Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2496,4,Mod(1,2496)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2496, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("2496.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2496 = 2^{6} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2496.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: | \(147.268767374\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 156) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 2496.1 |
$q$-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 | ||||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.00000 | 0.178885 | 0.0894427 | − | 0.995992i | \(-0.471491\pi\) | ||||
0.0894427 | + | 0.995992i | \(0.471491\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 32.0000 | 1.72784 | 0.863919 | − | 0.503631i | \(-0.168003\pi\) | ||||
0.863919 | + | 0.503631i | \(0.168003\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −68.0000 | −1.86389 | −0.931944 | − | 0.362602i | \(-0.881889\pi\) | ||||
−0.931944 | + | 0.362602i | \(0.881889\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −13.0000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6.00000 | 0.103280 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −14.0000 | −0.199735 | −0.0998676 | − | 0.995001i | \(-0.531842\pi\) | ||||
−0.0998676 | + | 0.995001i | \(0.531842\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.00000 | 0.0482980 | 0.0241490 | − | 0.999708i | \(-0.492312\pi\) | ||||
0.0241490 | + | 0.999708i | \(0.492312\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 96.0000 | 0.997567 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −72.0000 | −0.652741 | −0.326370 | − | 0.945242i | \(-0.605826\pi\) | ||||
−0.326370 | + | 0.945242i | \(0.605826\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −121.000 | −0.968000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −102.000 | −0.653135 | −0.326568 | − | 0.945174i | \(-0.605892\pi\) | ||||
−0.326568 | + | 0.945174i | \(0.605892\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 136.000 | 0.787946 | 0.393973 | − | 0.919122i | \(-0.371100\pi\) | ||||
0.393973 | + | 0.919122i | \(0.371100\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −204.000 | −1.07612 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 64.0000 | 0.309085 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 386.000 | 1.71508 | 0.857541 | − | 0.514416i | \(-0.171991\pi\) | ||||
0.857541 | + | 0.514416i | \(0.171991\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −39.0000 | −0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 250.000 | 0.952279 | 0.476140 | − | 0.879370i | \(-0.342036\pi\) | ||||
0.476140 | + | 0.879370i | \(0.342036\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −140.000 | −0.496507 | −0.248253 | − | 0.968695i | \(-0.579857\pi\) | ||||
−0.248253 | + | 0.968695i | \(0.579857\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 18.0000 | 0.0596285 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 296.000 | 0.918639 | 0.459320 | − | 0.888271i | \(-0.348093\pi\) | ||||
0.459320 | + | 0.888271i | \(0.348093\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 681.000 | 1.98542 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −42.0000 | −0.115317 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −526.000 | −1.36324 | −0.681619 | − | 0.731707i | \(-0.738724\pi\) | ||||
−0.681619 | + | 0.731707i | \(0.738724\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −136.000 | −0.333422 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 12.0000 | 0.0278849 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 332.000 | 0.732588 | 0.366294 | − | 0.930499i | \(-0.380626\pi\) | ||||
0.366294 | + | 0.930499i | \(0.380626\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 410.000 | 0.860576 | 0.430288 | − | 0.902692i | \(-0.358412\pi\) | ||||
0.430288 | + | 0.902692i | \(0.358412\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 288.000 | 0.575946 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −26.0000 | −0.0496139 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 596.000 | 1.08676 | 0.543381 | − | 0.839487i | \(-0.317144\pi\) | ||||
0.543381 | + | 0.839487i | \(0.317144\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −216.000 | −0.376860 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 880.000 | 1.47094 | 0.735470 | − | 0.677557i | \(-0.236961\pi\) | ||||
0.735470 | + | 0.677557i | \(0.236961\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 506.000 | 0.811272 | 0.405636 | − | 0.914035i | \(-0.367050\pi\) | ||||
0.405636 | + | 0.914035i | \(0.367050\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −363.000 | −0.558875 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2176.00 | −3.22050 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 640.000 | 0.911464 | 0.455732 | − | 0.890117i | \(-0.349378\pi\) | ||||
0.455732 | + | 0.890117i | \(0.349378\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1380.00 | 1.82500 | 0.912498 | − | 0.409081i | \(-0.134151\pi\) | ||||
0.912498 | + | 0.409081i | \(0.134151\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −28.0000 | −0.0357297 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −306.000 | −0.377088 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1450.00 | 1.72696 | 0.863481 | − | 0.504381i | \(-0.168279\pi\) | ||||
0.863481 | + | 0.504381i | \(0.168279\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −416.000 | −0.479216 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 408.000 | 0.454921 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8.00000 | 0.00863982 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −446.000 | −0.466850 | −0.233425 | − | 0.972375i | \(-0.574993\pi\) | ||||
−0.233425 | + | 0.972375i | \(0.574993\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −612.000 | −0.621296 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 610.000 | 0.600963 | 0.300482 | − | 0.953788i | \(-0.402853\pi\) | ||||
0.300482 | + | 0.953788i | \(0.402853\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1352.00 | 1.29336 | 0.646682 | − | 0.762760i | \(-0.276156\pi\) | ||||
0.646682 | + | 0.762760i | \(0.276156\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 192.000 | 0.178450 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −732.000 | −0.661356 | −0.330678 | − | 0.943744i | \(-0.607277\pi\) | ||||
−0.330678 | + | 0.943744i | \(0.607277\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1514.00 | 1.33041 | 0.665206 | − | 0.746660i | \(-0.268344\pi\) | ||||
0.665206 | + | 0.746660i | \(0.268344\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1158.00 | 0.990203 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1518.00 | −1.26373 | −0.631865 | − | 0.775079i | \(-0.717710\pi\) | ||||
−0.631865 | + | 0.775079i | \(0.717710\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −144.000 | −0.116766 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −117.000 | −0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −448.000 | −0.345110 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3293.00 | 2.47408 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 750.000 | 0.549799 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −492.000 | −0.352047 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 96.0000 | 0.0670758 | 0.0335379 | − | 0.999437i | \(-0.489323\pi\) | ||||
0.0335379 | + | 0.999437i | \(0.489323\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −420.000 | −0.286658 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2548.00 | −1.69939 | −0.849694 | − | 0.527276i | \(-0.823213\pi\) | ||||
−0.849694 | + | 0.527276i | \(0.823213\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 128.000 | 0.0834512 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 54.0000 | 0.0344265 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −230.000 | −0.143432 | −0.0717162 | − | 0.997425i | \(-0.522848\pi\) | ||||
−0.0717162 | + | 0.997425i | \(0.522848\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 516.000 | 0.314867 | 0.157434 | − | 0.987530i | \(-0.449678\pi\) | ||||
0.157434 | + | 0.987530i | \(0.449678\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 888.000 | 0.530377 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 884.000 | 0.516950 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −204.000 | −0.116836 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2043.00 | 1.14628 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1842.00 | 1.01277 | 0.506384 | − | 0.862308i | \(-0.330982\pi\) | ||||
0.506384 | + | 0.862308i | \(0.330982\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 528.000 | 0.284556 | 0.142278 | − | 0.989827i | \(-0.454557\pi\) | ||||
0.142278 | + | 0.989827i | \(0.454557\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −126.000 | −0.0665784 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 272.000 | 0.140952 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1306.00 | 0.663886 | 0.331943 | − | 0.943299i | \(-0.392296\pi\) | ||||
0.331943 | + | 0.943299i | \(0.392296\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1578.00 | −0.787066 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2304.00 | −1.12783 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3772.00 | −1.81255 | −0.906276 | − | 0.422687i | \(-0.861087\pi\) | ||||
−0.906276 | + | 0.422687i | \(0.861087\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −408.000 | −0.192502 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −384.000 | −0.177933 | −0.0889665 | − | 0.996035i | \(-0.528356\pi\) | ||||
−0.0889665 | + | 0.996035i | \(0.528356\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 169.000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 36.0000 | 0.0160993 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1462.00 | −0.642508 | −0.321254 | − | 0.946993i | \(-0.604104\pi\) | ||||
−0.321254 | + | 0.946993i | \(0.604104\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3872.00 | −1.67255 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 996.000 | 0.422960 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1332.00 | −0.556192 | −0.278096 | − | 0.960553i | \(-0.589703\pi\) | ||||
−0.278096 | + | 0.960553i | \(0.589703\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2030.00 | −0.833639 | −0.416820 | − | 0.908989i | \(-0.636855\pi\) | ||||
−0.416820 | + | 0.908989i | \(0.636855\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1230.00 | 0.496854 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 772.000 | 0.306803 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 952.000 | 0.372284 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 864.000 | 0.332522 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.0000 | 0.00606136 | 0.00303068 | − | 0.999995i | \(-0.499035\pi\) | ||||
0.00303068 | + | 0.999995i | \(0.499035\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2078.00 | −0.775014 | −0.387507 | − | 0.921867i | \(-0.626664\pi\) | ||||
−0.387507 | + | 0.921867i | \(0.626664\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −78.0000 | −0.0286446 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3486.00 | −1.26075 | −0.630374 | − | 0.776292i | \(-0.717098\pi\) | ||||
−0.630374 | + | 0.776292i | \(0.717098\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −568.000 | −0.202334 | −0.101167 | − | 0.994869i | \(-0.532258\pi\) | ||||
−0.101167 | + | 0.994869i | \(0.532258\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1788.00 | 0.627442 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3264.00 | −1.12851 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 500.000 | 0.170349 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −648.000 | −0.217580 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −272.000 | −0.0900222 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3804.00 | 1.24113 | 0.620564 | − | 0.784156i | \(-0.286904\pi\) | ||||
0.620564 | + | 0.784156i | \(0.286904\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2640.00 | 0.849248 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −280.000 | −0.0888179 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4352.00 | 1.36144 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1518.00 | 0.468388 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 182.000 | 0.0553966 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5912.00 | −1.77532 | −0.887661 | − | 0.460498i | \(-0.847671\pi\) | ||||
−0.887661 | + | 0.460498i | \(0.847671\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1089.00 | −0.322667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3308.00 | −0.967223 | −0.483612 | − | 0.875283i | \(-0.660675\pi\) | ||||
−0.483612 | + | 0.875283i | \(0.660675\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6050.00 | 1.74583 | 0.872915 | − | 0.487872i | \(-0.162227\pi\) | ||||
0.872915 | + | 0.487872i | \(0.162227\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6528.00 | −1.85935 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4794.00 | 1.34792 | 0.673960 | − | 0.738768i | \(-0.264592\pi\) | ||||
0.673960 | + | 0.738768i | \(0.264592\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 592.000 | 0.164331 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1920.00 | 0.526234 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4440.00 | 1.20167 | 0.600836 | − | 0.799372i | \(-0.294834\pi\) | ||||
0.600836 | + | 0.799372i | \(0.294834\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1330.00 | 0.355489 | 0.177744 | − | 0.984077i | \(-0.443120\pi\) | ||||
0.177744 | + | 0.984077i | \(0.443120\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1362.00 | 0.355163 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −52.0000 | −0.0133955 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4140.00 | 1.05366 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5116.00 | −1.28653 | −0.643265 | − | 0.765644i | \(-0.722421\pi\) | ||||
−0.643265 | + | 0.765644i | \(0.722421\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4896.00 | 1.21664 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −84.0000 | −0.0206286 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 642.000 | 0.155824 | 0.0779122 | − | 0.996960i | \(-0.475175\pi\) | ||||
0.0779122 | + | 0.996960i | \(0.475175\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 12352.0 | 2.96338 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −918.000 | −0.217712 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4264.00 | −0.999732 | −0.499866 | − | 0.866103i | \(-0.666617\pi\) | ||||
−0.499866 | + | 0.866103i | \(0.666617\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1052.00 | −0.243864 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4350.00 | 0.997062 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3850.00 | 0.872634 | 0.436317 | − | 0.899793i | \(-0.356283\pi\) | ||||
0.436317 | + | 0.899793i | \(0.356283\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2936.00 | −0.658115 | −0.329058 | − | 0.944310i | \(-0.606731\pi\) | ||||
−0.329058 | + | 0.944310i | \(0.606731\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1248.00 | −0.276675 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8228.00 | 1.80424 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2066.00 | 0.448137 | 0.224068 | − | 0.974573i | \(-0.428066\pi\) | ||||
0.224068 | + | 0.974573i | \(0.428066\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1224.00 | 0.262649 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −214.000 | −0.0454312 | −0.0227156 | − | 0.999742i | \(-0.507231\pi\) | ||||
−0.0227156 | + | 0.999742i | \(0.507231\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2620.00 | −0.550328 | −0.275164 | − | 0.961397i | \(-0.588732\pi\) | ||||
−0.275164 | + | 0.961397i | \(0.588732\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 24.0000 | 0.00498820 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8000.00 | 1.64538 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4717.00 | −0.960106 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1338.00 | −0.269536 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1154.00 | 0.230094 | 0.115047 | − | 0.993360i | \(-0.463298\pi\) | ||||
0.115047 | + | 0.993360i | \(0.463298\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 664.000 | 0.131049 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1836.00 | −0.358705 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 936.000 | 0.181038 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4480.00 | −0.857883 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1830.00 | 0.346966 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 820.000 | 0.153944 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4076.00 | −0.757751 | −0.378876 | − | 0.925448i | \(-0.623689\pi\) | ||||
−0.378876 | + | 0.925448i | \(0.623689\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4056.00 | 0.746724 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6456.00 | 1.17713 | 0.588563 | − | 0.808451i | \(-0.299694\pi\) | ||||
0.588563 | + | 0.808451i | \(0.299694\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5526.00 | −0.997917 | −0.498958 | − | 0.866626i | \(-0.666284\pi\) | ||||
−0.498958 | + | 0.866626i | \(0.666284\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 576.000 | 0.103028 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10458.0 | 1.85293 | 0.926467 | − | 0.376377i | \(-0.122830\pi\) | ||||
0.926467 | + | 0.376377i | \(0.122830\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6936.00 | 1.21737 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2196.00 | −0.381834 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −56.0000 | −0.00964682 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1573.00 | 0.268475 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4542.00 | 0.768114 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 9472.00 | 1.58726 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2348.00 | 0.389903 | 0.194951 | − | 0.980813i | \(-0.437545\pi\) | ||||
0.194951 | + | 0.980813i | \(0.437545\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3474.00 | 0.571694 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1192.00 | 0.194406 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5298.00 | 0.856381 | 0.428191 | − | 0.903688i | \(-0.359151\pi\) | ||||
0.428191 | + | 0.903688i | \(0.359151\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4554.00 | −0.729615 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9248.00 | −1.46864 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10816.0 | 1.70265 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −432.000 | −0.0674148 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9876.00 | 1.52787 | 0.763936 | − | 0.645292i | \(-0.223264\pi\) | ||||
0.763936 | + | 0.645292i | \(0.223264\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5370.00 | 0.823638 | 0.411819 | − | 0.911266i | \(-0.364894\pi\) | ||||
0.411819 | + | 0.911266i | \(0.364894\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −351.000 | −0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7330.00 | 1.10520 | 0.552601 | − | 0.833446i | \(-0.313635\pi\) | ||||
0.552601 | + | 0.833446i | \(0.313635\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1760.00 | 0.263130 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1344.00 | −0.199249 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7488.00 | −1.10084 | −0.550420 | − | 0.834888i | \(-0.685532\pi\) | ||||
−0.550420 | + | 0.834888i | \(0.685532\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6843.00 | −0.997667 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9879.00 | 1.42841 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1012.00 | 0.145125 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1504.00 | −0.213919 | −0.106959 | − | 0.994263i | \(-0.534111\pi\) | ||||
−0.106959 | + | 0.994263i | \(0.534111\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2250.00 | 0.317426 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −16832.0 | −2.35546 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6702.00 | −0.930339 | −0.465169 | − | 0.885222i | \(-0.654007\pi\) | ||||
−0.465169 | + | 0.885222i | \(0.654007\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1476.00 | −0.203254 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1326.00 | 0.181147 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5700.00 | −0.772531 | −0.386266 | − | 0.922388i | \(-0.626235\pi\) | ||||
−0.386266 | + | 0.922388i | \(0.626235\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 288.000 | 0.0387262 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2328.00 | −0.310588 | −0.155294 | − | 0.987868i | \(-0.549633\pi\) | ||||
−0.155294 | + | 0.987868i | \(0.549633\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4352.00 | −0.576100 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1260.00 | −0.165502 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11554.0 | 1.50594 | 0.752971 | − | 0.658054i | \(-0.228620\pi\) | ||||
0.752971 | + | 0.658054i | \(0.228620\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1008.00 | 0.130375 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7644.00 | −0.981142 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1280.00 | 0.163048 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6486.00 | −0.819957 | −0.409979 | − | 0.912095i | \(-0.634464\pi\) | ||||
−0.409979 | + | 0.912095i | \(0.634464\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 384.000 | 0.0481806 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7698.00 | 0.958653 | 0.479326 | − | 0.877637i | \(-0.340881\pi\) | ||||
0.479326 | + | 0.877637i | \(0.340881\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1768.00 | −0.218537 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 162.000 | 0.0198762 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −26248.0 | −3.19672 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3338.00 | 0.403554 | 0.201777 | − | 0.979432i | \(-0.435328\pi\) | ||||
0.201777 | + | 0.979432i | \(0.435328\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −690.000 | −0.0828107 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 10624.0 | 1.26579 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2760.00 | 0.326465 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1548.00 | 0.181789 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −52.0000 | −0.00606293 | −0.00303146 | − | 0.999995i | \(-0.500965\pi\) | ||||
−0.00303146 | + | 0.999995i | \(0.500965\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5858.00 | 0.678151 | 0.339075 | − | 0.940759i | \(-0.389886\pi\) | ||||
0.339075 | + | 0.940759i | \(0.389886\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2664.00 | 0.306213 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1694.00 | 0.193344 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13120.0 | 1.48694 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2652.00 | 0.298461 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8840.00 | −0.987953 | −0.493977 | − | 0.869475i | \(-0.664457\pi\) | ||||
−0.493977 | + | 0.869475i | \(0.664457\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11346.0 | 1.25925 | 0.629624 | − | 0.776900i | \(-0.283209\pi\) | ||||
0.629624 | + | 0.776900i | \(0.283209\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −612.000 | −0.0674555 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −288.000 | −0.0315261 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16456.0 | −1.78907 | −0.894535 | − | 0.446997i | \(-0.852493\pi\) | ||||
−0.894535 | + | 0.446997i | \(0.852493\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6129.00 | 0.661808 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3788.00 | −0.406260 | −0.203130 | − | 0.979152i | \(-0.565111\pi\) | ||||
−0.203130 | + | 0.979152i | \(0.565111\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2900.00 | 0.308929 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5526.00 | 0.584722 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 546.000 | 0.0573883 | 0.0286941 | − | 0.999588i | \(-0.490865\pi\) | ||||
0.0286941 | + | 0.999588i | \(0.490865\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −17000.0 | −1.77494 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1584.00 | 0.164289 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −832.000 | −0.0857248 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3546.00 | 0.362965 | 0.181482 | − | 0.983394i | \(-0.441910\pi\) | ||||
0.181482 | + | 0.983394i | \(0.441910\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −378.000 | −0.0384391 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12918.0 | −1.30510 | −0.652550 | − | 0.757746i | \(-0.726301\pi\) | ||||
−0.652550 | + | 0.757746i | \(0.726301\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18328.0 | −1.83969 | −0.919843 | − | 0.392287i | \(-0.871684\pi\) | ||||
−0.919843 | + | 0.392287i | \(0.871684\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 816.000 | 0.0813787 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11980.0 | 1.18708 | 0.593542 | − | 0.804803i | \(-0.297729\pi\) | ||||
0.593542 | + | 0.804803i | \(0.297729\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 19072.0 | 1.87775 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3918.00 | 0.383295 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9520.00 | 0.925434 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −484.000 | −0.0467525 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4734.00 | −0.454413 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12344.0 | 1.17748 | 0.588739 | − | 0.808323i | \(-0.299625\pi\) | ||||
0.588739 | + | 0.808323i | \(0.299625\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5018.00 | −0.475678 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6912.00 | −0.651153 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −892.000 | −0.0835126 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 80.0000 | 0.00744383 | 0.00372192 | − | 0.999993i | \(-0.498815\pi\) | ||||
0.00372192 | + | 0.999993i | \(0.498815\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −11316.0 | −1.04648 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15660.0 | −1.43936 | −0.719680 | − | 0.694306i | \(-0.755712\pi\) | ||||
−0.719680 | + | 0.694306i | \(0.755712\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1428.00 | 0.130454 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1224.00 | −0.111141 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 28160.0 | 2.54155 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −60.0000 | −0.00538270 | −0.00269135 | − | 0.999996i | \(-0.500857\pi\) | ||||
−0.00269135 | + | 0.999996i | \(0.500857\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1152.00 | −0.102730 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12248.0 | −1.08571 | −0.542854 | − | 0.839827i | \(-0.682656\pi\) | ||||
−0.542854 | + | 0.839827i | \(0.682656\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1220.00 | 0.107504 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 507.000 | 0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 90.0000 | 0.00783729 | 0.00391864 | − | 0.999992i | \(-0.498753\pi\) | ||||
0.00391864 | + | 0.999992i | \(0.498753\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16192.0 | 1.40175 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 108.000 | 0.00929496 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2704.00 | 0.231364 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −20128.0 | −1.71224 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4386.00 | −0.370952 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9818.00 | 0.825594 | 0.412797 | − | 0.910823i | \(-0.364552\pi\) | ||||
0.412797 | + | 0.910823i | \(0.364552\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −20252.0 | −1.69323 | −0.846614 | − | 0.532208i | \(-0.821363\pi\) | ||||
−0.846614 | + | 0.532208i | \(0.821363\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −11616.0 | −0.965645 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1904.00 | −0.157381 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6983.00 | −0.573929 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2988.00 | 0.244196 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3250.00 | −0.264115 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1464.00 | −0.118307 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3996.00 | −0.321118 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −46308.0 | −3.70061 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12634.0 | 1.00403 | 0.502013 | − | 0.864860i | \(-0.332593\pi\) | ||||
0.502013 | + | 0.864860i | \(0.332593\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6090.00 | −0.481302 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3028.00 | 0.237991 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11756.0 | 0.918922 | 0.459461 | − | 0.888198i | \(-0.348043\pi\) | ||||
0.459461 | + | 0.888198i | \(0.348043\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3690.00 | 0.286859 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −408.000 | −0.0315452 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 20480.0 | 1.57486 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2316.00 | 0.177133 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −17622.0 | −1.34052 | −0.670259 | − | 0.742128i | \(-0.733817\pi\) | ||||
−0.670259 | + | 0.742128i | \(0.733817\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1820.00 | 0.137706 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2856.00 | 0.214938 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −23092.0 | −1.72862 | −0.864309 | − | 0.502961i | \(-0.832244\pi\) | ||||
−0.864309 | + | 0.502961i | \(0.832244\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3036.00 | −0.226063 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2592.00 | 0.191982 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1302.00 | −0.0959274 | −0.0479637 | − | 0.998849i | \(-0.515273\pi\) | ||||
−0.0479637 | + | 0.998849i | \(0.515273\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24868.0 | 1.82258 | 0.911290 | − | 0.411765i | \(-0.135087\pi\) | ||||
0.911290 | + | 0.411765i | \(0.135087\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 48.0000 | 0.00349953 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8712.00 | 0.631853 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2562.00 | 0.184848 | 0.0924241 | − | 0.995720i | \(-0.470538\pi\) | ||||
0.0924241 | + | 0.995720i | \(0.470538\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6234.00 | −0.447455 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 44160.0 | 3.15330 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 35768.0 | 2.54092 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −234.000 | −0.0165380 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13484.0 | 0.948116 | 0.474058 | − | 0.880494i | \(-0.342789\pi\) | ||||
0.474058 | + | 0.880494i | \(0.342789\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 544.000 | 0.0380562 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −10458.0 | −0.727893 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −16974.0 | −1.17544 | −0.587722 | − | 0.809063i | \(-0.699975\pi\) | ||||
−0.587722 | + | 0.809063i | \(0.699975\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −896.000 | −0.0617352 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1704.00 | −0.116818 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3864.00 | −0.263571 | −0.131785 | − | 0.991278i | \(-0.542071\pi\) | ||||
−0.131785 | + | 0.991278i | \(0.542071\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17546.0 | 1.19088 | 0.595438 | − | 0.803401i | \(-0.296979\pi\) | ||||
0.595438 | + | 0.803401i | \(0.296979\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5364.00 | 0.362254 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6586.00 | 0.442577 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9296.00 | −0.621603 | −0.310801 | − | 0.950475i | \(-0.600597\pi\) | ||||
−0.310801 | + | 0.950475i | \(0.600597\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −9792.00 | −0.651547 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3848.00 | −0.254785 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6914.00 | 0.455553 | 0.227776 | − | 0.973713i | \(-0.426854\pi\) | ||||
0.227776 | + | 0.973713i | \(0.426854\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1500.00 | 0.0983510 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −25446.0 | −1.66032 | −0.830160 | − | 0.557525i | \(-0.811751\pi\) | ||||
−0.830160 | + | 0.557525i | \(0.811751\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11236.0 | −0.729585 | −0.364792 | − | 0.931089i | \(-0.618860\pi\) | ||||
−0.364792 | + | 0.931089i | \(0.618860\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1944.00 | −0.125620 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 46400.0 | 2.98391 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14141.0 | 0.905024 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −816.000 | −0.0519743 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5404.00 | −0.342562 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29424.0 | 1.85634 | 0.928170 | − | 0.372156i | \(-0.121381\pi\) | ||||
0.928170 | + | 0.372156i | \(0.121381\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 11412.0 | 0.716566 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 192.000 | 0.0119989 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8853.00 | −0.550657 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7920.00 | 0.490314 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5054.00 | −0.311421 | −0.155711 | − | 0.987803i | \(-0.549767\pi\) | ||||
−0.155711 | + | 0.987803i | \(0.549767\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1132.00 | −0.0694273 | −0.0347136 | − | 0.999397i | \(-0.511052\pi\) | ||||
−0.0347136 | + | 0.999397i | \(0.511052\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −840.000 | −0.0512790 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1464.00 | −0.0889579 | −0.0444790 | − | 0.999010i | \(-0.514163\pi\) | ||||
−0.0444790 | + | 0.999010i | \(0.514163\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −22576.0 | −1.36546 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 13056.0 | 0.786029 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5494.00 | −0.329245 | −0.164622 | − | 0.986357i | \(-0.552641\pi\) | ||||
−0.164622 | + | 0.986357i | \(0.552641\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5096.00 | −0.303996 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4554.00 | 0.270424 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11580.0 | 0.684511 | 0.342256 | − | 0.939607i | \(-0.388809\pi\) | ||||
0.342256 | + | 0.939607i | \(0.388809\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1298.00 | 0.0763787 | 0.0381894 | − | 0.999271i | \(-0.487841\pi\) | ||||
0.0381894 | + | 0.999271i | \(0.487841\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 546.000 | 0.0319832 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 256.000 | 0.0149282 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7344.00 | 0.426328 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −17736.0 | −1.02498 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −27880.0 | −1.60402 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16162.0 | 0.925705 | 0.462852 | − | 0.886435i | \(-0.346826\pi\) | ||||
0.462852 | + | 0.886435i | \(0.346826\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3267.00 | −0.186292 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9890.00 | 0.561453 | 0.280726 | − | 0.959788i | \(-0.409425\pi\) | ||||
0.280726 | + | 0.959788i | \(0.409425\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −14272.0 | −0.806641 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9924.00 | −0.558427 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 27100.0 | 1.51823 | 0.759116 | − | 0.650955i | \(-0.225631\pi\) | ||||
0.759116 | + | 0.650955i | \(0.225631\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −460.000 | −0.0256580 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 18150.0 | 1.00796 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6838.00 | 0.378094 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11132.0 | −0.612853 | −0.306426 | − | 0.951894i | \(-0.599133\pi\) | ||||
−0.306426 | + | 0.951894i | \(0.599133\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −19584.0 | −1.07350 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1032.00 | 0.0563252 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3500.00 | −0.190204 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 14382.0 | 0.778222 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1862.00 | −0.100323 | −0.0501617 | − | 0.998741i | \(-0.515974\pi\) | ||||
−0.0501617 | + | 0.998741i | \(0.515974\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1544.00 | 0.0828351 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1776.00 | 0.0948766 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 19520.0 | 1.03837 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7938.00 | 0.420477 | 0.210238 | − | 0.977650i | \(-0.432576\pi\) | ||||
0.210238 | + | 0.977650i | \(0.432576\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5760.00 | 0.303821 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9792.00 | −0.514324 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1768.00 | 0.0924748 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 13320.0 | 0.693786 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 24240.0 | 1.25730 | 0.628651 | − | 0.777688i | \(-0.283608\pi\) | ||||
0.628651 | + | 0.777688i | \(0.283608\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 43264.0 | 2.23472 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3990.00 | 0.205242 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 12342.0 | 0.632235 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13720.0 | 0.699927 | 0.349963 | − | 0.936763i | \(-0.386194\pi\) | ||||
0.349963 | + | 0.936763i | \(0.386194\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1960.00 | 0.0991699 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21958.0 | −1.10646 | −0.553231 | − | 0.833028i | \(-0.686605\pi\) | ||||
−0.553231 | + | 0.833028i | \(0.686605\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4086.00 | 0.205054 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −40528.0 | −2.02560 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13348.0 | 0.664430 | 0.332215 | − | 0.943204i | \(-0.392204\pi\) | ||||
0.332215 | + | 0.943204i | \(0.392204\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −156.000 | −0.00773388 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −20304.0 | −1.00253 | −0.501266 | − | 0.865293i | \(-0.667132\pi\) | ||||
−0.501266 | + | 0.865293i | \(0.667132\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3684.00 | 0.181170 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12420.0 | 0.608332 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −23424.0 | −1.14272 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3952.00 | 0.192025 | 0.0960123 | − | 0.995380i | \(-0.469391\pi\) | ||||
0.0960123 | + | 0.995380i | \(0.469391\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −15348.0 | −0.742779 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1056.00 | 0.0509030 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22386.0 | 1.07481 | 0.537406 | − | 0.843324i | \(-0.319404\pi\) | ||||
0.537406 | + | 0.843324i | \(0.319404\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 14688.0 | 0.702425 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12458.0 | 0.593433 | 0.296716 | − | 0.954966i | \(-0.404108\pi\) | ||||
0.296716 | + | 0.954966i | \(0.404108\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 48448.0 | 2.29874 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −252.000 | −0.0119099 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4316.00 | −0.203183 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28126.0 | −1.31892 | −0.659460 | − | 0.751740i | \(-0.729215\pi\) | ||||
−0.659460 | + | 0.751740i | \(0.729215\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1926.00 | 0.0899652 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 35778.0 | 1.66474 | 0.832371 | − | 0.554219i | \(-0.186983\pi\) | ||||
0.832371 | + | 0.554219i | \(0.186983\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −16456.0 | −0.762732 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 37056.0 | 1.71091 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1000.00 | 0.0459932 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −59840.0 | −2.74167 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2754.00 | −0.125696 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2612.00 | 0.118760 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7252.00 | 0.328470 | 0.164235 | − | 0.986421i | \(-0.447484\pi\) | ||||
0.164235 | + | 0.986421i | \(0.447484\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −12792.0 | −0.577196 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −48576.0 | −2.18352 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5330.00 | −0.238681 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3156.00 | −0.140795 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4454.00 | −0.197953 | −0.0989766 | − | 0.995090i | \(-0.531557\pi\) | ||||
−0.0989766 | + | 0.995090i | \(0.531557\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4144.00 | −0.183485 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 13050.0 | 0.575654 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −34408.0 | −1.51212 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4608.00 | −0.201752 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 11550.0 | 0.503816 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −34118.0 | −1.48273 | −0.741363 | − | 0.671104i | \(-0.765820\pi\) | ||||
−0.741363 | + | 0.671104i | \(0.765820\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16428.0 | 0.711301 | 0.355650 | − | 0.934619i | \(-0.384259\pi\) | ||||
0.355650 | + | 0.934619i | \(0.384259\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8808.00 | −0.379963 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7544.00 | −0.324239 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −560.000 | −0.0239803 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3744.00 | −0.159739 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18738.0 | 0.796542 | 0.398271 | − | 0.917268i | \(-0.369610\pi\) | ||||
0.398271 | + | 0.917268i | \(0.369610\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13928.0 | −0.589914 | −0.294957 | − | 0.955510i | \(-0.595305\pi\) | ||||
−0.294957 | + | 0.955510i | \(0.595305\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 24684.0 | 1.04168 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 41804.0 | 1.75776 | 0.878880 | − | 0.477043i | \(-0.158291\pi\) | ||||
0.878880 | + | 0.477043i | \(0.158291\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 43226.0 | 1.81098 | 0.905489 | − | 0.424369i | \(-0.139504\pi\) | ||||
0.905489 | + | 0.424369i | \(0.139504\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6198.00 | 0.258732 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −9534.00 | −0.396559 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −768.000 | −0.0318296 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3672.00 | 0.151640 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −10240.0 | −0.421364 | −0.210682 | − | 0.977555i | \(-0.567568\pi\) | ||||
−0.210682 | + | 0.977555i | \(0.567568\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13985.0 | −0.573414 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −642.000 | −0.0262297 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 338.000 | 0.0137604 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 105376. | 4.27481 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7860.00 | −0.317732 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −27792.0 | −1.11950 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 25682.0 | 1.03087 | 0.515437 | − | 0.856928i | \(-0.327630\pi\) | ||||
0.515437 | + | 0.856928i | \(0.327630\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 72.0000 | 0.00287994 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −21558.0 | −0.859285 | −0.429643 | − | 0.902999i | \(-0.641360\pi\) | ||||
−0.429643 | + | 0.902999i | \(0.641360\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14060.0 | −0.558465 | −0.279232 | − | 0.960224i | \(-0.590080\pi\) | ||||
−0.279232 | + | 0.960224i | \(0.590080\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 24000.0 | 0.949963 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −42008.0 | −1.65697 | −0.828487 | − | 0.560008i | \(-0.810798\pi\) | ||||
−0.828487 | + | 0.560008i | \(0.810798\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2924.00 | −0.114935 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −14151.0 | −0.554317 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −43520.0 | −1.69887 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7748.00 | −0.301413 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4014.00 | −0.155617 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −15744.0 | −0.608279 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23734.0 | −0.913843 | −0.456921 | − | 0.889507i | \(-0.651048\pi\) | ||||
−0.456921 | + | 0.889507i | \(0.651048\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3462.00 | 0.132845 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −37550.0 | −1.43597 | −0.717986 | − | 0.696057i | \(-0.754936\pi\) | ||||
−0.717986 | + | 0.696057i | \(0.754936\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12556.0 | 0.478531 | 0.239266 | − | 0.970954i | \(-0.423093\pi\) | ||||
0.239266 | + | 0.970954i | \(0.423093\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1992.00 | 0.0756614 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −37368.0 | −1.41454 | −0.707269 | − | 0.706945i | \(-0.750073\pi\) | ||||
−0.707269 | + | 0.706945i | \(0.750073\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3072.00 | 0.115896 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5508.00 | −0.207099 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1184.00 | 0.0443685 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2664.00 | −0.0994946 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2808.00 | 0.104522 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −13872.0 | −0.514635 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7364.00 | 0.272287 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −13440.0 | −0.495299 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4060.00 | −0.149126 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 33364.0 | 1.22143 | 0.610713 | − | 0.791852i | \(-0.290883\pi\) | ||||
0.610713 | + | 0.791852i | \(0.290883\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5490.00 | 0.200321 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −50432.0 | −1.83412 | −0.917062 | − | 0.398745i | \(-0.869446\pi\) | ||||
−0.917062 | + | 0.398745i | \(0.869446\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −93840.0 | −3.40159 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2460.00 | 0.0888799 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −81536.0 | −2.93627 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11864.0 | −0.425851 | −0.212926 | − | 0.977068i | \(-0.568299\pi\) | ||||
−0.212926 | + | 0.977068i | \(0.568299\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12228.0 | −0.437488 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −11440.0 | −0.407966 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −46706.0 | −1.66020 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 12168.0 | 0.431121 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −5950.00 | −0.210133 | −0.105066 | − | 0.994465i | \(-0.533505\pi\) | ||||
−0.105066 | + | 0.994465i | \(0.533505\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2724.00 | 0.0958920 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 19368.0 | 0.679614 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1904.00 | 0.0665962 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −20806.0 | −0.725403 | −0.362701 | − | 0.931905i | \(-0.618146\pi\) | ||||
−0.362701 | + | 0.931905i | \(0.618146\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −16578.0 | −0.576148 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 22346.0 | 0.774133 | 0.387066 | − | 0.922052i | \(-0.373488\pi\) | ||||
0.387066 | + | 0.922052i | \(0.373488\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −18000.0 | −0.621591 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1728.00 | 0.0594834 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 31636.0 | 1.08557 | 0.542783 | − | 0.839873i | \(-0.317370\pi\) | ||||
0.542783 | + | 0.839873i | \(0.317370\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6578.00 | −0.225006 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 31374.0 | 1.06979 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −23190.0 | −0.788245 | −0.394123 | − | 0.919058i | \(-0.628951\pi\) | ||||
−0.394123 | + | 0.919058i | \(0.628951\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 32.0000 | 0.00108429 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 20808.0 | 0.702850 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7360.00 | −0.247828 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11295.0 | −0.379141 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6588.00 | −0.220452 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4156.00 | −0.138639 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −304.000 | −0.0101096 | −0.00505480 | − | 0.999987i | \(-0.501609\pi\) | ||||
−0.00505480 | + | 0.999987i | \(0.501609\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −168.000 | −0.00556960 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −53372.0 | −1.76394 | −0.881972 | − | 0.471302i | \(-0.843784\pi\) | ||||
−0.881972 | + | 0.471302i | \(0.843784\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16512.0 | 0.544039 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4719.00 | 0.155004 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 13650.0 | 0.446983 | 0.223491 | − | 0.974706i | \(-0.428255\pi\) | ||||
0.223491 | + | 0.974706i | \(0.428255\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −98600.0 | −3.21887 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 13626.0 | 0.443471 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −34992.0 | −1.13537 | −0.567686 | − | 0.823245i | \(-0.692161\pi\) | ||||
−0.567686 | + | 0.823245i | \(0.692161\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6972.00 | −0.225529 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 28416.0 | 0.916405 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 10080.0 | 0.324090 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18096.0 | −0.580059 | −0.290029 | − | 0.957018i | \(-0.593665\pi\) | ||||
−0.290029 | + | 0.957018i | \(0.593665\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 7044.00 | 0.225110 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1136.00 | −0.0361946 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18914.0 | 0.600815 | 0.300407 | − | 0.953811i | \(-0.402877\pi\) | ||||
0.300407 | + | 0.953811i | \(0.402877\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 10422.0 | 0.330068 |
(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 | 2496.4.a.m.1.1 | 1 | ||
4.3 | odd | 2 | 2496.4.a.d.1.1 | 1 | |||
8.3 | odd | 2 | 156.4.a.b.1.1 | ✓ | 1 | ||
8.5 | even | 2 | 624.4.a.b.1.1 | 1 | |||
24.5 | odd | 2 | 1872.4.a.i.1.1 | 1 | |||
24.11 | even | 2 | 468.4.a.a.1.1 | 1 | |||
104.51 | odd | 2 | 2028.4.a.b.1.1 | 1 | |||
104.83 | even | 4 | 2028.4.b.d.337.2 | 2 | |||
104.99 | even | 4 | 2028.4.b.d.337.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
156.4.a.b.1.1 | ✓ | 1 | 8.3 | odd | 2 | ||
468.4.a.a.1.1 | 1 | 24.11 | even | 2 | |||
624.4.a.b.1.1 | 1 | 8.5 | even | 2 | |||
1872.4.a.i.1.1 | 1 | 24.5 | odd | 2 | |||
2028.4.a.b.1.1 | 1 | 104.51 | odd | 2 | |||
2028.4.b.d.337.1 | 2 | 104.99 | even | 4 | |||
2028.4.b.d.337.2 | 2 | 104.83 | even | 4 | |||
2496.4.a.d.1.1 | 1 | 4.3 | odd | 2 | |||
2496.4.a.m.1.1 | 1 | 1.1 | even | 1 | trivial |