Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [135,4,Mod(1,135)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(135, 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("135.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 135 = 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 135.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: | \(7.96525785077\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.5637.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 23x + 6 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.258712\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 135.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.258712 | −0.0914686 | −0.0457343 | − | 0.998954i | \(-0.514563\pi\) | ||||
−0.0457343 | + | 0.998954i | \(0.514563\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −7.93307 | −0.991633 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 14.5174 | 0.783867 | 0.391934 | − | 0.919993i | \(-0.371806\pi\) | ||||
0.391934 | + | 0.919993i | \(0.371806\pi\) | |||||||
\(8\) | 4.12208 | 0.182172 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.29356 | −0.0409060 | ||||||||
\(11\) | −49.2845 | −1.35090 | −0.675448 | − | 0.737408i | \(-0.736050\pi\) | ||||
−0.675448 | + | 0.737408i | \(0.736050\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 72.1800 | 1.53993 | 0.769967 | − | 0.638084i | \(-0.220273\pi\) | ||||
0.769967 | + | 0.638084i | \(0.220273\pi\) | |||||||
\(14\) | −3.75584 | −0.0716993 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 62.3981 | 0.974970 | ||||||||
\(17\) | 118.017 | 1.68372 | 0.841861 | − | 0.539694i | \(-0.181460\pi\) | ||||
0.841861 | + | 0.539694i | \(0.181460\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 123.389 | 1.48986 | 0.744932 | − | 0.667141i | \(-0.232482\pi\) | ||||
0.744932 | + | 0.667141i | \(0.232482\pi\) | |||||||
\(20\) | −39.6653 | −0.443472 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 12.7505 | 0.123565 | ||||||||
\(23\) | −91.4883 | −0.829419 | −0.414709 | − | 0.909954i | \(-0.636117\pi\) | ||||
−0.414709 | + | 0.909954i | \(0.636117\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | −18.6739 | −0.140856 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −115.168 | −0.777309 | ||||||||
\(29\) | 174.400 | 1.11673 | 0.558367 | − | 0.829594i | \(-0.311428\pi\) | ||||
0.558367 | + | 0.829594i | \(0.311428\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −46.2956 | −0.268224 | −0.134112 | − | 0.990966i | \(-0.542818\pi\) | ||||
−0.134112 | + | 0.990966i | \(0.542818\pi\) | |||||||
\(32\) | −49.1198 | −0.271351 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −30.5324 | −0.154008 | ||||||||
\(35\) | 72.5871 | 0.350556 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 154.977 | 0.688595 | 0.344297 | − | 0.938861i | \(-0.388117\pi\) | ||||
0.344297 | + | 0.938861i | \(0.388117\pi\) | |||||||
\(38\) | −31.9223 | −0.136276 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 20.6104 | 0.0814698 | ||||||||
\(41\) | −364.203 | −1.38729 | −0.693645 | − | 0.720317i | \(-0.743996\pi\) | ||||
−0.693645 | + | 0.720317i | \(0.743996\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 125.714 | 0.445841 | 0.222921 | − | 0.974837i | \(-0.428441\pi\) | ||||
0.222921 | + | 0.974837i | \(0.428441\pi\) | |||||||
\(44\) | 390.978 | 1.33959 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 23.6692 | 0.0758658 | ||||||||
\(47\) | −221.523 | −0.687499 | −0.343750 | − | 0.939061i | \(-0.611697\pi\) | ||||
−0.343750 | + | 0.939061i | \(0.611697\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −132.244 | −0.385552 | ||||||||
\(50\) | −6.46781 | −0.0182937 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −572.609 | −1.52705 | ||||||||
\(53\) | −13.6794 | −0.0354530 | −0.0177265 | − | 0.999843i | \(-0.505643\pi\) | ||||
−0.0177265 | + | 0.999843i | \(0.505643\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −246.423 | −0.604139 | ||||||||
\(56\) | 59.8420 | 0.142799 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −45.1195 | −0.102146 | ||||||||
\(59\) | 239.087 | 0.527567 | 0.263784 | − | 0.964582i | \(-0.415030\pi\) | ||||
0.263784 | + | 0.964582i | \(0.415030\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −54.5457 | −0.114490 | −0.0572448 | − | 0.998360i | \(-0.518232\pi\) | ||||
−0.0572448 | + | 0.998360i | \(0.518232\pi\) | |||||||
\(62\) | 11.9772 | 0.0245341 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −486.477 | −0.950150 | ||||||||
\(65\) | 360.900 | 0.688679 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −76.0558 | −0.138682 | −0.0693410 | − | 0.997593i | \(-0.522090\pi\) | ||||
−0.0693410 | + | 0.997593i | \(0.522090\pi\) | |||||||
\(68\) | −936.235 | −1.66964 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −18.7792 | −0.0320649 | ||||||||
\(71\) | 728.303 | 1.21738 | 0.608688 | − | 0.793410i | \(-0.291696\pi\) | ||||
0.608688 | + | 0.793410i | \(0.291696\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −501.815 | −0.804562 | −0.402281 | − | 0.915516i | \(-0.631782\pi\) | ||||
−0.402281 | + | 0.915516i | \(0.631782\pi\) | |||||||
\(74\) | −40.0944 | −0.0629848 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −978.854 | −1.47740 | ||||||||
\(77\) | −715.485 | −1.05892 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 397.610 | 0.566261 | 0.283130 | − | 0.959081i | \(-0.408627\pi\) | ||||
0.283130 | + | 0.959081i | \(0.408627\pi\) | |||||||
\(80\) | 311.991 | 0.436020 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 94.2237 | 0.126894 | ||||||||
\(83\) | −1369.46 | −1.81106 | −0.905530 | − | 0.424283i | \(-0.860526\pi\) | ||||
−0.905530 | + | 0.424283i | \(0.860526\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 590.084 | 0.752984 | ||||||||
\(86\) | −32.5237 | −0.0407805 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −203.155 | −0.246095 | ||||||||
\(89\) | 1468.13 | 1.74856 | 0.874278 | − | 0.485425i | \(-0.161335\pi\) | ||||
0.874278 | + | 0.485425i | \(0.161335\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1047.87 | 1.20710 | ||||||||
\(92\) | 725.783 | 0.822480 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 57.3108 | 0.0628846 | ||||||||
\(95\) | 616.945 | 0.666287 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 335.023 | 0.350685 | 0.175343 | − | 0.984507i | \(-0.443897\pi\) | ||||
0.175343 | + | 0.984507i | \(0.443897\pi\) | |||||||
\(98\) | 34.2133 | 0.0352659 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −198.327 | −0.198327 | ||||||||
\(101\) | −1206.09 | −1.18822 | −0.594109 | − | 0.804384i | \(-0.702495\pi\) | ||||
−0.594109 | + | 0.804384i | \(0.702495\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1061.11 | 1.01509 | 0.507545 | − | 0.861625i | \(-0.330553\pi\) | ||||
0.507545 | + | 0.861625i | \(0.330553\pi\) | |||||||
\(104\) | 297.532 | 0.280533 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.53903 | 0.00324284 | ||||||||
\(107\) | −475.578 | −0.429681 | −0.214841 | − | 0.976649i | \(-0.568923\pi\) | ||||
−0.214841 | + | 0.976649i | \(0.568923\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1320.42 | 1.16030 | 0.580152 | − | 0.814508i | \(-0.302993\pi\) | ||||
0.580152 | + | 0.814508i | \(0.302993\pi\) | |||||||
\(110\) | 63.7526 | 0.0552597 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 905.860 | 0.764247 | ||||||||
\(113\) | −68.1750 | −0.0567555 | −0.0283777 | − | 0.999597i | \(-0.509034\pi\) | ||||
−0.0283777 | + | 0.999597i | \(0.509034\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −457.442 | −0.370927 | ||||||||
\(116\) | −1383.53 | −1.10739 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −61.8547 | −0.0482559 | ||||||||
\(119\) | 1713.30 | 1.31981 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1097.97 | 0.824918 | ||||||||
\(122\) | 14.1117 | 0.0104722 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 367.266 | 0.265980 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −593.009 | −0.414339 | −0.207170 | − | 0.978305i | \(-0.566425\pi\) | ||||
−0.207170 | + | 0.978305i | \(0.566425\pi\) | |||||||
\(128\) | 518.816 | 0.358260 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −93.3693 | −0.0629925 | ||||||||
\(131\) | 338.937 | 0.226054 | 0.113027 | − | 0.993592i | \(-0.463945\pi\) | ||||
0.113027 | + | 0.993592i | \(0.463945\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1791.29 | 1.16785 | ||||||||
\(134\) | 19.6766 | 0.0126850 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 486.475 | 0.306727 | ||||||||
\(137\) | −811.442 | −0.506030 | −0.253015 | − | 0.967462i | \(-0.581422\pi\) | ||||
−0.253015 | + | 0.967462i | \(0.581422\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3106.13 | −1.89538 | −0.947691 | − | 0.319189i | \(-0.896590\pi\) | ||||
−0.947691 | + | 0.319189i | \(0.896590\pi\) | |||||||
\(140\) | −575.839 | −0.347623 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −188.421 | −0.111352 | ||||||||
\(143\) | −3557.36 | −2.08029 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 872.001 | 0.499419 | ||||||||
\(146\) | 129.826 | 0.0735922 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1229.44 | −0.682834 | ||||||||
\(149\) | 2541.01 | 1.39710 | 0.698550 | − | 0.715561i | \(-0.253829\pi\) | ||||
0.698550 | + | 0.715561i | \(0.253829\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1125.37 | −0.606499 | −0.303249 | − | 0.952911i | \(-0.598072\pi\) | ||||
−0.303249 | + | 0.952911i | \(0.598072\pi\) | |||||||
\(152\) | 508.620 | 0.271411 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 185.105 | 0.0968582 | ||||||||
\(155\) | −231.478 | −0.119953 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3230.05 | 1.64195 | 0.820975 | − | 0.570963i | \(-0.193430\pi\) | ||||
0.820975 | + | 0.570963i | \(0.193430\pi\) | |||||||
\(158\) | −102.867 | −0.0517951 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −245.599 | −0.121352 | ||||||||
\(161\) | −1328.17 | −0.650154 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −694.054 | −0.333512 | −0.166756 | − | 0.985998i | \(-0.553329\pi\) | ||||
−0.166756 | + | 0.985998i | \(0.553329\pi\) | |||||||
\(164\) | 2889.24 | 1.37568 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 354.297 | 0.165655 | ||||||||
\(167\) | 3216.04 | 1.49021 | 0.745103 | − | 0.666950i | \(-0.232400\pi\) | ||||
0.745103 | + | 0.666950i | \(0.232400\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3012.95 | 1.37139 | ||||||||
\(170\) | −152.662 | −0.0688744 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −997.296 | −0.442111 | ||||||||
\(173\) | 297.546 | 0.130763 | 0.0653816 | − | 0.997860i | \(-0.479174\pi\) | ||||
0.0653816 | + | 0.997860i | \(0.479174\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 362.936 | 0.156773 | ||||||||
\(176\) | −3075.26 | −1.31708 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −379.823 | −0.159938 | ||||||||
\(179\) | −3450.12 | −1.44064 | −0.720320 | − | 0.693642i | \(-0.756005\pi\) | ||||
−0.720320 | + | 0.693642i | \(0.756005\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3089.75 | −1.26883 | −0.634417 | − | 0.772991i | \(-0.718760\pi\) | ||||
−0.634417 | + | 0.772991i | \(0.718760\pi\) | |||||||
\(182\) | −271.096 | −0.110412 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −377.122 | −0.151097 | ||||||||
\(185\) | 774.883 | 0.307949 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5816.41 | −2.27453 | ||||||||
\(188\) | 1757.36 | 0.681748 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −159.611 | −0.0609444 | ||||||||
\(191\) | 1532.11 | 0.580419 | 0.290209 | − | 0.956963i | \(-0.406275\pi\) | ||||
0.290209 | + | 0.956963i | \(0.406275\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5194.42 | −1.93732 | −0.968660 | − | 0.248389i | \(-0.920099\pi\) | ||||
−0.968660 | + | 0.248389i | \(0.920099\pi\) | |||||||
\(194\) | −86.6747 | −0.0320767 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1049.10 | 0.382326 | ||||||||
\(197\) | −2005.61 | −0.725349 | −0.362674 | − | 0.931916i | \(-0.618136\pi\) | ||||
−0.362674 | + | 0.931916i | \(0.618136\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2874.68 | −1.02402 | −0.512011 | − | 0.858979i | \(-0.671099\pi\) | ||||
−0.512011 | + | 0.858979i | \(0.671099\pi\) | |||||||
\(200\) | 103.052 | 0.0364344 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 312.029 | 0.108685 | ||||||||
\(203\) | 2531.84 | 0.875372 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1821.01 | −0.620415 | ||||||||
\(206\) | −274.522 | −0.0928488 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4503.90 | 1.50139 | ||||||||
\(209\) | −6081.18 | −2.01265 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2749.94 | −0.897220 | −0.448610 | − | 0.893728i | \(-0.648081\pi\) | ||||
−0.448610 | + | 0.893728i | \(0.648081\pi\) | |||||||
\(212\) | 108.520 | 0.0351564 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 123.038 | 0.0393023 | ||||||||
\(215\) | 628.569 | 0.199386 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −672.093 | −0.210252 | ||||||||
\(218\) | −341.609 | −0.106131 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1954.89 | 0.599084 | ||||||||
\(221\) | 8518.45 | 2.59282 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −783.727 | −0.235346 | −0.117673 | − | 0.993052i | \(-0.537544\pi\) | ||||
−0.117673 | + | 0.993052i | \(0.537544\pi\) | |||||||
\(224\) | −713.093 | −0.212703 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 17.6377 | 0.00519134 | ||||||||
\(227\) | −145.665 | −0.0425909 | −0.0212955 | − | 0.999773i | \(-0.506779\pi\) | ||||
−0.0212955 | + | 0.999773i | \(0.506779\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3411.82 | −0.984539 | −0.492270 | − | 0.870443i | \(-0.663833\pi\) | ||||
−0.492270 | + | 0.870443i | \(0.663833\pi\) | |||||||
\(230\) | 118.346 | 0.0339282 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 718.892 | 0.203438 | ||||||||
\(233\) | 134.977 | 0.0379511 | 0.0189756 | − | 0.999820i | \(-0.493960\pi\) | ||||
0.0189756 | + | 0.999820i | \(0.493960\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1107.62 | −0.307459 | ||||||||
\(236\) | −1896.69 | −0.523153 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −443.252 | −0.120722 | ||||||||
\(239\) | −2245.32 | −0.607690 | −0.303845 | − | 0.952722i | \(-0.598270\pi\) | ||||
−0.303845 | + | 0.952722i | \(0.598270\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4158.54 | 1.11151 | 0.555757 | − | 0.831345i | \(-0.312428\pi\) | ||||
0.555757 | + | 0.831345i | \(0.312428\pi\) | |||||||
\(242\) | −284.057 | −0.0754542 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 432.715 | 0.113532 | ||||||||
\(245\) | −661.222 | −0.172424 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8906.22 | 2.29429 | ||||||||
\(248\) | −190.834 | −0.0488629 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −32.3390 | −0.00818120 | ||||||||
\(251\) | 3946.14 | 0.992343 | 0.496171 | − | 0.868225i | \(-0.334739\pi\) | ||||
0.496171 | + | 0.868225i | \(0.334739\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4508.96 | 1.12046 | ||||||||
\(254\) | 153.419 | 0.0378990 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3757.59 | 0.917381 | ||||||||
\(257\) | −5695.84 | −1.38248 | −0.691239 | − | 0.722626i | \(-0.742935\pi\) | ||||
−0.691239 | + | 0.722626i | \(0.742935\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2249.86 | 0.539767 | ||||||||
\(260\) | −2863.04 | −0.682917 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −87.6873 | −0.0206769 | ||||||||
\(263\) | 2814.06 | 0.659781 | 0.329891 | − | 0.944019i | \(-0.392988\pi\) | ||||
0.329891 | + | 0.944019i | \(0.392988\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −68.3970 | −0.0158551 | ||||||||
\(266\) | −463.429 | −0.106822 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 603.356 | 0.137522 | ||||||||
\(269\) | 200.985 | 0.0455548 | 0.0227774 | − | 0.999741i | \(-0.492749\pi\) | ||||
0.0227774 | + | 0.999741i | \(0.492749\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2406.05 | −0.539326 | −0.269663 | − | 0.962955i | \(-0.586912\pi\) | ||||
−0.269663 | + | 0.962955i | \(0.586912\pi\) | |||||||
\(272\) | 7364.03 | 1.64158 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 209.930 | 0.0462859 | ||||||||
\(275\) | −1232.11 | −0.270179 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8429.33 | −1.82841 | −0.914205 | − | 0.405253i | \(-0.867184\pi\) | ||||
−0.914205 | + | 0.405253i | \(0.867184\pi\) | |||||||
\(278\) | 803.593 | 0.173368 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 299.210 | 0.0638615 | ||||||||
\(281\) | 3974.26 | 0.843717 | 0.421859 | − | 0.906662i | \(-0.361378\pi\) | ||||
0.421859 | + | 0.906662i | \(0.361378\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3072.41 | −0.645356 | −0.322678 | − | 0.946509i | \(-0.604583\pi\) | ||||
−0.322678 | + | 0.946509i | \(0.604583\pi\) | |||||||
\(284\) | −5777.68 | −1.20719 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 920.333 | 0.190281 | ||||||||
\(287\) | −5287.28 | −1.08745 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9014.97 | 1.83492 | ||||||||
\(290\) | −225.597 | −0.0456812 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3980.93 | 0.797831 | ||||||||
\(293\) | 3982.21 | 0.794004 | 0.397002 | − | 0.917818i | \(-0.370051\pi\) | ||||
0.397002 | + | 0.917818i | \(0.370051\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1195.43 | 0.235935 | ||||||||
\(296\) | 638.826 | 0.125443 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −657.391 | −0.127791 | ||||||||
\(299\) | −6603.63 | −1.27725 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1825.04 | 0.349480 | ||||||||
\(302\) | 291.147 | 0.0554756 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 7699.25 | 1.45257 | ||||||||
\(305\) | −272.729 | −0.0512013 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2996.06 | −0.556984 | −0.278492 | − | 0.960439i | \(-0.589835\pi\) | ||||
−0.278492 | + | 0.960439i | \(0.589835\pi\) | |||||||
\(308\) | 5675.99 | 1.05006 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 59.8862 | 0.0109720 | ||||||||
\(311\) | −3079.94 | −0.561567 | −0.280783 | − | 0.959771i | \(-0.590594\pi\) | ||||
−0.280783 | + | 0.959771i | \(0.590594\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7953.65 | 1.43632 | 0.718158 | − | 0.695880i | \(-0.244986\pi\) | ||||
0.718158 | + | 0.695880i | \(0.244986\pi\) | |||||||
\(314\) | −835.655 | −0.150187 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3154.26 | −0.561523 | ||||||||
\(317\) | −6832.98 | −1.21066 | −0.605328 | − | 0.795976i | \(-0.706958\pi\) | ||||
−0.605328 | + | 0.795976i | \(0.706958\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8595.23 | −1.50859 | ||||||||
\(320\) | −2432.38 | −0.424920 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 343.615 | 0.0594687 | ||||||||
\(323\) | 14562.0 | 2.50852 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1804.50 | 0.307987 | ||||||||
\(326\) | 179.560 | 0.0305059 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1501.27 | −0.252725 | ||||||||
\(329\) | −3215.95 | −0.538908 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2296.57 | −0.381363 | −0.190682 | − | 0.981652i | \(-0.561070\pi\) | ||||
−0.190682 | + | 0.981652i | \(0.561070\pi\) | |||||||
\(332\) | 10864.0 | 1.79591 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −832.028 | −0.136307 | ||||||||
\(335\) | −380.279 | −0.0620205 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7261.48 | 1.17376 | 0.586881 | − | 0.809673i | \(-0.300355\pi\) | ||||
0.586881 | + | 0.809673i | \(0.300355\pi\) | |||||||
\(338\) | −779.488 | −0.125440 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4681.18 | −0.746684 | ||||||||
\(341\) | 2281.66 | 0.362342 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6899.32 | −1.08609 | ||||||||
\(344\) | 518.203 | 0.0812198 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −76.9789 | −0.0119607 | ||||||||
\(347\) | 7425.22 | 1.14872 | 0.574361 | − | 0.818602i | \(-0.305251\pi\) | ||||
0.574361 | + | 0.818602i | \(0.305251\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −478.160 | −0.0733390 | −0.0366695 | − | 0.999327i | \(-0.511675\pi\) | ||||
−0.0366695 | + | 0.999327i | \(0.511675\pi\) | |||||||
\(350\) | −93.8959 | −0.0143399 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2420.85 | 0.366567 | ||||||||
\(353\) | −4993.09 | −0.752847 | −0.376424 | − | 0.926448i | \(-0.622846\pi\) | ||||
−0.376424 | + | 0.926448i | \(0.622846\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3641.52 | 0.544427 | ||||||||
\(356\) | −11646.8 | −1.73393 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 892.590 | 0.131773 | ||||||||
\(359\) | −6873.09 | −1.01044 | −0.505219 | − | 0.862991i | \(-0.668588\pi\) | ||||
−0.505219 | + | 0.862991i | \(0.668588\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8365.87 | 1.21969 | ||||||||
\(362\) | 799.356 | 0.116059 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −8312.81 | −1.19700 | ||||||||
\(365\) | −2509.08 | −0.359811 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8688.72 | −1.23582 | −0.617912 | − | 0.786247i | \(-0.712021\pi\) | ||||
−0.617912 | + | 0.786247i | \(0.712021\pi\) | |||||||
\(368\) | −5708.70 | −0.808659 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −200.472 | −0.0281677 | ||||||||
\(371\) | −198.590 | −0.0277904 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3494.54 | 0.485095 | 0.242548 | − | 0.970140i | \(-0.422017\pi\) | ||||
0.242548 | + | 0.970140i | \(0.422017\pi\) | |||||||
\(374\) | 1504.78 | 0.208048 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −913.137 | −0.125243 | ||||||||
\(377\) | 12588.2 | 1.71970 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5802.83 | −0.786468 | −0.393234 | − | 0.919438i | \(-0.628644\pi\) | ||||
−0.393234 | + | 0.919438i | \(0.628644\pi\) | |||||||
\(380\) | −4894.27 | −0.660713 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −396.377 | −0.0530901 | ||||||||
\(383\) | −3358.56 | −0.448080 | −0.224040 | − | 0.974580i | \(-0.571925\pi\) | ||||
−0.224040 | + | 0.974580i | \(0.571925\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3577.42 | −0.473565 | ||||||||
\(386\) | 1343.86 | 0.177204 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2657.76 | −0.347751 | ||||||||
\(389\) | 19.1370 | 0.00249430 | 0.00124715 | − | 0.999999i | \(-0.499603\pi\) | ||||
0.00124715 | + | 0.999999i | \(0.499603\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10797.2 | −1.39651 | ||||||||
\(392\) | −545.122 | −0.0702368 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 518.876 | 0.0663467 | ||||||||
\(395\) | 1988.05 | 0.253239 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4348.59 | −0.549747 | −0.274873 | − | 0.961480i | \(-0.588636\pi\) | ||||
−0.274873 | + | 0.961480i | \(0.588636\pi\) | |||||||
\(398\) | 743.715 | 0.0936659 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1559.95 | 0.194994 | ||||||||
\(401\) | 8501.61 | 1.05873 | 0.529364 | − | 0.848395i | \(-0.322430\pi\) | ||||
0.529364 | + | 0.848395i | \(0.322430\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3341.62 | −0.413047 | ||||||||
\(404\) | 9567.96 | 1.17828 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −655.019 | −0.0800690 | ||||||||
\(407\) | −7637.95 | −0.930219 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2810.67 | −0.339801 | −0.169900 | − | 0.985461i | \(-0.554345\pi\) | ||||
−0.169900 | + | 0.985461i | \(0.554345\pi\) | |||||||
\(410\) | 471.119 | 0.0567485 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −8417.85 | −1.00660 | ||||||||
\(413\) | 3470.93 | 0.413543 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6847.31 | −0.809930 | ||||||||
\(416\) | −3545.47 | −0.417863 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1573.28 | 0.184094 | ||||||||
\(419\) | −16355.4 | −1.90696 | −0.953478 | − | 0.301461i | \(-0.902526\pi\) | ||||
−0.953478 | + | 0.301461i | \(0.902526\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4510.90 | −0.522204 | −0.261102 | − | 0.965311i | \(-0.584086\pi\) | ||||
−0.261102 | + | 0.965311i | \(0.584086\pi\) | |||||||
\(422\) | 711.443 | 0.0820675 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −56.3876 | −0.00645854 | ||||||||
\(425\) | 2950.42 | 0.336745 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −791.864 | −0.0897447 | ||||||||
\(428\) | 3772.79 | 0.426086 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −162.619 | −0.0182376 | ||||||||
\(431\) | 5850.47 | 0.653845 | 0.326923 | − | 0.945051i | \(-0.393988\pi\) | ||||
0.326923 | + | 0.945051i | \(0.393988\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3836.82 | −0.425833 | −0.212916 | − | 0.977070i | \(-0.568296\pi\) | ||||
−0.212916 | + | 0.977070i | \(0.568296\pi\) | |||||||
\(434\) | 173.879 | 0.0192314 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −10475.0 | −1.15060 | ||||||||
\(437\) | −11288.7 | −1.23572 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16227.3 | 1.76421 | 0.882106 | − | 0.471052i | \(-0.156125\pi\) | ||||
0.882106 | + | 0.471052i | \(0.156125\pi\) | |||||||
\(440\) | −1015.77 | −0.110057 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2203.83 | −0.237162 | ||||||||
\(443\) | 6705.13 | 0.719120 | 0.359560 | − | 0.933122i | \(-0.382927\pi\) | ||||
0.359560 | + | 0.933122i | \(0.382927\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7340.65 | 0.781978 | ||||||||
\(446\) | 202.760 | 0.0215268 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −7062.39 | −0.744792 | ||||||||
\(449\) | 213.100 | 0.0223982 | 0.0111991 | − | 0.999937i | \(-0.496435\pi\) | ||||
0.0111991 | + | 0.999937i | \(0.496435\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 17949.6 | 1.87408 | ||||||||
\(452\) | 540.837 | 0.0562806 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 37.6854 | 0.00389573 | ||||||||
\(455\) | 5239.34 | 0.539833 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16462.1 | 1.68504 | 0.842520 | − | 0.538665i | \(-0.181071\pi\) | ||||
0.842520 | + | 0.538665i | \(0.181071\pi\) | |||||||
\(458\) | 882.680 | 0.0900545 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3628.92 | 0.367824 | ||||||||
\(461\) | 1562.06 | 0.157814 | 0.0789071 | − | 0.996882i | \(-0.474857\pi\) | ||||
0.0789071 | + | 0.996882i | \(0.474857\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5924.27 | −0.594653 | −0.297326 | − | 0.954776i | \(-0.596095\pi\) | ||||
−0.297326 | + | 0.954776i | \(0.596095\pi\) | |||||||
\(464\) | 10882.2 | 1.08878 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −34.9201 | −0.00347134 | ||||||||
\(467\) | −17905.1 | −1.77420 | −0.887098 | − | 0.461582i | \(-0.847282\pi\) | ||||
−0.887098 | + | 0.461582i | \(0.847282\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1104.13 | −0.108708 | ||||||||
\(470\) | 286.554 | 0.0281229 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 985.536 | 0.0961080 | ||||||||
\(473\) | −6195.75 | −0.602285 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3084.73 | 0.297973 | ||||||||
\(476\) | −13591.7 | −1.30877 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 580.893 | 0.0555846 | ||||||||
\(479\) | 9915.44 | 0.945820 | 0.472910 | − | 0.881111i | \(-0.343204\pi\) | ||||
0.472910 | + | 0.881111i | \(0.343204\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11186.2 | 1.06039 | ||||||||
\(482\) | −1075.87 | −0.101669 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8710.24 | −0.818017 | ||||||||
\(485\) | 1675.12 | 0.156831 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11910.8 | 1.10828 | 0.554138 | − | 0.832425i | \(-0.313048\pi\) | ||||
0.554138 | + | 0.832425i | \(0.313048\pi\) | |||||||
\(488\) | −224.842 | −0.0208568 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 171.066 | 0.0157714 | ||||||||
\(491\) | 11063.8 | 1.01691 | 0.508453 | − | 0.861090i | \(-0.330218\pi\) | ||||
0.508453 | + | 0.861090i | \(0.330218\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 20582.2 | 1.88027 | ||||||||
\(494\) | −2304.15 | −0.209856 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2888.76 | −0.261510 | ||||||||
\(497\) | 10573.1 | 0.954261 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9347.25 | 0.838557 | 0.419279 | − | 0.907858i | \(-0.362283\pi\) | ||||
0.419279 | + | 0.907858i | \(0.362283\pi\) | |||||||
\(500\) | −991.633 | −0.0886944 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1020.91 | −0.0907682 | ||||||||
\(503\) | −19474.2 | −1.72627 | −0.863135 | − | 0.504973i | \(-0.831502\pi\) | ||||
−0.863135 | + | 0.504973i | \(0.831502\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6030.43 | −0.531387 | ||||||||
\(506\) | −1166.52 | −0.102487 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4704.38 | 0.410873 | ||||||||
\(509\) | 22164.1 | 1.93007 | 0.965035 | − | 0.262121i | \(-0.0844221\pi\) | ||||
0.965035 | + | 0.262121i | \(0.0844221\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7285.06 | −0.630670 | ||||||||
\(512\) | −5122.66 | −0.442172 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1473.58 | 0.126453 | ||||||||
\(515\) | 5305.55 | 0.453962 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10917.7 | 0.928740 | ||||||||
\(518\) | −582.067 | −0.0493717 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1487.66 | 0.125458 | ||||||||
\(521\) | −254.564 | −0.0214062 | −0.0107031 | − | 0.999943i | \(-0.503407\pi\) | ||||
−0.0107031 | + | 0.999943i | \(0.503407\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4049.92 | 0.338606 | 0.169303 | − | 0.985564i | \(-0.445848\pi\) | ||||
0.169303 | + | 0.985564i | \(0.445848\pi\) | |||||||
\(524\) | −2688.81 | −0.224163 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −728.033 | −0.0603493 | ||||||||
\(527\) | −5463.66 | −0.451614 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3796.89 | −0.312064 | ||||||||
\(530\) | 17.6951 | 0.00145024 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −14210.4 | −1.15808 | ||||||||
\(533\) | −26288.1 | −2.13633 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2377.89 | −0.192159 | ||||||||
\(536\) | −313.508 | −0.0252640 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −51.9972 | −0.00416684 | ||||||||
\(539\) | 6517.60 | 0.520841 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4085.88 | −0.324705 | −0.162353 | − | 0.986733i | \(-0.551908\pi\) | ||||
−0.162353 | + | 0.986733i | \(0.551908\pi\) | |||||||
\(542\) | 622.475 | 0.0493314 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5796.96 | −0.456880 | ||||||||
\(545\) | 6602.09 | 0.518904 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15392.2 | −1.20315 | −0.601575 | − | 0.798816i | \(-0.705460\pi\) | ||||
−0.601575 | + | 0.798816i | \(0.705460\pi\) | |||||||
\(548\) | 6437.22 | 0.501796 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 318.763 | 0.0247129 | ||||||||
\(551\) | 21519.1 | 1.66378 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5772.27 | 0.443873 | ||||||||
\(554\) | 2180.77 | 0.167242 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 24641.1 | 1.87952 | ||||||||
\(557\) | −10897.6 | −0.828987 | −0.414493 | − | 0.910052i | \(-0.636041\pi\) | ||||
−0.414493 | + | 0.910052i | \(0.636041\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9074.02 | 0.686566 | ||||||||
\(560\) | 4529.30 | 0.341782 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1028.19 | −0.0771737 | ||||||||
\(563\) | −1551.69 | −0.116156 | −0.0580781 | − | 0.998312i | \(-0.518497\pi\) | ||||
−0.0580781 | + | 0.998312i | \(0.518497\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −340.875 | −0.0253818 | ||||||||
\(566\) | 794.870 | 0.0590298 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3002.12 | 0.221772 | ||||||||
\(569\) | −1246.95 | −0.0918715 | −0.0459357 | − | 0.998944i | \(-0.514627\pi\) | ||||
−0.0459357 | + | 0.998944i | \(0.514627\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4196.58 | 0.307568 | 0.153784 | − | 0.988104i | \(-0.450854\pi\) | ||||
0.153784 | + | 0.988104i | \(0.450854\pi\) | |||||||
\(572\) | 28220.8 | 2.06288 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1367.89 | 0.0994677 | ||||||||
\(575\) | −2287.21 | −0.165884 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20585.1 | 1.48521 | 0.742607 | − | 0.669728i | \(-0.233589\pi\) | ||||
0.742607 | + | 0.669728i | \(0.233589\pi\) | |||||||
\(578\) | −2332.28 | −0.167838 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −6917.64 | −0.495240 | ||||||||
\(581\) | −19881.1 | −1.41963 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 674.183 | 0.0478933 | ||||||||
\(584\) | −2068.52 | −0.146569 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1030.25 | −0.0726265 | ||||||||
\(587\) | −4855.78 | −0.341430 | −0.170715 | − | 0.985320i | \(-0.554608\pi\) | ||||
−0.170715 | + | 0.985320i | \(0.554608\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5712.37 | −0.399617 | ||||||||
\(590\) | −309.274 | −0.0215807 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 9670.25 | 0.671360 | ||||||||
\(593\) | −23965.6 | −1.65961 | −0.829804 | − | 0.558055i | \(-0.811548\pi\) | ||||
−0.829804 | + | 0.558055i | \(0.811548\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8566.50 | 0.590239 | ||||||||
\(596\) | −20158.0 | −1.38541 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1708.44 | 0.116828 | ||||||||
\(599\) | 14229.1 | 0.970595 | 0.485297 | − | 0.874349i | \(-0.338711\pi\) | ||||
0.485297 | + | 0.874349i | \(0.338711\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8877.97 | −0.602562 | −0.301281 | − | 0.953535i | \(-0.597414\pi\) | ||||
−0.301281 | + | 0.953535i | \(0.597414\pi\) | |||||||
\(602\) | −472.161 | −0.0319665 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 8927.64 | 0.601424 | ||||||||
\(605\) | 5489.83 | 0.368915 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10876.7 | −0.727302 | −0.363651 | − | 0.931535i | \(-0.618470\pi\) | ||||
−0.363651 | + | 0.931535i | \(0.618470\pi\) | |||||||
\(608\) | −6060.85 | −0.404276 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 70.5583 | 0.00468331 | ||||||||
\(611\) | −15989.5 | −1.05870 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −19544.8 | −1.28778 | −0.643890 | − | 0.765118i | \(-0.722680\pi\) | ||||
−0.643890 | + | 0.765118i | \(0.722680\pi\) | |||||||
\(614\) | 775.118 | 0.0509466 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2949.29 | −0.192906 | ||||||||
\(617\) | 5041.75 | 0.328968 | 0.164484 | − | 0.986380i | \(-0.447404\pi\) | ||||
0.164484 | + | 0.986380i | \(0.447404\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5208.05 | −0.338173 | −0.169087 | − | 0.985601i | \(-0.554082\pi\) | ||||
−0.169087 | + | 0.985601i | \(0.554082\pi\) | |||||||
\(620\) | 1836.33 | 0.118950 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 796.818 | 0.0513657 | ||||||||
\(623\) | 21313.5 | 1.37064 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | −2057.71 | −0.131378 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −25624.2 | −1.62821 | ||||||||
\(629\) | 18289.9 | 1.15940 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20284.6 | −1.27974 | −0.639872 | − | 0.768482i | \(-0.721013\pi\) | ||||
−0.639872 | + | 0.768482i | \(0.721013\pi\) | |||||||
\(632\) | 1638.98 | 0.103157 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1767.78 | 0.110737 | ||||||||
\(635\) | −2965.05 | −0.185298 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9545.40 | −0.593724 | ||||||||
\(638\) | 2223.69 | 0.137989 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2594.08 | 0.160219 | ||||||||
\(641\) | −20852.4 | −1.28490 | −0.642449 | − | 0.766329i | \(-0.722081\pi\) | ||||
−0.642449 | + | 0.766329i | \(0.722081\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2187.22 | −0.134146 | −0.0670729 | − | 0.997748i | \(-0.521366\pi\) | ||||
−0.0670729 | + | 0.997748i | \(0.521366\pi\) | |||||||
\(644\) | 10536.5 | 0.644715 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3767.37 | −0.229451 | ||||||||
\(647\) | 17044.1 | 1.03566 | 0.517831 | − | 0.855483i | \(-0.326740\pi\) | ||||
0.517831 | + | 0.855483i | \(0.326740\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −11783.3 | −0.712688 | ||||||||
\(650\) | −466.846 | −0.0281711 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5505.98 | 0.330722 | ||||||||
\(653\) | 8474.26 | 0.507846 | 0.253923 | − | 0.967224i | \(-0.418279\pi\) | ||||
0.253923 | + | 0.967224i | \(0.418279\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1694.69 | 0.101094 | ||||||||
\(656\) | −22725.6 | −1.35257 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 832.005 | 0.0492932 | ||||||||
\(659\) | 25560.2 | 1.51090 | 0.755450 | − | 0.655207i | \(-0.227419\pi\) | ||||
0.755450 | + | 0.655207i | \(0.227419\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1209.59 | 0.0711766 | 0.0355883 | − | 0.999367i | \(-0.488670\pi\) | ||||
0.0355883 | + | 0.999367i | \(0.488670\pi\) | |||||||
\(662\) | 594.152 | 0.0348828 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −5645.03 | −0.329924 | ||||||||
\(665\) | 8956.46 | 0.522281 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −15955.6 | −0.926241 | ||||||||
\(668\) | −25513.0 | −1.47774 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 98.3828 | 0.00567293 | ||||||||
\(671\) | 2688.26 | 0.154664 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8698.21 | −0.498204 | −0.249102 | − | 0.968477i | \(-0.580135\pi\) | ||||
−0.249102 | + | 0.968477i | \(0.580135\pi\) | |||||||
\(674\) | −1878.64 | −0.107362 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −23902.0 | −1.35992 | ||||||||
\(677\) | −8424.49 | −0.478256 | −0.239128 | − | 0.970988i | \(-0.576862\pi\) | ||||
−0.239128 | + | 0.970988i | \(0.576862\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4863.68 | 0.274891 | ||||||||
\(680\) | 2432.37 | 0.137173 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −590.293 | −0.0331430 | ||||||||
\(683\) | −17828.6 | −0.998817 | −0.499408 | − | 0.866367i | \(-0.666449\pi\) | ||||
−0.499408 | + | 0.866367i | \(0.666449\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4057.21 | −0.226304 | ||||||||
\(686\) | 1784.94 | 0.0993431 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 7844.30 | 0.434682 | ||||||||
\(689\) | −987.378 | −0.0545952 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14525.1 | 0.799652 | 0.399826 | − | 0.916591i | \(-0.369070\pi\) | ||||
0.399826 | + | 0.916591i | \(0.369070\pi\) | |||||||
\(692\) | −2360.45 | −0.129669 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1921.00 | −0.105072 | ||||||||
\(695\) | −15530.6 | −0.847641 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −42982.0 | −2.33581 | ||||||||
\(698\) | 123.706 | 0.00670822 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2879.19 | −0.155462 | ||||||||
\(701\) | 18815.5 | 1.01377 | 0.506883 | − | 0.862015i | \(-0.330798\pi\) | ||||
0.506883 | + | 0.862015i | \(0.330798\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 19122.4 | 1.02591 | ||||||||
\(704\) | 23975.8 | 1.28355 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1291.77 | 0.0688619 | ||||||||
\(707\) | −17509.3 | −0.931405 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12934.4 | −0.685137 | −0.342569 | − | 0.939493i | \(-0.611297\pi\) | ||||
−0.342569 | + | 0.939493i | \(0.611297\pi\) | |||||||
\(710\) | −942.105 | −0.0497980 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6051.75 | 0.318538 | ||||||||
\(713\) | 4235.51 | 0.222470 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −17786.8 | −0.930333 | ||||||||
\(716\) | 27370.1 | 1.42859 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1778.15 | 0.0924235 | ||||||||
\(719\) | −8471.10 | −0.439386 | −0.219693 | − | 0.975569i | \(-0.570506\pi\) | ||||
−0.219693 | + | 0.975569i | \(0.570506\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15404.6 | 0.795695 | ||||||||
\(722\) | −2164.35 | −0.111564 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 24511.2 | 1.25822 | ||||||||
\(725\) | 4360.00 | 0.223347 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24369.5 | 1.24321 | 0.621605 | − | 0.783331i | \(-0.286481\pi\) | ||||
0.621605 | + | 0.783331i | \(0.286481\pi\) | |||||||
\(728\) | 4319.40 | 0.219900 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 649.129 | 0.0329114 | ||||||||
\(731\) | 14836.3 | 0.750673 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −35411.8 | −1.78440 | −0.892199 | − | 0.451642i | \(-0.850838\pi\) | ||||
−0.892199 | + | 0.451642i | \(0.850838\pi\) | |||||||
\(734\) | 2247.88 | 0.113039 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4493.89 | 0.225064 | ||||||||
\(737\) | 3748.37 | 0.187345 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −24447.0 | −1.21691 | −0.608456 | − | 0.793588i | \(-0.708211\pi\) | ||||
−0.608456 | + | 0.793588i | \(0.708211\pi\) | |||||||
\(740\) | −6147.20 | −0.305372 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 51.3776 | 0.00254195 | ||||||||
\(743\) | −24125.9 | −1.19125 | −0.595623 | − | 0.803264i | \(-0.703095\pi\) | ||||
−0.595623 | + | 0.803264i | \(0.703095\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12705.1 | 0.624802 | ||||||||
\(746\) | −904.081 | −0.0443710 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 46141.9 | 2.25550 | ||||||||
\(749\) | −6904.17 | −0.336813 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11882.4 | 0.577356 | 0.288678 | − | 0.957426i | \(-0.406784\pi\) | ||||
0.288678 | + | 0.957426i | \(0.406784\pi\) | |||||||
\(752\) | −13822.6 | −0.670292 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −3256.72 | −0.157298 | ||||||||
\(755\) | −5626.85 | −0.271234 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14601.3 | −0.701049 | −0.350525 | − | 0.936554i | \(-0.613997\pi\) | ||||
−0.350525 | + | 0.936554i | \(0.613997\pi\) | |||||||
\(758\) | 1501.26 | 0.0719372 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2543.10 | 0.121379 | ||||||||
\(761\) | −20296.3 | −0.966809 | −0.483404 | − | 0.875397i | \(-0.660600\pi\) | ||||
−0.483404 | + | 0.875397i | \(0.660600\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 19169.1 | 0.909524 | ||||||||
\(764\) | −12154.4 | −0.575562 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 868.902 | 0.0409853 | ||||||||
\(767\) | 17257.3 | 0.812418 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 36322.0 | 1.70326 | 0.851629 | − | 0.524146i | \(-0.175615\pi\) | ||||
0.851629 | + | 0.524146i | \(0.175615\pi\) | |||||||
\(770\) | 925.524 | 0.0433163 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 41207.7 | 1.92111 | ||||||||
\(773\) | 28930.9 | 1.34615 | 0.673073 | − | 0.739576i | \(-0.264974\pi\) | ||||
0.673073 | + | 0.739576i | \(0.264974\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1157.39 | −0.0536448 | ||||||||
\(776\) | 1380.99 | 0.0638850 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.95098 | −0.000228150 0 | ||||||||
\(779\) | −44938.6 | −2.06687 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −35894.1 | −1.64455 | ||||||||
\(782\) | 2793.36 | 0.127737 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −8251.80 | −0.375902 | ||||||||
\(785\) | 16150.3 | 0.734303 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21128.3 | 0.956978 | 0.478489 | − | 0.878094i | \(-0.341185\pi\) | ||||
0.478489 | + | 0.878094i | \(0.341185\pi\) | |||||||
\(788\) | 15910.6 | 0.719280 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −514.333 | −0.0231635 | ||||||||
\(791\) | −989.726 | −0.0444887 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3937.11 | −0.176306 | ||||||||
\(794\) | 1125.03 | 0.0502846 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 22805.0 | 1.01546 | ||||||||
\(797\) | −2765.87 | −0.122926 | −0.0614632 | − | 0.998109i | \(-0.519577\pi\) | ||||
−0.0614632 | + | 0.998109i | \(0.519577\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −26143.5 | −1.15756 | ||||||||
\(800\) | −1228.00 | −0.0542702 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −2199.47 | −0.0968405 | ||||||||
\(803\) | 24731.7 | 1.08688 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6640.87 | −0.290758 | ||||||||
\(806\) | 864.518 | 0.0377808 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −4971.59 | −0.216460 | ||||||||
\(809\) | 16756.6 | 0.728220 | 0.364110 | − | 0.931356i | \(-0.381373\pi\) | ||||
0.364110 | + | 0.931356i | \(0.381373\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17829.6 | 0.771987 | 0.385993 | − | 0.922502i | \(-0.373859\pi\) | ||||
0.385993 | + | 0.922502i | \(0.373859\pi\) | |||||||
\(812\) | −20085.3 | −0.868048 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1976.03 | 0.0850859 | ||||||||
\(815\) | −3470.27 | −0.149151 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 15511.7 | 0.664243 | ||||||||
\(818\) | 727.154 | 0.0310811 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 14446.2 | 0.615224 | ||||||||
\(821\) | −6757.48 | −0.287256 | −0.143628 | − | 0.989632i | \(-0.545877\pi\) | ||||
−0.143628 | + | 0.989632i | \(0.545877\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7121.28 | 0.301619 | 0.150809 | − | 0.988563i | \(-0.451812\pi\) | ||||
0.150809 | + | 0.988563i | \(0.451812\pi\) | |||||||
\(824\) | 4373.98 | 0.184921 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −897.972 | −0.0378262 | ||||||||
\(827\) | −1171.74 | −0.0492688 | −0.0246344 | − | 0.999697i | \(-0.507842\pi\) | ||||
−0.0246344 | + | 0.999697i | \(0.507842\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 23617.8 | 0.989483 | 0.494742 | − | 0.869040i | \(-0.335263\pi\) | ||||
0.494742 | + | 0.869040i | \(0.335263\pi\) | |||||||
\(830\) | 1771.48 | 0.0740832 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −35113.9 | −1.46317 | ||||||||
\(833\) | −15607.1 | −0.649163 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16080.2 | 0.666440 | ||||||||
\(836\) | 48242.4 | 1.99581 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 4231.35 | 0.174427 | ||||||||
\(839\) | −35054.3 | −1.44244 | −0.721222 | − | 0.692704i | \(-0.756419\pi\) | ||||
−0.721222 | + | 0.692704i | \(0.756419\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6026.42 | 0.247096 | ||||||||
\(842\) | 1167.02 | 0.0477652 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 21815.4 | 0.889714 | ||||||||
\(845\) | 15064.8 | 0.613306 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15939.6 | 0.646627 | ||||||||
\(848\) | −853.568 | −0.0345656 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −763.310 | −0.0308016 | ||||||||
\(851\) | −14178.6 | −0.571133 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −32772.3 | −1.31548 | −0.657740 | − | 0.753245i | \(-0.728487\pi\) | ||||
−0.657740 | + | 0.753245i | \(0.728487\pi\) | |||||||
\(854\) | 204.865 | 0.00820882 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1960.37 | −0.0782758 | ||||||||
\(857\) | −3503.93 | −0.139664 | −0.0698319 | − | 0.997559i | \(-0.522246\pi\) | ||||
−0.0698319 | + | 0.997559i | \(0.522246\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 31044.1 | 1.23307 | 0.616537 | − | 0.787326i | \(-0.288535\pi\) | ||||
0.616537 | + | 0.787326i | \(0.288535\pi\) | |||||||
\(860\) | −4986.48 | −0.197718 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1513.59 | −0.0598063 | ||||||||
\(863\) | 26333.6 | 1.03871 | 0.519354 | − | 0.854559i | \(-0.326173\pi\) | ||||
0.519354 | + | 0.854559i | \(0.326173\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1487.73 | 0.0584790 | ||||||||
\(866\) | 992.632 | 0.0389504 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 5331.76 | 0.208493 | ||||||||
\(869\) | −19596.0 | −0.764959 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5489.71 | −0.213561 | ||||||||
\(872\) | 5442.87 | 0.211375 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2920.52 | 0.113030 | ||||||||
\(875\) | 1814.68 | 0.0701112 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −40977.3 | −1.57777 | −0.788886 | − | 0.614540i | \(-0.789342\pi\) | ||||
−0.788886 | + | 0.614540i | \(0.789342\pi\) | |||||||
\(878\) | −4198.21 | −0.161370 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −15376.3 | −0.589017 | ||||||||
\(881\) | 37022.4 | 1.41579 | 0.707897 | − | 0.706315i | \(-0.249644\pi\) | ||||
0.707897 | + | 0.706315i | \(0.249644\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −36037.9 | −1.37347 | −0.686734 | − | 0.726909i | \(-0.740956\pi\) | ||||
−0.686734 | + | 0.726909i | \(0.740956\pi\) | |||||||
\(884\) | −67577.5 | −2.57113 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1734.70 | −0.0657769 | ||||||||
\(887\) | 1465.05 | 0.0554584 | 0.0277292 | − | 0.999615i | \(-0.491172\pi\) | ||||
0.0277292 | + | 0.999615i | \(0.491172\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8608.97 | −0.324787 | ||||||||
\(890\) | −1899.12 | −0.0715265 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 6217.36 | 0.233377 | ||||||||
\(893\) | −27333.5 | −1.02428 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −17250.6 | −0.644273 | ||||||||
\(896\) | 7531.87 | 0.280828 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −55.1315 | −0.00204873 | ||||||||
\(899\) | −8073.96 | −0.299535 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1614.40 | −0.0596930 | ||||||||
\(902\) | −4643.77 | −0.171420 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −281.023 | −0.0103393 | ||||||||
\(905\) | −15448.7 | −0.567440 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 33660.8 | 1.23229 | 0.616146 | − | 0.787632i | \(-0.288693\pi\) | ||||
0.616146 | + | 0.787632i | \(0.288693\pi\) | |||||||
\(908\) | 1155.57 | 0.0422346 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1355.48 | −0.0493778 | ||||||||
\(911\) | 25992.7 | 0.945311 | 0.472655 | − | 0.881247i | \(-0.343296\pi\) | ||||
0.472655 | + | 0.881247i | \(0.343296\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 67493.3 | 2.44655 | ||||||||
\(914\) | −4258.94 | −0.154128 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 27066.2 | 0.976302 | ||||||||
\(917\) | 4920.50 | 0.177196 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1149.54 | 0.0412620 | 0.0206310 | − | 0.999787i | \(-0.493432\pi\) | ||||
0.0206310 | + | 0.999787i | \(0.493432\pi\) | |||||||
\(920\) | −1885.61 | −0.0675726 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −404.124 | −0.0144350 | ||||||||
\(923\) | 52568.9 | 1.87468 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3874.42 | 0.137719 | ||||||||
\(926\) | 1532.68 | 0.0543921 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −8566.50 | −0.303027 | ||||||||
\(929\) | 1923.20 | 0.0679204 | 0.0339602 | − | 0.999423i | \(-0.489188\pi\) | ||||
0.0339602 | + | 0.999423i | \(0.489188\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −16317.5 | −0.574420 | ||||||||
\(932\) | −1070.78 | −0.0376336 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 4632.27 | 0.162283 | ||||||||
\(935\) | −29082.0 | −1.01720 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3511.90 | 0.122443 | 0.0612213 | − | 0.998124i | \(-0.480500\pi\) | ||||
0.0612213 | + | 0.998124i | \(0.480500\pi\) | |||||||
\(938\) | 285.653 | 0.00994339 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 8786.79 | 0.304887 | ||||||||
\(941\) | −6848.16 | −0.237241 | −0.118620 | − | 0.992940i | \(-0.537847\pi\) | ||||
−0.118620 | + | 0.992940i | \(0.537847\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 33320.3 | 1.15064 | ||||||||
\(944\) | 14918.6 | 0.514363 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1602.92 | 0.0550902 | ||||||||
\(947\) | 48357.3 | 1.65935 | 0.829673 | − | 0.558250i | \(-0.188527\pi\) | ||||
0.829673 | + | 0.558250i | \(0.188527\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −36221.0 | −1.23897 | ||||||||
\(950\) | −798.057 | −0.0272551 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 7062.36 | 0.240433 | ||||||||
\(953\) | 38701.1 | 1.31548 | 0.657740 | − | 0.753245i | \(-0.271512\pi\) | ||||
0.657740 | + | 0.753245i | \(0.271512\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7660.57 | 0.259571 | ||||||||
\(956\) | 17812.3 | 0.602606 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −2565.25 | −0.0865129 | ||||||||
\(959\) | −11780.0 | −0.396660 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27647.7 | −0.928056 | ||||||||
\(962\) | −2894.01 | −0.0969924 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −32990.0 | −1.10222 | ||||||||
\(965\) | −25972.1 | −0.866396 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24312.7 | −0.808526 | −0.404263 | − | 0.914643i | \(-0.632472\pi\) | ||||
−0.404263 | + | 0.914643i | \(0.632472\pi\) | |||||||
\(968\) | 4525.91 | 0.150277 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −433.373 | −0.0143451 | ||||||||
\(971\) | −37464.3 | −1.23820 | −0.619098 | − | 0.785314i | \(-0.712501\pi\) | ||||
−0.619098 | + | 0.785314i | \(0.712501\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −45092.9 | −1.48573 | ||||||||
\(974\) | −3081.47 | −0.101373 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3403.55 | −0.111624 | ||||||||
\(977\) | 3186.09 | 0.104332 | 0.0521659 | − | 0.998638i | \(-0.483388\pi\) | ||||
0.0521659 | + | 0.998638i | \(0.483388\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −72356.1 | −2.36212 | ||||||||
\(980\) | 5245.52 | 0.170982 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −2862.33 | −0.0930150 | ||||||||
\(983\) | 30345.6 | 0.984614 | 0.492307 | − | 0.870422i | \(-0.336154\pi\) | ||||
0.492307 | + | 0.870422i | \(0.336154\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10028.0 | −0.324386 | ||||||||
\(986\) | −5324.86 | −0.171986 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −70653.7 | −2.27509 | ||||||||
\(989\) | −11501.3 | −0.369789 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3443.75 | 0.110388 | 0.0551940 | − | 0.998476i | \(-0.482422\pi\) | ||||
0.0551940 | + | 0.998476i | \(0.482422\pi\) | |||||||
\(992\) | 2274.03 | 0.0727828 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2735.39 | −0.0872849 | ||||||||
\(995\) | −14373.4 | −0.457957 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4567.89 | −0.145102 | −0.0725510 | − | 0.997365i | \(-0.523114\pi\) | ||||
−0.0725510 | + | 0.997365i | \(0.523114\pi\) | |||||||
\(998\) | −2418.25 | −0.0767017 | ||||||||
\(999\) | 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 | 135.4.a.f.1.2 | ✓ | 3 | |
3.2 | odd | 2 | 135.4.a.g.1.2 | yes | 3 | ||
4.3 | odd | 2 | 2160.4.a.bm.1.2 | 3 | |||
5.2 | odd | 4 | 675.4.b.l.649.3 | 6 | |||
5.3 | odd | 4 | 675.4.b.l.649.4 | 6 | |||
5.4 | even | 2 | 675.4.a.r.1.2 | 3 | |||
9.2 | odd | 6 | 405.4.e.r.271.2 | 6 | |||
9.4 | even | 3 | 405.4.e.t.136.2 | 6 | |||
9.5 | odd | 6 | 405.4.e.r.136.2 | 6 | |||
9.7 | even | 3 | 405.4.e.t.271.2 | 6 | |||
12.11 | even | 2 | 2160.4.a.be.1.2 | 3 | |||
15.2 | even | 4 | 675.4.b.k.649.4 | 6 | |||
15.8 | even | 4 | 675.4.b.k.649.3 | 6 | |||
15.14 | odd | 2 | 675.4.a.q.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
135.4.a.f.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial | |
135.4.a.g.1.2 | yes | 3 | 3.2 | odd | 2 | ||
405.4.e.r.136.2 | 6 | 9.5 | odd | 6 | |||
405.4.e.r.271.2 | 6 | 9.2 | odd | 6 | |||
405.4.e.t.136.2 | 6 | 9.4 | even | 3 | |||
405.4.e.t.271.2 | 6 | 9.7 | even | 3 | |||
675.4.a.q.1.2 | 3 | 15.14 | odd | 2 | |||
675.4.a.r.1.2 | 3 | 5.4 | even | 2 | |||
675.4.b.k.649.3 | 6 | 15.8 | even | 4 | |||
675.4.b.k.649.4 | 6 | 15.2 | even | 4 | |||
675.4.b.l.649.3 | 6 | 5.2 | odd | 4 | |||
675.4.b.l.649.4 | 6 | 5.3 | odd | 4 | |||
2160.4.a.be.1.2 | 3 | 12.11 | even | 2 | |||
2160.4.a.bm.1.2 | 3 | 4.3 | odd | 2 |