Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1875,4,Mod(1,1875)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1875, 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("1875.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1875 = 3 \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1875.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: | \(110.628581261\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 81 x^{12} - 7 x^{11} + 2512 x^{10} + 517 x^{9} - 36970 x^{8} - 12987 x^{7} + 257291 x^{6} + 125779 x^{5} - 718713 x^{4} - 371750 x^{3} + 579848 x^{2} + \cdots + 42064 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2}\cdot 5^{3} \) |
Twist minimal: | no (minimal twist has level 75) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(1.73740\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1875.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.73740 | −0.614263 | −0.307131 | − | 0.951667i | \(-0.599369\pi\) | ||||
−0.307131 | + | 0.951667i | \(0.599369\pi\) | |||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | −4.98145 | −0.622681 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 5.21219 | 0.354645 | ||||||||
\(7\) | −7.66213 | −0.413716 | −0.206858 | − | 0.978371i | \(-0.566324\pi\) | ||||
−0.206858 | + | 0.978371i | \(0.566324\pi\) | |||||||
\(8\) | 22.5539 | 0.996753 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 20.4704 | 0.561095 | 0.280548 | − | 0.959840i | \(-0.409484\pi\) | ||||
0.280548 | + | 0.959840i | \(0.409484\pi\) | |||||||
\(12\) | 14.9443 | 0.359505 | ||||||||
\(13\) | 14.8079 | 0.315920 | 0.157960 | − | 0.987445i | \(-0.449508\pi\) | ||||
0.157960 | + | 0.987445i | \(0.449508\pi\) | |||||||
\(14\) | 13.3122 | 0.254130 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.666425 | 0.0104129 | ||||||||
\(17\) | 109.000 | 1.55508 | 0.777539 | − | 0.628835i | \(-0.216468\pi\) | ||||
0.777539 | + | 0.628835i | \(0.216468\pi\) | |||||||
\(18\) | −15.6366 | −0.204754 | ||||||||
\(19\) | 97.7849 | 1.18071 | 0.590353 | − | 0.807145i | \(-0.298989\pi\) | ||||
0.590353 | + | 0.807145i | \(0.298989\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 22.9864 | 0.238859 | ||||||||
\(22\) | −35.5652 | −0.344660 | ||||||||
\(23\) | 80.5714 | 0.730447 | 0.365224 | − | 0.930920i | \(-0.380992\pi\) | ||||
0.365224 | + | 0.930920i | \(0.380992\pi\) | |||||||
\(24\) | −67.6618 | −0.575475 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −25.7272 | −0.194058 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 38.1685 | 0.257613 | ||||||||
\(29\) | 59.0555 | 0.378149 | 0.189075 | − | 0.981963i | \(-0.439451\pi\) | ||||
0.189075 | + | 0.981963i | \(0.439451\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 176.318 | 1.02153 | 0.510767 | − | 0.859719i | \(-0.329361\pi\) | ||||
0.510767 | + | 0.859719i | \(0.329361\pi\) | |||||||
\(32\) | −181.589 | −1.00315 | ||||||||
\(33\) | −61.4111 | −0.323949 | ||||||||
\(34\) | −189.376 | −0.955226 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −44.8330 | −0.207560 | ||||||||
\(37\) | 230.536 | 1.02432 | 0.512161 | − | 0.858889i | \(-0.328845\pi\) | ||||
0.512161 | + | 0.858889i | \(0.328845\pi\) | |||||||
\(38\) | −169.891 | −0.725264 | ||||||||
\(39\) | −44.4236 | −0.182397 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 179.464 | 0.683600 | 0.341800 | − | 0.939773i | \(-0.388963\pi\) | ||||
0.341800 | + | 0.939773i | \(0.388963\pi\) | |||||||
\(42\) | −39.9365 | −0.146722 | ||||||||
\(43\) | 407.459 | 1.44505 | 0.722523 | − | 0.691347i | \(-0.242982\pi\) | ||||
0.722523 | + | 0.691347i | \(0.242982\pi\) | |||||||
\(44\) | −101.972 | −0.349384 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −139.985 | −0.448687 | ||||||||
\(47\) | −477.166 | −1.48089 | −0.740445 | − | 0.672117i | \(-0.765385\pi\) | ||||
−0.740445 | + | 0.672117i | \(0.765385\pi\) | |||||||
\(48\) | −1.99927 | −0.00601188 | ||||||||
\(49\) | −284.292 | −0.828839 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −326.999 | −0.897824 | ||||||||
\(52\) | −73.7647 | −0.196718 | ||||||||
\(53\) | 515.525 | 1.33609 | 0.668046 | − | 0.744120i | \(-0.267131\pi\) | ||||
0.668046 | + | 0.744120i | \(0.267131\pi\) | |||||||
\(54\) | 46.9097 | 0.118215 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −172.811 | −0.412372 | ||||||||
\(57\) | −293.355 | −0.681681 | ||||||||
\(58\) | −102.603 | −0.232283 | ||||||||
\(59\) | −571.444 | −1.26094 | −0.630472 | − | 0.776212i | \(-0.717139\pi\) | ||||
−0.630472 | + | 0.776212i | \(0.717139\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −52.3159 | −0.109809 | −0.0549046 | − | 0.998492i | \(-0.517485\pi\) | ||||
−0.0549046 | + | 0.998492i | \(0.517485\pi\) | |||||||
\(62\) | −306.334 | −0.627491 | ||||||||
\(63\) | −68.9591 | −0.137905 | ||||||||
\(64\) | 310.162 | 0.605784 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 106.696 | 0.198990 | ||||||||
\(67\) | 551.814 | 1.00619 | 0.503096 | − | 0.864231i | \(-0.332194\pi\) | ||||
0.503096 | + | 0.864231i | \(0.332194\pi\) | |||||||
\(68\) | −542.976 | −0.968317 | ||||||||
\(69\) | −241.714 | −0.421724 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 368.658 | 0.616220 | 0.308110 | − | 0.951351i | \(-0.400304\pi\) | ||||
0.308110 | + | 0.951351i | \(0.400304\pi\) | |||||||
\(72\) | 202.985 | 0.332251 | ||||||||
\(73\) | 406.465 | 0.651687 | 0.325843 | − | 0.945424i | \(-0.394352\pi\) | ||||
0.325843 | + | 0.945424i | \(0.394352\pi\) | |||||||
\(74\) | −400.533 | −0.629203 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −487.111 | −0.735203 | ||||||||
\(77\) | −156.847 | −0.232134 | ||||||||
\(78\) | 77.1815 | 0.112040 | ||||||||
\(79\) | −654.750 | −0.932470 | −0.466235 | − | 0.884661i | \(-0.654390\pi\) | ||||
−0.466235 | + | 0.884661i | \(0.654390\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −311.801 | −0.419910 | ||||||||
\(83\) | −421.856 | −0.557887 | −0.278944 | − | 0.960307i | \(-0.589984\pi\) | ||||
−0.278944 | + | 0.960307i | \(0.589984\pi\) | |||||||
\(84\) | −114.505 | −0.148733 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −707.919 | −0.887638 | ||||||||
\(87\) | −177.166 | −0.218325 | ||||||||
\(88\) | 461.688 | 0.559273 | ||||||||
\(89\) | 425.138 | 0.506343 | 0.253171 | − | 0.967421i | \(-0.418526\pi\) | ||||
0.253171 | + | 0.967421i | \(0.418526\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −113.460 | −0.130701 | ||||||||
\(92\) | −401.362 | −0.454836 | ||||||||
\(93\) | −528.953 | −0.589783 | ||||||||
\(94\) | 829.027 | 0.909655 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 544.768 | 0.579168 | ||||||||
\(97\) | −590.666 | −0.618279 | −0.309139 | − | 0.951017i | \(-0.600041\pi\) | ||||
−0.309139 | + | 0.951017i | \(0.600041\pi\) | |||||||
\(98\) | 493.928 | 0.509125 | ||||||||
\(99\) | 184.233 | 0.187032 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1533.55 | −1.51083 | −0.755417 | − | 0.655244i | \(-0.772566\pi\) | ||||
−0.755417 | + | 0.655244i | \(0.772566\pi\) | |||||||
\(102\) | 568.128 | 0.551500 | ||||||||
\(103\) | 718.897 | 0.687719 | 0.343859 | − | 0.939021i | \(-0.388266\pi\) | ||||
0.343859 | + | 0.939021i | \(0.388266\pi\) | |||||||
\(104\) | 333.976 | 0.314895 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −895.672 | −0.820711 | ||||||||
\(107\) | 944.844 | 0.853659 | 0.426830 | − | 0.904332i | \(-0.359630\pi\) | ||||
0.426830 | + | 0.904332i | \(0.359630\pi\) | |||||||
\(108\) | 134.499 | 0.119835 | ||||||||
\(109\) | 1472.33 | 1.29380 | 0.646899 | − | 0.762576i | \(-0.276066\pi\) | ||||
0.646899 | + | 0.762576i | \(0.276066\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −691.609 | −0.591393 | ||||||||
\(112\) | −5.10623 | −0.00430798 | ||||||||
\(113\) | 820.255 | 0.682859 | 0.341429 | − | 0.939907i | \(-0.389089\pi\) | ||||
0.341429 | + | 0.939907i | \(0.389089\pi\) | |||||||
\(114\) | 509.674 | 0.418731 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −294.182 | −0.235466 | ||||||||
\(117\) | 133.271 | 0.105307 | ||||||||
\(118\) | 992.826 | 0.774551 | ||||||||
\(119\) | −835.170 | −0.643360 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −911.964 | −0.685172 | ||||||||
\(122\) | 90.8935 | 0.0674517 | ||||||||
\(123\) | −538.393 | −0.394677 | ||||||||
\(124\) | −878.317 | −0.636090 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 119.809 | 0.0847101 | ||||||||
\(127\) | −1663.86 | −1.16255 | −0.581274 | − | 0.813708i | \(-0.697446\pi\) | ||||
−0.581274 | + | 0.813708i | \(0.697446\pi\) | |||||||
\(128\) | 913.841 | 0.631038 | ||||||||
\(129\) | −1222.38 | −0.834297 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2281.74 | −1.52180 | −0.760901 | − | 0.648868i | \(-0.775243\pi\) | ||||
−0.760901 | + | 0.648868i | \(0.775243\pi\) | |||||||
\(132\) | 305.916 | 0.201717 | ||||||||
\(133\) | −749.241 | −0.488477 | ||||||||
\(134\) | −958.721 | −0.618066 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2458.37 | 1.55003 | ||||||||
\(137\) | −934.992 | −0.583078 | −0.291539 | − | 0.956559i | \(-0.594167\pi\) | ||||
−0.291539 | + | 0.956559i | \(0.594167\pi\) | |||||||
\(138\) | 419.954 | 0.259049 | ||||||||
\(139\) | −2874.22 | −1.75387 | −0.876937 | − | 0.480605i | \(-0.840417\pi\) | ||||
−0.876937 | + | 0.480605i | \(0.840417\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1431.50 | 0.854992 | ||||||||
\(142\) | −640.505 | −0.378521 | ||||||||
\(143\) | 303.123 | 0.177262 | ||||||||
\(144\) | 5.99782 | 0.00347096 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −706.192 | −0.400307 | ||||||||
\(147\) | 852.875 | 0.478530 | ||||||||
\(148\) | −1148.40 | −0.637826 | ||||||||
\(149\) | 2275.13 | 1.25091 | 0.625457 | − | 0.780259i | \(-0.284913\pi\) | ||||
0.625457 | + | 0.780259i | \(0.284913\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2396.11 | 1.29134 | 0.645670 | − | 0.763617i | \(-0.276578\pi\) | ||||
0.645670 | + | 0.763617i | \(0.276578\pi\) | |||||||
\(152\) | 2205.44 | 1.17687 | ||||||||
\(153\) | 980.997 | 0.518359 | ||||||||
\(154\) | 272.505 | 0.142591 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 221.294 | 0.113575 | ||||||||
\(157\) | −902.424 | −0.458734 | −0.229367 | − | 0.973340i | \(-0.573666\pi\) | ||||
−0.229367 | + | 0.973340i | \(0.573666\pi\) | |||||||
\(158\) | 1137.56 | 0.572782 | ||||||||
\(159\) | −1546.58 | −0.771393 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −617.348 | −0.302198 | ||||||||
\(162\) | −140.729 | −0.0682514 | ||||||||
\(163\) | 4028.26 | 1.93569 | 0.967846 | − | 0.251543i | \(-0.0809380\pi\) | ||||
0.967846 | + | 0.251543i | \(0.0809380\pi\) | |||||||
\(164\) | −893.992 | −0.425665 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 732.931 | 0.342690 | ||||||||
\(167\) | 982.313 | 0.455172 | 0.227586 | − | 0.973758i | \(-0.426917\pi\) | ||||
0.227586 | + | 0.973758i | \(0.426917\pi\) | |||||||
\(168\) | 518.433 | 0.238083 | ||||||||
\(169\) | −1977.73 | −0.900194 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 880.065 | 0.393569 | ||||||||
\(172\) | −2029.74 | −0.899802 | ||||||||
\(173\) | −1265.10 | −0.555975 | −0.277988 | − | 0.960585i | \(-0.589667\pi\) | ||||
−0.277988 | + | 0.960585i | \(0.589667\pi\) | |||||||
\(174\) | 307.809 | 0.134109 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 13.6420 | 0.00584262 | ||||||||
\(177\) | 1714.33 | 0.728007 | ||||||||
\(178\) | −738.634 | −0.311028 | ||||||||
\(179\) | −1471.61 | −0.614488 | −0.307244 | − | 0.951631i | \(-0.599407\pi\) | ||||
−0.307244 | + | 0.951631i | \(0.599407\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3742.99 | −1.53709 | −0.768547 | − | 0.639794i | \(-0.779020\pi\) | ||||
−0.768547 | + | 0.639794i | \(0.779020\pi\) | |||||||
\(182\) | 197.125 | 0.0802850 | ||||||||
\(183\) | 156.948 | 0.0633984 | ||||||||
\(184\) | 1817.20 | 0.728075 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 919.001 | 0.362282 | ||||||||
\(187\) | 2231.26 | 0.872547 | ||||||||
\(188\) | 2376.98 | 0.922122 | ||||||||
\(189\) | 206.877 | 0.0796197 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3953.76 | 1.49782 | 0.748911 | − | 0.662670i | \(-0.230577\pi\) | ||||
0.748911 | + | 0.662670i | \(0.230577\pi\) | |||||||
\(192\) | −930.485 | −0.349750 | ||||||||
\(193\) | 4739.26 | 1.76756 | 0.883780 | − | 0.467903i | \(-0.154990\pi\) | ||||
0.883780 | + | 0.467903i | \(0.154990\pi\) | |||||||
\(194\) | 1026.22 | 0.379786 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1416.19 | 0.516102 | ||||||||
\(197\) | 1912.59 | 0.691708 | 0.345854 | − | 0.938288i | \(-0.387589\pi\) | ||||
0.345854 | + | 0.938288i | \(0.387589\pi\) | |||||||
\(198\) | −320.087 | −0.114887 | ||||||||
\(199\) | −3291.81 | −1.17262 | −0.586308 | − | 0.810089i | \(-0.699419\pi\) | ||||
−0.586308 | + | 0.810089i | \(0.699419\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1655.44 | −0.580925 | ||||||||
\(202\) | 2664.39 | 0.928050 | ||||||||
\(203\) | −452.491 | −0.156446 | ||||||||
\(204\) | 1628.93 | 0.559058 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1249.01 | −0.422440 | ||||||||
\(207\) | 725.142 | 0.243482 | ||||||||
\(208\) | 9.86833 | 0.00328964 | ||||||||
\(209\) | 2001.69 | 0.662489 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 713.739 | 0.232871 | 0.116436 | − | 0.993198i | \(-0.462853\pi\) | ||||
0.116436 | + | 0.993198i | \(0.462853\pi\) | |||||||
\(212\) | −2568.06 | −0.831959 | ||||||||
\(213\) | −1105.97 | −0.355775 | ||||||||
\(214\) | −1641.57 | −0.524371 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −608.956 | −0.191825 | ||||||||
\(217\) | −1350.97 | −0.422625 | ||||||||
\(218\) | −2558.03 | −0.794732 | ||||||||
\(219\) | −1219.40 | −0.376252 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1614.05 | 0.491281 | ||||||||
\(222\) | 1201.60 | 0.363271 | ||||||||
\(223\) | 4536.63 | 1.36231 | 0.681155 | − | 0.732140i | \(-0.261478\pi\) | ||||
0.681155 | + | 0.732140i | \(0.261478\pi\) | |||||||
\(224\) | 1391.36 | 0.415019 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1425.11 | −0.419455 | ||||||||
\(227\) | −49.5501 | −0.0144879 | −0.00724396 | − | 0.999974i | \(-0.502306\pi\) | ||||
−0.00724396 | + | 0.999974i | \(0.502306\pi\) | |||||||
\(228\) | 1461.33 | 0.424470 | ||||||||
\(229\) | −2354.73 | −0.679498 | −0.339749 | − | 0.940516i | \(-0.610342\pi\) | ||||
−0.339749 | + | 0.940516i | \(0.610342\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 470.540 | 0.134023 | ||||||||
\(232\) | 1331.93 | 0.376921 | ||||||||
\(233\) | 2899.04 | 0.815116 | 0.407558 | − | 0.913179i | \(-0.366380\pi\) | ||||
0.407558 | + | 0.913179i | \(0.366380\pi\) | |||||||
\(234\) | −231.545 | −0.0646861 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2846.62 | 0.785166 | ||||||||
\(237\) | 1964.25 | 0.538362 | ||||||||
\(238\) | 1451.02 | 0.395192 | ||||||||
\(239\) | −1054.21 | −0.285319 | −0.142660 | − | 0.989772i | \(-0.545565\pi\) | ||||
−0.142660 | + | 0.989772i | \(0.545565\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6842.40 | 1.82887 | 0.914435 | − | 0.404732i | \(-0.132635\pi\) | ||||
0.914435 | + | 0.404732i | \(0.132635\pi\) | |||||||
\(242\) | 1584.44 | 0.420876 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 260.609 | 0.0683761 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 935.403 | 0.242435 | ||||||||
\(247\) | 1447.99 | 0.373009 | ||||||||
\(248\) | 3976.66 | 1.01822 | ||||||||
\(249\) | 1265.57 | 0.322096 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6021.53 | −1.51424 | −0.757122 | − | 0.653273i | \(-0.773395\pi\) | ||||
−0.757122 | + | 0.653273i | \(0.773395\pi\) | |||||||
\(252\) | 343.516 | 0.0858710 | ||||||||
\(253\) | 1649.33 | 0.409851 | ||||||||
\(254\) | 2890.78 | 0.714110 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4069.00 | −0.993408 | ||||||||
\(257\) | 539.470 | 0.130939 | 0.0654693 | − | 0.997855i | \(-0.479146\pi\) | ||||
0.0654693 | + | 0.997855i | \(0.479146\pi\) | |||||||
\(258\) | 2123.76 | 0.512478 | ||||||||
\(259\) | −1766.40 | −0.423779 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 531.499 | 0.126050 | ||||||||
\(262\) | 3964.28 | 0.934787 | ||||||||
\(263\) | 707.750 | 0.165938 | 0.0829690 | − | 0.996552i | \(-0.473560\pi\) | ||||
0.0829690 | + | 0.996552i | \(0.473560\pi\) | |||||||
\(264\) | −1385.06 | −0.322897 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1301.73 | 0.300053 | ||||||||
\(267\) | −1275.41 | −0.292337 | ||||||||
\(268\) | −2748.83 | −0.626536 | ||||||||
\(269\) | −2877.92 | −0.652304 | −0.326152 | − | 0.945317i | \(-0.605752\pi\) | ||||
−0.326152 | + | 0.945317i | \(0.605752\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3569.27 | 0.800065 | 0.400033 | − | 0.916501i | \(-0.368999\pi\) | ||||
0.400033 | + | 0.916501i | \(0.368999\pi\) | |||||||
\(272\) | 72.6401 | 0.0161928 | ||||||||
\(273\) | 340.379 | 0.0754604 | ||||||||
\(274\) | 1624.45 | 0.358163 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1204.09 | 0.262600 | ||||||||
\(277\) | −6956.58 | −1.50895 | −0.754477 | − | 0.656327i | \(-0.772109\pi\) | ||||
−0.754477 | + | 0.656327i | \(0.772109\pi\) | |||||||
\(278\) | 4993.67 | 1.07734 | ||||||||
\(279\) | 1586.86 | 0.340512 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3329.41 | 0.706819 | 0.353409 | − | 0.935469i | \(-0.385022\pi\) | ||||
0.353409 | + | 0.935469i | \(0.385022\pi\) | |||||||
\(282\) | −2487.08 | −0.525190 | ||||||||
\(283\) | 613.980 | 0.128966 | 0.0644829 | − | 0.997919i | \(-0.479460\pi\) | ||||
0.0644829 | + | 0.997919i | \(0.479460\pi\) | |||||||
\(284\) | −1836.45 | −0.383709 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −526.645 | −0.108885 | ||||||||
\(287\) | −1375.08 | −0.282816 | ||||||||
\(288\) | −1634.30 | −0.334383 | ||||||||
\(289\) | 6967.94 | 1.41827 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1772.00 | 0.356963 | ||||||||
\(292\) | −2024.79 | −0.405793 | ||||||||
\(293\) | 6494.46 | 1.29492 | 0.647458 | − | 0.762101i | \(-0.275832\pi\) | ||||
0.647458 | + | 0.762101i | \(0.275832\pi\) | |||||||
\(294\) | −1481.78 | −0.293944 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 5199.50 | 1.02100 | ||||||||
\(297\) | −552.700 | −0.107983 | ||||||||
\(298\) | −3952.81 | −0.768390 | ||||||||
\(299\) | 1193.09 | 0.230763 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3122.00 | −0.597838 | ||||||||
\(302\) | −4162.99 | −0.793222 | ||||||||
\(303\) | 4600.66 | 0.872281 | ||||||||
\(304\) | 65.1663 | 0.0122946 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1704.38 | −0.318409 | ||||||||
\(307\) | 967.468 | 0.179858 | 0.0899289 | − | 0.995948i | \(-0.471336\pi\) | ||||
0.0899289 | + | 0.995948i | \(0.471336\pi\) | |||||||
\(308\) | 781.323 | 0.144546 | ||||||||
\(309\) | −2156.69 | −0.397055 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1530.33 | −0.279026 | −0.139513 | − | 0.990220i | \(-0.544554\pi\) | ||||
−0.139513 | + | 0.990220i | \(0.544554\pi\) | |||||||
\(312\) | −1001.93 | −0.181804 | ||||||||
\(313\) | −7983.61 | −1.44173 | −0.720863 | − | 0.693078i | \(-0.756254\pi\) | ||||
−0.720863 | + | 0.693078i | \(0.756254\pi\) | |||||||
\(314\) | 1567.87 | 0.281783 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3261.61 | 0.580632 | ||||||||
\(317\) | 5281.05 | 0.935689 | 0.467844 | − | 0.883811i | \(-0.345031\pi\) | ||||
0.467844 | + | 0.883811i | \(0.345031\pi\) | |||||||
\(318\) | 2687.02 | 0.473838 | ||||||||
\(319\) | 1208.89 | 0.212178 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2834.53 | −0.492860 | ||||||||
\(322\) | 1072.58 | 0.185629 | ||||||||
\(323\) | 10658.5 | 1.83609 | ||||||||
\(324\) | −403.497 | −0.0691868 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −6998.69 | −1.18902 | ||||||||
\(327\) | −4417.00 | −0.746975 | ||||||||
\(328\) | 4047.63 | 0.681381 | ||||||||
\(329\) | 3656.11 | 0.612667 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2082.60 | −0.345830 | −0.172915 | − | 0.984937i | \(-0.555319\pi\) | ||||
−0.172915 | + | 0.984937i | \(0.555319\pi\) | |||||||
\(332\) | 2101.45 | 0.347386 | ||||||||
\(333\) | 2074.83 | 0.341441 | ||||||||
\(334\) | −1706.67 | −0.279595 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 15.3187 | 0.00248721 | ||||||||
\(337\) | −6924.52 | −1.11930 | −0.559648 | − | 0.828730i | \(-0.689064\pi\) | ||||
−0.559648 | + | 0.828730i | \(0.689064\pi\) | |||||||
\(338\) | 3436.10 | 0.552956 | ||||||||
\(339\) | −2460.76 | −0.394249 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3609.29 | 0.573179 | ||||||||
\(342\) | −1529.02 | −0.241755 | ||||||||
\(343\) | 4806.39 | 0.756620 | ||||||||
\(344\) | 9189.81 | 1.44035 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2197.98 | 0.341515 | ||||||||
\(347\) | 2159.18 | 0.334037 | 0.167019 | − | 0.985954i | \(-0.446586\pi\) | ||||
0.167019 | + | 0.985954i | \(0.446586\pi\) | |||||||
\(348\) | 882.546 | 0.135947 | ||||||||
\(349\) | −11809.8 | −1.81136 | −0.905679 | − | 0.423963i | \(-0.860639\pi\) | ||||
−0.905679 | + | 0.423963i | \(0.860639\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −399.813 | −0.0607989 | ||||||||
\(352\) | −3717.20 | −0.562862 | ||||||||
\(353\) | −8267.86 | −1.24661 | −0.623306 | − | 0.781978i | \(-0.714211\pi\) | ||||
−0.623306 | + | 0.781978i | \(0.714211\pi\) | |||||||
\(354\) | −2978.48 | −0.447187 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −2117.80 | −0.315290 | ||||||||
\(357\) | 2505.51 | 0.371444 | ||||||||
\(358\) | 2556.77 | 0.377457 | ||||||||
\(359\) | 4656.29 | 0.684539 | 0.342269 | − | 0.939602i | \(-0.388804\pi\) | ||||
0.342269 | + | 0.939602i | \(0.388804\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2702.90 | 0.394066 | ||||||||
\(362\) | 6503.05 | 0.944179 | ||||||||
\(363\) | 2735.89 | 0.395584 | ||||||||
\(364\) | 565.194 | 0.0813852 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −272.680 | −0.0389433 | ||||||||
\(367\) | 519.600 | 0.0739044 | 0.0369522 | − | 0.999317i | \(-0.488235\pi\) | ||||
0.0369522 | + | 0.999317i | \(0.488235\pi\) | |||||||
\(368\) | 53.6947 | 0.00760606 | ||||||||
\(369\) | 1615.18 | 0.227867 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3950.02 | −0.552762 | ||||||||
\(372\) | 2634.95 | 0.367247 | ||||||||
\(373\) | 4202.26 | 0.583337 | 0.291669 | − | 0.956519i | \(-0.405790\pi\) | ||||
0.291669 | + | 0.956519i | \(0.405790\pi\) | |||||||
\(374\) | −3876.59 | −0.535973 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −10762.0 | −1.47608 | ||||||||
\(377\) | 874.486 | 0.119465 | ||||||||
\(378\) | −359.428 | −0.0489074 | ||||||||
\(379\) | 2855.16 | 0.386964 | 0.193482 | − | 0.981104i | \(-0.438022\pi\) | ||||
0.193482 | + | 0.981104i | \(0.438022\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4991.58 | 0.671197 | ||||||||
\(382\) | −6869.26 | −0.920057 | ||||||||
\(383\) | 5756.86 | 0.768046 | 0.384023 | − | 0.923324i | \(-0.374538\pi\) | ||||
0.384023 | + | 0.923324i | \(0.374538\pi\) | |||||||
\(384\) | −2741.52 | −0.364330 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −8233.97 | −1.08575 | ||||||||
\(387\) | 3667.13 | 0.481682 | ||||||||
\(388\) | 2942.37 | 0.384990 | ||||||||
\(389\) | 10994.1 | 1.43296 | 0.716481 | − | 0.697607i | \(-0.245752\pi\) | ||||
0.716481 | + | 0.697607i | \(0.245752\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8782.25 | 1.13590 | ||||||||
\(392\) | −6411.90 | −0.826148 | ||||||||
\(393\) | 6845.21 | 0.878613 | ||||||||
\(394\) | −3322.93 | −0.424890 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −917.749 | −0.116461 | ||||||||
\(397\) | 163.743 | 0.0207004 | 0.0103502 | − | 0.999946i | \(-0.496705\pi\) | ||||
0.0103502 | + | 0.999946i | \(0.496705\pi\) | |||||||
\(398\) | 5719.19 | 0.720294 | ||||||||
\(399\) | 2247.72 | 0.282022 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8096.74 | 1.00831 | 0.504154 | − | 0.863614i | \(-0.331804\pi\) | ||||
0.504154 | + | 0.863614i | \(0.331804\pi\) | |||||||
\(402\) | 2876.16 | 0.356841 | ||||||||
\(403\) | 2610.89 | 0.322724 | ||||||||
\(404\) | 7639.32 | 0.940768 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 786.156 | 0.0960992 | ||||||||
\(407\) | 4719.16 | 0.574743 | ||||||||
\(408\) | −7375.12 | −0.894909 | ||||||||
\(409\) | 5493.78 | 0.664181 | 0.332091 | − | 0.943247i | \(-0.392246\pi\) | ||||
0.332091 | + | 0.943247i | \(0.392246\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2804.98 | 0.336640 | ||||||||
\(412\) | −3581.15 | −0.428229 | ||||||||
\(413\) | 4378.48 | 0.521673 | ||||||||
\(414\) | −1259.86 | −0.149562 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2688.95 | −0.316915 | ||||||||
\(417\) | 8622.67 | 1.01260 | ||||||||
\(418\) | −3477.74 | −0.406942 | ||||||||
\(419\) | 11739.7 | 1.36879 | 0.684393 | − | 0.729114i | \(-0.260067\pi\) | ||||
0.684393 | + | 0.729114i | \(0.260067\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8506.36 | 0.984738 | 0.492369 | − | 0.870387i | \(-0.336131\pi\) | ||||
0.492369 | + | 0.870387i | \(0.336131\pi\) | |||||||
\(422\) | −1240.05 | −0.143044 | ||||||||
\(423\) | −4294.49 | −0.493630 | ||||||||
\(424\) | 11627.1 | 1.33175 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1921.52 | 0.218539 | ||||||||
\(427\) | 400.851 | 0.0454298 | ||||||||
\(428\) | −4706.69 | −0.531557 | ||||||||
\(429\) | −909.368 | −0.102342 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15772.5 | −1.76272 | −0.881362 | − | 0.472441i | \(-0.843373\pi\) | ||||
−0.881362 | + | 0.472441i | \(0.843373\pi\) | |||||||
\(432\) | −17.9935 | −0.00200396 | ||||||||
\(433\) | 5269.35 | 0.584824 | 0.292412 | − | 0.956292i | \(-0.405542\pi\) | ||||
0.292412 | + | 0.956292i | \(0.405542\pi\) | |||||||
\(434\) | 2347.17 | 0.259603 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7334.35 | −0.805624 | ||||||||
\(437\) | 7878.67 | 0.862443 | ||||||||
\(438\) | 2118.58 | 0.231117 | ||||||||
\(439\) | 6863.61 | 0.746201 | 0.373100 | − | 0.927791i | \(-0.378295\pi\) | ||||
0.373100 | + | 0.927791i | \(0.378295\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2558.63 | −0.276280 | ||||||||
\(442\) | −2804.25 | −0.301775 | ||||||||
\(443\) | −16108.2 | −1.72759 | −0.863795 | − | 0.503843i | \(-0.831919\pi\) | ||||
−0.863795 | + | 0.503843i | \(0.831919\pi\) | |||||||
\(444\) | 3445.21 | 0.368249 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −7881.92 | −0.836816 | ||||||||
\(447\) | −6825.40 | −0.722215 | ||||||||
\(448\) | −2376.50 | −0.250623 | ||||||||
\(449\) | 12908.2 | 1.35674 | 0.678370 | − | 0.734720i | \(-0.262687\pi\) | ||||
0.678370 | + | 0.734720i | \(0.262687\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3673.70 | 0.383565 | ||||||||
\(452\) | −4086.06 | −0.425203 | ||||||||
\(453\) | −7188.32 | −0.745556 | ||||||||
\(454\) | 86.0883 | 0.00889939 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6616.31 | −0.679467 | ||||||||
\(457\) | −10742.8 | −1.09962 | −0.549812 | − | 0.835288i | \(-0.685301\pi\) | ||||
−0.549812 | + | 0.835288i | \(0.685301\pi\) | |||||||
\(458\) | 4091.11 | 0.417390 | ||||||||
\(459\) | −2942.99 | −0.299275 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14421.4 | 1.45698 | 0.728492 | − | 0.685054i | \(-0.240222\pi\) | ||||
0.728492 | + | 0.685054i | \(0.240222\pi\) | |||||||
\(462\) | −817.515 | −0.0823252 | ||||||||
\(463\) | −11600.6 | −1.16442 | −0.582209 | − | 0.813039i | \(-0.697812\pi\) | ||||
−0.582209 | + | 0.813039i | \(0.697812\pi\) | |||||||
\(464\) | 39.3560 | 0.00393762 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5036.78 | −0.500696 | ||||||||
\(467\) | 3093.46 | 0.306527 | 0.153264 | − | 0.988185i | \(-0.451022\pi\) | ||||
0.153264 | + | 0.988185i | \(0.451022\pi\) | |||||||
\(468\) | −663.882 | −0.0655726 | ||||||||
\(469\) | −4228.07 | −0.416277 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2707.27 | 0.264850 | ||||||||
\(472\) | −12888.3 | −1.25685 | ||||||||
\(473\) | 8340.84 | 0.810808 | ||||||||
\(474\) | −3412.69 | −0.330696 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 4160.35 | 0.400608 | ||||||||
\(477\) | 4639.73 | 0.445364 | ||||||||
\(478\) | 1831.59 | 0.175261 | ||||||||
\(479\) | −17950.9 | −1.71231 | −0.856156 | − | 0.516717i | \(-0.827154\pi\) | ||||
−0.856156 | + | 0.516717i | \(0.827154\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3413.75 | 0.323604 | ||||||||
\(482\) | −11888.0 | −1.12341 | ||||||||
\(483\) | 1852.04 | 0.174474 | ||||||||
\(484\) | 4542.90 | 0.426644 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 422.188 | 0.0394050 | ||||||||
\(487\) | −17260.9 | −1.60609 | −0.803043 | − | 0.595921i | \(-0.796787\pi\) | ||||
−0.803043 | + | 0.595921i | \(0.796787\pi\) | |||||||
\(488\) | −1179.93 | −0.109453 | ||||||||
\(489\) | −12084.8 | −1.11757 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8189.74 | 0.752745 | 0.376372 | − | 0.926468i | \(-0.377171\pi\) | ||||
0.376372 | + | 0.926468i | \(0.377171\pi\) | |||||||
\(492\) | 2681.98 | 0.245758 | ||||||||
\(493\) | 6437.03 | 0.588051 | ||||||||
\(494\) | −2515.73 | −0.229126 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 117.502 | 0.0106371 | ||||||||
\(497\) | −2824.70 | −0.254940 | ||||||||
\(498\) | −2198.79 | −0.197852 | ||||||||
\(499\) | −10653.8 | −0.955767 | −0.477884 | − | 0.878423i | \(-0.658596\pi\) | ||||
−0.477884 | + | 0.878423i | \(0.658596\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2946.94 | −0.262793 | ||||||||
\(502\) | 10461.8 | 0.930144 | ||||||||
\(503\) | −6067.02 | −0.537803 | −0.268902 | − | 0.963168i | \(-0.586661\pi\) | ||||
−0.268902 | + | 0.963168i | \(0.586661\pi\) | |||||||
\(504\) | −1555.30 | −0.137457 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −2865.54 | −0.251756 | ||||||||
\(507\) | 5933.18 | 0.519727 | ||||||||
\(508\) | 8288.43 | 0.723897 | ||||||||
\(509\) | −3141.27 | −0.273545 | −0.136773 | − | 0.990602i | \(-0.543673\pi\) | ||||
−0.136773 | + | 0.990602i | \(0.543673\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3114.39 | −0.269613 | ||||||||
\(512\) | −241.260 | −0.0208247 | ||||||||
\(513\) | −2640.19 | −0.227227 | ||||||||
\(514\) | −937.275 | −0.0804308 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 6089.21 | 0.519501 | ||||||||
\(517\) | −9767.76 | −0.830920 | ||||||||
\(518\) | 3068.94 | 0.260311 | ||||||||
\(519\) | 3795.30 | 0.320992 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15548.5 | 1.30747 | 0.653737 | − | 0.756722i | \(-0.273200\pi\) | ||||
0.653737 | + | 0.756722i | \(0.273200\pi\) | |||||||
\(522\) | −923.426 | −0.0774277 | ||||||||
\(523\) | −19848.9 | −1.65952 | −0.829761 | − | 0.558119i | \(-0.811523\pi\) | ||||
−0.829761 | + | 0.558119i | \(0.811523\pi\) | |||||||
\(524\) | 11366.3 | 0.947598 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1229.64 | −0.101930 | ||||||||
\(527\) | 19218.6 | 1.58857 | ||||||||
\(528\) | −40.9259 | −0.00337324 | ||||||||
\(529\) | −5675.26 | −0.466447 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5143.00 | −0.420315 | ||||||||
\(532\) | 3732.30 | 0.304165 | ||||||||
\(533\) | 2657.49 | 0.215963 | ||||||||
\(534\) | 2215.90 | 0.179572 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 12445.6 | 1.00292 | ||||||||
\(537\) | 4414.83 | 0.354775 | ||||||||
\(538\) | 5000.09 | 0.400686 | ||||||||
\(539\) | −5819.56 | −0.465058 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13213.7 | −1.05010 | −0.525048 | − | 0.851072i | \(-0.675953\pi\) | ||||
−0.525048 | + | 0.851072i | \(0.675953\pi\) | |||||||
\(542\) | −6201.24 | −0.491451 | ||||||||
\(543\) | 11229.0 | 0.887441 | ||||||||
\(544\) | −19793.2 | −1.55997 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −591.374 | −0.0463525 | ||||||||
\(547\) | 6622.55 | 0.517660 | 0.258830 | − | 0.965923i | \(-0.416663\pi\) | ||||
0.258830 | + | 0.965923i | \(0.416663\pi\) | |||||||
\(548\) | 4657.61 | 0.363072 | ||||||||
\(549\) | −470.843 | −0.0366031 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5774.74 | 0.446483 | ||||||||
\(552\) | −5451.61 | −0.420355 | ||||||||
\(553\) | 5016.78 | 0.385778 | ||||||||
\(554\) | 12086.3 | 0.926894 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 14317.8 | 1.09210 | ||||||||
\(557\) | 15042.5 | 1.14430 | 0.572148 | − | 0.820150i | \(-0.306110\pi\) | ||||
0.572148 | + | 0.820150i | \(0.306110\pi\) | |||||||
\(558\) | −2757.00 | −0.209164 | ||||||||
\(559\) | 6033.61 | 0.456519 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6693.79 | −0.503765 | ||||||||
\(562\) | −5784.51 | −0.434173 | ||||||||
\(563\) | 3495.16 | 0.261641 | 0.130820 | − | 0.991406i | \(-0.458239\pi\) | ||||
0.130820 | + | 0.991406i | \(0.458239\pi\) | |||||||
\(564\) | −7130.93 | −0.532387 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1066.73 | −0.0792189 | ||||||||
\(567\) | −620.632 | −0.0459684 | ||||||||
\(568\) | 8314.68 | 0.614219 | ||||||||
\(569\) | 7467.34 | 0.550171 | 0.275085 | − | 0.961420i | \(-0.411294\pi\) | ||||
0.275085 | + | 0.961420i | \(0.411294\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15504.9 | −1.13635 | −0.568177 | − | 0.822906i | \(-0.692351\pi\) | ||||
−0.568177 | + | 0.822906i | \(0.692351\pi\) | |||||||
\(572\) | −1509.99 | −0.110377 | ||||||||
\(573\) | −11861.3 | −0.864768 | ||||||||
\(574\) | 2389.06 | 0.173724 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2791.45 | 0.201928 | ||||||||
\(577\) | 25877.8 | 1.86708 | 0.933542 | − | 0.358468i | \(-0.116701\pi\) | ||||
0.933542 | + | 0.358468i | \(0.116701\pi\) | |||||||
\(578\) | −12106.1 | −0.871188 | ||||||||
\(579\) | −14217.8 | −1.02050 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3232.31 | 0.230807 | ||||||||
\(582\) | −3078.66 | −0.219269 | ||||||||
\(583\) | 10553.0 | 0.749675 | ||||||||
\(584\) | 9167.39 | 0.649571 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −11283.5 | −0.795418 | ||||||||
\(587\) | 498.887 | 0.0350788 | 0.0175394 | − | 0.999846i | \(-0.494417\pi\) | ||||
0.0175394 | + | 0.999846i | \(0.494417\pi\) | |||||||
\(588\) | −4248.56 | −0.297972 | ||||||||
\(589\) | 17241.2 | 1.20613 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5737.77 | −0.399358 | ||||||||
\(592\) | 153.635 | 0.0106662 | ||||||||
\(593\) | −16095.6 | −1.11462 | −0.557309 | − | 0.830305i | \(-0.688166\pi\) | ||||
−0.557309 | + | 0.830305i | \(0.688166\pi\) | |||||||
\(594\) | 960.260 | 0.0663299 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −11333.5 | −0.778920 | ||||||||
\(597\) | 9875.44 | 0.677010 | ||||||||
\(598\) | −2072.87 | −0.141749 | ||||||||
\(599\) | −998.977 | −0.0681421 | −0.0340710 | − | 0.999419i | \(-0.510847\pi\) | ||||
−0.0340710 | + | 0.999419i | \(0.510847\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12876.3 | −0.873937 | −0.436968 | − | 0.899477i | \(-0.643948\pi\) | ||||
−0.436968 | + | 0.899477i | \(0.643948\pi\) | |||||||
\(602\) | 5424.16 | 0.367230 | ||||||||
\(603\) | 4966.33 | 0.335397 | ||||||||
\(604\) | −11936.1 | −0.804093 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −7993.18 | −0.535810 | ||||||||
\(607\) | 12236.9 | 0.818254 | 0.409127 | − | 0.912477i | \(-0.365833\pi\) | ||||
0.409127 | + | 0.912477i | \(0.365833\pi\) | |||||||
\(608\) | −17756.7 | −1.18442 | ||||||||
\(609\) | 1357.47 | 0.0903244 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7065.81 | −0.467843 | ||||||||
\(612\) | −4886.79 | −0.322772 | ||||||||
\(613\) | 1839.73 | 0.121217 | 0.0606085 | − | 0.998162i | \(-0.480696\pi\) | ||||
0.0606085 | + | 0.998162i | \(0.480696\pi\) | |||||||
\(614\) | −1680.88 | −0.110480 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3537.51 | −0.231380 | ||||||||
\(617\) | 3461.32 | 0.225847 | 0.112924 | − | 0.993604i | \(-0.463978\pi\) | ||||
0.112924 | + | 0.993604i | \(0.463978\pi\) | |||||||
\(618\) | 3747.03 | 0.243896 | ||||||||
\(619\) | −4899.75 | −0.318155 | −0.159077 | − | 0.987266i | \(-0.550852\pi\) | ||||
−0.159077 | + | 0.987266i | \(0.550852\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2175.43 | −0.140575 | ||||||||
\(622\) | 2658.80 | 0.171396 | ||||||||
\(623\) | −3257.46 | −0.209482 | ||||||||
\(624\) | −29.6050 | −0.00189928 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 13870.7 | 0.885599 | ||||||||
\(627\) | −6005.08 | −0.382488 | ||||||||
\(628\) | 4495.38 | 0.285645 | ||||||||
\(629\) | 25128.4 | 1.59290 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2129.24 | −0.134332 | −0.0671661 | − | 0.997742i | \(-0.521396\pi\) | ||||
−0.0671661 | + | 0.997742i | \(0.521396\pi\) | |||||||
\(632\) | −14767.2 | −0.929443 | ||||||||
\(633\) | −2141.22 | −0.134448 | ||||||||
\(634\) | −9175.29 | −0.574759 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 7704.19 | 0.480332 | ||||||||
\(637\) | −4209.76 | −0.261847 | ||||||||
\(638\) | −2100.32 | −0.130333 | ||||||||
\(639\) | 3317.92 | 0.205407 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20797.9 | −1.28154 | −0.640771 | − | 0.767732i | \(-0.721385\pi\) | ||||
−0.640771 | + | 0.767732i | \(0.721385\pi\) | |||||||
\(642\) | 4924.71 | 0.302746 | ||||||||
\(643\) | −6395.45 | −0.392243 | −0.196121 | − | 0.980580i | \(-0.562835\pi\) | ||||
−0.196121 | + | 0.980580i | \(0.562835\pi\) | |||||||
\(644\) | 3075.29 | 0.188173 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −18518.1 | −1.12784 | ||||||||
\(647\) | −9964.69 | −0.605491 | −0.302745 | − | 0.953071i | \(-0.597903\pi\) | ||||
−0.302745 | + | 0.953071i | \(0.597903\pi\) | |||||||
\(648\) | 1826.87 | 0.110750 | ||||||||
\(649\) | −11697.7 | −0.707510 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4052.90 | 0.244003 | ||||||||
\(652\) | −20066.6 | −1.20532 | ||||||||
\(653\) | −29629.0 | −1.77561 | −0.887803 | − | 0.460223i | \(-0.847769\pi\) | ||||
−0.887803 | + | 0.460223i | \(0.847769\pi\) | |||||||
\(654\) | 7674.09 | 0.458839 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 119.599 | 0.00711825 | ||||||||
\(657\) | 3658.19 | 0.217229 | ||||||||
\(658\) | −6352.11 | −0.376339 | ||||||||
\(659\) | 18698.2 | 1.10528 | 0.552640 | − | 0.833420i | \(-0.313621\pi\) | ||||
0.552640 | + | 0.833420i | \(0.313621\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16576.7 | 0.975430 | 0.487715 | − | 0.873003i | \(-0.337831\pi\) | ||||
0.487715 | + | 0.873003i | \(0.337831\pi\) | |||||||
\(662\) | 3618.30 | 0.212431 | ||||||||
\(663\) | −4842.16 | −0.283641 | ||||||||
\(664\) | −9514.50 | −0.556076 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3604.80 | −0.209734 | ||||||||
\(667\) | 4758.18 | 0.276218 | ||||||||
\(668\) | −4893.34 | −0.283427 | ||||||||
\(669\) | −13609.9 | −0.786530 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1070.93 | −0.0616135 | ||||||||
\(672\) | −4174.08 | −0.239611 | ||||||||
\(673\) | 8889.49 | 0.509160 | 0.254580 | − | 0.967052i | \(-0.418063\pi\) | ||||
0.254580 | + | 0.967052i | \(0.418063\pi\) | |||||||
\(674\) | 12030.7 | 0.687542 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 9851.95 | 0.560534 | ||||||||
\(677\) | −22803.3 | −1.29454 | −0.647270 | − | 0.762261i | \(-0.724089\pi\) | ||||
−0.647270 | + | 0.762261i | \(0.724089\pi\) | |||||||
\(678\) | 4275.33 | 0.242172 | ||||||||
\(679\) | 4525.76 | 0.255792 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 148.650 | 0.00836460 | ||||||||
\(682\) | −6270.77 | −0.352082 | ||||||||
\(683\) | 7599.47 | 0.425748 | 0.212874 | − | 0.977080i | \(-0.431718\pi\) | ||||
0.212874 | + | 0.977080i | \(0.431718\pi\) | |||||||
\(684\) | −4384.00 | −0.245068 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −8350.61 | −0.464764 | ||||||||
\(687\) | 7064.20 | 0.392308 | ||||||||
\(688\) | 271.541 | 0.0150471 | ||||||||
\(689\) | 7633.83 | 0.422099 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12622.0 | −0.694883 | −0.347441 | − | 0.937702i | \(-0.612949\pi\) | ||||
−0.347441 | + | 0.937702i | \(0.612949\pi\) | |||||||
\(692\) | 6302.03 | 0.346195 | ||||||||
\(693\) | −1411.62 | −0.0773780 | ||||||||
\(694\) | −3751.36 | −0.205187 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −3995.80 | −0.217616 | ||||||||
\(697\) | 19561.6 | 1.06305 | ||||||||
\(698\) | 20518.3 | 1.11265 | ||||||||
\(699\) | −8697.11 | −0.470608 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4783.64 | −0.257740 | −0.128870 | − | 0.991662i | \(-0.541135\pi\) | ||||
−0.128870 | + | 0.991662i | \(0.541135\pi\) | |||||||
\(702\) | 694.634 | 0.0373465 | ||||||||
\(703\) | 22543.0 | 1.20942 | ||||||||
\(704\) | 6349.12 | 0.339903 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 14364.6 | 0.765747 | ||||||||
\(707\) | 11750.3 | 0.625056 | ||||||||
\(708\) | −8539.86 | −0.453316 | ||||||||
\(709\) | −33251.4 | −1.76133 | −0.880664 | − | 0.473741i | \(-0.842903\pi\) | ||||
−0.880664 | + | 0.473741i | \(0.842903\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5892.75 | −0.310823 | ||||||||
\(712\) | 9588.53 | 0.504699 | ||||||||
\(713\) | 14206.1 | 0.746177 | ||||||||
\(714\) | −4353.06 | −0.228164 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 7330.76 | 0.382630 | ||||||||
\(717\) | 3162.64 | 0.164729 | ||||||||
\(718\) | −8089.82 | −0.420487 | ||||||||
\(719\) | 12428.5 | 0.644652 | 0.322326 | − | 0.946629i | \(-0.395535\pi\) | ||||
0.322326 | + | 0.946629i | \(0.395535\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5508.28 | −0.284520 | ||||||||
\(722\) | −4696.01 | −0.242060 | ||||||||
\(723\) | −20527.2 | −1.05590 | ||||||||
\(724\) | 18645.5 | 0.957119 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −4753.33 | −0.242993 | ||||||||
\(727\) | −8782.11 | −0.448020 | −0.224010 | − | 0.974587i | \(-0.571915\pi\) | ||||
−0.224010 | + | 0.974587i | \(0.571915\pi\) | |||||||
\(728\) | −2558.97 | −0.130277 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 44412.9 | 2.24716 | ||||||||
\(732\) | −781.827 | −0.0394770 | ||||||||
\(733\) | −26084.3 | −1.31438 | −0.657192 | − | 0.753723i | \(-0.728256\pi\) | ||||
−0.657192 | + | 0.753723i | \(0.728256\pi\) | |||||||
\(734\) | −902.753 | −0.0453967 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −14630.9 | −0.732748 | ||||||||
\(737\) | 11295.8 | 0.564569 | ||||||||
\(738\) | −2806.21 | −0.139970 | ||||||||
\(739\) | −23385.1 | −1.16405 | −0.582027 | − | 0.813170i | \(-0.697740\pi\) | ||||
−0.582027 | + | 0.813170i | \(0.697740\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4343.96 | −0.215357 | ||||||||
\(742\) | 6862.75 | 0.339541 | ||||||||
\(743\) | −26389.6 | −1.30302 | −0.651508 | − | 0.758642i | \(-0.725863\pi\) | ||||
−0.651508 | + | 0.758642i | \(0.725863\pi\) | |||||||
\(744\) | −11930.0 | −0.587868 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −7301.00 | −0.358322 | ||||||||
\(747\) | −3796.70 | −0.185962 | ||||||||
\(748\) | −11114.9 | −0.543318 | ||||||||
\(749\) | −7239.52 | −0.353172 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17725.3 | 0.861257 | 0.430629 | − | 0.902529i | \(-0.358292\pi\) | ||||
0.430629 | + | 0.902529i | \(0.358292\pi\) | |||||||
\(752\) | −317.995 | −0.0154203 | ||||||||
\(753\) | 18064.6 | 0.874250 | ||||||||
\(754\) | −1519.33 | −0.0733830 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1030.55 | −0.0495777 | ||||||||
\(757\) | 4478.94 | 0.215046 | 0.107523 | − | 0.994203i | \(-0.465708\pi\) | ||||
0.107523 | + | 0.994203i | \(0.465708\pi\) | |||||||
\(758\) | −4960.54 | −0.237698 | ||||||||
\(759\) | −4947.98 | −0.236627 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1368.09 | 0.0651683 | 0.0325841 | − | 0.999469i | \(-0.489626\pi\) | ||||
0.0325841 | + | 0.999469i | \(0.489626\pi\) | |||||||
\(762\) | −8672.35 | −0.412292 | ||||||||
\(763\) | −11281.2 | −0.535265 | ||||||||
\(764\) | −19695.5 | −0.932666 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −10001.9 | −0.471782 | ||||||||
\(767\) | −8461.88 | −0.398358 | ||||||||
\(768\) | 12207.0 | 0.573544 | ||||||||
\(769\) | 16530.6 | 0.775176 | 0.387588 | − | 0.921833i | \(-0.373308\pi\) | ||||
0.387588 | + | 0.921833i | \(0.373308\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1618.41 | −0.0755975 | ||||||||
\(772\) | −23608.4 | −1.10063 | ||||||||
\(773\) | 8002.04 | 0.372333 | 0.186166 | − | 0.982518i | \(-0.440394\pi\) | ||||
0.186166 | + | 0.982518i | \(0.440394\pi\) | |||||||
\(774\) | −6371.27 | −0.295879 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −13321.8 | −0.616271 | ||||||||
\(777\) | 5299.19 | 0.244669 | ||||||||
\(778\) | −19101.1 | −0.880215 | ||||||||
\(779\) | 17548.9 | 0.807131 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7546.56 | 0.345758 | ||||||||
\(782\) | −15258.3 | −0.697742 | ||||||||
\(783\) | −1594.50 | −0.0727749 | ||||||||
\(784\) | −189.459 | −0.00863061 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −11892.8 | −0.539699 | ||||||||
\(787\) | 19432.4 | 0.880166 | 0.440083 | − | 0.897957i | \(-0.354949\pi\) | ||||
0.440083 | + | 0.897957i | \(0.354949\pi\) | |||||||
\(788\) | −9527.47 | −0.430713 | ||||||||
\(789\) | −2123.25 | −0.0958044 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6284.89 | −0.282510 | ||||||||
\(792\) | 4155.19 | 0.186424 | ||||||||
\(793\) | −774.687 | −0.0346910 | ||||||||
\(794\) | −284.487 | −0.0127155 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 16398.0 | 0.730165 | ||||||||
\(797\) | 39528.1 | 1.75678 | 0.878391 | − | 0.477942i | \(-0.158617\pi\) | ||||
0.878391 | + | 0.477942i | \(0.158617\pi\) | |||||||
\(798\) | −3905.19 | −0.173236 | ||||||||
\(799\) | −52010.9 | −2.30290 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3826.24 | 0.168781 | ||||||||
\(802\) | −14067.3 | −0.619366 | ||||||||
\(803\) | 8320.49 | 0.365659 | ||||||||
\(804\) | 8246.50 | 0.361731 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −4536.15 | −0.198237 | ||||||||
\(807\) | 8633.76 | 0.376608 | ||||||||
\(808\) | −34587.7 | −1.50593 | ||||||||
\(809\) | −2308.05 | −0.100305 | −0.0501526 | − | 0.998742i | \(-0.515971\pi\) | ||||
−0.0501526 | + | 0.998742i | \(0.515971\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4243.29 | −0.183726 | −0.0918632 | − | 0.995772i | \(-0.529282\pi\) | ||||
−0.0918632 | + | 0.995772i | \(0.529282\pi\) | |||||||
\(812\) | 2254.06 | 0.0974162 | ||||||||
\(813\) | −10707.8 | −0.461918 | ||||||||
\(814\) | −8199.07 | −0.353043 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −217.920 | −0.00934894 | ||||||||
\(817\) | 39843.4 | 1.70617 | ||||||||
\(818\) | −9544.89 | −0.407982 | ||||||||
\(819\) | −1021.14 | −0.0435671 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 28705.4 | 1.22025 | 0.610124 | − | 0.792306i | \(-0.291120\pi\) | ||||
0.610124 | + | 0.792306i | \(0.291120\pi\) | |||||||
\(822\) | −4873.36 | −0.206786 | ||||||||
\(823\) | −28010.8 | −1.18639 | −0.593193 | − | 0.805061i | \(-0.702133\pi\) | ||||
−0.593193 | + | 0.805061i | \(0.702133\pi\) | |||||||
\(824\) | 16214.0 | 0.685486 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7607.16 | −0.320444 | ||||||||
\(827\) | −8868.42 | −0.372896 | −0.186448 | − | 0.982465i | \(-0.559698\pi\) | ||||
−0.186448 | + | 0.982465i | \(0.559698\pi\) | |||||||
\(828\) | −3612.26 | −0.151612 | ||||||||
\(829\) | −24216.6 | −1.01457 | −0.507283 | − | 0.861779i | \(-0.669350\pi\) | ||||
−0.507283 | + | 0.861779i | \(0.669350\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 20869.7 | 0.871195 | ||||||||
\(832\) | 4592.83 | 0.191380 | ||||||||
\(833\) | −30987.7 | −1.28891 | ||||||||
\(834\) | −14981.0 | −0.622003 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −9971.34 | −0.412519 | ||||||||
\(837\) | −4760.58 | −0.196594 | ||||||||
\(838\) | −20396.5 | −0.840794 | ||||||||
\(839\) | 33351.0 | 1.37235 | 0.686177 | − | 0.727435i | \(-0.259288\pi\) | ||||
0.686177 | + | 0.727435i | \(0.259288\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20901.4 | −0.857003 | ||||||||
\(842\) | −14778.9 | −0.604888 | ||||||||
\(843\) | −9988.24 | −0.408082 | ||||||||
\(844\) | −3555.45 | −0.145004 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 7461.24 | 0.303218 | ||||||||
\(847\) | 6987.58 | 0.283467 | ||||||||
\(848\) | 343.559 | 0.0139126 | ||||||||
\(849\) | −1841.94 | −0.0744585 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 18574.6 | 0.748214 | ||||||||
\(852\) | 5509.35 | 0.221534 | ||||||||
\(853\) | 25395.6 | 1.01938 | 0.509688 | − | 0.860359i | \(-0.329761\pi\) | ||||
0.509688 | + | 0.860359i | \(0.329761\pi\) | |||||||
\(854\) | −696.437 | −0.0279059 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 21310.0 | 0.850887 | ||||||||
\(857\) | −28013.4 | −1.11659 | −0.558296 | − | 0.829642i | \(-0.688545\pi\) | ||||
−0.558296 | + | 0.829642i | \(0.688545\pi\) | |||||||
\(858\) | 1579.93 | 0.0628649 | ||||||||
\(859\) | 7094.28 | 0.281786 | 0.140893 | − | 0.990025i | \(-0.455003\pi\) | ||||
0.140893 | + | 0.990025i | \(0.455003\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4125.23 | 0.163284 | ||||||||
\(862\) | 27403.1 | 1.08278 | ||||||||
\(863\) | 12168.3 | 0.479969 | 0.239984 | − | 0.970777i | \(-0.422858\pi\) | ||||
0.239984 | + | 0.970777i | \(0.422858\pi\) | |||||||
\(864\) | 4902.91 | 0.193056 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −9154.96 | −0.359236 | ||||||||
\(867\) | −20903.8 | −0.818836 | ||||||||
\(868\) | 6729.78 | 0.263161 | ||||||||
\(869\) | −13403.0 | −0.523205 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8171.20 | 0.317876 | ||||||||
\(872\) | 33206.9 | 1.28960 | ||||||||
\(873\) | −5315.99 | −0.206093 | ||||||||
\(874\) | −13688.4 | −0.529767 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 6074.36 | 0.234285 | ||||||||
\(877\) | 5576.23 | 0.214704 | 0.107352 | − | 0.994221i | \(-0.465763\pi\) | ||||
0.107352 | + | 0.994221i | \(0.465763\pi\) | |||||||
\(878\) | −11924.8 | −0.458364 | ||||||||
\(879\) | −19483.4 | −0.747620 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 44427.2 | 1.69897 | 0.849483 | − | 0.527616i | \(-0.176914\pi\) | ||||
0.849483 | + | 0.527616i | \(0.176914\pi\) | |||||||
\(882\) | 4445.35 | 0.169708 | ||||||||
\(883\) | −28781.0 | −1.09689 | −0.548447 | − | 0.836186i | \(-0.684781\pi\) | ||||
−0.548447 | + | 0.836186i | \(0.684781\pi\) | |||||||
\(884\) | −8040.33 | −0.305911 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 27986.3 | 1.06119 | ||||||||
\(887\) | −13229.3 | −0.500785 | −0.250392 | − | 0.968144i | \(-0.580560\pi\) | ||||
−0.250392 | + | 0.968144i | \(0.580560\pi\) | |||||||
\(888\) | −15598.5 | −0.589472 | ||||||||
\(889\) | 12748.7 | 0.480965 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1658.10 | 0.0623439 | ||||||||
\(892\) | −22599.0 | −0.848284 | ||||||||
\(893\) | −46659.6 | −1.74849 | ||||||||
\(894\) | 11858.4 | 0.443630 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −7001.96 | −0.261071 | ||||||||
\(897\) | −3579.27 | −0.133231 | ||||||||
\(898\) | −22426.7 | −0.833395 | ||||||||
\(899\) | 10412.5 | 0.386293 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 56192.1 | 2.07772 | ||||||||
\(902\) | −6382.68 | −0.235610 | ||||||||
\(903\) | 9366.01 | 0.345162 | ||||||||
\(904\) | 18500.0 | 0.680642 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 12489.0 | 0.457967 | ||||||||
\(907\) | 18849.7 | 0.690071 | 0.345035 | − | 0.938590i | \(-0.387867\pi\) | ||||
0.345035 | + | 0.938590i | \(0.387867\pi\) | |||||||
\(908\) | 246.831 | 0.00902135 | ||||||||
\(909\) | −13802.0 | −0.503611 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −20189.5 | −0.734258 | −0.367129 | − | 0.930170i | \(-0.619659\pi\) | ||||
−0.367129 | + | 0.930170i | \(0.619659\pi\) | |||||||
\(912\) | −195.499 | −0.00709826 | ||||||||
\(913\) | −8635.54 | −0.313028 | ||||||||
\(914\) | 18664.6 | 0.675459 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 11730.0 | 0.423111 | ||||||||
\(917\) | 17482.9 | 0.629594 | ||||||||
\(918\) | 5113.15 | 0.183833 | ||||||||
\(919\) | −9727.34 | −0.349157 | −0.174579 | − | 0.984643i | \(-0.555856\pi\) | ||||
−0.174579 | + | 0.984643i | \(0.555856\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2902.41 | −0.103841 | ||||||||
\(922\) | −25055.6 | −0.894971 | ||||||||
\(923\) | 5459.04 | 0.194676 | ||||||||
\(924\) | −2343.97 | −0.0834534 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 20154.9 | 0.715259 | ||||||||
\(927\) | 6470.07 | 0.229240 | ||||||||
\(928\) | −10723.8 | −0.379340 | ||||||||
\(929\) | −39516.5 | −1.39558 | −0.697790 | − | 0.716303i | \(-0.745833\pi\) | ||||
−0.697790 | + | 0.716303i | \(0.745833\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −27799.5 | −0.978615 | ||||||||
\(932\) | −14441.4 | −0.507558 | ||||||||
\(933\) | 4591.00 | 0.161096 | ||||||||
\(934\) | −5374.57 | −0.188288 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 3005.78 | 0.104965 | ||||||||
\(937\) | −32692.4 | −1.13982 | −0.569912 | − | 0.821706i | \(-0.693023\pi\) | ||||
−0.569912 | + | 0.821706i | \(0.693023\pi\) | |||||||
\(938\) | 7345.84 | 0.255704 | ||||||||
\(939\) | 23950.8 | 0.832381 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11482.8 | −0.397797 | −0.198899 | − | 0.980020i | \(-0.563736\pi\) | ||||
−0.198899 | + | 0.980020i | \(0.563736\pi\) | |||||||
\(942\) | −4703.61 | −0.162688 | ||||||||
\(943\) | 14459.7 | 0.499334 | ||||||||
\(944\) | −380.825 | −0.0131301 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −14491.4 | −0.498049 | ||||||||
\(947\) | −43381.4 | −1.48860 | −0.744300 | − | 0.667845i | \(-0.767217\pi\) | ||||
−0.744300 | + | 0.667845i | \(0.767217\pi\) | |||||||
\(948\) | −9784.82 | −0.335228 | ||||||||
\(949\) | 6018.89 | 0.205881 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −15843.2 | −0.540220 | ||||||||
\(952\) | −18836.4 | −0.641271 | ||||||||
\(953\) | −23222.7 | −0.789358 | −0.394679 | − | 0.918819i | \(-0.629144\pi\) | ||||
−0.394679 | + | 0.918819i | \(0.629144\pi\) | |||||||
\(954\) | −8061.05 | −0.273570 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 5251.51 | 0.177663 | ||||||||
\(957\) | −3626.66 | −0.122501 | ||||||||
\(958\) | 31187.8 | 1.05181 | ||||||||
\(959\) | 7164.03 | 0.241229 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1296.90 | 0.0435333 | ||||||||
\(962\) | −5931.05 | −0.198778 | ||||||||
\(963\) | 8503.60 | 0.284553 | ||||||||
\(964\) | −34085.1 | −1.13880 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −3217.74 | −0.107173 | ||||||||
\(967\) | −16334.6 | −0.543211 | −0.271605 | − | 0.962409i | \(-0.587555\pi\) | ||||
−0.271605 | + | 0.962409i | \(0.587555\pi\) | |||||||
\(968\) | −20568.4 | −0.682947 | ||||||||
\(969\) | −31975.6 | −1.06007 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −39066.5 | −1.29115 | −0.645574 | − | 0.763698i | \(-0.723382\pi\) | ||||
−0.645574 | + | 0.763698i | \(0.723382\pi\) | |||||||
\(972\) | 1210.49 | 0.0399450 | ||||||||
\(973\) | 22022.7 | 0.725606 | ||||||||
\(974\) | 29989.0 | 0.986559 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −34.8646 | −0.00114343 | ||||||||
\(977\) | 39942.7 | 1.30796 | 0.653982 | − | 0.756510i | \(-0.273097\pi\) | ||||
0.653982 | + | 0.756510i | \(0.273097\pi\) | |||||||
\(978\) | 20996.1 | 0.686483 | ||||||||
\(979\) | 8702.73 | 0.284107 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 13251.0 | 0.431266 | ||||||||
\(982\) | −14228.8 | −0.462383 | ||||||||
\(983\) | 23347.1 | 0.757534 | 0.378767 | − | 0.925492i | \(-0.376348\pi\) | ||||
0.378767 | + | 0.925492i | \(0.376348\pi\) | |||||||
\(984\) | −12142.9 | −0.393395 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −11183.7 | −0.361218 | ||||||||
\(987\) | −10968.3 | −0.353724 | ||||||||
\(988\) | −7213.08 | −0.232266 | ||||||||
\(989\) | 32829.5 | 1.05553 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1661.91 | 0.0532717 | 0.0266359 | − | 0.999645i | \(-0.491521\pi\) | ||||
0.0266359 | + | 0.999645i | \(0.491521\pi\) | |||||||
\(992\) | −32017.4 | −1.02475 | ||||||||
\(993\) | 6247.79 | 0.199665 | ||||||||
\(994\) | 4907.63 | 0.156600 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −6304.36 | −0.200563 | ||||||||
\(997\) | −4547.81 | −0.144464 | −0.0722320 | − | 0.997388i | \(-0.523012\pi\) | ||||
−0.0722320 | + | 0.997388i | \(0.523012\pi\) | |||||||
\(998\) | 18509.8 | 0.587092 | ||||||||
\(999\) | −6224.48 | −0.197131 |
(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 | 1875.4.a.f.1.5 | 14 | ||
5.4 | even | 2 | 1875.4.a.g.1.10 | 14 | |||
25.9 | even | 10 | 75.4.g.b.31.5 | ✓ | 28 | ||
25.14 | even | 10 | 75.4.g.b.46.5 | yes | 28 | ||
75.14 | odd | 10 | 225.4.h.a.46.3 | 28 | |||
75.59 | odd | 10 | 225.4.h.a.181.3 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.4.g.b.31.5 | ✓ | 28 | 25.9 | even | 10 | ||
75.4.g.b.46.5 | yes | 28 | 25.14 | even | 10 | ||
225.4.h.a.46.3 | 28 | 75.14 | odd | 10 | |||
225.4.h.a.181.3 | 28 | 75.59 | odd | 10 | |||
1875.4.a.f.1.5 | 14 | 1.1 | even | 1 | trivial | ||
1875.4.a.g.1.10 | 14 | 5.4 | even | 2 |