Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1216,4,Mod(1,1216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1216, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1216.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1216 = 2^{6} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1216.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(71.7463225670\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{57}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 14 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 152) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-3.27492\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1216.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.27492 | −0.630258 | −0.315129 | − | 0.949049i | \(-0.602048\pi\) | ||||
−0.315129 | + | 0.949049i | \(0.602048\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 6.27492 | 0.561246 | 0.280623 | − | 0.959818i | \(-0.409459\pi\) | ||||
0.280623 | + | 0.959818i | \(0.409459\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −18.0997 | −0.977290 | −0.488645 | − | 0.872483i | \(-0.662509\pi\) | ||||
−0.488645 | + | 0.872483i | \(0.662509\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −16.2749 | −0.602775 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 33.9244 | 0.929873 | 0.464936 | − | 0.885344i | \(-0.346077\pi\) | ||||
0.464936 | + | 0.885344i | \(0.346077\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.07558 | 0.0656163 | 0.0328082 | − | 0.999462i | \(-0.489555\pi\) | ||||
0.0328082 | + | 0.999462i | \(0.489555\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −20.5498 | −0.353730 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −14.2508 | −0.203314 | −0.101657 | − | 0.994820i | \(-0.532414\pi\) | ||||
−0.101657 | + | 0.994820i | \(0.532414\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 19.0000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 59.2749 | 0.615945 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 114.072 | 1.03416 | 0.517081 | − | 0.855937i | \(-0.327019\pi\) | ||||
0.517081 | + | 0.855937i | \(0.327019\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −85.6254 | −0.685003 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 141.722 | 1.01016 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 34.5257 | 0.221078 | 0.110539 | − | 0.993872i | \(-0.464742\pi\) | ||||
0.110539 | + | 0.993872i | \(0.464742\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 107.698 | 0.623970 | 0.311985 | − | 0.950087i | \(-0.399006\pi\) | ||||
0.311985 | + | 0.950087i | \(0.399006\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −111.100 | −0.586060 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −113.574 | −0.548500 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 181.698 | 0.807322 | 0.403661 | − | 0.914909i | \(-0.367738\pi\) | ||||
0.403661 | + | 0.914909i | \(0.367738\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −10.0723 | −0.0413552 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −444.743 | −1.69408 | −0.847038 | − | 0.531532i | \(-0.821616\pi\) | ||||
−0.847038 | + | 0.531532i | \(0.821616\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −120.323 | −0.426723 | −0.213362 | − | 0.976973i | \(-0.568441\pi\) | ||||
−0.213362 | + | 0.976973i | \(0.568441\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −102.124 | −0.338305 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 306.371 | 0.950826 | 0.475413 | − | 0.879763i | \(-0.342299\pi\) | ||||
0.475413 | + | 0.879763i | \(0.342299\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −15.4020 | −0.0449038 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 46.6703 | 0.128140 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −115.825 | −0.300184 | −0.150092 | − | 0.988672i | \(-0.547957\pi\) | ||||
−0.150092 | + | 0.988672i | \(0.547957\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 212.873 | 0.521887 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −62.2234 | −0.144591 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −161.680 | −0.356762 | −0.178381 | − | 0.983961i | \(-0.557086\pi\) | ||||
−0.178381 | + | 0.983961i | \(0.557086\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −274.571 | −0.576314 | −0.288157 | − | 0.957583i | \(-0.593043\pi\) | ||||
−0.288157 | + | 0.957583i | \(0.593043\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 294.571 | 0.589086 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 19.2990 | 0.0368269 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −81.6254 | −0.148838 | −0.0744189 | − | 0.997227i | \(-0.523710\pi\) | ||||
−0.0744189 | + | 0.997227i | \(0.523710\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −373.577 | −0.651789 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 773.492 | 1.29291 | 0.646455 | − | 0.762952i | \(-0.276251\pi\) | ||||
0.646455 | + | 0.762952i | \(0.276251\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 148.794 | 0.238562 | 0.119281 | − | 0.992861i | \(-0.461941\pi\) | ||||
0.119281 | + | 0.992861i | \(0.461941\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 280.416 | 0.431729 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −614.021 | −0.908755 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −557.341 | −0.793743 | −0.396872 | − | 0.917874i | \(-0.629904\pi\) | ||||
−0.396872 | + | 0.917874i | \(0.629904\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −24.7043 | −0.0338879 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −768.337 | −1.01610 | −0.508048 | − | 0.861329i | \(-0.669633\pi\) | ||||
−0.508048 | + | 0.861329i | \(0.669633\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −89.4228 | −0.114109 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −113.069 | −0.139336 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 457.884 | 0.545344 | 0.272672 | − | 0.962107i | \(-0.412093\pi\) | ||||
0.272672 | + | 0.962107i | \(0.412093\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −55.6670 | −0.0641262 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −352.701 | −0.393262 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 119.223 | 0.128759 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1500.82 | −1.57098 | −0.785490 | − | 0.618874i | \(-0.787589\pi\) | ||||
−0.785490 | + | 0.618874i | \(0.787589\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −552.117 | −0.560504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1731.06 | 1.70541 | 0.852707 | − | 0.522389i | \(-0.174959\pi\) | ||||
0.852707 | + | 0.522389i | \(0.174959\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1887.77 | −1.80590 | −0.902951 | − | 0.429743i | \(-0.858604\pi\) | ||||
−0.902951 | + | 0.429743i | \(0.858604\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 371.945 | 0.345697 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 411.468 | 0.371758 | 0.185879 | − | 0.982573i | \(-0.440487\pi\) | ||||
0.185879 | + | 0.982573i | \(0.440487\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1186.86 | −1.04294 | −0.521469 | − | 0.853270i | \(-0.674616\pi\) | ||||
−0.521469 | + | 0.853270i | \(0.674616\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −595.045 | −0.508821 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 509.478 | 0.424139 | 0.212069 | − | 0.977255i | \(-0.431980\pi\) | ||||
0.212069 | + | 0.977255i | \(0.431980\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 715.794 | 0.580419 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −50.0548 | −0.0395519 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 257.935 | 0.198697 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −180.134 | −0.135337 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1456.50 | 1.06771 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1321.66 | −0.945701 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1169.71 | −0.817284 | −0.408642 | − | 0.912695i | \(-0.633998\pi\) | ||||
−0.408642 | + | 0.912695i | \(0.633998\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 394.048 | 0.268946 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1052.31 | 0.701838 | 0.350919 | − | 0.936406i | \(-0.385869\pi\) | ||||
0.350919 | + | 0.936406i | \(0.385869\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −343.894 | −0.224206 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 889.292 | 0.566949 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2116.92 | −1.32015 | −0.660075 | − | 0.751200i | \(-0.729476\pi\) | ||||
−0.660075 | + | 0.751200i | \(0.729476\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1115.90 | 0.680929 | 0.340464 | − | 0.940257i | \(-0.389416\pi\) | ||||
0.340464 | + | 0.940257i | \(0.389416\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1003.34 | −0.599266 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 104.337 | 0.0610148 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 216.646 | 0.124079 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 50.4402 | 0.0283010 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −472.693 | −0.259896 | −0.129948 | − | 0.991521i | \(-0.541481\pi\) | ||||
−0.129948 | + | 0.991521i | \(0.541481\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1635.40 | −0.881372 | −0.440686 | − | 0.897661i | \(-0.645265\pi\) | ||||
−0.440686 | + | 0.897661i | \(0.645265\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 231.931 | 0.122552 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 675.794 | 0.350201 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 785.904 | 0.399503 | 0.199751 | − | 0.979847i | \(-0.435987\pi\) | ||||
0.199751 | + | 0.979847i | \(0.435987\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 379.316 | 0.189193 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2064.67 | −1.01068 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1224.95 | −0.588623 | −0.294311 | − | 0.955710i | \(-0.595090\pi\) | ||||
−0.294311 | + | 0.955710i | \(0.595090\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −697.141 | −0.328923 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1071.26 | 0.496386 | 0.248193 | − | 0.968711i | \(-0.420163\pi\) | ||||
0.248193 | + | 0.968711i | \(0.420163\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2187.54 | −0.995694 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −309.223 | −0.138286 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −825.821 | −0.362925 | −0.181462 | − | 0.983398i | \(-0.558083\pi\) | ||||
−0.181462 | + | 0.983398i | \(0.558083\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1549.79 | 0.669447 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 529.489 | 0.224852 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 465.802 | 0.194501 | 0.0972506 | − | 0.995260i | \(-0.468995\pi\) | ||||
0.0972506 | + | 0.995260i | \(0.468995\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1214.74 | 0.498847 | 0.249423 | − | 0.968395i | \(-0.419759\pi\) | ||||
0.249423 | + | 0.968395i | \(0.419759\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 899.196 | 0.363227 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1140.14 | 0.453106 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −483.451 | −0.189056 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2565.12 | −0.987221 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 154.943 | 0.0586980 | 0.0293490 | − | 0.999569i | \(-0.490657\pi\) | ||||
0.0293490 | + | 0.999569i | \(0.490657\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2776.64 | −1.03558 | −0.517790 | − | 0.855508i | \(-0.673245\pi\) | ||||
−0.517790 | + | 0.855508i | \(0.673245\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −63.2026 | −0.0232104 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4865.09 | −1.75951 | −0.879754 | − | 0.475429i | \(-0.842293\pi\) | ||||
−0.879754 | + | 0.475429i | \(0.842293\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3014.43 | −1.07381 | −0.536903 | − | 0.843644i | \(-0.680406\pi\) | ||||
−0.536903 | + | 0.843644i | \(0.680406\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 267.316 | 0.0938062 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −624.905 | −0.216058 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2790.72 | −0.950793 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1856.52 | −0.623366 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 644.564 | 0.213327 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3434.46 | −1.12056 | −0.560280 | − | 0.828303i | \(-0.689307\pi\) | ||||
−0.560280 | + | 0.828303i | \(0.689307\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2533.12 | −0.814867 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −755.017 | −0.239497 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1949.29 | −0.609800 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −487.288 | −0.150356 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −43.8296 | −0.0133407 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2247.73 | −0.674975 | −0.337488 | − | 0.941330i | \(-0.609577\pi\) | ||||
−0.337488 | + | 0.941330i | \(0.609577\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1393.55 | 0.412903 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1883.81 | −0.550806 | −0.275403 | − | 0.961329i | \(-0.588811\pi\) | ||||
−0.275403 | + | 0.961329i | \(0.588811\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3594.49 | −1.03725 | −0.518626 | − | 0.855001i | \(-0.673556\pi\) | ||||
−0.518626 | + | 0.855001i | \(0.673556\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2010.87 | 0.572750 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5530.01 | −1.55486 | −0.777431 | − | 0.628968i | \(-0.783478\pi\) | ||||
−0.777431 | + | 0.628968i | \(0.783478\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1922.45 | 0.533647 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1825.24 | 0.500263 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2587.82 | 0.700387 | 0.350193 | − | 0.936677i | \(-0.386116\pi\) | ||||
0.350193 | + | 0.936677i | \(0.386116\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3576.45 | −0.955932 | −0.477966 | − | 0.878378i | \(-0.658626\pi\) | ||||
−0.477966 | + | 0.878378i | \(0.658626\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3745.58 | −0.988804 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −96.6462 | −0.0252020 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 58.4360 | 0.0150534 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2516.24 | 0.640403 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5966.87 | −1.50050 | −0.750251 | − | 0.661154i | \(-0.770067\pi\) | ||||
−0.750251 | + | 0.661154i | \(0.770067\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3869.84 | 0.961638 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 292.852 | 0.0719181 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3841.01 | 0.932278 | 0.466139 | − | 0.884712i | \(-0.345645\pi\) | ||||
0.466139 | + | 0.884712i | \(0.345645\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3288.67 | −0.788988 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −561.904 | −0.133260 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3956.41 | 0.927614 | 0.463807 | − | 0.885936i | \(-0.346483\pi\) | ||||
0.463807 | + | 0.885936i | \(0.346483\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −726.791 | −0.168477 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1499.53 | −0.343707 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2158.66 | −0.489279 | −0.244639 | − | 0.969614i | \(-0.578670\pi\) | ||||
−0.244639 | + | 0.969614i | \(0.578670\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2321.77 | −0.520435 | −0.260217 | − | 0.965550i | \(-0.583794\pi\) | ||||
−0.260217 | + | 0.965550i | \(0.583794\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 182.305 | 0.0404161 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2904.79 | −0.636966 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6184.24 | 1.34143 | 0.670713 | − | 0.741717i | \(-0.265988\pi\) | ||||
0.670713 | + | 0.741717i | \(0.265988\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1752.77 | −0.376113 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7981.21 | −1.69437 | −0.847187 | − | 0.531294i | \(-0.821706\pi\) | ||||
−0.847187 | + | 0.531294i | \(0.821706\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4851.71 | 1.01910 | 0.509548 | − | 0.860442i | \(-0.329813\pi\) | ||||
0.509548 | + | 0.860442i | \(0.329813\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −390.447 | −0.0811511 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8049.69 | 1.65560 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4709.91 | −0.958664 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4915.06 | 0.990123 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1269.75 | 0.253172 | 0.126586 | − | 0.991956i | \(-0.459598\pi\) | ||||
0.126586 | + | 0.991956i | \(0.459598\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1014.53 | −0.200231 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4807.83 | 0.939322 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 350.838 | 0.0678579 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2177.81 | 0.417032 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5669.08 | −1.07485 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1722.91 | −0.323454 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9699.35 | 1.80316 | 0.901581 | − | 0.432610i | \(-0.142407\pi\) | ||||
0.901581 | + | 0.432610i | \(0.142407\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6182.30 | 1.13818 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −323.284 | −0.0589446 | −0.0294723 | − | 0.999566i | \(-0.509383\pi\) | ||||
−0.0294723 | + | 0.999566i | \(0.509383\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3251.29 | −0.587137 | −0.293569 | − | 0.955938i | \(-0.594843\pi\) | ||||
−0.293569 | + | 0.955938i | \(0.594843\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1848.41 | 0.330622 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7512.25 | 1.33101 | 0.665505 | − | 0.746393i | \(-0.268216\pi\) | ||||
0.665505 | + | 0.746393i | \(0.268216\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1171.27 | 0.205575 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1347.52 | −0.234303 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −270.766 | −0.0466434 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −263.348 | −0.0449474 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3886.86 | 0.657320 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5545.22 | −0.929233 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2857.14 | −0.474449 | −0.237225 | − | 0.971455i | \(-0.576238\pi\) | ||||
−0.237225 | + | 0.971455i | \(0.576238\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2957.11 | −0.486633 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −512.193 | −0.0835346 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10635.9 | 1.71921 | 0.859606 | − | 0.510958i | \(-0.170709\pi\) | ||||
0.859606 | + | 0.510958i | \(0.170709\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1668.50 | −0.267317 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3653.58 | 0.580213 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6486.96 | 1.02117 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2344.17 | −0.365814 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8357.08 | 1.29289 | 0.646443 | − | 0.762962i | \(-0.276256\pi\) | ||||
0.646443 | + | 0.762962i | \(0.276256\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7741.28 | −1.18734 | −0.593669 | − | 0.804709i | \(-0.702321\pi\) | ||||
−0.593669 | + | 0.804709i | \(0.702321\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 435.877 | 0.0662831 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2480.46 | 0.373999 | 0.186999 | − | 0.982360i | \(-0.440124\pi\) | ||||
0.186999 | + | 0.982360i | \(0.440124\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4853.60 | 0.725640 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −844.717 | −0.125230 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4310.17 | 0.633655 | 0.316827 | − | 0.948483i | \(-0.397382\pi\) | ||||
0.316827 | + | 0.948483i | \(0.397382\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 361.000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 589.923 | 0.0852973 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 933.670 | 0.133892 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8484.71 | −1.20681 | −0.603404 | − | 0.797436i | \(-0.706189\pi\) | ||||
−0.603404 | + | 0.797436i | \(0.706189\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 7238.15 | 1.02115 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2096.39 | 0.293367 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8039.16 | −1.11596 | −0.557978 | − | 0.829855i | \(-0.688423\pi\) | ||||
−0.557978 | + | 0.829855i | \(0.688423\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4328.32 | 0.596036 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 106.187 | 0.0145063 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2976.22 | 0.403372 | 0.201686 | − | 0.979450i | \(-0.435358\pi\) | ||||
0.201686 | + | 0.979450i | \(0.435358\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3830.71 | 0.515100 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5118.15 | −0.682834 | −0.341417 | − | 0.939912i | \(-0.610907\pi\) | ||||
−0.341417 | + | 0.939912i | \(0.610907\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3852.93 | −0.510035 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1958.25 | 0.257218 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6758.74 | 0.880929 | 0.440465 | − | 0.897770i | \(-0.354814\pi\) | ||||
0.440465 | + | 0.897770i | \(0.354814\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1625.62 | −0.210259 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3446.23 | −0.442339 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3497.27 | −0.445485 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14529.0 | −1.83675 | −0.918373 | − | 0.395716i | \(-0.870496\pi\) | ||||
−0.918373 | + | 0.395716i | \(0.870496\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1126.22 | 0.141308 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12416.4 | 1.54625 | 0.773124 | − | 0.634255i | \(-0.218693\pi\) | ||||
0.773124 | + | 0.634255i | \(0.218693\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 331.233 | 0.0409426 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −155.017 | −0.0190195 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6163.99 | 0.750707 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11615.8 | 1.40432 | 0.702159 | − | 0.712020i | \(-0.252220\pi\) | ||||
0.702159 | + | 0.712020i | \(0.252220\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6932.73 | 0.832035 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2926.36 | 0.348660 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4821.25 | −0.570279 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3654.47 | −0.429161 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16739.9 | −1.95179 | −0.975893 | − | 0.218248i | \(-0.929966\pi\) | ||||
−0.975893 | + | 0.218248i | \(0.929966\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6261.41 | −0.724852 | −0.362426 | − | 0.932013i | \(-0.618051\pi\) | ||||
−0.362426 | + | 0.932013i | \(0.618051\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4986.17 | −0.573134 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1220.23 | 0.139271 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4969.64 | 0.563226 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −341.696 | −0.0384551 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8893.01 | −0.993878 | −0.496939 | − | 0.867786i | \(-0.665543\pi\) | ||||
−0.496939 | + | 0.867786i | \(0.665543\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6326.61 | 0.702166 | 0.351083 | − | 0.936344i | \(-0.385814\pi\) | ||||
0.351083 | + | 0.936344i | \(0.385814\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −709.498 | −0.0782019 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2167.37 | 0.237253 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15823.4 | 1.72030 | 0.860149 | − | 0.510043i | \(-0.170370\pi\) | ||||
0.860149 | + | 0.510043i | \(0.170370\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 250.666 | 0.0270668 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14056.3 | 1.50753 | 0.753763 | − | 0.657147i | \(-0.228237\pi\) | ||||
0.753763 | + | 0.657147i | \(0.228237\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2873.18 | 0.306072 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1548.03 | 0.163802 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15412.9 | 1.62000 | 0.809999 | − | 0.586431i | \(-0.199468\pi\) | ||||
0.809999 | + | 0.586431i | \(0.199468\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −15087.6 | −1.57527 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5355.81 | 0.555492 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −349.306 | −0.0359906 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13336.9 | 1.36515 | 0.682573 | − | 0.730817i | \(-0.260861\pi\) | ||||
0.682573 | + | 0.730817i | \(0.260861\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2019.65 | −0.205380 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10226.9 | 1.03322 | 0.516612 | − | 0.856220i | \(-0.327193\pi\) | ||||
0.516612 | + | 0.856220i | \(0.327193\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17797.4 | −1.78642 | −0.893212 | − | 0.449636i | \(-0.851554\pi\) | ||||
−0.893212 | + | 0.449636i | \(0.851554\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2213.17 | −0.220717 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3100.03 | 0.307179 | 0.153589 | − | 0.988135i | \(-0.450917\pi\) | ||||
0.153589 | + | 0.988135i | \(0.450917\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1477.39 | 0.145458 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2573.77 | −0.251790 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4081.89 | −0.396798 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1626.88 | −0.157151 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1885.04 | 0.180943 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6280.67 | 0.599105 | 0.299552 | − | 0.954080i | \(-0.403163\pi\) | ||||
0.299552 | + | 0.954080i | \(0.403163\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 558.826 | 0.0529735 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6761.62 | 0.636987 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −9417.52 | −0.881706 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7940.07 | 0.738807 | 0.369403 | − | 0.929269i | \(-0.379562\pi\) | ||||
0.369403 | + | 0.929269i | \(0.379562\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4011.61 | 0.370984 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17276.3 | −1.58792 | −0.793959 | − | 0.607971i | \(-0.791984\pi\) | ||||
−0.793959 | + | 0.607971i | \(0.791984\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −492.020 | −0.0449482 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3464.49 | −0.314580 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −13999.9 | −1.26355 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14939.6 | −1.34026 | −0.670128 | − | 0.742246i | \(-0.733761\pi\) | ||||
−0.670128 | + | 0.742246i | \(0.733761\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3508.28 | −0.312851 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5559.39 | −0.492805 | −0.246402 | − | 0.969168i | \(-0.579248\pi\) | ||||
−0.246402 | + | 0.969168i | \(0.579248\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10862.3 | 0.957157 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7164.02 | 0.627545 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −11029.4 | −0.960452 | −0.480226 | − | 0.877145i | \(-0.659445\pi\) | ||||
−0.480226 | + | 0.877145i | \(0.659445\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2693.12 | −0.233144 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2692.71 | 0.231747 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11845.6 | −1.01355 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10393.5 | 0.884147 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2704.49 | 0.228736 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7802.02 | −0.656070 | −0.328035 | − | 0.944665i | \(-0.606386\pi\) | ||||
−0.328035 | + | 0.944665i | \(0.606386\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 23625.2 | 1.97525 | 0.987627 | − | 0.156820i | \(-0.0501241\pi\) | ||||
0.987627 | + | 0.156820i | \(0.0501241\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5075.44 | −0.421924 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1534.78 | −0.126862 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 845.482 | 0.0694898 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2631.33 | 0.215047 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1367.84 | −0.111159 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2581.93 | 0.208647 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1525.46 | −0.122586 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −522.503 | −0.0417548 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 24753.3 | 1.96715 | 0.983573 | − | 0.180509i | \(-0.0577744\pi\) | ||||
0.983573 | + | 0.180509i | \(0.0577744\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3978.19 | −0.314402 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7447.43 | −0.585344 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5655.38 | −0.442060 | −0.221030 | − | 0.975267i | \(-0.570942\pi\) | ||||
−0.221030 | + | 0.975267i | \(0.570942\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4468.61 | 0.347388 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 655.989 | 0.0507188 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10087.7 | 0.775717 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3733.86 | −0.285574 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14716.3 | 1.11948 | 0.559741 | − | 0.828668i | \(-0.310901\pi\) | ||||
0.559741 | + | 0.828668i | \(0.310901\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −370.063 | −0.0280000 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1583.26 | 0.119154 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4400.91 | 0.329443 | 0.164721 | − | 0.986340i | \(-0.447328\pi\) | ||||
0.164721 | + | 0.986340i | \(0.447328\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3196.94 | 0.238046 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 447.140 | 0.0331183 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10176.3 | 0.749758 | 0.374879 | − | 0.927074i | \(-0.377684\pi\) | ||||
0.374879 | + | 0.927074i | \(0.377684\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6775.74 | −0.496595 | −0.248298 | − | 0.968684i | \(-0.579871\pi\) | ||||
−0.248298 | + | 0.968684i | \(0.579871\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −507.427 | −0.0369949 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9767.49 | −0.708404 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3714.70 | −0.268016 | −0.134008 | − | 0.990980i | \(-0.542785\pi\) | ||||
−0.134008 | + | 0.990980i | \(0.542785\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9093.26 | 0.652683 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13906.6 | 0.993021 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3929.29 | −0.279133 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −314.090 | −0.0221983 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9362.24 | 0.658298 | 0.329149 | − | 0.944278i | \(-0.393238\pi\) | ||||
0.329149 | + | 0.944278i | \(0.393238\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2046.26 | 0.143149 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 15932.8 | 1.10894 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −14437.5 | −0.999793 | −0.499897 | − | 0.866085i | \(-0.666629\pi\) | ||||
−0.499897 | + | 0.866085i | \(0.666629\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1618.52 | 0.111518 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9872.02 | 0.676775 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −19992.7 | −1.36374 | −0.681871 | − | 0.731473i | \(-0.738833\pi\) | ||||
−0.681871 | + | 0.731473i | \(0.738833\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17371.4 | 1.17902 | 0.589511 | − | 0.807760i | \(-0.299320\pi\) | ||||
0.589511 | + | 0.807760i | \(0.299320\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1328.45 | 0.0897157 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1130.32 | −0.0759574 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14626.3 | −0.978025 | −0.489013 | − | 0.872277i | \(-0.662643\pi\) | ||||
−0.489013 | + | 0.872277i | \(0.662643\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2046.51 | 0.136172 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 942.269 | 0.0623897 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21052.2 | 1.38710 | 0.693549 | − | 0.720409i | \(-0.256046\pi\) | ||||
0.693549 | + | 0.720409i | \(0.256046\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 9139.39 | 0.599245 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1605.72 | 0.104771 | 0.0523855 | − | 0.998627i | \(-0.483318\pi\) | ||||
0.0523855 | + | 0.998627i | \(0.483318\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −21457.6 | −1.39330 | −0.696652 | − | 0.717410i | \(-0.745328\pi\) | ||||
−0.696652 | + | 0.717410i | \(0.745328\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 16166.5 | 1.04467 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8287.54 | −0.532959 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2409.89 | 0.154233 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2110.89 | −0.134451 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2589.34 | −0.164140 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9732.44 | 0.614013 | 0.307007 | − | 0.951707i | \(-0.400673\pi\) | ||||
0.307007 | + | 0.951707i | \(0.400673\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 11247.6 | 0.706242 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7339.84 | −0.458697 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −47.3700 | −0.00294642 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −12588.5 | −0.779333 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −25594.0 | −1.57707 | −0.788536 | − | 0.614989i | \(-0.789161\pi\) | ||||
−0.788536 | + | 0.614989i | \(0.789161\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11938.5 | 0.732207 | 0.366104 | − | 0.930574i | \(-0.380692\pi\) | ||||
0.366104 | + | 0.930574i | \(0.380692\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2472.62 | 0.150945 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 15685.4 | 0.953105 | 0.476552 | − | 0.879146i | \(-0.341886\pi\) | ||||
0.476552 | + | 0.879146i | \(0.341886\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5484.91 | −0.331743 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6383.77 | 0.384331 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11414.3 | −0.684037 | −0.342019 | − | 0.939693i | \(-0.611111\pi\) | ||||
−0.342019 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6603.16 | 0.393903 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2421.61 | −0.143799 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −24500.2 | −1.44824 | −0.724122 | − | 0.689672i | \(-0.757755\pi\) | ||||
−0.724122 | + | 0.689672i | \(0.757755\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24821.0 | −1.46055 | −0.730276 | − | 0.683152i | \(-0.760609\pi\) | ||||
−0.730276 | + | 0.683152i | \(0.760609\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 143.538 | 0.00840808 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2157.90 | −0.125835 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3938.43 | 0.228631 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7361.14 | 0.425408 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9314.65 | −0.535899 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14862.9 | −0.851297 | −0.425649 | − | 0.904888i | \(-0.639954\pi\) | ||||
−0.425649 | + | 0.904888i | \(0.639954\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −12135.0 | −0.691964 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1218.79 | 0.0691902 | 0.0345951 | − | 0.999401i | \(-0.488986\pi\) | ||||
0.0345951 | + | 0.999401i | \(0.488986\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 27164.3 | 1.53530 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6169.33 | 0.347150 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 10180.0 | 0.570319 | 0.285159 | − | 0.958480i | \(-0.407953\pi\) | ||||
0.285159 | + | 0.958480i | \(0.407953\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13283.5 | −0.740929 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 11771.7 | 0.653736 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −356.228 | −0.0196970 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13712.9 | −0.754941 | −0.377470 | − | 0.926022i | \(-0.623206\pi\) | ||||
−0.377470 | + | 0.926022i | \(0.623206\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 9993.14 | 0.547775 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7002.16 | 0.382168 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6337.95 | 0.344429 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 18110.3 | 0.979964 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 29853.2 | 1.60848 | 0.804238 | − | 0.594307i | \(-0.202574\pi\) | ||||
0.804238 | + | 0.594307i | \(0.202574\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3452.26 | 0.185212 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6295.88 | −0.336335 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −31331.6 | −1.66669 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11488.4 | 0.608541 | 0.304271 | − | 0.952586i | \(-0.401587\pi\) | ||||
0.304271 | + | 0.952586i | \(0.401587\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9070.67 | 0.478448 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 12285.3 | 0.645286 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 654.708 | 0.0342443 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −8474.91 | −0.441424 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −17536.5 | −0.909596 | −0.454798 | − | 0.890595i | \(-0.650289\pi\) | ||||
−0.454798 | + | 0.890595i | \(0.650289\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 34168.1 | 1.76489 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 11712.6 | 0.602484 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2956.28 | −0.151439 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 27607.0 | 1.40837 | 0.704185 | − | 0.710016i | \(-0.251312\pi\) | ||||
0.704185 | + | 0.710016i | \(0.251312\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 12933.5 | 0.657089 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1714.70 | 0.0867587 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3519.63 | 0.177354 | 0.0886770 | − | 0.996060i | \(-0.471736\pi\) | ||||
0.0886770 | + | 0.996060i | \(0.471736\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 316.508 | 0.0158838 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2769.09 | −0.138400 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4557.41 | −0.226857 | −0.113428 | − | 0.993546i | \(-0.536183\pi\) | ||||
−0.113428 | + | 0.993546i | \(0.536183\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −191.373 | −0.00948754 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5330.53 | 0.263201 | 0.131600 | − | 0.991303i | \(-0.457988\pi\) | ||||
0.131600 | + | 0.991303i | \(0.457988\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2966.11 | −0.145866 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12504.6 | 0.612477 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7447.43 | −0.363315 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22386.8 | 1.08776 | 0.543879 | − | 0.839163i | \(-0.316955\pi\) | ||||
0.543879 | + | 0.839163i | \(0.316955\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 19541.0 | 0.945703 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −10262.0 | −0.494666 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −25315.6 | −1.21547 | −0.607736 | − | 0.794139i | \(-0.707922\pi\) | ||||
−0.607736 | + | 0.794139i | \(0.707922\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −12673.4 | −0.606080 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18715.0 | −0.891485 | −0.445742 | − | 0.895161i | \(-0.647060\pi\) | ||||
−0.445742 | + | 0.895161i | \(0.647060\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 21481.7 | 1.01925 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1455.35 | 0.0687820 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −497.260 | −0.0234094 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20985.3 | 0.984070 | 0.492035 | − | 0.870575i | \(-0.336253\pi\) | ||||
0.492035 | + | 0.870575i | \(0.336253\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12579.0 | −0.587576 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −6302.27 | −0.293243 | −0.146622 | − | 0.989193i | \(-0.546840\pi\) | ||||
−0.146622 | + | 0.989193i | \(0.546840\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9221.66 | −0.427422 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 10770.1 | 0.497266 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8450.11 | −0.388648 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 26240.3 | 1.20224 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4893.05 | 0.223325 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4931.48 | 0.224219 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4124.73 | −0.186825 | −0.0934123 | − | 0.995628i | \(-0.529777\pi\) | ||||
−0.0934123 | + | 0.995628i | \(0.529777\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −12956.9 | −0.584636 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9221.39 | −0.414507 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −844.464 | −0.0378156 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2380.18 | 0.106184 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −8090.48 | −0.359573 | −0.179786 | − | 0.983706i | \(-0.557541\pi\) | ||||
−0.179786 | + | 0.983706i | \(0.557541\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4366.04 | −0.193316 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7452.02 | −0.328719 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5047.75 | 0.221832 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −12955.6 | −0.567237 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7069.44 | 0.308372 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −16735.9 | −0.727323 | −0.363662 | − | 0.931531i | \(-0.618474\pi\) | ||||
−0.363662 | + | 0.931531i | \(0.618474\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8476.59 | −0.367020 | −0.183510 | − | 0.983018i | \(-0.558746\pi\) | ||||
−0.183510 | + | 0.983018i | \(0.558746\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7603.62 | 0.328008 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7686.46 | −0.330362 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2286.14 | −0.0978970 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 905.975 | 0.0386537 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −902.399 | −0.0383605 | −0.0191802 | − | 0.999816i | \(-0.506106\pi\) | ||||
−0.0191802 | + | 0.999816i | \(0.506106\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −23266.2 | −0.985431 | −0.492716 | − | 0.870190i | \(-0.663996\pi\) | ||||
−0.492716 | + | 0.870190i | \(0.663996\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 9512.96 | 0.401453 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17103.5 | 0.719160 | 0.359580 | − | 0.933114i | \(-0.382920\pi\) | ||||
0.359580 | + | 0.933114i | \(0.382920\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6125.30 | 0.256623 | 0.128312 | − | 0.991734i | \(-0.459044\pi\) | ||||
0.128312 | + | 0.991734i | \(0.459044\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −20252.9 | −0.845445 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 219.491 | 0.00912955 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6722.05 | 0.278594 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 15263.1 | 0.630311 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 19918.5 | 0.819620 | 0.409810 | − | 0.912171i | \(-0.365595\pi\) | ||||
0.409810 | + | 0.912171i | \(0.365595\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23197.0 | −0.951124 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 26137.8 | 1.06789 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −13726.6 | −0.558829 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3260.36 | 0.132264 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −15889.0 | −0.642294 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 20726.7 | 0.834901 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −18785.3 | −0.754042 | −0.377021 | − | 0.926205i | \(-0.623052\pi\) | ||||
−0.377021 | + | 0.926205i | \(0.623052\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1940.35 | −0.0776124 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −33483.4 | −1.33462 | −0.667311 | − | 0.744779i | \(-0.732555\pi\) | ||||
−0.667311 | + | 0.744779i | \(0.732555\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7322.74 | −0.290860 | −0.145430 | − | 0.989369i | \(-0.546457\pi\) | ||||
−0.145430 | + | 0.989369i | \(0.546457\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −26362.1 | −1.04346 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 905.563 | 0.0357193 | 0.0178596 | − | 0.999841i | \(-0.494315\pi\) | ||||
0.0178596 | + | 0.999841i | \(0.494315\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5181.96 | −0.203690 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 15424.6 | 0.604205 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −18907.5 | −0.738080 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −251.045 | −0.00976619 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 24425.7 | 0.946947 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 23921.6 | 0.924224 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 27155.7 | 1.04559 | 0.522795 | − | 0.852459i | \(-0.324889\pi\) | ||||
0.522795 | + | 0.852459i | \(0.324889\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4158.32 | −0.159564 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 26094.1 | 0.997881 | 0.498941 | − | 0.866636i | \(-0.333723\pi\) | ||||
0.498941 | + | 0.866636i | \(0.333723\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −29674.6 | −1.13095 | −0.565476 | − | 0.824765i | \(-0.691307\pi\) | ||||
−0.565476 | + | 0.824765i | \(0.691307\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3322.50 | 0.126197 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1734.72 | −0.0656665 | −0.0328333 | − | 0.999461i | \(-0.510453\pi\) | ||||
−0.0328333 | + | 0.999461i | \(0.510453\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 21171.4 | 0.798724 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −838.079 | −0.0315115 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5821.05 | 0.218135 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2922.87 | 0.109163 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1148.97 | −0.0427680 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3718.34 | 0.137946 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1650.60 | 0.0610315 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7132.14 | −0.262838 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7622.42 | 0.279975 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6755.01 | −0.247295 | −0.123647 | − | 0.992326i | \(-0.539459\pi\) | ||||
−0.123647 | + | 0.992326i | \(0.539459\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −28172.9 | −1.02798 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −35150.7 | −1.27837 | −0.639184 | − | 0.769054i | \(-0.720728\pi\) | ||||
−0.639184 | + | 0.769054i | \(0.720728\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −26065.4 | −0.944840 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5642.38 | 0.203859 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −19046.5 | −0.685899 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −28684.2 | −1.02960 | −0.514802 | − | 0.857309i | \(-0.672134\pi\) | ||||
−0.514802 | + | 0.857309i | \(0.672134\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −31764.6 | −1.13646 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2378.94 | 0.0848360 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15557.9 | −0.553018 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 30723.4 | 1.08855 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3762.58 | −0.132881 | −0.0664405 | − | 0.997790i | \(-0.521164\pi\) | ||||
−0.0664405 | + | 0.997790i | \(0.521164\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −292.638 | −0.0103016 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1058.73 | 0.0371503 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3033.62 | −0.106107 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 25465.7 | 0.887863 | 0.443932 | − | 0.896061i | \(-0.353583\pi\) | ||||
0.443932 | + | 0.896061i | \(0.353583\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 10647.7 | 0.370048 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −40865.6 | −1.41571 | −0.707854 | − | 0.706359i | \(-0.750337\pi\) | ||||
−0.707854 | + | 0.706359i | \(0.750337\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −50732.8 | −1.75195 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −16095.9 | −0.554074 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8047.62 | 0.276148 | 0.138074 | − | 0.990422i | \(-0.455909\pi\) | ||||
0.138074 | + | 0.990422i | \(0.455909\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 457.628 | 0.0156536 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −24602.0 | −0.838880 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −21562.2 | −0.732915 | −0.366458 | − | 0.930435i | \(-0.619430\pi\) | ||||
−0.366458 | + | 0.930435i | \(0.619430\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 972.257 | 0.0329440 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3835.80 | −0.129565 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 38315.5 | 1.29017 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −18192.2 | −0.610661 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6696.60 | −0.224086 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −17423.2 | −0.581215 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −14667.4 | −0.487767 | −0.243883 | − | 0.969805i | \(-0.578421\pi\) | ||||
−0.243883 | + | 0.969805i | \(0.578421\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 886.735 | 0.0293974 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 60154.7 | 1.98811 | 0.994056 | − | 0.108867i | \(-0.0347221\pi\) | ||||
0.994056 | + | 0.108867i | \(0.0347221\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −20197.4 | −0.665465 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 862.442 | 0.0283285 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −29474.6 | −0.965176 | −0.482588 | − | 0.875848i | \(-0.660303\pi\) | ||||
−0.482588 | + | 0.875848i | \(0.660303\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15533.4 | 0.507100 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 19316.0 | 0.628657 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6813.42 | 0.221073 | 0.110536 | − | 0.993872i | \(-0.464743\pi\) | ||||
0.110536 | + | 0.993872i | \(0.464743\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −30528.0 | −0.987517 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 18160.1 | 0.585657 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −13725.5 | −0.441301 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11660.9 | −0.373786 | −0.186893 | − | 0.982380i | \(-0.559842\pi\) | ||||
−0.186893 | + | 0.982380i | \(0.559842\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 9356.91 | 0.299026 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −18915.3 | −0.602669 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 37537.3 | 1.19240 | 0.596198 | − | 0.802838i | \(-0.296677\pi\) | ||||
0.596198 | + | 0.802838i | \(0.296677\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 25750.5 | 0.815526 |
(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 | 1216.4.a.m.1.1 | 2 | ||
4.3 | odd | 2 | 1216.4.a.k.1.2 | 2 | |||
8.3 | odd | 2 | 304.4.a.e.1.1 | 2 | |||
8.5 | even | 2 | 152.4.a.a.1.2 | ✓ | 2 | ||
24.5 | odd | 2 | 1368.4.a.a.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
152.4.a.a.1.2 | ✓ | 2 | 8.5 | even | 2 | ||
304.4.a.e.1.1 | 2 | 8.3 | odd | 2 | |||
1216.4.a.k.1.2 | 2 | 4.3 | odd | 2 | |||
1216.4.a.m.1.1 | 2 | 1.1 | even | 1 | trivial | ||
1368.4.a.a.1.2 | 2 | 24.5 | odd | 2 |