Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [65,4,Mod(1,65)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(65, 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("65.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 65 = 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 65.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: | \(3.83512415037\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 65.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.56155 | 0.905646 | 0.452823 | − | 0.891601i | \(-0.350417\pi\) | ||||
0.452823 | + | 0.891601i | \(0.350417\pi\) | |||||||
\(3\) | 8.24621 | 1.58698 | 0.793492 | − | 0.608581i | \(-0.208261\pi\) | ||||
0.793492 | + | 0.608581i | \(0.208261\pi\) | |||||||
\(4\) | −1.43845 | −0.179806 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 21.1231 | 1.43725 | ||||||||
\(7\) | 24.8769 | 1.34323 | 0.671613 | − | 0.740902i | \(-0.265602\pi\) | ||||
0.671613 | + | 0.740902i | \(0.265602\pi\) | |||||||
\(8\) | −24.1771 | −1.06849 | ||||||||
\(9\) | 41.0000 | 1.51852 | ||||||||
\(10\) | −12.8078 | −0.405017 | ||||||||
\(11\) | −38.8769 | −1.06562 | −0.532810 | − | 0.846235i | \(-0.678864\pi\) | ||||
−0.532810 | + | 0.846235i | \(0.678864\pi\) | |||||||
\(12\) | −11.8617 | −0.285349 | ||||||||
\(13\) | −13.0000 | −0.277350 | ||||||||
\(14\) | 63.7235 | 1.21649 | ||||||||
\(15\) | −41.2311 | −0.709721 | ||||||||
\(16\) | −50.4233 | −0.787864 | ||||||||
\(17\) | −79.9697 | −1.14091 | −0.570456 | − | 0.821328i | \(-0.693233\pi\) | ||||
−0.570456 | + | 0.821328i | \(0.693233\pi\) | |||||||
\(18\) | 105.024 | 1.37524 | ||||||||
\(19\) | 128.354 | 1.54981 | 0.774907 | − | 0.632075i | \(-0.217797\pi\) | ||||
0.774907 | + | 0.632075i | \(0.217797\pi\) | |||||||
\(20\) | 7.19224 | 0.0804116 | ||||||||
\(21\) | 205.140 | 2.13168 | ||||||||
\(22\) | −99.5852 | −0.965075 | ||||||||
\(23\) | −101.939 | −0.924167 | −0.462083 | − | 0.886837i | \(-0.652898\pi\) | ||||
−0.462083 | + | 0.886837i | \(0.652898\pi\) | |||||||
\(24\) | −199.369 | −1.69567 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | −33.3002 | −0.251181 | ||||||||
\(27\) | 115.447 | 0.822881 | ||||||||
\(28\) | −35.7841 | −0.241520 | ||||||||
\(29\) | 117.723 | 0.753817 | 0.376909 | − | 0.926250i | \(-0.376987\pi\) | ||||
0.376909 | + | 0.926250i | \(0.376987\pi\) | |||||||
\(30\) | −105.616 | −0.642756 | ||||||||
\(31\) | −298.756 | −1.73091 | −0.865453 | − | 0.500990i | \(-0.832969\pi\) | ||||
−0.865453 | + | 0.500990i | \(0.832969\pi\) | |||||||
\(32\) | 64.2547 | 0.354961 | ||||||||
\(33\) | −320.587 | −1.69112 | ||||||||
\(34\) | −204.847 | −1.03326 | ||||||||
\(35\) | −124.384 | −0.600709 | ||||||||
\(36\) | −58.9763 | −0.273039 | ||||||||
\(37\) | 254.216 | 1.12954 | 0.564768 | − | 0.825250i | \(-0.308966\pi\) | ||||
0.564768 | + | 0.825250i | \(0.308966\pi\) | |||||||
\(38\) | 328.786 | 1.40358 | ||||||||
\(39\) | −107.201 | −0.440150 | ||||||||
\(40\) | 120.885 | 0.477842 | ||||||||
\(41\) | 219.633 | 0.836606 | 0.418303 | − | 0.908308i | \(-0.362625\pi\) | ||||
0.418303 | + | 0.908308i | \(0.362625\pi\) | |||||||
\(42\) | 525.477 | 1.93055 | ||||||||
\(43\) | −104.462 | −0.370473 | −0.185236 | − | 0.982694i | \(-0.559305\pi\) | ||||
−0.185236 | + | 0.982694i | \(0.559305\pi\) | |||||||
\(44\) | 55.9224 | 0.191605 | ||||||||
\(45\) | −205.000 | −0.679102 | ||||||||
\(46\) | −261.123 | −0.836967 | ||||||||
\(47\) | 308.816 | 0.958415 | 0.479207 | − | 0.877702i | \(-0.340924\pi\) | ||||
0.479207 | + | 0.877702i | \(0.340924\pi\) | |||||||
\(48\) | −415.801 | −1.25033 | ||||||||
\(49\) | 275.860 | 0.804256 | ||||||||
\(50\) | 64.0388 | 0.181129 | ||||||||
\(51\) | −659.447 | −1.81061 | ||||||||
\(52\) | 18.6998 | 0.0498692 | ||||||||
\(53\) | −0.0909300 | −0.000235664 0 | −0.000117832 | − | 1.00000i | \(-0.500038\pi\) | ||||
−0.000117832 | 1.00000i | \(0.500038\pi\) | ||||||||
\(54\) | 295.723 | 0.745238 | ||||||||
\(55\) | 194.384 | 0.476560 | ||||||||
\(56\) | −601.451 | −1.43522 | ||||||||
\(57\) | 1058.44 | 2.45953 | ||||||||
\(58\) | 301.555 | 0.682691 | ||||||||
\(59\) | −349.710 | −0.771668 | −0.385834 | − | 0.922568i | \(-0.626086\pi\) | ||||
−0.385834 | + | 0.922568i | \(0.626086\pi\) | |||||||
\(60\) | 59.3087 | 0.127612 | ||||||||
\(61\) | 442.000 | 0.927743 | 0.463871 | − | 0.885903i | \(-0.346460\pi\) | ||||
0.463871 | + | 0.885903i | \(0.346460\pi\) | |||||||
\(62\) | −765.278 | −1.56759 | ||||||||
\(63\) | 1019.95 | 2.03971 | ||||||||
\(64\) | 567.978 | 1.10933 | ||||||||
\(65\) | 65.0000 | 0.124035 | ||||||||
\(66\) | −821.201 | −1.53156 | ||||||||
\(67\) | 228.074 | 0.415876 | 0.207938 | − | 0.978142i | \(-0.433325\pi\) | ||||
0.207938 | + | 0.978142i | \(0.433325\pi\) | |||||||
\(68\) | 115.032 | 0.205143 | ||||||||
\(69\) | −840.614 | −1.46664 | ||||||||
\(70\) | −318.617 | −0.544029 | ||||||||
\(71\) | 964.328 | 1.61190 | 0.805948 | − | 0.591986i | \(-0.201656\pi\) | ||||
0.805948 | + | 0.591986i | \(0.201656\pi\) | |||||||
\(72\) | −991.260 | −1.62252 | ||||||||
\(73\) | 662.682 | 1.06248 | 0.531240 | − | 0.847221i | \(-0.321726\pi\) | ||||
0.531240 | + | 0.847221i | \(0.321726\pi\) | |||||||
\(74\) | 651.187 | 1.02296 | ||||||||
\(75\) | 206.155 | 0.317397 | ||||||||
\(76\) | −184.631 | −0.278666 | ||||||||
\(77\) | −967.136 | −1.43137 | ||||||||
\(78\) | −274.600 | −0.398620 | ||||||||
\(79\) | −65.2614 | −0.0929428 | −0.0464714 | − | 0.998920i | \(-0.514798\pi\) | ||||
−0.0464714 | + | 0.998920i | \(0.514798\pi\) | |||||||
\(80\) | 252.116 | 0.352343 | ||||||||
\(81\) | −155.000 | −0.212620 | ||||||||
\(82\) | 562.600 | 0.757669 | ||||||||
\(83\) | −92.4185 | −0.122220 | −0.0611099 | − | 0.998131i | \(-0.519464\pi\) | ||||
−0.0611099 | + | 0.998131i | \(0.519464\pi\) | |||||||
\(84\) | −295.083 | −0.383288 | ||||||||
\(85\) | 399.848 | 0.510231 | ||||||||
\(86\) | −267.585 | −0.335517 | ||||||||
\(87\) | 970.773 | 1.19630 | ||||||||
\(88\) | 939.930 | 1.13860 | ||||||||
\(89\) | −178.614 | −0.212730 | −0.106365 | − | 0.994327i | \(-0.533921\pi\) | ||||
−0.106365 | + | 0.994327i | \(0.533921\pi\) | |||||||
\(90\) | −525.118 | −0.615026 | ||||||||
\(91\) | −323.400 | −0.372544 | ||||||||
\(92\) | 146.634 | 0.166171 | ||||||||
\(93\) | −2463.60 | −2.74692 | ||||||||
\(94\) | 791.049 | 0.867984 | ||||||||
\(95\) | −641.771 | −0.693098 | ||||||||
\(96\) | 529.858 | 0.563317 | ||||||||
\(97\) | −1707.46 | −1.78728 | −0.893640 | − | 0.448785i | \(-0.851857\pi\) | ||||
−0.893640 | + | 0.448785i | \(0.851857\pi\) | |||||||
\(98\) | 706.630 | 0.728371 | ||||||||
\(99\) | −1593.95 | −1.61816 | ||||||||
\(100\) | −35.9612 | −0.0359612 | ||||||||
\(101\) | −1364.04 | −1.34383 | −0.671915 | − | 0.740628i | \(-0.734528\pi\) | ||||
−0.671915 | + | 0.740628i | \(0.734528\pi\) | |||||||
\(102\) | −1689.21 | −1.63977 | ||||||||
\(103\) | 355.167 | 0.339763 | 0.169882 | − | 0.985464i | \(-0.445661\pi\) | ||||
0.169882 | + | 0.985464i | \(0.445661\pi\) | |||||||
\(104\) | 314.302 | 0.296345 | ||||||||
\(105\) | −1025.70 | −0.953316 | ||||||||
\(106\) | −0.232922 | −0.000213428 0 | ||||||||
\(107\) | 325.905 | 0.294453 | 0.147226 | − | 0.989103i | \(-0.452965\pi\) | ||||
0.147226 | + | 0.989103i | \(0.452965\pi\) | |||||||
\(108\) | −166.064 | −0.147959 | ||||||||
\(109\) | 1738.93 | 1.52807 | 0.764034 | − | 0.645176i | \(-0.223216\pi\) | ||||
0.764034 | + | 0.645176i | \(0.223216\pi\) | |||||||
\(110\) | 497.926 | 0.431594 | ||||||||
\(111\) | 2096.32 | 1.79256 | ||||||||
\(112\) | −1254.37 | −1.05828 | ||||||||
\(113\) | −1628.89 | −1.35605 | −0.678024 | − | 0.735040i | \(-0.737164\pi\) | ||||
−0.678024 | + | 0.735040i | \(0.737164\pi\) | |||||||
\(114\) | 2711.24 | 2.22746 | ||||||||
\(115\) | 509.697 | 0.413300 | ||||||||
\(116\) | −169.339 | −0.135541 | ||||||||
\(117\) | −533.000 | −0.421161 | ||||||||
\(118\) | −895.801 | −0.698857 | ||||||||
\(119\) | −1989.40 | −1.53250 | ||||||||
\(120\) | 996.847 | 0.758327 | ||||||||
\(121\) | 180.413 | 0.135547 | ||||||||
\(122\) | 1132.21 | 0.840206 | ||||||||
\(123\) | 1811.14 | 1.32768 | ||||||||
\(124\) | 429.744 | 0.311227 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 2612.66 | 1.84726 | ||||||||
\(127\) | 165.333 | 0.115519 | 0.0577596 | − | 0.998331i | \(-0.481604\pi\) | ||||
0.0577596 | + | 0.998331i | \(0.481604\pi\) | |||||||
\(128\) | 940.868 | 0.649702 | ||||||||
\(129\) | −861.417 | −0.587934 | ||||||||
\(130\) | 166.501 | 0.112332 | ||||||||
\(131\) | −1867.49 | −1.24552 | −0.622760 | − | 0.782413i | \(-0.713989\pi\) | ||||
−0.622760 | + | 0.782413i | \(0.713989\pi\) | |||||||
\(132\) | 461.148 | 0.304074 | ||||||||
\(133\) | 3193.05 | 2.08175 | ||||||||
\(134\) | 584.223 | 0.376636 | ||||||||
\(135\) | −577.235 | −0.368003 | ||||||||
\(136\) | 1933.43 | 1.21905 | ||||||||
\(137\) | 1740.80 | 1.08560 | 0.542798 | − | 0.839864i | \(-0.317365\pi\) | ||||
0.542798 | + | 0.839864i | \(0.317365\pi\) | |||||||
\(138\) | −2153.28 | −1.32825 | ||||||||
\(139\) | −985.511 | −0.601367 | −0.300683 | − | 0.953724i | \(-0.597215\pi\) | ||||
−0.300683 | + | 0.953724i | \(0.597215\pi\) | |||||||
\(140\) | 178.920 | 0.108011 | ||||||||
\(141\) | 2546.56 | 1.52099 | ||||||||
\(142\) | 2470.18 | 1.45981 | ||||||||
\(143\) | 505.400 | 0.295550 | ||||||||
\(144\) | −2067.35 | −1.19639 | ||||||||
\(145\) | −588.617 | −0.337117 | ||||||||
\(146\) | 1697.49 | 0.962230 | ||||||||
\(147\) | 2274.80 | 1.27634 | ||||||||
\(148\) | −365.676 | −0.203097 | ||||||||
\(149\) | −2496.90 | −1.37285 | −0.686423 | − | 0.727202i | \(-0.740820\pi\) | ||||
−0.686423 | + | 0.727202i | \(0.740820\pi\) | |||||||
\(150\) | 528.078 | 0.287449 | ||||||||
\(151\) | 357.710 | 0.192782 | 0.0963909 | − | 0.995344i | \(-0.469270\pi\) | ||||
0.0963909 | + | 0.995344i | \(0.469270\pi\) | |||||||
\(152\) | −3103.23 | −1.65595 | ||||||||
\(153\) | −3278.76 | −1.73250 | ||||||||
\(154\) | −2477.37 | −1.29631 | ||||||||
\(155\) | 1493.78 | 0.774085 | ||||||||
\(156\) | 154.203 | 0.0791416 | ||||||||
\(157\) | −3218.32 | −1.63599 | −0.817993 | − | 0.575228i | \(-0.804913\pi\) | ||||
−0.817993 | + | 0.575228i | \(0.804913\pi\) | |||||||
\(158\) | −167.170 | −0.0841732 | ||||||||
\(159\) | −0.749828 | −0.000373995 0 | ||||||||
\(160\) | −321.274 | −0.158743 | ||||||||
\(161\) | −2535.94 | −1.24136 | ||||||||
\(162\) | −397.041 | −0.192558 | ||||||||
\(163\) | −2901.51 | −1.39425 | −0.697127 | − | 0.716948i | \(-0.745539\pi\) | ||||
−0.697127 | + | 0.716948i | \(0.745539\pi\) | |||||||
\(164\) | −315.930 | −0.150427 | ||||||||
\(165\) | 1602.94 | 0.756293 | ||||||||
\(166\) | −236.735 | −0.110688 | ||||||||
\(167\) | 531.036 | 0.246065 | 0.123032 | − | 0.992403i | \(-0.460738\pi\) | ||||
0.123032 | + | 0.992403i | \(0.460738\pi\) | |||||||
\(168\) | −4959.69 | −2.27767 | ||||||||
\(169\) | 169.000 | 0.0769231 | ||||||||
\(170\) | 1024.23 | 0.462089 | ||||||||
\(171\) | 5262.52 | 2.35342 | ||||||||
\(172\) | 150.263 | 0.0666132 | ||||||||
\(173\) | 809.826 | 0.355895 | 0.177948 | − | 0.984040i | \(-0.443054\pi\) | ||||
0.177948 | + | 0.984040i | \(0.443054\pi\) | |||||||
\(174\) | 2486.69 | 1.08342 | ||||||||
\(175\) | 621.922 | 0.268645 | ||||||||
\(176\) | 1960.30 | 0.839564 | ||||||||
\(177\) | −2883.78 | −1.22462 | ||||||||
\(178\) | −457.528 | −0.192658 | ||||||||
\(179\) | −1831.87 | −0.764919 | −0.382459 | − | 0.923972i | \(-0.624923\pi\) | ||||
−0.382459 | + | 0.923972i | \(0.624923\pi\) | |||||||
\(180\) | 294.882 | 0.122107 | ||||||||
\(181\) | 1046.76 | 0.429863 | 0.214931 | − | 0.976629i | \(-0.431047\pi\) | ||||
0.214931 | + | 0.976629i | \(0.431047\pi\) | |||||||
\(182\) | −828.405 | −0.337393 | ||||||||
\(183\) | 3644.83 | 1.47231 | ||||||||
\(184\) | 2464.60 | 0.987459 | ||||||||
\(185\) | −1271.08 | −0.505144 | ||||||||
\(186\) | −6310.65 | −2.48774 | ||||||||
\(187\) | 3108.97 | 1.21578 | ||||||||
\(188\) | −444.216 | −0.172329 | ||||||||
\(189\) | 2871.96 | 1.10531 | ||||||||
\(190\) | −1643.93 | −0.627701 | ||||||||
\(191\) | 759.973 | 0.287904 | 0.143952 | − | 0.989585i | \(-0.454019\pi\) | ||||
0.143952 | + | 0.989585i | \(0.454019\pi\) | |||||||
\(192\) | 4683.67 | 1.76049 | ||||||||
\(193\) | −411.618 | −0.153518 | −0.0767588 | − | 0.997050i | \(-0.524457\pi\) | ||||
−0.0767588 | + | 0.997050i | \(0.524457\pi\) | |||||||
\(194\) | −4373.74 | −1.61864 | ||||||||
\(195\) | 536.004 | 0.196841 | ||||||||
\(196\) | −396.810 | −0.144610 | ||||||||
\(197\) | −805.204 | −0.291210 | −0.145605 | − | 0.989343i | \(-0.546513\pi\) | ||||
−0.145605 | + | 0.989343i | \(0.546513\pi\) | |||||||
\(198\) | −4082.99 | −1.46548 | ||||||||
\(199\) | 2932.02 | 1.04445 | 0.522225 | − | 0.852808i | \(-0.325102\pi\) | ||||
0.522225 | + | 0.852808i | \(0.325102\pi\) | |||||||
\(200\) | −604.427 | −0.213697 | ||||||||
\(201\) | 1880.75 | 0.659988 | ||||||||
\(202\) | −3494.05 | −1.21703 | ||||||||
\(203\) | 2928.59 | 1.01255 | ||||||||
\(204\) | 948.580 | 0.325558 | ||||||||
\(205\) | −1098.16 | −0.374142 | ||||||||
\(206\) | 909.778 | 0.307705 | ||||||||
\(207\) | −4179.51 | −1.40336 | ||||||||
\(208\) | 655.503 | 0.218514 | ||||||||
\(209\) | −4990.01 | −1.65151 | ||||||||
\(210\) | −2627.39 | −0.863366 | ||||||||
\(211\) | −3922.57 | −1.27982 | −0.639908 | − | 0.768452i | \(-0.721027\pi\) | ||||
−0.639908 | + | 0.768452i | \(0.721027\pi\) | |||||||
\(212\) | 0.130798 | 4.23738e−5 0 | ||||||||
\(213\) | 7952.05 | 2.55805 | ||||||||
\(214\) | 834.824 | 0.266670 | ||||||||
\(215\) | 522.311 | 0.165680 | ||||||||
\(216\) | −2791.17 | −0.879237 | ||||||||
\(217\) | −7432.11 | −2.32500 | ||||||||
\(218\) | 4454.37 | 1.38389 | ||||||||
\(219\) | 5464.61 | 1.68614 | ||||||||
\(220\) | −279.612 | −0.0856883 | ||||||||
\(221\) | 1039.61 | 0.316432 | ||||||||
\(222\) | 5369.83 | 1.62342 | ||||||||
\(223\) | 6115.27 | 1.83636 | 0.918181 | − | 0.396162i | \(-0.129658\pi\) | ||||
0.918181 | + | 0.396162i | \(0.129658\pi\) | |||||||
\(224\) | 1598.46 | 0.476792 | ||||||||
\(225\) | 1025.00 | 0.303704 | ||||||||
\(226\) | −4172.50 | −1.22810 | ||||||||
\(227\) | 4216.13 | 1.23275 | 0.616376 | − | 0.787452i | \(-0.288600\pi\) | ||||
0.616376 | + | 0.787452i | \(0.288600\pi\) | |||||||
\(228\) | −1522.50 | −0.442238 | ||||||||
\(229\) | −299.451 | −0.0864116 | −0.0432058 | − | 0.999066i | \(-0.513757\pi\) | ||||
−0.0432058 | + | 0.999066i | \(0.513757\pi\) | |||||||
\(230\) | 1305.62 | 0.374303 | ||||||||
\(231\) | −7975.21 | −2.27156 | ||||||||
\(232\) | −2846.21 | −0.805443 | ||||||||
\(233\) | 1223.17 | 0.343916 | 0.171958 | − | 0.985104i | \(-0.444991\pi\) | ||||
0.171958 | + | 0.985104i | \(0.444991\pi\) | |||||||
\(234\) | −1365.31 | −0.381423 | ||||||||
\(235\) | −1544.08 | −0.428616 | ||||||||
\(236\) | 503.040 | 0.138750 | ||||||||
\(237\) | −538.159 | −0.147499 | ||||||||
\(238\) | −5095.95 | −1.38790 | ||||||||
\(239\) | −48.7253 | −0.0131874 | −0.00659368 | − | 0.999978i | \(-0.502099\pi\) | ||||
−0.00659368 | + | 0.999978i | \(0.502099\pi\) | |||||||
\(240\) | 2079.01 | 0.559163 | ||||||||
\(241\) | −4499.83 | −1.20274 | −0.601368 | − | 0.798972i | \(-0.705378\pi\) | ||||
−0.601368 | + | 0.798972i | \(0.705378\pi\) | |||||||
\(242\) | 462.137 | 0.122757 | ||||||||
\(243\) | −4395.23 | −1.16031 | ||||||||
\(244\) | −635.794 | −0.166814 | ||||||||
\(245\) | −1379.30 | −0.359674 | ||||||||
\(246\) | 4639.32 | 1.20241 | ||||||||
\(247\) | −1668.60 | −0.429841 | ||||||||
\(248\) | 7223.04 | 1.84945 | ||||||||
\(249\) | −762.103 | −0.193961 | ||||||||
\(250\) | −320.194 | −0.0810034 | ||||||||
\(251\) | −110.288 | −0.0277343 | −0.0138671 | − | 0.999904i | \(-0.504414\pi\) | ||||
−0.0138671 | + | 0.999904i | \(0.504414\pi\) | |||||||
\(252\) | −1467.15 | −0.366753 | ||||||||
\(253\) | 3963.09 | 0.984811 | ||||||||
\(254\) | 423.510 | 0.104620 | ||||||||
\(255\) | 3297.23 | 0.809729 | ||||||||
\(256\) | −2133.74 | −0.520933 | ||||||||
\(257\) | 7453.76 | 1.80916 | 0.904578 | − | 0.426308i | \(-0.140186\pi\) | ||||
0.904578 | + | 0.426308i | \(0.140186\pi\) | |||||||
\(258\) | −2206.56 | −0.532460 | ||||||||
\(259\) | 6324.10 | 1.51722 | ||||||||
\(260\) | −93.4991 | −0.0223022 | ||||||||
\(261\) | 4826.66 | 1.14469 | ||||||||
\(262\) | −4783.67 | −1.12800 | ||||||||
\(263\) | −225.156 | −0.0527897 | −0.0263948 | − | 0.999652i | \(-0.508403\pi\) | ||||
−0.0263948 | + | 0.999652i | \(0.508403\pi\) | |||||||
\(264\) | 7750.86 | 1.80694 | ||||||||
\(265\) | 0.454650 | 0.000105392 0 | ||||||||
\(266\) | 8179.17 | 1.88533 | ||||||||
\(267\) | −1472.89 | −0.337600 | ||||||||
\(268\) | −328.072 | −0.0747769 | ||||||||
\(269\) | −2742.09 | −0.621517 | −0.310758 | − | 0.950489i | \(-0.600583\pi\) | ||||
−0.310758 | + | 0.950489i | \(0.600583\pi\) | |||||||
\(270\) | −1478.62 | −0.333281 | ||||||||
\(271\) | 6749.69 | 1.51297 | 0.756484 | − | 0.654012i | \(-0.226916\pi\) | ||||
0.756484 | + | 0.654012i | \(0.226916\pi\) | |||||||
\(272\) | 4032.34 | 0.898883 | ||||||||
\(273\) | −2666.82 | −0.591221 | ||||||||
\(274\) | 4459.15 | 0.983164 | ||||||||
\(275\) | −971.922 | −0.213124 | ||||||||
\(276\) | 1209.18 | 0.263710 | ||||||||
\(277\) | 1511.65 | 0.327893 | 0.163946 | − | 0.986469i | \(-0.447578\pi\) | ||||
0.163946 | + | 0.986469i | \(0.447578\pi\) | |||||||
\(278\) | −2524.44 | −0.544625 | ||||||||
\(279\) | −12249.0 | −2.62841 | ||||||||
\(280\) | 3007.25 | 0.641849 | ||||||||
\(281\) | −5593.69 | −1.18751 | −0.593757 | − | 0.804645i | \(-0.702356\pi\) | ||||
−0.593757 | + | 0.804645i | \(0.702356\pi\) | |||||||
\(282\) | 6523.16 | 1.37748 | ||||||||
\(283\) | −3221.02 | −0.676572 | −0.338286 | − | 0.941043i | \(-0.609847\pi\) | ||||
−0.338286 | + | 0.941043i | \(0.609847\pi\) | |||||||
\(284\) | −1387.13 | −0.289828 | ||||||||
\(285\) | −5292.18 | −1.09994 | ||||||||
\(286\) | 1294.61 | 0.267664 | ||||||||
\(287\) | 5463.78 | 1.12375 | ||||||||
\(288\) | 2634.44 | 0.539014 | ||||||||
\(289\) | 1482.15 | 0.301679 | ||||||||
\(290\) | −1507.77 | −0.305309 | ||||||||
\(291\) | −14080.1 | −2.83638 | ||||||||
\(292\) | −953.233 | −0.191040 | ||||||||
\(293\) | 7809.84 | 1.55719 | 0.778594 | − | 0.627528i | \(-0.215933\pi\) | ||||
0.778594 | + | 0.627528i | \(0.215933\pi\) | |||||||
\(294\) | 5827.02 | 1.15591 | ||||||||
\(295\) | 1748.55 | 0.345100 | ||||||||
\(296\) | −6146.20 | −1.20689 | ||||||||
\(297\) | −4488.22 | −0.876878 | ||||||||
\(298\) | −6395.94 | −1.24331 | ||||||||
\(299\) | 1325.21 | 0.256318 | ||||||||
\(300\) | −296.543 | −0.0570698 | ||||||||
\(301\) | −2598.69 | −0.497628 | ||||||||
\(302\) | 916.294 | 0.174592 | ||||||||
\(303\) | −11248.1 | −2.13264 | ||||||||
\(304\) | −6472.04 | −1.22104 | ||||||||
\(305\) | −2210.00 | −0.414899 | ||||||||
\(306\) | −8398.71 | −1.56903 | ||||||||
\(307\) | 8581.07 | 1.59527 | 0.797634 | − | 0.603141i | \(-0.206084\pi\) | ||||
0.797634 | + | 0.603141i | \(0.206084\pi\) | |||||||
\(308\) | 1391.17 | 0.257369 | ||||||||
\(309\) | 2928.78 | 0.539199 | ||||||||
\(310\) | 3826.39 | 0.701047 | ||||||||
\(311\) | 9251.84 | 1.68689 | 0.843447 | − | 0.537213i | \(-0.180523\pi\) | ||||
0.843447 | + | 0.537213i | \(0.180523\pi\) | |||||||
\(312\) | 2591.80 | 0.470294 | ||||||||
\(313\) | 4386.17 | 0.792081 | 0.396040 | − | 0.918233i | \(-0.370384\pi\) | ||||
0.396040 | + | 0.918233i | \(0.370384\pi\) | |||||||
\(314\) | −8243.89 | −1.48162 | ||||||||
\(315\) | −5099.76 | −0.912188 | ||||||||
\(316\) | 93.8750 | 0.0167117 | ||||||||
\(317\) | −587.686 | −0.104125 | −0.0520626 | − | 0.998644i | \(-0.516580\pi\) | ||||
−0.0520626 | + | 0.998644i | \(0.516580\pi\) | |||||||
\(318\) | −1.92072 | −0.000338707 0 | ||||||||
\(319\) | −4576.72 | −0.803283 | ||||||||
\(320\) | −2839.89 | −0.496109 | ||||||||
\(321\) | 2687.48 | 0.467292 | ||||||||
\(322\) | −6495.93 | −1.12424 | ||||||||
\(323\) | −10264.4 | −1.76820 | ||||||||
\(324\) | 222.959 | 0.0382303 | ||||||||
\(325\) | −325.000 | −0.0554700 | ||||||||
\(326\) | −7432.36 | −1.26270 | ||||||||
\(327\) | 14339.6 | 2.42502 | ||||||||
\(328\) | −5310.07 | −0.893902 | ||||||||
\(329\) | 7682.39 | 1.28737 | ||||||||
\(330\) | 4106.00 | 0.684934 | ||||||||
\(331\) | −6559.71 | −1.08929 | −0.544644 | − | 0.838668i | \(-0.683335\pi\) | ||||
−0.544644 | + | 0.838668i | \(0.683335\pi\) | |||||||
\(332\) | 132.939 | 0.0219759 | ||||||||
\(333\) | 10422.9 | 1.71522 | ||||||||
\(334\) | 1360.28 | 0.222847 | ||||||||
\(335\) | −1140.37 | −0.185985 | ||||||||
\(336\) | −10343.8 | −1.67947 | ||||||||
\(337\) | 3316.98 | 0.536165 | 0.268083 | − | 0.963396i | \(-0.413610\pi\) | ||||
0.268083 | + | 0.963396i | \(0.413610\pi\) | |||||||
\(338\) | 432.902 | 0.0696651 | ||||||||
\(339\) | −13432.2 | −2.15203 | ||||||||
\(340\) | −575.161 | −0.0917426 | ||||||||
\(341\) | 11614.7 | 1.84449 | ||||||||
\(342\) | 13480.2 | 2.13137 | ||||||||
\(343\) | −1670.24 | −0.262928 | ||||||||
\(344\) | 2525.59 | 0.395845 | ||||||||
\(345\) | 4203.07 | 0.655900 | ||||||||
\(346\) | 2074.41 | 0.322315 | ||||||||
\(347\) | −3729.06 | −0.576906 | −0.288453 | − | 0.957494i | \(-0.593141\pi\) | ||||
−0.288453 | + | 0.957494i | \(0.593141\pi\) | |||||||
\(348\) | −1396.41 | −0.215101 | ||||||||
\(349\) | 3748.22 | 0.574892 | 0.287446 | − | 0.957797i | \(-0.407194\pi\) | ||||
0.287446 | + | 0.957797i | \(0.407194\pi\) | |||||||
\(350\) | 1593.09 | 0.243297 | ||||||||
\(351\) | −1500.81 | −0.228226 | ||||||||
\(352\) | −2498.02 | −0.378253 | ||||||||
\(353\) | −3353.90 | −0.505694 | −0.252847 | − | 0.967506i | \(-0.581367\pi\) | ||||
−0.252847 | + | 0.967506i | \(0.581367\pi\) | |||||||
\(354\) | −7386.97 | −1.10908 | ||||||||
\(355\) | −4821.64 | −0.720862 | ||||||||
\(356\) | 256.926 | 0.0382502 | ||||||||
\(357\) | −16405.0 | −2.43206 | ||||||||
\(358\) | −4692.44 | −0.692746 | ||||||||
\(359\) | −1041.87 | −0.153169 | −0.0765843 | − | 0.997063i | \(-0.524401\pi\) | ||||
−0.0765843 | + | 0.997063i | \(0.524401\pi\) | |||||||
\(360\) | 4956.30 | 0.725611 | ||||||||
\(361\) | 9615.79 | 1.40192 | ||||||||
\(362\) | 2681.33 | 0.389303 | ||||||||
\(363\) | 1487.72 | 0.215111 | ||||||||
\(364\) | 465.193 | 0.0669856 | ||||||||
\(365\) | −3313.41 | −0.475155 | ||||||||
\(366\) | 9336.41 | 1.33339 | ||||||||
\(367\) | 1099.95 | 0.156449 | 0.0782247 | − | 0.996936i | \(-0.475075\pi\) | ||||
0.0782247 | + | 0.996936i | \(0.475075\pi\) | |||||||
\(368\) | 5140.12 | 0.728117 | ||||||||
\(369\) | 9004.93 | 1.27040 | ||||||||
\(370\) | −3255.94 | −0.457481 | ||||||||
\(371\) | −2.26206 | −0.000316550 0 | ||||||||
\(372\) | 3543.76 | 0.493913 | ||||||||
\(373\) | 2967.14 | 0.411884 | 0.205942 | − | 0.978564i | \(-0.433974\pi\) | ||||
0.205942 | + | 0.978564i | \(0.433974\pi\) | |||||||
\(374\) | 7963.80 | 1.10106 | ||||||||
\(375\) | −1030.78 | −0.141944 | ||||||||
\(376\) | −7466.28 | −1.02405 | ||||||||
\(377\) | −1530.41 | −0.209071 | ||||||||
\(378\) | 7356.68 | 1.00102 | ||||||||
\(379\) | −9221.67 | −1.24983 | −0.624915 | − | 0.780693i | \(-0.714866\pi\) | ||||
−0.624915 | + | 0.780693i | \(0.714866\pi\) | |||||||
\(380\) | 923.153 | 0.124623 | ||||||||
\(381\) | 1363.37 | 0.183327 | ||||||||
\(382\) | 1946.71 | 0.260739 | ||||||||
\(383\) | −11048.0 | −1.47395 | −0.736976 | − | 0.675918i | \(-0.763747\pi\) | ||||
−0.736976 | + | 0.675918i | \(0.763747\pi\) | |||||||
\(384\) | 7758.60 | 1.03107 | ||||||||
\(385\) | 4835.68 | 0.640128 | ||||||||
\(386\) | −1054.38 | −0.139032 | ||||||||
\(387\) | −4282.95 | −0.562570 | ||||||||
\(388\) | 2456.09 | 0.321363 | ||||||||
\(389\) | −201.382 | −0.0262480 | −0.0131240 | − | 0.999914i | \(-0.504178\pi\) | ||||
−0.0131240 | + | 0.999914i | \(0.504178\pi\) | |||||||
\(390\) | 1373.00 | 0.178268 | ||||||||
\(391\) | 8152.06 | 1.05439 | ||||||||
\(392\) | −6669.49 | −0.859337 | ||||||||
\(393\) | −15399.7 | −1.97662 | ||||||||
\(394\) | −2062.57 | −0.263733 | ||||||||
\(395\) | 326.307 | 0.0415653 | ||||||||
\(396\) | 2292.82 | 0.290955 | ||||||||
\(397\) | −4354.09 | −0.550443 | −0.275221 | − | 0.961381i | \(-0.588751\pi\) | ||||
−0.275221 | + | 0.961381i | \(0.588751\pi\) | |||||||
\(398\) | 7510.53 | 0.945902 | ||||||||
\(399\) | 26330.6 | 3.30370 | ||||||||
\(400\) | −1260.58 | −0.157573 | ||||||||
\(401\) | 4241.31 | 0.528182 | 0.264091 | − | 0.964498i | \(-0.414928\pi\) | ||||
0.264091 | + | 0.964498i | \(0.414928\pi\) | |||||||
\(402\) | 4817.63 | 0.597715 | ||||||||
\(403\) | 3883.82 | 0.480067 | ||||||||
\(404\) | 1962.10 | 0.241629 | ||||||||
\(405\) | 775.000 | 0.0950866 | ||||||||
\(406\) | 7501.75 | 0.917009 | ||||||||
\(407\) | −9883.12 | −1.20366 | ||||||||
\(408\) | 15943.5 | 1.93461 | ||||||||
\(409\) | −1622.25 | −0.196124 | −0.0980622 | − | 0.995180i | \(-0.531264\pi\) | ||||
−0.0980622 | + | 0.995180i | \(0.531264\pi\) | |||||||
\(410\) | −2813.00 | −0.338840 | ||||||||
\(411\) | 14355.0 | 1.72282 | ||||||||
\(412\) | −510.889 | −0.0610914 | ||||||||
\(413\) | −8699.70 | −1.03652 | ||||||||
\(414\) | −10706.0 | −1.27095 | ||||||||
\(415\) | 462.093 | 0.0546584 | ||||||||
\(416\) | −835.311 | −0.0984483 | ||||||||
\(417\) | −8126.73 | −0.954359 | ||||||||
\(418\) | −12782.2 | −1.49569 | ||||||||
\(419\) | −6344.39 | −0.739723 | −0.369861 | − | 0.929087i | \(-0.620595\pi\) | ||||
−0.369861 | + | 0.929087i | \(0.620595\pi\) | |||||||
\(420\) | 1475.42 | 0.171412 | ||||||||
\(421\) | −7050.55 | −0.816206 | −0.408103 | − | 0.912936i | \(-0.633810\pi\) | ||||
−0.408103 | + | 0.912936i | \(0.633810\pi\) | |||||||
\(422\) | −10047.9 | −1.15906 | ||||||||
\(423\) | 12661.5 | 1.45537 | ||||||||
\(424\) | 2.19842 | 0.000251804 0 | ||||||||
\(425\) | −1999.24 | −0.228182 | ||||||||
\(426\) | 20369.6 | 2.31669 | ||||||||
\(427\) | 10995.6 | 1.24617 | ||||||||
\(428\) | −468.798 | −0.0529444 | ||||||||
\(429\) | 4167.63 | 0.469033 | ||||||||
\(430\) | 1337.93 | 0.150048 | ||||||||
\(431\) | −2749.74 | −0.307309 | −0.153655 | − | 0.988125i | \(-0.549104\pi\) | ||||
−0.153655 | + | 0.988125i | \(0.549104\pi\) | |||||||
\(432\) | −5821.22 | −0.648318 | ||||||||
\(433\) | −12718.7 | −1.41160 | −0.705798 | − | 0.708413i | \(-0.749411\pi\) | ||||
−0.705798 | + | 0.708413i | \(0.749411\pi\) | |||||||
\(434\) | −19037.7 | −2.10562 | ||||||||
\(435\) | −4853.86 | −0.535000 | ||||||||
\(436\) | −2501.36 | −0.274756 | ||||||||
\(437\) | −13084.3 | −1.43229 | ||||||||
\(438\) | 13997.9 | 1.52704 | ||||||||
\(439\) | 17656.7 | 1.91961 | 0.959807 | − | 0.280660i | \(-0.0905535\pi\) | ||||
0.959807 | + | 0.280660i | \(0.0905535\pi\) | |||||||
\(440\) | −4699.65 | −0.509198 | ||||||||
\(441\) | 11310.3 | 1.22128 | ||||||||
\(442\) | 2663.01 | 0.286575 | ||||||||
\(443\) | 18355.7 | 1.96864 | 0.984319 | − | 0.176397i | \(-0.0564444\pi\) | ||||
0.984319 | + | 0.176397i | \(0.0564444\pi\) | |||||||
\(444\) | −3015.44 | −0.322312 | ||||||||
\(445\) | 893.068 | 0.0951360 | ||||||||
\(446\) | 15664.6 | 1.66309 | ||||||||
\(447\) | −20590.0 | −2.17869 | ||||||||
\(448\) | 14129.5 | 1.49008 | ||||||||
\(449\) | −2675.78 | −0.281242 | −0.140621 | − | 0.990063i | \(-0.544910\pi\) | ||||
−0.140621 | + | 0.990063i | \(0.544910\pi\) | |||||||
\(450\) | 2625.59 | 0.275048 | ||||||||
\(451\) | −8538.63 | −0.891504 | ||||||||
\(452\) | 2343.08 | 0.243825 | ||||||||
\(453\) | 2949.75 | 0.305942 | ||||||||
\(454\) | 10799.9 | 1.11644 | ||||||||
\(455\) | 1617.00 | 0.166607 | ||||||||
\(456\) | −25589.9 | −2.62797 | ||||||||
\(457\) | 6114.51 | 0.625875 | 0.312937 | − | 0.949774i | \(-0.398687\pi\) | ||||
0.312937 | + | 0.949774i | \(0.398687\pi\) | |||||||
\(458\) | −767.059 | −0.0782583 | ||||||||
\(459\) | −9232.26 | −0.938834 | ||||||||
\(460\) | −733.172 | −0.0743137 | ||||||||
\(461\) | −13983.6 | −1.41275 | −0.706377 | − | 0.707836i | \(-0.749671\pi\) | ||||
−0.706377 | + | 0.707836i | \(0.749671\pi\) | |||||||
\(462\) | −20428.9 | −2.05723 | ||||||||
\(463\) | −5068.98 | −0.508802 | −0.254401 | − | 0.967099i | \(-0.581878\pi\) | ||||
−0.254401 | + | 0.967099i | \(0.581878\pi\) | |||||||
\(464\) | −5936.01 | −0.593905 | ||||||||
\(465\) | 12318.0 | 1.22846 | ||||||||
\(466\) | 3133.21 | 0.311466 | ||||||||
\(467\) | 2449.21 | 0.242689 | 0.121345 | − | 0.992610i | \(-0.461279\pi\) | ||||
0.121345 | + | 0.992610i | \(0.461279\pi\) | |||||||
\(468\) | 766.692 | 0.0757273 | ||||||||
\(469\) | 5673.77 | 0.558615 | ||||||||
\(470\) | −3955.25 | −0.388174 | ||||||||
\(471\) | −26538.9 | −2.59628 | ||||||||
\(472\) | 8454.97 | 0.824516 | ||||||||
\(473\) | 4061.16 | 0.394783 | ||||||||
\(474\) | −1378.52 | −0.133582 | ||||||||
\(475\) | 3208.85 | 0.309963 | ||||||||
\(476\) | 2861.64 | 0.275553 | ||||||||
\(477\) | −3.72813 | −0.000357860 0 | ||||||||
\(478\) | −124.813 | −0.0119431 | ||||||||
\(479\) | −14106.1 | −1.34556 | −0.672780 | − | 0.739842i | \(-0.734900\pi\) | ||||
−0.672780 | + | 0.739842i | \(0.734900\pi\) | |||||||
\(480\) | −2649.29 | −0.251923 | ||||||||
\(481\) | −3304.81 | −0.313277 | ||||||||
\(482\) | −11526.6 | −1.08925 | ||||||||
\(483\) | −20911.9 | −1.97003 | ||||||||
\(484\) | −259.514 | −0.0243721 | ||||||||
\(485\) | 8537.29 | 0.799296 | ||||||||
\(486\) | −11258.6 | −1.05083 | ||||||||
\(487\) | 11324.4 | 1.05371 | 0.526855 | − | 0.849955i | \(-0.323371\pi\) | ||||
0.526855 | + | 0.849955i | \(0.323371\pi\) | |||||||
\(488\) | −10686.3 | −0.991280 | ||||||||
\(489\) | −23926.4 | −2.21266 | ||||||||
\(490\) | −3533.15 | −0.325737 | ||||||||
\(491\) | −11824.8 | −1.08686 | −0.543430 | − | 0.839455i | \(-0.682875\pi\) | ||||
−0.543430 | + | 0.839455i | \(0.682875\pi\) | |||||||
\(492\) | −2605.22 | −0.238725 | ||||||||
\(493\) | −9414.31 | −0.860039 | ||||||||
\(494\) | −4274.22 | −0.389284 | ||||||||
\(495\) | 7969.76 | 0.723665 | ||||||||
\(496\) | 15064.2 | 1.36372 | ||||||||
\(497\) | 23989.5 | 2.16514 | ||||||||
\(498\) | −1952.17 | −0.175660 | ||||||||
\(499\) | 11462.3 | 1.02830 | 0.514150 | − | 0.857700i | \(-0.328108\pi\) | ||||
0.514150 | + | 0.857700i | \(0.328108\pi\) | |||||||
\(500\) | 179.806 | 0.0160823 | ||||||||
\(501\) | 4379.03 | 0.390501 | ||||||||
\(502\) | −282.508 | −0.0251174 | ||||||||
\(503\) | −13165.2 | −1.16701 | −0.583506 | − | 0.812109i | \(-0.698320\pi\) | ||||
−0.583506 | + | 0.812109i | \(0.698320\pi\) | |||||||
\(504\) | −24659.5 | −2.17941 | ||||||||
\(505\) | 6820.19 | 0.600979 | ||||||||
\(506\) | 10151.7 | 0.891890 | ||||||||
\(507\) | 1393.61 | 0.122076 | ||||||||
\(508\) | −237.823 | −0.0207710 | ||||||||
\(509\) | 8849.94 | 0.770661 | 0.385331 | − | 0.922779i | \(-0.374087\pi\) | ||||
0.385331 | + | 0.922779i | \(0.374087\pi\) | |||||||
\(510\) | 8446.04 | 0.733327 | ||||||||
\(511\) | 16485.5 | 1.42715 | ||||||||
\(512\) | −12992.6 | −1.12148 | ||||||||
\(513\) | 14818.1 | 1.27531 | ||||||||
\(514\) | 19093.2 | 1.63845 | ||||||||
\(515\) | −1775.83 | −0.151947 | ||||||||
\(516\) | 1239.10 | 0.105714 | ||||||||
\(517\) | −12005.8 | −1.02131 | ||||||||
\(518\) | 16199.5 | 1.37407 | ||||||||
\(519\) | 6677.99 | 0.564800 | ||||||||
\(520\) | −1571.51 | −0.132529 | ||||||||
\(521\) | 20509.2 | 1.72461 | 0.862306 | − | 0.506387i | \(-0.169019\pi\) | ||||
0.862306 | + | 0.506387i | \(0.169019\pi\) | |||||||
\(522\) | 12363.8 | 1.03668 | ||||||||
\(523\) | 434.056 | 0.0362906 | 0.0181453 | − | 0.999835i | \(-0.494224\pi\) | ||||
0.0181453 | + | 0.999835i | \(0.494224\pi\) | |||||||
\(524\) | 2686.28 | 0.223952 | ||||||||
\(525\) | 5128.50 | 0.426336 | ||||||||
\(526\) | −576.748 | −0.0478087 | ||||||||
\(527\) | 23891.4 | 1.97481 | ||||||||
\(528\) | 16165.1 | 1.33237 | ||||||||
\(529\) | −1775.36 | −0.145916 | ||||||||
\(530\) | 1.16461 | 9.54479e−5 0 | ||||||||
\(531\) | −14338.1 | −1.17179 | ||||||||
\(532\) | −4593.04 | −0.374311 | ||||||||
\(533\) | −2855.22 | −0.232033 | ||||||||
\(534\) | −3772.88 | −0.305746 | ||||||||
\(535\) | −1629.53 | −0.131683 | ||||||||
\(536\) | −5514.16 | −0.444357 | ||||||||
\(537\) | −15106.0 | −1.21391 | ||||||||
\(538\) | −7024.00 | −0.562874 | ||||||||
\(539\) | −10724.6 | −0.857032 | ||||||||
\(540\) | 830.322 | 0.0661692 | ||||||||
\(541\) | −5500.16 | −0.437099 | −0.218549 | − | 0.975826i | \(-0.570132\pi\) | ||||
−0.218549 | + | 0.975826i | \(0.570132\pi\) | |||||||
\(542\) | 17289.7 | 1.37021 | ||||||||
\(543\) | 8631.82 | 0.682185 | ||||||||
\(544\) | −5138.43 | −0.404979 | ||||||||
\(545\) | −8694.66 | −0.683373 | ||||||||
\(546\) | −6831.20 | −0.535437 | ||||||||
\(547\) | 8536.10 | 0.667235 | 0.333617 | − | 0.942709i | \(-0.391731\pi\) | ||||
0.333617 | + | 0.942709i | \(0.391731\pi\) | |||||||
\(548\) | −2504.05 | −0.195196 | ||||||||
\(549\) | 18122.0 | 1.40879 | ||||||||
\(550\) | −2489.63 | −0.193015 | ||||||||
\(551\) | 15110.3 | 1.16828 | ||||||||
\(552\) | 20323.6 | 1.56708 | ||||||||
\(553\) | −1623.50 | −0.124843 | ||||||||
\(554\) | 3872.18 | 0.296955 | ||||||||
\(555\) | −10481.6 | −0.801655 | ||||||||
\(556\) | 1417.61 | 0.108129 | ||||||||
\(557\) | −4701.29 | −0.357630 | −0.178815 | − | 0.983883i | \(-0.557226\pi\) | ||||
−0.178815 | + | 0.983883i | \(0.557226\pi\) | |||||||
\(558\) | −31376.4 | −2.38041 | ||||||||
\(559\) | 1358.01 | 0.102751 | ||||||||
\(560\) | 6271.87 | 0.473277 | ||||||||
\(561\) | 25637.2 | 1.92942 | ||||||||
\(562\) | −14328.5 | −1.07547 | ||||||||
\(563\) | 14613.9 | 1.09396 | 0.546981 | − | 0.837145i | \(-0.315777\pi\) | ||||
0.546981 | + | 0.837145i | \(0.315777\pi\) | |||||||
\(564\) | −3663.10 | −0.273483 | ||||||||
\(565\) | 8144.47 | 0.606443 | ||||||||
\(566\) | −8250.82 | −0.612735 | ||||||||
\(567\) | −3855.92 | −0.285597 | ||||||||
\(568\) | −23314.6 | −1.72229 | ||||||||
\(569\) | −10789.3 | −0.794921 | −0.397461 | − | 0.917619i | \(-0.630108\pi\) | ||||
−0.397461 | + | 0.917619i | \(0.630108\pi\) | |||||||
\(570\) | −13556.2 | −0.996152 | ||||||||
\(571\) | −1553.39 | −0.113848 | −0.0569240 | − | 0.998379i | \(-0.518129\pi\) | ||||
−0.0569240 | + | 0.998379i | \(0.518129\pi\) | |||||||
\(572\) | −726.991 | −0.0531416 | ||||||||
\(573\) | 6266.90 | 0.456900 | ||||||||
\(574\) | 13995.8 | 1.01772 | ||||||||
\(575\) | −2548.48 | −0.184833 | ||||||||
\(576\) | 23287.1 | 1.68454 | ||||||||
\(577\) | 11828.6 | 0.853431 | 0.426715 | − | 0.904386i | \(-0.359671\pi\) | ||||
0.426715 | + | 0.904386i | \(0.359671\pi\) | |||||||
\(578\) | 3796.61 | 0.273215 | ||||||||
\(579\) | −3394.29 | −0.243630 | ||||||||
\(580\) | 846.695 | 0.0606157 | ||||||||
\(581\) | −2299.09 | −0.164169 | ||||||||
\(582\) | −36066.8 | −2.56876 | ||||||||
\(583\) | 3.53507 | 0.000251128 0 | ||||||||
\(584\) | −16021.7 | −1.13525 | ||||||||
\(585\) | 2665.00 | 0.188349 | ||||||||
\(586\) | 20005.3 | 1.41026 | ||||||||
\(587\) | 2823.97 | 0.198565 | 0.0992825 | − | 0.995059i | \(-0.468345\pi\) | ||||
0.0992825 | + | 0.995059i | \(0.468345\pi\) | |||||||
\(588\) | −3272.18 | −0.229494 | ||||||||
\(589\) | −38346.5 | −2.68258 | ||||||||
\(590\) | 4479.01 | 0.312539 | ||||||||
\(591\) | −6639.89 | −0.462146 | ||||||||
\(592\) | −12818.4 | −0.889921 | ||||||||
\(593\) | 2016.22 | 0.139623 | 0.0698115 | − | 0.997560i | \(-0.477760\pi\) | ||||
0.0698115 | + | 0.997560i | \(0.477760\pi\) | |||||||
\(594\) | −11496.8 | −0.794141 | ||||||||
\(595\) | 9946.99 | 0.685356 | ||||||||
\(596\) | 3591.66 | 0.246846 | ||||||||
\(597\) | 24178.1 | 1.65753 | ||||||||
\(598\) | 3394.60 | 0.232133 | ||||||||
\(599\) | 9247.60 | 0.630796 | 0.315398 | − | 0.948960i | \(-0.397862\pi\) | ||||
0.315398 | + | 0.948960i | \(0.397862\pi\) | |||||||
\(600\) | −4984.23 | −0.339134 | ||||||||
\(601\) | 8105.84 | 0.550156 | 0.275078 | − | 0.961422i | \(-0.411296\pi\) | ||||
0.275078 | + | 0.961422i | \(0.411296\pi\) | |||||||
\(602\) | −6656.69 | −0.450675 | ||||||||
\(603\) | 9351.03 | 0.631515 | ||||||||
\(604\) | −514.547 | −0.0346633 | ||||||||
\(605\) | −902.065 | −0.0606184 | ||||||||
\(606\) | −28812.7 | −1.93141 | ||||||||
\(607\) | 11059.6 | 0.739534 | 0.369767 | − | 0.929124i | \(-0.379437\pi\) | ||||
0.369767 | + | 0.929124i | \(0.379437\pi\) | |||||||
\(608\) | 8247.36 | 0.550123 | ||||||||
\(609\) | 24149.8 | 1.60690 | ||||||||
\(610\) | −5661.03 | −0.375752 | ||||||||
\(611\) | −4014.61 | −0.265816 | ||||||||
\(612\) | 4716.32 | 0.311513 | ||||||||
\(613\) | −12579.3 | −0.828831 | −0.414416 | − | 0.910088i | \(-0.636014\pi\) | ||||
−0.414416 | + | 0.910088i | \(0.636014\pi\) | |||||||
\(614\) | 21980.9 | 1.44475 | ||||||||
\(615\) | −9055.68 | −0.593757 | ||||||||
\(616\) | 23382.5 | 1.52940 | ||||||||
\(617\) | 16915.6 | 1.10372 | 0.551862 | − | 0.833935i | \(-0.313917\pi\) | ||||
0.551862 | + | 0.833935i | \(0.313917\pi\) | |||||||
\(618\) | 7502.22 | 0.488323 | ||||||||
\(619\) | 10313.7 | 0.669697 | 0.334849 | − | 0.942272i | \(-0.391315\pi\) | ||||
0.334849 | + | 0.942272i | \(0.391315\pi\) | |||||||
\(620\) | −2148.72 | −0.139185 | ||||||||
\(621\) | −11768.6 | −0.760479 | ||||||||
\(622\) | 23699.1 | 1.52773 | ||||||||
\(623\) | −4443.35 | −0.285745 | ||||||||
\(624\) | 5405.41 | 0.346778 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 11235.4 | 0.717344 | ||||||||
\(627\) | −41148.7 | −2.62093 | ||||||||
\(628\) | 4629.38 | 0.294160 | ||||||||
\(629\) | −20329.6 | −1.28870 | ||||||||
\(630\) | −13063.3 | −0.826119 | ||||||||
\(631\) | −20558.9 | −1.29705 | −0.648524 | − | 0.761194i | \(-0.724613\pi\) | ||||
−0.648524 | + | 0.761194i | \(0.724613\pi\) | |||||||
\(632\) | 1577.83 | 0.0993080 | ||||||||
\(633\) | −32346.4 | −2.03105 | ||||||||
\(634\) | −1505.39 | −0.0943006 | ||||||||
\(635\) | −826.666 | −0.0516618 | ||||||||
\(636\) | 1.07859 | 6.72465e−5 0 | ||||||||
\(637\) | −3586.18 | −0.223061 | ||||||||
\(638\) | −11723.5 | −0.727490 | ||||||||
\(639\) | 39537.4 | 2.44769 | ||||||||
\(640\) | −4704.34 | −0.290555 | ||||||||
\(641\) | −5651.22 | −0.348221 | −0.174111 | − | 0.984726i | \(-0.555705\pi\) | ||||
−0.174111 | + | 0.984726i | \(0.555705\pi\) | |||||||
\(642\) | 6884.13 | 0.423201 | ||||||||
\(643\) | 2197.26 | 0.134761 | 0.0673805 | − | 0.997727i | \(-0.478536\pi\) | ||||
0.0673805 | + | 0.997727i | \(0.478536\pi\) | |||||||
\(644\) | 3647.81 | 0.223205 | ||||||||
\(645\) | 4307.08 | 0.262932 | ||||||||
\(646\) | −26292.9 | −1.60136 | ||||||||
\(647\) | 23529.6 | 1.42974 | 0.714872 | − | 0.699255i | \(-0.246485\pi\) | ||||
0.714872 | + | 0.699255i | \(0.246485\pi\) | |||||||
\(648\) | 3747.45 | 0.227182 | ||||||||
\(649\) | 13595.6 | 0.822305 | ||||||||
\(650\) | −832.505 | −0.0502362 | ||||||||
\(651\) | −61286.8 | −3.68974 | ||||||||
\(652\) | 4173.66 | 0.250695 | ||||||||
\(653\) | 26577.6 | 1.59275 | 0.796373 | − | 0.604806i | \(-0.206749\pi\) | ||||
0.796373 | + | 0.604806i | \(0.206749\pi\) | |||||||
\(654\) | 36731.6 | 2.19621 | ||||||||
\(655\) | 9337.44 | 0.557014 | ||||||||
\(656\) | −11074.6 | −0.659132 | ||||||||
\(657\) | 27170.0 | 1.61340 | ||||||||
\(658\) | 19678.8 | 1.16590 | ||||||||
\(659\) | −454.595 | −0.0268718 | −0.0134359 | − | 0.999910i | \(-0.504277\pi\) | ||||
−0.0134359 | + | 0.999910i | \(0.504277\pi\) | |||||||
\(660\) | −2305.74 | −0.135986 | ||||||||
\(661\) | −21367.3 | −1.25732 | −0.628662 | − | 0.777679i | \(-0.716397\pi\) | ||||
−0.628662 | + | 0.777679i | \(0.716397\pi\) | |||||||
\(662\) | −16803.0 | −0.986508 | ||||||||
\(663\) | 8572.81 | 0.502173 | ||||||||
\(664\) | 2234.41 | 0.130590 | ||||||||
\(665\) | −15965.3 | −0.930987 | ||||||||
\(666\) | 26698.7 | 1.55338 | ||||||||
\(667\) | −12000.7 | −0.696653 | ||||||||
\(668\) | −763.867 | −0.0442439 | ||||||||
\(669\) | 50427.8 | 2.91428 | ||||||||
\(670\) | −2921.12 | −0.168437 | ||||||||
\(671\) | −17183.6 | −0.988622 | ||||||||
\(672\) | 13181.2 | 0.756662 | ||||||||
\(673\) | −18710.7 | −1.07169 | −0.535843 | − | 0.844318i | \(-0.680006\pi\) | ||||
−0.535843 | + | 0.844318i | \(0.680006\pi\) | |||||||
\(674\) | 8496.63 | 0.485576 | ||||||||
\(675\) | 2886.17 | 0.164576 | ||||||||
\(676\) | −243.098 | −0.0138312 | ||||||||
\(677\) | −29181.5 | −1.65662 | −0.828312 | − | 0.560267i | \(-0.810699\pi\) | ||||
−0.828312 | + | 0.560267i | \(0.810699\pi\) | |||||||
\(678\) | −34407.3 | −1.94897 | ||||||||
\(679\) | −42476.3 | −2.40072 | ||||||||
\(680\) | −9667.17 | −0.545175 | ||||||||
\(681\) | 34767.1 | 1.95636 | ||||||||
\(682\) | 29751.6 | 1.67045 | ||||||||
\(683\) | 21953.8 | 1.22992 | 0.614961 | − | 0.788557i | \(-0.289172\pi\) | ||||
0.614961 | + | 0.788557i | \(0.289172\pi\) | |||||||
\(684\) | −7569.86 | −0.423159 | ||||||||
\(685\) | −8704.00 | −0.485493 | ||||||||
\(686\) | −4278.40 | −0.238120 | ||||||||
\(687\) | −2469.33 | −0.137134 | ||||||||
\(688\) | 5267.32 | 0.291882 | ||||||||
\(689\) | 1.18209 | 6.53614e−5 0 | ||||||||
\(690\) | 10766.4 | 0.594013 | ||||||||
\(691\) | 2242.59 | 0.123462 | 0.0617309 | − | 0.998093i | \(-0.480338\pi\) | ||||
0.0617309 | + | 0.998093i | \(0.480338\pi\) | |||||||
\(692\) | −1164.89 | −0.0639921 | ||||||||
\(693\) | −39652.6 | −2.17356 | ||||||||
\(694\) | −9552.18 | −0.522472 | ||||||||
\(695\) | 4927.56 | 0.268939 | ||||||||
\(696\) | −23470.4 | −1.27823 | ||||||||
\(697\) | −17563.9 | −0.954493 | ||||||||
\(698\) | 9601.25 | 0.520649 | ||||||||
\(699\) | 10086.5 | 0.545788 | ||||||||
\(700\) | −894.602 | −0.0483040 | ||||||||
\(701\) | 16013.4 | 0.862794 | 0.431397 | − | 0.902162i | \(-0.358021\pi\) | ||||
0.431397 | + | 0.902162i | \(0.358021\pi\) | |||||||
\(702\) | −3844.41 | −0.206692 | ||||||||
\(703\) | 32629.7 | 1.75057 | ||||||||
\(704\) | −22081.2 | −1.18213 | ||||||||
\(705\) | −12732.8 | −0.680207 | ||||||||
\(706\) | −8591.19 | −0.457980 | ||||||||
\(707\) | −33933.0 | −1.80507 | ||||||||
\(708\) | 4148.17 | 0.220195 | ||||||||
\(709\) | −34333.3 | −1.81864 | −0.909318 | − | 0.416102i | \(-0.863396\pi\) | ||||
−0.909318 | + | 0.416102i | \(0.863396\pi\) | |||||||
\(710\) | −12350.9 | −0.652845 | ||||||||
\(711\) | −2675.72 | −0.141135 | ||||||||
\(712\) | 4318.36 | 0.227300 | ||||||||
\(713\) | 30455.0 | 1.59965 | ||||||||
\(714\) | −42022.3 | −2.20258 | ||||||||
\(715\) | −2527.00 | −0.132174 | ||||||||
\(716\) | 2635.05 | 0.137537 | ||||||||
\(717\) | −401.799 | −0.0209281 | ||||||||
\(718\) | −2668.79 | −0.138717 | ||||||||
\(719\) | −4359.43 | −0.226119 | −0.113059 | − | 0.993588i | \(-0.536065\pi\) | ||||
−0.113059 | + | 0.993588i | \(0.536065\pi\) | |||||||
\(720\) | 10336.8 | 0.535040 | ||||||||
\(721\) | 8835.44 | 0.456379 | ||||||||
\(722\) | 24631.4 | 1.26965 | ||||||||
\(723\) | −37106.5 | −1.90872 | ||||||||
\(724\) | −1505.71 | −0.0772919 | ||||||||
\(725\) | 2943.09 | 0.150763 | ||||||||
\(726\) | 3810.88 | 0.194814 | ||||||||
\(727\) | −9626.47 | −0.491095 | −0.245547 | − | 0.969385i | \(-0.578968\pi\) | ||||
−0.245547 | + | 0.969385i | \(0.578968\pi\) | |||||||
\(728\) | 7818.86 | 0.398058 | ||||||||
\(729\) | −32059.0 | −1.62877 | ||||||||
\(730\) | −8487.47 | −0.430322 | ||||||||
\(731\) | 8353.80 | 0.422677 | ||||||||
\(732\) | −5242.89 | −0.264731 | ||||||||
\(733\) | −11224.3 | −0.565590 | −0.282795 | − | 0.959180i | \(-0.591262\pi\) | ||||
−0.282795 | + | 0.959180i | \(0.591262\pi\) | |||||||
\(734\) | 2817.58 | 0.141688 | ||||||||
\(735\) | −11374.0 | −0.570797 | ||||||||
\(736\) | −6550.09 | −0.328043 | ||||||||
\(737\) | −8866.81 | −0.443165 | ||||||||
\(738\) | 23066.6 | 1.15053 | ||||||||
\(739\) | 20190.6 | 1.00504 | 0.502519 | − | 0.864566i | \(-0.332407\pi\) | ||||
0.502519 | + | 0.864566i | \(0.332407\pi\) | |||||||
\(740\) | 1828.38 | 0.0908279 | ||||||||
\(741\) | −13759.7 | −0.682151 | ||||||||
\(742\) | −5.79437 | −0.000286682 0 | ||||||||
\(743\) | −19756.1 | −0.975479 | −0.487739 | − | 0.872989i | \(-0.662178\pi\) | ||||
−0.487739 | + | 0.872989i | \(0.662178\pi\) | |||||||
\(744\) | 59562.7 | 2.93505 | ||||||||
\(745\) | 12484.5 | 0.613956 | ||||||||
\(746\) | 7600.49 | 0.373021 | ||||||||
\(747\) | −3789.16 | −0.185593 | ||||||||
\(748\) | −4472.09 | −0.218604 | ||||||||
\(749\) | 8107.51 | 0.395517 | ||||||||
\(750\) | −2640.39 | −0.128551 | ||||||||
\(751\) | 17597.3 | 0.855040 | 0.427520 | − | 0.904006i | \(-0.359387\pi\) | ||||
0.427520 | + | 0.904006i | \(0.359387\pi\) | |||||||
\(752\) | −15571.5 | −0.755100 | ||||||||
\(753\) | −909.456 | −0.0440138 | ||||||||
\(754\) | −3920.21 | −0.189345 | ||||||||
\(755\) | −1788.55 | −0.0862146 | ||||||||
\(756\) | −4131.17 | −0.198742 | ||||||||
\(757\) | 29920.3 | 1.43655 | 0.718277 | − | 0.695757i | \(-0.244931\pi\) | ||||
0.718277 | + | 0.695757i | \(0.244931\pi\) | |||||||
\(758\) | −23621.8 | −1.13190 | ||||||||
\(759\) | 32680.4 | 1.56288 | ||||||||
\(760\) | 15516.1 | 0.740565 | ||||||||
\(761\) | 13040.7 | 0.621190 | 0.310595 | − | 0.950542i | \(-0.399472\pi\) | ||||
0.310595 | + | 0.950542i | \(0.399472\pi\) | |||||||
\(762\) | 3492.35 | 0.166030 | ||||||||
\(763\) | 43259.2 | 2.05254 | ||||||||
\(764\) | −1093.18 | −0.0517669 | ||||||||
\(765\) | 16393.8 | 0.774796 | ||||||||
\(766\) | −28299.9 | −1.33488 | ||||||||
\(767\) | 4546.23 | 0.214022 | ||||||||
\(768\) | −17595.3 | −0.826712 | ||||||||
\(769\) | 23856.2 | 1.11869 | 0.559347 | − | 0.828934i | \(-0.311052\pi\) | ||||
0.559347 | + | 0.828934i | \(0.311052\pi\) | |||||||
\(770\) | 12386.9 | 0.579729 | ||||||||
\(771\) | 61465.3 | 2.87110 | ||||||||
\(772\) | 592.090 | 0.0276034 | ||||||||
\(773\) | −20701.3 | −0.963224 | −0.481612 | − | 0.876384i | \(-0.659949\pi\) | ||||
−0.481612 | + | 0.876384i | \(0.659949\pi\) | |||||||
\(774\) | −10971.0 | −0.509489 | ||||||||
\(775\) | −7468.89 | −0.346181 | ||||||||
\(776\) | 41281.4 | 1.90968 | ||||||||
\(777\) | 52149.9 | 2.40781 | ||||||||
\(778\) | −515.851 | −0.0237714 | ||||||||
\(779\) | 28190.8 | 1.29658 | ||||||||
\(780\) | −771.013 | −0.0353932 | ||||||||
\(781\) | −37490.1 | −1.71767 | ||||||||
\(782\) | 20881.9 | 0.954906 | ||||||||
\(783\) | 13590.8 | 0.620302 | ||||||||
\(784\) | −13909.8 | −0.633644 | ||||||||
\(785\) | 16091.6 | 0.731635 | ||||||||
\(786\) | −39447.2 | −1.79012 | ||||||||
\(787\) | −4082.21 | −0.184899 | −0.0924493 | − | 0.995717i | \(-0.529470\pi\) | ||||
−0.0924493 | + | 0.995717i | \(0.529470\pi\) | |||||||
\(788\) | 1158.24 | 0.0523613 | ||||||||
\(789\) | −1856.68 | −0.0837764 | ||||||||
\(790\) | 835.852 | 0.0376434 | ||||||||
\(791\) | −40521.8 | −1.82148 | ||||||||
\(792\) | 38537.1 | 1.72899 | ||||||||
\(793\) | −5746.00 | −0.257310 | ||||||||
\(794\) | −11153.2 | −0.498506 | ||||||||
\(795\) | 3.74914 | 0.000167256 0 | ||||||||
\(796\) | −4217.56 | −0.187798 | ||||||||
\(797\) | 17269.3 | 0.767514 | 0.383757 | − | 0.923434i | \(-0.374630\pi\) | ||||
0.383757 | + | 0.923434i | \(0.374630\pi\) | |||||||
\(798\) | 67447.2 | 2.99199 | ||||||||
\(799\) | −24695.9 | −1.09347 | ||||||||
\(800\) | 1606.37 | 0.0709921 | ||||||||
\(801\) | −7323.16 | −0.323035 | ||||||||
\(802\) | 10864.3 | 0.478346 | ||||||||
\(803\) | −25763.0 | −1.13220 | ||||||||
\(804\) | −2705.35 | −0.118670 | ||||||||
\(805\) | 12679.7 | 0.555155 | ||||||||
\(806\) | 9948.62 | 0.434771 | ||||||||
\(807\) | −22611.8 | −0.986337 | ||||||||
\(808\) | 32978.5 | 1.43586 | ||||||||
\(809\) | −35166.8 | −1.52831 | −0.764153 | − | 0.645034i | \(-0.776843\pi\) | ||||
−0.764153 | + | 0.645034i | \(0.776843\pi\) | |||||||
\(810\) | 1985.20 | 0.0861147 | ||||||||
\(811\) | −40718.1 | −1.76302 | −0.881509 | − | 0.472167i | \(-0.843472\pi\) | ||||
−0.881509 | + | 0.472167i | \(0.843472\pi\) | |||||||
\(812\) | −4212.63 | −0.182062 | ||||||||
\(813\) | 55659.3 | 2.40106 | ||||||||
\(814\) | −25316.1 | −1.09009 | ||||||||
\(815\) | 14507.5 | 0.623529 | ||||||||
\(816\) | 33251.5 | 1.42651 | ||||||||
\(817\) | −13408.1 | −0.574164 | ||||||||
\(818\) | −4155.47 | −0.177619 | ||||||||
\(819\) | −13259.4 | −0.565715 | ||||||||
\(820\) | 1579.65 | 0.0672729 | ||||||||
\(821\) | −30057.8 | −1.27774 | −0.638870 | − | 0.769314i | \(-0.720598\pi\) | ||||
−0.638870 | + | 0.769314i | \(0.720598\pi\) | |||||||
\(822\) | 36771.1 | 1.56027 | ||||||||
\(823\) | 4548.10 | 0.192633 | 0.0963163 | − | 0.995351i | \(-0.469294\pi\) | ||||
0.0963163 | + | 0.995351i | \(0.469294\pi\) | |||||||
\(824\) | −8586.89 | −0.363032 | ||||||||
\(825\) | −8014.68 | −0.338225 | ||||||||
\(826\) | −22284.7 | −0.938724 | ||||||||
\(827\) | 9335.94 | 0.392554 | 0.196277 | − | 0.980548i | \(-0.437115\pi\) | ||||
0.196277 | + | 0.980548i | \(0.437115\pi\) | |||||||
\(828\) | 6012.01 | 0.252333 | ||||||||
\(829\) | −22765.0 | −0.953751 | −0.476876 | − | 0.878971i | \(-0.658231\pi\) | ||||
−0.476876 | + | 0.878971i | \(0.658231\pi\) | |||||||
\(830\) | 1183.67 | 0.0495011 | ||||||||
\(831\) | 12465.4 | 0.520361 | ||||||||
\(832\) | −7383.72 | −0.307673 | ||||||||
\(833\) | −22060.4 | −0.917585 | ||||||||
\(834\) | −20817.1 | −0.864312 | ||||||||
\(835\) | −2655.18 | −0.110043 | ||||||||
\(836\) | 7177.87 | 0.296952 | ||||||||
\(837\) | −34490.4 | −1.42433 | ||||||||
\(838\) | −16251.5 | −0.669927 | ||||||||
\(839\) | 28521.3 | 1.17362 | 0.586808 | − | 0.809726i | \(-0.300384\pi\) | ||||
0.586808 | + | 0.809726i | \(0.300384\pi\) | |||||||
\(840\) | 24798.4 | 1.01860 | ||||||||
\(841\) | −10530.2 | −0.431760 | ||||||||
\(842\) | −18060.3 | −0.739193 | ||||||||
\(843\) | −46126.7 | −1.88456 | ||||||||
\(844\) | 5642.41 | 0.230118 | ||||||||
\(845\) | −845.000 | −0.0344010 | ||||||||
\(846\) | 32433.0 | 1.31805 | ||||||||
\(847\) | 4488.11 | 0.182070 | ||||||||
\(848\) | 4.58499 | 0.000185671 0 | ||||||||
\(849\) | −26561.2 | −1.07371 | ||||||||
\(850\) | −5121.16 | −0.206652 | ||||||||
\(851\) | −25914.6 | −1.04388 | ||||||||
\(852\) | −11438.6 | −0.459953 | ||||||||
\(853\) | 5037.10 | 0.202189 | 0.101094 | − | 0.994877i | \(-0.467766\pi\) | ||||
0.101094 | + | 0.994877i | \(0.467766\pi\) | |||||||
\(854\) | 28165.8 | 1.12859 | ||||||||
\(855\) | −26312.6 | −1.05248 | ||||||||
\(856\) | −7879.44 | −0.314619 | ||||||||
\(857\) | −27178.6 | −1.08332 | −0.541658 | − | 0.840599i | \(-0.682203\pi\) | ||||
−0.541658 | + | 0.840599i | \(0.682203\pi\) | |||||||
\(858\) | 10675.6 | 0.424778 | ||||||||
\(859\) | 21916.5 | 0.870525 | 0.435262 | − | 0.900304i | \(-0.356656\pi\) | ||||
0.435262 | + | 0.900304i | \(0.356656\pi\) | |||||||
\(860\) | −751.316 | −0.0297903 | ||||||||
\(861\) | 45055.4 | 1.78337 | ||||||||
\(862\) | −7043.60 | −0.278313 | ||||||||
\(863\) | 38533.9 | 1.51994 | 0.759971 | − | 0.649957i | \(-0.225213\pi\) | ||||
0.759971 | + | 0.649957i | \(0.225213\pi\) | |||||||
\(864\) | 7418.01 | 0.292090 | ||||||||
\(865\) | −4049.13 | −0.159161 | ||||||||
\(866\) | −32579.6 | −1.27841 | ||||||||
\(867\) | 12222.1 | 0.478761 | ||||||||
\(868\) | 10690.7 | 0.418048 | ||||||||
\(869\) | 2537.16 | 0.0990417 | ||||||||
\(870\) | −12433.4 | −0.484520 | ||||||||
\(871\) | −2964.96 | −0.115343 | ||||||||
\(872\) | −42042.3 | −1.63272 | ||||||||
\(873\) | −70005.8 | −2.71402 | ||||||||
\(874\) | −33516.2 | −1.29714 | ||||||||
\(875\) | −3109.61 | −0.120142 | ||||||||
\(876\) | −7860.56 | −0.303178 | ||||||||
\(877\) | 4812.41 | 0.185295 | 0.0926475 | − | 0.995699i | \(-0.470467\pi\) | ||||
0.0926475 | + | 0.995699i | \(0.470467\pi\) | |||||||
\(878\) | 45228.7 | 1.73849 | ||||||||
\(879\) | 64401.6 | 2.47123 | ||||||||
\(880\) | −9801.51 | −0.375464 | ||||||||
\(881\) | −18910.3 | −0.723160 | −0.361580 | − | 0.932341i | \(-0.617763\pi\) | ||||
−0.361580 | + | 0.932341i | \(0.617763\pi\) | |||||||
\(882\) | 28971.8 | 1.10605 | ||||||||
\(883\) | −35174.6 | −1.34057 | −0.670283 | − | 0.742106i | \(-0.733827\pi\) | ||||
−0.670283 | + | 0.742106i | \(0.733827\pi\) | |||||||
\(884\) | −1495.42 | −0.0568963 | ||||||||
\(885\) | 14418.9 | 0.547669 | ||||||||
\(886\) | 47019.2 | 1.78289 | ||||||||
\(887\) | 38502.7 | 1.45749 | 0.728745 | − | 0.684785i | \(-0.240104\pi\) | ||||
0.728745 | + | 0.684785i | \(0.240104\pi\) | |||||||
\(888\) | −50682.9 | −1.91532 | ||||||||
\(889\) | 4112.98 | 0.155168 | ||||||||
\(890\) | 2287.64 | 0.0861595 | ||||||||
\(891\) | 6025.92 | 0.226572 | ||||||||
\(892\) | −8796.49 | −0.330189 | ||||||||
\(893\) | 39637.9 | 1.48536 | ||||||||
\(894\) | −52742.3 | −1.97312 | ||||||||
\(895\) | 9159.36 | 0.342082 | ||||||||
\(896\) | 23405.9 | 0.872696 | ||||||||
\(897\) | 10928.0 | 0.406772 | ||||||||
\(898\) | −6854.14 | −0.254706 | ||||||||
\(899\) | −35170.6 | −1.30479 | ||||||||
\(900\) | −1474.41 | −0.0546077 | ||||||||
\(901\) | 7.27164 | 0.000268872 0 | ||||||||
\(902\) | −21872.2 | −0.807387 | ||||||||
\(903\) | −21429.4 | −0.789728 | ||||||||
\(904\) | 39381.9 | 1.44892 | ||||||||
\(905\) | −5233.81 | −0.192240 | ||||||||
\(906\) | 7555.95 | 0.277075 | ||||||||
\(907\) | −52947.3 | −1.93835 | −0.969176 | − | 0.246368i | \(-0.920763\pi\) | ||||
−0.969176 | + | 0.246368i | \(0.920763\pi\) | |||||||
\(908\) | −6064.69 | −0.221656 | ||||||||
\(909\) | −55925.5 | −2.04063 | ||||||||
\(910\) | 4142.03 | 0.150887 | ||||||||
\(911\) | 11565.8 | 0.420627 | 0.210314 | − | 0.977634i | \(-0.432551\pi\) | ||||
0.210314 | + | 0.977634i | \(0.432551\pi\) | |||||||
\(912\) | −53369.8 | −1.93778 | ||||||||
\(913\) | 3592.94 | 0.130240 | ||||||||
\(914\) | 15662.6 | 0.566821 | ||||||||
\(915\) | −18224.1 | −0.658438 | ||||||||
\(916\) | 430.744 | 0.0155373 | ||||||||
\(917\) | −46457.3 | −1.67302 | ||||||||
\(918\) | −23648.9 | −0.850251 | ||||||||
\(919\) | −31800.9 | −1.14148 | −0.570738 | − | 0.821132i | \(-0.693343\pi\) | ||||
−0.570738 | + | 0.821132i | \(0.693343\pi\) | |||||||
\(920\) | −12323.0 | −0.441605 | ||||||||
\(921\) | 70761.3 | 2.53167 | ||||||||
\(922\) | −35819.6 | −1.27945 | ||||||||
\(923\) | −12536.3 | −0.447060 | ||||||||
\(924\) | 11471.9 | 0.408440 | ||||||||
\(925\) | 6355.40 | 0.225907 | ||||||||
\(926\) | −12984.5 | −0.460794 | ||||||||
\(927\) | 14561.8 | 0.515937 | ||||||||
\(928\) | 7564.29 | 0.267575 | ||||||||
\(929\) | 39306.1 | 1.38815 | 0.694075 | − | 0.719903i | \(-0.255814\pi\) | ||||
0.694075 | + | 0.719903i | \(0.255814\pi\) | |||||||
\(930\) | 31553.2 | 1.11255 | ||||||||
\(931\) | 35407.8 | 1.24645 | ||||||||
\(932\) | −1759.46 | −0.0618380 | ||||||||
\(933\) | 76292.6 | 2.67707 | ||||||||
\(934\) | 6273.78 | 0.219791 | ||||||||
\(935\) | −15544.9 | −0.543713 | ||||||||
\(936\) | 12886.4 | 0.450005 | ||||||||
\(937\) | 2554.39 | 0.0890589 | 0.0445294 | − | 0.999008i | \(-0.485821\pi\) | ||||
0.0445294 | + | 0.999008i | \(0.485821\pi\) | |||||||
\(938\) | 14533.7 | 0.505907 | ||||||||
\(939\) | 36169.3 | 1.25702 | ||||||||
\(940\) | 2221.08 | 0.0770677 | ||||||||
\(941\) | 17871.8 | 0.619133 | 0.309567 | − | 0.950878i | \(-0.399816\pi\) | ||||
0.309567 | + | 0.950878i | \(0.399816\pi\) | |||||||
\(942\) | −67980.9 | −2.35131 | ||||||||
\(943\) | −22389.2 | −0.773163 | ||||||||
\(944\) | 17633.5 | 0.607969 | ||||||||
\(945\) | −14359.8 | −0.494312 | ||||||||
\(946\) | 10402.9 | 0.357534 | ||||||||
\(947\) | 13013.0 | 0.446532 | 0.223266 | − | 0.974758i | \(-0.428328\pi\) | ||||
0.223266 | + | 0.974758i | \(0.428328\pi\) | |||||||
\(948\) | 774.113 | 0.0265211 | ||||||||
\(949\) | −8614.86 | −0.294679 | ||||||||
\(950\) | 8219.65 | 0.280716 | ||||||||
\(951\) | −4846.18 | −0.165245 | ||||||||
\(952\) | 48097.8 | 1.63746 | ||||||||
\(953\) | −11984.0 | −0.407345 | −0.203672 | − | 0.979039i | \(-0.565288\pi\) | ||||
−0.203672 | + | 0.979039i | \(0.565288\pi\) | |||||||
\(954\) | −9.54980 | −0.000324094 0 | ||||||||
\(955\) | −3799.87 | −0.128755 | ||||||||
\(956\) | 70.0888 | 0.00237117 | ||||||||
\(957\) | −37740.6 | −1.27480 | ||||||||
\(958\) | −36133.5 | −1.21860 | ||||||||
\(959\) | 43305.7 | 1.45820 | ||||||||
\(960\) | −23418.3 | −0.787316 | ||||||||
\(961\) | 59463.9 | 1.99604 | ||||||||
\(962\) | −8465.44 | −0.283718 | ||||||||
\(963\) | 13362.1 | 0.447132 | ||||||||
\(964\) | 6472.77 | 0.216259 | ||||||||
\(965\) | 2058.09 | 0.0686551 | ||||||||
\(966\) | −53566.8 | −1.78415 | ||||||||
\(967\) | 34643.6 | 1.15208 | 0.576041 | − | 0.817421i | \(-0.304597\pi\) | ||||
0.576041 | + | 0.817421i | \(0.304597\pi\) | |||||||
\(968\) | −4361.86 | −0.144830 | ||||||||
\(969\) | −84642.8 | −2.80611 | ||||||||
\(970\) | 21868.7 | 0.723879 | ||||||||
\(971\) | 11097.6 | 0.366776 | 0.183388 | − | 0.983041i | \(-0.441294\pi\) | ||||
0.183388 | + | 0.983041i | \(0.441294\pi\) | |||||||
\(972\) | 6322.31 | 0.208630 | ||||||||
\(973\) | −24516.5 | −0.807771 | ||||||||
\(974\) | 29008.0 | 0.954288 | ||||||||
\(975\) | −2680.02 | −0.0880300 | ||||||||
\(976\) | −22287.1 | −0.730935 | ||||||||
\(977\) | 6609.39 | 0.216431 | 0.108215 | − | 0.994127i | \(-0.465486\pi\) | ||||
0.108215 | + | 0.994127i | \(0.465486\pi\) | |||||||
\(978\) | −61288.8 | −2.00389 | ||||||||
\(979\) | 6943.94 | 0.226690 | ||||||||
\(980\) | 1984.05 | 0.0646716 | ||||||||
\(981\) | 71296.2 | 2.32040 | ||||||||
\(982\) | −30290.0 | −0.984309 | ||||||||
\(983\) | 30211.3 | 0.980254 | 0.490127 | − | 0.871651i | \(-0.336950\pi\) | ||||
0.490127 | + | 0.871651i | \(0.336950\pi\) | |||||||
\(984\) | −43788.0 | −1.41861 | ||||||||
\(985\) | 4026.02 | 0.130233 | ||||||||
\(986\) | −24115.3 | −0.778891 | ||||||||
\(987\) | 63350.6 | 2.04303 | ||||||||
\(988\) | 2400.20 | 0.0772880 | ||||||||
\(989\) | 10648.8 | 0.342378 | ||||||||
\(990\) | 20415.0 | 0.655384 | ||||||||
\(991\) | 36910.1 | 1.18313 | 0.591567 | − | 0.806256i | \(-0.298509\pi\) | ||||
0.591567 | + | 0.806256i | \(0.298509\pi\) | |||||||
\(992\) | −19196.5 | −0.614403 | ||||||||
\(993\) | −54092.7 | −1.72868 | ||||||||
\(994\) | 61450.3 | 1.96085 | ||||||||
\(995\) | −14660.1 | −0.467092 | ||||||||
\(996\) | 1096.24 | 0.0348753 | ||||||||
\(997\) | −42912.3 | −1.36313 | −0.681567 | − | 0.731755i | \(-0.738701\pi\) | ||||
−0.681567 | + | 0.731755i | \(0.738701\pi\) | |||||||
\(998\) | 29361.2 | 0.931275 | ||||||||
\(999\) | 29348.5 | 0.929473 |
(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 | 65.4.a.c.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 585.4.a.h.1.1 | 2 | |||
4.3 | odd | 2 | 1040.4.a.k.1.1 | 2 | |||
5.2 | odd | 4 | 325.4.b.f.274.4 | 4 | |||
5.3 | odd | 4 | 325.4.b.f.274.1 | 4 | |||
5.4 | even | 2 | 325.4.a.g.1.1 | 2 | |||
13.12 | even | 2 | 845.4.a.d.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
65.4.a.c.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
325.4.a.g.1.1 | 2 | 5.4 | even | 2 | |||
325.4.b.f.274.1 | 4 | 5.3 | odd | 4 | |||
325.4.b.f.274.4 | 4 | 5.2 | odd | 4 | |||
585.4.a.h.1.1 | 2 | 3.2 | odd | 2 | |||
845.4.a.d.1.1 | 2 | 13.12 | even | 2 | |||
1040.4.a.k.1.1 | 2 | 4.3 | odd | 2 |