Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5577,2,Mod(1,5577)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5577, 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("5577.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5577 = 3 \cdot 11 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5577.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: | \(44.5325692073\) |
Analytic rank: | \(1\) |
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: | \( x^{7} - 3x^{6} - 7x^{5} + 21x^{4} + 13x^{3} - 33x^{2} - 7x + 7 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 429) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-0.584778\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5577.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.584778 | 0.413501 | 0.206750 | − | 0.978394i | \(-0.433711\pi\) | ||||
0.206750 | + | 0.978394i | \(0.433711\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.65803 | −0.829017 | ||||||||
\(5\) | 1.95350 | 0.873633 | 0.436817 | − | 0.899551i | \(-0.356106\pi\) | ||||
0.436817 | + | 0.899551i | \(0.356106\pi\) | |||||||
\(6\) | 0.584778 | 0.238735 | ||||||||
\(7\) | −1.51078 | −0.571023 | −0.285511 | − | 0.958375i | \(-0.592163\pi\) | ||||
−0.285511 | + | 0.958375i | \(0.592163\pi\) | |||||||
\(8\) | −2.13914 | −0.756300 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.14237 | 0.361248 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −1.65803 | −0.478633 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −0.883474 | −0.236118 | ||||||||
\(15\) | 1.95350 | 0.504392 | ||||||||
\(16\) | 2.06515 | 0.516286 | ||||||||
\(17\) | 3.44198 | 0.834803 | 0.417401 | − | 0.908722i | \(-0.362941\pi\) | ||||
0.417401 | + | 0.908722i | \(0.362941\pi\) | |||||||
\(18\) | 0.584778 | 0.137834 | ||||||||
\(19\) | −5.09587 | −1.16907 | −0.584536 | − | 0.811368i | \(-0.698724\pi\) | ||||
−0.584536 | + | 0.811368i | \(0.698724\pi\) | |||||||
\(20\) | −3.23897 | −0.724257 | ||||||||
\(21\) | −1.51078 | −0.329680 | ||||||||
\(22\) | −0.584778 | −0.124675 | ||||||||
\(23\) | −0.701611 | −0.146296 | −0.0731480 | − | 0.997321i | \(-0.523305\pi\) | ||||
−0.0731480 | + | 0.997321i | \(0.523305\pi\) | |||||||
\(24\) | −2.13914 | −0.436650 | ||||||||
\(25\) | −1.18383 | −0.236765 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 2.50493 | 0.473388 | ||||||||
\(29\) | 5.04937 | 0.937645 | 0.468822 | − | 0.883292i | \(-0.344678\pi\) | ||||
0.468822 | + | 0.883292i | \(0.344678\pi\) | |||||||
\(30\) | 1.14237 | 0.208567 | ||||||||
\(31\) | −7.26957 | −1.30565 | −0.652827 | − | 0.757507i | \(-0.726417\pi\) | ||||
−0.652827 | + | 0.757507i | \(0.726417\pi\) | |||||||
\(32\) | 5.48593 | 0.969785 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | 2.01280 | 0.345192 | ||||||||
\(35\) | −2.95132 | −0.498864 | ||||||||
\(36\) | −1.65803 | −0.276339 | ||||||||
\(37\) | 2.08160 | 0.342213 | 0.171106 | − | 0.985253i | \(-0.445266\pi\) | ||||
0.171106 | + | 0.985253i | \(0.445266\pi\) | |||||||
\(38\) | −2.97995 | −0.483413 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.17882 | −0.660729 | ||||||||
\(41\) | −1.03658 | −0.161886 | −0.0809430 | − | 0.996719i | \(-0.525793\pi\) | ||||
−0.0809430 | + | 0.996719i | \(0.525793\pi\) | |||||||
\(42\) | −0.883474 | −0.136323 | ||||||||
\(43\) | −5.48659 | −0.836698 | −0.418349 | − | 0.908286i | \(-0.637391\pi\) | ||||
−0.418349 | + | 0.908286i | \(0.637391\pi\) | |||||||
\(44\) | 1.65803 | 0.249958 | ||||||||
\(45\) | 1.95350 | 0.291211 | ||||||||
\(46\) | −0.410287 | −0.0604935 | ||||||||
\(47\) | −3.75225 | −0.547322 | −0.273661 | − | 0.961826i | \(-0.588235\pi\) | ||||
−0.273661 | + | 0.961826i | \(0.588235\pi\) | |||||||
\(48\) | 2.06515 | 0.298078 | ||||||||
\(49\) | −4.71753 | −0.673933 | ||||||||
\(50\) | −0.692276 | −0.0979026 | ||||||||
\(51\) | 3.44198 | 0.481974 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.502747 | −0.0690575 | −0.0345288 | − | 0.999404i | \(-0.510993\pi\) | ||||
−0.0345288 | + | 0.999404i | \(0.510993\pi\) | |||||||
\(54\) | 0.584778 | 0.0795783 | ||||||||
\(55\) | −1.95350 | −0.263410 | ||||||||
\(56\) | 3.23178 | 0.431865 | ||||||||
\(57\) | −5.09587 | −0.674964 | ||||||||
\(58\) | 2.95276 | 0.387717 | ||||||||
\(59\) | 2.65023 | 0.345031 | 0.172515 | − | 0.985007i | \(-0.444811\pi\) | ||||
0.172515 | + | 0.985007i | \(0.444811\pi\) | |||||||
\(60\) | −3.23897 | −0.418150 | ||||||||
\(61\) | −5.38195 | −0.689088 | −0.344544 | − | 0.938770i | \(-0.611967\pi\) | ||||
−0.344544 | + | 0.938770i | \(0.611967\pi\) | |||||||
\(62\) | −4.25109 | −0.539889 | ||||||||
\(63\) | −1.51078 | −0.190341 | ||||||||
\(64\) | −0.922236 | −0.115279 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.584778 | −0.0719813 | ||||||||
\(67\) | 8.47197 | 1.03502 | 0.517508 | − | 0.855679i | \(-0.326860\pi\) | ||||
0.517508 | + | 0.855679i | \(0.326860\pi\) | |||||||
\(68\) | −5.70692 | −0.692066 | ||||||||
\(69\) | −0.701611 | −0.0844640 | ||||||||
\(70\) | −1.72587 | −0.206281 | ||||||||
\(71\) | 2.31533 | 0.274779 | 0.137390 | − | 0.990517i | \(-0.456129\pi\) | ||||
0.137390 | + | 0.990517i | \(0.456129\pi\) | |||||||
\(72\) | −2.13914 | −0.252100 | ||||||||
\(73\) | −2.21094 | −0.258771 | −0.129385 | − | 0.991594i | \(-0.541300\pi\) | ||||
−0.129385 | + | 0.991594i | \(0.541300\pi\) | |||||||
\(74\) | 1.21727 | 0.141505 | ||||||||
\(75\) | −1.18383 | −0.136696 | ||||||||
\(76\) | 8.44913 | 0.969181 | ||||||||
\(77\) | 1.51078 | 0.172170 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.54589 | −0.623961 | −0.311981 | − | 0.950088i | \(-0.600992\pi\) | ||||
−0.311981 | + | 0.950088i | \(0.600992\pi\) | |||||||
\(80\) | 4.03427 | 0.451045 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.606168 | −0.0669400 | ||||||||
\(83\) | −14.5137 | −1.59308 | −0.796541 | − | 0.604585i | \(-0.793339\pi\) | ||||
−0.796541 | + | 0.604585i | \(0.793339\pi\) | |||||||
\(84\) | 2.50493 | 0.273310 | ||||||||
\(85\) | 6.72392 | 0.729311 | ||||||||
\(86\) | −3.20844 | −0.345975 | ||||||||
\(87\) | 5.04937 | 0.541350 | ||||||||
\(88\) | 2.13914 | 0.228033 | ||||||||
\(89\) | 1.80966 | 0.191824 | 0.0959119 | − | 0.995390i | \(-0.469423\pi\) | ||||
0.0959119 | + | 0.995390i | \(0.469423\pi\) | |||||||
\(90\) | 1.14237 | 0.120416 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.16330 | 0.121282 | ||||||||
\(93\) | −7.26957 | −0.753819 | ||||||||
\(94\) | −2.19424 | −0.226318 | ||||||||
\(95\) | −9.95480 | −1.02134 | ||||||||
\(96\) | 5.48593 | 0.559906 | ||||||||
\(97\) | −14.5085 | −1.47312 | −0.736560 | − | 0.676372i | \(-0.763551\pi\) | ||||
−0.736560 | + | 0.676372i | \(0.763551\pi\) | |||||||
\(98\) | −2.75871 | −0.278672 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 1.96282 | 0.196282 | ||||||||
\(101\) | 8.63799 | 0.859512 | 0.429756 | − | 0.902945i | \(-0.358600\pi\) | ||||
0.429756 | + | 0.902945i | \(0.358600\pi\) | |||||||
\(102\) | 2.01280 | 0.199296 | ||||||||
\(103\) | −2.90048 | −0.285792 | −0.142896 | − | 0.989738i | \(-0.545642\pi\) | ||||
−0.142896 | + | 0.989738i | \(0.545642\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.95132 | −0.288019 | ||||||||
\(106\) | −0.293995 | −0.0285554 | ||||||||
\(107\) | −2.29234 | −0.221609 | −0.110805 | − | 0.993842i | \(-0.535343\pi\) | ||||
−0.110805 | + | 0.993842i | \(0.535343\pi\) | |||||||
\(108\) | −1.65803 | −0.159544 | ||||||||
\(109\) | −12.8818 | −1.23386 | −0.616929 | − | 0.787019i | \(-0.711623\pi\) | ||||
−0.616929 | + | 0.787019i | \(0.711623\pi\) | |||||||
\(110\) | −1.14237 | −0.108920 | ||||||||
\(111\) | 2.08160 | 0.197577 | ||||||||
\(112\) | −3.11999 | −0.294811 | ||||||||
\(113\) | −12.6273 | −1.18788 | −0.593940 | − | 0.804509i | \(-0.702428\pi\) | ||||
−0.593940 | + | 0.804509i | \(0.702428\pi\) | |||||||
\(114\) | −2.97995 | −0.279098 | ||||||||
\(115\) | −1.37060 | −0.127809 | ||||||||
\(116\) | −8.37203 | −0.777324 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.54980 | 0.142670 | ||||||||
\(119\) | −5.20009 | −0.476691 | ||||||||
\(120\) | −4.17882 | −0.381472 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −3.14725 | −0.284939 | ||||||||
\(123\) | −1.03658 | −0.0934649 | ||||||||
\(124\) | 12.0532 | 1.08241 | ||||||||
\(125\) | −12.0801 | −1.08048 | ||||||||
\(126\) | −0.883474 | −0.0787061 | ||||||||
\(127\) | 5.05085 | 0.448190 | 0.224095 | − | 0.974567i | \(-0.428057\pi\) | ||||
0.224095 | + | 0.974567i | \(0.428057\pi\) | |||||||
\(128\) | −11.5112 | −1.01745 | ||||||||
\(129\) | −5.48659 | −0.483068 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.9772 | 1.39594 | 0.697968 | − | 0.716129i | \(-0.254088\pi\) | ||||
0.697968 | + | 0.716129i | \(0.254088\pi\) | |||||||
\(132\) | 1.65803 | 0.144313 | ||||||||
\(133\) | 7.69876 | 0.667567 | ||||||||
\(134\) | 4.95422 | 0.427980 | ||||||||
\(135\) | 1.95350 | 0.168131 | ||||||||
\(136\) | −7.36288 | −0.631361 | ||||||||
\(137\) | 17.2582 | 1.47447 | 0.737233 | − | 0.675639i | \(-0.236132\pi\) | ||||
0.737233 | + | 0.675639i | \(0.236132\pi\) | |||||||
\(138\) | −0.410287 | −0.0349260 | ||||||||
\(139\) | −5.70544 | −0.483929 | −0.241965 | − | 0.970285i | \(-0.577792\pi\) | ||||
−0.241965 | + | 0.970285i | \(0.577792\pi\) | |||||||
\(140\) | 4.89339 | 0.413567 | ||||||||
\(141\) | −3.75225 | −0.315997 | ||||||||
\(142\) | 1.35395 | 0.113621 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 2.06515 | 0.172095 | ||||||||
\(145\) | 9.86396 | 0.819158 | ||||||||
\(146\) | −1.29291 | −0.107002 | ||||||||
\(147\) | −4.71753 | −0.389095 | ||||||||
\(148\) | −3.45136 | −0.283700 | ||||||||
\(149\) | 0.161015 | 0.0131908 | 0.00659542 | − | 0.999978i | \(-0.497901\pi\) | ||||
0.00659542 | + | 0.999978i | \(0.497901\pi\) | |||||||
\(150\) | −0.692276 | −0.0565241 | ||||||||
\(151\) | −16.3107 | −1.32734 | −0.663671 | − | 0.748025i | \(-0.731003\pi\) | ||||
−0.663671 | + | 0.748025i | \(0.731003\pi\) | |||||||
\(152\) | 10.9008 | 0.884170 | ||||||||
\(153\) | 3.44198 | 0.278268 | ||||||||
\(154\) | 0.883474 | 0.0711924 | ||||||||
\(155\) | −14.2011 | −1.14066 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.2192 | −1.13481 | −0.567407 | − | 0.823437i | \(-0.692053\pi\) | ||||
−0.567407 | + | 0.823437i | \(0.692053\pi\) | |||||||
\(158\) | −3.24312 | −0.258008 | ||||||||
\(159\) | −0.502747 | −0.0398704 | ||||||||
\(160\) | 10.7168 | 0.847236 | ||||||||
\(161\) | 1.05998 | 0.0835384 | ||||||||
\(162\) | 0.584778 | 0.0459445 | ||||||||
\(163\) | −13.0186 | −1.01970 | −0.509848 | − | 0.860264i | \(-0.670298\pi\) | ||||
−0.509848 | + | 0.860264i | \(0.670298\pi\) | |||||||
\(164\) | 1.71868 | 0.134206 | ||||||||
\(165\) | −1.95350 | −0.152080 | ||||||||
\(166\) | −8.48728 | −0.658740 | ||||||||
\(167\) | −14.0271 | −1.08545 | −0.542724 | − | 0.839911i | \(-0.682607\pi\) | ||||
−0.542724 | + | 0.839911i | \(0.682607\pi\) | |||||||
\(168\) | 3.23178 | 0.249337 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 3.93200 | 0.301571 | ||||||||
\(171\) | −5.09587 | −0.389691 | ||||||||
\(172\) | 9.09696 | 0.693637 | ||||||||
\(173\) | 17.8674 | 1.35844 | 0.679218 | − | 0.733936i | \(-0.262319\pi\) | ||||
0.679218 | + | 0.733936i | \(0.262319\pi\) | |||||||
\(174\) | 2.95276 | 0.223848 | ||||||||
\(175\) | 1.78851 | 0.135198 | ||||||||
\(176\) | −2.06515 | −0.155666 | ||||||||
\(177\) | 2.65023 | 0.199204 | ||||||||
\(178\) | 1.05825 | 0.0793193 | ||||||||
\(179\) | 17.2723 | 1.29099 | 0.645495 | − | 0.763764i | \(-0.276651\pi\) | ||||
0.645495 | + | 0.763764i | \(0.276651\pi\) | |||||||
\(180\) | −3.23897 | −0.241419 | ||||||||
\(181\) | 3.70318 | 0.275255 | 0.137628 | − | 0.990484i | \(-0.456052\pi\) | ||||
0.137628 | + | 0.990484i | \(0.456052\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.38195 | −0.397845 | ||||||||
\(184\) | 1.50084 | 0.110644 | ||||||||
\(185\) | 4.06641 | 0.298969 | ||||||||
\(186\) | −4.25109 | −0.311705 | ||||||||
\(187\) | −3.44198 | −0.251703 | ||||||||
\(188\) | 6.22136 | 0.453740 | ||||||||
\(189\) | −1.51078 | −0.109893 | ||||||||
\(190\) | −5.82135 | −0.422325 | ||||||||
\(191\) | −20.6259 | −1.49243 | −0.746217 | − | 0.665702i | \(-0.768132\pi\) | ||||
−0.746217 | + | 0.665702i | \(0.768132\pi\) | |||||||
\(192\) | −0.922236 | −0.0665566 | ||||||||
\(193\) | −18.8475 | −1.35667 | −0.678335 | − | 0.734753i | \(-0.737298\pi\) | ||||
−0.678335 | + | 0.734753i | \(0.737298\pi\) | |||||||
\(194\) | −8.48429 | −0.609136 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 7.82183 | 0.558702 | ||||||||
\(197\) | 7.18370 | 0.511818 | 0.255909 | − | 0.966701i | \(-0.417625\pi\) | ||||
0.255909 | + | 0.966701i | \(0.417625\pi\) | |||||||
\(198\) | −0.584778 | −0.0415584 | ||||||||
\(199\) | −18.9591 | −1.34398 | −0.671989 | − | 0.740562i | \(-0.734560\pi\) | ||||
−0.671989 | + | 0.740562i | \(0.734560\pi\) | |||||||
\(200\) | 2.53237 | 0.179066 | ||||||||
\(201\) | 8.47197 | 0.597566 | ||||||||
\(202\) | 5.05131 | 0.355409 | ||||||||
\(203\) | −7.62851 | −0.535417 | ||||||||
\(204\) | −5.70692 | −0.399564 | ||||||||
\(205\) | −2.02496 | −0.141429 | ||||||||
\(206\) | −1.69614 | −0.118175 | ||||||||
\(207\) | −0.701611 | −0.0487653 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.09587 | 0.352489 | ||||||||
\(210\) | −1.72587 | −0.119096 | ||||||||
\(211\) | −19.9916 | −1.37628 | −0.688139 | − | 0.725578i | \(-0.741572\pi\) | ||||
−0.688139 | + | 0.725578i | \(0.741572\pi\) | |||||||
\(212\) | 0.833571 | 0.0572499 | ||||||||
\(213\) | 2.31533 | 0.158644 | ||||||||
\(214\) | −1.34051 | −0.0916356 | ||||||||
\(215\) | −10.7181 | −0.730967 | ||||||||
\(216\) | −2.13914 | −0.145550 | ||||||||
\(217\) | 10.9828 | 0.745558 | ||||||||
\(218\) | −7.53303 | −0.510201 | ||||||||
\(219\) | −2.21094 | −0.149401 | ||||||||
\(220\) | 3.23897 | 0.218372 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 1.21727 | 0.0816981 | ||||||||
\(223\) | 27.7784 | 1.86018 | 0.930091 | − | 0.367330i | \(-0.119728\pi\) | ||||
0.930091 | + | 0.367330i | \(0.119728\pi\) | |||||||
\(224\) | −8.28806 | −0.553769 | ||||||||
\(225\) | −1.18383 | −0.0789218 | ||||||||
\(226\) | −7.38419 | −0.491189 | ||||||||
\(227\) | −28.6524 | −1.90173 | −0.950863 | − | 0.309612i | \(-0.899801\pi\) | ||||
−0.950863 | + | 0.309612i | \(0.899801\pi\) | |||||||
\(228\) | 8.44913 | 0.559557 | ||||||||
\(229\) | −4.83459 | −0.319479 | −0.159739 | − | 0.987159i | \(-0.551065\pi\) | ||||
−0.159739 | + | 0.987159i | \(0.551065\pi\) | |||||||
\(230\) | −0.801497 | −0.0528491 | ||||||||
\(231\) | 1.51078 | 0.0994023 | ||||||||
\(232\) | −10.8013 | −0.709141 | ||||||||
\(233\) | 13.6237 | 0.892518 | 0.446259 | − | 0.894904i | \(-0.352756\pi\) | ||||
0.446259 | + | 0.894904i | \(0.352756\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.33004 | −0.478159 | ||||||||
\(236\) | −4.39417 | −0.286036 | ||||||||
\(237\) | −5.54589 | −0.360244 | ||||||||
\(238\) | −3.04090 | −0.197112 | ||||||||
\(239\) | 5.99903 | 0.388045 | 0.194023 | − | 0.980997i | \(-0.437846\pi\) | ||||
0.194023 | + | 0.980997i | \(0.437846\pi\) | |||||||
\(240\) | 4.03427 | 0.260411 | ||||||||
\(241\) | 12.9290 | 0.832831 | 0.416416 | − | 0.909174i | \(-0.363286\pi\) | ||||
0.416416 | + | 0.909174i | \(0.363286\pi\) | |||||||
\(242\) | 0.584778 | 0.0375910 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 8.92346 | 0.571266 | ||||||||
\(245\) | −9.21571 | −0.588770 | ||||||||
\(246\) | −0.606168 | −0.0386478 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 15.5506 | 0.987466 | ||||||||
\(249\) | −14.5137 | −0.919766 | ||||||||
\(250\) | −7.06420 | −0.446779 | ||||||||
\(251\) | −23.9724 | −1.51313 | −0.756563 | − | 0.653921i | \(-0.773123\pi\) | ||||
−0.756563 | + | 0.653921i | \(0.773123\pi\) | |||||||
\(252\) | 2.50493 | 0.157796 | ||||||||
\(253\) | 0.701611 | 0.0441099 | ||||||||
\(254\) | 2.95363 | 0.185327 | ||||||||
\(255\) | 6.72392 | 0.421068 | ||||||||
\(256\) | −4.88701 | −0.305438 | ||||||||
\(257\) | 16.3441 | 1.01952 | 0.509758 | − | 0.860318i | \(-0.329735\pi\) | ||||
0.509758 | + | 0.860318i | \(0.329735\pi\) | |||||||
\(258\) | −3.20844 | −0.199749 | ||||||||
\(259\) | −3.14485 | −0.195411 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.04937 | 0.312548 | ||||||||
\(262\) | 9.34313 | 0.577220 | ||||||||
\(263\) | 10.1510 | 0.625936 | 0.312968 | − | 0.949764i | \(-0.398677\pi\) | ||||
0.312968 | + | 0.949764i | \(0.398677\pi\) | |||||||
\(264\) | 2.13914 | 0.131655 | ||||||||
\(265\) | −0.982117 | −0.0603310 | ||||||||
\(266\) | 4.50207 | 0.276040 | ||||||||
\(267\) | 1.80966 | 0.110750 | ||||||||
\(268\) | −14.0468 | −0.858045 | ||||||||
\(269\) | 16.5294 | 1.00781 | 0.503907 | − | 0.863758i | \(-0.331895\pi\) | ||||
0.503907 | + | 0.863758i | \(0.331895\pi\) | |||||||
\(270\) | 1.14237 | 0.0695222 | ||||||||
\(271\) | −20.8927 | −1.26914 | −0.634570 | − | 0.772865i | \(-0.718823\pi\) | ||||
−0.634570 | + | 0.772865i | \(0.718823\pi\) | |||||||
\(272\) | 7.10819 | 0.430997 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 10.0922 | 0.609693 | ||||||||
\(275\) | 1.18383 | 0.0713874 | ||||||||
\(276\) | 1.16330 | 0.0700221 | ||||||||
\(277\) | −17.3070 | −1.03988 | −0.519938 | − | 0.854204i | \(-0.674045\pi\) | ||||
−0.519938 | + | 0.854204i | \(0.674045\pi\) | |||||||
\(278\) | −3.33642 | −0.200105 | ||||||||
\(279\) | −7.26957 | −0.435218 | ||||||||
\(280\) | 6.31329 | 0.377291 | ||||||||
\(281\) | 16.0666 | 0.958450 | 0.479225 | − | 0.877692i | \(-0.340918\pi\) | ||||
0.479225 | + | 0.877692i | \(0.340918\pi\) | |||||||
\(282\) | −2.19424 | −0.130665 | ||||||||
\(283\) | −17.2180 | −1.02350 | −0.511751 | − | 0.859134i | \(-0.671003\pi\) | ||||
−0.511751 | + | 0.859134i | \(0.671003\pi\) | |||||||
\(284\) | −3.83890 | −0.227797 | ||||||||
\(285\) | −9.95480 | −0.589671 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.56604 | 0.0924406 | ||||||||
\(288\) | 5.48593 | 0.323262 | ||||||||
\(289\) | −5.15277 | −0.303104 | ||||||||
\(290\) | 5.76823 | 0.338722 | ||||||||
\(291\) | −14.5085 | −0.850506 | ||||||||
\(292\) | 3.66581 | 0.214525 | ||||||||
\(293\) | −5.29670 | −0.309436 | −0.154718 | − | 0.987959i | \(-0.549447\pi\) | ||||
−0.154718 | + | 0.987959i | \(0.549447\pi\) | |||||||
\(294\) | −2.75871 | −0.160891 | ||||||||
\(295\) | 5.17723 | 0.301430 | ||||||||
\(296\) | −4.45283 | −0.258816 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | 0.0941580 | 0.00545443 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 1.96282 | 0.113324 | ||||||||
\(301\) | 8.28906 | 0.477773 | ||||||||
\(302\) | −9.53812 | −0.548857 | ||||||||
\(303\) | 8.63799 | 0.496240 | ||||||||
\(304\) | −10.5237 | −0.603576 | ||||||||
\(305\) | −10.5137 | −0.602010 | ||||||||
\(306\) | 2.01280 | 0.115064 | ||||||||
\(307\) | −26.3020 | −1.50113 | −0.750567 | − | 0.660794i | \(-0.770220\pi\) | ||||
−0.750567 | + | 0.660794i | \(0.770220\pi\) | |||||||
\(308\) | −2.50493 | −0.142732 | ||||||||
\(309\) | −2.90048 | −0.165002 | ||||||||
\(310\) | −8.30451 | −0.471665 | ||||||||
\(311\) | 32.8590 | 1.86326 | 0.931632 | − | 0.363403i | \(-0.118385\pi\) | ||||
0.931632 | + | 0.363403i | \(0.118385\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 33.2130 | 1.87731 | 0.938655 | − | 0.344858i | \(-0.112073\pi\) | ||||
0.938655 | + | 0.344858i | \(0.112073\pi\) | |||||||
\(314\) | −8.31507 | −0.469247 | ||||||||
\(315\) | −2.95132 | −0.166288 | ||||||||
\(316\) | 9.19527 | 0.517274 | ||||||||
\(317\) | −30.8436 | −1.73235 | −0.866175 | − | 0.499740i | \(-0.833429\pi\) | ||||
−0.866175 | + | 0.499740i | \(0.833429\pi\) | |||||||
\(318\) | −0.293995 | −0.0164864 | ||||||||
\(319\) | −5.04937 | −0.282711 | ||||||||
\(320\) | −1.80159 | −0.100712 | ||||||||
\(321\) | −2.29234 | −0.127946 | ||||||||
\(322\) | 0.619855 | 0.0345432 | ||||||||
\(323\) | −17.5399 | −0.975945 | ||||||||
\(324\) | −1.65803 | −0.0921130 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −7.61300 | −0.421645 | ||||||||
\(327\) | −12.8818 | −0.712368 | ||||||||
\(328\) | 2.21738 | 0.122434 | ||||||||
\(329\) | 5.66884 | 0.312534 | ||||||||
\(330\) | −1.14237 | −0.0628852 | ||||||||
\(331\) | −5.75414 | −0.316276 | −0.158138 | − | 0.987417i | \(-0.550549\pi\) | ||||
−0.158138 | + | 0.987417i | \(0.550549\pi\) | |||||||
\(332\) | 24.0641 | 1.32069 | ||||||||
\(333\) | 2.08160 | 0.114071 | ||||||||
\(334\) | −8.20273 | −0.448833 | ||||||||
\(335\) | 16.5500 | 0.904224 | ||||||||
\(336\) | −3.11999 | −0.170209 | ||||||||
\(337\) | 10.9245 | 0.595094 | 0.297547 | − | 0.954707i | \(-0.403831\pi\) | ||||
0.297547 | + | 0.954707i | \(0.403831\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −12.6273 | −0.685823 | ||||||||
\(340\) | −11.1485 | −0.604612 | ||||||||
\(341\) | 7.26957 | 0.393669 | ||||||||
\(342\) | −2.97995 | −0.161138 | ||||||||
\(343\) | 17.7027 | 0.955854 | ||||||||
\(344\) | 11.7366 | 0.632795 | ||||||||
\(345\) | −1.37060 | −0.0737906 | ||||||||
\(346\) | 10.4485 | 0.561715 | ||||||||
\(347\) | 16.3474 | 0.877572 | 0.438786 | − | 0.898591i | \(-0.355409\pi\) | ||||
0.438786 | + | 0.898591i | \(0.355409\pi\) | |||||||
\(348\) | −8.37203 | −0.448788 | ||||||||
\(349\) | −8.62758 | −0.461824 | −0.230912 | − | 0.972975i | \(-0.574171\pi\) | ||||
−0.230912 | + | 0.972975i | \(0.574171\pi\) | |||||||
\(350\) | 1.04588 | 0.0559046 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −5.48593 | −0.292401 | ||||||||
\(353\) | −16.5793 | −0.882425 | −0.441212 | − | 0.897403i | \(-0.645451\pi\) | ||||
−0.441212 | + | 0.897403i | \(0.645451\pi\) | |||||||
\(354\) | 1.54980 | 0.0823708 | ||||||||
\(355\) | 4.52300 | 0.240056 | ||||||||
\(356\) | −3.00048 | −0.159025 | ||||||||
\(357\) | −5.20009 | −0.275218 | ||||||||
\(358\) | 10.1005 | 0.533826 | ||||||||
\(359\) | 15.5233 | 0.819289 | 0.409645 | − | 0.912245i | \(-0.365653\pi\) | ||||
0.409645 | + | 0.912245i | \(0.365653\pi\) | |||||||
\(360\) | −4.17882 | −0.220243 | ||||||||
\(361\) | 6.96788 | 0.366731 | ||||||||
\(362\) | 2.16554 | 0.113818 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.31907 | −0.226071 | ||||||||
\(366\) | −3.14725 | −0.164509 | ||||||||
\(367\) | 23.4682 | 1.22503 | 0.612514 | − | 0.790460i | \(-0.290158\pi\) | ||||
0.612514 | + | 0.790460i | \(0.290158\pi\) | |||||||
\(368\) | −1.44893 | −0.0755306 | ||||||||
\(369\) | −1.03658 | −0.0539620 | ||||||||
\(370\) | 2.37795 | 0.123624 | ||||||||
\(371\) | 0.759541 | 0.0394334 | ||||||||
\(372\) | 12.0532 | 0.624929 | ||||||||
\(373\) | 12.3222 | 0.638018 | 0.319009 | − | 0.947752i | \(-0.396650\pi\) | ||||
0.319009 | + | 0.947752i | \(0.396650\pi\) | |||||||
\(374\) | −2.01280 | −0.104079 | ||||||||
\(375\) | −12.0801 | −0.623815 | ||||||||
\(376\) | 8.02659 | 0.413940 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −0.883474 | −0.0454410 | ||||||||
\(379\) | 22.8695 | 1.17473 | 0.587365 | − | 0.809322i | \(-0.300165\pi\) | ||||
0.587365 | + | 0.809322i | \(0.300165\pi\) | |||||||
\(380\) | 16.5054 | 0.846709 | ||||||||
\(381\) | 5.05085 | 0.258763 | ||||||||
\(382\) | −12.0616 | −0.617123 | ||||||||
\(383\) | 35.5259 | 1.81529 | 0.907646 | − | 0.419737i | \(-0.137878\pi\) | ||||
0.907646 | + | 0.419737i | \(0.137878\pi\) | |||||||
\(384\) | −11.5112 | −0.587427 | ||||||||
\(385\) | 2.95132 | 0.150413 | ||||||||
\(386\) | −11.0216 | −0.560984 | ||||||||
\(387\) | −5.48659 | −0.278899 | ||||||||
\(388\) | 24.0557 | 1.22124 | ||||||||
\(389\) | −2.67074 | −0.135412 | −0.0677060 | − | 0.997705i | \(-0.521568\pi\) | ||||
−0.0677060 | + | 0.997705i | \(0.521568\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.41493 | −0.122128 | ||||||||
\(392\) | 10.0915 | 0.509696 | ||||||||
\(393\) | 15.9772 | 0.805944 | ||||||||
\(394\) | 4.20087 | 0.211637 | ||||||||
\(395\) | −10.8339 | −0.545113 | ||||||||
\(396\) | 1.65803 | 0.0833193 | ||||||||
\(397\) | 36.4406 | 1.82890 | 0.914451 | − | 0.404698i | \(-0.132623\pi\) | ||||
0.914451 | + | 0.404698i | \(0.132623\pi\) | |||||||
\(398\) | −11.0869 | −0.555736 | ||||||||
\(399\) | 7.69876 | 0.385420 | ||||||||
\(400\) | −2.44477 | −0.122239 | ||||||||
\(401\) | −13.6597 | −0.682132 | −0.341066 | − | 0.940039i | \(-0.610788\pi\) | ||||
−0.341066 | + | 0.940039i | \(0.610788\pi\) | |||||||
\(402\) | 4.95422 | 0.247094 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −14.3221 | −0.712550 | ||||||||
\(405\) | 1.95350 | 0.0970703 | ||||||||
\(406\) | −4.46099 | −0.221395 | ||||||||
\(407\) | −2.08160 | −0.103181 | ||||||||
\(408\) | −7.36288 | −0.364517 | ||||||||
\(409\) | −25.8507 | −1.27823 | −0.639117 | − | 0.769110i | \(-0.720700\pi\) | ||||
−0.639117 | + | 0.769110i | \(0.720700\pi\) | |||||||
\(410\) | −1.18415 | −0.0584810 | ||||||||
\(411\) | 17.2582 | 0.851283 | ||||||||
\(412\) | 4.80909 | 0.236927 | ||||||||
\(413\) | −4.00393 | −0.197020 | ||||||||
\(414\) | −0.410287 | −0.0201645 | ||||||||
\(415\) | −28.3525 | −1.39177 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.70544 | −0.279397 | ||||||||
\(418\) | 2.97995 | 0.145754 | ||||||||
\(419\) | 22.6067 | 1.10441 | 0.552205 | − | 0.833708i | \(-0.313787\pi\) | ||||
0.552205 | + | 0.833708i | \(0.313787\pi\) | |||||||
\(420\) | 4.89339 | 0.238773 | ||||||||
\(421\) | −24.6918 | −1.20341 | −0.601703 | − | 0.798720i | \(-0.705511\pi\) | ||||
−0.601703 | + | 0.798720i | \(0.705511\pi\) | |||||||
\(422\) | −11.6907 | −0.569092 | ||||||||
\(423\) | −3.75225 | −0.182441 | ||||||||
\(424\) | 1.07544 | 0.0522282 | ||||||||
\(425\) | −4.07471 | −0.197652 | ||||||||
\(426\) | 1.35395 | 0.0655993 | ||||||||
\(427\) | 8.13097 | 0.393485 | ||||||||
\(428\) | 3.80079 | 0.183718 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −6.26770 | −0.302255 | ||||||||
\(431\) | −30.1126 | −1.45047 | −0.725237 | − | 0.688499i | \(-0.758270\pi\) | ||||
−0.725237 | + | 0.688499i | \(0.758270\pi\) | |||||||
\(432\) | 2.06515 | 0.0993594 | ||||||||
\(433\) | 30.9402 | 1.48689 | 0.743445 | − | 0.668797i | \(-0.233191\pi\) | ||||
0.743445 | + | 0.668797i | \(0.233191\pi\) | |||||||
\(434\) | 6.42248 | 0.308289 | ||||||||
\(435\) | 9.86396 | 0.472941 | ||||||||
\(436\) | 21.3585 | 1.02289 | ||||||||
\(437\) | 3.57532 | 0.171031 | ||||||||
\(438\) | −1.29291 | −0.0617775 | ||||||||
\(439\) | −7.02158 | −0.335122 | −0.167561 | − | 0.985862i | \(-0.553589\pi\) | ||||
−0.167561 | + | 0.985862i | \(0.553589\pi\) | |||||||
\(440\) | 4.17882 | 0.199217 | ||||||||
\(441\) | −4.71753 | −0.224644 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −22.5411 | −1.07096 | −0.535480 | − | 0.844548i | \(-0.679869\pi\) | ||||
−0.535480 | + | 0.844548i | \(0.679869\pi\) | |||||||
\(444\) | −3.45136 | −0.163794 | ||||||||
\(445\) | 3.53518 | 0.167584 | ||||||||
\(446\) | 16.2442 | 0.769187 | ||||||||
\(447\) | 0.161015 | 0.00761574 | ||||||||
\(448\) | 1.39330 | 0.0658272 | ||||||||
\(449\) | 9.41670 | 0.444401 | 0.222201 | − | 0.975001i | \(-0.428676\pi\) | ||||
0.222201 | + | 0.975001i | \(0.428676\pi\) | |||||||
\(450\) | −0.692276 | −0.0326342 | ||||||||
\(451\) | 1.03658 | 0.0488105 | ||||||||
\(452\) | 20.9365 | 0.984772 | ||||||||
\(453\) | −16.3107 | −0.766341 | ||||||||
\(454\) | −16.7553 | −0.786365 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 10.9008 | 0.510476 | ||||||||
\(457\) | 3.48691 | 0.163111 | 0.0815554 | − | 0.996669i | \(-0.474011\pi\) | ||||
0.0815554 | + | 0.996669i | \(0.474011\pi\) | |||||||
\(458\) | −2.82717 | −0.132105 | ||||||||
\(459\) | 3.44198 | 0.160658 | ||||||||
\(460\) | 2.27250 | 0.105956 | ||||||||
\(461\) | −15.1983 | −0.707855 | −0.353928 | − | 0.935273i | \(-0.615154\pi\) | ||||
−0.353928 | + | 0.935273i | \(0.615154\pi\) | |||||||
\(462\) | 0.883474 | 0.0411029 | ||||||||
\(463\) | −15.9882 | −0.743035 | −0.371518 | − | 0.928426i | \(-0.621162\pi\) | ||||
−0.371518 | + | 0.928426i | \(0.621162\pi\) | |||||||
\(464\) | 10.4277 | 0.484093 | ||||||||
\(465\) | −14.2011 | −0.658562 | ||||||||
\(466\) | 7.96684 | 0.369057 | ||||||||
\(467\) | 32.9225 | 1.52347 | 0.761736 | − | 0.647888i | \(-0.224348\pi\) | ||||
0.761736 | + | 0.647888i | \(0.224348\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.7993 | −0.591017 | ||||||||
\(470\) | −4.28645 | −0.197719 | ||||||||
\(471\) | −14.2192 | −0.655185 | ||||||||
\(472\) | −5.66921 | −0.260947 | ||||||||
\(473\) | 5.48659 | 0.252274 | ||||||||
\(474\) | −3.24312 | −0.148961 | ||||||||
\(475\) | 6.03262 | 0.276796 | ||||||||
\(476\) | 8.62193 | 0.395185 | ||||||||
\(477\) | −0.502747 | −0.0230192 | ||||||||
\(478\) | 3.50811 | 0.160457 | ||||||||
\(479\) | −33.6023 | −1.53533 | −0.767664 | − | 0.640853i | \(-0.778581\pi\) | ||||
−0.767664 | + | 0.640853i | \(0.778581\pi\) | |||||||
\(480\) | 10.7168 | 0.489152 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 7.56061 | 0.344376 | ||||||||
\(483\) | 1.05998 | 0.0482309 | ||||||||
\(484\) | −1.65803 | −0.0753652 | ||||||||
\(485\) | −28.3425 | −1.28697 | ||||||||
\(486\) | 0.584778 | 0.0265261 | ||||||||
\(487\) | −3.70001 | −0.167663 | −0.0838316 | − | 0.996480i | \(-0.526716\pi\) | ||||
−0.0838316 | + | 0.996480i | \(0.526716\pi\) | |||||||
\(488\) | 11.5127 | 0.521158 | ||||||||
\(489\) | −13.0186 | −0.588722 | ||||||||
\(490\) | −5.38915 | −0.243457 | ||||||||
\(491\) | −10.1397 | −0.457599 | −0.228799 | − | 0.973474i | \(-0.573480\pi\) | ||||
−0.228799 | + | 0.973474i | \(0.573480\pi\) | |||||||
\(492\) | 1.71868 | 0.0774840 | ||||||||
\(493\) | 17.3798 | 0.782749 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.95350 | −0.0878034 | ||||||||
\(496\) | −15.0127 | −0.674091 | ||||||||
\(497\) | −3.49796 | −0.156905 | ||||||||
\(498\) | −8.48728 | −0.380324 | ||||||||
\(499\) | 15.1124 | 0.676525 | 0.338263 | − | 0.941052i | \(-0.390161\pi\) | ||||
0.338263 | + | 0.941052i | \(0.390161\pi\) | |||||||
\(500\) | 20.0293 | 0.895736 | ||||||||
\(501\) | −14.0271 | −0.626683 | ||||||||
\(502\) | −14.0185 | −0.625678 | ||||||||
\(503\) | 11.9190 | 0.531441 | 0.265721 | − | 0.964050i | \(-0.414390\pi\) | ||||
0.265721 | + | 0.964050i | \(0.414390\pi\) | |||||||
\(504\) | 3.23178 | 0.143955 | ||||||||
\(505\) | 16.8743 | 0.750898 | ||||||||
\(506\) | 0.410287 | 0.0182395 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8.37448 | −0.371558 | ||||||||
\(509\) | 35.2059 | 1.56047 | 0.780236 | − | 0.625485i | \(-0.215099\pi\) | ||||
0.780236 | + | 0.625485i | \(0.215099\pi\) | |||||||
\(510\) | 3.93200 | 0.174112 | ||||||||
\(511\) | 3.34025 | 0.147764 | ||||||||
\(512\) | 20.1645 | 0.891154 | ||||||||
\(513\) | −5.09587 | −0.224988 | ||||||||
\(514\) | 9.55767 | 0.421571 | ||||||||
\(515\) | −5.66609 | −0.249678 | ||||||||
\(516\) | 9.09696 | 0.400471 | ||||||||
\(517\) | 3.75225 | 0.165024 | ||||||||
\(518\) | −1.83904 | −0.0808028 | ||||||||
\(519\) | 17.8674 | 0.784294 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.84143 | −0.124485 | −0.0622426 | − | 0.998061i | \(-0.519825\pi\) | ||||
−0.0622426 | + | 0.998061i | \(0.519825\pi\) | |||||||
\(522\) | 2.95276 | 0.129239 | ||||||||
\(523\) | −17.8564 | −0.780804 | −0.390402 | − | 0.920644i | \(-0.627664\pi\) | ||||
−0.390402 | + | 0.920644i | \(0.627664\pi\) | |||||||
\(524\) | −26.4908 | −1.15725 | ||||||||
\(525\) | 1.78851 | 0.0780568 | ||||||||
\(526\) | 5.93607 | 0.258825 | ||||||||
\(527\) | −25.0217 | −1.08996 | ||||||||
\(528\) | −2.06515 | −0.0898739 | ||||||||
\(529\) | −22.5077 | −0.978597 | ||||||||
\(530\) | −0.574321 | −0.0249469 | ||||||||
\(531\) | 2.65023 | 0.115010 | ||||||||
\(532\) | −12.7648 | −0.553424 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 1.05825 | 0.0457950 | ||||||||
\(535\) | −4.47810 | −0.193605 | ||||||||
\(536\) | −18.1227 | −0.782782 | ||||||||
\(537\) | 17.2723 | 0.745354 | ||||||||
\(538\) | 9.66602 | 0.416732 | ||||||||
\(539\) | 4.71753 | 0.203198 | ||||||||
\(540\) | −3.23897 | −0.139383 | ||||||||
\(541\) | 3.56883 | 0.153436 | 0.0767179 | − | 0.997053i | \(-0.475556\pi\) | ||||
0.0767179 | + | 0.997053i | \(0.475556\pi\) | |||||||
\(542\) | −12.2176 | −0.524791 | ||||||||
\(543\) | 3.70318 | 0.158919 | ||||||||
\(544\) | 18.8825 | 0.809579 | ||||||||
\(545\) | −25.1647 | −1.07794 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.50639 | 0.149923 | 0.0749613 | − | 0.997186i | \(-0.476117\pi\) | ||||
0.0749613 | + | 0.997186i | \(0.476117\pi\) | |||||||
\(548\) | −28.6146 | −1.22236 | ||||||||
\(549\) | −5.38195 | −0.229696 | ||||||||
\(550\) | 0.692276 | 0.0295188 | ||||||||
\(551\) | −25.7309 | −1.09617 | ||||||||
\(552\) | 1.50084 | 0.0638802 | ||||||||
\(553\) | 8.37864 | 0.356296 | ||||||||
\(554\) | −10.1207 | −0.429989 | ||||||||
\(555\) | 4.06641 | 0.172610 | ||||||||
\(556\) | 9.45982 | 0.401186 | ||||||||
\(557\) | −7.38164 | −0.312770 | −0.156385 | − | 0.987696i | \(-0.549984\pi\) | ||||
−0.156385 | + | 0.987696i | \(0.549984\pi\) | |||||||
\(558\) | −4.25109 | −0.179963 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −6.09491 | −0.257557 | ||||||||
\(561\) | −3.44198 | −0.145321 | ||||||||
\(562\) | 9.39537 | 0.396320 | ||||||||
\(563\) | −35.5383 | −1.49776 | −0.748879 | − | 0.662706i | \(-0.769408\pi\) | ||||
−0.748879 | + | 0.662706i | \(0.769408\pi\) | |||||||
\(564\) | 6.22136 | 0.261967 | ||||||||
\(565\) | −24.6675 | −1.03777 | ||||||||
\(566\) | −10.0687 | −0.423219 | ||||||||
\(567\) | −1.51078 | −0.0634470 | ||||||||
\(568\) | −4.95281 | −0.207815 | ||||||||
\(569\) | −19.6546 | −0.823966 | −0.411983 | − | 0.911192i | \(-0.635164\pi\) | ||||
−0.411983 | + | 0.911192i | \(0.635164\pi\) | |||||||
\(570\) | −5.82135 | −0.243830 | ||||||||
\(571\) | −18.6081 | −0.778726 | −0.389363 | − | 0.921084i | \(-0.627305\pi\) | ||||
−0.389363 | + | 0.921084i | \(0.627305\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −20.6259 | −0.861658 | ||||||||
\(574\) | 0.915788 | 0.0382243 | ||||||||
\(575\) | 0.830586 | 0.0346378 | ||||||||
\(576\) | −0.922236 | −0.0384265 | ||||||||
\(577\) | −25.5485 | −1.06360 | −0.531799 | − | 0.846871i | \(-0.678484\pi\) | ||||
−0.531799 | + | 0.846871i | \(0.678484\pi\) | |||||||
\(578\) | −3.01323 | −0.125334 | ||||||||
\(579\) | −18.8475 | −0.783274 | ||||||||
\(580\) | −16.3548 | −0.679096 | ||||||||
\(581\) | 21.9270 | 0.909686 | ||||||||
\(582\) | −8.48429 | −0.351685 | ||||||||
\(583\) | 0.502747 | 0.0208216 | ||||||||
\(584\) | 4.72950 | 0.195708 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.09739 | −0.127952 | ||||||||
\(587\) | −2.35936 | −0.0973813 | −0.0486907 | − | 0.998814i | \(-0.515505\pi\) | ||||
−0.0486907 | + | 0.998814i | \(0.515505\pi\) | |||||||
\(588\) | 7.82183 | 0.322567 | ||||||||
\(589\) | 37.0448 | 1.52640 | ||||||||
\(590\) | 3.02753 | 0.124642 | ||||||||
\(591\) | 7.18370 | 0.295498 | ||||||||
\(592\) | 4.29881 | 0.176680 | ||||||||
\(593\) | −11.6707 | −0.479257 | −0.239628 | − | 0.970865i | \(-0.577026\pi\) | ||||
−0.239628 | + | 0.970865i | \(0.577026\pi\) | |||||||
\(594\) | −0.584778 | −0.0239938 | ||||||||
\(595\) | −10.1584 | −0.416453 | ||||||||
\(596\) | −0.266968 | −0.0109354 | ||||||||
\(597\) | −18.9591 | −0.775946 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.12181 | 0.372707 | 0.186354 | − | 0.982483i | \(-0.440333\pi\) | ||||
0.186354 | + | 0.982483i | \(0.440333\pi\) | |||||||
\(600\) | 2.53237 | 0.103384 | ||||||||
\(601\) | 6.90316 | 0.281586 | 0.140793 | − | 0.990039i | \(-0.455035\pi\) | ||||
0.140793 | + | 0.990039i | \(0.455035\pi\) | |||||||
\(602\) | 4.84726 | 0.197560 | ||||||||
\(603\) | 8.47197 | 0.345005 | ||||||||
\(604\) | 27.0436 | 1.10039 | ||||||||
\(605\) | 1.95350 | 0.0794212 | ||||||||
\(606\) | 5.05131 | 0.205196 | ||||||||
\(607\) | 11.5559 | 0.469038 | 0.234519 | − | 0.972112i | \(-0.424648\pi\) | ||||
0.234519 | + | 0.972112i | \(0.424648\pi\) | |||||||
\(608\) | −27.9556 | −1.13375 | ||||||||
\(609\) | −7.62851 | −0.309123 | ||||||||
\(610\) | −6.14816 | −0.248932 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −5.70692 | −0.230689 | ||||||||
\(613\) | 37.7362 | 1.52415 | 0.762075 | − | 0.647488i | \(-0.224181\pi\) | ||||
0.762075 | + | 0.647488i | \(0.224181\pi\) | |||||||
\(614\) | −15.3808 | −0.620720 | ||||||||
\(615\) | −2.02496 | −0.0816541 | ||||||||
\(616\) | −3.23178 | −0.130212 | ||||||||
\(617\) | 28.2159 | 1.13593 | 0.567964 | − | 0.823053i | \(-0.307731\pi\) | ||||
0.567964 | + | 0.823053i | \(0.307731\pi\) | |||||||
\(618\) | −1.69614 | −0.0682286 | ||||||||
\(619\) | 38.4407 | 1.54506 | 0.772530 | − | 0.634978i | \(-0.218991\pi\) | ||||
0.772530 | + | 0.634978i | \(0.218991\pi\) | |||||||
\(620\) | 23.5460 | 0.945628 | ||||||||
\(621\) | −0.701611 | −0.0281547 | ||||||||
\(622\) | 19.2152 | 0.770461 | ||||||||
\(623\) | −2.73401 | −0.109536 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17.6794 | −0.707177 | ||||||||
\(626\) | 19.4222 | 0.776269 | ||||||||
\(627\) | 5.09587 | 0.203509 | ||||||||
\(628\) | 23.5759 | 0.940781 | ||||||||
\(629\) | 7.16483 | 0.285680 | ||||||||
\(630\) | −1.72587 | −0.0687603 | ||||||||
\(631\) | −16.9688 | −0.675519 | −0.337759 | − | 0.941232i | \(-0.609669\pi\) | ||||
−0.337759 | + | 0.941232i | \(0.609669\pi\) | |||||||
\(632\) | 11.8634 | 0.471902 | ||||||||
\(633\) | −19.9916 | −0.794595 | ||||||||
\(634\) | −18.0367 | −0.716328 | ||||||||
\(635\) | 9.86685 | 0.391554 | ||||||||
\(636\) | 0.833571 | 0.0330532 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.95276 | −0.116901 | ||||||||
\(639\) | 2.31533 | 0.0915930 | ||||||||
\(640\) | −22.4871 | −0.888881 | ||||||||
\(641\) | 6.00876 | 0.237332 | 0.118666 | − | 0.992934i | \(-0.462138\pi\) | ||||
0.118666 | + | 0.992934i | \(0.462138\pi\) | |||||||
\(642\) | −1.34051 | −0.0529059 | ||||||||
\(643\) | 9.64269 | 0.380270 | 0.190135 | − | 0.981758i | \(-0.439107\pi\) | ||||
0.190135 | + | 0.981758i | \(0.439107\pi\) | |||||||
\(644\) | −1.75749 | −0.0692547 | ||||||||
\(645\) | −10.7181 | −0.422024 | ||||||||
\(646\) | −10.2569 | −0.403554 | ||||||||
\(647\) | −34.1912 | −1.34420 | −0.672098 | − | 0.740463i | \(-0.734606\pi\) | ||||
−0.672098 | + | 0.740463i | \(0.734606\pi\) | |||||||
\(648\) | −2.13914 | −0.0840333 | ||||||||
\(649\) | −2.65023 | −0.104031 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10.9828 | 0.430448 | ||||||||
\(652\) | 21.5853 | 0.845345 | ||||||||
\(653\) | −2.32307 | −0.0909086 | −0.0454543 | − | 0.998966i | \(-0.514474\pi\) | ||||
−0.0454543 | + | 0.998966i | \(0.514474\pi\) | |||||||
\(654\) | −7.53303 | −0.294565 | ||||||||
\(655\) | 31.2115 | 1.21954 | ||||||||
\(656\) | −2.14068 | −0.0835796 | ||||||||
\(657\) | −2.21094 | −0.0862568 | ||||||||
\(658\) | 3.31502 | 0.129233 | ||||||||
\(659\) | 4.07928 | 0.158906 | 0.0794532 | − | 0.996839i | \(-0.474683\pi\) | ||||
0.0794532 | + | 0.996839i | \(0.474683\pi\) | |||||||
\(660\) | 3.23897 | 0.126077 | ||||||||
\(661\) | 42.2740 | 1.64427 | 0.822135 | − | 0.569293i | \(-0.192783\pi\) | ||||
0.822135 | + | 0.569293i | \(0.192783\pi\) | |||||||
\(662\) | −3.36489 | −0.130780 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 31.0467 | 1.20485 | ||||||||
\(665\) | 15.0395 | 0.583209 | ||||||||
\(666\) | 1.21727 | 0.0471684 | ||||||||
\(667\) | −3.54270 | −0.137174 | ||||||||
\(668\) | 23.2574 | 0.899854 | ||||||||
\(669\) | 27.7784 | 1.07398 | ||||||||
\(670\) | 9.67809 | 0.373897 | ||||||||
\(671\) | 5.38195 | 0.207768 | ||||||||
\(672\) | −8.28806 | −0.319719 | ||||||||
\(673\) | −10.6688 | −0.411252 | −0.205626 | − | 0.978631i | \(-0.565923\pi\) | ||||
−0.205626 | + | 0.978631i | \(0.565923\pi\) | |||||||
\(674\) | 6.38840 | 0.246072 | ||||||||
\(675\) | −1.18383 | −0.0455655 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 24.2174 | 0.930752 | 0.465376 | − | 0.885113i | \(-0.345919\pi\) | ||||
0.465376 | + | 0.885113i | \(0.345919\pi\) | |||||||
\(678\) | −7.38419 | −0.283588 | ||||||||
\(679\) | 21.9193 | 0.841185 | ||||||||
\(680\) | −14.3834 | −0.551578 | ||||||||
\(681\) | −28.6524 | −1.09796 | ||||||||
\(682\) | 4.25109 | 0.162783 | ||||||||
\(683\) | −37.1698 | −1.42226 | −0.711132 | − | 0.703059i | \(-0.751817\pi\) | ||||
−0.711132 | + | 0.703059i | \(0.751817\pi\) | |||||||
\(684\) | 8.44913 | 0.323060 | ||||||||
\(685\) | 33.7139 | 1.28814 | ||||||||
\(686\) | 10.3521 | 0.395246 | ||||||||
\(687\) | −4.83459 | −0.184451 | ||||||||
\(688\) | −11.3306 | −0.431976 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −0.801497 | −0.0305125 | ||||||||
\(691\) | 15.9632 | 0.607268 | 0.303634 | − | 0.952789i | \(-0.401800\pi\) | ||||
0.303634 | + | 0.952789i | \(0.401800\pi\) | |||||||
\(692\) | −29.6248 | −1.12617 | ||||||||
\(693\) | 1.51078 | 0.0573899 | ||||||||
\(694\) | 9.55959 | 0.362877 | ||||||||
\(695\) | −11.1456 | −0.422777 | ||||||||
\(696\) | −10.8013 | −0.409423 | ||||||||
\(697\) | −3.56788 | −0.135143 | ||||||||
\(698\) | −5.04522 | −0.190965 | ||||||||
\(699\) | 13.6237 | 0.515295 | ||||||||
\(700\) | −2.96540 | −0.112082 | ||||||||
\(701\) | −2.01736 | −0.0761947 | −0.0380974 | − | 0.999274i | \(-0.512130\pi\) | ||||
−0.0380974 | + | 0.999274i | \(0.512130\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.6076 | −0.400072 | ||||||||
\(704\) | 0.922236 | 0.0347581 | ||||||||
\(705\) | −7.33004 | −0.276065 | ||||||||
\(706\) | −9.69519 | −0.364883 | ||||||||
\(707\) | −13.0501 | −0.490801 | ||||||||
\(708\) | −4.39417 | −0.165143 | ||||||||
\(709\) | 29.6428 | 1.11326 | 0.556629 | − | 0.830761i | \(-0.312095\pi\) | ||||
0.556629 | + | 0.830761i | \(0.312095\pi\) | |||||||
\(710\) | 2.64495 | 0.0992634 | ||||||||
\(711\) | −5.54589 | −0.207987 | ||||||||
\(712\) | −3.87112 | −0.145076 | ||||||||
\(713\) | 5.10041 | 0.191012 | ||||||||
\(714\) | −3.04090 | −0.113803 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −28.6380 | −1.07025 | ||||||||
\(717\) | 5.99903 | 0.224038 | ||||||||
\(718\) | 9.07770 | 0.338777 | ||||||||
\(719\) | 32.3389 | 1.20604 | 0.603018 | − | 0.797728i | \(-0.293965\pi\) | ||||
0.603018 | + | 0.797728i | \(0.293965\pi\) | |||||||
\(720\) | 4.03427 | 0.150348 | ||||||||
\(721\) | 4.38199 | 0.163194 | ||||||||
\(722\) | 4.07467 | 0.151643 | ||||||||
\(723\) | 12.9290 | 0.480835 | ||||||||
\(724\) | −6.13999 | −0.228191 | ||||||||
\(725\) | −5.97758 | −0.222002 | ||||||||
\(726\) | 0.584778 | 0.0217032 | ||||||||
\(727\) | 37.9325 | 1.40684 | 0.703419 | − | 0.710775i | \(-0.251656\pi\) | ||||
0.703419 | + | 0.710775i | \(0.251656\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −2.52570 | −0.0934803 | ||||||||
\(731\) | −18.8847 | −0.698478 | ||||||||
\(732\) | 8.92346 | 0.329821 | ||||||||
\(733\) | 16.7917 | 0.620217 | 0.310109 | − | 0.950701i | \(-0.399635\pi\) | ||||
0.310109 | + | 0.950701i | \(0.399635\pi\) | |||||||
\(734\) | 13.7237 | 0.506550 | ||||||||
\(735\) | −9.21571 | −0.339927 | ||||||||
\(736\) | −3.84899 | −0.141876 | ||||||||
\(737\) | −8.47197 | −0.312069 | ||||||||
\(738\) | −0.606168 | −0.0223133 | ||||||||
\(739\) | 25.4629 | 0.936668 | 0.468334 | − | 0.883551i | \(-0.344854\pi\) | ||||
0.468334 | + | 0.883551i | \(0.344854\pi\) | |||||||
\(740\) | −6.74225 | −0.247850 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.444164 | 0.0163058 | ||||||||
\(743\) | 4.81269 | 0.176560 | 0.0882802 | − | 0.996096i | \(-0.471863\pi\) | ||||
0.0882802 | + | 0.996096i | \(0.471863\pi\) | |||||||
\(744\) | 15.5506 | 0.570114 | ||||||||
\(745\) | 0.314543 | 0.0115240 | ||||||||
\(746\) | 7.20574 | 0.263821 | ||||||||
\(747\) | −14.5137 | −0.531027 | ||||||||
\(748\) | 5.70692 | 0.208666 | ||||||||
\(749\) | 3.46324 | 0.126544 | ||||||||
\(750\) | −7.06420 | −0.257948 | ||||||||
\(751\) | −24.9537 | −0.910574 | −0.455287 | − | 0.890345i | \(-0.650463\pi\) | ||||
−0.455287 | + | 0.890345i | \(0.650463\pi\) | |||||||
\(752\) | −7.74895 | −0.282575 | ||||||||
\(753\) | −23.9724 | −0.873603 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −31.8629 | −1.15961 | ||||||||
\(756\) | 2.50493 | 0.0911035 | ||||||||
\(757\) | −33.8373 | −1.22984 | −0.614919 | − | 0.788591i | \(-0.710811\pi\) | ||||
−0.614919 | + | 0.788591i | \(0.710811\pi\) | |||||||
\(758\) | 13.3736 | 0.485752 | ||||||||
\(759\) | 0.701611 | 0.0254669 | ||||||||
\(760\) | 21.2947 | 0.772440 | ||||||||
\(761\) | −50.5981 | −1.83418 | −0.917091 | − | 0.398679i | \(-0.869469\pi\) | ||||
−0.917091 | + | 0.398679i | \(0.869469\pi\) | |||||||
\(762\) | 2.95363 | 0.106999 | ||||||||
\(763\) | 19.4617 | 0.704561 | ||||||||
\(764\) | 34.1984 | 1.23725 | ||||||||
\(765\) | 6.72392 | 0.243104 | ||||||||
\(766\) | 20.7748 | 0.750624 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −4.88701 | −0.176345 | ||||||||
\(769\) | 26.1333 | 0.942389 | 0.471195 | − | 0.882029i | \(-0.343823\pi\) | ||||
0.471195 | + | 0.882029i | \(0.343823\pi\) | |||||||
\(770\) | 1.72587 | 0.0621960 | ||||||||
\(771\) | 16.3441 | 0.588618 | ||||||||
\(772\) | 31.2497 | 1.12470 | ||||||||
\(773\) | −0.778578 | −0.0280035 | −0.0140018 | − | 0.999902i | \(-0.504457\pi\) | ||||
−0.0140018 | + | 0.999902i | \(0.504457\pi\) | |||||||
\(774\) | −3.20844 | −0.115325 | ||||||||
\(775\) | 8.60591 | 0.309133 | ||||||||
\(776\) | 31.0358 | 1.11412 | ||||||||
\(777\) | −3.14485 | −0.112821 | ||||||||
\(778\) | −1.56179 | −0.0559930 | ||||||||
\(779\) | 5.28226 | 0.189257 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.31533 | −0.0828490 | ||||||||
\(782\) | −1.41220 | −0.0505002 | ||||||||
\(783\) | 5.04937 | 0.180450 | ||||||||
\(784\) | −9.74239 | −0.347942 | ||||||||
\(785\) | −27.7772 | −0.991411 | ||||||||
\(786\) | 9.34313 | 0.333258 | ||||||||
\(787\) | 33.9128 | 1.20886 | 0.604431 | − | 0.796658i | \(-0.293401\pi\) | ||||
0.604431 | + | 0.796658i | \(0.293401\pi\) | |||||||
\(788\) | −11.9108 | −0.424305 | ||||||||
\(789\) | 10.1510 | 0.361384 | ||||||||
\(790\) | −6.33544 | −0.225405 | ||||||||
\(791\) | 19.0772 | 0.678306 | ||||||||
\(792\) | 2.13914 | 0.0760110 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 21.3097 | 0.756252 | ||||||||
\(795\) | −0.982117 | −0.0348321 | ||||||||
\(796\) | 31.4349 | 1.11418 | ||||||||
\(797\) | 26.9305 | 0.953928 | 0.476964 | − | 0.878923i | \(-0.341737\pi\) | ||||
0.476964 | + | 0.878923i | \(0.341737\pi\) | |||||||
\(798\) | 4.50207 | 0.159372 | ||||||||
\(799\) | −12.9152 | −0.456906 | ||||||||
\(800\) | −6.49439 | −0.229611 | ||||||||
\(801\) | 1.80966 | 0.0639413 | ||||||||
\(802\) | −7.98789 | −0.282062 | ||||||||
\(803\) | 2.21094 | 0.0780223 | ||||||||
\(804\) | −14.0468 | −0.495393 | ||||||||
\(805\) | 2.07068 | 0.0729819 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 16.5294 | 0.581862 | ||||||||
\(808\) | −18.4779 | −0.650049 | ||||||||
\(809\) | 52.4814 | 1.84515 | 0.922575 | − | 0.385819i | \(-0.126081\pi\) | ||||
0.922575 | + | 0.385819i | \(0.126081\pi\) | |||||||
\(810\) | 1.14237 | 0.0401387 | ||||||||
\(811\) | −19.2236 | −0.675033 | −0.337516 | − | 0.941320i | \(-0.609587\pi\) | ||||
−0.337516 | + | 0.941320i | \(0.609587\pi\) | |||||||
\(812\) | 12.6483 | 0.443869 | ||||||||
\(813\) | −20.8927 | −0.732739 | ||||||||
\(814\) | −1.21727 | −0.0426655 | ||||||||
\(815\) | −25.4319 | −0.890840 | ||||||||
\(816\) | 7.10819 | 0.248836 | ||||||||
\(817\) | 27.9590 | 0.978160 | ||||||||
\(818\) | −15.1169 | −0.528551 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.35744 | 0.117247 | ||||||||
\(821\) | −30.4099 | −1.06131 | −0.530657 | − | 0.847587i | \(-0.678055\pi\) | ||||
−0.530657 | + | 0.847587i | \(0.678055\pi\) | |||||||
\(822\) | 10.0922 | 0.352006 | ||||||||
\(823\) | 16.1575 | 0.563216 | 0.281608 | − | 0.959530i | \(-0.409132\pi\) | ||||
0.281608 | + | 0.959530i | \(0.409132\pi\) | |||||||
\(824\) | 6.20452 | 0.216145 | ||||||||
\(825\) | 1.18383 | 0.0412155 | ||||||||
\(826\) | −2.34141 | −0.0814681 | ||||||||
\(827\) | 47.5066 | 1.65197 | 0.825983 | − | 0.563695i | \(-0.190621\pi\) | ||||
0.825983 | + | 0.563695i | \(0.190621\pi\) | |||||||
\(828\) | 1.16330 | 0.0404273 | ||||||||
\(829\) | 56.6932 | 1.96904 | 0.984519 | − | 0.175278i | \(-0.0560825\pi\) | ||||
0.984519 | + | 0.175278i | \(0.0560825\pi\) | |||||||
\(830\) | −16.5799 | −0.575497 | ||||||||
\(831\) | −17.3070 | −0.600372 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −16.2376 | −0.562601 | ||||||||
\(834\) | −3.33642 | −0.115531 | ||||||||
\(835\) | −27.4019 | −0.948283 | ||||||||
\(836\) | −8.44913 | −0.292219 | ||||||||
\(837\) | −7.26957 | −0.251273 | ||||||||
\(838\) | 13.2199 | 0.456674 | ||||||||
\(839\) | −35.2293 | −1.21625 | −0.608125 | − | 0.793841i | \(-0.708078\pi\) | ||||
−0.608125 | + | 0.793841i | \(0.708078\pi\) | |||||||
\(840\) | 6.31329 | 0.217829 | ||||||||
\(841\) | −3.50384 | −0.120822 | ||||||||
\(842\) | −14.4393 | −0.497610 | ||||||||
\(843\) | 16.0666 | 0.553361 | ||||||||
\(844\) | 33.1468 | 1.14096 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −2.19424 | −0.0754394 | ||||||||
\(847\) | −1.51078 | −0.0519112 | ||||||||
\(848\) | −1.03824 | −0.0356535 | ||||||||
\(849\) | −17.2180 | −0.590919 | ||||||||
\(850\) | −2.38280 | −0.0817294 | ||||||||
\(851\) | −1.46047 | −0.0500644 | ||||||||
\(852\) | −3.83890 | −0.131518 | ||||||||
\(853\) | −18.7185 | −0.640909 | −0.320454 | − | 0.947264i | \(-0.603836\pi\) | ||||
−0.320454 | + | 0.947264i | \(0.603836\pi\) | |||||||
\(854\) | 4.75482 | 0.162706 | ||||||||
\(855\) | −9.95480 | −0.340447 | ||||||||
\(856\) | 4.90365 | 0.167603 | ||||||||
\(857\) | 47.3032 | 1.61585 | 0.807924 | − | 0.589287i | \(-0.200591\pi\) | ||||
0.807924 | + | 0.589287i | \(0.200591\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −40.6908 | −1.38835 | −0.694176 | − | 0.719805i | \(-0.744231\pi\) | ||||
−0.694176 | + | 0.719805i | \(0.744231\pi\) | |||||||
\(860\) | 17.7709 | 0.605984 | ||||||||
\(861\) | 1.56604 | 0.0533706 | ||||||||
\(862\) | −17.6092 | −0.599772 | ||||||||
\(863\) | 1.42374 | 0.0484647 | 0.0242324 | − | 0.999706i | \(-0.492286\pi\) | ||||
0.0242324 | + | 0.999706i | \(0.492286\pi\) | |||||||
\(864\) | 5.48593 | 0.186635 | ||||||||
\(865\) | 34.9041 | 1.18678 | ||||||||
\(866\) | 18.0931 | 0.614830 | ||||||||
\(867\) | −5.15277 | −0.174997 | ||||||||
\(868\) | −18.2098 | −0.618080 | ||||||||
\(869\) | 5.54589 | 0.188131 | ||||||||
\(870\) | 5.76823 | 0.195561 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 27.5561 | 0.933166 | ||||||||
\(873\) | −14.5085 | −0.491040 | ||||||||
\(874\) | 2.09077 | 0.0707213 | ||||||||
\(875\) | 18.2505 | 0.616978 | ||||||||
\(876\) | 3.66581 | 0.123856 | ||||||||
\(877\) | −56.1060 | −1.89457 | −0.947283 | − | 0.320397i | \(-0.896184\pi\) | ||||
−0.947283 | + | 0.320397i | \(0.896184\pi\) | |||||||
\(878\) | −4.10607 | −0.138573 | ||||||||
\(879\) | −5.29670 | −0.178653 | ||||||||
\(880\) | −4.03427 | −0.135995 | ||||||||
\(881\) | 16.2234 | 0.546581 | 0.273290 | − | 0.961932i | \(-0.411888\pi\) | ||||
0.273290 | + | 0.961932i | \(0.411888\pi\) | |||||||
\(882\) | −2.75871 | −0.0928906 | ||||||||
\(883\) | −33.0296 | −1.11153 | −0.555767 | − | 0.831338i | \(-0.687575\pi\) | ||||
−0.555767 | + | 0.831338i | \(0.687575\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.17723 | 0.174031 | ||||||||
\(886\) | −13.1815 | −0.442843 | ||||||||
\(887\) | −54.6149 | −1.83379 | −0.916894 | − | 0.399130i | \(-0.869312\pi\) | ||||
−0.916894 | + | 0.399130i | \(0.869312\pi\) | |||||||
\(888\) | −4.45283 | −0.149427 | ||||||||
\(889\) | −7.63074 | −0.255927 | ||||||||
\(890\) | 2.06730 | 0.0692960 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | −46.0576 | −1.54212 | ||||||||
\(893\) | 19.1210 | 0.639860 | ||||||||
\(894\) | 0.0941580 | 0.00314911 | ||||||||
\(895\) | 33.7414 | 1.12785 | ||||||||
\(896\) | 17.3909 | 0.580989 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 5.50668 | 0.183760 | ||||||||
\(899\) | −36.7068 | −1.22424 | ||||||||
\(900\) | 1.96282 | 0.0654275 | ||||||||
\(901\) | −1.73044 | −0.0576494 | ||||||||
\(902\) | 0.606168 | 0.0201832 | ||||||||
\(903\) | 8.28906 | 0.275843 | ||||||||
\(904\) | 27.0116 | 0.898393 | ||||||||
\(905\) | 7.23417 | 0.240472 | ||||||||
\(906\) | −9.53812 | −0.316883 | ||||||||
\(907\) | 31.1937 | 1.03577 | 0.517884 | − | 0.855451i | \(-0.326720\pi\) | ||||
0.517884 | + | 0.855451i | \(0.326720\pi\) | |||||||
\(908\) | 47.5066 | 1.57656 | ||||||||
\(909\) | 8.63799 | 0.286504 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 53.7300 | 1.78015 | 0.890077 | − | 0.455810i | \(-0.150650\pi\) | ||||
0.890077 | + | 0.455810i | \(0.150650\pi\) | |||||||
\(912\) | −10.5237 | −0.348475 | ||||||||
\(913\) | 14.5137 | 0.480332 | ||||||||
\(914\) | 2.03907 | 0.0674464 | ||||||||
\(915\) | −10.5137 | −0.347571 | ||||||||
\(916\) | 8.01592 | 0.264853 | ||||||||
\(917\) | −24.1381 | −0.797111 | ||||||||
\(918\) | 2.01280 | 0.0664322 | ||||||||
\(919\) | 16.3202 | 0.538353 | 0.269177 | − | 0.963091i | \(-0.413248\pi\) | ||||
0.269177 | + | 0.963091i | \(0.413248\pi\) | |||||||
\(920\) | 2.93190 | 0.0966620 | ||||||||
\(921\) | −26.3020 | −0.866680 | ||||||||
\(922\) | −8.88764 | −0.292699 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −2.50493 | −0.0824062 | ||||||||
\(925\) | −2.46425 | −0.0810241 | ||||||||
\(926\) | −9.34956 | −0.307246 | ||||||||
\(927\) | −2.90048 | −0.0952641 | ||||||||
\(928\) | 27.7005 | 0.909314 | ||||||||
\(929\) | −56.4975 | −1.85362 | −0.926811 | − | 0.375527i | \(-0.877462\pi\) | ||||
−0.926811 | + | 0.375527i | \(0.877462\pi\) | |||||||
\(930\) | −8.30451 | −0.272316 | ||||||||
\(931\) | 24.0399 | 0.787877 | ||||||||
\(932\) | −22.5885 | −0.739912 | ||||||||
\(933\) | 32.8590 | 1.07576 | ||||||||
\(934\) | 19.2524 | 0.629957 | ||||||||
\(935\) | −6.72392 | −0.219896 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 52.5328 | 1.71617 | 0.858086 | − | 0.513506i | \(-0.171654\pi\) | ||||
0.858086 | + | 0.513506i | \(0.171654\pi\) | |||||||
\(938\) | −7.48476 | −0.244386 | ||||||||
\(939\) | 33.2130 | 1.08387 | ||||||||
\(940\) | 12.1535 | 0.396402 | ||||||||
\(941\) | −24.3963 | −0.795296 | −0.397648 | − | 0.917538i | \(-0.630174\pi\) | ||||
−0.397648 | + | 0.917538i | \(0.630174\pi\) | |||||||
\(942\) | −8.31507 | −0.270920 | ||||||||
\(943\) | 0.727273 | 0.0236833 | ||||||||
\(944\) | 5.47311 | 0.178135 | ||||||||
\(945\) | −2.95132 | −0.0960065 | ||||||||
\(946\) | 3.20844 | 0.104315 | ||||||||
\(947\) | 38.9960 | 1.26720 | 0.633600 | − | 0.773661i | \(-0.281577\pi\) | ||||
0.633600 | + | 0.773661i | \(0.281577\pi\) | |||||||
\(948\) | 9.19527 | 0.298648 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 3.52775 | 0.114455 | ||||||||
\(951\) | −30.8436 | −1.00017 | ||||||||
\(952\) | 11.1237 | 0.360522 | ||||||||
\(953\) | −30.9120 | −1.00134 | −0.500670 | − | 0.865638i | \(-0.666913\pi\) | ||||
−0.500670 | + | 0.865638i | \(0.666913\pi\) | |||||||
\(954\) | −0.293995 | −0.00951845 | ||||||||
\(955\) | −40.2927 | −1.30384 | ||||||||
\(956\) | −9.94660 | −0.321696 | ||||||||
\(957\) | −5.04937 | −0.163223 | ||||||||
\(958\) | −19.6499 | −0.634859 | ||||||||
\(959\) | −26.0734 | −0.841953 | ||||||||
\(960\) | −1.80159 | −0.0581461 | ||||||||
\(961\) | 21.8467 | 0.704731 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.29234 | −0.0738698 | ||||||||
\(964\) | −21.4367 | −0.690431 | ||||||||
\(965\) | −36.8186 | −1.18523 | ||||||||
\(966\) | 0.619855 | 0.0199435 | ||||||||
\(967\) | 31.5859 | 1.01573 | 0.507867 | − | 0.861435i | \(-0.330434\pi\) | ||||
0.507867 | + | 0.861435i | \(0.330434\pi\) | |||||||
\(968\) | −2.13914 | −0.0687546 | ||||||||
\(969\) | −17.5399 | −0.563462 | ||||||||
\(970\) | −16.5741 | −0.532162 | ||||||||
\(971\) | −32.5555 | −1.04476 | −0.522378 | − | 0.852714i | \(-0.674955\pi\) | ||||
−0.522378 | + | 0.852714i | \(0.674955\pi\) | |||||||
\(972\) | −1.65803 | −0.0531815 | ||||||||
\(973\) | 8.61969 | 0.276335 | ||||||||
\(974\) | −2.16368 | −0.0693289 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −11.1145 | −0.355767 | ||||||||
\(977\) | 3.54984 | 0.113569 | 0.0567847 | − | 0.998386i | \(-0.481915\pi\) | ||||
0.0567847 | + | 0.998386i | \(0.481915\pi\) | |||||||
\(978\) | −7.61300 | −0.243437 | ||||||||
\(979\) | −1.80966 | −0.0578371 | ||||||||
\(980\) | 15.2800 | 0.488101 | ||||||||
\(981\) | −12.8818 | −0.411286 | ||||||||
\(982\) | −5.92949 | −0.189218 | ||||||||
\(983\) | 16.6279 | 0.530349 | 0.265174 | − | 0.964200i | \(-0.414570\pi\) | ||||
0.265174 | + | 0.964200i | \(0.414570\pi\) | |||||||
\(984\) | 2.21738 | 0.0706875 | ||||||||
\(985\) | 14.0334 | 0.447141 | ||||||||
\(986\) | 10.1634 | 0.323667 | ||||||||
\(987\) | 5.66884 | 0.180441 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.84946 | 0.122406 | ||||||||
\(990\) | −1.14237 | −0.0363068 | ||||||||
\(991\) | 36.4447 | 1.15770 | 0.578852 | − | 0.815433i | \(-0.303501\pi\) | ||||
0.578852 | + | 0.815433i | \(0.303501\pi\) | |||||||
\(992\) | −39.8804 | −1.26620 | ||||||||
\(993\) | −5.75414 | −0.182602 | ||||||||
\(994\) | −2.04553 | −0.0648804 | ||||||||
\(995\) | −37.0367 | −1.17414 | ||||||||
\(996\) | 24.0641 | 0.762502 | ||||||||
\(997\) | −2.23772 | −0.0708692 | −0.0354346 | − | 0.999372i | \(-0.511282\pi\) | ||||
−0.0354346 | + | 0.999372i | \(0.511282\pi\) | |||||||
\(998\) | 8.83742 | 0.279744 | ||||||||
\(999\) | 2.08160 | 0.0658589 |
(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 | 5577.2.a.x.1.5 | 7 | ||
13.5 | odd | 4 | 429.2.b.b.298.6 | ✓ | 14 | ||
13.8 | odd | 4 | 429.2.b.b.298.9 | yes | 14 | ||
13.12 | even | 2 | 5577.2.a.y.1.3 | 7 | |||
39.5 | even | 4 | 1287.2.b.c.298.9 | 14 | |||
39.8 | even | 4 | 1287.2.b.c.298.6 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
429.2.b.b.298.6 | ✓ | 14 | 13.5 | odd | 4 | ||
429.2.b.b.298.9 | yes | 14 | 13.8 | odd | 4 | ||
1287.2.b.c.298.6 | 14 | 39.8 | even | 4 | |||
1287.2.b.c.298.9 | 14 | 39.5 | even | 4 | |||
5577.2.a.x.1.5 | 7 | 1.1 | even | 1 | trivial | ||
5577.2.a.y.1.3 | 7 | 13.12 | even | 2 |