Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1856,4,Mod(1,1856)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1856, 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("1856.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1856 = 2^{6} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1856.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: | \(109.507544971\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 58) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1856.1 |
$q$-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 | ||||||||
\(3\) | −7.00000 | −1.34715 | −0.673575 | − | 0.739119i | \(-0.735242\pi\) | ||||
−0.673575 | + | 0.739119i | \(0.735242\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 15.0000 | 1.34164 | 0.670820 | − | 0.741620i | \(-0.265942\pi\) | ||||
0.670820 | + | 0.741620i | \(0.265942\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 18.0000 | 0.971909 | 0.485954 | − | 0.873984i | \(-0.338472\pi\) | ||||
0.485954 | + | 0.873984i | \(0.338472\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 22.0000 | 0.814815 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 27.0000 | 0.740073 | 0.370037 | − | 0.929017i | \(-0.379345\pi\) | ||||
0.370037 | + | 0.929017i | \(0.379345\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 57.0000 | 1.21607 | 0.608037 | − | 0.793909i | \(-0.291957\pi\) | ||||
0.608037 | + | 0.793909i | \(0.291957\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −105.000 | −1.80739 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −44.0000 | −0.627739 | −0.313870 | − | 0.949466i | \(-0.601625\pi\) | ||||
−0.313870 | + | 0.949466i | \(0.601625\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 152.000 | 1.83533 | 0.917663 | − | 0.397360i | \(-0.130073\pi\) | ||||
0.917663 | + | 0.397360i | \(0.130073\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −126.000 | −1.30931 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 152.000 | 1.37801 | 0.689004 | − | 0.724757i | \(-0.258048\pi\) | ||||
0.689004 | + | 0.724757i | \(0.258048\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 100.000 | 0.800000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 35.0000 | 0.249472 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 29.0000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 173.000 | 1.00231 | 0.501157 | − | 0.865357i | \(-0.332908\pi\) | ||||
0.501157 | + | 0.865357i | \(0.332908\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −189.000 | −0.996990 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 270.000 | 1.30395 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 120.000 | 0.533186 | 0.266593 | − | 0.963809i | \(-0.414102\pi\) | ||||
0.266593 | + | 0.963809i | \(0.414102\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −399.000 | −1.63823 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −314.000 | −1.19606 | −0.598031 | − | 0.801473i | \(-0.704050\pi\) | ||||
−0.598031 | + | 0.801473i | \(0.704050\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 339.000 | 1.20226 | 0.601128 | − | 0.799153i | \(-0.294718\pi\) | ||||
0.601128 | + | 0.799153i | \(0.294718\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 330.000 | 1.09319 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 357.000 | 1.10795 | 0.553977 | − | 0.832532i | \(-0.313110\pi\) | ||||
0.553977 | + | 0.832532i | \(0.313110\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −19.0000 | −0.0553936 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 308.000 | 0.845659 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 59.0000 | 0.152911 | 0.0764554 | − | 0.997073i | \(-0.475640\pi\) | ||||
0.0764554 | + | 0.997073i | \(0.475640\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 405.000 | 0.992913 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1064.00 | −2.47246 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −572.000 | −1.26217 | −0.631085 | − | 0.775713i | \(-0.717390\pi\) | ||||
−0.631085 | + | 0.775713i | \(0.717390\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 420.000 | 0.881565 | 0.440783 | − | 0.897614i | \(-0.354701\pi\) | ||||
0.440783 | + | 0.897614i | \(0.354701\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 396.000 | 0.791926 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 855.000 | 1.63153 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 660.000 | 1.20346 | 0.601730 | − | 0.798699i | \(-0.294478\pi\) | ||||
0.601730 | + | 0.798699i | \(0.294478\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1064.00 | −1.85638 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −726.000 | −1.21353 | −0.606763 | − | 0.794883i | \(-0.707532\pi\) | ||||
−0.606763 | + | 0.794883i | \(0.707532\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1004.00 | 1.60972 | 0.804858 | − | 0.593467i | \(-0.202241\pi\) | ||||
0.804858 | + | 0.593467i | \(0.202241\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −700.000 | −1.07772 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 486.000 | 0.719284 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −361.000 | −0.514122 | −0.257061 | − | 0.966395i | \(-0.582754\pi\) | ||||
−0.257061 | + | 0.966395i | \(0.582754\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −839.000 | −1.15089 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −168.000 | −0.222173 | −0.111087 | − | 0.993811i | \(-0.535433\pi\) | ||||
−0.111087 | + | 0.993811i | \(0.535433\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −660.000 | −0.842201 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −203.000 | −0.250160 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 58.0000 | 0.0690785 | 0.0345393 | − | 0.999403i | \(-0.489004\pi\) | ||||
0.0345393 | + | 0.999403i | \(0.489004\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1026.00 | 1.18191 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1211.00 | −1.35027 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2280.00 | 2.46235 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1206.00 | −1.26238 | −0.631189 | − | 0.775629i | \(-0.717433\pi\) | ||||
−0.631189 | + | 0.775629i | \(0.717433\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 594.000 | 0.603023 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1440.00 | −1.41867 | −0.709333 | − | 0.704873i | \(-0.751004\pi\) | ||||
−0.709333 | + | 0.704873i | \(0.751004\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1858.00 | −1.77742 | −0.888710 | − | 0.458471i | \(-0.848397\pi\) | ||||
−0.888710 | + | 0.458471i | \(0.848397\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1890.00 | −1.75662 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1914.00 | −1.72928 | −0.864642 | − | 0.502389i | \(-0.832455\pi\) | ||||
−0.864642 | + | 0.502389i | \(0.832455\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −989.000 | −0.869074 | −0.434537 | − | 0.900654i | \(-0.643088\pi\) | ||||
−0.434537 | + | 0.900654i | \(0.643088\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −840.000 | −0.718282 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −278.000 | −0.231434 | −0.115717 | − | 0.993282i | \(-0.536917\pi\) | ||||
−0.115717 | + | 0.993282i | \(0.536917\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2280.00 | 1.84879 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1254.00 | 0.990875 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −792.000 | −0.610105 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −602.000 | −0.452292 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2198.00 | 1.61128 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −375.000 | −0.268328 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 600.000 | 0.419224 | 0.209612 | − | 0.977785i | \(-0.432780\pi\) | ||||
0.209612 | + | 0.977785i | \(0.432780\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2373.00 | −1.61962 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1652.00 | −1.10180 | −0.550900 | − | 0.834571i | \(-0.685716\pi\) | ||||
−0.550900 | + | 0.834571i | \(0.685716\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2736.00 | 1.78377 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 525.000 | 0.334702 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1212.00 | −0.755826 | −0.377913 | − | 0.925841i | \(-0.623358\pi\) | ||||
−0.377913 | + | 0.925841i | \(0.623358\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1328.00 | 0.810356 | 0.405178 | − | 0.914238i | \(-0.367210\pi\) | ||||
0.405178 | + | 0.914238i | \(0.367210\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2499.00 | −1.49258 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1539.00 | 0.899984 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 435.000 | 0.249136 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 133.000 | 0.0746235 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1777.00 | 0.977030 | 0.488515 | − | 0.872555i | \(-0.337539\pi\) | ||||
0.488515 | + | 0.872555i | \(0.337539\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1934.00 | 1.04230 | 0.521148 | − | 0.853466i | \(-0.325504\pi\) | ||||
0.521148 | + | 0.853466i | \(0.325504\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −968.000 | −0.511491 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2595.00 | 1.34474 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −734.000 | −0.373118 | −0.186559 | − | 0.982444i | \(-0.559734\pi\) | ||||
−0.186559 | + | 0.982444i | \(0.559734\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −413.000 | −0.205994 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2736.00 | 1.33930 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3337.00 | −1.60352 | −0.801761 | − | 0.597645i | \(-0.796103\pi\) | ||||
−0.801761 | + | 0.597645i | \(0.796103\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2835.00 | −1.33760 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 198.000 | 0.0917467 | 0.0458734 | − | 0.998947i | \(-0.485393\pi\) | ||||
0.0458734 | + | 0.998947i | \(0.485393\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1052.00 | 0.478835 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3344.00 | 1.49545 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2598.00 | 1.14175 | 0.570874 | − | 0.821038i | \(-0.306605\pi\) | ||||
0.570874 | + | 0.821038i | \(0.306605\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1800.00 | 0.777527 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4004.00 | 1.70033 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1510.00 | −0.630518 | −0.315259 | − | 0.949006i | \(-0.602091\pi\) | ||||
−0.315259 | + | 0.949006i | \(0.602091\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2865.00 | 1.17654 | 0.588270 | − | 0.808665i | \(-0.299809\pi\) | ||||
0.588270 | + | 0.808665i | \(0.299809\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2940.00 | −1.18760 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1800.00 | 0.715344 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1188.00 | −0.464573 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 630.000 | 0.242464 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1936.00 | 0.733424 | 0.366712 | − | 0.930334i | \(-0.380483\pi\) | ||||
0.366712 | + | 0.930334i | \(0.380483\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3850.00 | 1.43590 | 0.717951 | − | 0.696094i | \(-0.245080\pi\) | ||||
0.717951 | + | 0.696094i | \(0.245080\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5985.00 | −2.19792 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3034.00 | −1.09728 | −0.548638 | − | 0.836060i | \(-0.684854\pi\) | ||||
−0.548638 | + | 0.836060i | \(0.684854\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −246.000 | −0.0876305 | −0.0438153 | − | 0.999040i | \(-0.513951\pi\) | ||||
−0.0438153 | + | 0.999040i | \(0.513951\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4620.00 | −1.62124 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 522.000 | 0.180479 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4710.00 | −1.60469 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3344.00 | 1.12282 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4104.00 | 1.35828 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1493.00 | −0.487120 | −0.243560 | − | 0.969886i | \(-0.578315\pi\) | ||||
−0.243560 | + | 0.969886i | \(0.578315\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5082.00 | 1.63480 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5085.00 | 1.61300 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3114.00 | 0.974157 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7028.00 | −2.16853 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2508.00 | −0.763377 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1402.00 | −0.421008 | −0.210504 | − | 0.977593i | \(-0.567511\pi\) | ||||
−0.210504 | + | 0.977593i | \(0.567511\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2200.00 | 0.651852 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1166.00 | 0.340926 | 0.170463 | − | 0.985364i | \(-0.445474\pi\) | ||||
0.170463 | + | 0.985364i | \(0.445474\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1466.00 | 0.423039 | 0.211520 | − | 0.977374i | \(-0.432159\pi\) | ||||
0.211520 | + | 0.977374i | \(0.432159\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3402.00 | −0.968983 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 847.000 | 0.238149 | 0.119075 | − | 0.992885i | \(-0.462007\pi\) | ||||
0.119075 | + | 0.992885i | \(0.462007\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5355.00 | 1.48648 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2527.00 | 0.692600 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 444.000 | 0.120167 | 0.0600836 | − | 0.998193i | \(-0.480863\pi\) | ||||
0.0600836 | + | 0.998193i | \(0.480863\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5297.00 | 1.41581 | 0.707904 | − | 0.706309i | \(-0.249641\pi\) | ||||
0.707904 | + | 0.706309i | \(0.249641\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 4928.00 | 1.30095 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −285.000 | −0.0743183 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8664.00 | 2.23189 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1176.00 | 0.299301 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4061.00 | 1.02123 | 0.510614 | − | 0.859810i | \(-0.329418\pi\) | ||||
0.510614 | + | 0.859810i | \(0.329418\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4104.00 | 1.01983 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4620.00 | 1.13457 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6843.00 | −1.66091 | −0.830456 | − | 0.557084i | \(-0.811920\pi\) | ||||
−0.830456 | + | 0.557084i | \(0.811920\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2160.00 | 0.518208 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 638.000 | 0.151307 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3191.00 | −0.748158 | −0.374079 | − | 0.927397i | \(-0.622041\pi\) | ||||
−0.374079 | + | 0.927397i | \(0.622041\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 885.000 | 0.205151 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −406.000 | −0.0930592 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7436.00 | −1.68543 | −0.842715 | − | 0.538359i | \(-0.819044\pi\) | ||||
−0.842715 | + | 0.538359i | \(0.819044\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2755.00 | 0.617544 | 0.308772 | − | 0.951136i | \(-0.400082\pi\) | ||||
0.308772 | + | 0.951136i | \(0.400082\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −7182.00 | −1.59221 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2700.00 | 0.592059 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2410.00 | 0.522754 | 0.261377 | − | 0.965237i | \(-0.415823\pi\) | ||||
0.261377 | + | 0.965237i | \(0.415823\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3806.00 | 0.816700 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2235.00 | 0.474480 | 0.237240 | − | 0.971451i | \(-0.423757\pi\) | ||||
0.237240 | + | 0.971451i | \(0.423757\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1648.00 | −0.346161 | −0.173080 | − | 0.984908i | \(-0.555372\pi\) | ||||
−0.173080 | + | 0.984908i | \(0.555372\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −15960.0 | −3.31715 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5652.00 | −1.16246 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2977.00 | −0.605943 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8442.00 | 1.70061 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2878.00 | −0.573838 | −0.286919 | − | 0.957955i | \(-0.592631\pi\) | ||||
−0.286919 | + | 0.957955i | \(0.592631\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8580.00 | −1.69338 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 945.000 | 0.184628 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8664.00 | 1.67576 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6102.00 | 1.16848 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 10080.0 | 1.91116 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6300.00 | 1.18274 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4903.00 | 0.911495 | 0.455748 | − | 0.890109i | \(-0.349372\pi\) | ||||
0.455748 | + | 0.890109i | \(0.349372\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 13006.0 | 2.39445 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 32.0000 | 0.00583458 | 0.00291729 | − | 0.999996i | \(-0.499071\pi\) | ||||
0.00291729 | + | 0.999996i | \(0.499071\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5455.00 | −0.985095 | −0.492548 | − | 0.870285i | \(-0.663934\pi\) | ||||
−0.492548 | + | 0.870285i | \(0.663934\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5940.00 | 1.06248 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9552.00 | 1.69241 | 0.846205 | − | 0.532858i | \(-0.178882\pi\) | ||||
0.846205 | + | 0.532858i | \(0.178882\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 783.000 | 0.137428 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 13398.0 | 2.32961 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6688.00 | −1.15211 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5700.00 | 0.972859 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6923.00 | 1.17077 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6426.00 | 1.07683 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2433.00 | −0.404017 | −0.202009 | − | 0.979384i | \(-0.564747\pi\) | ||||
−0.202009 | + | 0.979384i | \(0.564747\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2640.00 | 0.434448 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9900.00 | 1.61461 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7460.00 | −1.20585 | −0.602926 | − | 0.797797i | \(-0.705999\pi\) | ||||
−0.602926 | + | 0.797797i | \(0.705999\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1946.00 | 0.311776 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4671.00 | 0.741785 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6516.00 | −1.02575 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −15960.0 | −2.49060 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4002.00 | 0.619131 | 0.309566 | − | 0.950878i | \(-0.399816\pi\) | ||||
0.309566 | + | 0.950878i | \(0.399816\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2167.00 | 0.332369 | 0.166185 | − | 0.986095i | \(-0.446855\pi\) | ||||
0.166185 | + | 0.986095i | \(0.446855\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1995.00 | 0.303377 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2354.00 | −0.354931 | −0.177466 | − | 0.984127i | \(-0.556790\pi\) | ||||
−0.177466 | + | 0.984127i | \(0.556790\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10890.0 | −1.62812 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5544.00 | 0.821904 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3471.00 | 0.510285 | 0.255143 | − | 0.966903i | \(-0.417878\pi\) | ||||
0.255143 | + | 0.966903i | \(0.417878\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16245.0 | 2.36842 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4214.00 | 0.609305 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15060.0 | 2.15966 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10880.0 | 1.54750 | 0.773748 | − | 0.633493i | \(-0.218379\pi\) | ||||
0.773748 | + | 0.633493i | \(0.218379\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6908.00 | −0.974569 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1062.00 | 0.148615 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8827.00 | −1.22532 | −0.612661 | − | 0.790346i | \(-0.709901\pi\) | ||||
−0.612661 | + | 0.790346i | \(0.709901\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2625.00 | 0.361478 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1653.00 | 0.225819 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −876.000 | −0.118726 | −0.0593629 | − | 0.998236i | \(-0.518907\pi\) | ||||
−0.0593629 | + | 0.998236i | \(0.518907\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4200.00 | −0.564757 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5446.00 | −0.726573 | −0.363287 | − | 0.931677i | \(-0.618345\pi\) | ||||
−0.363287 | + | 0.931677i | \(0.618345\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7290.00 | 0.965020 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7458.00 | 0.979616 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2216.00 | 0.288832 | 0.144416 | − | 0.989517i | \(-0.453870\pi\) | ||||
0.144416 | + | 0.989517i | \(0.453870\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6688.00 | −0.865030 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 11564.0 | 1.48429 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5415.00 | −0.689768 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6823.00 | −0.862561 | −0.431280 | − | 0.902218i | \(-0.641938\pi\) | ||||
−0.431280 | + | 0.902218i | \(0.641938\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −19152.0 | −2.40301 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5589.00 | −0.696013 | −0.348007 | − | 0.937492i | \(-0.613141\pi\) | ||||
−0.348007 | + | 0.937492i | \(0.613141\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9861.00 | 1.21889 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −12585.0 | −1.54408 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3240.00 | 0.394597 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8258.00 | −0.998366 | −0.499183 | − | 0.866496i | \(-0.666367\pi\) | ||||
−0.499183 | + | 0.866496i | \(0.666367\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8484.00 | 1.01821 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −10296.0 | −1.22671 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2520.00 | −0.298077 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9296.00 | −1.09167 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3946.00 | 0.460083 | 0.230041 | − | 0.973181i | \(-0.426114\pi\) | ||||
0.230041 | + | 0.973181i | \(0.426114\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1380.00 | −0.159756 | −0.0798778 | − | 0.996805i | \(-0.525453\pi\) | ||||
−0.0798778 | + | 0.996805i | \(0.525453\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7854.00 | 0.902777 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4400.00 | −0.502191 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7560.00 | 0.856801 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −10773.0 | −1.21241 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5820.00 | 0.650440 | 0.325220 | − | 0.945638i | \(-0.394562\pi\) | ||||
0.325220 | + | 0.945638i | \(0.394562\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14504.0 | −1.60974 | −0.804870 | − | 0.593451i | \(-0.797765\pi\) | ||||
−0.804870 | + | 0.593451i | \(0.797765\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3045.00 | −0.335624 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 23104.0 | 2.52909 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14912.0 | −1.62121 | −0.810605 | − | 0.585594i | \(-0.800861\pi\) | ||||
−0.810605 | + | 0.585594i | \(0.800861\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −418.000 | −0.0451355 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7180.00 | 0.770050 | 0.385025 | − | 0.922906i | \(-0.374193\pi\) | ||||
0.385025 | + | 0.922906i | \(0.374193\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 870.000 | 0.0926786 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −12439.0 | −1.31621 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1398.00 | 0.146939 | 0.0734696 | − | 0.997297i | \(-0.476593\pi\) | ||||
0.0734696 | + | 0.997297i | \(0.476593\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8478.00 | −0.885174 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −13538.0 | −1.40413 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 15390.0 | 1.58570 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5658.00 | −0.579147 | −0.289573 | − | 0.957156i | \(-0.593513\pi\) | ||||
−0.289573 | + | 0.957156i | \(0.593513\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1540.00 | −0.156604 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11410.0 | −1.15275 | −0.576374 | − | 0.817186i | \(-0.695533\pi\) | ||||
−0.576374 | + | 0.817186i | \(0.695533\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2560.00 | 0.256962 | 0.128481 | − | 0.991712i | \(-0.458990\pi\) | ||||
0.128481 | + | 0.991712i | \(0.458990\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −18165.0 | −1.81157 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10395.0 | 1.03003 | 0.515014 | − | 0.857182i | \(-0.327787\pi\) | ||||
0.515014 | + | 0.857182i | \(0.327787\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11880.0 | 1.16965 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5138.00 | 0.502647 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9153.00 | 0.889758 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 15200.0 | 1.46826 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1298.00 | 0.124594 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5627.00 | 0.536752 | 0.268376 | − | 0.963314i | \(-0.413513\pi\) | ||||
0.268376 | + | 0.963314i | \(0.413513\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6840.00 | 0.648393 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −19152.0 | −1.80424 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −18090.0 | −1.69366 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8738.00 | −0.813053 | −0.406526 | − | 0.913639i | \(-0.633260\pi\) | ||||
−0.406526 | + | 0.913639i | \(0.633260\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 23359.0 | 2.16019 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3177.00 | 0.292008 | 0.146004 | − | 0.989284i | \(-0.453359\pi\) | ||||
0.146004 | + | 0.989284i | \(0.453359\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1276.00 | −0.116568 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8910.00 | 0.809040 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −13068.0 | −1.17944 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5816.00 | −0.521763 | −0.260882 | − | 0.965371i | \(-0.584013\pi\) | ||||
−0.260882 | + | 0.965371i | \(0.584013\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1386.00 | −0.123597 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2267.00 | 0.200955 | 0.100478 | − | 0.994939i | \(-0.467963\pi\) | ||||
0.100478 | + | 0.994939i | \(0.467963\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −21600.0 | −1.90334 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7364.00 | −0.645063 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6481.00 | −0.564372 | −0.282186 | − | 0.959360i | \(-0.591060\pi\) | ||||
−0.282186 | + | 0.959360i | \(0.591060\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 18072.0 | 1.56450 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5320.00 | 0.457863 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −27870.0 | −2.38466 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9639.00 | 0.819967 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −18186.0 | −1.53811 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21357.0 | −1.79591 | −0.897953 | − | 0.440091i | \(-0.854946\pi\) | ||||
−0.897953 | + | 0.440091i | \(0.854946\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6192.00 | −0.517700 | −0.258850 | − | 0.965917i | \(-0.583344\pi\) | ||||
−0.258850 | + | 0.965917i | \(0.583344\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −12600.0 | −1.04745 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7612.00 | −0.629192 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10937.0 | 0.898907 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −12584.0 | −1.02844 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −17898.0 | −1.45450 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −28710.0 | −2.32008 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 10570.0 | 0.849403 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −513.000 | −0.0409953 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19800.0 | 1.57351 | 0.786755 | − | 0.617266i | \(-0.211760\pi\) | ||||
0.786755 | + | 0.617266i | \(0.211760\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −20055.0 | −1.58498 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −14835.0 | −1.16598 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10526.0 | 0.822777 | 0.411389 | − | 0.911460i | \(-0.365044\pi\) | ||||
0.411389 | + | 0.911460i | \(0.365044\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9240.00 | 0.718313 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4408.00 | 0.340811 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6498.00 | −0.499680 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −12600.0 | −0.963676 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11834.0 | 0.900220 | 0.450110 | − | 0.892973i | \(-0.351385\pi\) | ||||
0.450110 | + | 0.892973i | \(0.351385\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 19323.0 | 1.46203 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8316.00 | 0.625850 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 21771.0 | 1.62973 | 0.814865 | − | 0.579650i | \(-0.196811\pi\) | ||||
0.814865 | + | 0.579650i | \(0.196811\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4170.00 | −0.310501 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −15102.0 | −1.11856 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 20778.0 | 1.53086 | 0.765430 | − | 0.643519i | \(-0.222526\pi\) | ||||
0.765430 | + | 0.643519i | \(0.222526\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5596.00 | −0.410132 | −0.205066 | − | 0.978748i | \(-0.565741\pi\) | ||||
−0.205066 | + | 0.978748i | \(0.565741\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −13552.0 | −0.988033 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 15200.0 | 1.10241 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14908.0 | −1.07561 | −0.537806 | − | 0.843069i | \(-0.680747\pi\) | ||||
−0.537806 | + | 0.843069i | \(0.680747\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −26950.0 | −1.93438 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3024.00 | −0.215932 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1593.00 | 0.113165 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 18810.0 | 1.32940 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8136.00 | 0.572076 | 0.286038 | − | 0.958218i | \(-0.407662\pi\) | ||||
0.286038 | + | 0.958218i | \(0.407662\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 26296.0 | 1.83957 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 21238.0 | 1.47820 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3521.00 | −0.243828 | −0.121914 | − | 0.992541i | \(-0.538903\pi\) | ||||
−0.121914 | + | 0.992541i | \(0.538903\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −11880.0 | −0.818542 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1722.00 | 0.118052 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7749.00 | −0.528574 | −0.264287 | − | 0.964444i | \(-0.585137\pi\) | ||||
−0.264287 | + | 0.964444i | \(0.585137\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5054.00 | 0.343023 | 0.171512 | − | 0.985182i | \(-0.445135\pi\) | ||||
0.171512 | + | 0.985182i | \(0.445135\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14520.0 | 0.980597 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9030.00 | −0.606813 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −27389.0 | −1.83144 | −0.915721 | − | 0.401815i | \(-0.868380\pi\) | ||||
−0.915721 | + | 0.401815i | \(0.868380\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3654.00 | −0.243132 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 20349.0 | 1.34735 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2375.00 | 0.156485 | 0.0782425 | − | 0.996934i | \(-0.475069\pi\) | ||||
0.0782425 | + | 0.996934i | \(0.475069\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 32970.0 | 2.16175 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3412.00 | 0.222629 | 0.111314 | − | 0.993785i | \(-0.464494\pi\) | ||||
0.111314 | + | 0.993785i | \(0.464494\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17659.0 | 1.14665 | 0.573324 | − | 0.819329i | \(-0.305654\pi\) | ||||
0.573324 | + | 0.819329i | \(0.305654\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5320.00 | 0.343775 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1044.00 | 0.0671380 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −18125.0 | −1.16000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −28728.0 | −1.82980 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5280.00 | −0.334702 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12742.0 | −0.803884 | −0.401942 | − | 0.915665i | \(-0.631665\pi\) | ||||
−0.401942 | + | 0.915665i | \(0.631665\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 10451.0 | 0.656224 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9000.00 | 0.562447 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1083.00 | −0.0673627 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −15972.0 | −0.988799 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10988.0 | −0.677067 | −0.338533 | − | 0.940954i | \(-0.609931\pi\) | ||||
−0.338533 | + | 0.940954i | \(0.609931\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −13190.0 | −0.808962 | −0.404481 | − | 0.914546i | \(-0.632548\pi\) | ||||
−0.404481 | + | 0.914546i | \(0.632548\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −35595.0 | −2.17295 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −22924.0 | −1.39295 | −0.696473 | − | 0.717583i | \(-0.745248\pi\) | ||||
−0.696473 | + | 0.717583i | \(0.745248\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −15444.0 | −0.934099 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −21798.0 | −1.31234 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10278.0 | 0.615941 | 0.307970 | − | 0.951396i | \(-0.400350\pi\) | ||||
0.307970 | + | 0.951396i | \(0.400350\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −24780.0 | −1.47822 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 22088.0 | 1.31162 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10607.0 | −0.626996 | −0.313498 | − | 0.949589i | \(-0.601501\pi\) | ||||
−0.313498 | + | 0.949589i | \(0.601501\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24698.0 | 1.45331 | 0.726657 | − | 0.687000i | \(-0.241073\pi\) | ||||
0.726657 | + | 0.687000i | \(0.241073\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 17556.0 | 1.02838 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 41040.0 | 2.39318 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4408.00 | 0.255890 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9814.00 | 0.567162 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11340.0 | 0.652423 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16801.0 | 0.962305 | 0.481152 | − | 0.876637i | \(-0.340218\pi\) | ||||
0.481152 | + | 0.876637i | \(0.340218\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3500.00 | 0.199578 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1258.00 | 0.0714163 | 0.0357082 | − | 0.999362i | \(-0.488631\pi\) | ||||
0.0357082 | + | 0.999362i | \(0.488631\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −21708.0 | −1.22692 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8162.00 | −0.459278 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1256.00 | −0.0703653 | −0.0351827 | − | 0.999381i | \(-0.511201\pi\) | ||||
−0.0351827 | + | 0.999381i | \(0.511201\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −18180.0 | −1.01405 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −10262.0 | −0.569898 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3363.00 | 0.185951 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15996.0 | −0.880632 | −0.440316 | − | 0.897843i | \(-0.645134\pi\) | ||||
−0.440316 | + | 0.897843i | \(0.645134\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 10692.0 | 0.586083 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 19920.0 | 1.08721 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13816.0 | 0.750815 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5929.00 | −0.320823 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 189.000 | 0.0101832 | 0.00509161 | − | 0.999987i | \(-0.498379\pi\) | ||||
0.00509161 | + | 0.999987i | \(0.498379\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18240.0 | 0.978570 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −37485.0 | −2.00251 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −25920.0 | −1.37881 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2431.00 | −0.128770 | −0.0643851 | − | 0.997925i | \(-0.520509\pi\) | ||||
−0.0643851 | + | 0.997925i | \(0.520509\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7942.00 | −0.418915 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 26296.0 | 1.38120 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 23085.0 | 1.20745 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3108.00 | −0.161883 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3630.00 | 0.188284 | 0.0941420 | − | 0.995559i | \(-0.469989\pi\) | ||||
0.0941420 | + | 0.995559i | \(0.469989\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −33444.0 | −1.72749 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −37079.0 | −1.90731 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2900.00 | 0.148556 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1712.00 | 0.0873378 | 0.0436689 | − | 0.999046i | \(-0.486095\pi\) | ||||
0.0436689 | + | 0.999046i | \(0.486095\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −11843.0 | −0.601687 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −14916.0 | −0.754703 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −26584.0 | −1.33957 | −0.669783 | − | 0.742557i | \(-0.733613\pi\) | ||||
−0.669783 | + | 0.742557i | \(0.733613\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1995.00 | 0.100118 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 17820.0 | 0.890649 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8125.00 | 0.404442 | 0.202221 | − | 0.979340i | \(-0.435184\pi\) | ||||
0.202221 | + | 0.979340i | \(0.435184\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −60648.0 | −3.00669 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 31804.0 | 1.57036 | 0.785179 | − | 0.619269i | \(-0.212571\pi\) | ||||
0.785179 | + | 0.619269i | \(0.212571\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 26655.0 | 1.31082 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3696.00 | −0.181030 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −34452.0 | −1.68071 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 37504.0 | 1.82229 | 0.911145 | − | 0.412085i | \(-0.135199\pi\) | ||||
0.911145 | + | 0.412085i | \(0.135199\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −28427.0 | −1.37575 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 29010.0 | 1.39839 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 76.0000 | 0.00364897 | 0.00182448 | − | 0.999998i | \(-0.499419\pi\) | ||||
0.00182448 | + | 0.999998i | \(0.499419\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −28728.0 | −1.37386 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −23374.0 | −1.11341 | −0.556706 | − | 0.830709i | \(-0.687935\pi\) | ||||
−0.556706 | + | 0.830709i | \(0.687935\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −17802.0 | −0.844660 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −14520.0 | −0.686238 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −32604.0 | −1.53489 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5448.00 | −0.255475 | −0.127737 | − | 0.991808i | \(-0.540771\pi\) | ||||
−0.127737 | + | 0.991808i | \(0.540771\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 47901.0 | 2.23750 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 16062.0 | 0.747361 | 0.373680 | − | 0.927558i | \(-0.378096\pi\) | ||||
0.373680 | + | 0.927558i | \(0.378096\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 17300.0 | 0.801851 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −15120.0 | −0.698104 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −47728.0 | −2.19516 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19602.0 | −0.898098 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1015.00 | 0.0463259 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −11010.0 | −0.500591 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19182.0 | 0.868824 | 0.434412 | − | 0.900714i | \(-0.356956\pi\) | ||||
0.434412 | + | 0.900714i | \(0.356956\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 22337.0 | 1.00788 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5004.00 | −0.224933 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 23940.0 | 1.07205 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −6195.00 | −0.276370 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5556.00 | −0.246931 | −0.123465 | − | 0.992349i | \(-0.539401\pi\) | ||||
−0.123465 | + | 0.992349i | \(0.539401\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15708.0 | −0.695506 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1276.00 | 0.0562862 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 27108.0 | 1.19131 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 41040.0 | 1.79686 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 52052.0 | 2.27053 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2616.00 | 0.113688 | 0.0568440 | − | 0.998383i | \(-0.481896\pi\) | ||||
0.0568440 | + | 0.998383i | \(0.481896\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9626.00 | −0.416787 | −0.208394 | − | 0.978045i | \(-0.566824\pi\) | ||||
−0.208394 | + | 0.978045i | \(0.566824\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −19285.0 | −0.831924 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −50055.0 | −2.15135 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 51528.0 | 2.20653 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 22572.0 | 0.963040 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16007.0 | −0.680448 | −0.340224 | − | 0.940344i | \(-0.610503\pi\) | ||||
−0.340224 | + | 0.940344i | \(0.610503\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −23216.0 | −0.983304 | −0.491652 | − | 0.870792i | \(-0.663607\pi\) | ||||
−0.491652 | + | 0.870792i | \(0.663607\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −18900.0 | −0.797592 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −46765.0 | −1.96636 | −0.983179 | − | 0.182644i | \(-0.941535\pi\) | ||||
−0.983179 | + | 0.182644i | \(0.941535\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37820.0 | 1.58449 | 0.792245 | − | 0.610203i | \(-0.208912\pi\) | ||||
0.792245 | + | 0.610203i | \(0.208912\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −16870.0 | −0.704228 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 836.000 | 0.0347727 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2970.00 | 0.123091 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6055.00 | 0.250049 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −6747.00 | −0.277631 | −0.138815 | − | 0.990318i | \(-0.544329\pi\) | ||||
−0.138815 | + | 0.990318i | \(0.544329\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 841.000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −15645.0 | −0.639196 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 15780.0 | 0.642424 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10836.0 | −0.439586 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 11536.0 | 0.466330 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 18240.0 | 0.734735 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13274.0 | 0.532817 | 0.266409 | − | 0.963860i | \(-0.414163\pi\) | ||||
0.266409 | + | 0.963860i | \(0.414163\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 50160.0 | 2.00636 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 39069.0 | 1.55726 | 0.778630 | − | 0.627483i | \(-0.215915\pi\) | ||||
0.778630 | + | 0.627483i | \(0.215915\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 35329.0 | 1.40327 | 0.701636 | − | 0.712536i | \(-0.252453\pi\) | ||||
0.701636 | + | 0.712536i | \(0.252453\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 39564.0 | 1.56601 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 36378.0 | 1.43490 | 0.717452 | − | 0.696608i | \(-0.245308\pi\) | ||||
0.717452 | + | 0.696608i | \(0.245308\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 38970.0 | 1.53181 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 20839.0 | 0.816297 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9747.00 | −0.380488 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 37620.0 | 1.46350 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −26532.0 | −1.02860 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6750.00 | −0.260790 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 219.000 | 0.00843227 | 0.00421614 | − | 0.999991i | \(-0.498658\pi\) | ||||
0.00421614 | + | 0.999991i | \(0.498658\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 20146.0 | 0.773046 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5598.00 | −0.214077 | −0.107038 | − | 0.994255i | \(-0.534137\pi\) | ||||
−0.107038 | + | 0.994255i | \(0.534137\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5886.00 | 0.224326 | 0.112163 | − | 0.993690i | \(-0.464222\pi\) | ||||
0.112163 | + | 0.993690i | \(0.464222\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 60060.0 | 2.28124 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 29673.0 | 1.12325 | 0.561624 | − | 0.827392i | \(-0.310177\pi\) | ||||
0.561624 | + | 0.827392i | \(0.310177\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10800.0 | 0.407447 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −22653.0 | −0.851744 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 54264.0 | 2.03346 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −22650.0 | −0.845928 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −60648.0 | −2.25750 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5017.00 | 0.186125 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2596.00 | −0.0959881 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −42714.0 | −1.57412 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 42975.0 | 1.57849 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13668.0 | 0.500373 | 0.250187 | − | 0.968198i | \(-0.419508\pi\) | ||||
0.250187 | + | 0.968198i | \(0.419508\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −31680.0 | −1.15595 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4963.00 | 0.180496 | 0.0902478 | − | 0.995919i | \(-0.471234\pi\) | ||||
0.0902478 | + | 0.995919i | \(0.471234\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4536.00 | −0.164425 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −44100.0 | −1.59333 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −29736.0 | −1.07085 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9954.00 | −0.357293 | −0.178646 | − | 0.983913i | \(-0.557172\pi\) | ||||
−0.178646 | + | 0.983913i | \(0.557172\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −34321.0 | −1.22792 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −41382.0 | −1.47574 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12000.0 | 0.426549 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −40876.0 | −1.44827 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 30930.0 | 1.09234 | 0.546168 | − | 0.837676i | \(-0.316086\pi\) | ||||
0.546168 | + | 0.837676i | \(0.316086\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2888.00 | −0.101665 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −224.000 | −0.00786005 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −17820.0 | −0.623290 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −38770.0 | −1.35172 | −0.675859 | − | 0.737030i | \(-0.736227\pi\) | ||||
−0.675859 | + | 0.737030i | \(0.736227\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 38185.0 | 1.32707 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 30115.0 | 1.04327 | 0.521637 | − | 0.853167i | \(-0.325322\pi\) | ||||
0.521637 | + | 0.853167i | \(0.325322\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −47728.0 | −1.64818 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 9450.00 | 0.325300 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 31319.0 | 1.07469 | 0.537345 | − | 0.843363i | \(-0.319427\pi\) | ||||
0.537345 | + | 0.843363i | \(0.319427\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 57228.0 | 1.95753 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −66864.0 | −2.27993 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 7623.00 | 0.259111 | 0.129556 | − | 0.991572i | \(-0.458645\pi\) | ||||
0.129556 | + | 0.991572i | \(0.458645\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 29040.0 | 0.983992 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5481.00 | −0.185136 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −21816.0 | −0.734594 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 138.000 | 0.00463227 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −42108.0 | −1.40905 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 57750.0 | 1.92646 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6269.00 | 0.208477 | 0.104239 | − | 0.994552i | \(-0.466759\pi\) | ||||
0.104239 | + | 0.994552i | \(0.466759\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 46816.0 | 1.55206 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −34020.0 | −1.12436 | −0.562180 | − | 0.827015i | \(-0.690037\pi\) | ||||
−0.562180 | + | 0.827015i | \(0.690037\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 23904.0 | 0.787592 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −39900.0 | −1.31059 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −51291.0 | −1.67957 | −0.839787 | − | 0.542915i | \(-0.817320\pi\) | ||||
−0.839787 | + | 0.542915i | \(0.817320\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1566.00 | 0.0511232 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −21758.0 | −0.708134 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −38687.0 | −1.25526 | −0.627632 | − | 0.778511i | \(-0.715976\pi\) | ||||
−0.627632 | + | 0.778511i | \(0.715976\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −45510.0 | −1.47215 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −44982.0 | −1.45065 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 51528.0 | 1.65672 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3158.00 | 0.101228 | 0.0506141 | − | 0.998718i | \(-0.483882\pi\) | ||||
0.0506141 | + | 0.998718i | \(0.483882\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 17031.0 | 0.544272 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3690.00 | −0.117569 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21944.0 | 0.697065 | 0.348532 | − | 0.937297i | \(-0.386680\pi\) | ||||
0.348532 | + | 0.937297i | \(0.386680\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4200.00 | 0.133015 |
(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 | 1856.4.a.c.1.1 | 1 | ||
4.3 | odd | 2 | 1856.4.a.f.1.1 | 1 | |||
8.3 | odd | 2 | 58.4.a.b.1.1 | ✓ | 1 | ||
8.5 | even | 2 | 464.4.a.b.1.1 | 1 | |||
24.11 | even | 2 | 522.4.a.b.1.1 | 1 | |||
40.19 | odd | 2 | 1450.4.a.d.1.1 | 1 | |||
232.115 | odd | 2 | 1682.4.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
58.4.a.b.1.1 | ✓ | 1 | 8.3 | odd | 2 | ||
464.4.a.b.1.1 | 1 | 8.5 | even | 2 | |||
522.4.a.b.1.1 | 1 | 24.11 | even | 2 | |||
1450.4.a.d.1.1 | 1 | 40.19 | odd | 2 | |||
1682.4.a.a.1.1 | 1 | 232.115 | odd | 2 | |||
1856.4.a.c.1.1 | 1 | 1.1 | even | 1 | trivial | ||
1856.4.a.f.1.1 | 1 | 4.3 | odd | 2 |