Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [289,4,Mod(288,289)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(289, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("289.288");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 289 = 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 289.b (of order \(2\), degree \(1\), not 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: | \(17.0515519917\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.27793984.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{3} + 49x^{2} - 14x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | no (minimal twist has level 17) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 288.3 | ||
Root | \(-1.93854 - 1.93854i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 289.288 |
Dual form | 289.4.b.b.288.4 |
$q$-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 \(\left(\mathbb{Z}/289\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.36122 | −0.481264 | −0.240632 | − | 0.970616i | \(-0.577355\pi\) | ||||
−0.240632 | + | 0.970616i | \(0.577355\pi\) | |||||||
\(3\) | − 3.15463i | − 0.607109i | −0.952814 | − | 0.303555i | \(-0.901827\pi\) | ||||
0.952814 | − | 0.303555i | \(-0.0981735\pi\) | |||||||
\(4\) | −6.14708 | −0.768385 | ||||||||
\(5\) | − 3.03171i | − 0.271164i | −0.990766 | − | 0.135582i | \(-0.956710\pi\) | ||||
0.990766 | − | 0.135582i | \(-0.0432904\pi\) | |||||||
\(6\) | 4.29415i | 0.292180i | ||||||||
\(7\) | − 7.94049i | − 0.428746i | −0.976752 | − | 0.214373i | \(-0.931229\pi\) | ||||
0.976752 | − | 0.214373i | \(-0.0687708\pi\) | |||||||
\(8\) | 19.2573 | 0.851061 | ||||||||
\(9\) | 17.0483 | 0.631419 | ||||||||
\(10\) | 4.12682i | 0.130502i | ||||||||
\(11\) | 27.6161i | 0.756961i | 0.925609 | + | 0.378481i | \(0.123553\pi\) | ||||
−0.925609 | + | 0.378481i | \(0.876447\pi\) | |||||||
\(12\) | 19.3918i | 0.466493i | ||||||||
\(13\) | 58.1117 | 1.23979 | 0.619896 | − | 0.784684i | \(-0.287175\pi\) | ||||
0.619896 | + | 0.784684i | \(0.287175\pi\) | |||||||
\(14\) | 10.8088i | 0.206340i | ||||||||
\(15\) | −9.56391 | −0.164626 | ||||||||
\(16\) | 22.9632 | 0.358799 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | −23.2065 | −0.303879 | ||||||||
\(19\) | −89.1688 | −1.07667 | −0.538335 | − | 0.842731i | \(-0.680946\pi\) | ||||
−0.538335 | + | 0.842731i | \(0.680946\pi\) | |||||||
\(20\) | 18.6361i | 0.208358i | ||||||||
\(21\) | −25.0493 | −0.260296 | ||||||||
\(22\) | − 37.5916i | − 0.364298i | ||||||||
\(23\) | − 115.269i | − 1.04501i | −0.852635 | − | 0.522507i | \(-0.824997\pi\) | ||||
0.852635 | − | 0.522507i | \(-0.175003\pi\) | |||||||
\(24\) | − 60.7497i | − 0.516687i | ||||||||
\(25\) | 115.809 | 0.926470 | ||||||||
\(26\) | −79.1029 | −0.596668 | ||||||||
\(27\) | − 138.956i | − 0.990449i | ||||||||
\(28\) | 48.8108i | 0.329442i | ||||||||
\(29\) | 128.558i | 0.823191i | 0.911367 | + | 0.411596i | \(0.135028\pi\) | ||||
−0.911367 | + | 0.411596i | \(0.864972\pi\) | |||||||
\(30\) | 13.0186 | 0.0792287 | ||||||||
\(31\) | − 273.460i | − 1.58435i | −0.610295 | − | 0.792174i | \(-0.708949\pi\) | ||||
0.610295 | − | 0.792174i | \(-0.291051\pi\) | |||||||
\(32\) | −185.316 | −1.02374 | ||||||||
\(33\) | 87.1187 | 0.459558 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −24.0732 | −0.116260 | ||||||||
\(36\) | −104.797 | −0.485172 | ||||||||
\(37\) | 132.351i | 0.588063i | 0.955796 | + | 0.294031i | \(0.0949970\pi\) | ||||
−0.955796 | + | 0.294031i | \(0.905003\pi\) | |||||||
\(38\) | 121.379 | 0.518163 | ||||||||
\(39\) | − 183.321i | − 0.752689i | ||||||||
\(40\) | − 58.3825i | − 0.230777i | ||||||||
\(41\) | − 470.559i | − 1.79241i | −0.443636 | − | 0.896207i | \(-0.646312\pi\) | ||||
0.443636 | − | 0.896207i | \(-0.353688\pi\) | |||||||
\(42\) | 34.0977 | 0.125271 | ||||||||
\(43\) | −352.642 | −1.25064 | −0.625318 | − | 0.780370i | \(-0.715031\pi\) | ||||
−0.625318 | + | 0.780370i | \(0.715031\pi\) | |||||||
\(44\) | − 169.758i | − 0.581637i | ||||||||
\(45\) | − 51.6854i | − 0.171218i | ||||||||
\(46\) | 156.907i | 0.502928i | ||||||||
\(47\) | 152.598 | 0.473589 | 0.236795 | − | 0.971560i | \(-0.423903\pi\) | ||||
0.236795 | + | 0.971560i | \(0.423903\pi\) | |||||||
\(48\) | − 72.4403i | − 0.217830i | ||||||||
\(49\) | 279.949 | 0.816177 | ||||||||
\(50\) | −157.641 | −0.445877 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −357.217 | −0.952637 | ||||||||
\(53\) | −527.614 | −1.36742 | −0.683711 | − | 0.729753i | \(-0.739635\pi\) | ||||
−0.683711 | + | 0.729753i | \(0.739635\pi\) | |||||||
\(54\) | 189.150i | 0.476668i | ||||||||
\(55\) | 83.7239 | 0.205261 | ||||||||
\(56\) | − 152.912i | − 0.364889i | ||||||||
\(57\) | 281.295i | 0.653656i | ||||||||
\(58\) | − 174.995i | − 0.396173i | ||||||||
\(59\) | 292.020 | 0.644368 | 0.322184 | − | 0.946677i | \(-0.395583\pi\) | ||||
0.322184 | + | 0.946677i | \(0.395583\pi\) | |||||||
\(60\) | 58.7901 | 0.126496 | ||||||||
\(61\) | − 53.8962i | − 0.113126i | −0.998399 | − | 0.0565632i | \(-0.981986\pi\) | ||||
0.998399 | − | 0.0565632i | \(-0.0180142\pi\) | |||||||
\(62\) | 372.239i | 0.762490i | ||||||||
\(63\) | − 135.372i | − 0.270718i | ||||||||
\(64\) | 68.5514 | 0.133889 | ||||||||
\(65\) | − 176.178i | − 0.336187i | ||||||||
\(66\) | −118.588 | −0.221169 | ||||||||
\(67\) | 52.9572 | 0.0965635 | 0.0482817 | − | 0.998834i | \(-0.484625\pi\) | ||||
0.0482817 | + | 0.998834i | \(0.484625\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −363.632 | −0.634437 | ||||||||
\(70\) | 32.7690 | 0.0559520 | ||||||||
\(71\) | − 788.400i | − 1.31783i | −0.752218 | − | 0.658915i | \(-0.771016\pi\) | ||||
0.752218 | − | 0.658915i | \(-0.228984\pi\) | |||||||
\(72\) | 328.304 | 0.537375 | ||||||||
\(73\) | − 295.780i | − 0.474224i | −0.971482 | − | 0.237112i | \(-0.923799\pi\) | ||||
0.971482 | − | 0.237112i | \(-0.0762009\pi\) | |||||||
\(74\) | − 180.159i | − 0.283014i | ||||||||
\(75\) | − 365.334i | − 0.562468i | ||||||||
\(76\) | 548.127 | 0.827296 | ||||||||
\(77\) | 219.285 | 0.324544 | ||||||||
\(78\) | 249.541i | 0.362242i | ||||||||
\(79\) | − 720.325i | − 1.02586i | −0.858430 | − | 0.512930i | \(-0.828560\pi\) | ||||
0.858430 | − | 0.512930i | \(-0.171440\pi\) | |||||||
\(80\) | − 69.6175i | − 0.0972934i | ||||||||
\(81\) | 21.9487 | 0.0301079 | ||||||||
\(82\) | 640.535i | 0.862625i | ||||||||
\(83\) | 116.051 | 0.153473 | 0.0767363 | − | 0.997051i | \(-0.475550\pi\) | ||||
0.0767363 | + | 0.997051i | \(0.475550\pi\) | |||||||
\(84\) | 153.980 | 0.200007 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 480.024 | 0.601887 | ||||||||
\(87\) | 405.552 | 0.499767 | ||||||||
\(88\) | 531.812i | 0.644220i | ||||||||
\(89\) | −813.329 | −0.968682 | −0.484341 | − | 0.874879i | \(-0.660941\pi\) | ||||
−0.484341 | + | 0.874879i | \(0.660941\pi\) | |||||||
\(90\) | 70.3553i | 0.0824011i | ||||||||
\(91\) | − 461.435i | − 0.531556i | ||||||||
\(92\) | 708.569i | 0.802972i | ||||||||
\(93\) | −862.664 | −0.961872 | ||||||||
\(94\) | −207.720 | −0.227922 | ||||||||
\(95\) | 270.334i | 0.291954i | ||||||||
\(96\) | 584.605i | 0.621521i | ||||||||
\(97\) | − 794.693i | − 0.831844i | −0.909400 | − | 0.415922i | \(-0.863459\pi\) | ||||
0.909400 | − | 0.415922i | \(-0.136541\pi\) | |||||||
\(98\) | −381.072 | −0.392797 | ||||||||
\(99\) | 470.808i | 0.477959i | ||||||||
\(100\) | −711.885 | −0.711885 | ||||||||
\(101\) | 265.513 | 0.261579 | 0.130790 | − | 0.991410i | \(-0.458249\pi\) | ||||
0.130790 | + | 0.991410i | \(0.458249\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 523.107 | 0.500420 | 0.250210 | − | 0.968192i | \(-0.419500\pi\) | ||||
0.250210 | + | 0.968192i | \(0.419500\pi\) | |||||||
\(104\) | 1119.07 | 1.05514 | ||||||||
\(105\) | 75.9421i | 0.0705828i | ||||||||
\(106\) | 718.199 | 0.658091 | ||||||||
\(107\) | 986.039i | 0.890878i | 0.895312 | + | 0.445439i | \(0.146952\pi\) | ||||
−0.895312 | + | 0.445439i | \(0.853048\pi\) | |||||||
\(108\) | 854.174i | 0.761046i | ||||||||
\(109\) | 1814.39i | 1.59438i | 0.603732 | + | 0.797188i | \(0.293680\pi\) | ||||
−0.603732 | + | 0.797188i | \(0.706320\pi\) | |||||||
\(110\) | −113.967 | −0.0987846 | ||||||||
\(111\) | 417.518 | 0.357018 | ||||||||
\(112\) | − 182.339i | − 0.153834i | ||||||||
\(113\) | − 707.339i | − 0.588857i | −0.955673 | − | 0.294429i | \(-0.904871\pi\) | ||||
0.955673 | − | 0.294429i | \(-0.0951293\pi\) | |||||||
\(114\) | − 382.904i | − 0.314581i | ||||||||
\(115\) | −349.463 | −0.283370 | ||||||||
\(116\) | − 790.253i | − 0.632527i | ||||||||
\(117\) | 990.706 | 0.782827 | ||||||||
\(118\) | −397.503 | −0.310112 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −184.175 | −0.140107 | ||||||||
\(121\) | 568.350 | 0.427010 | ||||||||
\(122\) | 73.3647i | 0.0544437i | ||||||||
\(123\) | −1484.44 | −1.08819 | ||||||||
\(124\) | 1680.98i | 1.21739i | ||||||||
\(125\) | − 730.061i | − 0.522389i | ||||||||
\(126\) | 184.271i | 0.130287i | ||||||||
\(127\) | −2648.18 | −1.85030 | −0.925151 | − | 0.379600i | \(-0.876062\pi\) | ||||
−0.925151 | + | 0.379600i | \(0.876062\pi\) | |||||||
\(128\) | 1389.22 | 0.959302 | ||||||||
\(129\) | 1112.46i | 0.759273i | ||||||||
\(130\) | 239.817i | 0.161795i | ||||||||
\(131\) | 1979.08i | 1.31995i | 0.751289 | + | 0.659974i | \(0.229433\pi\) | ||||
−0.751289 | + | 0.659974i | \(0.770567\pi\) | |||||||
\(132\) | −535.525 | −0.353117 | ||||||||
\(133\) | 708.044i | 0.461618i | ||||||||
\(134\) | −72.0865 | −0.0464726 | ||||||||
\(135\) | −421.274 | −0.268574 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3141.92 | 1.95936 | 0.979679 | − | 0.200570i | \(-0.0642794\pi\) | ||||
0.979679 | + | 0.200570i | \(0.0642794\pi\) | |||||||
\(138\) | 494.984 | 0.305332 | ||||||||
\(139\) | − 1468.07i | − 0.895830i | −0.894076 | − | 0.447915i | \(-0.852167\pi\) | ||||
0.894076 | − | 0.447915i | \(-0.147833\pi\) | |||||||
\(140\) | 147.980 | 0.0893327 | ||||||||
\(141\) | − 481.390i | − 0.287520i | ||||||||
\(142\) | 1073.19i | 0.634224i | ||||||||
\(143\) | 1604.82i | 0.938474i | ||||||||
\(144\) | 391.483 | 0.226553 | ||||||||
\(145\) | 389.749 | 0.223220 | ||||||||
\(146\) | 402.621i | 0.228227i | ||||||||
\(147\) | − 883.135i | − 0.495508i | ||||||||
\(148\) | − 813.570i | − 0.451858i | ||||||||
\(149\) | −286.027 | −0.157263 | −0.0786316 | − | 0.996904i | \(-0.525055\pi\) | ||||
−0.0786316 | + | 0.996904i | \(0.525055\pi\) | |||||||
\(150\) | 497.300i | 0.270696i | ||||||||
\(151\) | 669.626 | 0.360883 | 0.180442 | − | 0.983586i | \(-0.442247\pi\) | ||||
0.180442 | + | 0.983586i | \(0.442247\pi\) | |||||||
\(152\) | −1717.15 | −0.916311 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −298.496 | −0.156191 | ||||||||
\(155\) | −829.049 | −0.429618 | ||||||||
\(156\) | 1126.89i | 0.578354i | ||||||||
\(157\) | 720.809 | 0.366413 | 0.183206 | − | 0.983074i | \(-0.441352\pi\) | ||||
0.183206 | + | 0.983074i | \(0.441352\pi\) | |||||||
\(158\) | 980.522i | 0.493710i | ||||||||
\(159\) | 1664.43i | 0.830174i | ||||||||
\(160\) | 561.825i | 0.277601i | ||||||||
\(161\) | −915.294 | −0.448045 | ||||||||
\(162\) | −29.8770 | −0.0144899 | ||||||||
\(163\) | − 676.599i | − 0.325125i | −0.986698 | − | 0.162562i | \(-0.948024\pi\) | ||||
0.986698 | − | 0.162562i | \(-0.0519759\pi\) | |||||||
\(164\) | 2892.56i | 1.37726i | ||||||||
\(165\) | − 264.118i | − 0.124616i | ||||||||
\(166\) | −157.971 | −0.0738609 | ||||||||
\(167\) | 2835.67i | 1.31396i | 0.753909 | + | 0.656979i | \(0.228166\pi\) | ||||
−0.753909 | + | 0.656979i | \(0.771834\pi\) | |||||||
\(168\) | −482.382 | −0.221527 | ||||||||
\(169\) | 1179.97 | 0.537083 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1520.18 | −0.679829 | ||||||||
\(172\) | 2167.72 | 0.960970 | ||||||||
\(173\) | 177.314i | 0.0779243i | 0.999241 | + | 0.0389621i | \(0.0124052\pi\) | ||||
−0.999241 | + | 0.0389621i | \(0.987595\pi\) | |||||||
\(174\) | −552.046 | −0.240520 | ||||||||
\(175\) | − 919.578i | − 0.397220i | ||||||||
\(176\) | 634.153i | 0.271597i | ||||||||
\(177\) | − 921.214i | − 0.391202i | ||||||||
\(178\) | 1107.12 | 0.466192 | ||||||||
\(179\) | 1023.76 | 0.427483 | 0.213741 | − | 0.976890i | \(-0.431435\pi\) | ||||
0.213741 | + | 0.976890i | \(0.431435\pi\) | |||||||
\(180\) | 317.714i | 0.131561i | ||||||||
\(181\) | − 3450.21i | − 1.41686i | −0.705779 | − | 0.708432i | \(-0.749403\pi\) | ||||
0.705779 | − | 0.708432i | \(-0.250597\pi\) | |||||||
\(182\) | 628.116i | 0.255819i | ||||||||
\(183\) | −170.023 | −0.0686800 | ||||||||
\(184\) | − 2219.78i | − 0.889370i | ||||||||
\(185\) | 401.248 | 0.159461 | ||||||||
\(186\) | 1174.28 | 0.462915 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −938.031 | −0.363899 | ||||||||
\(189\) | −1103.38 | −0.424651 | ||||||||
\(190\) | − 367.984i | − 0.140507i | ||||||||
\(191\) | −490.894 | −0.185968 | −0.0929839 | − | 0.995668i | \(-0.529640\pi\) | ||||
−0.0929839 | + | 0.995668i | \(0.529640\pi\) | |||||||
\(192\) | − 216.254i | − 0.0812855i | ||||||||
\(193\) | − 3548.80i | − 1.32357i | −0.749696 | − | 0.661783i | \(-0.769800\pi\) | ||||
0.749696 | − | 0.661783i | \(-0.230200\pi\) | |||||||
\(194\) | 1081.75i | 0.400337i | ||||||||
\(195\) | −555.775 | −0.204102 | ||||||||
\(196\) | −1720.87 | −0.627138 | ||||||||
\(197\) | 1363.15i | 0.492996i | 0.969143 | + | 0.246498i | \(0.0792799\pi\) | ||||
−0.969143 | + | 0.246498i | \(0.920720\pi\) | |||||||
\(198\) | − 640.874i | − 0.230025i | ||||||||
\(199\) | − 3737.46i | − 1.33137i | −0.746235 | − | 0.665683i | \(-0.768140\pi\) | ||||
0.746235 | − | 0.665683i | \(-0.231860\pi\) | |||||||
\(200\) | 2230.16 | 0.788482 | ||||||||
\(201\) | − 167.060i | − 0.0586246i | ||||||||
\(202\) | −361.422 | −0.125889 | ||||||||
\(203\) | 1020.81 | 0.352940 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1426.60 | −0.486038 | ||||||||
\(206\) | −712.064 | −0.240834 | ||||||||
\(207\) | − 1965.15i | − 0.659841i | ||||||||
\(208\) | 1334.43 | 0.444836 | ||||||||
\(209\) | − 2462.50i | − 0.814997i | ||||||||
\(210\) | − 103.374i | − 0.0339690i | ||||||||
\(211\) | − 5266.12i | − 1.71817i | −0.511829 | − | 0.859087i | \(-0.671032\pi\) | ||||
0.511829 | − | 0.859087i | \(-0.328968\pi\) | |||||||
\(212\) | 3243.28 | 1.05071 | ||||||||
\(213\) | −2487.11 | −0.800066 | ||||||||
\(214\) | − 1342.22i | − 0.428748i | ||||||||
\(215\) | 1069.11i | 0.339128i | ||||||||
\(216\) | − 2675.92i | − 0.842932i | ||||||||
\(217\) | −2171.40 | −0.679283 | ||||||||
\(218\) | − 2469.78i | − 0.767316i | ||||||||
\(219\) | −933.075 | −0.287906 | ||||||||
\(220\) | −514.657 | −0.157719 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −568.334 | −0.171820 | ||||||||
\(223\) | −704.546 | −0.211569 | −0.105785 | − | 0.994389i | \(-0.533735\pi\) | ||||
−0.105785 | + | 0.994389i | \(0.533735\pi\) | |||||||
\(224\) | 1471.50i | 0.438923i | ||||||||
\(225\) | 1974.34 | 0.584990 | ||||||||
\(226\) | 962.845i | 0.283396i | ||||||||
\(227\) | − 2151.26i | − 0.629006i | −0.949256 | − | 0.314503i | \(-0.898162\pi\) | ||||
0.949256 | − | 0.314503i | \(-0.101838\pi\) | |||||||
\(228\) | − 1729.14i | − 0.502259i | ||||||||
\(229\) | 3916.94 | 1.13030 | 0.565149 | − | 0.824989i | \(-0.308819\pi\) | ||||
0.565149 | + | 0.824989i | \(0.308819\pi\) | |||||||
\(230\) | 475.696 | 0.136376 | ||||||||
\(231\) | − 691.764i | − 0.197034i | ||||||||
\(232\) | 2475.67i | 0.700586i | ||||||||
\(233\) | 5192.74i | 1.46003i | 0.683429 | + | 0.730017i | \(0.260488\pi\) | ||||
−0.683429 | + | 0.730017i | \(0.739512\pi\) | |||||||
\(234\) | −1348.57 | −0.376747 | ||||||||
\(235\) | − 462.632i | − 0.128420i | ||||||||
\(236\) | −1795.07 | −0.495123 | ||||||||
\(237\) | −2272.36 | −0.622809 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 334.305 | 0.0904786 | 0.0452393 | − | 0.998976i | \(-0.485595\pi\) | ||||
0.0452393 | + | 0.998976i | \(0.485595\pi\) | |||||||
\(240\) | −219.618 | −0.0590677 | ||||||||
\(241\) | 1918.45i | 0.512773i | 0.966574 | + | 0.256386i | \(0.0825320\pi\) | ||||
−0.966574 | + | 0.256386i | \(0.917468\pi\) | |||||||
\(242\) | −773.651 | −0.205505 | ||||||||
\(243\) | − 3821.06i | − 1.00873i | ||||||||
\(244\) | 331.304i | 0.0869245i | ||||||||
\(245\) | − 848.722i | − 0.221318i | ||||||||
\(246\) | 2020.65 | 0.523708 | ||||||||
\(247\) | −5181.75 | −1.33485 | ||||||||
\(248\) | − 5266.09i | − 1.34838i | ||||||||
\(249\) | − 366.097i | − 0.0931746i | ||||||||
\(250\) | 993.775i | 0.251407i | ||||||||
\(251\) | 7695.71 | 1.93525 | 0.967627 | − | 0.252385i | \(-0.0812148\pi\) | ||||
0.967627 | + | 0.252385i | \(0.0812148\pi\) | |||||||
\(252\) | 832.141i | 0.208016i | ||||||||
\(253\) | 3183.29 | 0.791035 | ||||||||
\(254\) | 3604.76 | 0.890484 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2439.44 | −0.595567 | ||||||||
\(257\) | −5335.10 | −1.29492 | −0.647460 | − | 0.762099i | \(-0.724169\pi\) | ||||
−0.647460 | + | 0.762099i | \(0.724169\pi\) | |||||||
\(258\) | − 1514.30i | − 0.365411i | ||||||||
\(259\) | 1050.93 | 0.252130 | ||||||||
\(260\) | 1082.98i | 0.258321i | ||||||||
\(261\) | 2191.69i | 0.519778i | ||||||||
\(262\) | − 2693.97i | − 0.635244i | ||||||||
\(263\) | −3934.15 | −0.922396 | −0.461198 | − | 0.887297i | \(-0.652580\pi\) | ||||
−0.461198 | + | 0.887297i | \(0.652580\pi\) | |||||||
\(264\) | 1677.67 | 0.391112 | ||||||||
\(265\) | 1599.57i | 0.370795i | ||||||||
\(266\) | − 963.804i | − 0.222160i | ||||||||
\(267\) | 2565.75i | 0.588095i | ||||||||
\(268\) | −325.532 | −0.0741979 | ||||||||
\(269\) | − 3424.04i | − 0.776088i | −0.921641 | − | 0.388044i | \(-0.873151\pi\) | ||||
0.921641 | − | 0.388044i | \(-0.126849\pi\) | |||||||
\(270\) | 573.447 | 0.129255 | ||||||||
\(271\) | 549.034 | 0.123068 | 0.0615340 | − | 0.998105i | \(-0.480401\pi\) | ||||
0.0615340 | + | 0.998105i | \(0.480401\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1455.66 | −0.322712 | ||||||||
\(274\) | −4276.85 | −0.942970 | ||||||||
\(275\) | 3198.19i | 0.701302i | ||||||||
\(276\) | 2235.27 | 0.487492 | ||||||||
\(277\) | − 5203.65i | − 1.12873i | −0.825527 | − | 0.564363i | \(-0.809122\pi\) | ||||
0.825527 | − | 0.564363i | \(-0.190878\pi\) | |||||||
\(278\) | 1998.37i | 0.431131i | ||||||||
\(279\) | − 4662.02i | − 1.00039i | ||||||||
\(280\) | −463.585 | −0.0989447 | ||||||||
\(281\) | 1986.73 | 0.421774 | 0.210887 | − | 0.977510i | \(-0.432365\pi\) | ||||
0.210887 | + | 0.977510i | \(0.432365\pi\) | |||||||
\(282\) | 655.279i | 0.138373i | ||||||||
\(283\) | 753.696i | 0.158313i | 0.996862 | + | 0.0791565i | \(0.0252227\pi\) | ||||
−0.996862 | + | 0.0791565i | \(0.974777\pi\) | |||||||
\(284\) | 4846.36i | 1.01260i | ||||||||
\(285\) | 852.803 | 0.177248 | ||||||||
\(286\) | − 2184.51i | − 0.451654i | ||||||||
\(287\) | −3736.47 | −0.768490 | ||||||||
\(288\) | −3159.33 | −0.646407 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | −530.534 | −0.107428 | ||||||||
\(291\) | −2506.96 | −0.505020 | ||||||||
\(292\) | 1818.18i | 0.364387i | ||||||||
\(293\) | −7202.22 | −1.43603 | −0.718017 | − | 0.696025i | \(-0.754950\pi\) | ||||
−0.718017 | + | 0.696025i | \(0.754950\pi\) | |||||||
\(294\) | 1202.14i | 0.238471i | ||||||||
\(295\) | − 885.318i | − 0.174729i | ||||||||
\(296\) | 2548.72i | 0.500477i | ||||||||
\(297\) | 3837.43 | 0.749731 | ||||||||
\(298\) | 389.345 | 0.0756852 | ||||||||
\(299\) | − 6698.50i | − 1.29560i | ||||||||
\(300\) | 2245.74i | 0.432192i | ||||||||
\(301\) | 2800.15i | 0.536205i | ||||||||
\(302\) | −911.509 | −0.173680 | ||||||||
\(303\) | − 837.595i | − 0.158807i | ||||||||
\(304\) | −2047.60 | −0.386308 | ||||||||
\(305\) | −163.398 | −0.0306758 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2425.71 | 0.450953 | 0.225477 | − | 0.974249i | \(-0.427606\pi\) | ||||
0.225477 | + | 0.974249i | \(0.427606\pi\) | |||||||
\(308\) | −1347.96 | −0.249375 | ||||||||
\(309\) | − 1650.21i | − 0.303809i | ||||||||
\(310\) | 1128.52 | 0.206760 | ||||||||
\(311\) | 9544.94i | 1.74033i | 0.492757 | + | 0.870167i | \(0.335989\pi\) | ||||
−0.492757 | + | 0.870167i | \(0.664011\pi\) | |||||||
\(312\) | − 3530.27i | − 0.640584i | ||||||||
\(313\) | 588.379i | 0.106253i | 0.998588 | + | 0.0531264i | \(0.0169186\pi\) | ||||
−0.998588 | + | 0.0531264i | \(0.983081\pi\) | |||||||
\(314\) | −981.180 | −0.176341 | ||||||||
\(315\) | −410.407 | −0.0734090 | ||||||||
\(316\) | 4427.89i | 0.788255i | ||||||||
\(317\) | 7653.31i | 1.35600i | 0.735061 | + | 0.678001i | \(0.237154\pi\) | ||||
−0.735061 | + | 0.678001i | \(0.762846\pi\) | |||||||
\(318\) | − 2265.65i | − 0.399533i | ||||||||
\(319\) | −3550.26 | −0.623124 | ||||||||
\(320\) | − 207.828i | − 0.0363060i | ||||||||
\(321\) | 3110.59 | 0.540860 | ||||||||
\(322\) | 1245.92 | 0.215628 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −134.920 | −0.0231345 | ||||||||
\(325\) | 6729.85 | 1.14863 | ||||||||
\(326\) | 921.001i | 0.156471i | ||||||||
\(327\) | 5723.73 | 0.967960 | ||||||||
\(328\) | − 9061.70i | − 1.52545i | ||||||||
\(329\) | − 1211.70i | − 0.203050i | ||||||||
\(330\) | 359.523i | 0.0599730i | ||||||||
\(331\) | −752.266 | −0.124919 | −0.0624597 | − | 0.998047i | \(-0.519894\pi\) | ||||
−0.0624597 | + | 0.998047i | \(0.519894\pi\) | |||||||
\(332\) | −713.373 | −0.117926 | ||||||||
\(333\) | 2256.36i | 0.371314i | ||||||||
\(334\) | − 3859.98i | − 0.632361i | ||||||||
\(335\) | − 160.551i | − 0.0261845i | ||||||||
\(336\) | −575.211 | −0.0933939 | ||||||||
\(337\) | 1968.57i | 0.318204i | 0.987262 | + | 0.159102i | \(0.0508598\pi\) | ||||
−0.987262 | + | 0.159102i | \(0.949140\pi\) | |||||||
\(338\) | −1606.20 | −0.258479 | ||||||||
\(339\) | −2231.39 | −0.357501 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7551.89 | 1.19929 | ||||||||
\(342\) | 2069.30 | 0.327178 | ||||||||
\(343\) | − 4946.52i | − 0.778678i | ||||||||
\(344\) | −6790.93 | −1.06437 | ||||||||
\(345\) | 1102.43i | 0.172037i | ||||||||
\(346\) | − 241.363i | − 0.0375022i | ||||||||
\(347\) | 3983.10i | 0.616207i | 0.951353 | + | 0.308104i | \(0.0996944\pi\) | ||||
−0.951353 | + | 0.308104i | \(0.900306\pi\) | |||||||
\(348\) | −2492.96 | −0.384013 | ||||||||
\(349\) | −1495.61 | −0.229393 | −0.114697 | − | 0.993401i | \(-0.536590\pi\) | ||||
−0.114697 | + | 0.993401i | \(0.536590\pi\) | |||||||
\(350\) | 1251.75i | 0.191168i | ||||||||
\(351\) | − 8074.98i | − 1.22795i | ||||||||
\(352\) | − 5117.72i | − 0.774930i | ||||||||
\(353\) | 6482.49 | 0.977417 | 0.488708 | − | 0.872447i | \(-0.337468\pi\) | ||||
0.488708 | + | 0.872447i | \(0.337468\pi\) | |||||||
\(354\) | 1253.98i | 0.188272i | ||||||||
\(355\) | −2390.20 | −0.357348 | ||||||||
\(356\) | 4999.59 | 0.744320 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1393.56 | −0.205732 | ||||||||
\(359\) | 4943.42 | 0.726751 | 0.363376 | − | 0.931643i | \(-0.381624\pi\) | ||||
0.363376 | + | 0.931643i | \(0.381624\pi\) | |||||||
\(360\) | − 995.322i | − 0.145717i | ||||||||
\(361\) | 1092.08 | 0.159218 | ||||||||
\(362\) | 4696.50i | 0.681886i | ||||||||
\(363\) | − 1792.94i | − 0.259242i | ||||||||
\(364\) | 2836.48i | 0.408439i | ||||||||
\(365\) | −896.717 | −0.128593 | ||||||||
\(366\) | 231.439 | 0.0330533 | ||||||||
\(367\) | − 14.8871i | − 0.00211743i | −0.999999 | − | 0.00105872i | \(-0.999663\pi\) | ||||
0.999999 | − | 0.00105872i | \(-0.000337000\pi\) | |||||||
\(368\) | − 2646.95i | − 0.374950i | ||||||||
\(369\) | − 8022.23i | − 1.13176i | ||||||||
\(370\) | −546.188 | −0.0767431 | ||||||||
\(371\) | 4189.51i | 0.586276i | ||||||||
\(372\) | 5302.86 | 0.739088 | ||||||||
\(373\) | 1923.18 | 0.266966 | 0.133483 | − | 0.991051i | \(-0.457384\pi\) | ||||
0.133483 | + | 0.991051i | \(0.457384\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2303.07 | −0.317147 | ||||||||
\(376\) | 2938.63 | 0.403053 | ||||||||
\(377\) | 7470.70i | 1.02059i | ||||||||
\(378\) | 1501.94 | 0.204369 | ||||||||
\(379\) | 9592.87i | 1.30014i | 0.759875 | + | 0.650069i | \(0.225260\pi\) | ||||
−0.759875 | + | 0.650069i | \(0.774740\pi\) | |||||||
\(380\) | − 1661.76i | − 0.224333i | ||||||||
\(381\) | 8354.04i | 1.12333i | ||||||||
\(382\) | 668.215 | 0.0894996 | ||||||||
\(383\) | 9083.77 | 1.21190 | 0.605951 | − | 0.795502i | \(-0.292793\pi\) | ||||
0.605951 | + | 0.795502i | \(0.292793\pi\) | |||||||
\(384\) | − 4382.47i | − 0.582401i | ||||||||
\(385\) | − 664.809i | − 0.0880046i | ||||||||
\(386\) | 4830.70i | 0.636985i | ||||||||
\(387\) | −6011.95 | −0.789675 | ||||||||
\(388\) | 4885.04i | 0.639176i | ||||||||
\(389\) | 1143.78 | 0.149079 | 0.0745396 | − | 0.997218i | \(-0.476251\pi\) | ||||
0.0745396 | + | 0.997218i | \(0.476251\pi\) | |||||||
\(390\) | 756.533 | 0.0982271 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 5391.06 | 0.694616 | ||||||||
\(393\) | 6243.27 | 0.801352 | ||||||||
\(394\) | − 1855.55i | − 0.237262i | ||||||||
\(395\) | −2183.81 | −0.278176 | ||||||||
\(396\) | − 2894.09i | − 0.367256i | ||||||||
\(397\) | 10604.5i | 1.34061i | 0.742084 | + | 0.670307i | \(0.233838\pi\) | ||||
−0.742084 | + | 0.670307i | \(0.766162\pi\) | |||||||
\(398\) | 5087.51i | 0.640739i | ||||||||
\(399\) | 2233.62 | 0.280252 | ||||||||
\(400\) | 2659.33 | 0.332417 | ||||||||
\(401\) | 13785.4i | 1.71674i | 0.513035 | + | 0.858368i | \(0.328521\pi\) | ||||
−0.513035 | + | 0.858368i | \(0.671479\pi\) | |||||||
\(402\) | 227.406i | 0.0282139i | ||||||||
\(403\) | − 15891.2i | − 1.96426i | ||||||||
\(404\) | −1632.13 | −0.200993 | ||||||||
\(405\) | − 66.5420i | − 0.00816419i | ||||||||
\(406\) | −1389.55 | −0.169857 | ||||||||
\(407\) | −3655.01 | −0.445141 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9505.94 | −1.14924 | −0.574619 | − | 0.818421i | \(-0.694850\pi\) | ||||
−0.574619 | + | 0.818421i | \(0.694850\pi\) | |||||||
\(410\) | 1941.91 | 0.233913 | ||||||||
\(411\) | − 9911.59i | − 1.18954i | ||||||||
\(412\) | −3215.58 | −0.384515 | ||||||||
\(413\) | − 2318.78i | − 0.276270i | ||||||||
\(414\) | 2675.00i | 0.317558i | ||||||||
\(415\) | − 351.832i | − 0.0416162i | ||||||||
\(416\) | −10769.1 | −1.26922 | ||||||||
\(417\) | −4631.23 | −0.543866 | ||||||||
\(418\) | 3352.00i | 0.392229i | ||||||||
\(419\) | 9680.86i | 1.12874i | 0.825523 | + | 0.564369i | \(0.190880\pi\) | ||||
−0.825523 | + | 0.564369i | \(0.809120\pi\) | |||||||
\(420\) | − 466.822i | − 0.0542347i | ||||||||
\(421\) | −12360.3 | −1.43089 | −0.715444 | − | 0.698671i | \(-0.753775\pi\) | ||||
−0.715444 | + | 0.698671i | \(0.753775\pi\) | |||||||
\(422\) | 7168.36i | 0.826897i | ||||||||
\(423\) | 2601.54 | 0.299033 | ||||||||
\(424\) | −10160.4 | −1.16376 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 3385.51 | 0.385043 | ||||||||
\(427\) | −427.962 | −0.0485025 | ||||||||
\(428\) | − 6061.25i | − 0.684537i | ||||||||
\(429\) | 5062.61 | 0.569756 | ||||||||
\(430\) | − 1455.29i | − 0.163210i | ||||||||
\(431\) | 2970.58i | 0.331990i | 0.986127 | + | 0.165995i | \(0.0530835\pi\) | ||||
−0.986127 | + | 0.165995i | \(0.946916\pi\) | |||||||
\(432\) | − 3190.87i | − 0.355372i | ||||||||
\(433\) | −6131.50 | −0.680510 | −0.340255 | − | 0.940333i | \(-0.610513\pi\) | ||||
−0.340255 | + | 0.940333i | \(0.610513\pi\) | |||||||
\(434\) | 2955.76 | 0.326915 | ||||||||
\(435\) | − 1229.51i | − 0.135519i | ||||||||
\(436\) | − 11153.2i | − 1.22509i | ||||||||
\(437\) | 10278.4i | 1.12513i | ||||||||
\(438\) | 1270.12 | 0.138559 | ||||||||
\(439\) | 2544.91i | 0.276679i | 0.990385 | + | 0.138339i | \(0.0441765\pi\) | ||||
−0.990385 | + | 0.138339i | \(0.955824\pi\) | |||||||
\(440\) | 1612.30 | 0.174689 | ||||||||
\(441\) | 4772.65 | 0.515349 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8529.82 | 0.914817 | 0.457408 | − | 0.889257i | \(-0.348778\pi\) | ||||
0.457408 | + | 0.889257i | \(0.348778\pi\) | |||||||
\(444\) | −2566.51 | −0.274327 | ||||||||
\(445\) | 2465.77i | 0.262672i | ||||||||
\(446\) | 959.043 | 0.101821 | ||||||||
\(447\) | 902.308i | 0.0954759i | ||||||||
\(448\) | − 544.331i | − 0.0574046i | ||||||||
\(449\) | 8855.74i | 0.930798i | 0.885101 | + | 0.465399i | \(0.154089\pi\) | ||||
−0.885101 | + | 0.465399i | \(0.845911\pi\) | |||||||
\(450\) | −2687.52 | −0.281535 | ||||||||
\(451\) | 12995.0 | 1.35679 | ||||||||
\(452\) | 4348.07i | 0.452469i | ||||||||
\(453\) | − 2112.42i | − 0.219095i | ||||||||
\(454\) | 2928.35i | 0.302718i | ||||||||
\(455\) | −1398.94 | −0.144139 | ||||||||
\(456\) | 5416.98i | 0.556301i | ||||||||
\(457\) | 7154.78 | 0.732356 | 0.366178 | − | 0.930545i | \(-0.380666\pi\) | ||||
0.366178 | + | 0.930545i | \(0.380666\pi\) | |||||||
\(458\) | −5331.82 | −0.543973 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2148.17 | 0.217737 | ||||||||
\(461\) | 7263.06 | 0.733784 | 0.366892 | − | 0.930264i | \(-0.380422\pi\) | ||||
0.366892 | + | 0.930264i | \(0.380422\pi\) | |||||||
\(462\) | 941.645i | 0.0948253i | ||||||||
\(463\) | 352.898 | 0.0354224 | 0.0177112 | − | 0.999843i | \(-0.494362\pi\) | ||||
0.0177112 | + | 0.999843i | \(0.494362\pi\) | |||||||
\(464\) | 2952.09i | 0.295360i | ||||||||
\(465\) | 2615.34i | 0.260825i | ||||||||
\(466\) | − 7068.47i | − 0.702662i | ||||||||
\(467\) | −1483.02 | −0.146951 | −0.0734753 | − | 0.997297i | \(-0.523409\pi\) | ||||
−0.0734753 | + | 0.997297i | \(0.523409\pi\) | |||||||
\(468\) | −6089.94 | −0.601512 | ||||||||
\(469\) | − 420.506i | − 0.0414012i | ||||||||
\(470\) | 629.745i | 0.0618042i | ||||||||
\(471\) | − 2273.89i | − 0.222452i | ||||||||
\(472\) | 5623.51 | 0.548396 | ||||||||
\(473\) | − 9738.60i | − 0.946683i | ||||||||
\(474\) | 3093.19 | 0.299736 | ||||||||
\(475\) | −10326.5 | −0.997502 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8994.92 | −0.863415 | ||||||||
\(478\) | −455.063 | −0.0435441 | ||||||||
\(479\) | 9990.10i | 0.952942i | 0.879190 | + | 0.476471i | \(0.158084\pi\) | ||||
−0.879190 | + | 0.476471i | \(0.841916\pi\) | |||||||
\(480\) | 1772.35 | 0.168534 | ||||||||
\(481\) | 7691.13i | 0.729075i | ||||||||
\(482\) | − 2611.44i | − 0.246779i | ||||||||
\(483\) | 2887.42i | 0.272012i | ||||||||
\(484\) | −3493.69 | −0.328108 | ||||||||
\(485\) | −2409.27 | −0.225566 | ||||||||
\(486\) | 5201.30i | 0.485465i | ||||||||
\(487\) | − 1129.88i | − 0.105133i | −0.998617 | − | 0.0525663i | \(-0.983260\pi\) | ||||
0.998617 | − | 0.0525663i | \(-0.0167401\pi\) | |||||||
\(488\) | − 1037.90i | − 0.0962774i | ||||||||
\(489\) | −2134.42 | −0.197386 | ||||||||
\(490\) | 1155.30i | 0.106512i | ||||||||
\(491\) | −18774.9 | −1.72566 | −0.862832 | − | 0.505491i | \(-0.831311\pi\) | ||||
−0.862832 | + | 0.505491i | \(0.831311\pi\) | |||||||
\(492\) | 9124.97 | 0.836149 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 7053.51 | 0.642414 | ||||||||
\(495\) | 1427.35 | 0.129605 | ||||||||
\(496\) | − 6279.49i | − 0.568463i | ||||||||
\(497\) | −6260.28 | −0.565014 | ||||||||
\(498\) | 498.339i | 0.0448416i | ||||||||
\(499\) | 17329.1i | 1.55462i | 0.629118 | + | 0.777310i | \(0.283416\pi\) | ||||
−0.629118 | + | 0.777310i | \(0.716584\pi\) | |||||||
\(500\) | 4487.74i | 0.401396i | ||||||||
\(501\) | 8945.50 | 0.797716 | ||||||||
\(502\) | −10475.6 | −0.931369 | ||||||||
\(503\) | − 20837.0i | − 1.84707i | −0.383518 | − | 0.923533i | \(-0.625288\pi\) | ||||
0.383518 | − | 0.923533i | \(-0.374712\pi\) | |||||||
\(504\) | − 2606.90i | − 0.230398i | ||||||||
\(505\) | − 804.957i | − 0.0709309i | ||||||||
\(506\) | −4333.16 | −0.380697 | ||||||||
\(507\) | − 3722.37i | − 0.326068i | ||||||||
\(508\) | 16278.6 | 1.42174 | ||||||||
\(509\) | 11835.0 | 1.03060 | 0.515301 | − | 0.857009i | \(-0.327680\pi\) | ||||
0.515301 | + | 0.857009i | \(0.327680\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2348.63 | −0.203322 | ||||||||
\(512\) | −7793.12 | −0.672676 | ||||||||
\(513\) | 12390.6i | 1.06639i | ||||||||
\(514\) | 7262.26 | 0.623199 | ||||||||
\(515\) | − 1585.91i | − 0.135696i | ||||||||
\(516\) | − 6838.35i | − 0.583414i | ||||||||
\(517\) | 4214.16i | 0.358489i | ||||||||
\(518\) | −1430.55 | −0.121341 | ||||||||
\(519\) | 559.359 | 0.0473086 | ||||||||
\(520\) | − 3392.71i | − 0.286115i | ||||||||
\(521\) | 7686.37i | 0.646346i | 0.946340 | + | 0.323173i | \(0.104750\pi\) | ||||
−0.946340 | + | 0.323173i | \(0.895250\pi\) | |||||||
\(522\) | − 2983.37i | − 0.250151i | ||||||||
\(523\) | 11476.4 | 0.959518 | 0.479759 | − | 0.877400i | \(-0.340724\pi\) | ||||
0.479759 | + | 0.877400i | \(0.340724\pi\) | |||||||
\(524\) | − 12165.6i | − 1.01423i | ||||||||
\(525\) | −2900.93 | −0.241156 | ||||||||
\(526\) | 5355.25 | 0.443916 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 2000.52 | 0.164889 | ||||||||
\(529\) | −1120.01 | −0.0920535 | ||||||||
\(530\) | − 2177.37i | − 0.178451i | ||||||||
\(531\) | 4978.44 | 0.406866 | ||||||||
\(532\) | − 4352.40i | − 0.354700i | ||||||||
\(533\) | − 27345.0i | − 2.22222i | ||||||||
\(534\) | − 3492.56i | − 0.283029i | ||||||||
\(535\) | 2989.38 | 0.241574 | ||||||||
\(536\) | 1019.81 | 0.0821814 | ||||||||
\(537\) | − 3229.59i | − 0.259529i | ||||||||
\(538\) | 4660.88i | 0.373504i | ||||||||
\(539\) | 7731.09i | 0.617814i | ||||||||
\(540\) | 2589.60 | 0.206368 | ||||||||
\(541\) | 546.481i | 0.0434289i | 0.999764 | + | 0.0217145i | \(0.00691247\pi\) | ||||
−0.999764 | + | 0.0217145i | \(0.993088\pi\) | |||||||
\(542\) | −747.357 | −0.0592283 | ||||||||
\(543\) | −10884.1 | −0.860191 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5500.69 | 0.432337 | ||||||||
\(546\) | 1981.47 | 0.155310 | ||||||||
\(547\) | − 8397.33i | − 0.656388i | −0.944610 | − | 0.328194i | \(-0.893560\pi\) | ||||
0.944610 | − | 0.328194i | \(-0.106440\pi\) | |||||||
\(548\) | −19313.6 | −1.50554 | ||||||||
\(549\) | − 918.839i | − 0.0714301i | ||||||||
\(550\) | − 4353.44i | − 0.337512i | ||||||||
\(551\) | − 11463.3i | − 0.886305i | ||||||||
\(552\) | −7002.58 | −0.539945 | ||||||||
\(553\) | −5719.73 | −0.439833 | ||||||||
\(554\) | 7083.32i | 0.543215i | ||||||||
\(555\) | − 1265.79i | − 0.0968105i | ||||||||
\(556\) | 9024.36i | 0.688342i | ||||||||
\(557\) | −4881.65 | −0.371350 | −0.185675 | − | 0.982611i | \(-0.559447\pi\) | ||||
−0.185675 | + | 0.982611i | \(0.559447\pi\) | |||||||
\(558\) | 6346.04i | 0.481451i | ||||||||
\(559\) | −20492.6 | −1.55053 | ||||||||
\(560\) | −552.797 | −0.0417142 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2704.38 | −0.202985 | ||||||||
\(563\) | −7198.57 | −0.538870 | −0.269435 | − | 0.963019i | \(-0.586837\pi\) | ||||
−0.269435 | + | 0.963019i | \(0.586837\pi\) | |||||||
\(564\) | 2959.14i | 0.220926i | ||||||||
\(565\) | −2144.44 | −0.159677 | ||||||||
\(566\) | − 1025.95i | − 0.0761904i | ||||||||
\(567\) | − 174.283i | − 0.0129087i | ||||||||
\(568\) | − 15182.5i | − 1.12155i | ||||||||
\(569\) | 23946.9 | 1.76433 | 0.882167 | − | 0.470937i | \(-0.156084\pi\) | ||||
0.882167 | + | 0.470937i | \(0.156084\pi\) | |||||||
\(570\) | −1160.85 | −0.0853032 | ||||||||
\(571\) | 1593.15i | 0.116763i | 0.998294 | + | 0.0583813i | \(0.0185939\pi\) | ||||
−0.998294 | + | 0.0583813i | \(0.981406\pi\) | |||||||
\(572\) | − 9864.95i | − 0.721109i | ||||||||
\(573\) | 1548.59i | 0.112903i | ||||||||
\(574\) | 5086.16 | 0.369847 | ||||||||
\(575\) | − 13349.2i | − 0.968174i | ||||||||
\(576\) | 1168.69 | 0.0845403 | ||||||||
\(577\) | 12937.4 | 0.933435 | 0.466717 | − | 0.884406i | \(-0.345436\pi\) | ||||
0.466717 | + | 0.884406i | \(0.345436\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −11195.2 | −0.803549 | ||||||||
\(580\) | −2395.82 | −0.171519 | ||||||||
\(581\) | − 921.499i | − 0.0658007i | ||||||||
\(582\) | 3412.53 | 0.243048 | ||||||||
\(583\) | − 14570.6i | − 1.03508i | ||||||||
\(584\) | − 5695.92i | − 0.403594i | ||||||||
\(585\) | − 3003.53i | − 0.212275i | ||||||||
\(586\) | 9803.82 | 0.691112 | ||||||||
\(587\) | 12899.2 | 0.906998 | 0.453499 | − | 0.891257i | \(-0.350176\pi\) | ||||
0.453499 | + | 0.891257i | \(0.350176\pi\) | |||||||
\(588\) | 5428.70i | 0.380741i | ||||||||
\(589\) | 24384.1i | 1.70582i | ||||||||
\(590\) | 1205.11i | 0.0840911i | ||||||||
\(591\) | 4300.23 | 0.299302 | ||||||||
\(592\) | 3039.19i | 0.210997i | ||||||||
\(593\) | −4357.13 | −0.301730 | −0.150865 | − | 0.988554i | \(-0.548206\pi\) | ||||
−0.150865 | + | 0.988554i | \(0.548206\pi\) | |||||||
\(594\) | −5223.59 | −0.360819 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1758.23 | 0.120839 | ||||||||
\(597\) | −11790.3 | −0.808284 | ||||||||
\(598\) | 9118.14i | 0.623526i | ||||||||
\(599\) | 13726.8 | 0.936328 | 0.468164 | − | 0.883642i | \(-0.344916\pi\) | ||||
0.468164 | + | 0.883642i | \(0.344916\pi\) | |||||||
\(600\) | − 7035.35i | − 0.478695i | ||||||||
\(601\) | 2531.41i | 0.171811i | 0.996303 | + | 0.0859056i | \(0.0273783\pi\) | ||||
−0.996303 | + | 0.0859056i | \(0.972622\pi\) | |||||||
\(602\) | − 3811.62i | − 0.258057i | ||||||||
\(603\) | 902.830 | 0.0609720 | ||||||||
\(604\) | −4116.24 | −0.277297 | ||||||||
\(605\) | − 1723.07i | − 0.115790i | ||||||||
\(606\) | 1140.15i | 0.0764283i | ||||||||
\(607\) | − 185.004i | − 0.0123708i | −0.999981 | − | 0.00618540i | \(-0.998031\pi\) | ||||
0.999981 | − | 0.00618540i | \(-0.00196889\pi\) | |||||||
\(608\) | 16524.4 | 1.10223 | ||||||||
\(609\) | − 3220.28i | − 0.214273i | ||||||||
\(610\) | 222.420 | 0.0147632 | ||||||||
\(611\) | 8867.73 | 0.587152 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17706.9 | −1.16668 | −0.583339 | − | 0.812228i | \(-0.698254\pi\) | ||||
−0.583339 | + | 0.812228i | \(0.698254\pi\) | |||||||
\(614\) | −3301.93 | −0.217028 | ||||||||
\(615\) | 4500.39i | 0.295078i | ||||||||
\(616\) | 4222.84 | 0.276207 | ||||||||
\(617\) | 6183.89i | 0.403491i | 0.979438 | + | 0.201746i | \(0.0646614\pi\) | ||||
−0.979438 | + | 0.201746i | \(0.935339\pi\) | |||||||
\(618\) | 2246.30i | 0.146213i | ||||||||
\(619\) | − 1247.51i | − 0.0810046i | −0.999179 | − | 0.0405023i | \(-0.987104\pi\) | ||||
0.999179 | − | 0.0405023i | \(-0.0128958\pi\) | |||||||
\(620\) | 5096.23 | 0.330112 | ||||||||
\(621\) | −16017.4 | −1.03503 | ||||||||
\(622\) | − 12992.8i | − 0.837561i | ||||||||
\(623\) | 6458.23i | 0.415318i | ||||||||
\(624\) | − 4209.63i | − 0.270064i | ||||||||
\(625\) | 12262.8 | 0.784817 | ||||||||
\(626\) | − 800.914i | − 0.0511357i | ||||||||
\(627\) | −7768.27 | −0.494792 | ||||||||
\(628\) | −4430.87 | −0.281546 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 558.655 | 0.0353292 | ||||||||
\(631\) | −24053.3 | −1.51750 | −0.758752 | − | 0.651379i | \(-0.774191\pi\) | ||||
−0.758752 | + | 0.651379i | \(0.774191\pi\) | |||||||
\(632\) | − 13871.5i | − 0.873069i | ||||||||
\(633\) | −16612.7 | −1.04312 | ||||||||
\(634\) | − 10417.8i | − 0.652596i | ||||||||
\(635\) | 8028.51i | 0.501735i | ||||||||
\(636\) | − 10231.4i | − 0.637893i | ||||||||
\(637\) | 16268.3 | 1.01189 | ||||||||
\(638\) | 4832.69 | 0.299887 | ||||||||
\(639\) | − 13440.9i | − 0.832102i | ||||||||
\(640\) | − 4211.70i | − 0.260128i | ||||||||
\(641\) | 21286.8i | 1.31167i | 0.754905 | + | 0.655834i | \(0.227683\pi\) | ||||
−0.754905 | + | 0.655834i | \(0.772317\pi\) | |||||||
\(642\) | −4234.20 | −0.260297 | ||||||||
\(643\) | 1789.41i | 0.109747i | 0.998493 | + | 0.0548736i | \(0.0174756\pi\) | ||||
−0.998493 | + | 0.0548736i | \(0.982524\pi\) | |||||||
\(644\) | 5626.38 | 0.344271 | ||||||||
\(645\) | 3372.64 | 0.205888 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4378.61 | −0.266060 | −0.133030 | − | 0.991112i | \(-0.542471\pi\) | ||||
−0.133030 | + | 0.991112i | \(0.542471\pi\) | |||||||
\(648\) | 422.672 | 0.0256237 | ||||||||
\(649\) | 8064.45i | 0.487762i | ||||||||
\(650\) | −9160.81 | −0.552795 | ||||||||
\(651\) | 6849.97i | 0.412399i | ||||||||
\(652\) | 4159.11i | 0.249821i | ||||||||
\(653\) | − 7665.15i | − 0.459358i | −0.973266 | − | 0.229679i | \(-0.926232\pi\) | ||||
0.973266 | − | 0.229679i | \(-0.0737676\pi\) | |||||||
\(654\) | −7791.26 | −0.465845 | ||||||||
\(655\) | 5999.99 | 0.357922 | ||||||||
\(656\) | − 10805.5i | − 0.643117i | ||||||||
\(657\) | − 5042.54i | − 0.299434i | ||||||||
\(658\) | 1649.39i | 0.0977205i | ||||||||
\(659\) | −4710.22 | −0.278428 | −0.139214 | − | 0.990262i | \(-0.544458\pi\) | ||||
−0.139214 | + | 0.990262i | \(0.544458\pi\) | |||||||
\(660\) | 1623.55i | 0.0957527i | ||||||||
\(661\) | 31266.6 | 1.83983 | 0.919916 | − | 0.392116i | \(-0.128257\pi\) | ||||
0.919916 | + | 0.392116i | \(0.128257\pi\) | |||||||
\(662\) | 1024.00 | 0.0601192 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2234.82 | 0.130614 | ||||||||
\(665\) | 2146.58 | 0.125174 | ||||||||
\(666\) | − 3071.40i | − 0.178700i | ||||||||
\(667\) | 14818.7 | 0.860246 | ||||||||
\(668\) | − 17431.1i | − 1.00962i | ||||||||
\(669\) | 2222.58i | 0.128446i | ||||||||
\(670\) | 218.545i | 0.0126017i | ||||||||
\(671\) | 1488.40 | 0.0856322 | ||||||||
\(672\) | 4642.05 | 0.266474 | ||||||||
\(673\) | 11723.0i | 0.671454i | 0.941959 | + | 0.335727i | \(0.108982\pi\) | ||||
−0.941959 | + | 0.335727i | \(0.891018\pi\) | |||||||
\(674\) | − 2679.65i | − 0.153140i | ||||||||
\(675\) | − 16092.3i | − 0.917621i | ||||||||
\(676\) | −7253.37 | −0.412686 | ||||||||
\(677\) | 289.531i | 0.0164366i | 0.999966 | + | 0.00821829i | \(0.00261599\pi\) | ||||
−0.999966 | + | 0.00821829i | \(0.997384\pi\) | |||||||
\(678\) | 3037.42 | 0.172052 | ||||||||
\(679\) | −6310.25 | −0.356650 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6786.45 | −0.381875 | ||||||||
\(682\) | −10279.8 | −0.577175 | ||||||||
\(683\) | − 1720.10i | − 0.0963660i | −0.998839 | − | 0.0481830i | \(-0.984657\pi\) | ||||
0.998839 | − | 0.0481830i | \(-0.0153431\pi\) | |||||||
\(684\) | 9344.64 | 0.522370 | ||||||||
\(685\) | − 9525.37i | − 0.531308i | ||||||||
\(686\) | 6733.30i | 0.374750i | ||||||||
\(687\) | − 12356.5i | − 0.686215i | ||||||||
\(688\) | −8097.77 | −0.448728 | ||||||||
\(689\) | −30660.5 | −1.69532 | ||||||||
\(690\) | − 1500.65i | − 0.0827951i | ||||||||
\(691\) | − 16777.7i | − 0.923665i | −0.886967 | − | 0.461832i | \(-0.847192\pi\) | ||||
0.886967 | − | 0.461832i | \(-0.152808\pi\) | |||||||
\(692\) | − 1089.96i | − 0.0598758i | ||||||||
\(693\) | 3738.44 | 0.204923 | ||||||||
\(694\) | − 5421.88i | − 0.296559i | ||||||||
\(695\) | −4450.77 | −0.242917 | ||||||||
\(696\) | 7809.84 | 0.425332 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 2035.86 | 0.110399 | ||||||||
\(699\) | 16381.2 | 0.886400 | ||||||||
\(700\) | 5652.71i | 0.305218i | ||||||||
\(701\) | 23981.1 | 1.29209 | 0.646043 | − | 0.763301i | \(-0.276423\pi\) | ||||
0.646043 | + | 0.763301i | \(0.276423\pi\) | |||||||
\(702\) | 10991.8i | 0.590969i | ||||||||
\(703\) | − 11801.6i | − 0.633150i | ||||||||
\(704\) | 1893.12i | 0.101349i | ||||||||
\(705\) | −1459.43 | −0.0779652 | ||||||||
\(706\) | −8824.10 | −0.470396 | ||||||||
\(707\) | − 2108.30i | − 0.112151i | ||||||||
\(708\) | 5662.78i | 0.300593i | ||||||||
\(709\) | 7709.28i | 0.408361i | 0.978933 | + | 0.204181i | \(0.0654530\pi\) | ||||
−0.978933 | + | 0.204181i | \(0.934547\pi\) | |||||||
\(710\) | 3253.59 | 0.171979 | ||||||||
\(711\) | − 12280.3i | − 0.647747i | ||||||||
\(712\) | −15662.5 | −0.824407 | ||||||||
\(713\) | −31521.5 | −1.65567 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4865.34 | 0.254480 | ||||||||
\(716\) | −6293.13 | −0.328471 | ||||||||
\(717\) | − 1054.61i | − 0.0549304i | ||||||||
\(718\) | −6729.09 | −0.349760 | ||||||||
\(719\) | 11976.5i | 0.621209i | 0.950539 | + | 0.310605i | \(0.100532\pi\) | ||||
−0.950539 | + | 0.310605i | \(0.899468\pi\) | |||||||
\(720\) | − 1186.86i | − 0.0614329i | ||||||||
\(721\) | − 4153.72i | − 0.214553i | ||||||||
\(722\) | −1486.56 | −0.0766260 | ||||||||
\(723\) | 6052.00 | 0.311309 | ||||||||
\(724\) | 21208.7i | 1.08870i | ||||||||
\(725\) | 14888.1i | 0.762662i | ||||||||
\(726\) | 2440.58i | 0.124764i | ||||||||
\(727\) | −18597.3 | −0.948745 | −0.474372 | − | 0.880324i | \(-0.657325\pi\) | ||||
−0.474372 | + | 0.880324i | \(0.657325\pi\) | |||||||
\(728\) | − 8886.00i | − 0.452386i | ||||||||
\(729\) | −11461.4 | −0.582300 | ||||||||
\(730\) | 1220.63 | 0.0618870 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 1045.14 | 0.0527727 | ||||||||
\(733\) | 23569.5 | 1.18767 | 0.593833 | − | 0.804588i | \(-0.297614\pi\) | ||||
0.593833 | + | 0.804588i | \(0.297614\pi\) | |||||||
\(734\) | 20.2646i | 0.00101905i | ||||||||
\(735\) | −2677.41 | −0.134364 | ||||||||
\(736\) | 21361.3i | 1.06982i | ||||||||
\(737\) | 1462.47i | 0.0730948i | ||||||||
\(738\) | 10920.0i | 0.544678i | ||||||||
\(739\) | −10149.1 | −0.505199 | −0.252599 | − | 0.967571i | \(-0.581285\pi\) | ||||
−0.252599 | + | 0.967571i | \(0.581285\pi\) | |||||||
\(740\) | −2466.50 | −0.122528 | ||||||||
\(741\) | 16346.5i | 0.810397i | ||||||||
\(742\) | − 5702.85i | − 0.282154i | ||||||||
\(743\) | − 27758.0i | − 1.37058i | −0.728269 | − | 0.685291i | \(-0.759675\pi\) | ||||
0.728269 | − | 0.685291i | \(-0.240325\pi\) | |||||||
\(744\) | −16612.6 | −0.818611 | ||||||||
\(745\) | 867.148i | 0.0426441i | ||||||||
\(746\) | −2617.87 | −0.128481 | ||||||||
\(747\) | 1978.47 | 0.0969054 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7829.63 | 0.381960 | ||||||||
\(750\) | 3134.99 | 0.152632 | ||||||||
\(751\) | 815.225i | 0.0396112i | 0.999804 | + | 0.0198056i | \(0.00630473\pi\) | ||||
−0.999804 | + | 0.0198056i | \(0.993695\pi\) | |||||||
\(752\) | 3504.13 | 0.169924 | ||||||||
\(753\) | − 24277.1i | − 1.17491i | ||||||||
\(754\) | − 10169.3i | − 0.491172i | ||||||||
\(755\) | − 2030.11i | − 0.0978585i | ||||||||
\(756\) | 6782.56 | 0.326295 | ||||||||
\(757\) | 13239.4 | 0.635659 | 0.317829 | − | 0.948148i | \(-0.397046\pi\) | ||||
0.317829 | + | 0.948148i | \(0.397046\pi\) | |||||||
\(758\) | − 13058.0i | − 0.625710i | ||||||||
\(759\) | − 10042.1i | − 0.480244i | ||||||||
\(760\) | 5205.90i | 0.248471i | ||||||||
\(761\) | −11028.2 | −0.525324 | −0.262662 | − | 0.964888i | \(-0.584600\pi\) | ||||
−0.262662 | + | 0.964888i | \(0.584600\pi\) | |||||||
\(762\) | − 11371.7i | − 0.540621i | ||||||||
\(763\) | 14407.1 | 0.683582 | ||||||||
\(764\) | 3017.56 | 0.142895 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −12365.0 | −0.583246 | ||||||||
\(767\) | 16969.8 | 0.798882 | ||||||||
\(768\) | 7695.55i | 0.361574i | ||||||||
\(769\) | −18921.2 | −0.887277 | −0.443639 | − | 0.896206i | \(-0.646313\pi\) | ||||
−0.443639 | + | 0.896206i | \(0.646313\pi\) | |||||||
\(770\) | 904.952i | 0.0423535i | ||||||||
\(771\) | 16830.3i | 0.786158i | ||||||||
\(772\) | 21814.7i | 1.01701i | ||||||||
\(773\) | −38728.6 | −1.80203 | −0.901016 | − | 0.433786i | \(-0.857177\pi\) | ||||
−0.901016 | + | 0.433786i | \(0.857177\pi\) | |||||||
\(774\) | 8183.59 | 0.380043 | ||||||||
\(775\) | − 31669.0i | − 1.46785i | ||||||||
\(776\) | − 15303.6i | − 0.707949i | ||||||||
\(777\) | − 3315.29i | − 0.153070i | ||||||||
\(778\) | −1556.93 | −0.0717465 | ||||||||
\(779\) | 41959.2i | 1.92984i | ||||||||
\(780\) | 3416.39 | 0.156829 | ||||||||
\(781\) | 21772.5 | 0.997545 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 17863.9 | 0.815329 | ||||||||
\(784\) | 6428.50 | 0.292844 | ||||||||
\(785\) | − 2185.28i | − 0.0993579i | ||||||||
\(786\) | −8498.47 | −0.385662 | ||||||||
\(787\) | 20587.3i | 0.932477i | 0.884659 | + | 0.466239i | \(0.154391\pi\) | ||||
−0.884659 | + | 0.466239i | \(0.845609\pi\) | |||||||
\(788\) | − 8379.37i | − 0.378811i | ||||||||
\(789\) | 12410.8i | 0.559995i | ||||||||
\(790\) | 2972.66 | 0.133876 | ||||||||
\(791\) | −5616.62 | −0.252470 | ||||||||
\(792\) | 9066.49i | 0.406772i | ||||||||
\(793\) | − 3132.00i | − 0.140253i | ||||||||
\(794\) | − 14435.0i | − 0.645190i | ||||||||
\(795\) | 5046.05 | 0.225113 | ||||||||
\(796\) | 22974.5i | 1.02300i | ||||||||
\(797\) | 15871.4 | 0.705385 | 0.352693 | − | 0.935739i | \(-0.385266\pi\) | ||||
0.352693 | + | 0.935739i | \(0.385266\pi\) | |||||||
\(798\) | −3040.45 | −0.134876 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −21461.3 | −0.948463 | ||||||||
\(801\) | −13865.9 | −0.611644 | ||||||||
\(802\) | − 18765.0i | − 0.826204i | ||||||||
\(803\) | 8168.28 | 0.358969 | ||||||||
\(804\) | 1026.93i | 0.0450462i | ||||||||
\(805\) | 2774.90i | 0.121494i | ||||||||
\(806\) | 21631.4i | 0.945329i | ||||||||
\(807\) | −10801.6 | −0.471170 | ||||||||
\(808\) | 5113.06 | 0.222620 | ||||||||
\(809\) | 39667.1i | 1.72388i | 0.507007 | + | 0.861942i | \(0.330752\pi\) | ||||
−0.507007 | + | 0.861942i | \(0.669248\pi\) | |||||||
\(810\) | 90.5783i | 0.00392913i | ||||||||
\(811\) | − 8003.87i | − 0.346552i | −0.984873 | − | 0.173276i | \(-0.944565\pi\) | ||||
0.984873 | − | 0.173276i | \(-0.0554353\pi\) | |||||||
\(812\) | −6275.00 | −0.271194 | ||||||||
\(813\) | − 1732.00i | − 0.0747157i | ||||||||
\(814\) | 4975.28 | 0.214230 | ||||||||
\(815\) | −2051.25 | −0.0881621 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 31444.7 | 1.34652 | ||||||||
\(818\) | 12939.7 | 0.553088 | ||||||||
\(819\) | − 7866.69i | − 0.335634i | ||||||||
\(820\) | 8769.40 | 0.373464 | ||||||||
\(821\) | 13279.1i | 0.564489i | 0.959343 | + | 0.282244i | \(0.0910789\pi\) | ||||
−0.959343 | + | 0.282244i | \(0.908921\pi\) | |||||||
\(822\) | 13491.9i | 0.572486i | ||||||||
\(823\) | 28934.0i | 1.22549i | 0.790281 | + | 0.612745i | \(0.209935\pi\) | ||||
−0.790281 | + | 0.612745i | \(0.790065\pi\) | |||||||
\(824\) | 10073.6 | 0.425887 | ||||||||
\(825\) | 10089.1 | 0.425767 | ||||||||
\(826\) | 3156.37i | 0.132959i | ||||||||
\(827\) | − 13679.6i | − 0.575193i | −0.957752 | − | 0.287597i | \(-0.907144\pi\) | ||||
0.957752 | − | 0.287597i | \(-0.0928563\pi\) | |||||||
\(828\) | 12079.9i | 0.507012i | ||||||||
\(829\) | 16514.5 | 0.691886 | 0.345943 | − | 0.938256i | \(-0.387559\pi\) | ||||
0.345943 | + | 0.938256i | \(0.387559\pi\) | |||||||
\(830\) | 478.921i | 0.0200284i | ||||||||
\(831\) | −16415.6 | −0.685260 | ||||||||
\(832\) | 3983.64 | 0.165995 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 6304.13 | 0.261744 | ||||||||
\(835\) | 8596.93 | 0.356298 | ||||||||
\(836\) | 15137.1i | 0.626231i | ||||||||
\(837\) | −37998.9 | −1.56922 | ||||||||
\(838\) | − 13177.8i | − 0.543221i | ||||||||
\(839\) | − 87.9839i | − 0.00362043i | −0.999998 | − | 0.00181022i | \(-0.999424\pi\) | ||||
0.999998 | − | 0.00181022i | \(-0.000576210\pi\) | |||||||
\(840\) | 1462.44i | 0.0600702i | ||||||||
\(841\) | 7861.94 | 0.322356 | ||||||||
\(842\) | 16825.1 | 0.688635 | ||||||||
\(843\) | − 6267.41i | − 0.256063i | ||||||||
\(844\) | 32371.3i | 1.32022i | ||||||||
\(845\) | − 3577.33i | − 0.145638i | ||||||||
\(846\) | −3541.27 | −0.143914 | ||||||||
\(847\) | − 4512.98i | − 0.183079i | ||||||||
\(848\) | −12115.7 | −0.490630 | ||||||||
\(849\) | 2377.63 | 0.0961133 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 15256.0 | 0.614534 | ||||||||
\(852\) | 15288.5 | 0.614758 | ||||||||
\(853\) | − 8162.96i | − 0.327660i | −0.986489 | − | 0.163830i | \(-0.947615\pi\) | ||||
0.986489 | − | 0.163830i | \(-0.0523849\pi\) | |||||||
\(854\) | 582.551 | 0.0233425 | ||||||||
\(855\) | 4608.73i | 0.184345i | ||||||||
\(856\) | 18988.4i | 0.758191i | ||||||||
\(857\) | 18724.9i | 0.746361i | 0.927759 | + | 0.373181i | \(0.121733\pi\) | ||||
−0.927759 | + | 0.373181i | \(0.878267\pi\) | |||||||
\(858\) | −6891.34 | −0.274203 | ||||||||
\(859\) | 46422.5 | 1.84391 | 0.921953 | − | 0.387301i | \(-0.126593\pi\) | ||||
0.921953 | + | 0.387301i | \(0.126593\pi\) | |||||||
\(860\) | − 6571.88i | − 0.260580i | ||||||||
\(861\) | 11787.2i | 0.466557i | ||||||||
\(862\) | − 4043.61i | − 0.159775i | ||||||||
\(863\) | 29112.3 | 1.14831 | 0.574157 | − | 0.818746i | \(-0.305330\pi\) | ||||
0.574157 | + | 0.818746i | \(0.305330\pi\) | |||||||
\(864\) | 25750.8i | 1.01396i | ||||||||
\(865\) | 537.563 | 0.0211303 | ||||||||
\(866\) | 8346.33 | 0.327505 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 13347.8 | 0.521950 | ||||||||
\(869\) | 19892.6 | 0.776536 | ||||||||
\(870\) | 1673.64i | 0.0652204i | ||||||||
\(871\) | 3077.43 | 0.119719 | ||||||||
\(872\) | 34940.2i | 1.35691i | ||||||||
\(873\) | − 13548.2i | − 0.525241i | ||||||||
\(874\) | − 13991.2i | − 0.541487i | ||||||||
\(875\) | −5797.04 | −0.223972 | ||||||||
\(876\) | 5735.69 | 0.221222 | ||||||||
\(877\) | 39163.0i | 1.50791i | 0.656924 | + | 0.753957i | \(0.271857\pi\) | ||||
−0.656924 | + | 0.753957i | \(0.728143\pi\) | |||||||
\(878\) | − 3464.19i | − 0.133156i | ||||||||
\(879\) | 22720.3i | 0.871830i | ||||||||
\(880\) | 1922.57 | 0.0736473 | ||||||||
\(881\) | 35073.2i | 1.34125i | 0.741795 | + | 0.670627i | \(0.233975\pi\) | ||||
−0.741795 | + | 0.670627i | \(0.766025\pi\) | |||||||
\(882\) | −6496.63 | −0.248019 | ||||||||
\(883\) | −48775.7 | −1.85893 | −0.929463 | − | 0.368915i | \(-0.879729\pi\) | ||||
−0.929463 | + | 0.368915i | \(0.879729\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2792.85 | −0.106080 | ||||||||
\(886\) | −11611.0 | −0.440269 | ||||||||
\(887\) | − 13296.0i | − 0.503309i | −0.967817 | − | 0.251654i | \(-0.919025\pi\) | ||||
0.967817 | − | 0.251654i | \(-0.0809746\pi\) | |||||||
\(888\) | 8040.27 | 0.303844 | ||||||||
\(889\) | 21027.9i | 0.793309i | ||||||||
\(890\) | − 3356.46i | − 0.126415i | ||||||||
\(891\) | 606.137i | 0.0227905i | ||||||||
\(892\) | 4330.90 | 0.162566 | ||||||||
\(893\) | −13607.0 | −0.509899 | ||||||||
\(894\) | − 1228.24i | − 0.0459492i | ||||||||
\(895\) | − 3103.74i | − 0.115918i | ||||||||
\(896\) | − 11031.1i | − 0.411297i | ||||||||
\(897\) | −21131.3 | −0.786570 | ||||||||
\(898\) | − 12054.6i | − 0.447960i | ||||||||
\(899\) | 35155.3 | 1.30422 | ||||||||
\(900\) | −12136.4 | −0.449498 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −17689.1 | −0.652974 | ||||||||
\(903\) | 8833.44 | 0.325535 | ||||||||
\(904\) | − 13621.4i | − 0.501153i | ||||||||
\(905\) | −10460.0 | −0.384202 | ||||||||
\(906\) | 2875.47i | 0.105443i | ||||||||
\(907\) | − 11675.0i | − 0.427410i | −0.976898 | − | 0.213705i | \(-0.931447\pi\) | ||||
0.976898 | − | 0.213705i | \(-0.0685532\pi\) | |||||||
\(908\) | 13224.0i | 0.483319i | ||||||||
\(909\) | 4526.54 | 0.165166 | ||||||||
\(910\) | 1904.26 | 0.0693689 | ||||||||
\(911\) | 18552.9i | 0.674738i | 0.941372 | + | 0.337369i | \(0.109537\pi\) | ||||
−0.941372 | + | 0.337369i | \(0.890463\pi\) | |||||||
\(912\) | 6459.41i | 0.234531i | ||||||||
\(913\) | 3204.87i | 0.116173i | ||||||||
\(914\) | −9739.24 | −0.352457 | ||||||||
\(915\) | 515.459i | 0.0186235i | ||||||||
\(916\) | −24077.7 | −0.868504 | ||||||||
\(917\) | 15714.9 | 0.565922 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 33956.8 | 1.21886 | 0.609429 | − | 0.792841i | \(-0.291399\pi\) | ||||
0.609429 | + | 0.792841i | \(0.291399\pi\) | |||||||
\(920\) | −6729.71 | −0.241165 | ||||||||
\(921\) | − 7652.23i | − 0.273778i | ||||||||
\(922\) | −9886.63 | −0.353144 | ||||||||
\(923\) | − 45815.3i | − 1.63383i | ||||||||
\(924\) | 4252.33i | 0.151398i | ||||||||
\(925\) | 15327.4i | 0.544823i | ||||||||
\(926\) | −480.372 | −0.0170475 | ||||||||
\(927\) | 8918.08 | 0.315974 | ||||||||
\(928\) | − 23823.8i | − 0.842732i | ||||||||
\(929\) | − 23695.3i | − 0.836832i | −0.908256 | − | 0.418416i | \(-0.862585\pi\) | ||||
0.908256 | − | 0.418416i | \(-0.137415\pi\) | |||||||
\(930\) | − 3560.06i | − 0.125526i | ||||||||
\(931\) | −24962.7 | −0.878753 | ||||||||
\(932\) | − 31920.2i | − 1.12187i | ||||||||
\(933\) | 30110.8 | 1.05657 | ||||||||
\(934\) | 2018.72 | 0.0707221 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 19078.3 | 0.666234 | ||||||||
\(937\) | −7990.62 | −0.278593 | −0.139297 | − | 0.990251i | \(-0.544484\pi\) | ||||
−0.139297 | + | 0.990251i | \(0.544484\pi\) | |||||||
\(938\) | 572.402i | 0.0199249i | ||||||||
\(939\) | 1856.12 | 0.0645071 | ||||||||
\(940\) | 2843.83i | 0.0986762i | ||||||||
\(941\) | 24385.9i | 0.844799i | 0.906410 | + | 0.422400i | \(0.138812\pi\) | ||||
−0.906410 | + | 0.422400i | \(0.861188\pi\) | |||||||
\(942\) | 3095.26i | 0.107058i | ||||||||
\(943\) | −54241.0 | −1.87310 | ||||||||
\(944\) | 6705.69 | 0.231199 | ||||||||
\(945\) | 3345.12i | 0.115150i | ||||||||
\(946\) | 13256.4i | 0.455605i | ||||||||
\(947\) | 1174.62i | 0.0403064i | 0.999797 | + | 0.0201532i | \(0.00641539\pi\) | ||||
−0.999797 | + | 0.0201532i | \(0.993585\pi\) | |||||||
\(948\) | 13968.4 | 0.478557 | ||||||||
\(949\) | − 17188.3i | − 0.587939i | ||||||||
\(950\) | 14056.7 | 0.480063 | ||||||||
\(951\) | 24143.4 | 0.823241 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −33546.9 | −1.14029 | −0.570143 | − | 0.821546i | \(-0.693112\pi\) | ||||
−0.570143 | + | 0.821546i | \(0.693112\pi\) | |||||||
\(954\) | 12244.1 | 0.415531 | ||||||||
\(955\) | 1488.25i | 0.0504277i | ||||||||
\(956\) | −2055.00 | −0.0695224 | ||||||||
\(957\) | 11199.8i | 0.378304i | ||||||||
\(958\) | − 13598.7i | − 0.458617i | ||||||||
\(959\) | − 24948.4i | − 0.840067i | ||||||||
\(960\) | −655.620 | −0.0220417 | ||||||||
\(961\) | −44989.1 | −1.51016 | ||||||||
\(962\) | − 10469.3i | − 0.350878i | ||||||||
\(963\) | 16810.3i | 0.562517i | ||||||||
\(964\) | − 11792.9i | − 0.394007i | ||||||||
\(965\) | −10758.9 | −0.358903 | ||||||||
\(966\) | − 3930.41i | − 0.130910i | ||||||||
\(967\) | −24766.8 | −0.823625 | −0.411813 | − | 0.911269i | \(-0.635104\pi\) | ||||
−0.411813 | + | 0.911269i | \(0.635104\pi\) | |||||||
\(968\) | 10944.9 | 0.363411 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3279.56 | 0.108557 | ||||||||
\(971\) | −42324.3 | −1.39882 | −0.699409 | − | 0.714721i | \(-0.746553\pi\) | ||||
−0.699409 | + | 0.714721i | \(0.746553\pi\) | |||||||
\(972\) | 23488.3i | 0.775091i | ||||||||
\(973\) | −11657.2 | −0.384083 | ||||||||
\(974\) | 1538.01i | 0.0505966i | ||||||||
\(975\) | − 21230.2i | − 0.697344i | ||||||||
\(976\) | − 1237.63i | − 0.0405896i | ||||||||
\(977\) | 11320.4 | 0.370698 | 0.185349 | − | 0.982673i | \(-0.440658\pi\) | ||||
0.185349 | + | 0.982673i | \(0.440658\pi\) | |||||||
\(978\) | 2905.42 | 0.0949949 | ||||||||
\(979\) | − 22461.0i | − 0.733254i | ||||||||
\(980\) | 5217.16i | 0.170057i | ||||||||
\(981\) | 30932.2i | 1.00672i | ||||||||
\(982\) | 25556.8 | 0.830500 | ||||||||
\(983\) | 11311.9i | 0.367032i | 0.983017 | + | 0.183516i | \(0.0587478\pi\) | ||||
−0.983017 | + | 0.183516i | \(0.941252\pi\) | |||||||
\(984\) | −28586.3 | −0.926116 | ||||||||
\(985\) | 4132.66 | 0.133683 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3822.47 | −0.123273 | ||||||||
\(988\) | 31852.6 | 1.02568 | ||||||||
\(989\) | 40648.8i | 1.30693i | ||||||||
\(990\) | −1942.94 | −0.0623744 | ||||||||
\(991\) | 29405.5i | 0.942580i | 0.881978 | + | 0.471290i | \(0.156212\pi\) | ||||
−0.881978 | + | 0.471290i | \(0.843788\pi\) | |||||||
\(992\) | 50676.5i | 1.62196i | ||||||||
\(993\) | 2373.12i | 0.0758397i | ||||||||
\(994\) | 8521.63 | 0.271921 | ||||||||
\(995\) | −11330.9 | −0.361018 | ||||||||
\(996\) | 2250.43i | 0.0715939i | ||||||||
\(997\) | − 54905.9i | − 1.74412i | −0.489398 | − | 0.872060i | \(-0.662784\pi\) | ||||
0.489398 | − | 0.872060i | \(-0.337216\pi\) | |||||||
\(998\) | − 23588.7i | − 0.748183i | ||||||||
\(999\) | 18390.9 | 0.582446 |
(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 | 289.4.b.b.288.3 | 6 | ||
17.4 | even | 4 | 289.4.a.b.1.2 | 3 | |||
17.13 | even | 4 | 17.4.a.b.1.2 | ✓ | 3 | ||
17.16 | even | 2 | inner | 289.4.b.b.288.4 | 6 | ||
51.47 | odd | 4 | 153.4.a.g.1.2 | 3 | |||
68.47 | odd | 4 | 272.4.a.h.1.2 | 3 | |||
85.13 | odd | 4 | 425.4.b.f.324.3 | 6 | |||
85.47 | odd | 4 | 425.4.b.f.324.4 | 6 | |||
85.64 | even | 4 | 425.4.a.g.1.2 | 3 | |||
119.13 | odd | 4 | 833.4.a.d.1.2 | 3 | |||
136.13 | even | 4 | 1088.4.a.v.1.2 | 3 | |||
136.115 | odd | 4 | 1088.4.a.x.1.2 | 3 | |||
187.98 | odd | 4 | 2057.4.a.e.1.2 | 3 | |||
204.47 | even | 4 | 2448.4.a.bi.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
17.4.a.b.1.2 | ✓ | 3 | 17.13 | even | 4 | ||
153.4.a.g.1.2 | 3 | 51.47 | odd | 4 | |||
272.4.a.h.1.2 | 3 | 68.47 | odd | 4 | |||
289.4.a.b.1.2 | 3 | 17.4 | even | 4 | |||
289.4.b.b.288.3 | 6 | 1.1 | even | 1 | trivial | ||
289.4.b.b.288.4 | 6 | 17.16 | even | 2 | inner | ||
425.4.a.g.1.2 | 3 | 85.64 | even | 4 | |||
425.4.b.f.324.3 | 6 | 85.13 | odd | 4 | |||
425.4.b.f.324.4 | 6 | 85.47 | odd | 4 | |||
833.4.a.d.1.2 | 3 | 119.13 | odd | 4 | |||
1088.4.a.v.1.2 | 3 | 136.13 | even | 4 | |||
1088.4.a.x.1.2 | 3 | 136.115 | odd | 4 | |||
2057.4.a.e.1.2 | 3 | 187.98 | odd | 4 | |||
2448.4.a.bi.1.1 | 3 | 204.47 | even | 4 |