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: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 3x^{8} - 16x^{7} + 45x^{6} + 67x^{5} - 166x^{4} - 83x^{3} + 152x^{2} + 51x - 10 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 4008) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-0.482381\) 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 | ||||||||
\(5\) | −1.48238 | −0.662941 | −0.331470 | − | 0.943466i | \(-0.607545\pi\) | ||||
−0.331470 | + | 0.943466i | \(0.607545\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.03908 | 0.392735 | 0.196368 | − | 0.980530i | \(-0.437085\pi\) | ||||
0.196368 | + | 0.980530i | \(0.437085\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.64105 | −1.70084 | −0.850420 | − | 0.526105i | \(-0.823652\pi\) | ||||
−0.850420 | + | 0.526105i | \(0.823652\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.47983 | −1.24248 | −0.621241 | − | 0.783620i | \(-0.713371\pi\) | ||||
−0.621241 | + | 0.783620i | \(0.713371\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.48238 | 0.382749 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.13922 | −1.48898 | −0.744490 | − | 0.667634i | \(-0.767307\pi\) | ||||
−0.744490 | + | 0.667634i | \(0.767307\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.87154 | −1.34702 | −0.673511 | − | 0.739177i | \(-0.735215\pi\) | ||||
−0.673511 | + | 0.739177i | \(0.735215\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.03908 | −0.226746 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.22710 | 0.255869 | 0.127934 | − | 0.991783i | \(-0.459165\pi\) | ||||
0.127934 | + | 0.991783i | \(0.459165\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.80255 | −0.560509 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.91991 | −1.28500 | −0.642498 | − | 0.766288i | \(-0.722102\pi\) | ||||
−0.642498 | + | 0.766288i | \(0.722102\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.70123 | −0.664760 | −0.332380 | − | 0.943146i | \(-0.607852\pi\) | ||||
−0.332380 | + | 0.943146i | \(0.607852\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.64105 | 0.981980 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.54031 | −0.260360 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.62294 | −1.08880 | −0.544402 | − | 0.838824i | \(-0.683244\pi\) | ||||
−0.544402 | + | 0.838824i | \(0.683244\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.47983 | 0.717347 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.85846 | 0.290242 | 0.145121 | − | 0.989414i | \(-0.453643\pi\) | ||||
0.145121 | + | 0.989414i | \(0.453643\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.29781 | 0.350413 | 0.175207 | − | 0.984532i | \(-0.443941\pi\) | ||||
0.175207 | + | 0.984532i | \(0.443941\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.48238 | −0.220980 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.59229 | −0.523990 | −0.261995 | − | 0.965069i | \(-0.584380\pi\) | ||||
−0.261995 | + | 0.965069i | \(0.584380\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.92031 | −0.845759 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.13922 | 0.859663 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.299721 | −0.0411699 | −0.0205849 | − | 0.999788i | \(-0.506553\pi\) | ||||
−0.0205849 | + | 0.999788i | \(0.506553\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.36218 | 1.12756 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.87154 | 0.777704 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.102376 | −0.0133282 | −0.00666409 | − | 0.999978i | \(-0.502121\pi\) | ||||
−0.00666409 | + | 0.999978i | \(0.502121\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.64463 | 0.466647 | 0.233323 | − | 0.972399i | \(-0.425040\pi\) | ||||
0.233323 | + | 0.972399i | \(0.425040\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.03908 | 0.130912 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.64082 | 0.823692 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.27810 | 0.644823 | 0.322412 | − | 0.946600i | \(-0.395507\pi\) | ||||
0.322412 | + | 0.946600i | \(0.395507\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.22710 | −0.147726 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.00339 | −0.237759 | −0.118879 | − | 0.992909i | \(-0.537930\pi\) | ||||
−0.118879 | + | 0.992909i | \(0.537930\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.34023 | 1.09319 | 0.546596 | − | 0.837397i | \(-0.315923\pi\) | ||||
0.546596 | + | 0.837397i | \(0.315923\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.80255 | 0.323610 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.86150 | −0.667979 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.92469 | 0.441562 | 0.220781 | − | 0.975323i | \(-0.429139\pi\) | ||||
0.220781 | + | 0.975323i | \(0.429139\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.4441 | 1.25615 | 0.628075 | − | 0.778153i | \(-0.283843\pi\) | ||||
0.628075 | + | 0.778153i | \(0.283843\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.10067 | 0.987106 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.91991 | 0.741893 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.4583 | −1.10858 | −0.554290 | − | 0.832324i | \(-0.687010\pi\) | ||||
−0.554290 | + | 0.832324i | \(0.687010\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.65490 | −0.487966 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.70123 | 0.383799 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8.70385 | 0.892997 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.40524 | −0.345749 | −0.172875 | − | 0.984944i | \(-0.555306\pi\) | ||||
−0.172875 | + | 0.984944i | \(0.555306\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.64105 | −0.566947 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.6052 | −1.25426 | −0.627132 | − | 0.778913i | \(-0.715771\pi\) | ||||
−0.627132 | + | 0.778913i | \(0.715771\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.3704 | 1.51449 | 0.757245 | − | 0.653131i | \(-0.226545\pi\) | ||||
0.757245 | + | 0.653131i | \(0.226545\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.54031 | 0.150319 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.62482 | −0.640446 | −0.320223 | − | 0.947342i | \(-0.603758\pi\) | ||||
−0.320223 | + | 0.947342i | \(0.603758\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −18.9911 | −1.81901 | −0.909507 | − | 0.415690i | \(-0.863540\pi\) | ||||
−0.909507 | + | 0.415690i | \(0.863540\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.62294 | 0.628622 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.3656 | 1.53955 | 0.769774 | − | 0.638316i | \(-0.220369\pi\) | ||||
0.769774 | + | 0.638316i | \(0.220369\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.81903 | −0.169626 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.47983 | −0.414160 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.37914 | −0.584775 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 20.8214 | 1.89286 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.85846 | −0.167571 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.5663 | 1.03453 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.6141 | −1.56300 | −0.781499 | − | 0.623906i | \(-0.785545\pi\) | ||||
−0.781499 | + | 0.623906i | \(0.785545\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.29781 | −0.202311 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.79697 | −0.855965 | −0.427982 | − | 0.903787i | \(-0.640776\pi\) | ||||
−0.427982 | + | 0.903787i | \(0.640776\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.10099 | −0.529023 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.48238 | 0.127583 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.81856 | −0.582549 | −0.291274 | − | 0.956640i | \(-0.594079\pi\) | ||||
−0.291274 | + | 0.956640i | \(0.594079\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.34794 | 0.453606 | 0.226803 | − | 0.973941i | \(-0.427173\pi\) | ||||
0.226803 | + | 0.973941i | \(0.427173\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.59229 | 0.302526 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 25.2709 | 2.11326 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.2579 | 0.851876 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.92031 | 0.488299 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −20.0944 | −1.64620 | −0.823100 | − | 0.567896i | \(-0.807757\pi\) | ||||
−0.823100 | + | 0.567896i | \(0.807757\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.4596 | 1.25808 | 0.629041 | − | 0.777372i | \(-0.283448\pi\) | ||||
0.629041 | + | 0.777372i | \(0.283448\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.13922 | −0.496327 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.48663 | 0.440696 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.6576 | 0.850568 | 0.425284 | − | 0.905060i | \(-0.360174\pi\) | ||||
0.425284 | + | 0.905060i | \(0.360174\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.299721 | 0.0237694 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.27506 | 0.100489 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 21.2802 | 1.66680 | 0.833399 | − | 0.552672i | \(-0.186392\pi\) | ||||
0.833399 | + | 0.552672i | \(0.186392\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −8.36218 | −0.650995 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.00000 | 0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.06888 | 0.543760 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.87154 | −0.449008 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −16.4057 | −1.24730 | −0.623650 | − | 0.781704i | \(-0.714351\pi\) | ||||
−0.623650 | + | 0.781704i | \(0.714351\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.91207 | −0.220132 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.102376 | 0.00769503 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.21604 | −0.0908913 | −0.0454456 | − | 0.998967i | \(-0.514471\pi\) | ||||
−0.0454456 | + | 0.998967i | \(0.514471\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.24694 | −0.464331 | −0.232166 | − | 0.972676i | \(-0.574581\pi\) | ||||
−0.232166 | + | 0.972676i | \(0.574581\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.64463 | −0.269419 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9.81772 | 0.721813 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 34.6316 | 2.53252 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.03908 | −0.0755819 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.2291 | −1.17429 | −0.587146 | − | 0.809481i | \(-0.699749\pi\) | ||||
−0.587146 | + | 0.809481i | \(0.699749\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.97087 | −0.645737 | −0.322869 | − | 0.946444i | \(-0.604647\pi\) | ||||
−0.322869 | + | 0.946444i | \(0.604647\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.64082 | −0.475559 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −23.1926 | −1.65240 | −0.826201 | − | 0.563376i | \(-0.809502\pi\) | ||||
−0.826201 | + | 0.563376i | \(0.809502\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.8934 | 0.984876 | 0.492438 | − | 0.870348i | \(-0.336106\pi\) | ||||
0.492438 | + | 0.870348i | \(0.336106\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.27810 | −0.372289 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.19034 | −0.504663 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.75494 | −0.192413 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.22710 | 0.0852895 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 33.1216 | 2.29107 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.9560 | 0.823082 | 0.411541 | − | 0.911391i | \(-0.364991\pi\) | ||||
0.411541 | + | 0.911391i | \(0.364991\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.00339 | 0.137270 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.40623 | −0.232303 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.84587 | −0.261074 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −9.34023 | −0.631155 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 27.5027 | 1.85003 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 25.7496 | 1.72432 | 0.862159 | − | 0.506638i | \(-0.169112\pi\) | ||||
0.862159 | + | 0.506638i | \(0.169112\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.80255 | −0.186836 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −23.2899 | −1.54580 | −0.772901 | − | 0.634527i | \(-0.781195\pi\) | ||||
−0.772901 | + | 0.634527i | \(0.781195\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.4690 | −0.691813 | −0.345906 | − | 0.938269i | \(-0.612429\pi\) | ||||
−0.345906 | + | 0.938269i | \(0.612429\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.86150 | 0.385658 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −19.6195 | −1.28532 | −0.642658 | − | 0.766153i | \(-0.722168\pi\) | ||||
−0.642658 | + | 0.766153i | \(0.722168\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.32515 | 0.347374 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.92469 | −0.254936 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.5821 | −1.00793 | −0.503963 | − | 0.863725i | \(-0.668125\pi\) | ||||
−0.503963 | + | 0.863725i | \(0.668125\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −30.8313 | −1.98602 | −0.993011 | − | 0.118025i | \(-0.962344\pi\) | ||||
−0.993011 | + | 0.118025i | \(0.962344\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 8.77616 | 0.560688 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 26.3035 | 1.67365 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −11.4441 | −0.725238 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.66860 | 0.357799 | 0.178899 | − | 0.983867i | \(-0.442746\pi\) | ||||
0.178899 | + | 0.983867i | \(0.442746\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.92214 | −0.435191 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −9.10067 | −0.569906 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.81618 | −0.425182 | −0.212591 | − | 0.977141i | \(-0.568190\pi\) | ||||
−0.212591 | + | 0.977141i | \(0.568190\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.88176 | −0.427612 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.91991 | −0.428332 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.22632 | −0.260606 | −0.130303 | − | 0.991474i | \(-0.541595\pi\) | ||||
−0.130303 | + | 0.991474i | \(0.541595\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.444301 | 0.0272932 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.4583 | 0.640039 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 20.5783 | 1.25468 | 0.627340 | − | 0.778745i | \(-0.284144\pi\) | ||||
0.627340 | + | 0.778745i | \(0.284144\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.93172 | 0.421072 | 0.210536 | − | 0.977586i | \(-0.432479\pi\) | ||||
0.210536 | + | 0.977586i | \(0.432479\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.65490 | 0.281727 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 15.8093 | 0.953336 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.5380 | 1.35418 | 0.677088 | − | 0.735902i | \(-0.263242\pi\) | ||||
0.677088 | + | 0.735902i | \(0.263242\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.70123 | −0.221587 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.5684 | 1.22701 | 0.613504 | − | 0.789691i | \(-0.289759\pi\) | ||||
0.613504 | + | 0.789691i | \(0.289759\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −29.4021 | −1.74777 | −0.873886 | − | 0.486131i | \(-0.838408\pi\) | ||||
−0.873886 | + | 0.486131i | \(0.838408\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −8.70385 | −0.515572 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.93108 | 0.113988 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 20.6900 | 1.21706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.40524 | 0.199618 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 20.2839 | 1.18500 | 0.592500 | − | 0.805571i | \(-0.298141\pi\) | ||||
0.592500 | + | 0.805571i | \(0.298141\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.151760 | 0.00883580 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.64105 | 0.327327 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.49721 | −0.317912 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.38761 | 0.137619 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 12.6052 | 0.724149 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.40273 | −0.309359 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.9899 | −0.627224 | −0.313612 | − | 0.949551i | \(-0.601539\pi\) | ||||
−0.313612 | + | 0.949551i | \(0.601539\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −15.3704 | −0.874391 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −26.9703 | −1.52935 | −0.764673 | − | 0.644418i | \(-0.777100\pi\) | ||||
−0.764673 | + | 0.644418i | \(0.777100\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −32.1109 | −1.81501 | −0.907507 | − | 0.420036i | \(-0.862017\pi\) | ||||
−0.907507 | + | 0.420036i | \(0.862017\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.54031 | −0.0867867 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −21.3657 | −1.20002 | −0.600008 | − | 0.799994i | \(-0.704836\pi\) | ||||
−0.600008 | + | 0.799994i | \(0.704836\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 39.0356 | 2.18557 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.62482 | 0.369761 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 36.0467 | 2.00569 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.5549 | 0.696422 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 18.9911 | 1.05021 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.73268 | −0.205789 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −23.6701 | −1.30102 | −0.650512 | − | 0.759496i | \(-0.725446\pi\) | ||||
−0.650512 | + | 0.759496i | \(0.725446\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.62294 | −0.362935 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.82416 | −0.427480 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −23.6003 | −1.28559 | −0.642796 | − | 0.766037i | \(-0.722226\pi\) | ||||
−0.642796 | + | 0.766037i | \(0.722226\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −16.3656 | −0.888859 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 20.8788 | 1.13065 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.4252 | −0.724894 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.81903 | 0.0979335 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −17.2073 | −0.923736 | −0.461868 | − | 0.886949i | \(-0.652821\pi\) | ||||
−0.461868 | + | 0.886949i | \(0.652821\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.7148 | 1.10884 | 0.554419 | − | 0.832238i | \(-0.312941\pi\) | ||||
0.554419 | + | 0.832238i | \(0.312941\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.47983 | 0.239116 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.81530 | 0.0966187 | 0.0483094 | − | 0.998832i | \(-0.484617\pi\) | ||||
0.0483094 | + | 0.998832i | \(0.484617\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.96979 | 0.157620 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.37914 | 0.337620 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.55958 | 0.398979 | 0.199490 | − | 0.979900i | \(-0.436072\pi\) | ||||
0.199490 | + | 0.979900i | \(0.436072\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.4749 | 0.814471 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −20.8214 | −1.09284 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −13.8458 | −0.724722 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 24.2242 | 1.26449 | 0.632247 | − | 0.774767i | \(-0.282133\pi\) | ||||
0.632247 | + | 0.774767i | \(0.282133\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.85846 | 0.0967473 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.311434 | −0.0161689 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.50121 | 0.440176 | 0.220088 | − | 0.975480i | \(-0.429366\pi\) | ||||
0.220088 | + | 0.975480i | \(0.429366\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −11.5663 | −0.597284 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 31.0000 | 1.59658 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.72626 | 0.242772 | 0.121386 | − | 0.992605i | \(-0.461266\pi\) | ||||
0.121386 | + | 0.992605i | \(0.461266\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 17.6141 | 0.902398 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −22.7605 | −1.16301 | −0.581505 | − | 0.813543i | \(-0.697536\pi\) | ||||
−0.581505 | + | 0.813543i | \(0.697536\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.68897 | 0.442831 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.29781 | 0.116804 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 26.2141 | 1.32911 | 0.664554 | − | 0.747241i | \(-0.268622\pi\) | ||||
0.664554 | + | 0.747241i | \(0.268622\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.53346 | −0.380983 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9.79697 | 0.494192 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.81789 | −0.292730 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.99098 | 0.451244 | 0.225622 | − | 0.974215i | \(-0.427559\pi\) | ||||
0.225622 | + | 0.974215i | \(0.427559\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6.10099 | 0.305432 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.85669 | 0.242531 | 0.121266 | − | 0.992620i | \(-0.461305\pi\) | ||||
0.121266 | + | 0.992620i | \(0.461305\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 16.5809 | 0.825952 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.48238 | −0.0736601 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 37.3603 | 1.85188 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 28.4764 | 1.40807 | 0.704034 | − | 0.710166i | \(-0.251380\pi\) | ||||
0.704034 | + | 0.710166i | \(0.251380\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.81856 | 0.336335 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.106376 | −0.00523444 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −16.9645 | −0.832753 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.34794 | −0.261890 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −22.7505 | −1.11143 | −0.555717 | − | 0.831371i | \(-0.687556\pi\) | ||||
−0.555717 | + | 0.831371i | \(0.687556\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.05605 | 0.441365 | 0.220682 | − | 0.975346i | \(-0.429172\pi\) | ||||
0.220682 | + | 0.975346i | \(0.429172\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.59229 | −0.174663 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 17.2055 | 0.834587 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.78706 | 0.183269 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −25.2709 | −1.22009 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.21053 | −0.347319 | −0.173660 | − | 0.984806i | \(-0.555559\pi\) | ||||
−0.173660 | + | 0.984806i | \(0.555559\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −26.9366 | −1.29449 | −0.647246 | − | 0.762281i | \(-0.724079\pi\) | ||||
−0.647246 | + | 0.762281i | \(0.724079\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −10.2579 | −0.491831 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.20498 | −0.344661 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 24.4736 | 1.16806 | 0.584031 | − | 0.811731i | \(-0.301475\pi\) | ||||
0.584031 | + | 0.811731i | \(0.301475\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.92031 | −0.281920 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −32.1730 | −1.52858 | −0.764292 | − | 0.644870i | \(-0.776912\pi\) | ||||
−0.764292 | + | 0.644870i | \(0.776912\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 15.5032 | 0.734923 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 20.0944 | 0.950434 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 37.2697 | 1.75887 | 0.879434 | − | 0.476021i | \(-0.157921\pi\) | ||||
0.879434 | + | 0.476021i | \(0.157921\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.4836 | −0.493655 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −15.4596 | −0.726354 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.90033 | 0.323493 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.52936 | −0.165096 | −0.0825482 | − | 0.996587i | \(-0.526306\pi\) | ||||
−0.0825482 | + | 0.996587i | \(0.526306\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.13922 | 0.286554 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.01289 | −0.233474 | −0.116737 | − | 0.993163i | \(-0.537243\pi\) | ||||
−0.116737 | + | 0.993163i | \(0.537243\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.8928 | 0.552707 | 0.276353 | − | 0.961056i | \(-0.410874\pi\) | ||||
0.276353 | + | 0.961056i | \(0.410874\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.48663 | −0.254436 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.68147 | 0.401730 | 0.200865 | − | 0.979619i | \(-0.435625\pi\) | ||||
0.200865 | + | 0.979619i | \(0.435625\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.48437 | 0.253245 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.6576 | −0.491076 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −12.9621 | −0.595996 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 16.4553 | 0.755019 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.299721 | −0.0137233 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11.9188 | 0.544585 | 0.272293 | − | 0.962215i | \(-0.412218\pi\) | ||||
0.272293 | + | 0.962215i | \(0.412218\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 29.6697 | 1.35282 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.27506 | −0.0580171 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.04786 | 0.229211 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −34.7303 | −1.57378 | −0.786889 | − | 0.617095i | \(-0.788310\pi\) | ||||
−0.786889 | + | 0.617095i | \(0.788310\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −21.2802 | −0.962326 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.62022 | 0.389025 | 0.194513 | − | 0.980900i | \(-0.437687\pi\) | ||||
0.194513 | + | 0.980900i | \(0.437687\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 42.4829 | 1.91333 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8.36218 | 0.375852 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.08168 | −0.0933762 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19.1457 | −0.857080 | −0.428540 | − | 0.903523i | \(-0.640972\pi\) | ||||
−0.428540 | + | 0.903523i | \(0.640972\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.00000 | −0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 24.8619 | 1.10854 | 0.554269 | − | 0.832337i | \(-0.312998\pi\) | ||||
0.554269 | + | 0.832337i | \(0.312998\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.6857 | 0.831502 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.06888 | −0.313940 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.12427 | 0.0941567 | 0.0470783 | − | 0.998891i | \(-0.485009\pi\) | ||||
0.0470783 | + | 0.998891i | \(0.485009\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.70525 | 0.429335 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.87154 | 0.259235 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −22.7848 | −1.00402 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 20.2643 | 0.891222 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 16.4057 | 0.720129 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.08693 | −0.0914302 | −0.0457151 | − | 0.998955i | \(-0.514557\pi\) | ||||
−0.0457151 | + | 0.998955i | \(0.514557\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 21.6413 | 0.946306 | 0.473153 | − | 0.880980i | \(-0.343116\pi\) | ||||
0.473153 | + | 0.880980i | \(0.343116\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.91207 | 0.127093 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 22.7226 | 0.989814 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.4942 | −0.934531 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.102376 | −0.00444273 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.32556 | −0.360620 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.82051 | 0.424578 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.21604 | 0.0524761 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 33.3968 | 1.43850 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 24.7817 | 1.06545 | 0.532725 | − | 0.846289i | \(-0.321168\pi\) | ||||
0.532725 | + | 0.846289i | \(0.321168\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.24694 | 0.268082 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 28.1520 | 1.20590 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.13808 | −0.0914179 | −0.0457089 | − | 0.998955i | \(-0.514555\pi\) | ||||
−0.0457089 | + | 0.998955i | \(0.514555\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.64463 | 0.155549 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 40.6305 | 1.73092 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.07807 | 0.173417 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −9.81772 | −0.416739 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −11.7687 | −0.498656 | −0.249328 | − | 0.968419i | \(-0.580210\pi\) | ||||
−0.249328 | + | 0.968419i | \(0.580210\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.2938 | −0.435382 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −34.6316 | −1.46215 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −14.6893 | −0.619079 | −0.309540 | − | 0.950887i | \(-0.600175\pi\) | ||||
−0.309540 | + | 0.950887i | \(0.600175\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −24.2601 | −1.02063 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.03908 | 0.0436372 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −16.2827 | −0.682608 | −0.341304 | − | 0.939953i | \(-0.610869\pi\) | ||||
−0.341304 | + | 0.939953i | \(0.610869\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.0677 | −0.588714 | −0.294357 | − | 0.955696i | \(-0.595105\pi\) | ||||
−0.294357 | + | 0.955696i | \(0.595105\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 16.2291 | 0.677978 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.43901 | −0.143417 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15.5023 | 0.645369 | 0.322684 | − | 0.946507i | \(-0.395415\pi\) | ||||
0.322684 | + | 0.946507i | \(0.395415\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.97087 | 0.372816 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11.8913 | 0.493334 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.69074 | 0.0700234 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6.64082 | 0.274564 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22.7257 | 0.937989 | 0.468995 | − | 0.883201i | \(-0.344616\pi\) | ||||
0.468995 | + | 0.883201i | \(0.344616\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 21.7319 | 0.895447 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 23.1926 | 0.954015 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −34.1852 | −1.40382 | −0.701909 | − | 0.712267i | \(-0.747669\pi\) | ||||
−0.701909 | + | 0.712267i | \(0.747669\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.45631 | 0.387671 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −13.8934 | −0.568618 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.88943 | −0.240636 | −0.120318 | − | 0.992735i | \(-0.538391\pi\) | ||||
−0.120318 | + | 0.992735i | \(0.538391\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −39.0125 | −1.59135 | −0.795676 | − | 0.605723i | \(-0.792884\pi\) | ||||
−0.795676 | + | 0.605723i | \(0.792884\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.27810 | 0.214941 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −30.8653 | −1.25485 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.36469 | 0.217746 | 0.108873 | − | 0.994056i | \(-0.465276\pi\) | ||||
0.108873 | + | 0.994056i | \(0.465276\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7.19034 | 0.291367 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 16.0929 | 0.651047 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −44.6516 | −1.80346 | −0.901731 | − | 0.432297i | \(-0.857703\pi\) | ||||
−0.901731 | + | 0.432297i | \(0.857703\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.75494 | 0.111090 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15.1280 | −0.609030 | −0.304515 | − | 0.952508i | \(-0.598494\pi\) | ||||
−0.304515 | + | 0.952508i | \(0.598494\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 38.8437 | 1.56126 | 0.780631 | − | 0.624992i | \(-0.214898\pi\) | ||||
0.780631 | + | 0.624992i | \(0.214898\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.22710 | −0.0492419 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −10.8670 | −0.435378 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.13300 | −0.125320 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −33.1216 | −1.32275 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 40.6597 | 1.62121 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.0968 | −0.919470 | −0.459735 | − | 0.888056i | \(-0.652056\pi\) | ||||
−0.459735 | + | 0.888056i | \(0.652056\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −11.9560 | −0.475207 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 26.1108 | 1.03618 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 26.5220 | 1.05084 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.00339 | −0.0792529 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 28.3497 | 1.11974 | 0.559872 | − | 0.828579i | \(-0.310850\pi\) | ||||
0.559872 | + | 0.828579i | \(0.310850\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 40.8208 | 1.60981 | 0.804907 | − | 0.593401i | \(-0.202215\pi\) | ||||
0.804907 | + | 0.593401i | \(0.202215\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.40623 | 0.134120 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 31.6874 | 1.24576 | 0.622881 | − | 0.782317i | \(-0.285962\pi\) | ||||
0.622881 | + | 0.782317i | \(0.285962\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.577506 | 0.0226691 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.84587 | 0.150731 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 17.1808 | 0.672337 | 0.336169 | − | 0.941802i | \(-0.390869\pi\) | ||||
0.336169 | + | 0.941802i | \(0.390869\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.5228 | 0.567454 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9.34023 | 0.364397 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −29.0908 | −1.13322 | −0.566608 | − | 0.823988i | \(-0.691745\pi\) | ||||
−0.566608 | + | 0.823988i | \(0.691745\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.34936 | 0.0913794 | 0.0456897 | − | 0.998956i | \(-0.485451\pi\) | ||||
0.0456897 | + | 0.998956i | \(0.485451\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −27.5027 | −1.06812 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 9.04400 | 0.350711 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.49144 | −0.328790 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −25.7496 | −0.995535 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −20.5595 | −0.793691 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.7107 | 0.759792 | 0.379896 | − | 0.925029i | \(-0.375960\pi\) | ||||
0.379896 | + | 0.925029i | \(0.375960\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.80255 | 0.107870 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 13.2631 | 0.509744 | 0.254872 | − | 0.966975i | \(-0.417967\pi\) | ||||
0.254872 | + | 0.966975i | \(0.417967\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.53831 | −0.135788 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 23.2899 | 0.892469 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 32.2080 | 1.23241 | 0.616203 | − | 0.787587i | \(-0.288670\pi\) | ||||
0.616203 | + | 0.787587i | \(0.288670\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.1077 | 0.386195 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10.4690 | 0.399418 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.34270 | 0.0511528 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.3513 | 0.698115 | 0.349058 | − | 0.937101i | \(-0.386502\pi\) | ||||
0.349058 | + | 0.937101i | \(0.386502\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.86150 | −0.222660 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.92768 | −0.300714 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −11.4095 | −0.432164 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 19.6195 | 0.742078 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −15.0603 | −0.568821 | −0.284411 | − | 0.958703i | \(-0.591798\pi\) | ||||
−0.284411 | + | 0.958703i | \(0.591798\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 38.8868 | 1.46665 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.32515 | −0.200557 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −13.0978 | −0.492593 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22.7311 | 0.853684 | 0.426842 | − | 0.904326i | \(-0.359626\pi\) | ||||
0.426842 | + | 0.904326i | \(0.359626\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.92469 | 0.147187 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.54178 | −0.170091 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −37.4611 | −1.40097 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 15.5821 | 0.581926 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −22.0804 | −0.823460 | −0.411730 | − | 0.911306i | \(-0.635075\pi\) | ||||
−0.411730 | + | 0.911306i | \(0.635075\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.9711 | 0.594793 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 30.8313 | 1.14663 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 19.3934 | 0.720252 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.19378 | 0.0442749 | 0.0221374 | − | 0.999755i | \(-0.492953\pi\) | ||||
0.0221374 | + | 0.999755i | \(0.492953\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −14.1068 | −0.521758 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −40.8588 | −1.50915 | −0.754577 | − | 0.656212i | \(-0.772158\pi\) | ||||
−0.754577 | + | 0.656212i | \(0.772158\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −8.77616 | −0.323714 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −29.7740 | −1.09674 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −43.2993 | −1.59279 | −0.796396 | − | 0.604776i | \(-0.793263\pi\) | ||||
−0.796396 | + | 0.604776i | \(0.793263\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −26.3035 | −0.966283 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −30.6987 | −1.12622 | −0.563112 | − | 0.826380i | \(-0.690396\pi\) | ||||
−0.563112 | + | 0.826380i | \(0.690396\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 29.7876 | 1.09133 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 11.4441 | 0.418717 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.88372 | −0.251525 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −38.3723 | −1.40022 | −0.700112 | − | 0.714033i | \(-0.746867\pi\) | ||||
−0.700112 | + | 0.714033i | \(0.746867\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −5.66860 | −0.206575 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −22.9170 | −0.834034 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.5003 | 0.563367 | 0.281684 | − | 0.959507i | \(-0.409107\pi\) | ||||
0.281684 | + | 0.959507i | \(0.409107\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.92214 | 0.251258 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 41.5796 | 1.50726 | 0.753629 | − | 0.657300i | \(-0.228301\pi\) | ||||
0.753629 | + | 0.657300i | \(0.228301\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −19.7332 | −0.714390 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 9.10067 | 0.329035 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.458626 | 0.0165600 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 42.7687 | 1.54228 | 0.771140 | − | 0.636666i | \(-0.219687\pi\) | ||||
0.771140 | + | 0.636666i | \(0.219687\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.81618 | 0.245479 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 32.3512 | 1.16359 | 0.581795 | − | 0.813335i | \(-0.302350\pi\) | ||||
0.581795 | + | 0.813335i | \(0.302350\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.3729 | 0.372604 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6.88176 | 0.246882 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −10.9120 | −0.390963 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.3012 | 0.404389 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.91991 | 0.247298 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −15.7986 | −0.563877 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.830709 | −0.0296116 | −0.0148058 | − | 0.999890i | \(-0.504713\pi\) | ||||
−0.0148058 | + | 0.999890i | \(0.504713\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.22632 | 0.150461 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 17.0052 | 0.604635 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16.3273 | −0.579800 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.444301 | −0.0157577 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 44.9143 | 1.59095 | 0.795473 | − | 0.605988i | \(-0.207222\pi\) | ||||
0.795473 | + | 0.605988i | \(0.207222\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 22.0539 | 0.780210 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10.4583 | −0.369527 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −52.6887 | −1.85934 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.89012 | −0.0666180 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −20.5783 | −0.724390 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −25.0553 | −0.880897 | −0.440449 | − | 0.897778i | \(-0.645181\pi\) | ||||
−0.440449 | + | 0.897778i | \(0.645181\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −30.9063 | −1.08527 | −0.542634 | − | 0.839969i | \(-0.682573\pi\) | ||||
−0.542634 | + | 0.839969i | \(0.682573\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.93172 | −0.243106 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −31.5454 | −1.10499 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −13.4917 | −0.472014 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.65490 | −0.162655 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.78573 | 0.167023 | 0.0835115 | − | 0.996507i | \(-0.473386\pi\) | ||||
0.0835115 | + | 0.996507i | \(0.473386\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −21.7901 | −0.759555 | −0.379778 | − | 0.925078i | \(-0.623999\pi\) | ||||
−0.379778 | + | 0.925078i | \(0.623999\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −15.8093 | −0.550409 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −37.7470 | −1.31259 | −0.656295 | − | 0.754504i | \(-0.727877\pi\) | ||||
−0.656295 | + | 0.754504i | \(0.727877\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13.6115 | −0.472748 | −0.236374 | − | 0.971662i | \(-0.575959\pi\) | ||||
−0.236374 | + | 0.971662i | \(0.575959\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −22.5380 | −0.781833 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 36.3461 | 1.25932 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.48238 | −0.0512999 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.70123 | 0.127933 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 20.7228 | 0.715431 | 0.357715 | − | 0.933831i | \(-0.383556\pi\) | ||||
0.357715 | + | 0.933831i | \(0.383556\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 18.8852 | 0.651214 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −20.5684 | −0.708414 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −10.4788 | −0.360481 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 21.6351 | 0.743391 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 29.4021 | 1.00908 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.12703 | −0.278591 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −18.7796 | −0.643001 | −0.321501 | − | 0.946909i | \(-0.604187\pi\) | ||||
−0.321501 | + | 0.946909i | \(0.604187\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.70385 | 0.297666 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −47.7602 | −1.63146 | −0.815729 | − | 0.578434i | \(-0.803664\pi\) | ||||
−0.815729 | + | 0.578434i | \(0.803664\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −41.5608 | −1.41804 | −0.709018 | − | 0.705190i | \(-0.750862\pi\) | ||||
−0.709018 | + | 0.705190i | \(0.750862\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.93108 | −0.0658111 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −0.525151 | −0.0178764 | −0.00893818 | − | 0.999960i | \(-0.502845\pi\) | ||||
−0.00893818 | + | 0.999960i | \(0.502845\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 24.3194 | 0.826886 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −20.6900 | −0.702671 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −22.1394 | −0.751027 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −23.6450 | −0.801181 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.40524 | −0.115250 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 12.0184 | 0.406294 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.76515 | −0.127140 | −0.0635701 | − | 0.997977i | \(-0.520249\pi\) | ||||
−0.0635701 | + | 0.997977i | \(0.520249\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −20.2839 | −0.684160 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −30.4381 | −1.02549 | −0.512743 | − | 0.858542i | \(-0.671371\pi\) | ||||
−0.512743 | + | 0.858542i | \(0.671371\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.63578 | 0.122354 | 0.0611768 | − | 0.998127i | \(-0.480515\pi\) | ||||
0.0611768 | + | 0.998127i | \(0.480515\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.151760 | −0.00510135 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 19.9846 | 0.671018 | 0.335509 | − | 0.942037i | \(-0.391092\pi\) | ||||
0.335509 | + | 0.942037i | \(0.391092\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −18.3024 | −0.613844 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.64105 | −0.188982 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 21.0923 | 0.705826 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.80264 | 0.0602555 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.49721 | 0.183547 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 25.6122 | 0.854213 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.84006 | 0.0613011 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.38761 | −0.0794547 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9.26035 | 0.307824 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20.7963 | 0.690529 | 0.345264 | − | 0.938505i | \(-0.387789\pi\) | ||||
0.345264 | + | 0.938505i | \(0.387789\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −12.6052 | −0.418088 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −54.5814 | −1.80836 | −0.904181 | − | 0.427150i | \(-0.859518\pi\) | ||||
−0.904181 | + | 0.427150i | \(0.859518\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −64.5565 | −2.13651 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.40273 | 0.178609 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −10.1798 | −0.336168 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.31975 | −0.274443 | −0.137222 | − | 0.990540i | \(-0.543817\pi\) | ||||
−0.137222 | + | 0.990540i | \(0.543817\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.9899 | 0.362128 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8.97485 | 0.295411 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 18.5611 | 0.610285 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 15.3704 | 0.504830 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 14.6371 | 0.480229 | 0.240114 | − | 0.970745i | \(-0.422815\pi\) | ||||
0.240114 | + | 0.970745i | \(0.422815\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 34.7613 | 1.13926 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 26.9703 | 0.882969 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −51.3373 | −1.67891 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10.0788 | 0.329260 | 0.164630 | − | 0.986355i | \(-0.447357\pi\) | ||||
0.164630 | + | 0.986355i | \(0.447357\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 32.1109 | 1.04790 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12.5806 | 0.410116 | 0.205058 | − | 0.978750i | \(-0.434262\pi\) | ||||
0.205058 | + | 0.978750i | \(0.434262\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.28052 | 0.0742638 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.54031 | 0.0501063 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15.0438 | −0.488858 | −0.244429 | − | 0.969667i | \(-0.578601\pi\) | ||||
−0.244429 | + | 0.969667i | \(0.578601\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −41.8427 | −1.35827 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 21.3657 | 0.692830 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 61.0466 | 1.97749 | 0.988746 | − | 0.149603i | \(-0.0477996\pi\) | ||||
0.988746 | + | 0.149603i | \(0.0477996\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 24.0576 | 0.778487 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −39.0356 | −1.26184 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7.08502 | −0.228787 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17.3009 | −0.558095 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.62482 | −0.213482 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 13.2982 | 0.428085 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.42784 | −0.206705 | −0.103353 | − | 0.994645i | \(-0.532957\pi\) | ||||
−0.103353 | + | 0.994645i | \(0.532957\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −36.0467 | −1.15799 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −28.9135 | −0.927879 | −0.463940 | − | 0.885867i | \(-0.653565\pi\) | ||||
−0.463940 | + | 0.885867i | \(0.653565\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.55693 | 0.178147 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −12.5549 | −0.402080 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −5.12031 | −0.163813 | −0.0819066 | − | 0.996640i | \(-0.526101\pi\) | ||||
−0.0819066 | + | 0.996640i | \(0.526101\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 58.9959 | 1.88552 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −18.9911 | −0.606338 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 15.0970 | 0.481518 | 0.240759 | − | 0.970585i | \(-0.422604\pi\) | ||||
0.240759 | + | 0.970585i | \(0.422604\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 34.3802 | 1.09544 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.73268 | 0.118812 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.81965 | 0.0896597 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.5344 | 0.779360 | 0.389680 | − | 0.920950i | \(-0.372586\pi\) | ||||
0.389680 | + | 0.920950i | \(0.372586\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 23.6701 | 0.751147 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −20.5953 | −0.652915 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.08691 | −0.0660930 | −0.0330465 | − | 0.999454i | \(-0.510521\pi\) | ||||
−0.0330465 | + | 0.999454i | \(0.510521\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6.62294 | 0.209541 |
(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.ba.1.4 | 9 | ||
4.3 | odd | 2 | 4008.2.a.i.1.4 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4008.2.a.i.1.4 | ✓ | 9 | 4.3 | odd | 2 | ||
8016.2.a.ba.1.4 | 9 | 1.1 | even | 1 | trivial |