Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8016,2,Mod(1,8016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8016, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8016 = 2^{4} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8016.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: | \(64.0080822603\) |
Analytic rank: | \(0\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 2 x^{12} - 49 x^{11} + 99 x^{10} + 901 x^{9} - 1879 x^{8} - 7582 x^{7} + 16968 x^{6} + \cdots + 12144 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 4008) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(0.649069\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8016.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.649069 | 0.290273 | 0.145136 | − | 0.989412i | \(-0.453638\pi\) | ||||
0.145136 | + | 0.989412i | \(0.453638\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.19646 | −1.58611 | −0.793057 | − | 0.609147i | \(-0.791512\pi\) | ||||
−0.793057 | + | 0.609147i | \(0.791512\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.95286 | −0.588810 | −0.294405 | − | 0.955681i | \(-0.595121\pi\) | ||||
−0.294405 | + | 0.955681i | \(0.595121\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.07299 | 0.852293 | 0.426146 | − | 0.904654i | \(-0.359871\pi\) | ||||
0.426146 | + | 0.904654i | \(0.359871\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.649069 | −0.167589 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.85258 | 1.66200 | 0.830998 | − | 0.556276i | \(-0.187770\pi\) | ||||
0.830998 | + | 0.556276i | \(0.187770\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −8.04597 | −1.84587 | −0.922936 | − | 0.384954i | \(-0.874217\pi\) | ||||
−0.922936 | + | 0.384954i | \(0.874217\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.19646 | 0.915744 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.50672 | 1.35675 | 0.678373 | − | 0.734718i | \(-0.262686\pi\) | ||||
0.678373 | + | 0.734718i | \(0.262686\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.57871 | −0.915742 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.52529 | −0.468935 | −0.234468 | − | 0.972124i | \(-0.575335\pi\) | ||||
−0.234468 | + | 0.972124i | \(0.575335\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.14955 | −0.745281 | −0.372640 | − | 0.927976i | \(-0.621547\pi\) | ||||
−0.372640 | + | 0.927976i | \(0.621547\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.95286 | 0.339949 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.72380 | −0.460406 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.94625 | −0.813159 | −0.406579 | − | 0.913615i | \(-0.633279\pi\) | ||||
−0.406579 | + | 0.913615i | \(0.633279\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.07299 | −0.492072 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.05737 | 0.321308 | 0.160654 | − | 0.987011i | \(-0.448640\pi\) | ||||
0.160654 | + | 0.987011i | \(0.448640\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.35750 | −0.664512 | −0.332256 | − | 0.943189i | \(-0.607810\pi\) | ||||
−0.332256 | + | 0.943189i | \(0.607810\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.649069 | 0.0967576 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.2109 | 1.63528 | 0.817641 | − | 0.575728i | \(-0.195281\pi\) | ||||
0.817641 | + | 0.575728i | \(0.195281\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 10.6103 | 1.51576 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.85258 | −0.959554 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.69789 | −0.233224 | −0.116612 | − | 0.993178i | \(-0.537203\pi\) | ||||
−0.116612 | + | 0.993178i | \(0.537203\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.26754 | −0.170915 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.04597 | 1.06571 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.31745 | 0.952651 | 0.476326 | − | 0.879269i | \(-0.341968\pi\) | ||||
0.476326 | + | 0.879269i | \(0.341968\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.5360 | −1.60507 | −0.802534 | − | 0.596607i | \(-0.796515\pi\) | ||||
−0.802534 | + | 0.596607i | \(0.796515\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.19646 | −0.528705 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.99458 | 0.247397 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.97495 | 0.852126 | 0.426063 | − | 0.904694i | \(-0.359900\pi\) | ||||
0.426063 | + | 0.904694i | \(0.359900\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.50672 | −0.783317 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.84782 | −0.337974 | −0.168987 | − | 0.985618i | \(-0.554050\pi\) | ||||
−0.168987 | + | 0.985618i | \(0.554050\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.78221 | −0.910839 | −0.455420 | − | 0.890277i | \(-0.650511\pi\) | ||||
−0.455420 | + | 0.890277i | \(0.650511\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.57871 | 0.528704 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.19511 | 0.933920 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.29528 | 0.370747 | 0.185374 | − | 0.982668i | \(-0.440650\pi\) | ||||
0.185374 | + | 0.982668i | \(0.440650\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.99647 | −0.219141 | −0.109571 | − | 0.993979i | \(-0.534948\pi\) | ||||
−0.109571 | + | 0.993979i | \(0.534948\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.44780 | 0.482432 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.52529 | 0.270740 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −15.9262 | −1.68817 | −0.844086 | − | 0.536207i | \(-0.819857\pi\) | ||||
−0.844086 | + | 0.536207i | \(0.819857\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.8957 | −1.35183 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.14955 | 0.430288 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.22239 | −0.535806 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.7538 | 1.39649 | 0.698243 | − | 0.715861i | \(-0.253966\pi\) | ||||
0.698243 | + | 0.715861i | \(0.253966\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.95286 | −0.196270 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.39371 | −0.238183 | −0.119092 | − | 0.992883i | \(-0.537998\pi\) | ||||
−0.119092 | + | 0.992883i | \(0.537998\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.185299 | 0.0182581 | 0.00912904 | − | 0.999958i | \(-0.497094\pi\) | ||||
0.00912904 | + | 0.999958i | \(0.497094\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.72380 | 0.265815 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.1993 | 0.986002 | 0.493001 | − | 0.870029i | \(-0.335900\pi\) | ||||
0.493001 | + | 0.870029i | \(0.335900\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.3264 | −1.08487 | −0.542437 | − | 0.840097i | \(-0.682498\pi\) | ||||
−0.542437 | + | 0.840097i | \(0.682498\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.94625 | 0.469477 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.85199 | 0.174221 | 0.0871104 | − | 0.996199i | \(-0.472237\pi\) | ||||
0.0871104 | + | 0.996199i | \(0.472237\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.22331 | 0.393826 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.07299 | 0.284098 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −28.7566 | −2.63612 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.18633 | −0.653303 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.05737 | −0.185507 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.21725 | −0.556087 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.4107 | −0.923802 | −0.461901 | − | 0.886931i | \(-0.652833\pi\) | ||||
−0.461901 | + | 0.886931i | \(0.652833\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.35750 | 0.383656 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.5093 | 1.35506 | 0.677528 | − | 0.735497i | \(-0.263051\pi\) | ||||
0.677528 | + | 0.735497i | \(0.263051\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 33.7646 | 2.92776 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.649069 | −0.0558630 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 16.4624 | 1.40648 | 0.703239 | − | 0.710954i | \(-0.251736\pi\) | ||||
0.703239 | + | 0.710954i | \(0.251736\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −19.8190 | −1.68102 | −0.840512 | − | 0.541793i | \(-0.817746\pi\) | ||||
−0.840512 | + | 0.541793i | \(0.817746\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −11.2109 | −0.944131 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.00111 | −0.501838 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.63909 | −0.136119 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −10.6103 | −0.875124 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.90281 | 0.811269 | 0.405635 | − | 0.914035i | \(-0.367051\pi\) | ||||
0.405635 | + | 0.914035i | \(0.367051\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.84338 | −0.312770 | −0.156385 | − | 0.987696i | \(-0.549984\pi\) | ||||
−0.156385 | + | 0.987696i | \(0.549984\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.85258 | 0.553999 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.69334 | −0.216335 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.26403 | 0.499924 | 0.249962 | − | 0.968256i | \(-0.419582\pi\) | ||||
0.249962 | + | 0.968256i | \(0.419582\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.69789 | 0.134652 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −27.3052 | −2.15195 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.4625 | 1.21111 | 0.605557 | − | 0.795802i | \(-0.292950\pi\) | ||||
0.605557 | + | 0.795802i | \(0.292950\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.26754 | 0.0986780 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.00000 | 0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.55676 | −0.273597 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.04597 | −0.615290 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.68343 | −0.356075 | −0.178037 | − | 0.984024i | \(-0.556975\pi\) | ||||
−0.178037 | + | 0.984024i | \(0.556975\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 19.2144 | 1.45247 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −7.31745 | −0.550014 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 23.5932 | 1.76344 | 0.881720 | − | 0.471773i | \(-0.156386\pi\) | ||||
0.881720 | + | 0.471773i | \(0.156386\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.72533 | 0.499890 | 0.249945 | − | 0.968260i | \(-0.419588\pi\) | ||||
0.249945 | + | 0.968260i | \(0.419588\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 12.5360 | 0.926686 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.21046 | −0.236038 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −13.3821 | −0.978599 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.19646 | 0.305248 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.7649 | −0.778922 | −0.389461 | − | 0.921043i | \(-0.627339\pi\) | ||||
−0.389461 | + | 0.921043i | \(0.627339\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.0021 | 1.22384 | 0.611918 | − | 0.790921i | \(-0.290398\pi\) | ||||
0.611918 | + | 0.790921i | \(0.290398\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.99458 | −0.142835 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.7297 | 0.764461 | 0.382230 | − | 0.924067i | \(-0.375156\pi\) | ||||
0.382230 | + | 0.924067i | \(0.375156\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.9427 | 0.917486 | 0.458743 | − | 0.888569i | \(-0.348300\pi\) | ||||
0.458743 | + | 0.888569i | \(0.348300\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.97495 | −0.491975 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 10.5973 | 0.743785 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.33538 | 0.0932669 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.50672 | 0.452248 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 15.7127 | 1.08687 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.727181 | 0.0500612 | 0.0250306 | − | 0.999687i | \(-0.492032\pi\) | ||||
0.0250306 | + | 0.999687i | \(0.492032\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.84782 | 0.195129 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.82832 | −0.192890 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 17.4134 | 1.18210 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7.78221 | 0.525873 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 21.0579 | 1.41651 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 22.1726 | 1.48478 | 0.742392 | − | 0.669966i | \(-0.233691\pi\) | ||||
0.742392 | + | 0.669966i | \(0.233691\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.57871 | −0.305247 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.28074 | −0.416867 | −0.208434 | − | 0.978037i | \(-0.566837\pi\) | ||||
−0.208434 | + | 0.978037i | \(0.566837\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.3981 | 1.41402 | 0.707012 | − | 0.707201i | \(-0.250043\pi\) | ||||
0.707012 | + | 0.707201i | \(0.250043\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.19511 | −0.539199 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −22.8556 | −1.49732 | −0.748659 | − | 0.662956i | \(-0.769302\pi\) | ||||
−0.748659 | + | 0.662956i | \(0.769302\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.27667 | 0.474678 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.29528 | −0.214051 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 21.7956 | 1.40984 | 0.704920 | − | 0.709287i | \(-0.250983\pi\) | ||||
0.704920 | + | 0.709287i | \(0.250983\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.28924 | −0.211878 | −0.105939 | − | 0.994373i | \(-0.533785\pi\) | ||||
−0.105939 | + | 0.994373i | \(0.533785\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.88683 | 0.439983 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −24.7251 | −1.57322 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.99647 | 0.126521 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.5801 | −0.794050 | −0.397025 | − | 0.917808i | \(-0.629957\pi\) | ||||
−0.397025 | + | 0.917808i | \(0.629957\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.7067 | −0.798865 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.44780 | −0.278532 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.03469 | 0.251677 | 0.125839 | − | 0.992051i | \(-0.459838\pi\) | ||||
0.125839 | + | 0.992051i | \(0.459838\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 20.7568 | 1.28976 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.52529 | −0.156312 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.0597 | 0.743631 | 0.371815 | − | 0.928307i | \(-0.378735\pi\) | ||||
0.371815 | + | 0.928307i | \(0.378735\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.10205 | −0.0676984 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 15.9262 | 0.974667 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.441761 | −0.0269346 | −0.0134673 | − | 0.999909i | \(-0.504287\pi\) | ||||
−0.0134673 | + | 0.999909i | \(0.504287\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.7472 | 1.32105 | 0.660523 | − | 0.750806i | \(-0.270334\pi\) | ||||
0.660523 | + | 0.750806i | \(0.270334\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 12.8957 | 0.780482 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8.94158 | 0.539198 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.7062 | −0.763442 | −0.381721 | − | 0.924278i | \(-0.624669\pi\) | ||||
−0.381721 | + | 0.924278i | \(0.624669\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.14955 | −0.248427 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.6981 | 1.47336 | 0.736682 | − | 0.676240i | \(-0.236392\pi\) | ||||
0.736682 | + | 0.676240i | \(0.236392\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.77605 | −0.343350 | −0.171675 | − | 0.985154i | \(-0.554918\pi\) | ||||
−0.171675 | + | 0.985154i | \(0.554918\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.22239 | 0.309348 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.63370 | −0.509631 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 29.9579 | 1.76223 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −13.7538 | −0.806261 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.9087 | 0.870973 | 0.435486 | − | 0.900195i | \(-0.356576\pi\) | ||||
0.435486 | + | 0.900195i | \(0.356576\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.74954 | 0.276529 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.95286 | 0.113316 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 19.9951 | 1.15634 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 18.2861 | 1.05399 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.39371 | 0.137515 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.13672 | −0.465907 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.60592 | −0.148728 | −0.0743638 | − | 0.997231i | \(-0.523693\pi\) | ||||
−0.0743638 | + | 0.997231i | \(0.523693\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.185299 | −0.0105413 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.88680 | 0.333810 | 0.166905 | − | 0.985973i | \(-0.446623\pi\) | ||||
0.166905 | + | 0.985973i | \(0.446623\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 29.5589 | 1.67077 | 0.835384 | − | 0.549667i | \(-0.185245\pi\) | ||||
0.835384 | + | 0.549667i | \(0.185245\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.72380 | −0.153469 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 27.3897 | 1.53836 | 0.769180 | − | 0.639032i | \(-0.220665\pi\) | ||||
0.769180 | + | 0.639032i | \(0.220665\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.93155 | 0.276114 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10.1993 | −0.569268 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −55.1357 | −3.06783 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −14.0703 | −0.780480 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 11.3264 | 0.626352 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −47.0463 | −2.59375 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −25.0680 | −1.37786 | −0.688931 | − | 0.724827i | \(-0.741920\pi\) | ||||
−0.688931 | + | 0.724827i | \(0.741920\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.94625 | −0.271053 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.52723 | 0.247349 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.0351 | −1.09138 | −0.545691 | − | 0.837987i | \(-0.683733\pi\) | ||||
−0.545691 | + | 0.837987i | \(0.683733\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.85199 | −0.100586 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.10349 | 0.438829 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.1505 | −0.818052 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.22331 | −0.227376 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −27.6121 | −1.48229 | −0.741147 | − | 0.671343i | \(-0.765718\pi\) | ||||
−0.741147 | + | 0.671343i | \(0.765718\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.2868 | 1.24652 | 0.623258 | − | 0.782016i | \(-0.285809\pi\) | ||||
0.623258 | + | 0.782016i | \(0.285809\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.07299 | −0.164024 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −27.0763 | −1.44112 | −0.720562 | − | 0.693390i | \(-0.756116\pi\) | ||||
−0.720562 | + | 0.693390i | \(0.756116\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.84843 | −0.0981045 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 28.7566 | 1.52196 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10.5945 | 0.559156 | 0.279578 | − | 0.960123i | \(-0.409805\pi\) | ||||
0.279578 | + | 0.960123i | \(0.409805\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 45.7376 | 2.40724 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.18633 | 0.377185 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.05120 | −0.264392 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.01577 | −0.418420 | −0.209210 | − | 0.977871i | \(-0.567089\pi\) | ||||
−0.209210 | + | 0.977871i | \(0.567089\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.05737 | 0.107103 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.12515 | 0.369919 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.337791 | −0.0174902 | −0.00874508 | − | 0.999962i | \(-0.502784\pi\) | ||||
−0.00874508 | + | 0.999962i | \(0.502784\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6.21725 | 0.321057 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7.76019 | −0.399670 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −31.4233 | −1.61411 | −0.807054 | − | 0.590477i | \(-0.798940\pi\) | ||||
−0.807054 | + | 0.590477i | \(0.798940\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10.4107 | 0.533357 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 23.6461 | 1.20826 | 0.604129 | − | 0.796887i | \(-0.293521\pi\) | ||||
0.604129 | + | 0.796887i | \(0.293521\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.31920 | 0.271091 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.35750 | −0.221504 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.30638 | 0.471852 | 0.235926 | − | 0.971771i | \(-0.424188\pi\) | ||||
0.235926 | + | 0.971771i | \(0.424188\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 44.5879 | 2.25490 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −15.5093 | −0.782342 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.13886 | 0.107618 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.29743 | 0.265870 | 0.132935 | − | 0.991125i | \(-0.457560\pi\) | ||||
0.132935 | + | 0.991125i | \(0.457560\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −33.7646 | −1.69034 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 24.1903 | 1.20801 | 0.604004 | − | 0.796982i | \(-0.293571\pi\) | ||||
0.604004 | + | 0.796982i | \(0.293571\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12.7515 | −0.635198 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.649069 | 0.0322525 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.65934 | 0.478796 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −26.6321 | −1.31687 | −0.658436 | − | 0.752637i | \(-0.728782\pi\) | ||||
−0.658436 | + | 0.752637i | \(0.728782\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −16.4624 | −0.812030 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −30.7074 | −1.51101 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.29585 | −0.0636107 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 19.8190 | 0.970540 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16.8970 | 0.825473 | 0.412737 | − | 0.910850i | \(-0.364573\pi\) | ||||
0.412737 | + | 0.910850i | \(0.364573\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.6534 | 0.665428 | 0.332714 | − | 0.943028i | \(-0.392036\pi\) | ||||
0.332714 | + | 0.943028i | \(0.392036\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 11.2109 | 0.545094 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −31.3760 | −1.52196 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 52.6068 | 2.54582 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.00111 | 0.289737 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.15760 | −0.152096 | −0.0760481 | − | 0.997104i | \(-0.524230\pi\) | ||||
−0.0760481 | + | 0.997104i | \(0.524230\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.19183 | −0.153390 | −0.0766948 | − | 0.997055i | \(-0.524437\pi\) | ||||
−0.0766948 | + | 0.997055i | \(0.524437\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.63909 | 0.0785884 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −52.3529 | −2.50438 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −24.3383 | −1.16160 | −0.580801 | − | 0.814046i | \(-0.697261\pi\) | ||||
−0.580801 | + | 0.814046i | \(0.697261\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 10.6103 | 0.505253 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.32690 | 0.110554 | 0.0552772 | − | 0.998471i | \(-0.482396\pi\) | ||||
0.0552772 | + | 0.998471i | \(0.482396\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.3372 | −0.490030 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9.90281 | −0.468387 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.9408 | 0.893869 | 0.446935 | − | 0.894567i | \(-0.352516\pi\) | ||||
0.446935 | + | 0.894567i | \(0.352516\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.01777 | −0.189189 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.84338 | 0.180578 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −8.37019 | −0.392400 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.00613 | −0.327733 | −0.163867 | − | 0.986483i | \(-0.552397\pi\) | ||||
−0.163867 | + | 0.986483i | \(0.552397\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.85258 | −0.319851 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 29.9382 | 1.39436 | 0.697182 | − | 0.716895i | \(-0.254437\pi\) | ||||
0.697182 | + | 0.716895i | \(0.254437\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 28.6425 | 1.33113 | 0.665564 | − | 0.746341i | \(-0.268191\pi\) | ||||
0.665564 | + | 0.746341i | \(0.268191\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.69334 | 0.124901 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10.2858 | 0.475970 | 0.237985 | − | 0.971269i | \(-0.423513\pi\) | ||||
0.237985 | + | 0.971269i | \(0.423513\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −29.2701 | −1.35157 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.26403 | −0.288631 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.50959 | 0.391271 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 36.8401 | 1.69034 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.69789 | −0.0777412 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 35.9258 | 1.64149 | 0.820745 | − | 0.571295i | \(-0.193559\pi\) | ||||
0.820745 | + | 0.571295i | \(0.193559\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.1998 | −0.693050 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 27.3052 | 1.24243 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.92716 | 0.405362 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 24.5681 | 1.11329 | 0.556644 | − | 0.830751i | \(-0.312089\pi\) | ||||
0.556644 | + | 0.830751i | \(0.312089\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −15.4625 | −0.699237 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.0673 | 0.634848 | 0.317424 | − | 0.948284i | \(-0.397182\pi\) | ||||
0.317424 | + | 0.948284i | \(0.397182\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −17.3048 | −0.779368 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.26754 | −0.0569718 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 11.9508 | 0.536065 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −28.3654 | −1.26981 | −0.634905 | − | 0.772590i | \(-0.718961\pi\) | ||||
−0.634905 | + | 0.772590i | \(0.718961\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.00000 | −0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.29871 | 0.147082 | 0.0735412 | − | 0.997292i | \(-0.476570\pi\) | ||||
0.0735412 | + | 0.997292i | \(0.476570\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.55369 | −0.0691381 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.55676 | 0.157961 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13.2600 | −0.587738 | −0.293869 | − | 0.955846i | \(-0.594943\pi\) | ||||
−0.293869 | + | 0.955846i | \(0.594943\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 32.6578 | 1.44470 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.04597 | 0.355238 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.120272 | 0.00529982 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −21.8934 | −0.962870 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.68343 | 0.205580 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 23.0586 | 1.01022 | 0.505108 | − | 0.863056i | \(-0.331453\pi\) | ||||
0.505108 | + | 0.863056i | \(0.331453\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.08722 | 0.222449 | 0.111224 | − | 0.993795i | \(-0.464523\pi\) | ||||
0.111224 | + | 0.993795i | \(0.464523\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −19.2144 | −0.838585 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −28.4351 | −1.23865 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.3374 | 0.840758 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.31745 | 0.317550 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.32228 | 0.273848 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.62004 | 0.286209 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −23.5932 | −1.01812 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −20.7205 | −0.892493 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.83762 | 0.293972 | 0.146986 | − | 0.989139i | \(-0.453043\pi\) | ||||
0.146986 | + | 0.989139i | \(0.453043\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6.72533 | −0.288611 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.35163 | −0.314909 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.89764 | 0.123894 | 0.0619470 | − | 0.998079i | \(-0.480269\pi\) | ||||
0.0619470 | + | 0.998079i | \(0.480269\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −12.5360 | −0.535022 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 20.3184 | 0.865594 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13.8285 | −0.588048 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.21046 | 0.136276 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.11407 | 0.0472045 | 0.0236023 | − | 0.999721i | \(-0.492486\pi\) | ||||
0.0236023 | + | 0.999721i | \(0.492486\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −13.3905 | −0.566359 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 13.3821 | 0.564995 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 26.2894 | 1.10797 | 0.553984 | − | 0.832527i | \(-0.313107\pi\) | ||||
0.553984 | + | 0.832527i | \(0.313107\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.20207 | 0.0505715 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.19646 | −0.176235 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 29.5405 | 1.23840 | 0.619200 | − | 0.785233i | \(-0.287457\pi\) | ||||
0.619200 | + | 0.785233i | \(0.287457\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.4949 | 0.732139 | 0.366069 | − | 0.930588i | \(-0.380703\pi\) | ||||
0.366069 | + | 0.930588i | \(0.380703\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10.7649 | 0.449711 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −29.7924 | −1.24243 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −24.5885 | −1.02363 | −0.511816 | − | 0.859095i | \(-0.671027\pi\) | ||||
−0.511816 | + | 0.859095i | \(0.671027\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −17.0021 | −0.706582 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.37812 | 0.347583 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.31575 | 0.137324 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.99458 | 0.0824658 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7.38624 | −0.304863 | −0.152431 | − | 0.988314i | \(-0.548710\pi\) | ||||
−0.152431 | + | 0.988314i | \(0.548710\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 33.3871 | 1.37569 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −10.7297 | −0.441361 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.49026 | −0.143328 | −0.0716640 | − | 0.997429i | \(-0.522831\pi\) | ||||
−0.0716640 | + | 0.997429i | \(0.522831\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −18.6650 | −0.765192 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −12.9427 | −0.529711 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −19.5847 | −0.800211 | −0.400105 | − | 0.916469i | \(-0.631026\pi\) | ||||
−0.400105 | + | 0.916469i | \(0.631026\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.07252 | 0.370076 | 0.185038 | − | 0.982731i | \(-0.440759\pi\) | ||||
0.185038 | + | 0.982731i | \(0.440759\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.97495 | 0.284042 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.66443 | −0.189636 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −42.6413 | −1.73076 | −0.865379 | − | 0.501119i | \(-0.832922\pi\) | ||||
−0.865379 | + | 0.501119i | \(0.832922\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −10.5973 | −0.429424 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 34.4510 | 1.39374 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 30.2567 | 1.22206 | 0.611028 | − | 0.791609i | \(-0.290756\pi\) | ||||
0.611028 | + | 0.791609i | \(0.290756\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.33538 | −0.0538477 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22.7488 | 0.915831 | 0.457915 | − | 0.888996i | \(-0.348596\pi\) | ||||
0.457915 | + | 0.888996i | \(0.348596\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.82335 | 0.153674 | 0.0768368 | − | 0.997044i | \(-0.475518\pi\) | ||||
0.0768368 | + | 0.997044i | \(0.475518\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.50672 | −0.261106 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 66.8337 | 2.67764 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 18.8581 | 0.754325 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −15.7127 | −0.627503 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −33.8946 | −1.35147 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.5670 | 0.420666 | 0.210333 | − | 0.977630i | \(-0.432545\pi\) | ||||
0.210333 | + | 0.977630i | \(0.432545\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.727181 | −0.0289028 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.75728 | −0.268155 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 32.6053 | 1.29187 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.84782 | −0.112658 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −24.3166 | −0.960447 | −0.480223 | − | 0.877146i | \(-0.659444\pi\) | ||||
−0.480223 | + | 0.877146i | \(0.659444\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.6719 | −0.499733 | −0.249866 | − | 0.968280i | \(-0.580387\pi\) | ||||
−0.249866 | + | 0.968280i | \(0.580387\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.82832 | 0.111365 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −11.2943 | −0.444024 | −0.222012 | − | 0.975044i | \(-0.571262\pi\) | ||||
−0.222012 | + | 0.975044i | \(0.571262\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −14.2900 | −0.560930 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −17.4134 | −0.682486 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −40.4706 | −1.58374 | −0.791869 | − | 0.610691i | \(-0.790892\pi\) | ||||
−0.791869 | + | 0.610691i | \(0.790892\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10.0666 | 0.393336 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −7.78221 | −0.303613 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13.5779 | 0.528921 | 0.264460 | − | 0.964397i | \(-0.414806\pi\) | ||||
0.264460 | + | 0.964397i | \(0.414806\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −38.4128 | −1.49408 | −0.747041 | − | 0.664777i | \(-0.768526\pi\) | ||||
−0.747041 | + | 0.664777i | \(0.768526\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −21.0579 | −0.817821 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 21.9156 | 0.849849 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −16.4314 | −0.636226 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −22.1726 | −0.857240 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 24.4810 | 0.945079 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 33.7593 | 1.30132 | 0.650662 | − | 0.759367i | \(-0.274491\pi\) | ||||
0.650662 | + | 0.759367i | \(0.274491\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.57871 | 0.176235 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −0.268807 | −0.0103311 | −0.00516555 | − | 0.999987i | \(-0.501644\pi\) | ||||
−0.00516555 | + | 0.999987i | \(0.501644\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −57.7173 | −2.21499 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.28074 | 0.240678 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 42.6332 | 1.63131 | 0.815656 | − | 0.578537i | \(-0.196376\pi\) | ||||
0.815656 | + | 0.578537i | \(0.196376\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.6852 | 0.408262 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −21.3981 | −0.816387 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.21760 | −0.198775 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.9041 | −0.566979 | −0.283490 | − | 0.958975i | \(-0.591492\pi\) | ||||
−0.283490 | + | 0.958975i | \(0.591492\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8.19511 | 0.311307 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −12.8639 | −0.487955 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.0983 | 0.534012 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 22.8556 | 0.864476 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −46.9108 | −1.77180 | −0.885898 | − | 0.463880i | \(-0.846457\pi\) | ||||
−0.885898 | + | 0.463880i | \(0.846457\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 39.7974 | 1.50099 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7.27667 | −0.274055 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10.0451 | 0.377786 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 38.2929 | 1.43812 | 0.719059 | − | 0.694949i | \(-0.244573\pi\) | ||||
0.719059 | + | 0.694949i | \(0.244573\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.29528 | 0.123582 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −27.0000 | −1.01116 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.89514 | −0.145670 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −21.7956 | −0.813971 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −15.4361 | −0.575670 | −0.287835 | − | 0.957680i | \(-0.592936\pi\) | ||||
−0.287835 | + | 0.957680i | \(0.592936\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.777601 | −0.0289594 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.28924 | 0.122328 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 11.5626 | 0.429424 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −28.7752 | −1.06721 | −0.533606 | − | 0.845733i | \(-0.679163\pi\) | ||||
−0.533606 | + | 0.845733i | \(0.679163\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −29.8601 | −1.10442 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.2197 | 0.599088 | 0.299544 | − | 0.954082i | \(-0.403165\pi\) | ||||
0.299544 | + | 0.954082i | \(0.403165\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.88683 | −0.254024 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −13.6211 | −0.501740 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −40.9725 | −1.50720 | −0.753599 | − | 0.657334i | \(-0.771684\pi\) | ||||
−0.753599 | + | 0.657334i | \(0.771684\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 24.7251 | 0.908301 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.94574 | 0.364874 | 0.182437 | − | 0.983218i | \(-0.441601\pi\) | ||||
0.182437 | + | 0.983218i | \(0.441601\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.42761 | 0.235489 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.99647 | −0.0730471 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −42.8009 | −1.56391 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 36.5092 | 1.33224 | 0.666121 | − | 0.745844i | \(-0.267954\pi\) | ||||
0.666121 | + | 0.745844i | \(0.267954\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 12.5801 | 0.458445 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.49462 | −0.0907885 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 45.9732 | 1.67092 | 0.835462 | − | 0.549549i | \(-0.185200\pi\) | ||||
0.835462 | + | 0.549549i | \(0.185200\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 12.7067 | 0.461225 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.48336 | −0.343771 | −0.171886 | − | 0.985117i | \(-0.554986\pi\) | ||||
−0.171886 | + | 0.985117i | \(0.554986\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 47.5309 | 1.72073 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.44780 | 0.160811 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 22.4864 | 0.811938 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.3149 | 0.408027 | 0.204014 | − | 0.978968i | \(-0.434601\pi\) | ||||
0.204014 | + | 0.978968i | \(0.434601\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.03469 | −0.145306 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 22.0938 | 0.794659 | 0.397329 | − | 0.917676i | \(-0.369937\pi\) | ||||
0.397329 | + | 0.917676i | \(0.369937\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 18.9996 | 0.682485 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −20.7568 | −0.744645 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −16.5536 | −0.593093 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.56139 | 0.199002 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.52529 | 0.0902466 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.06579 | 0.145114 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 27.3069 | 0.973385 | 0.486692 | − | 0.873573i | \(-0.338203\pi\) | ||||
0.486692 | + | 0.873573i | \(0.338203\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −12.0597 | −0.429335 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.77182 | −0.276334 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −38.5229 | −1.36799 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.10205 | 0.0390857 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −28.3415 | −1.00391 | −0.501953 | − | 0.864895i | \(-0.667385\pi\) | ||||
−0.501953 | + | 0.864895i | \(0.667385\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 76.8239 | 2.71783 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −15.9262 | −0.562724 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 15.1976 | 0.536311 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −17.7230 | −0.624653 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.441761 | 0.0155507 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 33.8936 | 1.19163 | 0.595817 | − | 0.803120i | \(-0.296828\pi\) | ||||
0.595817 | + | 0.803120i | \(0.296828\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −22.7048 | −0.797275 | −0.398637 | − | 0.917109i | \(-0.630517\pi\) | ||||
−0.398637 | + | 0.917109i | \(0.630517\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −21.7472 | −0.762707 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10.0362 | 0.351553 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 35.0603 | 1.22660 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −12.8957 | −0.450611 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.663314 | 0.0231498 | 0.0115749 | − | 0.999933i | \(-0.496316\pi\) | ||||
0.0115749 | + | 0.999933i | \(0.496316\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 41.4039 | 1.44325 | 0.721624 | − | 0.692285i | \(-0.243396\pi\) | ||||
0.721624 | + | 0.692285i | \(0.243396\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −8.94158 | −0.311306 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −17.6369 | −0.613296 | −0.306648 | − | 0.951823i | \(-0.599207\pi\) | ||||
−0.306648 | + | 0.951823i | \(0.599207\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.8064 | 0.410053 | 0.205027 | − | 0.978756i | \(-0.434272\pi\) | ||||
0.205027 | + | 0.978756i | \(0.434272\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12.7062 | 0.440774 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 72.7080 | 2.51918 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.649069 | 0.0224620 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.14955 | 0.143429 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 42.9529 | 1.48290 | 0.741449 | − | 0.671010i | \(-0.234139\pi\) | ||||
0.741449 | + | 0.671010i | \(0.234139\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.6229 | −0.780100 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −24.6981 | −0.850647 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.30858 | −0.0794177 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 30.1572 | 1.03621 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.77605 | 0.198233 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −32.1839 | −1.10325 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 31.7110 | 1.08576 | 0.542882 | − | 0.839809i | \(-0.317333\pi\) | ||||
0.542882 | + | 0.839809i | \(0.317333\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.22239 | −0.178602 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −43.9632 | −1.50175 | −0.750877 | − | 0.660442i | \(-0.770369\pi\) | ||||
−0.750877 | + | 0.660442i | \(0.770369\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 28.7001 | 0.979234 | 0.489617 | − | 0.871938i | \(-0.337137\pi\) | ||||
0.489617 | + | 0.871938i | \(0.337137\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.63370 | 0.294236 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 42.6438 | 1.45161 | 0.725806 | − | 0.687899i | \(-0.241467\pi\) | ||||
0.725806 | + | 0.687899i | \(0.241467\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.03987 | −0.103359 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −29.9579 | −1.01742 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.43521 | −0.218300 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 21.4339 | 0.726261 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 13.7538 | 0.465495 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 26.0905 | 0.882018 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15.1091 | −0.510199 | −0.255099 | − | 0.966915i | \(-0.582108\pi\) | ||||
−0.255099 | + | 0.966915i | \(0.582108\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −14.9087 | −0.502856 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −14.5387 | −0.489820 | −0.244910 | − | 0.969546i | \(-0.578758\pi\) | ||||
−0.244910 | + | 0.969546i | \(0.578758\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.92350 | −0.232994 | −0.116497 | − | 0.993191i | \(-0.537167\pi\) | ||||
−0.116497 | + | 0.993191i | \(0.537167\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.74954 | −0.159654 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 45.7047 | 1.53461 | 0.767306 | − | 0.641281i | \(-0.221597\pi\) | ||||
0.767306 | + | 0.641281i | \(0.221597\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 43.6882 | 1.46526 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.95286 | −0.0654233 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −90.2028 | −3.01852 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 15.3136 | 0.511878 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −19.9951 | −0.667616 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 10.4788 | 0.349488 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.6350 | −0.387616 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −18.2861 | −0.608523 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.36520 | 0.145104 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −28.7584 | −0.954907 | −0.477453 | − | 0.878657i | \(-0.658440\pi\) | ||||
−0.477453 | + | 0.878657i | \(0.658440\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.39371 | −0.0793945 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.33280 | −0.110421 | −0.0552103 | − | 0.998475i | \(-0.517583\pi\) | ||||
−0.0552103 | + | 0.998475i | \(0.517583\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.89883 | 0.129032 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 8.13672 | 0.268992 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −65.0843 | −2.14927 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −45.6696 | −1.50650 | −0.753250 | − | 0.657735i | \(-0.771515\pi\) | ||||
−0.753250 | + | 0.657735i | \(0.771515\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.60592 | 0.0858679 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.75130 | −0.288052 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 22.6474 | 0.744643 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.185299 | 0.00608602 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 41.0210 | 1.34586 | 0.672928 | − | 0.739708i | \(-0.265037\pi\) | ||||
0.672928 | + | 0.739708i | \(0.265037\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −85.3702 | −2.79789 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.88680 | −0.192725 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.68594 | −0.284061 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.449676 | 0.0146903 | 0.00734514 | − | 0.999973i | \(-0.497662\pi\) | ||||
0.00734514 | + | 0.999973i | \(0.497662\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −29.5589 | −0.964618 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24.2530 | −0.790626 | −0.395313 | − | 0.918546i | \(-0.629364\pi\) | ||||
−0.395313 | + | 0.918546i | \(0.629364\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13.3868 | 0.435933 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.72380 | 0.0886051 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −42.4970 | −1.38097 | −0.690484 | − | 0.723348i | \(-0.742602\pi\) | ||||
−0.690484 | + | 0.723348i | \(0.742602\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −23.9146 | −0.776302 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −27.3897 | −0.888173 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 17.5025 | 0.566961 | 0.283480 | − | 0.958978i | \(-0.408511\pi\) | ||||
0.283480 | + | 0.958978i | \(0.408511\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.98718 | −0.226100 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.93155 | −0.159414 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −69.0839 | −2.23083 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.7813 | −0.444557 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10.1993 | 0.328667 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 11.0355 | 0.355246 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.8865 | 0.543032 | 0.271516 | − | 0.962434i | \(-0.412475\pi\) | ||||
0.271516 | + | 0.962434i | \(0.412475\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 55.1357 | 1.77121 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 54.6352 | 1.75333 | 0.876664 | − | 0.481103i | \(-0.159764\pi\) | ||||
0.876664 | + | 0.481103i | \(0.159764\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 83.1696 | 2.66630 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 14.0703 | 0.450610 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −18.6725 | −0.597386 | −0.298693 | − | 0.954349i | \(-0.596551\pi\) | ||||
−0.298693 | + | 0.954349i | \(0.596551\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 31.1016 | 0.994013 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11.3264 | −0.361625 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −46.7507 | −1.49112 | −0.745558 | − | 0.666441i | \(-0.767817\pi\) | ||||
−0.745558 | + | 0.666441i | \(0.767817\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.96433 | 0.221902 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 47.0463 | 1.49750 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −28.3530 | −0.901574 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 46.7105 | 1.48381 | 0.741904 | − | 0.670506i | \(-0.233923\pi\) | ||||
0.741904 | + | 0.670506i | \(0.233923\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 25.0680 | 0.795509 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.40074 | 0.266321 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −59.1332 | −1.87277 | −0.936383 | − | 0.350979i | \(-0.885849\pi\) | ||||
−0.936383 | + | 0.350979i | \(0.885849\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.94625 | 0.156492 |
(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 | 8016.2.a.bg.1.7 | 13 | ||
4.3 | odd | 2 | 4008.2.a.m.1.7 | ✓ | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4008.2.a.m.1.7 | ✓ | 13 | 4.3 | odd | 2 | ||
8016.2.a.bg.1.7 | 13 | 1.1 | even | 1 | trivial |