Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6027,2,Mod(1,6027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6027 = 3 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6027.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: | \(48.1258372982\) |
Analytic rank: | \(1\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} - 14 x^{14} + 68 x^{13} + 64 x^{12} - 456 x^{11} - 54 x^{10} + 1532 x^{9} - 400 x^{8} + \cdots - 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(1.04648\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6027.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.04648 | −0.739971 | −0.369986 | − | 0.929037i | \(-0.620637\pi\) | ||||
−0.369986 | + | 0.929037i | \(0.620637\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −0.904885 | −0.452442 | ||||||||
\(5\) | 1.81328 | 0.810922 | 0.405461 | − | 0.914112i | \(-0.367111\pi\) | ||||
0.405461 | + | 0.914112i | \(0.367111\pi\) | |||||||
\(6\) | −1.04648 | −0.427223 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 3.03990 | 1.07477 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.89755 | −0.600059 | ||||||||
\(11\) | −0.445995 | −0.134472 | −0.0672362 | − | 0.997737i | \(-0.521418\pi\) | ||||
−0.0672362 | + | 0.997737i | \(0.521418\pi\) | |||||||
\(12\) | −0.904885 | −0.261218 | ||||||||
\(13\) | −2.67032 | −0.740613 | −0.370307 | − | 0.928910i | \(-0.620747\pi\) | ||||
−0.370307 | + | 0.928910i | \(0.620747\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.81328 | 0.468186 | ||||||||
\(16\) | −1.37141 | −0.342854 | ||||||||
\(17\) | 2.86907 | 0.695853 | 0.347926 | − | 0.937522i | \(-0.386886\pi\) | ||||
0.347926 | + | 0.937522i | \(0.386886\pi\) | |||||||
\(18\) | −1.04648 | −0.246657 | ||||||||
\(19\) | −4.73993 | −1.08741 | −0.543707 | − | 0.839275i | \(-0.682980\pi\) | ||||
−0.543707 | + | 0.839275i | \(0.682980\pi\) | |||||||
\(20\) | −1.64081 | −0.366895 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.466723 | 0.0995058 | ||||||||
\(23\) | 3.59833 | 0.750303 | 0.375152 | − | 0.926963i | \(-0.377591\pi\) | ||||
0.375152 | + | 0.926963i | \(0.377591\pi\) | |||||||
\(24\) | 3.03990 | 0.620516 | ||||||||
\(25\) | −1.71203 | −0.342406 | ||||||||
\(26\) | 2.79443 | 0.548033 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.22128 | −0.783871 | −0.391936 | − | 0.919993i | \(-0.628194\pi\) | ||||
−0.391936 | + | 0.919993i | \(0.628194\pi\) | |||||||
\(30\) | −1.89755 | −0.346444 | ||||||||
\(31\) | 6.94583 | 1.24751 | 0.623754 | − | 0.781621i | \(-0.285607\pi\) | ||||
0.623754 | + | 0.781621i | \(0.285607\pi\) | |||||||
\(32\) | −4.64464 | −0.821064 | ||||||||
\(33\) | −0.445995 | −0.0776377 | ||||||||
\(34\) | −3.00242 | −0.514911 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.904885 | −0.150814 | ||||||||
\(37\) | −9.17863 | −1.50896 | −0.754479 | − | 0.656324i | \(-0.772110\pi\) | ||||
−0.754479 | + | 0.656324i | \(0.772110\pi\) | |||||||
\(38\) | 4.96023 | 0.804656 | ||||||||
\(39\) | −2.67032 | −0.427593 | ||||||||
\(40\) | 5.51217 | 0.871551 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.79959 | −1.18943 | −0.594713 | − | 0.803938i | \(-0.702735\pi\) | ||||
−0.594713 | + | 0.803938i | \(0.702735\pi\) | |||||||
\(44\) | 0.403574 | 0.0608410 | ||||||||
\(45\) | 1.81328 | 0.270307 | ||||||||
\(46\) | −3.76557 | −0.555203 | ||||||||
\(47\) | −11.4891 | −1.67585 | −0.837926 | − | 0.545783i | \(-0.816232\pi\) | ||||
−0.837926 | + | 0.545783i | \(0.816232\pi\) | |||||||
\(48\) | −1.37141 | −0.197947 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 1.79160 | 0.253370 | ||||||||
\(51\) | 2.86907 | 0.401751 | ||||||||
\(52\) | 2.41633 | 0.335085 | ||||||||
\(53\) | 10.4400 | 1.43405 | 0.717025 | − | 0.697048i | \(-0.245503\pi\) | ||||
0.717025 | + | 0.697048i | \(0.245503\pi\) | |||||||
\(54\) | −1.04648 | −0.142408 | ||||||||
\(55\) | −0.808712 | −0.109047 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.73993 | −0.627819 | ||||||||
\(58\) | 4.41747 | 0.580042 | ||||||||
\(59\) | 5.38717 | 0.701350 | 0.350675 | − | 0.936497i | \(-0.385952\pi\) | ||||
0.350675 | + | 0.936497i | \(0.385952\pi\) | |||||||
\(60\) | −1.64081 | −0.211827 | ||||||||
\(61\) | −7.26684 | −0.930423 | −0.465212 | − | 0.885199i | \(-0.654022\pi\) | ||||
−0.465212 | + | 0.885199i | \(0.654022\pi\) | |||||||
\(62\) | −7.26865 | −0.923120 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.60334 | 0.950417 | ||||||||
\(65\) | −4.84203 | −0.600580 | ||||||||
\(66\) | 0.466723 | 0.0574497 | ||||||||
\(67\) | −14.2182 | −1.73702 | −0.868512 | − | 0.495668i | \(-0.834923\pi\) | ||||
−0.868512 | + | 0.495668i | \(0.834923\pi\) | |||||||
\(68\) | −2.59618 | −0.314833 | ||||||||
\(69\) | 3.59833 | 0.433188 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15.4800 | 1.83713 | 0.918567 | − | 0.395265i | \(-0.129347\pi\) | ||||
0.918567 | + | 0.395265i | \(0.129347\pi\) | |||||||
\(72\) | 3.03990 | 0.358255 | ||||||||
\(73\) | −12.6484 | −1.48038 | −0.740192 | − | 0.672396i | \(-0.765265\pi\) | ||||
−0.740192 | + | 0.672396i | \(0.765265\pi\) | |||||||
\(74\) | 9.60523 | 1.11659 | ||||||||
\(75\) | −1.71203 | −0.197688 | ||||||||
\(76\) | 4.28909 | 0.491992 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2.79443 | 0.316407 | ||||||||
\(79\) | 5.02198 | 0.565017 | 0.282508 | − | 0.959265i | \(-0.408834\pi\) | ||||
0.282508 | + | 0.959265i | \(0.408834\pi\) | |||||||
\(80\) | −2.48675 | −0.278027 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −1.04648 | −0.115564 | ||||||||
\(83\) | −7.60824 | −0.835113 | −0.417557 | − | 0.908651i | \(-0.637113\pi\) | ||||
−0.417557 | + | 0.908651i | \(0.637113\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.20242 | 0.564282 | ||||||||
\(86\) | 8.16210 | 0.880142 | ||||||||
\(87\) | −4.22128 | −0.452568 | ||||||||
\(88\) | −1.35578 | −0.144526 | ||||||||
\(89\) | 2.20300 | 0.233518 | 0.116759 | − | 0.993160i | \(-0.462750\pi\) | ||||
0.116759 | + | 0.993160i | \(0.462750\pi\) | |||||||
\(90\) | −1.89755 | −0.200020 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3.25607 | −0.339469 | ||||||||
\(93\) | 6.94583 | 0.720249 | ||||||||
\(94\) | 12.0230 | 1.24008 | ||||||||
\(95\) | −8.59480 | −0.881808 | ||||||||
\(96\) | −4.64464 | −0.474042 | ||||||||
\(97\) | 1.75062 | 0.177748 | 0.0888742 | − | 0.996043i | \(-0.471673\pi\) | ||||
0.0888742 | + | 0.996043i | \(0.471673\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.445995 | −0.0448242 | ||||||||
\(100\) | 1.54919 | 0.154919 | ||||||||
\(101\) | −10.0727 | −1.00227 | −0.501134 | − | 0.865370i | \(-0.667084\pi\) | ||||
−0.501134 | + | 0.865370i | \(0.667084\pi\) | |||||||
\(102\) | −3.00242 | −0.297284 | ||||||||
\(103\) | −15.6394 | −1.54099 | −0.770496 | − | 0.637445i | \(-0.779991\pi\) | ||||
−0.770496 | + | 0.637445i | \(0.779991\pi\) | |||||||
\(104\) | −8.11749 | −0.795986 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.9253 | −1.06116 | ||||||||
\(107\) | −11.1705 | −1.07990 | −0.539948 | − | 0.841699i | \(-0.681556\pi\) | ||||
−0.539948 | + | 0.841699i | \(0.681556\pi\) | |||||||
\(108\) | −0.904885 | −0.0870726 | ||||||||
\(109\) | 14.9447 | 1.43145 | 0.715723 | − | 0.698384i | \(-0.246097\pi\) | ||||
0.715723 | + | 0.698384i | \(0.246097\pi\) | |||||||
\(110\) | 0.846299 | 0.0806914 | ||||||||
\(111\) | −9.17863 | −0.871197 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.9484 | 1.12401 | 0.562007 | − | 0.827133i | \(-0.310030\pi\) | ||||
0.562007 | + | 0.827133i | \(0.310030\pi\) | |||||||
\(114\) | 4.96023 | 0.464568 | ||||||||
\(115\) | 6.52477 | 0.608437 | ||||||||
\(116\) | 3.81977 | 0.354657 | ||||||||
\(117\) | −2.67032 | −0.246871 | ||||||||
\(118\) | −5.63755 | −0.518979 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 5.51217 | 0.503190 | ||||||||
\(121\) | −10.8011 | −0.981917 | ||||||||
\(122\) | 7.60458 | 0.688487 | ||||||||
\(123\) | 1.00000 | 0.0901670 | ||||||||
\(124\) | −6.28517 | −0.564425 | ||||||||
\(125\) | −12.1708 | −1.08859 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.63833 | −0.411586 | −0.205793 | − | 0.978596i | \(-0.565977\pi\) | ||||
−0.205793 | + | 0.978596i | \(0.565977\pi\) | |||||||
\(128\) | 1.33256 | 0.117782 | ||||||||
\(129\) | −7.79959 | −0.686716 | ||||||||
\(130\) | 5.06707 | 0.444412 | ||||||||
\(131\) | 7.50200 | 0.655453 | 0.327726 | − | 0.944773i | \(-0.393718\pi\) | ||||
0.327726 | + | 0.944773i | \(0.393718\pi\) | |||||||
\(132\) | 0.403574 | 0.0351266 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 14.8790 | 1.28535 | ||||||||
\(135\) | 1.81328 | 0.156062 | ||||||||
\(136\) | 8.72169 | 0.747879 | ||||||||
\(137\) | −18.9937 | −1.62274 | −0.811370 | − | 0.584533i | \(-0.801278\pi\) | ||||
−0.811370 | + | 0.584533i | \(0.801278\pi\) | |||||||
\(138\) | −3.76557 | −0.320547 | ||||||||
\(139\) | 12.7746 | 1.08353 | 0.541766 | − | 0.840530i | \(-0.317756\pi\) | ||||
0.541766 | + | 0.840530i | \(0.317756\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −11.4891 | −0.967554 | ||||||||
\(142\) | −16.1994 | −1.35943 | ||||||||
\(143\) | 1.19095 | 0.0995921 | ||||||||
\(144\) | −1.37141 | −0.114285 | ||||||||
\(145\) | −7.65434 | −0.635658 | ||||||||
\(146\) | 13.2363 | 1.09544 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 8.30561 | 0.682717 | ||||||||
\(149\) | −6.86535 | −0.562431 | −0.281216 | − | 0.959645i | \(-0.590738\pi\) | ||||
−0.281216 | + | 0.959645i | \(0.590738\pi\) | |||||||
\(150\) | 1.79160 | 0.146283 | ||||||||
\(151\) | −6.76282 | −0.550351 | −0.275175 | − | 0.961394i | \(-0.588736\pi\) | ||||
−0.275175 | + | 0.961394i | \(0.588736\pi\) | |||||||
\(152\) | −14.4089 | −1.16872 | ||||||||
\(153\) | 2.86907 | 0.231951 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 12.5947 | 1.01163 | ||||||||
\(156\) | 2.41633 | 0.193461 | ||||||||
\(157\) | 3.74193 | 0.298639 | 0.149319 | − | 0.988789i | \(-0.452292\pi\) | ||||
0.149319 | + | 0.988789i | \(0.452292\pi\) | |||||||
\(158\) | −5.25539 | −0.418096 | ||||||||
\(159\) | 10.4400 | 0.827949 | ||||||||
\(160\) | −8.42202 | −0.665819 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.04648 | −0.0822190 | ||||||||
\(163\) | −18.3200 | −1.43494 | −0.717468 | − | 0.696592i | \(-0.754699\pi\) | ||||
−0.717468 | + | 0.696592i | \(0.754699\pi\) | |||||||
\(164\) | −0.904885 | −0.0706596 | ||||||||
\(165\) | −0.808712 | −0.0629581 | ||||||||
\(166\) | 7.96186 | 0.617960 | ||||||||
\(167\) | 12.9443 | 1.00166 | 0.500829 | − | 0.865546i | \(-0.333029\pi\) | ||||
0.500829 | + | 0.865546i | \(0.333029\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.86940 | −0.451492 | ||||||||
\(170\) | −5.44422 | −0.417553 | ||||||||
\(171\) | −4.73993 | −0.362472 | ||||||||
\(172\) | 7.05773 | 0.538147 | ||||||||
\(173\) | 14.8684 | 1.13042 | 0.565212 | − | 0.824946i | \(-0.308795\pi\) | ||||
0.565212 | + | 0.824946i | \(0.308795\pi\) | |||||||
\(174\) | 4.41747 | 0.334888 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.611643 | 0.0461044 | ||||||||
\(177\) | 5.38717 | 0.404925 | ||||||||
\(178\) | −2.30539 | −0.172796 | ||||||||
\(179\) | −0.390628 | −0.0291969 | −0.0145984 | − | 0.999893i | \(-0.504647\pi\) | ||||
−0.0145984 | + | 0.999893i | \(0.504647\pi\) | |||||||
\(180\) | −1.64081 | −0.122298 | ||||||||
\(181\) | −1.88861 | −0.140380 | −0.0701898 | − | 0.997534i | \(-0.522360\pi\) | ||||
−0.0701898 | + | 0.997534i | \(0.522360\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.26684 | −0.537180 | ||||||||
\(184\) | 10.9385 | 0.806400 | ||||||||
\(185\) | −16.6434 | −1.22365 | ||||||||
\(186\) | −7.26865 | −0.532963 | ||||||||
\(187\) | −1.27959 | −0.0935730 | ||||||||
\(188\) | 10.3963 | 0.758227 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 8.99427 | 0.652513 | ||||||||
\(191\) | −8.98328 | −0.650007 | −0.325004 | − | 0.945713i | \(-0.605366\pi\) | ||||
−0.325004 | + | 0.945713i | \(0.605366\pi\) | |||||||
\(192\) | 7.60334 | 0.548724 | ||||||||
\(193\) | 16.2969 | 1.17307 | 0.586537 | − | 0.809922i | \(-0.300491\pi\) | ||||
0.586537 | + | 0.809922i | \(0.300491\pi\) | |||||||
\(194\) | −1.83198 | −0.131529 | ||||||||
\(195\) | −4.84203 | −0.346745 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.0411 | 1.28538 | 0.642688 | − | 0.766128i | \(-0.277819\pi\) | ||||
0.642688 | + | 0.766128i | \(0.277819\pi\) | |||||||
\(198\) | 0.466723 | 0.0331686 | ||||||||
\(199\) | 3.32264 | 0.235535 | 0.117768 | − | 0.993041i | \(-0.462426\pi\) | ||||
0.117768 | + | 0.993041i | \(0.462426\pi\) | |||||||
\(200\) | −5.20439 | −0.368006 | ||||||||
\(201\) | −14.2182 | −1.00287 | ||||||||
\(202\) | 10.5408 | 0.741650 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −2.59618 | −0.181769 | ||||||||
\(205\) | 1.81328 | 0.126645 | ||||||||
\(206\) | 16.3662 | 1.14029 | ||||||||
\(207\) | 3.59833 | 0.250101 | ||||||||
\(208\) | 3.66211 | 0.253922 | ||||||||
\(209\) | 2.11398 | 0.146227 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.3821 | 1.26547 | 0.632737 | − | 0.774367i | \(-0.281932\pi\) | ||||
0.632737 | + | 0.774367i | \(0.281932\pi\) | |||||||
\(212\) | −9.44703 | −0.648825 | ||||||||
\(213\) | 15.4800 | 1.06067 | ||||||||
\(214\) | 11.6897 | 0.799092 | ||||||||
\(215\) | −14.1428 | −0.964532 | ||||||||
\(216\) | 3.03990 | 0.206839 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −15.6393 | −1.05923 | ||||||||
\(219\) | −12.6484 | −0.854700 | ||||||||
\(220\) | 0.731791 | 0.0493373 | ||||||||
\(221\) | −7.66134 | −0.515358 | ||||||||
\(222\) | 9.60523 | 0.644661 | ||||||||
\(223\) | −8.28572 | −0.554853 | −0.277427 | − | 0.960747i | \(-0.589482\pi\) | ||||
−0.277427 | + | 0.960747i | \(0.589482\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.71203 | −0.114135 | ||||||||
\(226\) | −12.5038 | −0.831738 | ||||||||
\(227\) | −7.06231 | −0.468742 | −0.234371 | − | 0.972147i | \(-0.575303\pi\) | ||||
−0.234371 | + | 0.972147i | \(0.575303\pi\) | |||||||
\(228\) | 4.28909 | 0.284052 | ||||||||
\(229\) | −20.2997 | −1.34144 | −0.670720 | − | 0.741711i | \(-0.734015\pi\) | ||||
−0.670720 | + | 0.741711i | \(0.734015\pi\) | |||||||
\(230\) | −6.82802 | −0.450226 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −12.8322 | −0.842478 | ||||||||
\(233\) | 4.13151 | 0.270664 | 0.135332 | − | 0.990800i | \(-0.456790\pi\) | ||||
0.135332 | + | 0.990800i | \(0.456790\pi\) | |||||||
\(234\) | 2.79443 | 0.182678 | ||||||||
\(235\) | −20.8329 | −1.35899 | ||||||||
\(236\) | −4.87477 | −0.317320 | ||||||||
\(237\) | 5.02198 | 0.326213 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.65744 | −0.365950 | −0.182975 | − | 0.983118i | \(-0.558573\pi\) | ||||
−0.182975 | + | 0.983118i | \(0.558573\pi\) | |||||||
\(240\) | −2.48675 | −0.160519 | ||||||||
\(241\) | 18.0436 | 1.16229 | 0.581145 | − | 0.813800i | \(-0.302605\pi\) | ||||
0.581145 | + | 0.813800i | \(0.302605\pi\) | |||||||
\(242\) | 11.3031 | 0.726591 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 6.57565 | 0.420963 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.04648 | −0.0667210 | ||||||||
\(247\) | 12.6571 | 0.805354 | ||||||||
\(248\) | 21.1146 | 1.34078 | ||||||||
\(249\) | −7.60824 | −0.482153 | ||||||||
\(250\) | 12.7364 | 0.805523 | ||||||||
\(251\) | −16.5321 | −1.04349 | −0.521747 | − | 0.853100i | \(-0.674720\pi\) | ||||
−0.521747 | + | 0.853100i | \(0.674720\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.60484 | −0.100895 | ||||||||
\(254\) | 4.85391 | 0.304562 | ||||||||
\(255\) | 5.20242 | 0.325788 | ||||||||
\(256\) | −16.6012 | −1.03757 | ||||||||
\(257\) | −27.2214 | −1.69802 | −0.849012 | − | 0.528373i | \(-0.822802\pi\) | ||||
−0.849012 | + | 0.528373i | \(0.822802\pi\) | |||||||
\(258\) | 8.16210 | 0.508150 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 4.38148 | 0.271728 | ||||||||
\(261\) | −4.22128 | −0.261290 | ||||||||
\(262\) | −7.85067 | −0.485016 | ||||||||
\(263\) | 0.195115 | 0.0120313 | 0.00601567 | − | 0.999982i | \(-0.498085\pi\) | ||||
0.00601567 | + | 0.999982i | \(0.498085\pi\) | |||||||
\(264\) | −1.35578 | −0.0834424 | ||||||||
\(265\) | 18.9307 | 1.16290 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.20300 | 0.134822 | ||||||||
\(268\) | 12.8658 | 0.785904 | ||||||||
\(269\) | 23.1477 | 1.41134 | 0.705670 | − | 0.708541i | \(-0.250646\pi\) | ||||
0.705670 | + | 0.708541i | \(0.250646\pi\) | |||||||
\(270\) | −1.89755 | −0.115481 | ||||||||
\(271\) | 6.82658 | 0.414685 | 0.207343 | − | 0.978268i | \(-0.433519\pi\) | ||||
0.207343 | + | 0.978268i | \(0.433519\pi\) | |||||||
\(272\) | −3.93469 | −0.238575 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 19.8765 | 1.20078 | ||||||||
\(275\) | 0.763555 | 0.0460441 | ||||||||
\(276\) | −3.25607 | −0.195993 | ||||||||
\(277\) | 27.7102 | 1.66495 | 0.832474 | − | 0.554065i | \(-0.186924\pi\) | ||||
0.832474 | + | 0.554065i | \(0.186924\pi\) | |||||||
\(278\) | −13.3684 | −0.801782 | ||||||||
\(279\) | 6.94583 | 0.415836 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.97578 | −0.237175 | −0.118587 | − | 0.992944i | \(-0.537837\pi\) | ||||
−0.118587 | + | 0.992944i | \(0.537837\pi\) | |||||||
\(282\) | 12.0230 | 0.715962 | ||||||||
\(283\) | 12.5932 | 0.748590 | 0.374295 | − | 0.927310i | \(-0.377885\pi\) | ||||
0.374295 | + | 0.927310i | \(0.377885\pi\) | |||||||
\(284\) | −14.0076 | −0.831197 | ||||||||
\(285\) | −8.59480 | −0.509112 | ||||||||
\(286\) | −1.24630 | −0.0736953 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −4.64464 | −0.273688 | ||||||||
\(289\) | −8.76842 | −0.515789 | ||||||||
\(290\) | 8.01010 | 0.470369 | ||||||||
\(291\) | 1.75062 | 0.102623 | ||||||||
\(292\) | 11.4453 | 0.669788 | ||||||||
\(293\) | −18.7975 | −1.09816 | −0.549081 | − | 0.835769i | \(-0.685022\pi\) | ||||
−0.549081 | + | 0.835769i | \(0.685022\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.76843 | 0.568740 | ||||||||
\(296\) | −27.9021 | −1.62178 | ||||||||
\(297\) | −0.445995 | −0.0258792 | ||||||||
\(298\) | 7.18443 | 0.416183 | ||||||||
\(299\) | −9.60868 | −0.555685 | ||||||||
\(300\) | 1.54919 | 0.0894424 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 7.07714 | 0.407244 | ||||||||
\(303\) | −10.0727 | −0.578660 | ||||||||
\(304\) | 6.50041 | 0.372824 | ||||||||
\(305\) | −13.1768 | −0.754501 | ||||||||
\(306\) | −3.00242 | −0.171637 | ||||||||
\(307\) | 15.8413 | 0.904109 | 0.452055 | − | 0.891990i | \(-0.350691\pi\) | ||||
0.452055 | + | 0.891990i | \(0.350691\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −15.6394 | −0.889692 | ||||||||
\(310\) | −13.1801 | −0.748578 | ||||||||
\(311\) | −22.9872 | −1.30349 | −0.651743 | − | 0.758439i | \(-0.725962\pi\) | ||||
−0.651743 | + | 0.758439i | \(0.725962\pi\) | |||||||
\(312\) | −8.11749 | −0.459563 | ||||||||
\(313\) | 13.7375 | 0.776489 | 0.388244 | − | 0.921556i | \(-0.373082\pi\) | ||||
0.388244 | + | 0.921556i | \(0.373082\pi\) | |||||||
\(314\) | −3.91585 | −0.220984 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.54431 | −0.255638 | ||||||||
\(317\) | 2.04989 | 0.115133 | 0.0575666 | − | 0.998342i | \(-0.481666\pi\) | ||||
0.0575666 | + | 0.998342i | \(0.481666\pi\) | |||||||
\(318\) | −10.9253 | −0.612658 | ||||||||
\(319\) | 1.88267 | 0.105409 | ||||||||
\(320\) | 13.7870 | 0.770714 | ||||||||
\(321\) | −11.1705 | −0.623478 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −13.5992 | −0.756680 | ||||||||
\(324\) | −0.904885 | −0.0502714 | ||||||||
\(325\) | 4.57166 | 0.253590 | ||||||||
\(326\) | 19.1715 | 1.06181 | ||||||||
\(327\) | 14.9447 | 0.826446 | ||||||||
\(328\) | 3.03990 | 0.167850 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0.846299 | 0.0465872 | ||||||||
\(331\) | −29.0301 | −1.59564 | −0.797819 | − | 0.602897i | \(-0.794013\pi\) | ||||
−0.797819 | + | 0.602897i | \(0.794013\pi\) | |||||||
\(332\) | 6.88458 | 0.377841 | ||||||||
\(333\) | −9.17863 | −0.502986 | ||||||||
\(334\) | −13.5459 | −0.741198 | ||||||||
\(335\) | −25.7815 | −1.40859 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −23.8798 | −1.30082 | −0.650408 | − | 0.759585i | \(-0.725402\pi\) | ||||
−0.650408 | + | 0.759585i | \(0.725402\pi\) | |||||||
\(338\) | 6.14219 | 0.334091 | ||||||||
\(339\) | 11.9484 | 0.648949 | ||||||||
\(340\) | −4.70759 | −0.255305 | ||||||||
\(341\) | −3.09780 | −0.167755 | ||||||||
\(342\) | 4.96023 | 0.268219 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −23.7100 | −1.27836 | ||||||||
\(345\) | 6.52477 | 0.351282 | ||||||||
\(346\) | −15.5594 | −0.836481 | ||||||||
\(347\) | −6.57264 | −0.352838 | −0.176419 | − | 0.984315i | \(-0.556451\pi\) | ||||
−0.176419 | + | 0.984315i | \(0.556451\pi\) | |||||||
\(348\) | 3.81977 | 0.204761 | ||||||||
\(349\) | 9.91409 | 0.530689 | 0.265345 | − | 0.964154i | \(-0.414514\pi\) | ||||
0.265345 | + | 0.964154i | \(0.414514\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.67032 | −0.142531 | ||||||||
\(352\) | 2.07148 | 0.110411 | ||||||||
\(353\) | 6.00923 | 0.319839 | 0.159920 | − | 0.987130i | \(-0.448877\pi\) | ||||
0.159920 | + | 0.987130i | \(0.448877\pi\) | |||||||
\(354\) | −5.63755 | −0.299633 | ||||||||
\(355\) | 28.0695 | 1.48977 | ||||||||
\(356\) | −1.99346 | −0.105653 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.408783 | 0.0216049 | ||||||||
\(359\) | 17.1440 | 0.904826 | 0.452413 | − | 0.891808i | \(-0.350563\pi\) | ||||
0.452413 | + | 0.891808i | \(0.350563\pi\) | |||||||
\(360\) | 5.51217 | 0.290517 | ||||||||
\(361\) | 3.46694 | 0.182470 | ||||||||
\(362\) | 1.97639 | 0.103877 | ||||||||
\(363\) | −10.8011 | −0.566910 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −22.9351 | −1.20048 | ||||||||
\(366\) | 7.60458 | 0.397498 | ||||||||
\(367\) | 0.197446 | 0.0103066 | 0.00515330 | − | 0.999987i | \(-0.498360\pi\) | ||||
0.00515330 | + | 0.999987i | \(0.498360\pi\) | |||||||
\(368\) | −4.93480 | −0.257244 | ||||||||
\(369\) | 1.00000 | 0.0520579 | ||||||||
\(370\) | 17.4169 | 0.905464 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −6.28517 | −0.325871 | ||||||||
\(373\) | −35.1529 | −1.82015 | −0.910074 | − | 0.414447i | \(-0.863975\pi\) | ||||
−0.910074 | + | 0.414447i | \(0.863975\pi\) | |||||||
\(374\) | 1.33906 | 0.0692414 | ||||||||
\(375\) | −12.1708 | −0.628496 | ||||||||
\(376\) | −34.9256 | −1.80115 | ||||||||
\(377\) | 11.2722 | 0.580545 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −32.5491 | −1.67193 | −0.835967 | − | 0.548779i | \(-0.815093\pi\) | ||||
−0.835967 | + | 0.548779i | \(0.815093\pi\) | |||||||
\(380\) | 7.77731 | 0.398967 | ||||||||
\(381\) | −4.63833 | −0.237629 | ||||||||
\(382\) | 9.40080 | 0.480987 | ||||||||
\(383\) | 16.1072 | 0.823037 | 0.411519 | − | 0.911401i | \(-0.364999\pi\) | ||||
0.411519 | + | 0.911401i | \(0.364999\pi\) | |||||||
\(384\) | 1.33256 | 0.0680017 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −17.0543 | −0.868041 | ||||||||
\(387\) | −7.79959 | −0.396476 | ||||||||
\(388\) | −1.58411 | −0.0804209 | ||||||||
\(389\) | −33.7726 | −1.71234 | −0.856168 | − | 0.516697i | \(-0.827161\pi\) | ||||
−0.856168 | + | 0.516697i | \(0.827161\pi\) | |||||||
\(390\) | 5.06707 | 0.256581 | ||||||||
\(391\) | 10.3239 | 0.522101 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.50200 | 0.378426 | ||||||||
\(394\) | −18.8796 | −0.951141 | ||||||||
\(395\) | 9.10624 | 0.458184 | ||||||||
\(396\) | 0.403574 | 0.0202803 | ||||||||
\(397\) | −18.8905 | −0.948087 | −0.474044 | − | 0.880501i | \(-0.657206\pi\) | ||||
−0.474044 | + | 0.880501i | \(0.657206\pi\) | |||||||
\(398\) | −3.47706 | −0.174289 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.34790 | 0.117395 | ||||||||
\(401\) | −15.2704 | −0.762566 | −0.381283 | − | 0.924458i | \(-0.624518\pi\) | ||||
−0.381283 | + | 0.924458i | \(0.624518\pi\) | |||||||
\(402\) | 14.8790 | 0.742096 | ||||||||
\(403\) | −18.5476 | −0.923920 | ||||||||
\(404\) | 9.11461 | 0.453469 | ||||||||
\(405\) | 1.81328 | 0.0901024 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.09362 | 0.202913 | ||||||||
\(408\) | 8.72169 | 0.431788 | ||||||||
\(409\) | 32.9169 | 1.62764 | 0.813818 | − | 0.581119i | \(-0.197385\pi\) | ||||
0.813818 | + | 0.581119i | \(0.197385\pi\) | |||||||
\(410\) | −1.89755 | −0.0937135 | ||||||||
\(411\) | −18.9937 | −0.936889 | ||||||||
\(412\) | 14.1518 | 0.697210 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −3.76557 | −0.185068 | ||||||||
\(415\) | −13.7958 | −0.677212 | ||||||||
\(416\) | 12.4027 | 0.608091 | ||||||||
\(417\) | 12.7746 | 0.625577 | ||||||||
\(418\) | −2.21224 | −0.108204 | ||||||||
\(419\) | −36.0486 | −1.76109 | −0.880544 | − | 0.473964i | \(-0.842823\pi\) | ||||
−0.880544 | + | 0.473964i | \(0.842823\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.11308 | −0.102985 | −0.0514927 | − | 0.998673i | \(-0.516398\pi\) | ||||
−0.0514927 | + | 0.998673i | \(0.516398\pi\) | |||||||
\(422\) | −19.2364 | −0.936414 | ||||||||
\(423\) | −11.4891 | −0.558618 | ||||||||
\(424\) | 31.7366 | 1.54127 | ||||||||
\(425\) | −4.91193 | −0.238264 | ||||||||
\(426\) | −16.1994 | −0.784865 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 10.1080 | 0.488590 | ||||||||
\(429\) | 1.19095 | 0.0574995 | ||||||||
\(430\) | 14.8001 | 0.713726 | ||||||||
\(431\) | 25.2339 | 1.21547 | 0.607736 | − | 0.794139i | \(-0.292078\pi\) | ||||
0.607736 | + | 0.794139i | \(0.292078\pi\) | |||||||
\(432\) | −1.37141 | −0.0659822 | ||||||||
\(433\) | 23.1074 | 1.11047 | 0.555235 | − | 0.831694i | \(-0.312628\pi\) | ||||
0.555235 | + | 0.831694i | \(0.312628\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.65434 | −0.366998 | ||||||||
\(436\) | −13.5233 | −0.647647 | ||||||||
\(437\) | −17.0558 | −0.815891 | ||||||||
\(438\) | 13.2363 | 0.632454 | ||||||||
\(439\) | 21.0733 | 1.00577 | 0.502887 | − | 0.864352i | \(-0.332271\pi\) | ||||
0.502887 | + | 0.864352i | \(0.332271\pi\) | |||||||
\(440\) | −2.45840 | −0.117200 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 8.01742 | 0.381350 | ||||||||
\(443\) | 10.7771 | 0.512035 | 0.256017 | − | 0.966672i | \(-0.417590\pi\) | ||||
0.256017 | + | 0.966672i | \(0.417590\pi\) | |||||||
\(444\) | 8.30561 | 0.394167 | ||||||||
\(445\) | 3.99465 | 0.189365 | ||||||||
\(446\) | 8.67082 | 0.410575 | ||||||||
\(447\) | −6.86535 | −0.324720 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.96438 | −0.0927048 | −0.0463524 | − | 0.998925i | \(-0.514760\pi\) | ||||
−0.0463524 | + | 0.998925i | \(0.514760\pi\) | |||||||
\(450\) | 1.79160 | 0.0844568 | ||||||||
\(451\) | −0.445995 | −0.0210011 | ||||||||
\(452\) | −10.8119 | −0.508551 | ||||||||
\(453\) | −6.76282 | −0.317745 | ||||||||
\(454\) | 7.39055 | 0.346856 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −14.4089 | −0.674758 | ||||||||
\(457\) | 10.4268 | 0.487744 | 0.243872 | − | 0.969807i | \(-0.421582\pi\) | ||||
0.243872 | + | 0.969807i | \(0.421582\pi\) | |||||||
\(458\) | 21.2431 | 0.992627 | ||||||||
\(459\) | 2.86907 | 0.133917 | ||||||||
\(460\) | −5.90416 | −0.275283 | ||||||||
\(461\) | −28.1751 | −1.31224 | −0.656122 | − | 0.754655i | \(-0.727804\pi\) | ||||
−0.656122 | + | 0.754655i | \(0.727804\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.96875 | −0.277392 | −0.138696 | − | 0.990335i | \(-0.544291\pi\) | ||||
−0.138696 | + | 0.990335i | \(0.544291\pi\) | |||||||
\(464\) | 5.78912 | 0.268753 | ||||||||
\(465\) | 12.5947 | 0.584065 | ||||||||
\(466\) | −4.32353 | −0.200284 | ||||||||
\(467\) | −0.120608 | −0.00558107 | −0.00279053 | − | 0.999996i | \(-0.500888\pi\) | ||||
−0.00279053 | + | 0.999996i | \(0.500888\pi\) | |||||||
\(468\) | 2.41633 | 0.111695 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 21.8011 | 1.00561 | ||||||||
\(471\) | 3.74193 | 0.172419 | ||||||||
\(472\) | 16.3764 | 0.753787 | ||||||||
\(473\) | 3.47858 | 0.159945 | ||||||||
\(474\) | −5.25539 | −0.241388 | ||||||||
\(475\) | 8.11489 | 0.372337 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.4400 | 0.478016 | ||||||||
\(478\) | 5.92039 | 0.270792 | ||||||||
\(479\) | −40.6769 | −1.85858 | −0.929288 | − | 0.369356i | \(-0.879578\pi\) | ||||
−0.929288 | + | 0.369356i | \(0.879578\pi\) | |||||||
\(480\) | −8.42202 | −0.384411 | ||||||||
\(481\) | 24.5099 | 1.11755 | ||||||||
\(482\) | −18.8822 | −0.860061 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9.77374 | 0.444261 | ||||||||
\(485\) | 3.17436 | 0.144140 | ||||||||
\(486\) | −1.04648 | −0.0474692 | ||||||||
\(487\) | −28.6842 | −1.29981 | −0.649903 | − | 0.760017i | \(-0.725190\pi\) | ||||
−0.649903 | + | 0.760017i | \(0.725190\pi\) | |||||||
\(488\) | −22.0904 | −0.999987 | ||||||||
\(489\) | −18.3200 | −0.828460 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.32175 | 0.104779 | 0.0523896 | − | 0.998627i | \(-0.483316\pi\) | ||||
0.0523896 | + | 0.998627i | \(0.483316\pi\) | |||||||
\(492\) | −0.904885 | −0.0407954 | ||||||||
\(493\) | −12.1112 | −0.545459 | ||||||||
\(494\) | −13.2454 | −0.595939 | ||||||||
\(495\) | −0.808712 | −0.0363489 | ||||||||
\(496\) | −9.52560 | −0.427712 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 7.96186 | 0.356779 | ||||||||
\(499\) | 11.9822 | 0.536397 | 0.268198 | − | 0.963364i | \(-0.413572\pi\) | ||||
0.268198 | + | 0.963364i | \(0.413572\pi\) | |||||||
\(500\) | 11.0131 | 0.492523 | ||||||||
\(501\) | 12.9443 | 0.578307 | ||||||||
\(502\) | 17.3004 | 0.772156 | ||||||||
\(503\) | 8.06028 | 0.359390 | 0.179695 | − | 0.983722i | \(-0.442489\pi\) | ||||
0.179695 | + | 0.983722i | \(0.442489\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −18.2645 | −0.812762 | ||||||||
\(506\) | 1.67942 | 0.0746595 | ||||||||
\(507\) | −5.86940 | −0.260669 | ||||||||
\(508\) | 4.19716 | 0.186219 | ||||||||
\(509\) | 10.8090 | 0.479101 | 0.239550 | − | 0.970884i | \(-0.423000\pi\) | ||||
0.239550 | + | 0.970884i | \(0.423000\pi\) | |||||||
\(510\) | −5.44422 | −0.241074 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 14.7076 | 0.649992 | ||||||||
\(513\) | −4.73993 | −0.209273 | ||||||||
\(514\) | 28.4866 | 1.25649 | ||||||||
\(515\) | −28.3585 | −1.24962 | ||||||||
\(516\) | 7.05773 | 0.310699 | ||||||||
\(517\) | 5.12406 | 0.225356 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 14.8684 | 0.652650 | ||||||||
\(520\) | −14.7193 | −0.645482 | ||||||||
\(521\) | −14.9072 | −0.653095 | −0.326547 | − | 0.945181i | \(-0.605885\pi\) | ||||
−0.326547 | + | 0.945181i | \(0.605885\pi\) | |||||||
\(522\) | 4.41747 | 0.193347 | ||||||||
\(523\) | −24.1148 | −1.05447 | −0.527233 | − | 0.849721i | \(-0.676770\pi\) | ||||
−0.527233 | + | 0.849721i | \(0.676770\pi\) | |||||||
\(524\) | −6.78844 | −0.296554 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.204184 | −0.00890284 | ||||||||
\(527\) | 19.9281 | 0.868081 | ||||||||
\(528\) | 0.611643 | 0.0266184 | ||||||||
\(529\) | −10.0520 | −0.437045 | ||||||||
\(530\) | −19.8105 | −0.860514 | ||||||||
\(531\) | 5.38717 | 0.233783 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.67032 | −0.115664 | ||||||||
\(534\) | −2.30539 | −0.0997641 | ||||||||
\(535\) | −20.2553 | −0.875711 | ||||||||
\(536\) | −43.2217 | −1.86689 | ||||||||
\(537\) | −0.390628 | −0.0168568 | ||||||||
\(538\) | −24.2235 | −1.04435 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.64081 | −0.0706091 | ||||||||
\(541\) | −21.2142 | −0.912072 | −0.456036 | − | 0.889961i | \(-0.650731\pi\) | ||||
−0.456036 | + | 0.889961i | \(0.650731\pi\) | |||||||
\(542\) | −7.14386 | −0.306855 | ||||||||
\(543\) | −1.88861 | −0.0810482 | ||||||||
\(544\) | −13.3258 | −0.571339 | ||||||||
\(545\) | 27.0989 | 1.16079 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.39628 | −0.230728 | −0.115364 | − | 0.993323i | \(-0.536803\pi\) | ||||
−0.115364 | + | 0.993323i | \(0.536803\pi\) | |||||||
\(548\) | 17.1871 | 0.734196 | ||||||||
\(549\) | −7.26684 | −0.310141 | ||||||||
\(550\) | −0.799044 | −0.0340713 | ||||||||
\(551\) | 20.0086 | 0.852393 | ||||||||
\(552\) | 10.9385 | 0.465575 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −28.9981 | −1.23201 | ||||||||
\(555\) | −16.6434 | −0.706473 | ||||||||
\(556\) | −11.5596 | −0.490236 | ||||||||
\(557\) | −42.9811 | −1.82117 | −0.910584 | − | 0.413324i | \(-0.864368\pi\) | ||||
−0.910584 | + | 0.413324i | \(0.864368\pi\) | |||||||
\(558\) | −7.26865 | −0.307707 | ||||||||
\(559\) | 20.8274 | 0.880905 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.27959 | −0.0540244 | ||||||||
\(562\) | 4.16056 | 0.175503 | ||||||||
\(563\) | 43.8925 | 1.84985 | 0.924924 | − | 0.380153i | \(-0.124129\pi\) | ||||
0.924924 | + | 0.380153i | \(0.124129\pi\) | |||||||
\(564\) | 10.3963 | 0.437762 | ||||||||
\(565\) | 21.6658 | 0.911487 | ||||||||
\(566\) | −13.1785 | −0.553935 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 47.0575 | 1.97449 | ||||||||
\(569\) | −10.8598 | −0.455267 | −0.227634 | − | 0.973747i | \(-0.573099\pi\) | ||||
−0.227634 | + | 0.973747i | \(0.573099\pi\) | |||||||
\(570\) | 8.99427 | 0.376728 | ||||||||
\(571\) | 14.8272 | 0.620498 | 0.310249 | − | 0.950655i | \(-0.399588\pi\) | ||||
0.310249 | + | 0.950655i | \(0.399588\pi\) | |||||||
\(572\) | −1.07767 | −0.0450597 | ||||||||
\(573\) | −8.98328 | −0.375282 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.16044 | −0.256908 | ||||||||
\(576\) | 7.60334 | 0.316806 | ||||||||
\(577\) | −17.5161 | −0.729204 | −0.364602 | − | 0.931164i | \(-0.618795\pi\) | ||||
−0.364602 | + | 0.931164i | \(0.618795\pi\) | |||||||
\(578\) | 9.17595 | 0.381669 | ||||||||
\(579\) | 16.2969 | 0.677275 | ||||||||
\(580\) | 6.92630 | 0.287599 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −1.83198 | −0.0759381 | ||||||||
\(583\) | −4.65620 | −0.192840 | ||||||||
\(584\) | −38.4498 | −1.59107 | ||||||||
\(585\) | −4.84203 | −0.200193 | ||||||||
\(586\) | 19.6712 | 0.812608 | ||||||||
\(587\) | 17.4318 | 0.719488 | 0.359744 | − | 0.933051i | \(-0.382864\pi\) | ||||
0.359744 | + | 0.933051i | \(0.382864\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −32.9227 | −1.35656 | ||||||||
\(590\) | −10.2224 | −0.420851 | ||||||||
\(591\) | 18.0411 | 0.742112 | ||||||||
\(592\) | 12.5877 | 0.517352 | ||||||||
\(593\) | −33.0499 | −1.35720 | −0.678598 | − | 0.734510i | \(-0.737412\pi\) | ||||
−0.678598 | + | 0.734510i | \(0.737412\pi\) | |||||||
\(594\) | 0.466723 | 0.0191499 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.21235 | 0.254468 | ||||||||
\(597\) | 3.32264 | 0.135986 | ||||||||
\(598\) | 10.0553 | 0.411191 | ||||||||
\(599\) | 47.6320 | 1.94619 | 0.973095 | − | 0.230405i | \(-0.0740052\pi\) | ||||
0.973095 | + | 0.230405i | \(0.0740052\pi\) | |||||||
\(600\) | −5.20439 | −0.212468 | ||||||||
\(601\) | −14.1223 | −0.576060 | −0.288030 | − | 0.957621i | \(-0.593000\pi\) | ||||
−0.288030 | + | 0.957621i | \(0.593000\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −14.2182 | −0.579008 | ||||||||
\(604\) | 6.11957 | 0.249002 | ||||||||
\(605\) | −19.5854 | −0.796258 | ||||||||
\(606\) | 10.5408 | 0.428192 | ||||||||
\(607\) | 25.8046 | 1.04738 | 0.523688 | − | 0.851910i | \(-0.324556\pi\) | ||||
0.523688 | + | 0.851910i | \(0.324556\pi\) | |||||||
\(608\) | 22.0153 | 0.892837 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 13.7892 | 0.558309 | ||||||||
\(611\) | 30.6795 | 1.24116 | ||||||||
\(612\) | −2.59618 | −0.104944 | ||||||||
\(613\) | −7.36270 | −0.297377 | −0.148688 | − | 0.988884i | \(-0.547505\pi\) | ||||
−0.148688 | + | 0.988884i | \(0.547505\pi\) | |||||||
\(614\) | −16.5775 | −0.669015 | ||||||||
\(615\) | 1.81328 | 0.0731184 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −42.7294 | −1.72022 | −0.860110 | − | 0.510109i | \(-0.829605\pi\) | ||||
−0.860110 | + | 0.510109i | \(0.829605\pi\) | |||||||
\(618\) | 16.3662 | 0.658347 | ||||||||
\(619\) | −9.25040 | −0.371805 | −0.185902 | − | 0.982568i | \(-0.559521\pi\) | ||||
−0.185902 | + | 0.982568i | \(0.559521\pi\) | |||||||
\(620\) | −11.3968 | −0.457705 | ||||||||
\(621\) | 3.59833 | 0.144396 | ||||||||
\(622\) | 24.0556 | 0.964543 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 3.66211 | 0.146602 | ||||||||
\(625\) | −13.5088 | −0.540353 | ||||||||
\(626\) | −14.3760 | −0.574580 | ||||||||
\(627\) | 2.11398 | 0.0844244 | ||||||||
\(628\) | −3.38602 | −0.135117 | ||||||||
\(629\) | −26.3342 | −1.05001 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.08724 | −0.0830918 | −0.0415459 | − | 0.999137i | \(-0.513228\pi\) | ||||
−0.0415459 | + | 0.999137i | \(0.513228\pi\) | |||||||
\(632\) | 15.2663 | 0.607261 | ||||||||
\(633\) | 18.3821 | 0.730621 | ||||||||
\(634\) | −2.14516 | −0.0851953 | ||||||||
\(635\) | −8.41058 | −0.333764 | ||||||||
\(636\) | −9.44703 | −0.374599 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.97017 | −0.0779997 | ||||||||
\(639\) | 15.4800 | 0.612378 | ||||||||
\(640\) | 2.41629 | 0.0955123 | ||||||||
\(641\) | 8.30068 | 0.327857 | 0.163929 | − | 0.986472i | \(-0.447583\pi\) | ||||
0.163929 | + | 0.986472i | \(0.447583\pi\) | |||||||
\(642\) | 11.6897 | 0.461356 | ||||||||
\(643\) | −39.5985 | −1.56161 | −0.780807 | − | 0.624772i | \(-0.785192\pi\) | ||||
−0.780807 | + | 0.624772i | \(0.785192\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −14.1428 | −0.556873 | ||||||||
\(646\) | 14.2313 | 0.559922 | ||||||||
\(647\) | 7.17653 | 0.282139 | 0.141069 | − | 0.990000i | \(-0.454946\pi\) | ||||
0.141069 | + | 0.990000i | \(0.454946\pi\) | |||||||
\(648\) | 3.03990 | 0.119418 | ||||||||
\(649\) | −2.40265 | −0.0943123 | ||||||||
\(650\) | −4.78414 | −0.187649 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 16.5775 | 0.649226 | ||||||||
\(653\) | −25.7808 | −1.00888 | −0.504440 | − | 0.863447i | \(-0.668301\pi\) | ||||
−0.504440 | + | 0.863447i | \(0.668301\pi\) | |||||||
\(654\) | −15.6393 | −0.611546 | ||||||||
\(655\) | 13.6032 | 0.531521 | ||||||||
\(656\) | −1.37141 | −0.0535447 | ||||||||
\(657\) | −12.6484 | −0.493461 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.94995 | 0.114914 | 0.0574569 | − | 0.998348i | \(-0.481701\pi\) | ||||
0.0574569 | + | 0.998348i | \(0.481701\pi\) | |||||||
\(660\) | 0.731791 | 0.0284849 | ||||||||
\(661\) | 17.7965 | 0.692204 | 0.346102 | − | 0.938197i | \(-0.387505\pi\) | ||||
0.346102 | + | 0.938197i | \(0.387505\pi\) | |||||||
\(662\) | 30.3793 | 1.18073 | ||||||||
\(663\) | −7.66134 | −0.297542 | ||||||||
\(664\) | −23.1283 | −0.897551 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 9.60523 | 0.372195 | ||||||||
\(667\) | −15.1895 | −0.588141 | ||||||||
\(668\) | −11.7131 | −0.453193 | ||||||||
\(669\) | −8.28572 | −0.320345 | ||||||||
\(670\) | 26.9797 | 1.04232 | ||||||||
\(671\) | 3.24097 | 0.125116 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 35.0368 | 1.35057 | 0.675285 | − | 0.737557i | \(-0.264021\pi\) | ||||
0.675285 | + | 0.737557i | \(0.264021\pi\) | |||||||
\(674\) | 24.9897 | 0.962567 | ||||||||
\(675\) | −1.71203 | −0.0658960 | ||||||||
\(676\) | 5.31113 | 0.204274 | ||||||||
\(677\) | 32.5996 | 1.25291 | 0.626453 | − | 0.779459i | \(-0.284506\pi\) | ||||
0.626453 | + | 0.779459i | \(0.284506\pi\) | |||||||
\(678\) | −12.5038 | −0.480204 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 15.8148 | 0.606471 | ||||||||
\(681\) | −7.06231 | −0.270628 | ||||||||
\(682\) | 3.24178 | 0.124134 | ||||||||
\(683\) | −36.4205 | −1.39359 | −0.696796 | − | 0.717269i | \(-0.745392\pi\) | ||||
−0.696796 | + | 0.717269i | \(0.745392\pi\) | |||||||
\(684\) | 4.28909 | 0.163997 | ||||||||
\(685\) | −34.4408 | −1.31592 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −20.2997 | −0.774480 | ||||||||
\(688\) | 10.6965 | 0.407799 | ||||||||
\(689\) | −27.8782 | −1.06208 | ||||||||
\(690\) | −6.82802 | −0.259938 | ||||||||
\(691\) | 25.8214 | 0.982293 | 0.491147 | − | 0.871077i | \(-0.336578\pi\) | ||||
0.491147 | + | 0.871077i | \(0.336578\pi\) | |||||||
\(692\) | −13.4542 | −0.511451 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6.87812 | 0.261090 | ||||||||
\(695\) | 23.1640 | 0.878659 | ||||||||
\(696\) | −12.8322 | −0.486405 | ||||||||
\(697\) | 2.86907 | 0.108674 | ||||||||
\(698\) | −10.3749 | −0.392695 | ||||||||
\(699\) | 4.13151 | 0.156268 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.64248 | −0.288653 | −0.144326 | − | 0.989530i | \(-0.546101\pi\) | ||||
−0.144326 | + | 0.989530i | \(0.546101\pi\) | |||||||
\(702\) | 2.79443 | 0.105469 | ||||||||
\(703\) | 43.5061 | 1.64086 | ||||||||
\(704\) | −3.39105 | −0.127805 | ||||||||
\(705\) | −20.8329 | −0.784611 | ||||||||
\(706\) | −6.28853 | −0.236672 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −4.87477 | −0.183205 | ||||||||
\(709\) | −16.9791 | −0.637664 | −0.318832 | − | 0.947811i | \(-0.603290\pi\) | ||||
−0.318832 | + | 0.947811i | \(0.603290\pi\) | |||||||
\(710\) | −29.3741 | −1.10239 | ||||||||
\(711\) | 5.02198 | 0.188339 | ||||||||
\(712\) | 6.69690 | 0.250977 | ||||||||
\(713\) | 24.9934 | 0.936009 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.15952 | 0.0807614 | ||||||||
\(716\) | 0.353473 | 0.0132099 | ||||||||
\(717\) | −5.65744 | −0.211281 | ||||||||
\(718\) | −17.9408 | −0.669545 | ||||||||
\(719\) | −1.92341 | −0.0717310 | −0.0358655 | − | 0.999357i | \(-0.511419\pi\) | ||||
−0.0358655 | + | 0.999357i | \(0.511419\pi\) | |||||||
\(720\) | −2.48675 | −0.0926758 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −3.62807 | −0.135023 | ||||||||
\(723\) | 18.0436 | 0.671049 | ||||||||
\(724\) | 1.70898 | 0.0635137 | ||||||||
\(725\) | 7.22694 | 0.268402 | ||||||||
\(726\) | 11.3031 | 0.419497 | ||||||||
\(727\) | −5.46716 | −0.202766 | −0.101383 | − | 0.994847i | \(-0.532327\pi\) | ||||
−0.101383 | + | 0.994847i | \(0.532327\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 24.0010 | 0.888318 | ||||||||
\(731\) | −22.3776 | −0.827666 | ||||||||
\(732\) | 6.57565 | 0.243043 | ||||||||
\(733\) | 19.6346 | 0.725219 | 0.362609 | − | 0.931941i | \(-0.381886\pi\) | ||||
0.362609 | + | 0.931941i | \(0.381886\pi\) | |||||||
\(734\) | −0.206623 | −0.00762659 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −16.7129 | −0.616047 | ||||||||
\(737\) | 6.34122 | 0.233582 | ||||||||
\(738\) | −1.04648 | −0.0385214 | ||||||||
\(739\) | 33.1279 | 1.21863 | 0.609315 | − | 0.792929i | \(-0.291445\pi\) | ||||
0.609315 | + | 0.792929i | \(0.291445\pi\) | |||||||
\(740\) | 15.0604 | 0.553630 | ||||||||
\(741\) | 12.6571 | 0.464971 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14.1798 | −0.520206 | −0.260103 | − | 0.965581i | \(-0.583756\pi\) | ||||
−0.260103 | + | 0.965581i | \(0.583756\pi\) | |||||||
\(744\) | 21.1146 | 0.774099 | ||||||||
\(745\) | −12.4488 | −0.456088 | ||||||||
\(746\) | 36.7867 | 1.34686 | ||||||||
\(747\) | −7.60824 | −0.278371 | ||||||||
\(748\) | 1.15788 | 0.0423364 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 12.7364 | 0.465069 | ||||||||
\(751\) | −3.84986 | −0.140483 | −0.0702416 | − | 0.997530i | \(-0.522377\pi\) | ||||
−0.0702416 | + | 0.997530i | \(0.522377\pi\) | |||||||
\(752\) | 15.7563 | 0.574572 | ||||||||
\(753\) | −16.5321 | −0.602462 | ||||||||
\(754\) | −11.7961 | −0.429587 | ||||||||
\(755\) | −12.2629 | −0.446291 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −45.9774 | −1.67108 | −0.835539 | − | 0.549432i | \(-0.814844\pi\) | ||||
−0.835539 | + | 0.549432i | \(0.814844\pi\) | |||||||
\(758\) | 34.0619 | 1.23718 | ||||||||
\(759\) | −1.60484 | −0.0582518 | ||||||||
\(760\) | −26.1273 | −0.947737 | ||||||||
\(761\) | 44.3346 | 1.60713 | 0.803564 | − | 0.595218i | \(-0.202934\pi\) | ||||
0.803564 | + | 0.595218i | \(0.202934\pi\) | |||||||
\(762\) | 4.85391 | 0.175839 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 8.12883 | 0.294091 | ||||||||
\(765\) | 5.20242 | 0.188094 | ||||||||
\(766\) | −16.8558 | −0.609024 | ||||||||
\(767\) | −14.3855 | −0.519429 | ||||||||
\(768\) | −16.6012 | −0.599043 | ||||||||
\(769\) | −4.11151 | −0.148265 | −0.0741324 | − | 0.997248i | \(-0.523619\pi\) | ||||
−0.0741324 | + | 0.997248i | \(0.523619\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −27.2214 | −0.980355 | ||||||||
\(772\) | −14.7468 | −0.530749 | ||||||||
\(773\) | −19.1489 | −0.688737 | −0.344369 | − | 0.938835i | \(-0.611907\pi\) | ||||
−0.344369 | + | 0.938835i | \(0.611907\pi\) | |||||||
\(774\) | 8.16210 | 0.293381 | ||||||||
\(775\) | −11.8914 | −0.427153 | ||||||||
\(776\) | 5.32170 | 0.191038 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 35.3422 | 1.26708 | ||||||||
\(779\) | −4.73993 | −0.169826 | ||||||||
\(780\) | 4.38148 | 0.156882 | ||||||||
\(781\) | −6.90398 | −0.247044 | ||||||||
\(782\) | −10.8037 | −0.386339 | ||||||||
\(783\) | −4.22128 | −0.150856 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.78516 | 0.242173 | ||||||||
\(786\) | −7.85067 | −0.280024 | ||||||||
\(787\) | −42.9937 | −1.53256 | −0.766280 | − | 0.642506i | \(-0.777895\pi\) | ||||
−0.766280 | + | 0.642506i | \(0.777895\pi\) | |||||||
\(788\) | −16.3251 | −0.581558 | ||||||||
\(789\) | 0.195115 | 0.00694629 | ||||||||
\(790\) | −9.52947 | −0.339043 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −1.35578 | −0.0481755 | ||||||||
\(793\) | 19.4048 | 0.689084 | ||||||||
\(794\) | 19.7685 | 0.701557 | ||||||||
\(795\) | 18.9307 | 0.671402 | ||||||||
\(796\) | −3.00660 | −0.106566 | ||||||||
\(797\) | 14.2882 | 0.506116 | 0.253058 | − | 0.967451i | \(-0.418564\pi\) | ||||
0.253058 | + | 0.967451i | \(0.418564\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −32.9630 | −1.16615 | ||||||||
\(800\) | 7.95175 | 0.281137 | ||||||||
\(801\) | 2.20300 | 0.0778392 | ||||||||
\(802\) | 15.9801 | 0.564277 | ||||||||
\(803\) | 5.64112 | 0.199071 | ||||||||
\(804\) | 12.8658 | 0.453742 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 19.4096 | 0.683675 | ||||||||
\(807\) | 23.1477 | 0.814837 | ||||||||
\(808\) | −30.6199 | −1.07720 | ||||||||
\(809\) | −22.9124 | −0.805555 | −0.402778 | − | 0.915298i | \(-0.631955\pi\) | ||||
−0.402778 | + | 0.915298i | \(0.631955\pi\) | |||||||
\(810\) | −1.89755 | −0.0666732 | ||||||||
\(811\) | 33.4405 | 1.17425 | 0.587127 | − | 0.809495i | \(-0.300259\pi\) | ||||
0.587127 | + | 0.809495i | \(0.300259\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.82658 | 0.239419 | ||||||||
\(814\) | −4.28388 | −0.150150 | ||||||||
\(815\) | −33.2193 | −1.16362 | ||||||||
\(816\) | −3.93469 | −0.137742 | ||||||||
\(817\) | 36.9695 | 1.29340 | ||||||||
\(818\) | −34.4468 | −1.20440 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.64081 | −0.0572994 | ||||||||
\(821\) | −19.3510 | −0.675355 | −0.337677 | − | 0.941262i | \(-0.609641\pi\) | ||||
−0.337677 | + | 0.941262i | \(0.609641\pi\) | |||||||
\(822\) | 19.8765 | 0.693271 | ||||||||
\(823\) | 14.9217 | 0.520139 | 0.260070 | − | 0.965590i | \(-0.416255\pi\) | ||||
0.260070 | + | 0.965590i | \(0.416255\pi\) | |||||||
\(824\) | −47.5420 | −1.65621 | ||||||||
\(825\) | 0.763555 | 0.0265836 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −10.1637 | −0.353425 | −0.176713 | − | 0.984262i | \(-0.556546\pi\) | ||||
−0.176713 | + | 0.984262i | \(0.556546\pi\) | |||||||
\(828\) | −3.25607 | −0.113156 | ||||||||
\(829\) | 7.08509 | 0.246075 | 0.123038 | − | 0.992402i | \(-0.460736\pi\) | ||||
0.123038 | + | 0.992402i | \(0.460736\pi\) | |||||||
\(830\) | 14.4370 | 0.501117 | ||||||||
\(831\) | 27.7102 | 0.961258 | ||||||||
\(832\) | −20.3033 | −0.703892 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −13.3684 | −0.462909 | ||||||||
\(835\) | 23.4715 | 0.812266 | ||||||||
\(836\) | −1.91291 | −0.0661594 | ||||||||
\(837\) | 6.94583 | 0.240083 | ||||||||
\(838\) | 37.7240 | 1.30315 | ||||||||
\(839\) | 23.0788 | 0.796770 | 0.398385 | − | 0.917218i | \(-0.369571\pi\) | ||||
0.398385 | + | 0.917218i | \(0.369571\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.1808 | −0.385546 | ||||||||
\(842\) | 2.21129 | 0.0762062 | ||||||||
\(843\) | −3.97578 | −0.136933 | ||||||||
\(844\) | −16.6337 | −0.572554 | ||||||||
\(845\) | −10.6428 | −0.366125 | ||||||||
\(846\) | 12.0230 | 0.413361 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −14.3176 | −0.491669 | ||||||||
\(849\) | 12.5932 | 0.432199 | ||||||||
\(850\) | 5.14023 | 0.176308 | ||||||||
\(851\) | −33.0277 | −1.13218 | ||||||||
\(852\) | −14.0076 | −0.479892 | ||||||||
\(853\) | 55.1310 | 1.88765 | 0.943825 | − | 0.330446i | \(-0.107199\pi\) | ||||
0.943825 | + | 0.330446i | \(0.107199\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.59480 | −0.293936 | ||||||||
\(856\) | −33.9572 | −1.16063 | ||||||||
\(857\) | 21.0816 | 0.720135 | 0.360068 | − | 0.932926i | \(-0.382754\pi\) | ||||
0.360068 | + | 0.932926i | \(0.382754\pi\) | |||||||
\(858\) | −1.24630 | −0.0425480 | ||||||||
\(859\) | 35.7227 | 1.21884 | 0.609421 | − | 0.792847i | \(-0.291402\pi\) | ||||
0.609421 | + | 0.792847i | \(0.291402\pi\) | |||||||
\(860\) | 12.7976 | 0.436395 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −26.4067 | −0.899415 | ||||||||
\(863\) | −41.9838 | −1.42914 | −0.714572 | − | 0.699562i | \(-0.753378\pi\) | ||||
−0.714572 | + | 0.699562i | \(0.753378\pi\) | |||||||
\(864\) | −4.64464 | −0.158014 | ||||||||
\(865\) | 26.9605 | 0.916685 | ||||||||
\(866\) | −24.1814 | −0.821716 | ||||||||
\(867\) | −8.76842 | −0.297791 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.23978 | −0.0759792 | ||||||||
\(870\) | 8.01010 | 0.271568 | ||||||||
\(871\) | 37.9670 | 1.28646 | ||||||||
\(872\) | 45.4304 | 1.53847 | ||||||||
\(873\) | 1.75062 | 0.0592495 | ||||||||
\(874\) | 17.8485 | 0.603736 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 11.4453 | 0.386703 | ||||||||
\(877\) | −54.7628 | −1.84921 | −0.924604 | − | 0.380931i | \(-0.875604\pi\) | ||||
−0.924604 | + | 0.380931i | \(0.875604\pi\) | |||||||
\(878\) | −22.0527 | −0.744244 | ||||||||
\(879\) | −18.7975 | −0.634024 | ||||||||
\(880\) | 1.10908 | 0.0373870 | ||||||||
\(881\) | −25.1750 | −0.848166 | −0.424083 | − | 0.905623i | \(-0.639404\pi\) | ||||
−0.424083 | + | 0.905623i | \(0.639404\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 55.2757 | 1.86018 | 0.930088 | − | 0.367336i | \(-0.119730\pi\) | ||||
0.930088 | + | 0.367336i | \(0.119730\pi\) | |||||||
\(884\) | 6.93263 | 0.233170 | ||||||||
\(885\) | 9.76843 | 0.328362 | ||||||||
\(886\) | −11.2780 | −0.378891 | ||||||||
\(887\) | 10.4173 | 0.349780 | 0.174890 | − | 0.984588i | \(-0.444043\pi\) | ||||
0.174890 | + | 0.984588i | \(0.444043\pi\) | |||||||
\(888\) | −27.9021 | −0.936333 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −4.18031 | −0.140124 | ||||||||
\(891\) | −0.445995 | −0.0149414 | ||||||||
\(892\) | 7.49762 | 0.251039 | ||||||||
\(893\) | 54.4574 | 1.82235 | ||||||||
\(894\) | 7.18443 | 0.240283 | ||||||||
\(895\) | −0.708316 | −0.0236764 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9.60868 | −0.320825 | ||||||||
\(898\) | 2.05568 | 0.0685989 | ||||||||
\(899\) | −29.3202 | −0.977885 | ||||||||
\(900\) | 1.54919 | 0.0516396 | ||||||||
\(901\) | 29.9532 | 0.997887 | ||||||||
\(902\) | 0.466723 | 0.0155402 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 36.3220 | 1.20805 | ||||||||
\(905\) | −3.42458 | −0.113837 | ||||||||
\(906\) | 7.07714 | 0.235122 | ||||||||
\(907\) | 10.0366 | 0.333258 | 0.166629 | − | 0.986020i | \(-0.446712\pi\) | ||||
0.166629 | + | 0.986020i | \(0.446712\pi\) | |||||||
\(908\) | 6.39058 | 0.212079 | ||||||||
\(909\) | −10.0727 | −0.334089 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17.5250 | 0.580628 | 0.290314 | − | 0.956931i | \(-0.406240\pi\) | ||||
0.290314 | + | 0.956931i | \(0.406240\pi\) | |||||||
\(912\) | 6.50041 | 0.215250 | ||||||||
\(913\) | 3.39324 | 0.112300 | ||||||||
\(914\) | −10.9114 | −0.360917 | ||||||||
\(915\) | −13.1768 | −0.435611 | ||||||||
\(916\) | 18.3689 | 0.606924 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −3.00242 | −0.0990947 | ||||||||
\(919\) | −41.1561 | −1.35761 | −0.678807 | − | 0.734317i | \(-0.737503\pi\) | ||||
−0.678807 | + | 0.734317i | \(0.737503\pi\) | |||||||
\(920\) | 19.8346 | 0.653928 | ||||||||
\(921\) | 15.8413 | 0.521988 | ||||||||
\(922\) | 29.4846 | 0.971023 | ||||||||
\(923\) | −41.3365 | −1.36061 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15.7141 | 0.516676 | ||||||||
\(926\) | 6.24617 | 0.205262 | ||||||||
\(927\) | −15.6394 | −0.513664 | ||||||||
\(928\) | 19.6063 | 0.643608 | ||||||||
\(929\) | −19.3546 | −0.635002 | −0.317501 | − | 0.948258i | \(-0.602844\pi\) | ||||
−0.317501 | + | 0.948258i | \(0.602844\pi\) | |||||||
\(930\) | −13.1801 | −0.432192 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −3.73854 | −0.122460 | ||||||||
\(933\) | −22.9872 | −0.752569 | ||||||||
\(934\) | 0.126213 | 0.00412983 | ||||||||
\(935\) | −2.32025 | −0.0758804 | ||||||||
\(936\) | −8.11749 | −0.265329 | ||||||||
\(937\) | 16.6445 | 0.543753 | 0.271876 | − | 0.962332i | \(-0.412356\pi\) | ||||
0.271876 | + | 0.962332i | \(0.412356\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 13.7375 | 0.448306 | ||||||||
\(940\) | 18.8513 | 0.614863 | ||||||||
\(941\) | −11.3034 | −0.368480 | −0.184240 | − | 0.982881i | \(-0.558982\pi\) | ||||
−0.184240 | + | 0.982881i | \(0.558982\pi\) | |||||||
\(942\) | −3.91585 | −0.127585 | ||||||||
\(943\) | 3.59833 | 0.117178 | ||||||||
\(944\) | −7.38804 | −0.240460 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.64025 | −0.118355 | ||||||||
\(947\) | 4.08943 | 0.132889 | 0.0664443 | − | 0.997790i | \(-0.478835\pi\) | ||||
0.0664443 | + | 0.997790i | \(0.478835\pi\) | |||||||
\(948\) | −4.54431 | −0.147592 | ||||||||
\(949\) | 33.7753 | 1.09639 | ||||||||
\(950\) | −8.49205 | −0.275519 | ||||||||
\(951\) | 2.04989 | 0.0664722 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −14.0371 | −0.454707 | −0.227353 | − | 0.973812i | \(-0.573007\pi\) | ||||
−0.227353 | + | 0.973812i | \(0.573007\pi\) | |||||||
\(954\) | −10.9253 | −0.353718 | ||||||||
\(955\) | −16.2892 | −0.527105 | ||||||||
\(956\) | 5.11934 | 0.165571 | ||||||||
\(957\) | 1.88267 | 0.0608580 | ||||||||
\(958\) | 42.5675 | 1.37529 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 13.7870 | 0.444972 | ||||||||
\(961\) | 17.2445 | 0.556274 | ||||||||
\(962\) | −25.6490 | −0.826958 | ||||||||
\(963\) | −11.1705 | −0.359965 | ||||||||
\(964\) | −16.3274 | −0.525869 | ||||||||
\(965\) | 29.5507 | 0.951272 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 43.1943 | 1.38904 | 0.694518 | − | 0.719475i | \(-0.255618\pi\) | ||||
0.694518 | + | 0.719475i | \(0.255618\pi\) | |||||||
\(968\) | −32.8342 | −1.05533 | ||||||||
\(969\) | −13.5992 | −0.436869 | ||||||||
\(970\) | −3.32189 | −0.106660 | ||||||||
\(971\) | 34.2336 | 1.09861 | 0.549304 | − | 0.835623i | \(-0.314893\pi\) | ||||
0.549304 | + | 0.835623i | \(0.314893\pi\) | |||||||
\(972\) | −0.904885 | −0.0290242 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 30.0174 | 0.961819 | ||||||||
\(975\) | 4.57166 | 0.146410 | ||||||||
\(976\) | 9.96585 | 0.318999 | ||||||||
\(977\) | −25.7841 | −0.824908 | −0.412454 | − | 0.910978i | \(-0.635328\pi\) | ||||
−0.412454 | + | 0.910978i | \(0.635328\pi\) | |||||||
\(978\) | 19.1715 | 0.613037 | ||||||||
\(979\) | −0.982527 | −0.0314017 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.9447 | 0.477149 | ||||||||
\(982\) | −2.42966 | −0.0775336 | ||||||||
\(983\) | 15.7033 | 0.500858 | 0.250429 | − | 0.968135i | \(-0.419428\pi\) | ||||
0.250429 | + | 0.968135i | \(0.419428\pi\) | |||||||
\(984\) | 3.03990 | 0.0969084 | ||||||||
\(985\) | 32.7135 | 1.04234 | ||||||||
\(986\) | 12.6740 | 0.403624 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −11.4532 | −0.364376 | ||||||||
\(989\) | −28.0655 | −0.892431 | ||||||||
\(990\) | 0.846299 | 0.0268971 | ||||||||
\(991\) | 47.9872 | 1.52436 | 0.762182 | − | 0.647363i | \(-0.224128\pi\) | ||||
0.762182 | + | 0.647363i | \(0.224128\pi\) | |||||||
\(992\) | −32.2609 | −1.02428 | ||||||||
\(993\) | −29.0301 | −0.921242 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.02486 | 0.191001 | ||||||||
\(996\) | 6.88458 | 0.218146 | ||||||||
\(997\) | −32.6743 | −1.03481 | −0.517403 | − | 0.855742i | \(-0.673101\pi\) | ||||
−0.517403 | + | 0.855742i | \(0.673101\pi\) | |||||||
\(998\) | −12.5391 | −0.396918 | ||||||||
\(999\) | −9.17863 | −0.290399 |
(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 | 6027.2.a.bm.1.7 | yes | 16 | |
7.6 | odd | 2 | 6027.2.a.bl.1.7 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6027.2.a.bl.1.7 | ✓ | 16 | 7.6 | odd | 2 | ||
6027.2.a.bm.1.7 | yes | 16 | 1.1 | even | 1 | trivial |