Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2254,4,Mod(1,2254)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2254, 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("2254.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2254 = 2 \cdot 7^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2254.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: | \(132.990305153\) |
Analytic rank: | \(0\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{11} - 5 x^{10} - 165 x^{9} + 798 x^{8} + 8769 x^{7} - 38472 x^{6} - 184213 x^{5} + 644009 x^{4} + \cdots + 2848203 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 322) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(-6.47210\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2254.1 |
$q$-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 | ||||||||
\(3\) | 7.47210 | 1.43801 | 0.719003 | − | 0.695007i | \(-0.244599\pi\) | ||||
0.719003 | + | 0.695007i | \(0.244599\pi\) | |||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 5.30939 | 0.474886 | 0.237443 | − | 0.971401i | \(-0.423691\pi\) | ||||
0.237443 | + | 0.971401i | \(0.423691\pi\) | |||||||
\(6\) | 14.9442 | 1.01682 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 28.8323 | 1.06786 | ||||||||
\(10\) | 10.6188 | 0.335795 | ||||||||
\(11\) | 15.0723 | 0.413135 | 0.206567 | − | 0.978432i | \(-0.433771\pi\) | ||||
0.206567 | + | 0.978432i | \(0.433771\pi\) | |||||||
\(12\) | 29.8884 | 0.719003 | ||||||||
\(13\) | −19.5834 | −0.417804 | −0.208902 | − | 0.977937i | \(-0.566989\pi\) | ||||
−0.208902 | + | 0.977937i | \(0.566989\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 39.6723 | 0.682889 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 114.919 | 1.63953 | 0.819763 | − | 0.572702i | \(-0.194105\pi\) | ||||
0.819763 | + | 0.572702i | \(0.194105\pi\) | |||||||
\(18\) | 57.6646 | 0.755093 | ||||||||
\(19\) | −51.8349 | −0.625881 | −0.312940 | − | 0.949773i | \(-0.601314\pi\) | ||||
−0.312940 | + | 0.949773i | \(0.601314\pi\) | |||||||
\(20\) | 21.2376 | 0.237443 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 30.1447 | 0.292130 | ||||||||
\(23\) | −23.0000 | −0.208514 | ||||||||
\(24\) | 59.7768 | 0.508412 | ||||||||
\(25\) | −96.8104 | −0.774483 | ||||||||
\(26\) | −39.1667 | −0.295432 | ||||||||
\(27\) | 13.6912 | 0.0975881 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 227.585 | 1.45729 | 0.728646 | − | 0.684890i | \(-0.240150\pi\) | ||||
0.728646 | + | 0.684890i | \(0.240150\pi\) | |||||||
\(30\) | 79.3446 | 0.482876 | ||||||||
\(31\) | 178.024 | 1.03142 | 0.515712 | − | 0.856762i | \(-0.327528\pi\) | ||||
0.515712 | + | 0.856762i | \(0.327528\pi\) | |||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | 112.622 | 0.594090 | ||||||||
\(34\) | 229.838 | 1.15932 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 115.329 | 0.533932 | ||||||||
\(37\) | 20.7398 | 0.0921513 | 0.0460756 | − | 0.998938i | \(-0.485328\pi\) | ||||
0.0460756 | + | 0.998938i | \(0.485328\pi\) | |||||||
\(38\) | −103.670 | −0.442565 | ||||||||
\(39\) | −146.329 | −0.600804 | ||||||||
\(40\) | 42.4751 | 0.167898 | ||||||||
\(41\) | 107.492 | 0.409449 | 0.204724 | − | 0.978820i | \(-0.434370\pi\) | ||||
0.204724 | + | 0.978820i | \(0.434370\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 138.795 | 0.492232 | 0.246116 | − | 0.969240i | \(-0.420846\pi\) | ||||
0.246116 | + | 0.969240i | \(0.420846\pi\) | |||||||
\(44\) | 60.2894 | 0.206567 | ||||||||
\(45\) | 153.082 | 0.507113 | ||||||||
\(46\) | −46.0000 | −0.147442 | ||||||||
\(47\) | −21.4507 | −0.0665725 | −0.0332863 | − | 0.999446i | \(-0.510597\pi\) | ||||
−0.0332863 | + | 0.999446i | \(0.510597\pi\) | |||||||
\(48\) | 119.554 | 0.359502 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −193.621 | −0.547642 | ||||||||
\(51\) | 858.687 | 2.35765 | ||||||||
\(52\) | −78.3334 | −0.208902 | ||||||||
\(53\) | 429.203 | 1.11237 | 0.556185 | − | 0.831059i | \(-0.312265\pi\) | ||||
0.556185 | + | 0.831059i | \(0.312265\pi\) | |||||||
\(54\) | 27.3825 | 0.0690052 | ||||||||
\(55\) | 80.0249 | 0.196192 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −387.316 | −0.900021 | ||||||||
\(58\) | 455.170 | 1.03046 | ||||||||
\(59\) | −128.564 | −0.283689 | −0.141844 | − | 0.989889i | \(-0.545303\pi\) | ||||
−0.141844 | + | 0.989889i | \(0.545303\pi\) | |||||||
\(60\) | 158.689 | 0.341445 | ||||||||
\(61\) | −225.931 | −0.474222 | −0.237111 | − | 0.971483i | \(-0.576200\pi\) | ||||
−0.237111 | + | 0.971483i | \(0.576200\pi\) | |||||||
\(62\) | 356.049 | 0.729326 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −103.976 | −0.198409 | ||||||||
\(66\) | 225.244 | 0.420085 | ||||||||
\(67\) | 478.716 | 0.872902 | 0.436451 | − | 0.899728i | \(-0.356235\pi\) | ||||
0.436451 | + | 0.899728i | \(0.356235\pi\) | |||||||
\(68\) | 459.676 | 0.819763 | ||||||||
\(69\) | −171.858 | −0.299845 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 652.010 | 1.08985 | 0.544925 | − | 0.838485i | \(-0.316558\pi\) | ||||
0.544925 | + | 0.838485i | \(0.316558\pi\) | |||||||
\(72\) | 230.659 | 0.377547 | ||||||||
\(73\) | 516.418 | 0.827975 | 0.413987 | − | 0.910283i | \(-0.364136\pi\) | ||||
0.413987 | + | 0.910283i | \(0.364136\pi\) | |||||||
\(74\) | 41.4796 | 0.0651608 | ||||||||
\(75\) | −723.377 | −1.11371 | ||||||||
\(76\) | −207.340 | −0.312940 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −292.658 | −0.424833 | ||||||||
\(79\) | −349.397 | −0.497597 | −0.248799 | − | 0.968555i | \(-0.580036\pi\) | ||||
−0.248799 | + | 0.968555i | \(0.580036\pi\) | |||||||
\(80\) | 84.9502 | 0.118722 | ||||||||
\(81\) | −676.170 | −0.927531 | ||||||||
\(82\) | 214.984 | 0.289524 | ||||||||
\(83\) | −373.014 | −0.493297 | −0.246649 | − | 0.969105i | \(-0.579329\pi\) | ||||
−0.246649 | + | 0.969105i | \(0.579329\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 610.150 | 0.778588 | ||||||||
\(86\) | 277.589 | 0.348061 | ||||||||
\(87\) | 1700.54 | 2.09560 | ||||||||
\(88\) | 120.579 | 0.146065 | ||||||||
\(89\) | −896.694 | −1.06797 | −0.533985 | − | 0.845494i | \(-0.679306\pi\) | ||||
−0.533985 | + | 0.845494i | \(0.679306\pi\) | |||||||
\(90\) | 306.164 | 0.358583 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −92.0000 | −0.104257 | ||||||||
\(93\) | 1330.22 | 1.48319 | ||||||||
\(94\) | −42.9014 | −0.0470739 | ||||||||
\(95\) | −275.211 | −0.297222 | ||||||||
\(96\) | 239.107 | 0.254206 | ||||||||
\(97\) | 1294.92 | 1.35546 | 0.677729 | − | 0.735312i | \(-0.262964\pi\) | ||||
0.677729 | + | 0.735312i | \(0.262964\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 434.570 | 0.441171 | ||||||||
\(100\) | −387.242 | −0.387242 | ||||||||
\(101\) | −309.230 | −0.304649 | −0.152325 | − | 0.988331i | \(-0.548676\pi\) | ||||
−0.152325 | + | 0.988331i | \(0.548676\pi\) | |||||||
\(102\) | 1717.37 | 1.66711 | ||||||||
\(103\) | −617.628 | −0.590842 | −0.295421 | − | 0.955367i | \(-0.595460\pi\) | ||||
−0.295421 | + | 0.955367i | \(0.595460\pi\) | |||||||
\(104\) | −156.667 | −0.147716 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 858.407 | 0.786564 | ||||||||
\(107\) | −1225.20 | −1.10696 | −0.553481 | − | 0.832862i | \(-0.686701\pi\) | ||||
−0.553481 | + | 0.832862i | \(0.686701\pi\) | |||||||
\(108\) | 54.7649 | 0.0487941 | ||||||||
\(109\) | 157.245 | 0.138177 | 0.0690886 | − | 0.997611i | \(-0.477991\pi\) | ||||
0.0690886 | + | 0.997611i | \(0.477991\pi\) | |||||||
\(110\) | 160.050 | 0.138729 | ||||||||
\(111\) | 154.970 | 0.132514 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1226.97 | −1.02145 | −0.510723 | − | 0.859745i | \(-0.670622\pi\) | ||||
−0.510723 | + | 0.859745i | \(0.670622\pi\) | |||||||
\(114\) | −774.631 | −0.636411 | ||||||||
\(115\) | −122.116 | −0.0990206 | ||||||||
\(116\) | 910.340 | 0.728646 | ||||||||
\(117\) | −564.634 | −0.446157 | ||||||||
\(118\) | −257.128 | −0.200598 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 317.378 | 0.241438 | ||||||||
\(121\) | −1103.82 | −0.829320 | ||||||||
\(122\) | −451.862 | −0.335325 | ||||||||
\(123\) | 803.190 | 0.588790 | ||||||||
\(124\) | 712.097 | 0.515712 | ||||||||
\(125\) | −1177.68 | −0.842677 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1229.19 | 0.858840 | 0.429420 | − | 0.903105i | \(-0.358718\pi\) | ||||
0.429420 | + | 0.903105i | \(0.358718\pi\) | |||||||
\(128\) | 128.000 | 0.0883883 | ||||||||
\(129\) | 1037.09 | 0.707834 | ||||||||
\(130\) | −207.951 | −0.140296 | ||||||||
\(131\) | 2420.93 | 1.61464 | 0.807321 | − | 0.590113i | \(-0.200917\pi\) | ||||
0.807321 | + | 0.590113i | \(0.200917\pi\) | |||||||
\(132\) | 450.488 | 0.297045 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 957.432 | 0.617235 | ||||||||
\(135\) | 72.6921 | 0.0463432 | ||||||||
\(136\) | 919.352 | 0.579660 | ||||||||
\(137\) | 3202.71 | 1.99727 | 0.998635 | − | 0.0522373i | \(-0.0166352\pi\) | ||||
0.998635 | + | 0.0522373i | \(0.0166352\pi\) | |||||||
\(138\) | −343.717 | −0.212023 | ||||||||
\(139\) | 1710.35 | 1.04367 | 0.521833 | − | 0.853048i | \(-0.325248\pi\) | ||||
0.521833 | + | 0.853048i | \(0.325248\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −160.282 | −0.0957317 | ||||||||
\(142\) | 1304.02 | 0.770641 | ||||||||
\(143\) | −295.167 | −0.172609 | ||||||||
\(144\) | 461.317 | 0.266966 | ||||||||
\(145\) | 1208.34 | 0.692048 | ||||||||
\(146\) | 1032.84 | 0.585466 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 82.9591 | 0.0460756 | ||||||||
\(149\) | −2647.44 | −1.45561 | −0.727807 | − | 0.685782i | \(-0.759461\pi\) | ||||
−0.727807 | + | 0.685782i | \(0.759461\pi\) | |||||||
\(150\) | −1446.75 | −0.787513 | ||||||||
\(151\) | −1010.81 | −0.544761 | −0.272381 | − | 0.962190i | \(-0.587811\pi\) | ||||
−0.272381 | + | 0.962190i | \(0.587811\pi\) | |||||||
\(152\) | −414.679 | −0.221282 | ||||||||
\(153\) | 3313.38 | 1.75079 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 945.200 | 0.489809 | ||||||||
\(156\) | −585.315 | −0.300402 | ||||||||
\(157\) | −76.7891 | −0.0390347 | −0.0195173 | − | 0.999810i | \(-0.506213\pi\) | ||||
−0.0195173 | + | 0.999810i | \(0.506213\pi\) | |||||||
\(158\) | −698.793 | −0.351854 | ||||||||
\(159\) | 3207.05 | 1.59960 | ||||||||
\(160\) | 169.900 | 0.0839488 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1352.34 | −0.655864 | ||||||||
\(163\) | 2149.22 | 1.03276 | 0.516379 | − | 0.856360i | \(-0.327280\pi\) | ||||
0.516379 | + | 0.856360i | \(0.327280\pi\) | |||||||
\(164\) | 429.967 | 0.204724 | ||||||||
\(165\) | 597.954 | 0.282125 | ||||||||
\(166\) | −746.029 | −0.348814 | ||||||||
\(167\) | 2071.34 | 0.959791 | 0.479896 | − | 0.877326i | \(-0.340675\pi\) | ||||
0.479896 | + | 0.877326i | \(0.340675\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1813.49 | −0.825440 | ||||||||
\(170\) | 1220.30 | 0.550545 | ||||||||
\(171\) | −1494.52 | −0.668355 | ||||||||
\(172\) | 555.179 | 0.246116 | ||||||||
\(173\) | −3121.85 | −1.37197 | −0.685983 | − | 0.727618i | \(-0.740627\pi\) | ||||
−0.685983 | + | 0.727618i | \(0.740627\pi\) | |||||||
\(174\) | 3401.08 | 1.48181 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 241.157 | 0.103284 | ||||||||
\(177\) | −960.645 | −0.407946 | ||||||||
\(178\) | −1793.39 | −0.755169 | ||||||||
\(179\) | −3069.29 | −1.28162 | −0.640808 | − | 0.767701i | \(-0.721401\pi\) | ||||
−0.640808 | + | 0.767701i | \(0.721401\pi\) | |||||||
\(180\) | 612.328 | 0.253557 | ||||||||
\(181\) | −1108.70 | −0.455300 | −0.227650 | − | 0.973743i | \(-0.573104\pi\) | ||||
−0.227650 | + | 0.973743i | \(0.573104\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1688.18 | −0.681934 | ||||||||
\(184\) | −184.000 | −0.0737210 | ||||||||
\(185\) | 110.116 | 0.0437614 | ||||||||
\(186\) | 2660.43 | 1.04878 | ||||||||
\(187\) | 1732.10 | 0.677345 | ||||||||
\(188\) | −85.8028 | −0.0332863 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −550.423 | −0.210168 | ||||||||
\(191\) | −3180.62 | −1.20493 | −0.602465 | − | 0.798146i | \(-0.705815\pi\) | ||||
−0.602465 | + | 0.798146i | \(0.705815\pi\) | |||||||
\(192\) | 478.215 | 0.179751 | ||||||||
\(193\) | −812.325 | −0.302966 | −0.151483 | − | 0.988460i | \(-0.548405\pi\) | ||||
−0.151483 | + | 0.988460i | \(0.548405\pi\) | |||||||
\(194\) | 2589.84 | 0.958454 | ||||||||
\(195\) | −776.917 | −0.285314 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3772.40 | −1.36433 | −0.682164 | − | 0.731199i | \(-0.738961\pi\) | ||||
−0.682164 | + | 0.731199i | \(0.738961\pi\) | |||||||
\(198\) | 869.141 | 0.311955 | ||||||||
\(199\) | 1524.28 | 0.542980 | 0.271490 | − | 0.962441i | \(-0.412484\pi\) | ||||
0.271490 | + | 0.962441i | \(0.412484\pi\) | |||||||
\(200\) | −774.483 | −0.273821 | ||||||||
\(201\) | 3577.01 | 1.25524 | ||||||||
\(202\) | −618.460 | −0.215419 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 3434.75 | 1.17883 | ||||||||
\(205\) | 570.716 | 0.194441 | ||||||||
\(206\) | −1235.26 | −0.417788 | ||||||||
\(207\) | −663.143 | −0.222665 | ||||||||
\(208\) | −313.334 | −0.104451 | ||||||||
\(209\) | −781.273 | −0.258573 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 910.563 | 0.297089 | 0.148544 | − | 0.988906i | \(-0.452541\pi\) | ||||
0.148544 | + | 0.988906i | \(0.452541\pi\) | |||||||
\(212\) | 1716.81 | 0.556185 | ||||||||
\(213\) | 4871.89 | 1.56721 | ||||||||
\(214\) | −2450.41 | −0.782740 | ||||||||
\(215\) | 736.915 | 0.233754 | ||||||||
\(216\) | 109.530 | 0.0345026 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 314.489 | 0.0977060 | ||||||||
\(219\) | 3858.73 | 1.19063 | ||||||||
\(220\) | 320.100 | 0.0980959 | ||||||||
\(221\) | −2250.50 | −0.685000 | ||||||||
\(222\) | 309.939 | 0.0937017 | ||||||||
\(223\) | −1289.30 | −0.387166 | −0.193583 | − | 0.981084i | \(-0.562011\pi\) | ||||
−0.193583 | + | 0.981084i | \(0.562011\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2791.27 | −0.827042 | ||||||||
\(226\) | −2453.94 | −0.722272 | ||||||||
\(227\) | −1413.94 | −0.413419 | −0.206710 | − | 0.978402i | \(-0.566276\pi\) | ||||
−0.206710 | + | 0.978402i | \(0.566276\pi\) | |||||||
\(228\) | −1549.26 | −0.450010 | ||||||||
\(229\) | 799.165 | 0.230613 | 0.115306 | − | 0.993330i | \(-0.463215\pi\) | ||||
0.115306 | + | 0.993330i | \(0.463215\pi\) | |||||||
\(230\) | −244.232 | −0.0700181 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1820.68 | 0.515231 | ||||||||
\(233\) | 1554.41 | 0.437050 | 0.218525 | − | 0.975831i | \(-0.429875\pi\) | ||||
0.218525 | + | 0.975831i | \(0.429875\pi\) | |||||||
\(234\) | −1129.27 | −0.315481 | ||||||||
\(235\) | −113.890 | −0.0316144 | ||||||||
\(236\) | −514.257 | −0.141844 | ||||||||
\(237\) | −2610.73 | −0.715548 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6967.81 | −1.88582 | −0.942908 | − | 0.333052i | \(-0.891922\pi\) | ||||
−0.942908 | + | 0.333052i | \(0.891922\pi\) | |||||||
\(240\) | 634.757 | 0.170722 | ||||||||
\(241\) | 5058.24 | 1.35199 | 0.675996 | − | 0.736905i | \(-0.263714\pi\) | ||||
0.675996 | + | 0.736905i | \(0.263714\pi\) | |||||||
\(242\) | −2207.65 | −0.586418 | ||||||||
\(243\) | −5422.08 | −1.43138 | ||||||||
\(244\) | −903.725 | −0.237111 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1606.38 | 0.416337 | ||||||||
\(247\) | 1015.10 | 0.261495 | ||||||||
\(248\) | 1424.19 | 0.364663 | ||||||||
\(249\) | −2787.20 | −0.709365 | ||||||||
\(250\) | −2355.35 | −0.595863 | ||||||||
\(251\) | 3363.38 | 0.845796 | 0.422898 | − | 0.906177i | \(-0.361013\pi\) | ||||
0.422898 | + | 0.906177i | \(0.361013\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −346.664 | −0.0861445 | ||||||||
\(254\) | 2458.37 | 0.607292 | ||||||||
\(255\) | 4559.10 | 1.11962 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 7020.29 | 1.70394 | 0.851972 | − | 0.523588i | \(-0.175407\pi\) | ||||
0.851972 | + | 0.523588i | \(0.175407\pi\) | |||||||
\(258\) | 2074.18 | 0.500514 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −415.903 | −0.0992046 | ||||||||
\(261\) | 6561.80 | 1.55619 | ||||||||
\(262\) | 4841.87 | 1.14172 | ||||||||
\(263\) | −1118.57 | −0.262258 | −0.131129 | − | 0.991365i | \(-0.541860\pi\) | ||||
−0.131129 | + | 0.991365i | \(0.541860\pi\) | |||||||
\(264\) | 900.976 | 0.210043 | ||||||||
\(265\) | 2278.81 | 0.528249 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6700.19 | −1.53575 | ||||||||
\(268\) | 1914.86 | 0.436451 | ||||||||
\(269\) | 2785.87 | 0.631439 | 0.315720 | − | 0.948853i | \(-0.397754\pi\) | ||||
0.315720 | + | 0.948853i | \(0.397754\pi\) | |||||||
\(270\) | 145.384 | 0.0327696 | ||||||||
\(271\) | 2689.54 | 0.602870 | 0.301435 | − | 0.953487i | \(-0.402534\pi\) | ||||
0.301435 | + | 0.953487i | \(0.402534\pi\) | |||||||
\(272\) | 1838.70 | 0.409882 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6405.42 | 1.41228 | ||||||||
\(275\) | −1459.16 | −0.319966 | ||||||||
\(276\) | −687.433 | −0.149923 | ||||||||
\(277\) | −830.836 | −0.180217 | −0.0901085 | − | 0.995932i | \(-0.528721\pi\) | ||||
−0.0901085 | + | 0.995932i | \(0.528721\pi\) | |||||||
\(278\) | 3420.69 | 0.737984 | ||||||||
\(279\) | 5132.85 | 1.10142 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8850.37 | −1.87889 | −0.939447 | − | 0.342695i | \(-0.888660\pi\) | ||||
−0.939447 | + | 0.342695i | \(0.888660\pi\) | |||||||
\(282\) | −320.564 | −0.0676925 | ||||||||
\(283\) | 557.575 | 0.117118 | 0.0585590 | − | 0.998284i | \(-0.481349\pi\) | ||||
0.0585590 | + | 0.998284i | \(0.481349\pi\) | |||||||
\(284\) | 2608.04 | 0.544925 | ||||||||
\(285\) | −2056.41 | −0.427407 | ||||||||
\(286\) | −590.334 | −0.122053 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 922.634 | 0.188773 | ||||||||
\(289\) | 8293.38 | 1.68805 | ||||||||
\(290\) | 2416.67 | 0.489352 | ||||||||
\(291\) | 9675.79 | 1.94916 | ||||||||
\(292\) | 2065.67 | 0.413987 | ||||||||
\(293\) | 263.506 | 0.0525400 | 0.0262700 | − | 0.999655i | \(-0.491637\pi\) | ||||
0.0262700 | + | 0.999655i | \(0.491637\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −682.597 | −0.134720 | ||||||||
\(296\) | 165.918 | 0.0325804 | ||||||||
\(297\) | 206.359 | 0.0403170 | ||||||||
\(298\) | −5294.88 | −1.02928 | ||||||||
\(299\) | 450.417 | 0.0871181 | ||||||||
\(300\) | −2893.51 | −0.556856 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −2021.63 | −0.385204 | ||||||||
\(303\) | −2310.60 | −0.438087 | ||||||||
\(304\) | −829.358 | −0.156470 | ||||||||
\(305\) | −1199.56 | −0.225201 | ||||||||
\(306\) | 6626.76 | 1.23800 | ||||||||
\(307\) | −6200.77 | −1.15276 | −0.576379 | − | 0.817182i | \(-0.695535\pi\) | ||||
−0.576379 | + | 0.817182i | \(0.695535\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4614.98 | −0.849635 | ||||||||
\(310\) | 1890.40 | 0.346347 | ||||||||
\(311\) | −8424.24 | −1.53600 | −0.767999 | − | 0.640452i | \(-0.778747\pi\) | ||||
−0.767999 | + | 0.640452i | \(0.778747\pi\) | |||||||
\(312\) | −1170.63 | −0.212416 | ||||||||
\(313\) | 2421.11 | 0.437218 | 0.218609 | − | 0.975813i | \(-0.429848\pi\) | ||||
0.218609 | + | 0.975813i | \(0.429848\pi\) | |||||||
\(314\) | −153.578 | −0.0276017 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1397.59 | −0.248799 | ||||||||
\(317\) | −1032.26 | −0.182895 | −0.0914474 | − | 0.995810i | \(-0.529149\pi\) | ||||
−0.0914474 | + | 0.995810i | \(0.529149\pi\) | |||||||
\(318\) | 6414.10 | 1.13108 | ||||||||
\(319\) | 3430.24 | 0.602058 | ||||||||
\(320\) | 339.801 | 0.0593608 | ||||||||
\(321\) | −9154.85 | −1.59182 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5956.81 | −1.02615 | ||||||||
\(324\) | −2704.68 | −0.463766 | ||||||||
\(325\) | 1895.87 | 0.323582 | ||||||||
\(326\) | 4298.43 | 0.730270 | ||||||||
\(327\) | 1174.95 | 0.198700 | ||||||||
\(328\) | 859.934 | 0.144762 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 1195.91 | 0.199493 | ||||||||
\(331\) | 1815.35 | 0.301453 | 0.150726 | − | 0.988576i | \(-0.451839\pi\) | ||||
0.150726 | + | 0.988576i | \(0.451839\pi\) | |||||||
\(332\) | −1492.06 | −0.246649 | ||||||||
\(333\) | 597.976 | 0.0984050 | ||||||||
\(334\) | 4142.68 | 0.678675 | ||||||||
\(335\) | 2541.69 | 0.414529 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8160.36 | −1.31906 | −0.659530 | − | 0.751678i | \(-0.729245\pi\) | ||||
−0.659530 | + | 0.751678i | \(0.729245\pi\) | |||||||
\(338\) | −3626.98 | −0.583674 | ||||||||
\(339\) | −9168.03 | −1.46885 | ||||||||
\(340\) | 2440.60 | 0.389294 | ||||||||
\(341\) | 2683.24 | 0.426117 | ||||||||
\(342\) | −2989.04 | −0.472599 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 1110.36 | 0.174030 | ||||||||
\(345\) | −912.463 | −0.142392 | ||||||||
\(346\) | −6243.70 | −0.970126 | ||||||||
\(347\) | −5693.79 | −0.880861 | −0.440431 | − | 0.897787i | \(-0.645174\pi\) | ||||
−0.440431 | + | 0.897787i | \(0.645174\pi\) | |||||||
\(348\) | 6802.15 | 1.04780 | ||||||||
\(349\) | −4560.60 | −0.699494 | −0.349747 | − | 0.936844i | \(-0.613733\pi\) | ||||
−0.349747 | + | 0.936844i | \(0.613733\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −268.120 | −0.0407727 | ||||||||
\(352\) | 482.315 | 0.0730326 | ||||||||
\(353\) | −8580.49 | −1.29375 | −0.646874 | − | 0.762597i | \(-0.723924\pi\) | ||||
−0.646874 | + | 0.762597i | \(0.723924\pi\) | |||||||
\(354\) | −1921.29 | −0.288462 | ||||||||
\(355\) | 3461.78 | 0.517555 | ||||||||
\(356\) | −3586.78 | −0.533985 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6138.58 | −0.906240 | ||||||||
\(359\) | 1989.15 | 0.292433 | 0.146217 | − | 0.989253i | \(-0.453290\pi\) | ||||
0.146217 | + | 0.989253i | \(0.453290\pi\) | |||||||
\(360\) | 1224.66 | 0.179292 | ||||||||
\(361\) | −4172.15 | −0.608273 | ||||||||
\(362\) | −2217.41 | −0.321945 | ||||||||
\(363\) | −8247.89 | −1.19257 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2741.86 | 0.393194 | ||||||||
\(366\) | −3376.36 | −0.482200 | ||||||||
\(367\) | 114.888 | 0.0163409 | 0.00817046 | − | 0.999967i | \(-0.497399\pi\) | ||||
0.00817046 | + | 0.999967i | \(0.497399\pi\) | |||||||
\(368\) | −368.000 | −0.0521286 | ||||||||
\(369\) | 3099.24 | 0.437235 | ||||||||
\(370\) | 220.231 | 0.0309440 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 5320.87 | 0.741597 | ||||||||
\(373\) | 12568.7 | 1.74473 | 0.872363 | − | 0.488858i | \(-0.162586\pi\) | ||||
0.872363 | + | 0.488858i | \(0.162586\pi\) | |||||||
\(374\) | 3464.20 | 0.478956 | ||||||||
\(375\) | −8799.73 | −1.21178 | ||||||||
\(376\) | −171.606 | −0.0235369 | ||||||||
\(377\) | −4456.88 | −0.608862 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12075.5 | −1.63662 | −0.818308 | − | 0.574781i | \(-0.805087\pi\) | ||||
−0.818308 | + | 0.574781i | \(0.805087\pi\) | |||||||
\(380\) | −1100.85 | −0.148611 | ||||||||
\(381\) | 9184.61 | 1.23502 | ||||||||
\(382\) | −6361.24 | −0.852014 | ||||||||
\(383\) | 12228.0 | 1.63139 | 0.815695 | − | 0.578482i | \(-0.196355\pi\) | ||||
0.815695 | + | 0.578482i | \(0.196355\pi\) | |||||||
\(384\) | 956.429 | 0.127103 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1624.65 | −0.214229 | ||||||||
\(387\) | 4001.77 | 0.525637 | ||||||||
\(388\) | 5179.69 | 0.677729 | ||||||||
\(389\) | 3137.56 | 0.408948 | 0.204474 | − | 0.978872i | \(-0.434452\pi\) | ||||
0.204474 | + | 0.978872i | \(0.434452\pi\) | |||||||
\(390\) | −1553.83 | −0.201747 | ||||||||
\(391\) | −2643.14 | −0.341865 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 18089.5 | 2.32187 | ||||||||
\(394\) | −7544.81 | −0.964725 | ||||||||
\(395\) | −1855.08 | −0.236302 | ||||||||
\(396\) | 1738.28 | 0.220586 | ||||||||
\(397\) | −15489.8 | −1.95821 | −0.979106 | − | 0.203352i | \(-0.934816\pi\) | ||||
−0.979106 | + | 0.203352i | \(0.934816\pi\) | |||||||
\(398\) | 3048.55 | 0.383945 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1548.97 | −0.193621 | ||||||||
\(401\) | −6052.52 | −0.753737 | −0.376869 | − | 0.926267i | \(-0.622999\pi\) | ||||
−0.376869 | + | 0.926267i | \(0.622999\pi\) | |||||||
\(402\) | 7154.03 | 0.887588 | ||||||||
\(403\) | −3486.32 | −0.430932 | ||||||||
\(404\) | −1236.92 | −0.152325 | ||||||||
\(405\) | −3590.05 | −0.440472 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 312.597 | 0.0380709 | ||||||||
\(408\) | 6869.49 | 0.833555 | ||||||||
\(409\) | −11921.8 | −1.44130 | −0.720652 | − | 0.693297i | \(-0.756157\pi\) | ||||
−0.720652 | + | 0.693297i | \(0.756157\pi\) | |||||||
\(410\) | 1141.43 | 0.137491 | ||||||||
\(411\) | 23931.0 | 2.87209 | ||||||||
\(412\) | −2470.51 | −0.295421 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1326.29 | −0.157448 | ||||||||
\(415\) | −1980.48 | −0.234260 | ||||||||
\(416\) | −626.668 | −0.0738579 | ||||||||
\(417\) | 12779.9 | 1.50080 | ||||||||
\(418\) | −1562.55 | −0.182839 | ||||||||
\(419\) | 7468.53 | 0.870792 | 0.435396 | − | 0.900239i | \(-0.356608\pi\) | ||||
0.435396 | + | 0.900239i | \(0.356608\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6039.59 | 0.699172 | 0.349586 | − | 0.936904i | \(-0.386322\pi\) | ||||
0.349586 | + | 0.936904i | \(0.386322\pi\) | |||||||
\(422\) | 1821.13 | 0.210073 | ||||||||
\(423\) | −618.474 | −0.0710903 | ||||||||
\(424\) | 3433.63 | 0.393282 | ||||||||
\(425\) | −11125.4 | −1.26979 | ||||||||
\(426\) | 9743.78 | 1.10819 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −4900.81 | −0.553481 | ||||||||
\(429\) | −2205.52 | −0.248213 | ||||||||
\(430\) | 1473.83 | 0.165289 | ||||||||
\(431\) | 13552.1 | 1.51458 | 0.757289 | − | 0.653079i | \(-0.226523\pi\) | ||||
0.757289 | + | 0.653079i | \(0.226523\pi\) | |||||||
\(432\) | 219.060 | 0.0243970 | ||||||||
\(433\) | −2807.93 | −0.311641 | −0.155821 | − | 0.987785i | \(-0.549802\pi\) | ||||
−0.155821 | + | 0.987785i | \(0.549802\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 9028.82 | 0.995169 | ||||||||
\(436\) | 628.979 | 0.0690886 | ||||||||
\(437\) | 1192.20 | 0.130505 | ||||||||
\(438\) | 7717.45 | 0.841905 | ||||||||
\(439\) | 15898.7 | 1.72849 | 0.864243 | − | 0.503075i | \(-0.167798\pi\) | ||||
0.864243 | + | 0.503075i | \(0.167798\pi\) | |||||||
\(440\) | 640.199 | 0.0693643 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4501.00 | −0.484368 | ||||||||
\(443\) | −9194.64 | −0.986118 | −0.493059 | − | 0.869996i | \(-0.664121\pi\) | ||||
−0.493059 | + | 0.869996i | \(0.664121\pi\) | |||||||
\(444\) | 619.879 | 0.0662571 | ||||||||
\(445\) | −4760.90 | −0.507164 | ||||||||
\(446\) | −2578.61 | −0.273768 | ||||||||
\(447\) | −19781.9 | −2.09318 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11231.7 | −1.18053 | −0.590265 | − | 0.807209i | \(-0.700977\pi\) | ||||
−0.590265 | + | 0.807209i | \(0.700977\pi\) | |||||||
\(450\) | −5582.54 | −0.584807 | ||||||||
\(451\) | 1620.15 | 0.169157 | ||||||||
\(452\) | −4907.87 | −0.510723 | ||||||||
\(453\) | −7552.91 | −0.783370 | ||||||||
\(454\) | −2827.87 | −0.292332 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3098.52 | −0.318205 | ||||||||
\(457\) | −9751.96 | −0.998200 | −0.499100 | − | 0.866544i | \(-0.666336\pi\) | ||||
−0.499100 | + | 0.866544i | \(0.666336\pi\) | |||||||
\(458\) | 1598.33 | 0.163068 | ||||||||
\(459\) | 1573.38 | 0.159998 | ||||||||
\(460\) | −488.464 | −0.0495103 | ||||||||
\(461\) | 6728.85 | 0.679813 | 0.339906 | − | 0.940459i | \(-0.389605\pi\) | ||||
0.339906 | + | 0.940459i | \(0.389605\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7665.18 | −0.769398 | −0.384699 | − | 0.923042i | \(-0.625695\pi\) | ||||
−0.384699 | + | 0.923042i | \(0.625695\pi\) | |||||||
\(464\) | 3641.36 | 0.364323 | ||||||||
\(465\) | 7062.63 | 0.704348 | ||||||||
\(466\) | 3108.82 | 0.309041 | ||||||||
\(467\) | 16755.9 | 1.66033 | 0.830163 | − | 0.557521i | \(-0.188248\pi\) | ||||
0.830163 | + | 0.557521i | \(0.188248\pi\) | |||||||
\(468\) | −2258.53 | −0.223079 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −227.780 | −0.0223547 | ||||||||
\(471\) | −573.776 | −0.0561321 | ||||||||
\(472\) | −1028.51 | −0.100299 | ||||||||
\(473\) | 2091.96 | 0.203358 | ||||||||
\(474\) | −5221.45 | −0.505969 | ||||||||
\(475\) | 5018.16 | 0.484734 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 12374.9 | 1.18786 | ||||||||
\(478\) | −13935.6 | −1.33347 | ||||||||
\(479\) | −5518.57 | −0.526409 | −0.263205 | − | 0.964740i | \(-0.584779\pi\) | ||||
−0.263205 | + | 0.964740i | \(0.584779\pi\) | |||||||
\(480\) | 1269.51 | 0.120719 | ||||||||
\(481\) | −406.154 | −0.0385011 | ||||||||
\(482\) | 10116.5 | 0.956003 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4415.30 | −0.414660 | ||||||||
\(485\) | 6875.24 | 0.643688 | ||||||||
\(486\) | −10844.2 | −1.01214 | ||||||||
\(487\) | 3953.92 | 0.367904 | 0.183952 | − | 0.982935i | \(-0.441111\pi\) | ||||
0.183952 | + | 0.982935i | \(0.441111\pi\) | |||||||
\(488\) | −1807.45 | −0.167663 | ||||||||
\(489\) | 16059.2 | 1.48511 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12730.6 | 1.17011 | 0.585053 | − | 0.810995i | \(-0.301074\pi\) | ||||
0.585053 | + | 0.810995i | \(0.301074\pi\) | |||||||
\(492\) | 3212.76 | 0.294395 | ||||||||
\(493\) | 26153.8 | 2.38927 | ||||||||
\(494\) | 2030.20 | 0.184905 | ||||||||
\(495\) | 2307.30 | 0.209506 | ||||||||
\(496\) | 2848.39 | 0.257856 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −5574.40 | −0.501596 | ||||||||
\(499\) | −18019.9 | −1.61659 | −0.808297 | − | 0.588775i | \(-0.799611\pi\) | ||||
−0.808297 | + | 0.588775i | \(0.799611\pi\) | |||||||
\(500\) | −4710.71 | −0.421339 | ||||||||
\(501\) | 15477.3 | 1.38019 | ||||||||
\(502\) | 6726.77 | 0.598068 | ||||||||
\(503\) | 10200.1 | 0.904175 | 0.452087 | − | 0.891974i | \(-0.350680\pi\) | ||||
0.452087 | + | 0.891974i | \(0.350680\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1641.82 | −0.144674 | ||||||||
\(506\) | −693.328 | −0.0609134 | ||||||||
\(507\) | −13550.6 | −1.18699 | ||||||||
\(508\) | 4916.75 | 0.429420 | ||||||||
\(509\) | −12372.6 | −1.07741 | −0.538707 | − | 0.842493i | \(-0.681087\pi\) | ||||
−0.538707 | + | 0.842493i | \(0.681087\pi\) | |||||||
\(510\) | 9118.20 | 0.791688 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | −709.683 | −0.0610785 | ||||||||
\(514\) | 14040.6 | 1.20487 | ||||||||
\(515\) | −3279.23 | −0.280583 | ||||||||
\(516\) | 4148.35 | 0.353917 | ||||||||
\(517\) | −323.312 | −0.0275034 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −23326.8 | −1.97290 | ||||||||
\(520\) | −831.805 | −0.0701482 | ||||||||
\(521\) | −11660.6 | −0.980538 | −0.490269 | − | 0.871571i | \(-0.663101\pi\) | ||||
−0.490269 | + | 0.871571i | \(0.663101\pi\) | |||||||
\(522\) | 13123.6 | 1.10039 | ||||||||
\(523\) | 3985.38 | 0.333210 | 0.166605 | − | 0.986024i | \(-0.446720\pi\) | ||||
0.166605 | + | 0.986024i | \(0.446720\pi\) | |||||||
\(524\) | 9683.74 | 0.807321 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2237.13 | −0.185444 | ||||||||
\(527\) | 20458.4 | 1.69105 | ||||||||
\(528\) | 1801.95 | 0.148523 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | 4557.61 | 0.373528 | ||||||||
\(531\) | −3706.80 | −0.302941 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2105.05 | −0.171069 | ||||||||
\(534\) | −13400.4 | −1.08594 | ||||||||
\(535\) | −6505.08 | −0.525681 | ||||||||
\(536\) | 3829.73 | 0.308618 | ||||||||
\(537\) | −22934.0 | −1.84297 | ||||||||
\(538\) | 5571.73 | 0.446495 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 290.768 | 0.0231716 | ||||||||
\(541\) | 8567.19 | 0.680836 | 0.340418 | − | 0.940274i | \(-0.389431\pi\) | ||||
0.340418 | + | 0.940274i | \(0.389431\pi\) | |||||||
\(542\) | 5379.07 | 0.426293 | ||||||||
\(543\) | −8284.34 | −0.654724 | ||||||||
\(544\) | 3677.41 | 0.289830 | ||||||||
\(545\) | 834.873 | 0.0656184 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14381.3 | −1.12413 | −0.562067 | − | 0.827091i | \(-0.689994\pi\) | ||||
−0.562067 | + | 0.827091i | \(0.689994\pi\) | |||||||
\(548\) | 12810.8 | 0.998635 | ||||||||
\(549\) | −6514.12 | −0.506404 | ||||||||
\(550\) | −2918.32 | −0.226250 | ||||||||
\(551\) | −11796.8 | −0.912091 | ||||||||
\(552\) | −1374.87 | −0.106011 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −1661.67 | −0.127433 | ||||||||
\(555\) | 822.794 | 0.0629291 | ||||||||
\(556\) | 6841.38 | 0.521833 | ||||||||
\(557\) | −1759.65 | −0.133857 | −0.0669287 | − | 0.997758i | \(-0.521320\pi\) | ||||
−0.0669287 | + | 0.997758i | \(0.521320\pi\) | |||||||
\(558\) | 10265.7 | 0.778821 | ||||||||
\(559\) | −2718.07 | −0.205656 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12942.4 | 0.974027 | ||||||||
\(562\) | −17700.7 | −1.32858 | ||||||||
\(563\) | 12597.1 | 0.942989 | 0.471495 | − | 0.881869i | \(-0.343715\pi\) | ||||
0.471495 | + | 0.881869i | \(0.343715\pi\) | |||||||
\(564\) | −641.128 | −0.0478659 | ||||||||
\(565\) | −6514.45 | −0.485071 | ||||||||
\(566\) | 1115.15 | 0.0828149 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5216.08 | 0.385320 | ||||||||
\(569\) | −6429.70 | −0.473721 | −0.236860 | − | 0.971544i | \(-0.576118\pi\) | ||||
−0.236860 | + | 0.971544i | \(0.576118\pi\) | |||||||
\(570\) | −4112.82 | −0.302223 | ||||||||
\(571\) | −5090.14 | −0.373057 | −0.186529 | − | 0.982450i | \(-0.559724\pi\) | ||||
−0.186529 | + | 0.982450i | \(0.559724\pi\) | |||||||
\(572\) | −1180.67 | −0.0863046 | ||||||||
\(573\) | −23765.9 | −1.73270 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2226.64 | 0.161491 | ||||||||
\(576\) | 1845.27 | 0.133483 | ||||||||
\(577\) | 12748.9 | 0.919834 | 0.459917 | − | 0.887962i | \(-0.347879\pi\) | ||||
0.459917 | + | 0.887962i | \(0.347879\pi\) | |||||||
\(578\) | 16586.8 | 1.19363 | ||||||||
\(579\) | −6069.78 | −0.435667 | ||||||||
\(580\) | 4833.35 | 0.346024 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 19351.6 | 1.37826 | ||||||||
\(583\) | 6469.10 | 0.459559 | ||||||||
\(584\) | 4131.34 | 0.292733 | ||||||||
\(585\) | −2997.86 | −0.211874 | ||||||||
\(586\) | 527.013 | 0.0371514 | ||||||||
\(587\) | −7455.98 | −0.524261 | −0.262131 | − | 0.965032i | \(-0.584425\pi\) | ||||
−0.262131 | + | 0.965032i | \(0.584425\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9227.87 | −0.645548 | ||||||||
\(590\) | −1365.19 | −0.0952613 | ||||||||
\(591\) | −28187.8 | −1.96191 | ||||||||
\(592\) | 331.836 | 0.0230378 | ||||||||
\(593\) | −9005.60 | −0.623635 | −0.311817 | − | 0.950142i | \(-0.600938\pi\) | ||||
−0.311817 | + | 0.950142i | \(0.600938\pi\) | |||||||
\(594\) | 412.718 | 0.0285084 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −10589.8 | −0.727807 | ||||||||
\(597\) | 11389.5 | 0.780809 | ||||||||
\(598\) | 900.835 | 0.0616018 | ||||||||
\(599\) | −14196.3 | −0.968359 | −0.484179 | − | 0.874969i | \(-0.660882\pi\) | ||||
−0.484179 | + | 0.874969i | \(0.660882\pi\) | |||||||
\(600\) | −5787.02 | −0.393757 | ||||||||
\(601\) | −4208.80 | −0.285658 | −0.142829 | − | 0.989747i | \(-0.545620\pi\) | ||||
−0.142829 | + | 0.989747i | \(0.545620\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 13802.5 | 0.932140 | ||||||||
\(604\) | −4043.26 | −0.272381 | ||||||||
\(605\) | −5860.63 | −0.393832 | ||||||||
\(606\) | −4621.20 | −0.309775 | ||||||||
\(607\) | 13431.8 | 0.898155 | 0.449078 | − | 0.893493i | \(-0.351753\pi\) | ||||
0.449078 | + | 0.893493i | \(0.351753\pi\) | |||||||
\(608\) | −1658.72 | −0.110641 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2399.11 | −0.159241 | ||||||||
\(611\) | 420.077 | 0.0278142 | ||||||||
\(612\) | 13253.5 | 0.875395 | ||||||||
\(613\) | 27774.2 | 1.83000 | 0.914999 | − | 0.403456i | \(-0.132191\pi\) | ||||
0.914999 | + | 0.403456i | \(0.132191\pi\) | |||||||
\(614\) | −12401.5 | −0.815123 | ||||||||
\(615\) | 4264.44 | 0.279608 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10560.5 | 0.689061 | 0.344530 | − | 0.938775i | \(-0.388038\pi\) | ||||
0.344530 | + | 0.938775i | \(0.388038\pi\) | |||||||
\(618\) | −9229.96 | −0.600782 | ||||||||
\(619\) | 20438.9 | 1.32715 | 0.663577 | − | 0.748108i | \(-0.269038\pi\) | ||||
0.663577 | + | 0.748108i | \(0.269038\pi\) | |||||||
\(620\) | 3780.80 | 0.244904 | ||||||||
\(621\) | −314.898 | −0.0203485 | ||||||||
\(622\) | −16848.5 | −1.08611 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −2341.26 | −0.150201 | ||||||||
\(625\) | 5848.55 | 0.374308 | ||||||||
\(626\) | 4842.22 | 0.309160 | ||||||||
\(627\) | −5837.75 | −0.371830 | ||||||||
\(628\) | −307.157 | −0.0195173 | ||||||||
\(629\) | 2383.39 | 0.151085 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15693.6 | −0.990099 | −0.495049 | − | 0.868865i | \(-0.664850\pi\) | ||||
−0.495049 | + | 0.868865i | \(0.664850\pi\) | |||||||
\(632\) | −2795.17 | −0.175927 | ||||||||
\(633\) | 6803.82 | 0.427216 | ||||||||
\(634\) | −2064.53 | −0.129326 | ||||||||
\(635\) | 6526.23 | 0.407851 | ||||||||
\(636\) | 12828.2 | 0.799798 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 6860.48 | 0.425719 | ||||||||
\(639\) | 18799.0 | 1.16381 | ||||||||
\(640\) | 679.602 | 0.0419744 | ||||||||
\(641\) | −13898.9 | −0.856434 | −0.428217 | − | 0.903676i | \(-0.640858\pi\) | ||||
−0.428217 | + | 0.903676i | \(0.640858\pi\) | |||||||
\(642\) | −18309.7 | −1.12559 | ||||||||
\(643\) | −18032.4 | −1.10595 | −0.552977 | − | 0.833196i | \(-0.686508\pi\) | ||||
−0.552977 | + | 0.833196i | \(0.686508\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5506.30 | 0.336140 | ||||||||
\(646\) | −11913.6 | −0.725597 | ||||||||
\(647\) | 2023.00 | 0.122925 | 0.0614624 | − | 0.998109i | \(-0.480424\pi\) | ||||
0.0614624 | + | 0.998109i | \(0.480424\pi\) | |||||||
\(648\) | −5409.36 | −0.327932 | ||||||||
\(649\) | −1937.76 | −0.117202 | ||||||||
\(650\) | 3791.75 | 0.228807 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 8596.86 | 0.516379 | ||||||||
\(653\) | −153.043 | −0.00917154 | −0.00458577 | − | 0.999989i | \(-0.501460\pi\) | ||||
−0.00458577 | + | 0.999989i | \(0.501460\pi\) | |||||||
\(654\) | 2349.90 | 0.140502 | ||||||||
\(655\) | 12853.7 | 0.766771 | ||||||||
\(656\) | 1719.87 | 0.102362 | ||||||||
\(657\) | 14889.5 | 0.884164 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5171.29 | −0.305683 | −0.152841 | − | 0.988251i | \(-0.548842\pi\) | ||||
−0.152841 | + | 0.988251i | \(0.548842\pi\) | |||||||
\(660\) | 2391.82 | 0.141063 | ||||||||
\(661\) | 4426.43 | 0.260466 | 0.130233 | − | 0.991483i | \(-0.458427\pi\) | ||||
0.130233 | + | 0.991483i | \(0.458427\pi\) | |||||||
\(662\) | 3630.71 | 0.213159 | ||||||||
\(663\) | −16816.0 | −0.985035 | ||||||||
\(664\) | −2984.12 | −0.174407 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1195.95 | 0.0695828 | ||||||||
\(667\) | −5234.46 | −0.303866 | ||||||||
\(668\) | 8285.36 | 0.479896 | ||||||||
\(669\) | −9633.80 | −0.556748 | ||||||||
\(670\) | 5083.38 | 0.293116 | ||||||||
\(671\) | −3405.31 | −0.195917 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19846.7 | 1.13675 | 0.568377 | − | 0.822768i | \(-0.307571\pi\) | ||||
0.568377 | + | 0.822768i | \(0.307571\pi\) | |||||||
\(674\) | −16320.7 | −0.932717 | ||||||||
\(675\) | −1325.45 | −0.0755804 | ||||||||
\(676\) | −7253.97 | −0.412720 | ||||||||
\(677\) | 23737.7 | 1.34758 | 0.673792 | − | 0.738921i | \(-0.264664\pi\) | ||||
0.673792 | + | 0.738921i | \(0.264664\pi\) | |||||||
\(678\) | −18336.1 | −1.03863 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 4881.20 | 0.275273 | ||||||||
\(681\) | −10565.1 | −0.594500 | ||||||||
\(682\) | 5366.49 | 0.301310 | ||||||||
\(683\) | −4733.62 | −0.265193 | −0.132597 | − | 0.991170i | \(-0.542332\pi\) | ||||
−0.132597 | + | 0.991170i | \(0.542332\pi\) | |||||||
\(684\) | −5978.08 | −0.334178 | ||||||||
\(685\) | 17004.4 | 0.948475 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5971.45 | 0.331623 | ||||||||
\(688\) | 2220.72 | 0.123058 | ||||||||
\(689\) | −8405.24 | −0.464752 | ||||||||
\(690\) | −1824.93 | −0.100687 | ||||||||
\(691\) | 275.544 | 0.0151696 | 0.00758480 | − | 0.999971i | \(-0.497586\pi\) | ||||
0.00758480 | + | 0.999971i | \(0.497586\pi\) | |||||||
\(692\) | −12487.4 | −0.685983 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −11387.6 | −0.622863 | ||||||||
\(695\) | 9080.89 | 0.495623 | ||||||||
\(696\) | 13604.3 | 0.740905 | ||||||||
\(697\) | 12352.9 | 0.671302 | ||||||||
\(698\) | −9121.21 | −0.494617 | ||||||||
\(699\) | 11614.7 | 0.628481 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15236.5 | 0.820933 | 0.410467 | − | 0.911876i | \(-0.365366\pi\) | ||||
0.410467 | + | 0.911876i | \(0.365366\pi\) | |||||||
\(702\) | −536.241 | −0.0288306 | ||||||||
\(703\) | −1075.04 | −0.0576757 | ||||||||
\(704\) | 964.630 | 0.0516418 | ||||||||
\(705\) | −850.999 | −0.0454617 | ||||||||
\(706\) | −17161.0 | −0.914819 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −3842.58 | −0.203973 | ||||||||
\(709\) | 20262.7 | 1.07332 | 0.536659 | − | 0.843799i | \(-0.319686\pi\) | ||||
0.536659 | + | 0.843799i | \(0.319686\pi\) | |||||||
\(710\) | 6923.55 | 0.365967 | ||||||||
\(711\) | −10073.9 | −0.531366 | ||||||||
\(712\) | −7173.55 | −0.377585 | ||||||||
\(713\) | −4094.56 | −0.215067 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1567.16 | −0.0819697 | ||||||||
\(716\) | −12277.2 | −0.640808 | ||||||||
\(717\) | −52064.2 | −2.71182 | ||||||||
\(718\) | 3978.30 | 0.206781 | ||||||||
\(719\) | −4018.57 | −0.208439 | −0.104219 | − | 0.994554i | \(-0.533234\pi\) | ||||
−0.104219 | + | 0.994554i | \(0.533234\pi\) | |||||||
\(720\) | 2449.31 | 0.126778 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −8344.29 | −0.430114 | ||||||||
\(723\) | 37795.7 | 1.94417 | ||||||||
\(724\) | −4434.81 | −0.227650 | ||||||||
\(725\) | −22032.6 | −1.12865 | ||||||||
\(726\) | −16495.8 | −0.843273 | ||||||||
\(727\) | −31658.7 | −1.61507 | −0.807536 | − | 0.589819i | \(-0.799199\pi\) | ||||
−0.807536 | + | 0.589819i | \(0.799199\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −22257.7 | −1.13081 | ||||||||
\(730\) | 5483.73 | 0.278030 | ||||||||
\(731\) | 15950.2 | 0.807028 | ||||||||
\(732\) | −6752.72 | −0.340967 | ||||||||
\(733\) | −35997.8 | −1.81393 | −0.906963 | − | 0.421210i | \(-0.861605\pi\) | ||||
−0.906963 | + | 0.421210i | \(0.861605\pi\) | |||||||
\(734\) | 229.776 | 0.0115548 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −736.000 | −0.0368605 | ||||||||
\(737\) | 7215.37 | 0.360626 | ||||||||
\(738\) | 6198.47 | 0.309172 | ||||||||
\(739\) | 8160.48 | 0.406209 | 0.203104 | − | 0.979157i | \(-0.434897\pi\) | ||||
0.203104 | + | 0.979157i | \(0.434897\pi\) | |||||||
\(740\) | 440.462 | 0.0218807 | ||||||||
\(741\) | 7584.94 | 0.376032 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2264.67 | −0.111821 | −0.0559104 | − | 0.998436i | \(-0.517806\pi\) | ||||
−0.0559104 | + | 0.998436i | \(0.517806\pi\) | |||||||
\(744\) | 10641.7 | 0.524388 | ||||||||
\(745\) | −14056.3 | −0.691251 | ||||||||
\(746\) | 25137.4 | 1.23371 | ||||||||
\(747\) | −10754.9 | −0.526774 | ||||||||
\(748\) | 6928.39 | 0.338673 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −17599.5 | −0.856855 | ||||||||
\(751\) | −20177.1 | −0.980391 | −0.490195 | − | 0.871613i | \(-0.663075\pi\) | ||||
−0.490195 | + | 0.871613i | \(0.663075\pi\) | |||||||
\(752\) | −343.211 | −0.0166431 | ||||||||
\(753\) | 25131.5 | 1.21626 | ||||||||
\(754\) | −8913.76 | −0.430530 | ||||||||
\(755\) | −5366.81 | −0.258700 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2404.49 | 0.115446 | 0.0577231 | − | 0.998333i | \(-0.481616\pi\) | ||||
0.0577231 | + | 0.998333i | \(0.481616\pi\) | |||||||
\(758\) | −24151.0 | −1.15726 | ||||||||
\(759\) | −2590.31 | −0.123876 | ||||||||
\(760\) | −2201.69 | −0.105084 | ||||||||
\(761\) | −36396.7 | −1.73374 | −0.866871 | − | 0.498532i | \(-0.833873\pi\) | ||||
−0.866871 | + | 0.498532i | \(0.833873\pi\) | |||||||
\(762\) | 18369.2 | 0.873290 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −12722.5 | −0.602465 | ||||||||
\(765\) | 17592.0 | 0.831426 | ||||||||
\(766\) | 24456.0 | 1.15357 | ||||||||
\(767\) | 2517.72 | 0.118526 | ||||||||
\(768\) | 1912.86 | 0.0898754 | ||||||||
\(769\) | 29050.2 | 1.36226 | 0.681129 | − | 0.732163i | \(-0.261489\pi\) | ||||
0.681129 | + | 0.732163i | \(0.261489\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 52456.3 | 2.45028 | ||||||||
\(772\) | −3249.30 | −0.151483 | ||||||||
\(773\) | 30769.4 | 1.43169 | 0.715847 | − | 0.698257i | \(-0.246041\pi\) | ||||
0.715847 | + | 0.698257i | \(0.246041\pi\) | |||||||
\(774\) | 8003.54 | 0.371681 | ||||||||
\(775\) | −17234.6 | −0.798820 | ||||||||
\(776\) | 10359.4 | 0.479227 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 6275.12 | 0.289170 | ||||||||
\(779\) | −5571.82 | −0.256266 | ||||||||
\(780\) | −3107.67 | −0.142657 | ||||||||
\(781\) | 9827.32 | 0.450255 | ||||||||
\(782\) | −5286.27 | −0.241735 | ||||||||
\(783\) | 3115.92 | 0.142214 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −407.703 | −0.0185370 | ||||||||
\(786\) | 36178.9 | 1.64181 | ||||||||
\(787\) | −11172.5 | −0.506043 | −0.253022 | − | 0.967461i | \(-0.581424\pi\) | ||||
−0.253022 | + | 0.967461i | \(0.581424\pi\) | |||||||
\(788\) | −15089.6 | −0.682164 | ||||||||
\(789\) | −8358.04 | −0.377128 | ||||||||
\(790\) | −3710.16 | −0.167091 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 3476.56 | 0.155978 | ||||||||
\(793\) | 4424.49 | 0.198132 | ||||||||
\(794\) | −30979.6 | −1.38466 | ||||||||
\(795\) | 17027.5 | 0.759626 | ||||||||
\(796\) | 6097.10 | 0.271490 | ||||||||
\(797\) | 7065.60 | 0.314023 | 0.157012 | − | 0.987597i | \(-0.449814\pi\) | ||||
0.157012 | + | 0.987597i | \(0.449814\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2465.09 | −0.109147 | ||||||||
\(800\) | −3097.93 | −0.136911 | ||||||||
\(801\) | −25853.8 | −1.14045 | ||||||||
\(802\) | −12105.0 | −0.532973 | ||||||||
\(803\) | 7783.63 | 0.342065 | ||||||||
\(804\) | 14308.1 | 0.627620 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −6972.63 | −0.304715 | ||||||||
\(807\) | 20816.3 | 0.908014 | ||||||||
\(808\) | −2473.84 | −0.107710 | ||||||||
\(809\) | 37869.3 | 1.64575 | 0.822875 | − | 0.568222i | \(-0.192368\pi\) | ||||
0.822875 | + | 0.568222i | \(0.192368\pi\) | |||||||
\(810\) | −7180.10 | −0.311460 | ||||||||
\(811\) | −33563.4 | −1.45323 | −0.726616 | − | 0.687044i | \(-0.758908\pi\) | ||||
−0.726616 | + | 0.687044i | \(0.758908\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 20096.5 | 0.866931 | ||||||||
\(814\) | 625.194 | 0.0269202 | ||||||||
\(815\) | 11411.0 | 0.490442 | ||||||||
\(816\) | 13739.0 | 0.589413 | ||||||||
\(817\) | −7194.41 | −0.308079 | ||||||||
\(818\) | −23843.5 | −1.01916 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2282.86 | 0.0972207 | ||||||||
\(821\) | −17903.5 | −0.761069 | −0.380534 | − | 0.924767i | \(-0.624260\pi\) | ||||
−0.380534 | + | 0.924767i | \(0.624260\pi\) | |||||||
\(822\) | 47861.9 | 2.03087 | ||||||||
\(823\) | 6635.99 | 0.281064 | 0.140532 | − | 0.990076i | \(-0.455119\pi\) | ||||
0.140532 | + | 0.990076i | \(0.455119\pi\) | |||||||
\(824\) | −4941.02 | −0.208894 | ||||||||
\(825\) | −10903.0 | −0.460113 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 30086.7 | 1.26508 | 0.632538 | − | 0.774529i | \(-0.282013\pi\) | ||||
0.632538 | + | 0.774529i | \(0.282013\pi\) | |||||||
\(828\) | −2652.57 | −0.111332 | ||||||||
\(829\) | −18965.3 | −0.794562 | −0.397281 | − | 0.917697i | \(-0.630046\pi\) | ||||
−0.397281 | + | 0.917697i | \(0.630046\pi\) | |||||||
\(830\) | −3960.96 | −0.165647 | ||||||||
\(831\) | −6208.09 | −0.259153 | ||||||||
\(832\) | −1253.34 | −0.0522254 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 25559.8 | 1.06123 | ||||||||
\(835\) | 10997.5 | 0.455791 | ||||||||
\(836\) | −3125.09 | −0.129287 | ||||||||
\(837\) | 2437.37 | 0.100655 | ||||||||
\(838\) | 14937.1 | 0.615743 | ||||||||
\(839\) | 5909.42 | 0.243166 | 0.121583 | − | 0.992581i | \(-0.461203\pi\) | ||||
0.121583 | + | 0.992581i | \(0.461203\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27405.9 | 1.12370 | ||||||||
\(842\) | 12079.2 | 0.494389 | ||||||||
\(843\) | −66130.9 | −2.70186 | ||||||||
\(844\) | 3642.25 | 0.148544 | ||||||||
\(845\) | −9628.53 | −0.391990 | ||||||||
\(846\) | −1236.95 | −0.0502685 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 6867.25 | 0.278092 | ||||||||
\(849\) | 4166.26 | 0.168416 | ||||||||
\(850\) | −22250.7 | −0.897874 | ||||||||
\(851\) | −477.015 | −0.0192149 | ||||||||
\(852\) | 19487.6 | 0.783606 | ||||||||
\(853\) | 4235.96 | 0.170031 | 0.0850156 | − | 0.996380i | \(-0.472906\pi\) | ||||
0.0850156 | + | 0.996380i | \(0.472906\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −7934.98 | −0.317393 | ||||||||
\(856\) | −9801.63 | −0.391370 | ||||||||
\(857\) | −22565.0 | −0.899424 | −0.449712 | − | 0.893174i | \(-0.648473\pi\) | ||||
−0.449712 | + | 0.893174i | \(0.648473\pi\) | |||||||
\(858\) | −4411.04 | −0.175513 | ||||||||
\(859\) | 3340.91 | 0.132701 | 0.0663505 | − | 0.997796i | \(-0.478864\pi\) | ||||
0.0663505 | + | 0.997796i | \(0.478864\pi\) | |||||||
\(860\) | 2947.66 | 0.116877 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 27104.3 | 1.07097 | ||||||||
\(863\) | −49888.4 | −1.96781 | −0.983905 | − | 0.178691i | \(-0.942814\pi\) | ||||
−0.983905 | + | 0.178691i | \(0.942814\pi\) | |||||||
\(864\) | 438.119 | 0.0172513 | ||||||||
\(865\) | −16575.1 | −0.651527 | ||||||||
\(866\) | −5615.86 | −0.220364 | ||||||||
\(867\) | 61969.0 | 2.42742 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5266.22 | −0.205575 | ||||||||
\(870\) | 18057.6 | 0.703691 | ||||||||
\(871\) | −9374.86 | −0.364702 | ||||||||
\(872\) | 1257.96 | 0.0488530 | ||||||||
\(873\) | 37335.6 | 1.44744 | ||||||||
\(874\) | 2384.40 | 0.0922811 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 15434.9 | 0.595316 | ||||||||
\(877\) | 41188.0 | 1.58588 | 0.792942 | − | 0.609297i | \(-0.208548\pi\) | ||||
0.792942 | + | 0.609297i | \(0.208548\pi\) | |||||||
\(878\) | 31797.5 | 1.22222 | ||||||||
\(879\) | 1968.95 | 0.0755528 | ||||||||
\(880\) | 1280.40 | 0.0490480 | ||||||||
\(881\) | −19351.1 | −0.740018 | −0.370009 | − | 0.929028i | \(-0.620645\pi\) | ||||
−0.370009 | + | 0.929028i | \(0.620645\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −31330.1 | −1.19404 | −0.597022 | − | 0.802225i | \(-0.703649\pi\) | ||||
−0.597022 | + | 0.802225i | \(0.703649\pi\) | |||||||
\(884\) | −9002.00 | −0.342500 | ||||||||
\(885\) | −5100.44 | −0.193728 | ||||||||
\(886\) | −18389.3 | −0.697291 | ||||||||
\(887\) | 18838.7 | 0.713124 | 0.356562 | − | 0.934272i | \(-0.383949\pi\) | ||||
0.356562 | + | 0.934272i | \(0.383949\pi\) | |||||||
\(888\) | 1239.76 | 0.0468508 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −9521.79 | −0.358619 | ||||||||
\(891\) | −10191.5 | −0.383195 | ||||||||
\(892\) | −5157.21 | −0.193583 | ||||||||
\(893\) | 1111.90 | 0.0416665 | ||||||||
\(894\) | −39563.9 | −1.48010 | ||||||||
\(895\) | −16296.0 | −0.608622 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3365.56 | 0.125276 | ||||||||
\(898\) | −22463.5 | −0.834761 | ||||||||
\(899\) | 40515.7 | 1.50309 | ||||||||
\(900\) | −11165.1 | −0.413521 | ||||||||
\(901\) | 49323.6 | 1.82376 | ||||||||
\(902\) | 3240.31 | 0.119612 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −9815.75 | −0.361136 | ||||||||
\(905\) | −5886.53 | −0.216215 | ||||||||
\(906\) | −15105.8 | −0.553926 | ||||||||
\(907\) | −28754.5 | −1.05268 | −0.526339 | − | 0.850275i | \(-0.676436\pi\) | ||||
−0.526339 | + | 0.850275i | \(0.676436\pi\) | |||||||
\(908\) | −5655.74 | −0.206710 | ||||||||
\(909\) | −8915.82 | −0.325324 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7679.37 | 0.279285 | 0.139643 | − | 0.990202i | \(-0.455405\pi\) | ||||
0.139643 | + | 0.990202i | \(0.455405\pi\) | |||||||
\(912\) | −6197.05 | −0.225005 | ||||||||
\(913\) | −5622.20 | −0.203798 | ||||||||
\(914\) | −19503.9 | −0.705834 | ||||||||
\(915\) | −8963.21 | −0.323841 | ||||||||
\(916\) | 3196.66 | 0.115306 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 3146.77 | 0.113136 | ||||||||
\(919\) | 45937.0 | 1.64888 | 0.824440 | − | 0.565950i | \(-0.191490\pi\) | ||||
0.824440 | + | 0.565950i | \(0.191490\pi\) | |||||||
\(920\) | −976.927 | −0.0350091 | ||||||||
\(921\) | −46332.8 | −1.65767 | ||||||||
\(922\) | 13457.7 | 0.480700 | ||||||||
\(923\) | −12768.6 | −0.455344 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2007.83 | −0.0713696 | ||||||||
\(926\) | −15330.4 | −0.544046 | ||||||||
\(927\) | −17807.6 | −0.630938 | ||||||||
\(928\) | 7282.72 | 0.257615 | ||||||||
\(929\) | 35684.8 | 1.26026 | 0.630129 | − | 0.776490i | \(-0.283002\pi\) | ||||
0.630129 | + | 0.776490i | \(0.283002\pi\) | |||||||
\(930\) | 14125.3 | 0.498049 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 6217.64 | 0.218525 | ||||||||
\(933\) | −62946.8 | −2.20877 | ||||||||
\(934\) | 33511.9 | 1.17403 | ||||||||
\(935\) | 9196.38 | 0.321662 | ||||||||
\(936\) | −4517.07 | −0.157740 | ||||||||
\(937\) | −4161.99 | −0.145108 | −0.0725540 | − | 0.997364i | \(-0.523115\pi\) | ||||
−0.0725540 | + | 0.997364i | \(0.523115\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 18090.8 | 0.628722 | ||||||||
\(940\) | −455.561 | −0.0158072 | ||||||||
\(941\) | 30661.7 | 1.06221 | 0.531106 | − | 0.847305i | \(-0.321776\pi\) | ||||
0.531106 | + | 0.847305i | \(0.321776\pi\) | |||||||
\(942\) | −1147.55 | −0.0396914 | ||||||||
\(943\) | −2472.31 | −0.0853760 | ||||||||
\(944\) | −2057.03 | −0.0709222 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4183.92 | 0.143796 | ||||||||
\(947\) | 9165.36 | 0.314503 | 0.157251 | − | 0.987559i | \(-0.449737\pi\) | ||||
0.157251 | + | 0.987559i | \(0.449737\pi\) | |||||||
\(948\) | −10442.9 | −0.357774 | ||||||||
\(949\) | −10113.2 | −0.345931 | ||||||||
\(950\) | 10036.3 | 0.342759 | ||||||||
\(951\) | −7713.18 | −0.263004 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −27150.4 | −0.922862 | −0.461431 | − | 0.887176i | \(-0.652664\pi\) | ||||
−0.461431 | + | 0.887176i | \(0.652664\pi\) | |||||||
\(954\) | 24749.8 | 0.839943 | ||||||||
\(955\) | −16887.1 | −0.572204 | ||||||||
\(956\) | −27871.2 | −0.942908 | ||||||||
\(957\) | 25631.1 | 0.865763 | ||||||||
\(958\) | −11037.1 | −0.372227 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 2539.03 | 0.0853612 | ||||||||
\(961\) | 1901.68 | 0.0638340 | ||||||||
\(962\) | −812.309 | −0.0272244 | ||||||||
\(963\) | −35325.5 | −1.18208 | ||||||||
\(964\) | 20233.0 | 0.675996 | ||||||||
\(965\) | −4312.95 | −0.143874 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −34024.7 | −1.13150 | −0.565750 | − | 0.824577i | \(-0.691413\pi\) | ||||
−0.565750 | + | 0.824577i | \(0.691413\pi\) | |||||||
\(968\) | −8830.60 | −0.293209 | ||||||||
\(969\) | −44509.9 | −1.47561 | ||||||||
\(970\) | 13750.5 | 0.455156 | ||||||||
\(971\) | −18794.4 | −0.621154 | −0.310577 | − | 0.950548i | \(-0.600522\pi\) | ||||
−0.310577 | + | 0.950548i | \(0.600522\pi\) | |||||||
\(972\) | −21688.3 | −0.715692 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 7907.83 | 0.260147 | ||||||||
\(975\) | 14166.2 | 0.465313 | ||||||||
\(976\) | −3614.90 | −0.118555 | ||||||||
\(977\) | −60427.0 | −1.97874 | −0.989371 | − | 0.145411i | \(-0.953549\pi\) | ||||
−0.989371 | + | 0.145411i | \(0.953549\pi\) | |||||||
\(978\) | 32118.3 | 1.05013 | ||||||||
\(979\) | −13515.3 | −0.441216 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4533.73 | 0.147554 | ||||||||
\(982\) | 25461.1 | 0.827390 | ||||||||
\(983\) | −38938.6 | −1.26343 | −0.631713 | − | 0.775203i | \(-0.717648\pi\) | ||||
−0.631713 | + | 0.775203i | \(0.717648\pi\) | |||||||
\(984\) | 6425.52 | 0.208169 | ||||||||
\(985\) | −20029.1 | −0.647900 | ||||||||
\(986\) | 52307.7 | 1.68947 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4060.40 | 0.130748 | ||||||||
\(989\) | −3192.28 | −0.102638 | ||||||||
\(990\) | 4614.61 | 0.148143 | ||||||||
\(991\) | −31599.6 | −1.01291 | −0.506455 | − | 0.862267i | \(-0.669044\pi\) | ||||
−0.506455 | + | 0.862267i | \(0.669044\pi\) | |||||||
\(992\) | 5696.78 | 0.182332 | ||||||||
\(993\) | 13564.5 | 0.433491 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8092.97 | 0.257854 | ||||||||
\(996\) | −11148.8 | −0.354682 | ||||||||
\(997\) | −38706.6 | −1.22954 | −0.614770 | − | 0.788707i | \(-0.710751\pi\) | ||||
−0.614770 | + | 0.788707i | \(0.710751\pi\) | |||||||
\(998\) | −36039.8 | −1.14310 | ||||||||
\(999\) | 283.953 | 0.00899287 |
(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 | 2254.4.a.x.1.10 | 11 | ||
7.3 | odd | 6 | 322.4.e.b.93.10 | ✓ | 22 | ||
7.5 | odd | 6 | 322.4.e.b.277.10 | yes | 22 | ||
7.6 | odd | 2 | 2254.4.a.w.1.2 | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
322.4.e.b.93.10 | ✓ | 22 | 7.3 | odd | 6 | ||
322.4.e.b.277.10 | yes | 22 | 7.5 | odd | 6 | ||
2254.4.a.w.1.2 | 11 | 7.6 | odd | 2 | |||
2254.4.a.x.1.10 | 11 | 1.1 | even | 1 | trivial |