Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2312,4,Mod(1,2312)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2312, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2312.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2312 = 2^{3} \cdot 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2312.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: | \(136.412415933\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 294 x^{16} - 14 x^{15} + 34371 x^{14} + 2670 x^{13} - 2054705 x^{12} - 160284 x^{11} + 67981059 x^{10} + 2824200 x^{9} - 1279285428 x^{8} + \cdots - 176969301147 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{15}\cdot 17^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Root | \(-9.04549\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2312.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 10.0455 | 1.93326 | 0.966628 | − | 0.256186i | \(-0.0824658\pi\) | ||||
0.966628 | + | 0.256186i | \(0.0824658\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −13.8476 | −1.23856 | −0.619282 | − | 0.785169i | \(-0.712576\pi\) | ||||
−0.619282 | + | 0.785169i | \(0.712576\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 18.1085 | 0.977767 | 0.488883 | − | 0.872349i | \(-0.337404\pi\) | ||||
0.488883 | + | 0.872349i | \(0.337404\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 73.9118 | 2.73748 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −46.2930 | −1.26890 | −0.634448 | − | 0.772965i | \(-0.718773\pi\) | ||||
−0.634448 | + | 0.772965i | \(0.718773\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 65.8265 | 1.40438 | 0.702192 | − | 0.711988i | \(-0.252205\pi\) | ||||
0.702192 | + | 0.711988i | \(0.252205\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −139.106 | −2.39446 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −19.0550 | −0.230079 | −0.115040 | − | 0.993361i | \(-0.536700\pi\) | ||||
−0.115040 | + | 0.993361i | \(0.536700\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 181.909 | 1.89027 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 194.354 | 1.76199 | 0.880993 | − | 0.473128i | \(-0.156875\pi\) | ||||
0.880993 | + | 0.473128i | \(0.156875\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 66.7550 | 0.534040 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 471.252 | 3.35898 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −118.661 | −0.759823 | −0.379911 | − | 0.925023i | \(-0.624046\pi\) | ||||
−0.379911 | + | 0.925023i | \(0.624046\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.17687 | 0.0241996 | 0.0120998 | − | 0.999927i | \(-0.496148\pi\) | ||||
0.0120998 | + | 0.999927i | \(0.496148\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −465.036 | −2.45310 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −250.759 | −1.21103 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 270.949 | 1.20388 | 0.601942 | − | 0.798540i | \(-0.294394\pi\) | ||||
0.601942 | + | 0.798540i | \(0.294394\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 661.259 | 2.71503 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −31.6127 | −0.120416 | −0.0602082 | − | 0.998186i | \(-0.519176\pi\) | ||||
−0.0602082 | + | 0.998186i | \(0.519176\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.51835 | 0.0337566 | 0.0168783 | − | 0.999858i | \(-0.494627\pi\) | ||||
0.0168783 | + | 0.999858i | \(0.494627\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1023.50 | −3.39054 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −471.665 | −1.46382 | −0.731909 | − | 0.681402i | \(-0.761371\pi\) | ||||
−0.731909 | + | 0.681402i | \(0.761371\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −15.0824 | −0.0439721 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −96.9167 | −0.251180 | −0.125590 | − | 0.992082i | \(-0.540082\pi\) | ||||
−0.125590 | + | 0.992082i | \(0.540082\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 641.045 | 1.57161 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −191.416 | −0.444802 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 854.508 | 1.88555 | 0.942775 | − | 0.333429i | \(-0.108206\pi\) | ||||
0.942775 | + | 0.333429i | \(0.108206\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −171.489 | −0.359950 | −0.179975 | − | 0.983671i | \(-0.557602\pi\) | ||||
−0.179975 | + | 0.983671i | \(0.557602\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1338.43 | 2.67661 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −911.536 | −1.73942 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.33083 | −0.0151906 | −0.00759532 | − | 0.999971i | \(-0.502418\pi\) | ||||
−0.00759532 | + | 0.999971i | \(0.502418\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1952.39 | 3.40637 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 51.0425 | 0.0853187 | 0.0426594 | − | 0.999090i | \(-0.486417\pi\) | ||||
0.0426594 | + | 0.999090i | \(0.486417\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 946.835 | 1.51806 | 0.759032 | − | 0.651053i | \(-0.225673\pi\) | ||||
0.759032 | + | 0.651053i | \(0.225673\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 670.587 | 1.03244 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −838.297 | −1.24069 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 16.0587 | 0.0228702 | 0.0114351 | − | 0.999935i | \(-0.496360\pi\) | ||||
0.0114351 | + | 0.999935i | \(0.496360\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2738.34 | 3.75630 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1243.38 | 1.64432 | 0.822161 | − | 0.569254i | \(-0.192768\pi\) | ||||
0.822161 | + | 0.569254i | \(0.192768\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1192.01 | −1.46893 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1364.62 | −1.62527 | −0.812635 | − | 0.582773i | \(-0.801968\pi\) | ||||
−0.812635 | + | 0.582773i | \(0.801968\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1192.02 | 1.37316 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 41.9587 | 0.0467840 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 263.865 | 0.284968 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1166.56 | 1.22110 | 0.610550 | − | 0.791978i | \(-0.290949\pi\) | ||||
0.610550 | + | 0.791978i | \(0.290949\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3421.60 | −3.47357 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −647.569 | −0.637976 | −0.318988 | − | 0.947759i | \(-0.603343\pi\) | ||||
−0.318988 | + | 0.947759i | \(0.603343\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −167.539 | −0.160273 | −0.0801363 | − | 0.996784i | \(-0.525536\pi\) | ||||
−0.0801363 | + | 0.996784i | \(0.525536\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2518.99 | −2.34122 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −541.412 | −0.489161 | −0.244581 | − | 0.969629i | \(-0.578650\pi\) | ||||
−0.244581 | + | 0.969629i | \(0.578650\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 212.961 | 0.187137 | 0.0935685 | − | 0.995613i | \(-0.470173\pi\) | ||||
0.0935685 | + | 0.995613i | \(0.470173\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2721.81 | 2.32741 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 888.160 | 0.739390 | 0.369695 | − | 0.929153i | \(-0.379462\pi\) | ||||
0.369695 | + | 0.929153i | \(0.379462\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2691.34 | −2.18233 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4865.36 | 3.84447 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 812.042 | 0.610099 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −317.565 | −0.232796 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 806.551 | 0.577121 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 530.718 | 0.370816 | 0.185408 | − | 0.982662i | \(-0.440639\pi\) | ||||
0.185408 | + | 0.982662i | \(0.440639\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 95.6165 | 0.0652602 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 644.014 | 0.429525 | 0.214763 | − | 0.976666i | \(-0.431102\pi\) | ||||
0.214763 | + | 0.976666i | \(0.431102\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −345.057 | −0.224964 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −6525.70 | −4.16032 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2424.52 | 1.51198 | 0.755988 | − | 0.654585i | \(-0.227157\pi\) | ||||
0.755988 | + | 0.654585i | \(0.227157\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2242.69 | −1.36850 | −0.684252 | − | 0.729246i | \(-0.739871\pi\) | ||||
−0.684252 | + | 0.729246i | \(0.739871\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4738.11 | −2.82994 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3047.31 | −1.78202 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1643.17 | 0.941089 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −151.510 | −0.0850092 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −455.171 | −0.250262 | −0.125131 | − | 0.992140i | \(-0.539935\pi\) | ||||
−0.125131 | + | 0.992140i | \(0.539935\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −746.455 | −0.402289 | −0.201145 | − | 0.979562i | \(-0.564466\pi\) | ||||
−0.201145 | + | 0.979562i | \(0.564466\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −57.8395 | −0.0299728 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1565.75 | 0.795926 | 0.397963 | − | 0.917401i | \(-0.369717\pi\) | ||||
0.397963 | + | 0.917401i | \(0.369717\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −973.576 | −0.485595 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3519.47 | 1.72281 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1510.00 | 0.725596 | 0.362798 | − | 0.931868i | \(-0.381822\pi\) | ||||
0.362798 | + | 0.931868i | \(0.381822\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6439.61 | 3.03832 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −961.994 | −0.445756 | −0.222878 | − | 0.974846i | \(-0.571545\pi\) | ||||
−0.222878 | + | 0.974846i | \(0.571545\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2136.13 | 0.972292 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1408.39 | −0.629837 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 756.380 | 0.332407 | 0.166204 | − | 0.986091i | \(-0.446849\pi\) | ||||
0.166204 | + | 0.986091i | \(0.446849\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1208.83 | 0.522167 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8583.95 | 3.64525 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 390.689 | 0.163137 | 0.0815683 | − | 0.996668i | \(-0.474007\pi\) | ||||
0.0815683 | + | 0.996668i | \(0.474007\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1969.73 | −0.808888 | −0.404444 | − | 0.914563i | \(-0.632535\pi\) | ||||
−0.404444 | + | 0.914563i | \(0.632535\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1722.70 | −0.695876 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3751.98 | −1.49109 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 8533.67 | 3.28430 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 422.510 | 0.160061 | 0.0800307 | − | 0.996792i | \(-0.474498\pi\) | ||||
0.0800307 | + | 0.996792i | \(0.474498\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1790.64 | 0.667839 | 0.333919 | − | 0.942602i | \(-0.391629\pi\) | ||||
0.333919 | + | 0.942602i | \(0.391629\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −9156.83 | −3.36274 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2580.69 | 0.933331 | 0.466666 | − | 0.884434i | \(-0.345455\pi\) | ||||
0.466666 | + | 0.884434i | \(0.345455\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1201.62 | −0.428043 | −0.214022 | − | 0.976829i | \(-0.568656\pi\) | ||||
−0.214022 | + | 0.976829i | \(0.568656\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −83.6873 | −0.0293674 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2148.78 | −0.742929 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 437.759 | 0.149143 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 14365.1 | 4.82340 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 882.112 | 0.291947 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5001.53 | 1.63185 | 0.815924 | − | 0.578160i | \(-0.196229\pi\) | ||||
0.815924 | + | 0.578160i | \(0.196229\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 512.747 | 0.164943 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −131.806 | −0.0418097 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 75.6369 | 0.0236616 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9511.42 | 2.93481 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5961.70 | 1.79025 | 0.895123 | − | 0.445819i | \(-0.147088\pi\) | ||||
0.895123 | + | 0.445819i | \(0.147088\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4933.99 | 1.46192 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5697.72 | 1.66595 | 0.832976 | − | 0.553309i | \(-0.186635\pi\) | ||||
0.832976 | + | 0.553309i | \(0.186635\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5833.82 | 1.68345 | 0.841724 | − | 0.539909i | \(-0.181541\pi\) | ||||
0.841724 | + | 0.539909i | \(0.181541\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8421.10 | −2.39856 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2251.11 | −0.632942 | −0.316471 | − | 0.948602i | \(-0.602498\pi\) | ||||
−0.316471 | + | 0.948602i | \(0.602498\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6531.42 | 1.81303 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 161.318 | 0.0442140 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2723.39 | −0.737076 | −0.368538 | − | 0.929613i | \(-0.620142\pi\) | ||||
−0.368538 | + | 0.929613i | \(0.620142\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2762.12 | 0.738272 | 0.369136 | − | 0.929375i | \(-0.379654\pi\) | ||||
0.369136 | + | 0.929375i | \(0.379654\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14784.2 | 3.90290 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 208.855 | 0.0544622 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1254.32 | −0.323120 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12490.4 | 3.17890 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2857.56 | −0.718596 | −0.359298 | − | 0.933223i | \(-0.616984\pi\) | ||||
−0.359298 | + | 0.933223i | \(0.616984\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8997.25 | −2.23578 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5620.28 | −1.36414 | −0.682069 | − | 0.731288i | \(-0.738920\pi\) | ||||
−0.682069 | + | 0.731288i | \(0.738920\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4906.47 | 1.17712 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8770.48 | −2.08000 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3064.10 | −0.718404 | −0.359202 | − | 0.933260i | \(-0.616951\pi\) | ||||
−0.359202 | + | 0.933260i | \(0.616951\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1342.06 | 0.311102 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −13708.2 | −3.14206 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1166.34 | −0.264360 | −0.132180 | − | 0.991226i | \(-0.542198\pi\) | ||||
−0.132180 | + | 0.991226i | \(0.542198\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8580.83 | −1.92343 | −0.961713 | − | 0.274058i | \(-0.911634\pi\) | ||||
−0.961713 | + | 0.274058i | \(0.911634\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 11974.4 | 2.65467 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3090.29 | −0.677642 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6463.59 | −1.40202 | −0.701010 | − | 0.713152i | \(-0.747267\pi\) | ||||
−0.701010 | + | 0.713152i | \(0.747267\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 308.720 | 0.0662459 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5531.65 | −1.17434 | −0.587172 | − | 0.809462i | \(-0.699759\pi\) | ||||
−0.587172 | + | 0.809462i | \(0.699759\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1092.62 | 0.229504 | 0.114752 | − | 0.993394i | \(-0.463393\pi\) | ||||
0.114752 | + | 0.993394i | \(0.463393\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2650.65 | 0.550916 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −572.458 | −0.117739 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11718.7 | 2.36070 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3169.97 | −0.632052 | −0.316026 | − | 0.948750i | \(-0.602349\pi\) | ||||
−0.316026 | + | 0.948750i | \(0.602349\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11832.9 | −2.33537 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −21815.7 | −4.26220 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12793.7 | 2.47450 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 172.363 | 0.0330061 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6505.15 | −1.23337 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2374.71 | 0.445821 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2627.50 | −0.488467 | −0.244234 | − | 0.969716i | \(-0.578536\pi\) | ||||
−0.244234 | + | 0.969716i | \(0.578536\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1683.01 | −0.309848 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3985.35 | −0.726650 | −0.363325 | − | 0.931662i | \(-0.618359\pi\) | ||||
−0.363325 | + | 0.931662i | \(0.618359\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3505.16 | 0.632983 | 0.316491 | − | 0.948595i | \(-0.397495\pi\) | ||||
0.316491 | + | 0.948595i | \(0.397495\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −18534.0 | −3.31516 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1649.79 | 0.292308 | 0.146154 | − | 0.989262i | \(-0.453311\pi\) | ||||
0.146154 | + | 0.989262i | \(0.453311\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5493.19 | 0.964137 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5438.75 | −0.945674 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4394.25 | 0.749997 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2139.29 | 0.361783 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8541.15 | −1.43127 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4301.09 | 0.714228 | 0.357114 | − | 0.934061i | \(-0.383761\pi\) | ||||
0.357114 | + | 0.934061i | \(0.383761\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 20026.3 | 3.29560 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 115.362 | 0.0188146 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6835.65 | 1.10493 | 0.552465 | − | 0.833536i | \(-0.313687\pi\) | ||||
0.552465 | + | 0.833536i | \(0.313687\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 8922.00 | 1.42943 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −193.360 | −0.0307068 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6484.33 | −1.02076 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −27035.8 | −4.21901 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5608.80 | −0.867712 | −0.433856 | − | 0.900982i | \(-0.642847\pi\) | ||||
−0.433856 | + | 0.900982i | \(0.642847\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8300.72 | 1.27314 | 0.636572 | − | 0.771217i | \(-0.280352\pi\) | ||||
0.636572 | + | 0.771217i | \(0.280352\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 31020.9 | 4.71730 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1181.71 | −0.178176 | −0.0890880 | − | 0.996024i | \(-0.528395\pi\) | ||||
−0.0890880 | + | 0.996024i | \(0.528395\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −706.814 | −0.105673 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10863.5 | −1.59709 | −0.798546 | − | 0.601934i | \(-0.794397\pi\) | ||||
−0.798546 | + | 0.601934i | \(0.794397\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6495.91 | −0.947063 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8157.36 | 1.17948 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −13111.4 | −1.88022 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3724.19 | 0.529704 | 0.264852 | − | 0.964289i | \(-0.414677\pi\) | ||||
0.264852 | + | 0.964289i | \(0.414677\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2336.55 | −0.329637 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1755.02 | −0.245595 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9169.41 | 1.27285 | 0.636426 | − | 0.771338i | \(-0.280412\pi\) | ||||
0.636426 | + | 0.771338i | \(0.280412\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 8102.20 | 1.11572 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7811.06 | −1.06708 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5969.10 | 0.809004 | 0.404502 | − | 0.914537i | \(-0.367445\pi\) | ||||
0.404502 | + | 0.914537i | \(0.367445\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5331.32 | 0.716881 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3025.44 | −0.403637 | −0.201818 | − | 0.979423i | \(-0.564685\pi\) | ||||
−0.201818 | + | 0.979423i | \(0.564685\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 11608.4 | 1.53667 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 703.519 | 0.0924080 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11596.8 | 1.51152 | 0.755758 | − | 0.654851i | \(-0.227269\pi\) | ||||
0.755758 | + | 0.654851i | \(0.227269\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6469.44 | 0.830382 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −222.374 | −0.0283263 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1680.42 | −0.212438 | −0.106219 | − | 0.994343i | \(-0.533874\pi\) | ||||
−0.106219 | + | 0.994343i | \(0.533874\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3466.26 | −0.434913 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8962.57 | −1.11613 | −0.558066 | − | 0.829796i | \(-0.688457\pi\) | ||||
−0.558066 | + | 0.829796i | \(0.688457\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 274.949 | 0.0339855 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −37919.4 | −4.65241 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −12543.0 | −1.52760 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7158.94 | −0.865494 | −0.432747 | − | 0.901516i | \(-0.642456\pi\) | ||||
−0.432747 | + | 0.901516i | \(0.642456\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 24355.5 | 2.92304 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 15473.9 | 1.84363 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −17217.8 | −2.03660 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −22528.9 | −2.64567 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14813.8 | 1.72722 | 0.863608 | − | 0.504164i | \(-0.168199\pi\) | ||||
0.863608 | + | 0.504164i | \(0.168199\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7260.01 | −0.840454 | −0.420227 | − | 0.907419i | \(-0.638050\pi\) | ||||
−0.420227 | + | 0.907419i | \(0.638050\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −34861.7 | −4.00717 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3105.42 | −0.351947 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −30611.7 | −3.44510 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2370.15 | −0.264887 | −0.132443 | − | 0.991191i | \(-0.542282\pi\) | ||||
−0.132443 | + | 0.991191i | \(0.542282\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3056.05 | −0.339178 | −0.169589 | − | 0.985515i | \(-0.554244\pi\) | ||||
−0.169589 | + | 0.985515i | \(0.554244\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 16506.5 | 1.81936 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3703.42 | −0.405397 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2584.92 | 0.281029 | 0.140514 | − | 0.990079i | \(-0.455124\pi\) | ||||
0.140514 | + | 0.990079i | \(0.455124\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1114.77 | −0.120372 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9354.57 | −1.00327 | −0.501635 | − | 0.865079i | \(-0.667268\pi\) | ||||
−0.501635 | + | 0.865079i | \(0.667268\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 18896.6 | 2.01300 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4572.42 | −0.483821 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2103.48 | 0.221090 | 0.110545 | − | 0.993871i | \(-0.464740\pi\) | ||||
0.110545 | + | 0.993871i | \(0.464740\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1463.45 | 0.152796 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7498.51 | −0.777728 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −16506.6 | −1.70075 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8869.30 | 0.907852 | 0.453926 | − | 0.891039i | \(-0.350023\pi\) | ||||
0.453926 | + | 0.891039i | \(0.350023\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16376.3 | −1.65449 | −0.827244 | − | 0.561843i | \(-0.810092\pi\) | ||||
−0.827244 | + | 0.561843i | \(0.810092\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6611.44 | −0.663628 | −0.331814 | − | 0.943345i | \(-0.607661\pi\) | ||||
−0.331814 | + | 0.943345i | \(0.607661\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −581.026 | −0.0579450 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1589.77 | 0.157528 | 0.0787640 | − | 0.996893i | \(-0.474903\pi\) | ||||
0.0787640 | + | 0.996893i | \(0.474903\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −150.859 | −0.0148529 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 15728.7 | 1.53873 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −440.633 | −0.0428337 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1272.01 | −0.122872 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7163.29 | −0.687599 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 317.589 | 0.0302944 | 0.0151472 | − | 0.999885i | \(-0.495178\pi\) | ||||
0.0151472 | + | 0.999885i | \(0.495178\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 17835.6 | 1.69071 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 35354.8 | 3.33064 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −16154.1 | −1.51241 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12005.6 | −1.11710 | −0.558549 | − | 0.829472i | \(-0.688642\pi\) | ||||
−0.558549 | + | 0.829472i | \(0.688642\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 15168.7 | 1.40276 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12537.5 | −1.15236 | −0.576179 | − | 0.817324i | \(-0.695457\pi\) | ||||
−0.576179 | + | 0.817324i | \(0.695457\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 47380.8 | 4.30224 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 924.303 | 0.0834218 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7088.85 | −0.635953 | −0.317977 | − | 0.948099i | \(-0.603003\pi\) | ||||
−0.317977 | + | 0.948099i | \(0.603003\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9663.70 | −0.861761 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −13957.4 | −1.23724 | −0.618618 | − | 0.785692i | \(-0.712307\pi\) | ||||
−0.618618 | + | 0.785692i | \(0.712307\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8967.25 | 0.790173 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 21458.4 | 1.87969 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −21328.4 | −1.85729 | −0.928647 | − | 0.370964i | \(-0.879027\pi\) | ||||
−0.928647 | + | 0.370964i | \(0.879027\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 17145.8 | 1.48431 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −8979.70 | −0.772833 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2320.00 | 0.198508 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 21834.8 | 1.85744 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7598.20 | 0.642628 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2588.63 | −0.217677 | −0.108839 | − | 0.994059i | \(-0.534713\pi\) | ||||
−0.108839 | + | 0.994059i | \(0.534713\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20409.3 | 1.70638 | 0.853191 | − | 0.521599i | \(-0.174664\pi\) | ||||
0.853191 | + | 0.521599i | \(0.174664\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 12143.3 | 1.00948 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 25606.6 | 2.10460 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 63158.3 | 5.16165 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2080.95 | −0.169111 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7497.23 | 0.605857 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3924.66 | 0.315385 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 698.211 | 0.0557960 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4762.23 | 0.378455 | 0.189227 | − | 0.981933i | \(-0.439402\pi\) | ||||
0.189227 | + | 0.981933i | \(0.439402\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −19786.9 | −1.56379 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2948.98 | −0.231781 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16094.3 | −1.25803 | −0.629013 | − | 0.777395i | \(-0.716541\pi\) | ||||
−0.629013 | + | 0.777395i | \(0.716541\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −12675.1 | −0.985355 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2261.09 | 0.174820 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 290.800 | 0.0223618 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −37690.5 | −2.88265 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6505.51 | −0.494879 | −0.247439 | − | 0.968903i | \(-0.579589\pi\) | ||||
−0.247439 | + | 0.968903i | \(0.579589\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 626.560 | 0.0474072 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4057.45 | −0.303732 | −0.151866 | − | 0.988401i | \(-0.548528\pi\) | ||||
−0.151866 | + | 0.988401i | \(0.548528\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12298.9 | −0.915782 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 49587.2 | 3.67278 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 14345.2 | 1.05691 | 0.528456 | − | 0.848961i | \(-0.322771\pi\) | ||||
0.528456 | + | 0.848961i | \(0.322771\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 760.937 | 0.0557692 | 0.0278846 | − | 0.999611i | \(-0.491123\pi\) | ||||
0.0278846 | + | 0.999611i | \(0.491123\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4244.32 | 0.309440 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 12974.1 | 0.940972 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3549.57 | −0.256101 | −0.128051 | − | 0.991768i | \(-0.540872\pi\) | ||||
−0.128051 | + | 0.991768i | \(0.540872\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 17987.8 | 1.29110 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 22515.8 | 1.60776 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4486.57 | 0.318721 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −67373.3 | −4.76162 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3839.58 | 0.269977 | 0.134988 | − | 0.990847i | \(-0.456900\pi\) | ||||
0.134988 | + | 0.990847i | \(0.456900\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −79.5902 | −0.00556784 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 25924.2 | 1.80437 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 22417.1 | 1.55238 | 0.776189 | − | 0.630500i | \(-0.217150\pi\) | ||||
0.776189 | + | 0.630500i | \(0.217150\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −12070.9 | −0.827517 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5574.76 | 0.380265 | 0.190132 | − | 0.981758i | \(-0.439108\pi\) | ||||
0.190132 | + | 0.981758i | \(0.439108\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25055.3 | −1.70054 | −0.850272 | − | 0.526344i | \(-0.823562\pi\) | ||||
−0.850272 | + | 0.526344i | \(0.823562\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −615.747 | −0.0415840 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −11244.8 | −0.755647 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1371.15 | −0.0916857 | −0.0458428 | − | 0.998949i | \(-0.514597\pi\) | ||||
−0.0458428 | + | 0.998949i | \(0.514597\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −21585.5 | −1.43627 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −31048.1 | −2.05576 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4685.73 | −0.308736 | −0.154368 | − | 0.988013i | \(-0.549334\pi\) | ||||
−0.154368 | + | 0.988013i | \(0.549334\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4397.50 | 0.288332 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 24700.7 | 1.61169 | 0.805846 | − | 0.592125i | \(-0.201711\pi\) | ||||
0.805846 | + | 0.592125i | \(0.201711\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18824.1 | 1.22230 | 0.611151 | − | 0.791514i | \(-0.290707\pi\) | ||||
0.611151 | + | 0.791514i | \(0.290707\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 91590.0 | 5.91849 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −24711.1 | −1.58914 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19513.1 | −1.24884 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8861.24 | 0.564408 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15571.9 | −0.982420 | −0.491210 | − | 0.871041i | \(-0.663445\pi\) | ||||
−0.491210 | + | 0.871041i | \(0.663445\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 50242.8 | 3.15478 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7349.15 | −0.459279 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −992.823 | −0.0617536 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3772.64 | 0.233558 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −27035.7 | −1.66591 | −0.832954 | − | 0.553342i | \(-0.813352\pi\) | ||||
−0.832954 | + | 0.553342i | \(0.813352\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19405.7 | −1.19018 | −0.595090 | − | 0.803659i | \(-0.702883\pi\) | ||||
−0.595090 | + | 0.803659i | \(0.702883\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1324.06 | −0.0808289 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −20930.2 | −1.27179 | −0.635897 | − | 0.771774i | \(-0.719370\pi\) | ||||
−0.635897 | + | 0.771774i | \(0.719370\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −39557.8 | −2.39257 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 759.809 | 0.0457439 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5277.55 | 0.316273 | 0.158137 | − | 0.987417i | \(-0.449451\pi\) | ||||
0.158137 | + | 0.987417i | \(0.449451\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8918.03 | −0.531994 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 69982.3 | 4.15566 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7954.54 | −0.470205 | −0.235102 | − | 0.971971i | \(-0.575543\pi\) | ||||
−0.235102 | + | 0.971971i | \(0.575543\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11489.7 | 0.676094 | 0.338047 | − | 0.941129i | \(-0.390234\pi\) | ||||
0.338047 | + | 0.941129i | \(0.390234\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4778.20 | 0.278632 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −23062.4 | −1.33880 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 59888.2 | 3.46100 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7938.76 | 0.456740 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1213.00 | −0.0694766 | −0.0347383 | − | 0.999396i | \(-0.511060\pi\) | ||||
−0.0347383 | + | 0.999396i | \(0.511060\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 31458.5 | 1.79383 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8069.13 | 0.458083 | 0.229041 | − | 0.973417i | \(-0.426441\pi\) | ||||
0.229041 | + | 0.973417i | \(0.426441\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 21124.7 | 1.19395 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 57236.4 | 3.22071 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12540.1 | 0.702537 | 0.351268 | − | 0.936275i | \(-0.385750\pi\) | ||||
0.351268 | + | 0.936275i | \(0.385750\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −33573.7 | −1.87268 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 58603.5 | 3.25453 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6379.69 | −0.352753 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6511.86 | −0.358499 | −0.179250 | − | 0.983804i | \(-0.557367\pi\) | ||||
−0.179250 | + | 0.983804i | \(0.557367\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −61960.1 | −3.39635 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 31055.7 | 1.69498 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −22613.5 | −1.22364 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8151.13 | −0.439178 | −0.219589 | − | 0.975592i | \(-0.570472\pi\) | ||||
−0.219589 | + | 0.975592i | \(0.570472\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5162.92 | −0.276989 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 65611.3 | 3.50505 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −11726.5 | −0.623791 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19489.6 | 1.03237 | 0.516184 | − | 0.856478i | \(-0.327352\pi\) | ||||
0.516184 | + | 0.856478i | \(0.327352\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1186.93 | 0.0626068 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 811.794 | 0.0426394 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 42197.8 | 2.20714 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −27357.7 | −1.42496 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9234.85 | −0.479001 | −0.239501 | − | 0.970896i | \(-0.576984\pi\) | ||||
−0.239501 | + | 0.970896i | \(0.576984\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3033.87 | −0.156709 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 27746.8 | 1.42727 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7921.24 | −0.405776 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21248.2 | 1.08398 | 0.541989 | − | 0.840386i | \(-0.317671\pi\) | ||||
0.541989 | + | 0.840386i | \(0.317671\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 74578.9 | 3.78900 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −33363.0 | −1.68116 | −0.840579 | − | 0.541689i | \(-0.817785\pi\) | ||||
−0.840579 | + | 0.541689i | \(0.817785\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2098.05 | 0.105289 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 385.659 | 0.0192754 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15082.8 | 0.750784 | 0.375392 | − | 0.926866i | \(-0.377508\pi\) | ||||
0.375392 | + | 0.926866i | \(0.377508\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −12600.3 | −0.624673 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1869.09 | 0.0922883 | 0.0461442 | − | 0.998935i | \(-0.485307\pi\) | ||||
0.0461442 | + | 0.998935i | \(0.485307\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6303.01 | 0.309966 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 91900.6 | 4.50129 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9804.15 | −0.478286 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20231.4 | −0.983026 | −0.491513 | − | 0.870870i | \(-0.663556\pi\) | ||||
−0.491513 | + | 0.870870i | \(0.663556\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −28705.6 | −1.38923 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10336.6 | 0.498261 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4216.92 | −0.202466 | −0.101233 | − | 0.994863i | \(-0.532279\pi\) | ||||
−0.101233 | + | 0.994863i | \(0.532279\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −90381.8 | −4.32233 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7638.77 | −0.363870 | −0.181935 | − | 0.983311i | \(-0.558236\pi\) | ||||
−0.181935 | + | 0.983311i | \(0.558236\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3856.40 | 0.182976 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 56249.3 | 2.64804 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −32633.5 | −1.53029 | −0.765145 | − | 0.643858i | \(-0.777333\pi\) | ||||
−0.765145 | + | 0.643858i | \(0.777333\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −56458.4 | −2.63723 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5125.84 | −0.238504 | −0.119252 | − | 0.992864i | \(-0.538050\pi\) | ||||
−0.119252 | + | 0.992864i | \(0.538050\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 278.827 | 0.0129236 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 49287.9 | 2.27567 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 602.379 | 0.0277053 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2362.91 | −0.108261 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −55919.4 | −2.55223 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −21681.8 | −0.985806 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16716.9 | 0.757169 | 0.378584 | − | 0.925567i | \(-0.376411\pi\) | ||||
0.378584 | + | 0.925567i | \(0.376411\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −30780.4 | −1.38886 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 16083.2 | 0.722951 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −11288.5 | −0.505508 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 13481.7 | 0.601440 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 16430.8 | 0.730248 | 0.365124 | − | 0.930959i | \(-0.381027\pi\) | ||||
0.365124 | + | 0.930959i | \(0.381027\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −100861. | −4.44914 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −43831.9 | −1.92627 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −48736.0 | −2.13381 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −11716.4 | −0.511075 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 13144.4 | 0.571237 | 0.285619 | − | 0.958343i | \(-0.407801\pi\) | ||||
0.285619 | + | 0.958343i | \(0.407801\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 21400.7 | 0.926608 | 0.463304 | − | 0.886199i | \(-0.346664\pi\) | ||||
0.463304 | + | 0.886199i | \(0.346664\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −86198.7 | −3.71847 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −20909.8 | −0.898696 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −181.372 | −0.00776671 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 88104.3 | 3.75899 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2678.59 | −0.113865 | −0.0569327 | − | 0.998378i | \(-0.518132\pi\) | ||||
−0.0569327 | + | 0.998378i | \(0.518132\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2939.29 | 0.124493 | 0.0622463 | − | 0.998061i | \(-0.480174\pi\) | ||||
0.0622463 | + | 0.998061i | \(0.480174\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −31043.5 | −1.31005 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4542.99 | −0.191022 | −0.0955110 | − | 0.995428i | \(-0.530449\pi\) | ||||
−0.0955110 | + | 0.995428i | \(0.530449\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −28672.1 | −1.20124 | −0.600618 | − | 0.799536i | \(-0.705079\pi\) | ||||
−0.600618 | + | 0.799536i | \(0.705079\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −64929.9 | −2.71046 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 13321.3 | 0.552098 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1968.36 | 0.0812862 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 20351.7 | 0.837449 | 0.418724 | − | 0.908113i | \(-0.362477\pi\) | ||||
0.418724 | + | 0.908113i | \(0.362477\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10308.5 | −0.422669 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −55568.2 | −2.27031 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −29580.1 | −1.20425 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 14704.9 | 0.596535 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 10975.9 | 0.443691 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 52660.1 | 2.12123 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −18949.3 | −0.760625 | −0.380313 | − | 0.924858i | \(-0.624184\pi\) | ||||
−0.380313 | + | 0.924858i | \(0.624184\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 19502.7 | 0.780093 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −41367.8 | −1.64889 | −0.824444 | − | 0.565943i | \(-0.808512\pi\) | ||||
−0.824444 | + | 0.565943i | \(0.808512\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17909.6 | 0.711370 | 0.355685 | − | 0.934606i | \(-0.384248\pi\) | ||||
0.355685 | + | 0.934606i | \(0.384248\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5750.62 | −0.227620 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −28855.9 | −1.13820 | −0.569099 | − | 0.822269i | \(-0.692708\pi\) | ||||
−0.569099 | + | 0.822269i | \(0.692708\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10474.0 | −0.411708 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −743.407 | −0.0290200 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −548.389 | −0.0213335 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 86222.9 | 3.34273 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 14605.4 | 0.564290 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 36116.6 | 1.39062 | 0.695309 | − | 0.718711i | \(-0.255268\pi\) | ||||
0.695309 | + | 0.718711i | \(0.255268\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −31843.8 | −1.22192 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31133.0 | 1.19058 | 0.595289 | − | 0.803512i | \(-0.297038\pi\) | ||||
0.595289 | + | 0.803512i | \(0.297038\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −44665.2 | −1.70227 | −0.851135 | − | 0.524946i | \(-0.824085\pi\) | ||||
−0.851135 | + | 0.524946i | \(0.824085\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −118867. | −4.51488 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −36950.4 | −1.39873 | −0.699365 | − | 0.714765i | \(-0.746534\pi\) | ||||
−0.699365 | + | 0.714765i | \(0.746534\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9610.50 | 0.362571 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −126766. | −4.76635 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8987.57 | 0.336795 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5410.09 | −0.202055 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 128519. | 4.78385 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −495.633 | −0.0183874 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1731.47 | 0.0638092 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 27275.9 | 1.00186 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1462.19 | −0.0535296 | −0.0267648 | − | 0.999642i | \(-0.508521\pi\) | ||||
−0.0267648 | + | 0.999642i | \(0.508521\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −47863.0 | −1.74644 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 993.504 | 0.0361320 | 0.0180660 | − | 0.999837i | \(-0.494249\pi\) | ||||
0.0180660 | + | 0.999837i | \(0.494249\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −57559.8 | −2.08648 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 23855.1 | 0.861887 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 11662.1 | 0.419976 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −12596.0 | −0.452125 | −0.226063 | − | 0.974113i | \(-0.572585\pi\) | ||||
−0.226063 | + | 0.974113i | \(0.572585\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −26394.5 | −0.944332 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3359.95 | 0.119820 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 18087.2 | 0.642922 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −12383.1 | −0.438742 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 26013.8 | 0.918713 | 0.459357 | − | 0.888252i | \(-0.348080\pi\) | ||||
0.459357 | + | 0.888252i | \(0.348080\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 287.395 | 0.0101171 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −40034.8 | −1.40480 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22507.8 | 0.784737 | 0.392368 | − | 0.919808i | \(-0.371656\pi\) | ||||
0.392368 | + | 0.919808i | \(0.371656\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 35211.1 | 1.22372 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −35241.7 | −1.22088 | −0.610439 | − | 0.792063i | \(-0.709007\pi\) | ||||
−0.610439 | + | 0.792063i | \(0.709007\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6144.07 | −0.212172 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −118171. | −4.06782 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −35820.8 | −1.22917 | −0.614583 | − | 0.788852i | \(-0.710676\pi\) | ||||
−0.614583 | + | 0.788852i | \(0.710676\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 62326.8 | 2.13194 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 16573.0 | 0.565106 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 25732.2 | 0.874658 | 0.437329 | − | 0.899302i | \(-0.355925\pi\) | ||||
0.437329 | + | 0.899302i | \(0.355925\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5850.73 | −0.198246 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 55181.8 | 1.86392 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 43904.4 | 1.47836 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29773.6 | −0.999414 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −40016.7 | −1.33907 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −24796.0 | −0.827161 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −34792.6 | −1.15704 | −0.578518 | − | 0.815669i | \(-0.696369\pi\) | ||||
−0.578518 | + | 0.815669i | \(0.696369\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19826.3 | −0.655260 | −0.327630 | − | 0.944806i | \(-0.606250\pi\) | ||||
−0.327630 | + | 0.944806i | \(0.606250\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −40611.7 | −1.33808 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 44142.4 | 1.44994 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4133.51 | 0.135356 | 0.0676779 | − | 0.997707i | \(-0.478441\pi\) | ||||
0.0676779 | + | 0.997707i | \(0.478441\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 63172.2 | 2.06230 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15740.3 | 0.512283 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 41660.6 | 1.35175 | 0.675873 | − | 0.737018i | \(-0.263767\pi\) | ||||
0.675873 | + | 0.737018i | \(0.263767\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −35736.2 | −1.15599 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −85800.0 | −2.76702 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1849.93 | 0.0594787 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2903.34 | −0.0930652 | −0.0465326 | − | 0.998917i | \(-0.514817\pi\) | ||||
−0.0465326 | + | 0.998917i | \(0.514817\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 43206.6 | 1.38079 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 16639.5 | 0.530159 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −43692.3 | −1.38791 | −0.693957 | − | 0.720017i | \(-0.744134\pi\) | ||||
−0.693957 | + | 0.720017i | \(0.744134\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 127685. | 4.04382 |
(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 | 2312.4.a.q.1.18 | yes | 18 | |
17.16 | even | 2 | 2312.4.a.n.1.1 | ✓ | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2312.4.a.n.1.1 | ✓ | 18 | 17.16 | even | 2 | ||
2312.4.a.q.1.18 | yes | 18 | 1.1 | even | 1 | trivial |