Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1849,4,Mod(1,1849)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1849, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1849.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1849 = 43^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1849.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: | \(109.094531601\) |
Analytic rank: | \(1\) |
Dimension: | \(60\) |
Twist minimal: | no (minimal twist has level 43) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 1849.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.24990 | −1.85612 | −0.928060 | − | 0.372432i | \(-0.878524\pi\) | ||||
−0.928060 | + | 0.372432i | \(0.878524\pi\) | |||||||
\(3\) | −9.69865 | −1.86651 | −0.933253 | − | 0.359220i | \(-0.883043\pi\) | ||||
−0.933253 | + | 0.359220i | \(0.883043\pi\) | |||||||
\(4\) | 19.5614 | 2.44518 | ||||||||
\(5\) | −5.59920 | −0.500807 | −0.250404 | − | 0.968142i | \(-0.580563\pi\) | ||||
−0.250404 | + | 0.968142i | \(0.580563\pi\) | |||||||
\(6\) | 50.9169 | 3.46446 | ||||||||
\(7\) | 0.820208 | 0.0442870 | 0.0221435 | − | 0.999755i | \(-0.492951\pi\) | ||||
0.0221435 | + | 0.999755i | \(0.492951\pi\) | |||||||
\(8\) | −60.6963 | −2.68242 | ||||||||
\(9\) | 67.0638 | 2.48384 | ||||||||
\(10\) | 29.3952 | 0.929558 | ||||||||
\(11\) | −48.4653 | −1.32844 | −0.664220 | − | 0.747537i | \(-0.731236\pi\) | ||||
−0.664220 | + | 0.747537i | \(0.731236\pi\) | |||||||
\(12\) | −189.719 | −4.56394 | ||||||||
\(13\) | 4.57016 | 0.0975025 | 0.0487513 | − | 0.998811i | \(-0.484476\pi\) | ||||
0.0487513 | + | 0.998811i | \(0.484476\pi\) | |||||||
\(14\) | −4.30601 | −0.0822020 | ||||||||
\(15\) | 54.3046 | 0.934760 | ||||||||
\(16\) | 162.158 | 2.53372 | ||||||||
\(17\) | 108.420 | 1.54680 | 0.773400 | − | 0.633918i | \(-0.218554\pi\) | ||||
0.773400 | + | 0.633918i | \(0.218554\pi\) | |||||||
\(18\) | −352.078 | −4.61031 | ||||||||
\(19\) | 24.1770 | 0.291925 | 0.145962 | − | 0.989290i | \(-0.453372\pi\) | ||||
0.145962 | + | 0.989290i | \(0.453372\pi\) | |||||||
\(20\) | −109.528 | −1.22456 | ||||||||
\(21\) | −7.95490 | −0.0826620 | ||||||||
\(22\) | 254.438 | 2.46574 | ||||||||
\(23\) | −1.18989 | −0.0107873 | −0.00539366 | − | 0.999985i | \(-0.501717\pi\) | ||||
−0.00539366 | + | 0.999985i | \(0.501717\pi\) | |||||||
\(24\) | 588.672 | 5.00676 | ||||||||
\(25\) | −93.6490 | −0.749192 | ||||||||
\(26\) | −23.9928 | −0.180976 | ||||||||
\(27\) | −388.564 | −2.76960 | ||||||||
\(28\) | 16.0444 | 0.108290 | ||||||||
\(29\) | 32.2620 | 0.206583 | 0.103291 | − | 0.994651i | \(-0.467063\pi\) | ||||
0.103291 | + | 0.994651i | \(0.467063\pi\) | |||||||
\(30\) | −285.094 | −1.73503 | ||||||||
\(31\) | −59.1739 | −0.342837 | −0.171419 | − | 0.985198i | \(-0.554835\pi\) | ||||
−0.171419 | + | 0.985198i | \(0.554835\pi\) | |||||||
\(32\) | −365.742 | −2.02046 | ||||||||
\(33\) | 470.048 | 2.47954 | ||||||||
\(34\) | −569.192 | −2.87105 | ||||||||
\(35\) | −4.59250 | −0.0221793 | ||||||||
\(36\) | 1311.86 | 6.07344 | ||||||||
\(37\) | 353.501 | 1.57068 | 0.785340 | − | 0.619065i | \(-0.212488\pi\) | ||||
0.785340 | + | 0.619065i | \(0.212488\pi\) | |||||||
\(38\) | −126.927 | −0.541847 | ||||||||
\(39\) | −44.3243 | −0.181989 | ||||||||
\(40\) | 339.850 | 1.34338 | ||||||||
\(41\) | −62.8277 | −0.239318 | −0.119659 | − | 0.992815i | \(-0.538180\pi\) | ||||
−0.119659 | + | 0.992815i | \(0.538180\pi\) | |||||||
\(42\) | 41.7624 | 0.153431 | ||||||||
\(43\) | 0 | 0 | ||||||||
\(44\) | −948.050 | −3.24827 | ||||||||
\(45\) | −375.503 | −1.24393 | ||||||||
\(46\) | 6.24678 | 0.0200226 | ||||||||
\(47\) | −213.247 | −0.661816 | −0.330908 | − | 0.943663i | \(-0.607355\pi\) | ||||
−0.330908 | + | 0.943663i | \(0.607355\pi\) | |||||||
\(48\) | −1572.71 | −4.72920 | ||||||||
\(49\) | −342.327 | −0.998039 | ||||||||
\(50\) | 491.648 | 1.39059 | ||||||||
\(51\) | −1051.52 | −2.88711 | ||||||||
\(52\) | 89.3987 | 0.238411 | ||||||||
\(53\) | −119.382 | −0.309402 | −0.154701 | − | 0.987961i | \(-0.549441\pi\) | ||||
−0.154701 | + | 0.987961i | \(0.549441\pi\) | |||||||
\(54\) | 2039.92 | 5.14071 | ||||||||
\(55\) | 271.367 | 0.665292 | ||||||||
\(56\) | −49.7835 | −0.118797 | ||||||||
\(57\) | −234.484 | −0.544880 | ||||||||
\(58\) | −169.372 | −0.383442 | ||||||||
\(59\) | −367.191 | −0.810240 | −0.405120 | − | 0.914264i | \(-0.632770\pi\) | ||||
−0.405120 | + | 0.914264i | \(0.632770\pi\) | |||||||
\(60\) | 1062.28 | 2.28565 | ||||||||
\(61\) | −36.8200 | −0.0772839 | −0.0386419 | − | 0.999253i | \(-0.512303\pi\) | ||||
−0.0386419 | + | 0.999253i | \(0.512303\pi\) | |||||||
\(62\) | 310.657 | 0.636347 | ||||||||
\(63\) | 55.0062 | 0.110002 | ||||||||
\(64\) | 622.845 | 1.21649 | ||||||||
\(65\) | −25.5892 | −0.0488300 | ||||||||
\(66\) | −2467.70 | −4.60232 | ||||||||
\(67\) | 173.580 | 0.316510 | 0.158255 | − | 0.987398i | \(-0.449413\pi\) | ||||
0.158255 | + | 0.987398i | \(0.449413\pi\) | |||||||
\(68\) | 2120.84 | 3.78220 | ||||||||
\(69\) | 11.5403 | 0.0201346 | ||||||||
\(70\) | 24.1102 | 0.0411674 | ||||||||
\(71\) | −918.269 | −1.53491 | −0.767454 | − | 0.641104i | \(-0.778477\pi\) | ||||
−0.767454 | + | 0.641104i | \(0.778477\pi\) | |||||||
\(72\) | −4070.52 | −6.66272 | ||||||||
\(73\) | −33.8560 | −0.0542814 | −0.0271407 | − | 0.999632i | \(-0.508640\pi\) | ||||
−0.0271407 | + | 0.999632i | \(0.508640\pi\) | |||||||
\(74\) | −1855.84 | −2.91537 | ||||||||
\(75\) | 908.269 | 1.39837 | ||||||||
\(76\) | 472.936 | 0.713808 | ||||||||
\(77\) | −39.7516 | −0.0588327 | ||||||||
\(78\) | 232.698 | 0.337793 | ||||||||
\(79\) | −612.712 | −0.872601 | −0.436301 | − | 0.899801i | \(-0.643712\pi\) | ||||
−0.436301 | + | 0.899801i | \(0.643712\pi\) | |||||||
\(80\) | −907.954 | −1.26890 | ||||||||
\(81\) | 1957.83 | 2.68564 | ||||||||
\(82\) | 329.839 | 0.444202 | ||||||||
\(83\) | −416.023 | −0.550174 | −0.275087 | − | 0.961419i | \(-0.588707\pi\) | ||||
−0.275087 | + | 0.961419i | \(0.588707\pi\) | |||||||
\(84\) | −155.609 | −0.202123 | ||||||||
\(85\) | −607.063 | −0.774649 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −312.898 | −0.385588 | ||||||||
\(88\) | 2941.66 | 3.56344 | ||||||||
\(89\) | −921.950 | −1.09805 | −0.549025 | − | 0.835806i | \(-0.685001\pi\) | ||||
−0.549025 | + | 0.835806i | \(0.685001\pi\) | |||||||
\(90\) | 1971.35 | 2.30888 | ||||||||
\(91\) | 3.74848 | 0.00431810 | ||||||||
\(92\) | −23.2759 | −0.0263769 | ||||||||
\(93\) | 573.907 | 0.639908 | ||||||||
\(94\) | 1119.53 | 1.22841 | ||||||||
\(95\) | −135.372 | −0.146198 | ||||||||
\(96\) | 3547.20 | 3.77120 | ||||||||
\(97\) | 431.946 | 0.452139 | 0.226070 | − | 0.974111i | \(-0.427412\pi\) | ||||
0.226070 | + | 0.974111i | \(0.427412\pi\) | |||||||
\(98\) | 1797.18 | 1.85248 | ||||||||
\(99\) | −3250.27 | −3.29964 | ||||||||
\(100\) | −1831.91 | −1.83191 | ||||||||
\(101\) | 793.557 | 0.781801 | 0.390900 | − | 0.920433i | \(-0.372164\pi\) | ||||
0.390900 | + | 0.920433i | \(0.372164\pi\) | |||||||
\(102\) | 5520.39 | 5.35882 | ||||||||
\(103\) | 1475.90 | 1.41189 | 0.705945 | − | 0.708266i | \(-0.250522\pi\) | ||||
0.705945 | + | 0.708266i | \(0.250522\pi\) | |||||||
\(104\) | −277.391 | −0.261543 | ||||||||
\(105\) | 44.5411 | 0.0413978 | ||||||||
\(106\) | 626.741 | 0.574288 | ||||||||
\(107\) | 524.938 | 0.474277 | 0.237139 | − | 0.971476i | \(-0.423790\pi\) | ||||
0.237139 | + | 0.971476i | \(0.423790\pi\) | |||||||
\(108\) | −7600.87 | −6.77217 | ||||||||
\(109\) | 1931.34 | 1.69714 | 0.848572 | − | 0.529081i | \(-0.177463\pi\) | ||||
0.848572 | + | 0.529081i | \(0.177463\pi\) | |||||||
\(110\) | −1424.65 | −1.23486 | ||||||||
\(111\) | −3428.48 | −2.93168 | ||||||||
\(112\) | 133.003 | 0.112211 | ||||||||
\(113\) | −1163.28 | −0.968424 | −0.484212 | − | 0.874951i | \(-0.660894\pi\) | ||||
−0.484212 | + | 0.874951i | \(0.660894\pi\) | |||||||
\(114\) | 1231.02 | 1.01136 | ||||||||
\(115\) | 6.66241 | 0.00540237 | ||||||||
\(116\) | 631.091 | 0.505132 | ||||||||
\(117\) | 306.492 | 0.242181 | ||||||||
\(118\) | 1927.71 | 1.50390 | ||||||||
\(119\) | 88.9266 | 0.0685032 | ||||||||
\(120\) | −3296.09 | −2.50742 | ||||||||
\(121\) | 1017.88 | 0.764752 | ||||||||
\(122\) | 193.301 | 0.143448 | ||||||||
\(123\) | 609.343 | 0.446688 | ||||||||
\(124\) | −1157.53 | −0.838298 | ||||||||
\(125\) | 1224.26 | 0.876008 | ||||||||
\(126\) | −288.777 | −0.204177 | ||||||||
\(127\) | 1801.72 | 1.25887 | 0.629437 | − | 0.777051i | \(-0.283285\pi\) | ||||
0.629437 | + | 0.777051i | \(0.283285\pi\) | |||||||
\(128\) | −343.935 | −0.237499 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 134.341 | 0.0906343 | ||||||||
\(131\) | 670.848 | 0.447422 | 0.223711 | − | 0.974656i | \(-0.428183\pi\) | ||||
0.223711 | + | 0.974656i | \(0.428183\pi\) | |||||||
\(132\) | 9194.80 | 6.06292 | ||||||||
\(133\) | 19.8301 | 0.0129285 | ||||||||
\(134\) | −911.277 | −0.587480 | ||||||||
\(135\) | 2175.65 | 1.38704 | ||||||||
\(136\) | −6580.67 | −4.14917 | ||||||||
\(137\) | 1536.94 | 0.958462 | 0.479231 | − | 0.877689i | \(-0.340916\pi\) | ||||
0.479231 | + | 0.877689i | \(0.340916\pi\) | |||||||
\(138\) | −60.5853 | −0.0373722 | ||||||||
\(139\) | 1697.23 | 1.03566 | 0.517831 | − | 0.855483i | \(-0.326739\pi\) | ||||
0.517831 | + | 0.855483i | \(0.326739\pi\) | |||||||
\(140\) | −89.8359 | −0.0542323 | ||||||||
\(141\) | 2068.21 | 1.23528 | ||||||||
\(142\) | 4820.82 | 2.84897 | ||||||||
\(143\) | −221.494 | −0.129526 | ||||||||
\(144\) | 10874.9 | 6.29336 | ||||||||
\(145\) | −180.641 | −0.103458 | ||||||||
\(146\) | 177.740 | 0.100753 | ||||||||
\(147\) | 3320.11 | 1.86284 | ||||||||
\(148\) | 6914.98 | 3.84059 | ||||||||
\(149\) | 2923.14 | 1.60720 | 0.803600 | − | 0.595170i | \(-0.202915\pi\) | ||||
0.803600 | + | 0.595170i | \(0.202915\pi\) | |||||||
\(150\) | −4768.32 | −2.59554 | ||||||||
\(151\) | 1455.71 | 0.784529 | 0.392265 | − | 0.919852i | \(-0.371692\pi\) | ||||
0.392265 | + | 0.919852i | \(0.371692\pi\) | |||||||
\(152\) | −1467.45 | −0.783066 | ||||||||
\(153\) | 7271.03 | 3.84201 | ||||||||
\(154\) | 208.692 | 0.109200 | ||||||||
\(155\) | 331.327 | 0.171695 | ||||||||
\(156\) | −867.047 | −0.444996 | ||||||||
\(157\) | −1258.86 | −0.639921 | −0.319961 | − | 0.947431i | \(-0.603670\pi\) | ||||
−0.319961 | + | 0.947431i | \(0.603670\pi\) | |||||||
\(158\) | 3216.68 | 1.61965 | ||||||||
\(159\) | 1157.84 | 0.577501 | ||||||||
\(160\) | 2047.86 | 1.01186 | ||||||||
\(161\) | −0.975954 | −0.000477739 0 | ||||||||
\(162\) | −10278.4 | −4.98486 | ||||||||
\(163\) | 2717.96 | 1.30606 | 0.653029 | − | 0.757333i | \(-0.273498\pi\) | ||||
0.653029 | + | 0.757333i | \(0.273498\pi\) | |||||||
\(164\) | −1229.00 | −0.585175 | ||||||||
\(165\) | −2631.89 | −1.24177 | ||||||||
\(166\) | 2184.08 | 1.02119 | ||||||||
\(167\) | −3875.29 | −1.79568 | −0.897841 | − | 0.440319i | \(-0.854865\pi\) | ||||
−0.897841 | + | 0.440319i | \(0.854865\pi\) | |||||||
\(168\) | 482.833 | 0.221734 | ||||||||
\(169\) | −2176.11 | −0.990493 | ||||||||
\(170\) | 3187.02 | 1.43784 | ||||||||
\(171\) | 1621.40 | 0.725096 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3701.24 | −1.62659 | −0.813296 | − | 0.581851i | \(-0.802329\pi\) | ||||
−0.813296 | + | 0.581851i | \(0.802329\pi\) | |||||||
\(174\) | 1642.68 | 0.715697 | ||||||||
\(175\) | −76.8116 | −0.0331795 | ||||||||
\(176\) | −7859.03 | −3.36589 | ||||||||
\(177\) | 3561.25 | 1.51232 | ||||||||
\(178\) | 4840.14 | 2.03811 | ||||||||
\(179\) | −1787.48 | −0.746382 | −0.373191 | − | 0.927755i | \(-0.621736\pi\) | ||||
−0.373191 | + | 0.927755i | \(0.621736\pi\) | |||||||
\(180\) | −7345.38 | −3.04162 | ||||||||
\(181\) | 3722.70 | 1.52876 | 0.764381 | − | 0.644765i | \(-0.223045\pi\) | ||||
0.764381 | + | 0.644765i | \(0.223045\pi\) | |||||||
\(182\) | −19.6791 | −0.00801491 | ||||||||
\(183\) | 357.104 | 0.144251 | ||||||||
\(184\) | 72.2217 | 0.0289362 | ||||||||
\(185\) | −1979.32 | −0.786608 | ||||||||
\(186\) | −3012.95 | −1.18774 | ||||||||
\(187\) | −5254.59 | −2.05483 | ||||||||
\(188\) | −4171.42 | −1.61826 | ||||||||
\(189\) | −318.704 | −0.122658 | ||||||||
\(190\) | 710.687 | 0.271361 | ||||||||
\(191\) | −4238.79 | −1.60580 | −0.802900 | − | 0.596114i | \(-0.796711\pi\) | ||||
−0.802900 | + | 0.596114i | \(0.796711\pi\) | |||||||
\(192\) | −6040.75 | −2.27059 | ||||||||
\(193\) | 2087.86 | 0.778691 | 0.389345 | − | 0.921092i | \(-0.372701\pi\) | ||||
0.389345 | + | 0.921092i | \(0.372701\pi\) | |||||||
\(194\) | −2267.67 | −0.839224 | ||||||||
\(195\) | 248.181 | 0.0911414 | ||||||||
\(196\) | −6696.41 | −2.44038 | ||||||||
\(197\) | 2825.59 | 1.02190 | 0.510952 | − | 0.859609i | \(-0.329293\pi\) | ||||
0.510952 | + | 0.859609i | \(0.329293\pi\) | |||||||
\(198\) | 17063.6 | 6.12452 | ||||||||
\(199\) | −44.6321 | −0.0158989 | −0.00794945 | − | 0.999968i | \(-0.502530\pi\) | ||||
−0.00794945 | + | 0.999968i | \(0.502530\pi\) | |||||||
\(200\) | 5684.15 | 2.00965 | ||||||||
\(201\) | −1683.49 | −0.590768 | ||||||||
\(202\) | −4166.09 | −1.45112 | ||||||||
\(203\) | 26.4615 | 0.00914894 | ||||||||
\(204\) | −20569.3 | −7.05950 | ||||||||
\(205\) | 351.784 | 0.119852 | ||||||||
\(206\) | −7748.32 | −2.62064 | ||||||||
\(207\) | −79.7983 | −0.0267940 | ||||||||
\(208\) | 741.087 | 0.247044 | ||||||||
\(209\) | −1171.74 | −0.387805 | ||||||||
\(210\) | −233.836 | −0.0768392 | ||||||||
\(211\) | −4090.17 | −1.33450 | −0.667249 | − | 0.744835i | \(-0.732528\pi\) | ||||
−0.667249 | + | 0.744835i | \(0.732528\pi\) | |||||||
\(212\) | −2335.27 | −0.756544 | ||||||||
\(213\) | 8905.97 | 2.86492 | ||||||||
\(214\) | −2755.87 | −0.880315 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 23584.4 | 7.42924 | ||||||||
\(217\) | −48.5349 | −0.0151832 | ||||||||
\(218\) | −10139.3 | −3.15010 | ||||||||
\(219\) | 328.357 | 0.101317 | ||||||||
\(220\) | 5308.32 | 1.62676 | ||||||||
\(221\) | 495.494 | 0.150817 | ||||||||
\(222\) | 17999.2 | 5.44155 | ||||||||
\(223\) | 1439.56 | 0.432288 | 0.216144 | − | 0.976362i | \(-0.430652\pi\) | ||||
0.216144 | + | 0.976362i | \(0.430652\pi\) | |||||||
\(224\) | −299.984 | −0.0894801 | ||||||||
\(225\) | −6280.46 | −1.86088 | ||||||||
\(226\) | 6107.08 | 1.79751 | ||||||||
\(227\) | 3376.13 | 0.987143 | 0.493571 | − | 0.869705i | \(-0.335691\pi\) | ||||
0.493571 | + | 0.869705i | \(0.335691\pi\) | |||||||
\(228\) | −4586.84 | −1.33233 | ||||||||
\(229\) | 3863.41 | 1.11485 | 0.557427 | − | 0.830226i | \(-0.311789\pi\) | ||||
0.557427 | + | 0.830226i | \(0.311789\pi\) | |||||||
\(230\) | −34.9770 | −0.0100274 | ||||||||
\(231\) | 385.537 | 0.109812 | ||||||||
\(232\) | −1958.18 | −0.554142 | ||||||||
\(233\) | −1421.57 | −0.399701 | −0.199850 | − | 0.979826i | \(-0.564046\pi\) | ||||
−0.199850 | + | 0.979826i | \(0.564046\pi\) | |||||||
\(234\) | −1609.05 | −0.449517 | ||||||||
\(235\) | 1194.01 | 0.331442 | ||||||||
\(236\) | −7182.77 | −1.98118 | ||||||||
\(237\) | 5942.48 | 1.62872 | ||||||||
\(238\) | −466.855 | −0.127150 | ||||||||
\(239\) | 4388.76 | 1.18780 | 0.593902 | − | 0.804537i | \(-0.297587\pi\) | ||||
0.593902 | + | 0.804537i | \(0.297587\pi\) | |||||||
\(240\) | 8805.92 | 2.36842 | ||||||||
\(241\) | 2027.92 | 0.542031 | 0.271016 | − | 0.962575i | \(-0.412641\pi\) | ||||
0.271016 | + | 0.962575i | \(0.412641\pi\) | |||||||
\(242\) | −5343.79 | −1.41947 | ||||||||
\(243\) | −8497.05 | −2.24315 | ||||||||
\(244\) | −720.251 | −0.188973 | ||||||||
\(245\) | 1916.76 | 0.499825 | ||||||||
\(246\) | −3198.99 | −0.829106 | ||||||||
\(247\) | 110.492 | 0.0284634 | ||||||||
\(248\) | 3591.64 | 0.919634 | ||||||||
\(249\) | 4034.86 | 1.02690 | ||||||||
\(250\) | −6427.23 | −1.62598 | ||||||||
\(251\) | −2680.07 | −0.673962 | −0.336981 | − | 0.941511i | \(-0.609406\pi\) | ||||
−0.336981 | + | 0.941511i | \(0.609406\pi\) | |||||||
\(252\) | 1076.00 | 0.268975 | ||||||||
\(253\) | 57.6682 | 0.0143303 | ||||||||
\(254\) | −9458.86 | −2.33662 | ||||||||
\(255\) | 5887.69 | 1.44589 | ||||||||
\(256\) | −3177.13 | −0.775668 | ||||||||
\(257\) | 5500.90 | 1.33516 | 0.667581 | − | 0.744537i | \(-0.267330\pi\) | ||||
0.667581 | + | 0.744537i | \(0.267330\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 289.944 | 0.0695608 | ||||||||
\(260\) | −500.561 | −0.119398 | ||||||||
\(261\) | 2163.61 | 0.513119 | ||||||||
\(262\) | −3521.88 | −0.830468 | ||||||||
\(263\) | 842.845 | 0.197612 | 0.0988062 | − | 0.995107i | \(-0.468498\pi\) | ||||
0.0988062 | + | 0.995107i | \(0.468498\pi\) | |||||||
\(264\) | −28530.2 | −6.65117 | ||||||||
\(265\) | 668.441 | 0.154951 | ||||||||
\(266\) | −104.106 | −0.0239968 | ||||||||
\(267\) | 8941.67 | 2.04952 | ||||||||
\(268\) | 3395.47 | 0.773923 | ||||||||
\(269\) | −2415.99 | −0.547605 | −0.273802 | − | 0.961786i | \(-0.588281\pi\) | ||||
−0.273802 | + | 0.961786i | \(0.588281\pi\) | |||||||
\(270\) | −11421.9 | −2.57451 | ||||||||
\(271\) | −4315.30 | −0.967290 | −0.483645 | − | 0.875264i | \(-0.660687\pi\) | ||||
−0.483645 | + | 0.875264i | \(0.660687\pi\) | |||||||
\(272\) | 17581.1 | 3.91916 | ||||||||
\(273\) | −36.3551 | −0.00805976 | ||||||||
\(274\) | −8068.76 | −1.77902 | ||||||||
\(275\) | 4538.73 | 0.995256 | ||||||||
\(276\) | 225.745 | 0.0492327 | ||||||||
\(277\) | 6373.76 | 1.38253 | 0.691267 | − | 0.722599i | \(-0.257053\pi\) | ||||
0.691267 | + | 0.722599i | \(0.257053\pi\) | |||||||
\(278\) | −8910.28 | −1.92231 | ||||||||
\(279\) | −3968.43 | −0.851554 | ||||||||
\(280\) | 278.748 | 0.0594942 | ||||||||
\(281\) | −6639.69 | −1.40958 | −0.704788 | − | 0.709418i | \(-0.748958\pi\) | ||||
−0.704788 | + | 0.709418i | \(0.748958\pi\) | |||||||
\(282\) | −10857.9 | −2.29283 | ||||||||
\(283\) | −2035.59 | −0.427573 | −0.213787 | − | 0.976880i | \(-0.568580\pi\) | ||||
−0.213787 | + | 0.976880i | \(0.568580\pi\) | |||||||
\(284\) | −17962.7 | −3.75312 | ||||||||
\(285\) | 1312.92 | 0.272880 | ||||||||
\(286\) | 1162.82 | 0.240416 | ||||||||
\(287\) | −51.5317 | −0.0105987 | ||||||||
\(288\) | −24528.0 | −5.01850 | ||||||||
\(289\) | 6841.81 | 1.39259 | ||||||||
\(290\) | 948.348 | 0.192031 | ||||||||
\(291\) | −4189.29 | −0.843920 | ||||||||
\(292\) | −662.271 | −0.132728 | ||||||||
\(293\) | −3279.18 | −0.653829 | −0.326915 | − | 0.945054i | \(-0.606009\pi\) | ||||
−0.326915 | + | 0.945054i | \(0.606009\pi\) | |||||||
\(294\) | −17430.2 | −3.45766 | ||||||||
\(295\) | 2055.97 | 0.405774 | ||||||||
\(296\) | −21456.2 | −4.21323 | ||||||||
\(297\) | 18831.9 | 3.67925 | ||||||||
\(298\) | −15346.2 | −2.98315 | ||||||||
\(299\) | −5.43797 | −0.00105179 | ||||||||
\(300\) | 17767.0 | 3.41927 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −7642.33 | −1.45618 | ||||||||
\(303\) | −7696.43 | −1.45924 | ||||||||
\(304\) | 3920.48 | 0.739655 | ||||||||
\(305\) | 206.162 | 0.0387043 | ||||||||
\(306\) | −38172.1 | −7.13123 | ||||||||
\(307\) | 5716.06 | 1.06265 | 0.531324 | − | 0.847169i | \(-0.321695\pi\) | ||||
0.531324 | + | 0.847169i | \(0.321695\pi\) | |||||||
\(308\) | −777.598 | −0.143856 | ||||||||
\(309\) | −14314.2 | −2.63530 | ||||||||
\(310\) | −1739.43 | −0.318687 | ||||||||
\(311\) | 5282.52 | 0.963165 | 0.481583 | − | 0.876401i | \(-0.340062\pi\) | ||||
0.481583 | + | 0.876401i | \(0.340062\pi\) | |||||||
\(312\) | 2690.32 | 0.488171 | ||||||||
\(313\) | 1343.26 | 0.242575 | 0.121287 | − | 0.992617i | \(-0.461298\pi\) | ||||
0.121287 | + | 0.992617i | \(0.461298\pi\) | |||||||
\(314\) | 6608.86 | 1.18777 | ||||||||
\(315\) | −307.991 | −0.0550899 | ||||||||
\(316\) | −11985.5 | −2.13367 | ||||||||
\(317\) | 1907.98 | 0.338054 | 0.169027 | − | 0.985611i | \(-0.445937\pi\) | ||||
0.169027 | + | 0.985611i | \(0.445937\pi\) | |||||||
\(318\) | −6078.54 | −1.07191 | ||||||||
\(319\) | −1563.59 | −0.274433 | ||||||||
\(320\) | −3487.43 | −0.609229 | ||||||||
\(321\) | −5091.19 | −0.885242 | ||||||||
\(322\) | 5.12366 | 0.000886740 0 | ||||||||
\(323\) | 2621.26 | 0.451550 | ||||||||
\(324\) | 38297.9 | 6.56686 | ||||||||
\(325\) | −427.990 | −0.0730481 | ||||||||
\(326\) | −14269.0 | −2.42420 | ||||||||
\(327\) | −18731.4 | −3.16773 | ||||||||
\(328\) | 3813.41 | 0.641952 | ||||||||
\(329\) | −174.907 | −0.0293099 | ||||||||
\(330\) | 13817.2 | 2.30488 | ||||||||
\(331\) | −9225.01 | −1.53188 | −0.765940 | − | 0.642912i | \(-0.777726\pi\) | ||||
−0.765940 | + | 0.642912i | \(0.777726\pi\) | |||||||
\(332\) | −8138.00 | −1.34527 | ||||||||
\(333\) | 23707.1 | 3.90132 | ||||||||
\(334\) | 20344.9 | 3.33300 | ||||||||
\(335\) | −971.908 | −0.158511 | ||||||||
\(336\) | −1289.95 | −0.209442 | ||||||||
\(337\) | 2193.66 | 0.354589 | 0.177295 | − | 0.984158i | \(-0.443265\pi\) | ||||
0.177295 | + | 0.984158i | \(0.443265\pi\) | |||||||
\(338\) | 11424.4 | 1.83847 | ||||||||
\(339\) | 11282.2 | 1.80757 | ||||||||
\(340\) | −11875.0 | −1.89416 | ||||||||
\(341\) | 2867.88 | 0.455439 | ||||||||
\(342\) | −8512.17 | −1.34586 | ||||||||
\(343\) | −562.111 | −0.0884872 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −64.6164 | −0.0100836 | ||||||||
\(346\) | 19431.1 | 3.01915 | ||||||||
\(347\) | 7606.27 | 1.17673 | 0.588366 | − | 0.808595i | \(-0.299771\pi\) | ||||
0.588366 | + | 0.808595i | \(0.299771\pi\) | |||||||
\(348\) | −6120.72 | −0.942831 | ||||||||
\(349\) | 11139.6 | 1.70857 | 0.854285 | − | 0.519805i | \(-0.173995\pi\) | ||||
0.854285 | + | 0.519805i | \(0.173995\pi\) | |||||||
\(350\) | 403.253 | 0.0615851 | ||||||||
\(351\) | −1775.80 | −0.270043 | ||||||||
\(352\) | 17725.8 | 2.68406 | ||||||||
\(353\) | −6695.74 | −1.00957 | −0.504785 | − | 0.863245i | \(-0.668428\pi\) | ||||
−0.504785 | + | 0.863245i | \(0.668428\pi\) | |||||||
\(354\) | −18696.2 | −2.80704 | ||||||||
\(355\) | 5141.57 | 0.768694 | ||||||||
\(356\) | −18034.7 | −2.68493 | ||||||||
\(357\) | −862.468 | −0.127862 | ||||||||
\(358\) | 9384.08 | 1.38537 | ||||||||
\(359\) | 1450.57 | 0.213253 | 0.106627 | − | 0.994299i | \(-0.465995\pi\) | ||||
0.106627 | + | 0.994299i | \(0.465995\pi\) | |||||||
\(360\) | 22791.7 | 3.33674 | ||||||||
\(361\) | −6274.47 | −0.914780 | ||||||||
\(362\) | −19543.8 | −2.83756 | ||||||||
\(363\) | −9872.10 | −1.42741 | ||||||||
\(364\) | 73.3255 | 0.0105585 | ||||||||
\(365\) | 189.566 | 0.0271845 | ||||||||
\(366\) | −1874.76 | −0.267747 | ||||||||
\(367\) | 852.755 | 0.121290 | 0.0606450 | − | 0.998159i | \(-0.480684\pi\) | ||||
0.0606450 | + | 0.998159i | \(0.480684\pi\) | |||||||
\(368\) | −192.949 | −0.0273320 | ||||||||
\(369\) | −4213.46 | −0.594428 | ||||||||
\(370\) | 10391.2 | 1.46004 | ||||||||
\(371\) | −97.9177 | −0.0137025 | ||||||||
\(372\) | 11226.4 | 1.56469 | ||||||||
\(373\) | −5505.36 | −0.764228 | −0.382114 | − | 0.924115i | \(-0.624804\pi\) | ||||
−0.382114 | + | 0.924115i | \(0.624804\pi\) | |||||||
\(374\) | 27586.0 | 3.81401 | ||||||||
\(375\) | −11873.7 | −1.63507 | ||||||||
\(376\) | 12943.3 | 1.77527 | ||||||||
\(377\) | 147.442 | 0.0201423 | ||||||||
\(378\) | 1673.16 | 0.227667 | ||||||||
\(379\) | −1565.31 | −0.212149 | −0.106074 | − | 0.994358i | \(-0.533828\pi\) | ||||
−0.106074 | + | 0.994358i | \(0.533828\pi\) | |||||||
\(380\) | −2648.06 | −0.357480 | ||||||||
\(381\) | −17474.3 | −2.34970 | ||||||||
\(382\) | 22253.2 | 2.98056 | ||||||||
\(383\) | 9163.31 | 1.22251 | 0.611257 | − | 0.791432i | \(-0.290664\pi\) | ||||
0.611257 | + | 0.791432i | \(0.290664\pi\) | |||||||
\(384\) | 3335.70 | 0.443292 | ||||||||
\(385\) | 222.577 | 0.0294638 | ||||||||
\(386\) | −10961.0 | −1.44534 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 8449.48 | 1.10556 | ||||||||
\(389\) | −6892.14 | −0.898318 | −0.449159 | − | 0.893452i | \(-0.648276\pi\) | ||||
−0.449159 | + | 0.893452i | \(0.648276\pi\) | |||||||
\(390\) | −1302.92 | −0.169169 | ||||||||
\(391\) | −129.007 | −0.0166858 | ||||||||
\(392\) | 20778.0 | 2.67716 | ||||||||
\(393\) | −6506.32 | −0.835116 | ||||||||
\(394\) | −14834.1 | −1.89678 | ||||||||
\(395\) | 3430.70 | 0.437005 | ||||||||
\(396\) | −63579.8 | −8.06820 | ||||||||
\(397\) | −9704.76 | −1.22687 | −0.613436 | − | 0.789744i | \(-0.710213\pi\) | ||||
−0.613436 | + | 0.789744i | \(0.710213\pi\) | |||||||
\(398\) | 234.314 | 0.0295103 | ||||||||
\(399\) | −192.325 | −0.0241311 | ||||||||
\(400\) | −15185.9 | −1.89824 | ||||||||
\(401\) | −6933.44 | −0.863440 | −0.431720 | − | 0.902008i | \(-0.642093\pi\) | ||||
−0.431720 | + | 0.902008i | \(0.642093\pi\) | |||||||
\(402\) | 8838.16 | 1.09654 | ||||||||
\(403\) | −270.434 | −0.0334275 | ||||||||
\(404\) | 15523.1 | 1.91164 | ||||||||
\(405\) | −10962.3 | −1.34499 | ||||||||
\(406\) | −138.920 | −0.0169815 | ||||||||
\(407\) | −17132.5 | −2.08655 | ||||||||
\(408\) | 63823.6 | 7.74445 | ||||||||
\(409\) | 3733.75 | 0.451399 | 0.225699 | − | 0.974197i | \(-0.427533\pi\) | ||||
0.225699 | + | 0.974197i | \(0.427533\pi\) | |||||||
\(410\) | −1846.83 | −0.222460 | ||||||||
\(411\) | −14906.2 | −1.78898 | ||||||||
\(412\) | 28870.7 | 3.45232 | ||||||||
\(413\) | −301.173 | −0.0358831 | ||||||||
\(414\) | 418.933 | 0.0497329 | ||||||||
\(415\) | 2329.39 | 0.275531 | ||||||||
\(416\) | −1671.50 | −0.197000 | ||||||||
\(417\) | −16460.8 | −1.93307 | ||||||||
\(418\) | 6151.53 | 0.719812 | ||||||||
\(419\) | −7400.59 | −0.862869 | −0.431435 | − | 0.902144i | \(-0.641992\pi\) | ||||
−0.431435 | + | 0.902144i | \(0.641992\pi\) | |||||||
\(420\) | 871.287 | 0.101225 | ||||||||
\(421\) | −813.451 | −0.0941691 | −0.0470845 | − | 0.998891i | \(-0.514993\pi\) | ||||
−0.0470845 | + | 0.998891i | \(0.514993\pi\) | |||||||
\(422\) | 21473.0 | 2.47699 | ||||||||
\(423\) | −14301.2 | −1.64385 | ||||||||
\(424\) | 7246.02 | 0.829948 | ||||||||
\(425\) | −10153.4 | −1.15885 | ||||||||
\(426\) | −46755.4 | −5.31763 | ||||||||
\(427\) | −30.2000 | −0.00342267 | ||||||||
\(428\) | 10268.5 | 1.15969 | ||||||||
\(429\) | 2148.19 | 0.241761 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6470.90 | −0.723184 | −0.361592 | − | 0.932337i | \(-0.617767\pi\) | ||||
−0.361592 | + | 0.932337i | \(0.617767\pi\) | |||||||
\(432\) | −63008.8 | −7.01739 | ||||||||
\(433\) | −11614.5 | −1.28905 | −0.644523 | − | 0.764585i | \(-0.722944\pi\) | ||||
−0.644523 | + | 0.764585i | \(0.722944\pi\) | |||||||
\(434\) | 254.803 | 0.0281819 | ||||||||
\(435\) | 1751.98 | 0.193105 | ||||||||
\(436\) | 37779.7 | 4.14982 | ||||||||
\(437\) | −28.7678 | −0.00314909 | ||||||||
\(438\) | −1723.84 | −0.188056 | ||||||||
\(439\) | 7410.59 | 0.805668 | 0.402834 | − | 0.915273i | \(-0.368025\pi\) | ||||
0.402834 | + | 0.915273i | \(0.368025\pi\) | |||||||
\(440\) | −16470.9 | −1.78459 | ||||||||
\(441\) | −22957.8 | −2.47897 | ||||||||
\(442\) | −2601.29 | −0.279934 | ||||||||
\(443\) | 10749.4 | 1.15287 | 0.576433 | − | 0.817145i | \(-0.304444\pi\) | ||||
0.576433 | + | 0.817145i | \(0.304444\pi\) | |||||||
\(444\) | −67065.9 | −7.16849 | ||||||||
\(445\) | 5162.18 | 0.549912 | ||||||||
\(446\) | −7557.55 | −0.802378 | ||||||||
\(447\) | −28350.5 | −2.99985 | ||||||||
\(448\) | 510.862 | 0.0538749 | ||||||||
\(449\) | −2958.61 | −0.310970 | −0.155485 | − | 0.987838i | \(-0.549694\pi\) | ||||
−0.155485 | + | 0.987838i | \(0.549694\pi\) | |||||||
\(450\) | 32971.7 | 3.45401 | ||||||||
\(451\) | 3044.96 | 0.317919 | ||||||||
\(452\) | −22755.4 | −2.36797 | ||||||||
\(453\) | −14118.4 | −1.46433 | ||||||||
\(454\) | −17724.3 | −1.83225 | ||||||||
\(455\) | −20.9885 | −0.00216254 | ||||||||
\(456\) | 14232.3 | 1.46160 | ||||||||
\(457\) | 7447.46 | 0.762314 | 0.381157 | − | 0.924510i | \(-0.375526\pi\) | ||||
0.381157 | + | 0.924510i | \(0.375526\pi\) | |||||||
\(458\) | −20282.5 | −2.06930 | ||||||||
\(459\) | −42128.0 | −4.28402 | ||||||||
\(460\) | 130.326 | 0.0132098 | ||||||||
\(461\) | 13145.0 | 1.32803 | 0.664015 | − | 0.747719i | \(-0.268851\pi\) | ||||
0.664015 | + | 0.747719i | \(0.268851\pi\) | |||||||
\(462\) | −2024.03 | −0.203823 | ||||||||
\(463\) | −8298.41 | −0.832958 | −0.416479 | − | 0.909145i | \(-0.636736\pi\) | ||||
−0.416479 | + | 0.909145i | \(0.636736\pi\) | |||||||
\(464\) | 5231.54 | 0.523422 | ||||||||
\(465\) | −3213.42 | −0.320470 | ||||||||
\(466\) | 7463.10 | 0.741892 | ||||||||
\(467\) | 5139.31 | 0.509248 | 0.254624 | − | 0.967040i | \(-0.418048\pi\) | ||||
0.254624 | + | 0.967040i | \(0.418048\pi\) | |||||||
\(468\) | 5995.42 | 0.592176 | ||||||||
\(469\) | 142.372 | 0.0140173 | ||||||||
\(470\) | −6268.45 | −0.615196 | ||||||||
\(471\) | 12209.2 | 1.19442 | ||||||||
\(472\) | 22287.1 | 2.17340 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −31197.4 | −3.02309 | ||||||||
\(475\) | −2264.15 | −0.218708 | ||||||||
\(476\) | 1739.53 | 0.167503 | ||||||||
\(477\) | −8006.18 | −0.768507 | ||||||||
\(478\) | −23040.5 | −2.20471 | ||||||||
\(479\) | 10403.5 | 0.992377 | 0.496188 | − | 0.868215i | \(-0.334733\pi\) | ||||
0.496188 | + | 0.868215i | \(0.334733\pi\) | |||||||
\(480\) | −19861.5 | −1.88864 | ||||||||
\(481\) | 1615.55 | 0.153145 | ||||||||
\(482\) | −10646.3 | −1.00607 | ||||||||
\(483\) | 9.46543 | 0.000891702 0 | ||||||||
\(484\) | 19911.3 | 1.86995 | ||||||||
\(485\) | −2418.55 | −0.226435 | ||||||||
\(486\) | 44608.6 | 4.16356 | ||||||||
\(487\) | 130.371 | 0.0121308 | 0.00606538 | − | 0.999982i | \(-0.498069\pi\) | ||||
0.00606538 | + | 0.999982i | \(0.498069\pi\) | |||||||
\(488\) | 2234.84 | 0.207308 | ||||||||
\(489\) | −26360.6 | −2.43776 | ||||||||
\(490\) | −10062.8 | −0.927735 | ||||||||
\(491\) | 6549.97 | 0.602029 | 0.301014 | − | 0.953620i | \(-0.402675\pi\) | ||||
0.301014 | + | 0.953620i | \(0.402675\pi\) | |||||||
\(492\) | 11919.6 | 1.09223 | ||||||||
\(493\) | 3497.83 | 0.319543 | ||||||||
\(494\) | −580.074 | −0.0528315 | ||||||||
\(495\) | 18198.9 | 1.65248 | ||||||||
\(496\) | −9595.52 | −0.868652 | ||||||||
\(497\) | −753.171 | −0.0679766 | ||||||||
\(498\) | −21182.6 | −1.90606 | ||||||||
\(499\) | −12423.5 | −1.11454 | −0.557268 | − | 0.830333i | \(-0.688150\pi\) | ||||
−0.557268 | + | 0.830333i | \(0.688150\pi\) | |||||||
\(500\) | 23948.2 | 2.14200 | ||||||||
\(501\) | 37585.1 | 3.35165 | ||||||||
\(502\) | 14070.1 | 1.25095 | ||||||||
\(503\) | 16203.4 | 1.43633 | 0.718166 | − | 0.695871i | \(-0.244982\pi\) | ||||
0.718166 | + | 0.695871i | \(0.244982\pi\) | |||||||
\(504\) | −3338.67 | −0.295072 | ||||||||
\(505\) | −4443.28 | −0.391532 | ||||||||
\(506\) | −302.752 | −0.0265988 | ||||||||
\(507\) | 21105.4 | 1.84876 | ||||||||
\(508\) | 35244.3 | 3.07817 | ||||||||
\(509\) | 21966.2 | 1.91283 | 0.956417 | − | 0.292004i | \(-0.0943222\pi\) | ||||
0.956417 | + | 0.292004i | \(0.0943222\pi\) | |||||||
\(510\) | −30909.8 | −2.68374 | ||||||||
\(511\) | −27.7689 | −0.00240396 | ||||||||
\(512\) | 19431.1 | 1.67723 | ||||||||
\(513\) | −9394.31 | −0.808516 | ||||||||
\(514\) | −28879.2 | −2.47822 | ||||||||
\(515\) | −8263.85 | −0.707085 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10335.1 | 0.879182 | ||||||||
\(518\) | −1522.18 | −0.129113 | ||||||||
\(519\) | 35897.1 | 3.03604 | ||||||||
\(520\) | 1553.17 | 0.130983 | ||||||||
\(521\) | −15304.4 | −1.28694 | −0.643471 | − | 0.765470i | \(-0.722506\pi\) | ||||
−0.643471 | + | 0.765470i | \(0.722506\pi\) | |||||||
\(522\) | −11358.7 | −0.952411 | ||||||||
\(523\) | −5101.60 | −0.426534 | −0.213267 | − | 0.976994i | \(-0.568410\pi\) | ||||
−0.213267 | + | 0.976994i | \(0.568410\pi\) | |||||||
\(524\) | 13122.7 | 1.09403 | ||||||||
\(525\) | 744.969 | 0.0619297 | ||||||||
\(526\) | −4424.85 | −0.366792 | ||||||||
\(527\) | −6415.62 | −0.530301 | ||||||||
\(528\) | 76222.0 | 6.28245 | ||||||||
\(529\) | −12165.6 | −0.999884 | ||||||||
\(530\) | −3509.25 | −0.287607 | ||||||||
\(531\) | −24625.2 | −2.01251 | ||||||||
\(532\) | 387.905 | 0.0316125 | ||||||||
\(533\) | −287.132 | −0.0233341 | ||||||||
\(534\) | −46942.9 | −3.80415 | ||||||||
\(535\) | −2939.23 | −0.237522 | ||||||||
\(536\) | −10535.7 | −0.849013 | ||||||||
\(537\) | 17336.1 | 1.39313 | ||||||||
\(538\) | 12683.7 | 1.01642 | ||||||||
\(539\) | 16591.0 | 1.32583 | ||||||||
\(540\) | 42558.8 | 3.39155 | ||||||||
\(541\) | 3790.76 | 0.301253 | 0.150626 | − | 0.988591i | \(-0.451871\pi\) | ||||
0.150626 | + | 0.988591i | \(0.451871\pi\) | |||||||
\(542\) | 22654.9 | 1.79540 | ||||||||
\(543\) | −36105.1 | −2.85344 | ||||||||
\(544\) | −39653.6 | −3.12525 | ||||||||
\(545\) | −10813.9 | −0.849942 | ||||||||
\(546\) | 190.861 | 0.0149599 | ||||||||
\(547\) | 3861.12 | 0.301809 | 0.150905 | − | 0.988548i | \(-0.451781\pi\) | ||||
0.150905 | + | 0.988548i | \(0.451781\pi\) | |||||||
\(548\) | 30064.7 | 2.34361 | ||||||||
\(549\) | −2469.29 | −0.191961 | ||||||||
\(550\) | −23827.8 | −1.84731 | ||||||||
\(551\) | 779.997 | 0.0603067 | ||||||||
\(552\) | −700.453 | −0.0540095 | ||||||||
\(553\) | −502.551 | −0.0386449 | ||||||||
\(554\) | −33461.6 | −2.56615 | ||||||||
\(555\) | 19196.7 | 1.46821 | ||||||||
\(556\) | 33200.2 | 2.53238 | ||||||||
\(557\) | 14089.2 | 1.07177 | 0.535886 | − | 0.844290i | \(-0.319978\pi\) | ||||
0.535886 | + | 0.844290i | \(0.319978\pi\) | |||||||
\(558\) | 20833.8 | 1.58059 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −744.711 | −0.0561960 | ||||||||
\(561\) | 50962.4 | 3.83535 | ||||||||
\(562\) | 34857.7 | 2.61634 | ||||||||
\(563\) | −4417.45 | −0.330681 | −0.165340 | − | 0.986237i | \(-0.552872\pi\) | ||||
−0.165340 | + | 0.986237i | \(0.552872\pi\) | |||||||
\(564\) | 40457.2 | 3.02049 | ||||||||
\(565\) | 6513.42 | 0.484994 | ||||||||
\(566\) | 10686.6 | 0.793627 | ||||||||
\(567\) | 1605.83 | 0.118939 | ||||||||
\(568\) | 55735.5 | 4.11727 | ||||||||
\(569\) | −2935.33 | −0.216266 | −0.108133 | − | 0.994136i | \(-0.534487\pi\) | ||||
−0.108133 | + | 0.994136i | \(0.534487\pi\) | |||||||
\(570\) | −6892.70 | −0.506497 | ||||||||
\(571\) | −14735.7 | −1.07998 | −0.539990 | − | 0.841672i | \(-0.681572\pi\) | ||||
−0.539990 | + | 0.841672i | \(0.681572\pi\) | |||||||
\(572\) | −4332.74 | −0.316715 | ||||||||
\(573\) | 41110.5 | 2.99723 | ||||||||
\(574\) | 270.536 | 0.0196724 | ||||||||
\(575\) | 111.432 | 0.00808178 | ||||||||
\(576\) | 41770.3 | 3.02158 | ||||||||
\(577\) | 12632.7 | 0.911450 | 0.455725 | − | 0.890121i | \(-0.349380\pi\) | ||||
0.455725 | + | 0.890121i | \(0.349380\pi\) | |||||||
\(578\) | −35918.8 | −2.58482 | ||||||||
\(579\) | −20249.4 | −1.45343 | ||||||||
\(580\) | −3533.60 | −0.252974 | ||||||||
\(581\) | −341.225 | −0.0243656 | ||||||||
\(582\) | 21993.4 | 1.56642 | ||||||||
\(583\) | 5785.86 | 0.411022 | ||||||||
\(584\) | 2054.93 | 0.145606 | ||||||||
\(585\) | −1716.11 | −0.121286 | ||||||||
\(586\) | 17215.4 | 1.21358 | ||||||||
\(587\) | −11971.0 | −0.841730 | −0.420865 | − | 0.907123i | \(-0.638273\pi\) | ||||
−0.420865 | + | 0.907123i | \(0.638273\pi\) | |||||||
\(588\) | 64946.1 | 4.55499 | ||||||||
\(589\) | −1430.65 | −0.100083 | ||||||||
\(590\) | −10793.6 | −0.753165 | ||||||||
\(591\) | −27404.4 | −1.90739 | ||||||||
\(592\) | 57322.9 | 3.97966 | ||||||||
\(593\) | −25205.0 | −1.74544 | −0.872719 | − | 0.488223i | \(-0.837645\pi\) | ||||
−0.872719 | + | 0.488223i | \(0.837645\pi\) | |||||||
\(594\) | −98865.5 | −6.82913 | ||||||||
\(595\) | −497.917 | −0.0343069 | ||||||||
\(596\) | 57180.7 | 3.92989 | ||||||||
\(597\) | 432.871 | 0.0296754 | ||||||||
\(598\) | 28.5488 | 0.00195225 | ||||||||
\(599\) | 10917.1 | 0.744674 | 0.372337 | − | 0.928098i | \(-0.378557\pi\) | ||||
0.372337 | + | 0.928098i | \(0.378557\pi\) | |||||||
\(600\) | −55128.5 | −3.75102 | ||||||||
\(601\) | 7264.54 | 0.493056 | 0.246528 | − | 0.969136i | \(-0.420710\pi\) | ||||
0.246528 | + | 0.969136i | \(0.420710\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 11640.9 | 0.786161 | ||||||||
\(604\) | 28475.7 | 1.91831 | ||||||||
\(605\) | −5699.34 | −0.382993 | ||||||||
\(606\) | 40405.5 | 2.70852 | ||||||||
\(607\) | −21342.0 | −1.42709 | −0.713547 | − | 0.700607i | \(-0.752913\pi\) | ||||
−0.713547 | + | 0.700607i | \(0.752913\pi\) | |||||||
\(608\) | −8842.53 | −0.589822 | ||||||||
\(609\) | −256.641 | −0.0170766 | ||||||||
\(610\) | −1082.33 | −0.0718398 | ||||||||
\(611\) | −974.574 | −0.0645287 | ||||||||
\(612\) | 142232. | 9.39440 | ||||||||
\(613\) | −11531.3 | −0.759779 | −0.379889 | − | 0.925032i | \(-0.624038\pi\) | ||||
−0.379889 | + | 0.925032i | \(0.624038\pi\) | |||||||
\(614\) | −30008.7 | −1.97240 | ||||||||
\(615\) | −3411.83 | −0.223705 | ||||||||
\(616\) | 2412.77 | 0.157814 | ||||||||
\(617\) | 9055.91 | 0.590887 | 0.295444 | − | 0.955360i | \(-0.404533\pi\) | ||||
0.295444 | + | 0.955360i | \(0.404533\pi\) | |||||||
\(618\) | 75148.3 | 4.89143 | ||||||||
\(619\) | −4260.01 | −0.276615 | −0.138307 | − | 0.990389i | \(-0.544166\pi\) | ||||
−0.138307 | + | 0.990389i | \(0.544166\pi\) | |||||||
\(620\) | 6481.22 | 0.419826 | ||||||||
\(621\) | 462.348 | 0.0298766 | ||||||||
\(622\) | −27732.7 | −1.78775 | ||||||||
\(623\) | −756.191 | −0.0486294 | ||||||||
\(624\) | −7187.54 | −0.461109 | ||||||||
\(625\) | 4851.26 | 0.310481 | ||||||||
\(626\) | −7052.00 | −0.450247 | ||||||||
\(627\) | 11364.3 | 0.723840 | ||||||||
\(628\) | −24625.0 | −1.56472 | ||||||||
\(629\) | 38326.4 | 2.42953 | ||||||||
\(630\) | 1616.92 | 0.102253 | ||||||||
\(631\) | 5353.21 | 0.337731 | 0.168865 | − | 0.985639i | \(-0.445990\pi\) | ||||
0.168865 | + | 0.985639i | \(0.445990\pi\) | |||||||
\(632\) | 37189.4 | 2.34069 | ||||||||
\(633\) | 39669.1 | 2.49085 | ||||||||
\(634\) | −10016.7 | −0.627468 | ||||||||
\(635\) | −10088.2 | −0.630454 | ||||||||
\(636\) | 22649.0 | 1.41209 | ||||||||
\(637\) | −1564.49 | −0.0973113 | ||||||||
\(638\) | 8208.67 | 0.509380 | ||||||||
\(639\) | −61582.6 | −3.81247 | ||||||||
\(640\) | 1925.76 | 0.118941 | ||||||||
\(641\) | 18014.6 | 1.11004 | 0.555020 | − | 0.831837i | \(-0.312711\pi\) | ||||
0.555020 | + | 0.831837i | \(0.312711\pi\) | |||||||
\(642\) | 26728.2 | 1.64311 | ||||||||
\(643\) | 13215.0 | 0.810496 | 0.405248 | − | 0.914207i | \(-0.367185\pi\) | ||||
0.405248 | + | 0.914207i | \(0.367185\pi\) | |||||||
\(644\) | −19.0910 | −0.00116816 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −13761.3 | −0.838130 | ||||||||
\(647\) | 9446.10 | 0.573979 | 0.286989 | − | 0.957934i | \(-0.407346\pi\) | ||||
0.286989 | + | 0.957934i | \(0.407346\pi\) | |||||||
\(648\) | −118833. | −7.20401 | ||||||||
\(649\) | 17796.0 | 1.07635 | ||||||||
\(650\) | 2246.91 | 0.135586 | ||||||||
\(651\) | 470.723 | 0.0283396 | ||||||||
\(652\) | 53167.2 | 3.19354 | ||||||||
\(653\) | −16070.1 | −0.963048 | −0.481524 | − | 0.876433i | \(-0.659917\pi\) | ||||
−0.481524 | + | 0.876433i | \(0.659917\pi\) | |||||||
\(654\) | 98337.7 | 5.87968 | ||||||||
\(655\) | −3756.21 | −0.224072 | ||||||||
\(656\) | −10188.0 | −0.606364 | ||||||||
\(657\) | −2270.51 | −0.134826 | ||||||||
\(658\) | 918.245 | 0.0544026 | ||||||||
\(659\) | 24256.6 | 1.43385 | 0.716923 | − | 0.697152i | \(-0.245550\pi\) | ||||
0.716923 | + | 0.697152i | \(0.245550\pi\) | |||||||
\(660\) | −51483.5 | −3.03635 | ||||||||
\(661\) | −14345.2 | −0.844123 | −0.422061 | − | 0.906567i | \(-0.638693\pi\) | ||||
−0.422061 | + | 0.906567i | \(0.638693\pi\) | |||||||
\(662\) | 48430.4 | 2.84335 | ||||||||
\(663\) | −4805.63 | −0.281501 | ||||||||
\(664\) | 25251.1 | 1.47580 | ||||||||
\(665\) | −111.033 | −0.00647468 | ||||||||
\(666\) | −124460. | −7.24132 | ||||||||
\(667\) | −38.3881 | −0.00222848 | ||||||||
\(668\) | −75806.2 | −4.39076 | ||||||||
\(669\) | −13961.8 | −0.806868 | ||||||||
\(670\) | 5102.42 | 0.294214 | ||||||||
\(671\) | 1784.49 | 0.102667 | ||||||||
\(672\) | 2909.44 | 0.167015 | ||||||||
\(673\) | −19972.6 | −1.14397 | −0.571983 | − | 0.820266i | \(-0.693826\pi\) | ||||
−0.571983 | + | 0.820266i | \(0.693826\pi\) | |||||||
\(674\) | −11516.5 | −0.658160 | ||||||||
\(675\) | 36388.7 | 2.07496 | ||||||||
\(676\) | −42567.9 | −2.42193 | ||||||||
\(677\) | −4701.00 | −0.266874 | −0.133437 | − | 0.991057i | \(-0.542601\pi\) | ||||
−0.133437 | + | 0.991057i | \(0.542601\pi\) | |||||||
\(678\) | −59230.5 | −3.35506 | ||||||||
\(679\) | 354.286 | 0.0200239 | ||||||||
\(680\) | 36846.4 | 2.07794 | ||||||||
\(681\) | −32743.9 | −1.84251 | ||||||||
\(682\) | −15056.1 | −0.845348 | ||||||||
\(683\) | −9546.69 | −0.534838 | −0.267419 | − | 0.963580i | \(-0.586171\pi\) | ||||
−0.267419 | + | 0.963580i | \(0.586171\pi\) | |||||||
\(684\) | 31716.8 | 1.77299 | ||||||||
\(685\) | −8605.61 | −0.480005 | ||||||||
\(686\) | 2951.02 | 0.164243 | ||||||||
\(687\) | −37469.9 | −2.08088 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −545.592 | −0.0301675 | ||||||||
\(690\) | 339.229 | 0.0187163 | ||||||||
\(691\) | 5642.15 | 0.310619 | 0.155309 | − | 0.987866i | \(-0.450363\pi\) | ||||
0.155309 | + | 0.987866i | \(0.450363\pi\) | |||||||
\(692\) | −72401.6 | −3.97731 | ||||||||
\(693\) | −2665.89 | −0.146131 | ||||||||
\(694\) | −39932.2 | −2.18416 | ||||||||
\(695\) | −9503.12 | −0.518668 | ||||||||
\(696\) | 18991.7 | 1.03431 | ||||||||
\(697\) | −6811.75 | −0.370177 | ||||||||
\(698\) | −58481.9 | −3.17131 | ||||||||
\(699\) | 13787.3 | 0.746043 | ||||||||
\(700\) | −1502.54 | −0.0811298 | ||||||||
\(701\) | 4272.35 | 0.230192 | 0.115096 | − | 0.993354i | \(-0.463282\pi\) | ||||
0.115096 | + | 0.993354i | \(0.463282\pi\) | |||||||
\(702\) | 9322.77 | 0.501232 | ||||||||
\(703\) | 8546.57 | 0.458521 | ||||||||
\(704\) | −30186.3 | −1.61604 | ||||||||
\(705\) | −11580.3 | −0.618639 | ||||||||
\(706\) | 35151.9 | 1.87388 | ||||||||
\(707\) | 650.882 | 0.0346236 | ||||||||
\(708\) | 69663.2 | 3.69788 | ||||||||
\(709\) | −5618.45 | −0.297610 | −0.148805 | − | 0.988867i | \(-0.547543\pi\) | ||||
−0.148805 | + | 0.988867i | \(0.547543\pi\) | |||||||
\(710\) | −26992.7 | −1.42679 | ||||||||
\(711\) | −41090.8 | −2.16741 | ||||||||
\(712\) | 55959.0 | 2.94544 | ||||||||
\(713\) | 70.4103 | 0.00369830 | ||||||||
\(714\) | 4527.87 | 0.237327 | ||||||||
\(715\) | 1240.19 | 0.0648677 | ||||||||
\(716\) | −34965.6 | −1.82504 | ||||||||
\(717\) | −42565.0 | −2.21704 | ||||||||
\(718\) | −7615.32 | −0.395824 | ||||||||
\(719\) | −20888.3 | −1.08345 | −0.541726 | − | 0.840555i | \(-0.682229\pi\) | ||||
−0.541726 | + | 0.840555i | \(0.682229\pi\) | |||||||
\(720\) | −60890.8 | −3.15176 | ||||||||
\(721\) | 1210.54 | 0.0625285 | ||||||||
\(722\) | 32940.3 | 1.69794 | ||||||||
\(723\) | −19668.0 | −1.01170 | ||||||||
\(724\) | 72821.3 | 3.73810 | ||||||||
\(725\) | −3021.30 | −0.154770 | ||||||||
\(726\) | 51827.5 | 2.64945 | ||||||||
\(727\) | −22269.4 | −1.13607 | −0.568036 | − | 0.823004i | \(-0.692297\pi\) | ||||
−0.568036 | + | 0.823004i | \(0.692297\pi\) | |||||||
\(728\) | −227.519 | −0.0115830 | ||||||||
\(729\) | 29548.5 | 1.50122 | ||||||||
\(730\) | −995.203 | −0.0504577 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 6985.46 | 0.352719 | ||||||||
\(733\) | −3529.35 | −0.177844 | −0.0889219 | − | 0.996039i | \(-0.528342\pi\) | ||||
−0.0889219 | + | 0.996039i | \(0.528342\pi\) | |||||||
\(734\) | −4476.88 | −0.225129 | ||||||||
\(735\) | −18590.0 | −0.932926 | ||||||||
\(736\) | 435.191 | 0.0217953 | ||||||||
\(737\) | −8412.60 | −0.420464 | ||||||||
\(738\) | 22120.2 | 1.10333 | ||||||||
\(739\) | −2076.61 | −0.103369 | −0.0516843 | − | 0.998663i | \(-0.516459\pi\) | ||||
−0.0516843 | + | 0.998663i | \(0.516459\pi\) | |||||||
\(740\) | −38718.3 | −1.92340 | ||||||||
\(741\) | −1071.63 | −0.0531271 | ||||||||
\(742\) | 514.058 | 0.0254335 | ||||||||
\(743\) | 13559.1 | 0.669496 | 0.334748 | − | 0.942308i | \(-0.391349\pi\) | ||||
0.334748 | + | 0.942308i | \(0.391349\pi\) | |||||||
\(744\) | −34834.0 | −1.71650 | ||||||||
\(745\) | −16367.2 | −0.804898 | ||||||||
\(746\) | 28902.6 | 1.41850 | ||||||||
\(747\) | −27900.1 | −1.36655 | ||||||||
\(748\) | −102787. | −5.02443 | ||||||||
\(749\) | 430.558 | 0.0210043 | ||||||||
\(750\) | 62335.5 | 3.03489 | ||||||||
\(751\) | −26360.2 | −1.28082 | −0.640410 | − | 0.768033i | \(-0.721236\pi\) | ||||
−0.640410 | + | 0.768033i | \(0.721236\pi\) | |||||||
\(752\) | −34579.8 | −1.67685 | ||||||||
\(753\) | 25993.0 | 1.25795 | ||||||||
\(754\) | −774.057 | −0.0373866 | ||||||||
\(755\) | −8150.80 | −0.392898 | ||||||||
\(756\) | −6234.29 | −0.299919 | ||||||||
\(757\) | −6025.87 | −0.289318 | −0.144659 | − | 0.989482i | \(-0.546209\pi\) | ||||
−0.144659 | + | 0.989482i | \(0.546209\pi\) | |||||||
\(758\) | 8217.70 | 0.393774 | ||||||||
\(759\) | −559.304 | −0.0267476 | ||||||||
\(760\) | 8216.55 | 0.392165 | ||||||||
\(761\) | 11127.9 | 0.530073 | 0.265037 | − | 0.964238i | \(-0.414616\pi\) | ||||
0.265037 | + | 0.964238i | \(0.414616\pi\) | |||||||
\(762\) | 91738.2 | 4.36132 | ||||||||
\(763\) | 1584.10 | 0.0751615 | ||||||||
\(764\) | −82916.7 | −3.92647 | ||||||||
\(765\) | −40711.9 | −1.92411 | ||||||||
\(766\) | −48106.4 | −2.26913 | ||||||||
\(767\) | −1678.12 | −0.0790004 | ||||||||
\(768\) | 30813.9 | 1.44779 | ||||||||
\(769\) | 26446.7 | 1.24017 | 0.620085 | − | 0.784534i | \(-0.287098\pi\) | ||||
0.620085 | + | 0.784534i | \(0.287098\pi\) | |||||||
\(770\) | −1168.51 | −0.0546884 | ||||||||
\(771\) | −53351.3 | −2.49209 | ||||||||
\(772\) | 40841.5 | 1.90404 | ||||||||
\(773\) | −3081.60 | −0.143386 | −0.0716930 | − | 0.997427i | \(-0.522840\pi\) | ||||
−0.0716930 | + | 0.997427i | \(0.522840\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5541.58 | 0.256851 | ||||||||
\(776\) | −26217.5 | −1.21283 | ||||||||
\(777\) | −2812.06 | −0.129836 | ||||||||
\(778\) | 36183.1 | 1.66738 | ||||||||
\(779\) | −1518.98 | −0.0698629 | ||||||||
\(780\) | 4854.77 | 0.222857 | ||||||||
\(781\) | 44504.2 | 2.03903 | ||||||||
\(782\) | 677.274 | 0.0309709 | ||||||||
\(783\) | −12535.9 | −0.572152 | ||||||||
\(784\) | −55511.1 | −2.52875 | ||||||||
\(785\) | 7048.58 | 0.320477 | ||||||||
\(786\) | 34157.5 | 1.55007 | ||||||||
\(787\) | −17984.9 | −0.814605 | −0.407302 | − | 0.913293i | \(-0.633530\pi\) | ||||
−0.407302 | + | 0.913293i | \(0.633530\pi\) | |||||||
\(788\) | 55272.6 | 2.49874 | ||||||||
\(789\) | −8174.46 | −0.368845 | ||||||||
\(790\) | −18010.8 | −0.811134 | ||||||||
\(791\) | −954.129 | −0.0428886 | ||||||||
\(792\) | 197279. | 8.85102 | ||||||||
\(793\) | −168.273 | −0.00753537 | ||||||||
\(794\) | 50949.0 | 2.27722 | ||||||||
\(795\) | −6482.97 | −0.289217 | ||||||||
\(796\) | −873.067 | −0.0388757 | ||||||||
\(797\) | 35163.6 | 1.56281 | 0.781403 | − | 0.624026i | \(-0.214504\pi\) | ||||
0.781403 | + | 0.624026i | \(0.214504\pi\) | |||||||
\(798\) | 1009.69 | 0.0447902 | ||||||||
\(799\) | −23120.2 | −1.02370 | ||||||||
\(800\) | 34251.4 | 1.51371 | ||||||||
\(801\) | −61829.5 | −2.72739 | ||||||||
\(802\) | 36399.8 | 1.60265 | ||||||||
\(803\) | 1640.84 | 0.0721095 | ||||||||
\(804\) | −32931.5 | −1.44453 | ||||||||
\(805\) | 5.46456 | 0.000239255 0 | ||||||||
\(806\) | 1419.75 | 0.0620454 | ||||||||
\(807\) | 23431.9 | 1.02211 | ||||||||
\(808\) | −48166.0 | −2.09712 | ||||||||
\(809\) | 4623.40 | 0.200927 | 0.100464 | − | 0.994941i | \(-0.467967\pi\) | ||||
0.100464 | + | 0.994941i | \(0.467967\pi\) | |||||||
\(810\) | 57550.8 | 2.49645 | ||||||||
\(811\) | 20925.5 | 0.906034 | 0.453017 | − | 0.891502i | \(-0.350348\pi\) | ||||
0.453017 | + | 0.891502i | \(0.350348\pi\) | |||||||
\(812\) | 517.625 | 0.0223708 | ||||||||
\(813\) | 41852.5 | 1.80545 | ||||||||
\(814\) | 89944.0 | 3.87289 | ||||||||
\(815\) | −15218.4 | −0.654083 | ||||||||
\(816\) | −170513. | −7.31513 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −19601.8 | −0.837850 | ||||||||
\(819\) | 251.387 | 0.0107255 | ||||||||
\(820\) | 6881.40 | 0.293060 | ||||||||
\(821\) | −10907.2 | −0.463658 | −0.231829 | − | 0.972757i | \(-0.574471\pi\) | ||||
−0.231829 | + | 0.972757i | \(0.574471\pi\) | |||||||
\(822\) | 78256.0 | 3.32055 | ||||||||
\(823\) | 15600.9 | 0.660769 | 0.330384 | − | 0.943846i | \(-0.392822\pi\) | ||||
0.330384 | + | 0.943846i | \(0.392822\pi\) | |||||||
\(824\) | −89581.6 | −3.78729 | ||||||||
\(825\) | −44019.5 | −1.85765 | ||||||||
\(826\) | 1581.12 | 0.0666033 | ||||||||
\(827\) | 15888.5 | 0.668075 | 0.334038 | − | 0.942560i | \(-0.391589\pi\) | ||||
0.334038 | + | 0.942560i | \(0.391589\pi\) | |||||||
\(828\) | −1560.97 | −0.0655162 | ||||||||
\(829\) | 44098.8 | 1.84754 | 0.923772 | − | 0.382942i | \(-0.125089\pi\) | ||||
0.923772 | + | 0.382942i | \(0.125089\pi\) | |||||||
\(830\) | −12229.1 | −0.511419 | ||||||||
\(831\) | −61816.9 | −2.58051 | ||||||||
\(832\) | 2846.50 | 0.118611 | ||||||||
\(833\) | −37115.0 | −1.54377 | ||||||||
\(834\) | 86417.7 | 3.58801 | ||||||||
\(835\) | 21698.5 | 0.899291 | ||||||||
\(836\) | −22921.0 | −0.948251 | ||||||||
\(837\) | 22992.9 | 0.949523 | ||||||||
\(838\) | 38852.3 | 1.60159 | ||||||||
\(839\) | −36334.9 | −1.49514 | −0.747569 | − | 0.664184i | \(-0.768779\pi\) | ||||
−0.747569 | + | 0.664184i | \(0.768779\pi\) | |||||||
\(840\) | −2703.48 | −0.111046 | ||||||||
\(841\) | −23348.2 | −0.957324 | ||||||||
\(842\) | 4270.54 | 0.174789 | ||||||||
\(843\) | 64396.1 | 2.63098 | ||||||||
\(844\) | −80009.5 | −3.26308 | ||||||||
\(845\) | 12184.5 | 0.496046 | ||||||||
\(846\) | 75079.7 | 3.05118 | ||||||||
\(847\) | 834.877 | 0.0338686 | ||||||||
\(848\) | −19358.7 | −0.783938 | ||||||||
\(849\) | 19742.5 | 0.798068 | ||||||||
\(850\) | 53304.2 | 2.15097 | ||||||||
\(851\) | −420.626 | −0.0169434 | ||||||||
\(852\) | 174213. | 7.00523 | ||||||||
\(853\) | −35791.3 | −1.43666 | −0.718330 | − | 0.695703i | \(-0.755093\pi\) | ||||
−0.718330 | + | 0.695703i | \(0.755093\pi\) | |||||||
\(854\) | 158.547 | 0.00635289 | ||||||||
\(855\) | −9078.53 | −0.363133 | ||||||||
\(856\) | −31861.8 | −1.27221 | ||||||||
\(857\) | −21314.2 | −0.849566 | −0.424783 | − | 0.905295i | \(-0.639650\pi\) | ||||
−0.424783 | + | 0.905295i | \(0.639650\pi\) | |||||||
\(858\) | −11277.8 | −0.448738 | ||||||||
\(859\) | 20018.3 | 0.795129 | 0.397565 | − | 0.917574i | \(-0.369855\pi\) | ||||
0.397565 | + | 0.917574i | \(0.369855\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 499.788 | 0.0197825 | ||||||||
\(862\) | 33971.5 | 1.34231 | ||||||||
\(863\) | −19104.2 | −0.753550 | −0.376775 | − | 0.926305i | \(-0.622967\pi\) | ||||
−0.376775 | + | 0.926305i | \(0.622967\pi\) | |||||||
\(864\) | 142114. | 5.59586 | ||||||||
\(865\) | 20724.0 | 0.814609 | ||||||||
\(866\) | 60974.9 | 2.39262 | ||||||||
\(867\) | −66356.3 | −2.59928 | ||||||||
\(868\) | −949.412 | −0.0371257 | ||||||||
\(869\) | 29695.3 | 1.15920 | ||||||||
\(870\) | −9197.69 | −0.358426 | ||||||||
\(871\) | 793.287 | 0.0308605 | ||||||||
\(872\) | −117225. | −4.55245 | ||||||||
\(873\) | 28967.9 | 1.12304 | ||||||||
\(874\) | 151.028 | 0.00584508 | ||||||||
\(875\) | 1004.15 | 0.0387958 | ||||||||
\(876\) | 6423.13 | 0.247737 | ||||||||
\(877\) | −2573.42 | −0.0990859 | −0.0495430 | − | 0.998772i | \(-0.515776\pi\) | ||||
−0.0495430 | + | 0.998772i | \(0.515776\pi\) | |||||||
\(878\) | −38904.8 | −1.49542 | ||||||||
\(879\) | 31803.6 | 1.22038 | ||||||||
\(880\) | 44004.2 | 1.68566 | ||||||||
\(881\) | −2855.96 | −0.109217 | −0.0546083 | − | 0.998508i | \(-0.517391\pi\) | ||||
−0.0546083 | + | 0.998508i | \(0.517391\pi\) | |||||||
\(882\) | 120526. | 4.60127 | ||||||||
\(883\) | −38336.8 | −1.46108 | −0.730541 | − | 0.682869i | \(-0.760732\pi\) | ||||
−0.730541 | + | 0.682869i | \(0.760732\pi\) | |||||||
\(884\) | 9692.57 | 0.368774 | ||||||||
\(885\) | −19940.2 | −0.757379 | ||||||||
\(886\) | −56433.2 | −2.13986 | ||||||||
\(887\) | −18543.8 | −0.701960 | −0.350980 | − | 0.936383i | \(-0.614152\pi\) | ||||
−0.350980 | + | 0.936383i | \(0.614152\pi\) | |||||||
\(888\) | 208096. | 7.86401 | ||||||||
\(889\) | 1477.79 | 0.0557519 | ||||||||
\(890\) | −27100.9 | −1.02070 | ||||||||
\(891\) | −94886.7 | −3.56770 | ||||||||
\(892\) | 28159.9 | 1.05702 | ||||||||
\(893\) | −5155.67 | −0.193201 | ||||||||
\(894\) | 148837. | 5.56808 | ||||||||
\(895\) | 10008.4 | 0.373794 | ||||||||
\(896\) | −282.098 | −0.0105181 | ||||||||
\(897\) | 52.7409 | 0.00196318 | ||||||||
\(898\) | 15532.4 | 0.577197 | ||||||||
\(899\) | −1909.07 | −0.0708243 | ||||||||
\(900\) | −122855. | −4.55017 | ||||||||
\(901\) | −12943.3 | −0.478584 | ||||||||
\(902\) | −15985.7 | −0.590096 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 70606.6 | 2.59772 | ||||||||
\(905\) | −20844.1 | −0.765615 | ||||||||
\(906\) | 74120.2 | 2.71797 | ||||||||
\(907\) | 27448.6 | 1.00487 | 0.502434 | − | 0.864615i | \(-0.332438\pi\) | ||||
0.502434 | + | 0.864615i | \(0.332438\pi\) | |||||||
\(908\) | 66041.8 | 2.41374 | ||||||||
\(909\) | 53218.9 | 1.94187 | ||||||||
\(910\) | 110.187 | 0.00401392 | ||||||||
\(911\) | −21983.3 | −0.799495 | −0.399748 | − | 0.916625i | \(-0.630902\pi\) | ||||
−0.399748 | + | 0.916625i | \(0.630902\pi\) | |||||||
\(912\) | −38023.4 | −1.38057 | ||||||||
\(913\) | 20162.7 | 0.730873 | ||||||||
\(914\) | −39098.4 | −1.41495 | ||||||||
\(915\) | −1999.50 | −0.0722418 | ||||||||
\(916\) | 75573.9 | 2.72602 | ||||||||
\(917\) | 550.235 | 0.0198150 | ||||||||
\(918\) | 221168. | 7.95166 | ||||||||
\(919\) | 44001.0 | 1.57939 | 0.789695 | − | 0.613499i | \(-0.210239\pi\) | ||||
0.789695 | + | 0.613499i | \(0.210239\pi\) | |||||||
\(920\) | −404.383 | −0.0144914 | ||||||||
\(921\) | −55438.1 | −1.98344 | ||||||||
\(922\) | −69009.7 | −2.46498 | ||||||||
\(923\) | −4196.63 | −0.149657 | ||||||||
\(924\) | 7541.65 | 0.268509 | ||||||||
\(925\) | −33105.0 | −1.17674 | ||||||||
\(926\) | 43565.8 | 1.54607 | ||||||||
\(927\) | 98979.4 | 3.50692 | ||||||||
\(928\) | −11799.6 | −0.417392 | ||||||||
\(929\) | −7977.00 | −0.281719 | −0.140860 | − | 0.990030i | \(-0.544987\pi\) | ||||
−0.140860 | + | 0.990030i | \(0.544987\pi\) | |||||||
\(930\) | 16870.1 | 0.594831 | ||||||||
\(931\) | −8276.43 | −0.291352 | ||||||||
\(932\) | −27808.0 | −0.977339 | ||||||||
\(933\) | −51233.3 | −1.79775 | ||||||||
\(934\) | −26980.8 | −0.945225 | ||||||||
\(935\) | 29421.5 | 1.02907 | ||||||||
\(936\) | −18602.9 | −0.649632 | ||||||||
\(937\) | −16116.5 | −0.561904 | −0.280952 | − | 0.959722i | \(-0.590650\pi\) | ||||
−0.280952 | + | 0.959722i | \(0.590650\pi\) | |||||||
\(938\) | −747.436 | −0.0260178 | ||||||||
\(939\) | −13027.9 | −0.452767 | ||||||||
\(940\) | 23356.6 | 0.810435 | ||||||||
\(941\) | 24389.1 | 0.844912 | 0.422456 | − | 0.906384i | \(-0.361168\pi\) | ||||
0.422456 | + | 0.906384i | \(0.361168\pi\) | |||||||
\(942\) | −64097.0 | −2.21698 | ||||||||
\(943\) | 74.7578 | 0.00258160 | ||||||||
\(944\) | −59542.8 | −2.05292 | ||||||||
\(945\) | 1784.48 | 0.0614278 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −6934.33 | −0.237946 | −0.118973 | − | 0.992897i | \(-0.537960\pi\) | ||||
−0.118973 | + | 0.992897i | \(0.537960\pi\) | |||||||
\(948\) | 116243. | 3.98250 | ||||||||
\(949\) | −154.727 | −0.00529257 | ||||||||
\(950\) | 11886.5 | 0.405948 | ||||||||
\(951\) | −18504.9 | −0.630980 | ||||||||
\(952\) | −5397.51 | −0.183755 | ||||||||
\(953\) | −507.536 | −0.0172515 | −0.00862577 | − | 0.999963i | \(-0.502746\pi\) | ||||
−0.00862577 | + | 0.999963i | \(0.502746\pi\) | |||||||
\(954\) | 42031.6 | 1.42644 | ||||||||
\(955\) | 23733.8 | 0.804196 | ||||||||
\(956\) | 85850.3 | 2.90439 | ||||||||
\(957\) | 15164.7 | 0.512230 | ||||||||
\(958\) | −54617.4 | −1.84197 | ||||||||
\(959\) | 1260.61 | 0.0424475 | ||||||||
\(960\) | 33823.3 | 1.13713 | ||||||||
\(961\) | −26289.4 | −0.882463 | ||||||||
\(962\) | −8481.49 | −0.284256 | ||||||||
\(963\) | 35204.3 | 1.17803 | ||||||||
\(964\) | 39668.9 | 1.32536 | ||||||||
\(965\) | −11690.3 | −0.389974 | ||||||||
\(966\) | −49.6926 | −0.00165511 | ||||||||
\(967\) | −35811.1 | −1.19091 | −0.595454 | − | 0.803389i | \(-0.703028\pi\) | ||||
−0.595454 | + | 0.803389i | \(0.703028\pi\) | |||||||
\(968\) | −61781.8 | −2.05139 | ||||||||
\(969\) | −25422.6 | −0.842820 | ||||||||
\(970\) | 12697.1 | 0.420290 | ||||||||
\(971\) | −46854.8 | −1.54855 | −0.774275 | − | 0.632849i | \(-0.781885\pi\) | ||||
−0.774275 | + | 0.632849i | \(0.781885\pi\) | |||||||
\(972\) | −166214. | −5.48490 | ||||||||
\(973\) | 1392.08 | 0.0458664 | ||||||||
\(974\) | −684.435 | −0.0225161 | ||||||||
\(975\) | 4150.93 | 0.136345 | ||||||||
\(976\) | −5970.65 | −0.195815 | ||||||||
\(977\) | 4116.58 | 0.134802 | 0.0674008 | − | 0.997726i | \(-0.478529\pi\) | ||||
0.0674008 | + | 0.997726i | \(0.478529\pi\) | |||||||
\(978\) | 138390. | 4.52478 | ||||||||
\(979\) | 44682.6 | 1.45869 | ||||||||
\(980\) | 37494.5 | 1.22216 | ||||||||
\(981\) | 129523. | 4.21544 | ||||||||
\(982\) | −34386.7 | −1.11744 | ||||||||
\(983\) | 18015.4 | 0.584539 | 0.292270 | − | 0.956336i | \(-0.405590\pi\) | ||||
0.292270 | + | 0.956336i | \(0.405590\pi\) | |||||||
\(984\) | −36984.9 | −1.19821 | ||||||||
\(985\) | −15821.0 | −0.511777 | ||||||||
\(986\) | −18363.3 | −0.593109 | ||||||||
\(987\) | 1696.36 | 0.0547070 | ||||||||
\(988\) | 2161.39 | 0.0695981 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −95542.2 | −3.06720 | ||||||||
\(991\) | −51294.1 | −1.64421 | −0.822105 | − | 0.569336i | \(-0.807200\pi\) | ||||
−0.822105 | + | 0.569336i | \(0.807200\pi\) | |||||||
\(992\) | 21642.4 | 0.692688 | ||||||||
\(993\) | 89470.1 | 2.85926 | ||||||||
\(994\) | 3954.07 | 0.126173 | ||||||||
\(995\) | 249.904 | 0.00796229 | ||||||||
\(996\) | 78927.6 | 2.51096 | ||||||||
\(997\) | −17610.7 | −0.559415 | −0.279707 | − | 0.960085i | \(-0.590237\pi\) | ||||
−0.279707 | + | 0.960085i | \(0.590237\pi\) | |||||||
\(998\) | 65222.3 | 2.06871 | ||||||||
\(999\) | −137358. | −4.35016 |
(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 | 1849.4.a.k.1.5 | 60 | ||
43.3 | odd | 42 | 43.4.g.a.9.10 | ✓ | 120 | ||
43.29 | odd | 42 | 43.4.g.a.24.10 | yes | 120 | ||
43.42 | odd | 2 | 1849.4.a.l.1.56 | 60 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.4.g.a.9.10 | ✓ | 120 | 43.3 | odd | 42 | ||
43.4.g.a.24.10 | yes | 120 | 43.29 | odd | 42 | ||
1849.4.a.k.1.5 | 60 | 1.1 | even | 1 | trivial | ||
1849.4.a.l.1.56 | 60 | 43.42 | odd | 2 |