Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8034,2,Mod(1,8034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8034, 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("8034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8034.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: | \(64.1518129839\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 4x^{9} - 15x^{8} + 72x^{7} - 27x^{6} - 115x^{5} + 54x^{4} + 68x^{3} - 15x^{2} - 15x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.671383\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8034.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.82988 | −0.818346 | −0.409173 | − | 0.912457i | \(-0.634183\pi\) | ||||
−0.409173 | + | 0.912457i | \(0.634183\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 1.45707 | 0.550719 | 0.275360 | − | 0.961341i | \(-0.411203\pi\) | ||||
0.275360 | + | 0.961341i | \(0.411203\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.82988 | 0.578658 | ||||||||
\(11\) | −0.513205 | −0.154737 | −0.0773686 | − | 0.997003i | \(-0.524652\pi\) | ||||
−0.0773686 | + | 0.997003i | \(0.524652\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | −1.45707 | −0.389417 | ||||||||
\(15\) | 1.82988 | 0.472472 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.785684 | −0.190556 | −0.0952781 | − | 0.995451i | \(-0.530374\pi\) | ||||
−0.0952781 | + | 0.995451i | \(0.530374\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −1.12864 | −0.258928 | −0.129464 | − | 0.991584i | \(-0.541326\pi\) | ||||
−0.129464 | + | 0.991584i | \(0.541326\pi\) | |||||||
\(20\) | −1.82988 | −0.409173 | ||||||||
\(21\) | −1.45707 | −0.317958 | ||||||||
\(22\) | 0.513205 | 0.109416 | ||||||||
\(23\) | 5.13440 | 1.07060 | 0.535298 | − | 0.844663i | \(-0.320199\pi\) | ||||
0.535298 | + | 0.844663i | \(0.320199\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −1.65155 | −0.330310 | ||||||||
\(26\) | 1.00000 | 0.196116 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.45707 | 0.275360 | ||||||||
\(29\) | 3.60480 | 0.669394 | 0.334697 | − | 0.942326i | \(-0.391366\pi\) | ||||
0.334697 | + | 0.942326i | \(0.391366\pi\) | |||||||
\(30\) | −1.82988 | −0.334088 | ||||||||
\(31\) | −8.18455 | −1.46999 | −0.734994 | − | 0.678074i | \(-0.762815\pi\) | ||||
−0.734994 | + | 0.678074i | \(0.762815\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0.513205 | 0.0893375 | ||||||||
\(34\) | 0.785684 | 0.134744 | ||||||||
\(35\) | −2.66625 | −0.450679 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 2.66489 | 0.438106 | 0.219053 | − | 0.975713i | \(-0.429703\pi\) | ||||
0.219053 | + | 0.975713i | \(0.429703\pi\) | |||||||
\(38\) | 1.12864 | 0.183090 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 1.82988 | 0.289329 | ||||||||
\(41\) | 5.68841 | 0.888381 | 0.444190 | − | 0.895932i | \(-0.353491\pi\) | ||||
0.444190 | + | 0.895932i | \(0.353491\pi\) | |||||||
\(42\) | 1.45707 | 0.224830 | ||||||||
\(43\) | 5.80579 | 0.885375 | 0.442688 | − | 0.896676i | \(-0.354025\pi\) | ||||
0.442688 | + | 0.896676i | \(0.354025\pi\) | |||||||
\(44\) | −0.513205 | −0.0773686 | ||||||||
\(45\) | −1.82988 | −0.272782 | ||||||||
\(46\) | −5.13440 | −0.757026 | ||||||||
\(47\) | 4.47220 | 0.652337 | 0.326168 | − | 0.945312i | \(-0.394242\pi\) | ||||
0.326168 | + | 0.945312i | \(0.394242\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −4.87696 | −0.696708 | ||||||||
\(50\) | 1.65155 | 0.233564 | ||||||||
\(51\) | 0.785684 | 0.110018 | ||||||||
\(52\) | −1.00000 | −0.138675 | ||||||||
\(53\) | −9.91273 | −1.36162 | −0.680809 | − | 0.732461i | \(-0.738372\pi\) | ||||
−0.680809 | + | 0.732461i | \(0.738372\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0.939102 | 0.126629 | ||||||||
\(56\) | −1.45707 | −0.194709 | ||||||||
\(57\) | 1.12864 | 0.149492 | ||||||||
\(58\) | −3.60480 | −0.473333 | ||||||||
\(59\) | 10.2889 | 1.33951 | 0.669753 | − | 0.742584i | \(-0.266400\pi\) | ||||
0.669753 | + | 0.742584i | \(0.266400\pi\) | |||||||
\(60\) | 1.82988 | 0.236236 | ||||||||
\(61\) | −9.58790 | −1.22760 | −0.613802 | − | 0.789460i | \(-0.710361\pi\) | ||||
−0.613802 | + | 0.789460i | \(0.710361\pi\) | |||||||
\(62\) | 8.18455 | 1.03944 | ||||||||
\(63\) | 1.45707 | 0.183573 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.82988 | 0.226968 | ||||||||
\(66\) | −0.513205 | −0.0631712 | ||||||||
\(67\) | −11.1866 | −1.36667 | −0.683333 | − | 0.730107i | \(-0.739470\pi\) | ||||
−0.683333 | + | 0.730107i | \(0.739470\pi\) | |||||||
\(68\) | −0.785684 | −0.0952781 | ||||||||
\(69\) | −5.13440 | −0.618109 | ||||||||
\(70\) | 2.66625 | 0.318678 | ||||||||
\(71\) | 4.34398 | 0.515536 | 0.257768 | − | 0.966207i | \(-0.417013\pi\) | ||||
0.257768 | + | 0.966207i | \(0.417013\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 0.434059 | 0.0508027 | 0.0254014 | − | 0.999677i | \(-0.491914\pi\) | ||||
0.0254014 | + | 0.999677i | \(0.491914\pi\) | |||||||
\(74\) | −2.66489 | −0.309788 | ||||||||
\(75\) | 1.65155 | 0.190704 | ||||||||
\(76\) | −1.12864 | −0.129464 | ||||||||
\(77\) | −0.747774 | −0.0852167 | ||||||||
\(78\) | −1.00000 | −0.113228 | ||||||||
\(79\) | 7.70913 | 0.867345 | 0.433672 | − | 0.901071i | \(-0.357218\pi\) | ||||
0.433672 | + | 0.901071i | \(0.357218\pi\) | |||||||
\(80\) | −1.82988 | −0.204587 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −5.68841 | −0.628180 | ||||||||
\(83\) | −0.451085 | −0.0495130 | −0.0247565 | − | 0.999694i | \(-0.507881\pi\) | ||||
−0.0247565 | + | 0.999694i | \(0.507881\pi\) | |||||||
\(84\) | −1.45707 | −0.158979 | ||||||||
\(85\) | 1.43770 | 0.155941 | ||||||||
\(86\) | −5.80579 | −0.626055 | ||||||||
\(87\) | −3.60480 | −0.386475 | ||||||||
\(88\) | 0.513205 | 0.0547078 | ||||||||
\(89\) | 0.196823 | 0.0208632 | 0.0104316 | − | 0.999946i | \(-0.496679\pi\) | ||||
0.0104316 | + | 0.999946i | \(0.496679\pi\) | |||||||
\(90\) | 1.82988 | 0.192886 | ||||||||
\(91\) | −1.45707 | −0.152742 | ||||||||
\(92\) | 5.13440 | 0.535298 | ||||||||
\(93\) | 8.18455 | 0.848698 | ||||||||
\(94\) | −4.47220 | −0.461272 | ||||||||
\(95\) | 2.06528 | 0.211893 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 0.774045 | 0.0785923 | 0.0392962 | − | 0.999228i | \(-0.487488\pi\) | ||||
0.0392962 | + | 0.999228i | \(0.487488\pi\) | |||||||
\(98\) | 4.87696 | 0.492647 | ||||||||
\(99\) | −0.513205 | −0.0515790 | ||||||||
\(100\) | −1.65155 | −0.165155 | ||||||||
\(101\) | 13.7255 | 1.36574 | 0.682870 | − | 0.730540i | \(-0.260731\pi\) | ||||
0.682870 | + | 0.730540i | \(0.260731\pi\) | |||||||
\(102\) | −0.785684 | −0.0777943 | ||||||||
\(103\) | −1.00000 | −0.0985329 | ||||||||
\(104\) | 1.00000 | 0.0980581 | ||||||||
\(105\) | 2.66625 | 0.260200 | ||||||||
\(106\) | 9.91273 | 0.962809 | ||||||||
\(107\) | 11.3226 | 1.09460 | 0.547301 | − | 0.836936i | \(-0.315655\pi\) | ||||
0.547301 | + | 0.836936i | \(0.315655\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 4.23121 | 0.405276 | 0.202638 | − | 0.979254i | \(-0.435049\pi\) | ||||
0.202638 | + | 0.979254i | \(0.435049\pi\) | |||||||
\(110\) | −0.939102 | −0.0895399 | ||||||||
\(111\) | −2.66489 | −0.252940 | ||||||||
\(112\) | 1.45707 | 0.137680 | ||||||||
\(113\) | −17.2827 | −1.62582 | −0.812910 | − | 0.582389i | \(-0.802118\pi\) | ||||
−0.812910 | + | 0.582389i | \(0.802118\pi\) | |||||||
\(114\) | −1.12864 | −0.105707 | ||||||||
\(115\) | −9.39533 | −0.876119 | ||||||||
\(116\) | 3.60480 | 0.334697 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | −10.2889 | −0.947173 | ||||||||
\(119\) | −1.14479 | −0.104943 | ||||||||
\(120\) | −1.82988 | −0.167044 | ||||||||
\(121\) | −10.7366 | −0.976056 | ||||||||
\(122\) | 9.58790 | 0.868048 | ||||||||
\(123\) | −5.68841 | −0.512907 | ||||||||
\(124\) | −8.18455 | −0.734994 | ||||||||
\(125\) | 12.1715 | 1.08865 | ||||||||
\(126\) | −1.45707 | −0.129806 | ||||||||
\(127\) | −9.36539 | −0.831044 | −0.415522 | − | 0.909583i | \(-0.636401\pi\) | ||||
−0.415522 | + | 0.909583i | \(0.636401\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −5.80579 | −0.511172 | ||||||||
\(130\) | −1.82988 | −0.160491 | ||||||||
\(131\) | −11.5102 | −1.00565 | −0.502826 | − | 0.864388i | \(-0.667706\pi\) | ||||
−0.502826 | + | 0.864388i | \(0.667706\pi\) | |||||||
\(132\) | 0.513205 | 0.0446688 | ||||||||
\(133\) | −1.64451 | −0.142597 | ||||||||
\(134\) | 11.1866 | 0.966378 | ||||||||
\(135\) | 1.82988 | 0.157491 | ||||||||
\(136\) | 0.785684 | 0.0673718 | ||||||||
\(137\) | −2.77252 | −0.236872 | −0.118436 | − | 0.992962i | \(-0.537788\pi\) | ||||
−0.118436 | + | 0.992962i | \(0.537788\pi\) | |||||||
\(138\) | 5.13440 | 0.437069 | ||||||||
\(139\) | −11.4546 | −0.971568 | −0.485784 | − | 0.874079i | \(-0.661466\pi\) | ||||
−0.485784 | + | 0.874079i | \(0.661466\pi\) | |||||||
\(140\) | −2.66625 | −0.225340 | ||||||||
\(141\) | −4.47220 | −0.376627 | ||||||||
\(142\) | −4.34398 | −0.364539 | ||||||||
\(143\) | 0.513205 | 0.0429164 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −6.59634 | −0.547796 | ||||||||
\(146\) | −0.434059 | −0.0359230 | ||||||||
\(147\) | 4.87696 | 0.402245 | ||||||||
\(148\) | 2.66489 | 0.219053 | ||||||||
\(149\) | −14.3197 | −1.17311 | −0.586556 | − | 0.809909i | \(-0.699517\pi\) | ||||
−0.586556 | + | 0.809909i | \(0.699517\pi\) | |||||||
\(150\) | −1.65155 | −0.134848 | ||||||||
\(151\) | −9.19404 | −0.748200 | −0.374100 | − | 0.927388i | \(-0.622048\pi\) | ||||
−0.374100 | + | 0.927388i | \(0.622048\pi\) | |||||||
\(152\) | 1.12864 | 0.0915449 | ||||||||
\(153\) | −0.785684 | −0.0635188 | ||||||||
\(154\) | 0.747774 | 0.0602573 | ||||||||
\(155\) | 14.9767 | 1.20296 | ||||||||
\(156\) | 1.00000 | 0.0800641 | ||||||||
\(157\) | 22.9121 | 1.82858 | 0.914291 | − | 0.405058i | \(-0.132749\pi\) | ||||
0.914291 | + | 0.405058i | \(0.132749\pi\) | |||||||
\(158\) | −7.70913 | −0.613305 | ||||||||
\(159\) | 9.91273 | 0.786131 | ||||||||
\(160\) | 1.82988 | 0.144665 | ||||||||
\(161\) | 7.48116 | 0.589598 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −13.1323 | −1.02860 | −0.514301 | − | 0.857610i | \(-0.671949\pi\) | ||||
−0.514301 | + | 0.857610i | \(0.671949\pi\) | |||||||
\(164\) | 5.68841 | 0.444190 | ||||||||
\(165\) | −0.939102 | −0.0731090 | ||||||||
\(166\) | 0.451085 | 0.0350110 | ||||||||
\(167\) | 12.9880 | 1.00504 | 0.502521 | − | 0.864565i | \(-0.332406\pi\) | ||||
0.502521 | + | 0.864565i | \(0.332406\pi\) | |||||||
\(168\) | 1.45707 | 0.112415 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −1.43770 | −0.110267 | ||||||||
\(171\) | −1.12864 | −0.0863094 | ||||||||
\(172\) | 5.80579 | 0.442688 | ||||||||
\(173\) | 25.8509 | 1.96541 | 0.982705 | − | 0.185176i | \(-0.0592855\pi\) | ||||
0.982705 | + | 0.185176i | \(0.0592855\pi\) | |||||||
\(174\) | 3.60480 | 0.273279 | ||||||||
\(175\) | −2.40641 | −0.181908 | ||||||||
\(176\) | −0.513205 | −0.0386843 | ||||||||
\(177\) | −10.2889 | −0.773364 | ||||||||
\(178\) | −0.196823 | −0.0147525 | ||||||||
\(179\) | 17.2268 | 1.28759 | 0.643797 | − | 0.765196i | \(-0.277358\pi\) | ||||
0.643797 | + | 0.765196i | \(0.277358\pi\) | |||||||
\(180\) | −1.82988 | −0.136391 | ||||||||
\(181\) | 9.57039 | 0.711361 | 0.355681 | − | 0.934608i | \(-0.384249\pi\) | ||||
0.355681 | + | 0.934608i | \(0.384249\pi\) | |||||||
\(182\) | 1.45707 | 0.108005 | ||||||||
\(183\) | 9.58790 | 0.708758 | ||||||||
\(184\) | −5.13440 | −0.378513 | ||||||||
\(185\) | −4.87643 | −0.358522 | ||||||||
\(186\) | −8.18455 | −0.600120 | ||||||||
\(187\) | 0.403217 | 0.0294861 | ||||||||
\(188\) | 4.47220 | 0.326168 | ||||||||
\(189\) | −1.45707 | −0.105986 | ||||||||
\(190\) | −2.06528 | −0.149831 | ||||||||
\(191\) | 12.4477 | 0.900685 | 0.450343 | − | 0.892856i | \(-0.351302\pi\) | ||||
0.450343 | + | 0.892856i | \(0.351302\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 5.35638 | 0.385561 | 0.192780 | − | 0.981242i | \(-0.438250\pi\) | ||||
0.192780 | + | 0.981242i | \(0.438250\pi\) | |||||||
\(194\) | −0.774045 | −0.0555732 | ||||||||
\(195\) | −1.82988 | −0.131040 | ||||||||
\(196\) | −4.87696 | −0.348354 | ||||||||
\(197\) | 5.23510 | 0.372985 | 0.186493 | − | 0.982456i | \(-0.440288\pi\) | ||||
0.186493 | + | 0.982456i | \(0.440288\pi\) | |||||||
\(198\) | 0.513205 | 0.0364719 | ||||||||
\(199\) | 10.4226 | 0.738836 | 0.369418 | − | 0.929263i | \(-0.379557\pi\) | ||||
0.369418 | + | 0.929263i | \(0.379557\pi\) | |||||||
\(200\) | 1.65155 | 0.116782 | ||||||||
\(201\) | 11.1866 | 0.789044 | ||||||||
\(202\) | −13.7255 | −0.965725 | ||||||||
\(203\) | 5.25243 | 0.368648 | ||||||||
\(204\) | 0.785684 | 0.0550089 | ||||||||
\(205\) | −10.4091 | −0.727003 | ||||||||
\(206\) | 1.00000 | 0.0696733 | ||||||||
\(207\) | 5.13440 | 0.356866 | ||||||||
\(208\) | −1.00000 | −0.0693375 | ||||||||
\(209\) | 0.579225 | 0.0400658 | ||||||||
\(210\) | −2.66625 | −0.183989 | ||||||||
\(211\) | 25.9138 | 1.78398 | 0.891990 | − | 0.452054i | \(-0.149309\pi\) | ||||
0.891990 | + | 0.452054i | \(0.149309\pi\) | |||||||
\(212\) | −9.91273 | −0.680809 | ||||||||
\(213\) | −4.34398 | −0.297645 | ||||||||
\(214\) | −11.3226 | −0.774000 | ||||||||
\(215\) | −10.6239 | −0.724543 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −11.9254 | −0.809551 | ||||||||
\(218\) | −4.23121 | −0.286573 | ||||||||
\(219\) | −0.434059 | −0.0293310 | ||||||||
\(220\) | 0.939102 | 0.0633143 | ||||||||
\(221\) | 0.785684 | 0.0528508 | ||||||||
\(222\) | 2.66489 | 0.178856 | ||||||||
\(223\) | −23.7842 | −1.59271 | −0.796355 | − | 0.604829i | \(-0.793241\pi\) | ||||
−0.796355 | + | 0.604829i | \(0.793241\pi\) | |||||||
\(224\) | −1.45707 | −0.0973543 | ||||||||
\(225\) | −1.65155 | −0.110103 | ||||||||
\(226\) | 17.2827 | 1.14963 | ||||||||
\(227\) | −12.9676 | −0.860690 | −0.430345 | − | 0.902664i | \(-0.641608\pi\) | ||||
−0.430345 | + | 0.902664i | \(0.641608\pi\) | |||||||
\(228\) | 1.12864 | 0.0747461 | ||||||||
\(229\) | −13.2509 | −0.875642 | −0.437821 | − | 0.899062i | \(-0.644250\pi\) | ||||
−0.437821 | + | 0.899062i | \(0.644250\pi\) | |||||||
\(230\) | 9.39533 | 0.619509 | ||||||||
\(231\) | 0.747774 | 0.0491999 | ||||||||
\(232\) | −3.60480 | −0.236666 | ||||||||
\(233\) | −19.7166 | −1.29168 | −0.645839 | − | 0.763474i | \(-0.723492\pi\) | ||||
−0.645839 | + | 0.763474i | \(0.723492\pi\) | |||||||
\(234\) | 1.00000 | 0.0653720 | ||||||||
\(235\) | −8.18357 | −0.533837 | ||||||||
\(236\) | 10.2889 | 0.669753 | ||||||||
\(237\) | −7.70913 | −0.500762 | ||||||||
\(238\) | 1.14479 | 0.0742059 | ||||||||
\(239\) | −24.4023 | −1.57846 | −0.789228 | − | 0.614101i | \(-0.789519\pi\) | ||||
−0.789228 | + | 0.614101i | \(0.789519\pi\) | |||||||
\(240\) | 1.82988 | 0.118118 | ||||||||
\(241\) | −7.27230 | −0.468450 | −0.234225 | − | 0.972182i | \(-0.575255\pi\) | ||||
−0.234225 | + | 0.972182i | \(0.575255\pi\) | |||||||
\(242\) | 10.7366 | 0.690176 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −9.58790 | −0.613802 | ||||||||
\(245\) | 8.92424 | 0.570149 | ||||||||
\(246\) | 5.68841 | 0.362680 | ||||||||
\(247\) | 1.12864 | 0.0718137 | ||||||||
\(248\) | 8.18455 | 0.519719 | ||||||||
\(249\) | 0.451085 | 0.0285864 | ||||||||
\(250\) | −12.1715 | −0.769794 | ||||||||
\(251\) | −5.76786 | −0.364064 | −0.182032 | − | 0.983293i | \(-0.558267\pi\) | ||||
−0.182032 | + | 0.983293i | \(0.558267\pi\) | |||||||
\(252\) | 1.45707 | 0.0917865 | ||||||||
\(253\) | −2.63500 | −0.165661 | ||||||||
\(254\) | 9.36539 | 0.587637 | ||||||||
\(255\) | −1.43770 | −0.0900326 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −7.06058 | −0.440427 | −0.220213 | − | 0.975452i | \(-0.570675\pi\) | ||||
−0.220213 | + | 0.975452i | \(0.570675\pi\) | |||||||
\(258\) | 5.80579 | 0.361453 | ||||||||
\(259\) | 3.88293 | 0.241273 | ||||||||
\(260\) | 1.82988 | 0.113484 | ||||||||
\(261\) | 3.60480 | 0.223131 | ||||||||
\(262\) | 11.5102 | 0.711103 | ||||||||
\(263\) | −27.5232 | −1.69715 | −0.848575 | − | 0.529075i | \(-0.822539\pi\) | ||||
−0.848575 | + | 0.529075i | \(0.822539\pi\) | |||||||
\(264\) | −0.513205 | −0.0315856 | ||||||||
\(265\) | 18.1391 | 1.11428 | ||||||||
\(266\) | 1.64451 | 0.100831 | ||||||||
\(267\) | −0.196823 | −0.0120454 | ||||||||
\(268\) | −11.1866 | −0.683333 | ||||||||
\(269\) | 15.1132 | 0.921467 | 0.460733 | − | 0.887539i | \(-0.347586\pi\) | ||||
0.460733 | + | 0.887539i | \(0.347586\pi\) | |||||||
\(270\) | −1.82988 | −0.111363 | ||||||||
\(271\) | −8.91417 | −0.541497 | −0.270749 | − | 0.962650i | \(-0.587271\pi\) | ||||
−0.270749 | + | 0.962650i | \(0.587271\pi\) | |||||||
\(272\) | −0.785684 | −0.0476391 | ||||||||
\(273\) | 1.45707 | 0.0881857 | ||||||||
\(274\) | 2.77252 | 0.167494 | ||||||||
\(275\) | 0.847583 | 0.0511112 | ||||||||
\(276\) | −5.13440 | −0.309055 | ||||||||
\(277\) | −2.29177 | −0.137699 | −0.0688495 | − | 0.997627i | \(-0.521933\pi\) | ||||
−0.0688495 | + | 0.997627i | \(0.521933\pi\) | |||||||
\(278\) | 11.4546 | 0.687003 | ||||||||
\(279\) | −8.18455 | −0.489996 | ||||||||
\(280\) | 2.66625 | 0.159339 | ||||||||
\(281\) | 29.9684 | 1.78776 | 0.893882 | − | 0.448303i | \(-0.147971\pi\) | ||||
0.893882 | + | 0.448303i | \(0.147971\pi\) | |||||||
\(282\) | 4.47220 | 0.266315 | ||||||||
\(283\) | 27.0645 | 1.60882 | 0.804410 | − | 0.594075i | \(-0.202482\pi\) | ||||
0.804410 | + | 0.594075i | \(0.202482\pi\) | |||||||
\(284\) | 4.34398 | 0.257768 | ||||||||
\(285\) | −2.06528 | −0.122336 | ||||||||
\(286\) | −0.513205 | −0.0303465 | ||||||||
\(287\) | 8.28840 | 0.489248 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −16.3827 | −0.963688 | ||||||||
\(290\) | 6.59634 | 0.387350 | ||||||||
\(291\) | −0.774045 | −0.0453753 | ||||||||
\(292\) | 0.434059 | 0.0254014 | ||||||||
\(293\) | −16.0466 | −0.937454 | −0.468727 | − | 0.883343i | \(-0.655287\pi\) | ||||
−0.468727 | + | 0.883343i | \(0.655287\pi\) | |||||||
\(294\) | −4.87696 | −0.284430 | ||||||||
\(295\) | −18.8275 | −1.09618 | ||||||||
\(296\) | −2.66489 | −0.154894 | ||||||||
\(297\) | 0.513205 | 0.0297792 | ||||||||
\(298\) | 14.3197 | 0.829515 | ||||||||
\(299\) | −5.13440 | −0.296930 | ||||||||
\(300\) | 1.65155 | 0.0953522 | ||||||||
\(301\) | 8.45943 | 0.487593 | ||||||||
\(302\) | 9.19404 | 0.529057 | ||||||||
\(303\) | −13.7255 | −0.788511 | ||||||||
\(304\) | −1.12864 | −0.0647320 | ||||||||
\(305\) | 17.5447 | 1.00461 | ||||||||
\(306\) | 0.785684 | 0.0449145 | ||||||||
\(307\) | −0.570165 | −0.0325410 | −0.0162705 | − | 0.999868i | \(-0.505179\pi\) | ||||
−0.0162705 | + | 0.999868i | \(0.505179\pi\) | |||||||
\(308\) | −0.747774 | −0.0426084 | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | −14.9767 | −0.850620 | ||||||||
\(311\) | −13.7186 | −0.777909 | −0.388954 | − | 0.921257i | \(-0.627164\pi\) | ||||
−0.388954 | + | 0.921257i | \(0.627164\pi\) | |||||||
\(312\) | −1.00000 | −0.0566139 | ||||||||
\(313\) | −8.93255 | −0.504898 | −0.252449 | − | 0.967610i | \(-0.581236\pi\) | ||||
−0.252449 | + | 0.967610i | \(0.581236\pi\) | |||||||
\(314\) | −22.9121 | −1.29300 | ||||||||
\(315\) | −2.66625 | −0.150226 | ||||||||
\(316\) | 7.70913 | 0.433672 | ||||||||
\(317\) | 2.51336 | 0.141164 | 0.0705821 | − | 0.997506i | \(-0.477514\pi\) | ||||
0.0705821 | + | 0.997506i | \(0.477514\pi\) | |||||||
\(318\) | −9.91273 | −0.555878 | ||||||||
\(319\) | −1.85000 | −0.103580 | ||||||||
\(320\) | −1.82988 | −0.102293 | ||||||||
\(321\) | −11.3226 | −0.631968 | ||||||||
\(322\) | −7.48116 | −0.416909 | ||||||||
\(323\) | 0.886755 | 0.0493404 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 1.65155 | 0.0916114 | ||||||||
\(326\) | 13.1323 | 0.727332 | ||||||||
\(327\) | −4.23121 | −0.233986 | ||||||||
\(328\) | −5.68841 | −0.314090 | ||||||||
\(329\) | 6.51629 | 0.359254 | ||||||||
\(330\) | 0.939102 | 0.0516959 | ||||||||
\(331\) | −6.17555 | −0.339439 | −0.169719 | − | 0.985492i | \(-0.554286\pi\) | ||||
−0.169719 | + | 0.985492i | \(0.554286\pi\) | |||||||
\(332\) | −0.451085 | −0.0247565 | ||||||||
\(333\) | 2.66489 | 0.146035 | ||||||||
\(334\) | −12.9880 | −0.710672 | ||||||||
\(335\) | 20.4702 | 1.11841 | ||||||||
\(336\) | −1.45707 | −0.0794895 | ||||||||
\(337\) | 22.9070 | 1.24782 | 0.623911 | − | 0.781496i | \(-0.285543\pi\) | ||||
0.623911 | + | 0.781496i | \(0.285543\pi\) | |||||||
\(338\) | −1.00000 | −0.0543928 | ||||||||
\(339\) | 17.2827 | 0.938668 | ||||||||
\(340\) | 1.43770 | 0.0779705 | ||||||||
\(341\) | 4.20035 | 0.227462 | ||||||||
\(342\) | 1.12864 | 0.0610299 | ||||||||
\(343\) | −17.3055 | −0.934410 | ||||||||
\(344\) | −5.80579 | −0.313027 | ||||||||
\(345\) | 9.39533 | 0.505827 | ||||||||
\(346\) | −25.8509 | −1.38976 | ||||||||
\(347\) | 20.6315 | 1.10756 | 0.553779 | − | 0.832663i | \(-0.313185\pi\) | ||||
0.553779 | + | 0.832663i | \(0.313185\pi\) | |||||||
\(348\) | −3.60480 | −0.193237 | ||||||||
\(349\) | 10.8998 | 0.583452 | 0.291726 | − | 0.956502i | \(-0.405770\pi\) | ||||
0.291726 | + | 0.956502i | \(0.405770\pi\) | |||||||
\(350\) | 2.40641 | 0.128628 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 0.513205 | 0.0273539 | ||||||||
\(353\) | −1.25568 | −0.0668332 | −0.0334166 | − | 0.999442i | \(-0.510639\pi\) | ||||
−0.0334166 | + | 0.999442i | \(0.510639\pi\) | |||||||
\(354\) | 10.2889 | 0.546851 | ||||||||
\(355\) | −7.94896 | −0.421887 | ||||||||
\(356\) | 0.196823 | 0.0104316 | ||||||||
\(357\) | 1.14479 | 0.0605889 | ||||||||
\(358\) | −17.2268 | −0.910467 | ||||||||
\(359\) | −19.3745 | −1.02255 | −0.511274 | − | 0.859418i | \(-0.670826\pi\) | ||||
−0.511274 | + | 0.859418i | \(0.670826\pi\) | |||||||
\(360\) | 1.82988 | 0.0964430 | ||||||||
\(361\) | −17.7262 | −0.932956 | ||||||||
\(362\) | −9.57039 | −0.503009 | ||||||||
\(363\) | 10.7366 | 0.563526 | ||||||||
\(364\) | −1.45707 | −0.0763710 | ||||||||
\(365\) | −0.794274 | −0.0415742 | ||||||||
\(366\) | −9.58790 | −0.501168 | ||||||||
\(367\) | 12.8242 | 0.669417 | 0.334709 | − | 0.942322i | \(-0.391362\pi\) | ||||
0.334709 | + | 0.942322i | \(0.391362\pi\) | |||||||
\(368\) | 5.13440 | 0.267649 | ||||||||
\(369\) | 5.68841 | 0.296127 | ||||||||
\(370\) | 4.87643 | 0.253513 | ||||||||
\(371\) | −14.4435 | −0.749869 | ||||||||
\(372\) | 8.18455 | 0.424349 | ||||||||
\(373\) | 14.3607 | 0.743570 | 0.371785 | − | 0.928319i | \(-0.378746\pi\) | ||||
0.371785 | + | 0.928319i | \(0.378746\pi\) | |||||||
\(374\) | −0.403217 | −0.0208498 | ||||||||
\(375\) | −12.1715 | −0.628535 | ||||||||
\(376\) | −4.47220 | −0.230636 | ||||||||
\(377\) | −3.60480 | −0.185656 | ||||||||
\(378\) | 1.45707 | 0.0749434 | ||||||||
\(379\) | 9.96185 | 0.511706 | 0.255853 | − | 0.966716i | \(-0.417644\pi\) | ||||
0.255853 | + | 0.966716i | \(0.417644\pi\) | |||||||
\(380\) | 2.06528 | 0.105946 | ||||||||
\(381\) | 9.36539 | 0.479803 | ||||||||
\(382\) | −12.4477 | −0.636881 | ||||||||
\(383\) | −5.93297 | −0.303161 | −0.151580 | − | 0.988445i | \(-0.548436\pi\) | ||||
−0.151580 | + | 0.988445i | \(0.548436\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 1.36833 | 0.0697368 | ||||||||
\(386\) | −5.35638 | −0.272633 | ||||||||
\(387\) | 5.80579 | 0.295125 | ||||||||
\(388\) | 0.774045 | 0.0392962 | ||||||||
\(389\) | −25.3451 | −1.28505 | −0.642523 | − | 0.766267i | \(-0.722112\pi\) | ||||
−0.642523 | + | 0.766267i | \(0.722112\pi\) | |||||||
\(390\) | 1.82988 | 0.0926595 | ||||||||
\(391\) | −4.03401 | −0.204009 | ||||||||
\(392\) | 4.87696 | 0.246324 | ||||||||
\(393\) | 11.5102 | 0.580613 | ||||||||
\(394\) | −5.23510 | −0.263740 | ||||||||
\(395\) | −14.1068 | −0.709788 | ||||||||
\(396\) | −0.513205 | −0.0257895 | ||||||||
\(397\) | −27.8148 | −1.39599 | −0.697993 | − | 0.716104i | \(-0.745923\pi\) | ||||
−0.697993 | + | 0.716104i | \(0.745923\pi\) | |||||||
\(398\) | −10.4226 | −0.522436 | ||||||||
\(399\) | 1.64451 | 0.0823283 | ||||||||
\(400\) | −1.65155 | −0.0825774 | ||||||||
\(401\) | −37.3383 | −1.86459 | −0.932293 | − | 0.361704i | \(-0.882195\pi\) | ||||
−0.932293 | + | 0.361704i | \(0.882195\pi\) | |||||||
\(402\) | −11.1866 | −0.557939 | ||||||||
\(403\) | 8.18455 | 0.407701 | ||||||||
\(404\) | 13.7255 | 0.682870 | ||||||||
\(405\) | −1.82988 | −0.0909273 | ||||||||
\(406\) | −5.25243 | −0.260674 | ||||||||
\(407\) | −1.36764 | −0.0677912 | ||||||||
\(408\) | −0.785684 | −0.0388971 | ||||||||
\(409\) | −18.2282 | −0.901326 | −0.450663 | − | 0.892694i | \(-0.648812\pi\) | ||||
−0.450663 | + | 0.892694i | \(0.648812\pi\) | |||||||
\(410\) | 10.4091 | 0.514069 | ||||||||
\(411\) | 2.77252 | 0.136758 | ||||||||
\(412\) | −1.00000 | −0.0492665 | ||||||||
\(413\) | 14.9917 | 0.737691 | ||||||||
\(414\) | −5.13440 | −0.252342 | ||||||||
\(415\) | 0.825431 | 0.0405188 | ||||||||
\(416\) | 1.00000 | 0.0490290 | ||||||||
\(417\) | 11.4546 | 0.560935 | ||||||||
\(418\) | −0.579225 | −0.0283308 | ||||||||
\(419\) | 23.0355 | 1.12536 | 0.562680 | − | 0.826675i | \(-0.309770\pi\) | ||||
0.562680 | + | 0.826675i | \(0.309770\pi\) | |||||||
\(420\) | 2.66625 | 0.130100 | ||||||||
\(421\) | −37.1791 | −1.81200 | −0.905999 | − | 0.423279i | \(-0.860879\pi\) | ||||
−0.905999 | + | 0.423279i | \(0.860879\pi\) | |||||||
\(422\) | −25.9138 | −1.26146 | ||||||||
\(423\) | 4.47220 | 0.217446 | ||||||||
\(424\) | 9.91273 | 0.481405 | ||||||||
\(425\) | 1.29759 | 0.0629426 | ||||||||
\(426\) | 4.34398 | 0.210467 | ||||||||
\(427\) | −13.9702 | −0.676066 | ||||||||
\(428\) | 11.3226 | 0.547301 | ||||||||
\(429\) | −0.513205 | −0.0247778 | ||||||||
\(430\) | 10.6239 | 0.512330 | ||||||||
\(431\) | −9.91314 | −0.477499 | −0.238750 | − | 0.971081i | \(-0.576738\pi\) | ||||
−0.238750 | + | 0.971081i | \(0.576738\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 0.898037 | 0.0431569 | 0.0215785 | − | 0.999767i | \(-0.493131\pi\) | ||||
0.0215785 | + | 0.999767i | \(0.493131\pi\) | |||||||
\(434\) | 11.9254 | 0.572439 | ||||||||
\(435\) | 6.59634 | 0.316270 | ||||||||
\(436\) | 4.23121 | 0.202638 | ||||||||
\(437\) | −5.79490 | −0.277208 | ||||||||
\(438\) | 0.434059 | 0.0207401 | ||||||||
\(439\) | −20.9744 | −1.00105 | −0.500527 | − | 0.865721i | \(-0.666860\pi\) | ||||
−0.500527 | + | 0.865721i | \(0.666860\pi\) | |||||||
\(440\) | −0.939102 | −0.0447700 | ||||||||
\(441\) | −4.87696 | −0.232236 | ||||||||
\(442\) | −0.785684 | −0.0373712 | ||||||||
\(443\) | −12.8861 | −0.612237 | −0.306118 | − | 0.951993i | \(-0.599030\pi\) | ||||
−0.306118 | + | 0.951993i | \(0.599030\pi\) | |||||||
\(444\) | −2.66489 | −0.126470 | ||||||||
\(445\) | −0.360162 | −0.0170733 | ||||||||
\(446\) | 23.7842 | 1.12622 | ||||||||
\(447\) | 14.3197 | 0.677296 | ||||||||
\(448\) | 1.45707 | 0.0688399 | ||||||||
\(449\) | −1.17918 | −0.0556489 | −0.0278245 | − | 0.999613i | \(-0.508858\pi\) | ||||
−0.0278245 | + | 0.999613i | \(0.508858\pi\) | |||||||
\(450\) | 1.65155 | 0.0778547 | ||||||||
\(451\) | −2.91932 | −0.137466 | ||||||||
\(452\) | −17.2827 | −0.812910 | ||||||||
\(453\) | 9.19404 | 0.431973 | ||||||||
\(454\) | 12.9676 | 0.608600 | ||||||||
\(455\) | 2.66625 | 0.124996 | ||||||||
\(456\) | −1.12864 | −0.0528535 | ||||||||
\(457\) | −22.1846 | −1.03775 | −0.518876 | − | 0.854849i | \(-0.673649\pi\) | ||||
−0.518876 | + | 0.854849i | \(0.673649\pi\) | |||||||
\(458\) | 13.2509 | 0.619172 | ||||||||
\(459\) | 0.785684 | 0.0366726 | ||||||||
\(460\) | −9.39533 | −0.438059 | ||||||||
\(461\) | −1.97709 | −0.0920822 | −0.0460411 | − | 0.998940i | \(-0.514661\pi\) | ||||
−0.0460411 | + | 0.998940i | \(0.514661\pi\) | |||||||
\(462\) | −0.747774 | −0.0347896 | ||||||||
\(463\) | 29.1462 | 1.35454 | 0.677268 | − | 0.735736i | \(-0.263164\pi\) | ||||
0.677268 | + | 0.735736i | \(0.263164\pi\) | |||||||
\(464\) | 3.60480 | 0.167348 | ||||||||
\(465\) | −14.9767 | −0.694529 | ||||||||
\(466\) | 19.7166 | 0.913354 | ||||||||
\(467\) | −1.07865 | −0.0499138 | −0.0249569 | − | 0.999689i | \(-0.507945\pi\) | ||||
−0.0249569 | + | 0.999689i | \(0.507945\pi\) | |||||||
\(468\) | −1.00000 | −0.0462250 | ||||||||
\(469\) | −16.2997 | −0.752649 | ||||||||
\(470\) | 8.18357 | 0.377480 | ||||||||
\(471\) | −22.9121 | −1.05573 | ||||||||
\(472\) | −10.2889 | −0.473587 | ||||||||
\(473\) | −2.97956 | −0.137000 | ||||||||
\(474\) | 7.70913 | 0.354092 | ||||||||
\(475\) | 1.86401 | 0.0855264 | ||||||||
\(476\) | −1.14479 | −0.0524715 | ||||||||
\(477\) | −9.91273 | −0.453873 | ||||||||
\(478\) | 24.4023 | 1.11614 | ||||||||
\(479\) | 43.5747 | 1.99098 | 0.995488 | − | 0.0948823i | \(-0.0302475\pi\) | ||||
0.995488 | + | 0.0948823i | \(0.0302475\pi\) | |||||||
\(480\) | −1.82988 | −0.0835221 | ||||||||
\(481\) | −2.66489 | −0.121509 | ||||||||
\(482\) | 7.27230 | 0.331244 | ||||||||
\(483\) | −7.48116 | −0.340405 | ||||||||
\(484\) | −10.7366 | −0.488028 | ||||||||
\(485\) | −1.41641 | −0.0643157 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 2.28651 | 0.103612 | 0.0518059 | − | 0.998657i | \(-0.483502\pi\) | ||||
0.0518059 | + | 0.998657i | \(0.483502\pi\) | |||||||
\(488\) | 9.58790 | 0.434024 | ||||||||
\(489\) | 13.1323 | 0.593864 | ||||||||
\(490\) | −8.92424 | −0.403156 | ||||||||
\(491\) | −2.07996 | −0.0938672 | −0.0469336 | − | 0.998898i | \(-0.514945\pi\) | ||||
−0.0469336 | + | 0.998898i | \(0.514945\pi\) | |||||||
\(492\) | −5.68841 | −0.256453 | ||||||||
\(493\) | −2.83223 | −0.127557 | ||||||||
\(494\) | −1.12864 | −0.0507800 | ||||||||
\(495\) | 0.939102 | 0.0422095 | ||||||||
\(496\) | −8.18455 | −0.367497 | ||||||||
\(497\) | 6.32947 | 0.283916 | ||||||||
\(498\) | −0.451085 | −0.0202136 | ||||||||
\(499\) | −5.05021 | −0.226078 | −0.113039 | − | 0.993591i | \(-0.536059\pi\) | ||||
−0.113039 | + | 0.993591i | \(0.536059\pi\) | |||||||
\(500\) | 12.1715 | 0.544327 | ||||||||
\(501\) | −12.9880 | −0.580261 | ||||||||
\(502\) | 5.76786 | 0.257432 | ||||||||
\(503\) | −25.8794 | −1.15391 | −0.576953 | − | 0.816777i | \(-0.695759\pi\) | ||||
−0.576953 | + | 0.816777i | \(0.695759\pi\) | |||||||
\(504\) | −1.45707 | −0.0649029 | ||||||||
\(505\) | −25.1160 | −1.11765 | ||||||||
\(506\) | 2.63500 | 0.117140 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | −9.36539 | −0.415522 | ||||||||
\(509\) | −35.6770 | −1.58135 | −0.790677 | − | 0.612233i | \(-0.790271\pi\) | ||||
−0.790677 | + | 0.612233i | \(0.790271\pi\) | |||||||
\(510\) | 1.43770 | 0.0636626 | ||||||||
\(511\) | 0.632452 | 0.0279780 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 1.12864 | 0.0498307 | ||||||||
\(514\) | 7.06058 | 0.311429 | ||||||||
\(515\) | 1.82988 | 0.0806340 | ||||||||
\(516\) | −5.80579 | −0.255586 | ||||||||
\(517\) | −2.29515 | −0.100941 | ||||||||
\(518\) | −3.88293 | −0.170606 | ||||||||
\(519\) | −25.8509 | −1.13473 | ||||||||
\(520\) | −1.82988 | −0.0802454 | ||||||||
\(521\) | −19.1843 | −0.840481 | −0.420240 | − | 0.907413i | \(-0.638054\pi\) | ||||
−0.420240 | + | 0.907413i | \(0.638054\pi\) | |||||||
\(522\) | −3.60480 | −0.157778 | ||||||||
\(523\) | 27.2070 | 1.18968 | 0.594840 | − | 0.803844i | \(-0.297215\pi\) | ||||
0.594840 | + | 0.803844i | \(0.297215\pi\) | |||||||
\(524\) | −11.5102 | −0.502826 | ||||||||
\(525\) | 2.40641 | 0.105025 | ||||||||
\(526\) | 27.5232 | 1.20007 | ||||||||
\(527\) | 6.43046 | 0.280115 | ||||||||
\(528\) | 0.513205 | 0.0223344 | ||||||||
\(529\) | 3.36207 | 0.146177 | ||||||||
\(530\) | −18.1391 | −0.787911 | ||||||||
\(531\) | 10.2889 | 0.446502 | ||||||||
\(532\) | −1.64451 | −0.0712984 | ||||||||
\(533\) | −5.68841 | −0.246393 | ||||||||
\(534\) | 0.196823 | 0.00851736 | ||||||||
\(535\) | −20.7191 | −0.895763 | ||||||||
\(536\) | 11.1866 | 0.483189 | ||||||||
\(537\) | −17.2268 | −0.743393 | ||||||||
\(538\) | −15.1132 | −0.651575 | ||||||||
\(539\) | 2.50288 | 0.107807 | ||||||||
\(540\) | 1.82988 | 0.0787454 | ||||||||
\(541\) | 10.1326 | 0.435633 | 0.217816 | − | 0.975990i | \(-0.430107\pi\) | ||||
0.217816 | + | 0.975990i | \(0.430107\pi\) | |||||||
\(542\) | 8.91417 | 0.382896 | ||||||||
\(543\) | −9.57039 | −0.410705 | ||||||||
\(544\) | 0.785684 | 0.0336859 | ||||||||
\(545\) | −7.74259 | −0.331656 | ||||||||
\(546\) | −1.45707 | −0.0623567 | ||||||||
\(547\) | −2.67032 | −0.114175 | −0.0570874 | − | 0.998369i | \(-0.518181\pi\) | ||||
−0.0570874 | + | 0.998369i | \(0.518181\pi\) | |||||||
\(548\) | −2.77252 | −0.118436 | ||||||||
\(549\) | −9.58790 | −0.409202 | ||||||||
\(550\) | −0.847583 | −0.0361410 | ||||||||
\(551\) | −4.06852 | −0.173325 | ||||||||
\(552\) | 5.13440 | 0.218535 | ||||||||
\(553\) | 11.2327 | 0.477663 | ||||||||
\(554\) | 2.29177 | 0.0973679 | ||||||||
\(555\) | 4.87643 | 0.206993 | ||||||||
\(556\) | −11.4546 | −0.485784 | ||||||||
\(557\) | −36.9005 | −1.56352 | −0.781762 | − | 0.623577i | \(-0.785679\pi\) | ||||
−0.781762 | + | 0.623577i | \(0.785679\pi\) | |||||||
\(558\) | 8.18455 | 0.346479 | ||||||||
\(559\) | −5.80579 | −0.245559 | ||||||||
\(560\) | −2.66625 | −0.112670 | ||||||||
\(561\) | −0.403217 | −0.0170238 | ||||||||
\(562\) | −29.9684 | −1.26414 | ||||||||
\(563\) | −12.5724 | −0.529865 | −0.264933 | − | 0.964267i | \(-0.585350\pi\) | ||||
−0.264933 | + | 0.964267i | \(0.585350\pi\) | |||||||
\(564\) | −4.47220 | −0.188313 | ||||||||
\(565\) | 31.6252 | 1.33048 | ||||||||
\(566\) | −27.0645 | −1.13761 | ||||||||
\(567\) | 1.45707 | 0.0611910 | ||||||||
\(568\) | −4.34398 | −0.182270 | ||||||||
\(569\) | −37.7583 | −1.58291 | −0.791455 | − | 0.611228i | \(-0.790676\pi\) | ||||
−0.791455 | + | 0.611228i | \(0.790676\pi\) | |||||||
\(570\) | 2.06528 | 0.0865049 | ||||||||
\(571\) | −17.5934 | −0.736259 | −0.368130 | − | 0.929774i | \(-0.620002\pi\) | ||||
−0.368130 | + | 0.929774i | \(0.620002\pi\) | |||||||
\(572\) | 0.513205 | 0.0214582 | ||||||||
\(573\) | −12.4477 | −0.520011 | ||||||||
\(574\) | −8.28840 | −0.345951 | ||||||||
\(575\) | −8.47971 | −0.353628 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 26.8868 | 1.11931 | 0.559656 | − | 0.828725i | \(-0.310933\pi\) | ||||
0.559656 | + | 0.828725i | \(0.310933\pi\) | |||||||
\(578\) | 16.3827 | 0.681431 | ||||||||
\(579\) | −5.35638 | −0.222604 | ||||||||
\(580\) | −6.59634 | −0.273898 | ||||||||
\(581\) | −0.657261 | −0.0272678 | ||||||||
\(582\) | 0.774045 | 0.0320852 | ||||||||
\(583\) | 5.08726 | 0.210693 | ||||||||
\(584\) | −0.434059 | −0.0179615 | ||||||||
\(585\) | 1.82988 | 0.0756561 | ||||||||
\(586\) | 16.0466 | 0.662880 | ||||||||
\(587\) | 13.7189 | 0.566242 | 0.283121 | − | 0.959084i | \(-0.408630\pi\) | ||||
0.283121 | + | 0.959084i | \(0.408630\pi\) | |||||||
\(588\) | 4.87696 | 0.201122 | ||||||||
\(589\) | 9.23742 | 0.380621 | ||||||||
\(590\) | 18.8275 | 0.775116 | ||||||||
\(591\) | −5.23510 | −0.215343 | ||||||||
\(592\) | 2.66489 | 0.109526 | ||||||||
\(593\) | 16.5470 | 0.679504 | 0.339752 | − | 0.940515i | \(-0.389657\pi\) | ||||
0.339752 | + | 0.940515i | \(0.389657\pi\) | |||||||
\(594\) | −0.513205 | −0.0210571 | ||||||||
\(595\) | 2.09483 | 0.0858797 | ||||||||
\(596\) | −14.3197 | −0.586556 | ||||||||
\(597\) | −10.4226 | −0.426567 | ||||||||
\(598\) | 5.13440 | 0.209961 | ||||||||
\(599\) | −44.4217 | −1.81502 | −0.907511 | − | 0.420028i | \(-0.862020\pi\) | ||||
−0.907511 | + | 0.420028i | \(0.862020\pi\) | |||||||
\(600\) | −1.65155 | −0.0674242 | ||||||||
\(601\) | 0.0157036 | 0.000640562 0 | 0.000320281 | − | 1.00000i | \(-0.499898\pi\) | ||||
0.000320281 | 1.00000i | \(0.499898\pi\) | ||||||||
\(602\) | −8.45943 | −0.344780 | ||||||||
\(603\) | −11.1866 | −0.455555 | ||||||||
\(604\) | −9.19404 | −0.374100 | ||||||||
\(605\) | 19.6467 | 0.798752 | ||||||||
\(606\) | 13.7255 | 0.557561 | ||||||||
\(607\) | −34.7387 | −1.41000 | −0.705001 | − | 0.709207i | \(-0.749053\pi\) | ||||
−0.705001 | + | 0.709207i | \(0.749053\pi\) | |||||||
\(608\) | 1.12864 | 0.0457725 | ||||||||
\(609\) | −5.25243 | −0.212839 | ||||||||
\(610\) | −17.5447 | −0.710363 | ||||||||
\(611\) | −4.47220 | −0.180926 | ||||||||
\(612\) | −0.785684 | −0.0317594 | ||||||||
\(613\) | −38.7813 | −1.56636 | −0.783181 | − | 0.621794i | \(-0.786404\pi\) | ||||
−0.783181 | + | 0.621794i | \(0.786404\pi\) | |||||||
\(614\) | 0.570165 | 0.0230100 | ||||||||
\(615\) | 10.4091 | 0.419735 | ||||||||
\(616\) | 0.747774 | 0.0301287 | ||||||||
\(617\) | −3.46954 | −0.139679 | −0.0698393 | − | 0.997558i | \(-0.522249\pi\) | ||||
−0.0698393 | + | 0.997558i | \(0.522249\pi\) | |||||||
\(618\) | −1.00000 | −0.0402259 | ||||||||
\(619\) | −34.6311 | −1.39194 | −0.695971 | − | 0.718069i | \(-0.745026\pi\) | ||||
−0.695971 | + | 0.718069i | \(0.745026\pi\) | |||||||
\(620\) | 14.9767 | 0.601479 | ||||||||
\(621\) | −5.13440 | −0.206036 | ||||||||
\(622\) | 13.7186 | 0.550065 | ||||||||
\(623\) | 0.286784 | 0.0114898 | ||||||||
\(624\) | 1.00000 | 0.0400320 | ||||||||
\(625\) | −14.0146 | −0.560586 | ||||||||
\(626\) | 8.93255 | 0.357017 | ||||||||
\(627\) | −0.579225 | −0.0231320 | ||||||||
\(628\) | 22.9121 | 0.914291 | ||||||||
\(629\) | −2.09376 | −0.0834838 | ||||||||
\(630\) | 2.66625 | 0.106226 | ||||||||
\(631\) | −5.31616 | −0.211633 | −0.105816 | − | 0.994386i | \(-0.533746\pi\) | ||||
−0.105816 | + | 0.994386i | \(0.533746\pi\) | |||||||
\(632\) | −7.70913 | −0.306653 | ||||||||
\(633\) | −25.9138 | −1.02998 | ||||||||
\(634\) | −2.51336 | −0.0998182 | ||||||||
\(635\) | 17.1375 | 0.680081 | ||||||||
\(636\) | 9.91273 | 0.393065 | ||||||||
\(637\) | 4.87696 | 0.193232 | ||||||||
\(638\) | 1.85000 | 0.0732422 | ||||||||
\(639\) | 4.34398 | 0.171845 | ||||||||
\(640\) | 1.82988 | 0.0723323 | ||||||||
\(641\) | −34.6319 | −1.36788 | −0.683940 | − | 0.729539i | \(-0.739735\pi\) | ||||
−0.683940 | + | 0.729539i | \(0.739735\pi\) | |||||||
\(642\) | 11.3226 | 0.446869 | ||||||||
\(643\) | 14.2684 | 0.562690 | 0.281345 | − | 0.959607i | \(-0.409220\pi\) | ||||
0.281345 | + | 0.959607i | \(0.409220\pi\) | |||||||
\(644\) | 7.48116 | 0.294799 | ||||||||
\(645\) | 10.6239 | 0.418315 | ||||||||
\(646\) | −0.886755 | −0.0348889 | ||||||||
\(647\) | −32.7461 | −1.28738 | −0.643690 | − | 0.765286i | \(-0.722597\pi\) | ||||
−0.643690 | + | 0.765286i | \(0.722597\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −5.28033 | −0.207271 | ||||||||
\(650\) | −1.65155 | −0.0647790 | ||||||||
\(651\) | 11.9254 | 0.467394 | ||||||||
\(652\) | −13.1323 | −0.514301 | ||||||||
\(653\) | −42.3825 | −1.65855 | −0.829277 | − | 0.558838i | \(-0.811247\pi\) | ||||
−0.829277 | + | 0.558838i | \(0.811247\pi\) | |||||||
\(654\) | 4.23121 | 0.165453 | ||||||||
\(655\) | 21.0623 | 0.822971 | ||||||||
\(656\) | 5.68841 | 0.222095 | ||||||||
\(657\) | 0.434059 | 0.0169342 | ||||||||
\(658\) | −6.51629 | −0.254031 | ||||||||
\(659\) | −14.8469 | −0.578352 | −0.289176 | − | 0.957276i | \(-0.593381\pi\) | ||||
−0.289176 | + | 0.957276i | \(0.593381\pi\) | |||||||
\(660\) | −0.939102 | −0.0365545 | ||||||||
\(661\) | 2.53869 | 0.0987436 | 0.0493718 | − | 0.998780i | \(-0.484278\pi\) | ||||
0.0493718 | + | 0.998780i | \(0.484278\pi\) | |||||||
\(662\) | 6.17555 | 0.240019 | ||||||||
\(663\) | −0.785684 | −0.0305134 | ||||||||
\(664\) | 0.451085 | 0.0175055 | ||||||||
\(665\) | 3.00924 | 0.116693 | ||||||||
\(666\) | −2.66489 | −0.103263 | ||||||||
\(667\) | 18.5085 | 0.716651 | ||||||||
\(668\) | 12.9880 | 0.502521 | ||||||||
\(669\) | 23.7842 | 0.919552 | ||||||||
\(670\) | −20.4702 | −0.790832 | ||||||||
\(671\) | 4.92056 | 0.189956 | ||||||||
\(672\) | 1.45707 | 0.0562076 | ||||||||
\(673\) | 38.2772 | 1.47548 | 0.737739 | − | 0.675086i | \(-0.235893\pi\) | ||||
0.737739 | + | 0.675086i | \(0.235893\pi\) | |||||||
\(674\) | −22.9070 | −0.882343 | ||||||||
\(675\) | 1.65155 | 0.0635681 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | −4.80497 | −0.184670 | −0.0923350 | − | 0.995728i | \(-0.529433\pi\) | ||||
−0.0923350 | + | 0.995728i | \(0.529433\pi\) | |||||||
\(678\) | −17.2827 | −0.663738 | ||||||||
\(679\) | 1.12783 | 0.0432823 | ||||||||
\(680\) | −1.43770 | −0.0551335 | ||||||||
\(681\) | 12.9676 | 0.496920 | ||||||||
\(682\) | −4.20035 | −0.160840 | ||||||||
\(683\) | −41.1100 | −1.57303 | −0.786514 | − | 0.617572i | \(-0.788116\pi\) | ||||
−0.786514 | + | 0.617572i | \(0.788116\pi\) | |||||||
\(684\) | −1.12864 | −0.0431547 | ||||||||
\(685\) | 5.07337 | 0.193843 | ||||||||
\(686\) | 17.3055 | 0.660728 | ||||||||
\(687\) | 13.2509 | 0.505552 | ||||||||
\(688\) | 5.80579 | 0.221344 | ||||||||
\(689\) | 9.91273 | 0.377645 | ||||||||
\(690\) | −9.39533 | −0.357674 | ||||||||
\(691\) | −36.1423 | −1.37492 | −0.687458 | − | 0.726224i | \(-0.741274\pi\) | ||||
−0.687458 | + | 0.726224i | \(0.741274\pi\) | |||||||
\(692\) | 25.8509 | 0.982705 | ||||||||
\(693\) | −0.747774 | −0.0284056 | ||||||||
\(694\) | −20.6315 | −0.783162 | ||||||||
\(695\) | 20.9606 | 0.795079 | ||||||||
\(696\) | 3.60480 | 0.136639 | ||||||||
\(697\) | −4.46929 | −0.169287 | ||||||||
\(698\) | −10.8998 | −0.412563 | ||||||||
\(699\) | 19.7166 | 0.745750 | ||||||||
\(700\) | −2.40641 | −0.0909539 | ||||||||
\(701\) | 42.6017 | 1.60904 | 0.804522 | − | 0.593923i | \(-0.202422\pi\) | ||||
0.804522 | + | 0.593923i | \(0.202422\pi\) | |||||||
\(702\) | −1.00000 | −0.0377426 | ||||||||
\(703\) | −3.00771 | −0.113438 | ||||||||
\(704\) | −0.513205 | −0.0193421 | ||||||||
\(705\) | 8.18357 | 0.308211 | ||||||||
\(706\) | 1.25568 | 0.0472582 | ||||||||
\(707\) | 19.9990 | 0.752140 | ||||||||
\(708\) | −10.2889 | −0.386682 | ||||||||
\(709\) | −12.9681 | −0.487027 | −0.243513 | − | 0.969898i | \(-0.578300\pi\) | ||||
−0.243513 | + | 0.969898i | \(0.578300\pi\) | |||||||
\(710\) | 7.94896 | 0.298319 | ||||||||
\(711\) | 7.70913 | 0.289115 | ||||||||
\(712\) | −0.196823 | −0.00737625 | ||||||||
\(713\) | −42.0227 | −1.57376 | ||||||||
\(714\) | −1.14479 | −0.0428428 | ||||||||
\(715\) | −0.939102 | −0.0351204 | ||||||||
\(716\) | 17.2268 | 0.643797 | ||||||||
\(717\) | 24.4023 | 0.911322 | ||||||||
\(718\) | 19.3745 | 0.723050 | ||||||||
\(719\) | 28.7639 | 1.07271 | 0.536356 | − | 0.843992i | \(-0.319800\pi\) | ||||
0.536356 | + | 0.843992i | \(0.319800\pi\) | |||||||
\(720\) | −1.82988 | −0.0681955 | ||||||||
\(721\) | −1.45707 | −0.0542640 | ||||||||
\(722\) | 17.7262 | 0.659700 | ||||||||
\(723\) | 7.27230 | 0.270460 | ||||||||
\(724\) | 9.57039 | 0.355681 | ||||||||
\(725\) | −5.95349 | −0.221107 | ||||||||
\(726\) | −10.7366 | −0.398473 | ||||||||
\(727\) | −0.295380 | −0.0109550 | −0.00547751 | − | 0.999985i | \(-0.501744\pi\) | ||||
−0.00547751 | + | 0.999985i | \(0.501744\pi\) | |||||||
\(728\) | 1.45707 | 0.0540025 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0.794274 | 0.0293974 | ||||||||
\(731\) | −4.56152 | −0.168714 | ||||||||
\(732\) | 9.58790 | 0.354379 | ||||||||
\(733\) | 8.63759 | 0.319037 | 0.159518 | − | 0.987195i | \(-0.449006\pi\) | ||||
0.159518 | + | 0.987195i | \(0.449006\pi\) | |||||||
\(734\) | −12.8242 | −0.473350 | ||||||||
\(735\) | −8.92424 | −0.329175 | ||||||||
\(736\) | −5.13440 | −0.189257 | ||||||||
\(737\) | 5.74104 | 0.211474 | ||||||||
\(738\) | −5.68841 | −0.209393 | ||||||||
\(739\) | −13.6062 | −0.500513 | −0.250256 | − | 0.968180i | \(-0.580515\pi\) | ||||
−0.250256 | + | 0.968180i | \(0.580515\pi\) | |||||||
\(740\) | −4.87643 | −0.179261 | ||||||||
\(741\) | −1.12864 | −0.0414617 | ||||||||
\(742\) | 14.4435 | 0.530238 | ||||||||
\(743\) | 5.71623 | 0.209708 | 0.104854 | − | 0.994488i | \(-0.466562\pi\) | ||||
0.104854 | + | 0.994488i | \(0.466562\pi\) | |||||||
\(744\) | −8.18455 | −0.300060 | ||||||||
\(745\) | 26.2032 | 0.960012 | ||||||||
\(746\) | −14.3607 | −0.525784 | ||||||||
\(747\) | −0.451085 | −0.0165043 | ||||||||
\(748\) | 0.403217 | 0.0147431 | ||||||||
\(749\) | 16.4978 | 0.602818 | ||||||||
\(750\) | 12.1715 | 0.444441 | ||||||||
\(751\) | −10.6900 | −0.390084 | −0.195042 | − | 0.980795i | \(-0.562484\pi\) | ||||
−0.195042 | + | 0.980795i | \(0.562484\pi\) | |||||||
\(752\) | 4.47220 | 0.163084 | ||||||||
\(753\) | 5.76786 | 0.210192 | ||||||||
\(754\) | 3.60480 | 0.131279 | ||||||||
\(755\) | 16.8240 | 0.612287 | ||||||||
\(756\) | −1.45707 | −0.0529930 | ||||||||
\(757\) | −20.4338 | −0.742678 | −0.371339 | − | 0.928497i | \(-0.621101\pi\) | ||||
−0.371339 | + | 0.928497i | \(0.621101\pi\) | |||||||
\(758\) | −9.96185 | −0.361831 | ||||||||
\(759\) | 2.63500 | 0.0956445 | ||||||||
\(760\) | −2.06528 | −0.0749154 | ||||||||
\(761\) | 15.5349 | 0.563140 | 0.281570 | − | 0.959541i | \(-0.409145\pi\) | ||||
0.281570 | + | 0.959541i | \(0.409145\pi\) | |||||||
\(762\) | −9.36539 | −0.339272 | ||||||||
\(763\) | 6.16515 | 0.223193 | ||||||||
\(764\) | 12.4477 | 0.450343 | ||||||||
\(765\) | 1.43770 | 0.0519803 | ||||||||
\(766\) | 5.93297 | 0.214367 | ||||||||
\(767\) | −10.2889 | −0.371512 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −20.4423 | −0.737167 | −0.368583 | − | 0.929595i | \(-0.620157\pi\) | ||||
−0.368583 | + | 0.929595i | \(0.620157\pi\) | |||||||
\(770\) | −1.36833 | −0.0493114 | ||||||||
\(771\) | 7.06058 | 0.254281 | ||||||||
\(772\) | 5.35638 | 0.192780 | ||||||||
\(773\) | 36.3765 | 1.30837 | 0.654186 | − | 0.756334i | \(-0.273011\pi\) | ||||
0.654186 | + | 0.756334i | \(0.273011\pi\) | |||||||
\(774\) | −5.80579 | −0.208685 | ||||||||
\(775\) | 13.5172 | 0.485551 | ||||||||
\(776\) | −0.774045 | −0.0277866 | ||||||||
\(777\) | −3.88293 | −0.139299 | ||||||||
\(778\) | 25.3451 | 0.908665 | ||||||||
\(779\) | −6.42018 | −0.230027 | ||||||||
\(780\) | −1.82988 | −0.0655201 | ||||||||
\(781\) | −2.22935 | −0.0797726 | ||||||||
\(782\) | 4.03401 | 0.144256 | ||||||||
\(783\) | −3.60480 | −0.128825 | ||||||||
\(784\) | −4.87696 | −0.174177 | ||||||||
\(785\) | −41.9263 | −1.49641 | ||||||||
\(786\) | −11.5102 | −0.410556 | ||||||||
\(787\) | −47.6154 | −1.69730 | −0.848652 | − | 0.528951i | \(-0.822585\pi\) | ||||
−0.848652 | + | 0.528951i | \(0.822585\pi\) | |||||||
\(788\) | 5.23510 | 0.186493 | ||||||||
\(789\) | 27.5232 | 0.979850 | ||||||||
\(790\) | 14.1068 | 0.501896 | ||||||||
\(791\) | −25.1820 | −0.895370 | ||||||||
\(792\) | 0.513205 | 0.0182359 | ||||||||
\(793\) | 9.58790 | 0.340476 | ||||||||
\(794\) | 27.8148 | 0.987111 | ||||||||
\(795\) | −18.1391 | −0.643327 | ||||||||
\(796\) | 10.4226 | 0.369418 | ||||||||
\(797\) | 4.78644 | 0.169544 | 0.0847722 | − | 0.996400i | \(-0.472984\pi\) | ||||
0.0847722 | + | 0.996400i | \(0.472984\pi\) | |||||||
\(798\) | −1.64451 | −0.0582149 | ||||||||
\(799\) | −3.51373 | −0.124307 | ||||||||
\(800\) | 1.65155 | 0.0583910 | ||||||||
\(801\) | 0.196823 | 0.00695439 | ||||||||
\(802\) | 37.3383 | 1.31846 | ||||||||
\(803\) | −0.222761 | −0.00786107 | ||||||||
\(804\) | 11.1866 | 0.394522 | ||||||||
\(805\) | −13.6896 | −0.482495 | ||||||||
\(806\) | −8.18455 | −0.288288 | ||||||||
\(807\) | −15.1132 | −0.532009 | ||||||||
\(808\) | −13.7255 | −0.482862 | ||||||||
\(809\) | 33.5579 | 1.17983 | 0.589916 | − | 0.807465i | \(-0.299161\pi\) | ||||
0.589916 | + | 0.807465i | \(0.299161\pi\) | |||||||
\(810\) | 1.82988 | 0.0642953 | ||||||||
\(811\) | −6.88017 | −0.241596 | −0.120798 | − | 0.992677i | \(-0.538545\pi\) | ||||
−0.120798 | + | 0.992677i | \(0.538545\pi\) | |||||||
\(812\) | 5.25243 | 0.184324 | ||||||||
\(813\) | 8.91417 | 0.312633 | ||||||||
\(814\) | 1.36764 | 0.0479356 | ||||||||
\(815\) | 24.0305 | 0.841753 | ||||||||
\(816\) | 0.785684 | 0.0275044 | ||||||||
\(817\) | −6.55266 | −0.229249 | ||||||||
\(818\) | 18.2282 | 0.637334 | ||||||||
\(819\) | −1.45707 | −0.0509140 | ||||||||
\(820\) | −10.4091 | −0.363502 | ||||||||
\(821\) | 8.51374 | 0.297131 | 0.148566 | − | 0.988903i | \(-0.452534\pi\) | ||||
0.148566 | + | 0.988903i | \(0.452534\pi\) | |||||||
\(822\) | −2.77252 | −0.0967027 | ||||||||
\(823\) | −50.3331 | −1.75450 | −0.877252 | − | 0.480031i | \(-0.840625\pi\) | ||||
−0.877252 | + | 0.480031i | \(0.840625\pi\) | |||||||
\(824\) | 1.00000 | 0.0348367 | ||||||||
\(825\) | −0.847583 | −0.0295090 | ||||||||
\(826\) | −14.9917 | −0.521627 | ||||||||
\(827\) | −0.219786 | −0.00764271 | −0.00382135 | − | 0.999993i | \(-0.501216\pi\) | ||||
−0.00382135 | + | 0.999993i | \(0.501216\pi\) | |||||||
\(828\) | 5.13440 | 0.178433 | ||||||||
\(829\) | 3.17717 | 0.110348 | 0.0551739 | − | 0.998477i | \(-0.482429\pi\) | ||||
0.0551739 | + | 0.998477i | \(0.482429\pi\) | |||||||
\(830\) | −0.825431 | −0.0286511 | ||||||||
\(831\) | 2.29177 | 0.0795005 | ||||||||
\(832\) | −1.00000 | −0.0346688 | ||||||||
\(833\) | 3.83175 | 0.132762 | ||||||||
\(834\) | −11.4546 | −0.396641 | ||||||||
\(835\) | −23.7664 | −0.822472 | ||||||||
\(836\) | 0.579225 | 0.0200329 | ||||||||
\(837\) | 8.18455 | 0.282899 | ||||||||
\(838\) | −23.0355 | −0.795750 | ||||||||
\(839\) | 40.7319 | 1.40622 | 0.703111 | − | 0.711080i | \(-0.251794\pi\) | ||||
0.703111 | + | 0.711080i | \(0.251794\pi\) | |||||||
\(840\) | −2.66625 | −0.0919945 | ||||||||
\(841\) | −16.0054 | −0.551912 | ||||||||
\(842\) | 37.1791 | 1.28128 | ||||||||
\(843\) | −29.9684 | −1.03217 | ||||||||
\(844\) | 25.9138 | 0.891990 | ||||||||
\(845\) | −1.82988 | −0.0629497 | ||||||||
\(846\) | −4.47220 | −0.153757 | ||||||||
\(847\) | −15.6440 | −0.537533 | ||||||||
\(848\) | −9.91273 | −0.340405 | ||||||||
\(849\) | −27.0645 | −0.928852 | ||||||||
\(850\) | −1.29759 | −0.0445071 | ||||||||
\(851\) | 13.6826 | 0.469035 | ||||||||
\(852\) | −4.34398 | −0.148822 | ||||||||
\(853\) | 26.0115 | 0.890616 | 0.445308 | − | 0.895378i | \(-0.353094\pi\) | ||||
0.445308 | + | 0.895378i | \(0.353094\pi\) | |||||||
\(854\) | 13.9702 | 0.478051 | ||||||||
\(855\) | 2.06528 | 0.0706309 | ||||||||
\(856\) | −11.3226 | −0.387000 | ||||||||
\(857\) | 7.99227 | 0.273011 | 0.136505 | − | 0.990639i | \(-0.456413\pi\) | ||||
0.136505 | + | 0.990639i | \(0.456413\pi\) | |||||||
\(858\) | 0.513205 | 0.0175205 | ||||||||
\(859\) | −14.4445 | −0.492841 | −0.246421 | − | 0.969163i | \(-0.579254\pi\) | ||||
−0.246421 | + | 0.969163i | \(0.579254\pi\) | |||||||
\(860\) | −10.6239 | −0.362272 | ||||||||
\(861\) | −8.28840 | −0.282468 | ||||||||
\(862\) | 9.91314 | 0.337643 | ||||||||
\(863\) | 3.73344 | 0.127088 | 0.0635439 | − | 0.997979i | \(-0.479760\pi\) | ||||
0.0635439 | + | 0.997979i | \(0.479760\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −47.3041 | −1.60839 | ||||||||
\(866\) | −0.898037 | −0.0305165 | ||||||||
\(867\) | 16.3827 | 0.556386 | ||||||||
\(868\) | −11.9254 | −0.404775 | ||||||||
\(869\) | −3.95636 | −0.134210 | ||||||||
\(870\) | −6.59634 | −0.223637 | ||||||||
\(871\) | 11.1866 | 0.379045 | ||||||||
\(872\) | −4.23121 | −0.143287 | ||||||||
\(873\) | 0.774045 | 0.0261974 | ||||||||
\(874\) | 5.79490 | 0.196015 | ||||||||
\(875\) | 17.7347 | 0.599543 | ||||||||
\(876\) | −0.434059 | −0.0146655 | ||||||||
\(877\) | 53.4114 | 1.80357 | 0.901787 | − | 0.432181i | \(-0.142256\pi\) | ||||
0.901787 | + | 0.432181i | \(0.142256\pi\) | |||||||
\(878\) | 20.9744 | 0.707852 | ||||||||
\(879\) | 16.0466 | 0.541239 | ||||||||
\(880\) | 0.939102 | 0.0316571 | ||||||||
\(881\) | 6.04164 | 0.203548 | 0.101774 | − | 0.994808i | \(-0.467548\pi\) | ||||
0.101774 | + | 0.994808i | \(0.467548\pi\) | |||||||
\(882\) | 4.87696 | 0.164216 | ||||||||
\(883\) | −57.7805 | −1.94447 | −0.972234 | − | 0.234012i | \(-0.924814\pi\) | ||||
−0.972234 | + | 0.234012i | \(0.924814\pi\) | |||||||
\(884\) | 0.785684 | 0.0264254 | ||||||||
\(885\) | 18.8275 | 0.632879 | ||||||||
\(886\) | 12.8861 | 0.432917 | ||||||||
\(887\) | −40.6851 | −1.36607 | −0.683037 | − | 0.730384i | \(-0.739341\pi\) | ||||
−0.683037 | + | 0.730384i | \(0.739341\pi\) | |||||||
\(888\) | 2.66489 | 0.0894280 | ||||||||
\(889\) | −13.6460 | −0.457672 | ||||||||
\(890\) | 0.360162 | 0.0120727 | ||||||||
\(891\) | −0.513205 | −0.0171930 | ||||||||
\(892\) | −23.7842 | −0.796355 | ||||||||
\(893\) | −5.04751 | −0.168908 | ||||||||
\(894\) | −14.3197 | −0.478921 | ||||||||
\(895\) | −31.5230 | −1.05370 | ||||||||
\(896\) | −1.45707 | −0.0486772 | ||||||||
\(897\) | 5.13440 | 0.171433 | ||||||||
\(898\) | 1.17918 | 0.0393497 | ||||||||
\(899\) | −29.5036 | −0.984001 | ||||||||
\(900\) | −1.65155 | −0.0550516 | ||||||||
\(901\) | 7.78827 | 0.259465 | ||||||||
\(902\) | 2.91932 | 0.0972028 | ||||||||
\(903\) | −8.45943 | −0.281512 | ||||||||
\(904\) | 17.2827 | 0.574814 | ||||||||
\(905\) | −17.5126 | −0.582140 | ||||||||
\(906\) | −9.19404 | −0.305451 | ||||||||
\(907\) | 26.4114 | 0.876975 | 0.438487 | − | 0.898737i | \(-0.355514\pi\) | ||||
0.438487 | + | 0.898737i | \(0.355514\pi\) | |||||||
\(908\) | −12.9676 | −0.430345 | ||||||||
\(909\) | 13.7255 | 0.455247 | ||||||||
\(910\) | −2.66625 | −0.0883854 | ||||||||
\(911\) | −5.31146 | −0.175977 | −0.0879883 | − | 0.996122i | \(-0.528044\pi\) | ||||
−0.0879883 | + | 0.996122i | \(0.528044\pi\) | |||||||
\(912\) | 1.12864 | 0.0373731 | ||||||||
\(913\) | 0.231499 | 0.00766151 | ||||||||
\(914\) | 22.1846 | 0.733802 | ||||||||
\(915\) | −17.5447 | −0.580009 | ||||||||
\(916\) | −13.2509 | −0.437821 | ||||||||
\(917\) | −16.7711 | −0.553832 | ||||||||
\(918\) | −0.785684 | −0.0259314 | ||||||||
\(919\) | 11.1230 | 0.366915 | 0.183457 | − | 0.983028i | \(-0.441271\pi\) | ||||
0.183457 | + | 0.983028i | \(0.441271\pi\) | |||||||
\(920\) | 9.39533 | 0.309755 | ||||||||
\(921\) | 0.570165 | 0.0187876 | ||||||||
\(922\) | 1.97709 | 0.0651119 | ||||||||
\(923\) | −4.34398 | −0.142984 | ||||||||
\(924\) | 0.747774 | 0.0246000 | ||||||||
\(925\) | −4.40120 | −0.144711 | ||||||||
\(926\) | −29.1462 | −0.957802 | ||||||||
\(927\) | −1.00000 | −0.0328443 | ||||||||
\(928\) | −3.60480 | −0.118333 | ||||||||
\(929\) | −13.4206 | −0.440315 | −0.220158 | − | 0.975464i | \(-0.570657\pi\) | ||||
−0.220158 | + | 0.975464i | \(0.570657\pi\) | |||||||
\(930\) | 14.9767 | 0.491106 | ||||||||
\(931\) | 5.50434 | 0.180397 | ||||||||
\(932\) | −19.7166 | −0.645839 | ||||||||
\(933\) | 13.7186 | 0.449126 | ||||||||
\(934\) | 1.07865 | 0.0352944 | ||||||||
\(935\) | −0.737837 | −0.0241299 | ||||||||
\(936\) | 1.00000 | 0.0326860 | ||||||||
\(937\) | −15.0557 | −0.491847 | −0.245923 | − | 0.969289i | \(-0.579091\pi\) | ||||
−0.245923 | + | 0.969289i | \(0.579091\pi\) | |||||||
\(938\) | 16.2997 | 0.532203 | ||||||||
\(939\) | 8.93255 | 0.291503 | ||||||||
\(940\) | −8.18357 | −0.266919 | ||||||||
\(941\) | 5.11672 | 0.166800 | 0.0834001 | − | 0.996516i | \(-0.473422\pi\) | ||||
0.0834001 | + | 0.996516i | \(0.473422\pi\) | |||||||
\(942\) | 22.9121 | 0.746516 | ||||||||
\(943\) | 29.2066 | 0.951098 | ||||||||
\(944\) | 10.2889 | 0.334876 | ||||||||
\(945\) | 2.66625 | 0.0867332 | ||||||||
\(946\) | 2.97956 | 0.0968739 | ||||||||
\(947\) | 3.79903 | 0.123452 | 0.0617260 | − | 0.998093i | \(-0.480340\pi\) | ||||
0.0617260 | + | 0.998093i | \(0.480340\pi\) | |||||||
\(948\) | −7.70913 | −0.250381 | ||||||||
\(949\) | −0.434059 | −0.0140901 | ||||||||
\(950\) | −1.86401 | −0.0604763 | ||||||||
\(951\) | −2.51336 | −0.0815012 | ||||||||
\(952\) | 1.14479 | 0.0371030 | ||||||||
\(953\) | 47.8946 | 1.55146 | 0.775729 | − | 0.631066i | \(-0.217382\pi\) | ||||
0.775729 | + | 0.631066i | \(0.217382\pi\) | |||||||
\(954\) | 9.91273 | 0.320936 | ||||||||
\(955\) | −22.7778 | −0.737072 | ||||||||
\(956\) | −24.4023 | −0.789228 | ||||||||
\(957\) | 1.85000 | 0.0598020 | ||||||||
\(958\) | −43.5747 | −1.40783 | ||||||||
\(959\) | −4.03974 | −0.130450 | ||||||||
\(960\) | 1.82988 | 0.0590590 | ||||||||
\(961\) | 35.9868 | 1.16086 | ||||||||
\(962\) | 2.66489 | 0.0859196 | ||||||||
\(963\) | 11.3226 | 0.364867 | ||||||||
\(964\) | −7.27230 | −0.234225 | ||||||||
\(965\) | −9.80152 | −0.315522 | ||||||||
\(966\) | 7.48116 | 0.240702 | ||||||||
\(967\) | 33.3006 | 1.07087 | 0.535437 | − | 0.844575i | \(-0.320147\pi\) | ||||
0.535437 | + | 0.844575i | \(0.320147\pi\) | |||||||
\(968\) | 10.7366 | 0.345088 | ||||||||
\(969\) | −0.886755 | −0.0284867 | ||||||||
\(970\) | 1.41641 | 0.0454781 | ||||||||
\(971\) | −22.6344 | −0.726371 | −0.363186 | − | 0.931717i | \(-0.618311\pi\) | ||||
−0.363186 | + | 0.931717i | \(0.618311\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −16.6901 | −0.535061 | ||||||||
\(974\) | −2.28651 | −0.0732646 | ||||||||
\(975\) | −1.65155 | −0.0528919 | ||||||||
\(976\) | −9.58790 | −0.306901 | ||||||||
\(977\) | −55.6987 | −1.78196 | −0.890979 | − | 0.454044i | \(-0.849981\pi\) | ||||
−0.890979 | + | 0.454044i | \(0.849981\pi\) | |||||||
\(978\) | −13.1323 | −0.419925 | ||||||||
\(979\) | −0.101010 | −0.00322831 | ||||||||
\(980\) | 8.92424 | 0.285074 | ||||||||
\(981\) | 4.23121 | 0.135092 | ||||||||
\(982\) | 2.07996 | 0.0663741 | ||||||||
\(983\) | 32.7830 | 1.04562 | 0.522808 | − | 0.852450i | \(-0.324884\pi\) | ||||
0.522808 | + | 0.852450i | \(0.324884\pi\) | |||||||
\(984\) | 5.68841 | 0.181340 | ||||||||
\(985\) | −9.57959 | −0.305231 | ||||||||
\(986\) | 2.83223 | 0.0901966 | ||||||||
\(987\) | −6.51629 | −0.207416 | ||||||||
\(988\) | 1.12864 | 0.0359069 | ||||||||
\(989\) | 29.8093 | 0.947880 | ||||||||
\(990\) | −0.939102 | −0.0298466 | ||||||||
\(991\) | −26.8844 | −0.854011 | −0.427005 | − | 0.904249i | \(-0.640431\pi\) | ||||
−0.427005 | + | 0.904249i | \(0.640431\pi\) | |||||||
\(992\) | 8.18455 | 0.259860 | ||||||||
\(993\) | 6.17555 | 0.195975 | ||||||||
\(994\) | −6.32947 | −0.200759 | ||||||||
\(995\) | −19.0720 | −0.604623 | ||||||||
\(996\) | 0.451085 | 0.0142932 | ||||||||
\(997\) | 38.3685 | 1.21514 | 0.607571 | − | 0.794266i | \(-0.292144\pi\) | ||||
0.607571 | + | 0.794266i | \(0.292144\pi\) | |||||||
\(998\) | 5.05021 | 0.159862 | ||||||||
\(999\) | −2.66489 | −0.0843135 |
(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 | 8034.2.a.s.1.3 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8034.2.a.s.1.3 | ✓ | 10 | 1.1 | even | 1 | trivial |