Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [725,4,Mod(1,725)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(725, 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("725.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 725 = 5^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 725.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: | \(42.7763847542\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 29) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 725.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.41421 | 0.853553 | 0.426777 | − | 0.904357i | \(-0.359649\pi\) | ||||
0.426777 | + | 0.904357i | \(0.359649\pi\) | |||||||
\(3\) | 0.757359 | 0.145754 | 0.0728769 | − | 0.997341i | \(-0.476782\pi\) | ||||
0.0728769 | + | 0.997341i | \(0.476782\pi\) | |||||||
\(4\) | −2.17157 | −0.271447 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.82843 | 0.124409 | ||||||||
\(7\) | 22.1421 | 1.19556 | 0.597781 | − | 0.801659i | \(-0.296049\pi\) | ||||
0.597781 | + | 0.801659i | \(0.296049\pi\) | |||||||
\(8\) | −24.5563 | −1.08525 | ||||||||
\(9\) | −26.4264 | −0.978756 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 39.3259 | 1.07793 | 0.538964 | − | 0.842329i | \(-0.318816\pi\) | ||||
0.538964 | + | 0.842329i | \(0.318816\pi\) | |||||||
\(12\) | −1.64466 | −0.0395644 | ||||||||
\(13\) | −23.7696 | −0.507114 | −0.253557 | − | 0.967320i | \(-0.581601\pi\) | ||||
−0.253557 | + | 0.967320i | \(0.581601\pi\) | |||||||
\(14\) | 53.4558 | 1.02048 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −41.9117 | −0.654870 | ||||||||
\(17\) | −4.54416 | −0.0648306 | −0.0324153 | − | 0.999474i | \(-0.510320\pi\) | ||||
−0.0324153 | + | 0.999474i | \(0.510320\pi\) | |||||||
\(18\) | −63.7990 | −0.835420 | ||||||||
\(19\) | −155.255 | −1.87463 | −0.937313 | − | 0.348488i | \(-0.886695\pi\) | ||||
−0.937313 | + | 0.348488i | \(0.886695\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 16.7696 | 0.174258 | ||||||||
\(22\) | 94.9411 | 0.920069 | ||||||||
\(23\) | 41.8823 | 0.379698 | 0.189849 | − | 0.981813i | \(-0.439200\pi\) | ||||
0.189849 | + | 0.981813i | \(0.439200\pi\) | |||||||
\(24\) | −18.5980 | −0.158179 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −57.3848 | −0.432849 | ||||||||
\(27\) | −40.4630 | −0.288411 | ||||||||
\(28\) | −48.0833 | −0.324532 | ||||||||
\(29\) | 29.0000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −57.9045 | −0.335483 | −0.167741 | − | 0.985831i | \(-0.553647\pi\) | ||||
−0.167741 | + | 0.985831i | \(0.553647\pi\) | |||||||
\(32\) | 95.2670 | 0.526281 | ||||||||
\(33\) | 29.7838 | 0.157112 | ||||||||
\(34\) | −10.9706 | −0.0553364 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 57.3869 | 0.265680 | ||||||||
\(37\) | −235.196 | −1.04503 | −0.522513 | − | 0.852631i | \(-0.675005\pi\) | ||||
−0.522513 | + | 0.852631i | \(0.675005\pi\) | |||||||
\(38\) | −374.818 | −1.60009 | ||||||||
\(39\) | −18.0021 | −0.0739139 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −175.161 | −0.667210 | −0.333605 | − | 0.942713i | \(-0.608265\pi\) | ||||
−0.333605 | + | 0.942713i | \(0.608265\pi\) | |||||||
\(42\) | 40.4853 | 0.148738 | ||||||||
\(43\) | 402.831 | 1.42863 | 0.714315 | − | 0.699824i | \(-0.246738\pi\) | ||||
0.714315 | + | 0.699824i | \(0.246738\pi\) | |||||||
\(44\) | −85.3991 | −0.292600 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 101.113 | 0.324092 | ||||||||
\(47\) | −227.742 | −0.706800 | −0.353400 | − | 0.935472i | \(-0.614975\pi\) | ||||
−0.353400 | + | 0.935472i | \(0.614975\pi\) | |||||||
\(48\) | −31.7422 | −0.0954499 | ||||||||
\(49\) | 147.274 | 0.429371 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.44156 | −0.00944931 | ||||||||
\(52\) | 51.6173 | 0.137654 | ||||||||
\(53\) | −673.534 | −1.74560 | −0.872802 | − | 0.488074i | \(-0.837699\pi\) | ||||
−0.872802 | + | 0.488074i | \(0.837699\pi\) | |||||||
\(54\) | −97.6863 | −0.246174 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −543.730 | −1.29748 | ||||||||
\(57\) | −117.584 | −0.273234 | ||||||||
\(58\) | 70.0122 | 0.158501 | ||||||||
\(59\) | −800.725 | −1.76687 | −0.883437 | − | 0.468551i | \(-0.844776\pi\) | ||||
−0.883437 | + | 0.468551i | \(0.844776\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −222.270 | −0.466537 | −0.233268 | − | 0.972412i | \(-0.574942\pi\) | ||||
−0.233268 | + | 0.972412i | \(0.574942\pi\) | |||||||
\(62\) | −139.794 | −0.286352 | ||||||||
\(63\) | −585.137 | −1.17016 | ||||||||
\(64\) | 565.288 | 1.10408 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 71.9045 | 0.134104 | ||||||||
\(67\) | 524.479 | 0.956349 | 0.478174 | − | 0.878265i | \(-0.341299\pi\) | ||||
0.478174 | + | 0.878265i | \(0.341299\pi\) | |||||||
\(68\) | 9.86797 | 0.0175980 | ||||||||
\(69\) | 31.7199 | 0.0553424 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −281.917 | −0.471230 | −0.235615 | − | 0.971846i | \(-0.575711\pi\) | ||||
−0.235615 | + | 0.971846i | \(0.575711\pi\) | |||||||
\(72\) | 648.936 | 1.06219 | ||||||||
\(73\) | −1229.10 | −1.97061 | −0.985307 | − | 0.170790i | \(-0.945368\pi\) | ||||
−0.985307 | + | 0.170790i | \(0.945368\pi\) | |||||||
\(74\) | −567.813 | −0.891986 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 337.147 | 0.508861 | ||||||||
\(77\) | 870.759 | 1.28873 | ||||||||
\(78\) | −43.4609 | −0.0630895 | ||||||||
\(79\) | 611.247 | 0.870514 | 0.435257 | − | 0.900306i | \(-0.356657\pi\) | ||||
0.435257 | + | 0.900306i | \(0.356657\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 682.868 | 0.936719 | ||||||||
\(82\) | −422.877 | −0.569500 | ||||||||
\(83\) | −515.490 | −0.681716 | −0.340858 | − | 0.940115i | \(-0.610718\pi\) | ||||
−0.340858 | + | 0.940115i | \(0.610718\pi\) | |||||||
\(84\) | −36.4163 | −0.0473017 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 972.519 | 1.21941 | ||||||||
\(87\) | 21.9634 | 0.0270658 | ||||||||
\(88\) | −965.701 | −1.16982 | ||||||||
\(89\) | −358.219 | −0.426643 | −0.213321 | − | 0.976982i | \(-0.568428\pi\) | ||||
−0.213321 | + | 0.976982i | \(0.568428\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −526.309 | −0.606287 | ||||||||
\(92\) | −90.9504 | −0.103068 | ||||||||
\(93\) | −43.8545 | −0.0488979 | ||||||||
\(94\) | −549.818 | −0.603292 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 72.1514 | 0.0767075 | ||||||||
\(97\) | −829.415 | −0.868189 | −0.434095 | − | 0.900867i | \(-0.642932\pi\) | ||||
−0.434095 | + | 0.900867i | \(0.642932\pi\) | |||||||
\(98\) | 355.551 | 0.366491 | ||||||||
\(99\) | −1039.24 | −1.05503 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −978.010 | −0.963521 | −0.481761 | − | 0.876303i | \(-0.660003\pi\) | ||||
−0.481761 | + | 0.876303i | \(0.660003\pi\) | |||||||
\(102\) | −8.30866 | −0.00806549 | ||||||||
\(103\) | 1217.33 | 1.16453 | 0.582266 | − | 0.812998i | \(-0.302166\pi\) | ||||
0.582266 | + | 0.812998i | \(0.302166\pi\) | |||||||
\(104\) | 583.693 | 0.550345 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1626.06 | −1.48997 | ||||||||
\(107\) | 707.044 | 0.638808 | 0.319404 | − | 0.947619i | \(-0.396517\pi\) | ||||
0.319404 | + | 0.947619i | \(0.396517\pi\) | |||||||
\(108\) | 87.8683 | 0.0782883 | ||||||||
\(109\) | −1496.14 | −1.31471 | −0.657357 | − | 0.753580i | \(-0.728326\pi\) | ||||
−0.657357 | + | 0.753580i | \(0.728326\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −178.128 | −0.152317 | ||||||||
\(112\) | −928.014 | −0.782938 | ||||||||
\(113\) | 1067.23 | 0.888469 | 0.444234 | − | 0.895911i | \(-0.353476\pi\) | ||||
0.444234 | + | 0.895911i | \(0.353476\pi\) | |||||||
\(114\) | −283.872 | −0.233220 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −62.9756 | −0.0504064 | ||||||||
\(117\) | 628.144 | 0.496341 | ||||||||
\(118\) | −1933.12 | −1.50812 | ||||||||
\(119\) | −100.617 | −0.0775090 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 215.527 | 0.161928 | ||||||||
\(122\) | −536.607 | −0.398214 | ||||||||
\(123\) | −132.660 | −0.0972485 | ||||||||
\(124\) | 125.744 | 0.0910656 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1412.65 | −0.998798 | ||||||||
\(127\) | 1179.58 | 0.824177 | 0.412088 | − | 0.911144i | \(-0.364799\pi\) | ||||
0.412088 | + | 0.911144i | \(0.364799\pi\) | |||||||
\(128\) | 602.591 | 0.416109 | ||||||||
\(129\) | 305.087 | 0.208228 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2357.47 | −1.57231 | −0.786156 | − | 0.618028i | \(-0.787932\pi\) | ||||
−0.786156 | + | 0.618028i | \(0.787932\pi\) | |||||||
\(132\) | −64.6778 | −0.0426476 | ||||||||
\(133\) | −3437.67 | −2.24123 | ||||||||
\(134\) | 1266.21 | 0.816295 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 111.588 | 0.0703572 | ||||||||
\(137\) | −722.489 | −0.450558 | −0.225279 | − | 0.974294i | \(-0.572329\pi\) | ||||
−0.225279 | + | 0.974294i | \(0.572329\pi\) | |||||||
\(138\) | 76.5786 | 0.0472377 | ||||||||
\(139\) | 1398.24 | 0.853219 | 0.426610 | − | 0.904436i | \(-0.359708\pi\) | ||||
0.426610 | + | 0.904436i | \(0.359708\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −172.483 | −0.103019 | ||||||||
\(142\) | −680.607 | −0.402220 | ||||||||
\(143\) | −934.759 | −0.546633 | ||||||||
\(144\) | 1107.58 | 0.640958 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2967.30 | −1.68203 | ||||||||
\(147\) | 111.539 | 0.0625824 | ||||||||
\(148\) | 510.745 | 0.283669 | ||||||||
\(149\) | 2830.63 | 1.55634 | 0.778168 | − | 0.628056i | \(-0.216149\pi\) | ||||
0.778168 | + | 0.628056i | \(0.216149\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1705.58 | 0.919194 | 0.459597 | − | 0.888128i | \(-0.347994\pi\) | ||||
0.459597 | + | 0.888128i | \(0.347994\pi\) | |||||||
\(152\) | 3812.49 | 2.03443 | ||||||||
\(153\) | 120.086 | 0.0634533 | ||||||||
\(154\) | 2102.20 | 1.10000 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 39.0929 | 0.0200637 | ||||||||
\(157\) | 2670.84 | 1.35768 | 0.678841 | − | 0.734286i | \(-0.262483\pi\) | ||||
0.678841 | + | 0.734286i | \(0.262483\pi\) | |||||||
\(158\) | 1475.68 | 0.743031 | ||||||||
\(159\) | −510.107 | −0.254429 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 927.362 | 0.453953 | ||||||||
\(162\) | 1648.59 | 0.799539 | ||||||||
\(163\) | 2151.92 | 1.03406 | 0.517028 | − | 0.855968i | \(-0.327038\pi\) | ||||
0.517028 | + | 0.855968i | \(0.327038\pi\) | |||||||
\(164\) | 380.376 | 0.181112 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1244.50 | −0.581881 | ||||||||
\(167\) | −999.387 | −0.463083 | −0.231542 | − | 0.972825i | \(-0.574377\pi\) | ||||
−0.231542 | + | 0.972825i | \(0.574377\pi\) | |||||||
\(168\) | −411.799 | −0.189113 | ||||||||
\(169\) | −1632.01 | −0.742835 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4102.83 | 1.83480 | ||||||||
\(172\) | −874.776 | −0.387797 | ||||||||
\(173\) | 2534.30 | 1.11375 | 0.556877 | − | 0.830595i | \(-0.311999\pi\) | ||||
0.556877 | + | 0.830595i | \(0.311999\pi\) | |||||||
\(174\) | 53.0244 | 0.0231021 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1648.21 | −0.705903 | ||||||||
\(177\) | −606.437 | −0.257529 | ||||||||
\(178\) | −864.818 | −0.364162 | ||||||||
\(179\) | 3550.27 | 1.48245 | 0.741227 | − | 0.671254i | \(-0.234244\pi\) | ||||
0.741227 | + | 0.671254i | \(0.234244\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3034.68 | −1.24622 | −0.623110 | − | 0.782135i | \(-0.714131\pi\) | ||||
−0.623110 | + | 0.782135i | \(0.714131\pi\) | |||||||
\(182\) | −1270.62 | −0.517499 | ||||||||
\(183\) | −168.338 | −0.0679996 | ||||||||
\(184\) | −1028.48 | −0.412066 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −105.874 | −0.0417370 | ||||||||
\(187\) | −178.703 | −0.0698827 | ||||||||
\(188\) | 494.559 | 0.191859 | ||||||||
\(189\) | −895.937 | −0.344814 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2224.00 | 0.842529 | 0.421265 | − | 0.906938i | \(-0.361586\pi\) | ||||
0.421265 | + | 0.906938i | \(0.361586\pi\) | |||||||
\(192\) | 428.126 | 0.160924 | ||||||||
\(193\) | 632.830 | 0.236021 | 0.118011 | − | 0.993012i | \(-0.462348\pi\) | ||||
0.118011 | + | 0.993012i | \(0.462348\pi\) | |||||||
\(194\) | −2002.39 | −0.741046 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −319.817 | −0.116551 | ||||||||
\(197\) | −1369.80 | −0.495404 | −0.247702 | − | 0.968836i | \(-0.579675\pi\) | ||||
−0.247702 | + | 0.968836i | \(0.579675\pi\) | |||||||
\(198\) | −2508.95 | −0.900523 | ||||||||
\(199\) | 1416.38 | 0.504544 | 0.252272 | − | 0.967656i | \(-0.418822\pi\) | ||||
0.252272 | + | 0.967656i | \(0.418822\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 397.219 | 0.139391 | ||||||||
\(202\) | −2361.13 | −0.822417 | ||||||||
\(203\) | 642.122 | 0.222010 | ||||||||
\(204\) | 7.47360 | 0.00256498 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2938.89 | 0.993991 | ||||||||
\(207\) | −1106.80 | −0.371632 | ||||||||
\(208\) | 996.222 | 0.332094 | ||||||||
\(209\) | −6105.54 | −2.02071 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −896.432 | −0.292478 | −0.146239 | − | 0.989249i | \(-0.546717\pi\) | ||||
−0.146239 | + | 0.989249i | \(0.546717\pi\) | |||||||
\(212\) | 1462.63 | 0.473838 | ||||||||
\(213\) | −213.512 | −0.0686837 | ||||||||
\(214\) | 1706.95 | 0.545257 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 993.623 | 0.312998 | ||||||||
\(217\) | −1282.13 | −0.401091 | ||||||||
\(218\) | −3611.99 | −1.12218 | ||||||||
\(219\) | −930.868 | −0.287225 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 108.013 | 0.0328765 | ||||||||
\(222\) | −430.039 | −0.130010 | ||||||||
\(223\) | 2268.94 | 0.681344 | 0.340672 | − | 0.940182i | \(-0.389345\pi\) | ||||
0.340672 | + | 0.940182i | \(0.389345\pi\) | |||||||
\(224\) | 2109.42 | 0.629202 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2576.53 | 0.758356 | ||||||||
\(227\) | 2078.09 | 0.607610 | 0.303805 | − | 0.952734i | \(-0.401743\pi\) | ||||
0.303805 | + | 0.952734i | \(0.401743\pi\) | |||||||
\(228\) | 255.342 | 0.0741685 | ||||||||
\(229\) | −3715.05 | −1.07204 | −0.536020 | − | 0.844205i | \(-0.680073\pi\) | ||||
−0.536020 | + | 0.844205i | \(0.680073\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 659.478 | 0.187837 | ||||||||
\(232\) | −712.134 | −0.201525 | ||||||||
\(233\) | −2521.35 | −0.708923 | −0.354461 | − | 0.935071i | \(-0.615336\pi\) | ||||
−0.354461 | + | 0.935071i | \(0.615336\pi\) | |||||||
\(234\) | 1516.47 | 0.423654 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1738.83 | 0.479612 | ||||||||
\(237\) | 462.933 | 0.126881 | ||||||||
\(238\) | −242.912 | −0.0661581 | ||||||||
\(239\) | 3940.04 | 1.06636 | 0.533179 | − | 0.846002i | \(-0.320997\pi\) | ||||
0.533179 | + | 0.846002i | \(0.320997\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1973.06 | −0.527369 | −0.263684 | − | 0.964609i | \(-0.584938\pi\) | ||||
−0.263684 | + | 0.964609i | \(0.584938\pi\) | |||||||
\(242\) | 520.327 | 0.138214 | ||||||||
\(243\) | 1609.68 | 0.424942 | ||||||||
\(244\) | 482.675 | 0.126640 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −320.270 | −0.0830068 | ||||||||
\(247\) | 3690.34 | 0.950650 | ||||||||
\(248\) | 1421.92 | 0.364082 | ||||||||
\(249\) | −390.411 | −0.0993627 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1236.65 | −0.310982 | −0.155491 | − | 0.987837i | \(-0.549696\pi\) | ||||
−0.155491 | + | 0.987837i | \(0.549696\pi\) | |||||||
\(252\) | 1270.67 | 0.317637 | ||||||||
\(253\) | 1647.06 | 0.409287 | ||||||||
\(254\) | 2847.75 | 0.703479 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3067.52 | −0.748907 | ||||||||
\(257\) | −2918.10 | −0.708272 | −0.354136 | − | 0.935194i | \(-0.615225\pi\) | ||||
−0.354136 | + | 0.935194i | \(0.615225\pi\) | |||||||
\(258\) | 736.546 | 0.177734 | ||||||||
\(259\) | −5207.74 | −1.24939 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −766.366 | −0.181750 | ||||||||
\(262\) | −5691.43 | −1.34205 | ||||||||
\(263\) | 310.789 | 0.0728673 | 0.0364336 | − | 0.999336i | \(-0.488400\pi\) | ||||
0.0364336 | + | 0.999336i | \(0.488400\pi\) | |||||||
\(264\) | −731.382 | −0.170506 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −8299.28 | −1.91301 | ||||||||
\(267\) | −271.301 | −0.0621848 | ||||||||
\(268\) | −1138.95 | −0.259598 | ||||||||
\(269\) | −1839.98 | −0.417047 | −0.208523 | − | 0.978017i | \(-0.566866\pi\) | ||||
−0.208523 | + | 0.978017i | \(0.566866\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5187.35 | 1.16277 | 0.581383 | − | 0.813630i | \(-0.302512\pi\) | ||||
0.581383 | + | 0.813630i | \(0.302512\pi\) | |||||||
\(272\) | 190.453 | 0.0424556 | ||||||||
\(273\) | −398.605 | −0.0883687 | ||||||||
\(274\) | −1744.24 | −0.384575 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −68.8821 | −0.0150225 | ||||||||
\(277\) | −8666.41 | −1.87983 | −0.939917 | − | 0.341403i | \(-0.889098\pi\) | ||||
−0.939917 | + | 0.341403i | \(0.889098\pi\) | |||||||
\(278\) | 3375.66 | 0.728268 | ||||||||
\(279\) | 1530.21 | 0.328356 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7856.96 | 1.66800 | 0.833998 | − | 0.551767i | \(-0.186046\pi\) | ||||
0.833998 | + | 0.551767i | \(0.186046\pi\) | |||||||
\(282\) | −416.410 | −0.0879321 | ||||||||
\(283\) | 3054.71 | 0.641638 | 0.320819 | − | 0.947141i | \(-0.396042\pi\) | ||||
0.320819 | + | 0.947141i | \(0.396042\pi\) | |||||||
\(284\) | 612.203 | 0.127914 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2256.71 | −0.466580 | ||||||||
\(287\) | −3878.45 | −0.797692 | ||||||||
\(288\) | −2517.57 | −0.515101 | ||||||||
\(289\) | −4892.35 | −0.995797 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −628.166 | −0.126542 | ||||||||
\(292\) | 2669.07 | 0.534917 | ||||||||
\(293\) | −2847.83 | −0.567822 | −0.283911 | − | 0.958851i | \(-0.591632\pi\) | ||||
−0.283911 | + | 0.958851i | \(0.591632\pi\) | |||||||
\(294\) | 269.280 | 0.0534175 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 5775.55 | 1.13411 | ||||||||
\(297\) | −1591.24 | −0.310887 | ||||||||
\(298\) | 6833.74 | 1.32842 | ||||||||
\(299\) | −995.522 | −0.192550 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8919.53 | 1.70802 | ||||||||
\(302\) | 4117.64 | 0.784581 | ||||||||
\(303\) | −740.705 | −0.140437 | ||||||||
\(304\) | 6506.99 | 1.22764 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 289.913 | 0.0541608 | ||||||||
\(307\) | 2470.79 | 0.459334 | 0.229667 | − | 0.973269i | \(-0.426236\pi\) | ||||
0.229667 | + | 0.973269i | \(0.426236\pi\) | |||||||
\(308\) | −1890.92 | −0.349822 | ||||||||
\(309\) | 921.955 | 0.169735 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5653.29 | −1.03077 | −0.515384 | − | 0.856959i | \(-0.672351\pi\) | ||||
−0.515384 | + | 0.856959i | \(0.672351\pi\) | |||||||
\(312\) | 442.066 | 0.0802149 | ||||||||
\(313\) | 8289.72 | 1.49701 | 0.748503 | − | 0.663132i | \(-0.230773\pi\) | ||||
0.748503 | + | 0.663132i | \(0.230773\pi\) | |||||||
\(314\) | 6447.97 | 1.15885 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1327.37 | −0.236298 | ||||||||
\(317\) | −2577.06 | −0.456600 | −0.228300 | − | 0.973591i | \(-0.573317\pi\) | ||||
−0.228300 | + | 0.973591i | \(0.573317\pi\) | |||||||
\(318\) | −1231.51 | −0.217168 | ||||||||
\(319\) | 1140.45 | 0.200166 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 535.486 | 0.0931088 | ||||||||
\(322\) | 2238.85 | 0.387473 | ||||||||
\(323\) | 705.502 | 0.121533 | ||||||||
\(324\) | −1482.90 | −0.254269 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5195.19 | 0.882622 | ||||||||
\(327\) | −1133.11 | −0.191625 | ||||||||
\(328\) | 4301.33 | 0.724088 | ||||||||
\(329\) | −5042.70 | −0.845024 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7672.12 | 1.27401 | 0.637006 | − | 0.770859i | \(-0.280173\pi\) | ||||
0.637006 | + | 0.770859i | \(0.280173\pi\) | |||||||
\(332\) | 1119.42 | 0.185049 | ||||||||
\(333\) | 6215.38 | 1.02283 | ||||||||
\(334\) | −2412.73 | −0.395266 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −702.840 | −0.114116 | ||||||||
\(337\) | −3650.77 | −0.590120 | −0.295060 | − | 0.955479i | \(-0.595340\pi\) | ||||
−0.295060 | + | 0.955479i | \(0.595340\pi\) | |||||||
\(338\) | −3940.02 | −0.634049 | ||||||||
\(339\) | 808.280 | 0.129498 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2277.15 | −0.361626 | ||||||||
\(342\) | 9905.10 | 1.56610 | ||||||||
\(343\) | −4333.79 | −0.682223 | ||||||||
\(344\) | −9892.05 | −1.55042 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6118.35 | 0.950649 | ||||||||
\(347\) | 8737.06 | 1.35167 | 0.675835 | − | 0.737053i | \(-0.263783\pi\) | ||||
0.675835 | + | 0.737053i | \(0.263783\pi\) | |||||||
\(348\) | −47.6952 | −0.00734692 | ||||||||
\(349\) | −2143.83 | −0.328816 | −0.164408 | − | 0.986392i | \(-0.552571\pi\) | ||||
−0.164408 | + | 0.986392i | \(0.552571\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 961.787 | 0.146258 | ||||||||
\(352\) | 3746.46 | 0.567293 | ||||||||
\(353\) | 5111.17 | 0.770651 | 0.385326 | − | 0.922781i | \(-0.374089\pi\) | ||||
0.385326 | + | 0.922781i | \(0.374089\pi\) | |||||||
\(354\) | −1464.07 | −0.219814 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 777.900 | 0.115811 | ||||||||
\(357\) | −76.2035 | −0.0112972 | ||||||||
\(358\) | 8571.10 | 1.26535 | ||||||||
\(359\) | 4520.87 | 0.664630 | 0.332315 | − | 0.943168i | \(-0.392170\pi\) | ||||
0.332315 | + | 0.943168i | \(0.392170\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17245.1 | 2.51422 | ||||||||
\(362\) | −7326.35 | −1.06371 | ||||||||
\(363\) | 163.231 | 0.0236017 | ||||||||
\(364\) | 1142.92 | 0.164575 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −406.404 | −0.0580413 | ||||||||
\(367\) | 486.272 | 0.0691641 | 0.0345820 | − | 0.999402i | \(-0.488990\pi\) | ||||
0.0345820 | + | 0.999402i | \(0.488990\pi\) | |||||||
\(368\) | −1755.36 | −0.248653 | ||||||||
\(369\) | 4628.89 | 0.653036 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −14913.5 | −2.08698 | ||||||||
\(372\) | 95.2333 | 0.0132732 | ||||||||
\(373\) | −10053.1 | −1.39552 | −0.697758 | − | 0.716333i | \(-0.745819\pi\) | ||||
−0.697758 | + | 0.716333i | \(0.745819\pi\) | |||||||
\(374\) | −431.427 | −0.0596486 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5592.52 | 0.767053 | ||||||||
\(377\) | −689.317 | −0.0941688 | ||||||||
\(378\) | −2162.98 | −0.294317 | ||||||||
\(379\) | −11602.8 | −1.57255 | −0.786273 | − | 0.617879i | \(-0.787992\pi\) | ||||
−0.786273 | + | 0.617879i | \(0.787992\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 893.363 | 0.120127 | ||||||||
\(382\) | 5369.22 | 0.719144 | ||||||||
\(383\) | 4161.38 | 0.555187 | 0.277593 | − | 0.960699i | \(-0.410463\pi\) | ||||
0.277593 | + | 0.960699i | \(0.410463\pi\) | |||||||
\(384\) | 456.378 | 0.0606496 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1527.79 | 0.201457 | ||||||||
\(387\) | −10645.4 | −1.39828 | ||||||||
\(388\) | 1801.14 | 0.235667 | ||||||||
\(389\) | −6843.95 | −0.892036 | −0.446018 | − | 0.895024i | \(-0.647158\pi\) | ||||
−0.446018 | + | 0.895024i | \(0.647158\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −190.319 | −0.0246160 | ||||||||
\(392\) | −3616.52 | −0.465974 | ||||||||
\(393\) | −1785.45 | −0.229171 | ||||||||
\(394\) | −3307.00 | −0.422854 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2256.79 | 0.286384 | ||||||||
\(397\) | −5474.73 | −0.692112 | −0.346056 | − | 0.938214i | \(-0.612479\pi\) | ||||
−0.346056 | + | 0.938214i | \(0.612479\pi\) | |||||||
\(398\) | 3419.43 | 0.430655 | ||||||||
\(399\) | −2603.55 | −0.326669 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 890.013 | 0.110836 | 0.0554178 | − | 0.998463i | \(-0.482351\pi\) | ||||
0.0554178 | + | 0.998463i | \(0.482351\pi\) | |||||||
\(402\) | 958.972 | 0.118978 | ||||||||
\(403\) | 1376.37 | 0.170128 | ||||||||
\(404\) | 2123.82 | 0.261545 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1550.22 | 0.189498 | ||||||||
\(407\) | −9249.29 | −1.12646 | ||||||||
\(408\) | 84.5121 | 0.0102548 | ||||||||
\(409\) | 8107.81 | 0.980209 | 0.490104 | − | 0.871664i | \(-0.336959\pi\) | ||||
0.490104 | + | 0.871664i | \(0.336959\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −547.184 | −0.0656706 | ||||||||
\(412\) | −2643.52 | −0.316109 | ||||||||
\(413\) | −17729.8 | −2.11241 | ||||||||
\(414\) | −2672.05 | −0.317207 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2264.45 | −0.266885 | ||||||||
\(417\) | 1058.97 | 0.124360 | ||||||||
\(418\) | −14740.1 | −1.72479 | ||||||||
\(419\) | 4237.59 | 0.494080 | 0.247040 | − | 0.969005i | \(-0.420542\pi\) | ||||
0.247040 | + | 0.969005i | \(0.420542\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −953.634 | −0.110397 | −0.0551987 | − | 0.998475i | \(-0.517579\pi\) | ||||
−0.0551987 | + | 0.998475i | \(0.517579\pi\) | |||||||
\(422\) | −2164.18 | −0.249646 | ||||||||
\(423\) | 6018.41 | 0.691785 | ||||||||
\(424\) | 16539.5 | 1.89441 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −515.464 | −0.0586252 | ||||||||
\(427\) | −4921.53 | −0.557774 | ||||||||
\(428\) | −1535.40 | −0.173402 | ||||||||
\(429\) | −707.949 | −0.0796738 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10098.8 | −1.12864 | −0.564318 | − | 0.825557i | \(-0.690861\pi\) | ||||
−0.564318 | + | 0.825557i | \(0.690861\pi\) | |||||||
\(432\) | 1695.87 | 0.188872 | ||||||||
\(433\) | 12833.1 | 1.42430 | 0.712148 | − | 0.702029i | \(-0.247722\pi\) | ||||
0.712148 | + | 0.702029i | \(0.247722\pi\) | |||||||
\(434\) | −3095.34 | −0.342352 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3248.97 | 0.356875 | ||||||||
\(437\) | −6502.42 | −0.711792 | ||||||||
\(438\) | −2247.31 | −0.245162 | ||||||||
\(439\) | −14434.8 | −1.56932 | −0.784662 | − | 0.619924i | \(-0.787164\pi\) | ||||
−0.784662 | + | 0.619924i | \(0.787164\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3891.93 | −0.420249 | ||||||||
\(442\) | 260.765 | 0.0280619 | ||||||||
\(443\) | 7020.65 | 0.752959 | 0.376480 | − | 0.926425i | \(-0.377134\pi\) | ||||
0.376480 | + | 0.926425i | \(0.377134\pi\) | |||||||
\(444\) | 386.818 | 0.0413458 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 5477.71 | 0.581563 | ||||||||
\(447\) | 2143.80 | 0.226842 | ||||||||
\(448\) | 12516.7 | 1.32000 | ||||||||
\(449\) | 13210.5 | 1.38851 | 0.694254 | − | 0.719730i | \(-0.255735\pi\) | ||||
0.694254 | + | 0.719730i | \(0.255735\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6888.38 | −0.719205 | ||||||||
\(452\) | −2317.58 | −0.241172 | ||||||||
\(453\) | 1291.74 | 0.133976 | ||||||||
\(454\) | 5016.95 | 0.518628 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2887.43 | 0.296527 | ||||||||
\(457\) | 2811.18 | 0.287749 | 0.143875 | − | 0.989596i | \(-0.454044\pi\) | ||||
0.143875 | + | 0.989596i | \(0.454044\pi\) | |||||||
\(458\) | −8968.92 | −0.915044 | ||||||||
\(459\) | 183.870 | 0.0186979 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9645.10 | −0.974441 | −0.487220 | − | 0.873279i | \(-0.661989\pi\) | ||||
−0.487220 | + | 0.873279i | \(0.661989\pi\) | |||||||
\(462\) | 1592.12 | 0.160329 | ||||||||
\(463\) | −6923.23 | −0.694924 | −0.347462 | − | 0.937694i | \(-0.612956\pi\) | ||||
−0.347462 | + | 0.937694i | \(0.612956\pi\) | |||||||
\(464\) | −1215.44 | −0.121606 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6087.07 | −0.605103 | ||||||||
\(467\) | 124.351 | 0.0123218 | 0.00616089 | − | 0.999981i | \(-0.498039\pi\) | ||||
0.00616089 | + | 0.999981i | \(0.498039\pi\) | |||||||
\(468\) | −1364.06 | −0.134730 | ||||||||
\(469\) | 11613.1 | 1.14337 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2022.78 | 0.197887 | ||||||||
\(472\) | 19662.9 | 1.91749 | ||||||||
\(473\) | 15841.7 | 1.53996 | ||||||||
\(474\) | 1117.62 | 0.108300 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 218.498 | 0.0210396 | ||||||||
\(477\) | 17799.1 | 1.70852 | ||||||||
\(478\) | 9512.09 | 0.910194 | ||||||||
\(479\) | −4461.48 | −0.425575 | −0.212788 | − | 0.977098i | \(-0.568254\pi\) | ||||
−0.212788 | + | 0.977098i | \(0.568254\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5590.50 | 0.529948 | ||||||||
\(482\) | −4763.39 | −0.450137 | ||||||||
\(483\) | 702.347 | 0.0661654 | ||||||||
\(484\) | −468.032 | −0.0439549 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 3886.10 | 0.362710 | ||||||||
\(487\) | 5660.72 | 0.526718 | 0.263359 | − | 0.964698i | \(-0.415170\pi\) | ||||
0.263359 | + | 0.964698i | \(0.415170\pi\) | |||||||
\(488\) | 5458.14 | 0.506308 | ||||||||
\(489\) | 1629.77 | 0.150718 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5587.50 | 0.513565 | 0.256782 | − | 0.966469i | \(-0.417338\pi\) | ||||
0.256782 | + | 0.966469i | \(0.417338\pi\) | |||||||
\(492\) | 288.081 | 0.0263978 | ||||||||
\(493\) | −131.781 | −0.0120387 | ||||||||
\(494\) | 8909.26 | 0.811431 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2426.88 | 0.219698 | ||||||||
\(497\) | −6242.24 | −0.563386 | ||||||||
\(498\) | −942.537 | −0.0848114 | ||||||||
\(499\) | −4210.19 | −0.377703 | −0.188851 | − | 0.982006i | \(-0.560476\pi\) | ||||
−0.188851 | + | 0.982006i | \(0.560476\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −756.895 | −0.0674962 | ||||||||
\(502\) | −2985.53 | −0.265440 | ||||||||
\(503\) | −10796.7 | −0.957063 | −0.478532 | − | 0.878070i | \(-0.658831\pi\) | ||||
−0.478532 | + | 0.878070i | \(0.658831\pi\) | |||||||
\(504\) | 14368.8 | 1.26992 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3976.35 | 0.349348 | ||||||||
\(507\) | −1236.02 | −0.108271 | ||||||||
\(508\) | −2561.54 | −0.223720 | ||||||||
\(509\) | 14983.6 | 1.30479 | 0.652395 | − | 0.757879i | \(-0.273764\pi\) | ||||
0.652395 | + | 0.757879i | \(0.273764\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −27214.8 | −2.35599 | ||||||||
\(512\) | −12226.4 | −1.05534 | ||||||||
\(513\) | 6282.07 | 0.540663 | ||||||||
\(514\) | −7044.91 | −0.604548 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −662.520 | −0.0565229 | ||||||||
\(517\) | −8956.17 | −0.761880 | ||||||||
\(518\) | −12572.6 | −1.06643 | ||||||||
\(519\) | 1919.38 | 0.162334 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10770.3 | −0.905671 | −0.452836 | − | 0.891594i | \(-0.649588\pi\) | ||||
−0.452836 | + | 0.891594i | \(0.649588\pi\) | |||||||
\(522\) | −1850.17 | −0.155134 | ||||||||
\(523\) | 7538.93 | 0.630314 | 0.315157 | − | 0.949040i | \(-0.397943\pi\) | ||||
0.315157 | + | 0.949040i | \(0.397943\pi\) | |||||||
\(524\) | 5119.41 | 0.426799 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 750.312 | 0.0621961 | ||||||||
\(527\) | 263.127 | 0.0217495 | ||||||||
\(528\) | −1248.29 | −0.102888 | ||||||||
\(529\) | −10412.9 | −0.855829 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 21160.3 | 1.72934 | ||||||||
\(532\) | 7465.16 | 0.608375 | ||||||||
\(533\) | 4163.51 | 0.338352 | ||||||||
\(534\) | −654.978 | −0.0530781 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −12879.3 | −1.03787 | ||||||||
\(537\) | 2688.83 | 0.216073 | ||||||||
\(538\) | −4442.11 | −0.355972 | ||||||||
\(539\) | 5791.69 | 0.462831 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 595.816 | 0.0473496 | 0.0236748 | − | 0.999720i | \(-0.492463\pi\) | ||||
0.0236748 | + | 0.999720i | \(0.492463\pi\) | |||||||
\(542\) | 12523.4 | 0.992482 | ||||||||
\(543\) | −2298.34 | −0.181641 | ||||||||
\(544\) | −432.908 | −0.0341191 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −962.317 | −0.0754274 | ||||||||
\(547\) | −12703.4 | −0.992978 | −0.496489 | − | 0.868043i | \(-0.665378\pi\) | ||||
−0.496489 | + | 0.868043i | \(0.665378\pi\) | |||||||
\(548\) | 1568.94 | 0.122302 | ||||||||
\(549\) | 5873.80 | 0.456626 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4502.39 | −0.348109 | ||||||||
\(552\) | −778.925 | −0.0600603 | ||||||||
\(553\) | 13534.3 | 1.04075 | ||||||||
\(554\) | −20922.6 | −1.60454 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3036.39 | −0.231604 | ||||||||
\(557\) | 14973.0 | 1.13901 | 0.569503 | − | 0.821990i | \(-0.307136\pi\) | ||||
0.569503 | + | 0.821990i | \(0.307136\pi\) | |||||||
\(558\) | 3694.25 | 0.280269 | ||||||||
\(559\) | −9575.10 | −0.724479 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −135.342 | −0.0101857 | ||||||||
\(562\) | 18968.4 | 1.42372 | ||||||||
\(563\) | 10439.3 | 0.781466 | 0.390733 | − | 0.920504i | \(-0.372222\pi\) | ||||
0.390733 | + | 0.920504i | \(0.372222\pi\) | |||||||
\(564\) | 374.559 | 0.0279641 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 7374.71 | 0.547672 | ||||||||
\(567\) | 15120.2 | 1.11991 | ||||||||
\(568\) | 6922.85 | 0.511402 | ||||||||
\(569\) | −8859.72 | −0.652757 | −0.326379 | − | 0.945239i | \(-0.605828\pi\) | ||||
−0.326379 | + | 0.945239i | \(0.605828\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5078.17 | −0.372180 | −0.186090 | − | 0.982533i | \(-0.559582\pi\) | ||||
−0.186090 | + | 0.982533i | \(0.559582\pi\) | |||||||
\(572\) | 2029.90 | 0.148382 | ||||||||
\(573\) | 1684.37 | 0.122802 | ||||||||
\(574\) | −9363.40 | −0.680873 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −14938.5 | −1.08062 | ||||||||
\(577\) | −20457.2 | −1.47599 | −0.737994 | − | 0.674808i | \(-0.764227\pi\) | ||||
−0.737994 | + | 0.674808i | \(0.764227\pi\) | |||||||
\(578\) | −11811.2 | −0.849966 | ||||||||
\(579\) | 479.280 | 0.0344010 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11414.1 | −0.815034 | ||||||||
\(582\) | −1516.53 | −0.108010 | ||||||||
\(583\) | −26487.3 | −1.88164 | ||||||||
\(584\) | 30182.1 | 2.13860 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6875.27 | −0.484667 | ||||||||
\(587\) | −4355.22 | −0.306234 | −0.153117 | − | 0.988208i | \(-0.548931\pi\) | ||||
−0.153117 | + | 0.988208i | \(0.548931\pi\) | |||||||
\(588\) | −242.216 | −0.0169878 | ||||||||
\(589\) | 8989.96 | 0.628905 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1037.43 | −0.0722070 | ||||||||
\(592\) | 9857.46 | 0.684357 | ||||||||
\(593\) | −4342.49 | −0.300716 | −0.150358 | − | 0.988632i | \(-0.548043\pi\) | ||||
−0.150358 | + | 0.988632i | \(0.548043\pi\) | |||||||
\(594\) | −3841.60 | −0.265358 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6146.92 | −0.422462 | ||||||||
\(597\) | 1072.71 | 0.0735392 | ||||||||
\(598\) | −2403.40 | −0.164352 | ||||||||
\(599\) | −12761.8 | −0.870506 | −0.435253 | − | 0.900308i | \(-0.643341\pi\) | ||||
−0.435253 | + | 0.900308i | \(0.643341\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2804.87 | −0.190371 | −0.0951857 | − | 0.995460i | \(-0.530344\pi\) | ||||
−0.0951857 | + | 0.995460i | \(0.530344\pi\) | |||||||
\(602\) | 21533.6 | 1.45788 | ||||||||
\(603\) | −13860.1 | −0.936032 | ||||||||
\(604\) | −3703.80 | −0.249512 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1788.22 | −0.119870 | ||||||||
\(607\) | −12033.5 | −0.804654 | −0.402327 | − | 0.915496i | \(-0.631798\pi\) | ||||
−0.402327 | + | 0.915496i | \(0.631798\pi\) | |||||||
\(608\) | −14790.7 | −0.986580 | ||||||||
\(609\) | 486.317 | 0.0323589 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5413.33 | 0.358429 | ||||||||
\(612\) | −260.775 | −0.0172242 | ||||||||
\(613\) | −7993.67 | −0.526690 | −0.263345 | − | 0.964702i | \(-0.584826\pi\) | ||||
−0.263345 | + | 0.964702i | \(0.584826\pi\) | |||||||
\(614\) | 5965.02 | 0.392066 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −21382.7 | −1.39859 | ||||||||
\(617\) | −9922.51 | −0.647432 | −0.323716 | − | 0.946154i | \(-0.604932\pi\) | ||||
−0.323716 | + | 0.946154i | \(0.604932\pi\) | |||||||
\(618\) | 2225.80 | 0.144878 | ||||||||
\(619\) | −15401.4 | −1.00005 | −0.500027 | − | 0.866010i | \(-0.666676\pi\) | ||||
−0.500027 | + | 0.866010i | \(0.666676\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1694.68 | −0.109509 | ||||||||
\(622\) | −13648.3 | −0.879816 | ||||||||
\(623\) | −7931.74 | −0.510078 | ||||||||
\(624\) | 754.498 | 0.0484040 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 20013.2 | 1.27777 | ||||||||
\(627\) | −4624.08 | −0.294527 | ||||||||
\(628\) | −5799.92 | −0.368538 | ||||||||
\(629\) | 1068.77 | 0.0677497 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3776.97 | −0.238287 | −0.119143 | − | 0.992877i | \(-0.538015\pi\) | ||||
−0.119143 | + | 0.992877i | \(0.538015\pi\) | |||||||
\(632\) | −15010.0 | −0.944724 | ||||||||
\(633\) | −678.921 | −0.0426298 | ||||||||
\(634\) | −6221.57 | −0.389732 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1107.74 | 0.0690638 | ||||||||
\(637\) | −3500.64 | −0.217740 | ||||||||
\(638\) | 2753.29 | 0.170853 | ||||||||
\(639\) | 7450.05 | 0.461220 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 464.125 | 0.0285988 | 0.0142994 | − | 0.999898i | \(-0.495448\pi\) | ||||
0.0142994 | + | 0.999898i | \(0.495448\pi\) | |||||||
\(642\) | 1292.78 | 0.0794733 | ||||||||
\(643\) | −7607.61 | −0.466586 | −0.233293 | − | 0.972406i | \(-0.574950\pi\) | ||||
−0.233293 | + | 0.972406i | \(0.574950\pi\) | |||||||
\(644\) | −2013.84 | −0.123224 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1703.23 | 0.103735 | ||||||||
\(647\) | −7776.85 | −0.472550 | −0.236275 | − | 0.971686i | \(-0.575927\pi\) | ||||
−0.236275 | + | 0.971686i | \(0.575927\pi\) | |||||||
\(648\) | −16768.7 | −1.01657 | ||||||||
\(649\) | −31489.2 | −1.90456 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −971.033 | −0.0584605 | ||||||||
\(652\) | −4673.04 | −0.280691 | ||||||||
\(653\) | 24486.1 | 1.46740 | 0.733702 | − | 0.679471i | \(-0.237791\pi\) | ||||
0.733702 | + | 0.679471i | \(0.237791\pi\) | |||||||
\(654\) | −2735.57 | −0.163562 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 7341.31 | 0.436936 | ||||||||
\(657\) | 32480.6 | 1.92875 | ||||||||
\(658\) | −12174.2 | −0.721273 | ||||||||
\(659\) | 910.966 | 0.0538486 | 0.0269243 | − | 0.999637i | \(-0.491429\pi\) | ||||
0.0269243 | + | 0.999637i | \(0.491429\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5826.64 | 0.342859 | 0.171430 | − | 0.985196i | \(-0.445161\pi\) | ||||
0.171430 | + | 0.985196i | \(0.445161\pi\) | |||||||
\(662\) | 18522.1 | 1.08744 | ||||||||
\(663\) | 81.8043 | 0.00479188 | ||||||||
\(664\) | 12658.6 | 0.739830 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 15005.3 | 0.873036 | ||||||||
\(667\) | 1214.59 | 0.0705081 | ||||||||
\(668\) | 2170.24 | 0.125702 | ||||||||
\(669\) | 1718.40 | 0.0993085 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8740.97 | −0.502893 | ||||||||
\(672\) | 1597.59 | 0.0917086 | ||||||||
\(673\) | −27236.0 | −1.55999 | −0.779994 | − | 0.625788i | \(-0.784778\pi\) | ||||
−0.779994 | + | 0.625788i | \(0.784778\pi\) | |||||||
\(674\) | −8813.75 | −0.503699 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3544.03 | 0.201640 | ||||||||
\(677\) | −8989.70 | −0.510343 | −0.255172 | − | 0.966896i | \(-0.582132\pi\) | ||||
−0.255172 | + | 0.966896i | \(0.582132\pi\) | |||||||
\(678\) | 1951.36 | 0.110533 | ||||||||
\(679\) | −18365.0 | −1.03798 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1573.86 | 0.0885616 | ||||||||
\(682\) | −5497.52 | −0.308667 | ||||||||
\(683\) | −6934.65 | −0.388502 | −0.194251 | − | 0.980952i | \(-0.562228\pi\) | ||||
−0.194251 | + | 0.980952i | \(0.562228\pi\) | |||||||
\(684\) | −8909.59 | −0.498051 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −10462.7 | −0.582314 | ||||||||
\(687\) | −2813.63 | −0.156254 | ||||||||
\(688\) | −16883.3 | −0.935567 | ||||||||
\(689\) | 16009.6 | 0.885221 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5234.54 | 0.288178 | 0.144089 | − | 0.989565i | \(-0.453975\pi\) | ||||
0.144089 | + | 0.989565i | \(0.453975\pi\) | |||||||
\(692\) | −5503.43 | −0.302325 | ||||||||
\(693\) | −23011.0 | −1.26135 | ||||||||
\(694\) | 21093.1 | 1.15372 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −539.341 | −0.0293731 | ||||||||
\(697\) | 795.961 | 0.0432556 | ||||||||
\(698\) | −5175.67 | −0.280662 | ||||||||
\(699\) | −1909.57 | −0.103328 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −33713.7 | −1.81647 | −0.908237 | − | 0.418457i | \(-0.862571\pi\) | ||||
−0.908237 | + | 0.418457i | \(0.862571\pi\) | |||||||
\(702\) | 2321.96 | 0.124839 | ||||||||
\(703\) | 36515.3 | 1.95903 | ||||||||
\(704\) | 22230.5 | 1.19012 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 12339.4 | 0.657792 | ||||||||
\(707\) | −21655.2 | −1.15195 | ||||||||
\(708\) | 1316.92 | 0.0699053 | ||||||||
\(709\) | −12687.3 | −0.672049 | −0.336025 | − | 0.941853i | \(-0.609083\pi\) | ||||
−0.336025 | + | 0.941853i | \(0.609083\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −16153.1 | −0.852021 | ||||||||
\(712\) | 8796.56 | 0.463013 | ||||||||
\(713\) | −2425.17 | −0.127382 | ||||||||
\(714\) | −183.971 | −0.00964280 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −7709.66 | −0.402407 | ||||||||
\(717\) | 2984.02 | 0.155426 | ||||||||
\(718\) | 10914.3 | 0.567297 | ||||||||
\(719\) | 30604.9 | 1.58744 | 0.793720 | − | 0.608283i | \(-0.208141\pi\) | ||||
0.793720 | + | 0.608283i | \(0.208141\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 26954.2 | 1.39227 | ||||||||
\(722\) | 41633.3 | 2.14602 | ||||||||
\(723\) | −1494.31 | −0.0768661 | ||||||||
\(724\) | 6590.02 | 0.338282 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 394.075 | 0.0201453 | ||||||||
\(727\) | −3727.96 | −0.190182 | −0.0950911 | − | 0.995469i | \(-0.530314\pi\) | ||||
−0.0950911 | + | 0.995469i | \(0.530314\pi\) | |||||||
\(728\) | 12924.2 | 0.657972 | ||||||||
\(729\) | −17218.3 | −0.874782 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1830.52 | −0.0926189 | ||||||||
\(732\) | 365.559 | 0.0184583 | ||||||||
\(733\) | −1107.21 | −0.0557921 | −0.0278960 | − | 0.999611i | \(-0.508881\pi\) | ||||
−0.0278960 | + | 0.999611i | \(0.508881\pi\) | |||||||
\(734\) | 1173.97 | 0.0590352 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3990.00 | 0.199828 | ||||||||
\(737\) | 20625.6 | 1.03087 | ||||||||
\(738\) | 11175.1 | 0.557401 | ||||||||
\(739\) | −29127.7 | −1.44991 | −0.724953 | − | 0.688798i | \(-0.758139\pi\) | ||||
−0.724953 | + | 0.688798i | \(0.758139\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2794.91 | 0.138561 | ||||||||
\(742\) | −36004.3 | −1.78135 | ||||||||
\(743\) | −12162.8 | −0.600552 | −0.300276 | − | 0.953852i | \(-0.597079\pi\) | ||||
−0.300276 | + | 0.953852i | \(0.597079\pi\) | |||||||
\(744\) | 1076.91 | 0.0530663 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −24270.2 | −1.19115 | ||||||||
\(747\) | 13622.6 | 0.667233 | ||||||||
\(748\) | 388.067 | 0.0189694 | ||||||||
\(749\) | 15655.5 | 0.763736 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25067.6 | −1.21802 | −0.609008 | − | 0.793164i | \(-0.708432\pi\) | ||||
−0.609008 | + | 0.793164i | \(0.708432\pi\) | |||||||
\(752\) | 9545.06 | 0.462862 | ||||||||
\(753\) | −936.587 | −0.0453269 | ||||||||
\(754\) | −1664.16 | −0.0803781 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1945.59 | 0.0935986 | ||||||||
\(757\) | 12020.6 | 0.577140 | 0.288570 | − | 0.957459i | \(-0.406820\pi\) | ||||
0.288570 | + | 0.957459i | \(0.406820\pi\) | |||||||
\(758\) | −28011.6 | −1.34225 | ||||||||
\(759\) | 1247.41 | 0.0596552 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9255.42 | 0.440879 | 0.220439 | − | 0.975401i | \(-0.429251\pi\) | ||||
0.220439 | + | 0.975401i | \(0.429251\pi\) | |||||||
\(762\) | 2156.77 | 0.102535 | ||||||||
\(763\) | −33127.6 | −1.57182 | ||||||||
\(764\) | −4829.58 | −0.228702 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 10046.5 | 0.473881 | ||||||||
\(767\) | 19032.9 | 0.896007 | ||||||||
\(768\) | −2323.22 | −0.109156 | ||||||||
\(769\) | 28690.1 | 1.34537 | 0.672687 | − | 0.739928i | \(-0.265140\pi\) | ||||
0.672687 | + | 0.739928i | \(0.265140\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2210.05 | −0.103233 | ||||||||
\(772\) | −1374.24 | −0.0640672 | ||||||||
\(773\) | 8984.36 | 0.418040 | 0.209020 | − | 0.977911i | \(-0.432973\pi\) | ||||
0.209020 | + | 0.977911i | \(0.432973\pi\) | |||||||
\(774\) | −25700.2 | −1.19351 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 20367.4 | 0.942201 | ||||||||
\(777\) | −3944.13 | −0.182104 | ||||||||
\(778\) | −16522.8 | −0.761400 | ||||||||
\(779\) | 27194.7 | 1.25077 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11086.6 | −0.507952 | ||||||||
\(782\) | −459.472 | −0.0210111 | ||||||||
\(783\) | −1173.43 | −0.0535566 | ||||||||
\(784\) | −6172.51 | −0.281182 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −4310.46 | −0.195609 | ||||||||
\(787\) | 5257.13 | 0.238115 | 0.119058 | − | 0.992887i | \(-0.462013\pi\) | ||||
0.119058 | + | 0.992887i | \(0.462013\pi\) | |||||||
\(788\) | 2974.63 | 0.134476 | ||||||||
\(789\) | 235.379 | 0.0106207 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 23630.9 | 1.06222 | ||||||||
\(792\) | 25520.0 | 1.14497 | ||||||||
\(793\) | 5283.26 | 0.236588 | ||||||||
\(794\) | −13217.2 | −0.590755 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3075.76 | −0.136957 | ||||||||
\(797\) | −7623.92 | −0.338837 | −0.169419 | − | 0.985544i | \(-0.554189\pi\) | ||||
−0.169419 | + | 0.985544i | \(0.554189\pi\) | |||||||
\(798\) | −6285.54 | −0.278829 | ||||||||
\(799\) | 1034.90 | 0.0458223 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9466.45 | 0.417579 | ||||||||
\(802\) | 2148.68 | 0.0946042 | ||||||||
\(803\) | −48335.3 | −2.12418 | ||||||||
\(804\) | −862.591 | −0.0378373 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3322.84 | 0.145213 | ||||||||
\(807\) | −1393.53 | −0.0607862 | ||||||||
\(808\) | 24016.4 | 1.04566 | ||||||||
\(809\) | −28238.7 | −1.22722 | −0.613609 | − | 0.789610i | \(-0.710283\pi\) | ||||
−0.613609 | + | 0.789610i | \(0.710283\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29851.2 | 1.29250 | 0.646251 | − | 0.763125i | \(-0.276336\pi\) | ||||
0.646251 | + | 0.763125i | \(0.276336\pi\) | |||||||
\(812\) | −1394.41 | −0.0602640 | ||||||||
\(813\) | 3928.69 | 0.169478 | ||||||||
\(814\) | −22329.8 | −0.961496 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 144.242 | 0.00618807 | ||||||||
\(817\) | −62541.4 | −2.67815 | ||||||||
\(818\) | 19574.0 | 0.836661 | ||||||||
\(819\) | 13908.4 | 0.593407 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2043.20 | 0.0868552 | 0.0434276 | − | 0.999057i | \(-0.486172\pi\) | ||||
0.0434276 | + | 0.999057i | \(0.486172\pi\) | |||||||
\(822\) | −1321.02 | −0.0560533 | ||||||||
\(823\) | −123.242 | −0.00521988 | −0.00260994 | − | 0.999997i | \(-0.500831\pi\) | ||||
−0.00260994 | + | 0.999997i | \(0.500831\pi\) | |||||||
\(824\) | −29893.1 | −1.26381 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −42803.4 | −1.80305 | ||||||||
\(827\) | −34335.2 | −1.44371 | −0.721857 | − | 0.692043i | \(-0.756711\pi\) | ||||
−0.721857 | + | 0.692043i | \(0.756711\pi\) | |||||||
\(828\) | 2403.49 | 0.100878 | ||||||||
\(829\) | −14705.0 | −0.616073 | −0.308037 | − | 0.951375i | \(-0.599672\pi\) | ||||
−0.308037 | + | 0.951375i | \(0.599672\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6563.58 | −0.273993 | ||||||||
\(832\) | −13436.7 | −0.559894 | ||||||||
\(833\) | −669.237 | −0.0278364 | ||||||||
\(834\) | 2556.59 | 0.106148 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 13258.6 | 0.548515 | ||||||||
\(837\) | 2342.99 | 0.0967570 | ||||||||
\(838\) | 10230.4 | 0.421724 | ||||||||
\(839\) | −22204.3 | −0.913679 | −0.456840 | − | 0.889549i | \(-0.651019\pi\) | ||||
−0.456840 | + | 0.889549i | \(0.651019\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 841.000 | 0.0344828 | ||||||||
\(842\) | −2302.28 | −0.0942300 | ||||||||
\(843\) | 5950.54 | 0.243117 | ||||||||
\(844\) | 1946.67 | 0.0793922 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 14529.7 | 0.590475 | ||||||||
\(847\) | 4772.22 | 0.193595 | ||||||||
\(848\) | 28228.9 | 1.14314 | ||||||||
\(849\) | 2313.51 | 0.0935212 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9850.54 | −0.396794 | ||||||||
\(852\) | 463.657 | 0.0186439 | ||||||||
\(853\) | 40095.2 | 1.60942 | 0.804710 | − | 0.593669i | \(-0.202321\pi\) | ||||
0.804710 | + | 0.593669i | \(0.202321\pi\) | |||||||
\(854\) | −11881.6 | −0.476090 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −17362.4 | −0.693265 | ||||||||
\(857\) | 12883.7 | 0.513536 | 0.256768 | − | 0.966473i | \(-0.417342\pi\) | ||||
0.256768 | + | 0.966473i | \(0.417342\pi\) | |||||||
\(858\) | −1709.14 | −0.0680059 | ||||||||
\(859\) | −34336.9 | −1.36386 | −0.681932 | − | 0.731416i | \(-0.738860\pi\) | ||||
−0.681932 | + | 0.731416i | \(0.738860\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2937.38 | −0.116267 | ||||||||
\(862\) | −24380.7 | −0.963351 | ||||||||
\(863\) | −10864.2 | −0.428531 | −0.214266 | − | 0.976775i | \(-0.568736\pi\) | ||||
−0.214266 | + | 0.976775i | \(0.568736\pi\) | |||||||
\(864\) | −3854.79 | −0.151785 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 30981.9 | 1.21571 | ||||||||
\(867\) | −3705.27 | −0.145141 | ||||||||
\(868\) | 2784.24 | 0.108875 | ||||||||
\(869\) | 24037.8 | 0.938352 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12466.6 | −0.484978 | ||||||||
\(872\) | 36739.6 | 1.42679 | ||||||||
\(873\) | 21918.5 | 0.849745 | ||||||||
\(874\) | −15698.2 | −0.607552 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2021.45 | 0.0779662 | ||||||||
\(877\) | −4818.40 | −0.185525 | −0.0927626 | − | 0.995688i | \(-0.529570\pi\) | ||||
−0.0927626 | + | 0.995688i | \(0.529570\pi\) | |||||||
\(878\) | −34848.6 | −1.33950 | ||||||||
\(879\) | −2156.83 | −0.0827623 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −30195.7 | −1.15473 | −0.577366 | − | 0.816485i | \(-0.695920\pi\) | ||||
−0.577366 | + | 0.816485i | \(0.695920\pi\) | |||||||
\(882\) | −9395.94 | −0.358705 | ||||||||
\(883\) | −30734.0 | −1.17133 | −0.585663 | − | 0.810555i | \(-0.699166\pi\) | ||||
−0.585663 | + | 0.810555i | \(0.699166\pi\) | |||||||
\(884\) | −234.557 | −0.00892422 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 16949.3 | 0.642691 | ||||||||
\(887\) | 43409.3 | 1.64323 | 0.821614 | − | 0.570045i | \(-0.193074\pi\) | ||||
0.821614 | + | 0.570045i | \(0.193074\pi\) | |||||||
\(888\) | 4374.17 | 0.165301 | ||||||||
\(889\) | 26118.3 | 0.985355 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 26854.4 | 1.00972 | ||||||||
\(892\) | −4927.17 | −0.184948 | ||||||||
\(893\) | 35358.1 | 1.32499 | ||||||||
\(894\) | 5175.60 | 0.193622 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 13342.6 | 0.497485 | ||||||||
\(897\) | −753.968 | −0.0280650 | ||||||||
\(898\) | 31892.9 | 1.18517 | ||||||||
\(899\) | −1679.23 | −0.0622976 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3060.64 | 0.113169 | ||||||||
\(902\) | −16630.0 | −0.613880 | ||||||||
\(903\) | 6755.29 | 0.248950 | ||||||||
\(904\) | −26207.4 | −0.964209 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 3118.53 | 0.114356 | ||||||||
\(907\) | 7991.51 | 0.292562 | 0.146281 | − | 0.989243i | \(-0.453270\pi\) | ||||
0.146281 | + | 0.989243i | \(0.453270\pi\) | |||||||
\(908\) | −4512.72 | −0.164934 | ||||||||
\(909\) | 25845.3 | 0.943052 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24188.5 | 0.879694 | 0.439847 | − | 0.898073i | \(-0.355033\pi\) | ||||
0.439847 | + | 0.898073i | \(0.355033\pi\) | |||||||
\(912\) | 4928.13 | 0.178933 | ||||||||
\(913\) | −20272.1 | −0.734840 | ||||||||
\(914\) | 6786.79 | 0.245609 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8067.50 | 0.291002 | ||||||||
\(917\) | −52199.4 | −1.87980 | ||||||||
\(918\) | 443.902 | 0.0159596 | ||||||||
\(919\) | 27421.3 | 0.984273 | 0.492136 | − | 0.870518i | \(-0.336216\pi\) | ||||
0.492136 | + | 0.870518i | \(0.336216\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1871.28 | 0.0669497 | ||||||||
\(922\) | −23285.3 | −0.831737 | ||||||||
\(923\) | 6701.03 | 0.238968 | ||||||||
\(924\) | −1432.10 | −0.0509878 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −16714.1 | −0.593154 | ||||||||
\(927\) | −32169.6 | −1.13979 | ||||||||
\(928\) | 2762.74 | 0.0977279 | ||||||||
\(929\) | −9284.12 | −0.327882 | −0.163941 | − | 0.986470i | \(-0.552421\pi\) | ||||
−0.163941 | + | 0.986470i | \(0.552421\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −22865.0 | −0.804910 | ||||||||
\(932\) | 5475.29 | 0.192435 | ||||||||
\(933\) | −4281.57 | −0.150238 | ||||||||
\(934\) | 300.210 | 0.0105173 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −15424.9 | −0.538653 | ||||||||
\(937\) | 1891.00 | 0.0659297 | 0.0329649 | − | 0.999457i | \(-0.489505\pi\) | ||||
0.0329649 | + | 0.999457i | \(0.489505\pi\) | |||||||
\(938\) | 28036.5 | 0.975932 | ||||||||
\(939\) | 6278.30 | 0.218194 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15163.9 | 0.525322 | 0.262661 | − | 0.964888i | \(-0.415400\pi\) | ||||
0.262661 | + | 0.964888i | \(0.415400\pi\) | |||||||
\(942\) | 4883.43 | 0.168907 | ||||||||
\(943\) | −7336.16 | −0.253338 | ||||||||
\(944\) | 33559.7 | 1.15707 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 38245.2 | 1.31444 | ||||||||
\(947\) | 31251.8 | 1.07238 | 0.536192 | − | 0.844096i | \(-0.319862\pi\) | ||||
0.536192 | + | 0.844096i | \(0.319862\pi\) | |||||||
\(948\) | −1005.29 | −0.0344414 | ||||||||
\(949\) | 29215.1 | 0.999327 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1951.76 | −0.0665512 | ||||||||
\(952\) | 2470.79 | 0.0841165 | ||||||||
\(953\) | 12521.4 | 0.425612 | 0.212806 | − | 0.977094i | \(-0.431740\pi\) | ||||
0.212806 | + | 0.977094i | \(0.431740\pi\) | |||||||
\(954\) | 42970.8 | 1.45831 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −8556.07 | −0.289459 | ||||||||
\(957\) | 863.731 | 0.0291750 | ||||||||
\(958\) | −10771.0 | −0.363251 | ||||||||
\(959\) | −15997.5 | −0.538670 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26438.1 | −0.887451 | ||||||||
\(962\) | 13496.7 | 0.452339 | ||||||||
\(963\) | −18684.6 | −0.625237 | ||||||||
\(964\) | 4284.64 | 0.143152 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1695.61 | 0.0564757 | ||||||||
\(967\) | 18348.5 | 0.610183 | 0.305091 | − | 0.952323i | \(-0.401313\pi\) | ||||
0.305091 | + | 0.952323i | \(0.401313\pi\) | |||||||
\(968\) | −5292.55 | −0.175732 | ||||||||
\(969\) | 534.319 | 0.0177139 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 27188.0 | 0.898564 | 0.449282 | − | 0.893390i | \(-0.351680\pi\) | ||||
0.449282 | + | 0.893390i | \(0.351680\pi\) | |||||||
\(972\) | −3495.53 | −0.115349 | ||||||||
\(973\) | 30960.1 | 1.02008 | ||||||||
\(974\) | 13666.2 | 0.449582 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 9315.71 | 0.305521 | ||||||||
\(977\) | −4733.67 | −0.155009 | −0.0775044 | − | 0.996992i | \(-0.524695\pi\) | ||||
−0.0775044 | + | 0.996992i | \(0.524695\pi\) | |||||||
\(978\) | 3934.62 | 0.128646 | ||||||||
\(979\) | −14087.3 | −0.459890 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 39537.5 | 1.28678 | ||||||||
\(982\) | 13489.4 | 0.438355 | ||||||||
\(983\) | 43971.5 | 1.42673 | 0.713363 | − | 0.700795i | \(-0.247171\pi\) | ||||
0.713363 | + | 0.700795i | \(0.247171\pi\) | |||||||
\(984\) | 3257.65 | 0.105539 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −318.146 | −0.0102757 | ||||||||
\(987\) | −3819.13 | −0.123166 | ||||||||
\(988\) | −8013.84 | −0.258051 | ||||||||
\(989\) | 16871.4 | 0.542448 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −14031.4 | −0.449769 | −0.224885 | − | 0.974385i | \(-0.572201\pi\) | ||||
−0.224885 | + | 0.974385i | \(0.572201\pi\) | |||||||
\(992\) | −5516.39 | −0.176558 | ||||||||
\(993\) | 5810.56 | 0.185692 | ||||||||
\(994\) | −15070.1 | −0.480880 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 847.807 | 0.0269717 | ||||||||
\(997\) | −43177.4 | −1.37156 | −0.685779 | − | 0.727810i | \(-0.740538\pi\) | ||||
−0.685779 | + | 0.727810i | \(0.740538\pi\) | |||||||
\(998\) | −10164.3 | −0.322390 | ||||||||
\(999\) | 9516.73 | 0.301397 |
(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 | 725.4.a.b.1.2 | 2 | ||
5.4 | even | 2 | 29.4.a.a.1.1 | ✓ | 2 | ||
15.14 | odd | 2 | 261.4.a.b.1.2 | 2 | |||
20.19 | odd | 2 | 464.4.a.f.1.1 | 2 | |||
35.34 | odd | 2 | 1421.4.a.c.1.1 | 2 | |||
40.19 | odd | 2 | 1856.4.a.h.1.2 | 2 | |||
40.29 | even | 2 | 1856.4.a.n.1.1 | 2 | |||
145.144 | even | 2 | 841.4.a.a.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
29.4.a.a.1.1 | ✓ | 2 | 5.4 | even | 2 | ||
261.4.a.b.1.2 | 2 | 15.14 | odd | 2 | |||
464.4.a.f.1.1 | 2 | 20.19 | odd | 2 | |||
725.4.a.b.1.2 | 2 | 1.1 | even | 1 | trivial | ||
841.4.a.a.1.2 | 2 | 145.144 | even | 2 | |||
1421.4.a.c.1.1 | 2 | 35.34 | odd | 2 | |||
1856.4.a.h.1.2 | 2 | 40.19 | odd | 2 | |||
1856.4.a.n.1.1 | 2 | 40.29 | even | 2 |