Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [405,4,Mod(1,405)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(405, 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("405.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 405 = 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 405.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: | \(23.8957735523\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.2292.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 13x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 45) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-3.18296\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 405.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.74857 | 1.32532 | 0.662659 | − | 0.748921i | \(-0.269428\pi\) | ||||
0.662659 | + | 0.748921i | \(0.269428\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 6.05174 | 0.756468 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −31.3492 | −1.69270 | −0.846348 | − | 0.532630i | \(-0.821204\pi\) | ||||
−0.846348 | + | 0.532630i | \(0.821204\pi\) | |||||||
\(8\) | −7.30318 | −0.322758 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 18.7428 | 0.592700 | ||||||||
\(11\) | −20.8333 | −0.571043 | −0.285522 | − | 0.958372i | \(-0.592167\pi\) | ||||
−0.285522 | + | 0.958372i | \(0.592167\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 59.9310 | 1.27861 | 0.639303 | − | 0.768955i | \(-0.279223\pi\) | ||||
0.639303 | + | 0.768955i | \(0.279223\pi\) | |||||||
\(14\) | −117.514 | −2.24336 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −75.7904 | −1.18422 | ||||||||
\(17\) | −74.0460 | −1.05640 | −0.528200 | − | 0.849120i | \(-0.677133\pi\) | ||||
−0.528200 | + | 0.849120i | \(0.677133\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −63.8390 | −0.770825 | −0.385413 | − | 0.922744i | \(-0.625941\pi\) | ||||
−0.385413 | + | 0.922744i | \(0.625941\pi\) | |||||||
\(20\) | 30.2587 | 0.338303 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −78.0950 | −0.756814 | ||||||||
\(23\) | −32.8494 | −0.297807 | −0.148904 | − | 0.988852i | \(-0.547574\pi\) | ||||
−0.148904 | + | 0.988852i | \(0.547574\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 224.655 | 1.69456 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −189.717 | −1.28047 | ||||||||
\(29\) | −160.009 | −1.02458 | −0.512291 | − | 0.858812i | \(-0.671203\pi\) | ||||
−0.512291 | + | 0.858812i | \(0.671203\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −254.373 | −1.47377 | −0.736884 | − | 0.676019i | \(-0.763704\pi\) | ||||
−0.736884 | + | 0.676019i | \(0.763704\pi\) | |||||||
\(32\) | −225.680 | −1.24672 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −277.566 | −1.40007 | ||||||||
\(35\) | −156.746 | −0.756997 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 215.365 | 0.956914 | 0.478457 | − | 0.878111i | \(-0.341196\pi\) | ||||
0.478457 | + | 0.878111i | \(0.341196\pi\) | |||||||
\(38\) | −239.305 | −1.02159 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −36.5159 | −0.144342 | ||||||||
\(41\) | 141.681 | 0.539681 | 0.269841 | − | 0.962905i | \(-0.413029\pi\) | ||||
0.269841 | + | 0.962905i | \(0.413029\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 137.906 | 0.489080 | 0.244540 | − | 0.969639i | \(-0.421363\pi\) | ||||
0.244540 | + | 0.969639i | \(0.421363\pi\) | |||||||
\(44\) | −126.078 | −0.431976 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −123.138 | −0.394689 | ||||||||
\(47\) | 33.5790 | 0.104213 | 0.0521064 | − | 0.998642i | \(-0.483407\pi\) | ||||
0.0521064 | + | 0.998642i | \(0.483407\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 639.771 | 1.86522 | ||||||||
\(50\) | 93.7141 | 0.265064 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 362.687 | 0.967224 | ||||||||
\(53\) | −41.9914 | −0.108829 | −0.0544147 | − | 0.998518i | \(-0.517329\pi\) | ||||
−0.0544147 | + | 0.998518i | \(0.517329\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −104.166 | −0.255378 | ||||||||
\(56\) | 228.949 | 0.546331 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −599.803 | −1.35790 | ||||||||
\(59\) | 615.142 | 1.35737 | 0.678683 | − | 0.734431i | \(-0.262551\pi\) | ||||
0.678683 | + | 0.734431i | \(0.262551\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −134.307 | −0.281906 | −0.140953 | − | 0.990016i | \(-0.545017\pi\) | ||||
−0.140953 | + | 0.990016i | \(0.545017\pi\) | |||||||
\(62\) | −953.535 | −1.95321 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −239.652 | −0.468071 | ||||||||
\(65\) | 299.655 | 0.571810 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −857.533 | −1.56365 | −0.781824 | − | 0.623500i | \(-0.785710\pi\) | ||||
−0.781824 | + | 0.623500i | \(0.785710\pi\) | |||||||
\(68\) | −448.107 | −0.799132 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −587.572 | −1.00326 | ||||||||
\(71\) | 588.665 | 0.983968 | 0.491984 | − | 0.870604i | \(-0.336272\pi\) | ||||
0.491984 | + | 0.870604i | \(0.336272\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −618.191 | −0.991148 | −0.495574 | − | 0.868566i | \(-0.665042\pi\) | ||||
−0.495574 | + | 0.868566i | \(0.665042\pi\) | |||||||
\(74\) | 807.311 | 1.26822 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −386.337 | −0.583104 | ||||||||
\(77\) | 653.107 | 0.966603 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −345.288 | −0.491747 | −0.245873 | − | 0.969302i | \(-0.579075\pi\) | ||||
−0.245873 | + | 0.969302i | \(0.579075\pi\) | |||||||
\(80\) | −378.952 | −0.529601 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 531.102 | 0.715249 | ||||||||
\(83\) | −1093.17 | −1.44567 | −0.722836 | − | 0.691020i | \(-0.757162\pi\) | ||||
−0.722836 | + | 0.691020i | \(0.757162\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −370.230 | −0.472436 | ||||||||
\(86\) | 516.949 | 0.648186 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 152.149 | 0.184309 | ||||||||
\(89\) | 414.849 | 0.494089 | 0.247045 | − | 0.969004i | \(-0.420541\pi\) | ||||
0.247045 | + | 0.969004i | \(0.420541\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1878.79 | −2.16429 | ||||||||
\(92\) | −198.796 | −0.225282 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 125.873 | 0.138115 | ||||||||
\(95\) | −319.195 | −0.344724 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −201.411 | −0.210826 | −0.105413 | − | 0.994429i | \(-0.533617\pi\) | ||||
−0.105413 | + | 0.994429i | \(0.533617\pi\) | |||||||
\(98\) | 2398.22 | 2.47201 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 151.294 | 0.151294 | ||||||||
\(101\) | 265.383 | 0.261451 | 0.130726 | − | 0.991419i | \(-0.458269\pi\) | ||||
0.130726 | + | 0.991419i | \(0.458269\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −527.618 | −0.504735 | −0.252368 | − | 0.967631i | \(-0.581209\pi\) | ||||
−0.252368 | + | 0.967631i | \(0.581209\pi\) | |||||||
\(104\) | −437.687 | −0.412680 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −157.408 | −0.144234 | ||||||||
\(107\) | 2084.24 | 1.88310 | 0.941549 | − | 0.336877i | \(-0.109371\pi\) | ||||
0.941549 | + | 0.336877i | \(0.109371\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 925.651 | 0.813406 | 0.406703 | − | 0.913560i | \(-0.366678\pi\) | ||||
0.406703 | + | 0.913560i | \(0.366678\pi\) | |||||||
\(110\) | −390.475 | −0.338457 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2375.97 | 2.00453 | ||||||||
\(113\) | 546.019 | 0.454559 | 0.227279 | − | 0.973830i | \(-0.427017\pi\) | ||||
0.227279 | + | 0.973830i | \(0.427017\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −164.247 | −0.133183 | ||||||||
\(116\) | −968.332 | −0.775063 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2305.90 | 1.79894 | ||||||||
\(119\) | 2321.28 | 1.78816 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −896.974 | −0.673910 | ||||||||
\(122\) | −503.458 | −0.373614 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1539.40 | −1.11486 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −975.972 | −0.681918 | −0.340959 | − | 0.940078i | \(-0.610752\pi\) | ||||
−0.340959 | + | 0.940078i | \(0.610752\pi\) | |||||||
\(128\) | 907.086 | 0.626374 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1123.28 | 0.757830 | ||||||||
\(131\) | −1629.23 | −1.08661 | −0.543307 | − | 0.839534i | \(-0.682828\pi\) | ||||
−0.543307 | + | 0.839534i | \(0.682828\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2001.30 | 1.30477 | ||||||||
\(134\) | −3214.52 | −2.07233 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 540.771 | 0.340961 | ||||||||
\(137\) | 661.451 | 0.412493 | 0.206246 | − | 0.978500i | \(-0.433875\pi\) | ||||
0.206246 | + | 0.978500i | \(0.433875\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1382.99 | 0.843911 | 0.421955 | − | 0.906617i | \(-0.361344\pi\) | ||||
0.421955 | + | 0.906617i | \(0.361344\pi\) | |||||||
\(140\) | −948.586 | −0.572644 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2206.65 | 1.30407 | ||||||||
\(143\) | −1248.56 | −0.730139 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −800.044 | −0.458207 | ||||||||
\(146\) | −2317.33 | −1.31359 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1303.33 | 0.723875 | ||||||||
\(149\) | 3163.49 | 1.73935 | 0.869676 | − | 0.493624i | \(-0.164328\pi\) | ||||
0.869676 | + | 0.493624i | \(0.164328\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2558.80 | −1.37902 | −0.689509 | − | 0.724277i | \(-0.742174\pi\) | ||||
−0.689509 | + | 0.724277i | \(0.742174\pi\) | |||||||
\(152\) | 466.228 | 0.248790 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2448.21 | 1.28106 | ||||||||
\(155\) | −1271.87 | −0.659089 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3500.96 | 1.77966 | 0.889832 | − | 0.456288i | \(-0.150821\pi\) | ||||
0.889832 | + | 0.456288i | \(0.150821\pi\) | |||||||
\(158\) | −1294.34 | −0.651721 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1128.40 | −0.557548 | ||||||||
\(161\) | 1029.80 | 0.504097 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 263.950 | 0.126835 | 0.0634176 | − | 0.997987i | \(-0.479800\pi\) | ||||
0.0634176 | + | 0.997987i | \(0.479800\pi\) | |||||||
\(164\) | 857.419 | 0.408251 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4097.81 | −1.91597 | ||||||||
\(167\) | −3589.05 | −1.66305 | −0.831524 | − | 0.555489i | \(-0.812531\pi\) | ||||
−0.831524 | + | 0.555489i | \(0.812531\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1394.73 | 0.634834 | ||||||||
\(170\) | −1387.83 | −0.626128 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 834.570 | 0.369973 | ||||||||
\(173\) | 370.456 | 0.162805 | 0.0814024 | − | 0.996681i | \(-0.474060\pi\) | ||||
0.0814024 | + | 0.996681i | \(0.474060\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −783.729 | −0.338539 | ||||||||
\(176\) | 1578.96 | 0.676243 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1555.09 | 0.654825 | ||||||||
\(179\) | 446.898 | 0.186607 | 0.0933036 | − | 0.995638i | \(-0.470257\pi\) | ||||
0.0933036 | + | 0.995638i | \(0.470257\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −904.046 | −0.371255 | −0.185628 | − | 0.982620i | \(-0.559432\pi\) | ||||
−0.185628 | + | 0.982620i | \(0.559432\pi\) | |||||||
\(182\) | −7042.76 | −2.86838 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 239.905 | 0.0961196 | ||||||||
\(185\) | 1076.83 | 0.427945 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1542.62 | 0.603250 | ||||||||
\(188\) | 203.211 | 0.0788336 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1196.52 | −0.456868 | ||||||||
\(191\) | −599.587 | −0.227144 | −0.113572 | − | 0.993530i | \(-0.536229\pi\) | ||||
−0.113572 | + | 0.993530i | \(0.536229\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4413.73 | −1.64615 | −0.823076 | − | 0.567931i | \(-0.807744\pi\) | ||||
−0.823076 | + | 0.567931i | \(0.807744\pi\) | |||||||
\(194\) | −755.001 | −0.279412 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3871.73 | 1.41098 | ||||||||
\(197\) | −4807.15 | −1.73855 | −0.869277 | − | 0.494325i | \(-0.835415\pi\) | ||||
−0.869277 | + | 0.494325i | \(0.835415\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 313.833 | 0.111794 | 0.0558970 | − | 0.998437i | \(-0.482198\pi\) | ||||
0.0558970 | + | 0.998437i | \(0.482198\pi\) | |||||||
\(200\) | −182.579 | −0.0645516 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 994.805 | 0.346506 | ||||||||
\(203\) | 5016.14 | 1.73431 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 708.407 | 0.241353 | ||||||||
\(206\) | −1977.81 | −0.668935 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4542.20 | −1.51416 | ||||||||
\(209\) | 1329.98 | 0.440175 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2438.82 | 0.795711 | 0.397856 | − | 0.917448i | \(-0.369754\pi\) | ||||
0.397856 | + | 0.917448i | \(0.369754\pi\) | |||||||
\(212\) | −254.121 | −0.0823260 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 7812.92 | 2.49570 | ||||||||
\(215\) | 689.529 | 0.218723 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7974.40 | 2.49464 | ||||||||
\(218\) | 3469.86 | 1.07802 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −630.389 | −0.193185 | ||||||||
\(221\) | −4437.65 | −1.35072 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2333.41 | −0.700703 | −0.350352 | − | 0.936618i | \(-0.613938\pi\) | ||||
−0.350352 | + | 0.936618i | \(0.613938\pi\) | |||||||
\(224\) | 7074.87 | 2.11031 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2046.79 | 0.602435 | ||||||||
\(227\) | −2723.69 | −0.796378 | −0.398189 | − | 0.917303i | \(-0.630361\pi\) | ||||
−0.398189 | + | 0.917303i | \(0.630361\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3314.16 | −0.956358 | −0.478179 | − | 0.878262i | \(-0.658703\pi\) | ||||
−0.478179 | + | 0.878262i | \(0.658703\pi\) | |||||||
\(230\) | −615.690 | −0.176510 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1168.57 | 0.330692 | ||||||||
\(233\) | −3175.44 | −0.892833 | −0.446416 | − | 0.894825i | \(-0.647300\pi\) | ||||
−0.446416 | + | 0.894825i | \(0.647300\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 167.895 | 0.0466054 | ||||||||
\(236\) | 3722.68 | 1.02680 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 8701.47 | 2.36989 | ||||||||
\(239\) | −246.125 | −0.0666129 | −0.0333064 | − | 0.999445i | \(-0.510604\pi\) | ||||
−0.0333064 | + | 0.999445i | \(0.510604\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5287.73 | −1.41333 | −0.706666 | − | 0.707547i | \(-0.749802\pi\) | ||||
−0.706666 | + | 0.707547i | \(0.749802\pi\) | |||||||
\(242\) | −3362.36 | −0.893144 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −812.791 | −0.213252 | ||||||||
\(245\) | 3198.85 | 0.834152 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3825.94 | −0.985582 | ||||||||
\(248\) | 1857.73 | 0.475670 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 468.571 | 0.118540 | ||||||||
\(251\) | 2821.23 | 0.709459 | 0.354730 | − | 0.934969i | \(-0.384573\pi\) | ||||
0.354730 | + | 0.934969i | \(0.384573\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 684.361 | 0.170061 | ||||||||
\(254\) | −3658.50 | −0.903758 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5317.49 | 1.29821 | ||||||||
\(257\) | −1884.19 | −0.457326 | −0.228663 | − | 0.973506i | \(-0.573435\pi\) | ||||
−0.228663 | + | 0.973506i | \(0.573435\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6751.52 | −1.61977 | ||||||||
\(260\) | 1813.44 | 0.432556 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6107.27 | −1.44011 | ||||||||
\(263\) | 553.011 | 0.129658 | 0.0648292 | − | 0.997896i | \(-0.479350\pi\) | ||||
0.0648292 | + | 0.997896i | \(0.479350\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −209.957 | −0.0486700 | ||||||||
\(266\) | 7502.01 | 1.72924 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5189.57 | −1.18285 | ||||||||
\(269\) | 3363.48 | 0.762361 | 0.381180 | − | 0.924501i | \(-0.375518\pi\) | ||||
0.381180 | + | 0.924501i | \(0.375518\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3333.85 | −0.747295 | −0.373648 | − | 0.927571i | \(-0.621893\pi\) | ||||
−0.373648 | + | 0.927571i | \(0.621893\pi\) | |||||||
\(272\) | 5611.97 | 1.25101 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2479.49 | 0.546684 | ||||||||
\(275\) | −520.832 | −0.114209 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5387.25 | −1.16855 | −0.584275 | − | 0.811555i | \(-0.698621\pi\) | ||||
−0.584275 | + | 0.811555i | \(0.698621\pi\) | |||||||
\(278\) | 5184.23 | 1.11845 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1144.74 | 0.244327 | ||||||||
\(281\) | 3716.70 | 0.789038 | 0.394519 | − | 0.918888i | \(-0.370911\pi\) | ||||
0.394519 | + | 0.918888i | \(0.370911\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2768.76 | 0.581574 | 0.290787 | − | 0.956788i | \(-0.406083\pi\) | ||||
0.290787 | + | 0.956788i | \(0.406083\pi\) | |||||||
\(284\) | 3562.45 | 0.744340 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4680.31 | −0.967667 | ||||||||
\(287\) | −4441.60 | −0.913516 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 569.810 | 0.115980 | ||||||||
\(290\) | −2999.02 | −0.607270 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3741.13 | −0.749771 | ||||||||
\(293\) | −3479.99 | −0.693868 | −0.346934 | − | 0.937890i | \(-0.612777\pi\) | ||||
−0.346934 | + | 0.937890i | \(0.612777\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3075.71 | 0.607033 | ||||||||
\(296\) | −1572.85 | −0.308852 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 11858.6 | 2.30519 | ||||||||
\(299\) | −1968.70 | −0.380778 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4323.23 | −0.827864 | ||||||||
\(302\) | −9591.81 | −1.82764 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4838.38 | 0.912830 | ||||||||
\(305\) | −671.535 | −0.126072 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1810.36 | −0.336555 | −0.168278 | − | 0.985740i | \(-0.553821\pi\) | ||||
−0.168278 | + | 0.985740i | \(0.553821\pi\) | |||||||
\(308\) | 3952.43 | 0.731204 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4767.68 | −0.873503 | ||||||||
\(311\) | −887.298 | −0.161781 | −0.0808907 | − | 0.996723i | \(-0.525776\pi\) | ||||
−0.0808907 | + | 0.996723i | \(0.525776\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2215.13 | −0.400022 | −0.200011 | − | 0.979794i | \(-0.564098\pi\) | ||||
−0.200011 | + | 0.979794i | \(0.564098\pi\) | |||||||
\(314\) | 13123.6 | 2.35862 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2089.60 | −0.371990 | ||||||||
\(317\) | −658.046 | −0.116592 | −0.0582958 | − | 0.998299i | \(-0.518567\pi\) | ||||
−0.0582958 | + | 0.998299i | \(0.518567\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3333.51 | 0.585081 | ||||||||
\(320\) | −1198.26 | −0.209328 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3860.28 | 0.668089 | ||||||||
\(323\) | 4727.03 | 0.814299 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1498.28 | 0.255721 | ||||||||
\(326\) | 989.433 | 0.168097 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1034.72 | −0.174186 | ||||||||
\(329\) | −1052.67 | −0.176401 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5276.44 | 0.876192 | 0.438096 | − | 0.898928i | \(-0.355653\pi\) | ||||
0.438096 | + | 0.898928i | \(0.355653\pi\) | |||||||
\(332\) | −6615.57 | −1.09360 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −13453.8 | −2.20407 | ||||||||
\(335\) | −4287.67 | −0.699284 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3361.27 | −0.543324 | −0.271662 | − | 0.962393i | \(-0.587573\pi\) | ||||
−0.271662 | + | 0.962393i | \(0.587573\pi\) | |||||||
\(338\) | 5228.24 | 0.841357 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2240.54 | −0.357383 | ||||||||
\(341\) | 5299.44 | 0.841586 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9303.52 | −1.46456 | ||||||||
\(344\) | −1007.15 | −0.157854 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1388.68 | 0.215768 | ||||||||
\(347\) | 9355.54 | 1.44735 | 0.723677 | − | 0.690139i | \(-0.242451\pi\) | ||||
0.723677 | + | 0.690139i | \(0.242451\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7039.30 | 1.07967 | 0.539836 | − | 0.841770i | \(-0.318486\pi\) | ||||
0.539836 | + | 0.841770i | \(0.318486\pi\) | |||||||
\(350\) | −2937.86 | −0.448672 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4701.65 | 0.711929 | ||||||||
\(353\) | 4202.18 | 0.633596 | 0.316798 | − | 0.948493i | \(-0.397392\pi\) | ||||
0.316798 | + | 0.948493i | \(0.397392\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2943.33 | 0.440044 | ||||||||
\(356\) | 2510.56 | 0.373762 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1675.22 | 0.247314 | ||||||||
\(359\) | 588.013 | 0.0864461 | 0.0432230 | − | 0.999065i | \(-0.486237\pi\) | ||||
0.0432230 | + | 0.999065i | \(0.486237\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2783.58 | −0.405828 | ||||||||
\(362\) | −3388.87 | −0.492031 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −11369.9 | −1.63722 | ||||||||
\(365\) | −3090.95 | −0.443255 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7785.11 | −1.10730 | −0.553650 | − | 0.832749i | \(-0.686766\pi\) | ||||
−0.553650 | + | 0.832749i | \(0.686766\pi\) | |||||||
\(368\) | 2489.67 | 0.352671 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 4036.55 | 0.567163 | ||||||||
\(371\) | 1316.40 | 0.184215 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7824.03 | −1.08609 | −0.543047 | − | 0.839702i | \(-0.682729\pi\) | ||||
−0.543047 | + | 0.839702i | \(0.682729\pi\) | |||||||
\(374\) | 5782.62 | 0.799498 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −245.233 | −0.0336355 | ||||||||
\(377\) | −9589.49 | −1.31004 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4679.90 | −0.634275 | −0.317138 | − | 0.948379i | \(-0.602722\pi\) | ||||
−0.317138 | + | 0.948379i | \(0.602722\pi\) | |||||||
\(380\) | −1931.69 | −0.260772 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2247.59 | −0.301038 | ||||||||
\(383\) | −6727.65 | −0.897563 | −0.448782 | − | 0.893641i | \(-0.648142\pi\) | ||||
−0.448782 | + | 0.893641i | \(0.648142\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3265.53 | 0.432278 | ||||||||
\(386\) | −16545.2 | −2.18167 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1218.89 | −0.159483 | ||||||||
\(389\) | −4772.88 | −0.622094 | −0.311047 | − | 0.950395i | \(-0.600680\pi\) | ||||
−0.311047 | + | 0.950395i | \(0.600680\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2432.36 | 0.314603 | ||||||||
\(392\) | −4672.36 | −0.602015 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −18019.9 | −2.30414 | ||||||||
\(395\) | −1726.44 | −0.219916 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4688.95 | −0.592775 | −0.296388 | − | 0.955068i | \(-0.595782\pi\) | ||||
−0.296388 | + | 0.955068i | \(0.595782\pi\) | |||||||
\(398\) | 1176.42 | 0.148163 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1894.76 | −0.236845 | ||||||||
\(401\) | 1533.83 | 0.191012 | 0.0955061 | − | 0.995429i | \(-0.469553\pi\) | ||||
0.0955061 | + | 0.995429i | \(0.469553\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −15244.9 | −1.88437 | ||||||||
\(404\) | 1606.03 | 0.197780 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 18803.3 | 2.29851 | ||||||||
\(407\) | −4486.77 | −0.546439 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8778.82 | −1.06133 | −0.530666 | − | 0.847581i | \(-0.678058\pi\) | ||||
−0.530666 | + | 0.847581i | \(0.678058\pi\) | |||||||
\(410\) | 2655.51 | 0.319869 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3193.01 | −0.381816 | ||||||||
\(413\) | −19284.2 | −2.29761 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5465.84 | −0.646524 | ||||||||
\(416\) | −13525.2 | −1.59406 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 4985.51 | 0.583371 | ||||||||
\(419\) | −4276.05 | −0.498565 | −0.249282 | − | 0.968431i | \(-0.580195\pi\) | ||||
−0.249282 | + | 0.968431i | \(0.580195\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14463.3 | 1.67434 | 0.837169 | − | 0.546944i | \(-0.184209\pi\) | ||||
0.837169 | + | 0.546944i | \(0.184209\pi\) | |||||||
\(422\) | 9142.07 | 1.05457 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 306.671 | 0.0351256 | ||||||||
\(425\) | −1851.15 | −0.211280 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4210.41 | 0.477181 | ||||||||
\(428\) | 12613.3 | 1.42450 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2584.74 | 0.289878 | ||||||||
\(431\) | −2208.11 | −0.246777 | −0.123389 | − | 0.992358i | \(-0.539376\pi\) | ||||
−0.123389 | + | 0.992358i | \(0.539376\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10062.3 | −1.11677 | −0.558386 | − | 0.829581i | \(-0.688579\pi\) | ||||
−0.558386 | + | 0.829581i | \(0.688579\pi\) | |||||||
\(434\) | 29892.6 | 3.30619 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5601.80 | 0.615315 | ||||||||
\(437\) | 2097.07 | 0.229557 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13317.2 | 1.44783 | 0.723915 | − | 0.689889i | \(-0.242341\pi\) | ||||
0.723915 | + | 0.689889i | \(0.242341\pi\) | |||||||
\(440\) | 760.746 | 0.0824253 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −16634.8 | −1.79013 | ||||||||
\(443\) | −14275.1 | −1.53099 | −0.765497 | − | 0.643439i | \(-0.777507\pi\) | ||||
−0.765497 | + | 0.643439i | \(0.777507\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2074.25 | 0.220963 | ||||||||
\(446\) | −8746.95 | −0.928654 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 7512.90 | 0.792302 | ||||||||
\(449\) | −1690.02 | −0.177632 | −0.0888162 | − | 0.996048i | \(-0.528308\pi\) | ||||
−0.0888162 | + | 0.996048i | \(0.528308\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2951.69 | −0.308181 | ||||||||
\(452\) | 3304.36 | 0.343859 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −10209.9 | −1.05545 | ||||||||
\(455\) | −9393.94 | −0.967901 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6664.39 | −0.682159 | −0.341080 | − | 0.940034i | \(-0.610793\pi\) | ||||
−0.341080 | + | 0.940034i | \(0.610793\pi\) | |||||||
\(458\) | −12423.3 | −1.26748 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −993.979 | −0.100749 | ||||||||
\(461\) | 1667.42 | 0.168459 | 0.0842295 | − | 0.996446i | \(-0.473157\pi\) | ||||
0.0842295 | + | 0.996446i | \(0.473157\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5832.02 | −0.585393 | −0.292697 | − | 0.956205i | \(-0.594553\pi\) | ||||
−0.292697 | + | 0.956205i | \(0.594553\pi\) | |||||||
\(464\) | 12127.1 | 1.21334 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −11903.3 | −1.18329 | ||||||||
\(467\) | 17410.6 | 1.72519 | 0.862597 | − | 0.505892i | \(-0.168837\pi\) | ||||
0.862597 | + | 0.505892i | \(0.168837\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 26883.0 | 2.64678 | ||||||||
\(470\) | 629.366 | 0.0617670 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −4492.49 | −0.438101 | ||||||||
\(473\) | −2873.03 | −0.279286 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1595.98 | −0.154165 | ||||||||
\(476\) | 14047.8 | 1.35269 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −922.614 | −0.0882832 | ||||||||
\(479\) | −3279.34 | −0.312812 | −0.156406 | − | 0.987693i | \(-0.549991\pi\) | ||||
−0.156406 | + | 0.987693i | \(0.549991\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12907.1 | 1.22352 | ||||||||
\(482\) | −19821.4 | −1.87311 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5428.25 | −0.509791 | ||||||||
\(485\) | −1007.05 | −0.0942844 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10506.7 | −0.977624 | −0.488812 | − | 0.872389i | \(-0.662570\pi\) | ||||
−0.488812 | + | 0.872389i | \(0.662570\pi\) | |||||||
\(488\) | 980.867 | 0.0909872 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 11991.1 | 1.10552 | ||||||||
\(491\) | −14264.5 | −1.31110 | −0.655548 | − | 0.755154i | \(-0.727562\pi\) | ||||
−0.655548 | + | 0.755154i | \(0.727562\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11848.0 | 1.08237 | ||||||||
\(494\) | −14341.8 | −1.30621 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 19279.1 | 1.74527 | ||||||||
\(497\) | −18454.2 | −1.66556 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9447.40 | 0.847542 | 0.423771 | − | 0.905769i | \(-0.360706\pi\) | ||||
0.423771 | + | 0.905769i | \(0.360706\pi\) | |||||||
\(500\) | 756.468 | 0.0676605 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 10575.6 | 0.940259 | ||||||||
\(503\) | 14579.2 | 1.29235 | 0.646177 | − | 0.763188i | \(-0.276367\pi\) | ||||
0.646177 | + | 0.763188i | \(0.276367\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1326.91 | 0.116925 | ||||||||
\(506\) | 2565.37 | 0.225385 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −5906.33 | −0.515849 | ||||||||
\(509\) | 8410.65 | 0.732407 | 0.366204 | − | 0.930535i | \(-0.380657\pi\) | ||||
0.366204 | + | 0.930535i | \(0.380657\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 19379.8 | 1.67771 | ||||||||
\(512\) | 12676.3 | 1.09417 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −7063.02 | −0.606102 | ||||||||
\(515\) | −2638.09 | −0.225725 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −699.562 | −0.0595100 | ||||||||
\(518\) | −25308.5 | −2.14670 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2188.43 | −0.184556 | ||||||||
\(521\) | 10058.1 | 0.845781 | 0.422890 | − | 0.906181i | \(-0.361016\pi\) | ||||
0.422890 | + | 0.906181i | \(0.361016\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20006.3 | 1.67269 | 0.836344 | − | 0.548205i | \(-0.184688\pi\) | ||||
0.836344 | + | 0.548205i | \(0.184688\pi\) | |||||||
\(524\) | −9859.67 | −0.821988 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2073.00 | 0.171838 | ||||||||
\(527\) | 18835.3 | 1.55689 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11087.9 | −0.911311 | ||||||||
\(530\) | −787.038 | −0.0645033 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 12111.4 | 0.987019 | ||||||||
\(533\) | 8491.12 | 0.690040 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10421.2 | 0.842147 | ||||||||
\(536\) | 6262.72 | 0.504679 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 12608.2 | 1.01037 | ||||||||
\(539\) | −13328.5 | −1.06512 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1884.15 | −0.149734 | −0.0748668 | − | 0.997194i | \(-0.523853\pi\) | ||||
−0.0748668 | + | 0.997194i | \(0.523853\pi\) | |||||||
\(542\) | −12497.2 | −0.990404 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 16710.7 | 1.31703 | ||||||||
\(545\) | 4628.25 | 0.363766 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17996.5 | −1.40672 | −0.703358 | − | 0.710836i | \(-0.748317\pi\) | ||||
−0.703358 | + | 0.710836i | \(0.748317\pi\) | |||||||
\(548\) | 4002.93 | 0.312038 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1952.37 | −0.151363 | ||||||||
\(551\) | 10214.8 | 0.789774 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10824.5 | 0.832378 | ||||||||
\(554\) | −20194.5 | −1.54870 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 8369.49 | 0.638391 | ||||||||
\(557\) | −3615.76 | −0.275054 | −0.137527 | − | 0.990498i | \(-0.543915\pi\) | ||||
−0.137527 | + | 0.990498i | \(0.543915\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8264.84 | 0.625341 | ||||||||
\(560\) | 11879.8 | 0.896454 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 13932.3 | 1.04573 | ||||||||
\(563\) | 14821.8 | 1.10953 | 0.554765 | − | 0.832007i | \(-0.312808\pi\) | ||||
0.554765 | + | 0.832007i | \(0.312808\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2730.09 | 0.203285 | ||||||||
\(566\) | 10378.9 | 0.770771 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4299.13 | −0.317583 | ||||||||
\(569\) | 22449.5 | 1.65401 | 0.827005 | − | 0.562195i | \(-0.190043\pi\) | ||||
0.827005 | + | 0.562195i | \(0.190043\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16013.5 | −1.17363 | −0.586817 | − | 0.809720i | \(-0.699619\pi\) | ||||
−0.586817 | + | 0.809720i | \(0.699619\pi\) | |||||||
\(572\) | −7555.97 | −0.552327 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −16649.6 | −1.21070 | ||||||||
\(575\) | −821.234 | −0.0595615 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3096.97 | 0.223446 | 0.111723 | − | 0.993739i | \(-0.464363\pi\) | ||||
0.111723 | + | 0.993739i | \(0.464363\pi\) | |||||||
\(578\) | 2135.97 | 0.153711 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −4841.66 | −0.346619 | ||||||||
\(581\) | 34269.9 | 2.44708 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 874.820 | 0.0621464 | ||||||||
\(584\) | 4514.76 | 0.319901 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −13045.0 | −0.919595 | ||||||||
\(587\) | 24624.7 | 1.73147 | 0.865734 | − | 0.500504i | \(-0.166852\pi\) | ||||
0.865734 | + | 0.500504i | \(0.166852\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16239.0 | 1.13602 | ||||||||
\(590\) | 11529.5 | 0.804511 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −16322.6 | −1.13320 | ||||||||
\(593\) | 27128.8 | 1.87866 | 0.939330 | − | 0.343014i | \(-0.111448\pi\) | ||||
0.939330 | + | 0.343014i | \(0.111448\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11606.4 | 0.799691 | ||||||||
\(596\) | 19144.6 | 1.31576 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −7379.79 | −0.504652 | ||||||||
\(599\) | 5631.75 | 0.384152 | 0.192076 | − | 0.981380i | \(-0.438478\pi\) | ||||
0.192076 | + | 0.981380i | \(0.438478\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14751.8 | −1.00123 | −0.500613 | − | 0.865671i | \(-0.666892\pi\) | ||||
−0.500613 | + | 0.865671i | \(0.666892\pi\) | |||||||
\(602\) | −16205.9 | −1.09718 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −15485.2 | −1.04318 | ||||||||
\(605\) | −4484.87 | −0.301382 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14782.1 | −0.988445 | −0.494222 | − | 0.869336i | \(-0.664547\pi\) | ||||
−0.494222 | + | 0.869336i | \(0.664547\pi\) | |||||||
\(608\) | 14407.2 | 0.961000 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2517.29 | −0.167085 | ||||||||
\(611\) | 2012.43 | 0.133247 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4947.28 | 0.325969 | 0.162984 | − | 0.986629i | \(-0.447888\pi\) | ||||
0.162984 | + | 0.986629i | \(0.447888\pi\) | |||||||
\(614\) | −6786.24 | −0.446043 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4769.75 | −0.311979 | ||||||||
\(617\) | −3743.65 | −0.244268 | −0.122134 | − | 0.992514i | \(-0.538974\pi\) | ||||
−0.122134 | + | 0.992514i | \(0.538974\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6138.74 | 0.398605 | 0.199303 | − | 0.979938i | \(-0.436132\pi\) | ||||
0.199303 | + | 0.979938i | \(0.436132\pi\) | |||||||
\(620\) | −7697.01 | −0.498580 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −3326.09 | −0.214412 | ||||||||
\(623\) | −13005.2 | −0.836343 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | −8303.57 | −0.530156 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 21186.9 | 1.34626 | ||||||||
\(629\) | −15946.9 | −1.01088 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5548.00 | −0.350019 | −0.175010 | − | 0.984567i | \(-0.555996\pi\) | ||||
−0.175010 | + | 0.984567i | \(0.555996\pi\) | |||||||
\(632\) | 2521.70 | 0.158715 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −2466.73 | −0.154521 | ||||||||
\(635\) | −4879.86 | −0.304963 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 38342.1 | 2.38488 | ||||||||
\(638\) | 12495.9 | 0.775418 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 4535.43 | 0.280123 | ||||||||
\(641\) | −11608.1 | −0.715277 | −0.357639 | − | 0.933860i | \(-0.616418\pi\) | ||||
−0.357639 | + | 0.933860i | \(0.616418\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12721.7 | −0.780240 | −0.390120 | − | 0.920764i | \(-0.627567\pi\) | ||||
−0.390120 | + | 0.920764i | \(0.627567\pi\) | |||||||
\(644\) | 6232.09 | 0.381333 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 17719.6 | 1.07921 | ||||||||
\(647\) | −28203.7 | −1.71376 | −0.856879 | − | 0.515518i | \(-0.827600\pi\) | ||||
−0.856879 | + | 0.515518i | \(0.827600\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12815.4 | −0.775115 | ||||||||
\(650\) | 5616.39 | 0.338912 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1597.36 | 0.0959468 | ||||||||
\(653\) | −22692.8 | −1.35993 | −0.679966 | − | 0.733243i | \(-0.738006\pi\) | ||||
−0.679966 | + | 0.733243i | \(0.738006\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8146.14 | −0.485948 | ||||||||
\(656\) | −10738.1 | −0.639103 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −3946.02 | −0.233787 | ||||||||
\(659\) | 6004.00 | 0.354905 | 0.177453 | − | 0.984129i | \(-0.443214\pi\) | ||||
0.177453 | + | 0.984129i | \(0.443214\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11916.4 | 0.701199 | 0.350600 | − | 0.936525i | \(-0.385978\pi\) | ||||
0.350600 | + | 0.936525i | \(0.385978\pi\) | |||||||
\(662\) | 19779.1 | 1.16123 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 7983.59 | 0.466602 | ||||||||
\(665\) | 10006.5 | 0.583512 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5256.19 | 0.305128 | ||||||||
\(668\) | −21720.0 | −1.25804 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −16072.6 | −0.926774 | ||||||||
\(671\) | 2798.06 | 0.160980 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16033.7 | −0.918356 | −0.459178 | − | 0.888344i | \(-0.651856\pi\) | ||||
−0.459178 | + | 0.888344i | \(0.651856\pi\) | |||||||
\(674\) | −12599.9 | −0.720077 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 8440.54 | 0.480231 | ||||||||
\(677\) | 11311.9 | 0.642173 | 0.321086 | − | 0.947050i | \(-0.395952\pi\) | ||||
0.321086 | + | 0.947050i | \(0.395952\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6314.06 | 0.356865 | ||||||||
\(680\) | 2703.85 | 0.152483 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 19865.3 | 1.11537 | ||||||||
\(683\) | −652.395 | −0.0365493 | −0.0182747 | − | 0.999833i | \(-0.505817\pi\) | ||||
−0.0182747 | + | 0.999833i | \(0.505817\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3307.25 | 0.184472 | ||||||||
\(686\) | −34874.9 | −1.94100 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −10451.9 | −0.579180 | ||||||||
\(689\) | −2516.59 | −0.139150 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12537.9 | 0.690250 | 0.345125 | − | 0.938557i | \(-0.387837\pi\) | ||||
0.345125 | + | 0.938557i | \(0.387837\pi\) | |||||||
\(692\) | 2241.90 | 0.123157 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 35069.8 | 1.91820 | ||||||||
\(695\) | 6914.95 | 0.377408 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10490.9 | −0.570119 | ||||||||
\(698\) | 26387.3 | 1.43091 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −4742.93 | −0.256094 | ||||||||
\(701\) | 5880.60 | 0.316844 | 0.158422 | − | 0.987372i | \(-0.449359\pi\) | ||||
0.158422 | + | 0.987372i | \(0.449359\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13748.7 | −0.737614 | ||||||||
\(704\) | 4992.75 | 0.267289 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 15752.1 | 0.839716 | ||||||||
\(707\) | −8319.54 | −0.442558 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6406.66 | 0.339361 | 0.169681 | − | 0.985499i | \(-0.445726\pi\) | ||||
0.169681 | + | 0.985499i | \(0.445726\pi\) | |||||||
\(710\) | 11033.3 | 0.583198 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3029.72 | −0.159471 | ||||||||
\(713\) | 8356.01 | 0.438899 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6242.81 | −0.326528 | ||||||||
\(716\) | 2704.51 | 0.141162 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 2204.21 | 0.114569 | ||||||||
\(719\) | 21907.0 | 1.13629 | 0.568144 | − | 0.822929i | \(-0.307662\pi\) | ||||
0.568144 | + | 0.822929i | \(0.307662\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16540.4 | 0.854364 | ||||||||
\(722\) | −10434.4 | −0.537852 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −5471.05 | −0.280843 | ||||||||
\(725\) | −4000.22 | −0.204916 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13370.9 | 0.682118 | 0.341059 | − | 0.940042i | \(-0.389214\pi\) | ||||
0.341059 | + | 0.940042i | \(0.389214\pi\) | |||||||
\(728\) | 13721.1 | 0.698542 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −11586.6 | −0.587453 | ||||||||
\(731\) | −10211.4 | −0.516664 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 30191.1 | 1.52133 | 0.760663 | − | 0.649147i | \(-0.224874\pi\) | ||||
0.760663 | + | 0.649147i | \(0.224874\pi\) | |||||||
\(734\) | −29183.0 | −1.46752 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7413.44 | 0.371281 | ||||||||
\(737\) | 17865.2 | 0.892910 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −11624.7 | −0.578650 | −0.289325 | − | 0.957231i | \(-0.593431\pi\) | ||||
−0.289325 | + | 0.957231i | \(0.593431\pi\) | |||||||
\(740\) | 6516.67 | 0.323727 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4934.60 | 0.244144 | ||||||||
\(743\) | −5254.37 | −0.259440 | −0.129720 | − | 0.991551i | \(-0.541408\pi\) | ||||
−0.129720 | + | 0.991551i | \(0.541408\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15817.5 | 0.777862 | ||||||||
\(746\) | −29328.9 | −1.43942 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 9335.55 | 0.456339 | ||||||||
\(749\) | −65339.3 | −3.18751 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29228.8 | −1.42020 | −0.710102 | − | 0.704099i | \(-0.751351\pi\) | ||||
−0.710102 | + | 0.704099i | \(0.751351\pi\) | |||||||
\(752\) | −2544.97 | −0.123411 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −35946.8 | −1.73622 | ||||||||
\(755\) | −12794.0 | −0.616716 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32885.9 | 1.57894 | 0.789470 | − | 0.613789i | \(-0.210355\pi\) | ||||
0.789470 | + | 0.613789i | \(0.210355\pi\) | |||||||
\(758\) | −17542.9 | −0.840617 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2331.14 | 0.111262 | ||||||||
\(761\) | −13268.2 | −0.632027 | −0.316014 | − | 0.948755i | \(-0.602345\pi\) | ||||
−0.316014 | + | 0.948755i | \(0.602345\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −29018.4 | −1.37685 | ||||||||
\(764\) | −3628.54 | −0.171827 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −25219.0 | −1.18956 | ||||||||
\(767\) | 36866.1 | 1.73554 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 34285.8 | 1.60777 | 0.803887 | − | 0.594782i | \(-0.202762\pi\) | ||||
0.803887 | + | 0.594782i | \(0.202762\pi\) | |||||||
\(770\) | 12241.1 | 0.572906 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −26710.8 | −1.24526 | ||||||||
\(773\) | −27987.1 | −1.30223 | −0.651117 | − | 0.758978i | \(-0.725699\pi\) | ||||
−0.651117 | + | 0.758978i | \(0.725699\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6359.34 | −0.294754 | ||||||||
\(776\) | 1470.94 | 0.0680458 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −17891.4 | −0.824472 | ||||||||
\(779\) | −9044.81 | −0.416000 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12263.8 | −0.561888 | ||||||||
\(782\) | 9117.88 | 0.416950 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −48488.5 | −2.20884 | ||||||||
\(785\) | 17504.8 | 0.795890 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 354.799 | 0.0160702 | 0.00803509 | − | 0.999968i | \(-0.497442\pi\) | ||||
0.00803509 | + | 0.999968i | \(0.497442\pi\) | |||||||
\(788\) | −29091.6 | −1.31516 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −6471.68 | −0.291458 | ||||||||
\(791\) | −17117.2 | −0.769430 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8049.15 | −0.360446 | ||||||||
\(794\) | −17576.8 | −0.785616 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1899.23 | 0.0845686 | ||||||||
\(797\) | 12801.3 | 0.568940 | 0.284470 | − | 0.958685i | \(-0.408182\pi\) | ||||
0.284470 | + | 0.958685i | \(0.408182\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2486.39 | −0.110090 | ||||||||
\(800\) | −5641.99 | −0.249343 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 5749.67 | 0.253152 | ||||||||
\(803\) | 12879.0 | 0.565988 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5149.00 | 0.225439 | ||||||||
\(806\) | −57146.4 | −2.49739 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1938.14 | −0.0843855 | ||||||||
\(809\) | −16374.9 | −0.711632 | −0.355816 | − | 0.934556i | \(-0.615797\pi\) | ||||
−0.355816 | + | 0.934556i | \(0.615797\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −35518.2 | −1.53787 | −0.768936 | − | 0.639326i | \(-0.779214\pi\) | ||||
−0.768936 | + | 0.639326i | \(0.779214\pi\) | |||||||
\(812\) | 30356.4 | 1.31195 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −16818.9 | −0.724206 | ||||||||
\(815\) | 1319.75 | 0.0567225 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8803.77 | −0.376995 | ||||||||
\(818\) | −32908.0 | −1.40660 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4287.10 | 0.182576 | ||||||||
\(821\) | 42943.9 | 1.82552 | 0.912760 | − | 0.408496i | \(-0.133947\pi\) | ||||
0.912760 | + | 0.408496i | \(0.133947\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7916.93 | −0.335318 | −0.167659 | − | 0.985845i | \(-0.553621\pi\) | ||||
−0.167659 | + | 0.985845i | \(0.553621\pi\) | |||||||
\(824\) | 3853.29 | 0.162907 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −72288.0 | −3.04506 | ||||||||
\(827\) | 18774.4 | 0.789421 | 0.394710 | − | 0.918806i | \(-0.370845\pi\) | ||||
0.394710 | + | 0.918806i | \(0.370845\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 22166.1 | 0.928661 | 0.464330 | − | 0.885662i | \(-0.346295\pi\) | ||||
0.464330 | + | 0.885662i | \(0.346295\pi\) | |||||||
\(830\) | −20489.0 | −0.856850 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −14362.6 | −0.598478 | ||||||||
\(833\) | −47372.5 | −1.97042 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −17945.3 | −0.743738 | ||||||||
\(836\) | 8048.68 | 0.332978 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −16029.1 | −0.660757 | ||||||||
\(839\) | 42590.8 | 1.75256 | 0.876279 | − | 0.481804i | \(-0.160018\pi\) | ||||
0.876279 | + | 0.481804i | \(0.160018\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1213.82 | 0.0497690 | ||||||||
\(842\) | 54216.5 | 2.21903 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 14759.1 | 0.601930 | ||||||||
\(845\) | 6973.65 | 0.283906 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 28119.4 | 1.14072 | ||||||||
\(848\) | 3182.54 | 0.128879 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −6939.16 | −0.280013 | ||||||||
\(851\) | −7074.61 | −0.284976 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26461.1 | 1.06215 | 0.531074 | − | 0.847326i | \(-0.321789\pi\) | ||||
0.531074 | + | 0.847326i | \(0.321789\pi\) | |||||||
\(854\) | 15783.0 | 0.632416 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −15221.6 | −0.607784 | ||||||||
\(857\) | −20009.0 | −0.797543 | −0.398772 | − | 0.917050i | \(-0.630563\pi\) | ||||
−0.398772 | + | 0.917050i | \(0.630563\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17818.1 | −0.707735 | −0.353868 | − | 0.935296i | \(-0.615134\pi\) | ||||
−0.353868 | + | 0.935296i | \(0.615134\pi\) | |||||||
\(860\) | 4172.85 | 0.165457 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −8277.26 | −0.327059 | ||||||||
\(863\) | 12769.5 | 0.503683 | 0.251841 | − | 0.967769i | \(-0.418964\pi\) | ||||
0.251841 | + | 0.967769i | \(0.418964\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1852.28 | 0.0728085 | ||||||||
\(866\) | −37719.1 | −1.48008 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 48259.0 | 1.88712 | ||||||||
\(869\) | 7193.50 | 0.280809 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −51392.9 | −1.99929 | ||||||||
\(872\) | −6760.19 | −0.262533 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 7861.01 | 0.304236 | ||||||||
\(875\) | −3918.65 | −0.151399 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 27477.3 | 1.05797 | 0.528986 | − | 0.848630i | \(-0.322572\pi\) | ||||
0.528986 | + | 0.848630i | \(0.322572\pi\) | |||||||
\(878\) | 49920.5 | 1.91883 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 7894.82 | 0.302425 | ||||||||
\(881\) | 31509.1 | 1.20496 | 0.602480 | − | 0.798134i | \(-0.294179\pi\) | ||||
0.602480 | + | 0.798134i | \(0.294179\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5271.46 | 0.200905 | 0.100452 | − | 0.994942i | \(-0.467971\pi\) | ||||
0.100452 | + | 0.994942i | \(0.467971\pi\) | |||||||
\(884\) | −26855.5 | −1.02178 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −53511.1 | −2.02905 | ||||||||
\(887\) | 10433.8 | 0.394963 | 0.197481 | − | 0.980307i | \(-0.436724\pi\) | ||||
0.197481 | + | 0.980307i | \(0.436724\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 30595.9 | 1.15428 | ||||||||
\(890\) | 7775.45 | 0.292847 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −14121.2 | −0.530059 | ||||||||
\(893\) | −2143.65 | −0.0803299 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2234.49 | 0.0834533 | ||||||||
\(896\) | −28436.4 | −1.06026 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −6335.15 | −0.235419 | ||||||||
\(899\) | 40702.0 | 1.51000 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3109.30 | 0.114967 | ||||||||
\(902\) | −11064.6 | −0.408438 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3987.67 | −0.146712 | ||||||||
\(905\) | −4520.23 | −0.166030 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20686.6 | 0.757317 | 0.378659 | − | 0.925536i | \(-0.376385\pi\) | ||||
0.378659 | + | 0.925536i | \(0.376385\pi\) | |||||||
\(908\) | −16483.1 | −0.602434 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −35213.8 | −1.28278 | ||||||||
\(911\) | −23640.1 | −0.859748 | −0.429874 | − | 0.902889i | \(-0.641442\pi\) | ||||
−0.429874 | + | 0.902889i | \(0.641442\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 22774.3 | 0.825541 | ||||||||
\(914\) | −24981.9 | −0.904078 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −20056.4 | −0.723454 | ||||||||
\(917\) | 51075.0 | 1.83931 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 27335.2 | 0.981180 | 0.490590 | − | 0.871390i | \(-0.336781\pi\) | ||||
0.490590 | + | 0.871390i | \(0.336781\pi\) | |||||||
\(920\) | 1199.52 | 0.0429860 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 6250.44 | 0.223262 | ||||||||
\(923\) | 35279.3 | 1.25811 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5384.13 | 0.191383 | ||||||||
\(926\) | −21861.7 | −0.775832 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 36110.7 | 1.27736 | ||||||||
\(929\) | −13228.6 | −0.467185 | −0.233593 | − | 0.972335i | \(-0.575048\pi\) | ||||
−0.233593 | + | 0.972335i | \(0.575048\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −40842.4 | −1.43776 | ||||||||
\(932\) | −19216.9 | −0.675399 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 65264.7 | 2.28643 | ||||||||
\(935\) | 7713.11 | 0.269782 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −18740.4 | −0.653387 | −0.326693 | − | 0.945130i | \(-0.605934\pi\) | ||||
−0.326693 | + | 0.945130i | \(0.605934\pi\) | |||||||
\(938\) | 100773. | 3.50783 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1016.06 | 0.0352555 | ||||||||
\(941\) | 54489.0 | 1.88766 | 0.943832 | − | 0.330427i | \(-0.107193\pi\) | ||||
0.943832 | + | 0.330427i | \(0.107193\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4654.15 | −0.160721 | ||||||||
\(944\) | −46621.8 | −1.60743 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −10769.7 | −0.370142 | ||||||||
\(947\) | −11282.7 | −0.387158 | −0.193579 | − | 0.981085i | \(-0.562010\pi\) | ||||
−0.193579 | + | 0.981085i | \(0.562010\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −37048.8 | −1.26729 | ||||||||
\(950\) | −5982.62 | −0.204318 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −16952.7 | −0.577144 | ||||||||
\(953\) | −51190.0 | −1.73999 | −0.869994 | − | 0.493063i | \(-0.835877\pi\) | ||||
−0.869994 | + | 0.493063i | \(0.835877\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2997.93 | −0.101582 | ||||||||
\(956\) | −1489.48 | −0.0503905 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −12292.8 | −0.414575 | ||||||||
\(959\) | −20735.9 | −0.698225 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 34914.9 | 1.17199 | ||||||||
\(962\) | 48383.0 | 1.62155 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −32000.0 | −1.06914 | ||||||||
\(965\) | −22068.7 | −0.736182 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23143.5 | 0.769643 | 0.384822 | − | 0.922991i | \(-0.374263\pi\) | ||||
0.384822 | + | 0.922991i | \(0.374263\pi\) | |||||||
\(968\) | 6550.76 | 0.217510 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −3775.00 | −0.124957 | ||||||||
\(971\) | −34124.5 | −1.12782 | −0.563908 | − | 0.825838i | \(-0.690703\pi\) | ||||
−0.563908 | + | 0.825838i | \(0.690703\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −43355.6 | −1.42848 | ||||||||
\(974\) | −39384.9 | −1.29566 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10179.2 | 0.333839 | ||||||||
\(977\) | −36463.7 | −1.19404 | −0.597020 | − | 0.802226i | \(-0.703649\pi\) | ||||
−0.597020 | + | 0.802226i | \(0.703649\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8642.68 | −0.282146 | ||||||||
\(980\) | 19358.6 | 0.631009 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −53471.4 | −1.73762 | ||||||||
\(983\) | −51541.6 | −1.67235 | −0.836176 | − | 0.548462i | \(-0.815214\pi\) | ||||
−0.836176 | + | 0.548462i | \(0.815214\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −24035.7 | −0.777505 | ||||||||
\(986\) | 44413.0 | 1.43448 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −23153.6 | −0.745561 | ||||||||
\(989\) | −4530.12 | −0.145652 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 34299.1 | 1.09944 | 0.549721 | − | 0.835348i | \(-0.314734\pi\) | ||||
0.549721 | + | 0.835348i | \(0.314734\pi\) | |||||||
\(992\) | 57406.9 | 1.83737 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −69176.7 | −2.20740 | ||||||||
\(995\) | 1569.16 | 0.0499958 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21297.0 | 0.676512 | 0.338256 | − | 0.941054i | \(-0.390163\pi\) | ||||
0.338256 | + | 0.941054i | \(0.390163\pi\) | |||||||
\(998\) | 35414.2 | 1.12326 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 405.4.a.h.1.3 | 3 | ||
3.2 | odd | 2 | 405.4.a.j.1.1 | 3 | |||
5.4 | even | 2 | 2025.4.a.s.1.1 | 3 | |||
9.2 | odd | 6 | 135.4.e.b.91.3 | 6 | |||
9.4 | even | 3 | 45.4.e.b.16.1 | ✓ | 6 | ||
9.5 | odd | 6 | 135.4.e.b.46.3 | 6 | |||
9.7 | even | 3 | 45.4.e.b.31.1 | yes | 6 | ||
15.14 | odd | 2 | 2025.4.a.q.1.3 | 3 | |||
45.4 | even | 6 | 225.4.e.c.151.3 | 6 | |||
45.7 | odd | 12 | 225.4.k.c.49.5 | 12 | |||
45.13 | odd | 12 | 225.4.k.c.124.5 | 12 | |||
45.22 | odd | 12 | 225.4.k.c.124.2 | 12 | |||
45.34 | even | 6 | 225.4.e.c.76.3 | 6 | |||
45.43 | odd | 12 | 225.4.k.c.49.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.4.e.b.16.1 | ✓ | 6 | 9.4 | even | 3 | ||
45.4.e.b.31.1 | yes | 6 | 9.7 | even | 3 | ||
135.4.e.b.46.3 | 6 | 9.5 | odd | 6 | |||
135.4.e.b.91.3 | 6 | 9.2 | odd | 6 | |||
225.4.e.c.76.3 | 6 | 45.34 | even | 6 | |||
225.4.e.c.151.3 | 6 | 45.4 | even | 6 | |||
225.4.k.c.49.2 | 12 | 45.43 | odd | 12 | |||
225.4.k.c.49.5 | 12 | 45.7 | odd | 12 | |||
225.4.k.c.124.2 | 12 | 45.22 | odd | 12 | |||
225.4.k.c.124.5 | 12 | 45.13 | odd | 12 | |||
405.4.a.h.1.3 | 3 | 1.1 | even | 1 | trivial | ||
405.4.a.j.1.1 | 3 | 3.2 | odd | 2 | |||
2025.4.a.q.1.3 | 3 | 15.14 | odd | 2 | |||
2025.4.a.s.1.1 | 3 | 5.4 | even | 2 |