 | − | 0.632762i | \(-0.781921\pi\) | ||||
−0.774346 | + | 0.632762i | \(0.781921\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −675.808 | −0.0719918 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3668.53 | −0.388178 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9707.39 | −1.02031 | −0.510156 | − | 0.860082i | \(-0.670412\pi\) | ||||
−0.510156 | + | 0.860082i | \(0.670412\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1536.44 | −0.160417 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1862.42 | −0.193166 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −590.123 | −0.0608031 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4495.06 | 0.460109 | 0.230055 | − | 0.973178i | \(-0.426110\pi\) | ||||
0.230055 | + | 0.973178i | \(0.426110\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1290.69 | 0.131251 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1092.31 | 0.110355 | 0.0551777 | − | 0.998477i | \(-0.482427\pi\) | ||||
0.0551777 | + | 0.998477i | \(0.482427\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8212.83 | −0.824368 | −0.412184 | − | 0.911101i | \(-0.635234\pi\) | ||||
−0.412184 | + | 0.911101i | \(0.635234\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −253.004 | −0.0252318 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8826.37 | −0.874595 | −0.437297 | − | 0.899317i | \(-0.644064\pi\) | ||||
−0.437297 | + | 0.899317i | \(0.644064\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6233.94 | 0.613767 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 261.091 | 0.0255423 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9026.20 | 0.877432 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 14354.9 | 1.38662 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5344.00 | 0.512966 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16888.5 | 1.61097 | 0.805484 | − | 0.592617i | \(-0.201905\pi\) | ||||
0.805484 | + | 0.592617i | \(0.201905\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20204.5 | −1.91527 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −719.571 | −0.0677881 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −196.770 | −0.0184224 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5325.78 | −0.495552 | −0.247776 | − | 0.968817i | \(-0.579700\pi\) | ||||
−0.247776 | + | 0.968817i | \(0.579700\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5141.77 | −0.475499 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18743.1 | −1.72274 | −0.861368 | − | 0.507982i | \(-0.830392\pi\) | ||||
−0.861368 | + | 0.507982i | \(0.830392\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4897.13 | 0.447375 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 808.282 | 0.0733930 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7311.60 | 0.659899 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −557.533 | −0.0500172 | −0.0250086 | − | 0.999687i | \(-0.507961\pi\) | ||||
−0.0250086 | + | 0.999687i | \(0.507961\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −633.742 | −0.0565140 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9888.07 | −0.876515 | −0.438257 | − | 0.898849i | \(-0.644404\pi\) | ||||
−0.438257 | + | 0.898849i | \(0.644404\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −803.395 | −0.0707933 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7008.38 | −0.613912 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8219.25 | −0.715740 | −0.357870 | − | 0.933771i | \(-0.616497\pi\) | ||||
−0.357870 | + | 0.933771i | \(0.616497\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2605.03 | −0.225518 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −8779.43 | −0.755597 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −716.801 | −0.0613321 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1406.72 | 0.119667 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3423.29 | 0.289529 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12967.4 | −1.09042 | −0.545212 | − | 0.838298i | \(-0.683551\pi\) | ||||
−0.545212 | + | 0.838298i | \(0.683551\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12391.5 | 1.03603 | 0.518014 | − | 0.855372i | \(-0.326671\pi\) | ||||
0.518014 | + | 0.855372i | \(0.326671\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1382.71 | 0.114945 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3164.92 | −0.261605 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7993.51 | −0.656983 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −14563.7 | −1.19023 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3665.05 | −0.297844 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2042.26 | 0.165037 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1481.30 | 0.119037 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −9988.80 | −0.798234 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20467.6 | 1.62657 | 0.813283 | − | 0.581868i | \(-0.197678\pi\) | ||||
0.813283 | + | 0.581868i | \(0.197678\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2904.24 | −0.229527 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −37.0471 | −0.00291179 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2410.39 | 0.188411 | 0.0942056 | − | 0.995553i | \(-0.469969\pi\) | ||||
0.0942056 | + | 0.995553i | \(0.469969\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8246.33 | 0.641065 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −33310.8 | −2.57548 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3904.95 | 0.300281 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −328.560 | −0.0251290 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8165.50 | 0.621155 | 0.310577 | − | 0.950548i | \(-0.399478\pi\) | ||||
0.310577 | + | 0.950548i | \(0.399478\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 21531.3 | 1.62912 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −871.970 | −0.0656232 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19714.5 | 1.47579 | 0.737893 | − | 0.674918i | \(-0.235821\pi\) | ||||
0.737893 | + | 0.674918i | \(0.235821\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 764.582 | 0.0569314 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4260.03 | 0.315528 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6808.46 | 0.501627 | 0.250813 | − | 0.968035i | \(-0.419302\pi\) | ||||
0.250813 | + | 0.968035i | \(0.419302\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11660.8 | 0.854621 | 0.427311 | − | 0.904105i | \(-0.359461\pi\) | ||||
0.427311 | + | 0.904105i | \(0.359461\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3156.68 | 0.230143 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8019.66 | −0.581640 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17508.0 | −1.26320 | −0.631600 | − | 0.775294i | \(-0.717602\pi\) | ||||
−0.631600 | + | 0.775294i | \(0.717602\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2865.66 | −0.205687 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2060.83 | 0.147156 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7531.98 | −0.535065 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1928.09 | 0.136268 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 19549.2 | 1.37459 | 0.687293 | − | 0.726380i | \(-0.258799\pi\) | ||||
0.687293 | + | 0.726380i | \(0.258799\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 21528.1 | 1.50603 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2667.78 | 0.185682 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 22738.3 | 1.57462 | 0.787310 | − | 0.616558i | \(-0.211473\pi\) | ||||
0.787310 | + | 0.616558i | \(0.211473\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −120.045 | −0.00827122 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5842.56 | −0.400536 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3679.68 | 0.250998 | 0.125499 | − | 0.992094i | \(-0.459947\pi\) | ||||
0.125499 | + | 0.992094i | \(0.459947\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2834.52 | 0.192384 | 0.0961918 | − | 0.995363i | \(-0.469334\pi\) | ||||
0.0961918 | + | 0.995363i | \(0.469334\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −20368.0 | −1.37554 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 96.2235 | 0.00646618 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7728.36 | −0.516778 | −0.258389 | − | 0.966041i | \(-0.583192\pi\) | ||||
−0.258389 | + | 0.966041i | \(0.583192\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3208.61 | −0.213497 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3355.63 | 0.222184 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3729.75 | 0.245748 | 0.122874 | − | 0.992422i | \(-0.460789\pi\) | ||||
0.122874 | + | 0.992422i | \(0.460789\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −59.6001 | −0.00390782 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10148.2 | 0.662156 | 0.331078 | − | 0.943603i | \(-0.392588\pi\) | ||||
0.331078 | + | 0.943603i | \(0.392588\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −24975.6 | −1.62174 | −0.810868 | − | 0.585229i | \(-0.801005\pi\) | ||||
−0.810868 | + | 0.585229i | \(0.801005\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4904.82 | 0.316946 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5539.02 | 0.356206 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15302.7 | 0.979370 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5931.23 | 0.377784 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4110.08 | −0.260540 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10577.2 | 0.667310 | 0.333655 | − | 0.942695i | \(-0.391718\pi\) | ||||
0.333655 | + | 0.942695i | \(0.391718\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8742.92 | −0.548973 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1961.09 | −0.122557 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −23827.5 | −1.48207 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −23889.0 | −1.47893 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4744.60 | −0.292357 | −0.146178 | − | 0.989258i | \(-0.546697\pi\) | ||||
−0.146178 | + | 0.989258i | \(0.546697\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13420.1 | 0.823075 | 0.411537 | − | 0.911393i | \(-0.364992\pi\) | ||||
0.411537 | + | 0.911393i | \(0.364992\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 350.137 | 0.0213746 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −30769.7 | −1.86968 | −0.934839 | − | 0.355072i | \(-0.884456\pi\) | ||||
−0.934839 | + | 0.355072i | \(0.884456\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 20526.5 | 1.24150 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2073.66 | 0.124844 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 30697.6 | 1.83965 | 0.919825 | − | 0.392328i | \(-0.128330\pi\) | ||||
0.919825 | + | 0.392328i | \(0.128330\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 855.163 | 0.0510137 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8511.34 | 0.505417 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6532.13 | −0.386124 | −0.193062 | − | 0.981187i | \(-0.561842\pi\) | ||||
−0.193062 | + | 0.981187i | \(0.561842\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −25064.2 | −1.47486 | −0.737432 | − | 0.675421i | \(-0.763962\pi\) | ||||
−0.737432 | + | 0.675421i | \(0.763962\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2080.02 | −0.121842 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 816.561 | 0.0476164 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18609.8 | 1.08032 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2714.83 | 0.156893 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −11622.6 | −0.668683 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28852.3 | −1.65256 | −0.826280 | − | 0.563260i | \(-0.809547\pi\) | ||||
−0.826280 | + | 0.563260i | \(0.809547\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −9424.97 | −0.537433 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −17281.2 | −0.981050 | −0.490525 | − | 0.871427i | \(-0.663195\pi\) | ||||
−0.490525 | + | 0.871427i | \(0.663195\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1612.75 | 0.0911514 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2867.31 | −0.161344 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −11782.9 | −0.660117 | −0.330058 | − | 0.943961i | \(-0.607068\pi\) | ||||
−0.330058 | + | 0.943961i | \(0.607068\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −639.213 | −0.0356541 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4987.69 | −0.276990 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −17967.0 | −0.993449 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8292.73 | 0.456541 | 0.228271 | − | 0.973598i | \(-0.426693\pi\) | ||||
0.228271 | + | 0.973598i | \(0.426693\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6624.80 | −0.363139 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1978.97 | −0.108009 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −745.559 | −0.0405166 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1639.67 | 0.0887241 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1920.82 | 0.103493 | 0.0517464 | − | 0.998660i | \(-0.483521\pi\) | ||||
0.0517464 | + | 0.998660i | \(0.483521\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 27957.2 | 1.49989 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 54.5685 | 0.00291513 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6584.75 | 0.350276 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −34241.4 | −1.81377 | −0.906886 | − | 0.421377i | \(-0.861547\pi\) | ||||
−0.906886 | + | 0.421377i | \(0.861547\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −12758.5 | −0.672971 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −12027.2 | −0.631727 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2717.51 | −0.142138 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −7085.74 | −0.369068 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1945.22 | 0.100896 | 0.0504482 | − | 0.998727i | \(-0.483935\pi\) | ||||
0.0504482 | + | 0.998727i | \(0.483935\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5875.01 | 0.303463 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 8882.98 | 0.456932 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −35760.1 | −1.83186 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 27193.9 | 1.38730 | 0.693650 | − | 0.720313i | \(-0.256002\pi\) | ||||
0.693650 | + | 0.720313i | \(0.256002\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −10917.4 | −0.554661 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4379.98 | 0.221614 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15351.2 | −0.773545 | −0.386773 | − | 0.922175i | \(-0.626410\pi\) | ||||
−0.386773 | + | 0.922175i | \(0.626410\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −387.478 | −0.0194453 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 28707.2 | 1.43479 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10027.3 | −0.499133 | −0.249566 | − | 0.968358i | \(-0.580288\pi\) | ||||
−0.249566 | + | 0.968358i | \(0.580288\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 14148.5 | 0.701428 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 17396.2 | 0.858955 | 0.429477 | − | 0.903078i | \(-0.358698\pi\) | ||||
0.429477 | + | 0.903078i | \(0.358698\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2325.75 | −0.114375 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6733.28 | −0.329796 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −16738.7 | −0.816581 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3286.42 | −0.159685 | −0.0798423 | − | 0.996808i | \(-0.525442\pi\) | ||||
−0.0798423 | + | 0.996808i | \(0.525442\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4339.49 | 0.210013 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1180.73 | −0.0569153 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33578.7 | 1.61220 | 0.806101 | − | 0.591777i | \(-0.201574\pi\) | ||||
0.806101 | + | 0.591777i | \(0.201574\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3313.62 | −0.158467 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 31225.7 | 1.48742 | 0.743712 | − | 0.668500i | \(-0.233063\pi\) | ||||
0.743712 | + | 0.668500i | \(0.233063\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 303.644 | 0.0144071 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 392.221 | 0.0185369 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 48964.3 | 2.30508 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17386.4 | 0.815304 | 0.407652 | − | 0.913137i | \(-0.366348\pi\) | ||||
0.407652 | + | 0.913137i | \(0.366348\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5500.43 | −0.256930 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9764.68 | 0.454348 | 0.227174 | − | 0.973854i | \(-0.427051\pi\) | ||||
0.227174 | + | 0.973854i | \(0.427051\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 23111.1 | 1.07119 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2692.93 | 0.124335 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5071.37 | 0.233249 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 33669.8 | 1.54264 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 21870.9 | 0.998215 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 165.525 | 0.00752591 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 27285.8 | 1.23588 | 0.617939 | − | 0.786226i | \(-0.287968\pi\) | ||||
0.617939 | + | 0.786226i | \(0.287968\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −7149.60 | −0.322601 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6266.63 | −0.281689 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −27724.8 | −1.24154 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −292.175 | −0.0130344 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 18419.4 | 0.818632 | 0.409316 | − | 0.912393i | \(-0.365767\pi\) | ||||
0.409316 | + | 0.912393i | \(0.365767\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 682.616 | 0.0302243 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −18097.5 | −0.798307 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −11996.1 | −0.527191 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −456.190 | −0.0199734 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6265.28 | −0.273294 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −34203.0 | −1.48642 | −0.743211 | − | 0.669057i | \(-0.766698\pi\) | ||||
−0.743211 | + | 0.669057i | \(0.766698\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4605.05 | 0.199390 | 0.0996950 | − | 0.995018i | \(-0.468213\pi\) | ||||
0.0996950 | + | 0.995018i | \(0.468213\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9343.22 | 0.403052 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3259.75 | −0.140103 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −29793.1 | −1.27580 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −15802.9 | −0.674236 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11557.4 | 0.491298 | 0.245649 | − | 0.969359i | \(-0.420999\pi\) | ||||
0.245649 | + | 0.969359i | \(0.420999\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16810.8 | −0.712016 | −0.356008 | − | 0.934483i | \(-0.615862\pi\) | ||||
−0.356008 | + | 0.934483i | \(0.615862\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6367.35 | 0.268706 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −15832.7 | −0.665726 | −0.332863 | − | 0.942975i | \(-0.608015\pi\) | ||||
−0.332863 | + | 0.942975i | \(0.608015\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −28451.0 | −1.19197 | −0.595986 | − | 0.802995i | \(-0.703239\pi\) | ||||
−0.595986 | + | 0.802995i | \(0.703239\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −11013.6 | −0.459757 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4847.09 | −0.201611 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −401.776 | −0.0166516 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −14134.7 | −0.583713 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 20249.1 | 0.833226 | 0.416613 | − | 0.909084i | \(-0.363217\pi\) | ||||
0.416613 | + | 0.909084i | \(0.363217\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 58593.4 | 2.40245 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 9604.31 | 0.392396 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4443.14 | −0.180886 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −788.663 | −0.0319938 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2575.53 | 0.104113 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −15618.9 | −0.629153 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16346.3 | −0.656140 | −0.328070 | − | 0.944653i | \(-0.606398\pi\) | ||||
−0.328070 | + | 0.944653i | \(0.606398\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2667.93 | −0.106715 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 15549.0 | 0.619770 | 0.309885 | − | 0.950774i | \(-0.399709\pi\) | ||||
0.309885 | + | 0.950774i | \(0.399709\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17843.1 | −0.708728 | −0.354364 | − | 0.935107i | \(-0.615303\pi\) | ||||
−0.354364 | + | 0.935107i | \(0.615303\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 488.492 | 0.0193354 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −29343.7 | −1.15744 | −0.578721 | − | 0.815526i | \(-0.696448\pi\) | ||||
−0.578721 | + | 0.815526i | \(0.696448\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2170.28 | 0.0853082 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −423.125 | −0.0165745 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17982.2 | 0.701963 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 68478.8 | 2.66397 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5269.30 | −0.204283 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1759.29 | 0.0679712 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9538.17 | 0.367253 | 0.183627 | − | 0.982996i | \(-0.441216\pi\) | ||||
0.183627 | + | 0.982996i | \(0.441216\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4508.58 | 0.173004 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −35280.5 | −1.34918 | −0.674591 | − | 0.738192i | \(-0.735680\pi\) | ||||
−0.674591 | + | 0.738192i | \(0.735680\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8515.92 | −0.324557 | −0.162278 | − | 0.986745i | \(-0.551884\pi\) | ||||
−0.162278 | + | 0.986745i | \(0.551884\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 796.246 | 0.0302435 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 39734.0 | 1.50410 | 0.752051 | − | 0.659105i | \(-0.229065\pi\) | ||||
0.752051 | + | 0.659105i | \(0.229065\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16073.4 | 0.606395 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 19617.4 | 0.737607 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4643.23 | −0.173998 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 939.108 | 0.0350737 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7904.37 | −0.294224 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −53629.9 | −1.98961 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3654.91 | −0.135142 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2869.78 | −0.105759 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1841.22 | −0.0676288 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22025.4 | 0.806329 | 0.403165 | − | 0.915128i | \(-0.367910\pi\) | ||||
0.403165 | + | 0.915128i | \(0.367910\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −21514.2 | −0.785017 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4187.78 | −0.152302 | −0.0761512 | − | 0.997096i | \(-0.524263\pi\) | ||||
−0.0761512 | + | 0.997096i | \(0.524263\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9490.07 | 0.344004 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −450.855 | −0.0162894 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7009.05 | −0.252409 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9322.61 | 0.334629 | 0.167315 | − | 0.985904i | \(-0.446490\pi\) | ||||
0.167315 | + | 0.985904i | \(0.446490\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10587.7 | −0.378801 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 80316.7 | 2.86420 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 30012.8 | 1.06683 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −19195.3 | −0.680103 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 25028.1 | 0.883901 | 0.441950 | − | 0.897040i | \(-0.354287\pi\) | ||||
0.441950 | + | 0.897040i | \(0.354287\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 32970.4 | 1.16065 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −12510.8 | −0.438998 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −552.807 | −0.0193355 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 36634.8 | 1.27727 | 0.638637 | − | 0.769508i | \(-0.279498\pi\) | ||||
0.638637 | + | 0.769508i | \(0.279498\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 8503.71 | 0.295536 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 56248.4 | 1.94861 | 0.974307 | − | 0.225225i | \(-0.0723116\pi\) | ||||
0.974307 | + | 0.225225i | \(0.0723116\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2833.24 | −0.0978397 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −536.130 | −0.0184553 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 44981.0 | 1.54349 | 0.771745 | − | 0.635932i | \(-0.219384\pi\) | ||||
0.771745 | + | 0.635932i | \(0.219384\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −28615.8 | −0.978829 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5092.33 | −0.173638 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5346.14 | −0.181719 | −0.0908596 | − | 0.995864i | \(-0.528961\pi\) | ||||
−0.0908596 | + | 0.995864i | \(0.528961\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2001.25 | 0.0678105 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −14775.6 | −0.499089 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5239.09 | 0.176412 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4868.92 | 0.163436 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 54689.9 | 1.83007 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1816.75 | −0.0606046 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32790.2 | 1.09045 | 0.545223 | − | 0.838291i | \(-0.316445\pi\) | ||||
0.545223 | + | 0.838291i | \(0.316445\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2878.15 | 0.0954173 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3313.57 | −0.109513 | −0.0547567 | − | 0.998500i | \(-0.517438\pi\) | ||||
−0.0547567 | + | 0.998500i | \(0.517438\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16219.9 | 0.534416 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 15188.8 | 0.498904 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −44576.3 | −1.45970 | −0.729848 | − | 0.683609i | \(-0.760409\pi\) | ||||
−0.729848 | + | 0.683609i | \(0.760409\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 25507.1 | 0.832698 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −992.087 | −0.0322884 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −11436.7 | −0.371081 | −0.185541 | − | 0.982637i | \(-0.559404\pi\) | ||||
−0.185541 | + | 0.982637i | \(0.559404\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1691.30 | 0.0547101 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −447.252 | −0.0144237 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16644.6 | 0.535154 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1965.50 | 0.0630033 | 0.0315017 | − | 0.999504i | \(-0.489971\pi\) | ||||
0.0315017 | + | 0.999504i | \(0.489971\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3996.44 | 0.127717 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3704.04 | −0.118016 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2878.40 | 0.0914343 | 0.0457171 | − | 0.998954i | \(-0.485443\pi\) | ||||
0.0457171 | + | 0.998954i | \(0.485443\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −18355.9 | −0.581335 |
(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 | 1088.4.a.p.1.1 | 2 | ||
4.3 | odd | 2 | 1088.4.a.n.1.2 | 2 | |||
8.3 | odd | 2 | 136.4.a.a.1.1 | ✓ | 2 | ||
8.5 | even | 2 | 272.4.a.f.1.2 | 2 | |||
24.5 | odd | 2 | 2448.4.a.z.1.1 | 2 | |||
24.11 | even | 2 | 1224.4.a.d.1.1 | 2 | |||
136.67 | odd | 2 | 2312.4.a.b.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
136.4.a.a.1.1 | ✓ | 2 | 8.3 | odd | 2 | ||
272.4.a.f.1.2 | 2 | 8.5 | even | 2 | |||
1088.4.a.n.1.2 | 2 | 4.3 | odd | 2 | |||
1088.4.a.p.1.1 | 2 | 1.1 | even | 1 | trivial | ||
1224.4.a.d.1.1 | 2 | 24.11 | even | 2 | |||
2312.4.a.b.1.2 | 2 | 136.67 | odd | 2 | |||
2448.4.a.z.1.1 | 2 | 24.5 | odd | 2 |