Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6025,2,Mod(1,6025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6025, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6025 = 5^{2} \cdot 241 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6025.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: | \(48.1098672178\) |
Analytic rank: | \(1\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 6025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.17490 | −1.53788 | −0.768942 | − | 0.639318i | \(-0.779217\pi\) | ||||
−0.768942 | + | 0.639318i | \(0.779217\pi\) | |||||||
\(3\) | 0.995168 | 0.574561 | 0.287280 | − | 0.957847i | \(-0.407249\pi\) | ||||
0.287280 | + | 0.957847i | \(0.407249\pi\) | |||||||
\(4\) | 2.73018 | 1.36509 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.16439 | −0.883608 | ||||||||
\(7\) | 3.57474 | 1.35113 | 0.675563 | − | 0.737302i | \(-0.263901\pi\) | ||||
0.675563 | + | 0.737302i | \(0.263901\pi\) | |||||||
\(8\) | −1.58807 | −0.561467 | ||||||||
\(9\) | −2.00964 | −0.669880 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.14280 | −0.646078 | −0.323039 | − | 0.946386i | \(-0.604705\pi\) | ||||
−0.323039 | + | 0.946386i | \(0.604705\pi\) | |||||||
\(12\) | 2.71699 | 0.784327 | ||||||||
\(13\) | 1.64478 | 0.456181 | 0.228091 | − | 0.973640i | \(-0.426752\pi\) | ||||
0.228091 | + | 0.973640i | \(0.426752\pi\) | |||||||
\(14\) | −7.77470 | −2.07788 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00648 | −0.501619 | ||||||||
\(17\) | 0.660538 | 0.160204 | 0.0801020 | − | 0.996787i | \(-0.474475\pi\) | ||||
0.0801020 | + | 0.996787i | \(0.474475\pi\) | |||||||
\(18\) | 4.37076 | 1.03020 | ||||||||
\(19\) | 4.16594 | 0.955732 | 0.477866 | − | 0.878433i | \(-0.341410\pi\) | ||||
0.477866 | + | 0.878433i | \(0.341410\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.55747 | 0.776304 | ||||||||
\(22\) | 4.66037 | 0.993594 | ||||||||
\(23\) | −0.236291 | −0.0492702 | −0.0246351 | − | 0.999697i | \(-0.507842\pi\) | ||||
−0.0246351 | + | 0.999697i | \(0.507842\pi\) | |||||||
\(24\) | −1.58039 | −0.322597 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.57724 | −0.701554 | ||||||||
\(27\) | −4.98544 | −0.959448 | ||||||||
\(28\) | 9.75969 | 1.84441 | ||||||||
\(29\) | −6.17856 | −1.14733 | −0.573665 | − | 0.819090i | \(-0.694479\pi\) | ||||
−0.573665 | + | 0.819090i | \(0.694479\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.0561187 | −0.0100792 | −0.00503961 | − | 0.999987i | \(-0.501604\pi\) | ||||
−0.00503961 | + | 0.999987i | \(0.501604\pi\) | |||||||
\(32\) | 7.54002 | 1.33290 | ||||||||
\(33\) | −2.13245 | −0.371211 | ||||||||
\(34\) | −1.43660 | −0.246375 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −5.48668 | −0.914446 | ||||||||
\(37\) | −10.8833 | −1.78920 | −0.894602 | − | 0.446865i | \(-0.852541\pi\) | ||||
−0.894602 | + | 0.446865i | \(0.852541\pi\) | |||||||
\(38\) | −9.06049 | −1.46981 | ||||||||
\(39\) | 1.63684 | 0.262104 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.65875 | 1.50844 | 0.754221 | − | 0.656620i | \(-0.228014\pi\) | ||||
0.754221 | + | 0.656620i | \(0.228014\pi\) | |||||||
\(42\) | −7.73714 | −1.19387 | ||||||||
\(43\) | −11.8970 | −1.81427 | −0.907137 | − | 0.420836i | \(-0.861737\pi\) | ||||
−0.907137 | + | 0.420836i | \(0.861737\pi\) | |||||||
\(44\) | −5.85023 | −0.881955 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.513910 | 0.0757718 | ||||||||
\(47\) | −10.6445 | −1.55265 | −0.776327 | − | 0.630331i | \(-0.782919\pi\) | ||||
−0.776327 | + | 0.630331i | \(0.782919\pi\) | |||||||
\(48\) | −1.99678 | −0.288211 | ||||||||
\(49\) | 5.77878 | 0.825541 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.657347 | 0.0920470 | ||||||||
\(52\) | 4.49056 | 0.622728 | ||||||||
\(53\) | 0.824478 | 0.113251 | 0.0566254 | − | 0.998395i | \(-0.481966\pi\) | ||||
0.0566254 | + | 0.998395i | \(0.481966\pi\) | |||||||
\(54\) | 10.8428 | 1.47552 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −5.67693 | −0.758612 | ||||||||
\(57\) | 4.14581 | 0.549126 | ||||||||
\(58\) | 13.4377 | 1.76446 | ||||||||
\(59\) | 0.481563 | 0.0626942 | 0.0313471 | − | 0.999509i | \(-0.490020\pi\) | ||||
0.0313471 | + | 0.999509i | \(0.490020\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 15.0106 | 1.92191 | 0.960955 | − | 0.276704i | \(-0.0892421\pi\) | ||||
0.960955 | + | 0.276704i | \(0.0892421\pi\) | |||||||
\(62\) | 0.122053 | 0.0155007 | ||||||||
\(63\) | −7.18394 | −0.905092 | ||||||||
\(64\) | −12.3858 | −1.54823 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.63785 | 0.570880 | ||||||||
\(67\) | −1.76662 | −0.215826 | −0.107913 | − | 0.994160i | \(-0.534417\pi\) | ||||
−0.107913 | + | 0.994160i | \(0.534417\pi\) | |||||||
\(68\) | 1.80339 | 0.218693 | ||||||||
\(69\) | −0.235150 | −0.0283087 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.6191 | −1.37893 | −0.689465 | − | 0.724319i | \(-0.742154\pi\) | ||||
−0.689465 | + | 0.724319i | \(0.742154\pi\) | |||||||
\(72\) | 3.19144 | 0.376115 | ||||||||
\(73\) | 10.5925 | 1.23976 | 0.619882 | − | 0.784695i | \(-0.287181\pi\) | ||||
0.619882 | + | 0.784695i | \(0.287181\pi\) | |||||||
\(74\) | 23.6701 | 2.75159 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 11.3738 | 1.30466 | ||||||||
\(77\) | −7.65995 | −0.872933 | ||||||||
\(78\) | −3.55995 | −0.403085 | ||||||||
\(79\) | −12.4857 | −1.40476 | −0.702378 | − | 0.711804i | \(-0.747878\pi\) | ||||
−0.702378 | + | 0.711804i | \(0.747878\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.06757 | 0.118619 | ||||||||
\(82\) | −21.0068 | −2.31981 | ||||||||
\(83\) | −7.30251 | −0.801555 | −0.400777 | − | 0.916175i | \(-0.631260\pi\) | ||||
−0.400777 | + | 0.916175i | \(0.631260\pi\) | |||||||
\(84\) | 9.71254 | 1.05972 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 25.8747 | 2.79014 | ||||||||
\(87\) | −6.14871 | −0.659211 | ||||||||
\(88\) | 3.40291 | 0.362751 | ||||||||
\(89\) | 8.65772 | 0.917717 | 0.458858 | − | 0.888509i | \(-0.348259\pi\) | ||||
0.458858 | + | 0.888509i | \(0.348259\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.87968 | 0.616358 | ||||||||
\(92\) | −0.645118 | −0.0672582 | ||||||||
\(93\) | −0.0558476 | −0.00579113 | ||||||||
\(94\) | 23.1506 | 2.38780 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 7.50359 | 0.765831 | ||||||||
\(97\) | −2.57045 | −0.260990 | −0.130495 | − | 0.991449i | \(-0.541657\pi\) | ||||
−0.130495 | + | 0.991449i | \(0.541657\pi\) | |||||||
\(98\) | −12.5683 | −1.26959 | ||||||||
\(99\) | 4.30625 | 0.432795 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −15.3863 | −1.53099 | −0.765497 | − | 0.643439i | \(-0.777507\pi\) | ||||
−0.765497 | + | 0.643439i | \(0.777507\pi\) | |||||||
\(102\) | −1.42966 | −0.141558 | ||||||||
\(103\) | 13.0326 | 1.28414 | 0.642070 | − | 0.766646i | \(-0.278076\pi\) | ||||
0.642070 | + | 0.766646i | \(0.278076\pi\) | |||||||
\(104\) | −2.61203 | −0.256131 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.79315 | −0.174167 | ||||||||
\(107\) | −9.27514 | −0.896662 | −0.448331 | − | 0.893868i | \(-0.647981\pi\) | ||||
−0.448331 | + | 0.893868i | \(0.647981\pi\) | |||||||
\(108\) | −13.6111 | −1.30973 | ||||||||
\(109\) | 1.70201 | 0.163023 | 0.0815117 | − | 0.996672i | \(-0.474025\pi\) | ||||
0.0815117 | + | 0.996672i | \(0.474025\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.8307 | −1.02801 | ||||||||
\(112\) | −7.17264 | −0.677750 | ||||||||
\(113\) | −10.1146 | −0.951503 | −0.475752 | − | 0.879580i | \(-0.657824\pi\) | ||||
−0.475752 | + | 0.879580i | \(0.657824\pi\) | |||||||
\(114\) | −9.01671 | −0.844493 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −16.8686 | −1.56621 | ||||||||
\(117\) | −3.30542 | −0.305587 | ||||||||
\(118\) | −1.04735 | −0.0964165 | ||||||||
\(119\) | 2.36125 | 0.216456 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.40842 | −0.582583 | ||||||||
\(122\) | −32.6465 | −2.95568 | ||||||||
\(123\) | 9.61208 | 0.866692 | ||||||||
\(124\) | −0.153214 | −0.0137590 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 15.6243 | 1.39193 | ||||||||
\(127\) | −14.5083 | −1.28740 | −0.643700 | − | 0.765278i | \(-0.722601\pi\) | ||||
−0.643700 | + | 0.765278i | \(0.722601\pi\) | |||||||
\(128\) | 11.8578 | 1.04809 | ||||||||
\(129\) | −11.8395 | −1.04241 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.7901 | −0.942740 | −0.471370 | − | 0.881936i | \(-0.656240\pi\) | ||||
−0.471370 | + | 0.881936i | \(0.656240\pi\) | |||||||
\(132\) | −5.82196 | −0.506737 | ||||||||
\(133\) | 14.8922 | 1.29131 | ||||||||
\(134\) | 3.84221 | 0.331916 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.04898 | −0.0899492 | ||||||||
\(137\) | −2.13394 | −0.182315 | −0.0911574 | − | 0.995836i | \(-0.529057\pi\) | ||||
−0.0911574 | + | 0.995836i | \(0.529057\pi\) | |||||||
\(138\) | 0.511427 | 0.0435355 | ||||||||
\(139\) | 2.33824 | 0.198327 | 0.0991636 | − | 0.995071i | \(-0.468383\pi\) | ||||
0.0991636 | + | 0.995071i | \(0.468383\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.5930 | −0.892094 | ||||||||
\(142\) | 25.2703 | 2.12064 | ||||||||
\(143\) | −3.52444 | −0.294729 | ||||||||
\(144\) | 4.03229 | 0.336025 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −23.0377 | −1.90661 | ||||||||
\(147\) | 5.75086 | 0.474323 | ||||||||
\(148\) | −29.7134 | −2.44242 | ||||||||
\(149\) | −11.6752 | −0.956473 | −0.478237 | − | 0.878231i | \(-0.658724\pi\) | ||||
−0.478237 | + | 0.878231i | \(0.658724\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.2124 | −0.993828 | −0.496914 | − | 0.867800i | \(-0.665534\pi\) | ||||
−0.496914 | + | 0.867800i | \(0.665534\pi\) | |||||||
\(152\) | −6.61579 | −0.536612 | ||||||||
\(153\) | −1.32744 | −0.107317 | ||||||||
\(154\) | 16.6596 | 1.34247 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 4.46886 | 0.357795 | ||||||||
\(157\) | 9.76433 | 0.779279 | 0.389639 | − | 0.920968i | \(-0.372600\pi\) | ||||
0.389639 | + | 0.920968i | \(0.372600\pi\) | |||||||
\(158\) | 27.1552 | 2.16035 | ||||||||
\(159\) | 0.820494 | 0.0650694 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.844681 | −0.0665702 | ||||||||
\(162\) | −2.32186 | −0.182422 | ||||||||
\(163\) | 23.3726 | 1.83069 | 0.915343 | − | 0.402674i | \(-0.131919\pi\) | ||||
0.915343 | + | 0.402674i | \(0.131919\pi\) | |||||||
\(164\) | 26.3701 | 2.05916 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 15.8822 | 1.23270 | ||||||||
\(167\) | −20.0872 | −1.55439 | −0.777197 | − | 0.629257i | \(-0.783359\pi\) | ||||
−0.777197 | + | 0.629257i | \(0.783359\pi\) | |||||||
\(168\) | −5.64950 | −0.435869 | ||||||||
\(169\) | −10.2947 | −0.791899 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.37204 | −0.640226 | ||||||||
\(172\) | −32.4809 | −2.47665 | ||||||||
\(173\) | −15.7577 | −1.19803 | −0.599017 | − | 0.800736i | \(-0.704442\pi\) | ||||
−0.599017 | + | 0.800736i | \(0.704442\pi\) | |||||||
\(174\) | 13.3728 | 1.01379 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.29947 | 0.324085 | ||||||||
\(177\) | 0.479237 | 0.0360216 | ||||||||
\(178\) | −18.8297 | −1.41134 | ||||||||
\(179\) | 19.0820 | 1.42626 | 0.713130 | − | 0.701032i | \(-0.247277\pi\) | ||||
0.713130 | + | 0.701032i | \(0.247277\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.0266 | 1.41424 | 0.707119 | − | 0.707094i | \(-0.249994\pi\) | ||||
0.707119 | + | 0.707094i | \(0.249994\pi\) | |||||||
\(182\) | −12.7877 | −0.947888 | ||||||||
\(183\) | 14.9381 | 1.10425 | ||||||||
\(184\) | 0.375247 | 0.0276636 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.121463 | 0.00890609 | ||||||||
\(187\) | −1.41540 | −0.103504 | ||||||||
\(188\) | −29.0613 | −2.11951 | ||||||||
\(189\) | −17.8216 | −1.29633 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.5103 | −1.19465 | −0.597323 | − | 0.802001i | \(-0.703769\pi\) | ||||
−0.597323 | + | 0.802001i | \(0.703769\pi\) | |||||||
\(192\) | −12.3260 | −0.889550 | ||||||||
\(193\) | 16.9004 | 1.21652 | 0.608258 | − | 0.793740i | \(-0.291869\pi\) | ||||
0.608258 | + | 0.793740i | \(0.291869\pi\) | |||||||
\(194\) | 5.59047 | 0.401372 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 15.7771 | 1.12694 | ||||||||
\(197\) | −20.2646 | −1.44379 | −0.721897 | − | 0.692001i | \(-0.756729\pi\) | ||||
−0.721897 | + | 0.692001i | \(0.756729\pi\) | |||||||
\(198\) | −9.36566 | −0.665588 | ||||||||
\(199\) | 15.3572 | 1.08864 | 0.544321 | − | 0.838877i | \(-0.316787\pi\) | ||||
0.544321 | + | 0.838877i | \(0.316787\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.75808 | −0.124005 | ||||||||
\(202\) | 33.4636 | 2.35449 | ||||||||
\(203\) | −22.0868 | −1.55019 | ||||||||
\(204\) | 1.79468 | 0.125652 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −28.3446 | −1.97486 | ||||||||
\(207\) | 0.474861 | 0.0330051 | ||||||||
\(208\) | −3.30022 | −0.228829 | ||||||||
\(209\) | −8.92677 | −0.617477 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.96591 | 0.273025 | 0.136512 | − | 0.990638i | \(-0.456411\pi\) | ||||
0.136512 | + | 0.990638i | \(0.456411\pi\) | |||||||
\(212\) | 2.25097 | 0.154597 | ||||||||
\(213\) | −11.5629 | −0.792279 | ||||||||
\(214\) | 20.1725 | 1.37896 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 7.91721 | 0.538698 | ||||||||
\(217\) | −0.200610 | −0.0136183 | ||||||||
\(218\) | −3.70171 | −0.250711 | ||||||||
\(219\) | 10.5414 | 0.712319 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.08644 | 0.0730821 | ||||||||
\(222\) | 23.5557 | 1.58095 | ||||||||
\(223\) | 1.06015 | 0.0709926 | 0.0354963 | − | 0.999370i | \(-0.488699\pi\) | ||||
0.0354963 | + | 0.999370i | \(0.488699\pi\) | |||||||
\(224\) | 26.9536 | 1.80091 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 21.9983 | 1.46330 | ||||||||
\(227\) | −0.472126 | −0.0313361 | −0.0156681 | − | 0.999877i | \(-0.504987\pi\) | ||||
−0.0156681 | + | 0.999877i | \(0.504987\pi\) | |||||||
\(228\) | 11.3188 | 0.749607 | ||||||||
\(229\) | 19.8682 | 1.31293 | 0.656464 | − | 0.754358i | \(-0.272052\pi\) | ||||
0.656464 | + | 0.754358i | \(0.272052\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.62294 | −0.501553 | ||||||||
\(232\) | 9.81197 | 0.644188 | ||||||||
\(233\) | 28.8434 | 1.88959 | 0.944797 | − | 0.327655i | \(-0.106258\pi\) | ||||
0.944797 | + | 0.327655i | \(0.106258\pi\) | |||||||
\(234\) | 7.18896 | 0.469957 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.31475 | 0.0855832 | ||||||||
\(237\) | −12.4254 | −0.807117 | ||||||||
\(238\) | −5.13549 | −0.332884 | ||||||||
\(239\) | 30.0843 | 1.94599 | 0.972995 | − | 0.230825i | \(-0.0741426\pi\) | ||||
0.972995 | + | 0.230825i | \(0.0741426\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.00000 | −0.0644157 | ||||||||
\(242\) | 13.9376 | 0.895946 | ||||||||
\(243\) | 16.0187 | 1.02760 | ||||||||
\(244\) | 40.9816 | 2.62358 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −20.9053 | −1.33287 | ||||||||
\(247\) | 6.85207 | 0.435987 | ||||||||
\(248\) | 0.0891203 | 0.00565915 | ||||||||
\(249\) | −7.26723 | −0.460542 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.493643 | −0.0311585 | −0.0155792 | − | 0.999879i | \(-0.504959\pi\) | ||||
−0.0155792 | + | 0.999879i | \(0.504959\pi\) | |||||||
\(252\) | −19.6135 | −1.23553 | ||||||||
\(253\) | 0.506325 | 0.0318324 | ||||||||
\(254\) | 31.5540 | 1.97987 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.01797 | −0.0636232 | ||||||||
\(257\) | −0.629762 | −0.0392835 | −0.0196417 | − | 0.999807i | \(-0.506253\pi\) | ||||
−0.0196417 | + | 0.999807i | \(0.506253\pi\) | |||||||
\(258\) | 25.7497 | 1.60311 | ||||||||
\(259\) | −38.9050 | −2.41744 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 12.4167 | 0.768573 | ||||||||
\(262\) | 23.4675 | 1.44983 | ||||||||
\(263\) | −20.2647 | −1.24958 | −0.624789 | − | 0.780794i | \(-0.714815\pi\) | ||||
−0.624789 | + | 0.780794i | \(0.714815\pi\) | |||||||
\(264\) | 3.38647 | 0.208423 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −32.3889 | −1.98589 | ||||||||
\(267\) | 8.61589 | 0.527284 | ||||||||
\(268\) | −4.82318 | −0.294622 | ||||||||
\(269\) | −4.53269 | −0.276363 | −0.138181 | − | 0.990407i | \(-0.544126\pi\) | ||||
−0.138181 | + | 0.990407i | \(0.544126\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.6497 | −1.19364 | −0.596818 | − | 0.802377i | \(-0.703568\pi\) | ||||
−0.596818 | + | 0.802377i | \(0.703568\pi\) | |||||||
\(272\) | −1.32535 | −0.0803614 | ||||||||
\(273\) | 5.85127 | 0.354135 | ||||||||
\(274\) | 4.64110 | 0.280379 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.642001 | −0.0386439 | ||||||||
\(277\) | −20.6266 | −1.23933 | −0.619665 | − | 0.784866i | \(-0.712732\pi\) | ||||
−0.619665 | + | 0.784866i | \(0.712732\pi\) | |||||||
\(278\) | −5.08544 | −0.305004 | ||||||||
\(279\) | 0.112778 | 0.00675187 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.79009 | 0.464718 | 0.232359 | − | 0.972630i | \(-0.425356\pi\) | ||||
0.232359 | + | 0.972630i | \(0.425356\pi\) | |||||||
\(282\) | 23.0387 | 1.37194 | ||||||||
\(283\) | 12.2038 | 0.725442 | 0.362721 | − | 0.931898i | \(-0.381848\pi\) | ||||
0.362721 | + | 0.931898i | \(0.381848\pi\) | |||||||
\(284\) | −31.7222 | −1.88236 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 7.66530 | 0.453259 | ||||||||
\(287\) | 34.5275 | 2.03810 | ||||||||
\(288\) | −15.1527 | −0.892882 | ||||||||
\(289\) | −16.5637 | −0.974335 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.55803 | −0.149955 | ||||||||
\(292\) | 28.9195 | 1.69239 | ||||||||
\(293\) | 0.941948 | 0.0550292 | 0.0275146 | − | 0.999621i | \(-0.491241\pi\) | ||||
0.0275146 | + | 0.999621i | \(0.491241\pi\) | |||||||
\(294\) | −12.5075 | −0.729455 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 17.2834 | 1.00458 | ||||||||
\(297\) | 10.6828 | 0.619878 | ||||||||
\(298\) | 25.3925 | 1.47095 | ||||||||
\(299\) | −0.388648 | −0.0224761 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −42.5287 | −2.45131 | ||||||||
\(302\) | 26.5606 | 1.52839 | ||||||||
\(303\) | −15.3120 | −0.879650 | ||||||||
\(304\) | −8.35886 | −0.479413 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 2.88705 | 0.165042 | ||||||||
\(307\) | 11.0615 | 0.631314 | 0.315657 | − | 0.948873i | \(-0.397775\pi\) | ||||
0.315657 | + | 0.948873i | \(0.397775\pi\) | |||||||
\(308\) | −20.9131 | −1.19163 | ||||||||
\(309\) | 12.9696 | 0.737817 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.89176 | 0.504205 | 0.252103 | − | 0.967700i | \(-0.418878\pi\) | ||||
0.252103 | + | 0.967700i | \(0.418878\pi\) | |||||||
\(312\) | −2.59941 | −0.147163 | ||||||||
\(313\) | −27.4866 | −1.55364 | −0.776818 | − | 0.629725i | \(-0.783167\pi\) | ||||
−0.776818 | + | 0.629725i | \(0.783167\pi\) | |||||||
\(314\) | −21.2364 | −1.19844 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −34.0883 | −1.91762 | ||||||||
\(317\) | −10.6883 | −0.600318 | −0.300159 | − | 0.953889i | \(-0.597040\pi\) | ||||
−0.300159 | + | 0.953889i | \(0.597040\pi\) | |||||||
\(318\) | −1.78449 | −0.100069 | ||||||||
\(319\) | 13.2394 | 0.741265 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.23033 | −0.515187 | ||||||||
\(322\) | 1.83709 | 0.102377 | ||||||||
\(323\) | 2.75176 | 0.153112 | ||||||||
\(324\) | 2.91466 | 0.161926 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −50.8331 | −2.81539 | ||||||||
\(327\) | 1.69379 | 0.0936669 | ||||||||
\(328\) | −15.3387 | −0.846940 | ||||||||
\(329\) | −38.0512 | −2.09783 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 32.7774 | 1.80161 | 0.900805 | − | 0.434224i | \(-0.142977\pi\) | ||||
0.900805 | + | 0.434224i | \(0.142977\pi\) | |||||||
\(332\) | −19.9372 | −1.09419 | ||||||||
\(333\) | 21.8715 | 1.19855 | ||||||||
\(334\) | 43.6876 | 2.39048 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −7.13798 | −0.389409 | ||||||||
\(337\) | −18.1201 | −0.987064 | −0.493532 | − | 0.869728i | \(-0.664294\pi\) | ||||
−0.493532 | + | 0.869728i | \(0.664294\pi\) | |||||||
\(338\) | 22.3899 | 1.21785 | ||||||||
\(339\) | −10.0658 | −0.546697 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.120251 | 0.00651196 | ||||||||
\(342\) | 18.2083 | 0.984593 | ||||||||
\(343\) | −4.36553 | −0.235717 | ||||||||
\(344\) | 18.8932 | 1.01865 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 34.2713 | 1.84244 | ||||||||
\(347\) | 11.6120 | 0.623366 | 0.311683 | − | 0.950186i | \(-0.399107\pi\) | ||||
0.311683 | + | 0.950186i | \(0.399107\pi\) | |||||||
\(348\) | −16.7871 | −0.899882 | ||||||||
\(349\) | −0.628561 | −0.0336461 | −0.0168230 | − | 0.999858i | \(-0.505355\pi\) | ||||
−0.0168230 | + | 0.999858i | \(0.505355\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.19997 | −0.437682 | ||||||||
\(352\) | −16.1567 | −0.861157 | ||||||||
\(353\) | 10.6295 | 0.565753 | 0.282876 | − | 0.959156i | \(-0.408711\pi\) | ||||
0.282876 | + | 0.959156i | \(0.408711\pi\) | |||||||
\(354\) | −1.04229 | −0.0553971 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 23.6371 | 1.25277 | ||||||||
\(357\) | 2.34985 | 0.124367 | ||||||||
\(358\) | −41.5015 | −2.19342 | ||||||||
\(359\) | 1.54110 | 0.0813361 | 0.0406680 | − | 0.999173i | \(-0.487051\pi\) | ||||
0.0406680 | + | 0.999173i | \(0.487051\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.64495 | −0.0865766 | ||||||||
\(362\) | −41.3810 | −2.17494 | ||||||||
\(363\) | −6.37745 | −0.334729 | ||||||||
\(364\) | 16.0526 | 0.841384 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −32.4888 | −1.69822 | ||||||||
\(367\) | −33.3459 | −1.74064 | −0.870320 | − | 0.492487i | \(-0.836088\pi\) | ||||
−0.870320 | + | 0.492487i | \(0.836088\pi\) | |||||||
\(368\) | 0.474113 | 0.0247149 | ||||||||
\(369\) | −19.4106 | −1.01048 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.94730 | 0.153016 | ||||||||
\(372\) | −0.152474 | −0.00790541 | ||||||||
\(373\) | −30.4228 | −1.57523 | −0.787617 | − | 0.616165i | \(-0.788685\pi\) | ||||
−0.787617 | + | 0.616165i | \(0.788685\pi\) | |||||||
\(374\) | 3.07835 | 0.159178 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 16.9041 | 0.871763 | ||||||||
\(377\) | −10.1624 | −0.523390 | ||||||||
\(378\) | 38.7603 | 1.99361 | ||||||||
\(379\) | 24.9206 | 1.28008 | 0.640042 | − | 0.768340i | \(-0.278917\pi\) | ||||
0.640042 | + | 0.768340i | \(0.278917\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −14.4382 | −0.739689 | ||||||||
\(382\) | 35.9083 | 1.83723 | ||||||||
\(383\) | −3.42197 | −0.174854 | −0.0874272 | − | 0.996171i | \(-0.527865\pi\) | ||||
−0.0874272 | + | 0.996171i | \(0.527865\pi\) | |||||||
\(384\) | 11.8005 | 0.602194 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −36.7566 | −1.87086 | ||||||||
\(387\) | 23.9087 | 1.21535 | ||||||||
\(388\) | −7.01780 | −0.356275 | ||||||||
\(389\) | 0.0531094 | 0.00269276 | 0.00134638 | − | 0.999999i | \(-0.499571\pi\) | ||||
0.00134638 | + | 0.999999i | \(0.499571\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.156080 | −0.00789328 | ||||||||
\(392\) | −9.17710 | −0.463514 | ||||||||
\(393\) | −10.7380 | −0.541661 | ||||||||
\(394\) | 44.0734 | 2.22039 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 11.7568 | 0.590804 | ||||||||
\(397\) | 2.75259 | 0.138149 | 0.0690744 | − | 0.997612i | \(-0.477995\pi\) | ||||
0.0690744 | + | 0.997612i | \(0.477995\pi\) | |||||||
\(398\) | −33.4003 | −1.67421 | ||||||||
\(399\) | 14.8202 | 0.741938 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.3416 | 0.766123 | 0.383062 | − | 0.923723i | \(-0.374870\pi\) | ||||
0.383062 | + | 0.923723i | \(0.374870\pi\) | |||||||
\(402\) | 3.82364 | 0.190706 | ||||||||
\(403\) | −0.0923032 | −0.00459795 | ||||||||
\(404\) | −42.0074 | −2.08995 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 48.0365 | 2.38401 | ||||||||
\(407\) | 23.3207 | 1.15596 | ||||||||
\(408\) | −1.04391 | −0.0516813 | ||||||||
\(409\) | −37.6394 | −1.86115 | −0.930573 | − | 0.366106i | \(-0.880691\pi\) | ||||
−0.930573 | + | 0.366106i | \(0.880691\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.12363 | −0.104751 | ||||||||
\(412\) | 35.5814 | 1.75297 | ||||||||
\(413\) | 1.72147 | 0.0847078 | ||||||||
\(414\) | −1.03277 | −0.0507580 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 12.4017 | 0.608043 | ||||||||
\(417\) | 2.32695 | 0.113951 | ||||||||
\(418\) | 19.4148 | 0.949609 | ||||||||
\(419\) | −27.4474 | −1.34089 | −0.670447 | − | 0.741958i | \(-0.733898\pi\) | ||||
−0.670447 | + | 0.741958i | \(0.733898\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.9065 | 0.921448 | 0.460724 | − | 0.887543i | \(-0.347590\pi\) | ||||
0.460724 | + | 0.887543i | \(0.347590\pi\) | |||||||
\(422\) | −8.62545 | −0.419880 | ||||||||
\(423\) | 21.3915 | 1.04009 | ||||||||
\(424\) | −1.30933 | −0.0635865 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 25.1482 | 1.21843 | ||||||||
\(427\) | 53.6590 | 2.59674 | ||||||||
\(428\) | −25.3228 | −1.22402 | ||||||||
\(429\) | −3.50741 | −0.169339 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 35.3247 | 1.70153 | 0.850766 | − | 0.525545i | \(-0.176139\pi\) | ||||
0.850766 | + | 0.525545i | \(0.176139\pi\) | |||||||
\(432\) | 10.0032 | 0.481277 | ||||||||
\(433\) | 4.12878 | 0.198417 | 0.0992083 | − | 0.995067i | \(-0.468369\pi\) | ||||
0.0992083 | + | 0.995067i | \(0.468369\pi\) | |||||||
\(434\) | 0.436306 | 0.0209434 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.64681 | 0.222542 | ||||||||
\(437\) | −0.984376 | −0.0470891 | ||||||||
\(438\) | −22.9264 | −1.09547 | ||||||||
\(439\) | 0.720721 | 0.0343981 | 0.0171991 | − | 0.999852i | \(-0.494525\pi\) | ||||
0.0171991 | + | 0.999852i | \(0.494525\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −11.6133 | −0.553013 | ||||||||
\(442\) | −2.36290 | −0.112392 | ||||||||
\(443\) | −5.08399 | −0.241547 | −0.120774 | − | 0.992680i | \(-0.538538\pi\) | ||||
−0.120774 | + | 0.992680i | \(0.538538\pi\) | |||||||
\(444\) | −29.5698 | −1.40332 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −2.30571 | −0.109178 | ||||||||
\(447\) | −11.6188 | −0.549552 | ||||||||
\(448\) | −44.2761 | −2.09185 | ||||||||
\(449\) | 11.4515 | 0.540427 | 0.270214 | − | 0.962800i | \(-0.412906\pi\) | ||||
0.270214 | + | 0.962800i | \(0.412906\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −20.6967 | −0.974572 | ||||||||
\(452\) | −27.6147 | −1.29889 | ||||||||
\(453\) | −12.1534 | −0.571015 | ||||||||
\(454\) | 1.02683 | 0.0481913 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6.58383 | −0.308316 | ||||||||
\(457\) | 28.6494 | 1.34016 | 0.670082 | − | 0.742287i | \(-0.266259\pi\) | ||||
0.670082 | + | 0.742287i | \(0.266259\pi\) | |||||||
\(458\) | −43.2113 | −2.01913 | ||||||||
\(459\) | −3.29307 | −0.153707 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 20.4489 | 0.952401 | 0.476201 | − | 0.879337i | \(-0.342014\pi\) | ||||
0.476201 | + | 0.879337i | \(0.342014\pi\) | |||||||
\(462\) | 16.5791 | 0.771331 | ||||||||
\(463\) | 22.5059 | 1.04594 | 0.522969 | − | 0.852352i | \(-0.324824\pi\) | ||||
0.522969 | + | 0.852352i | \(0.324824\pi\) | |||||||
\(464\) | 12.3971 | 0.575523 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −62.7315 | −2.90598 | ||||||||
\(467\) | −29.8571 | −1.38162 | −0.690810 | − | 0.723036i | \(-0.742746\pi\) | ||||
−0.690810 | + | 0.723036i | \(0.742746\pi\) | |||||||
\(468\) | −9.02440 | −0.417153 | ||||||||
\(469\) | −6.31519 | −0.291609 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.71715 | 0.447743 | ||||||||
\(472\) | −0.764755 | −0.0352007 | ||||||||
\(473\) | 25.4928 | 1.17216 | ||||||||
\(474\) | 27.0240 | 1.24125 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 6.44665 | 0.295482 | ||||||||
\(477\) | −1.65690 | −0.0758644 | ||||||||
\(478\) | −65.4302 | −2.99271 | ||||||||
\(479\) | −27.7402 | −1.26748 | −0.633742 | − | 0.773545i | \(-0.718482\pi\) | ||||
−0.633742 | + | 0.773545i | \(0.718482\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −17.9007 | −0.816201 | ||||||||
\(482\) | 2.17490 | 0.0990639 | ||||||||
\(483\) | −0.840600 | −0.0382486 | ||||||||
\(484\) | −17.4961 | −0.795279 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −34.8391 | −1.58033 | ||||||||
\(487\) | −26.9173 | −1.21974 | −0.609870 | − | 0.792502i | \(-0.708778\pi\) | ||||
−0.609870 | + | 0.792502i | \(0.708778\pi\) | |||||||
\(488\) | −23.8378 | −1.07909 | ||||||||
\(489\) | 23.2597 | 1.05184 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 37.3841 | 1.68712 | 0.843561 | − | 0.537033i | \(-0.180455\pi\) | ||||
0.843561 | + | 0.537033i | \(0.180455\pi\) | |||||||
\(492\) | 26.2427 | 1.18311 | ||||||||
\(493\) | −4.08118 | −0.183807 | ||||||||
\(494\) | −14.9026 | −0.670498 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.112601 | 0.00505593 | ||||||||
\(497\) | −41.5352 | −1.86311 | ||||||||
\(498\) | 15.8055 | 0.708261 | ||||||||
\(499\) | −7.31755 | −0.327578 | −0.163789 | − | 0.986495i | \(-0.552372\pi\) | ||||
−0.163789 | + | 0.986495i | \(0.552372\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −19.9902 | −0.893094 | ||||||||
\(502\) | 1.07362 | 0.0479181 | ||||||||
\(503\) | −13.8428 | −0.617220 | −0.308610 | − | 0.951189i | \(-0.599864\pi\) | ||||
−0.308610 | + | 0.951189i | \(0.599864\pi\) | |||||||
\(504\) | 11.4086 | 0.508179 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.10120 | −0.0489545 | ||||||||
\(507\) | −10.2449 | −0.454994 | ||||||||
\(508\) | −39.6102 | −1.75742 | ||||||||
\(509\) | 16.3327 | 0.723935 | 0.361967 | − | 0.932191i | \(-0.382105\pi\) | ||||
0.361967 | + | 0.932191i | \(0.382105\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 37.8656 | 1.67508 | ||||||||
\(512\) | −21.5017 | −0.950250 | ||||||||
\(513\) | −20.7690 | −0.916975 | ||||||||
\(514\) | 1.36967 | 0.0604134 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −32.3240 | −1.42298 | ||||||||
\(517\) | 22.8089 | 1.00314 | ||||||||
\(518\) | 84.6144 | 3.71774 | ||||||||
\(519\) | −15.6815 | −0.688343 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19.4267 | −0.851097 | −0.425549 | − | 0.904936i | \(-0.639919\pi\) | ||||
−0.425549 | + | 0.904936i | \(0.639919\pi\) | |||||||
\(522\) | −27.0050 | −1.18198 | ||||||||
\(523\) | 9.84831 | 0.430637 | 0.215318 | − | 0.976544i | \(-0.430921\pi\) | ||||
0.215318 | + | 0.976544i | \(0.430921\pi\) | |||||||
\(524\) | −29.4591 | −1.28692 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 44.0737 | 1.92171 | ||||||||
\(527\) | −0.0370686 | −0.00161473 | ||||||||
\(528\) | 4.27870 | 0.186207 | ||||||||
\(529\) | −22.9442 | −0.997572 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.967769 | −0.0419976 | ||||||||
\(532\) | 40.6583 | 1.76276 | ||||||||
\(533\) | 15.8866 | 0.688123 | ||||||||
\(534\) | −18.7387 | −0.810902 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.80550 | 0.121179 | ||||||||
\(537\) | 18.9899 | 0.819473 | ||||||||
\(538\) | 9.85813 | 0.425014 | ||||||||
\(539\) | −12.3828 | −0.533364 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.30937 | 0.271261 | 0.135631 | − | 0.990759i | \(-0.456694\pi\) | ||||
0.135631 | + | 0.990759i | \(0.456694\pi\) | |||||||
\(542\) | 42.7361 | 1.83567 | ||||||||
\(543\) | 18.9347 | 0.812566 | ||||||||
\(544\) | 4.98047 | 0.213536 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −12.7259 | −0.544619 | ||||||||
\(547\) | −25.9302 | −1.10870 | −0.554348 | − | 0.832285i | \(-0.687032\pi\) | ||||
−0.554348 | + | 0.832285i | \(0.687032\pi\) | |||||||
\(548\) | −5.82604 | −0.248876 | ||||||||
\(549\) | −30.1659 | −1.28745 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −25.7395 | −1.09654 | ||||||||
\(552\) | 0.373434 | 0.0158944 | ||||||||
\(553\) | −44.6333 | −1.89800 | ||||||||
\(554\) | 44.8607 | 1.90595 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.38382 | 0.270734 | ||||||||
\(557\) | 16.0326 | 0.679325 | 0.339663 | − | 0.940547i | \(-0.389687\pi\) | ||||
0.339663 | + | 0.940547i | \(0.389687\pi\) | |||||||
\(558\) | −0.245282 | −0.0103836 | ||||||||
\(559\) | −19.5680 | −0.827637 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.40856 | −0.0594695 | ||||||||
\(562\) | −16.9426 | −0.714683 | ||||||||
\(563\) | −39.7361 | −1.67468 | −0.837340 | − | 0.546683i | \(-0.815890\pi\) | ||||
−0.837340 | + | 0.546683i | \(0.815890\pi\) | |||||||
\(564\) | −28.9209 | −1.21779 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −26.5421 | −1.11565 | ||||||||
\(567\) | 3.81629 | 0.160269 | ||||||||
\(568\) | 18.4519 | 0.774223 | ||||||||
\(569\) | 8.62464 | 0.361564 | 0.180782 | − | 0.983523i | \(-0.442137\pi\) | ||||
0.180782 | + | 0.983523i | \(0.442137\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 35.2994 | 1.47724 | 0.738618 | − | 0.674124i | \(-0.235479\pi\) | ||||
0.738618 | + | 0.674124i | \(0.235479\pi\) | |||||||
\(572\) | −9.62236 | −0.402331 | ||||||||
\(573\) | −16.4306 | −0.686396 | ||||||||
\(574\) | −75.0939 | −3.13436 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 24.8910 | 1.03713 | ||||||||
\(577\) | 20.8857 | 0.869481 | 0.434741 | − | 0.900556i | \(-0.356840\pi\) | ||||
0.434741 | + | 0.900556i | \(0.356840\pi\) | |||||||
\(578\) | 36.0243 | 1.49841 | ||||||||
\(579\) | 16.8187 | 0.698962 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −26.1046 | −1.08300 | ||||||||
\(582\) | 5.56346 | 0.230613 | ||||||||
\(583\) | −1.76669 | −0.0731688 | ||||||||
\(584\) | −16.8217 | −0.696086 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.04864 | −0.0846285 | ||||||||
\(587\) | −20.0720 | −0.828460 | −0.414230 | − | 0.910172i | \(-0.635949\pi\) | ||||
−0.414230 | + | 0.910172i | \(0.635949\pi\) | |||||||
\(588\) | 15.7009 | 0.647494 | ||||||||
\(589\) | −0.233787 | −0.00963303 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −20.1667 | −0.829547 | ||||||||
\(592\) | 21.8371 | 0.897498 | ||||||||
\(593\) | 29.9449 | 1.22969 | 0.614845 | − | 0.788648i | \(-0.289219\pi\) | ||||
0.614845 | + | 0.788648i | \(0.289219\pi\) | |||||||
\(594\) | −23.2340 | −0.953301 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −31.8755 | −1.30567 | ||||||||
\(597\) | 15.2830 | 0.625491 | ||||||||
\(598\) | 0.845271 | 0.0345657 | ||||||||
\(599\) | −16.8384 | −0.687998 | −0.343999 | − | 0.938970i | \(-0.611782\pi\) | ||||
−0.343999 | + | 0.938970i | \(0.611782\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.0027 | 0.489599 | 0.244799 | − | 0.969574i | \(-0.421278\pi\) | ||||
0.244799 | + | 0.969574i | \(0.421278\pi\) | |||||||
\(602\) | 92.4955 | 3.76983 | ||||||||
\(603\) | 3.55026 | 0.144578 | ||||||||
\(604\) | −33.3420 | −1.35667 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 33.3020 | 1.35280 | ||||||||
\(607\) | −49.0077 | −1.98916 | −0.994580 | − | 0.103973i | \(-0.966844\pi\) | ||||
−0.994580 | + | 0.103973i | \(0.966844\pi\) | |||||||
\(608\) | 31.4112 | 1.27389 | ||||||||
\(609\) | −21.9801 | −0.890677 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −17.5078 | −0.708291 | ||||||||
\(612\) | −3.62416 | −0.146498 | ||||||||
\(613\) | 14.6513 | 0.591760 | 0.295880 | − | 0.955225i | \(-0.404387\pi\) | ||||
0.295880 | + | 0.955225i | \(0.404387\pi\) | |||||||
\(614\) | −24.0577 | −0.970888 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 12.1645 | 0.490123 | ||||||||
\(617\) | −36.8232 | −1.48245 | −0.741224 | − | 0.671258i | \(-0.765754\pi\) | ||||
−0.741224 | + | 0.671258i | \(0.765754\pi\) | |||||||
\(618\) | −28.2076 | −1.13468 | ||||||||
\(619\) | 45.4722 | 1.82768 | 0.913841 | − | 0.406072i | \(-0.133102\pi\) | ||||
0.913841 | + | 0.406072i | \(0.133102\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.17802 | 0.0472721 | ||||||||
\(622\) | −19.3387 | −0.775410 | ||||||||
\(623\) | 30.9491 | 1.23995 | ||||||||
\(624\) | −3.28428 | −0.131476 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 59.7806 | 2.38931 | ||||||||
\(627\) | −8.88364 | −0.354778 | ||||||||
\(628\) | 26.6584 | 1.06379 | ||||||||
\(629\) | −7.18883 | −0.286638 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.2437 | −0.805890 | −0.402945 | − | 0.915224i | \(-0.632013\pi\) | ||||
−0.402945 | + | 0.915224i | \(0.632013\pi\) | |||||||
\(632\) | 19.8282 | 0.788723 | ||||||||
\(633\) | 3.94675 | 0.156869 | ||||||||
\(634\) | 23.2461 | 0.923219 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.24010 | 0.0888256 | ||||||||
\(637\) | 9.50485 | 0.376596 | ||||||||
\(638\) | −28.7944 | −1.13998 | ||||||||
\(639\) | 23.3502 | 0.923718 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −41.7882 | −1.65054 | −0.825268 | − | 0.564741i | \(-0.808976\pi\) | ||||
−0.825268 | + | 0.564741i | \(0.808976\pi\) | |||||||
\(642\) | 20.0750 | 0.792298 | ||||||||
\(643\) | −40.3083 | −1.58961 | −0.794803 | − | 0.606868i | \(-0.792426\pi\) | ||||
−0.794803 | + | 0.606868i | \(0.792426\pi\) | |||||||
\(644\) | −2.30613 | −0.0908743 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5.98480 | −0.235469 | ||||||||
\(647\) | −44.8702 | −1.76403 | −0.882014 | − | 0.471223i | \(-0.843813\pi\) | ||||
−0.882014 | + | 0.471223i | \(0.843813\pi\) | |||||||
\(648\) | −1.69538 | −0.0666006 | ||||||||
\(649\) | −1.03189 | −0.0405053 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.199641 | −0.00782454 | ||||||||
\(652\) | 63.8115 | 2.49905 | ||||||||
\(653\) | 2.92608 | 0.114507 | 0.0572533 | − | 0.998360i | \(-0.481766\pi\) | ||||
0.0572533 | + | 0.998360i | \(0.481766\pi\) | |||||||
\(654\) | −3.68382 | −0.144049 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −19.3800 | −0.756664 | ||||||||
\(657\) | −21.2872 | −0.830492 | ||||||||
\(658\) | 82.7574 | 3.22622 | ||||||||
\(659\) | −21.9078 | −0.853406 | −0.426703 | − | 0.904392i | \(-0.640325\pi\) | ||||
−0.426703 | + | 0.904392i | \(0.640325\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.9734 | 1.01025 | 0.505125 | − | 0.863046i | \(-0.331446\pi\) | ||||
0.505125 | + | 0.863046i | \(0.331446\pi\) | |||||||
\(662\) | −71.2875 | −2.77067 | ||||||||
\(663\) | 1.08119 | 0.0419901 | ||||||||
\(664\) | 11.5969 | 0.450046 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −47.5683 | −1.84323 | ||||||||
\(667\) | 1.45994 | 0.0565291 | ||||||||
\(668\) | −54.8417 | −2.12189 | ||||||||
\(669\) | 1.05502 | 0.0407896 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −32.1647 | −1.24170 | ||||||||
\(672\) | 26.8234 | 1.03473 | ||||||||
\(673\) | −19.5900 | −0.755138 | −0.377569 | − | 0.925981i | \(-0.623240\pi\) | ||||
−0.377569 | + | 0.925981i | \(0.623240\pi\) | |||||||
\(674\) | 39.4094 | 1.51799 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −28.1063 | −1.08101 | ||||||||
\(677\) | 21.7156 | 0.834596 | 0.417298 | − | 0.908770i | \(-0.362977\pi\) | ||||
0.417298 | + | 0.908770i | \(0.362977\pi\) | |||||||
\(678\) | 21.8920 | 0.840756 | ||||||||
\(679\) | −9.18871 | −0.352630 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.469845 | −0.0180045 | ||||||||
\(682\) | −0.261534 | −0.0100147 | ||||||||
\(683\) | −9.02292 | −0.345252 | −0.172626 | − | 0.984987i | \(-0.555225\pi\) | ||||
−0.172626 | + | 0.984987i | \(0.555225\pi\) | |||||||
\(684\) | −22.8572 | −0.873966 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 9.49459 | 0.362505 | ||||||||
\(687\) | 19.7722 | 0.754356 | ||||||||
\(688\) | 23.8710 | 0.910074 | ||||||||
\(689\) | 1.35609 | 0.0516628 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.0698 | −0.953700 | −0.476850 | − | 0.878985i | \(-0.658221\pi\) | ||||
−0.476850 | + | 0.878985i | \(0.658221\pi\) | |||||||
\(692\) | −43.0213 | −1.63542 | ||||||||
\(693\) | 15.3937 | 0.584760 | ||||||||
\(694\) | −25.2550 | −0.958666 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 9.76457 | 0.370125 | ||||||||
\(697\) | 6.37997 | 0.241659 | ||||||||
\(698\) | 1.36706 | 0.0517438 | ||||||||
\(699\) | 28.7041 | 1.08569 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.1409 | −0.685172 | −0.342586 | − | 0.939486i | \(-0.611303\pi\) | ||||
−0.342586 | + | 0.939486i | \(0.611303\pi\) | |||||||
\(702\) | 17.8341 | 0.673104 | ||||||||
\(703\) | −45.3391 | −1.71000 | ||||||||
\(704\) | 26.5403 | 1.00027 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −23.1181 | −0.870062 | ||||||||
\(707\) | −55.0021 | −2.06857 | ||||||||
\(708\) | 1.30840 | 0.0491728 | ||||||||
\(709\) | −20.2193 | −0.759352 | −0.379676 | − | 0.925120i | \(-0.623965\pi\) | ||||
−0.379676 | + | 0.925120i | \(0.623965\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 25.0918 | 0.941017 | ||||||||
\(712\) | −13.7490 | −0.515267 | ||||||||
\(713\) | 0.0132604 | 0.000496605 0 | ||||||||
\(714\) | −5.11067 | −0.191262 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 52.0974 | 1.94697 | ||||||||
\(717\) | 29.9389 | 1.11809 | ||||||||
\(718\) | −3.35173 | −0.125086 | ||||||||
\(719\) | 1.41119 | 0.0526286 | 0.0263143 | − | 0.999654i | \(-0.491623\pi\) | ||||
0.0263143 | + | 0.999654i | \(0.491623\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 46.5882 | 1.73504 | ||||||||
\(722\) | 3.57761 | 0.133145 | ||||||||
\(723\) | −0.995168 | −0.0370107 | ||||||||
\(724\) | 51.9461 | 1.93056 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 13.8703 | 0.514775 | ||||||||
\(727\) | 16.0736 | 0.596135 | 0.298068 | − | 0.954545i | \(-0.403658\pi\) | ||||
0.298068 | + | 0.954545i | \(0.403658\pi\) | |||||||
\(728\) | −9.33733 | −0.346065 | ||||||||
\(729\) | 12.7386 | 0.471800 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.85841 | −0.290654 | ||||||||
\(732\) | 40.7836 | 1.50741 | ||||||||
\(733\) | −21.5338 | −0.795369 | −0.397684 | − | 0.917522i | \(-0.630186\pi\) | ||||
−0.397684 | + | 0.917522i | \(0.630186\pi\) | |||||||
\(734\) | 72.5238 | 2.67690 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.78164 | −0.0656722 | ||||||||
\(737\) | 3.78550 | 0.139441 | ||||||||
\(738\) | 42.2161 | 1.55400 | ||||||||
\(739\) | −19.5469 | −0.719043 | −0.359522 | − | 0.933137i | \(-0.617060\pi\) | ||||
−0.359522 | + | 0.933137i | \(0.617060\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.81897 | 0.250501 | ||||||||
\(742\) | −6.41007 | −0.235321 | ||||||||
\(743\) | −17.2158 | −0.631588 | −0.315794 | − | 0.948828i | \(-0.602271\pi\) | ||||
−0.315794 | + | 0.948828i | \(0.602271\pi\) | |||||||
\(744\) | 0.0886898 | 0.00325152 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 66.1665 | 2.42253 | ||||||||
\(747\) | 14.6754 | 0.536946 | ||||||||
\(748\) | −3.86430 | −0.141293 | ||||||||
\(749\) | −33.1562 | −1.21150 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.294980 | 0.0107640 | 0.00538199 | − | 0.999986i | \(-0.498287\pi\) | ||||
0.00538199 | + | 0.999986i | \(0.498287\pi\) | |||||||
\(752\) | 21.3578 | 0.778840 | ||||||||
\(753\) | −0.491258 | −0.0179024 | ||||||||
\(754\) | 22.1022 | 0.804914 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −48.6563 | −1.76961 | ||||||||
\(757\) | −5.06019 | −0.183916 | −0.0919579 | − | 0.995763i | \(-0.529313\pi\) | ||||
−0.0919579 | + | 0.995763i | \(0.529313\pi\) | |||||||
\(758\) | −54.1997 | −1.96862 | ||||||||
\(759\) | 0.503878 | 0.0182896 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −22.1767 | −0.803903 | −0.401952 | − | 0.915661i | \(-0.631668\pi\) | ||||
−0.401952 | + | 0.915661i | \(0.631668\pi\) | |||||||
\(762\) | 31.4015 | 1.13756 | ||||||||
\(763\) | 6.08426 | 0.220265 | ||||||||
\(764\) | −45.0762 | −1.63080 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.44243 | 0.268906 | ||||||||
\(767\) | 0.792068 | 0.0285999 | ||||||||
\(768\) | −1.01305 | −0.0365554 | ||||||||
\(769\) | 24.1094 | 0.869409 | 0.434704 | − | 0.900573i | \(-0.356853\pi\) | ||||
0.434704 | + | 0.900573i | \(0.356853\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.626719 | −0.0225707 | ||||||||
\(772\) | 46.1411 | 1.66065 | ||||||||
\(773\) | 1.32362 | 0.0476074 | 0.0238037 | − | 0.999717i | \(-0.492422\pi\) | ||||
0.0238037 | + | 0.999717i | \(0.492422\pi\) | |||||||
\(774\) | −51.9989 | −1.86906 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 4.08205 | 0.146537 | ||||||||
\(777\) | −38.7170 | −1.38897 | ||||||||
\(778\) | −0.115508 | −0.00414115 | ||||||||
\(779\) | 40.2378 | 1.44167 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 24.8973 | 0.890897 | ||||||||
\(782\) | 0.339457 | 0.0121390 | ||||||||
\(783\) | 30.8028 | 1.10080 | ||||||||
\(784\) | −11.5950 | −0.414107 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 23.3541 | 0.833013 | ||||||||
\(787\) | −21.2362 | −0.756988 | −0.378494 | − | 0.925604i | \(-0.623558\pi\) | ||||
−0.378494 | + | 0.925604i | \(0.623558\pi\) | |||||||
\(788\) | −55.3260 | −1.97091 | ||||||||
\(789\) | −20.1668 | −0.717958 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −36.1572 | −1.28560 | ||||||||
\(792\) | −6.83862 | −0.243000 | ||||||||
\(793\) | 24.6892 | 0.876739 | ||||||||
\(794\) | −5.98661 | −0.212457 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 41.9279 | 1.48610 | ||||||||
\(797\) | −20.0623 | −0.710644 | −0.355322 | − | 0.934744i | \(-0.615629\pi\) | ||||
−0.355322 | + | 0.934744i | \(0.615629\pi\) | |||||||
\(798\) | −32.2324 | −1.14102 | ||||||||
\(799\) | −7.03107 | −0.248741 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −17.3989 | −0.614760 | ||||||||
\(802\) | −33.3664 | −1.17821 | ||||||||
\(803\) | −22.6977 | −0.800984 | ||||||||
\(804\) | −4.79987 | −0.169279 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.200750 | 0.00707112 | ||||||||
\(807\) | −4.51079 | −0.158787 | ||||||||
\(808\) | 24.4345 | 0.859603 | ||||||||
\(809\) | −16.7286 | −0.588145 | −0.294072 | − | 0.955783i | \(-0.595011\pi\) | ||||
−0.294072 | + | 0.955783i | \(0.595011\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.27147 | 0.290451 | 0.145225 | − | 0.989399i | \(-0.453609\pi\) | ||||
0.145225 | + | 0.989399i | \(0.453609\pi\) | |||||||
\(812\) | −60.3009 | −2.11615 | ||||||||
\(813\) | −19.5548 | −0.685816 | ||||||||
\(814\) | −50.7202 | −1.77774 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.31895 | −0.0461725 | ||||||||
\(817\) | −49.5621 | −1.73396 | ||||||||
\(818\) | 81.8618 | 2.86223 | ||||||||
\(819\) | −11.8160 | −0.412886 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 44.3275 | 1.54704 | 0.773521 | − | 0.633771i | \(-0.218494\pi\) | ||||
0.773521 | + | 0.633771i | \(0.218494\pi\) | |||||||
\(822\) | 4.61868 | 0.161095 | ||||||||
\(823\) | −44.8565 | −1.56360 | −0.781800 | − | 0.623529i | \(-0.785698\pi\) | ||||
−0.781800 | + | 0.623529i | \(0.785698\pi\) | |||||||
\(824\) | −20.6967 | −0.721002 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.74401 | −0.130271 | ||||||||
\(827\) | 48.8334 | 1.69810 | 0.849052 | − | 0.528309i | \(-0.177174\pi\) | ||||
0.849052 | + | 0.528309i | \(0.177174\pi\) | |||||||
\(828\) | 1.29646 | 0.0450549 | ||||||||
\(829\) | −37.5847 | −1.30537 | −0.652685 | − | 0.757630i | \(-0.726357\pi\) | ||||
−0.652685 | + | 0.757630i | \(0.726357\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −20.5269 | −0.712070 | ||||||||
\(832\) | −20.3720 | −0.706272 | ||||||||
\(833\) | 3.81711 | 0.132255 | ||||||||
\(834\) | −5.06087 | −0.175244 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −24.3717 | −0.842912 | ||||||||
\(837\) | 0.279776 | 0.00967048 | ||||||||
\(838\) | 59.6953 | 2.06214 | ||||||||
\(839\) | 12.6371 | 0.436283 | 0.218141 | − | 0.975917i | \(-0.430001\pi\) | ||||
0.218141 | + | 0.975917i | \(0.430001\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.17463 | 0.316367 | ||||||||
\(842\) | −41.1198 | −1.41708 | ||||||||
\(843\) | 7.75245 | 0.267009 | ||||||||
\(844\) | 10.8277 | 0.372703 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −46.5244 | −1.59954 | ||||||||
\(847\) | −22.9084 | −0.787143 | ||||||||
\(848\) | −1.65429 | −0.0568087 | ||||||||
\(849\) | 12.1449 | 0.416811 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.57163 | 0.0881543 | ||||||||
\(852\) | −31.5689 | −1.08153 | ||||||||
\(853\) | −6.32445 | −0.216545 | −0.108273 | − | 0.994121i | \(-0.534532\pi\) | ||||
−0.108273 | + | 0.994121i | \(0.534532\pi\) | |||||||
\(854\) | −116.703 | −3.99349 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 14.7296 | 0.503446 | ||||||||
\(857\) | 20.0524 | 0.684978 | 0.342489 | − | 0.939522i | \(-0.388730\pi\) | ||||
0.342489 | + | 0.939522i | \(0.388730\pi\) | |||||||
\(858\) | 7.62826 | 0.260425 | ||||||||
\(859\) | −20.6809 | −0.705623 | −0.352812 | − | 0.935694i | \(-0.614774\pi\) | ||||
−0.352812 | + | 0.935694i | \(0.614774\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 34.3607 | 1.17101 | ||||||||
\(862\) | −76.8276 | −2.61676 | ||||||||
\(863\) | −9.35107 | −0.318314 | −0.159157 | − | 0.987253i | \(-0.550878\pi\) | ||||
−0.159157 | + | 0.987253i | \(0.550878\pi\) | |||||||
\(864\) | −37.5903 | −1.27885 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −8.97968 | −0.305142 | ||||||||
\(867\) | −16.4837 | −0.559814 | ||||||||
\(868\) | −0.547702 | −0.0185902 | ||||||||
\(869\) | 26.7544 | 0.907582 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.90570 | −0.0984559 | ||||||||
\(872\) | −2.70291 | −0.0915322 | ||||||||
\(873\) | 5.16568 | 0.174832 | ||||||||
\(874\) | 2.14092 | 0.0724176 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 28.7798 | 0.972380 | ||||||||
\(877\) | 34.8026 | 1.17520 | 0.587600 | − | 0.809151i | \(-0.300073\pi\) | ||||
0.587600 | + | 0.809151i | \(0.300073\pi\) | |||||||
\(878\) | −1.56749 | −0.0529003 | ||||||||
\(879\) | 0.937397 | 0.0316176 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −52.5693 | −1.77110 | −0.885552 | − | 0.464541i | \(-0.846220\pi\) | ||||
−0.885552 | + | 0.464541i | \(0.846220\pi\) | |||||||
\(882\) | 25.2577 | 0.850470 | ||||||||
\(883\) | −5.46583 | −0.183940 | −0.0919700 | − | 0.995762i | \(-0.529316\pi\) | ||||
−0.0919700 | + | 0.995762i | \(0.529316\pi\) | |||||||
\(884\) | 2.96619 | 0.0997636 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 11.0572 | 0.371472 | ||||||||
\(887\) | 4.29456 | 0.144197 | 0.0720986 | − | 0.997398i | \(-0.477030\pi\) | ||||
0.0720986 | + | 0.997398i | \(0.477030\pi\) | |||||||
\(888\) | 17.1999 | 0.577191 | ||||||||
\(889\) | −51.8633 | −1.73944 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.28759 | −0.0766371 | ||||||||
\(892\) | 2.89439 | 0.0969113 | ||||||||
\(893\) | −44.3441 | −1.48392 | ||||||||
\(894\) | 25.2698 | 0.845148 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 42.3887 | 1.41611 | ||||||||
\(897\) | −0.386771 | −0.0129139 | ||||||||
\(898\) | −24.9057 | −0.831115 | ||||||||
\(899\) | 0.346733 | 0.0115642 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.544599 | 0.0181432 | ||||||||
\(902\) | 45.0133 | 1.49878 | ||||||||
\(903\) | −42.3232 | −1.40843 | ||||||||
\(904\) | 16.0627 | 0.534237 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 26.4323 | 0.878155 | ||||||||
\(907\) | −15.4572 | −0.513249 | −0.256625 | − | 0.966511i | \(-0.582610\pi\) | ||||
−0.256625 | + | 0.966511i | \(0.582610\pi\) | |||||||
\(908\) | −1.28899 | −0.0427766 | ||||||||
\(909\) | 30.9209 | 1.02558 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 53.1696 | 1.76159 | 0.880793 | − | 0.473502i | \(-0.157010\pi\) | ||||
0.880793 | + | 0.473502i | \(0.157010\pi\) | |||||||
\(912\) | −8.31847 | −0.275452 | ||||||||
\(913\) | 15.6478 | 0.517867 | ||||||||
\(914\) | −62.3096 | −2.06102 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 54.2437 | 1.79226 | ||||||||
\(917\) | −38.5720 | −1.27376 | ||||||||
\(918\) | 7.16209 | 0.236384 | ||||||||
\(919\) | −23.4129 | −0.772321 | −0.386160 | − | 0.922432i | \(-0.626199\pi\) | ||||
−0.386160 | + | 0.922432i | \(0.626199\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 11.0081 | 0.362728 | ||||||||
\(922\) | −44.4743 | −1.46468 | ||||||||
\(923\) | −19.1109 | −0.629042 | ||||||||
\(924\) | −20.8120 | −0.684665 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −48.9480 | −1.60853 | ||||||||
\(927\) | −26.1908 | −0.860220 | ||||||||
\(928\) | −46.5865 | −1.52928 | ||||||||
\(929\) | −54.3893 | −1.78445 | −0.892227 | − | 0.451587i | \(-0.850858\pi\) | ||||
−0.892227 | + | 0.451587i | \(0.850858\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 24.0741 | 0.788995 | ||||||||
\(932\) | 78.7477 | 2.57947 | ||||||||
\(933\) | 8.84880 | 0.289697 | ||||||||
\(934\) | 64.9361 | 2.12477 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 5.24924 | 0.171577 | ||||||||
\(937\) | 37.2899 | 1.21821 | 0.609105 | − | 0.793090i | \(-0.291529\pi\) | ||||
0.609105 | + | 0.793090i | \(0.291529\pi\) | |||||||
\(938\) | 13.7349 | 0.448460 | ||||||||
\(939\) | −27.3538 | −0.892658 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −20.4028 | −0.665112 | −0.332556 | − | 0.943083i | \(-0.607911\pi\) | ||||
−0.332556 | + | 0.943083i | \(0.607911\pi\) | |||||||
\(942\) | −21.1338 | −0.688577 | ||||||||
\(943\) | −2.28228 | −0.0743212 | ||||||||
\(944\) | −0.966245 | −0.0314486 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −55.4443 | −1.80265 | ||||||||
\(947\) | 40.1120 | 1.30347 | 0.651733 | − | 0.758449i | \(-0.274042\pi\) | ||||
0.651733 | + | 0.758449i | \(0.274042\pi\) | |||||||
\(948\) | −33.9236 | −1.10179 | ||||||||
\(949\) | 17.4224 | 0.565557 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −10.6367 | −0.344919 | ||||||||
\(952\) | −3.74983 | −0.121533 | ||||||||
\(953\) | −21.9176 | −0.709982 | −0.354991 | − | 0.934870i | \(-0.615516\pi\) | ||||
−0.354991 | + | 0.934870i | \(0.615516\pi\) | |||||||
\(954\) | 3.60359 | 0.116671 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 82.1355 | 2.65645 | ||||||||
\(957\) | 13.1754 | 0.425902 | ||||||||
\(958\) | 60.3321 | 1.94924 | ||||||||
\(959\) | −7.62829 | −0.246330 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9969 | −0.999898 | ||||||||
\(962\) | 38.9321 | 1.25522 | ||||||||
\(963\) | 18.6397 | 0.600656 | ||||||||
\(964\) | −2.73018 | −0.0879332 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.82822 | 0.0588220 | ||||||||
\(967\) | −31.4765 | −1.01222 | −0.506109 | − | 0.862470i | \(-0.668917\pi\) | ||||
−0.506109 | + | 0.862470i | \(0.668917\pi\) | |||||||
\(968\) | 10.1770 | 0.327101 | ||||||||
\(969\) | 2.73847 | 0.0879722 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15.0675 | −0.483539 | −0.241769 | − | 0.970334i | \(-0.577728\pi\) | ||||
−0.241769 | + | 0.970334i | \(0.577728\pi\) | |||||||
\(972\) | 43.7340 | 1.40277 | ||||||||
\(973\) | 8.35862 | 0.267965 | ||||||||
\(974\) | 58.5424 | 1.87582 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −30.1184 | −0.964067 | ||||||||
\(977\) | −29.5053 | −0.943959 | −0.471979 | − | 0.881610i | \(-0.656460\pi\) | ||||
−0.471979 | + | 0.881610i | \(0.656460\pi\) | |||||||
\(978\) | −50.5875 | −1.61761 | ||||||||
\(979\) | −18.5518 | −0.592917 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.42044 | −0.109206 | ||||||||
\(982\) | −81.3067 | −2.59460 | ||||||||
\(983\) | 54.1116 | 1.72589 | 0.862946 | − | 0.505295i | \(-0.168616\pi\) | ||||
0.862946 | + | 0.505295i | \(0.168616\pi\) | |||||||
\(984\) | −15.2646 | −0.486619 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 8.87614 | 0.282674 | ||||||||
\(987\) | −37.8673 | −1.20533 | ||||||||
\(988\) | 18.7074 | 0.595161 | ||||||||
\(989\) | 2.81116 | 0.0893895 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −37.3910 | −1.18777 | −0.593883 | − | 0.804552i | \(-0.702406\pi\) | ||||
−0.593883 | + | 0.804552i | \(0.702406\pi\) | |||||||
\(992\) | −0.423136 | −0.0134346 | ||||||||
\(993\) | 32.6191 | 1.03513 | ||||||||
\(994\) | 90.3348 | 2.86525 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −19.8408 | −0.628681 | ||||||||
\(997\) | 44.7165 | 1.41618 | 0.708092 | − | 0.706120i | \(-0.249556\pi\) | ||||
0.708092 | + | 0.706120i | \(0.249556\pi\) | |||||||
\(998\) | 15.9149 | 0.503778 | ||||||||
\(999\) | 54.2580 | 1.71665 |
(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 | 6025.2.a.l.1.8 | ✓ | 40 | |
5.4 | even | 2 | 6025.2.a.o.1.33 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6025.2.a.l.1.8 | ✓ | 40 | 1.1 | even | 1 | trivial | |
6025.2.a.o.1.33 | yes | 40 | 5.4 | even | 2 |