Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6027,2,Mod(1,6027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6027 = 3 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6027.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.1258372982\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 3x^{6} - 6x^{5} + 16x^{4} + 14x^{3} - 20x^{2} - 10x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 861) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-1.32604\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6027.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.32604 | 1.64476 | 0.822379 | − | 0.568941i | \(-0.192647\pi\) | ||||
0.822379 | + | 0.568941i | \(0.192647\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 3.41045 | 1.70523 | ||||||||
\(5\) | −0.0978008 | −0.0437378 | −0.0218689 | − | 0.999761i | \(-0.506962\pi\) | ||||
−0.0218689 | + | 0.999761i | \(0.506962\pi\) | |||||||
\(6\) | −2.32604 | −0.949601 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 3.28076 | 1.15993 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.227488 | −0.0719381 | ||||||||
\(11\) | −0.582422 | −0.175607 | −0.0878035 | − | 0.996138i | \(-0.527985\pi\) | ||||
−0.0878035 | + | 0.996138i | \(0.527985\pi\) | |||||||
\(12\) | −3.41045 | −0.984513 | ||||||||
\(13\) | −3.95129 | −1.09589 | −0.547946 | − | 0.836514i | \(-0.684590\pi\) | ||||
−0.547946 | + | 0.836514i | \(0.684590\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.0978008 | 0.0252520 | ||||||||
\(16\) | 0.810278 | 0.202570 | ||||||||
\(17\) | 3.98906 | 0.967489 | 0.483745 | − | 0.875209i | \(-0.339276\pi\) | ||||
0.483745 | + | 0.875209i | \(0.339276\pi\) | |||||||
\(18\) | 2.32604 | 0.548252 | ||||||||
\(19\) | 4.96154 | 1.13826 | 0.569128 | − | 0.822249i | \(-0.307281\pi\) | ||||
0.569128 | + | 0.822249i | \(0.307281\pi\) | |||||||
\(20\) | −0.333545 | −0.0745829 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.35474 | −0.288831 | ||||||||
\(23\) | 7.14176 | 1.48916 | 0.744580 | − | 0.667533i | \(-0.232650\pi\) | ||||
0.744580 | + | 0.667533i | \(0.232650\pi\) | |||||||
\(24\) | −3.28076 | −0.669683 | ||||||||
\(25\) | −4.99044 | −0.998087 | ||||||||
\(26\) | −9.19086 | −1.80248 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.15477 | 0.400131 | 0.200065 | − | 0.979783i | \(-0.435885\pi\) | ||||
0.200065 | + | 0.979783i | \(0.435885\pi\) | |||||||
\(30\) | 0.227488 | 0.0415335 | ||||||||
\(31\) | 3.43209 | 0.616422 | 0.308211 | − | 0.951318i | \(-0.400270\pi\) | ||||
0.308211 | + | 0.951318i | \(0.400270\pi\) | |||||||
\(32\) | −4.67679 | −0.826748 | ||||||||
\(33\) | 0.582422 | 0.101387 | ||||||||
\(34\) | 9.27871 | 1.59129 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.41045 | 0.568409 | ||||||||
\(37\) | −2.57517 | −0.423355 | −0.211678 | − | 0.977340i | \(-0.567893\pi\) | ||||
−0.211678 | + | 0.977340i | \(0.567893\pi\) | |||||||
\(38\) | 11.5407 | 1.87215 | ||||||||
\(39\) | 3.95129 | 0.632713 | ||||||||
\(40\) | −0.320861 | −0.0507326 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.59636 | 0.548440 | 0.274220 | − | 0.961667i | \(-0.411580\pi\) | ||||
0.274220 | + | 0.961667i | \(0.411580\pi\) | |||||||
\(44\) | −1.98632 | −0.299450 | ||||||||
\(45\) | −0.0978008 | −0.0145793 | ||||||||
\(46\) | 16.6120 | 2.44931 | ||||||||
\(47\) | 2.71266 | 0.395682 | 0.197841 | − | 0.980234i | \(-0.436607\pi\) | ||||
0.197841 | + | 0.980234i | \(0.436607\pi\) | |||||||
\(48\) | −0.810278 | −0.116954 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −11.6079 | −1.64161 | ||||||||
\(51\) | −3.98906 | −0.558580 | ||||||||
\(52\) | −13.4757 | −1.86874 | ||||||||
\(53\) | 12.7249 | 1.74790 | 0.873952 | − | 0.486012i | \(-0.161549\pi\) | ||||
0.873952 | + | 0.486012i | \(0.161549\pi\) | |||||||
\(54\) | −2.32604 | −0.316534 | ||||||||
\(55\) | 0.0569614 | 0.00768067 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.96154 | −0.657172 | ||||||||
\(58\) | 5.01208 | 0.658118 | ||||||||
\(59\) | 2.48011 | 0.322882 | 0.161441 | − | 0.986882i | \(-0.448386\pi\) | ||||
0.161441 | + | 0.986882i | \(0.448386\pi\) | |||||||
\(60\) | 0.333545 | 0.0430604 | ||||||||
\(61\) | 12.5132 | 1.60215 | 0.801076 | − | 0.598563i | \(-0.204261\pi\) | ||||
0.801076 | + | 0.598563i | \(0.204261\pi\) | |||||||
\(62\) | 7.98318 | 1.01387 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −12.4989 | −1.56237 | ||||||||
\(65\) | 0.386440 | 0.0479319 | ||||||||
\(66\) | 1.35474 | 0.166757 | ||||||||
\(67\) | −5.99051 | −0.731858 | −0.365929 | − | 0.930643i | \(-0.619249\pi\) | ||||
−0.365929 | + | 0.930643i | \(0.619249\pi\) | |||||||
\(68\) | 13.6045 | 1.64979 | ||||||||
\(69\) | −7.14176 | −0.859767 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.246186 | −0.0292169 | −0.0146084 | − | 0.999893i | \(-0.504650\pi\) | ||||
−0.0146084 | + | 0.999893i | \(0.504650\pi\) | |||||||
\(72\) | 3.28076 | 0.386642 | ||||||||
\(73\) | 3.11493 | 0.364575 | 0.182287 | − | 0.983245i | \(-0.441650\pi\) | ||||
0.182287 | + | 0.983245i | \(0.441650\pi\) | |||||||
\(74\) | −5.98994 | −0.696316 | ||||||||
\(75\) | 4.99044 | 0.576246 | ||||||||
\(76\) | 16.9211 | 1.94098 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 9.19086 | 1.04066 | ||||||||
\(79\) | 2.27858 | 0.256360 | 0.128180 | − | 0.991751i | \(-0.459086\pi\) | ||||
0.128180 | + | 0.991751i | \(0.459086\pi\) | |||||||
\(80\) | −0.0792458 | −0.00885995 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −2.32604 | −0.256868 | ||||||||
\(83\) | 6.99712 | 0.768034 | 0.384017 | − | 0.923326i | \(-0.374540\pi\) | ||||
0.384017 | + | 0.923326i | \(0.374540\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.390133 | −0.0423159 | ||||||||
\(86\) | 8.36527 | 0.902050 | ||||||||
\(87\) | −2.15477 | −0.231016 | ||||||||
\(88\) | −1.91079 | −0.203691 | ||||||||
\(89\) | −4.58259 | −0.485754 | −0.242877 | − | 0.970057i | \(-0.578091\pi\) | ||||
−0.242877 | + | 0.970057i | \(0.578091\pi\) | |||||||
\(90\) | −0.227488 | −0.0239794 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 24.3566 | 2.53936 | ||||||||
\(93\) | −3.43209 | −0.355892 | ||||||||
\(94\) | 6.30975 | 0.650801 | ||||||||
\(95\) | −0.485242 | −0.0497848 | ||||||||
\(96\) | 4.67679 | 0.477323 | ||||||||
\(97\) | 10.2253 | 1.03822 | 0.519109 | − | 0.854708i | \(-0.326264\pi\) | ||||
0.519109 | + | 0.854708i | \(0.326264\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.582422 | −0.0585357 | ||||||||
\(100\) | −17.0196 | −1.70196 | ||||||||
\(101\) | 9.97712 | 0.992761 | 0.496380 | − | 0.868105i | \(-0.334662\pi\) | ||||
0.496380 | + | 0.868105i | \(0.334662\pi\) | |||||||
\(102\) | −9.27871 | −0.918729 | ||||||||
\(103\) | −10.2103 | −1.00605 | −0.503023 | − | 0.864273i | \(-0.667779\pi\) | ||||
−0.503023 | + | 0.864273i | \(0.667779\pi\) | |||||||
\(104\) | −12.9633 | −1.27115 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 29.5987 | 2.87488 | ||||||||
\(107\) | 14.5942 | 1.41087 | 0.705436 | − | 0.708773i | \(-0.250751\pi\) | ||||
0.705436 | + | 0.708773i | \(0.250751\pi\) | |||||||
\(108\) | −3.41045 | −0.328171 | ||||||||
\(109\) | 1.33598 | 0.127964 | 0.0639820 | − | 0.997951i | \(-0.479620\pi\) | ||||
0.0639820 | + | 0.997951i | \(0.479620\pi\) | |||||||
\(110\) | 0.132494 | 0.0126328 | ||||||||
\(111\) | 2.57517 | 0.244424 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.0543 | −1.03990 | −0.519952 | − | 0.854195i | \(-0.674050\pi\) | ||||
−0.519952 | + | 0.854195i | \(0.674050\pi\) | |||||||
\(114\) | −11.5407 | −1.08089 | ||||||||
\(115\) | −0.698470 | −0.0651327 | ||||||||
\(116\) | 7.34874 | 0.682313 | ||||||||
\(117\) | −3.95129 | −0.365297 | ||||||||
\(118\) | 5.76882 | 0.531063 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0.320861 | 0.0292905 | ||||||||
\(121\) | −10.6608 | −0.969162 | ||||||||
\(122\) | 29.1062 | 2.63515 | ||||||||
\(123\) | 1.00000 | 0.0901670 | ||||||||
\(124\) | 11.7050 | 1.05114 | ||||||||
\(125\) | 0.977072 | 0.0873920 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.7303 | 1.48457 | 0.742287 | − | 0.670082i | \(-0.233741\pi\) | ||||
0.742287 | + | 0.670082i | \(0.233741\pi\) | |||||||
\(128\) | −19.7194 | −1.74297 | ||||||||
\(129\) | −3.59636 | −0.316642 | ||||||||
\(130\) | 0.898873 | 0.0788364 | ||||||||
\(131\) | 12.9305 | 1.12975 | 0.564874 | − | 0.825177i | \(-0.308925\pi\) | ||||
0.564874 | + | 0.825177i | \(0.308925\pi\) | |||||||
\(132\) | 1.98632 | 0.172887 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −13.9342 | −1.20373 | ||||||||
\(135\) | 0.0978008 | 0.00841735 | ||||||||
\(136\) | 13.0872 | 1.12222 | ||||||||
\(137\) | 21.9250 | 1.87318 | 0.936588 | − | 0.350433i | \(-0.113966\pi\) | ||||
0.936588 | + | 0.350433i | \(0.113966\pi\) | |||||||
\(138\) | −16.6120 | −1.41411 | ||||||||
\(139\) | −10.9812 | −0.931417 | −0.465709 | − | 0.884938i | \(-0.654201\pi\) | ||||
−0.465709 | + | 0.884938i | \(0.654201\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.71266 | −0.228447 | ||||||||
\(142\) | −0.572638 | −0.0480547 | ||||||||
\(143\) | 2.30132 | 0.192446 | ||||||||
\(144\) | 0.810278 | 0.0675232 | ||||||||
\(145\) | −0.210738 | −0.0175009 | ||||||||
\(146\) | 7.24544 | 0.599637 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −8.78249 | −0.721916 | ||||||||
\(149\) | −8.01535 | −0.656643 | −0.328321 | − | 0.944566i | \(-0.606483\pi\) | ||||
−0.328321 | + | 0.944566i | \(0.606483\pi\) | |||||||
\(150\) | 11.6079 | 0.947784 | ||||||||
\(151\) | 8.48267 | 0.690310 | 0.345155 | − | 0.938546i | \(-0.387826\pi\) | ||||
0.345155 | + | 0.938546i | \(0.387826\pi\) | |||||||
\(152\) | 16.2776 | 1.32029 | ||||||||
\(153\) | 3.98906 | 0.322496 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.335661 | −0.0269610 | ||||||||
\(156\) | 13.4757 | 1.07892 | ||||||||
\(157\) | −11.6378 | −0.928795 | −0.464398 | − | 0.885627i | \(-0.653729\pi\) | ||||
−0.464398 | + | 0.885627i | \(0.653729\pi\) | |||||||
\(158\) | 5.30006 | 0.421650 | ||||||||
\(159\) | −12.7249 | −1.00915 | ||||||||
\(160\) | 0.457394 | 0.0361601 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 2.32604 | 0.182751 | ||||||||
\(163\) | −17.5198 | −1.37225 | −0.686127 | − | 0.727482i | \(-0.740691\pi\) | ||||
−0.686127 | + | 0.727482i | \(0.740691\pi\) | |||||||
\(164\) | −3.41045 | −0.266312 | ||||||||
\(165\) | −0.0569614 | −0.00443444 | ||||||||
\(166\) | 16.2756 | 1.26323 | ||||||||
\(167\) | −13.2750 | −1.02725 | −0.513626 | − | 0.858014i | \(-0.671698\pi\) | ||||
−0.513626 | + | 0.858014i | \(0.671698\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.61273 | 0.200979 | ||||||||
\(170\) | −0.907465 | −0.0695994 | ||||||||
\(171\) | 4.96154 | 0.379418 | ||||||||
\(172\) | 12.2652 | 0.935214 | ||||||||
\(173\) | −20.1883 | −1.53489 | −0.767444 | − | 0.641116i | \(-0.778472\pi\) | ||||
−0.767444 | + | 0.641116i | \(0.778472\pi\) | |||||||
\(174\) | −5.01208 | −0.379965 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.471924 | −0.0355726 | ||||||||
\(177\) | −2.48011 | −0.186416 | ||||||||
\(178\) | −10.6593 | −0.798947 | ||||||||
\(179\) | 0.347661 | 0.0259854 | 0.0129927 | − | 0.999916i | \(-0.495864\pi\) | ||||
0.0129927 | + | 0.999916i | \(0.495864\pi\) | |||||||
\(180\) | −0.333545 | −0.0248610 | ||||||||
\(181\) | 1.09311 | 0.0812503 | 0.0406251 | − | 0.999174i | \(-0.487065\pi\) | ||||
0.0406251 | + | 0.999174i | \(0.487065\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12.5132 | −0.925003 | ||||||||
\(184\) | 23.4304 | 1.72732 | ||||||||
\(185\) | 0.251853 | 0.0185166 | ||||||||
\(186\) | −7.98318 | −0.585355 | ||||||||
\(187\) | −2.32332 | −0.169898 | ||||||||
\(188\) | 9.25140 | 0.674728 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.12869 | −0.0818839 | ||||||||
\(191\) | −7.50981 | −0.543391 | −0.271695 | − | 0.962383i | \(-0.587584\pi\) | ||||
−0.271695 | + | 0.962383i | \(0.587584\pi\) | |||||||
\(192\) | 12.4989 | 0.902034 | ||||||||
\(193\) | −1.85067 | −0.133214 | −0.0666071 | − | 0.997779i | \(-0.521217\pi\) | ||||
−0.0666071 | + | 0.997779i | \(0.521217\pi\) | |||||||
\(194\) | 23.7843 | 1.70762 | ||||||||
\(195\) | −0.386440 | −0.0276735 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.9892 | 1.35293 | 0.676464 | − | 0.736476i | \(-0.263512\pi\) | ||||
0.676464 | + | 0.736476i | \(0.263512\pi\) | |||||||
\(198\) | −1.35474 | −0.0962769 | ||||||||
\(199\) | 19.0072 | 1.34738 | 0.673691 | − | 0.739013i | \(-0.264708\pi\) | ||||
0.673691 | + | 0.739013i | \(0.264708\pi\) | |||||||
\(200\) | −16.3724 | −1.15771 | ||||||||
\(201\) | 5.99051 | 0.422538 | ||||||||
\(202\) | 23.2072 | 1.63285 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −13.6045 | −0.952506 | ||||||||
\(205\) | 0.0978008 | 0.00683070 | ||||||||
\(206\) | −23.7495 | −1.65470 | ||||||||
\(207\) | 7.14176 | 0.496387 | ||||||||
\(208\) | −3.20165 | −0.221994 | ||||||||
\(209\) | −2.88971 | −0.199886 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.1684 | 1.59498 | 0.797489 | − | 0.603334i | \(-0.206161\pi\) | ||||
0.797489 | + | 0.603334i | \(0.206161\pi\) | |||||||
\(212\) | 43.3978 | 2.98057 | ||||||||
\(213\) | 0.246186 | 0.0168684 | ||||||||
\(214\) | 33.9466 | 2.32054 | ||||||||
\(215\) | −0.351727 | −0.0239876 | ||||||||
\(216\) | −3.28076 | −0.223228 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 3.10755 | 0.210470 | ||||||||
\(219\) | −3.11493 | −0.210487 | ||||||||
\(220\) | 0.194264 | 0.0130973 | ||||||||
\(221\) | −15.7620 | −1.06026 | ||||||||
\(222\) | 5.98994 | 0.402018 | ||||||||
\(223\) | 7.61730 | 0.510092 | 0.255046 | − | 0.966929i | \(-0.417909\pi\) | ||||
0.255046 | + | 0.966929i | \(0.417909\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.99044 | −0.332696 | ||||||||
\(226\) | −25.7128 | −1.71039 | ||||||||
\(227\) | 20.5812 | 1.36603 | 0.683013 | − | 0.730407i | \(-0.260669\pi\) | ||||
0.683013 | + | 0.730407i | \(0.260669\pi\) | |||||||
\(228\) | −16.9211 | −1.12063 | ||||||||
\(229\) | −10.9117 | −0.721063 | −0.360531 | − | 0.932747i | \(-0.617405\pi\) | ||||
−0.360531 | + | 0.932747i | \(0.617405\pi\) | |||||||
\(230\) | −1.62467 | −0.107127 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.06929 | 0.464122 | ||||||||
\(233\) | 19.1646 | 1.25552 | 0.627758 | − | 0.778409i | \(-0.283973\pi\) | ||||
0.627758 | + | 0.778409i | \(0.283973\pi\) | |||||||
\(234\) | −9.19086 | −0.600825 | ||||||||
\(235\) | −0.265300 | −0.0173063 | ||||||||
\(236\) | 8.45828 | 0.550587 | ||||||||
\(237\) | −2.27858 | −0.148010 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 23.8019 | 1.53961 | 0.769807 | − | 0.638277i | \(-0.220352\pi\) | ||||
0.769807 | + | 0.638277i | \(0.220352\pi\) | |||||||
\(240\) | 0.0792458 | 0.00511530 | ||||||||
\(241\) | 20.7925 | 1.33936 | 0.669681 | − | 0.742649i | \(-0.266431\pi\) | ||||
0.669681 | + | 0.742649i | \(0.266431\pi\) | |||||||
\(242\) | −24.7974 | −1.59404 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 42.6757 | 2.73203 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.32604 | 0.148303 | ||||||||
\(247\) | −19.6045 | −1.24740 | ||||||||
\(248\) | 11.2599 | 0.715004 | ||||||||
\(249\) | −6.99712 | −0.443424 | ||||||||
\(250\) | 2.27271 | 0.143739 | ||||||||
\(251\) | −26.1674 | −1.65167 | −0.825835 | − | 0.563912i | \(-0.809296\pi\) | ||||
−0.825835 | + | 0.563912i | \(0.809296\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.15952 | −0.261507 | ||||||||
\(254\) | 38.9153 | 2.44176 | ||||||||
\(255\) | 0.390133 | 0.0244311 | ||||||||
\(256\) | −20.8703 | −1.30439 | ||||||||
\(257\) | −26.6554 | −1.66272 | −0.831359 | − | 0.555735i | \(-0.812437\pi\) | ||||
−0.831359 | + | 0.555735i | \(0.812437\pi\) | |||||||
\(258\) | −8.36527 | −0.520799 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1.31793 | 0.0817348 | ||||||||
\(261\) | 2.15477 | 0.133377 | ||||||||
\(262\) | 30.0769 | 1.85816 | ||||||||
\(263\) | −14.4582 | −0.891533 | −0.445767 | − | 0.895149i | \(-0.647069\pi\) | ||||
−0.445767 | + | 0.895149i | \(0.647069\pi\) | |||||||
\(264\) | 1.91079 | 0.117601 | ||||||||
\(265\) | −1.24451 | −0.0764495 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.58259 | 0.280450 | ||||||||
\(268\) | −20.4304 | −1.24798 | ||||||||
\(269\) | 0.964369 | 0.0587986 | 0.0293993 | − | 0.999568i | \(-0.490641\pi\) | ||||
0.0293993 | + | 0.999568i | \(0.490641\pi\) | |||||||
\(270\) | 0.227488 | 0.0138445 | ||||||||
\(271\) | −23.3860 | −1.42060 | −0.710298 | − | 0.703901i | \(-0.751440\pi\) | ||||
−0.710298 | + | 0.703901i | \(0.751440\pi\) | |||||||
\(272\) | 3.23225 | 0.195984 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 50.9983 | 3.08092 | ||||||||
\(275\) | 2.90654 | 0.175271 | ||||||||
\(276\) | −24.3566 | −1.46610 | ||||||||
\(277\) | 1.72664 | 0.103744 | 0.0518720 | − | 0.998654i | \(-0.483481\pi\) | ||||
0.0518720 | + | 0.998654i | \(0.483481\pi\) | |||||||
\(278\) | −25.5428 | −1.53196 | ||||||||
\(279\) | 3.43209 | 0.205474 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.4609 | −0.922322 | −0.461161 | − | 0.887316i | \(-0.652567\pi\) | ||||
−0.461161 | + | 0.887316i | \(0.652567\pi\) | |||||||
\(282\) | −6.30975 | −0.375740 | ||||||||
\(283\) | 1.79710 | 0.106826 | 0.0534132 | − | 0.998572i | \(-0.482990\pi\) | ||||
0.0534132 | + | 0.998572i | \(0.482990\pi\) | |||||||
\(284\) | −0.839605 | −0.0498214 | ||||||||
\(285\) | 0.485242 | 0.0287433 | ||||||||
\(286\) | 5.35296 | 0.316527 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −4.67679 | −0.275583 | ||||||||
\(289\) | −1.08739 | −0.0639643 | ||||||||
\(290\) | −0.490185 | −0.0287847 | ||||||||
\(291\) | −10.2253 | −0.599415 | ||||||||
\(292\) | 10.6233 | 0.621682 | ||||||||
\(293\) | −12.3247 | −0.720018 | −0.360009 | − | 0.932949i | \(-0.617226\pi\) | ||||
−0.360009 | + | 0.932949i | \(0.617226\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.242556 | −0.0141222 | ||||||||
\(296\) | −8.44852 | −0.491060 | ||||||||
\(297\) | 0.582422 | 0.0337956 | ||||||||
\(298\) | −18.6440 | −1.08002 | ||||||||
\(299\) | −28.2192 | −1.63196 | ||||||||
\(300\) | 17.0196 | 0.982629 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 19.7310 | 1.13539 | ||||||||
\(303\) | −9.97712 | −0.573171 | ||||||||
\(304\) | 4.02023 | 0.230576 | ||||||||
\(305\) | −1.22380 | −0.0700746 | ||||||||
\(306\) | 9.27871 | 0.530428 | ||||||||
\(307\) | 8.89441 | 0.507631 | 0.253815 | − | 0.967253i | \(-0.418314\pi\) | ||||
0.253815 | + | 0.967253i | \(0.418314\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.2103 | 0.580841 | ||||||||
\(310\) | −0.780761 | −0.0443443 | ||||||||
\(311\) | −7.36424 | −0.417588 | −0.208794 | − | 0.977960i | \(-0.566954\pi\) | ||||
−0.208794 | + | 0.977960i | \(0.566954\pi\) | |||||||
\(312\) | 12.9633 | 0.733900 | ||||||||
\(313\) | −9.03728 | −0.510817 | −0.255409 | − | 0.966833i | \(-0.582210\pi\) | ||||
−0.255409 | + | 0.966833i | \(0.582210\pi\) | |||||||
\(314\) | −27.0699 | −1.52764 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.77098 | 0.437152 | ||||||||
\(317\) | −0.357106 | −0.0200571 | −0.0100285 | − | 0.999950i | \(-0.503192\pi\) | ||||
−0.0100285 | + | 0.999950i | \(0.503192\pi\) | |||||||
\(318\) | −29.5987 | −1.65981 | ||||||||
\(319\) | −1.25499 | −0.0702658 | ||||||||
\(320\) | 1.22241 | 0.0683346 | ||||||||
\(321\) | −14.5942 | −0.814568 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 19.7919 | 1.10125 | ||||||||
\(324\) | 3.41045 | 0.189470 | ||||||||
\(325\) | 19.7187 | 1.09380 | ||||||||
\(326\) | −40.7516 | −2.25702 | ||||||||
\(327\) | −1.33598 | −0.0738801 | ||||||||
\(328\) | −3.28076 | −0.181150 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −0.132494 | −0.00729357 | ||||||||
\(331\) | −11.3319 | −0.622858 | −0.311429 | − | 0.950269i | \(-0.600808\pi\) | ||||
−0.311429 | + | 0.950269i | \(0.600808\pi\) | |||||||
\(332\) | 23.8633 | 1.30967 | ||||||||
\(333\) | −2.57517 | −0.141118 | ||||||||
\(334\) | −30.8782 | −1.68958 | ||||||||
\(335\) | 0.585877 | 0.0320099 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.50898 | −0.300093 | −0.150047 | − | 0.988679i | \(-0.547942\pi\) | ||||
−0.150047 | + | 0.988679i | \(0.547942\pi\) | |||||||
\(338\) | 6.07730 | 0.330562 | ||||||||
\(339\) | 11.0543 | 0.600389 | ||||||||
\(340\) | −1.33053 | −0.0721581 | ||||||||
\(341\) | −1.99893 | −0.108248 | ||||||||
\(342\) | 11.5407 | 0.624051 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 11.7988 | 0.636149 | ||||||||
\(345\) | 0.698470 | 0.0376044 | ||||||||
\(346\) | −46.9587 | −2.52452 | ||||||||
\(347\) | 8.24953 | 0.442858 | 0.221429 | − | 0.975177i | \(-0.428928\pi\) | ||||
0.221429 | + | 0.975177i | \(0.428928\pi\) | |||||||
\(348\) | −7.34874 | −0.393934 | ||||||||
\(349\) | 16.3307 | 0.874162 | 0.437081 | − | 0.899422i | \(-0.356012\pi\) | ||||
0.437081 | + | 0.899422i | \(0.356012\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.95129 | 0.210904 | ||||||||
\(352\) | 2.72387 | 0.145183 | ||||||||
\(353\) | −9.97755 | −0.531051 | −0.265526 | − | 0.964104i | \(-0.585545\pi\) | ||||
−0.265526 | + | 0.964104i | \(0.585545\pi\) | |||||||
\(354\) | −5.76882 | −0.306609 | ||||||||
\(355\) | 0.0240772 | 0.00127788 | ||||||||
\(356\) | −15.6287 | −0.828320 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.808672 | 0.0427397 | ||||||||
\(359\) | 12.3374 | 0.651141 | 0.325571 | − | 0.945518i | \(-0.394444\pi\) | ||||
0.325571 | + | 0.945518i | \(0.394444\pi\) | |||||||
\(360\) | −0.320861 | −0.0169109 | ||||||||
\(361\) | 5.61687 | 0.295625 | ||||||||
\(362\) | 2.54262 | 0.133637 | ||||||||
\(363\) | 10.6608 | 0.559546 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.304642 | −0.0159457 | ||||||||
\(366\) | −29.1062 | −1.52140 | ||||||||
\(367\) | −10.5212 | −0.549204 | −0.274602 | − | 0.961558i | \(-0.588546\pi\) | ||||
−0.274602 | + | 0.961558i | \(0.588546\pi\) | |||||||
\(368\) | 5.78682 | 0.301659 | ||||||||
\(369\) | −1.00000 | −0.0520579 | ||||||||
\(370\) | 0.585821 | 0.0304554 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −11.7050 | −0.606876 | ||||||||
\(373\) | −23.2163 | −1.20209 | −0.601046 | − | 0.799214i | \(-0.705249\pi\) | ||||
−0.601046 | + | 0.799214i | \(0.705249\pi\) | |||||||
\(374\) | −5.40413 | −0.279441 | ||||||||
\(375\) | −0.977072 | −0.0504558 | ||||||||
\(376\) | 8.89960 | 0.458962 | ||||||||
\(377\) | −8.51413 | −0.438500 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.66512 | −0.445097 | −0.222549 | − | 0.974922i | \(-0.571438\pi\) | ||||
−0.222549 | + | 0.974922i | \(0.571438\pi\) | |||||||
\(380\) | −1.65490 | −0.0848943 | ||||||||
\(381\) | −16.7303 | −0.857119 | ||||||||
\(382\) | −17.4681 | −0.893746 | ||||||||
\(383\) | −7.45570 | −0.380969 | −0.190484 | − | 0.981690i | \(-0.561006\pi\) | ||||
−0.190484 | + | 0.981690i | \(0.561006\pi\) | |||||||
\(384\) | 19.7194 | 1.00630 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.30473 | −0.219105 | ||||||||
\(387\) | 3.59636 | 0.182813 | ||||||||
\(388\) | 34.8727 | 1.77040 | ||||||||
\(389\) | −8.66253 | −0.439208 | −0.219604 | − | 0.975589i | \(-0.570476\pi\) | ||||
−0.219604 | + | 0.975589i | \(0.570476\pi\) | |||||||
\(390\) | −0.898873 | −0.0455162 | ||||||||
\(391\) | 28.4889 | 1.44075 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −12.9305 | −0.652260 | ||||||||
\(394\) | 44.1697 | 2.22524 | ||||||||
\(395\) | −0.222847 | −0.0112126 | ||||||||
\(396\) | −1.98632 | −0.0998165 | ||||||||
\(397\) | −14.6556 | −0.735546 | −0.367773 | − | 0.929916i | \(-0.619880\pi\) | ||||
−0.367773 | + | 0.929916i | \(0.619880\pi\) | |||||||
\(398\) | 44.2114 | 2.21611 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.04364 | −0.202182 | ||||||||
\(401\) | −14.6728 | −0.732722 | −0.366361 | − | 0.930473i | \(-0.619397\pi\) | ||||
−0.366361 | + | 0.930473i | \(0.619397\pi\) | |||||||
\(402\) | 13.9342 | 0.694973 | ||||||||
\(403\) | −13.5612 | −0.675532 | ||||||||
\(404\) | 34.0265 | 1.69288 | ||||||||
\(405\) | −0.0978008 | −0.00485976 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.49984 | 0.0743441 | ||||||||
\(408\) | −13.0872 | −0.647911 | ||||||||
\(409\) | 2.76287 | 0.136615 | 0.0683075 | − | 0.997664i | \(-0.478240\pi\) | ||||
0.0683075 | + | 0.997664i | \(0.478240\pi\) | |||||||
\(410\) | 0.227488 | 0.0112348 | ||||||||
\(411\) | −21.9250 | −1.08148 | ||||||||
\(412\) | −34.8216 | −1.71554 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 16.6120 | 0.816436 | ||||||||
\(415\) | −0.684324 | −0.0335921 | ||||||||
\(416\) | 18.4794 | 0.906026 | ||||||||
\(417\) | 10.9812 | 0.537754 | ||||||||
\(418\) | −6.72158 | −0.328763 | ||||||||
\(419\) | −30.1742 | −1.47411 | −0.737054 | − | 0.675834i | \(-0.763784\pi\) | ||||
−0.737054 | + | 0.675834i | \(0.763784\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.93295 | −0.337891 | −0.168946 | − | 0.985625i | \(-0.554036\pi\) | ||||
−0.168946 | + | 0.985625i | \(0.554036\pi\) | |||||||
\(422\) | 53.8906 | 2.62335 | ||||||||
\(423\) | 2.71266 | 0.131894 | ||||||||
\(424\) | 41.7475 | 2.02744 | ||||||||
\(425\) | −19.9071 | −0.965639 | ||||||||
\(426\) | 0.572638 | 0.0277444 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 49.7727 | 2.40586 | ||||||||
\(429\) | −2.30132 | −0.111109 | ||||||||
\(430\) | −0.818130 | −0.0394537 | ||||||||
\(431\) | −18.9984 | −0.915119 | −0.457559 | − | 0.889179i | \(-0.651276\pi\) | ||||
−0.457559 | + | 0.889179i | \(0.651276\pi\) | |||||||
\(432\) | −0.810278 | −0.0389845 | ||||||||
\(433\) | 28.4832 | 1.36881 | 0.684407 | − | 0.729100i | \(-0.260061\pi\) | ||||
0.684407 | + | 0.729100i | \(0.260061\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.210738 | 0.0101041 | ||||||||
\(436\) | 4.55631 | 0.218208 | ||||||||
\(437\) | 35.4341 | 1.69504 | ||||||||
\(438\) | −7.24544 | −0.346200 | ||||||||
\(439\) | −18.3921 | −0.877809 | −0.438904 | − | 0.898534i | \(-0.644633\pi\) | ||||
−0.438904 | + | 0.898534i | \(0.644633\pi\) | |||||||
\(440\) | 0.186877 | 0.00890900 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −36.6629 | −1.74388 | ||||||||
\(443\) | 5.49006 | 0.260841 | 0.130420 | − | 0.991459i | \(-0.458367\pi\) | ||||
0.130420 | + | 0.991459i | \(0.458367\pi\) | |||||||
\(444\) | 8.78249 | 0.416798 | ||||||||
\(445\) | 0.448181 | 0.0212458 | ||||||||
\(446\) | 17.7181 | 0.838978 | ||||||||
\(447\) | 8.01535 | 0.379113 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −25.1872 | −1.18866 | −0.594329 | − | 0.804222i | \(-0.702582\pi\) | ||||
−0.594329 | + | 0.804222i | \(0.702582\pi\) | |||||||
\(450\) | −11.6079 | −0.547204 | ||||||||
\(451\) | 0.582422 | 0.0274252 | ||||||||
\(452\) | −37.7003 | −1.77327 | ||||||||
\(453\) | −8.48267 | −0.398551 | ||||||||
\(454\) | 47.8728 | 2.24678 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −16.2776 | −0.762270 | ||||||||
\(457\) | 37.8522 | 1.77065 | 0.885326 | − | 0.464971i | \(-0.153935\pi\) | ||||
0.885326 | + | 0.464971i | \(0.153935\pi\) | |||||||
\(458\) | −25.3809 | −1.18597 | ||||||||
\(459\) | −3.98906 | −0.186193 | ||||||||
\(460\) | −2.38210 | −0.111066 | ||||||||
\(461\) | −9.06531 | −0.422213 | −0.211107 | − | 0.977463i | \(-0.567707\pi\) | ||||
−0.211107 | + | 0.977463i | \(0.567707\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.59721 | 0.306598 | 0.153299 | − | 0.988180i | \(-0.451010\pi\) | ||||
0.153299 | + | 0.988180i | \(0.451010\pi\) | |||||||
\(464\) | 1.74596 | 0.0810543 | ||||||||
\(465\) | 0.335661 | 0.0155659 | ||||||||
\(466\) | 44.5776 | 2.06502 | ||||||||
\(467\) | −4.20780 | −0.194714 | −0.0973569 | − | 0.995250i | \(-0.531039\pi\) | ||||
−0.0973569 | + | 0.995250i | \(0.531039\pi\) | |||||||
\(468\) | −13.4757 | −0.622914 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −0.617099 | −0.0284646 | ||||||||
\(471\) | 11.6378 | 0.536240 | ||||||||
\(472\) | 8.13664 | 0.374519 | ||||||||
\(473\) | −2.09460 | −0.0963098 | ||||||||
\(474\) | −5.30006 | −0.243440 | ||||||||
\(475\) | −24.7602 | −1.13608 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 12.7249 | 0.582635 | ||||||||
\(478\) | 55.3640 | 2.53229 | ||||||||
\(479\) | 8.07101 | 0.368774 | 0.184387 | − | 0.982854i | \(-0.440970\pi\) | ||||
0.184387 | + | 0.982854i | \(0.440970\pi\) | |||||||
\(480\) | −0.457394 | −0.0208771 | ||||||||
\(481\) | 10.1752 | 0.463951 | ||||||||
\(482\) | 48.3641 | 2.20292 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −36.3581 | −1.65264 | ||||||||
\(485\) | −1.00004 | −0.0454094 | ||||||||
\(486\) | −2.32604 | −0.105511 | ||||||||
\(487\) | −24.1297 | −1.09342 | −0.546711 | − | 0.837322i | \(-0.684120\pi\) | ||||
−0.546711 | + | 0.837322i | \(0.684120\pi\) | |||||||
\(488\) | 41.0529 | 1.85838 | ||||||||
\(489\) | 17.5198 | 0.792271 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 37.6556 | 1.69937 | 0.849687 | − | 0.527287i | \(-0.176791\pi\) | ||||
0.849687 | + | 0.527287i | \(0.176791\pi\) | |||||||
\(492\) | 3.41045 | 0.153755 | ||||||||
\(493\) | 8.59551 | 0.387122 | ||||||||
\(494\) | −45.6008 | −2.05168 | ||||||||
\(495\) | 0.0569614 | 0.00256022 | ||||||||
\(496\) | 2.78095 | 0.124868 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −16.2756 | −0.729325 | ||||||||
\(499\) | 34.3383 | 1.53719 | 0.768596 | − | 0.639735i | \(-0.220956\pi\) | ||||
0.768596 | + | 0.639735i | \(0.220956\pi\) | |||||||
\(500\) | 3.33226 | 0.149023 | ||||||||
\(501\) | 13.2750 | 0.593084 | ||||||||
\(502\) | −60.8663 | −2.71660 | ||||||||
\(503\) | −33.8797 | −1.51062 | −0.755310 | − | 0.655368i | \(-0.772514\pi\) | ||||
−0.755310 | + | 0.655368i | \(0.772514\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.975770 | −0.0434212 | ||||||||
\(506\) | −9.67521 | −0.430116 | ||||||||
\(507\) | −2.61273 | −0.116035 | ||||||||
\(508\) | 57.0579 | 2.53153 | ||||||||
\(509\) | 12.2614 | 0.543476 | 0.271738 | − | 0.962371i | \(-0.412402\pi\) | ||||
0.271738 | + | 0.962371i | \(0.412402\pi\) | |||||||
\(510\) | 0.907465 | 0.0401832 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −9.10617 | −0.402439 | ||||||||
\(513\) | −4.96154 | −0.219057 | ||||||||
\(514\) | −62.0015 | −2.73477 | ||||||||
\(515\) | 0.998571 | 0.0440023 | ||||||||
\(516\) | −12.2652 | −0.539946 | ||||||||
\(517\) | −1.57991 | −0.0694846 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 20.1883 | 0.886168 | ||||||||
\(520\) | 1.26782 | 0.0555975 | ||||||||
\(521\) | 29.4757 | 1.29135 | 0.645676 | − | 0.763611i | \(-0.276576\pi\) | ||||
0.645676 | + | 0.763611i | \(0.276576\pi\) | |||||||
\(522\) | 5.01208 | 0.219373 | ||||||||
\(523\) | 41.1371 | 1.79880 | 0.899399 | − | 0.437129i | \(-0.144005\pi\) | ||||
0.899399 | + | 0.437129i | \(0.144005\pi\) | |||||||
\(524\) | 44.0990 | 1.92647 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −33.6304 | −1.46636 | ||||||||
\(527\) | 13.6908 | 0.596382 | ||||||||
\(528\) | 0.471924 | 0.0205379 | ||||||||
\(529\) | 28.0048 | 1.21760 | ||||||||
\(530\) | −2.89477 | −0.125741 | ||||||||
\(531\) | 2.48011 | 0.107627 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.95129 | 0.171150 | ||||||||
\(534\) | 10.6593 | 0.461272 | ||||||||
\(535\) | −1.42732 | −0.0617085 | ||||||||
\(536\) | −19.6535 | −0.848900 | ||||||||
\(537\) | −0.347661 | −0.0150027 | ||||||||
\(538\) | 2.24316 | 0.0967095 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.333545 | 0.0143535 | ||||||||
\(541\) | −15.5031 | −0.666529 | −0.333264 | − | 0.942833i | \(-0.608150\pi\) | ||||
−0.333264 | + | 0.942833i | \(0.608150\pi\) | |||||||
\(542\) | −54.3967 | −2.33654 | ||||||||
\(543\) | −1.09311 | −0.0469099 | ||||||||
\(544\) | −18.6560 | −0.799870 | ||||||||
\(545\) | −0.130660 | −0.00559687 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 25.8851 | 1.10677 | 0.553384 | − | 0.832926i | \(-0.313336\pi\) | ||||
0.553384 | + | 0.832926i | \(0.313336\pi\) | |||||||
\(548\) | 74.7740 | 3.19419 | ||||||||
\(549\) | 12.5132 | 0.534051 | ||||||||
\(550\) | 6.76072 | 0.288278 | ||||||||
\(551\) | 10.6910 | 0.455451 | ||||||||
\(552\) | −23.4304 | −0.997266 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 4.01624 | 0.170634 | ||||||||
\(555\) | −0.251853 | −0.0106906 | ||||||||
\(556\) | −37.4510 | −1.58828 | ||||||||
\(557\) | −19.3798 | −0.821148 | −0.410574 | − | 0.911827i | \(-0.634672\pi\) | ||||
−0.410574 | + | 0.911827i | \(0.634672\pi\) | |||||||
\(558\) | 7.98318 | 0.337955 | ||||||||
\(559\) | −14.2103 | −0.601031 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.32332 | 0.0980906 | ||||||||
\(562\) | −35.9627 | −1.51700 | ||||||||
\(563\) | 2.07786 | 0.0875715 | 0.0437857 | − | 0.999041i | \(-0.486058\pi\) | ||||
0.0437857 | + | 0.999041i | \(0.486058\pi\) | |||||||
\(564\) | −9.25140 | −0.389554 | ||||||||
\(565\) | 1.08112 | 0.0454832 | ||||||||
\(566\) | 4.18012 | 0.175704 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −0.807678 | −0.0338894 | ||||||||
\(569\) | −3.58169 | −0.150152 | −0.0750762 | − | 0.997178i | \(-0.523920\pi\) | ||||
−0.0750762 | + | 0.997178i | \(0.523920\pi\) | |||||||
\(570\) | 1.12869 | 0.0472757 | ||||||||
\(571\) | 34.8356 | 1.45783 | 0.728913 | − | 0.684607i | \(-0.240026\pi\) | ||||
0.728913 | + | 0.684607i | \(0.240026\pi\) | |||||||
\(572\) | 7.84855 | 0.328164 | ||||||||
\(573\) | 7.50981 | 0.313727 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −35.6405 | −1.48631 | ||||||||
\(576\) | −12.4989 | −0.520790 | ||||||||
\(577\) | 10.9314 | 0.455080 | 0.227540 | − | 0.973769i | \(-0.426932\pi\) | ||||
0.227540 | + | 0.973769i | \(0.426932\pi\) | |||||||
\(578\) | −2.52932 | −0.105206 | ||||||||
\(579\) | 1.85067 | 0.0769112 | ||||||||
\(580\) | −0.718712 | −0.0298429 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −23.7843 | −0.985892 | ||||||||
\(583\) | −7.41129 | −0.306944 | ||||||||
\(584\) | 10.2193 | 0.422879 | ||||||||
\(585\) | 0.386440 | 0.0159773 | ||||||||
\(586\) | −28.6678 | −1.18426 | ||||||||
\(587\) | −12.0086 | −0.495647 | −0.247823 | − | 0.968805i | \(-0.579715\pi\) | ||||
−0.247823 | + | 0.968805i | \(0.579715\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.0285 | 0.701646 | ||||||||
\(590\) | −0.564195 | −0.0232275 | ||||||||
\(591\) | −18.9892 | −0.781113 | ||||||||
\(592\) | −2.08660 | −0.0857589 | ||||||||
\(593\) | 28.7042 | 1.17874 | 0.589370 | − | 0.807863i | \(-0.299376\pi\) | ||||
0.589370 | + | 0.807863i | \(0.299376\pi\) | |||||||
\(594\) | 1.35474 | 0.0555855 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −27.3360 | −1.11972 | ||||||||
\(597\) | −19.0072 | −0.777911 | ||||||||
\(598\) | −65.6390 | −2.68418 | ||||||||
\(599\) | −31.7023 | −1.29532 | −0.647661 | − | 0.761929i | \(-0.724253\pi\) | ||||
−0.647661 | + | 0.761929i | \(0.724253\pi\) | |||||||
\(600\) | 16.3724 | 0.668402 | ||||||||
\(601\) | 11.5206 | 0.469933 | 0.234967 | − | 0.972003i | \(-0.424502\pi\) | ||||
0.234967 | + | 0.972003i | \(0.424502\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.99051 | −0.243953 | ||||||||
\(604\) | 28.9297 | 1.17713 | ||||||||
\(605\) | 1.04263 | 0.0423891 | ||||||||
\(606\) | −23.2072 | −0.942726 | ||||||||
\(607\) | −0.0495832 | −0.00201252 | −0.00100626 | − | 0.999999i | \(-0.500320\pi\) | ||||
−0.00100626 | + | 0.999999i | \(0.500320\pi\) | |||||||
\(608\) | −23.2041 | −0.941050 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.84661 | −0.115256 | ||||||||
\(611\) | −10.7185 | −0.433625 | ||||||||
\(612\) | 13.6045 | 0.549929 | ||||||||
\(613\) | −35.4076 | −1.43010 | −0.715050 | − | 0.699073i | \(-0.753596\pi\) | ||||
−0.715050 | + | 0.699073i | \(0.753596\pi\) | |||||||
\(614\) | 20.6887 | 0.834929 | ||||||||
\(615\) | −0.0978008 | −0.00394371 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −27.3399 | −1.10066 | −0.550332 | − | 0.834946i | \(-0.685499\pi\) | ||||
−0.550332 | + | 0.834946i | \(0.685499\pi\) | |||||||
\(618\) | 23.7495 | 0.955343 | ||||||||
\(619\) | −40.2579 | −1.61810 | −0.809051 | − | 0.587739i | \(-0.800018\pi\) | ||||
−0.809051 | + | 0.587739i | \(0.800018\pi\) | |||||||
\(620\) | −1.14476 | −0.0459746 | ||||||||
\(621\) | −7.14176 | −0.286589 | ||||||||
\(622\) | −17.1295 | −0.686830 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 3.20165 | 0.128168 | ||||||||
\(625\) | 24.8566 | 0.994265 | ||||||||
\(626\) | −21.0211 | −0.840171 | ||||||||
\(627\) | 2.88971 | 0.115404 | ||||||||
\(628\) | −39.6901 | −1.58381 | ||||||||
\(629\) | −10.2725 | −0.409592 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −42.6224 | −1.69677 | −0.848385 | − | 0.529380i | \(-0.822425\pi\) | ||||
−0.848385 | + | 0.529380i | \(0.822425\pi\) | |||||||
\(632\) | 7.47548 | 0.297359 | ||||||||
\(633\) | −23.1684 | −0.920861 | ||||||||
\(634\) | −0.830643 | −0.0329890 | ||||||||
\(635\) | −1.63624 | −0.0649321 | ||||||||
\(636\) | −43.3978 | −1.72083 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.91915 | −0.115570 | ||||||||
\(639\) | −0.246186 | −0.00973896 | ||||||||
\(640\) | 1.92858 | 0.0762337 | ||||||||
\(641\) | 35.9301 | 1.41915 | 0.709577 | − | 0.704628i | \(-0.248886\pi\) | ||||
0.709577 | + | 0.704628i | \(0.248886\pi\) | |||||||
\(642\) | −33.9466 | −1.33977 | ||||||||
\(643\) | −18.9359 | −0.746760 | −0.373380 | − | 0.927678i | \(-0.621801\pi\) | ||||
−0.373380 | + | 0.927678i | \(0.621801\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.351727 | 0.0138492 | ||||||||
\(646\) | 46.0367 | 1.81129 | ||||||||
\(647\) | 0.964507 | 0.0379187 | 0.0189593 | − | 0.999820i | \(-0.493965\pi\) | ||||
0.0189593 | + | 0.999820i | \(0.493965\pi\) | |||||||
\(648\) | 3.28076 | 0.128881 | ||||||||
\(649\) | −1.44447 | −0.0567004 | ||||||||
\(650\) | 45.8664 | 1.79903 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −59.7503 | −2.34000 | ||||||||
\(653\) | −4.40352 | −0.172323 | −0.0861615 | − | 0.996281i | \(-0.527460\pi\) | ||||
−0.0861615 | + | 0.996281i | \(0.527460\pi\) | |||||||
\(654\) | −3.10755 | −0.121515 | ||||||||
\(655\) | −1.26462 | −0.0494127 | ||||||||
\(656\) | −0.810278 | −0.0316360 | ||||||||
\(657\) | 3.11493 | 0.121525 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −11.0759 | −0.431455 | −0.215728 | − | 0.976454i | \(-0.569212\pi\) | ||||
−0.215728 | + | 0.976454i | \(0.569212\pi\) | |||||||
\(660\) | −0.194264 | −0.00756171 | ||||||||
\(661\) | 45.7318 | 1.77876 | 0.889381 | − | 0.457167i | \(-0.151136\pi\) | ||||
0.889381 | + | 0.457167i | \(0.151136\pi\) | |||||||
\(662\) | −26.3584 | −1.02445 | ||||||||
\(663\) | 15.7620 | 0.612144 | ||||||||
\(664\) | 22.9559 | 0.890862 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5.98994 | −0.232105 | ||||||||
\(667\) | 15.3889 | 0.595859 | ||||||||
\(668\) | −45.2738 | −1.75170 | ||||||||
\(669\) | −7.61730 | −0.294502 | ||||||||
\(670\) | 1.36277 | 0.0526485 | ||||||||
\(671\) | −7.28797 | −0.281349 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 42.4285 | 1.63550 | 0.817750 | − | 0.575574i | \(-0.195221\pi\) | ||||
0.817750 | + | 0.575574i | \(0.195221\pi\) | |||||||
\(674\) | −12.8141 | −0.493580 | ||||||||
\(675\) | 4.99044 | 0.192082 | ||||||||
\(676\) | 8.91058 | 0.342715 | ||||||||
\(677\) | −12.5797 | −0.483478 | −0.241739 | − | 0.970341i | \(-0.577718\pi\) | ||||
−0.241739 | + | 0.970341i | \(0.577718\pi\) | |||||||
\(678\) | 25.7128 | 0.987494 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −1.27994 | −0.0490833 | ||||||||
\(681\) | −20.5812 | −0.788675 | ||||||||
\(682\) | −4.64958 | −0.178042 | ||||||||
\(683\) | −0.545437 | −0.0208706 | −0.0104353 | − | 0.999946i | \(-0.503322\pi\) | ||||
−0.0104353 | + | 0.999946i | \(0.503322\pi\) | |||||||
\(684\) | 16.9211 | 0.646994 | ||||||||
\(685\) | −2.14428 | −0.0819286 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10.9117 | 0.416306 | ||||||||
\(688\) | 2.91405 | 0.111097 | ||||||||
\(689\) | −50.2800 | −1.91551 | ||||||||
\(690\) | 1.62467 | 0.0618500 | ||||||||
\(691\) | −40.0206 | −1.52246 | −0.761228 | − | 0.648484i | \(-0.775403\pi\) | ||||
−0.761228 | + | 0.648484i | \(0.775403\pi\) | |||||||
\(692\) | −68.8512 | −2.61733 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 19.1887 | 0.728393 | ||||||||
\(695\) | 1.07397 | 0.0407382 | ||||||||
\(696\) | −7.06929 | −0.267961 | ||||||||
\(697\) | −3.98906 | −0.151096 | ||||||||
\(698\) | 37.9858 | 1.43778 | ||||||||
\(699\) | −19.1646 | −0.724872 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −33.0999 | −1.25017 | −0.625083 | − | 0.780558i | \(-0.714935\pi\) | ||||
−0.625083 | + | 0.780558i | \(0.714935\pi\) | |||||||
\(702\) | 9.19086 | 0.346887 | ||||||||
\(703\) | −12.7768 | −0.481886 | ||||||||
\(704\) | 7.27967 | 0.274363 | ||||||||
\(705\) | 0.265300 | 0.00999179 | ||||||||
\(706\) | −23.2082 | −0.873450 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −8.45828 | −0.317882 | ||||||||
\(709\) | 18.6301 | 0.699669 | 0.349835 | − | 0.936811i | \(-0.386238\pi\) | ||||
0.349835 | + | 0.936811i | \(0.386238\pi\) | |||||||
\(710\) | 0.0560044 | 0.00210181 | ||||||||
\(711\) | 2.27858 | 0.0854534 | ||||||||
\(712\) | −15.0344 | −0.563438 | ||||||||
\(713\) | 24.5112 | 0.917952 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.225071 | −0.00841718 | ||||||||
\(716\) | 1.18568 | 0.0443110 | ||||||||
\(717\) | −23.8019 | −0.888897 | ||||||||
\(718\) | 28.6972 | 1.07097 | ||||||||
\(719\) | −1.94161 | −0.0724099 | −0.0362050 | − | 0.999344i | \(-0.511527\pi\) | ||||
−0.0362050 | + | 0.999344i | \(0.511527\pi\) | |||||||
\(720\) | −0.0792458 | −0.00295332 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 13.0650 | 0.486231 | ||||||||
\(723\) | −20.7925 | −0.773281 | ||||||||
\(724\) | 3.72800 | 0.138550 | ||||||||
\(725\) | −10.7532 | −0.399365 | ||||||||
\(726\) | 24.7974 | 0.920317 | ||||||||
\(727\) | −29.7690 | −1.10407 | −0.552036 | − | 0.833820i | \(-0.686149\pi\) | ||||
−0.552036 | + | 0.833820i | \(0.686149\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −0.708609 | −0.0262268 | ||||||||
\(731\) | 14.3461 | 0.530610 | ||||||||
\(732\) | −42.6757 | −1.57734 | ||||||||
\(733\) | 45.3347 | 1.67448 | 0.837238 | − | 0.546839i | \(-0.184169\pi\) | ||||
0.837238 | + | 0.546839i | \(0.184169\pi\) | |||||||
\(734\) | −24.4728 | −0.903307 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −33.4005 | −1.23116 | ||||||||
\(737\) | 3.48901 | 0.128519 | ||||||||
\(738\) | −2.32604 | −0.0856226 | ||||||||
\(739\) | 18.5022 | 0.680614 | 0.340307 | − | 0.940314i | \(-0.389469\pi\) | ||||
0.340307 | + | 0.940314i | \(0.389469\pi\) | |||||||
\(740\) | 0.858934 | 0.0315750 | ||||||||
\(741\) | 19.6045 | 0.720189 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.94213 | 0.144623 | 0.0723114 | − | 0.997382i | \(-0.476962\pi\) | ||||
0.0723114 | + | 0.997382i | \(0.476962\pi\) | |||||||
\(744\) | −11.2599 | −0.412808 | ||||||||
\(745\) | 0.783907 | 0.0287201 | ||||||||
\(746\) | −54.0019 | −1.97715 | ||||||||
\(747\) | 6.99712 | 0.256011 | ||||||||
\(748\) | −7.92357 | −0.289714 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −2.27271 | −0.0829875 | ||||||||
\(751\) | −41.1338 | −1.50099 | −0.750496 | − | 0.660875i | \(-0.770185\pi\) | ||||
−0.750496 | + | 0.660875i | \(0.770185\pi\) | |||||||
\(752\) | 2.19801 | 0.0801532 | ||||||||
\(753\) | 26.1674 | 0.953592 | ||||||||
\(754\) | −19.8042 | −0.721226 | ||||||||
\(755\) | −0.829612 | −0.0301927 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16.5287 | −0.600747 | −0.300373 | − | 0.953822i | \(-0.597111\pi\) | ||||
−0.300373 | + | 0.953822i | \(0.597111\pi\) | |||||||
\(758\) | −20.1554 | −0.732077 | ||||||||
\(759\) | 4.15952 | 0.150981 | ||||||||
\(760\) | −1.59197 | −0.0577467 | ||||||||
\(761\) | 5.60469 | 0.203170 | 0.101585 | − | 0.994827i | \(-0.467609\pi\) | ||||
0.101585 | + | 0.994827i | \(0.467609\pi\) | |||||||
\(762\) | −38.9153 | −1.40975 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −25.6118 | −0.926604 | ||||||||
\(765\) | −0.390133 | −0.0141053 | ||||||||
\(766\) | −17.3422 | −0.626601 | ||||||||
\(767\) | −9.79963 | −0.353844 | ||||||||
\(768\) | 20.8703 | 0.753091 | ||||||||
\(769\) | −2.94131 | −0.106066 | −0.0530331 | − | 0.998593i | \(-0.516889\pi\) | ||||
−0.0530331 | + | 0.998593i | \(0.516889\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 26.6554 | 0.959971 | ||||||||
\(772\) | −6.31162 | −0.227160 | ||||||||
\(773\) | 12.8639 | 0.462683 | 0.231342 | − | 0.972873i | \(-0.425688\pi\) | ||||
0.231342 | + | 0.972873i | \(0.425688\pi\) | |||||||
\(774\) | 8.36527 | 0.300683 | ||||||||
\(775\) | −17.1276 | −0.615243 | ||||||||
\(776\) | 33.5467 | 1.20425 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −20.1494 | −0.722390 | ||||||||
\(779\) | −4.96154 | −0.177766 | ||||||||
\(780\) | −1.31793 | −0.0471896 | ||||||||
\(781\) | 0.143384 | 0.00513069 | ||||||||
\(782\) | 66.2663 | 2.36968 | ||||||||
\(783\) | −2.15477 | −0.0770052 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.13818 | 0.0406235 | ||||||||
\(786\) | −30.0769 | −1.07281 | ||||||||
\(787\) | −10.8028 | −0.385078 | −0.192539 | − | 0.981289i | \(-0.561672\pi\) | ||||
−0.192539 | + | 0.981289i | \(0.561672\pi\) | |||||||
\(788\) | 64.7619 | 2.30705 | ||||||||
\(789\) | 14.4582 | 0.514727 | ||||||||
\(790\) | −0.518350 | −0.0184421 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −1.91079 | −0.0678970 | ||||||||
\(793\) | −49.4434 | −1.75578 | ||||||||
\(794\) | −34.0896 | −1.20979 | ||||||||
\(795\) | 1.24451 | 0.0441382 | ||||||||
\(796\) | 64.8230 | 2.29759 | ||||||||
\(797\) | 32.2200 | 1.14129 | 0.570645 | − | 0.821197i | \(-0.306693\pi\) | ||||
0.570645 | + | 0.821197i | \(0.306693\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.8210 | 0.382818 | ||||||||
\(800\) | 23.3392 | 0.825166 | ||||||||
\(801\) | −4.58259 | −0.161918 | ||||||||
\(802\) | −34.1294 | −1.20515 | ||||||||
\(803\) | −1.81420 | −0.0640218 | ||||||||
\(804\) | 20.4304 | 0.720523 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −31.5439 | −1.11109 | ||||||||
\(807\) | −0.964369 | −0.0339474 | ||||||||
\(808\) | 32.7326 | 1.15153 | ||||||||
\(809\) | −30.0911 | −1.05795 | −0.528973 | − | 0.848639i | \(-0.677423\pi\) | ||||
−0.528973 | + | 0.848639i | \(0.677423\pi\) | |||||||
\(810\) | −0.227488 | −0.00799312 | ||||||||
\(811\) | −46.8676 | −1.64574 | −0.822871 | − | 0.568228i | \(-0.807629\pi\) | ||||
−0.822871 | + | 0.568228i | \(0.807629\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 23.3860 | 0.820182 | ||||||||
\(814\) | 3.48867 | 0.122278 | ||||||||
\(815\) | 1.71345 | 0.0600194 | ||||||||
\(816\) | −3.23225 | −0.113151 | ||||||||
\(817\) | 17.8435 | 0.624264 | ||||||||
\(818\) | 6.42653 | 0.224698 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.333545 | 0.0116479 | ||||||||
\(821\) | −41.4566 | −1.44684 | −0.723422 | − | 0.690406i | \(-0.757432\pi\) | ||||
−0.723422 | + | 0.690406i | \(0.757432\pi\) | |||||||
\(822\) | −50.9983 | −1.77877 | ||||||||
\(823\) | −36.4738 | −1.27140 | −0.635699 | − | 0.771937i | \(-0.719288\pi\) | ||||
−0.635699 | + | 0.771937i | \(0.719288\pi\) | |||||||
\(824\) | −33.4975 | −1.16694 | ||||||||
\(825\) | −2.90654 | −0.101193 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −5.77420 | −0.200789 | −0.100394 | − | 0.994948i | \(-0.532010\pi\) | ||||
−0.100394 | + | 0.994948i | \(0.532010\pi\) | |||||||
\(828\) | 24.3566 | 0.846452 | ||||||||
\(829\) | 19.1399 | 0.664755 | 0.332378 | − | 0.943146i | \(-0.392149\pi\) | ||||
0.332378 | + | 0.943146i | \(0.392149\pi\) | |||||||
\(830\) | −1.59176 | −0.0552509 | ||||||||
\(831\) | −1.72664 | −0.0598966 | ||||||||
\(832\) | 49.3870 | 1.71219 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 25.5428 | 0.884475 | ||||||||
\(835\) | 1.29831 | 0.0449297 | ||||||||
\(836\) | −9.85522 | −0.340850 | ||||||||
\(837\) | −3.43209 | −0.118631 | ||||||||
\(838\) | −70.1864 | −2.42455 | ||||||||
\(839\) | 32.7657 | 1.13120 | 0.565599 | − | 0.824680i | \(-0.308645\pi\) | ||||
0.565599 | + | 0.824680i | \(0.308645\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.3570 | −0.839895 | ||||||||
\(842\) | −16.1263 | −0.555749 | ||||||||
\(843\) | 15.4609 | 0.532503 | ||||||||
\(844\) | 79.0147 | 2.71980 | ||||||||
\(845\) | −0.255527 | −0.00879039 | ||||||||
\(846\) | 6.30975 | 0.216934 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 10.3107 | 0.354072 | ||||||||
\(849\) | −1.79710 | −0.0616763 | ||||||||
\(850\) | −46.3048 | −1.58824 | ||||||||
\(851\) | −18.3912 | −0.630444 | ||||||||
\(852\) | 0.839605 | 0.0287644 | ||||||||
\(853\) | 42.3085 | 1.44862 | 0.724308 | − | 0.689477i | \(-0.242159\pi\) | ||||
0.724308 | + | 0.689477i | \(0.242159\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.485242 | −0.0165949 | ||||||||
\(856\) | 47.8801 | 1.63651 | ||||||||
\(857\) | 23.3694 | 0.798283 | 0.399141 | − | 0.916889i | \(-0.369308\pi\) | ||||
0.399141 | + | 0.916889i | \(0.369308\pi\) | |||||||
\(858\) | −5.35296 | −0.182747 | ||||||||
\(859\) | −5.02568 | −0.171474 | −0.0857371 | − | 0.996318i | \(-0.527324\pi\) | ||||
−0.0857371 | + | 0.996318i | \(0.527324\pi\) | |||||||
\(860\) | −1.19955 | −0.0409042 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −44.1909 | −1.50515 | ||||||||
\(863\) | 17.7022 | 0.602591 | 0.301296 | − | 0.953531i | \(-0.402581\pi\) | ||||
0.301296 | + | 0.953531i | \(0.402581\pi\) | |||||||
\(864\) | 4.67679 | 0.159108 | ||||||||
\(865\) | 1.97443 | 0.0671327 | ||||||||
\(866\) | 66.2530 | 2.25137 | ||||||||
\(867\) | 1.08739 | 0.0369298 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.32710 | −0.0450186 | ||||||||
\(870\) | 0.490185 | 0.0166188 | ||||||||
\(871\) | 23.6703 | 0.802037 | ||||||||
\(872\) | 4.38305 | 0.148429 | ||||||||
\(873\) | 10.2253 | 0.346072 | ||||||||
\(874\) | 82.4212 | 2.78794 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −10.6233 | −0.358928 | ||||||||
\(877\) | 4.97821 | 0.168102 | 0.0840512 | − | 0.996461i | \(-0.473214\pi\) | ||||
0.0840512 | + | 0.996461i | \(0.473214\pi\) | |||||||
\(878\) | −42.7808 | −1.44378 | ||||||||
\(879\) | 12.3247 | 0.415703 | ||||||||
\(880\) | 0.0461545 | 0.00155587 | ||||||||
\(881\) | −31.4164 | −1.05844 | −0.529222 | − | 0.848483i | \(-0.677516\pi\) | ||||
−0.529222 | + | 0.848483i | \(0.677516\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −55.3269 | −1.86190 | −0.930950 | − | 0.365148i | \(-0.881019\pi\) | ||||
−0.930950 | + | 0.365148i | \(0.881019\pi\) | |||||||
\(884\) | −53.7554 | −1.80799 | ||||||||
\(885\) | 0.242556 | 0.00815344 | ||||||||
\(886\) | 12.7701 | 0.429020 | ||||||||
\(887\) | 0.897270 | 0.0301274 | 0.0150637 | − | 0.999887i | \(-0.495205\pi\) | ||||
0.0150637 | + | 0.999887i | \(0.495205\pi\) | |||||||
\(888\) | 8.44852 | 0.283514 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 1.04249 | 0.0349442 | ||||||||
\(891\) | −0.582422 | −0.0195119 | ||||||||
\(892\) | 25.9784 | 0.869822 | ||||||||
\(893\) | 13.4590 | 0.450387 | ||||||||
\(894\) | 18.6440 | 0.623549 | ||||||||
\(895\) | −0.0340015 | −0.00113654 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 28.2192 | 0.942212 | ||||||||
\(898\) | −58.5864 | −1.95505 | ||||||||
\(899\) | 7.39538 | 0.246650 | ||||||||
\(900\) | −17.0196 | −0.567321 | ||||||||
\(901\) | 50.7605 | 1.69108 | ||||||||
\(902\) | 1.35474 | 0.0451078 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −36.2667 | −1.20621 | ||||||||
\(905\) | −0.106907 | −0.00355371 | ||||||||
\(906\) | −19.7310 | −0.655519 | ||||||||
\(907\) | −16.4250 | −0.545383 | −0.272691 | − | 0.962102i | \(-0.587914\pi\) | ||||
−0.272691 | + | 0.962102i | \(0.587914\pi\) | |||||||
\(908\) | 70.1913 | 2.32938 | ||||||||
\(909\) | 9.97712 | 0.330920 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −54.6545 | −1.81078 | −0.905391 | − | 0.424578i | \(-0.860423\pi\) | ||||
−0.905391 | + | 0.424578i | \(0.860423\pi\) | |||||||
\(912\) | −4.02023 | −0.133123 | ||||||||
\(913\) | −4.07528 | −0.134872 | ||||||||
\(914\) | 88.0457 | 2.91229 | ||||||||
\(915\) | 1.22380 | 0.0404576 | ||||||||
\(916\) | −37.2137 | −1.22958 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −9.27871 | −0.306243 | ||||||||
\(919\) | −38.7201 | −1.27726 | −0.638629 | − | 0.769515i | \(-0.720498\pi\) | ||||
−0.638629 | + | 0.769515i | \(0.720498\pi\) | |||||||
\(920\) | −2.29152 | −0.0755490 | ||||||||
\(921\) | −8.89441 | −0.293081 | ||||||||
\(922\) | −21.0862 | −0.694439 | ||||||||
\(923\) | 0.972753 | 0.0320186 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12.8512 | 0.422545 | ||||||||
\(926\) | 15.3454 | 0.504280 | ||||||||
\(927\) | −10.2103 | −0.335349 | ||||||||
\(928\) | −10.0774 | −0.330807 | ||||||||
\(929\) | 3.66975 | 0.120400 | 0.0602002 | − | 0.998186i | \(-0.480826\pi\) | ||||
0.0602002 | + | 0.998186i | \(0.480826\pi\) | |||||||
\(930\) | 0.780761 | 0.0256022 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 65.3600 | 2.14094 | ||||||||
\(933\) | 7.36424 | 0.241094 | ||||||||
\(934\) | −9.78750 | −0.320257 | ||||||||
\(935\) | 0.227222 | 0.00743096 | ||||||||
\(936\) | −12.9633 | −0.423718 | ||||||||
\(937\) | −9.05184 | −0.295711 | −0.147855 | − | 0.989009i | \(-0.547237\pi\) | ||||
−0.147855 | + | 0.989009i | \(0.547237\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.03728 | 0.294921 | ||||||||
\(940\) | −0.904794 | −0.0295111 | ||||||||
\(941\) | 53.8288 | 1.75477 | 0.877384 | − | 0.479789i | \(-0.159287\pi\) | ||||
0.877384 | + | 0.479789i | \(0.159287\pi\) | |||||||
\(942\) | 27.0699 | 0.881985 | ||||||||
\(943\) | −7.14176 | −0.232568 | ||||||||
\(944\) | 2.00958 | 0.0654061 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.87212 | −0.158406 | ||||||||
\(947\) | −24.9164 | −0.809674 | −0.404837 | − | 0.914389i | \(-0.632672\pi\) | ||||
−0.404837 | + | 0.914389i | \(0.632672\pi\) | |||||||
\(948\) | −7.77098 | −0.252390 | ||||||||
\(949\) | −12.3080 | −0.399534 | ||||||||
\(950\) | −57.5932 | −1.86857 | ||||||||
\(951\) | 0.357106 | 0.0115800 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14.1959 | 0.459850 | 0.229925 | − | 0.973208i | \(-0.426152\pi\) | ||||
0.229925 | + | 0.973208i | \(0.426152\pi\) | |||||||
\(954\) | 29.5987 | 0.958293 | ||||||||
\(955\) | 0.734465 | 0.0237667 | ||||||||
\(956\) | 81.1751 | 2.62539 | ||||||||
\(957\) | 1.25499 | 0.0405680 | ||||||||
\(958\) | 18.7735 | 0.606544 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.22241 | −0.0394530 | ||||||||
\(961\) | −19.2207 | −0.620024 | ||||||||
\(962\) | 23.6680 | 0.763087 | ||||||||
\(963\) | 14.5942 | 0.470291 | ||||||||
\(964\) | 70.9118 | 2.28391 | ||||||||
\(965\) | 0.180997 | 0.00582650 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15.5411 | −0.499768 | −0.249884 | − | 0.968276i | \(-0.580392\pi\) | ||||
−0.249884 | + | 0.968276i | \(0.580392\pi\) | |||||||
\(968\) | −34.9755 | −1.12416 | ||||||||
\(969\) | −19.7919 | −0.635807 | ||||||||
\(970\) | −2.32613 | −0.0746874 | ||||||||
\(971\) | 43.8807 | 1.40820 | 0.704100 | − | 0.710101i | \(-0.251351\pi\) | ||||
0.704100 | + | 0.710101i | \(0.251351\pi\) | |||||||
\(972\) | −3.41045 | −0.109390 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −56.1266 | −1.79841 | ||||||||
\(975\) | −19.7187 | −0.631503 | ||||||||
\(976\) | 10.1392 | 0.324547 | ||||||||
\(977\) | −35.5556 | −1.13753 | −0.568763 | − | 0.822501i | \(-0.692578\pi\) | ||||
−0.568763 | + | 0.822501i | \(0.692578\pi\) | |||||||
\(978\) | 40.7516 | 1.30309 | ||||||||
\(979\) | 2.66900 | 0.0853018 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.33598 | 0.0426547 | ||||||||
\(982\) | 87.5884 | 2.79506 | ||||||||
\(983\) | −47.3823 | −1.51126 | −0.755630 | − | 0.654999i | \(-0.772669\pi\) | ||||
−0.755630 | + | 0.654999i | \(0.772669\pi\) | |||||||
\(984\) | 3.28076 | 0.104587 | ||||||||
\(985\) | −1.85716 | −0.0591741 | ||||||||
\(986\) | 19.9935 | 0.636722 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −66.8602 | −2.12711 | ||||||||
\(989\) | 25.6844 | 0.816715 | ||||||||
\(990\) | 0.132494 | 0.00421094 | ||||||||
\(991\) | −15.5951 | −0.495395 | −0.247697 | − | 0.968837i | \(-0.579674\pi\) | ||||
−0.247697 | + | 0.968837i | \(0.579674\pi\) | |||||||
\(992\) | −16.0512 | −0.509626 | ||||||||
\(993\) | 11.3319 | 0.359607 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.85891 | −0.0589315 | ||||||||
\(996\) | −23.8633 | −0.756139 | ||||||||
\(997\) | 42.2473 | 1.33799 | 0.668993 | − | 0.743269i | \(-0.266726\pi\) | ||||
0.668993 | + | 0.743269i | \(0.266726\pi\) | |||||||
\(998\) | 79.8721 | 2.52831 | ||||||||
\(999\) | 2.57517 | 0.0814747 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6027.2.a.y.1.6 | 7 | ||
7.6 | odd | 2 | 861.2.a.m.1.6 | ✓ | 7 | ||
21.20 | even | 2 | 2583.2.a.u.1.2 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
861.2.a.m.1.6 | ✓ | 7 | 7.6 | odd | 2 | ||
2583.2.a.u.1.2 | 7 | 21.20 | even | 2 | |||
6027.2.a.y.1.6 | 7 | 1.1 | even | 1 | trivial |