Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [435,4,Mod(1,435)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(435, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("435.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 435 = 3 \cdot 5 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 435.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: | \(25.6658308525\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - x^{6} - 35x^{5} + 18x^{4} + 329x^{3} - 167x^{2} - 767x + 638 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.26184\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 435.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.26184 | −0.446128 | −0.223064 | − | 0.974804i | \(-0.571606\pi\) | ||||
−0.223064 | + | 0.974804i | \(0.571606\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | −6.40776 | −0.800970 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | −3.78552 | −0.257572 | ||||||||
\(7\) | −13.4311 | −0.725213 | −0.362606 | − | 0.931942i | \(-0.618113\pi\) | ||||
−0.362606 | + | 0.931942i | \(0.618113\pi\) | |||||||
\(8\) | 18.1803 | 0.803463 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 6.30920 | 0.199514 | ||||||||
\(11\) | −1.30869 | −0.0358713 | −0.0179357 | − | 0.999839i | \(-0.505709\pi\) | ||||
−0.0179357 | + | 0.999839i | \(0.505709\pi\) | |||||||
\(12\) | −19.2233 | −0.462440 | ||||||||
\(13\) | 85.6641 | 1.82761 | 0.913806 | − | 0.406151i | \(-0.133129\pi\) | ||||
0.913806 | + | 0.406151i | \(0.133129\pi\) | |||||||
\(14\) | 16.9479 | 0.323538 | ||||||||
\(15\) | −15.0000 | −0.258199 | ||||||||
\(16\) | 28.3214 | 0.442523 | ||||||||
\(17\) | 67.9685 | 0.969693 | 0.484846 | − | 0.874599i | \(-0.338876\pi\) | ||||
0.484846 | + | 0.874599i | \(0.338876\pi\) | |||||||
\(18\) | −11.3566 | −0.148709 | ||||||||
\(19\) | −63.3429 | −0.764834 | −0.382417 | − | 0.923990i | \(-0.624908\pi\) | ||||
−0.382417 | + | 0.923990i | \(0.624908\pi\) | |||||||
\(20\) | 32.0388 | 0.358205 | ||||||||
\(21\) | −40.2934 | −0.418702 | ||||||||
\(22\) | 1.65136 | 0.0160032 | ||||||||
\(23\) | −139.990 | −1.26913 | −0.634565 | − | 0.772870i | \(-0.718821\pi\) | ||||
−0.634565 | + | 0.772870i | \(0.718821\pi\) | |||||||
\(24\) | 54.5409 | 0.463880 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | −108.094 | −0.815349 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 86.0634 | 0.580874 | ||||||||
\(29\) | −29.0000 | −0.185695 | ||||||||
\(30\) | 18.9276 | 0.115190 | ||||||||
\(31\) | −170.385 | −0.987164 | −0.493582 | − | 0.869699i | \(-0.664313\pi\) | ||||
−0.493582 | + | 0.869699i | \(0.664313\pi\) | |||||||
\(32\) | −181.179 | −1.00088 | ||||||||
\(33\) | −3.92607 | −0.0207103 | ||||||||
\(34\) | −85.7654 | −0.432607 | ||||||||
\(35\) | 67.1557 | 0.324325 | ||||||||
\(36\) | −57.6698 | −0.266990 | ||||||||
\(37\) | −405.970 | −1.80381 | −0.901905 | − | 0.431934i | \(-0.857831\pi\) | ||||
−0.901905 | + | 0.431934i | \(0.857831\pi\) | |||||||
\(38\) | 79.9286 | 0.341214 | ||||||||
\(39\) | 256.992 | 1.05517 | ||||||||
\(40\) | −90.9015 | −0.359320 | ||||||||
\(41\) | −447.863 | −1.70596 | −0.852982 | − | 0.521940i | \(-0.825208\pi\) | ||||
−0.852982 | + | 0.521940i | \(0.825208\pi\) | |||||||
\(42\) | 50.8438 | 0.186795 | ||||||||
\(43\) | 407.779 | 1.44618 | 0.723090 | − | 0.690754i | \(-0.242721\pi\) | ||||
0.723090 | + | 0.690754i | \(0.242721\pi\) | |||||||
\(44\) | 8.38576 | 0.0287318 | ||||||||
\(45\) | −45.0000 | −0.149071 | ||||||||
\(46\) | 176.645 | 0.566194 | ||||||||
\(47\) | −178.857 | −0.555086 | −0.277543 | − | 0.960713i | \(-0.589520\pi\) | ||||
−0.277543 | + | 0.960713i | \(0.589520\pi\) | |||||||
\(48\) | 84.9643 | 0.255491 | ||||||||
\(49\) | −162.605 | −0.474066 | ||||||||
\(50\) | −31.5460 | −0.0892256 | ||||||||
\(51\) | 203.905 | 0.559852 | ||||||||
\(52\) | −548.915 | −1.46386 | ||||||||
\(53\) | 93.3357 | 0.241899 | 0.120949 | − | 0.992659i | \(-0.461406\pi\) | ||||
0.120949 | + | 0.992659i | \(0.461406\pi\) | |||||||
\(54\) | −34.0697 | −0.0858574 | ||||||||
\(55\) | 6.54344 | 0.0160421 | ||||||||
\(56\) | −244.182 | −0.582682 | ||||||||
\(57\) | −190.029 | −0.441577 | ||||||||
\(58\) | 36.5934 | 0.0828439 | ||||||||
\(59\) | 279.796 | 0.617396 | 0.308698 | − | 0.951160i | \(-0.400107\pi\) | ||||
0.308698 | + | 0.951160i | \(0.400107\pi\) | |||||||
\(60\) | 96.1164 | 0.206810 | ||||||||
\(61\) | −793.549 | −1.66563 | −0.832816 | − | 0.553550i | \(-0.813273\pi\) | ||||
−0.832816 | + | 0.553550i | \(0.813273\pi\) | |||||||
\(62\) | 214.999 | 0.440402 | ||||||||
\(63\) | −120.880 | −0.241738 | ||||||||
\(64\) | 2.04805 | 0.00400010 | ||||||||
\(65\) | −428.321 | −0.817333 | ||||||||
\(66\) | 4.95407 | 0.00923945 | ||||||||
\(67\) | 460.471 | 0.839635 | 0.419818 | − | 0.907609i | \(-0.362094\pi\) | ||||
0.419818 | + | 0.907609i | \(0.362094\pi\) | |||||||
\(68\) | −435.526 | −0.776695 | ||||||||
\(69\) | −419.971 | −0.732732 | ||||||||
\(70\) | −84.7397 | −0.144690 | ||||||||
\(71\) | 803.153 | 1.34249 | 0.671244 | − | 0.741236i | \(-0.265760\pi\) | ||||
0.671244 | + | 0.741236i | \(0.265760\pi\) | |||||||
\(72\) | 163.623 | 0.267821 | ||||||||
\(73\) | −150.833 | −0.241832 | −0.120916 | − | 0.992663i | \(-0.538583\pi\) | ||||
−0.120916 | + | 0.992663i | \(0.538583\pi\) | |||||||
\(74\) | 512.269 | 0.804730 | ||||||||
\(75\) | 75.0000 | 0.115470 | ||||||||
\(76\) | 405.886 | 0.612609 | ||||||||
\(77\) | 17.5772 | 0.0260143 | ||||||||
\(78\) | −324.283 | −0.470742 | ||||||||
\(79\) | −313.814 | −0.446922 | −0.223461 | − | 0.974713i | \(-0.571735\pi\) | ||||
−0.223461 | + | 0.974713i | \(0.571735\pi\) | |||||||
\(80\) | −141.607 | −0.197902 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 565.132 | 0.761078 | ||||||||
\(83\) | 250.514 | 0.331295 | 0.165648 | − | 0.986185i | \(-0.447029\pi\) | ||||
0.165648 | + | 0.986185i | \(0.447029\pi\) | |||||||
\(84\) | 258.190 | 0.335368 | ||||||||
\(85\) | −339.842 | −0.433660 | ||||||||
\(86\) | −514.552 | −0.645181 | ||||||||
\(87\) | −87.0000 | −0.107211 | ||||||||
\(88\) | −23.7923 | −0.0288213 | ||||||||
\(89\) | −97.2972 | −0.115882 | −0.0579409 | − | 0.998320i | \(-0.518453\pi\) | ||||
−0.0579409 | + | 0.998320i | \(0.518453\pi\) | |||||||
\(90\) | 56.7828 | 0.0665048 | ||||||||
\(91\) | −1150.57 | −1.32541 | ||||||||
\(92\) | 897.024 | 1.01653 | ||||||||
\(93\) | −511.156 | −0.569940 | ||||||||
\(94\) | 225.689 | 0.247639 | ||||||||
\(95\) | 316.714 | 0.342044 | ||||||||
\(96\) | −543.538 | −0.577861 | ||||||||
\(97\) | −1342.23 | −1.40497 | −0.702487 | − | 0.711697i | \(-0.747927\pi\) | ||||
−0.702487 | + | 0.711697i | \(0.747927\pi\) | |||||||
\(98\) | 205.181 | 0.211494 | ||||||||
\(99\) | −11.7782 | −0.0119571 | ||||||||
\(100\) | −160.194 | −0.160194 | ||||||||
\(101\) | 73.7087 | 0.0726167 | 0.0363084 | − | 0.999341i | \(-0.488440\pi\) | ||||
0.0363084 | + | 0.999341i | \(0.488440\pi\) | |||||||
\(102\) | −257.296 | −0.249766 | ||||||||
\(103\) | −1307.09 | −1.25040 | −0.625199 | − | 0.780465i | \(-0.714982\pi\) | ||||
−0.625199 | + | 0.780465i | \(0.714982\pi\) | |||||||
\(104\) | 1557.40 | 1.46842 | ||||||||
\(105\) | 201.467 | 0.187249 | ||||||||
\(106\) | −117.775 | −0.107918 | ||||||||
\(107\) | 845.454 | 0.763861 | 0.381930 | − | 0.924191i | \(-0.375259\pi\) | ||||
0.381930 | + | 0.924191i | \(0.375259\pi\) | |||||||
\(108\) | −173.009 | −0.154147 | ||||||||
\(109\) | −1502.99 | −1.32074 | −0.660370 | − | 0.750941i | \(-0.729600\pi\) | ||||
−0.660370 | + | 0.750941i | \(0.729600\pi\) | |||||||
\(110\) | −8.25678 | −0.00715685 | ||||||||
\(111\) | −1217.91 | −1.04143 | ||||||||
\(112\) | −380.389 | −0.320923 | ||||||||
\(113\) | −317.218 | −0.264083 | −0.132042 | − | 0.991244i | \(-0.542153\pi\) | ||||
−0.132042 | + | 0.991244i | \(0.542153\pi\) | |||||||
\(114\) | 239.786 | 0.197000 | ||||||||
\(115\) | 699.951 | 0.567572 | ||||||||
\(116\) | 185.825 | 0.148736 | ||||||||
\(117\) | 770.977 | 0.609204 | ||||||||
\(118\) | −353.058 | −0.275438 | ||||||||
\(119\) | −912.893 | −0.703234 | ||||||||
\(120\) | −272.704 | −0.207453 | ||||||||
\(121\) | −1329.29 | −0.998713 | ||||||||
\(122\) | 1001.33 | 0.743085 | ||||||||
\(123\) | −1343.59 | −0.984939 | ||||||||
\(124\) | 1091.79 | 0.790689 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 152.531 | 0.107846 | ||||||||
\(127\) | −1936.01 | −1.35270 | −0.676349 | − | 0.736581i | \(-0.736439\pi\) | ||||
−0.676349 | + | 0.736581i | \(0.736439\pi\) | |||||||
\(128\) | 1446.85 | 0.999100 | ||||||||
\(129\) | 1223.34 | 0.834952 | ||||||||
\(130\) | 540.472 | 0.364635 | ||||||||
\(131\) | −1234.54 | −0.823379 | −0.411689 | − | 0.911324i | \(-0.635061\pi\) | ||||
−0.411689 | + | 0.911324i | \(0.635061\pi\) | |||||||
\(132\) | 25.1573 | 0.0165883 | ||||||||
\(133\) | 850.767 | 0.554668 | ||||||||
\(134\) | −581.042 | −0.374585 | ||||||||
\(135\) | −135.000 | −0.0860663 | ||||||||
\(136\) | 1235.69 | 0.779112 | ||||||||
\(137\) | −886.190 | −0.552645 | −0.276322 | − | 0.961065i | \(-0.589116\pi\) | ||||
−0.276322 | + | 0.961065i | \(0.589116\pi\) | |||||||
\(138\) | 529.936 | 0.326892 | ||||||||
\(139\) | 1582.12 | 0.965421 | 0.482711 | − | 0.875780i | \(-0.339652\pi\) | ||||
0.482711 | + | 0.875780i | \(0.339652\pi\) | |||||||
\(140\) | −430.317 | −0.259775 | ||||||||
\(141\) | −536.572 | −0.320479 | ||||||||
\(142\) | −1013.45 | −0.598922 | ||||||||
\(143\) | −112.108 | −0.0655588 | ||||||||
\(144\) | 254.893 | 0.147508 | ||||||||
\(145\) | 145.000 | 0.0830455 | ||||||||
\(146\) | 190.328 | 0.107888 | ||||||||
\(147\) | −487.814 | −0.273702 | ||||||||
\(148\) | 2601.36 | 1.44480 | ||||||||
\(149\) | −1649.57 | −0.906969 | −0.453485 | − | 0.891264i | \(-0.649819\pi\) | ||||
−0.453485 | + | 0.891264i | \(0.649819\pi\) | |||||||
\(150\) | −94.6380 | −0.0515144 | ||||||||
\(151\) | 343.852 | 0.185313 | 0.0926565 | − | 0.995698i | \(-0.470464\pi\) | ||||
0.0926565 | + | 0.995698i | \(0.470464\pi\) | |||||||
\(152\) | −1151.59 | −0.614516 | ||||||||
\(153\) | 611.716 | 0.323231 | ||||||||
\(154\) | −22.1796 | −0.0116057 | ||||||||
\(155\) | 851.926 | 0.441473 | ||||||||
\(156\) | −1646.75 | −0.845161 | ||||||||
\(157\) | 2493.83 | 1.26770 | 0.633851 | − | 0.773455i | \(-0.281473\pi\) | ||||
0.633851 | + | 0.773455i | \(0.281473\pi\) | |||||||
\(158\) | 395.983 | 0.199384 | ||||||||
\(159\) | 280.007 | 0.139660 | ||||||||
\(160\) | 905.897 | 0.447609 | ||||||||
\(161\) | 1880.23 | 0.920389 | ||||||||
\(162\) | −102.209 | −0.0495698 | ||||||||
\(163\) | −1915.12 | −0.920270 | −0.460135 | − | 0.887849i | \(-0.652199\pi\) | ||||
−0.460135 | + | 0.887849i | \(0.652199\pi\) | |||||||
\(164\) | 2869.80 | 1.36643 | ||||||||
\(165\) | 19.6303 | 0.00926194 | ||||||||
\(166\) | −316.109 | −0.147800 | ||||||||
\(167\) | 99.5806 | 0.0461424 | 0.0230712 | − | 0.999734i | \(-0.492656\pi\) | ||||
0.0230712 | + | 0.999734i | \(0.492656\pi\) | |||||||
\(168\) | −732.546 | −0.336411 | ||||||||
\(169\) | 5141.34 | 2.34016 | ||||||||
\(170\) | 428.827 | 0.193468 | ||||||||
\(171\) | −570.086 | −0.254945 | ||||||||
\(172\) | −2612.95 | −1.15835 | ||||||||
\(173\) | 2139.30 | 0.940160 | 0.470080 | − | 0.882624i | \(-0.344225\pi\) | ||||
0.470080 | + | 0.882624i | \(0.344225\pi\) | |||||||
\(174\) | 109.780 | 0.0478299 | ||||||||
\(175\) | −335.778 | −0.145043 | ||||||||
\(176\) | −37.0640 | −0.0158739 | ||||||||
\(177\) | 839.389 | 0.356454 | ||||||||
\(178\) | 122.773 | 0.0516981 | ||||||||
\(179\) | 1863.54 | 0.778142 | 0.389071 | − | 0.921208i | \(-0.372796\pi\) | ||||
0.389071 | + | 0.921208i | \(0.372796\pi\) | |||||||
\(180\) | 288.349 | 0.119402 | ||||||||
\(181\) | −3008.76 | −1.23558 | −0.617788 | − | 0.786345i | \(-0.711971\pi\) | ||||
−0.617788 | + | 0.786345i | \(0.711971\pi\) | |||||||
\(182\) | 1451.83 | 0.591301 | ||||||||
\(183\) | −2380.65 | −0.961653 | ||||||||
\(184\) | −2545.06 | −1.01970 | ||||||||
\(185\) | 2029.85 | 0.806689 | ||||||||
\(186\) | 644.997 | 0.254266 | ||||||||
\(187\) | −88.9496 | −0.0347842 | ||||||||
\(188\) | 1146.07 | 0.444607 | ||||||||
\(189\) | −362.641 | −0.139567 | ||||||||
\(190\) | −399.643 | −0.152596 | ||||||||
\(191\) | 5175.24 | 1.96056 | 0.980280 | − | 0.197611i | \(-0.0633184\pi\) | ||||
0.980280 | + | 0.197611i | \(0.0633184\pi\) | |||||||
\(192\) | 6.14415 | 0.00230946 | ||||||||
\(193\) | −3407.89 | −1.27101 | −0.635505 | − | 0.772097i | \(-0.719208\pi\) | ||||
−0.635505 | + | 0.772097i | \(0.719208\pi\) | |||||||
\(194\) | 1693.68 | 0.626798 | ||||||||
\(195\) | −1284.96 | −0.471887 | ||||||||
\(196\) | 1041.93 | 0.379713 | ||||||||
\(197\) | −2662.23 | −0.962823 | −0.481412 | − | 0.876495i | \(-0.659876\pi\) | ||||
−0.481412 | + | 0.876495i | \(0.659876\pi\) | |||||||
\(198\) | 14.8622 | 0.00533440 | ||||||||
\(199\) | 1124.12 | 0.400437 | 0.200218 | − | 0.979751i | \(-0.435835\pi\) | ||||
0.200218 | + | 0.979751i | \(0.435835\pi\) | |||||||
\(200\) | 454.507 | 0.160693 | ||||||||
\(201\) | 1381.41 | 0.484764 | ||||||||
\(202\) | −93.0086 | −0.0323964 | ||||||||
\(203\) | 389.503 | 0.134669 | ||||||||
\(204\) | −1306.58 | −0.448425 | ||||||||
\(205\) | 2239.32 | 0.762930 | ||||||||
\(206\) | 1649.33 | 0.557837 | ||||||||
\(207\) | −1259.91 | −0.423043 | ||||||||
\(208\) | 2426.13 | 0.808759 | ||||||||
\(209\) | 82.8961 | 0.0274356 | ||||||||
\(210\) | −254.219 | −0.0835371 | ||||||||
\(211\) | 109.248 | 0.0356442 | 0.0178221 | − | 0.999841i | \(-0.494327\pi\) | ||||
0.0178221 | + | 0.999841i | \(0.494327\pi\) | |||||||
\(212\) | −598.072 | −0.193754 | ||||||||
\(213\) | 2409.46 | 0.775086 | ||||||||
\(214\) | −1066.83 | −0.340780 | ||||||||
\(215\) | −2038.89 | −0.646751 | ||||||||
\(216\) | 490.868 | 0.154627 | ||||||||
\(217\) | 2288.47 | 0.715904 | ||||||||
\(218\) | 1896.54 | 0.589219 | ||||||||
\(219\) | −452.500 | −0.139622 | ||||||||
\(220\) | −41.9288 | −0.0128493 | ||||||||
\(221\) | 5822.46 | 1.77222 | ||||||||
\(222\) | 1536.81 | 0.464611 | ||||||||
\(223\) | −4655.65 | −1.39805 | −0.699026 | − | 0.715097i | \(-0.746383\pi\) | ||||
−0.699026 | + | 0.715097i | \(0.746383\pi\) | |||||||
\(224\) | 2433.45 | 0.725854 | ||||||||
\(225\) | 225.000 | 0.0666667 | ||||||||
\(226\) | 400.279 | 0.117815 | ||||||||
\(227\) | 3715.56 | 1.08639 | 0.543195 | − | 0.839606i | \(-0.317214\pi\) | ||||
0.543195 | + | 0.839606i | \(0.317214\pi\) | |||||||
\(228\) | 1217.66 | 0.353690 | ||||||||
\(229\) | 2437.74 | 0.703451 | 0.351726 | − | 0.936103i | \(-0.385595\pi\) | ||||
0.351726 | + | 0.936103i | \(0.385595\pi\) | |||||||
\(230\) | −883.227 | −0.253210 | ||||||||
\(231\) | 52.7315 | 0.0150194 | ||||||||
\(232\) | −527.228 | −0.149199 | ||||||||
\(233\) | −2704.29 | −0.760360 | −0.380180 | − | 0.924912i | \(-0.624138\pi\) | ||||
−0.380180 | + | 0.924912i | \(0.624138\pi\) | |||||||
\(234\) | −972.850 | −0.271783 | ||||||||
\(235\) | 894.287 | 0.248242 | ||||||||
\(236\) | −1792.87 | −0.494516 | ||||||||
\(237\) | −941.441 | −0.258030 | ||||||||
\(238\) | 1151.93 | 0.313732 | ||||||||
\(239\) | 6018.67 | 1.62893 | 0.814467 | − | 0.580210i | \(-0.197030\pi\) | ||||
0.814467 | + | 0.580210i | \(0.197030\pi\) | |||||||
\(240\) | −424.822 | −0.114259 | ||||||||
\(241\) | −1244.90 | −0.332743 | −0.166372 | − | 0.986063i | \(-0.553205\pi\) | ||||
−0.166372 | + | 0.986063i | \(0.553205\pi\) | |||||||
\(242\) | 1677.35 | 0.445554 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 5084.87 | 1.33412 | ||||||||
\(245\) | 813.024 | 0.212009 | ||||||||
\(246\) | 1695.40 | 0.439409 | ||||||||
\(247\) | −5426.21 | −1.39782 | ||||||||
\(248\) | −3097.65 | −0.793150 | ||||||||
\(249\) | 751.543 | 0.191273 | ||||||||
\(250\) | 157.730 | 0.0399029 | ||||||||
\(251\) | 2477.48 | 0.623016 | 0.311508 | − | 0.950244i | \(-0.399166\pi\) | ||||
0.311508 | + | 0.950244i | \(0.399166\pi\) | |||||||
\(252\) | 774.571 | 0.193625 | ||||||||
\(253\) | 183.204 | 0.0455254 | ||||||||
\(254\) | 2442.93 | 0.603477 | ||||||||
\(255\) | −1019.53 | −0.250374 | ||||||||
\(256\) | −1842.08 | −0.449727 | ||||||||
\(257\) | −4778.08 | −1.15972 | −0.579860 | − | 0.814716i | \(-0.696893\pi\) | ||||
−0.579860 | + | 0.814716i | \(0.696893\pi\) | |||||||
\(258\) | −1543.66 | −0.372495 | ||||||||
\(259\) | 5452.63 | 1.30815 | ||||||||
\(260\) | 2744.58 | 0.654659 | ||||||||
\(261\) | −261.000 | −0.0618984 | ||||||||
\(262\) | 1557.80 | 0.367332 | ||||||||
\(263\) | −1571.56 | −0.368467 | −0.184233 | − | 0.982883i | \(-0.558980\pi\) | ||||
−0.184233 | + | 0.982883i | \(0.558980\pi\) | |||||||
\(264\) | −71.3770 | −0.0166400 | ||||||||
\(265\) | −466.678 | −0.108180 | ||||||||
\(266\) | −1073.53 | −0.247453 | ||||||||
\(267\) | −291.892 | −0.0669044 | ||||||||
\(268\) | −2950.59 | −0.672522 | ||||||||
\(269\) | 4946.58 | 1.12118 | 0.560591 | − | 0.828093i | \(-0.310574\pi\) | ||||
0.560591 | + | 0.828093i | \(0.310574\pi\) | |||||||
\(270\) | 170.348 | 0.0383966 | ||||||||
\(271\) | −914.942 | −0.205088 | −0.102544 | − | 0.994728i | \(-0.532698\pi\) | ||||
−0.102544 | + | 0.994728i | \(0.532698\pi\) | |||||||
\(272\) | 1924.97 | 0.429111 | ||||||||
\(273\) | −3451.70 | −0.765224 | ||||||||
\(274\) | 1118.23 | 0.246550 | ||||||||
\(275\) | −32.7172 | −0.00717426 | ||||||||
\(276\) | 2691.07 | 0.586896 | ||||||||
\(277\) | −2441.56 | −0.529599 | −0.264799 | − | 0.964304i | \(-0.585306\pi\) | ||||
−0.264799 | + | 0.964304i | \(0.585306\pi\) | |||||||
\(278\) | −1996.38 | −0.430701 | ||||||||
\(279\) | −1533.47 | −0.329055 | ||||||||
\(280\) | 1220.91 | 0.260583 | ||||||||
\(281\) | −5311.04 | −1.12751 | −0.563755 | − | 0.825942i | \(-0.690644\pi\) | ||||
−0.563755 | + | 0.825942i | \(0.690644\pi\) | |||||||
\(282\) | 677.068 | 0.142975 | ||||||||
\(283\) | 669.167 | 0.140558 | 0.0702789 | − | 0.997527i | \(-0.477611\pi\) | ||||
0.0702789 | + | 0.997527i | \(0.477611\pi\) | |||||||
\(284\) | −5146.41 | −1.07529 | ||||||||
\(285\) | 950.143 | 0.197479 | ||||||||
\(286\) | 141.462 | 0.0292476 | ||||||||
\(287\) | 6015.31 | 1.23719 | ||||||||
\(288\) | −1630.62 | −0.333628 | ||||||||
\(289\) | −293.286 | −0.0596960 | ||||||||
\(290\) | −182.967 | −0.0370489 | ||||||||
\(291\) | −4026.68 | −0.811162 | ||||||||
\(292\) | 966.504 | 0.193700 | ||||||||
\(293\) | −7468.02 | −1.48903 | −0.744516 | − | 0.667604i | \(-0.767320\pi\) | ||||
−0.744516 | + | 0.667604i | \(0.767320\pi\) | |||||||
\(294\) | 615.544 | 0.122106 | ||||||||
\(295\) | −1398.98 | −0.276108 | ||||||||
\(296\) | −7380.65 | −1.44930 | ||||||||
\(297\) | −35.3346 | −0.00690344 | ||||||||
\(298\) | 2081.50 | 0.404624 | ||||||||
\(299\) | −11992.1 | −2.31948 | ||||||||
\(300\) | −480.582 | −0.0924880 | ||||||||
\(301\) | −5476.93 | −1.04879 | ||||||||
\(302\) | −433.886 | −0.0826733 | ||||||||
\(303\) | 221.126 | 0.0419253 | ||||||||
\(304\) | −1793.96 | −0.338456 | ||||||||
\(305\) | 3967.74 | 0.744893 | ||||||||
\(306\) | −771.888 | −0.144202 | ||||||||
\(307\) | −9927.63 | −1.84560 | −0.922801 | − | 0.385278i | \(-0.874106\pi\) | ||||
−0.922801 | + | 0.385278i | \(0.874106\pi\) | |||||||
\(308\) | −112.630 | −0.0208367 | ||||||||
\(309\) | −3921.26 | −0.721918 | ||||||||
\(310\) | −1075.00 | −0.196954 | ||||||||
\(311\) | 3131.42 | 0.570953 | 0.285477 | − | 0.958386i | \(-0.407848\pi\) | ||||
0.285477 | + | 0.958386i | \(0.407848\pi\) | |||||||
\(312\) | 4672.20 | 0.847792 | ||||||||
\(313\) | 8434.75 | 1.52320 | 0.761598 | − | 0.648050i | \(-0.224415\pi\) | ||||
0.761598 | + | 0.648050i | \(0.224415\pi\) | |||||||
\(314\) | −3146.82 | −0.565558 | ||||||||
\(315\) | 604.401 | 0.108108 | ||||||||
\(316\) | 2010.84 | 0.357971 | ||||||||
\(317\) | −9162.80 | −1.62345 | −0.811725 | − | 0.584039i | \(-0.801471\pi\) | ||||
−0.811725 | + | 0.584039i | \(0.801471\pi\) | |||||||
\(318\) | −353.324 | −0.0623064 | ||||||||
\(319\) | 37.9520 | 0.00666114 | ||||||||
\(320\) | −10.2403 | −0.00178890 | ||||||||
\(321\) | 2536.36 | 0.441015 | ||||||||
\(322\) | −2372.55 | −0.410611 | ||||||||
\(323\) | −4305.32 | −0.741654 | ||||||||
\(324\) | −519.028 | −0.0889966 | ||||||||
\(325\) | 2141.60 | 0.365522 | ||||||||
\(326\) | 2416.58 | 0.410558 | ||||||||
\(327\) | −4508.98 | −0.762529 | ||||||||
\(328\) | −8142.29 | −1.37068 | ||||||||
\(329\) | 2402.26 | 0.402555 | ||||||||
\(330\) | −24.7703 | −0.00413201 | ||||||||
\(331\) | 5194.87 | 0.862647 | 0.431323 | − | 0.902197i | \(-0.358047\pi\) | ||||
0.431323 | + | 0.902197i | \(0.358047\pi\) | |||||||
\(332\) | −1605.23 | −0.265357 | ||||||||
\(333\) | −3653.73 | −0.601270 | ||||||||
\(334\) | −125.655 | −0.0205854 | ||||||||
\(335\) | −2302.36 | −0.375496 | ||||||||
\(336\) | −1141.17 | −0.185285 | ||||||||
\(337\) | −3217.15 | −0.520027 | −0.260014 | − | 0.965605i | \(-0.583727\pi\) | ||||
−0.260014 | + | 0.965605i | \(0.583727\pi\) | |||||||
\(338\) | −6487.55 | −1.04401 | ||||||||
\(339\) | −951.655 | −0.152468 | ||||||||
\(340\) | 2177.63 | 0.347348 | ||||||||
\(341\) | 222.981 | 0.0354109 | ||||||||
\(342\) | 719.358 | 0.113738 | ||||||||
\(343\) | 6790.84 | 1.06901 | ||||||||
\(344\) | 7413.54 | 1.16195 | ||||||||
\(345\) | 2099.85 | 0.327688 | ||||||||
\(346\) | −2699.45 | −0.419432 | ||||||||
\(347\) | −609.761 | −0.0943334 | −0.0471667 | − | 0.998887i | \(-0.515019\pi\) | ||||
−0.0471667 | + | 0.998887i | \(0.515019\pi\) | |||||||
\(348\) | 557.475 | 0.0858730 | ||||||||
\(349\) | 4406.40 | 0.675843 | 0.337921 | − | 0.941174i | \(-0.390276\pi\) | ||||
0.337921 | + | 0.941174i | \(0.390276\pi\) | |||||||
\(350\) | 423.699 | 0.0647075 | ||||||||
\(351\) | 2312.93 | 0.351724 | ||||||||
\(352\) | 237.108 | 0.0359031 | ||||||||
\(353\) | 2480.09 | 0.373943 | 0.186971 | − | 0.982365i | \(-0.440133\pi\) | ||||
0.186971 | + | 0.982365i | \(0.440133\pi\) | |||||||
\(354\) | −1059.18 | −0.159024 | ||||||||
\(355\) | −4015.76 | −0.600379 | ||||||||
\(356\) | 623.457 | 0.0928178 | ||||||||
\(357\) | −2738.68 | −0.406012 | ||||||||
\(358\) | −2351.49 | −0.347151 | ||||||||
\(359\) | 6578.82 | 0.967177 | 0.483589 | − | 0.875295i | \(-0.339333\pi\) | ||||
0.483589 | + | 0.875295i | \(0.339333\pi\) | |||||||
\(360\) | −818.113 | −0.119773 | ||||||||
\(361\) | −2846.68 | −0.415028 | ||||||||
\(362\) | 3796.57 | 0.551225 | ||||||||
\(363\) | −3987.86 | −0.576607 | ||||||||
\(364\) | 7372.55 | 1.06161 | ||||||||
\(365\) | 754.167 | 0.108150 | ||||||||
\(366\) | 3004.00 | 0.429020 | ||||||||
\(367\) | −731.114 | −0.103989 | −0.0519943 | − | 0.998647i | \(-0.516558\pi\) | ||||
−0.0519943 | + | 0.998647i | \(0.516558\pi\) | |||||||
\(368\) | −3964.72 | −0.561618 | ||||||||
\(369\) | −4030.77 | −0.568655 | ||||||||
\(370\) | −2561.34 | −0.359886 | ||||||||
\(371\) | −1253.60 | −0.175428 | ||||||||
\(372\) | 3275.36 | 0.456504 | ||||||||
\(373\) | −1673.03 | −0.232242 | −0.116121 | − | 0.993235i | \(-0.537046\pi\) | ||||
−0.116121 | + | 0.993235i | \(0.537046\pi\) | |||||||
\(374\) | 112.240 | 0.0155182 | ||||||||
\(375\) | −375.000 | −0.0516398 | ||||||||
\(376\) | −3251.68 | −0.445991 | ||||||||
\(377\) | −2484.26 | −0.339379 | ||||||||
\(378\) | 457.594 | 0.0622649 | ||||||||
\(379\) | 3760.44 | 0.509659 | 0.254830 | − | 0.966986i | \(-0.417981\pi\) | ||||
0.254830 | + | 0.966986i | \(0.417981\pi\) | |||||||
\(380\) | −2029.43 | −0.273967 | ||||||||
\(381\) | −5808.02 | −0.780981 | ||||||||
\(382\) | −6530.33 | −0.874661 | ||||||||
\(383\) | −12540.8 | −1.67312 | −0.836562 | − | 0.547872i | \(-0.815438\pi\) | ||||
−0.836562 | + | 0.547872i | \(0.815438\pi\) | |||||||
\(384\) | 4340.55 | 0.576831 | ||||||||
\(385\) | −87.8859 | −0.0116340 | ||||||||
\(386\) | 4300.21 | 0.567033 | ||||||||
\(387\) | 3670.01 | 0.482060 | ||||||||
\(388\) | 8600.66 | 1.12534 | ||||||||
\(389\) | 5779.21 | 0.753259 | 0.376629 | − | 0.926364i | \(-0.377083\pi\) | ||||
0.376629 | + | 0.926364i | \(0.377083\pi\) | |||||||
\(390\) | 1621.42 | 0.210522 | ||||||||
\(391\) | −9514.92 | −1.23067 | ||||||||
\(392\) | −2956.20 | −0.380895 | ||||||||
\(393\) | −3703.63 | −0.475378 | ||||||||
\(394\) | 3359.31 | 0.429542 | ||||||||
\(395\) | 1569.07 | 0.199869 | ||||||||
\(396\) | 75.4719 | 0.00957728 | ||||||||
\(397\) | 14394.6 | 1.81976 | 0.909881 | − | 0.414869i | \(-0.136173\pi\) | ||||
0.909881 | + | 0.414869i | \(0.136173\pi\) | |||||||
\(398\) | −1418.46 | −0.178646 | ||||||||
\(399\) | 2552.30 | 0.320238 | ||||||||
\(400\) | 708.036 | 0.0885045 | ||||||||
\(401\) | 8620.31 | 1.07351 | 0.536756 | − | 0.843738i | \(-0.319650\pi\) | ||||
0.536756 | + | 0.843738i | \(0.319650\pi\) | |||||||
\(402\) | −1743.12 | −0.216267 | ||||||||
\(403\) | −14595.9 | −1.80415 | ||||||||
\(404\) | −472.308 | −0.0581638 | ||||||||
\(405\) | −405.000 | −0.0496904 | ||||||||
\(406\) | −491.490 | −0.0600795 | ||||||||
\(407\) | 531.288 | 0.0647051 | ||||||||
\(408\) | 3707.06 | 0.449821 | ||||||||
\(409\) | −14058.0 | −1.69957 | −0.849783 | − | 0.527133i | \(-0.823267\pi\) | ||||
−0.849783 | + | 0.527133i | \(0.823267\pi\) | |||||||
\(410\) | −2825.66 | −0.340365 | ||||||||
\(411\) | −2658.57 | −0.319070 | ||||||||
\(412\) | 8375.49 | 1.00153 | ||||||||
\(413\) | −3757.98 | −0.447744 | ||||||||
\(414\) | 1589.81 | 0.188731 | ||||||||
\(415\) | −1252.57 | −0.148160 | ||||||||
\(416\) | −15520.6 | −1.82923 | ||||||||
\(417\) | 4746.36 | 0.557386 | ||||||||
\(418\) | −104.602 | −0.0122398 | ||||||||
\(419\) | −308.722 | −0.0359954 | −0.0179977 | − | 0.999838i | \(-0.505729\pi\) | ||||
−0.0179977 | + | 0.999838i | \(0.505729\pi\) | |||||||
\(420\) | −1290.95 | −0.149981 | ||||||||
\(421\) | 7341.48 | 0.849886 | 0.424943 | − | 0.905220i | \(-0.360294\pi\) | ||||
0.424943 | + | 0.905220i | \(0.360294\pi\) | |||||||
\(422\) | −137.853 | −0.0159019 | ||||||||
\(423\) | −1609.72 | −0.185029 | ||||||||
\(424\) | 1696.87 | 0.194357 | ||||||||
\(425\) | 1699.21 | 0.193939 | ||||||||
\(426\) | −3040.35 | −0.345788 | ||||||||
\(427\) | 10658.3 | 1.20794 | ||||||||
\(428\) | −5417.47 | −0.611830 | ||||||||
\(429\) | −336.323 | −0.0378504 | ||||||||
\(430\) | 2572.76 | 0.288534 | ||||||||
\(431\) | −16660.8 | −1.86201 | −0.931003 | − | 0.365013i | \(-0.881065\pi\) | ||||
−0.931003 | + | 0.365013i | \(0.881065\pi\) | |||||||
\(432\) | 764.679 | 0.0851635 | ||||||||
\(433\) | 10091.5 | 1.12001 | 0.560006 | − | 0.828488i | \(-0.310799\pi\) | ||||
0.560006 | + | 0.828488i | \(0.310799\pi\) | |||||||
\(434\) | −2887.68 | −0.319385 | ||||||||
\(435\) | 435.000 | 0.0479463 | ||||||||
\(436\) | 9630.82 | 1.05787 | ||||||||
\(437\) | 8867.38 | 0.970674 | ||||||||
\(438\) | 570.983 | 0.0622891 | ||||||||
\(439\) | 5149.74 | 0.559871 | 0.279936 | − | 0.960019i | \(-0.409687\pi\) | ||||
0.279936 | + | 0.960019i | \(0.409687\pi\) | |||||||
\(440\) | 118.962 | 0.0128893 | ||||||||
\(441\) | −1463.44 | −0.158022 | ||||||||
\(442\) | −7347.02 | −0.790638 | ||||||||
\(443\) | 15820.5 | 1.69674 | 0.848371 | − | 0.529402i | \(-0.177584\pi\) | ||||
0.848371 | + | 0.529402i | \(0.177584\pi\) | |||||||
\(444\) | 7804.07 | 0.834154 | ||||||||
\(445\) | 486.486 | 0.0518239 | ||||||||
\(446\) | 5874.69 | 0.623710 | ||||||||
\(447\) | −4948.72 | −0.523639 | ||||||||
\(448\) | −27.5076 | −0.00290092 | ||||||||
\(449\) | −13903.0 | −1.46130 | −0.730651 | − | 0.682751i | \(-0.760783\pi\) | ||||
−0.730651 | + | 0.682751i | \(0.760783\pi\) | |||||||
\(450\) | −283.914 | −0.0297419 | ||||||||
\(451\) | 586.114 | 0.0611952 | ||||||||
\(452\) | 2032.66 | 0.211523 | ||||||||
\(453\) | 1031.55 | 0.106990 | ||||||||
\(454\) | −4688.45 | −0.484669 | ||||||||
\(455\) | 5752.83 | 0.592740 | ||||||||
\(456\) | −3454.78 | −0.354791 | ||||||||
\(457\) | 4315.24 | 0.441704 | 0.220852 | − | 0.975307i | \(-0.429116\pi\) | ||||
0.220852 | + | 0.975307i | \(0.429116\pi\) | |||||||
\(458\) | −3076.04 | −0.313829 | ||||||||
\(459\) | 1835.15 | 0.186617 | ||||||||
\(460\) | −4485.12 | −0.454608 | ||||||||
\(461\) | 5936.08 | 0.599720 | 0.299860 | − | 0.953983i | \(-0.403060\pi\) | ||||
0.299860 | + | 0.953983i | \(0.403060\pi\) | |||||||
\(462\) | −66.5388 | −0.00670057 | ||||||||
\(463\) | −12894.4 | −1.29428 | −0.647141 | − | 0.762370i | \(-0.724036\pi\) | ||||
−0.647141 | + | 0.762370i | \(0.724036\pi\) | |||||||
\(464\) | −821.322 | −0.0821744 | ||||||||
\(465\) | 2555.78 | 0.254885 | ||||||||
\(466\) | 3412.38 | 0.339218 | ||||||||
\(467\) | 12653.8 | 1.25385 | 0.626924 | − | 0.779081i | \(-0.284314\pi\) | ||||
0.626924 | + | 0.779081i | \(0.284314\pi\) | |||||||
\(468\) | −4940.24 | −0.487954 | ||||||||
\(469\) | −6184.65 | −0.608914 | ||||||||
\(470\) | −1128.45 | −0.110748 | ||||||||
\(471\) | 7481.49 | 0.731909 | ||||||||
\(472\) | 5086.78 | 0.496055 | ||||||||
\(473\) | −533.656 | −0.0518764 | ||||||||
\(474\) | 1187.95 | 0.115115 | ||||||||
\(475\) | −1583.57 | −0.152967 | ||||||||
\(476\) | 5849.60 | 0.563269 | ||||||||
\(477\) | 840.021 | 0.0806330 | ||||||||
\(478\) | −7594.60 | −0.726713 | ||||||||
\(479\) | 8991.57 | 0.857694 | 0.428847 | − | 0.903377i | \(-0.358920\pi\) | ||||
0.428847 | + | 0.903377i | \(0.358920\pi\) | |||||||
\(480\) | 2717.69 | 0.258427 | ||||||||
\(481\) | −34777.0 | −3.29667 | ||||||||
\(482\) | 1570.87 | 0.148446 | ||||||||
\(483\) | 5640.68 | 0.531387 | ||||||||
\(484\) | 8517.75 | 0.799939 | ||||||||
\(485\) | 6711.13 | 0.628323 | ||||||||
\(486\) | −306.627 | −0.0286191 | ||||||||
\(487\) | 7671.39 | 0.713806 | 0.356903 | − | 0.934141i | \(-0.383833\pi\) | ||||
0.356903 | + | 0.934141i | \(0.383833\pi\) | |||||||
\(488\) | −14426.9 | −1.33827 | ||||||||
\(489\) | −5745.37 | −0.531318 | ||||||||
\(490\) | −1025.91 | −0.0945831 | ||||||||
\(491\) | 10322.9 | 0.948809 | 0.474405 | − | 0.880307i | \(-0.342663\pi\) | ||||
0.474405 | + | 0.880307i | \(0.342663\pi\) | |||||||
\(492\) | 8609.40 | 0.788906 | ||||||||
\(493\) | −1971.09 | −0.180067 | ||||||||
\(494\) | 6847.01 | 0.623607 | ||||||||
\(495\) | 58.8910 | 0.00534738 | ||||||||
\(496\) | −4825.56 | −0.436843 | ||||||||
\(497\) | −10787.3 | −0.973590 | ||||||||
\(498\) | −948.327 | −0.0853324 | ||||||||
\(499\) | −4385.18 | −0.393402 | −0.196701 | − | 0.980464i | \(-0.563023\pi\) | ||||
−0.196701 | + | 0.980464i | \(0.563023\pi\) | |||||||
\(500\) | 800.970 | 0.0716409 | ||||||||
\(501\) | 298.742 | 0.0266403 | ||||||||
\(502\) | −3126.18 | −0.277945 | ||||||||
\(503\) | 8327.07 | 0.738143 | 0.369071 | − | 0.929401i | \(-0.379676\pi\) | ||||
0.369071 | + | 0.929401i | \(0.379676\pi\) | |||||||
\(504\) | −2197.64 | −0.194227 | ||||||||
\(505\) | −368.544 | −0.0324752 | ||||||||
\(506\) | −231.174 | −0.0203101 | ||||||||
\(507\) | 15424.0 | 1.35109 | ||||||||
\(508\) | 12405.5 | 1.08347 | ||||||||
\(509\) | −20580.8 | −1.79220 | −0.896098 | − | 0.443856i | \(-0.853610\pi\) | ||||
−0.896098 | + | 0.443856i | \(0.853610\pi\) | |||||||
\(510\) | 1286.48 | 0.111699 | ||||||||
\(511\) | 2025.86 | 0.175379 | ||||||||
\(512\) | −9250.40 | −0.798465 | ||||||||
\(513\) | −1710.26 | −0.147192 | ||||||||
\(514\) | 6029.17 | 0.517384 | ||||||||
\(515\) | 6535.43 | 0.559195 | ||||||||
\(516\) | −7838.85 | −0.668771 | ||||||||
\(517\) | 234.069 | 0.0199117 | ||||||||
\(518\) | −6880.35 | −0.583601 | ||||||||
\(519\) | 6417.89 | 0.542802 | ||||||||
\(520\) | −7786.99 | −0.656697 | ||||||||
\(521\) | −15109.3 | −1.27054 | −0.635270 | − | 0.772290i | \(-0.719111\pi\) | ||||
−0.635270 | + | 0.772290i | \(0.719111\pi\) | |||||||
\(522\) | 329.340 | 0.0276146 | ||||||||
\(523\) | −507.100 | −0.0423976 | −0.0211988 | − | 0.999775i | \(-0.506748\pi\) | ||||
−0.0211988 | + | 0.999775i | \(0.506748\pi\) | |||||||
\(524\) | 7910.66 | 0.659502 | ||||||||
\(525\) | −1007.33 | −0.0837404 | ||||||||
\(526\) | 1983.06 | 0.164383 | ||||||||
\(527\) | −11580.8 | −0.957246 | ||||||||
\(528\) | −111.192 | −0.00916478 | ||||||||
\(529\) | 7430.26 | 0.610690 | ||||||||
\(530\) | 588.874 | 0.0482623 | ||||||||
\(531\) | 2518.17 | 0.205799 | ||||||||
\(532\) | −5451.51 | −0.444272 | ||||||||
\(533\) | −38365.8 | −3.11784 | ||||||||
\(534\) | 368.320 | 0.0298479 | ||||||||
\(535\) | −4227.27 | −0.341609 | ||||||||
\(536\) | 8371.51 | 0.674616 | ||||||||
\(537\) | 5590.61 | 0.449260 | ||||||||
\(538\) | −6241.79 | −0.500191 | ||||||||
\(539\) | 212.799 | 0.0170054 | ||||||||
\(540\) | 865.047 | 0.0689365 | ||||||||
\(541\) | 8249.02 | 0.655551 | 0.327776 | − | 0.944756i | \(-0.393701\pi\) | ||||
0.327776 | + | 0.944756i | \(0.393701\pi\) | |||||||
\(542\) | 1154.51 | 0.0914954 | ||||||||
\(543\) | −9026.27 | −0.713360 | ||||||||
\(544\) | −12314.5 | −0.970551 | ||||||||
\(545\) | 7514.96 | 0.590653 | ||||||||
\(546\) | 4355.49 | 0.341388 | ||||||||
\(547\) | −19432.6 | −1.51897 | −0.759486 | − | 0.650524i | \(-0.774550\pi\) | ||||
−0.759486 | + | 0.650524i | \(0.774550\pi\) | |||||||
\(548\) | 5678.49 | 0.442652 | ||||||||
\(549\) | −7141.94 | −0.555210 | ||||||||
\(550\) | 41.2839 | 0.00320064 | ||||||||
\(551\) | 1836.94 | 0.142026 | ||||||||
\(552\) | −7635.19 | −0.588723 | ||||||||
\(553\) | 4214.87 | 0.324113 | ||||||||
\(554\) | 3080.85 | 0.236269 | ||||||||
\(555\) | 6089.54 | 0.465742 | ||||||||
\(556\) | −10137.8 | −0.773273 | ||||||||
\(557\) | 18807.6 | 1.43071 | 0.715354 | − | 0.698762i | \(-0.246265\pi\) | ||||
0.715354 | + | 0.698762i | \(0.246265\pi\) | |||||||
\(558\) | 1934.99 | 0.146801 | ||||||||
\(559\) | 34932.0 | 2.64305 | ||||||||
\(560\) | 1901.94 | 0.143521 | ||||||||
\(561\) | −266.849 | −0.0200826 | ||||||||
\(562\) | 6701.69 | 0.503013 | ||||||||
\(563\) | 7337.15 | 0.549243 | 0.274622 | − | 0.961552i | \(-0.411447\pi\) | ||||
0.274622 | + | 0.961552i | \(0.411447\pi\) | |||||||
\(564\) | 3438.22 | 0.256694 | ||||||||
\(565\) | 1586.09 | 0.118102 | ||||||||
\(566\) | −844.382 | −0.0627068 | ||||||||
\(567\) | −1087.92 | −0.0805792 | ||||||||
\(568\) | 14601.6 | 1.07864 | ||||||||
\(569\) | 5459.12 | 0.402211 | 0.201106 | − | 0.979570i | \(-0.435547\pi\) | ||||
0.201106 | + | 0.979570i | \(0.435547\pi\) | |||||||
\(570\) | −1198.93 | −0.0881011 | ||||||||
\(571\) | 5306.93 | 0.388946 | 0.194473 | − | 0.980908i | \(-0.437700\pi\) | ||||
0.194473 | + | 0.980908i | \(0.437700\pi\) | |||||||
\(572\) | 718.359 | 0.0525107 | ||||||||
\(573\) | 15525.7 | 1.13193 | ||||||||
\(574\) | −7590.36 | −0.551944 | ||||||||
\(575\) | −3499.76 | −0.253826 | ||||||||
\(576\) | 18.4325 | 0.00133337 | ||||||||
\(577\) | 16127.1 | 1.16357 | 0.581785 | − | 0.813343i | \(-0.302355\pi\) | ||||
0.581785 | + | 0.813343i | \(0.302355\pi\) | |||||||
\(578\) | 370.081 | 0.0266320 | ||||||||
\(579\) | −10223.7 | −0.733818 | ||||||||
\(580\) | −929.125 | −0.0665169 | ||||||||
\(581\) | −3364.69 | −0.240260 | ||||||||
\(582\) | 5081.03 | 0.361882 | ||||||||
\(583\) | −122.147 | −0.00867723 | ||||||||
\(584\) | −2742.19 | −0.194303 | ||||||||
\(585\) | −3854.89 | −0.272444 | ||||||||
\(586\) | 9423.45 | 0.664299 | ||||||||
\(587\) | 9109.13 | 0.640501 | 0.320250 | − | 0.947333i | \(-0.396233\pi\) | ||||
0.320250 | + | 0.947333i | \(0.396233\pi\) | |||||||
\(588\) | 3125.80 | 0.219227 | ||||||||
\(589\) | 10792.7 | 0.755017 | ||||||||
\(590\) | 1765.29 | 0.123180 | ||||||||
\(591\) | −7986.69 | −0.555886 | ||||||||
\(592\) | −11497.6 | −0.798227 | ||||||||
\(593\) | 28352.1 | 1.96337 | 0.981687 | − | 0.190500i | \(-0.0610110\pi\) | ||||
0.981687 | + | 0.190500i | \(0.0610110\pi\) | |||||||
\(594\) | 44.5866 | 0.00307982 | ||||||||
\(595\) | 4564.47 | 0.314496 | ||||||||
\(596\) | 10570.1 | 0.726455 | ||||||||
\(597\) | 3372.37 | 0.231192 | ||||||||
\(598\) | 15132.2 | 1.03478 | ||||||||
\(599\) | −15496.1 | −1.05702 | −0.528508 | − | 0.848928i | \(-0.677248\pi\) | ||||
−0.528508 | + | 0.848928i | \(0.677248\pi\) | |||||||
\(600\) | 1363.52 | 0.0927759 | ||||||||
\(601\) | 7637.92 | 0.518398 | 0.259199 | − | 0.965824i | \(-0.416541\pi\) | ||||
0.259199 | + | 0.965824i | \(0.416541\pi\) | |||||||
\(602\) | 6911.01 | 0.467894 | ||||||||
\(603\) | 4144.24 | 0.279878 | ||||||||
\(604\) | −2203.32 | −0.148430 | ||||||||
\(605\) | 6646.44 | 0.446638 | ||||||||
\(606\) | −279.026 | −0.0187040 | ||||||||
\(607\) | −12012.8 | −0.803268 | −0.401634 | − | 0.915800i | \(-0.631558\pi\) | ||||
−0.401634 | + | 0.915800i | \(0.631558\pi\) | |||||||
\(608\) | 11476.4 | 0.765511 | ||||||||
\(609\) | 1168.51 | 0.0777510 | ||||||||
\(610\) | −5006.66 | −0.332318 | ||||||||
\(611\) | −15321.7 | −1.01448 | ||||||||
\(612\) | −3919.73 | −0.258898 | ||||||||
\(613\) | −6113.47 | −0.402807 | −0.201404 | − | 0.979508i | \(-0.564550\pi\) | ||||
−0.201404 | + | 0.979508i | \(0.564550\pi\) | |||||||
\(614\) | 12527.1 | 0.823374 | ||||||||
\(615\) | 6717.95 | 0.440478 | ||||||||
\(616\) | 319.558 | 0.0209016 | ||||||||
\(617\) | −28775.9 | −1.87759 | −0.938797 | − | 0.344472i | \(-0.888058\pi\) | ||||
−0.938797 | + | 0.344472i | \(0.888058\pi\) | |||||||
\(618\) | 4948.00 | 0.322068 | ||||||||
\(619\) | −7092.81 | −0.460556 | −0.230278 | − | 0.973125i | \(-0.573964\pi\) | ||||
−0.230278 | + | 0.973125i | \(0.573964\pi\) | |||||||
\(620\) | −5458.94 | −0.353607 | ||||||||
\(621\) | −3779.74 | −0.244244 | ||||||||
\(622\) | −3951.35 | −0.254718 | ||||||||
\(623\) | 1306.81 | 0.0840390 | ||||||||
\(624\) | 7278.39 | 0.466937 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | −10643.3 | −0.679540 | ||||||||
\(627\) | 248.688 | 0.0158400 | ||||||||
\(628\) | −15979.9 | −1.01539 | ||||||||
\(629\) | −27593.1 | −1.74914 | ||||||||
\(630\) | −762.657 | −0.0482302 | ||||||||
\(631\) | −2283.67 | −0.144075 | −0.0720377 | − | 0.997402i | \(-0.522950\pi\) | ||||
−0.0720377 | + | 0.997402i | \(0.522950\pi\) | |||||||
\(632\) | −5705.23 | −0.359085 | ||||||||
\(633\) | 327.743 | 0.0205792 | ||||||||
\(634\) | 11562.0 | 0.724267 | ||||||||
\(635\) | 9680.03 | 0.604945 | ||||||||
\(636\) | −1794.22 | −0.111864 | ||||||||
\(637\) | −13929.4 | −0.866409 | ||||||||
\(638\) | −47.8893 | −0.00297172 | ||||||||
\(639\) | 7228.38 | 0.447496 | ||||||||
\(640\) | −7234.26 | −0.446811 | ||||||||
\(641\) | −17599.2 | −1.08444 | −0.542220 | − | 0.840236i | \(-0.682416\pi\) | ||||
−0.542220 | + | 0.840236i | \(0.682416\pi\) | |||||||
\(642\) | −3200.48 | −0.196749 | ||||||||
\(643\) | 9248.80 | 0.567242 | 0.283621 | − | 0.958936i | \(-0.408464\pi\) | ||||
0.283621 | + | 0.958936i | \(0.408464\pi\) | |||||||
\(644\) | −12048.0 | −0.737204 | ||||||||
\(645\) | −6116.68 | −0.373402 | ||||||||
\(646\) | 5432.63 | 0.330873 | ||||||||
\(647\) | −12201.5 | −0.741409 | −0.370704 | − | 0.928751i | \(-0.620884\pi\) | ||||
−0.370704 | + | 0.928751i | \(0.620884\pi\) | |||||||
\(648\) | 1472.60 | 0.0892737 | ||||||||
\(649\) | −366.166 | −0.0221468 | ||||||||
\(650\) | −2702.36 | −0.163070 | ||||||||
\(651\) | 6865.40 | 0.413328 | ||||||||
\(652\) | 12271.6 | 0.737108 | ||||||||
\(653\) | 9769.75 | 0.585482 | 0.292741 | − | 0.956192i | \(-0.405433\pi\) | ||||
0.292741 | + | 0.956192i | \(0.405433\pi\) | |||||||
\(654\) | 5689.61 | 0.340186 | ||||||||
\(655\) | 6172.72 | 0.368226 | ||||||||
\(656\) | −12684.1 | −0.754927 | ||||||||
\(657\) | −1357.50 | −0.0806105 | ||||||||
\(658\) | −3031.26 | −0.179591 | ||||||||
\(659\) | −15386.3 | −0.909506 | −0.454753 | − | 0.890618i | \(-0.650272\pi\) | ||||
−0.454753 | + | 0.890618i | \(0.650272\pi\) | |||||||
\(660\) | −125.786 | −0.00741853 | ||||||||
\(661\) | 16886.7 | 0.993671 | 0.496835 | − | 0.867845i | \(-0.334495\pi\) | ||||
0.496835 | + | 0.867845i | \(0.334495\pi\) | |||||||
\(662\) | −6555.10 | −0.384851 | ||||||||
\(663\) | 17467.4 | 1.02319 | ||||||||
\(664\) | 4554.42 | 0.266183 | ||||||||
\(665\) | −4253.83 | −0.248055 | ||||||||
\(666\) | 4610.42 | 0.268243 | ||||||||
\(667\) | 4059.72 | 0.235671 | ||||||||
\(668\) | −638.089 | −0.0369587 | ||||||||
\(669\) | −13967.0 | −0.807165 | ||||||||
\(670\) | 2905.21 | 0.167519 | ||||||||
\(671\) | 1038.51 | 0.0597484 | ||||||||
\(672\) | 7300.34 | 0.419072 | ||||||||
\(673\) | 26462.8 | 1.51570 | 0.757851 | − | 0.652428i | \(-0.226249\pi\) | ||||
0.757851 | + | 0.652428i | \(0.226249\pi\) | |||||||
\(674\) | 4059.53 | 0.231999 | ||||||||
\(675\) | 675.000 | 0.0384900 | ||||||||
\(676\) | −32944.5 | −1.87440 | ||||||||
\(677\) | 28533.1 | 1.61982 | 0.809908 | − | 0.586556i | \(-0.199517\pi\) | ||||
0.809908 | + | 0.586556i | \(0.199517\pi\) | |||||||
\(678\) | 1200.84 | 0.0680204 | ||||||||
\(679\) | 18027.6 | 1.01890 | ||||||||
\(680\) | −6178.43 | −0.348430 | ||||||||
\(681\) | 11146.7 | 0.627228 | ||||||||
\(682\) | −281.367 | −0.0157978 | ||||||||
\(683\) | 27990.7 | 1.56813 | 0.784066 | − | 0.620677i | \(-0.213142\pi\) | ||||
0.784066 | + | 0.620677i | \(0.213142\pi\) | |||||||
\(684\) | 3652.97 | 0.204203 | ||||||||
\(685\) | 4430.95 | 0.247150 | ||||||||
\(686\) | −8568.96 | −0.476916 | ||||||||
\(687\) | 7313.22 | 0.406138 | ||||||||
\(688\) | 11548.9 | 0.639967 | ||||||||
\(689\) | 7995.52 | 0.442097 | ||||||||
\(690\) | −2649.68 | −0.146191 | ||||||||
\(691\) | 9248.47 | 0.509158 | 0.254579 | − | 0.967052i | \(-0.418063\pi\) | ||||
0.254579 | + | 0.967052i | \(0.418063\pi\) | |||||||
\(692\) | −13708.1 | −0.753040 | ||||||||
\(693\) | 158.195 | 0.00867145 | ||||||||
\(694\) | 769.421 | 0.0420848 | ||||||||
\(695\) | −7910.59 | −0.431749 | ||||||||
\(696\) | −1581.69 | −0.0861403 | ||||||||
\(697\) | −30440.6 | −1.65426 | ||||||||
\(698\) | −5560.17 | −0.301512 | ||||||||
\(699\) | −8112.87 | −0.438994 | ||||||||
\(700\) | 2151.59 | 0.116175 | ||||||||
\(701\) | 16805.6 | 0.905474 | 0.452737 | − | 0.891644i | \(-0.350448\pi\) | ||||
0.452737 | + | 0.891644i | \(0.350448\pi\) | |||||||
\(702\) | −2918.55 | −0.156914 | ||||||||
\(703\) | 25715.3 | 1.37962 | ||||||||
\(704\) | −2.68026 | −0.000143489 0 | ||||||||
\(705\) | 2682.86 | 0.143322 | ||||||||
\(706\) | −3129.48 | −0.166826 | ||||||||
\(707\) | −989.991 | −0.0526626 | ||||||||
\(708\) | −5378.60 | −0.285509 | ||||||||
\(709\) | 28586.0 | 1.51421 | 0.757103 | − | 0.653296i | \(-0.226614\pi\) | ||||
0.757103 | + | 0.653296i | \(0.226614\pi\) | |||||||
\(710\) | 5067.25 | 0.267846 | ||||||||
\(711\) | −2824.32 | −0.148974 | ||||||||
\(712\) | −1768.89 | −0.0931067 | ||||||||
\(713\) | 23852.3 | 1.25284 | ||||||||
\(714\) | 3455.78 | 0.181133 | ||||||||
\(715\) | 560.538 | 0.0293188 | ||||||||
\(716\) | −11941.1 | −0.623268 | ||||||||
\(717\) | 18056.0 | 0.940465 | ||||||||
\(718\) | −8301.42 | −0.431485 | ||||||||
\(719\) | −37753.6 | −1.95824 | −0.979119 | − | 0.203289i | \(-0.934837\pi\) | ||||
−0.979119 | + | 0.203289i | \(0.934837\pi\) | |||||||
\(720\) | −1274.46 | −0.0659674 | ||||||||
\(721\) | 17555.6 | 0.906805 | ||||||||
\(722\) | 3592.05 | 0.185156 | ||||||||
\(723\) | −3734.70 | −0.192109 | ||||||||
\(724\) | 19279.4 | 0.989659 | ||||||||
\(725\) | −725.000 | −0.0371391 | ||||||||
\(726\) | 5032.05 | 0.257241 | ||||||||
\(727\) | −10769.6 | −0.549412 | −0.274706 | − | 0.961528i | \(-0.588581\pi\) | ||||
−0.274706 | + | 0.961528i | \(0.588581\pi\) | |||||||
\(728\) | −20917.6 | −1.06492 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −951.638 | −0.0482489 | ||||||||
\(731\) | 27716.1 | 1.40235 | ||||||||
\(732\) | 15254.6 | 0.770255 | ||||||||
\(733\) | −29083.9 | −1.46554 | −0.732768 | − | 0.680479i | \(-0.761772\pi\) | ||||
−0.732768 | + | 0.680479i | \(0.761772\pi\) | |||||||
\(734\) | 922.549 | 0.0463923 | ||||||||
\(735\) | 2439.07 | 0.122403 | ||||||||
\(736\) | 25363.4 | 1.27025 | ||||||||
\(737\) | −602.614 | −0.0301188 | ||||||||
\(738\) | 5086.19 | 0.253693 | ||||||||
\(739\) | 5594.45 | 0.278478 | 0.139239 | − | 0.990259i | \(-0.455534\pi\) | ||||
0.139239 | + | 0.990259i | \(0.455534\pi\) | |||||||
\(740\) | −13006.8 | −0.646133 | ||||||||
\(741\) | −16278.6 | −0.807032 | ||||||||
\(742\) | 1581.85 | 0.0782634 | ||||||||
\(743\) | 8984.59 | 0.443624 | 0.221812 | − | 0.975089i | \(-0.428803\pi\) | ||||
0.221812 | + | 0.975089i | \(0.428803\pi\) | |||||||
\(744\) | −9292.96 | −0.457925 | ||||||||
\(745\) | 8247.87 | 0.405609 | ||||||||
\(746\) | 2111.10 | 0.103610 | ||||||||
\(747\) | 2254.63 | 0.110432 | ||||||||
\(748\) | 569.967 | 0.0278611 | ||||||||
\(749\) | −11355.4 | −0.553962 | ||||||||
\(750\) | 473.190 | 0.0230379 | ||||||||
\(751\) | 4621.64 | 0.224562 | 0.112281 | − | 0.993676i | \(-0.464184\pi\) | ||||
0.112281 | + | 0.993676i | \(0.464184\pi\) | |||||||
\(752\) | −5065.50 | −0.245638 | ||||||||
\(753\) | 7432.44 | 0.359699 | ||||||||
\(754\) | 3134.74 | 0.151406 | ||||||||
\(755\) | −1719.26 | −0.0828745 | ||||||||
\(756\) | 2323.71 | 0.111789 | ||||||||
\(757\) | −5554.76 | −0.266699 | −0.133349 | − | 0.991069i | \(-0.542573\pi\) | ||||
−0.133349 | + | 0.991069i | \(0.542573\pi\) | |||||||
\(758\) | −4745.07 | −0.227373 | ||||||||
\(759\) | 549.611 | 0.0262841 | ||||||||
\(760\) | 5757.96 | 0.274820 | ||||||||
\(761\) | 28686.9 | 1.36649 | 0.683245 | − | 0.730189i | \(-0.260568\pi\) | ||||
0.683245 | + | 0.730189i | \(0.260568\pi\) | |||||||
\(762\) | 7328.79 | 0.348417 | ||||||||
\(763\) | 20186.9 | 0.957817 | ||||||||
\(764\) | −33161.7 | −1.57035 | ||||||||
\(765\) | −3058.58 | −0.144553 | ||||||||
\(766\) | 15824.5 | 0.746427 | ||||||||
\(767\) | 23968.5 | 1.12836 | ||||||||
\(768\) | −5526.24 | −0.259650 | ||||||||
\(769\) | 26311.7 | 1.23384 | 0.616921 | − | 0.787025i | \(-0.288380\pi\) | ||||
0.616921 | + | 0.787025i | \(0.288380\pi\) | |||||||
\(770\) | 110.898 | 0.00519024 | ||||||||
\(771\) | −14334.2 | −0.669565 | ||||||||
\(772\) | 21836.9 | 1.01804 | ||||||||
\(773\) | −25176.4 | −1.17145 | −0.585727 | − | 0.810508i | \(-0.699191\pi\) | ||||
−0.585727 | + | 0.810508i | \(0.699191\pi\) | |||||||
\(774\) | −4630.97 | −0.215060 | ||||||||
\(775\) | −4259.63 | −0.197433 | ||||||||
\(776\) | −24402.1 | −1.12884 | ||||||||
\(777\) | 16357.9 | 0.755259 | ||||||||
\(778\) | −7292.44 | −0.336050 | ||||||||
\(779\) | 28369.0 | 1.30478 | ||||||||
\(780\) | 8233.73 | 0.377968 | ||||||||
\(781\) | −1051.08 | −0.0481568 | ||||||||
\(782\) | 12006.3 | 0.549034 | ||||||||
\(783\) | −783.000 | −0.0357371 | ||||||||
\(784\) | −4605.20 | −0.209785 | ||||||||
\(785\) | −12469.2 | −0.566934 | ||||||||
\(786\) | 4673.39 | 0.212079 | ||||||||
\(787\) | −27651.8 | −1.25245 | −0.626226 | − | 0.779641i | \(-0.715401\pi\) | ||||
−0.626226 | + | 0.779641i | \(0.715401\pi\) | |||||||
\(788\) | 17058.9 | 0.771192 | ||||||||
\(789\) | −4714.69 | −0.212734 | ||||||||
\(790\) | −1979.91 | −0.0891673 | ||||||||
\(791\) | 4260.60 | 0.191516 | ||||||||
\(792\) | −214.131 | −0.00960709 | ||||||||
\(793\) | −67978.7 | −3.04413 | ||||||||
\(794\) | −18163.7 | −0.811847 | ||||||||
\(795\) | −1400.03 | −0.0624580 | ||||||||
\(796\) | −7203.11 | −0.320738 | ||||||||
\(797\) | −35053.5 | −1.55792 | −0.778958 | − | 0.627076i | \(-0.784252\pi\) | ||||
−0.778958 | + | 0.627076i | \(0.784252\pi\) | |||||||
\(798\) | −3220.59 | −0.142867 | ||||||||
\(799\) | −12156.7 | −0.538262 | ||||||||
\(800\) | −4529.49 | −0.200177 | ||||||||
\(801\) | −875.675 | −0.0386273 | ||||||||
\(802\) | −10877.5 | −0.478923 | ||||||||
\(803\) | 197.394 | 0.00867482 | ||||||||
\(804\) | −8851.77 | −0.388281 | ||||||||
\(805\) | −9401.13 | −0.411610 | ||||||||
\(806\) | 18417.7 | 0.804883 | ||||||||
\(807\) | 14839.7 | 0.647315 | ||||||||
\(808\) | 1340.05 | 0.0583449 | ||||||||
\(809\) | −23824.8 | −1.03540 | −0.517699 | − | 0.855563i | \(-0.673211\pi\) | ||||
−0.517699 | + | 0.855563i | \(0.673211\pi\) | |||||||
\(810\) | 511.045 | 0.0221683 | ||||||||
\(811\) | 19361.6 | 0.838322 | 0.419161 | − | 0.907912i | \(-0.362324\pi\) | ||||
0.419161 | + | 0.907912i | \(0.362324\pi\) | |||||||
\(812\) | −2495.84 | −0.107866 | ||||||||
\(813\) | −2744.83 | −0.118407 | ||||||||
\(814\) | −670.401 | −0.0288667 | ||||||||
\(815\) | 9575.61 | 0.411557 | ||||||||
\(816\) | 5774.90 | 0.247747 | ||||||||
\(817\) | −25829.9 | −1.10609 | ||||||||
\(818\) | 17738.9 | 0.758224 | ||||||||
\(819\) | −10355.1 | −0.441803 | ||||||||
\(820\) | −14349.0 | −0.611084 | ||||||||
\(821\) | −14914.6 | −0.634012 | −0.317006 | − | 0.948424i | \(-0.602678\pi\) | ||||
−0.317006 | + | 0.948424i | \(0.602678\pi\) | |||||||
\(822\) | 3354.69 | 0.142346 | ||||||||
\(823\) | 7639.98 | 0.323588 | 0.161794 | − | 0.986825i | \(-0.448272\pi\) | ||||
0.161794 | + | 0.986825i | \(0.448272\pi\) | |||||||
\(824\) | −23763.2 | −1.00465 | ||||||||
\(825\) | −98.1517 | −0.00414206 | ||||||||
\(826\) | 4741.97 | 0.199751 | ||||||||
\(827\) | 12462.1 | 0.524003 | 0.262001 | − | 0.965068i | \(-0.415618\pi\) | ||||
0.262001 | + | 0.965068i | \(0.415618\pi\) | |||||||
\(828\) | 8073.21 | 0.338845 | ||||||||
\(829\) | −26986.5 | −1.13062 | −0.565309 | − | 0.824880i | \(-0.691243\pi\) | ||||
−0.565309 | + | 0.824880i | \(0.691243\pi\) | |||||||
\(830\) | 1580.54 | 0.0660982 | ||||||||
\(831\) | −7324.67 | −0.305764 | ||||||||
\(832\) | 175.444 | 0.00731063 | ||||||||
\(833\) | −11052.0 | −0.459699 | ||||||||
\(834\) | −5989.14 | −0.248666 | ||||||||
\(835\) | −497.903 | −0.0206355 | ||||||||
\(836\) | −531.178 | −0.0219751 | ||||||||
\(837\) | −4600.40 | −0.189980 | ||||||||
\(838\) | 389.558 | 0.0160585 | ||||||||
\(839\) | 23448.1 | 0.964860 | 0.482430 | − | 0.875935i | \(-0.339754\pi\) | ||||
0.482430 | + | 0.875935i | \(0.339754\pi\) | |||||||
\(840\) | 3662.73 | 0.150448 | ||||||||
\(841\) | 841.000 | 0.0344828 | ||||||||
\(842\) | −9263.78 | −0.379158 | ||||||||
\(843\) | −15933.1 | −0.650968 | ||||||||
\(844\) | −700.034 | −0.0285499 | ||||||||
\(845\) | −25706.7 | −1.04655 | ||||||||
\(846\) | 2031.20 | 0.0825464 | ||||||||
\(847\) | 17853.8 | 0.724280 | ||||||||
\(848\) | 2643.40 | 0.107046 | ||||||||
\(849\) | 2007.50 | 0.0811511 | ||||||||
\(850\) | −2144.13 | −0.0865214 | ||||||||
\(851\) | 56831.8 | 2.28927 | ||||||||
\(852\) | −15439.2 | −0.620821 | ||||||||
\(853\) | −30230.4 | −1.21344 | −0.606722 | − | 0.794914i | \(-0.707516\pi\) | ||||
−0.606722 | + | 0.794914i | \(0.707516\pi\) | |||||||
\(854\) | −13449.0 | −0.538895 | ||||||||
\(855\) | 2850.43 | 0.114015 | ||||||||
\(856\) | 15370.6 | 0.613734 | ||||||||
\(857\) | 32088.1 | 1.27900 | 0.639502 | − | 0.768789i | \(-0.279140\pi\) | ||||
0.639502 | + | 0.768789i | \(0.279140\pi\) | |||||||
\(858\) | 424.386 | 0.0168861 | ||||||||
\(859\) | −43201.3 | −1.71596 | −0.857980 | − | 0.513683i | \(-0.828281\pi\) | ||||
−0.857980 | + | 0.513683i | \(0.828281\pi\) | |||||||
\(860\) | 13064.7 | 0.518028 | ||||||||
\(861\) | 18045.9 | 0.714290 | ||||||||
\(862\) | 21023.3 | 0.830692 | ||||||||
\(863\) | −15650.5 | −0.617323 | −0.308662 | − | 0.951172i | \(-0.599881\pi\) | ||||
−0.308662 | + | 0.951172i | \(0.599881\pi\) | |||||||
\(864\) | −4891.85 | −0.192620 | ||||||||
\(865\) | −10696.5 | −0.420452 | ||||||||
\(866\) | −12733.8 | −0.499669 | ||||||||
\(867\) | −879.859 | −0.0344655 | ||||||||
\(868\) | −14663.9 | −0.573418 | ||||||||
\(869\) | 410.685 | 0.0160317 | ||||||||
\(870\) | −548.901 | −0.0213902 | ||||||||
\(871\) | 39445.9 | 1.53453 | ||||||||
\(872\) | −27324.9 | −1.06117 | ||||||||
\(873\) | −12080.0 | −0.468324 | ||||||||
\(874\) | −11189.2 | −0.433045 | ||||||||
\(875\) | 1678.89 | 0.0648650 | ||||||||
\(876\) | 2899.51 | 0.111833 | ||||||||
\(877\) | −37921.1 | −1.46010 | −0.730049 | − | 0.683395i | \(-0.760503\pi\) | ||||
−0.730049 | + | 0.683395i | \(0.760503\pi\) | |||||||
\(878\) | −6498.14 | −0.249774 | ||||||||
\(879\) | −22404.1 | −0.859693 | ||||||||
\(880\) | 185.320 | 0.00709901 | ||||||||
\(881\) | 19844.4 | 0.758881 | 0.379441 | − | 0.925216i | \(-0.376116\pi\) | ||||
0.379441 | + | 0.925216i | \(0.376116\pi\) | |||||||
\(882\) | 1846.63 | 0.0704981 | ||||||||
\(883\) | 33386.5 | 1.27242 | 0.636210 | − | 0.771516i | \(-0.280501\pi\) | ||||
0.636210 | + | 0.771516i | \(0.280501\pi\) | |||||||
\(884\) | −37308.9 | −1.41950 | ||||||||
\(885\) | −4196.95 | −0.159411 | ||||||||
\(886\) | −19963.0 | −0.756964 | ||||||||
\(887\) | −25988.8 | −0.983788 | −0.491894 | − | 0.870655i | \(-0.663695\pi\) | ||||
−0.491894 | + | 0.870655i | \(0.663695\pi\) | |||||||
\(888\) | −22141.9 | −0.836751 | ||||||||
\(889\) | 26002.7 | 0.980994 | ||||||||
\(890\) | −613.867 | −0.0231201 | ||||||||
\(891\) | −106.004 | −0.00398570 | ||||||||
\(892\) | 29832.3 | 1.11980 | ||||||||
\(893\) | 11329.3 | 0.424549 | ||||||||
\(894\) | 6244.50 | 0.233610 | ||||||||
\(895\) | −9317.69 | −0.347996 | ||||||||
\(896\) | −19432.9 | −0.724560 | ||||||||
\(897\) | −35976.4 | −1.33915 | ||||||||
\(898\) | 17543.4 | 0.651928 | ||||||||
\(899\) | 4941.17 | 0.183312 | ||||||||
\(900\) | −1441.75 | −0.0533980 | ||||||||
\(901\) | 6343.88 | 0.234568 | ||||||||
\(902\) | −739.582 | −0.0273009 | ||||||||
\(903\) | −16430.8 | −0.605518 | ||||||||
\(904\) | −5767.12 | −0.212181 | ||||||||
\(905\) | 15043.8 | 0.552566 | ||||||||
\(906\) | −1301.66 | −0.0477314 | ||||||||
\(907\) | −26383.8 | −0.965887 | −0.482943 | − | 0.875652i | \(-0.660432\pi\) | ||||
−0.482943 | + | 0.875652i | \(0.660432\pi\) | |||||||
\(908\) | −23808.4 | −0.870166 | ||||||||
\(909\) | 663.378 | 0.0242056 | ||||||||
\(910\) | −7259.15 | −0.264438 | ||||||||
\(911\) | −23448.5 | −0.852779 | −0.426390 | − | 0.904540i | \(-0.640215\pi\) | ||||
−0.426390 | + | 0.904540i | \(0.640215\pi\) | |||||||
\(912\) | −5381.89 | −0.195408 | ||||||||
\(913\) | −327.845 | −0.0118840 | ||||||||
\(914\) | −5445.15 | −0.197056 | ||||||||
\(915\) | 11903.2 | 0.430064 | ||||||||
\(916\) | −15620.4 | −0.563443 | ||||||||
\(917\) | 16581.3 | 0.597125 | ||||||||
\(918\) | −2315.66 | −0.0832553 | ||||||||
\(919\) | −1649.45 | −0.0592060 | −0.0296030 | − | 0.999562i | \(-0.509424\pi\) | ||||
−0.0296030 | + | 0.999562i | \(0.509424\pi\) | |||||||
\(920\) | 12725.3 | 0.456023 | ||||||||
\(921\) | −29782.9 | −1.06556 | ||||||||
\(922\) | −7490.39 | −0.267552 | ||||||||
\(923\) | 68801.4 | 2.45355 | ||||||||
\(924\) | −337.891 | −0.0120301 | ||||||||
\(925\) | −10149.2 | −0.360762 | ||||||||
\(926\) | 16270.7 | 0.577415 | ||||||||
\(927\) | −11763.8 | −0.416799 | ||||||||
\(928\) | 5254.20 | 0.185860 | ||||||||
\(929\) | 48039.5 | 1.69658 | 0.848291 | − | 0.529531i | \(-0.177632\pi\) | ||||
0.848291 | + | 0.529531i | \(0.177632\pi\) | |||||||
\(930\) | −3224.99 | −0.113711 | ||||||||
\(931\) | 10299.9 | 0.362582 | ||||||||
\(932\) | 17328.4 | 0.609026 | ||||||||
\(933\) | 9394.26 | 0.329640 | ||||||||
\(934\) | −15967.0 | −0.559376 | ||||||||
\(935\) | 444.748 | 0.0155559 | ||||||||
\(936\) | 14016.6 | 0.489473 | ||||||||
\(937\) | −28647.5 | −0.998796 | −0.499398 | − | 0.866373i | \(-0.666445\pi\) | ||||
−0.499398 | + | 0.866373i | \(0.666445\pi\) | |||||||
\(938\) | 7804.04 | 0.271654 | ||||||||
\(939\) | 25304.2 | 0.879417 | ||||||||
\(940\) | −5730.37 | −0.198834 | ||||||||
\(941\) | 9541.12 | 0.330533 | 0.165267 | − | 0.986249i | \(-0.447152\pi\) | ||||
0.165267 | + | 0.986249i | \(0.447152\pi\) | |||||||
\(942\) | −9440.45 | −0.326525 | ||||||||
\(943\) | 62696.5 | 2.16509 | ||||||||
\(944\) | 7924.24 | 0.273212 | ||||||||
\(945\) | 1813.20 | 0.0624164 | ||||||||
\(946\) | 673.388 | 0.0231435 | ||||||||
\(947\) | 44596.6 | 1.53030 | 0.765151 | − | 0.643851i | \(-0.222664\pi\) | ||||
0.765151 | + | 0.643851i | \(0.222664\pi\) | |||||||
\(948\) | 6032.53 | 0.206674 | ||||||||
\(949\) | −12921.0 | −0.441974 | ||||||||
\(950\) | 1998.22 | 0.0682428 | ||||||||
\(951\) | −27488.4 | −0.937300 | ||||||||
\(952\) | −16596.7 | −0.565022 | ||||||||
\(953\) | 437.931 | 0.0148856 | 0.00744279 | − | 0.999972i | \(-0.497631\pi\) | ||||
0.00744279 | + | 0.999972i | \(0.497631\pi\) | |||||||
\(954\) | −1059.97 | −0.0359726 | ||||||||
\(955\) | −25876.2 | −0.876790 | ||||||||
\(956\) | −38566.2 | −1.30473 | ||||||||
\(957\) | 113.856 | 0.00384581 | ||||||||
\(958\) | −11345.9 | −0.382641 | ||||||||
\(959\) | 11902.5 | 0.400785 | ||||||||
\(960\) | −30.7208 | −0.00103282 | ||||||||
\(961\) | −759.861 | −0.0255064 | ||||||||
\(962\) | 43883.1 | 1.47073 | ||||||||
\(963\) | 7609.09 | 0.254620 | ||||||||
\(964\) | 7977.02 | 0.266517 | ||||||||
\(965\) | 17039.4 | 0.568413 | ||||||||
\(966\) | −7117.64 | −0.237067 | ||||||||
\(967\) | −37762.6 | −1.25580 | −0.627902 | − | 0.778292i | \(-0.716086\pi\) | ||||
−0.627902 | + | 0.778292i | \(0.716086\pi\) | |||||||
\(968\) | −24166.8 | −0.802429 | ||||||||
\(969\) | −12916.0 | −0.428194 | ||||||||
\(970\) | −8468.38 | −0.280313 | ||||||||
\(971\) | 16153.0 | 0.533858 | 0.266929 | − | 0.963716i | \(-0.413991\pi\) | ||||
0.266929 | + | 0.963716i | \(0.413991\pi\) | |||||||
\(972\) | −1557.09 | −0.0513822 | ||||||||
\(973\) | −21249.6 | −0.700136 | ||||||||
\(974\) | −9680.07 | −0.318449 | ||||||||
\(975\) | 6424.81 | 0.211034 | ||||||||
\(976\) | −22474.4 | −0.737079 | ||||||||
\(977\) | 33700.3 | 1.10355 | 0.551775 | − | 0.833993i | \(-0.313951\pi\) | ||||
0.551775 | + | 0.833993i | \(0.313951\pi\) | |||||||
\(978\) | 7249.74 | 0.237036 | ||||||||
\(979\) | 127.332 | 0.00415683 | ||||||||
\(980\) | −5209.66 | −0.169813 | ||||||||
\(981\) | −13526.9 | −0.440247 | ||||||||
\(982\) | −13025.8 | −0.423290 | ||||||||
\(983\) | −7637.13 | −0.247799 | −0.123900 | − | 0.992295i | \(-0.539540\pi\) | ||||
−0.123900 | + | 0.992295i | \(0.539540\pi\) | |||||||
\(984\) | −24426.9 | −0.791362 | ||||||||
\(985\) | 13311.2 | 0.430588 | ||||||||
\(986\) | 2487.20 | 0.0803331 | ||||||||
\(987\) | 7206.77 | 0.232415 | ||||||||
\(988\) | 34769.9 | 1.11961 | ||||||||
\(989\) | −57085.1 | −1.83539 | ||||||||
\(990\) | −74.3110 | −0.00238562 | ||||||||
\(991\) | 9339.90 | 0.299386 | 0.149693 | − | 0.988733i | \(-0.452171\pi\) | ||||
0.149693 | + | 0.988733i | \(0.452171\pi\) | |||||||
\(992\) | 30870.3 | 0.988038 | ||||||||
\(993\) | 15584.6 | 0.498049 | ||||||||
\(994\) | 13611.8 | 0.434346 | ||||||||
\(995\) | −5620.61 | −0.179081 | ||||||||
\(996\) | −4815.70 | −0.153204 | ||||||||
\(997\) | −11144.7 | −0.354017 | −0.177009 | − | 0.984209i | \(-0.556642\pi\) | ||||
−0.177009 | + | 0.984209i | \(0.556642\pi\) | |||||||
\(998\) | 5533.39 | 0.175508 | ||||||||
\(999\) | −10961.2 | −0.347144 |
(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 | 435.4.a.j.1.3 | ✓ | 7 | |
3.2 | odd | 2 | 1305.4.a.m.1.5 | 7 | |||
5.4 | even | 2 | 2175.4.a.m.1.5 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
435.4.a.j.1.3 | ✓ | 7 | 1.1 | even | 1 | trivial | |
1305.4.a.m.1.5 | 7 | 3.2 | odd | 2 | |||
2175.4.a.m.1.5 | 7 | 5.4 | even | 2 |