Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,5,Mod(55,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.55");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.d (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(11.1639560131\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 38x^{14} + 1016x^{12} + 13512x^{10} + 130640x^{8} + 569472x^{6} + 1783808x^{4} + 352256x^{2} + 65536 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{32}\cdot 3^{24} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 55.12 | ||
Root | \(-1.78073 + 3.08431i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 108.55 |
Dual form | 108.5.d.b.55.11 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.54696 | + | 3.08431i | 0.636740 | + | 0.771078i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −3.02598 | + | 15.7113i | −0.189124 | + | 0.981953i | ||||
\(5\) | −3.58334 | −0.143334 | −0.0716668 | − | 0.997429i | \(-0.522832\pi\) | ||||
−0.0716668 | + | 0.997429i | \(0.522832\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 16.2605i | 0.331847i | 0.986139 | + | 0.165923i | \(0.0530604\pi\) | ||||
−0.986139 | + | 0.165923i | \(0.946940\pi\) | |||||||
\(8\) | −56.1655 | + | 30.6829i | −0.877586 | + | 0.479420i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −9.12663 | − | 11.0521i | −0.0912663 | − | 0.110521i | ||||
\(11\) | 144.712i | 1.19597i | 0.801508 | + | 0.597985i | \(0.204032\pi\) | ||||
−0.801508 | + | 0.597985i | \(0.795968\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −223.658 | −1.32342 | −0.661709 | − | 0.749761i | \(-0.730169\pi\) | ||||
−0.661709 | + | 0.749761i | \(0.730169\pi\) | |||||||
\(14\) | −50.1524 | + | 41.4148i | −0.255880 | + | 0.211300i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −237.687 | − | 95.0838i | −0.928464 | − | 0.371421i | ||||
\(17\) | 1.80372 | 0.00624125 | 0.00312062 | − | 0.999995i | \(-0.499007\pi\) | ||||
0.00312062 | + | 0.999995i | \(0.499007\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 70.1406i | − | 0.194295i | −0.995270 | − | 0.0971476i | \(-0.969028\pi\) | ||
0.995270 | − | 0.0971476i | \(-0.0309719\pi\) | |||||||
\(20\) | 10.8431 | − | 56.2988i | 0.0271078 | − | 0.140747i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −446.338 | + | 368.577i | −0.922186 | + | 0.761522i | ||||
\(23\) | 251.394i | 0.475225i | 0.971360 | + | 0.237612i | \(0.0763648\pi\) | ||||
−0.971360 | + | 0.237612i | \(0.923635\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −612.160 | −0.979455 | ||||||||
\(26\) | −569.647 | − | 689.830i | −0.842674 | − | 1.02046i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −255.473 | − | 49.2039i | −0.325858 | − | 0.0627601i | ||||
\(29\) | 1641.50 | 1.95185 | 0.975924 | − | 0.218110i | \(-0.0699891\pi\) | ||||
0.975924 | + | 0.218110i | \(0.0699891\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1047.19i | 1.08968i | 0.838539 | + | 0.544842i | \(0.183410\pi\) | ||||
−0.838539 | + | 0.544842i | \(0.816590\pi\) | |||||||
\(32\) | −312.111 | − | 975.276i | −0.304796 | − | 0.952418i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.59401 | + | 5.56324i | 0.00397405 | + | 0.00481249i | ||||
\(35\) | − | 58.2669i | − | 0.0475648i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −690.791 | −0.504596 | −0.252298 | − | 0.967650i | \(-0.581186\pi\) | ||||
−0.252298 | + | 0.967650i | \(0.581186\pi\) | |||||||
\(38\) | 216.336 | − | 178.645i | 0.149817 | − | 0.123716i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 201.260 | − | 109.947i | 0.125788 | − | 0.0687170i | ||||
\(41\) | 993.138 | 0.590802 | 0.295401 | − | 0.955373i | \(-0.404547\pi\) | ||||
0.295401 | + | 0.955373i | \(0.404547\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 1983.63i | − | 1.07281i | −0.843959 | − | 0.536407i | \(-0.819781\pi\) | ||
0.843959 | − | 0.536407i | \(-0.180219\pi\) | |||||||
\(44\) | −2273.61 | − | 437.896i | −1.17439 | − | 0.226186i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −775.377 | + | 640.290i | −0.366435 | + | 0.302595i | ||||
\(47\) | 3199.12i | 1.44822i | 0.689683 | + | 0.724111i | \(0.257750\pi\) | ||||
−0.689683 | + | 0.724111i | \(0.742250\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2136.60 | 0.889878 | ||||||||
\(50\) | −1559.15 | − | 1888.09i | −0.623659 | − | 0.755237i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 676.783 | − | 3513.94i | 0.250290 | − | 1.29953i | ||||
\(53\) | 2863.25 | 1.01931 | 0.509657 | − | 0.860378i | \(-0.329772\pi\) | ||||
0.509657 | + | 0.860378i | \(0.329772\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 518.553i | − | 0.171423i | ||||||
\(56\) | −498.919 | − | 913.278i | −0.159094 | − | 0.291224i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4180.85 | + | 5062.91i | 1.24282 | + | 1.50503i | ||||
\(59\) | 5577.97i | 1.60241i | 0.598393 | + | 0.801203i | \(0.295806\pi\) | ||||
−0.598393 | + | 0.801203i | \(0.704194\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2838.27 | 0.762770 | 0.381385 | − | 0.924416i | \(-0.375447\pi\) | ||||
0.381385 | + | 0.924416i | \(0.375447\pi\) | |||||||
\(62\) | −3229.85 | + | 2667.14i | −0.840232 | + | 0.693846i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2213.12 | − | 3446.64i | 0.540313 | − | 0.841464i | ||||
\(65\) | 801.442 | 0.189690 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5289.13i | 1.17824i | 0.808045 | + | 0.589121i | \(0.200526\pi\) | ||||
−0.808045 | + | 0.589121i | \(0.799474\pi\) | |||||||
\(68\) | −5.45802 | + | 28.3387i | −0.00118037 | + | 0.00612861i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 179.713 | − | 148.403i | 0.0366762 | − | 0.0302864i | ||||
\(71\) | − | 1873.59i | − | 0.371671i | −0.982581 | − | 0.185835i | \(-0.940501\pi\) | ||
0.982581 | − | 0.185835i | \(-0.0594991\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4523.42 | 0.848830 | 0.424415 | − | 0.905468i | \(-0.360480\pi\) | ||||
0.424415 | + | 0.905468i | \(0.360480\pi\) | |||||||
\(74\) | −1759.42 | − | 2130.62i | −0.321296 | − | 0.389083i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1102.00 | + | 212.244i | 0.190789 | + | 0.0367458i | ||||
\(77\) | −2353.09 | −0.396879 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 7360.48i | − | 1.17937i | −0.807632 | − | 0.589687i | \(-0.799251\pi\) | ||
0.807632 | − | 0.589687i | \(-0.200749\pi\) | |||||||
\(80\) | 851.713 | + | 340.718i | 0.133080 | + | 0.0532371i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2529.48 | + | 3063.15i | 0.376187 | + | 0.455555i | ||||
\(83\) | − | 5006.55i | − | 0.726745i | −0.931644 | − | 0.363372i | \(-0.881625\pi\) | ||
0.931644 | − | 0.363372i | \(-0.118375\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.46335 | −0.000894581 | ||||||||
\(86\) | 6118.15 | − | 5052.24i | 0.827224 | − | 0.683104i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4440.19 | − | 8127.83i | −0.573372 | − | 1.04957i | ||||
\(89\) | 11438.5 | 1.44407 | 0.722034 | − | 0.691858i | \(-0.243208\pi\) | ||||
0.722034 | + | 0.691858i | \(0.243208\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 3636.78i | − | 0.439172i | ||||||
\(92\) | −3949.71 | − | 760.712i | −0.466648 | − | 0.0898762i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −9867.10 | + | 8148.04i | −1.11669 | + | 0.922142i | ||||
\(95\) | 251.338i | 0.0278490i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9022.44 | −0.958916 | −0.479458 | − | 0.877565i | \(-0.659167\pi\) | ||||
−0.479458 | + | 0.877565i | \(0.659167\pi\) | |||||||
\(98\) | 5441.83 | + | 6589.93i | 0.566621 | + | 0.686165i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1852.38 | − | 9617.80i | 0.185238 | − | 0.961780i | ||||
\(101\) | −14876.5 | −1.45833 | −0.729167 | − | 0.684336i | \(-0.760092\pi\) | ||||
−0.729167 | + | 0.684336i | \(0.760092\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12827.6i | 1.20912i | 0.796558 | + | 0.604562i | \(0.206652\pi\) | ||||
−0.796558 | + | 0.604562i | \(0.793348\pi\) | |||||||
\(104\) | 12561.8 | − | 6862.46i | 1.16141 | − | 0.634473i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7292.59 | + | 8831.17i | 0.649038 | + | 0.785971i | ||||
\(107\) | − | 18333.9i | − | 1.60136i | −0.599095 | − | 0.800678i | \(-0.704473\pi\) | ||
0.599095 | − | 0.800678i | \(-0.295527\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10407.4 | −0.875974 | −0.437987 | − | 0.898981i | \(-0.644308\pi\) | ||||
−0.437987 | + | 0.898981i | \(0.644308\pi\) | |||||||
\(110\) | 1599.38 | − | 1320.74i | 0.132180 | − | 0.109152i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1546.11 | − | 3864.91i | 0.123255 | − | 0.308108i | ||||
\(113\) | −21057.9 | −1.64914 | −0.824572 | − | 0.565758i | \(-0.808584\pi\) | ||||
−0.824572 | + | 0.565758i | \(0.808584\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 900.829i | − | 0.0681156i | ||||||
\(116\) | −4967.16 | + | 25790.1i | −0.369141 | + | 1.91662i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −17204.2 | + | 14206.9i | −1.23558 | + | 1.02032i | ||||
\(119\) | 29.3294i | 0.00207114i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6300.65 | −0.430343 | ||||||||
\(122\) | 7228.95 | + | 8754.10i | 0.485686 | + | 0.588155i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −16452.6 | − | 3168.76i | −1.07002 | − | 0.206085i | ||||
\(125\) | 4433.16 | 0.283723 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8341.04i | 0.517145i | 0.965992 | + | 0.258573i | \(0.0832521\pi\) | ||||
−0.965992 | + | 0.258573i | \(0.916748\pi\) | |||||||
\(128\) | 16267.2 | − | 1952.49i | 0.992874 | − | 0.119171i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2041.24 | + | 2471.90i | 0.120783 | + | 0.146266i | ||||
\(131\) | 17537.0i | 1.02191i | 0.859608 | + | 0.510955i | \(0.170708\pi\) | ||||
−0.859608 | + | 0.510955i | \(0.829292\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1140.52 | 0.0644762 | ||||||||
\(134\) | −16313.3 | + | 13471.2i | −0.908516 | + | 0.750234i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −101.307 | + | 55.3434i | −0.00547723 | + | 0.00299218i | ||||
\(137\) | −15233.4 | −0.811627 | −0.405814 | − | 0.913956i | \(-0.633012\pi\) | ||||
−0.405814 | + | 0.913956i | \(0.633012\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 29455.9i | − | 1.52455i | −0.647250 | − | 0.762277i | \(-0.724081\pi\) | ||
0.647250 | − | 0.762277i | \(-0.275919\pi\) | |||||||
\(140\) | 915.445 | + | 176.314i | 0.0467064 | + | 0.00899563i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 5778.75 | − | 4771.97i | 0.286587 | − | 0.236658i | ||||
\(143\) | − | 32366.0i | − | 1.58277i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5882.07 | −0.279766 | ||||||||
\(146\) | 11521.0 | + | 13951.6i | 0.540484 | + | 0.654515i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2090.32 | − | 10853.2i | 0.0954309 | − | 0.495489i | ||||
\(149\) | −25630.4 | −1.15447 | −0.577234 | − | 0.816579i | \(-0.695868\pi\) | ||||
−0.577234 | + | 0.816579i | \(0.695868\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 26662.5i | 1.16936i | 0.811265 | + | 0.584679i | \(0.198780\pi\) | ||||
−0.811265 | + | 0.584679i | \(0.801220\pi\) | |||||||
\(152\) | 2152.11 | + | 3939.48i | 0.0931490 | + | 0.170511i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −5993.24 | − | 7257.68i | −0.252709 | − | 0.306024i | ||||
\(155\) | − | 3752.43i | − | 0.156188i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4902.53 | 0.198894 | 0.0994468 | − | 0.995043i | \(-0.468293\pi\) | ||||
0.0994468 | + | 0.995043i | \(0.468293\pi\) | |||||||
\(158\) | 22702.0 | − | 18746.8i | 0.909390 | − | 0.750955i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1118.40 | + | 3494.74i | 0.0436875 | + | 0.136513i | ||||
\(161\) | −4087.79 | −0.157702 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 5606.70i | − | 0.211024i | −0.994418 | − | 0.105512i | \(-0.966352\pi\) | ||
0.994418 | − | 0.105512i | \(-0.0336481\pi\) | |||||||
\(164\) | −3005.21 | + | 15603.4i | −0.111735 | + | 0.580140i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 15441.8 | − | 12751.5i | 0.560377 | − | 0.462748i | ||||
\(167\) | 8055.50i | 0.288842i | 0.989516 | + | 0.144421i | \(0.0461319\pi\) | ||||
−0.989516 | + | 0.144421i | \(0.953868\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 21461.8 | 0.751436 | ||||||||
\(170\) | −16.4619 | − | 19.9350i | −0.000569616 | − | 0.000689792i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 31165.4 | + | 6002.43i | 1.05345 | + | 0.202894i | ||||
\(173\) | 37584.7 | 1.25580 | 0.627898 | − | 0.778296i | \(-0.283915\pi\) | ||||
0.627898 | + | 0.778296i | \(0.283915\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 9954.02i | − | 0.325029i | ||||||
\(176\) | 13759.8 | − | 34396.2i | 0.444208 | − | 1.11042i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 29133.3 | + | 35279.8i | 0.919496 | + | 1.11349i | ||||
\(179\) | − | 34709.7i | − | 1.08329i | −0.840608 | − | 0.541645i | \(-0.817802\pi\) | ||
0.840608 | − | 0.541645i | \(-0.182198\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 45374.3 | 1.38501 | 0.692504 | − | 0.721414i | \(-0.256507\pi\) | ||||
0.692504 | + | 0.721414i | \(0.256507\pi\) | |||||||
\(182\) | 11217.0 | − | 9262.75i | 0.338636 | − | 0.279638i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −7713.49 | − | 14119.7i | −0.227832 | − | 0.417050i | ||||
\(185\) | 2475.34 | 0.0723255 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 261.021i | 0.00746434i | ||||||||
\(188\) | −50262.2 | − | 9680.48i | −1.42209 | − | 0.273893i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −775.204 | + | 640.147i | −0.0214738 | + | 0.0177326i | ||||
\(191\) | 24475.4i | 0.670907i | 0.942057 | + | 0.335454i | \(0.108890\pi\) | ||||
−0.942057 | + | 0.335454i | \(0.891110\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13113.8 | 0.352058 | 0.176029 | − | 0.984385i | \(-0.443675\pi\) | ||||
0.176029 | + | 0.984385i | \(0.443675\pi\) | |||||||
\(194\) | −22979.8 | − | 27828.0i | −0.610581 | − | 0.739400i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6465.29 | + | 33568.6i | −0.168297 | + | 0.873818i | ||||
\(197\) | 32666.7 | 0.841730 | 0.420865 | − | 0.907123i | \(-0.361727\pi\) | ||||
0.420865 | + | 0.907123i | \(0.361727\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8800.86i | 0.222238i | 0.993807 | + | 0.111119i | \(0.0354435\pi\) | ||||
−0.993807 | + | 0.111119i | \(0.964556\pi\) | |||||||
\(200\) | 34382.2 | − | 18782.8i | 0.859556 | − | 0.469571i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −37889.8 | − | 45883.7i | −0.928580 | − | 1.12449i | ||||
\(203\) | 26691.7i | 0.647715i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3558.75 | −0.0846818 | ||||||||
\(206\) | −39564.3 | + | 32671.4i | −0.932329 | + | 0.769898i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 53160.5 | + | 21266.2i | 1.22875 | + | 0.491546i | ||||
\(209\) | 10150.2 | 0.232371 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 49061.2i | − | 1.10198i | −0.834513 | − | 0.550989i | \(-0.814251\pi\) | ||
0.834513 | − | 0.550989i | \(-0.185749\pi\) | |||||||
\(212\) | −8664.14 | + | 44985.3i | −0.192776 | + | 1.00092i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 56547.6 | − | 46695.8i | 1.23477 | − | 1.01965i | ||||
\(215\) | 7108.03i | 0.153770i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −17027.8 | −0.361608 | ||||||||
\(218\) | −26507.4 | − | 32099.8i | −0.557768 | − | 0.675445i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 8147.12 | + | 1569.13i | 0.168329 | + | 0.0324201i | ||||
\(221\) | −403.416 | −0.00825978 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 47153.5i | 0.948210i | 0.880468 | + | 0.474105i | \(0.157228\pi\) | ||||
−0.880468 | + | 0.474105i | \(0.842772\pi\) | |||||||
\(224\) | 15858.5 | − | 5075.08i | 0.316057 | − | 0.101146i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −53633.7 | − | 64949.2i | −1.05008 | − | 1.27162i | ||||
\(227\) | 61125.3i | 1.18623i | 0.805117 | + | 0.593116i | \(0.202102\pi\) | ||||
−0.805117 | + | 0.593116i | \(0.797898\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −42983.0 | −0.819645 | −0.409823 | − | 0.912165i | \(-0.634409\pi\) | ||||
−0.409823 | + | 0.912165i | \(0.634409\pi\) | |||||||
\(230\) | 2778.44 | − | 2294.38i | 0.0525225 | − | 0.0433720i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −92195.9 | + | 50366.1i | −1.71291 | + | 0.935755i | ||||
\(233\) | 63194.6 | 1.16404 | 0.582020 | − | 0.813175i | \(-0.302263\pi\) | ||||
0.582020 | + | 0.813175i | \(0.302263\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 11463.5i | − | 0.207579i | ||||||
\(236\) | −87637.0 | − | 16878.8i | −1.57349 | − | 0.303053i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −90.4610 | + | 74.7008i | −0.00159701 | + | 0.00131878i | ||||
\(239\) | 67281.6i | 1.17788i | 0.808177 | + | 0.588940i | \(0.200454\pi\) | ||||
−0.808177 | + | 0.588940i | \(0.799546\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14307.7 | 0.246341 | 0.123171 | − | 0.992386i | \(-0.460694\pi\) | ||||
0.123171 | + | 0.992386i | \(0.460694\pi\) | |||||||
\(242\) | −16047.5 | − | 19433.2i | −0.274016 | − | 0.331828i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −8588.53 | + | 44592.7i | −0.144258 | + | 0.749004i | ||||
\(245\) | −7656.15 | −0.127549 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 15687.5i | 0.257134i | ||||||||
\(248\) | −32130.7 | − | 58815.8i | −0.522417 | − | 0.956291i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 11291.1 | + | 13673.3i | 0.180658 | + | 0.218772i | ||||
\(251\) | 92024.1i | 1.46068i | 0.683085 | + | 0.730339i | \(0.260638\pi\) | ||||
−0.683085 | + | 0.730339i | \(0.739362\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −36379.8 | −0.568354 | ||||||||
\(254\) | −25726.4 | + | 21244.3i | −0.398760 | + | 0.329287i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 47454.1 | + | 45200.4i | 0.724093 | + | 0.689703i | ||||
\(257\) | 47095.9 | 0.713045 | 0.356523 | − | 0.934287i | \(-0.383962\pi\) | ||||
0.356523 | + | 0.934287i | \(0.383962\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 11232.6i | − | 0.167448i | ||||||
\(260\) | −2425.14 | + | 12591.7i | −0.0358749 | + | 0.186267i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −54089.5 | + | 44666.0i | −0.787972 | + | 0.650691i | ||||
\(263\) | − | 64791.0i | − | 0.936706i | −0.883542 | − | 0.468353i | \(-0.844848\pi\) | ||
0.883542 | − | 0.468353i | \(-0.155152\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10260.0 | −0.146102 | ||||||||
\(266\) | 2904.86 | + | 3517.72i | 0.0410546 | + | 0.0497162i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −83098.8 | − | 16004.8i | −1.15698 | − | 0.222833i | ||||
\(269\) | −13020.2 | −0.179934 | −0.0899669 | − | 0.995945i | \(-0.528676\pi\) | ||||
−0.0899669 | + | 0.995945i | \(0.528676\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 86544.0i | 1.17842i | 0.807981 | + | 0.589208i | \(0.200560\pi\) | ||||
−0.807981 | + | 0.589208i | \(0.799440\pi\) | |||||||
\(272\) | −428.721 | − | 171.505i | −0.00579478 | − | 0.00231813i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −38799.0 | − | 46984.7i | −0.516796 | − | 0.625828i | ||||
\(275\) | − | 88587.0i | − | 1.17140i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −71659.6 | −0.933931 | −0.466966 | − | 0.884275i | \(-0.654653\pi\) | ||||
−0.466966 | + | 0.884275i | \(0.654653\pi\) | |||||||
\(278\) | 90851.3 | − | 75023.1i | 1.17555 | − | 0.970745i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1787.80 | + | 3272.59i | 0.0228035 | + | 0.0417422i | ||||
\(281\) | 15636.0 | 0.198022 | 0.0990110 | − | 0.995086i | \(-0.468432\pi\) | ||||
0.0990110 | + | 0.995086i | \(0.468432\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 34109.5i | − | 0.425895i | −0.977064 | − | 0.212947i | \(-0.931694\pi\) | ||
0.977064 | − | 0.212947i | \(-0.0683063\pi\) | |||||||
\(284\) | 29436.5 | + | 5669.45i | 0.364964 | + | 0.0702918i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 99826.9 | − | 82435.0i | 1.22044 | − | 1.00781i | ||||
\(287\) | 16148.9i | 0.196056i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −83517.7 | −0.999961 | ||||||||
\(290\) | −14981.4 | − | 18142.1i | −0.178138 | − | 0.215721i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −13687.8 | + | 71068.5i | −0.160534 | + | 0.833512i | ||||
\(293\) | 82967.5 | 0.966436 | 0.483218 | − | 0.875500i | \(-0.339468\pi\) | ||||
0.483218 | + | 0.875500i | \(0.339468\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 19987.8i | − | 0.229679i | ||||||
\(296\) | 38798.6 | − | 21195.5i | 0.442826 | − | 0.241913i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −65279.5 | − | 79052.1i | −0.735097 | − | 0.890186i | ||||
\(299\) | − | 56226.1i | − | 0.628921i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 32254.8 | 0.356010 | ||||||||
\(302\) | −82235.6 | + | 67908.4i | −0.901667 | + | 0.744577i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −6669.23 | + | 16671.5i | −0.0721654 | + | 0.180396i | ||||
\(305\) | −10170.5 | −0.109331 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 156067.i | − | 1.65590i | −0.560802 | − | 0.827950i | \(-0.689507\pi\) | ||
0.560802 | − | 0.827950i | \(-0.310493\pi\) | |||||||
\(308\) | 7120.41 | − | 36970.0i | 0.0750591 | − | 0.389716i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 11573.7 | − | 9557.29i | 0.120434 | − | 0.0994515i | ||||
\(311\) | − | 23137.2i | − | 0.239216i | −0.992821 | − | 0.119608i | \(-0.961836\pi\) | ||
0.992821 | − | 0.119608i | \(-0.0381638\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21035.4 | 0.214715 | 0.107358 | − | 0.994220i | \(-0.465761\pi\) | ||||
0.107358 | + | 0.994220i | \(0.465761\pi\) | |||||||
\(314\) | 12486.5 | + | 15120.9i | 0.126644 | + | 0.153363i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 115642. | + | 22272.6i | 1.15809 | + | 0.223048i | ||||
\(317\) | −106440. | −1.05922 | −0.529611 | − | 0.848240i | \(-0.677662\pi\) | ||||
−0.529611 | + | 0.848240i | \(0.677662\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 237546.i | 2.33435i | ||||||||
\(320\) | −7930.37 | + | 12350.5i | −0.0774450 | + | 0.120610i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −10411.4 | − | 12608.0i | −0.100415 | − | 0.121600i | ||||
\(323\) | − | 126.514i | − | 0.00121264i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 136914. | 1.29623 | ||||||||
\(326\) | 17292.8 | − | 14280.0i | 0.162716 | − | 0.134367i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −55780.1 | + | 30472.3i | −0.518479 | + | 0.283242i | ||||
\(329\) | −52019.3 | −0.480588 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 194535.i | − | 1.77559i | −0.460239 | − | 0.887795i | \(-0.652236\pi\) | ||
0.460239 | − | 0.887795i | \(-0.347764\pi\) | |||||||
\(332\) | 78659.1 | + | 15149.7i | 0.713630 | + | 0.137445i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −24845.7 | + | 20517.1i | −0.222720 | + | 0.183917i | ||||
\(335\) | − | 18952.7i | − | 0.168882i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 81272.1 | 0.715618 | 0.357809 | − | 0.933795i | \(-0.383524\pi\) | ||||
0.357809 | + | 0.933795i | \(0.383524\pi\) | |||||||
\(338\) | 54662.2 | + | 66194.8i | 0.478469 | + | 0.579416i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 19.5579 | − | 101.547i | 0.000169186 | − | 0.000878436i | ||||
\(341\) | −151541. | −1.30323 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 73783.5i | 0.627150i | ||||||||
\(344\) | 60863.6 | + | 111412.i | 0.514328 | + | 0.941486i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 95726.8 | + | 115923.i | 0.799616 | + | 0.968317i | ||||
\(347\) | − | 113947.i | − | 0.946331i | −0.880974 | − | 0.473165i | \(-0.843111\pi\) | ||
0.880974 | − | 0.473165i | \(-0.156889\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 25419.8 | 0.208700 | 0.104350 | − | 0.994541i | \(-0.466724\pi\) | ||||
0.104350 | + | 0.994541i | \(0.466724\pi\) | |||||||
\(350\) | 30701.3 | − | 25352.5i | 0.250623 | − | 0.206959i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 141134. | − | 45166.3i | 1.13906 | − | 0.364527i | ||||
\(353\) | −39576.0 | −0.317601 | −0.158801 | − | 0.987311i | \(-0.550763\pi\) | ||||
−0.158801 | + | 0.987311i | \(0.550763\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6713.72i | 0.0532729i | ||||||||
\(356\) | −34612.5 | + | 179712.i | −0.273107 | + | 1.41801i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 107056. | − | 88404.2i | 0.835301 | − | 0.689774i | ||||
\(359\) | 120831.i | 0.937541i | 0.883320 | + | 0.468771i | \(0.155303\pi\) | ||||
−0.883320 | + | 0.468771i | \(0.844697\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 125401. | 0.962249 | ||||||||
\(362\) | 115566. | + | 139948.i | 0.881891 | + | 1.06795i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 57138.4 | + | 11004.8i | 0.431246 | + | 0.0830578i | ||||
\(365\) | −16208.9 | −0.121666 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 113429.i | 0.842156i | 0.907024 | + | 0.421078i | \(0.138348\pi\) | ||||
−0.907024 | + | 0.421078i | \(0.861652\pi\) | |||||||
\(368\) | 23903.5 | − | 59753.0i | 0.176508 | − | 0.441229i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 6304.60 | + | 7634.73i | 0.0460526 | + | 0.0557686i | ||||
\(371\) | 46557.9i | 0.338256i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −23277.7 | −0.167310 | −0.0836551 | − | 0.996495i | \(-0.526659\pi\) | ||||
−0.0836551 | + | 0.996495i | \(0.526659\pi\) | |||||||
\(374\) | −805.069 | + | 664.809i | −0.00575559 | + | 0.00475285i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −98158.3 | − | 179680.i | −0.694307 | − | 1.27094i | ||||
\(377\) | −367135. | −2.58311 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 89977.3i | − | 0.626404i | −0.949686 | − | 0.313202i | \(-0.898598\pi\) | ||
0.949686 | − | 0.313202i | \(-0.101402\pi\) | |||||||
\(380\) | −3948.83 | − | 760.542i | −0.0273465 | − | 0.00526691i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −75489.7 | + | 62337.8i | −0.517322 | + | 0.427194i | ||||
\(383\) | − | 242067.i | − | 1.65020i | −0.564984 | − | 0.825102i | \(-0.691118\pi\) | ||
0.564984 | − | 0.825102i | \(-0.308882\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8431.93 | 0.0568860 | ||||||||
\(386\) | 33400.3 | + | 40447.1i | 0.224169 | + | 0.271464i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 27301.7 | − | 141754.i | 0.181354 | − | 0.941611i | ||||
\(389\) | 229775. | 1.51846 | 0.759230 | − | 0.650823i | \(-0.225576\pi\) | ||||
0.759230 | + | 0.650823i | \(0.225576\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 453.444i | 0.00296599i | ||||||||
\(392\) | −120003. | + | 65556.9i | −0.780944 | + | 0.426625i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 83200.8 | + | 100754.i | 0.535963 | + | 0.649040i | ||||
\(395\) | 26375.1i | 0.169044i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −78709.5 | −0.499397 | −0.249699 | − | 0.968324i | \(-0.580332\pi\) | ||||
−0.249699 | + | 0.968324i | \(0.580332\pi\) | |||||||
\(398\) | −27144.6 | + | 22415.4i | −0.171363 | + | 0.141508i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 145502. | + | 58206.5i | 0.909390 | + | 0.363791i | ||||
\(401\) | 42894.9 | 0.266757 | 0.133379 | − | 0.991065i | \(-0.457417\pi\) | ||||
0.133379 | + | 0.991065i | \(0.457417\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 234211.i | − | 1.44211i | ||||||
\(404\) | 45015.9 | − | 233728.i | 0.275805 | − | 1.43202i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −82325.5 | + | 67982.6i | −0.499439 | + | 0.412426i | ||||
\(407\) | − | 99966.0i | − | 0.603481i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7021.98 | −0.0419771 | −0.0209886 | − | 0.999780i | \(-0.506681\pi\) | ||||
−0.0209886 | + | 0.999780i | \(0.506681\pi\) | |||||||
\(410\) | −9064.00 | − | 10976.3i | −0.0539203 | − | 0.0652963i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −201538. | − | 38816.0i | −1.18730 | − | 0.228674i | ||||
\(413\) | −90700.6 | −0.531753 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 17940.2i | 0.104167i | ||||||||
\(416\) | 69806.0 | + | 218128.i | 0.403372 | + | 1.26045i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 25852.2 | + | 31306.4i | 0.147960 | + | 0.179176i | ||||
\(419\) | − | 93841.8i | − | 0.534525i | −0.963624 | − | 0.267263i | \(-0.913881\pi\) | ||
0.963624 | − | 0.267263i | \(-0.0861191\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 131807. | 0.743662 | 0.371831 | − | 0.928300i | \(-0.378730\pi\) | ||||
0.371831 | + | 0.928300i | \(0.378730\pi\) | |||||||
\(422\) | 151320. | − | 124957.i | 0.849711 | − | 0.701674i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −160816. | + | 87852.8i | −0.894535 | + | 0.488679i | ||||
\(425\) | −1104.17 | −0.00611302 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 46151.6i | 0.253123i | ||||||||
\(428\) | 288049. | + | 55478.1i | 1.57246 | + | 0.302854i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −21923.4 | + | 18103.9i | −0.118569 | + | 0.0979117i | ||||
\(431\) | 14141.6i | 0.0761279i | 0.999275 | + | 0.0380640i | \(0.0121191\pi\) | ||||
−0.999275 | + | 0.0380640i | \(0.987881\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −224082. | −1.19517 | −0.597586 | − | 0.801805i | \(-0.703873\pi\) | ||||
−0.597586 | + | 0.801805i | \(0.703873\pi\) | |||||||
\(434\) | −43369.1 | − | 52519.0i | −0.230251 | − | 0.278828i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 31492.7 | − | 163514.i | 0.165667 | − | 0.860166i | ||||
\(437\) | 17632.9 | 0.0923338 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 168793.i | 0.875842i | 0.899013 | + | 0.437921i | \(0.144285\pi\) | ||||
−0.899013 | + | 0.437921i | \(0.855715\pi\) | |||||||
\(440\) | 15910.7 | + | 29124.8i | 0.0821834 | + | 0.150438i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1027.48 | − | 1244.26i | −0.00525934 | − | 0.00636894i | ||||
\(443\) | − | 129808.i | − | 0.661446i | −0.943728 | − | 0.330723i | \(-0.892707\pi\) | ||
0.943728 | − | 0.330723i | \(-0.107293\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −40987.9 | −0.206983 | ||||||||
\(446\) | −145436. | + | 120098.i | −0.731144 | + | 0.603764i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 56044.0 | + | 35986.4i | 0.279237 | + | 0.179301i | ||||
\(449\) | 107176. | 0.531623 | 0.265811 | − | 0.964025i | \(-0.414360\pi\) | ||||
0.265811 | + | 0.964025i | \(0.414360\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 143719.i | 0.706581i | ||||||||
\(452\) | 63720.8 | − | 330846.i | 0.311892 | − | 1.61938i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −188530. | + | 155684.i | −0.914677 | + | 0.755321i | ||||
\(455\) | 13031.8i | 0.0629481i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −345116. | −1.65247 | −0.826234 | − | 0.563327i | \(-0.809521\pi\) | ||||
−0.826234 | + | 0.563327i | \(0.809521\pi\) | |||||||
\(458\) | −109476. | − | 132573.i | −0.521901 | − | 0.632011i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 14153.2 | + | 2725.89i | 0.0668864 | + | 0.0128823i | ||||
\(461\) | −26097.1 | −0.122798 | −0.0613988 | − | 0.998113i | \(-0.519556\pi\) | ||||
−0.0613988 | + | 0.998113i | \(0.519556\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6582.77i | 0.0307077i | 0.999882 | + | 0.0153538i | \(0.00488747\pi\) | ||||
−0.999882 | + | 0.0153538i | \(0.995113\pi\) | |||||||
\(464\) | −390164. | − | 156081.i | −1.81222 | − | 0.724958i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 160954. | + | 194912.i | 0.741191 | + | 0.897566i | ||||
\(467\) | 107337.i | 0.492171i | 0.969248 | + | 0.246085i | \(0.0791443\pi\) | ||||
−0.969248 | + | 0.246085i | \(0.920856\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −86003.8 | −0.390996 | ||||||||
\(470\) | 35357.2 | − | 29197.2i | 0.160060 | − | 0.132174i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −171148. | − | 313290.i | −0.768225 | − | 1.40625i | ||||
\(473\) | 287056. | 1.28305 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 42937.2i | 0.190304i | ||||||||
\(476\) | −460.801 | − | 88.7501i | −0.00203376 | − | 0.000391701i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −207518. | + | 171364.i | −0.908237 | + | 0.750003i | ||||
\(479\) | 348828.i | 1.52034i | 0.649724 | + | 0.760170i | \(0.274884\pi\) | ||||
−0.649724 | + | 0.760170i | \(0.725116\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 154501. | 0.667791 | ||||||||
\(482\) | 36441.3 | + | 44129.6i | 0.156855 | + | 0.189948i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 19065.6 | − | 98991.0i | 0.0813880 | − | 0.422576i | ||||
\(485\) | 32330.5 | 0.137445 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 104528.i | 0.440732i | 0.975417 | + | 0.220366i | \(0.0707251\pi\) | ||||
−0.975417 | + | 0.220366i | \(0.929275\pi\) | |||||||
\(488\) | −159413. | + | 87086.2i | −0.669396 | + | 0.365687i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −19499.9 | − | 23614.0i | −0.0812158 | − | 0.0983506i | ||||
\(491\) | 181720.i | 0.753770i | 0.926260 | + | 0.376885i | \(0.123005\pi\) | ||||
−0.926260 | + | 0.376885i | \(0.876995\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2960.82 | 0.0121820 | ||||||||
\(494\) | −48385.1 | + | 39955.4i | −0.198270 | + | 0.163727i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 99570.5 | − | 248903.i | 0.404732 | − | 1.01173i | ||||
\(497\) | 30465.5 | 0.123338 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 329701.i | − | 1.32409i | −0.749462 | − | 0.662047i | \(-0.769688\pi\) | ||
0.749462 | − | 0.662047i | \(-0.230312\pi\) | |||||||
\(500\) | −13414.7 | + | 69650.6i | −0.0536586 | + | 0.278602i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −283831. | + | 234382.i | −1.12630 | + | 0.930072i | ||||
\(503\) | 225559.i | 0.891507i | 0.895156 | + | 0.445753i | \(0.147064\pi\) | ||||
−0.895156 | + | 0.445753i | \(0.852936\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 53307.4 | 0.209028 | ||||||||
\(506\) | −92657.9 | − | 112207.i | −0.361894 | − | 0.438245i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −131048. | − | 25239.8i | −0.507813 | − | 0.0978044i | ||||
\(509\) | 71361.2 | 0.275440 | 0.137720 | − | 0.990471i | \(-0.456023\pi\) | ||||
0.137720 | + | 0.990471i | \(0.456023\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 73553.0i | 0.281682i | ||||||||
\(512\) | −18548.2 | + | 261487.i | −0.0707559 | + | 0.997494i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 119952. | + | 145259.i | 0.454025 | + | 0.549814i | ||||
\(515\) | − | 45965.6i | − | 0.173308i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −462952. | −1.73203 | ||||||||
\(518\) | 34644.9 | − | 28609.0i | 0.129116 | − | 0.106621i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −45013.3 | + | 24590.5i | −0.166469 | + | 0.0909413i | ||||
\(521\) | 254162. | 0.936344 | 0.468172 | − | 0.883637i | \(-0.344913\pi\) | ||||
0.468172 | + | 0.883637i | \(0.344913\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 449711.i | − | 1.64411i | −0.569410 | − | 0.822054i | \(-0.692828\pi\) | ||
0.569410 | − | 0.822054i | \(-0.307172\pi\) | |||||||
\(524\) | −275528. | − | 53066.5i | −1.00347 | − | 0.193267i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 199836. | − | 165020.i | 0.722273 | − | 0.596438i | ||||
\(527\) | 1888.83i | 0.00680099i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 216642. | 0.774162 | ||||||||
\(530\) | −26131.8 | − | 31645.1i | −0.0930290 | − | 0.112656i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3451.19 | + | 17919.0i | −0.0121940 | + | 0.0633126i | ||||
\(533\) | −222123. | −0.781878 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 65696.7i | 0.229528i | ||||||||
\(536\) | −162286. | − | 297066.i | −0.564873 | − | 1.03401i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −33161.9 | − | 40158.4i | −0.114571 | − | 0.138743i | ||||
\(539\) | 309192.i | 1.06427i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 479811. | 1.63936 | 0.819682 | − | 0.572819i | \(-0.194150\pi\) | ||||
0.819682 | + | 0.572819i | \(0.194150\pi\) | |||||||
\(542\) | −266929. | + | 220424.i | −0.908651 | + | 0.750345i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −562.961 | − | 1759.13i | −0.00190231 | − | 0.00594428i | ||||
\(545\) | 37293.4 | 0.125557 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 352931.i | 1.17955i | 0.807569 | + | 0.589773i | \(0.200783\pi\) | ||||
−0.807569 | + | 0.589773i | \(0.799217\pi\) | |||||||
\(548\) | 46096.0 | − | 239336.i | 0.153498 | − | 0.796980i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 273230. | − | 225628.i | 0.903240 | − | 0.745877i | ||||
\(551\) | − | 115136.i | − | 0.379235i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 119685. | 0.391372 | ||||||||
\(554\) | −182514. | − | 221021.i | −0.594672 | − | 0.720134i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 462789. | + | 89133.0i | 1.49704 | + | 0.288329i | ||||
\(557\) | 360746. | 1.16276 | 0.581382 | − | 0.813631i | \(-0.302512\pi\) | ||||
0.581382 | + | 0.813631i | \(0.302512\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 443655.i | 1.41978i | ||||||||
\(560\) | −5540.24 | + | 13849.3i | −0.0176666 | + | 0.0441622i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 39824.3 | + | 48226.4i | 0.126089 | + | 0.152691i | ||||
\(563\) | 466715.i | 1.47243i | 0.676747 | + | 0.736216i | \(0.263389\pi\) | ||||
−0.676747 | + | 0.736216i | \(0.736611\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 75457.6 | 0.236378 | ||||||||
\(566\) | 105204. | − | 86875.6i | 0.328398 | − | 0.271184i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 57487.2 | + | 105231.i | 0.178187 | + | 0.326173i | ||||
\(569\) | 264863. | 0.818083 | 0.409041 | − | 0.912516i | \(-0.365863\pi\) | ||||
0.409041 | + | 0.912516i | \(0.365863\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 605767.i | − | 1.85795i | −0.370146 | − | 0.928974i | \(-0.620692\pi\) | ||
0.370146 | − | 0.928974i | \(-0.379308\pi\) | |||||||
\(572\) | 508511. | + | 97938.9i | 1.55420 | + | 0.299339i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −49808.3 | + | 41130.7i | −0.151174 | + | 0.124837i | ||||
\(575\) | − | 153893.i | − | 0.465461i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −160301. | −0.481488 | −0.240744 | − | 0.970589i | \(-0.577391\pi\) | ||||
−0.240744 | + | 0.970589i | \(0.577391\pi\) | |||||||
\(578\) | −212716. | − | 257595.i | −0.636715 | − | 0.771048i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 17799.0 | − | 92414.7i | 0.0529103 | − | 0.274717i | ||||
\(581\) | 81408.9 | 0.241168 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 414348.i | 1.21907i | ||||||||
\(584\) | −254060. | + | 138791.i | −0.744921 | + | 0.406946i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 211315. | + | 255898.i | 0.615369 | + | 0.745198i | ||||
\(587\) | − | 64997.1i | − | 0.188633i | −0.995542 | − | 0.0943165i | \(-0.969933\pi\) | ||
0.995542 | − | 0.0943165i | \(-0.0300665\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 73450.3 | 0.211721 | ||||||||
\(590\) | 61648.6 | − | 50908.1i | 0.177100 | − | 0.146246i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 164192. | + | 65683.1i | 0.468499 | + | 0.187417i | ||||
\(593\) | 150269. | 0.427326 | 0.213663 | − | 0.976907i | \(-0.431461\pi\) | ||||
0.213663 | + | 0.976907i | \(0.431461\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 105.097i | − | 0.000296864i | ||||||
\(596\) | 77556.9 | − | 402685.i | 0.218337 | − | 1.13363i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 173419. | − | 143206.i | 0.484947 | − | 0.400459i | ||||
\(599\) | − | 133110.i | − | 0.370985i | −0.982646 | − | 0.185492i | \(-0.940612\pi\) | ||
0.982646 | − | 0.185492i | \(-0.0593880\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 462021. | 1.27913 | 0.639563 | − | 0.768739i | \(-0.279115\pi\) | ||||
0.639563 | + | 0.768739i | \(0.279115\pi\) | |||||||
\(602\) | 82151.8 | + | 99484.0i | 0.226686 | + | 0.274511i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −418902. | − | 80680.3i | −1.14826 | − | 0.221153i | ||||
\(605\) | 22577.4 | 0.0616826 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 223633.i | − | 0.606959i | −0.952838 | − | 0.303479i | \(-0.901852\pi\) | ||
0.952838 | − | 0.303479i | \(-0.0981484\pi\) | |||||||
\(608\) | −68406.4 | + | 21891.6i | −0.185050 | + | 0.0592204i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −25903.8 | − | 31368.9i | −0.0696152 | − | 0.0843024i | ||||
\(611\) | − | 715508.i | − | 1.91660i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 383985. | 1.02187 | 0.510933 | − | 0.859621i | \(-0.329300\pi\) | ||||
0.510933 | + | 0.859621i | \(0.329300\pi\) | |||||||
\(614\) | 481359. | − | 397496.i | 1.27683 | − | 1.05438i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 132163. | − | 72199.7i | 0.348295 | − | 0.190272i | ||||
\(617\) | −608003. | −1.59711 | −0.798555 | − | 0.601921i | \(-0.794402\pi\) | ||||
−0.798555 | + | 0.601921i | \(0.794402\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 573813.i | − | 1.49758i | −0.662810 | − | 0.748788i | \(-0.730636\pi\) | ||
0.662810 | − | 0.748788i | \(-0.269364\pi\) | |||||||
\(620\) | 58955.3 | + | 11354.8i | 0.153370 | + | 0.0295389i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 71362.5 | − | 58929.6i | 0.184454 | − | 0.152319i | ||||
\(623\) | 185995.i | 0.479209i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 366714. | 0.938789 | ||||||||
\(626\) | 53576.5 | + | 64879.9i | 0.136718 | + | 0.165562i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −14834.9 | + | 77024.8i | −0.0376155 | + | 0.195304i | ||||
\(629\) | −1245.99 | −0.00314931 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 367125.i | − | 0.922053i | −0.887386 | − | 0.461026i | \(-0.847481\pi\) | ||
0.887386 | − | 0.461026i | \(-0.152519\pi\) | |||||||
\(632\) | 225841. | + | 413405.i | 0.565416 | + | 1.03500i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −271099. | − | 328295.i | −0.674450 | − | 0.816744i | ||||
\(635\) | − | 29888.8i | − | 0.0741243i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −477866. | −1.17768 | ||||||||
\(638\) | −732666. | + | 605020.i | −1.79997 | + | 1.48638i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −58291.1 | + | 6996.44i | −0.142312 | + | 0.0170812i | ||||
\(641\) | −161096. | −0.392075 | −0.196037 | − | 0.980596i | \(-0.562807\pi\) | ||||
−0.196037 | + | 0.980596i | \(0.562807\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 658474.i | 1.59264i | 0.604878 | + | 0.796318i | \(0.293222\pi\) | ||||
−0.604878 | + | 0.796318i | \(0.706778\pi\) | |||||||
\(644\) | 12369.6 | − | 64224.2i | 0.0298251 | − | 0.154856i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 390.209 | − | 322.226i | 0.000935044 | − | 0.000772140i | ||||
\(647\) | − | 410472.i | − | 0.980563i | −0.871564 | − | 0.490281i | \(-0.836894\pi\) | ||
0.871564 | − | 0.490281i | \(-0.163106\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −807201. | −1.91643 | ||||||||
\(650\) | 348715. | + | 422286.i | 0.825361 | + | 0.999494i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 88088.2 | + | 16965.7i | 0.207216 | + | 0.0399096i | ||||
\(653\) | 23202.5 | 0.0544136 | 0.0272068 | − | 0.999630i | \(-0.491339\pi\) | ||||
0.0272068 | + | 0.999630i | \(0.491339\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 62841.0i | − | 0.146474i | ||||||
\(656\) | −236056. | − | 94431.4i | −0.548539 | − | 0.219436i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −132491. | − | 160444.i | −0.306010 | − | 0.370571i | ||||
\(659\) | 210220.i | 0.484064i | 0.970268 | + | 0.242032i | \(0.0778139\pi\) | ||||
−0.970268 | + | 0.242032i | \(0.922186\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21515.2 | −0.0492428 | −0.0246214 | − | 0.999697i | \(-0.507838\pi\) | ||||
−0.0246214 | + | 0.999697i | \(0.507838\pi\) | |||||||
\(662\) | 600008. | − | 495474.i | 1.36912 | − | 1.13059i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 153615. | + | 281195.i | 0.348416 | + | 0.637781i | ||||
\(665\) | −4086.87 | −0.00924161 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 412664.i | 0.927566i | ||||||||
\(668\) | −126562. | − | 24375.8i | −0.283629 | − | 0.0546268i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 58456.2 | − | 48271.9i | 0.130221 | − | 0.107534i | ||||
\(671\) | 410732.i | 0.912249i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 79154.4 | 0.174761 | 0.0873806 | − | 0.996175i | \(-0.472150\pi\) | ||||
0.0873806 | + | 0.996175i | \(0.472150\pi\) | |||||||
\(674\) | 206997. | + | 250668.i | 0.455663 | + | 0.551798i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −64942.8 | + | 337191.i | −0.142114 | + | 0.737875i | ||||
\(677\) | −94999.9 | −0.207274 | −0.103637 | − | 0.994615i | \(-0.533048\pi\) | ||||
−0.103637 | + | 0.994615i | \(0.533048\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 146709.i | − | 0.318213i | ||||||
\(680\) | 363.017 | − | 198.314i | 0.000785071 | − | 0.000428880i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −385969. | − | 467399.i | −0.829819 | − | 1.00489i | ||||
\(683\) | − | 265559.i | − | 0.569272i | −0.958636 | − | 0.284636i | \(-0.908127\pi\) | ||
0.958636 | − | 0.284636i | \(-0.0918727\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 54586.6 | 0.116333 | ||||||||
\(686\) | −227572. | + | 187924.i | −0.483582 | + | 0.399332i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −188611. | + | 471484.i | −0.398466 | + | 0.996070i | ||||
\(689\) | −640388. | −1.34898 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 497888.i | 1.04274i | 0.853331 | + | 0.521369i | \(0.174579\pi\) | ||||
−0.853331 | + | 0.521369i | \(0.825421\pi\) | |||||||
\(692\) | −113731. | + | 590503.i | −0.237501 | + | 1.23313i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 351448. | − | 290218.i | 0.729695 | − | 0.602567i | ||||
\(695\) | 105551.i | 0.218520i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1791.34 | 0.00368734 | ||||||||
\(698\) | 64743.3 | + | 78402.8i | 0.132888 | + | 0.160924i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 156390. | + | 30120.6i | 0.319163 | + | 0.0614707i | ||||
\(701\) | −102403. | −0.208389 | −0.104195 | − | 0.994557i | \(-0.533226\pi\) | ||||
−0.104195 | + | 0.994557i | \(0.533226\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 48452.5i | 0.0980405i | ||||||||
\(704\) | 498771. | + | 320266.i | 1.00637 | + | 0.646198i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −100798. | − | 122065.i | −0.202230 | − | 0.244896i | ||||
\(707\) | − | 241899.i | − | 0.483943i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −557443. | −1.10894 | −0.554470 | − | 0.832204i | \(-0.687079\pi\) | ||||
−0.554470 | + | 0.832204i | \(0.687079\pi\) | |||||||
\(710\) | −20707.2 | + | 17099.6i | −0.0410776 | + | 0.0339210i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −642446. | + | 350965.i | −1.26729 | + | 0.692315i | ||||
\(713\) | −263256. | −0.517845 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 115978.i | 0.226864i | ||||||||
\(716\) | 545332. | + | 105031.i | 1.06374 | + | 0.204876i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −372682. | + | 307753.i | −0.722918 | + | 0.596970i | ||||
\(719\) | − | 665001.i | − | 1.28637i | −0.765713 | − | 0.643183i | \(-0.777614\pi\) | ||
0.765713 | − | 0.643183i | \(-0.222386\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −208583. | −0.401244 | ||||||||
\(722\) | 319392. | + | 386777.i | 0.612703 | + | 0.741970i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −137302. | + | 712887.i | −0.261938 | + | 1.36001i | ||||
\(725\) | −1.00486e6 | −1.91175 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 903006.i | − | 1.70853i | −0.519841 | − | 0.854263i | \(-0.674009\pi\) | ||
0.519841 | − | 0.854263i | \(-0.325991\pi\) | |||||||
\(728\) | 111587. | + | 204262.i | 0.210548 | + | 0.385411i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −41283.5 | − | 49993.5i | −0.0774696 | − | 0.0938140i | ||||
\(731\) | − | 3577.92i | − | 0.00669570i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −633281. | −1.17866 | −0.589330 | − | 0.807893i | \(-0.700608\pi\) | ||||
−0.589330 | + | 0.807893i | \(0.700608\pi\) | |||||||
\(734\) | −349851. | + | 288900.i | −0.649368 | + | 0.536235i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 245178. | − | 78462.8i | 0.452612 | − | 0.144846i | ||||
\(737\) | −765401. | −1.40914 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 72439.1i | − | 0.132643i | −0.997798 | − | 0.0663215i | \(-0.978874\pi\) | ||
0.997798 | − | 0.0663215i | \(-0.0211263\pi\) | |||||||
\(740\) | −7490.33 | + | 38890.7i | −0.0136785 | + | 0.0710203i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −143599. | + | 118581.i | −0.260822 | + | 0.215381i | ||||
\(743\) | 600017.i | 1.08689i | 0.839444 | + | 0.543446i | \(0.182881\pi\) | ||||
−0.839444 | + | 0.543446i | \(0.817119\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 91842.3 | 0.165474 | ||||||||
\(746\) | −59287.4 | − | 71795.7i | −0.106533 | − | 0.129009i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −4100.96 | − | 789.843i | −0.00732963 | − | 0.00141168i | ||||
\(749\) | 298119. | 0.531405 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 710454.i | 1.25967i | 0.776730 | + | 0.629834i | \(0.216877\pi\) | ||||
−0.776730 | + | 0.629834i | \(0.783123\pi\) | |||||||
\(752\) | 304185. | − | 760390.i | 0.537900 | − | 1.34462i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −935079. | − | 1.13236e6i | −1.64477 | − | 1.99178i | ||||
\(755\) | − | 95540.9i | − | 0.167608i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 577805. | 1.00830 | 0.504150 | − | 0.863616i | \(-0.331806\pi\) | ||||
0.504150 | + | 0.863616i | \(0.331806\pi\) | |||||||
\(758\) | 277518. | − | 229169.i | 0.483007 | − | 0.398857i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −7711.76 | − | 14116.5i | −0.0133514 | − | 0.0244399i | ||||
\(761\) | 751658. | 1.29793 | 0.648965 | − | 0.760818i | \(-0.275202\pi\) | ||||
0.648965 | + | 0.760818i | \(0.275202\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 169230.i | − | 0.290689i | ||||||
\(764\) | −384539. | − | 74061.9i | −0.658800 | − | 0.126884i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 746610. | − | 616535.i | 1.27244 | − | 1.05075i | ||||
\(767\) | − | 1.24756e6i | − | 2.12065i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −416567. | −0.704421 | −0.352211 | − | 0.935921i | \(-0.614570\pi\) | ||||
−0.352211 | + | 0.935921i | \(0.614570\pi\) | |||||||
\(770\) | 21475.8 | + | 26006.7i | 0.0362216 | + | 0.0438636i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −39682.1 | + | 206034.i | −0.0665824 | + | 0.345704i | ||||
\(773\) | 611604. | 1.02356 | 0.511778 | − | 0.859118i | \(-0.328987\pi\) | ||||
0.511778 | + | 0.859118i | \(0.328987\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 641046.i | − | 1.06730i | ||||||
\(776\) | 506750. | − | 276835.i | 0.841531 | − | 0.459724i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 585228. | + | 708698.i | 0.966864 | + | 1.17085i | ||||
\(779\) | − | 69659.3i | − | 0.114790i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 271132. | 0.444507 | ||||||||
\(782\) | −1398.56 | + | 1154.90i | −0.00228701 | + | 0.00188857i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −507841. | − | 203156.i | −0.826220 | − | 0.330519i | ||||
\(785\) | −17567.4 | −0.0285081 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 462322.i | 0.746440i | 0.927743 | + | 0.373220i | \(0.121746\pi\) | ||||
−0.927743 | + | 0.373220i | \(0.878254\pi\) | |||||||
\(788\) | −98848.7 | + | 513235.i | −0.159191 | + | 0.826540i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −81349.0 | + | 67176.3i | −0.130346 | + | 0.107637i | ||||
\(791\) | − | 342412.i | − | 0.547263i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −634800. | −1.00946 | ||||||||
\(794\) | −200470. | − | 242765.i | −0.317986 | − | 0.385075i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −138272. | − | 26631.2i | −0.218228 | − | 0.0420305i | ||||
\(797\) | −515899. | −0.812173 | −0.406086 | − | 0.913835i | \(-0.633107\pi\) | ||||
−0.406086 | + | 0.913835i | \(0.633107\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5770.33i | 0.00903872i | ||||||||
\(800\) | 191062. | + | 597024.i | 0.298534 | + | 0.932851i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 109252. | + | 132301.i | 0.169855 | + | 0.205691i | ||||
\(803\) | 654594.i | 1.01517i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 14647.9 | 0.0226040 | ||||||||
\(806\) | 722381. | − | 596527.i | 1.11198 | − | 0.918248i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 835544. | − | 456453.i | 1.27981 | − | 0.699155i | ||||
\(809\) | 1.06734e6 | 1.63081 | 0.815406 | − | 0.578889i | \(-0.196513\pi\) | ||||
0.815406 | + | 0.578889i | \(0.196513\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 255259.i | 0.388096i | 0.980992 | + | 0.194048i | \(0.0621618\pi\) | ||||
−0.980992 | + | 0.194048i | \(0.937838\pi\) | |||||||
\(812\) | −419360. | − | 80768.4i | −0.636025 | − | 0.122498i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 308326. | − | 254609.i | 0.465331 | − | 0.384261i | ||||
\(815\) | 20090.7i | 0.0302468i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −139133. | −0.208443 | ||||||||
\(818\) | −17884.7 | − | 21658.0i | −0.0267285 | − | 0.0323677i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 10768.7 | − | 55912.5i | 0.0160153 | − | 0.0831536i | ||||
\(821\) | −509001. | −0.755148 | −0.377574 | − | 0.925979i | \(-0.623242\pi\) | ||||
−0.377574 | + | 0.925979i | \(0.623242\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 29019.0i | − | 0.0428432i | −0.999771 | − | 0.0214216i | \(-0.993181\pi\) | ||
0.999771 | − | 0.0214216i | \(-0.00681923\pi\) | |||||||
\(824\) | −393588. | − | 720468.i | −0.579678 | − | 1.06111i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −231011. | − | 279749.i | −0.338589 | − | 0.410023i | ||||
\(827\) | − | 934276.i | − | 1.36604i | −0.730399 | − | 0.683021i | \(-0.760666\pi\) | ||
0.730399 | − | 0.683021i | \(-0.239334\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.06294e6 | 1.54667 | 0.773336 | − | 0.633996i | \(-0.218586\pi\) | ||||
0.773336 | + | 0.633996i | \(0.218586\pi\) | |||||||
\(830\) | −55333.1 | + | 45692.9i | −0.0803209 | + | 0.0663273i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −494982. | + | 770867.i | −0.715060 | + | 1.11361i | ||||
\(833\) | 3853.82 | 0.00555395 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 28865.6i | − | 0.0414007i | ||||||
\(836\) | −30714.3 | + | 159472.i | −0.0439469 | + | 0.228178i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 289438. | − | 239011.i | 0.412161 | − | 0.340354i | ||||
\(839\) | 532910.i | 0.757060i | 0.925589 | + | 0.378530i | \(0.123570\pi\) | ||||
−0.925589 | + | 0.378530i | \(0.876430\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.98726e6 | 2.80971 | ||||||||
\(842\) | 335708. | + | 406535.i | 0.473519 | + | 0.573421i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 770812. | + | 148458.i | 1.08209 | + | 0.208410i | ||||
\(845\) | −76904.8 | −0.107706 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 102452.i | − | 0.142808i | ||||||
\(848\) | −680558. | − | 272249.i | −0.946397 | − | 0.378595i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2812.27 | − | 3405.59i | −0.00389241 | − | 0.00471362i | ||||
\(851\) | − | 173661.i | − | 0.239796i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 154337. | 0.212115 | 0.106057 | − | 0.994360i | \(-0.466177\pi\) | ||||
0.106057 | + | 0.994360i | \(0.466177\pi\) | |||||||
\(854\) | −142346. | + | 117546.i | −0.195177 | + | 0.161173i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 562538. | + | 1.02973e6i | 0.767722 | + | 1.40533i | ||||
\(857\) | −614991. | −0.837350 | −0.418675 | − | 0.908136i | \(-0.637505\pi\) | ||||
−0.418675 | + | 0.908136i | \(0.637505\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 371191.i | 0.503049i | 0.967851 | + | 0.251525i | \(0.0809320\pi\) | ||||
−0.967851 | + | 0.251525i | \(0.919068\pi\) | |||||||
\(860\) | −111676. | − | 21508.8i | −0.150995 | − | 0.0290816i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −43617.1 | + | 36018.1i | −0.0587006 | + | 0.0484737i | ||||
\(863\) | 1.25171e6i | 1.68067i | 0.542067 | + | 0.840335i | \(0.317642\pi\) | ||||
−0.542067 | + | 0.840335i | \(0.682358\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −134679. | −0.179998 | ||||||||
\(866\) | −570727. | − | 691138.i | −0.761014 | − | 0.921571i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 51525.7 | − | 267528.i | 0.0683887 | − | 0.355082i | ||||
\(869\) | 1.06515e6 | 1.41050 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 1.18295e6i | − | 1.55931i | ||||||
\(872\) | 584539. | − | 319331.i | 0.768742 | − | 0.419960i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 44910.3 | + | 54385.4i | 0.0587927 | + | 0.0711966i | ||||
\(875\) | 72085.4i | 0.0941524i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −413992. | −0.538261 | −0.269130 | − | 0.963104i | \(-0.586736\pi\) | ||||
−0.269130 | + | 0.963104i | \(0.586736\pi\) | |||||||
\(878\) | −520611. | + | 429910.i | −0.675343 | + | 0.557684i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −49306.0 | + | 123253.i | −0.0636700 | + | 0.159160i | ||||
\(881\) | 974575. | 1.25563 | 0.627817 | − | 0.778361i | \(-0.283948\pi\) | ||||
0.627817 | + | 0.778361i | \(0.283948\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 269401.i | 0.345524i | 0.984964 | + | 0.172762i | \(0.0552691\pi\) | ||||
−0.984964 | + | 0.172762i | \(0.944731\pi\) | |||||||
\(884\) | 1220.73 | − | 6338.17i | 0.00156212 | − | 0.00811072i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 400369. | − | 330616.i | 0.510027 | − | 0.421170i | ||||
\(887\) | 609409.i | 0.774572i | 0.921960 | + | 0.387286i | \(0.126587\pi\) | ||||
−0.921960 | + | 0.387286i | \(0.873413\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −135629. | −0.171613 | ||||||||
\(890\) | −104395. | − | 126419.i | −0.131795 | − | 0.159600i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −740841. | − | 142686.i | −0.931098 | − | 0.179329i | ||||
\(893\) | 224388. | 0.281383 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 124377.i | 0.155272i | ||||||||
\(896\) | 31748.5 | + | 264513.i | 0.0395464 | + | 0.329482i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 272972. | + | 330563.i | 0.338506 | + | 0.409923i | ||||
\(899\) | 1.71896e6i | 2.12690i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5164.51 | 0.00636179 | ||||||||
\(902\) | −443275. | + | 366047.i | −0.544829 | + | 0.449909i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.18273e6 | − | 646117.i | 1.44726 | − | 0.790632i | ||||
\(905\) | −162591. | −0.198518 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 379792.i | 0.461669i | 0.972993 | + | 0.230835i | \(0.0741456\pi\) | ||||
−0.972993 | + | 0.230835i | \(0.925854\pi\) | |||||||
\(908\) | −960355. | − | 184964.i | −1.16482 | − | 0.224344i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −40194.3 | + | 33191.6i | −0.0485379 | + | 0.0400816i | ||||
\(911\) | 659379.i | 0.794509i | 0.917709 | + | 0.397254i | \(0.130037\pi\) | ||||
−0.917709 | + | 0.397254i | \(0.869963\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 724509. | 0.869165 | ||||||||
\(914\) | −878998. | − | 1.06445e6i | −1.05219 | − | 1.27418i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 130066. | − | 675317.i | 0.155014 | − | 0.804853i | ||||
\(917\) | −285160. | −0.339117 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 404939.i | − | 0.479466i | −0.970839 | − | 0.239733i | \(-0.922940\pi\) | ||
0.970839 | − | 0.239733i | \(-0.0770600\pi\) | |||||||
\(920\) | 27640.0 | + | 50595.5i | 0.0326560 | + | 0.0597773i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −66468.2 | − | 80491.5i | −0.0781902 | − | 0.0946866i | ||||
\(923\) | 419044.i | 0.491876i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 422875. | 0.494229 | ||||||||
\(926\) | −20303.3 | + | 16766.1i | −0.0236780 | + | 0.0195528i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −512332. | − | 1.60092e6i | −0.594915 | − | 1.85898i | ||||
\(929\) | 1.39702e6 | 1.61872 | 0.809361 | − | 0.587312i | \(-0.199814\pi\) | ||||
0.809361 | + | 0.587312i | \(0.199814\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 149862.i | − | 0.172899i | ||||||
\(932\) | −191225. | + | 992866.i | −0.220147 | + | 1.14303i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −331061. | + | 273383.i | −0.379502 | + | 0.313385i | ||||
\(935\) | − | 935.325i | − | 0.00106989i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.10888e6 | −1.26301 | −0.631506 | − | 0.775371i | \(-0.717563\pi\) | ||||
−0.631506 | + | 0.775371i | \(0.717563\pi\) | |||||||
\(938\) | −219048. | − | 265263.i | −0.248963 | − | 0.301488i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 180107. | + | 34688.4i | 0.203833 | + | 0.0392581i | ||||
\(941\) | 163801. | 0.184986 | 0.0924928 | − | 0.995713i | \(-0.470516\pi\) | ||||
0.0924928 | + | 0.995713i | \(0.470516\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 249669.i | 0.280764i | ||||||||
\(944\) | 530375. | − | 1.32581e6i | 0.595167 | − | 1.48778i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 731121. | + | 885371.i | 0.816971 | + | 0.989334i | ||||
\(947\) | − | 1.36349e6i | − | 1.52038i | −0.649701 | − | 0.760190i | \(-0.725106\pi\) | ||
0.649701 | − | 0.760190i | \(-0.274894\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.01170e6 | −1.12336 | ||||||||
\(950\) | −132432. | + | 109359.i | −0.146739 | + | 0.121174i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −899.910 | − | 1647.30i | −0.000992945 | − | 0.00181760i | ||||
\(953\) | −814580. | −0.896908 | −0.448454 | − | 0.893806i | \(-0.648025\pi\) | ||||
−0.448454 | + | 0.893806i | \(0.648025\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 87703.6i | − | 0.0961636i | ||||||
\(956\) | −1.05708e6 | − | 203593.i | −1.15662 | − | 0.222765i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.07590e6 | + | 888452.i | −1.17230 | + | 0.968062i | ||||
\(959\) | − | 247703.i | − | 0.269336i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −173079. | −0.187413 | ||||||||
\(962\) | 393507. | + | 476529.i | 0.425209 | + | 0.514919i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −43294.9 | + | 224793.i | −0.0465890 | + | 0.241896i | ||||
\(965\) | −46991.2 | −0.0504617 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 1.64661e6i | − | 1.76091i | −0.474131 | − | 0.880454i | \(-0.657238\pi\) | ||
0.474131 | − | 0.880454i | \(-0.342762\pi\) | |||||||
\(968\) | 353879. | − | 193322.i | 0.377662 | − | 0.206315i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 82344.5 | + | 99717.4i | 0.0875167 | + | 0.105981i | ||||
\(971\) | 804225.i | 0.852981i | 0.904492 | + | 0.426490i | \(0.140250\pi\) | ||||
−0.904492 | + | 0.426490i | \(0.859750\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 478968. | 0.505919 | ||||||||
\(974\) | −322397. | + | 266228.i | −0.339839 | + | 0.280632i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −674619. | − | 269873.i | −0.708205 | − | 0.283309i | ||||
\(977\) | 772285. | 0.809074 | 0.404537 | − | 0.914522i | \(-0.367433\pi\) | ||||
0.404537 | + | 0.914522i | \(0.367433\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.65529e6i | 1.72706i | ||||||||
\(980\) | 23167.4 | − | 120288.i | 0.0241226 | − | 0.125248i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −560480. | + | 462833.i | −0.581216 | + | 0.479956i | ||||
\(983\) | − | 366034.i | − | 0.378804i | −0.981900 | − | 0.189402i | \(-0.939345\pi\) | ||
0.981900 | − | 0.189402i | \(-0.0606550\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −117056. | −0.120648 | ||||||||
\(986\) | 7541.08 | + | 9132.08i | 0.00775675 | + | 0.00939325i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −246470. | − | 47470.0i | −0.252493 | − | 0.0486301i | ||||
\(989\) | 498673. | 0.509827 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 518534.i | 0.527996i | 0.964523 | + | 0.263998i | \(0.0850412\pi\) | ||||
−0.964523 | + | 0.263998i | \(0.914959\pi\) | |||||||
\(992\) | 1.02130e6 | − | 326839.i | 1.03783 | − | 0.332131i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 77594.6 | + | 93965.3i | 0.0785341 | + | 0.0951031i | ||||
\(995\) | − | 31536.5i | − | 0.0318542i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 399223. | 0.401629 | 0.200814 | − | 0.979629i | \(-0.435641\pi\) | ||||
0.200814 | + | 0.979629i | \(0.435641\pi\) | |||||||
\(998\) | 1.01690e6 | − | 839735.i | 1.02098 | − | 0.843104i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 108.5.d.b.55.12 | yes | 16 | |
3.2 | odd | 2 | inner | 108.5.d.b.55.5 | ✓ | 16 | |
4.3 | odd | 2 | inner | 108.5.d.b.55.11 | yes | 16 | |
12.11 | even | 2 | inner | 108.5.d.b.55.6 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.5.d.b.55.5 | ✓ | 16 | 3.2 | odd | 2 | inner | |
108.5.d.b.55.6 | yes | 16 | 12.11 | even | 2 | inner | |
108.5.d.b.55.11 | yes | 16 | 4.3 | odd | 2 | inner | |
108.5.d.b.55.12 | yes | 16 | 1.1 | even | 1 | trivial |