Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6045,2,Mod(1,6045)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6045, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6045.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6045 = 3 \cdot 5 \cdot 13 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6045.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: | \(48.2695680219\) |
Analytic rank: | \(0\) |
Dimension: | \(17\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{17} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{17} - 2 x^{16} - 25 x^{15} + 47 x^{14} + 252 x^{13} - 437 x^{12} - 1319 x^{11} + 2056 x^{10} + \cdots + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Root | \(1.42963\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6045.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.42963 | 1.01090 | 0.505450 | − | 0.862856i | \(-0.331327\pi\) | ||||
0.505450 | + | 0.862856i | \(0.331327\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0.0438374 | 0.0219187 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −1.42963 | −0.583643 | ||||||||
\(7\) | −4.47441 | −1.69117 | −0.845584 | − | 0.533842i | \(-0.820748\pi\) | ||||
−0.845584 | + | 0.533842i | \(0.820748\pi\) | |||||||
\(8\) | −2.79659 | −0.988742 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.42963 | 0.452088 | ||||||||
\(11\) | −2.86949 | −0.865185 | −0.432592 | − | 0.901590i | \(-0.642401\pi\) | ||||
−0.432592 | + | 0.901590i | \(0.642401\pi\) | |||||||
\(12\) | −0.0438374 | −0.0126548 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | −6.39675 | −1.70960 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | −4.08575 | −1.02144 | ||||||||
\(17\) | −6.35442 | −1.54117 | −0.770587 | − | 0.637335i | \(-0.780037\pi\) | ||||
−0.770587 | + | 0.637335i | \(0.780037\pi\) | |||||||
\(18\) | 1.42963 | 0.336967 | ||||||||
\(19\) | 2.17027 | 0.497895 | 0.248947 | − | 0.968517i | \(-0.419915\pi\) | ||||
0.248947 | + | 0.968517i | \(0.419915\pi\) | |||||||
\(20\) | 0.0438374 | 0.00980233 | ||||||||
\(21\) | 4.47441 | 0.976397 | ||||||||
\(22\) | −4.10231 | −0.874615 | ||||||||
\(23\) | 1.22473 | 0.255374 | 0.127687 | − | 0.991815i | \(-0.459245\pi\) | ||||
0.127687 | + | 0.991815i | \(0.459245\pi\) | |||||||
\(24\) | 2.79659 | 0.570851 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 1.42963 | 0.280373 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −0.196146 | −0.0370682 | ||||||||
\(29\) | −3.42572 | −0.636141 | −0.318070 | − | 0.948067i | \(-0.603035\pi\) | ||||
−0.318070 | + | 0.948067i | \(0.603035\pi\) | |||||||
\(30\) | −1.42963 | −0.261013 | ||||||||
\(31\) | 1.00000 | 0.179605 | ||||||||
\(32\) | −0.247937 | −0.0438295 | ||||||||
\(33\) | 2.86949 | 0.499515 | ||||||||
\(34\) | −9.08446 | −1.55797 | ||||||||
\(35\) | −4.47441 | −0.756314 | ||||||||
\(36\) | 0.0438374 | 0.00730623 | ||||||||
\(37\) | −1.26022 | −0.207179 | −0.103589 | − | 0.994620i | \(-0.533033\pi\) | ||||
−0.103589 | + | 0.994620i | \(0.533033\pi\) | |||||||
\(38\) | 3.10268 | 0.503322 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | −2.79659 | −0.442179 | ||||||||
\(41\) | −8.39821 | −1.31158 | −0.655790 | − | 0.754943i | \(-0.727664\pi\) | ||||
−0.655790 | + | 0.754943i | \(0.727664\pi\) | |||||||
\(42\) | 6.39675 | 0.987039 | ||||||||
\(43\) | 6.39998 | 0.975987 | 0.487994 | − | 0.872847i | \(-0.337729\pi\) | ||||
0.487994 | + | 0.872847i | \(0.337729\pi\) | |||||||
\(44\) | −0.125791 | −0.0189637 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 1.75091 | 0.258158 | ||||||||
\(47\) | −4.53772 | −0.661894 | −0.330947 | − | 0.943649i | \(-0.607368\pi\) | ||||
−0.330947 | + | 0.943649i | \(0.607368\pi\) | |||||||
\(48\) | 4.08575 | 0.589728 | ||||||||
\(49\) | 13.0204 | 1.86005 | ||||||||
\(50\) | 1.42963 | 0.202180 | ||||||||
\(51\) | 6.35442 | 0.889797 | ||||||||
\(52\) | 0.0438374 | 0.00607915 | ||||||||
\(53\) | −9.61892 | −1.32126 | −0.660630 | − | 0.750711i | \(-0.729711\pi\) | ||||
−0.660630 | + | 0.750711i | \(0.729711\pi\) | |||||||
\(54\) | −1.42963 | −0.194548 | ||||||||
\(55\) | −2.86949 | −0.386922 | ||||||||
\(56\) | 12.5131 | 1.67213 | ||||||||
\(57\) | −2.17027 | −0.287460 | ||||||||
\(58\) | −4.89751 | −0.643075 | ||||||||
\(59\) | −6.33107 | −0.824235 | −0.412118 | − | 0.911131i | \(-0.635211\pi\) | ||||
−0.412118 | + | 0.911131i | \(0.635211\pi\) | |||||||
\(60\) | −0.0438374 | −0.00565938 | ||||||||
\(61\) | 1.51919 | 0.194513 | 0.0972564 | − | 0.995259i | \(-0.468993\pi\) | ||||
0.0972564 | + | 0.995259i | \(0.468993\pi\) | |||||||
\(62\) | 1.42963 | 0.181563 | ||||||||
\(63\) | −4.47441 | −0.563723 | ||||||||
\(64\) | 7.81705 | 0.977131 | ||||||||
\(65\) | 1.00000 | 0.124035 | ||||||||
\(66\) | 4.10231 | 0.504959 | ||||||||
\(67\) | 13.7987 | 1.68578 | 0.842889 | − | 0.538087i | \(-0.180853\pi\) | ||||
0.842889 | + | 0.538087i | \(0.180853\pi\) | |||||||
\(68\) | −0.278561 | −0.0337805 | ||||||||
\(69\) | −1.22473 | −0.147440 | ||||||||
\(70\) | −6.39675 | −0.764557 | ||||||||
\(71\) | 7.05201 | 0.836919 | 0.418460 | − | 0.908235i | \(-0.362570\pi\) | ||||
0.418460 | + | 0.908235i | \(0.362570\pi\) | |||||||
\(72\) | −2.79659 | −0.329581 | ||||||||
\(73\) | 11.0374 | 1.29183 | 0.645917 | − | 0.763407i | \(-0.276475\pi\) | ||||
0.645917 | + | 0.763407i | \(0.276475\pi\) | |||||||
\(74\) | −1.80165 | −0.209437 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0.0951390 | 0.0109132 | ||||||||
\(77\) | 12.8393 | 1.46317 | ||||||||
\(78\) | −1.42963 | −0.161874 | ||||||||
\(79\) | −9.26634 | −1.04254 | −0.521272 | − | 0.853390i | \(-0.674542\pi\) | ||||
−0.521272 | + | 0.853390i | \(0.674542\pi\) | |||||||
\(80\) | −4.08575 | −0.456801 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −12.0063 | −1.32588 | ||||||||
\(83\) | 15.6062 | 1.71300 | 0.856501 | − | 0.516145i | \(-0.172633\pi\) | ||||
0.856501 | + | 0.516145i | \(0.172633\pi\) | |||||||
\(84\) | 0.196146 | 0.0214013 | ||||||||
\(85\) | −6.35442 | −0.689234 | ||||||||
\(86\) | 9.14959 | 0.986625 | ||||||||
\(87\) | 3.42572 | 0.367276 | ||||||||
\(88\) | 8.02478 | 0.855445 | ||||||||
\(89\) | −9.24557 | −0.980029 | −0.490014 | − | 0.871714i | \(-0.663008\pi\) | ||||
−0.490014 | + | 0.871714i | \(0.663008\pi\) | |||||||
\(90\) | 1.42963 | 0.150696 | ||||||||
\(91\) | −4.47441 | −0.469046 | ||||||||
\(92\) | 0.0536890 | 0.00559746 | ||||||||
\(93\) | −1.00000 | −0.103695 | ||||||||
\(94\) | −6.48725 | −0.669109 | ||||||||
\(95\) | 2.17027 | 0.222665 | ||||||||
\(96\) | 0.247937 | 0.0253050 | ||||||||
\(97\) | 17.8425 | 1.81163 | 0.905816 | − | 0.423671i | \(-0.139259\pi\) | ||||
0.905816 | + | 0.423671i | \(0.139259\pi\) | |||||||
\(98\) | 18.6143 | 1.88033 | ||||||||
\(99\) | −2.86949 | −0.288395 | ||||||||
\(100\) | 0.0438374 | 0.00438374 | ||||||||
\(101\) | −9.77269 | −0.972419 | −0.486210 | − | 0.873842i | \(-0.661621\pi\) | ||||
−0.486210 | + | 0.873842i | \(0.661621\pi\) | |||||||
\(102\) | 9.08446 | 0.899495 | ||||||||
\(103\) | −1.18727 | −0.116985 | −0.0584925 | − | 0.998288i | \(-0.518629\pi\) | ||||
−0.0584925 | + | 0.998288i | \(0.518629\pi\) | |||||||
\(104\) | −2.79659 | −0.274228 | ||||||||
\(105\) | 4.47441 | 0.436658 | ||||||||
\(106\) | −13.7515 | −1.33566 | ||||||||
\(107\) | −4.53205 | −0.438130 | −0.219065 | − | 0.975710i | \(-0.570301\pi\) | ||||
−0.219065 | + | 0.975710i | \(0.570301\pi\) | |||||||
\(108\) | −0.0438374 | −0.00421825 | ||||||||
\(109\) | −3.16623 | −0.303270 | −0.151635 | − | 0.988437i | \(-0.548454\pi\) | ||||
−0.151635 | + | 0.988437i | \(0.548454\pi\) | |||||||
\(110\) | −4.10231 | −0.391140 | ||||||||
\(111\) | 1.26022 | 0.119615 | ||||||||
\(112\) | 18.2813 | 1.72742 | ||||||||
\(113\) | 1.99869 | 0.188021 | 0.0940105 | − | 0.995571i | \(-0.470031\pi\) | ||||
0.0940105 | + | 0.995571i | \(0.470031\pi\) | |||||||
\(114\) | −3.10268 | −0.290593 | ||||||||
\(115\) | 1.22473 | 0.114207 | ||||||||
\(116\) | −0.150175 | −0.0139434 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | −9.05108 | −0.833219 | ||||||||
\(119\) | 28.4323 | 2.60638 | ||||||||
\(120\) | 2.79659 | 0.255292 | ||||||||
\(121\) | −2.76601 | −0.251455 | ||||||||
\(122\) | 2.17188 | 0.196633 | ||||||||
\(123\) | 8.39821 | 0.757241 | ||||||||
\(124\) | 0.0438374 | 0.00393671 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −6.39675 | −0.569867 | ||||||||
\(127\) | 12.0482 | 1.06910 | 0.534552 | − | 0.845135i | \(-0.320480\pi\) | ||||
0.534552 | + | 0.845135i | \(0.320480\pi\) | |||||||
\(128\) | 11.6713 | 1.03161 | ||||||||
\(129\) | −6.39998 | −0.563486 | ||||||||
\(130\) | 1.42963 | 0.125387 | ||||||||
\(131\) | 12.8368 | 1.12156 | 0.560780 | − | 0.827965i | \(-0.310501\pi\) | ||||
0.560780 | + | 0.827965i | \(0.310501\pi\) | |||||||
\(132\) | 0.125791 | 0.0109487 | ||||||||
\(133\) | −9.71069 | −0.842024 | ||||||||
\(134\) | 19.7270 | 1.70415 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 17.7707 | 1.52382 | ||||||||
\(137\) | −10.4020 | −0.888701 | −0.444350 | − | 0.895853i | \(-0.646565\pi\) | ||||
−0.444350 | + | 0.895853i | \(0.646565\pi\) | |||||||
\(138\) | −1.75091 | −0.149047 | ||||||||
\(139\) | 9.07898 | 0.770069 | 0.385034 | − | 0.922902i | \(-0.374190\pi\) | ||||
0.385034 | + | 0.922902i | \(0.374190\pi\) | |||||||
\(140\) | −0.196146 | −0.0165774 | ||||||||
\(141\) | 4.53772 | 0.382145 | ||||||||
\(142\) | 10.0817 | 0.846041 | ||||||||
\(143\) | −2.86949 | −0.239959 | ||||||||
\(144\) | −4.08575 | −0.340479 | ||||||||
\(145\) | −3.42572 | −0.284491 | ||||||||
\(146\) | 15.7794 | 1.30592 | ||||||||
\(147\) | −13.0204 | −1.07390 | ||||||||
\(148\) | −0.0552448 | −0.00454109 | ||||||||
\(149\) | −6.37098 | −0.521931 | −0.260966 | − | 0.965348i | \(-0.584041\pi\) | ||||
−0.260966 | + | 0.965348i | \(0.584041\pi\) | |||||||
\(150\) | −1.42963 | −0.116729 | ||||||||
\(151\) | 2.49069 | 0.202689 | 0.101345 | − | 0.994851i | \(-0.467686\pi\) | ||||
0.101345 | + | 0.994851i | \(0.467686\pi\) | |||||||
\(152\) | −6.06935 | −0.492290 | ||||||||
\(153\) | −6.35442 | −0.513724 | ||||||||
\(154\) | 18.3554 | 1.47912 | ||||||||
\(155\) | 1.00000 | 0.0803219 | ||||||||
\(156\) | −0.0438374 | −0.00350980 | ||||||||
\(157\) | 18.1588 | 1.44923 | 0.724615 | − | 0.689154i | \(-0.242018\pi\) | ||||
0.724615 | + | 0.689154i | \(0.242018\pi\) | |||||||
\(158\) | −13.2474 | −1.05391 | ||||||||
\(159\) | 9.61892 | 0.762830 | ||||||||
\(160\) | −0.247937 | −0.0196012 | ||||||||
\(161\) | −5.47995 | −0.431881 | ||||||||
\(162\) | 1.42963 | 0.112322 | ||||||||
\(163\) | −2.14427 | −0.167952 | −0.0839762 | − | 0.996468i | \(-0.526762\pi\) | ||||
−0.0839762 | + | 0.996468i | \(0.526762\pi\) | |||||||
\(164\) | −0.368156 | −0.0287481 | ||||||||
\(165\) | 2.86949 | 0.223390 | ||||||||
\(166\) | 22.3111 | 1.73167 | ||||||||
\(167\) | −2.50366 | −0.193739 | −0.0968696 | − | 0.995297i | \(-0.530883\pi\) | ||||
−0.0968696 | + | 0.995297i | \(0.530883\pi\) | |||||||
\(168\) | −12.5131 | −0.965405 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −9.08446 | −0.696746 | ||||||||
\(171\) | 2.17027 | 0.165965 | ||||||||
\(172\) | 0.280558 | 0.0213924 | ||||||||
\(173\) | 19.5084 | 1.48319 | 0.741597 | − | 0.670845i | \(-0.234068\pi\) | ||||
0.741597 | + | 0.670845i | \(0.234068\pi\) | |||||||
\(174\) | 4.89751 | 0.371279 | ||||||||
\(175\) | −4.47441 | −0.338234 | ||||||||
\(176\) | 11.7240 | 0.883733 | ||||||||
\(177\) | 6.33107 | 0.475872 | ||||||||
\(178\) | −13.2177 | −0.990711 | ||||||||
\(179\) | 17.3760 | 1.29875 | 0.649373 | − | 0.760470i | \(-0.275032\pi\) | ||||
0.649373 | + | 0.760470i | \(0.275032\pi\) | |||||||
\(180\) | 0.0438374 | 0.00326744 | ||||||||
\(181\) | 14.1087 | 1.04869 | 0.524346 | − | 0.851505i | \(-0.324310\pi\) | ||||
0.524346 | + | 0.851505i | \(0.324310\pi\) | |||||||
\(182\) | −6.39675 | −0.474158 | ||||||||
\(183\) | −1.51919 | −0.112302 | ||||||||
\(184\) | −3.42506 | −0.252499 | ||||||||
\(185\) | −1.26022 | −0.0926533 | ||||||||
\(186\) | −1.42963 | −0.104825 | ||||||||
\(187\) | 18.2340 | 1.33340 | ||||||||
\(188\) | −0.198922 | −0.0145079 | ||||||||
\(189\) | 4.47441 | 0.325466 | ||||||||
\(190\) | 3.10268 | 0.225092 | ||||||||
\(191\) | −0.672943 | −0.0486924 | −0.0243462 | − | 0.999704i | \(-0.507750\pi\) | ||||
−0.0243462 | + | 0.999704i | \(0.507750\pi\) | |||||||
\(192\) | −7.81705 | −0.564147 | ||||||||
\(193\) | 11.1627 | 0.803507 | 0.401754 | − | 0.915748i | \(-0.368401\pi\) | ||||
0.401754 | + | 0.915748i | \(0.368401\pi\) | |||||||
\(194\) | 25.5082 | 1.83138 | ||||||||
\(195\) | −1.00000 | −0.0716115 | ||||||||
\(196\) | 0.570779 | 0.0407699 | ||||||||
\(197\) | −16.7711 | −1.19489 | −0.597446 | − | 0.801909i | \(-0.703818\pi\) | ||||
−0.597446 | + | 0.801909i | \(0.703818\pi\) | |||||||
\(198\) | −4.10231 | −0.291538 | ||||||||
\(199\) | 1.29278 | 0.0916425 | 0.0458212 | − | 0.998950i | \(-0.485410\pi\) | ||||
0.0458212 | + | 0.998950i | \(0.485410\pi\) | |||||||
\(200\) | −2.79659 | −0.197748 | ||||||||
\(201\) | −13.7987 | −0.973284 | ||||||||
\(202\) | −13.9713 | −0.983019 | ||||||||
\(203\) | 15.3281 | 1.07582 | ||||||||
\(204\) | 0.278561 | 0.0195032 | ||||||||
\(205\) | −8.39821 | −0.586557 | ||||||||
\(206\) | −1.69735 | −0.118260 | ||||||||
\(207\) | 1.22473 | 0.0851247 | ||||||||
\(208\) | −4.08575 | −0.283296 | ||||||||
\(209\) | −6.22758 | −0.430771 | ||||||||
\(210\) | 6.39675 | 0.441417 | ||||||||
\(211\) | −15.3133 | −1.05421 | −0.527106 | − | 0.849800i | \(-0.676723\pi\) | ||||
−0.527106 | + | 0.849800i | \(0.676723\pi\) | |||||||
\(212\) | −0.421668 | −0.0289603 | ||||||||
\(213\) | −7.05201 | −0.483195 | ||||||||
\(214\) | −6.47915 | −0.442906 | ||||||||
\(215\) | 6.39998 | 0.436475 | ||||||||
\(216\) | 2.79659 | 0.190284 | ||||||||
\(217\) | −4.47441 | −0.303743 | ||||||||
\(218\) | −4.52653 | −0.306576 | ||||||||
\(219\) | −11.0374 | −0.745841 | ||||||||
\(220\) | −0.125791 | −0.00848083 | ||||||||
\(221\) | −6.35442 | −0.427444 | ||||||||
\(222\) | 1.80165 | 0.120919 | ||||||||
\(223\) | 16.5103 | 1.10561 | 0.552806 | − | 0.833310i | \(-0.313557\pi\) | ||||
0.552806 | + | 0.833310i | \(0.313557\pi\) | |||||||
\(224\) | 1.10937 | 0.0741231 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 2.85739 | 0.190070 | ||||||||
\(227\) | 14.6303 | 0.971045 | 0.485522 | − | 0.874224i | \(-0.338629\pi\) | ||||
0.485522 | + | 0.874224i | \(0.338629\pi\) | |||||||
\(228\) | −0.0951390 | −0.00630074 | ||||||||
\(229\) | −16.1703 | −1.06856 | −0.534280 | − | 0.845307i | \(-0.679417\pi\) | ||||
−0.534280 | + | 0.845307i | \(0.679417\pi\) | |||||||
\(230\) | 1.75091 | 0.115452 | ||||||||
\(231\) | −12.8393 | −0.844764 | ||||||||
\(232\) | 9.58033 | 0.628979 | ||||||||
\(233\) | 16.8377 | 1.10307 | 0.551537 | − | 0.834150i | \(-0.314041\pi\) | ||||
0.551537 | + | 0.834150i | \(0.314041\pi\) | |||||||
\(234\) | 1.42963 | 0.0934577 | ||||||||
\(235\) | −4.53772 | −0.296008 | ||||||||
\(236\) | −0.277537 | −0.0180661 | ||||||||
\(237\) | 9.26634 | 0.601913 | ||||||||
\(238\) | 40.6476 | 2.63479 | ||||||||
\(239\) | 1.02344 | 0.0662007 | 0.0331003 | − | 0.999452i | \(-0.489462\pi\) | ||||
0.0331003 | + | 0.999452i | \(0.489462\pi\) | |||||||
\(240\) | 4.08575 | 0.263734 | ||||||||
\(241\) | −21.4332 | −1.38063 | −0.690317 | − | 0.723507i | \(-0.742529\pi\) | ||||
−0.690317 | + | 0.723507i | \(0.742529\pi\) | |||||||
\(242\) | −3.95437 | −0.254196 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0.0665974 | 0.00426346 | ||||||||
\(245\) | 13.0204 | 0.831841 | ||||||||
\(246\) | 12.0063 | 0.765495 | ||||||||
\(247\) | 2.17027 | 0.138091 | ||||||||
\(248\) | −2.79659 | −0.177583 | ||||||||
\(249\) | −15.6062 | −0.989003 | ||||||||
\(250\) | 1.42963 | 0.0904176 | ||||||||
\(251\) | −21.2923 | −1.34396 | −0.671980 | − | 0.740570i | \(-0.734556\pi\) | ||||
−0.671980 | + | 0.740570i | \(0.734556\pi\) | |||||||
\(252\) | −0.196146 | −0.0123561 | ||||||||
\(253\) | −3.51436 | −0.220946 | ||||||||
\(254\) | 17.2244 | 1.08076 | ||||||||
\(255\) | 6.35442 | 0.397929 | ||||||||
\(256\) | 1.05160 | 0.0657247 | ||||||||
\(257\) | 0.0868775 | 0.00541927 | 0.00270964 | − | 0.999996i | \(-0.499137\pi\) | ||||
0.00270964 | + | 0.999996i | \(0.499137\pi\) | |||||||
\(258\) | −9.14959 | −0.569628 | ||||||||
\(259\) | 5.63875 | 0.350375 | ||||||||
\(260\) | 0.0438374 | 0.00271868 | ||||||||
\(261\) | −3.42572 | −0.212047 | ||||||||
\(262\) | 18.3519 | 1.13379 | ||||||||
\(263\) | 11.6286 | 0.717050 | 0.358525 | − | 0.933520i | \(-0.383280\pi\) | ||||
0.358525 | + | 0.933520i | \(0.383280\pi\) | |||||||
\(264\) | −8.02478 | −0.493891 | ||||||||
\(265\) | −9.61892 | −0.590886 | ||||||||
\(266\) | −13.8827 | −0.851202 | ||||||||
\(267\) | 9.24557 | 0.565820 | ||||||||
\(268\) | 0.604898 | 0.0369500 | ||||||||
\(269\) | 2.49992 | 0.152423 | 0.0762114 | − | 0.997092i | \(-0.475718\pi\) | ||||
0.0762114 | + | 0.997092i | \(0.475718\pi\) | |||||||
\(270\) | −1.42963 | −0.0870044 | ||||||||
\(271\) | −24.5200 | −1.48949 | −0.744743 | − | 0.667351i | \(-0.767428\pi\) | ||||
−0.744743 | + | 0.667351i | \(0.767428\pi\) | |||||||
\(272\) | 25.9626 | 1.57421 | ||||||||
\(273\) | 4.47441 | 0.270804 | ||||||||
\(274\) | −14.8710 | −0.898387 | ||||||||
\(275\) | −2.86949 | −0.173037 | ||||||||
\(276\) | −0.0536890 | −0.00323170 | ||||||||
\(277\) | −32.3790 | −1.94547 | −0.972734 | − | 0.231925i | \(-0.925497\pi\) | ||||
−0.972734 | + | 0.231925i | \(0.925497\pi\) | |||||||
\(278\) | 12.9796 | 0.778463 | ||||||||
\(279\) | 1.00000 | 0.0598684 | ||||||||
\(280\) | 12.5131 | 0.747799 | ||||||||
\(281\) | 2.24157 | 0.133721 | 0.0668604 | − | 0.997762i | \(-0.478702\pi\) | ||||
0.0668604 | + | 0.997762i | \(0.478702\pi\) | |||||||
\(282\) | 6.48725 | 0.386310 | ||||||||
\(283\) | −31.3068 | −1.86100 | −0.930499 | − | 0.366295i | \(-0.880626\pi\) | ||||
−0.930499 | + | 0.366295i | \(0.880626\pi\) | |||||||
\(284\) | 0.309141 | 0.0183442 | ||||||||
\(285\) | −2.17027 | −0.128556 | ||||||||
\(286\) | −4.10231 | −0.242575 | ||||||||
\(287\) | 37.5771 | 2.21810 | ||||||||
\(288\) | −0.247937 | −0.0146098 | ||||||||
\(289\) | 23.3786 | 1.37521 | ||||||||
\(290\) | −4.89751 | −0.287592 | ||||||||
\(291\) | −17.8425 | −1.04595 | ||||||||
\(292\) | 0.483852 | 0.0283153 | ||||||||
\(293\) | −33.1790 | −1.93834 | −0.969168 | − | 0.246402i | \(-0.920752\pi\) | ||||
−0.969168 | + | 0.246402i | \(0.920752\pi\) | |||||||
\(294\) | −18.6143 | −1.08561 | ||||||||
\(295\) | −6.33107 | −0.368609 | ||||||||
\(296\) | 3.52431 | 0.204847 | ||||||||
\(297\) | 2.86949 | 0.166505 | ||||||||
\(298\) | −9.10814 | −0.527620 | ||||||||
\(299\) | 1.22473 | 0.0708280 | ||||||||
\(300\) | −0.0438374 | −0.00253095 | ||||||||
\(301\) | −28.6361 | −1.65056 | ||||||||
\(302\) | 3.56076 | 0.204899 | ||||||||
\(303\) | 9.77269 | 0.561427 | ||||||||
\(304\) | −8.86720 | −0.508569 | ||||||||
\(305\) | 1.51919 | 0.0869887 | ||||||||
\(306\) | −9.08446 | −0.519324 | ||||||||
\(307\) | −3.40426 | −0.194291 | −0.0971457 | − | 0.995270i | \(-0.530971\pi\) | ||||
−0.0971457 | + | 0.995270i | \(0.530971\pi\) | |||||||
\(308\) | 0.562841 | 0.0320708 | ||||||||
\(309\) | 1.18727 | 0.0675414 | ||||||||
\(310\) | 1.42963 | 0.0811974 | ||||||||
\(311\) | −19.1888 | −1.08810 | −0.544048 | − | 0.839054i | \(-0.683109\pi\) | ||||
−0.544048 | + | 0.839054i | \(0.683109\pi\) | |||||||
\(312\) | 2.79659 | 0.158325 | ||||||||
\(313\) | 20.4573 | 1.15632 | 0.578158 | − | 0.815925i | \(-0.303772\pi\) | ||||
0.578158 | + | 0.815925i | \(0.303772\pi\) | |||||||
\(314\) | 25.9603 | 1.46503 | ||||||||
\(315\) | −4.47441 | −0.252105 | ||||||||
\(316\) | −0.406212 | −0.0228512 | ||||||||
\(317\) | 12.9611 | 0.727968 | 0.363984 | − | 0.931405i | \(-0.381416\pi\) | ||||
0.363984 | + | 0.931405i | \(0.381416\pi\) | |||||||
\(318\) | 13.7515 | 0.771145 | ||||||||
\(319\) | 9.83009 | 0.550379 | ||||||||
\(320\) | 7.81705 | 0.436986 | ||||||||
\(321\) | 4.53205 | 0.252954 | ||||||||
\(322\) | −7.83429 | −0.436588 | ||||||||
\(323\) | −13.7908 | −0.767342 | ||||||||
\(324\) | 0.0438374 | 0.00243541 | ||||||||
\(325\) | 1.00000 | 0.0554700 | ||||||||
\(326\) | −3.06551 | −0.169783 | ||||||||
\(327\) | 3.16623 | 0.175093 | ||||||||
\(328\) | 23.4863 | 1.29682 | ||||||||
\(329\) | 20.3036 | 1.11937 | ||||||||
\(330\) | 4.10231 | 0.225825 | ||||||||
\(331\) | −6.79424 | −0.373445 | −0.186723 | − | 0.982413i | \(-0.559787\pi\) | ||||
−0.186723 | + | 0.982413i | \(0.559787\pi\) | |||||||
\(332\) | 0.684135 | 0.0375468 | ||||||||
\(333\) | −1.26022 | −0.0690597 | ||||||||
\(334\) | −3.57931 | −0.195851 | ||||||||
\(335\) | 13.7987 | 0.753903 | ||||||||
\(336\) | −18.2813 | −0.997329 | ||||||||
\(337\) | 32.0169 | 1.74407 | 0.872036 | − | 0.489442i | \(-0.162799\pi\) | ||||
0.872036 | + | 0.489442i | \(0.162799\pi\) | |||||||
\(338\) | 1.42963 | 0.0777615 | ||||||||
\(339\) | −1.99869 | −0.108554 | ||||||||
\(340\) | −0.278561 | −0.0151071 | ||||||||
\(341\) | −2.86949 | −0.155392 | ||||||||
\(342\) | 3.10268 | 0.167774 | ||||||||
\(343\) | −26.9376 | −1.45449 | ||||||||
\(344\) | −17.8981 | −0.965000 | ||||||||
\(345\) | −1.22473 | −0.0659373 | ||||||||
\(346\) | 27.8897 | 1.49936 | ||||||||
\(347\) | 30.1269 | 1.61730 | 0.808648 | − | 0.588293i | \(-0.200200\pi\) | ||||
0.808648 | + | 0.588293i | \(0.200200\pi\) | |||||||
\(348\) | 0.150175 | 0.00805021 | ||||||||
\(349\) | 14.2671 | 0.763703 | 0.381852 | − | 0.924224i | \(-0.375287\pi\) | ||||
0.381852 | + | 0.924224i | \(0.375287\pi\) | |||||||
\(350\) | −6.39675 | −0.341920 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 0.711454 | 0.0379206 | ||||||||
\(353\) | 16.9210 | 0.900614 | 0.450307 | − | 0.892874i | \(-0.351315\pi\) | ||||
0.450307 | + | 0.892874i | \(0.351315\pi\) | |||||||
\(354\) | 9.05108 | 0.481059 | ||||||||
\(355\) | 7.05201 | 0.374282 | ||||||||
\(356\) | −0.405302 | −0.0214809 | ||||||||
\(357\) | −28.4323 | −1.50480 | ||||||||
\(358\) | 24.8413 | 1.31290 | ||||||||
\(359\) | 5.63749 | 0.297535 | 0.148768 | − | 0.988872i | \(-0.452469\pi\) | ||||
0.148768 | + | 0.988872i | \(0.452469\pi\) | |||||||
\(360\) | −2.79659 | −0.147393 | ||||||||
\(361\) | −14.2899 | −0.752101 | ||||||||
\(362\) | 20.1702 | 1.06012 | ||||||||
\(363\) | 2.76601 | 0.145178 | ||||||||
\(364\) | −0.196146 | −0.0102809 | ||||||||
\(365\) | 11.0374 | 0.577726 | ||||||||
\(366\) | −2.17188 | −0.113526 | ||||||||
\(367\) | −2.66057 | −0.138880 | −0.0694402 | − | 0.997586i | \(-0.522121\pi\) | ||||
−0.0694402 | + | 0.997586i | \(0.522121\pi\) | |||||||
\(368\) | −5.00395 | −0.260849 | ||||||||
\(369\) | −8.39821 | −0.437193 | ||||||||
\(370\) | −1.80165 | −0.0936632 | ||||||||
\(371\) | 43.0390 | 2.23447 | ||||||||
\(372\) | −0.0438374 | −0.00227286 | ||||||||
\(373\) | −19.4992 | −1.00963 | −0.504816 | − | 0.863227i | \(-0.668440\pi\) | ||||
−0.504816 | + | 0.863227i | \(0.668440\pi\) | |||||||
\(374\) | 26.0678 | 1.34793 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 12.6901 | 0.654443 | ||||||||
\(377\) | −3.42572 | −0.176434 | ||||||||
\(378\) | 6.39675 | 0.329013 | ||||||||
\(379\) | 22.0893 | 1.13465 | 0.567327 | − | 0.823493i | \(-0.307978\pi\) | ||||
0.567327 | + | 0.823493i | \(0.307978\pi\) | |||||||
\(380\) | 0.0951390 | 0.00488053 | ||||||||
\(381\) | −12.0482 | −0.617248 | ||||||||
\(382\) | −0.962058 | −0.0492232 | ||||||||
\(383\) | −23.5864 | −1.20521 | −0.602603 | − | 0.798041i | \(-0.705870\pi\) | ||||
−0.602603 | + | 0.798041i | \(0.705870\pi\) | |||||||
\(384\) | −11.6713 | −0.595601 | ||||||||
\(385\) | 12.8393 | 0.654351 | ||||||||
\(386\) | 15.9585 | 0.812265 | ||||||||
\(387\) | 6.39998 | 0.325329 | ||||||||
\(388\) | 0.782169 | 0.0397086 | ||||||||
\(389\) | 9.84561 | 0.499192 | 0.249596 | − | 0.968350i | \(-0.419702\pi\) | ||||
0.249596 | + | 0.968350i | \(0.419702\pi\) | |||||||
\(390\) | −1.42963 | −0.0723920 | ||||||||
\(391\) | −7.78245 | −0.393576 | ||||||||
\(392\) | −36.4126 | −1.83911 | ||||||||
\(393\) | −12.8368 | −0.647533 | ||||||||
\(394\) | −23.9764 | −1.20792 | ||||||||
\(395\) | −9.26634 | −0.466240 | ||||||||
\(396\) | −0.125791 | −0.00632124 | ||||||||
\(397\) | 20.2353 | 1.01558 | 0.507791 | − | 0.861480i | \(-0.330462\pi\) | ||||
0.507791 | + | 0.861480i | \(0.330462\pi\) | |||||||
\(398\) | 1.84819 | 0.0926414 | ||||||||
\(399\) | 9.71069 | 0.486143 | ||||||||
\(400\) | −4.08575 | −0.204288 | ||||||||
\(401\) | 23.5324 | 1.17515 | 0.587575 | − | 0.809170i | \(-0.300083\pi\) | ||||
0.587575 | + | 0.809170i | \(0.300083\pi\) | |||||||
\(402\) | −19.7270 | −0.983893 | ||||||||
\(403\) | 1.00000 | 0.0498135 | ||||||||
\(404\) | −0.428409 | −0.0213142 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 21.9135 | 1.08755 | ||||||||
\(407\) | 3.61619 | 0.179248 | ||||||||
\(408\) | −17.7707 | −0.879780 | ||||||||
\(409\) | 0.0984305 | 0.00486707 | 0.00243354 | − | 0.999997i | \(-0.499225\pi\) | ||||
0.00243354 | + | 0.999997i | \(0.499225\pi\) | |||||||
\(410\) | −12.0063 | −0.592950 | ||||||||
\(411\) | 10.4020 | 0.513092 | ||||||||
\(412\) | −0.0520467 | −0.00256416 | ||||||||
\(413\) | 28.3278 | 1.39392 | ||||||||
\(414\) | 1.75091 | 0.0860525 | ||||||||
\(415\) | 15.6062 | 0.766078 | ||||||||
\(416\) | −0.247937 | −0.0121561 | ||||||||
\(417\) | −9.07898 | −0.444599 | ||||||||
\(418\) | −8.90313 | −0.435466 | ||||||||
\(419\) | 3.69507 | 0.180516 | 0.0902580 | − | 0.995918i | \(-0.471231\pi\) | ||||
0.0902580 | + | 0.995918i | \(0.471231\pi\) | |||||||
\(420\) | 0.196146 | 0.00957097 | ||||||||
\(421\) | −29.0769 | −1.41712 | −0.708561 | − | 0.705649i | \(-0.750655\pi\) | ||||
−0.708561 | + | 0.705649i | \(0.750655\pi\) | |||||||
\(422\) | −21.8924 | −1.06570 | ||||||||
\(423\) | −4.53772 | −0.220631 | ||||||||
\(424\) | 26.9001 | 1.30639 | ||||||||
\(425\) | −6.35442 | −0.308235 | ||||||||
\(426\) | −10.0817 | −0.488462 | ||||||||
\(427\) | −6.79750 | −0.328954 | ||||||||
\(428\) | −0.198673 | −0.00960323 | ||||||||
\(429\) | 2.86949 | 0.138540 | ||||||||
\(430\) | 9.14959 | 0.441232 | ||||||||
\(431\) | 5.34712 | 0.257562 | 0.128781 | − | 0.991673i | \(-0.458894\pi\) | ||||
0.128781 | + | 0.991673i | \(0.458894\pi\) | |||||||
\(432\) | 4.08575 | 0.196576 | ||||||||
\(433\) | −19.1267 | −0.919171 | −0.459585 | − | 0.888134i | \(-0.652002\pi\) | ||||
−0.459585 | + | 0.888134i | \(0.652002\pi\) | |||||||
\(434\) | −6.39675 | −0.307054 | ||||||||
\(435\) | 3.42572 | 0.164251 | ||||||||
\(436\) | −0.138799 | −0.00664728 | ||||||||
\(437\) | 2.65800 | 0.127149 | ||||||||
\(438\) | −15.7794 | −0.753971 | ||||||||
\(439\) | 22.6415 | 1.08062 | 0.540309 | − | 0.841466i | \(-0.318307\pi\) | ||||
0.540309 | + | 0.841466i | \(0.318307\pi\) | |||||||
\(440\) | 8.02478 | 0.382567 | ||||||||
\(441\) | 13.0204 | 0.620017 | ||||||||
\(442\) | −9.08446 | −0.432104 | ||||||||
\(443\) | 40.0442 | 1.90256 | 0.951279 | − | 0.308332i | \(-0.0997707\pi\) | ||||
0.951279 | + | 0.308332i | \(0.0997707\pi\) | |||||||
\(444\) | 0.0552448 | 0.00262180 | ||||||||
\(445\) | −9.24557 | −0.438282 | ||||||||
\(446\) | 23.6036 | 1.11766 | ||||||||
\(447\) | 6.37098 | 0.301337 | ||||||||
\(448\) | −34.9767 | −1.65249 | ||||||||
\(449\) | −8.19922 | −0.386945 | −0.193473 | − | 0.981106i | \(-0.561975\pi\) | ||||
−0.193473 | + | 0.981106i | \(0.561975\pi\) | |||||||
\(450\) | 1.42963 | 0.0673933 | ||||||||
\(451\) | 24.0986 | 1.13476 | ||||||||
\(452\) | 0.0876173 | 0.00412117 | ||||||||
\(453\) | −2.49069 | −0.117023 | ||||||||
\(454\) | 20.9158 | 0.981629 | ||||||||
\(455\) | −4.47441 | −0.209764 | ||||||||
\(456\) | 6.06935 | 0.284224 | ||||||||
\(457\) | 7.05261 | 0.329907 | 0.164954 | − | 0.986301i | \(-0.447253\pi\) | ||||
0.164954 | + | 0.986301i | \(0.447253\pi\) | |||||||
\(458\) | −23.1175 | −1.08021 | ||||||||
\(459\) | 6.35442 | 0.296599 | ||||||||
\(460\) | 0.0536890 | 0.00250326 | ||||||||
\(461\) | −25.3718 | −1.18168 | −0.590842 | − | 0.806787i | \(-0.701204\pi\) | ||||
−0.590842 | + | 0.806787i | \(0.701204\pi\) | |||||||
\(462\) | −18.3554 | −0.853971 | ||||||||
\(463\) | 10.6373 | 0.494356 | 0.247178 | − | 0.968970i | \(-0.420497\pi\) | ||||
0.247178 | + | 0.968970i | \(0.420497\pi\) | |||||||
\(464\) | 13.9967 | 0.649778 | ||||||||
\(465\) | −1.00000 | −0.0463739 | ||||||||
\(466\) | 24.0717 | 1.11510 | ||||||||
\(467\) | −8.19953 | −0.379429 | −0.189714 | − | 0.981839i | \(-0.560756\pi\) | ||||
−0.189714 | + | 0.981839i | \(0.560756\pi\) | |||||||
\(468\) | 0.0438374 | 0.00202638 | ||||||||
\(469\) | −61.7410 | −2.85094 | ||||||||
\(470\) | −6.48725 | −0.299235 | ||||||||
\(471\) | −18.1588 | −0.836713 | ||||||||
\(472\) | 17.7054 | 0.814956 | ||||||||
\(473\) | −18.3647 | −0.844409 | ||||||||
\(474\) | 13.2474 | 0.608474 | ||||||||
\(475\) | 2.17027 | 0.0995789 | ||||||||
\(476\) | 1.24640 | 0.0571285 | ||||||||
\(477\) | −9.61892 | −0.440420 | ||||||||
\(478\) | 1.46314 | 0.0669223 | ||||||||
\(479\) | 20.8450 | 0.952433 | 0.476216 | − | 0.879328i | \(-0.342008\pi\) | ||||
0.476216 | + | 0.879328i | \(0.342008\pi\) | |||||||
\(480\) | 0.247937 | 0.0113167 | ||||||||
\(481\) | −1.26022 | −0.0574611 | ||||||||
\(482\) | −30.6415 | −1.39568 | ||||||||
\(483\) | 5.47995 | 0.249346 | ||||||||
\(484\) | −0.121255 | −0.00551157 | ||||||||
\(485\) | 17.8425 | 0.810186 | ||||||||
\(486\) | −1.42963 | −0.0648493 | ||||||||
\(487\) | 26.4623 | 1.19912 | 0.599561 | − | 0.800329i | \(-0.295342\pi\) | ||||
0.599561 | + | 0.800329i | \(0.295342\pi\) | |||||||
\(488\) | −4.24855 | −0.192323 | ||||||||
\(489\) | 2.14427 | 0.0969674 | ||||||||
\(490\) | 18.6143 | 0.840908 | ||||||||
\(491\) | −28.2812 | −1.27631 | −0.638156 | − | 0.769907i | \(-0.720303\pi\) | ||||
−0.638156 | + | 0.769907i | \(0.720303\pi\) | |||||||
\(492\) | 0.368156 | 0.0165977 | ||||||||
\(493\) | 21.7685 | 0.980403 | ||||||||
\(494\) | 3.10268 | 0.139596 | ||||||||
\(495\) | −2.86949 | −0.128974 | ||||||||
\(496\) | −4.08575 | −0.183456 | ||||||||
\(497\) | −31.5536 | −1.41537 | ||||||||
\(498\) | −22.3111 | −0.999783 | ||||||||
\(499\) | −30.8430 | −1.38072 | −0.690360 | − | 0.723466i | \(-0.742548\pi\) | ||||
−0.690360 | + | 0.723466i | \(0.742548\pi\) | |||||||
\(500\) | 0.0438374 | 0.00196047 | ||||||||
\(501\) | 2.50366 | 0.111855 | ||||||||
\(502\) | −30.4401 | −1.35861 | ||||||||
\(503\) | 8.18657 | 0.365021 | 0.182511 | − | 0.983204i | \(-0.441578\pi\) | ||||
0.182511 | + | 0.983204i | \(0.441578\pi\) | |||||||
\(504\) | 12.5131 | 0.557377 | ||||||||
\(505\) | −9.77269 | −0.434879 | ||||||||
\(506\) | −5.02422 | −0.223354 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 0.528161 | 0.0234334 | ||||||||
\(509\) | 29.7467 | 1.31850 | 0.659250 | − | 0.751924i | \(-0.270874\pi\) | ||||
0.659250 | + | 0.751924i | \(0.270874\pi\) | |||||||
\(510\) | 9.08446 | 0.402267 | ||||||||
\(511\) | −49.3861 | −2.18471 | ||||||||
\(512\) | −21.8393 | −0.965170 | ||||||||
\(513\) | −2.17027 | −0.0958199 | ||||||||
\(514\) | 0.124203 | 0.00547834 | ||||||||
\(515\) | −1.18727 | −0.0523173 | ||||||||
\(516\) | −0.280558 | −0.0123509 | ||||||||
\(517\) | 13.0210 | 0.572661 | ||||||||
\(518\) | 8.06131 | 0.354194 | ||||||||
\(519\) | −19.5084 | −0.856323 | ||||||||
\(520\) | −2.79659 | −0.122638 | ||||||||
\(521\) | −5.45918 | −0.239171 | −0.119586 | − | 0.992824i | \(-0.538157\pi\) | ||||
−0.119586 | + | 0.992824i | \(0.538157\pi\) | |||||||
\(522\) | −4.89751 | −0.214358 | ||||||||
\(523\) | −8.19069 | −0.358154 | −0.179077 | − | 0.983835i | \(-0.557311\pi\) | ||||
−0.179077 | + | 0.983835i | \(0.557311\pi\) | |||||||
\(524\) | 0.562733 | 0.0245831 | ||||||||
\(525\) | 4.47441 | 0.195279 | ||||||||
\(526\) | 16.6246 | 0.724866 | ||||||||
\(527\) | −6.35442 | −0.276803 | ||||||||
\(528\) | −11.7240 | −0.510223 | ||||||||
\(529\) | −21.5000 | −0.934784 | ||||||||
\(530\) | −13.7515 | −0.597326 | ||||||||
\(531\) | −6.33107 | −0.274745 | ||||||||
\(532\) | −0.425691 | −0.0184561 | ||||||||
\(533\) | −8.39821 | −0.363767 | ||||||||
\(534\) | 13.2177 | 0.571987 | ||||||||
\(535\) | −4.53205 | −0.195938 | ||||||||
\(536\) | −38.5892 | −1.66680 | ||||||||
\(537\) | −17.3760 | −0.749831 | ||||||||
\(538\) | 3.57396 | 0.154084 | ||||||||
\(539\) | −37.3618 | −1.60929 | ||||||||
\(540\) | −0.0438374 | −0.00188646 | ||||||||
\(541\) | 8.91629 | 0.383341 | 0.191671 | − | 0.981459i | \(-0.438609\pi\) | ||||
0.191671 | + | 0.981459i | \(0.438609\pi\) | |||||||
\(542\) | −35.0545 | −1.50572 | ||||||||
\(543\) | −14.1087 | −0.605462 | ||||||||
\(544\) | 1.57550 | 0.0675489 | ||||||||
\(545\) | −3.16623 | −0.135626 | ||||||||
\(546\) | 6.39675 | 0.273755 | ||||||||
\(547\) | 18.1506 | 0.776066 | 0.388033 | − | 0.921646i | \(-0.373155\pi\) | ||||
0.388033 | + | 0.921646i | \(0.373155\pi\) | |||||||
\(548\) | −0.455995 | −0.0194791 | ||||||||
\(549\) | 1.51919 | 0.0648376 | ||||||||
\(550\) | −4.10231 | −0.174923 | ||||||||
\(551\) | −7.43475 | −0.316731 | ||||||||
\(552\) | 3.42506 | 0.145780 | ||||||||
\(553\) | 41.4614 | 1.76312 | ||||||||
\(554\) | −46.2900 | −1.96667 | ||||||||
\(555\) | 1.26022 | 0.0534934 | ||||||||
\(556\) | 0.397999 | 0.0168789 | ||||||||
\(557\) | −18.8315 | −0.797916 | −0.398958 | − | 0.916969i | \(-0.630628\pi\) | ||||
−0.398958 | + | 0.916969i | \(0.630628\pi\) | |||||||
\(558\) | 1.42963 | 0.0605210 | ||||||||
\(559\) | 6.39998 | 0.270690 | ||||||||
\(560\) | 18.2813 | 0.772528 | ||||||||
\(561\) | −18.2340 | −0.769838 | ||||||||
\(562\) | 3.20461 | 0.135178 | ||||||||
\(563\) | −30.7279 | −1.29503 | −0.647514 | − | 0.762053i | \(-0.724191\pi\) | ||||
−0.647514 | + | 0.762053i | \(0.724191\pi\) | |||||||
\(564\) | 0.198922 | 0.00837611 | ||||||||
\(565\) | 1.99869 | 0.0840856 | ||||||||
\(566\) | −44.7571 | −1.88128 | ||||||||
\(567\) | −4.47441 | −0.187908 | ||||||||
\(568\) | −19.7215 | −0.827497 | ||||||||
\(569\) | 21.3290 | 0.894160 | 0.447080 | − | 0.894494i | \(-0.352464\pi\) | ||||
0.447080 | + | 0.894494i | \(0.352464\pi\) | |||||||
\(570\) | −3.10268 | −0.129957 | ||||||||
\(571\) | 40.2346 | 1.68376 | 0.841882 | − | 0.539661i | \(-0.181448\pi\) | ||||
0.841882 | + | 0.539661i | \(0.181448\pi\) | |||||||
\(572\) | −0.125791 | −0.00525959 | ||||||||
\(573\) | 0.672943 | 0.0281126 | ||||||||
\(574\) | 53.7212 | 2.24228 | ||||||||
\(575\) | 1.22473 | 0.0510748 | ||||||||
\(576\) | 7.81705 | 0.325710 | ||||||||
\(577\) | 5.41816 | 0.225561 | 0.112781 | − | 0.993620i | \(-0.464024\pi\) | ||||
0.112781 | + | 0.993620i | \(0.464024\pi\) | |||||||
\(578\) | 33.4228 | 1.39020 | ||||||||
\(579\) | −11.1627 | −0.463905 | ||||||||
\(580\) | −0.150175 | −0.00623566 | ||||||||
\(581\) | −69.8286 | −2.89698 | ||||||||
\(582\) | −25.5082 | −1.05735 | ||||||||
\(583\) | 27.6014 | 1.14313 | ||||||||
\(584\) | −30.8671 | −1.27729 | ||||||||
\(585\) | 1.00000 | 0.0413449 | ||||||||
\(586\) | −47.4336 | −1.95946 | ||||||||
\(587\) | 29.0990 | 1.20104 | 0.600521 | − | 0.799609i | \(-0.294960\pi\) | ||||
0.600521 | + | 0.799609i | \(0.294960\pi\) | |||||||
\(588\) | −0.570779 | −0.0235385 | ||||||||
\(589\) | 2.17027 | 0.0894245 | ||||||||
\(590\) | −9.05108 | −0.372627 | ||||||||
\(591\) | 16.7711 | 0.689871 | ||||||||
\(592\) | 5.14895 | 0.211621 | ||||||||
\(593\) | −6.09138 | −0.250143 | −0.125072 | − | 0.992148i | \(-0.539916\pi\) | ||||
−0.125072 | + | 0.992148i | \(0.539916\pi\) | |||||||
\(594\) | 4.10231 | 0.168320 | ||||||||
\(595\) | 28.4323 | 1.16561 | ||||||||
\(596\) | −0.279287 | −0.0114400 | ||||||||
\(597\) | −1.29278 | −0.0529098 | ||||||||
\(598\) | 1.75091 | 0.0716000 | ||||||||
\(599\) | 29.5761 | 1.20845 | 0.604223 | − | 0.796816i | \(-0.293484\pi\) | ||||
0.604223 | + | 0.796816i | \(0.293484\pi\) | |||||||
\(600\) | 2.79659 | 0.114170 | ||||||||
\(601\) | −24.5755 | −1.00246 | −0.501228 | − | 0.865315i | \(-0.667118\pi\) | ||||
−0.501228 | + | 0.865315i | \(0.667118\pi\) | |||||||
\(602\) | −40.9390 | −1.66855 | ||||||||
\(603\) | 13.7987 | 0.561926 | ||||||||
\(604\) | 0.109185 | 0.00444268 | ||||||||
\(605\) | −2.76601 | −0.112454 | ||||||||
\(606\) | 13.9713 | 0.567546 | ||||||||
\(607\) | −11.1444 | −0.452338 | −0.226169 | − | 0.974088i | \(-0.572620\pi\) | ||||
−0.226169 | + | 0.974088i | \(0.572620\pi\) | |||||||
\(608\) | −0.538091 | −0.0218225 | ||||||||
\(609\) | −15.3281 | −0.621126 | ||||||||
\(610\) | 2.17188 | 0.0879369 | ||||||||
\(611\) | −4.53772 | −0.183576 | ||||||||
\(612\) | −0.278561 | −0.0112602 | ||||||||
\(613\) | 1.41311 | 0.0570748 | 0.0285374 | − | 0.999593i | \(-0.490915\pi\) | ||||
0.0285374 | + | 0.999593i | \(0.490915\pi\) | |||||||
\(614\) | −4.86683 | −0.196409 | ||||||||
\(615\) | 8.39821 | 0.338649 | ||||||||
\(616\) | −35.9062 | −1.44670 | ||||||||
\(617\) | −40.9484 | −1.64852 | −0.824261 | − | 0.566211i | \(-0.808409\pi\) | ||||
−0.824261 | + | 0.566211i | \(0.808409\pi\) | |||||||
\(618\) | 1.69735 | 0.0682776 | ||||||||
\(619\) | 21.2520 | 0.854190 | 0.427095 | − | 0.904207i | \(-0.359537\pi\) | ||||
0.427095 | + | 0.904207i | \(0.359537\pi\) | |||||||
\(620\) | 0.0438374 | 0.00176055 | ||||||||
\(621\) | −1.22473 | −0.0491468 | ||||||||
\(622\) | −27.4328 | −1.09996 | ||||||||
\(623\) | 41.3685 | 1.65739 | ||||||||
\(624\) | 4.08575 | 0.163561 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 29.2463 | 1.16892 | ||||||||
\(627\) | 6.22758 | 0.248706 | ||||||||
\(628\) | 0.796034 | 0.0317652 | ||||||||
\(629\) | 8.00797 | 0.319299 | ||||||||
\(630\) | −6.39675 | −0.254852 | ||||||||
\(631\) | 0.769178 | 0.0306205 | 0.0153102 | − | 0.999883i | \(-0.495126\pi\) | ||||
0.0153102 | + | 0.999883i | \(0.495126\pi\) | |||||||
\(632\) | 25.9141 | 1.03081 | ||||||||
\(633\) | 15.3133 | 0.608650 | ||||||||
\(634\) | 18.5296 | 0.735903 | ||||||||
\(635\) | 12.0482 | 0.478118 | ||||||||
\(636\) | 0.421668 | 0.0167202 | ||||||||
\(637\) | 13.0204 | 0.515886 | ||||||||
\(638\) | 14.0534 | 0.556378 | ||||||||
\(639\) | 7.05201 | 0.278973 | ||||||||
\(640\) | 11.6713 | 0.461351 | ||||||||
\(641\) | −11.3508 | −0.448328 | −0.224164 | − | 0.974551i | \(-0.571965\pi\) | ||||
−0.224164 | + | 0.974551i | \(0.571965\pi\) | |||||||
\(642\) | 6.47915 | 0.255712 | ||||||||
\(643\) | 13.3069 | 0.524772 | 0.262386 | − | 0.964963i | \(-0.415491\pi\) | ||||
0.262386 | + | 0.964963i | \(0.415491\pi\) | |||||||
\(644\) | −0.240227 | −0.00946625 | ||||||||
\(645\) | −6.39998 | −0.251999 | ||||||||
\(646\) | −19.7158 | −0.775706 | ||||||||
\(647\) | −28.5035 | −1.12059 | −0.560295 | − | 0.828293i | \(-0.689312\pi\) | ||||
−0.560295 | + | 0.828293i | \(0.689312\pi\) | |||||||
\(648\) | −2.79659 | −0.109860 | ||||||||
\(649\) | 18.1670 | 0.713116 | ||||||||
\(650\) | 1.42963 | 0.0560746 | ||||||||
\(651\) | 4.47441 | 0.175366 | ||||||||
\(652\) | −0.0939993 | −0.00368130 | ||||||||
\(653\) | 5.82199 | 0.227832 | 0.113916 | − | 0.993490i | \(-0.463661\pi\) | ||||
0.113916 | + | 0.993490i | \(0.463661\pi\) | |||||||
\(654\) | 4.52653 | 0.177001 | ||||||||
\(655\) | 12.8368 | 0.501577 | ||||||||
\(656\) | 34.3130 | 1.33970 | ||||||||
\(657\) | 11.0374 | 0.430612 | ||||||||
\(658\) | 29.0266 | 1.13158 | ||||||||
\(659\) | −24.2352 | −0.944068 | −0.472034 | − | 0.881580i | \(-0.656480\pi\) | ||||
−0.472034 | + | 0.881580i | \(0.656480\pi\) | |||||||
\(660\) | 0.125791 | 0.00489641 | ||||||||
\(661\) | −10.8467 | −0.421888 | −0.210944 | − | 0.977498i | \(-0.567654\pi\) | ||||
−0.210944 | + | 0.977498i | \(0.567654\pi\) | |||||||
\(662\) | −9.71324 | −0.377516 | ||||||||
\(663\) | 6.35442 | 0.246785 | ||||||||
\(664\) | −43.6441 | −1.69372 | ||||||||
\(665\) | −9.71069 | −0.376565 | ||||||||
\(666\) | −1.80165 | −0.0698124 | ||||||||
\(667\) | −4.19559 | −0.162454 | ||||||||
\(668\) | −0.109754 | −0.00424651 | ||||||||
\(669\) | −16.5103 | −0.638325 | ||||||||
\(670\) | 19.7270 | 0.762120 | ||||||||
\(671\) | −4.35931 | −0.168289 | ||||||||
\(672\) | −1.10937 | −0.0427950 | ||||||||
\(673\) | −26.1167 | −1.00672 | −0.503362 | − | 0.864076i | \(-0.667904\pi\) | ||||
−0.503362 | + | 0.864076i | \(0.667904\pi\) | |||||||
\(674\) | 45.7723 | 1.76308 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0.0438374 | 0.00168605 | ||||||||
\(677\) | −3.93495 | −0.151232 | −0.0756161 | − | 0.997137i | \(-0.524092\pi\) | ||||
−0.0756161 | + | 0.997137i | \(0.524092\pi\) | |||||||
\(678\) | −2.85739 | −0.109737 | ||||||||
\(679\) | −79.8347 | −3.06378 | ||||||||
\(680\) | 17.7707 | 0.681474 | ||||||||
\(681\) | −14.6303 | −0.560633 | ||||||||
\(682\) | −4.10231 | −0.157086 | ||||||||
\(683\) | 8.94105 | 0.342120 | 0.171060 | − | 0.985261i | \(-0.445281\pi\) | ||||
0.171060 | + | 0.985261i | \(0.445281\pi\) | |||||||
\(684\) | 0.0951390 | 0.00363773 | ||||||||
\(685\) | −10.4020 | −0.397439 | ||||||||
\(686\) | −38.5107 | −1.47035 | ||||||||
\(687\) | 16.1703 | 0.616934 | ||||||||
\(688\) | −26.1487 | −0.996911 | ||||||||
\(689\) | −9.61892 | −0.366452 | ||||||||
\(690\) | −1.75091 | −0.0666560 | ||||||||
\(691\) | 21.1885 | 0.806048 | 0.403024 | − | 0.915189i | \(-0.367959\pi\) | ||||
0.403024 | + | 0.915189i | \(0.367959\pi\) | |||||||
\(692\) | 0.855196 | 0.0325097 | ||||||||
\(693\) | 12.8393 | 0.487724 | ||||||||
\(694\) | 43.0703 | 1.63492 | ||||||||
\(695\) | 9.07898 | 0.344385 | ||||||||
\(696\) | −9.58033 | −0.363141 | ||||||||
\(697\) | 53.3658 | 2.02137 | ||||||||
\(698\) | 20.3967 | 0.772027 | ||||||||
\(699\) | −16.8377 | −0.636860 | ||||||||
\(700\) | −0.196146 | −0.00741364 | ||||||||
\(701\) | 16.9080 | 0.638607 | 0.319303 | − | 0.947653i | \(-0.396551\pi\) | ||||
0.319303 | + | 0.947653i | \(0.396551\pi\) | |||||||
\(702\) | −1.42963 | −0.0539578 | ||||||||
\(703\) | −2.73502 | −0.103153 | ||||||||
\(704\) | −22.4310 | −0.845399 | ||||||||
\(705\) | 4.53772 | 0.170900 | ||||||||
\(706\) | 24.1907 | 0.910431 | ||||||||
\(707\) | 43.7271 | 1.64453 | ||||||||
\(708\) | 0.277537 | 0.0104305 | ||||||||
\(709\) | 35.8118 | 1.34494 | 0.672470 | − | 0.740125i | \(-0.265233\pi\) | ||||
0.672470 | + | 0.740125i | \(0.265233\pi\) | |||||||
\(710\) | 10.0817 | 0.378361 | ||||||||
\(711\) | −9.26634 | −0.347515 | ||||||||
\(712\) | 25.8560 | 0.968996 | ||||||||
\(713\) | 1.22473 | 0.0458665 | ||||||||
\(714\) | −40.6476 | −1.52120 | ||||||||
\(715\) | −2.86949 | −0.107313 | ||||||||
\(716\) | 0.761719 | 0.0284668 | ||||||||
\(717\) | −1.02344 | −0.0382210 | ||||||||
\(718\) | 8.05951 | 0.300778 | ||||||||
\(719\) | 50.8109 | 1.89493 | 0.947464 | − | 0.319862i | \(-0.103637\pi\) | ||||
0.947464 | + | 0.319862i | \(0.103637\pi\) | |||||||
\(720\) | −4.08575 | −0.152267 | ||||||||
\(721\) | 5.31233 | 0.197841 | ||||||||
\(722\) | −20.4293 | −0.760299 | ||||||||
\(723\) | 21.4332 | 0.797109 | ||||||||
\(724\) | 0.618488 | 0.0229859 | ||||||||
\(725\) | −3.42572 | −0.127228 | ||||||||
\(726\) | 3.95437 | 0.146760 | ||||||||
\(727\) | 11.1760 | 0.414496 | 0.207248 | − | 0.978288i | \(-0.433549\pi\) | ||||
0.207248 | + | 0.978288i | \(0.433549\pi\) | |||||||
\(728\) | 12.5131 | 0.463765 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 15.7794 | 0.584023 | ||||||||
\(731\) | −40.6681 | −1.50417 | ||||||||
\(732\) | −0.0665974 | −0.00246151 | ||||||||
\(733\) | −34.4498 | −1.27243 | −0.636217 | − | 0.771510i | \(-0.719502\pi\) | ||||
−0.636217 | + | 0.771510i | \(0.719502\pi\) | |||||||
\(734\) | −3.80362 | −0.140394 | ||||||||
\(735\) | −13.0204 | −0.480263 | ||||||||
\(736\) | −0.303656 | −0.0111929 | ||||||||
\(737\) | −39.5952 | −1.45851 | ||||||||
\(738\) | −12.0063 | −0.441959 | ||||||||
\(739\) | 12.8309 | 0.471994 | 0.235997 | − | 0.971754i | \(-0.424164\pi\) | ||||
0.235997 | + | 0.971754i | \(0.424164\pi\) | |||||||
\(740\) | −0.0552448 | −0.00203084 | ||||||||
\(741\) | −2.17027 | −0.0797270 | ||||||||
\(742\) | 61.5298 | 2.25883 | ||||||||
\(743\) | −46.6391 | −1.71102 | −0.855512 | − | 0.517783i | \(-0.826757\pi\) | ||||
−0.855512 | + | 0.517783i | \(0.826757\pi\) | |||||||
\(744\) | 2.79659 | 0.102528 | ||||||||
\(745\) | −6.37098 | −0.233415 | ||||||||
\(746\) | −27.8767 | −1.02064 | ||||||||
\(747\) | 15.6062 | 0.571001 | ||||||||
\(748\) | 0.799329 | 0.0292264 | ||||||||
\(749\) | 20.2783 | 0.740952 | ||||||||
\(750\) | −1.42963 | −0.0522026 | ||||||||
\(751\) | −44.3609 | −1.61875 | −0.809376 | − | 0.587291i | \(-0.800194\pi\) | ||||
−0.809376 | + | 0.587291i | \(0.800194\pi\) | |||||||
\(752\) | 18.5400 | 0.676084 | ||||||||
\(753\) | 21.2923 | 0.775935 | ||||||||
\(754\) | −4.89751 | −0.178357 | ||||||||
\(755\) | 2.49069 | 0.0906454 | ||||||||
\(756\) | 0.196146 | 0.00713378 | ||||||||
\(757\) | −25.2583 | −0.918028 | −0.459014 | − | 0.888429i | \(-0.651797\pi\) | ||||
−0.459014 | + | 0.888429i | \(0.651797\pi\) | |||||||
\(758\) | 31.5795 | 1.14702 | ||||||||
\(759\) | 3.51436 | 0.127563 | ||||||||
\(760\) | −6.06935 | −0.220159 | ||||||||
\(761\) | 28.2240 | 1.02312 | 0.511560 | − | 0.859247i | \(-0.329068\pi\) | ||||
0.511560 | + | 0.859247i | \(0.329068\pi\) | |||||||
\(762\) | −17.2244 | −0.623976 | ||||||||
\(763\) | 14.1670 | 0.512881 | ||||||||
\(764\) | −0.0295000 | −0.00106727 | ||||||||
\(765\) | −6.35442 | −0.229745 | ||||||||
\(766\) | −33.7197 | −1.21834 | ||||||||
\(767\) | −6.33107 | −0.228602 | ||||||||
\(768\) | −1.05160 | −0.0379462 | ||||||||
\(769\) | −14.7443 | −0.531692 | −0.265846 | − | 0.964016i | \(-0.585651\pi\) | ||||
−0.265846 | + | 0.964016i | \(0.585651\pi\) | |||||||
\(770\) | 18.3554 | 0.661483 | ||||||||
\(771\) | −0.0868775 | −0.00312882 | ||||||||
\(772\) | 0.489342 | 0.0176118 | ||||||||
\(773\) | −37.3466 | −1.34326 | −0.671632 | − | 0.740885i | \(-0.734407\pi\) | ||||
−0.671632 | + | 0.740885i | \(0.734407\pi\) | |||||||
\(774\) | 9.14959 | 0.328875 | ||||||||
\(775\) | 1.00000 | 0.0359211 | ||||||||
\(776\) | −49.8981 | −1.79124 | ||||||||
\(777\) | −5.63875 | −0.202289 | ||||||||
\(778\) | 14.0756 | 0.504633 | ||||||||
\(779\) | −18.2264 | −0.653029 | ||||||||
\(780\) | −0.0438374 | −0.00156963 | ||||||||
\(781\) | −20.2357 | −0.724090 | ||||||||
\(782\) | −11.1260 | −0.397865 | ||||||||
\(783\) | 3.42572 | 0.122425 | ||||||||
\(784\) | −53.1980 | −1.89993 | ||||||||
\(785\) | 18.1588 | 0.648115 | ||||||||
\(786\) | −18.3519 | −0.654591 | ||||||||
\(787\) | 46.1830 | 1.64625 | 0.823123 | − | 0.567863i | \(-0.192230\pi\) | ||||
0.823123 | + | 0.567863i | \(0.192230\pi\) | |||||||
\(788\) | −0.735201 | −0.0261904 | ||||||||
\(789\) | −11.6286 | −0.413989 | ||||||||
\(790\) | −13.2474 | −0.471322 | ||||||||
\(791\) | −8.94297 | −0.317975 | ||||||||
\(792\) | 8.02478 | 0.285148 | ||||||||
\(793\) | 1.51919 | 0.0539481 | ||||||||
\(794\) | 28.9290 | 1.02665 | ||||||||
\(795\) | 9.61892 | 0.341148 | ||||||||
\(796\) | 0.0566719 | 0.00200868 | ||||||||
\(797\) | −49.0737 | −1.73828 | −0.869139 | − | 0.494567i | \(-0.835327\pi\) | ||||
−0.869139 | + | 0.494567i | \(0.835327\pi\) | |||||||
\(798\) | 13.8827 | 0.491442 | ||||||||
\(799\) | 28.8346 | 1.02009 | ||||||||
\(800\) | −0.247937 | −0.00876591 | ||||||||
\(801\) | −9.24557 | −0.326676 | ||||||||
\(802\) | 33.6425 | 1.18796 | ||||||||
\(803\) | −31.6719 | −1.11768 | ||||||||
\(804\) | −0.604898 | −0.0213331 | ||||||||
\(805\) | −5.47995 | −0.193143 | ||||||||
\(806\) | 1.42963 | 0.0503565 | ||||||||
\(807\) | −2.49992 | −0.0880014 | ||||||||
\(808\) | 27.3302 | 0.961472 | ||||||||
\(809\) | −27.4385 | −0.964686 | −0.482343 | − | 0.875982i | \(-0.660214\pi\) | ||||
−0.482343 | + | 0.875982i | \(0.660214\pi\) | |||||||
\(810\) | 1.42963 | 0.0502320 | ||||||||
\(811\) | 2.50285 | 0.0878868 | 0.0439434 | − | 0.999034i | \(-0.486008\pi\) | ||||
0.0439434 | + | 0.999034i | \(0.486008\pi\) | |||||||
\(812\) | 0.671943 | 0.0235806 | ||||||||
\(813\) | 24.5200 | 0.859955 | ||||||||
\(814\) | 5.16981 | 0.181202 | ||||||||
\(815\) | −2.14427 | −0.0751106 | ||||||||
\(816\) | −25.9626 | −0.908872 | ||||||||
\(817\) | 13.8897 | 0.485939 | ||||||||
\(818\) | 0.140719 | 0.00492013 | ||||||||
\(819\) | −4.47441 | −0.156349 | ||||||||
\(820\) | −0.368156 | −0.0128565 | ||||||||
\(821\) | 38.6751 | 1.34977 | 0.674886 | − | 0.737922i | \(-0.264193\pi\) | ||||
0.674886 | + | 0.737922i | \(0.264193\pi\) | |||||||
\(822\) | 14.8710 | 0.518684 | ||||||||
\(823\) | 21.7932 | 0.759663 | 0.379832 | − | 0.925056i | \(-0.375982\pi\) | ||||
0.379832 | + | 0.925056i | \(0.375982\pi\) | |||||||
\(824\) | 3.32030 | 0.115668 | ||||||||
\(825\) | 2.86949 | 0.0999029 | ||||||||
\(826\) | 40.4982 | 1.40911 | ||||||||
\(827\) | 2.81434 | 0.0978642 | 0.0489321 | − | 0.998802i | \(-0.484418\pi\) | ||||
0.0489321 | + | 0.998802i | \(0.484418\pi\) | |||||||
\(828\) | 0.0536890 | 0.00186582 | ||||||||
\(829\) | 12.5417 | 0.435592 | 0.217796 | − | 0.975994i | \(-0.430113\pi\) | ||||
0.217796 | + | 0.975994i | \(0.430113\pi\) | |||||||
\(830\) | 22.3111 | 0.774428 | ||||||||
\(831\) | 32.3790 | 1.12322 | ||||||||
\(832\) | 7.81705 | 0.271007 | ||||||||
\(833\) | −82.7369 | −2.86666 | ||||||||
\(834\) | −12.9796 | −0.449446 | ||||||||
\(835\) | −2.50366 | −0.0866428 | ||||||||
\(836\) | −0.273001 | −0.00944193 | ||||||||
\(837\) | −1.00000 | −0.0345651 | ||||||||
\(838\) | 5.28258 | 0.182484 | ||||||||
\(839\) | 7.22990 | 0.249604 | 0.124802 | − | 0.992182i | \(-0.460170\pi\) | ||||
0.124802 | + | 0.992182i | \(0.460170\pi\) | |||||||
\(840\) | −12.5131 | −0.431742 | ||||||||
\(841\) | −17.2644 | −0.595325 | ||||||||
\(842\) | −41.5692 | −1.43257 | ||||||||
\(843\) | −2.24157 | −0.0772038 | ||||||||
\(844\) | −0.671295 | −0.0231069 | ||||||||
\(845\) | 1.00000 | 0.0344010 | ||||||||
\(846\) | −6.48725 | −0.223036 | ||||||||
\(847\) | 12.3763 | 0.425253 | ||||||||
\(848\) | 39.3005 | 1.34959 | ||||||||
\(849\) | 31.3068 | 1.07445 | ||||||||
\(850\) | −9.08446 | −0.311594 | ||||||||
\(851\) | −1.54343 | −0.0529081 | ||||||||
\(852\) | −0.309141 | −0.0105910 | ||||||||
\(853\) | −54.6938 | −1.87268 | −0.936340 | − | 0.351093i | \(-0.885810\pi\) | ||||
−0.936340 | + | 0.351093i | \(0.885810\pi\) | |||||||
\(854\) | −9.71789 | −0.332539 | ||||||||
\(855\) | 2.17027 | 0.0742218 | ||||||||
\(856\) | 12.6743 | 0.433198 | ||||||||
\(857\) | 28.4315 | 0.971201 | 0.485601 | − | 0.874181i | \(-0.338601\pi\) | ||||
0.485601 | + | 0.874181i | \(0.338601\pi\) | |||||||
\(858\) | 4.10231 | 0.140051 | ||||||||
\(859\) | 38.3246 | 1.30762 | 0.653810 | − | 0.756659i | \(-0.273170\pi\) | ||||
0.653810 | + | 0.756659i | \(0.273170\pi\) | |||||||
\(860\) | 0.280558 | 0.00956695 | ||||||||
\(861\) | −37.5771 | −1.28062 | ||||||||
\(862\) | 7.64440 | 0.260369 | ||||||||
\(863\) | 50.7220 | 1.72660 | 0.863298 | − | 0.504694i | \(-0.168395\pi\) | ||||
0.863298 | + | 0.504694i | \(0.168395\pi\) | |||||||
\(864\) | 0.247937 | 0.00843500 | ||||||||
\(865\) | 19.5084 | 0.663305 | ||||||||
\(866\) | −27.3441 | −0.929190 | ||||||||
\(867\) | −23.3786 | −0.793980 | ||||||||
\(868\) | −0.196146 | −0.00665764 | ||||||||
\(869\) | 26.5897 | 0.901994 | ||||||||
\(870\) | 4.89751 | 0.166041 | ||||||||
\(871\) | 13.7987 | 0.467551 | ||||||||
\(872\) | 8.85464 | 0.299856 | ||||||||
\(873\) | 17.8425 | 0.603877 | ||||||||
\(874\) | 3.79995 | 0.128535 | ||||||||
\(875\) | −4.47441 | −0.151263 | ||||||||
\(876\) | −0.483852 | −0.0163479 | ||||||||
\(877\) | 19.7064 | 0.665438 | 0.332719 | − | 0.943026i | \(-0.392034\pi\) | ||||
0.332719 | + | 0.943026i | \(0.392034\pi\) | |||||||
\(878\) | 32.3689 | 1.09240 | ||||||||
\(879\) | 33.1790 | 1.11910 | ||||||||
\(880\) | 11.7240 | 0.395217 | ||||||||
\(881\) | −42.1093 | −1.41870 | −0.709349 | − | 0.704857i | \(-0.751011\pi\) | ||||
−0.709349 | + | 0.704857i | \(0.751011\pi\) | |||||||
\(882\) | 18.6143 | 0.626775 | ||||||||
\(883\) | 8.01981 | 0.269888 | 0.134944 | − | 0.990853i | \(-0.456915\pi\) | ||||
0.134944 | + | 0.990853i | \(0.456915\pi\) | |||||||
\(884\) | −0.278561 | −0.00936902 | ||||||||
\(885\) | 6.33107 | 0.212817 | ||||||||
\(886\) | 57.2483 | 1.92330 | ||||||||
\(887\) | −7.04175 | −0.236439 | −0.118219 | − | 0.992988i | \(-0.537719\pi\) | ||||
−0.118219 | + | 0.992988i | \(0.537719\pi\) | |||||||
\(888\) | −3.52431 | −0.118268 | ||||||||
\(889\) | −53.9086 | −1.80804 | ||||||||
\(890\) | −13.2177 | −0.443059 | ||||||||
\(891\) | −2.86949 | −0.0961316 | ||||||||
\(892\) | 0.723769 | 0.0242336 | ||||||||
\(893\) | −9.84809 | −0.329554 | ||||||||
\(894\) | 9.10814 | 0.304622 | ||||||||
\(895\) | 17.3760 | 0.580816 | ||||||||
\(896\) | −52.2224 | −1.74463 | ||||||||
\(897\) | −1.22473 | −0.0408926 | ||||||||
\(898\) | −11.7218 | −0.391163 | ||||||||
\(899\) | −3.42572 | −0.114254 | ||||||||
\(900\) | 0.0438374 | 0.00146125 | ||||||||
\(901\) | 61.1227 | 2.03629 | ||||||||
\(902\) | 34.4521 | 1.14713 | ||||||||
\(903\) | 28.6361 | 0.952951 | ||||||||
\(904\) | −5.58951 | −0.185904 | ||||||||
\(905\) | 14.1087 | 0.468989 | ||||||||
\(906\) | −3.56076 | −0.118298 | ||||||||
\(907\) | −5.01811 | −0.166624 | −0.0833118 | − | 0.996524i | \(-0.526550\pi\) | ||||
−0.0833118 | + | 0.996524i | \(0.526550\pi\) | |||||||
\(908\) | 0.641352 | 0.0212840 | ||||||||
\(909\) | −9.77269 | −0.324140 | ||||||||
\(910\) | −6.39675 | −0.212050 | ||||||||
\(911\) | 16.3645 | 0.542180 | 0.271090 | − | 0.962554i | \(-0.412616\pi\) | ||||
0.271090 | + | 0.962554i | \(0.412616\pi\) | |||||||
\(912\) | 8.86720 | 0.293622 | ||||||||
\(913\) | −44.7819 | −1.48206 | ||||||||
\(914\) | 10.0826 | 0.333503 | ||||||||
\(915\) | −1.51919 | −0.0502230 | ||||||||
\(916\) | −0.708861 | −0.0234214 | ||||||||
\(917\) | −57.4373 | −1.89675 | ||||||||
\(918\) | 9.08446 | 0.299832 | ||||||||
\(919\) | 24.2024 | 0.798362 | 0.399181 | − | 0.916872i | \(-0.369294\pi\) | ||||
0.399181 | + | 0.916872i | \(0.369294\pi\) | |||||||
\(920\) | −3.42506 | −0.112921 | ||||||||
\(921\) | 3.40426 | 0.112174 | ||||||||
\(922\) | −36.2723 | −1.19456 | ||||||||
\(923\) | 7.05201 | 0.232120 | ||||||||
\(924\) | −0.562841 | −0.0185161 | ||||||||
\(925\) | −1.26022 | −0.0414358 | ||||||||
\(926\) | 15.2073 | 0.499744 | ||||||||
\(927\) | −1.18727 | −0.0389950 | ||||||||
\(928\) | 0.849364 | 0.0278817 | ||||||||
\(929\) | −3.59466 | −0.117937 | −0.0589685 | − | 0.998260i | \(-0.518781\pi\) | ||||
−0.0589685 | + | 0.998260i | \(0.518781\pi\) | |||||||
\(930\) | −1.42963 | −0.0468794 | ||||||||
\(931\) | 28.2577 | 0.926110 | ||||||||
\(932\) | 0.738120 | 0.0241779 | ||||||||
\(933\) | 19.1888 | 0.628212 | ||||||||
\(934\) | −11.7223 | −0.383565 | ||||||||
\(935\) | 18.2340 | 0.596314 | ||||||||
\(936\) | −2.79659 | −0.0914093 | ||||||||
\(937\) | 48.1916 | 1.57435 | 0.787175 | − | 0.616730i | \(-0.211543\pi\) | ||||
0.787175 | + | 0.616730i | \(0.211543\pi\) | |||||||
\(938\) | −88.2667 | −2.88201 | ||||||||
\(939\) | −20.4573 | −0.667599 | ||||||||
\(940\) | −0.198922 | −0.00648811 | ||||||||
\(941\) | 9.75622 | 0.318044 | 0.159022 | − | 0.987275i | \(-0.449166\pi\) | ||||
0.159022 | + | 0.987275i | \(0.449166\pi\) | |||||||
\(942\) | −25.9603 | −0.845833 | ||||||||
\(943\) | −10.2855 | −0.334944 | ||||||||
\(944\) | 25.8672 | 0.841905 | ||||||||
\(945\) | 4.47441 | 0.145553 | ||||||||
\(946\) | −26.2547 | −0.853613 | ||||||||
\(947\) | −0.0463227 | −0.00150529 | −0.000752643 | − | 1.00000i | \(-0.500240\pi\) | ||||
−0.000752643 | 1.00000i | \(0.500240\pi\) | ||||||||
\(948\) | 0.406212 | 0.0131932 | ||||||||
\(949\) | 11.0374 | 0.358290 | ||||||||
\(950\) | 3.10268 | 0.100664 | ||||||||
\(951\) | −12.9611 | −0.420292 | ||||||||
\(952\) | −79.5133 | −2.57704 | ||||||||
\(953\) | −29.3351 | −0.950257 | −0.475129 | − | 0.879916i | \(-0.657598\pi\) | ||||
−0.475129 | + | 0.879916i | \(0.657598\pi\) | |||||||
\(954\) | −13.7515 | −0.445221 | ||||||||
\(955\) | −0.672943 | −0.0217759 | ||||||||
\(956\) | 0.0448648 | 0.00145103 | ||||||||
\(957\) | −9.83009 | −0.317762 | ||||||||
\(958\) | 29.8006 | 0.962814 | ||||||||
\(959\) | 46.5427 | 1.50294 | ||||||||
\(960\) | −7.81705 | −0.252294 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | −1.80165 | −0.0580874 | ||||||||
\(963\) | −4.53205 | −0.146043 | ||||||||
\(964\) | −0.939575 | −0.0302617 | ||||||||
\(965\) | 11.1627 | 0.359339 | ||||||||
\(966\) | 7.83429 | 0.252064 | ||||||||
\(967\) | 0.665964 | 0.0214160 | 0.0107080 | − | 0.999943i | \(-0.496591\pi\) | ||||
0.0107080 | + | 0.999943i | \(0.496591\pi\) | |||||||
\(968\) | 7.73538 | 0.248625 | ||||||||
\(969\) | 13.7908 | 0.443025 | ||||||||
\(970\) | 25.5082 | 0.819017 | ||||||||
\(971\) | 14.2368 | 0.456882 | 0.228441 | − | 0.973558i | \(-0.426637\pi\) | ||||
0.228441 | + | 0.973558i | \(0.426637\pi\) | |||||||
\(972\) | −0.0438374 | −0.00140608 | ||||||||
\(973\) | −40.6231 | −1.30232 | ||||||||
\(974\) | 37.8313 | 1.21219 | ||||||||
\(975\) | −1.00000 | −0.0320256 | ||||||||
\(976\) | −6.20705 | −0.198683 | ||||||||
\(977\) | 7.56467 | 0.242015 | 0.121008 | − | 0.992652i | \(-0.461387\pi\) | ||||
0.121008 | + | 0.992652i | \(0.461387\pi\) | |||||||
\(978\) | 3.06551 | 0.0980243 | ||||||||
\(979\) | 26.5301 | 0.847906 | ||||||||
\(980\) | 0.570779 | 0.0182329 | ||||||||
\(981\) | −3.16623 | −0.101090 | ||||||||
\(982\) | −40.4316 | −1.29022 | ||||||||
\(983\) | 21.2236 | 0.676929 | 0.338465 | − | 0.940979i | \(-0.390092\pi\) | ||||
0.338465 | + | 0.940979i | \(0.390092\pi\) | |||||||
\(984\) | −23.4863 | −0.748717 | ||||||||
\(985\) | −16.7711 | −0.534372 | ||||||||
\(986\) | 31.1208 | 0.991089 | ||||||||
\(987\) | −20.3036 | −0.646271 | ||||||||
\(988\) | 0.0951390 | 0.00302678 | ||||||||
\(989\) | 7.83825 | 0.249242 | ||||||||
\(990\) | −4.10231 | −0.130380 | ||||||||
\(991\) | 25.2831 | 0.803145 | 0.401572 | − | 0.915827i | \(-0.368464\pi\) | ||||
0.401572 | + | 0.915827i | \(0.368464\pi\) | |||||||
\(992\) | −0.247937 | −0.00787202 | ||||||||
\(993\) | 6.79424 | 0.215609 | ||||||||
\(994\) | −45.1099 | −1.43080 | ||||||||
\(995\) | 1.29278 | 0.0409838 | ||||||||
\(996\) | −0.684135 | −0.0216776 | ||||||||
\(997\) | 9.55424 | 0.302586 | 0.151293 | − | 0.988489i | \(-0.451656\pi\) | ||||
0.151293 | + | 0.988489i | \(0.451656\pi\) | |||||||
\(998\) | −44.0940 | −1.39577 | ||||||||
\(999\) | 1.26022 | 0.0398716 |
(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 | 6045.2.a.bh.1.13 | ✓ | 17 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6045.2.a.bh.1.13 | ✓ | 17 | 1.1 | even | 1 | trivial |