Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [490,4,Mod(1,490)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(490, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("490.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 490 = 2 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 490.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: | \(28.9109359028\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.115880.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 66x + 90 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 70) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(7.90730\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 490.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000 | 0.707107 | ||||||||
\(3\) | −8.90730 | −1.71421 | −0.857105 | − | 0.515141i | \(-0.827740\pi\) | ||||
−0.857105 | + | 0.515141i | \(0.827740\pi\) | |||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | −17.8146 | −1.21213 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 52.3400 | 1.93852 | ||||||||
\(10\) | −10.0000 | −0.316228 | ||||||||
\(11\) | −49.9692 | −1.36966 | −0.684831 | − | 0.728702i | \(-0.740124\pi\) | ||||
−0.684831 | + | 0.728702i | \(0.740124\pi\) | |||||||
\(12\) | −35.6292 | −0.857105 | ||||||||
\(13\) | 18.5254 | 0.395233 | 0.197616 | − | 0.980279i | \(-0.436680\pi\) | ||||
0.197616 | + | 0.980279i | \(0.436680\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 44.5365 | 0.766618 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | −100.888 | −1.43934 | −0.719672 | − | 0.694314i | \(-0.755708\pi\) | ||||
−0.719672 | + | 0.694314i | \(0.755708\pi\) | |||||||
\(18\) | 104.680 | 1.37074 | ||||||||
\(19\) | −101.205 | −1.22201 | −0.611003 | − | 0.791628i | \(-0.709234\pi\) | ||||
−0.611003 | + | 0.791628i | \(0.709234\pi\) | |||||||
\(20\) | −20.0000 | −0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −99.9384 | −0.968498 | ||||||||
\(23\) | 92.2187 | 0.836040 | 0.418020 | − | 0.908438i | \(-0.362724\pi\) | ||||
0.418020 | + | 0.908438i | \(0.362724\pi\) | |||||||
\(24\) | −71.2584 | −0.606065 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 37.0508 | 0.279472 | ||||||||
\(27\) | −225.711 | −1.60882 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 37.8740 | 0.242518 | 0.121259 | − | 0.992621i | \(-0.461307\pi\) | ||||
0.121259 | + | 0.992621i | \(0.461307\pi\) | |||||||
\(30\) | 89.0730 | 0.542081 | ||||||||
\(31\) | 127.545 | 0.738963 | 0.369481 | − | 0.929238i | \(-0.379535\pi\) | ||||
0.369481 | + | 0.929238i | \(0.379535\pi\) | |||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | 445.091 | 2.34789 | ||||||||
\(34\) | −201.775 | −1.01777 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 209.360 | 0.969260 | ||||||||
\(37\) | 283.104 | 1.25789 | 0.628946 | − | 0.777449i | \(-0.283487\pi\) | ||||
0.628946 | + | 0.777449i | \(0.283487\pi\) | |||||||
\(38\) | −202.411 | −0.864089 | ||||||||
\(39\) | −165.011 | −0.677512 | ||||||||
\(40\) | −40.0000 | −0.158114 | ||||||||
\(41\) | 250.157 | 0.952879 | 0.476439 | − | 0.879207i | \(-0.341927\pi\) | ||||
0.476439 | + | 0.879207i | \(0.341927\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −260.330 | −0.923254 | −0.461627 | − | 0.887074i | \(-0.652734\pi\) | ||||
−0.461627 | + | 0.887074i | \(0.652734\pi\) | |||||||
\(44\) | −199.877 | −0.684831 | ||||||||
\(45\) | −261.700 | −0.866932 | ||||||||
\(46\) | 184.437 | 0.591170 | ||||||||
\(47\) | 604.345 | 1.87559 | 0.937796 | − | 0.347188i | \(-0.112863\pi\) | ||||
0.937796 | + | 0.347188i | \(0.112863\pi\) | |||||||
\(48\) | −142.517 | −0.428553 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 50.0000 | 0.141421 | ||||||||
\(51\) | 898.636 | 2.46734 | ||||||||
\(52\) | 74.1017 | 0.197616 | ||||||||
\(53\) | 411.510 | 1.06652 | 0.533258 | − | 0.845953i | \(-0.320968\pi\) | ||||
0.533258 | + | 0.845953i | \(0.320968\pi\) | |||||||
\(54\) | −451.422 | −1.13761 | ||||||||
\(55\) | 249.846 | 0.612532 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 901.467 | 2.09478 | ||||||||
\(58\) | 75.7481 | 0.171486 | ||||||||
\(59\) | 381.449 | 0.841702 | 0.420851 | − | 0.907130i | \(-0.361732\pi\) | ||||
0.420851 | + | 0.907130i | \(0.361732\pi\) | |||||||
\(60\) | 178.146 | 0.383309 | ||||||||
\(61\) | −75.1332 | −0.157702 | −0.0788510 | − | 0.996886i | \(-0.525125\pi\) | ||||
−0.0788510 | + | 0.996886i | \(0.525125\pi\) | |||||||
\(62\) | 255.091 | 0.522526 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −92.6271 | −0.176753 | ||||||||
\(66\) | 890.182 | 1.66021 | ||||||||
\(67\) | −630.948 | −1.15049 | −0.575243 | − | 0.817982i | \(-0.695093\pi\) | ||||
−0.575243 | + | 0.817982i | \(0.695093\pi\) | |||||||
\(68\) | −403.550 | −0.719672 | ||||||||
\(69\) | −821.419 | −1.43315 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −214.755 | −0.358967 | −0.179484 | − | 0.983761i | \(-0.557443\pi\) | ||||
−0.179484 | + | 0.983761i | \(0.557443\pi\) | |||||||
\(72\) | 418.720 | 0.685370 | ||||||||
\(73\) | 1049.04 | 1.68193 | 0.840964 | − | 0.541091i | \(-0.181988\pi\) | ||||
0.840964 | + | 0.541091i | \(0.181988\pi\) | |||||||
\(74\) | 566.208 | 0.889463 | ||||||||
\(75\) | −222.683 | −0.342842 | ||||||||
\(76\) | −404.822 | −0.611003 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −330.023 | −0.479074 | ||||||||
\(79\) | −1060.77 | −1.51071 | −0.755354 | − | 0.655317i | \(-0.772535\pi\) | ||||
−0.755354 | + | 0.655317i | \(0.772535\pi\) | |||||||
\(80\) | −80.0000 | −0.111803 | ||||||||
\(81\) | 597.297 | 0.819338 | ||||||||
\(82\) | 500.315 | 0.673787 | ||||||||
\(83\) | 289.875 | 0.383349 | 0.191674 | − | 0.981459i | \(-0.438608\pi\) | ||||
0.191674 | + | 0.981459i | \(0.438608\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 504.438 | 0.643694 | ||||||||
\(86\) | −520.659 | −0.652839 | ||||||||
\(87\) | −337.355 | −0.415728 | ||||||||
\(88\) | −399.754 | −0.484249 | ||||||||
\(89\) | 994.158 | 1.18405 | 0.592026 | − | 0.805919i | \(-0.298328\pi\) | ||||
0.592026 | + | 0.805919i | \(0.298328\pi\) | |||||||
\(90\) | −523.400 | −0.613014 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 368.875 | 0.418020 | ||||||||
\(93\) | −1136.09 | −1.26674 | ||||||||
\(94\) | 1208.69 | 1.32624 | ||||||||
\(95\) | 506.027 | 0.546498 | ||||||||
\(96\) | −285.034 | −0.303033 | ||||||||
\(97\) | 281.931 | 0.295111 | 0.147556 | − | 0.989054i | \(-0.452859\pi\) | ||||
0.147556 | + | 0.989054i | \(0.452859\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2615.39 | −2.65512 | ||||||||
\(100\) | 100.000 | 0.100000 | ||||||||
\(101\) | −238.249 | −0.234720 | −0.117360 | − | 0.993089i | \(-0.537443\pi\) | ||||
−0.117360 | + | 0.993089i | \(0.537443\pi\) | |||||||
\(102\) | 1797.27 | 1.74467 | ||||||||
\(103\) | −956.179 | −0.914710 | −0.457355 | − | 0.889284i | \(-0.651203\pi\) | ||||
−0.457355 | + | 0.889284i | \(0.651203\pi\) | |||||||
\(104\) | 148.203 | 0.139736 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 823.021 | 0.754140 | ||||||||
\(107\) | 1527.21 | 1.37982 | 0.689911 | − | 0.723894i | \(-0.257649\pi\) | ||||
0.689911 | + | 0.723894i | \(0.257649\pi\) | |||||||
\(108\) | −902.845 | −0.804410 | ||||||||
\(109\) | −10.2326 | −0.00899182 | −0.00449591 | − | 0.999990i | \(-0.501431\pi\) | ||||
−0.00449591 | + | 0.999990i | \(0.501431\pi\) | |||||||
\(110\) | 499.692 | 0.433125 | ||||||||
\(111\) | −2521.69 | −2.15629 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1287.33 | 1.07170 | 0.535849 | − | 0.844314i | \(-0.319992\pi\) | ||||
0.535849 | + | 0.844314i | \(0.319992\pi\) | |||||||
\(114\) | 1802.93 | 1.48123 | ||||||||
\(115\) | −461.093 | −0.373888 | ||||||||
\(116\) | 151.496 | 0.121259 | ||||||||
\(117\) | 969.621 | 0.766166 | ||||||||
\(118\) | 762.898 | 0.595173 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 356.292 | 0.271041 | ||||||||
\(121\) | 1165.92 | 0.875975 | ||||||||
\(122\) | −150.266 | −0.111512 | ||||||||
\(123\) | −2228.23 | −1.63344 | ||||||||
\(124\) | 510.182 | 0.369481 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1243.53 | 0.868859 | 0.434430 | − | 0.900706i | \(-0.356950\pi\) | ||||
0.434430 | + | 0.900706i | \(0.356950\pi\) | |||||||
\(128\) | 128.000 | 0.0883883 | ||||||||
\(129\) | 2318.83 | 1.58265 | ||||||||
\(130\) | −185.254 | −0.124984 | ||||||||
\(131\) | 557.884 | 0.372081 | 0.186040 | − | 0.982542i | \(-0.440435\pi\) | ||||
0.186040 | + | 0.982542i | \(0.440435\pi\) | |||||||
\(132\) | 1780.36 | 1.17395 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1261.90 | −0.813517 | ||||||||
\(135\) | 1128.56 | 0.719486 | ||||||||
\(136\) | −807.101 | −0.508885 | ||||||||
\(137\) | 763.931 | 0.476402 | 0.238201 | − | 0.971216i | \(-0.423442\pi\) | ||||
0.238201 | + | 0.971216i | \(0.423442\pi\) | |||||||
\(138\) | −1642.84 | −1.01339 | ||||||||
\(139\) | −551.104 | −0.336288 | −0.168144 | − | 0.985762i | \(-0.553777\pi\) | ||||
−0.168144 | + | 0.985762i | \(0.553777\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5383.08 | −3.21516 | ||||||||
\(142\) | −429.509 | −0.253828 | ||||||||
\(143\) | −925.701 | −0.541336 | ||||||||
\(144\) | 837.440 | 0.484630 | ||||||||
\(145\) | −189.370 | −0.108457 | ||||||||
\(146\) | 2098.08 | 1.18930 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1132.42 | 0.628946 | ||||||||
\(149\) | −2557.21 | −1.40601 | −0.703003 | − | 0.711187i | \(-0.748158\pi\) | ||||
−0.703003 | + | 0.711187i | \(0.748158\pi\) | |||||||
\(150\) | −445.365 | −0.242426 | ||||||||
\(151\) | −757.655 | −0.408325 | −0.204163 | − | 0.978937i | \(-0.565447\pi\) | ||||
−0.204163 | + | 0.978937i | \(0.565447\pi\) | |||||||
\(152\) | −809.644 | −0.432045 | ||||||||
\(153\) | −5280.46 | −2.79020 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −637.727 | −0.330474 | ||||||||
\(156\) | −660.046 | −0.338756 | ||||||||
\(157\) | −982.388 | −0.499383 | −0.249691 | − | 0.968325i | \(-0.580329\pi\) | ||||
−0.249691 | + | 0.968325i | \(0.580329\pi\) | |||||||
\(158\) | −2121.54 | −1.06823 | ||||||||
\(159\) | −3665.45 | −1.82823 | ||||||||
\(160\) | −160.000 | −0.0790569 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1194.59 | 0.579359 | ||||||||
\(163\) | 2267.52 | 1.08960 | 0.544802 | − | 0.838564i | \(-0.316605\pi\) | ||||
0.544802 | + | 0.838564i | \(0.316605\pi\) | |||||||
\(164\) | 1000.63 | 0.476439 | ||||||||
\(165\) | −2225.45 | −1.05001 | ||||||||
\(166\) | 579.750 | 0.271068 | ||||||||
\(167\) | 1079.84 | 0.500364 | 0.250182 | − | 0.968199i | \(-0.419509\pi\) | ||||
0.250182 | + | 0.968199i | \(0.419509\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1853.81 | −0.843791 | ||||||||
\(170\) | 1008.88 | 0.455160 | ||||||||
\(171\) | −5297.10 | −2.36888 | ||||||||
\(172\) | −1041.32 | −0.461627 | ||||||||
\(173\) | −2597.42 | −1.14149 | −0.570746 | − | 0.821126i | \(-0.693346\pi\) | ||||
−0.570746 | + | 0.821126i | \(0.693346\pi\) | |||||||
\(174\) | −674.711 | −0.293964 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −799.508 | −0.342416 | ||||||||
\(177\) | −3397.68 | −1.44285 | ||||||||
\(178\) | 1988.32 | 0.837251 | ||||||||
\(179\) | −2087.69 | −0.871740 | −0.435870 | − | 0.900010i | \(-0.643559\pi\) | ||||
−0.435870 | + | 0.900010i | \(0.643559\pi\) | |||||||
\(180\) | −1046.80 | −0.433466 | ||||||||
\(181\) | 1911.11 | 0.784815 | 0.392408 | − | 0.919791i | \(-0.371642\pi\) | ||||
0.392408 | + | 0.919791i | \(0.371642\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 669.234 | 0.270334 | ||||||||
\(184\) | 737.749 | 0.295585 | ||||||||
\(185\) | −1415.52 | −0.562546 | ||||||||
\(186\) | −2272.17 | −0.895719 | ||||||||
\(187\) | 5041.28 | 1.97142 | ||||||||
\(188\) | 2417.38 | 0.937796 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1012.05 | 0.386432 | ||||||||
\(191\) | 458.990 | 0.173881 | 0.0869407 | − | 0.996213i | \(-0.472291\pi\) | ||||
0.0869407 | + | 0.996213i | \(0.472291\pi\) | |||||||
\(192\) | −570.067 | −0.214276 | ||||||||
\(193\) | 1746.32 | 0.651312 | 0.325656 | − | 0.945488i | \(-0.394415\pi\) | ||||
0.325656 | + | 0.945488i | \(0.394415\pi\) | |||||||
\(194\) | 563.863 | 0.208675 | ||||||||
\(195\) | 825.057 | 0.302993 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4099.78 | 1.48273 | 0.741363 | − | 0.671105i | \(-0.234180\pi\) | ||||
0.741363 | + | 0.671105i | \(0.234180\pi\) | |||||||
\(198\) | −5230.78 | −1.87745 | ||||||||
\(199\) | −4303.31 | −1.53293 | −0.766466 | − | 0.642285i | \(-0.777987\pi\) | ||||
−0.766466 | + | 0.642285i | \(0.777987\pi\) | |||||||
\(200\) | 200.000 | 0.0707107 | ||||||||
\(201\) | 5620.05 | 1.97218 | ||||||||
\(202\) | −476.498 | −0.165972 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 3594.55 | 1.23367 | ||||||||
\(205\) | −1250.79 | −0.426140 | ||||||||
\(206\) | −1912.36 | −0.646798 | ||||||||
\(207\) | 4826.73 | 1.62068 | ||||||||
\(208\) | 296.407 | 0.0988082 | ||||||||
\(209\) | 5057.16 | 1.67374 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 812.214 | 0.265000 | 0.132500 | − | 0.991183i | \(-0.457699\pi\) | ||||
0.132500 | + | 0.991183i | \(0.457699\pi\) | |||||||
\(212\) | 1646.04 | 0.533258 | ||||||||
\(213\) | 1912.88 | 0.615346 | ||||||||
\(214\) | 3054.42 | 0.975682 | ||||||||
\(215\) | 1301.65 | 0.412892 | ||||||||
\(216\) | −1805.69 | −0.568804 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −20.4653 | −0.00635818 | ||||||||
\(219\) | −9344.11 | −2.88318 | ||||||||
\(220\) | 999.384 | 0.306266 | ||||||||
\(221\) | −1868.99 | −0.568876 | ||||||||
\(222\) | −5043.38 | −1.52473 | ||||||||
\(223\) | 1293.12 | 0.388313 | 0.194156 | − | 0.980971i | \(-0.437803\pi\) | ||||
0.194156 | + | 0.980971i | \(0.437803\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1308.50 | 0.387704 | ||||||||
\(226\) | 2574.66 | 0.757805 | ||||||||
\(227\) | 5072.38 | 1.48311 | 0.741555 | − | 0.670892i | \(-0.234089\pi\) | ||||
0.741555 | + | 0.670892i | \(0.234089\pi\) | |||||||
\(228\) | 3605.87 | 1.04739 | ||||||||
\(229\) | −1945.18 | −0.561316 | −0.280658 | − | 0.959808i | \(-0.590553\pi\) | ||||
−0.280658 | + | 0.959808i | \(0.590553\pi\) | |||||||
\(230\) | −922.187 | −0.264379 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 302.992 | 0.0857432 | ||||||||
\(233\) | −683.447 | −0.192164 | −0.0960818 | − | 0.995373i | \(-0.530631\pi\) | ||||
−0.0960818 | + | 0.995373i | \(0.530631\pi\) | |||||||
\(234\) | 1939.24 | 0.541761 | ||||||||
\(235\) | −3021.73 | −0.838790 | ||||||||
\(236\) | 1525.80 | 0.420851 | ||||||||
\(237\) | 9448.60 | 2.58967 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4579.46 | 1.23942 | 0.619708 | − | 0.784832i | \(-0.287251\pi\) | ||||
0.619708 | + | 0.784832i | \(0.287251\pi\) | |||||||
\(240\) | 712.584 | 0.191655 | ||||||||
\(241\) | 5068.07 | 1.35462 | 0.677309 | − | 0.735699i | \(-0.263146\pi\) | ||||
0.677309 | + | 0.735699i | \(0.263146\pi\) | |||||||
\(242\) | 2331.85 | 0.619408 | ||||||||
\(243\) | 773.897 | 0.204303 | ||||||||
\(244\) | −300.533 | −0.0788510 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −4456.46 | −1.15501 | ||||||||
\(247\) | −1874.87 | −0.482977 | ||||||||
\(248\) | 1020.36 | 0.261263 | ||||||||
\(249\) | −2582.01 | −0.657140 | ||||||||
\(250\) | −250.000 | −0.0632456 | ||||||||
\(251\) | −1416.11 | −0.356112 | −0.178056 | − | 0.984020i | \(-0.556981\pi\) | ||||
−0.178056 | + | 0.984020i | \(0.556981\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4608.10 | −1.14509 | ||||||||
\(254\) | 2487.05 | 0.614376 | ||||||||
\(255\) | −4493.18 | −1.10343 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −3522.33 | −0.854929 | −0.427464 | − | 0.904032i | \(-0.640593\pi\) | ||||
−0.427464 | + | 0.904032i | \(0.640593\pi\) | |||||||
\(258\) | 4637.67 | 1.11910 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −370.508 | −0.0883767 | ||||||||
\(261\) | 1982.33 | 0.470126 | ||||||||
\(262\) | 1115.77 | 0.263101 | ||||||||
\(263\) | −3163.61 | −0.741736 | −0.370868 | − | 0.928686i | \(-0.620940\pi\) | ||||
−0.370868 | + | 0.928686i | \(0.620940\pi\) | |||||||
\(264\) | 3560.73 | 0.830105 | ||||||||
\(265\) | −2057.55 | −0.476960 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8855.27 | −2.02971 | ||||||||
\(268\) | −2523.79 | −0.575243 | ||||||||
\(269\) | 3903.37 | 0.884731 | 0.442366 | − | 0.896835i | \(-0.354139\pi\) | ||||
0.442366 | + | 0.896835i | \(0.354139\pi\) | |||||||
\(270\) | 2257.11 | 0.508754 | ||||||||
\(271\) | −2969.11 | −0.665538 | −0.332769 | − | 0.943008i | \(-0.607983\pi\) | ||||
−0.332769 | + | 0.943008i | \(0.607983\pi\) | |||||||
\(272\) | −1614.20 | −0.359836 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1527.86 | 0.336867 | ||||||||
\(275\) | −1249.23 | −0.273933 | ||||||||
\(276\) | −3285.68 | −0.716575 | ||||||||
\(277\) | −4308.50 | −0.934558 | −0.467279 | − | 0.884110i | \(-0.654766\pi\) | ||||
−0.467279 | + | 0.884110i | \(0.654766\pi\) | |||||||
\(278\) | −1102.21 | −0.237792 | ||||||||
\(279\) | 6675.73 | 1.43249 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3116.17 | 0.661550 | 0.330775 | − | 0.943710i | \(-0.392690\pi\) | ||||
0.330775 | + | 0.943710i | \(0.392690\pi\) | |||||||
\(282\) | −10766.2 | −2.27346 | ||||||||
\(283\) | −7611.17 | −1.59872 | −0.799359 | − | 0.600854i | \(-0.794827\pi\) | ||||
−0.799359 | + | 0.600854i | \(0.794827\pi\) | |||||||
\(284\) | −859.018 | −0.179484 | ||||||||
\(285\) | −4507.34 | −0.936813 | ||||||||
\(286\) | −1851.40 | −0.382782 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1674.88 | 0.342685 | ||||||||
\(289\) | 5265.31 | 1.07171 | ||||||||
\(290\) | −378.740 | −0.0766910 | ||||||||
\(291\) | −2511.25 | −0.505883 | ||||||||
\(292\) | 4196.16 | 0.840964 | ||||||||
\(293\) | 2351.74 | 0.468908 | 0.234454 | − | 0.972127i | \(-0.424670\pi\) | ||||
0.234454 | + | 0.972127i | \(0.424670\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1907.24 | −0.376420 | ||||||||
\(296\) | 2264.83 | 0.444732 | ||||||||
\(297\) | 11278.6 | 2.20354 | ||||||||
\(298\) | −5114.42 | −0.994197 | ||||||||
\(299\) | 1708.39 | 0.330430 | ||||||||
\(300\) | −890.730 | −0.171421 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1515.31 | −0.288730 | ||||||||
\(303\) | 2122.16 | 0.402359 | ||||||||
\(304\) | −1619.29 | −0.305502 | ||||||||
\(305\) | 375.666 | 0.0705265 | ||||||||
\(306\) | −10560.9 | −1.97297 | ||||||||
\(307\) | −2261.80 | −0.420480 | −0.210240 | − | 0.977650i | \(-0.567425\pi\) | ||||
−0.210240 | + | 0.977650i | \(0.567425\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8516.98 | 1.56801 | ||||||||
\(310\) | −1275.45 | −0.233681 | ||||||||
\(311\) | −1476.22 | −0.269160 | −0.134580 | − | 0.990903i | \(-0.542969\pi\) | ||||
−0.134580 | + | 0.990903i | \(0.542969\pi\) | |||||||
\(312\) | −1320.09 | −0.239537 | ||||||||
\(313\) | 6028.15 | 1.08860 | 0.544299 | − | 0.838891i | \(-0.316796\pi\) | ||||
0.544299 | + | 0.838891i | \(0.316796\pi\) | |||||||
\(314\) | −1964.78 | −0.353117 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4243.08 | −0.755354 | ||||||||
\(317\) | 1966.33 | 0.348392 | 0.174196 | − | 0.984711i | \(-0.444267\pi\) | ||||
0.174196 | + | 0.984711i | \(0.444267\pi\) | |||||||
\(318\) | −7330.90 | −1.29276 | ||||||||
\(319\) | −1892.54 | −0.332168 | ||||||||
\(320\) | −320.000 | −0.0559017 | ||||||||
\(321\) | −13603.3 | −2.36531 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10210.4 | 1.75889 | ||||||||
\(324\) | 2389.19 | 0.409669 | ||||||||
\(325\) | 463.135 | 0.0790466 | ||||||||
\(326\) | 4535.03 | 0.770467 | ||||||||
\(327\) | 91.1451 | 0.0154139 | ||||||||
\(328\) | 2001.26 | 0.336894 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −4450.91 | −0.742468 | ||||||||
\(331\) | 7753.43 | 1.28751 | 0.643757 | − | 0.765230i | \(-0.277375\pi\) | ||||
0.643757 | + | 0.765230i | \(0.277375\pi\) | |||||||
\(332\) | 1159.50 | 0.191674 | ||||||||
\(333\) | 14817.7 | 2.43845 | ||||||||
\(334\) | 2159.69 | 0.353811 | ||||||||
\(335\) | 3154.74 | 0.514513 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3258.06 | 0.526640 | 0.263320 | − | 0.964709i | \(-0.415182\pi\) | ||||
0.263320 | + | 0.964709i | \(0.415182\pi\) | |||||||
\(338\) | −3707.62 | −0.596650 | ||||||||
\(339\) | −11466.6 | −1.83712 | ||||||||
\(340\) | 2017.75 | 0.321847 | ||||||||
\(341\) | −6373.35 | −1.01213 | ||||||||
\(342\) | −10594.2 | −1.67505 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −2082.64 | −0.326419 | ||||||||
\(345\) | 4107.10 | 0.640924 | ||||||||
\(346\) | −5194.84 | −0.807157 | ||||||||
\(347\) | −10949.1 | −1.69388 | −0.846940 | − | 0.531689i | \(-0.821558\pi\) | ||||
−0.846940 | + | 0.531689i | \(0.821558\pi\) | |||||||
\(348\) | −1349.42 | −0.207864 | ||||||||
\(349\) | 2498.45 | 0.383206 | 0.191603 | − | 0.981473i | \(-0.438631\pi\) | ||||
0.191603 | + | 0.981473i | \(0.438631\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4181.39 | −0.635858 | ||||||||
\(352\) | −1599.02 | −0.242124 | ||||||||
\(353\) | −8789.58 | −1.32527 | −0.662637 | − | 0.748940i | \(-0.730563\pi\) | ||||
−0.662637 | + | 0.748940i | \(0.730563\pi\) | |||||||
\(354\) | −6795.36 | −1.02025 | ||||||||
\(355\) | 1073.77 | 0.160535 | ||||||||
\(356\) | 3976.63 | 0.592026 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4175.39 | −0.616413 | ||||||||
\(359\) | −2169.34 | −0.318923 | −0.159462 | − | 0.987204i | \(-0.550976\pi\) | ||||
−0.159462 | + | 0.987204i | \(0.550976\pi\) | |||||||
\(360\) | −2093.60 | −0.306507 | ||||||||
\(361\) | 3383.54 | 0.493300 | ||||||||
\(362\) | 3822.22 | 0.554948 | ||||||||
\(363\) | −10385.2 | −1.50161 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5245.20 | −0.752181 | ||||||||
\(366\) | 1338.47 | 0.191155 | ||||||||
\(367\) | 13002.5 | 1.84938 | 0.924692 | − | 0.380715i | \(-0.124322\pi\) | ||||
0.924692 | + | 0.380715i | \(0.124322\pi\) | |||||||
\(368\) | 1475.50 | 0.209010 | ||||||||
\(369\) | 13093.2 | 1.84717 | ||||||||
\(370\) | −2831.04 | −0.397780 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −4544.34 | −0.633369 | ||||||||
\(373\) | 5107.50 | 0.708998 | 0.354499 | − | 0.935056i | \(-0.384651\pi\) | ||||
0.354499 | + | 0.935056i | \(0.384651\pi\) | |||||||
\(374\) | 10082.6 | 1.39400 | ||||||||
\(375\) | 1113.41 | 0.153324 | ||||||||
\(376\) | 4834.76 | 0.663122 | ||||||||
\(377\) | 701.632 | 0.0958512 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12391.9 | −1.67950 | −0.839749 | − | 0.542975i | \(-0.817298\pi\) | ||||
−0.839749 | + | 0.542975i | \(0.817298\pi\) | |||||||
\(380\) | 2024.11 | 0.273249 | ||||||||
\(381\) | −11076.5 | −1.48941 | ||||||||
\(382\) | 917.980 | 0.122953 | ||||||||
\(383\) | −9130.21 | −1.21810 | −0.609049 | − | 0.793132i | \(-0.708449\pi\) | ||||
−0.609049 | + | 0.793132i | \(0.708449\pi\) | |||||||
\(384\) | −1140.13 | −0.151516 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3492.65 | 0.460547 | ||||||||
\(387\) | −13625.7 | −1.78974 | ||||||||
\(388\) | 1127.73 | 0.147556 | ||||||||
\(389\) | 12312.2 | 1.60477 | 0.802385 | − | 0.596806i | \(-0.203564\pi\) | ||||
0.802385 | + | 0.596806i | \(0.203564\pi\) | |||||||
\(390\) | 1650.11 | 0.214248 | ||||||||
\(391\) | −9303.72 | −1.20335 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4969.24 | −0.637825 | ||||||||
\(394\) | 8199.55 | 1.04845 | ||||||||
\(395\) | 5303.85 | 0.675609 | ||||||||
\(396\) | −10461.6 | −1.32756 | ||||||||
\(397\) | 1359.39 | 0.171854 | 0.0859270 | − | 0.996301i | \(-0.472615\pi\) | ||||
0.0859270 | + | 0.996301i | \(0.472615\pi\) | |||||||
\(398\) | −8606.62 | −1.08395 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 400.000 | 0.0500000 | ||||||||
\(401\) | 11142.3 | 1.38758 | 0.693790 | − | 0.720177i | \(-0.255939\pi\) | ||||
0.693790 | + | 0.720177i | \(0.255939\pi\) | |||||||
\(402\) | 11240.1 | 1.39454 | ||||||||
\(403\) | 2362.83 | 0.292062 | ||||||||
\(404\) | −952.997 | −0.117360 | ||||||||
\(405\) | −2986.49 | −0.366419 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −14146.5 | −1.72289 | ||||||||
\(408\) | 7189.09 | 0.872336 | ||||||||
\(409\) | 10378.0 | 1.25466 | 0.627331 | − | 0.778753i | \(-0.284147\pi\) | ||||
0.627331 | + | 0.778753i | \(0.284147\pi\) | |||||||
\(410\) | −2501.57 | −0.301327 | ||||||||
\(411\) | −6804.57 | −0.816653 | ||||||||
\(412\) | −3824.72 | −0.457355 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 9653.45 | 1.14599 | ||||||||
\(415\) | −1449.38 | −0.171439 | ||||||||
\(416\) | 592.813 | 0.0698679 | ||||||||
\(417\) | 4908.85 | 0.576469 | ||||||||
\(418\) | 10114.3 | 1.18351 | ||||||||
\(419\) | 477.650 | 0.0556915 | 0.0278458 | − | 0.999612i | \(-0.491135\pi\) | ||||
0.0278458 | + | 0.999612i | \(0.491135\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7877.72 | 0.911963 | 0.455981 | − | 0.889989i | \(-0.349288\pi\) | ||||
0.455981 | + | 0.889989i | \(0.349288\pi\) | |||||||
\(422\) | 1624.43 | 0.187384 | ||||||||
\(423\) | 31631.4 | 3.63587 | ||||||||
\(424\) | 3292.08 | 0.377070 | ||||||||
\(425\) | −2522.19 | −0.287869 | ||||||||
\(426\) | 3825.77 | 0.435115 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 6108.84 | 0.689911 | ||||||||
\(429\) | 8245.49 | 0.927963 | ||||||||
\(430\) | 2603.30 | 0.291958 | ||||||||
\(431\) | 9425.11 | 1.05334 | 0.526672 | − | 0.850068i | \(-0.323439\pi\) | ||||
0.526672 | + | 0.850068i | \(0.323439\pi\) | |||||||
\(432\) | −3611.38 | −0.402205 | ||||||||
\(433\) | 2438.58 | 0.270648 | 0.135324 | − | 0.990801i | \(-0.456792\pi\) | ||||
0.135324 | + | 0.990801i | \(0.456792\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1686.78 | 0.185919 | ||||||||
\(436\) | −40.9305 | −0.00449591 | ||||||||
\(437\) | −9333.03 | −1.02165 | ||||||||
\(438\) | −18688.2 | −2.03872 | ||||||||
\(439\) | −6785.52 | −0.737711 | −0.368856 | − | 0.929487i | \(-0.620250\pi\) | ||||
−0.368856 | + | 0.929487i | \(0.620250\pi\) | |||||||
\(440\) | 1998.77 | 0.216563 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3737.97 | −0.402256 | ||||||||
\(443\) | −7317.41 | −0.784787 | −0.392393 | − | 0.919797i | \(-0.628353\pi\) | ||||
−0.392393 | + | 0.919797i | \(0.628353\pi\) | |||||||
\(444\) | −10086.8 | −1.07815 | ||||||||
\(445\) | −4970.79 | −0.529524 | ||||||||
\(446\) | 2586.24 | 0.274578 | ||||||||
\(447\) | 22777.9 | 2.41019 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5411.83 | 0.568820 | 0.284410 | − | 0.958703i | \(-0.408202\pi\) | ||||
0.284410 | + | 0.958703i | \(0.408202\pi\) | |||||||
\(450\) | 2617.00 | 0.274148 | ||||||||
\(451\) | −12500.2 | −1.30512 | ||||||||
\(452\) | 5149.32 | 0.535849 | ||||||||
\(453\) | 6748.67 | 0.699956 | ||||||||
\(454\) | 10144.8 | 1.04872 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7211.74 | 0.740615 | ||||||||
\(457\) | −4074.35 | −0.417046 | −0.208523 | − | 0.978017i | \(-0.566866\pi\) | ||||
−0.208523 | + | 0.978017i | \(0.566866\pi\) | |||||||
\(458\) | −3890.37 | −0.396910 | ||||||||
\(459\) | 22771.5 | 2.31564 | ||||||||
\(460\) | −1844.37 | −0.186944 | ||||||||
\(461\) | −2259.32 | −0.228258 | −0.114129 | − | 0.993466i | \(-0.536408\pi\) | ||||
−0.114129 | + | 0.993466i | \(0.536408\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11153.8 | 1.11957 | 0.559786 | − | 0.828637i | \(-0.310883\pi\) | ||||
0.559786 | + | 0.828637i | \(0.310883\pi\) | |||||||
\(464\) | 605.984 | 0.0606296 | ||||||||
\(465\) | 5680.43 | 0.566502 | ||||||||
\(466\) | −1366.89 | −0.135880 | ||||||||
\(467\) | −15304.5 | −1.51651 | −0.758253 | − | 0.651961i | \(-0.773947\pi\) | ||||
−0.758253 | + | 0.651961i | \(0.773947\pi\) | |||||||
\(468\) | 3878.48 | 0.383083 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −6043.45 | −0.593114 | ||||||||
\(471\) | 8750.43 | 0.856048 | ||||||||
\(472\) | 3051.59 | 0.297587 | ||||||||
\(473\) | 13008.5 | 1.26455 | ||||||||
\(474\) | 18897.2 | 1.83118 | ||||||||
\(475\) | −2530.14 | −0.244401 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 21538.5 | 2.06746 | ||||||||
\(478\) | 9158.92 | 0.876400 | ||||||||
\(479\) | 2452.16 | 0.233909 | 0.116954 | − | 0.993137i | \(-0.462687\pi\) | ||||
0.116954 | + | 0.993137i | \(0.462687\pi\) | |||||||
\(480\) | 1425.17 | 0.135520 | ||||||||
\(481\) | 5244.62 | 0.497160 | ||||||||
\(482\) | 10136.1 | 0.957859 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4663.69 | 0.437988 | ||||||||
\(485\) | −1409.66 | −0.131978 | ||||||||
\(486\) | 1547.79 | 0.144464 | ||||||||
\(487\) | 14248.5 | 1.32580 | 0.662899 | − | 0.748709i | \(-0.269326\pi\) | ||||
0.662899 | + | 0.748709i | \(0.269326\pi\) | |||||||
\(488\) | −601.065 | −0.0557561 | ||||||||
\(489\) | −20197.5 | −1.86781 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10764.1 | 0.989364 | 0.494682 | − | 0.869074i | \(-0.335285\pi\) | ||||
0.494682 | + | 0.869074i | \(0.335285\pi\) | |||||||
\(492\) | −8912.91 | −0.816718 | ||||||||
\(493\) | −3821.02 | −0.349067 | ||||||||
\(494\) | −3749.75 | −0.341516 | ||||||||
\(495\) | 13077.0 | 1.18740 | ||||||||
\(496\) | 2040.73 | 0.184741 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −5164.01 | −0.464668 | ||||||||
\(499\) | −7294.82 | −0.654431 | −0.327216 | − | 0.944950i | \(-0.606110\pi\) | ||||
−0.327216 | + | 0.944950i | \(0.606110\pi\) | |||||||
\(500\) | −500.000 | −0.0447214 | ||||||||
\(501\) | −9618.50 | −0.857730 | ||||||||
\(502\) | −2832.22 | −0.251809 | ||||||||
\(503\) | 11064.2 | 0.980774 | 0.490387 | − | 0.871505i | \(-0.336855\pi\) | ||||
0.490387 | + | 0.871505i | \(0.336855\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1191.25 | 0.104970 | ||||||||
\(506\) | −9216.19 | −0.809703 | ||||||||
\(507\) | 16512.4 | 1.44644 | ||||||||
\(508\) | 4974.10 | 0.434430 | ||||||||
\(509\) | −14890.7 | −1.29669 | −0.648347 | − | 0.761345i | \(-0.724539\pi\) | ||||
−0.648347 | + | 0.761345i | \(0.724539\pi\) | |||||||
\(510\) | −8986.36 | −0.780241 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | 22843.2 | 1.96599 | ||||||||
\(514\) | −7044.65 | −0.604526 | ||||||||
\(515\) | 4780.90 | 0.409071 | ||||||||
\(516\) | 9275.34 | 0.791326 | ||||||||
\(517\) | −30198.7 | −2.56893 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 23136.0 | 1.95676 | ||||||||
\(520\) | −741.017 | −0.0624918 | ||||||||
\(521\) | −6360.27 | −0.534834 | −0.267417 | − | 0.963581i | \(-0.586170\pi\) | ||||
−0.267417 | + | 0.963581i | \(0.586170\pi\) | |||||||
\(522\) | 3964.65 | 0.332430 | ||||||||
\(523\) | 42.8271 | 0.00358069 | 0.00179034 | − | 0.999998i | \(-0.499430\pi\) | ||||
0.00179034 | + | 0.999998i | \(0.499430\pi\) | |||||||
\(524\) | 2231.54 | 0.186040 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6327.22 | −0.524486 | ||||||||
\(527\) | −12867.8 | −1.06362 | ||||||||
\(528\) | 7121.46 | 0.586973 | ||||||||
\(529\) | −3662.72 | −0.301037 | ||||||||
\(530\) | −4115.10 | −0.337262 | ||||||||
\(531\) | 19965.0 | 1.63166 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4634.27 | 0.376609 | ||||||||
\(534\) | −17710.5 | −1.43522 | ||||||||
\(535\) | −7636.05 | −0.617076 | ||||||||
\(536\) | −5047.59 | −0.406758 | ||||||||
\(537\) | 18595.7 | 1.49435 | ||||||||
\(538\) | 7806.74 | 0.625600 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 4514.22 | 0.359743 | ||||||||
\(541\) | −3293.75 | −0.261755 | −0.130877 | − | 0.991399i | \(-0.541779\pi\) | ||||
−0.130877 | + | 0.991399i | \(0.541779\pi\) | |||||||
\(542\) | −5938.23 | −0.470607 | ||||||||
\(543\) | −17022.8 | −1.34534 | ||||||||
\(544\) | −3228.40 | −0.254442 | ||||||||
\(545\) | 51.1632 | 0.00402126 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12786.8 | 0.999492 | 0.499746 | − | 0.866172i | \(-0.333427\pi\) | ||||
0.499746 | + | 0.866172i | \(0.333427\pi\) | |||||||
\(548\) | 3055.73 | 0.238201 | ||||||||
\(549\) | −3932.47 | −0.305708 | ||||||||
\(550\) | −2498.46 | −0.193700 | ||||||||
\(551\) | −3833.06 | −0.296359 | ||||||||
\(552\) | −6571.36 | −0.506695 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −8617.00 | −0.660833 | ||||||||
\(555\) | 12608.5 | 0.964323 | ||||||||
\(556\) | −2204.42 | −0.168144 | ||||||||
\(557\) | 16913.1 | 1.28659 | 0.643295 | − | 0.765618i | \(-0.277567\pi\) | ||||
0.643295 | + | 0.765618i | \(0.277567\pi\) | |||||||
\(558\) | 13351.5 | 1.01293 | ||||||||
\(559\) | −4822.72 | −0.364900 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −44904.2 | −3.37942 | ||||||||
\(562\) | 6232.35 | 0.467786 | ||||||||
\(563\) | 17336.2 | 1.29775 | 0.648877 | − | 0.760893i | \(-0.275239\pi\) | ||||
0.648877 | + | 0.760893i | \(0.275239\pi\) | |||||||
\(564\) | −21532.3 | −1.60758 | ||||||||
\(565\) | −6436.65 | −0.479278 | ||||||||
\(566\) | −15222.3 | −1.13046 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1718.04 | −0.126914 | ||||||||
\(569\) | −3143.79 | −0.231625 | −0.115812 | − | 0.993271i | \(-0.536947\pi\) | ||||
−0.115812 | + | 0.993271i | \(0.536947\pi\) | |||||||
\(570\) | −9014.67 | −0.662427 | ||||||||
\(571\) | −9794.82 | −0.717865 | −0.358932 | − | 0.933364i | \(-0.616859\pi\) | ||||
−0.358932 | + | 0.933364i | \(0.616859\pi\) | |||||||
\(572\) | −3702.80 | −0.270668 | ||||||||
\(573\) | −4088.36 | −0.298069 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2305.47 | 0.167208 | ||||||||
\(576\) | 3349.76 | 0.242315 | ||||||||
\(577\) | 8386.30 | 0.605071 | 0.302536 | − | 0.953138i | \(-0.402167\pi\) | ||||
0.302536 | + | 0.953138i | \(0.402167\pi\) | |||||||
\(578\) | 10530.6 | 0.757813 | ||||||||
\(579\) | −15555.0 | −1.11649 | ||||||||
\(580\) | −757.481 | −0.0542287 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −5022.49 | −0.357713 | ||||||||
\(583\) | −20562.9 | −1.46077 | ||||||||
\(584\) | 8392.32 | 0.594651 | ||||||||
\(585\) | −4848.10 | −0.342640 | ||||||||
\(586\) | 4703.47 | 0.331568 | ||||||||
\(587\) | 21032.1 | 1.47886 | 0.739428 | − | 0.673236i | \(-0.235096\pi\) | ||||
0.739428 | + | 0.673236i | \(0.235096\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12908.3 | −0.903017 | ||||||||
\(590\) | −3814.49 | −0.266169 | ||||||||
\(591\) | −36517.9 | −2.54170 | ||||||||
\(592\) | 4529.66 | 0.314473 | ||||||||
\(593\) | 10818.4 | 0.749171 | 0.374585 | − | 0.927192i | \(-0.377785\pi\) | ||||
0.374585 | + | 0.927192i | \(0.377785\pi\) | |||||||
\(594\) | 22557.2 | 1.55814 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −10228.8 | −0.703003 | ||||||||
\(597\) | 38330.9 | 2.62777 | ||||||||
\(598\) | 3416.78 | 0.233650 | ||||||||
\(599\) | 8595.40 | 0.586308 | 0.293154 | − | 0.956065i | \(-0.405295\pi\) | ||||
0.293154 | + | 0.956065i | \(0.405295\pi\) | |||||||
\(600\) | −1781.46 | −0.121213 | ||||||||
\(601\) | −18316.3 | −1.24316 | −0.621579 | − | 0.783351i | \(-0.713509\pi\) | ||||
−0.621579 | + | 0.783351i | \(0.713509\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −33023.8 | −2.23024 | ||||||||
\(604\) | −3030.62 | −0.204163 | ||||||||
\(605\) | −5829.62 | −0.391748 | ||||||||
\(606\) | 4244.32 | 0.284511 | ||||||||
\(607\) | 13568.7 | 0.907310 | 0.453655 | − | 0.891177i | \(-0.350120\pi\) | ||||
0.453655 | + | 0.891177i | \(0.350120\pi\) | |||||||
\(608\) | −3238.57 | −0.216022 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 751.332 | 0.0498697 | ||||||||
\(611\) | 11195.7 | 0.741295 | ||||||||
\(612\) | −21121.8 | −1.39510 | ||||||||
\(613\) | −12346.3 | −0.813477 | −0.406739 | − | 0.913545i | \(-0.633334\pi\) | ||||
−0.406739 | + | 0.913545i | \(0.633334\pi\) | |||||||
\(614\) | −4523.59 | −0.297325 | ||||||||
\(615\) | 11141.1 | 0.730495 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 17639.2 | 1.15094 | 0.575469 | − | 0.817824i | \(-0.304820\pi\) | ||||
0.575469 | + | 0.817824i | \(0.304820\pi\) | |||||||
\(618\) | 17034.0 | 1.10875 | ||||||||
\(619\) | 690.919 | 0.0448633 | 0.0224317 | − | 0.999748i | \(-0.492859\pi\) | ||||
0.0224317 | + | 0.999748i | \(0.492859\pi\) | |||||||
\(620\) | −2550.91 | −0.165237 | ||||||||
\(621\) | −20814.8 | −1.34504 | ||||||||
\(622\) | −2952.44 | −0.190325 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −2640.18 | −0.169378 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 12056.3 | 0.769755 | ||||||||
\(627\) | −45045.6 | −2.86914 | ||||||||
\(628\) | −3929.55 | −0.249691 | ||||||||
\(629\) | −28561.7 | −1.81054 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7403.38 | 0.467074 | 0.233537 | − | 0.972348i | \(-0.424970\pi\) | ||||
0.233537 | + | 0.972348i | \(0.424970\pi\) | |||||||
\(632\) | −8486.16 | −0.534116 | ||||||||
\(633\) | −7234.63 | −0.454267 | ||||||||
\(634\) | 3932.66 | 0.246350 | ||||||||
\(635\) | −6217.63 | −0.388566 | ||||||||
\(636\) | −14661.8 | −0.914116 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −3785.07 | −0.234878 | ||||||||
\(639\) | −11240.3 | −0.695865 | ||||||||
\(640\) | −640.000 | −0.0395285 | ||||||||
\(641\) | 13280.4 | 0.818325 | 0.409162 | − | 0.912462i | \(-0.365821\pi\) | ||||
0.409162 | + | 0.912462i | \(0.365821\pi\) | |||||||
\(642\) | −27206.7 | −1.67252 | ||||||||
\(643\) | 13586.5 | 0.833279 | 0.416640 | − | 0.909072i | \(-0.363208\pi\) | ||||
0.416640 | + | 0.909072i | \(0.363208\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −11594.2 | −0.707783 | ||||||||
\(646\) | 20420.8 | 1.24372 | ||||||||
\(647\) | −16389.1 | −0.995861 | −0.497931 | − | 0.867217i | \(-0.665907\pi\) | ||||
−0.497931 | + | 0.867217i | \(0.665907\pi\) | |||||||
\(648\) | 4778.38 | 0.289680 | ||||||||
\(649\) | −19060.7 | −1.15285 | ||||||||
\(650\) | 926.271 | 0.0558944 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9070.07 | 0.544802 | ||||||||
\(653\) | −18282.5 | −1.09563 | −0.547817 | − | 0.836599i | \(-0.684541\pi\) | ||||
−0.547817 | + | 0.836599i | \(0.684541\pi\) | |||||||
\(654\) | 182.290 | 0.0108993 | ||||||||
\(655\) | −2789.42 | −0.166399 | ||||||||
\(656\) | 4002.52 | 0.238220 | ||||||||
\(657\) | 54906.7 | 3.26045 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3419.09 | −0.202108 | −0.101054 | − | 0.994881i | \(-0.532221\pi\) | ||||
−0.101054 | + | 0.994881i | \(0.532221\pi\) | |||||||
\(660\) | −8901.82 | −0.525004 | ||||||||
\(661\) | 9950.75 | 0.585536 | 0.292768 | − | 0.956183i | \(-0.405424\pi\) | ||||
0.292768 | + | 0.956183i | \(0.405424\pi\) | |||||||
\(662\) | 15506.9 | 0.910409 | ||||||||
\(663\) | 16647.6 | 0.975173 | ||||||||
\(664\) | 2319.00 | 0.135534 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 29635.3 | 1.72424 | ||||||||
\(667\) | 3492.69 | 0.202755 | ||||||||
\(668\) | 4319.38 | 0.250182 | ||||||||
\(669\) | −11518.2 | −0.665650 | ||||||||
\(670\) | 6309.48 | 0.363816 | ||||||||
\(671\) | 3754.35 | 0.215998 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15363.3 | −0.879957 | −0.439978 | − | 0.898008i | \(-0.645014\pi\) | ||||
−0.439978 | + | 0.898008i | \(0.645014\pi\) | |||||||
\(674\) | 6516.12 | 0.372391 | ||||||||
\(675\) | −5642.78 | −0.321764 | ||||||||
\(676\) | −7415.24 | −0.421896 | ||||||||
\(677\) | 3687.29 | 0.209326 | 0.104663 | − | 0.994508i | \(-0.466624\pi\) | ||||
0.104663 | + | 0.994508i | \(0.466624\pi\) | |||||||
\(678\) | −22933.3 | −1.29904 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 4035.50 | 0.227580 | ||||||||
\(681\) | −45181.2 | −2.54236 | ||||||||
\(682\) | −12746.7 | −0.715684 | ||||||||
\(683\) | 15116.1 | 0.846854 | 0.423427 | − | 0.905930i | \(-0.360827\pi\) | ||||
0.423427 | + | 0.905930i | \(0.360827\pi\) | |||||||
\(684\) | −21188.4 | −1.18444 | ||||||||
\(685\) | −3819.66 | −0.213053 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 17326.3 | 0.962214 | ||||||||
\(688\) | −4165.27 | −0.230813 | ||||||||
\(689\) | 7623.40 | 0.421522 | ||||||||
\(690\) | 8214.19 | 0.453202 | ||||||||
\(691\) | 5427.11 | 0.298780 | 0.149390 | − | 0.988778i | \(-0.452269\pi\) | ||||
0.149390 | + | 0.988778i | \(0.452269\pi\) | |||||||
\(692\) | −10389.7 | −0.570746 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −21898.1 | −1.19775 | ||||||||
\(695\) | 2755.52 | 0.150393 | ||||||||
\(696\) | −2698.84 | −0.146982 | ||||||||
\(697\) | −25237.8 | −1.37152 | ||||||||
\(698\) | 4996.89 | 0.270967 | ||||||||
\(699\) | 6087.67 | 0.329409 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1857.26 | 0.100068 | 0.0500340 | − | 0.998748i | \(-0.484067\pi\) | ||||
0.0500340 | + | 0.998748i | \(0.484067\pi\) | |||||||
\(702\) | −8362.79 | −0.449620 | ||||||||
\(703\) | −28651.6 | −1.53715 | ||||||||
\(704\) | −3198.03 | −0.171208 | ||||||||
\(705\) | 26915.4 | 1.43786 | ||||||||
\(706\) | −17579.2 | −0.937111 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −13590.7 | −0.721427 | ||||||||
\(709\) | −4592.23 | −0.243251 | −0.121625 | − | 0.992576i | \(-0.538811\pi\) | ||||
−0.121625 | + | 0.992576i | \(0.538811\pi\) | |||||||
\(710\) | 2147.55 | 0.113515 | ||||||||
\(711\) | −55520.7 | −2.92854 | ||||||||
\(712\) | 7953.27 | 0.418625 | ||||||||
\(713\) | 11762.1 | 0.617802 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4628.50 | 0.242093 | ||||||||
\(716\) | −8350.77 | −0.435870 | ||||||||
\(717\) | −40790.6 | −2.12462 | ||||||||
\(718\) | −4338.68 | −0.225513 | ||||||||
\(719\) | 14986.9 | 0.777355 | 0.388678 | − | 0.921374i | \(-0.372932\pi\) | ||||
0.388678 | + | 0.921374i | \(0.372932\pi\) | |||||||
\(720\) | −4187.20 | −0.216733 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 6767.09 | 0.348816 | ||||||||
\(723\) | −45142.8 | −2.32210 | ||||||||
\(724\) | 7644.43 | 0.392408 | ||||||||
\(725\) | 946.851 | 0.0485037 | ||||||||
\(726\) | −20770.5 | −1.06180 | ||||||||
\(727\) | 8473.49 | 0.432276 | 0.216138 | − | 0.976363i | \(-0.430654\pi\) | ||||
0.216138 | + | 0.976363i | \(0.430654\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −23020.4 | −1.16956 | ||||||||
\(730\) | −10490.4 | −0.531872 | ||||||||
\(731\) | 26264.0 | 1.32888 | ||||||||
\(732\) | 2676.94 | 0.135167 | ||||||||
\(733\) | −31462.8 | −1.58541 | −0.792706 | − | 0.609604i | \(-0.791328\pi\) | ||||
−0.792706 | + | 0.609604i | \(0.791328\pi\) | |||||||
\(734\) | 26005.0 | 1.30771 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2951.00 | 0.147792 | ||||||||
\(737\) | 31528.0 | 1.57578 | ||||||||
\(738\) | 26186.5 | 1.30615 | ||||||||
\(739\) | 384.770 | 0.0191529 | 0.00957645 | − | 0.999954i | \(-0.496952\pi\) | ||||
0.00957645 | + | 0.999954i | \(0.496952\pi\) | |||||||
\(740\) | −5662.08 | −0.281273 | ||||||||
\(741\) | 16700.1 | 0.827924 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −13573.4 | −0.670201 | −0.335100 | − | 0.942182i | \(-0.608770\pi\) | ||||
−0.335100 | + | 0.942182i | \(0.608770\pi\) | |||||||
\(744\) | −9088.69 | −0.447859 | ||||||||
\(745\) | 12786.1 | 0.628785 | ||||||||
\(746\) | 10215.0 | 0.501337 | ||||||||
\(747\) | 15172.1 | 0.743129 | ||||||||
\(748\) | 20165.1 | 0.985708 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 2226.83 | 0.108416 | ||||||||
\(751\) | −34266.9 | −1.66500 | −0.832501 | − | 0.554023i | \(-0.813092\pi\) | ||||
−0.832501 | + | 0.554023i | \(0.813092\pi\) | |||||||
\(752\) | 9669.52 | 0.468898 | ||||||||
\(753\) | 12613.7 | 0.610451 | ||||||||
\(754\) | 1403.26 | 0.0677770 | ||||||||
\(755\) | 3788.28 | 0.182609 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9605.37 | 0.461180 | 0.230590 | − | 0.973051i | \(-0.425934\pi\) | ||||
0.230590 | + | 0.973051i | \(0.425934\pi\) | |||||||
\(758\) | −24783.8 | −1.18758 | ||||||||
\(759\) | 41045.7 | 1.96293 | ||||||||
\(760\) | 4048.22 | 0.193216 | ||||||||
\(761\) | −20928.3 | −0.996911 | −0.498455 | − | 0.866915i | \(-0.666099\pi\) | ||||
−0.498455 | + | 0.866915i | \(0.666099\pi\) | |||||||
\(762\) | −22152.9 | −1.05317 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 1835.96 | 0.0869407 | ||||||||
\(765\) | 26402.3 | 1.24781 | ||||||||
\(766\) | −18260.4 | −0.861326 | ||||||||
\(767\) | 7066.50 | 0.332668 | ||||||||
\(768\) | −2280.27 | −0.107138 | ||||||||
\(769\) | −18338.3 | −0.859940 | −0.429970 | − | 0.902843i | \(-0.641476\pi\) | ||||
−0.429970 | + | 0.902843i | \(0.641476\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 31374.4 | 1.46553 | ||||||||
\(772\) | 6985.29 | 0.325656 | ||||||||
\(773\) | −5647.02 | −0.262755 | −0.131377 | − | 0.991332i | \(-0.541940\pi\) | ||||
−0.131377 | + | 0.991332i | \(0.541940\pi\) | |||||||
\(774\) | −27251.3 | −1.26554 | ||||||||
\(775\) | 3188.64 | 0.147793 | ||||||||
\(776\) | 2255.45 | 0.104338 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 24624.5 | 1.13474 | ||||||||
\(779\) | −25317.3 | −1.16442 | ||||||||
\(780\) | 3300.23 | 0.151496 | ||||||||
\(781\) | 10731.1 | 0.491664 | ||||||||
\(782\) | −18607.4 | −0.850896 | ||||||||
\(783\) | −8548.59 | −0.390168 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4911.94 | 0.223331 | ||||||||
\(786\) | −9938.48 | −0.451010 | ||||||||
\(787\) | 28407.3 | 1.28667 | 0.643336 | − | 0.765584i | \(-0.277550\pi\) | ||||
0.643336 | + | 0.765584i | \(0.277550\pi\) | |||||||
\(788\) | 16399.1 | 0.741363 | ||||||||
\(789\) | 28179.2 | 1.27149 | ||||||||
\(790\) | 10607.7 | 0.477728 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −20923.1 | −0.938726 | ||||||||
\(793\) | −1391.87 | −0.0623290 | ||||||||
\(794\) | 2718.79 | 0.121519 | ||||||||
\(795\) | 18327.2 | 0.817610 | ||||||||
\(796\) | −17213.2 | −0.766466 | ||||||||
\(797\) | −5120.09 | −0.227557 | −0.113778 | − | 0.993506i | \(-0.536295\pi\) | ||||
−0.113778 | + | 0.993506i | \(0.536295\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −60970.9 | −2.69962 | ||||||||
\(800\) | 800.000 | 0.0353553 | ||||||||
\(801\) | 52034.3 | 2.29531 | ||||||||
\(802\) | 22284.6 | 0.981168 | ||||||||
\(803\) | −52419.7 | −2.30367 | ||||||||
\(804\) | 22480.2 | 0.986088 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 4725.67 | 0.206519 | ||||||||
\(807\) | −34768.5 | −1.51662 | ||||||||
\(808\) | −1905.99 | −0.0829859 | ||||||||
\(809\) | 26387.6 | 1.14677 | 0.573386 | − | 0.819285i | \(-0.305629\pi\) | ||||
0.573386 | + | 0.819285i | \(0.305629\pi\) | |||||||
\(810\) | −5972.97 | −0.259097 | ||||||||
\(811\) | 43383.4 | 1.87842 | 0.939210 | − | 0.343343i | \(-0.111559\pi\) | ||||
0.939210 | + | 0.343343i | \(0.111559\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 26446.8 | 1.14087 | ||||||||
\(814\) | −28293.0 | −1.21826 | ||||||||
\(815\) | −11337.6 | −0.487286 | ||||||||
\(816\) | 14378.2 | 0.616835 | ||||||||
\(817\) | 26346.8 | 1.12822 | ||||||||
\(818\) | 20755.9 | 0.887180 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −5003.15 | −0.213070 | ||||||||
\(821\) | 29558.8 | 1.25653 | 0.628263 | − | 0.778001i | \(-0.283766\pi\) | ||||
0.628263 | + | 0.778001i | \(0.283766\pi\) | |||||||
\(822\) | −13609.1 | −0.577461 | ||||||||
\(823\) | −29015.4 | −1.22894 | −0.614468 | − | 0.788942i | \(-0.710629\pi\) | ||||
−0.614468 | + | 0.788942i | \(0.710629\pi\) | |||||||
\(824\) | −7649.44 | −0.323399 | ||||||||
\(825\) | 11127.3 | 0.469578 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 425.416 | 0.0178878 | 0.00894388 | − | 0.999960i | \(-0.497153\pi\) | ||||
0.00894388 | + | 0.999960i | \(0.497153\pi\) | |||||||
\(828\) | 19306.9 | 0.810340 | ||||||||
\(829\) | 8113.77 | 0.339931 | 0.169965 | − | 0.985450i | \(-0.445634\pi\) | ||||
0.169965 | + | 0.985450i | \(0.445634\pi\) | |||||||
\(830\) | −2898.75 | −0.121225 | ||||||||
\(831\) | 38377.1 | 1.60203 | ||||||||
\(832\) | 1185.63 | 0.0494041 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 9817.71 | 0.407625 | ||||||||
\(835\) | −5399.22 | −0.223770 | ||||||||
\(836\) | 20228.6 | 0.836868 | ||||||||
\(837\) | −28788.4 | −1.18886 | ||||||||
\(838\) | 955.301 | 0.0393799 | ||||||||
\(839\) | −17633.8 | −0.725609 | −0.362804 | − | 0.931865i | \(-0.618181\pi\) | ||||
−0.362804 | + | 0.931865i | \(0.618181\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22954.6 | −0.941185 | ||||||||
\(842\) | 15755.4 | 0.644855 | ||||||||
\(843\) | −27756.7 | −1.13404 | ||||||||
\(844\) | 3248.85 | 0.132500 | ||||||||
\(845\) | 9269.04 | 0.377355 | ||||||||
\(846\) | 63262.9 | 2.57095 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 6584.17 | 0.266629 | ||||||||
\(849\) | 67795.0 | 2.74054 | ||||||||
\(850\) | −5044.38 | −0.203554 | ||||||||
\(851\) | 26107.5 | 1.05165 | ||||||||
\(852\) | 7651.53 | 0.307673 | ||||||||
\(853\) | −33769.2 | −1.35549 | −0.677746 | − | 0.735296i | \(-0.737043\pi\) | ||||
−0.677746 | + | 0.735296i | \(0.737043\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 26485.5 | 1.05940 | ||||||||
\(856\) | 12217.7 | 0.487841 | ||||||||
\(857\) | −19414.0 | −0.773827 | −0.386914 | − | 0.922116i | \(-0.626459\pi\) | ||||
−0.386914 | + | 0.922116i | \(0.626459\pi\) | |||||||
\(858\) | 16491.0 | 0.656169 | ||||||||
\(859\) | 22824.2 | 0.906580 | 0.453290 | − | 0.891363i | \(-0.350250\pi\) | ||||
0.453290 | + | 0.891363i | \(0.350250\pi\) | |||||||
\(860\) | 5206.59 | 0.206446 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 18850.2 | 0.744827 | ||||||||
\(863\) | 30871.7 | 1.21771 | 0.608856 | − | 0.793281i | \(-0.291629\pi\) | ||||
0.608856 | + | 0.793281i | \(0.291629\pi\) | |||||||
\(864\) | −7222.76 | −0.284402 | ||||||||
\(865\) | 12987.1 | 0.510491 | ||||||||
\(866\) | 4877.16 | 0.191377 | ||||||||
\(867\) | −46899.7 | −1.83714 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 53005.9 | 2.06916 | ||||||||
\(870\) | 3373.55 | 0.131465 | ||||||||
\(871\) | −11688.6 | −0.454710 | ||||||||
\(872\) | −81.8611 | −0.00317909 | ||||||||
\(873\) | 14756.3 | 0.572079 | ||||||||
\(874\) | −18666.1 | −0.722413 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −37376.4 | −1.44159 | ||||||||
\(877\) | −39162.1 | −1.50788 | −0.753939 | − | 0.656944i | \(-0.771849\pi\) | ||||
−0.753939 | + | 0.656944i | \(0.771849\pi\) | |||||||
\(878\) | −13571.0 | −0.521641 | ||||||||
\(879\) | −20947.6 | −0.803807 | ||||||||
\(880\) | 3997.54 | 0.153133 | ||||||||
\(881\) | −7446.38 | −0.284762 | −0.142381 | − | 0.989812i | \(-0.545476\pi\) | ||||
−0.142381 | + | 0.989812i | \(0.545476\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −43961.2 | −1.67544 | −0.837720 | − | 0.546100i | \(-0.816112\pi\) | ||||
−0.837720 | + | 0.546100i | \(0.816112\pi\) | |||||||
\(884\) | −7475.94 | −0.284438 | ||||||||
\(885\) | 16988.4 | 0.645264 | ||||||||
\(886\) | −14634.8 | −0.554928 | ||||||||
\(887\) | −19329.2 | −0.731692 | −0.365846 | − | 0.930675i | \(-0.619220\pi\) | ||||
−0.365846 | + | 0.930675i | \(0.619220\pi\) | |||||||
\(888\) | −20173.5 | −0.762364 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −9941.58 | −0.374430 | ||||||||
\(891\) | −29846.5 | −1.12222 | ||||||||
\(892\) | 5172.48 | 0.194156 | ||||||||
\(893\) | −61163.0 | −2.29198 | ||||||||
\(894\) | 45555.7 | 1.70426 | ||||||||
\(895\) | 10438.5 | 0.389854 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −15217.1 | −0.566427 | ||||||||
\(898\) | 10823.7 | 0.402217 | ||||||||
\(899\) | 4830.66 | 0.179212 | ||||||||
\(900\) | 5234.00 | 0.193852 | ||||||||
\(901\) | −41516.3 | −1.53508 | ||||||||
\(902\) | −25000.4 | −0.922861 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 10298.6 | 0.378902 | ||||||||
\(905\) | −9555.54 | −0.350980 | ||||||||
\(906\) | 13497.3 | 0.494943 | ||||||||
\(907\) | −27330.8 | −1.00056 | −0.500278 | − | 0.865865i | \(-0.666769\pi\) | ||||
−0.500278 | + | 0.865865i | \(0.666769\pi\) | |||||||
\(908\) | 20289.5 | 0.741555 | ||||||||
\(909\) | −12470.0 | −0.455009 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 35141.2 | 1.27803 | 0.639013 | − | 0.769196i | \(-0.279343\pi\) | ||||
0.639013 | + | 0.769196i | \(0.279343\pi\) | |||||||
\(912\) | 14423.5 | 0.523694 | ||||||||
\(913\) | −14484.8 | −0.525058 | ||||||||
\(914\) | −8148.71 | −0.294896 | ||||||||
\(915\) | −3346.17 | −0.120897 | ||||||||
\(916\) | −7780.74 | −0.280658 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 45542.9 | 1.63741 | ||||||||
\(919\) | 2857.06 | 0.102553 | 0.0512763 | − | 0.998685i | \(-0.483671\pi\) | ||||
0.0512763 | + | 0.998685i | \(0.483671\pi\) | |||||||
\(920\) | −3688.75 | −0.132190 | ||||||||
\(921\) | 20146.5 | 0.720792 | ||||||||
\(922\) | −4518.63 | −0.161403 | ||||||||
\(923\) | −3978.42 | −0.141876 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7077.59 | 0.251578 | ||||||||
\(926\) | 22307.6 | 0.791657 | ||||||||
\(927\) | −50046.4 | −1.77318 | ||||||||
\(928\) | 1211.97 | 0.0428716 | ||||||||
\(929\) | −10875.4 | −0.384081 | −0.192040 | − | 0.981387i | \(-0.561510\pi\) | ||||
−0.192040 | + | 0.981387i | \(0.561510\pi\) | |||||||
\(930\) | 11360.9 | 0.400578 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −2733.79 | −0.0960818 | ||||||||
\(933\) | 13149.1 | 0.461397 | ||||||||
\(934\) | −30609.0 | −1.07233 | ||||||||
\(935\) | −25206.4 | −0.881644 | ||||||||
\(936\) | 7756.96 | 0.270881 | ||||||||
\(937\) | 31754.7 | 1.10713 | 0.553566 | − | 0.832805i | \(-0.313267\pi\) | ||||
0.553566 | + | 0.832805i | \(0.313267\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −53694.5 | −1.86609 | ||||||||
\(940\) | −12086.9 | −0.419395 | ||||||||
\(941\) | 33296.9 | 1.15350 | 0.576752 | − | 0.816919i | \(-0.304320\pi\) | ||||
0.576752 | + | 0.816919i | \(0.304320\pi\) | |||||||
\(942\) | 17500.9 | 0.605317 | ||||||||
\(943\) | 23069.2 | 0.796645 | ||||||||
\(944\) | 6103.18 | 0.210425 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 26016.9 | 0.894169 | ||||||||
\(947\) | 57116.0 | 1.95990 | 0.979948 | − | 0.199254i | \(-0.0638518\pi\) | ||||
0.979948 | + | 0.199254i | \(0.0638518\pi\) | |||||||
\(948\) | 37794.4 | 1.29484 | ||||||||
\(949\) | 19433.9 | 0.664753 | ||||||||
\(950\) | −5060.27 | −0.172818 | ||||||||
\(951\) | −17514.7 | −0.597217 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −15228.5 | −0.517630 | −0.258815 | − | 0.965927i | \(-0.583332\pi\) | ||||
−0.258815 | + | 0.965927i | \(0.583332\pi\) | |||||||
\(954\) | 43076.9 | 1.46192 | ||||||||
\(955\) | −2294.95 | −0.0777621 | ||||||||
\(956\) | 18317.8 | 0.619708 | ||||||||
\(957\) | 16857.4 | 0.569406 | ||||||||
\(958\) | 4904.33 | 0.165398 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 2850.34 | 0.0958273 | ||||||||
\(961\) | −13523.2 | −0.453934 | ||||||||
\(962\) | 10489.2 | 0.351545 | ||||||||
\(963\) | 79934.2 | 2.67481 | ||||||||
\(964\) | 20272.3 | 0.677309 | ||||||||
\(965\) | −8731.62 | −0.291275 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −52050.8 | −1.73096 | −0.865481 | − | 0.500942i | \(-0.832987\pi\) | ||||
−0.865481 | + | 0.500942i | \(0.832987\pi\) | |||||||
\(968\) | 9327.39 | 0.309704 | ||||||||
\(969\) | −90946.9 | −3.01510 | ||||||||
\(970\) | −2819.31 | −0.0933223 | ||||||||
\(971\) | 32256.3 | 1.06607 | 0.533034 | − | 0.846094i | \(-0.321052\pi\) | ||||
0.533034 | + | 0.846094i | \(0.321052\pi\) | |||||||
\(972\) | 3095.59 | 0.102151 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 28497.1 | 0.937480 | ||||||||
\(975\) | −4125.29 | −0.135502 | ||||||||
\(976\) | −1202.13 | −0.0394255 | ||||||||
\(977\) | 47733.6 | 1.56308 | 0.781542 | − | 0.623853i | \(-0.214434\pi\) | ||||
0.781542 | + | 0.623853i | \(0.214434\pi\) | |||||||
\(978\) | −40394.9 | −1.32074 | ||||||||
\(979\) | −49677.3 | −1.62175 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −535.576 | −0.0174308 | ||||||||
\(982\) | 21528.2 | 0.699586 | ||||||||
\(983\) | 14046.2 | 0.455753 | 0.227877 | − | 0.973690i | \(-0.426822\pi\) | ||||
0.227877 | + | 0.973690i | \(0.426822\pi\) | |||||||
\(984\) | −17825.8 | −0.577507 | ||||||||
\(985\) | −20498.9 | −0.663095 | ||||||||
\(986\) | −7642.04 | −0.246828 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7499.49 | −0.241489 | ||||||||
\(989\) | −24007.3 | −0.771877 | ||||||||
\(990\) | 26153.9 | 0.839622 | ||||||||
\(991\) | 50650.8 | 1.62359 | 0.811793 | − | 0.583945i | \(-0.198492\pi\) | ||||
0.811793 | + | 0.583945i | \(0.198492\pi\) | |||||||
\(992\) | 4081.46 | 0.130631 | ||||||||
\(993\) | −69062.1 | −2.20707 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 21516.5 | 0.685548 | ||||||||
\(996\) | −10328.0 | −0.328570 | ||||||||
\(997\) | −25849.6 | −0.821128 | −0.410564 | − | 0.911832i | \(-0.634668\pi\) | ||||
−0.410564 | + | 0.911832i | \(0.634668\pi\) | |||||||
\(998\) | −14589.6 | −0.462753 | ||||||||
\(999\) | −63899.7 | −2.02372 |
(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 | 490.4.a.v.1.1 | 3 | ||
5.4 | even | 2 | 2450.4.a.ce.1.3 | 3 | |||
7.2 | even | 3 | 490.4.e.y.361.3 | 6 | |||
7.3 | odd | 6 | 70.4.e.e.51.1 | yes | 6 | ||
7.4 | even | 3 | 490.4.e.y.471.3 | 6 | |||
7.5 | odd | 6 | 70.4.e.e.11.1 | ✓ | 6 | ||
7.6 | odd | 2 | 490.4.a.w.1.3 | 3 | |||
21.5 | even | 6 | 630.4.k.r.361.1 | 6 | |||
21.17 | even | 6 | 630.4.k.r.541.1 | 6 | |||
28.3 | even | 6 | 560.4.q.m.401.3 | 6 | |||
28.19 | even | 6 | 560.4.q.m.81.3 | 6 | |||
35.3 | even | 12 | 350.4.j.i.149.6 | 12 | |||
35.12 | even | 12 | 350.4.j.i.249.6 | 12 | |||
35.17 | even | 12 | 350.4.j.i.149.1 | 12 | |||
35.19 | odd | 6 | 350.4.e.k.151.3 | 6 | |||
35.24 | odd | 6 | 350.4.e.k.51.3 | 6 | |||
35.33 | even | 12 | 350.4.j.i.249.1 | 12 | |||
35.34 | odd | 2 | 2450.4.a.cb.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
70.4.e.e.11.1 | ✓ | 6 | 7.5 | odd | 6 | ||
70.4.e.e.51.1 | yes | 6 | 7.3 | odd | 6 | ||
350.4.e.k.51.3 | 6 | 35.24 | odd | 6 | |||
350.4.e.k.151.3 | 6 | 35.19 | odd | 6 | |||
350.4.j.i.149.1 | 12 | 35.17 | even | 12 | |||
350.4.j.i.149.6 | 12 | 35.3 | even | 12 | |||
350.4.j.i.249.1 | 12 | 35.33 | even | 12 | |||
350.4.j.i.249.6 | 12 | 35.12 | even | 12 | |||
490.4.a.v.1.1 | 3 | 1.1 | even | 1 | trivial | ||
490.4.a.w.1.3 | 3 | 7.6 | odd | 2 | |||
490.4.e.y.361.3 | 6 | 7.2 | even | 3 | |||
490.4.e.y.471.3 | 6 | 7.4 | even | 3 | |||
560.4.q.m.81.3 | 6 | 28.19 | even | 6 | |||
560.4.q.m.401.3 | 6 | 28.3 | even | 6 | |||
630.4.k.r.361.1 | 6 | 21.5 | even | 6 | |||
630.4.k.r.541.1 | 6 | 21.17 | even | 6 | |||
2450.4.a.cb.1.1 | 3 | 35.34 | odd | 2 | |||
2450.4.a.ce.1.3 | 3 | 5.4 | even | 2 |