Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2205,4,Mod(1,2205)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2205, 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("2205.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2205.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: | \(130.099211563\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 35) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 2205.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.353553 | −0.176777 | − | 0.984251i | \(-0.556567\pi\) | ||||
−0.176777 | + | 0.984251i | \(0.556567\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −7.00000 | −0.875000 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 15.0000 | 0.662913 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 5.00000 | 0.158114 | ||||||||
\(11\) | −12.0000 | −0.328921 | −0.164461 | − | 0.986384i | \(-0.552588\pi\) | ||||
−0.164461 | + | 0.986384i | \(0.552588\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 78.0000 | 1.66410 | 0.832050 | − | 0.554700i | \(-0.187167\pi\) | ||||
0.832050 | + | 0.554700i | \(0.187167\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 41.0000 | 0.640625 | ||||||||
\(17\) | −94.0000 | −1.34108 | −0.670540 | − | 0.741874i | \(-0.733937\pi\) | ||||
−0.670540 | + | 0.741874i | \(0.733937\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −40.0000 | −0.482980 | −0.241490 | − | 0.970403i | \(-0.577636\pi\) | ||||
−0.241490 | + | 0.970403i | \(0.577636\pi\) | |||||||
\(20\) | 35.0000 | 0.391312 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 12.0000 | 0.116291 | ||||||||
\(23\) | −32.0000 | −0.290107 | −0.145054 | − | 0.989424i | \(-0.546335\pi\) | ||||
−0.145054 | + | 0.989424i | \(0.546335\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | −78.0000 | −0.588348 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 50.0000 | 0.320164 | 0.160082 | − | 0.987104i | \(-0.448824\pi\) | ||||
0.160082 | + | 0.987104i | \(0.448824\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 248.000 | 1.43684 | 0.718421 | − | 0.695608i | \(-0.244865\pi\) | ||||
0.718421 | + | 0.695608i | \(0.244865\pi\) | |||||||
\(32\) | −161.000 | −0.889408 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 94.0000 | 0.474143 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −434.000 | −1.92836 | −0.964178 | − | 0.265257i | \(-0.914543\pi\) | ||||
−0.964178 | + | 0.265257i | \(0.914543\pi\) | |||||||
\(38\) | 40.0000 | 0.170759 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −75.0000 | −0.296464 | ||||||||
\(41\) | 402.000 | 1.53126 | 0.765632 | − | 0.643278i | \(-0.222426\pi\) | ||||
0.765632 | + | 0.643278i | \(0.222426\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −68.0000 | −0.241161 | −0.120580 | − | 0.992704i | \(-0.538476\pi\) | ||||
−0.120580 | + | 0.992704i | \(0.538476\pi\) | |||||||
\(44\) | 84.0000 | 0.287806 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 32.0000 | 0.102568 | ||||||||
\(47\) | 536.000 | 1.66348 | 0.831741 | − | 0.555164i | \(-0.187345\pi\) | ||||
0.831741 | + | 0.555164i | \(0.187345\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −25.0000 | −0.0707107 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −546.000 | −1.45609 | ||||||||
\(53\) | −22.0000 | −0.0570176 | −0.0285088 | − | 0.999594i | \(-0.509076\pi\) | ||||
−0.0285088 | + | 0.999594i | \(0.509076\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 60.0000 | 0.147098 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −50.0000 | −0.113195 | ||||||||
\(59\) | −560.000 | −1.23569 | −0.617846 | − | 0.786299i | \(-0.711994\pi\) | ||||
−0.617846 | + | 0.786299i | \(0.711994\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 278.000 | 0.583512 | 0.291756 | − | 0.956493i | \(-0.405760\pi\) | ||||
0.291756 | + | 0.956493i | \(0.405760\pi\) | |||||||
\(62\) | −248.000 | −0.508001 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −167.000 | −0.326172 | ||||||||
\(65\) | −390.000 | −0.744208 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −164.000 | −0.299042 | −0.149521 | − | 0.988759i | \(-0.547773\pi\) | ||||
−0.149521 | + | 0.988759i | \(0.547773\pi\) | |||||||
\(68\) | 658.000 | 1.17344 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −672.000 | −1.12326 | −0.561632 | − | 0.827387i | \(-0.689826\pi\) | ||||
−0.561632 | + | 0.827387i | \(0.689826\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −82.0000 | −0.131471 | −0.0657354 | − | 0.997837i | \(-0.520939\pi\) | ||||
−0.0657354 | + | 0.997837i | \(0.520939\pi\) | |||||||
\(74\) | 434.000 | 0.681777 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 280.000 | 0.422608 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1000.00 | −1.42416 | −0.712081 | − | 0.702097i | \(-0.752247\pi\) | ||||
−0.712081 | + | 0.702097i | \(0.752247\pi\) | |||||||
\(80\) | −205.000 | −0.286496 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −402.000 | −0.541384 | ||||||||
\(83\) | −448.000 | −0.592463 | −0.296231 | − | 0.955116i | \(-0.595730\pi\) | ||||
−0.296231 | + | 0.955116i | \(0.595730\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 470.000 | 0.599749 | ||||||||
\(86\) | 68.0000 | 0.0852631 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −180.000 | −0.218046 | ||||||||
\(89\) | −870.000 | −1.03618 | −0.518089 | − | 0.855327i | \(-0.673356\pi\) | ||||
−0.518089 | + | 0.855327i | \(0.673356\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 224.000 | 0.253844 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −536.000 | −0.588130 | ||||||||
\(95\) | 200.000 | 0.215995 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1026.00 | −1.07396 | −0.536982 | − | 0.843594i | \(-0.680436\pi\) | ||||
−0.536982 | + | 0.843594i | \(0.680436\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −175.000 | −0.175000 | ||||||||
\(101\) | 482.000 | 0.474859 | 0.237430 | − | 0.971405i | \(-0.423695\pi\) | ||||
0.237430 | + | 0.971405i | \(0.423695\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −272.000 | −0.260203 | −0.130102 | − | 0.991501i | \(-0.541530\pi\) | ||||
−0.130102 | + | 0.991501i | \(0.541530\pi\) | |||||||
\(104\) | 1170.00 | 1.10315 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 22.0000 | 0.0201588 | ||||||||
\(107\) | 444.000 | 0.401150 | 0.200575 | − | 0.979678i | \(-0.435719\pi\) | ||||
0.200575 | + | 0.979678i | \(0.435719\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1170.00 | −1.02813 | −0.514063 | − | 0.857753i | \(-0.671860\pi\) | ||||
−0.514063 | + | 0.857753i | \(0.671860\pi\) | |||||||
\(110\) | −60.0000 | −0.0520071 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 798.000 | 0.664332 | 0.332166 | − | 0.943221i | \(-0.392221\pi\) | ||||
0.332166 | + | 0.943221i | \(0.392221\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 160.000 | 0.129740 | ||||||||
\(116\) | −350.000 | −0.280144 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 560.000 | 0.436883 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1187.00 | −0.891811 | ||||||||
\(122\) | −278.000 | −0.206303 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1736.00 | −1.25724 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 776.000 | 0.542196 | 0.271098 | − | 0.962552i | \(-0.412613\pi\) | ||||
0.271098 | + | 0.962552i | \(0.412613\pi\) | |||||||
\(128\) | 1455.00 | 1.00473 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 390.000 | 0.263117 | ||||||||
\(131\) | 1112.00 | 0.741648 | 0.370824 | − | 0.928703i | \(-0.379075\pi\) | ||||
0.370824 | + | 0.928703i | \(0.379075\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 164.000 | 0.105727 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1410.00 | −0.889018 | ||||||||
\(137\) | 694.000 | 0.432791 | 0.216396 | − | 0.976306i | \(-0.430570\pi\) | ||||
0.216396 | + | 0.976306i | \(0.430570\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −360.000 | −0.219675 | −0.109837 | − | 0.993950i | \(-0.535033\pi\) | ||||
−0.109837 | + | 0.993950i | \(0.535033\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 672.000 | 0.397134 | ||||||||
\(143\) | −936.000 | −0.547358 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −250.000 | −0.143182 | ||||||||
\(146\) | 82.0000 | 0.0464820 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3038.00 | 1.68731 | ||||||||
\(149\) | −2270.00 | −1.24809 | −0.624046 | − | 0.781388i | \(-0.714512\pi\) | ||||
−0.624046 | + | 0.781388i | \(0.714512\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 632.000 | 0.340606 | 0.170303 | − | 0.985392i | \(-0.445525\pi\) | ||||
0.170303 | + | 0.985392i | \(0.445525\pi\) | |||||||
\(152\) | −600.000 | −0.320174 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1240.00 | −0.642575 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 734.000 | 0.373118 | 0.186559 | − | 0.982444i | \(-0.440266\pi\) | ||||
0.186559 | + | 0.982444i | \(0.440266\pi\) | |||||||
\(158\) | 1000.00 | 0.503517 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 805.000 | 0.397755 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2532.00 | 1.21670 | 0.608348 | − | 0.793670i | \(-0.291832\pi\) | ||||
0.608348 | + | 0.793670i | \(0.291832\pi\) | |||||||
\(164\) | −2814.00 | −1.33986 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 448.000 | 0.209467 | ||||||||
\(167\) | 416.000 | 0.192761 | 0.0963804 | − | 0.995345i | \(-0.469273\pi\) | ||||
0.0963804 | + | 0.995345i | \(0.469273\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3887.00 | 1.76923 | ||||||||
\(170\) | −470.000 | −0.212043 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 476.000 | 0.211015 | ||||||||
\(173\) | 3042.00 | 1.33687 | 0.668436 | − | 0.743769i | \(-0.266964\pi\) | ||||
0.668436 | + | 0.743769i | \(0.266964\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −492.000 | −0.210715 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 870.000 | 0.366344 | ||||||||
\(179\) | 180.000 | 0.0751611 | 0.0375805 | − | 0.999294i | \(-0.488035\pi\) | ||||
0.0375805 | + | 0.999294i | \(0.488035\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1958.00 | 0.804072 | 0.402036 | − | 0.915624i | \(-0.368303\pi\) | ||||
0.402036 | + | 0.915624i | \(0.368303\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −480.000 | −0.192316 | ||||||||
\(185\) | 2170.00 | 0.862387 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1128.00 | 0.441110 | ||||||||
\(188\) | −3752.00 | −1.45555 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −200.000 | −0.0763659 | ||||||||
\(191\) | 2888.00 | 1.09408 | 0.547038 | − | 0.837108i | \(-0.315755\pi\) | ||||
0.547038 | + | 0.837108i | \(0.315755\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1602.00 | 0.597484 | 0.298742 | − | 0.954334i | \(-0.403433\pi\) | ||||
0.298742 | + | 0.954334i | \(0.403433\pi\) | |||||||
\(194\) | 1026.00 | 0.379704 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4794.00 | 1.73380 | 0.866899 | − | 0.498483i | \(-0.166109\pi\) | ||||
0.866899 | + | 0.498483i | \(0.166109\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1280.00 | −0.455964 | −0.227982 | − | 0.973665i | \(-0.573213\pi\) | ||||
−0.227982 | + | 0.973665i | \(0.573213\pi\) | |||||||
\(200\) | 375.000 | 0.132583 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −482.000 | −0.167888 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2010.00 | −0.684802 | ||||||||
\(206\) | 272.000 | 0.0919958 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3198.00 | 1.06606 | ||||||||
\(209\) | 480.000 | 0.158863 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −68.0000 | −0.0221863 | −0.0110932 | − | 0.999938i | \(-0.503531\pi\) | ||||
−0.0110932 | + | 0.999938i | \(0.503531\pi\) | |||||||
\(212\) | 154.000 | 0.0498904 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −444.000 | −0.141828 | ||||||||
\(215\) | 340.000 | 0.107850 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1170.00 | 0.363497 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −420.000 | −0.128711 | ||||||||
\(221\) | −7332.00 | −2.23169 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1728.00 | 0.518903 | 0.259452 | − | 0.965756i | \(-0.416458\pi\) | ||||
0.259452 | + | 0.965756i | \(0.416458\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −798.000 | −0.234877 | ||||||||
\(227\) | −4864.00 | −1.42218 | −0.711090 | − | 0.703101i | \(-0.751798\pi\) | ||||
−0.711090 | + | 0.703101i | \(0.751798\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5510.00 | 1.59000 | 0.795002 | − | 0.606606i | \(-0.207470\pi\) | ||||
0.795002 | + | 0.606606i | \(0.207470\pi\) | |||||||
\(230\) | −160.000 | −0.0458699 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 750.000 | 0.212241 | ||||||||
\(233\) | −5322.00 | −1.49638 | −0.748188 | − | 0.663486i | \(-0.769076\pi\) | ||||
−0.748188 | + | 0.663486i | \(0.769076\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2680.00 | −0.743932 | ||||||||
\(236\) | 3920.00 | 1.08123 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1840.00 | 0.497990 | 0.248995 | − | 0.968505i | \(-0.419900\pi\) | ||||
0.248995 | + | 0.968505i | \(0.419900\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 438.000 | 0.117071 | 0.0585354 | − | 0.998285i | \(-0.481357\pi\) | ||||
0.0585354 | + | 0.998285i | \(0.481357\pi\) | |||||||
\(242\) | 1187.00 | 0.315303 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1946.00 | −0.510573 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3120.00 | −0.803728 | ||||||||
\(248\) | 3720.00 | 0.952501 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 125.000 | 0.0316228 | ||||||||
\(251\) | 5592.00 | 1.40623 | 0.703115 | − | 0.711076i | \(-0.251792\pi\) | ||||
0.703115 | + | 0.711076i | \(0.251792\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 384.000 | 0.0954224 | ||||||||
\(254\) | −776.000 | −0.191695 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −119.000 | −0.0290527 | ||||||||
\(257\) | −1974.00 | −0.479123 | −0.239562 | − | 0.970881i | \(-0.577004\pi\) | ||||
−0.239562 | + | 0.970881i | \(0.577004\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 2730.00 | 0.651182 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1112.00 | −0.262212 | ||||||||
\(263\) | 728.000 | 0.170686 | 0.0853430 | − | 0.996352i | \(-0.472801\pi\) | ||||
0.0853430 | + | 0.996352i | \(0.472801\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 110.000 | 0.0254990 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1148.00 | 0.261661 | ||||||||
\(269\) | 5810.00 | 1.31688 | 0.658442 | − | 0.752631i | \(-0.271216\pi\) | ||||
0.658442 | + | 0.752631i | \(0.271216\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6528.00 | 1.46328 | 0.731638 | − | 0.681693i | \(-0.238756\pi\) | ||||
0.731638 | + | 0.681693i | \(0.238756\pi\) | |||||||
\(272\) | −3854.00 | −0.859129 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −694.000 | −0.153015 | ||||||||
\(275\) | −300.000 | −0.0657843 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5126.00 | 1.11188 | 0.555941 | − | 0.831222i | \(-0.312358\pi\) | ||||
0.555941 | + | 0.831222i | \(0.312358\pi\) | |||||||
\(278\) | 360.000 | 0.0776668 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2358.00 | 0.500592 | 0.250296 | − | 0.968169i | \(-0.419472\pi\) | ||||
0.250296 | + | 0.968169i | \(0.419472\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −392.000 | −0.0823392 | −0.0411696 | − | 0.999152i | \(-0.513108\pi\) | ||||
−0.0411696 | + | 0.999152i | \(0.513108\pi\) | |||||||
\(284\) | 4704.00 | 0.982856 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 936.000 | 0.193520 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3923.00 | 0.798494 | ||||||||
\(290\) | 250.000 | 0.0506224 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 574.000 | 0.115037 | ||||||||
\(293\) | 1202.00 | 0.239664 | 0.119832 | − | 0.992794i | \(-0.461764\pi\) | ||||
0.119832 | + | 0.992794i | \(0.461764\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2800.00 | 0.552618 | ||||||||
\(296\) | −6510.00 | −1.27833 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2270.00 | 0.441267 | ||||||||
\(299\) | −2496.00 | −0.482767 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −632.000 | −0.120422 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1640.00 | −0.309409 | ||||||||
\(305\) | −1390.00 | −0.260955 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6384.00 | 1.18682 | 0.593411 | − | 0.804900i | \(-0.297781\pi\) | ||||
0.593411 | + | 0.804900i | \(0.297781\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1240.00 | 0.227185 | ||||||||
\(311\) | −4968.00 | −0.905818 | −0.452909 | − | 0.891557i | \(-0.649614\pi\) | ||||
−0.452909 | + | 0.891557i | \(0.649614\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2758.00 | 0.498056 | 0.249028 | − | 0.968496i | \(-0.419889\pi\) | ||||
0.249028 | + | 0.968496i | \(0.419889\pi\) | |||||||
\(314\) | −734.000 | −0.131917 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7000.00 | 1.24614 | ||||||||
\(317\) | 6274.00 | 1.11162 | 0.555809 | − | 0.831310i | \(-0.312409\pi\) | ||||
0.555809 | + | 0.831310i | \(0.312409\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −600.000 | −0.105309 | ||||||||
\(320\) | 835.000 | 0.145868 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3760.00 | 0.647715 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1950.00 | 0.332820 | ||||||||
\(326\) | −2532.00 | −0.430167 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6030.00 | 1.01509 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1932.00 | 0.320823 | 0.160411 | − | 0.987050i | \(-0.448718\pi\) | ||||
0.160411 | + | 0.987050i | \(0.448718\pi\) | |||||||
\(332\) | 3136.00 | 0.518405 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −416.000 | −0.0681512 | ||||||||
\(335\) | 820.000 | 0.133735 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2386.00 | 0.385679 | 0.192839 | − | 0.981230i | \(-0.438230\pi\) | ||||
0.192839 | + | 0.981230i | \(0.438230\pi\) | |||||||
\(338\) | −3887.00 | −0.625518 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3290.00 | −0.524780 | ||||||||
\(341\) | −2976.00 | −0.472608 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1020.00 | −0.159868 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3042.00 | −0.472656 | ||||||||
\(347\) | −6076.00 | −0.939991 | −0.469995 | − | 0.882669i | \(-0.655744\pi\) | ||||
−0.469995 | + | 0.882669i | \(0.655744\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2210.00 | −0.338964 | −0.169482 | − | 0.985533i | \(-0.554210\pi\) | ||||
−0.169482 | + | 0.985533i | \(0.554210\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1932.00 | 0.292545 | ||||||||
\(353\) | −2598.00 | −0.391721 | −0.195861 | − | 0.980632i | \(-0.562750\pi\) | ||||
−0.195861 | + | 0.980632i | \(0.562750\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3360.00 | 0.502339 | ||||||||
\(356\) | 6090.00 | 0.906655 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −180.000 | −0.0265735 | ||||||||
\(359\) | 13320.0 | 1.95822 | 0.979112 | − | 0.203320i | \(-0.0651731\pi\) | ||||
0.979112 | + | 0.203320i | \(0.0651731\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5259.00 | −0.766730 | ||||||||
\(362\) | −1958.00 | −0.284282 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 410.000 | 0.0587956 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10816.0 | −1.53839 | −0.769197 | − | 0.639012i | \(-0.779344\pi\) | ||||
−0.769197 | + | 0.639012i | \(0.779344\pi\) | |||||||
\(368\) | −1312.00 | −0.185850 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2170.00 | −0.304900 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11098.0 | −1.54057 | −0.770285 | − | 0.637700i | \(-0.779886\pi\) | ||||
−0.770285 | + | 0.637700i | \(0.779886\pi\) | |||||||
\(374\) | −1128.00 | −0.155956 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 8040.00 | 1.10274 | ||||||||
\(377\) | 3900.00 | 0.532786 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7100.00 | 0.962276 | 0.481138 | − | 0.876645i | \(-0.340224\pi\) | ||||
0.481138 | + | 0.876645i | \(0.340224\pi\) | |||||||
\(380\) | −1400.00 | −0.188996 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2888.00 | −0.386814 | ||||||||
\(383\) | −728.000 | −0.0971255 | −0.0485627 | − | 0.998820i | \(-0.515464\pi\) | ||||
−0.0485627 | + | 0.998820i | \(0.515464\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1602.00 | −0.211243 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 7182.00 | 0.939719 | ||||||||
\(389\) | 6810.00 | 0.887611 | 0.443806 | − | 0.896123i | \(-0.353628\pi\) | ||||
0.443806 | + | 0.896123i | \(0.353628\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3008.00 | 0.389057 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −4794.00 | −0.612990 | ||||||||
\(395\) | 5000.00 | 0.636905 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 574.000 | 0.0725648 | 0.0362824 | − | 0.999342i | \(-0.488448\pi\) | ||||
0.0362824 | + | 0.999342i | \(0.488448\pi\) | |||||||
\(398\) | 1280.00 | 0.161208 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1025.00 | 0.128125 | ||||||||
\(401\) | −6162.00 | −0.767371 | −0.383685 | − | 0.923464i | \(-0.625345\pi\) | ||||
−0.383685 | + | 0.923464i | \(0.625345\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 19344.0 | 2.39105 | ||||||||
\(404\) | −3374.00 | −0.415502 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5208.00 | 0.634278 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8210.00 | −0.992563 | −0.496282 | − | 0.868162i | \(-0.665302\pi\) | ||||
−0.496282 | + | 0.868162i | \(0.665302\pi\) | |||||||
\(410\) | 2010.00 | 0.242114 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1904.00 | 0.227678 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2240.00 | 0.264957 | ||||||||
\(416\) | −12558.0 | −1.48006 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −480.000 | −0.0561664 | ||||||||
\(419\) | 4800.00 | 0.559655 | 0.279827 | − | 0.960050i | \(-0.409723\pi\) | ||||
0.279827 | + | 0.960050i | \(0.409723\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9938.00 | −1.15047 | −0.575236 | − | 0.817988i | \(-0.695090\pi\) | ||||
−0.575236 | + | 0.817988i | \(0.695090\pi\) | |||||||
\(422\) | 68.0000 | 0.00784405 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −330.000 | −0.0377977 | ||||||||
\(425\) | −2350.00 | −0.268216 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −3108.00 | −0.351007 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −340.000 | −0.0381308 | ||||||||
\(431\) | 9248.00 | 1.03355 | 0.516776 | − | 0.856121i | \(-0.327132\pi\) | ||||
0.516776 | + | 0.856121i | \(0.327132\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1118.00 | 0.124082 | 0.0620412 | − | 0.998074i | \(-0.480239\pi\) | ||||
0.0620412 | + | 0.998074i | \(0.480239\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8190.00 | 0.899610 | ||||||||
\(437\) | 1280.00 | 0.140116 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11960.0 | 1.30027 | 0.650136 | − | 0.759818i | \(-0.274712\pi\) | ||||
0.650136 | + | 0.759818i | \(0.274712\pi\) | |||||||
\(440\) | 900.000 | 0.0975132 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 7332.00 | 0.789022 | ||||||||
\(443\) | −7332.00 | −0.786352 | −0.393176 | − | 0.919463i | \(-0.628624\pi\) | ||||
−0.393176 | + | 0.919463i | \(0.628624\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4350.00 | 0.463393 | ||||||||
\(446\) | −1728.00 | −0.183460 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1890.00 | −0.198652 | −0.0993259 | − | 0.995055i | \(-0.531669\pi\) | ||||
−0.0993259 | + | 0.995055i | \(0.531669\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4824.00 | −0.503666 | ||||||||
\(452\) | −5586.00 | −0.581291 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4864.00 | 0.502817 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7014.00 | −0.717945 | −0.358973 | − | 0.933348i | \(-0.616873\pi\) | ||||
−0.358973 | + | 0.933348i | \(0.616873\pi\) | |||||||
\(458\) | −5510.00 | −0.562152 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1120.00 | −0.113522 | ||||||||
\(461\) | −8318.00 | −0.840364 | −0.420182 | − | 0.907440i | \(-0.638034\pi\) | ||||
−0.420182 | + | 0.907440i | \(0.638034\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6432.00 | 0.645616 | 0.322808 | − | 0.946464i | \(-0.395373\pi\) | ||||
0.322808 | + | 0.946464i | \(0.395373\pi\) | |||||||
\(464\) | 2050.00 | 0.205105 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5322.00 | 0.529049 | ||||||||
\(467\) | −10064.0 | −0.997230 | −0.498615 | − | 0.866824i | \(-0.666158\pi\) | ||||
−0.498615 | + | 0.866824i | \(0.666158\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 2680.00 | 0.263020 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −8400.00 | −0.819155 | ||||||||
\(473\) | 816.000 | 0.0793229 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1000.00 | −0.0965961 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1840.00 | −0.176066 | ||||||||
\(479\) | 1400.00 | 0.133544 | 0.0667721 | − | 0.997768i | \(-0.478730\pi\) | ||||
0.0667721 | + | 0.997768i | \(0.478730\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −33852.0 | −3.20898 | ||||||||
\(482\) | −438.000 | −0.0413908 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8309.00 | 0.780334 | ||||||||
\(485\) | 5130.00 | 0.480291 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13376.0 | 1.24461 | 0.622304 | − | 0.782775i | \(-0.286197\pi\) | ||||
0.622304 | + | 0.782775i | \(0.286197\pi\) | |||||||
\(488\) | 4170.00 | 0.386818 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7092.00 | −0.651848 | −0.325924 | − | 0.945396i | \(-0.605675\pi\) | ||||
−0.325924 | + | 0.945396i | \(0.605675\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4700.00 | −0.429366 | ||||||||
\(494\) | 3120.00 | 0.284161 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 10168.0 | 0.920477 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −820.000 | −0.0735636 | −0.0367818 | − | 0.999323i | \(-0.511711\pi\) | ||||
−0.0367818 | + | 0.999323i | \(0.511711\pi\) | |||||||
\(500\) | 875.000 | 0.0782624 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −5592.00 | −0.497178 | ||||||||
\(503\) | −4568.00 | −0.404925 | −0.202462 | − | 0.979290i | \(-0.564894\pi\) | ||||
−0.202462 | + | 0.979290i | \(0.564894\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2410.00 | −0.212364 | ||||||||
\(506\) | −384.000 | −0.0337369 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −5432.00 | −0.474421 | ||||||||
\(509\) | 19810.0 | 1.72507 | 0.862537 | − | 0.505994i | \(-0.168874\pi\) | ||||
0.862537 | + | 0.505994i | \(0.168874\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −11521.0 | −0.994455 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1974.00 | 0.169396 | ||||||||
\(515\) | 1360.00 | 0.116367 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6432.00 | −0.547155 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −5850.00 | −0.493345 | ||||||||
\(521\) | −1838.00 | −0.154557 | −0.0772785 | − | 0.997010i | \(-0.524623\pi\) | ||||
−0.0772785 | + | 0.997010i | \(0.524623\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2072.00 | −0.173236 | −0.0866178 | − | 0.996242i | \(-0.527606\pi\) | ||||
−0.0866178 | + | 0.996242i | \(0.527606\pi\) | |||||||
\(524\) | −7784.00 | −0.648942 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −728.000 | −0.0603466 | ||||||||
\(527\) | −23312.0 | −1.92692 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11143.0 | −0.915838 | ||||||||
\(530\) | −110.000 | −0.00901527 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 31356.0 | 2.54818 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2220.00 | −0.179400 | ||||||||
\(536\) | −2460.00 | −0.198238 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −5810.00 | −0.465589 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3498.00 | −0.277987 | −0.138993 | − | 0.990293i | \(-0.544387\pi\) | ||||
−0.138993 | + | 0.990293i | \(0.544387\pi\) | |||||||
\(542\) | −6528.00 | −0.517346 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 15134.0 | 1.19277 | ||||||||
\(545\) | 5850.00 | 0.459792 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5076.00 | 0.396772 | 0.198386 | − | 0.980124i | \(-0.436430\pi\) | ||||
0.198386 | + | 0.980124i | \(0.436430\pi\) | |||||||
\(548\) | −4858.00 | −0.378692 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 300.000 | 0.0232583 | ||||||||
\(551\) | −2000.00 | −0.154633 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −5126.00 | −0.393110 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2520.00 | 0.192215 | ||||||||
\(557\) | 8674.00 | 0.659837 | 0.329918 | − | 0.944009i | \(-0.392979\pi\) | ||||
0.329918 | + | 0.944009i | \(0.392979\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5304.00 | −0.401315 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2358.00 | −0.176986 | ||||||||
\(563\) | 16072.0 | 1.20312 | 0.601558 | − | 0.798829i | \(-0.294547\pi\) | ||||
0.601558 | + | 0.798829i | \(0.294547\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3990.00 | −0.297098 | ||||||||
\(566\) | 392.000 | 0.0291113 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −10080.0 | −0.744626 | ||||||||
\(569\) | −2730.00 | −0.201138 | −0.100569 | − | 0.994930i | \(-0.532066\pi\) | ||||
−0.100569 | + | 0.994930i | \(0.532066\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19932.0 | 1.46082 | 0.730410 | − | 0.683009i | \(-0.239329\pi\) | ||||
0.730410 | + | 0.683009i | \(0.239329\pi\) | |||||||
\(572\) | 6552.00 | 0.478939 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −800.000 | −0.0580214 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20054.0 | 1.44690 | 0.723448 | − | 0.690379i | \(-0.242556\pi\) | ||||
0.723448 | + | 0.690379i | \(0.242556\pi\) | |||||||
\(578\) | −3923.00 | −0.282310 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1750.00 | 0.125284 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 264.000 | 0.0187543 | ||||||||
\(584\) | −1230.00 | −0.0871537 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1202.00 | −0.0847341 | ||||||||
\(587\) | −2544.00 | −0.178879 | −0.0894396 | − | 0.995992i | \(-0.528508\pi\) | ||||
−0.0894396 | + | 0.995992i | \(0.528508\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9920.00 | −0.693967 | ||||||||
\(590\) | −2800.00 | −0.195380 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −17794.0 | −1.23535 | ||||||||
\(593\) | 14202.0 | 0.983484 | 0.491742 | − | 0.870741i | \(-0.336360\pi\) | ||||
0.491742 | + | 0.870741i | \(0.336360\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 15890.0 | 1.09208 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2496.00 | 0.170684 | ||||||||
\(599\) | 19600.0 | 1.33695 | 0.668476 | − | 0.743734i | \(-0.266947\pi\) | ||||
0.668476 | + | 0.743734i | \(0.266947\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 27078.0 | 1.83783 | 0.918914 | − | 0.394458i | \(-0.129068\pi\) | ||||
0.918914 | + | 0.394458i | \(0.129068\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4424.00 | −0.298030 | ||||||||
\(605\) | 5935.00 | 0.398830 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2704.00 | 0.180811 | 0.0904053 | − | 0.995905i | \(-0.471184\pi\) | ||||
0.0904053 | + | 0.995905i | \(0.471184\pi\) | |||||||
\(608\) | 6440.00 | 0.429567 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1390.00 | 0.0922614 | ||||||||
\(611\) | 41808.0 | 2.76820 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12702.0 | 0.836915 | 0.418458 | − | 0.908236i | \(-0.362571\pi\) | ||||
0.418458 | + | 0.908236i | \(0.362571\pi\) | |||||||
\(614\) | −6384.00 | −0.419605 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12666.0 | −0.826441 | −0.413220 | − | 0.910631i | \(-0.635596\pi\) | ||||
−0.413220 | + | 0.910631i | \(0.635596\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −960.000 | −0.0623355 | −0.0311677 | − | 0.999514i | \(-0.509923\pi\) | ||||
−0.0311677 | + | 0.999514i | \(0.509923\pi\) | |||||||
\(620\) | 8680.00 | 0.562254 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 4968.00 | 0.320255 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | −2758.00 | −0.176089 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −5138.00 | −0.326479 | ||||||||
\(629\) | 40796.0 | 2.58608 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23232.0 | 1.46569 | 0.732846 | − | 0.680395i | \(-0.238192\pi\) | ||||
0.732846 | + | 0.680395i | \(0.238192\pi\) | |||||||
\(632\) | −15000.0 | −0.944095 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −6274.00 | −0.393016 | ||||||||
\(635\) | −3880.00 | −0.242477 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 600.000 | 0.0372323 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −7275.00 | −0.449328 | ||||||||
\(641\) | −12162.0 | −0.749407 | −0.374704 | − | 0.927145i | \(-0.622256\pi\) | ||||
−0.374704 | + | 0.927145i | \(0.622256\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 488.000 | 0.0299298 | 0.0149649 | − | 0.999888i | \(-0.495236\pi\) | ||||
0.0149649 | + | 0.999888i | \(0.495236\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3760.00 | −0.229002 | ||||||||
\(647\) | −3984.00 | −0.242082 | −0.121041 | − | 0.992647i | \(-0.538623\pi\) | ||||
−0.121041 | + | 0.992647i | \(0.538623\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6720.00 | 0.406445 | ||||||||
\(650\) | −1950.00 | −0.117670 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −17724.0 | −1.06461 | ||||||||
\(653\) | 30538.0 | 1.83008 | 0.915042 | − | 0.403360i | \(-0.132158\pi\) | ||||
0.915042 | + | 0.403360i | \(0.132158\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5560.00 | −0.331675 | ||||||||
\(656\) | 16482.0 | 0.980966 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22740.0 | −1.34420 | −0.672098 | − | 0.740463i | \(-0.734606\pi\) | ||||
−0.672098 | + | 0.740463i | \(0.734606\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18718.0 | 1.10143 | 0.550715 | − | 0.834693i | \(-0.314355\pi\) | ||||
0.550715 | + | 0.834693i | \(0.314355\pi\) | |||||||
\(662\) | −1932.00 | −0.113428 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6720.00 | −0.392751 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1600.00 | −0.0928819 | ||||||||
\(668\) | −2912.00 | −0.168666 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −820.000 | −0.0472826 | ||||||||
\(671\) | −3336.00 | −0.191930 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10802.0 | 0.618702 | 0.309351 | − | 0.950948i | \(-0.399888\pi\) | ||||
0.309351 | + | 0.950948i | \(0.399888\pi\) | |||||||
\(674\) | −2386.00 | −0.136358 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −27209.0 | −1.54808 | ||||||||
\(677\) | 346.000 | 0.0196423 | 0.00982117 | − | 0.999952i | \(-0.496874\pi\) | ||||
0.00982117 | + | 0.999952i | \(0.496874\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 7050.00 | 0.397581 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2976.00 | 0.167092 | ||||||||
\(683\) | 11628.0 | 0.651439 | 0.325720 | − | 0.945466i | \(-0.394393\pi\) | ||||
0.325720 | + | 0.945466i | \(0.394393\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3470.00 | −0.193550 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2788.00 | −0.154493 | ||||||||
\(689\) | −1716.00 | −0.0948830 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2472.00 | −0.136092 | −0.0680458 | − | 0.997682i | \(-0.521676\pi\) | ||||
−0.0680458 | + | 0.997682i | \(0.521676\pi\) | |||||||
\(692\) | −21294.0 | −1.16976 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6076.00 | 0.332337 | ||||||||
\(695\) | 1800.00 | 0.0982416 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −37788.0 | −2.05355 | ||||||||
\(698\) | 2210.00 | 0.119842 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2018.00 | 0.108729 | 0.0543643 | − | 0.998521i | \(-0.482687\pi\) | ||||
0.0543643 | + | 0.998521i | \(0.482687\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17360.0 | 0.931358 | ||||||||
\(704\) | 2004.00 | 0.107285 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2598.00 | 0.138494 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 790.000 | 0.0418464 | 0.0209232 | − | 0.999781i | \(-0.493339\pi\) | ||||
0.0209232 | + | 0.999781i | \(0.493339\pi\) | |||||||
\(710\) | −3360.00 | −0.177604 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −13050.0 | −0.686895 | ||||||||
\(713\) | −7936.00 | −0.416838 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4680.00 | 0.244786 | ||||||||
\(716\) | −1260.00 | −0.0657659 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −13320.0 | −0.692337 | ||||||||
\(719\) | 18200.0 | 0.944013 | 0.472007 | − | 0.881595i | \(-0.343530\pi\) | ||||
0.472007 | + | 0.881595i | \(0.343530\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 5259.00 | 0.271080 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −13706.0 | −0.703563 | ||||||||
\(725\) | 1250.00 | 0.0640329 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −29056.0 | −1.48229 | −0.741147 | − | 0.671343i | \(-0.765718\pi\) | ||||
−0.741147 | + | 0.671343i | \(0.765718\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −410.000 | −0.0207874 | ||||||||
\(731\) | 6392.00 | 0.323415 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7082.00 | −0.356862 | −0.178431 | − | 0.983952i | \(-0.557102\pi\) | ||||
−0.178431 | + | 0.983952i | \(0.557102\pi\) | |||||||
\(734\) | 10816.0 | 0.543904 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5152.00 | 0.258023 | ||||||||
\(737\) | 1968.00 | 0.0983612 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11060.0 | 0.550539 | 0.275270 | − | 0.961367i | \(-0.411233\pi\) | ||||
0.275270 | + | 0.961367i | \(0.411233\pi\) | |||||||
\(740\) | −15190.0 | −0.754589 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −33072.0 | −1.63297 | −0.816483 | − | 0.577369i | \(-0.804079\pi\) | ||||
−0.816483 | + | 0.577369i | \(0.804079\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11350.0 | 0.558164 | ||||||||
\(746\) | 11098.0 | 0.544674 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −7896.00 | −0.385971 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 29072.0 | 1.41259 | 0.706293 | − | 0.707919i | \(-0.250366\pi\) | ||||
0.706293 | + | 0.707919i | \(0.250366\pi\) | |||||||
\(752\) | 21976.0 | 1.06567 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −3900.00 | −0.188368 | ||||||||
\(755\) | −3160.00 | −0.152323 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13234.0 | −0.635400 | −0.317700 | − | 0.948191i | \(-0.602911\pi\) | ||||
−0.317700 | + | 0.948191i | \(0.602911\pi\) | |||||||
\(758\) | −7100.00 | −0.340216 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3000.00 | 0.143186 | ||||||||
\(761\) | −22398.0 | −1.06692 | −0.533460 | − | 0.845825i | \(-0.679109\pi\) | ||||
−0.533460 | + | 0.845825i | \(0.679109\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −20216.0 | −0.957316 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 728.000 | 0.0343390 | ||||||||
\(767\) | −43680.0 | −2.05631 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6890.00 | −0.323095 | −0.161547 | − | 0.986865i | \(-0.551648\pi\) | ||||
−0.161547 | + | 0.986865i | \(0.551648\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −11214.0 | −0.522799 | ||||||||
\(773\) | 16722.0 | 0.778071 | 0.389035 | − | 0.921223i | \(-0.372808\pi\) | ||||
0.389035 | + | 0.921223i | \(0.372808\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6200.00 | 0.287368 | ||||||||
\(776\) | −15390.0 | −0.711944 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −6810.00 | −0.313818 | ||||||||
\(779\) | −16080.0 | −0.739571 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8064.00 | 0.369466 | ||||||||
\(782\) | −3008.00 | −0.137552 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3670.00 | −0.166864 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 32624.0 | 1.47766 | 0.738831 | − | 0.673891i | \(-0.235378\pi\) | ||||
0.738831 | + | 0.673891i | \(0.235378\pi\) | |||||||
\(788\) | −33558.0 | −1.51707 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −5000.00 | −0.225180 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 21684.0 | 0.971023 | ||||||||
\(794\) | −574.000 | −0.0256555 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8960.00 | 0.398968 | ||||||||
\(797\) | 11346.0 | 0.504261 | 0.252130 | − | 0.967693i | \(-0.418869\pi\) | ||||
0.252130 | + | 0.967693i | \(0.418869\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −50384.0 | −2.23086 | ||||||||
\(800\) | −4025.00 | −0.177882 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 6162.00 | 0.271306 | ||||||||
\(803\) | 984.000 | 0.0432436 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −19344.0 | −0.845364 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 7230.00 | 0.314790 | ||||||||
\(809\) | 35190.0 | 1.52931 | 0.764657 | − | 0.644438i | \(-0.222909\pi\) | ||||
0.764657 | + | 0.644438i | \(0.222909\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −30432.0 | −1.31765 | −0.658824 | − | 0.752297i | \(-0.728946\pi\) | ||||
−0.658824 | + | 0.752297i | \(0.728946\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −5208.00 | −0.224251 | ||||||||
\(815\) | −12660.0 | −0.544123 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2720.00 | 0.116476 | ||||||||
\(818\) | 8210.00 | 0.350924 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 14070.0 | 0.599202 | ||||||||
\(821\) | −12702.0 | −0.539955 | −0.269977 | − | 0.962867i | \(-0.587016\pi\) | ||||
−0.269977 | + | 0.962867i | \(0.587016\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16952.0 | 0.717995 | 0.358997 | − | 0.933339i | \(-0.383119\pi\) | ||||
0.358997 | + | 0.933339i | \(0.383119\pi\) | |||||||
\(824\) | −4080.00 | −0.172492 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25404.0 | 1.06818 | 0.534089 | − | 0.845428i | \(-0.320655\pi\) | ||||
0.534089 | + | 0.845428i | \(0.320655\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −26250.0 | −1.09976 | −0.549879 | − | 0.835244i | \(-0.685326\pi\) | ||||
−0.549879 | + | 0.835244i | \(0.685326\pi\) | |||||||
\(830\) | −2240.00 | −0.0936765 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −13026.0 | −0.542783 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2080.00 | −0.0862052 | ||||||||
\(836\) | −3360.00 | −0.139005 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −4800.00 | −0.197868 | ||||||||
\(839\) | −15360.0 | −0.632045 | −0.316023 | − | 0.948752i | \(-0.602348\pi\) | ||||
−0.316023 | + | 0.948752i | \(0.602348\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21889.0 | −0.897495 | ||||||||
\(842\) | 9938.00 | 0.406753 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 476.000 | 0.0194130 | ||||||||
\(845\) | −19435.0 | −0.791224 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −902.000 | −0.0365269 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2350.00 | 0.0948286 | ||||||||
\(851\) | 13888.0 | 0.559430 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10362.0 | −0.415930 | −0.207965 | − | 0.978136i | \(-0.566684\pi\) | ||||
−0.207965 | + | 0.978136i | \(0.566684\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6660.00 | 0.265928 | ||||||||
\(857\) | 4506.00 | 0.179606 | 0.0898028 | − | 0.995960i | \(-0.471376\pi\) | ||||
0.0898028 | + | 0.995960i | \(0.471376\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24200.0 | −0.961226 | −0.480613 | − | 0.876933i | \(-0.659586\pi\) | ||||
−0.480613 | + | 0.876933i | \(0.659586\pi\) | |||||||
\(860\) | −2380.00 | −0.0943690 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −9248.00 | −0.365415 | ||||||||
\(863\) | 37008.0 | 1.45975 | 0.729877 | − | 0.683579i | \(-0.239578\pi\) | ||||
0.729877 | + | 0.683579i | \(0.239578\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −15210.0 | −0.597868 | ||||||||
\(866\) | −1118.00 | −0.0438697 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12000.0 | 0.468437 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12792.0 | −0.497635 | ||||||||
\(872\) | −17550.0 | −0.681557 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1280.00 | −0.0495385 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3446.00 | 0.132683 | 0.0663416 | − | 0.997797i | \(-0.478867\pi\) | ||||
0.0663416 | + | 0.997797i | \(0.478867\pi\) | |||||||
\(878\) | −11960.0 | −0.459716 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2460.00 | 0.0942348 | ||||||||
\(881\) | −16158.0 | −0.617908 | −0.308954 | − | 0.951077i | \(-0.599979\pi\) | ||||
−0.308954 | + | 0.951077i | \(0.599979\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −44708.0 | −1.70390 | −0.851950 | − | 0.523623i | \(-0.824580\pi\) | ||||
−0.851950 | + | 0.523623i | \(0.824580\pi\) | |||||||
\(884\) | 51324.0 | 1.95273 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 7332.00 | 0.278017 | ||||||||
\(887\) | −23504.0 | −0.889726 | −0.444863 | − | 0.895599i | \(-0.646748\pi\) | ||||
−0.444863 | + | 0.895599i | \(0.646748\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −4350.00 | −0.163834 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −12096.0 | −0.454040 | ||||||||
\(893\) | −21440.0 | −0.803429 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −900.000 | −0.0336131 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1890.00 | 0.0702340 | ||||||||
\(899\) | 12400.0 | 0.460026 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2068.00 | 0.0764651 | ||||||||
\(902\) | 4824.00 | 0.178073 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 11970.0 | 0.440394 | ||||||||
\(905\) | −9790.00 | −0.359592 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 42436.0 | 1.55354 | 0.776772 | − | 0.629782i | \(-0.216856\pi\) | ||||
0.776772 | + | 0.629782i | \(0.216856\pi\) | |||||||
\(908\) | 34048.0 | 1.24441 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7968.00 | 0.289782 | 0.144891 | − | 0.989448i | \(-0.453717\pi\) | ||||
0.144891 | + | 0.989448i | \(0.453717\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5376.00 | 0.194874 | ||||||||
\(914\) | 7014.00 | 0.253832 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −38570.0 | −1.39125 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14880.0 | 0.534109 | 0.267054 | − | 0.963681i | \(-0.413950\pi\) | ||||
0.267054 | + | 0.963681i | \(0.413950\pi\) | |||||||
\(920\) | 2400.00 | 0.0860061 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 8318.00 | 0.297114 | ||||||||
\(923\) | −52416.0 | −1.86922 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10850.0 | −0.385671 | ||||||||
\(926\) | −6432.00 | −0.228260 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −8050.00 | −0.284757 | ||||||||
\(929\) | 27610.0 | 0.975086 | 0.487543 | − | 0.873099i | \(-0.337893\pi\) | ||||
0.487543 | + | 0.873099i | \(0.337893\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 37254.0 | 1.30933 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 10064.0 | 0.352574 | ||||||||
\(935\) | −5640.00 | −0.197270 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28094.0 | 0.979499 | 0.489750 | − | 0.871863i | \(-0.337088\pi\) | ||||
0.489750 | + | 0.871863i | \(0.337088\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 18760.0 | 0.650940 | ||||||||
\(941\) | −12198.0 | −0.422575 | −0.211288 | − | 0.977424i | \(-0.567766\pi\) | ||||
−0.211288 | + | 0.977424i | \(0.567766\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −12864.0 | −0.444231 | ||||||||
\(944\) | −22960.0 | −0.791615 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −816.000 | −0.0280449 | ||||||||
\(947\) | −31316.0 | −1.07459 | −0.537293 | − | 0.843396i | \(-0.680553\pi\) | ||||
−0.537293 | + | 0.843396i | \(0.680553\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6396.00 | −0.218781 | ||||||||
\(950\) | 1000.00 | 0.0341519 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −27322.0 | −0.928695 | −0.464348 | − | 0.885653i | \(-0.653711\pi\) | ||||
−0.464348 | + | 0.885653i | \(0.653711\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −14440.0 | −0.489285 | ||||||||
\(956\) | −12880.0 | −0.435742 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1400.00 | −0.0472150 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 31713.0 | 1.06452 | ||||||||
\(962\) | 33852.0 | 1.13454 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −3066.00 | −0.102437 | ||||||||
\(965\) | −8010.00 | −0.267203 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5296.00 | 0.176120 | 0.0880599 | − | 0.996115i | \(-0.471933\pi\) | ||||
0.0880599 | + | 0.996115i | \(0.471933\pi\) | |||||||
\(968\) | −17805.0 | −0.591193 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −5130.00 | −0.169809 | ||||||||
\(971\) | 512.000 | 0.0169216 | 0.00846079 | − | 0.999964i | \(-0.497307\pi\) | ||||
0.00846079 | + | 0.999964i | \(0.497307\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −13376.0 | −0.440036 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 11398.0 | 0.373813 | ||||||||
\(977\) | 20734.0 | 0.678955 | 0.339478 | − | 0.940614i | \(-0.389750\pi\) | ||||
0.339478 | + | 0.940614i | \(0.389750\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10440.0 | 0.340821 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 7092.00 | 0.230463 | ||||||||
\(983\) | −61168.0 | −1.98470 | −0.992348 | − | 0.123472i | \(-0.960597\pi\) | ||||
−0.992348 | + | 0.123472i | \(0.960597\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −23970.0 | −0.775378 | ||||||||
\(986\) | 4700.00 | 0.151804 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 21840.0 | 0.703262 | ||||||||
\(989\) | 2176.00 | 0.0699624 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −47928.0 | −1.53631 | −0.768155 | − | 0.640264i | \(-0.778825\pi\) | ||||
−0.768155 | + | 0.640264i | \(0.778825\pi\) | |||||||
\(992\) | −39928.0 | −1.27794 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6400.00 | 0.203913 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9454.00 | 0.300312 | 0.150156 | − | 0.988662i | \(-0.452022\pi\) | ||||
0.150156 | + | 0.988662i | \(0.452022\pi\) | |||||||
\(998\) | 820.000 | 0.0260087 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2205.4.a.i.1.1 | 1 | ||
3.2 | odd | 2 | 245.4.a.d.1.1 | 1 | |||
7.6 | odd | 2 | 315.4.a.c.1.1 | 1 | |||
15.14 | odd | 2 | 1225.4.a.e.1.1 | 1 | |||
21.2 | odd | 6 | 245.4.e.b.116.1 | 2 | |||
21.5 | even | 6 | 245.4.e.e.116.1 | 2 | |||
21.11 | odd | 6 | 245.4.e.b.226.1 | 2 | |||
21.17 | even | 6 | 245.4.e.e.226.1 | 2 | |||
21.20 | even | 2 | 35.4.a.a.1.1 | ✓ | 1 | ||
35.34 | odd | 2 | 1575.4.a.g.1.1 | 1 | |||
84.83 | odd | 2 | 560.4.a.p.1.1 | 1 | |||
105.62 | odd | 4 | 175.4.b.a.99.2 | 2 | |||
105.83 | odd | 4 | 175.4.b.a.99.1 | 2 | |||
105.104 | even | 2 | 175.4.a.a.1.1 | 1 | |||
168.83 | odd | 2 | 2240.4.a.b.1.1 | 1 | |||
168.125 | even | 2 | 2240.4.a.bk.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.4.a.a.1.1 | ✓ | 1 | 21.20 | even | 2 | ||
175.4.a.a.1.1 | 1 | 105.104 | even | 2 | |||
175.4.b.a.99.1 | 2 | 105.83 | odd | 4 | |||
175.4.b.a.99.2 | 2 | 105.62 | odd | 4 | |||
245.4.a.d.1.1 | 1 | 3.2 | odd | 2 | |||
245.4.e.b.116.1 | 2 | 21.2 | odd | 6 | |||
245.4.e.b.226.1 | 2 | 21.11 | odd | 6 | |||
245.4.e.e.116.1 | 2 | 21.5 | even | 6 | |||
245.4.e.e.226.1 | 2 | 21.17 | even | 6 | |||
315.4.a.c.1.1 | 1 | 7.6 | odd | 2 | |||
560.4.a.p.1.1 | 1 | 84.83 | odd | 2 | |||
1225.4.a.e.1.1 | 1 | 15.14 | odd | 2 | |||
1575.4.a.g.1.1 | 1 | 35.34 | odd | 2 | |||
2205.4.a.i.1.1 | 1 | 1.1 | even | 1 | trivial | ||
2240.4.a.b.1.1 | 1 | 168.83 | odd | 2 | |||
2240.4.a.bk.1.1 | 1 | 168.125 | even | 2 |