Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1690,2,Mod(1,1690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1690, 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("1690.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1690 = 2 \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1690.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: | \(13.4947179416\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{14})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.24698\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1690.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.24698 | −0.719944 | −0.359972 | − | 0.932963i | \(-0.617214\pi\) | ||||
−0.359972 | + | 0.932963i | \(0.617214\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 1.24698 | 0.509077 | ||||||||
\(7\) | −0.198062 | −0.0748605 | −0.0374302 | − | 0.999299i | \(-0.511917\pi\) | ||||
−0.0374302 | + | 0.999299i | \(0.511917\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −1.44504 | −0.481681 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | −1.10992 | −0.334652 | −0.167326 | − | 0.985902i | \(-0.553513\pi\) | ||||
−0.167326 | + | 0.985902i | \(0.553513\pi\) | |||||||
\(12\) | −1.24698 | −0.359972 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0.198062 | 0.0529344 | ||||||||
\(15\) | −1.24698 | −0.321969 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.49396 | 1.57502 | 0.787508 | − | 0.616304i | \(-0.211371\pi\) | ||||
0.787508 | + | 0.616304i | \(0.211371\pi\) | |||||||
\(18\) | 1.44504 | 0.340600 | ||||||||
\(19\) | 0.493959 | 0.113322 | 0.0566610 | − | 0.998393i | \(-0.481955\pi\) | ||||
0.0566610 | + | 0.998393i | \(0.481955\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 0.246980 | 0.0538954 | ||||||||
\(22\) | 1.10992 | 0.236635 | ||||||||
\(23\) | −6.76271 | −1.41012 | −0.705061 | − | 0.709147i | \(-0.749080\pi\) | ||||
−0.705061 | + | 0.709147i | \(0.749080\pi\) | |||||||
\(24\) | 1.24698 | 0.254539 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.54288 | 1.06673 | ||||||||
\(28\) | −0.198062 | −0.0374302 | ||||||||
\(29\) | −0.356896 | −0.0662739 | −0.0331369 | − | 0.999451i | \(-0.510550\pi\) | ||||
−0.0331369 | + | 0.999451i | \(0.510550\pi\) | |||||||
\(30\) | 1.24698 | 0.227666 | ||||||||
\(31\) | −6.27413 | −1.12687 | −0.563433 | − | 0.826162i | \(-0.690520\pi\) | ||||
−0.563433 | + | 0.826162i | \(0.690520\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 1.38404 | 0.240931 | ||||||||
\(34\) | −6.49396 | −1.11370 | ||||||||
\(35\) | −0.198062 | −0.0334786 | ||||||||
\(36\) | −1.44504 | −0.240840 | ||||||||
\(37\) | −2.21983 | −0.364938 | −0.182469 | − | 0.983212i | \(-0.558409\pi\) | ||||
−0.182469 | + | 0.983212i | \(0.558409\pi\) | |||||||
\(38\) | −0.493959 | −0.0801308 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −8.96615 | −1.40028 | −0.700139 | − | 0.714007i | \(-0.746878\pi\) | ||||
−0.700139 | + | 0.714007i | \(0.746878\pi\) | |||||||
\(42\) | −0.246980 | −0.0381098 | ||||||||
\(43\) | 5.65279 | 0.862043 | 0.431021 | − | 0.902342i | \(-0.358153\pi\) | ||||
0.431021 | + | 0.902342i | \(0.358153\pi\) | |||||||
\(44\) | −1.10992 | −0.167326 | ||||||||
\(45\) | −1.44504 | −0.215414 | ||||||||
\(46\) | 6.76271 | 0.997107 | ||||||||
\(47\) | 1.43296 | 0.209019 | 0.104509 | − | 0.994524i | \(-0.466673\pi\) | ||||
0.104509 | + | 0.994524i | \(0.466673\pi\) | |||||||
\(48\) | −1.24698 | −0.179986 | ||||||||
\(49\) | −6.96077 | −0.994396 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | −8.09783 | −1.13392 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.92154 | 1.36283 | 0.681414 | − | 0.731898i | \(-0.261365\pi\) | ||||
0.681414 | + | 0.731898i | \(0.261365\pi\) | |||||||
\(54\) | −5.54288 | −0.754290 | ||||||||
\(55\) | −1.10992 | −0.149661 | ||||||||
\(56\) | 0.198062 | 0.0264672 | ||||||||
\(57\) | −0.615957 | −0.0815855 | ||||||||
\(58\) | 0.356896 | 0.0468627 | ||||||||
\(59\) | −4.61596 | −0.600946 | −0.300473 | − | 0.953790i | \(-0.597145\pi\) | ||||
−0.300473 | + | 0.953790i | \(0.597145\pi\) | |||||||
\(60\) | −1.24698 | −0.160984 | ||||||||
\(61\) | 5.50365 | 0.704670 | 0.352335 | − | 0.935874i | \(-0.385388\pi\) | ||||
0.352335 | + | 0.935874i | \(0.385388\pi\) | |||||||
\(62\) | 6.27413 | 0.796815 | ||||||||
\(63\) | 0.286208 | 0.0360589 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.38404 | −0.170364 | ||||||||
\(67\) | 3.87263 | 0.473116 | 0.236558 | − | 0.971617i | \(-0.423981\pi\) | ||||
0.236558 | + | 0.971617i | \(0.423981\pi\) | |||||||
\(68\) | 6.49396 | 0.787508 | ||||||||
\(69\) | 8.43296 | 1.01521 | ||||||||
\(70\) | 0.198062 | 0.0236730 | ||||||||
\(71\) | −13.6039 | −1.61448 | −0.807241 | − | 0.590221i | \(-0.799040\pi\) | ||||
−0.807241 | + | 0.590221i | \(0.799040\pi\) | |||||||
\(72\) | 1.44504 | 0.170300 | ||||||||
\(73\) | −0.591794 | −0.0692642 | −0.0346321 | − | 0.999400i | \(-0.511026\pi\) | ||||
−0.0346321 | + | 0.999400i | \(0.511026\pi\) | |||||||
\(74\) | 2.21983 | 0.258050 | ||||||||
\(75\) | −1.24698 | −0.143989 | ||||||||
\(76\) | 0.493959 | 0.0566610 | ||||||||
\(77\) | 0.219833 | 0.0250522 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.93362 | 0.330059 | 0.165029 | − | 0.986289i | \(-0.447228\pi\) | ||||
0.165029 | + | 0.986289i | \(0.447228\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | −2.57673 | −0.286303 | ||||||||
\(82\) | 8.96615 | 0.990145 | ||||||||
\(83\) | −15.6625 | −1.71918 | −0.859590 | − | 0.510984i | \(-0.829281\pi\) | ||||
−0.859590 | + | 0.510984i | \(0.829281\pi\) | |||||||
\(84\) | 0.246980 | 0.0269477 | ||||||||
\(85\) | 6.49396 | 0.704369 | ||||||||
\(86\) | −5.65279 | −0.609556 | ||||||||
\(87\) | 0.445042 | 0.0477135 | ||||||||
\(88\) | 1.10992 | 0.118317 | ||||||||
\(89\) | 17.0804 | 1.81052 | 0.905258 | − | 0.424862i | \(-0.139677\pi\) | ||||
0.905258 | + | 0.424862i | \(0.139677\pi\) | |||||||
\(90\) | 1.44504 | 0.152321 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −6.76271 | −0.705061 | ||||||||
\(93\) | 7.82371 | 0.811281 | ||||||||
\(94\) | −1.43296 | −0.147799 | ||||||||
\(95\) | 0.493959 | 0.0506791 | ||||||||
\(96\) | 1.24698 | 0.127269 | ||||||||
\(97\) | −13.5797 | −1.37881 | −0.689405 | − | 0.724376i | \(-0.742128\pi\) | ||||
−0.689405 | + | 0.724376i | \(0.742128\pi\) | |||||||
\(98\) | 6.96077 | 0.703144 | ||||||||
\(99\) | 1.60388 | 0.161196 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −5.55496 | −0.552739 | −0.276369 | − | 0.961051i | \(-0.589131\pi\) | ||||
−0.276369 | + | 0.961051i | \(0.589131\pi\) | |||||||
\(102\) | 8.09783 | 0.801805 | ||||||||
\(103\) | −4.39373 | −0.432927 | −0.216464 | − | 0.976291i | \(-0.569452\pi\) | ||||
−0.216464 | + | 0.976291i | \(0.569452\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.246980 | 0.0241027 | ||||||||
\(106\) | −9.92154 | −0.963665 | ||||||||
\(107\) | −17.9758 | −1.73779 | −0.868895 | − | 0.494997i | \(-0.835169\pi\) | ||||
−0.868895 | + | 0.494997i | \(0.835169\pi\) | |||||||
\(108\) | 5.54288 | 0.533364 | ||||||||
\(109\) | −6.73556 | −0.645150 | −0.322575 | − | 0.946544i | \(-0.604548\pi\) | ||||
−0.322575 | + | 0.946544i | \(0.604548\pi\) | |||||||
\(110\) | 1.10992 | 0.105826 | ||||||||
\(111\) | 2.76809 | 0.262735 | ||||||||
\(112\) | −0.198062 | −0.0187151 | ||||||||
\(113\) | 2.27413 | 0.213932 | 0.106966 | − | 0.994263i | \(-0.465886\pi\) | ||||
0.106966 | + | 0.994263i | \(0.465886\pi\) | |||||||
\(114\) | 0.615957 | 0.0576897 | ||||||||
\(115\) | −6.76271 | −0.630626 | ||||||||
\(116\) | −0.356896 | −0.0331369 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.61596 | 0.424933 | ||||||||
\(119\) | −1.28621 | −0.117907 | ||||||||
\(120\) | 1.24698 | 0.113833 | ||||||||
\(121\) | −9.76809 | −0.888008 | ||||||||
\(122\) | −5.50365 | −0.498277 | ||||||||
\(123\) | 11.1806 | 1.00812 | ||||||||
\(124\) | −6.27413 | −0.563433 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −0.286208 | −0.0254975 | ||||||||
\(127\) | 13.7778 | 1.22258 | 0.611290 | − | 0.791407i | \(-0.290651\pi\) | ||||
0.611290 | + | 0.791407i | \(0.290651\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −7.04892 | −0.620623 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −19.3056 | −1.68674 | −0.843368 | − | 0.537336i | \(-0.819431\pi\) | ||||
−0.843368 | + | 0.537336i | \(0.819431\pi\) | |||||||
\(132\) | 1.38404 | 0.120465 | ||||||||
\(133\) | −0.0978347 | −0.00848334 | ||||||||
\(134\) | −3.87263 | −0.334544 | ||||||||
\(135\) | 5.54288 | 0.477055 | ||||||||
\(136\) | −6.49396 | −0.556852 | ||||||||
\(137\) | −19.5362 | −1.66909 | −0.834544 | − | 0.550941i | \(-0.814269\pi\) | ||||
−0.834544 | + | 0.550941i | \(0.814269\pi\) | |||||||
\(138\) | −8.43296 | −0.717861 | ||||||||
\(139\) | −18.4155 | −1.56198 | −0.780991 | − | 0.624542i | \(-0.785286\pi\) | ||||
−0.780991 | + | 0.624542i | \(0.785286\pi\) | |||||||
\(140\) | −0.198062 | −0.0167393 | ||||||||
\(141\) | −1.78687 | −0.150482 | ||||||||
\(142\) | 13.6039 | 1.14161 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1.44504 | −0.120420 | ||||||||
\(145\) | −0.356896 | −0.0296386 | ||||||||
\(146\) | 0.591794 | 0.0489772 | ||||||||
\(147\) | 8.67994 | 0.715909 | ||||||||
\(148\) | −2.21983 | −0.182469 | ||||||||
\(149\) | −17.2664 | −1.41452 | −0.707258 | − | 0.706956i | \(-0.750068\pi\) | ||||
−0.707258 | + | 0.706956i | \(0.750068\pi\) | |||||||
\(150\) | 1.24698 | 0.101815 | ||||||||
\(151\) | −3.97584 | −0.323549 | −0.161775 | − | 0.986828i | \(-0.551722\pi\) | ||||
−0.161775 | + | 0.986828i | \(0.551722\pi\) | |||||||
\(152\) | −0.493959 | −0.0400654 | ||||||||
\(153\) | −9.38404 | −0.758655 | ||||||||
\(154\) | −0.219833 | −0.0177146 | ||||||||
\(155\) | −6.27413 | −0.503950 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.4034 | 1.38894 | 0.694472 | − | 0.719520i | \(-0.255638\pi\) | ||||
0.694472 | + | 0.719520i | \(0.255638\pi\) | |||||||
\(158\) | −2.93362 | −0.233387 | ||||||||
\(159\) | −12.3720 | −0.981160 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 1.33944 | 0.105562 | ||||||||
\(162\) | 2.57673 | 0.202447 | ||||||||
\(163\) | 9.16852 | 0.718134 | 0.359067 | − | 0.933312i | \(-0.383095\pi\) | ||||
0.359067 | + | 0.933312i | \(0.383095\pi\) | |||||||
\(164\) | −8.96615 | −0.700139 | ||||||||
\(165\) | 1.38404 | 0.107748 | ||||||||
\(166\) | 15.6625 | 1.21564 | ||||||||
\(167\) | −7.36227 | −0.569710 | −0.284855 | − | 0.958571i | \(-0.591945\pi\) | ||||
−0.284855 | + | 0.958571i | \(0.591945\pi\) | |||||||
\(168\) | −0.246980 | −0.0190549 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −6.49396 | −0.498064 | ||||||||
\(171\) | −0.713792 | −0.0545850 | ||||||||
\(172\) | 5.65279 | 0.431021 | ||||||||
\(173\) | −8.59179 | −0.653222 | −0.326611 | − | 0.945159i | \(-0.605907\pi\) | ||||
−0.326611 | + | 0.945159i | \(0.605907\pi\) | |||||||
\(174\) | −0.445042 | −0.0337385 | ||||||||
\(175\) | −0.198062 | −0.0149721 | ||||||||
\(176\) | −1.10992 | −0.0836631 | ||||||||
\(177\) | 5.75600 | 0.432648 | ||||||||
\(178\) | −17.0804 | −1.28023 | ||||||||
\(179\) | −0.659498 | −0.0492932 | −0.0246466 | − | 0.999696i | \(-0.507846\pi\) | ||||
−0.0246466 | + | 0.999696i | \(0.507846\pi\) | |||||||
\(180\) | −1.44504 | −0.107707 | ||||||||
\(181\) | −20.4101 | −1.51707 | −0.758536 | − | 0.651631i | \(-0.774085\pi\) | ||||
−0.758536 | + | 0.651631i | \(0.774085\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.86294 | −0.507323 | ||||||||
\(184\) | 6.76271 | 0.498554 | ||||||||
\(185\) | −2.21983 | −0.163205 | ||||||||
\(186\) | −7.82371 | −0.573662 | ||||||||
\(187\) | −7.20775 | −0.527083 | ||||||||
\(188\) | 1.43296 | 0.104509 | ||||||||
\(189\) | −1.09783 | −0.0798557 | ||||||||
\(190\) | −0.493959 | −0.0358356 | ||||||||
\(191\) | 12.7332 | 0.921340 | 0.460670 | − | 0.887572i | \(-0.347609\pi\) | ||||
0.460670 | + | 0.887572i | \(0.347609\pi\) | |||||||
\(192\) | −1.24698 | −0.0899930 | ||||||||
\(193\) | −8.68963 | −0.625493 | −0.312747 | − | 0.949837i | \(-0.601249\pi\) | ||||
−0.312747 | + | 0.949837i | \(0.601249\pi\) | |||||||
\(194\) | 13.5797 | 0.974967 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.96077 | −0.497198 | ||||||||
\(197\) | −5.28621 | −0.376627 | −0.188313 | − | 0.982109i | \(-0.560302\pi\) | ||||
−0.188313 | + | 0.982109i | \(0.560302\pi\) | |||||||
\(198\) | −1.60388 | −0.113982 | ||||||||
\(199\) | −10.9444 | −0.775826 | −0.387913 | − | 0.921696i | \(-0.626804\pi\) | ||||
−0.387913 | + | 0.921696i | \(0.626804\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | −4.82908 | −0.340617 | ||||||||
\(202\) | 5.55496 | 0.390845 | ||||||||
\(203\) | 0.0706876 | 0.00496130 | ||||||||
\(204\) | −8.09783 | −0.566962 | ||||||||
\(205\) | −8.96615 | −0.626223 | ||||||||
\(206\) | 4.39373 | 0.306126 | ||||||||
\(207\) | 9.77240 | 0.679229 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.548253 | −0.0379235 | ||||||||
\(210\) | −0.246980 | −0.0170432 | ||||||||
\(211\) | 3.30559 | 0.227566 | 0.113783 | − | 0.993506i | \(-0.463703\pi\) | ||||
0.113783 | + | 0.993506i | \(0.463703\pi\) | |||||||
\(212\) | 9.92154 | 0.681414 | ||||||||
\(213\) | 16.9638 | 1.16234 | ||||||||
\(214\) | 17.9758 | 1.22880 | ||||||||
\(215\) | 5.65279 | 0.385517 | ||||||||
\(216\) | −5.54288 | −0.377145 | ||||||||
\(217\) | 1.24267 | 0.0843578 | ||||||||
\(218\) | 6.73556 | 0.456190 | ||||||||
\(219\) | 0.737955 | 0.0498664 | ||||||||
\(220\) | −1.10992 | −0.0748305 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −2.76809 | −0.185782 | ||||||||
\(223\) | 16.6310 | 1.11370 | 0.556848 | − | 0.830615i | \(-0.312011\pi\) | ||||
0.556848 | + | 0.830615i | \(0.312011\pi\) | |||||||
\(224\) | 0.198062 | 0.0132336 | ||||||||
\(225\) | −1.44504 | −0.0963361 | ||||||||
\(226\) | −2.27413 | −0.151273 | ||||||||
\(227\) | 10.8616 | 0.720910 | 0.360455 | − | 0.932777i | \(-0.382621\pi\) | ||||
0.360455 | + | 0.932777i | \(0.382621\pi\) | |||||||
\(228\) | −0.615957 | −0.0407928 | ||||||||
\(229\) | 23.3991 | 1.54626 | 0.773128 | − | 0.634250i | \(-0.218691\pi\) | ||||
0.773128 | + | 0.634250i | \(0.218691\pi\) | |||||||
\(230\) | 6.76271 | 0.445920 | ||||||||
\(231\) | −0.274127 | −0.0180362 | ||||||||
\(232\) | 0.356896 | 0.0234314 | ||||||||
\(233\) | 14.3913 | 0.942808 | 0.471404 | − | 0.881917i | \(-0.343747\pi\) | ||||
0.471404 | + | 0.881917i | \(0.343747\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.43296 | 0.0934760 | ||||||||
\(236\) | −4.61596 | −0.300473 | ||||||||
\(237\) | −3.65817 | −0.237624 | ||||||||
\(238\) | 1.28621 | 0.0833725 | ||||||||
\(239\) | −3.56033 | −0.230299 | −0.115149 | − | 0.993348i | \(-0.536735\pi\) | ||||
−0.115149 | + | 0.993348i | \(0.536735\pi\) | |||||||
\(240\) | −1.24698 | −0.0804922 | ||||||||
\(241\) | 29.1890 | 1.88023 | 0.940113 | − | 0.340862i | \(-0.110719\pi\) | ||||
0.940113 | + | 0.340862i | \(0.110719\pi\) | |||||||
\(242\) | 9.76809 | 0.627916 | ||||||||
\(243\) | −13.4155 | −0.860605 | ||||||||
\(244\) | 5.50365 | 0.352335 | ||||||||
\(245\) | −6.96077 | −0.444707 | ||||||||
\(246\) | −11.1806 | −0.712849 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 6.27413 | 0.398407 | ||||||||
\(249\) | 19.5308 | 1.23771 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −29.3599 | −1.85318 | −0.926590 | − | 0.376074i | \(-0.877274\pi\) | ||||
−0.926590 | + | 0.376074i | \(0.877274\pi\) | |||||||
\(252\) | 0.286208 | 0.0180294 | ||||||||
\(253\) | 7.50604 | 0.471901 | ||||||||
\(254\) | −13.7778 | −0.864494 | ||||||||
\(255\) | −8.09783 | −0.507106 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 21.5362 | 1.34339 | 0.671695 | − | 0.740828i | \(-0.265567\pi\) | ||||
0.671695 | + | 0.740828i | \(0.265567\pi\) | |||||||
\(258\) | 7.04892 | 0.438846 | ||||||||
\(259\) | 0.439665 | 0.0273195 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.515729 | 0.0319229 | ||||||||
\(262\) | 19.3056 | 1.19270 | ||||||||
\(263\) | −6.57002 | −0.405125 | −0.202563 | − | 0.979269i | \(-0.564927\pi\) | ||||
−0.202563 | + | 0.979269i | \(0.564927\pi\) | |||||||
\(264\) | −1.38404 | −0.0851820 | ||||||||
\(265\) | 9.92154 | 0.609476 | ||||||||
\(266\) | 0.0978347 | 0.00599863 | ||||||||
\(267\) | −21.2989 | −1.30347 | ||||||||
\(268\) | 3.87263 | 0.236558 | ||||||||
\(269\) | 7.36898 | 0.449294 | 0.224647 | − | 0.974440i | \(-0.427877\pi\) | ||||
0.224647 | + | 0.974440i | \(0.427877\pi\) | |||||||
\(270\) | −5.54288 | −0.337329 | ||||||||
\(271\) | −15.5797 | −0.946400 | −0.473200 | − | 0.880955i | \(-0.656901\pi\) | ||||
−0.473200 | + | 0.880955i | \(0.656901\pi\) | |||||||
\(272\) | 6.49396 | 0.393754 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 19.5362 | 1.18022 | ||||||||
\(275\) | −1.10992 | −0.0669305 | ||||||||
\(276\) | 8.43296 | 0.507605 | ||||||||
\(277\) | −13.9952 | −0.840891 | −0.420445 | − | 0.907318i | \(-0.638126\pi\) | ||||
−0.420445 | + | 0.907318i | \(0.638126\pi\) | |||||||
\(278\) | 18.4155 | 1.10449 | ||||||||
\(279\) | 9.06638 | 0.542790 | ||||||||
\(280\) | 0.198062 | 0.0118365 | ||||||||
\(281\) | −13.3341 | −0.795443 | −0.397722 | − | 0.917506i | \(-0.630199\pi\) | ||||
−0.397722 | + | 0.917506i | \(0.630199\pi\) | |||||||
\(282\) | 1.78687 | 0.106407 | ||||||||
\(283\) | −20.7289 | −1.23220 | −0.616101 | − | 0.787667i | \(-0.711289\pi\) | ||||
−0.616101 | + | 0.787667i | \(0.711289\pi\) | |||||||
\(284\) | −13.6039 | −0.807241 | ||||||||
\(285\) | −0.615957 | −0.0364861 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.77586 | 0.104825 | ||||||||
\(288\) | 1.44504 | 0.0851499 | ||||||||
\(289\) | 25.1715 | 1.48068 | ||||||||
\(290\) | 0.356896 | 0.0209576 | ||||||||
\(291\) | 16.9336 | 0.992667 | ||||||||
\(292\) | −0.591794 | −0.0346321 | ||||||||
\(293\) | −16.3913 | −0.957592 | −0.478796 | − | 0.877926i | \(-0.658927\pi\) | ||||
−0.478796 | + | 0.877926i | \(0.658927\pi\) | |||||||
\(294\) | −8.67994 | −0.506224 | ||||||||
\(295\) | −4.61596 | −0.268751 | ||||||||
\(296\) | 2.21983 | 0.129025 | ||||||||
\(297\) | −6.15213 | −0.356983 | ||||||||
\(298\) | 17.2664 | 1.00021 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1.24698 | −0.0719944 | ||||||||
\(301\) | −1.11960 | −0.0645330 | ||||||||
\(302\) | 3.97584 | 0.228784 | ||||||||
\(303\) | 6.92692 | 0.397941 | ||||||||
\(304\) | 0.493959 | 0.0283305 | ||||||||
\(305\) | 5.50365 | 0.315138 | ||||||||
\(306\) | 9.38404 | 0.536450 | ||||||||
\(307\) | 6.94869 | 0.396583 | 0.198291 | − | 0.980143i | \(-0.436461\pi\) | ||||
0.198291 | + | 0.980143i | \(0.436461\pi\) | |||||||
\(308\) | 0.219833 | 0.0125261 | ||||||||
\(309\) | 5.47889 | 0.311683 | ||||||||
\(310\) | 6.27413 | 0.356346 | ||||||||
\(311\) | −24.3612 | −1.38140 | −0.690699 | − | 0.723143i | \(-0.742697\pi\) | ||||
−0.690699 | + | 0.723143i | \(0.742697\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.89008 | 0.163357 | 0.0816786 | − | 0.996659i | \(-0.473972\pi\) | ||||
0.0816786 | + | 0.996659i | \(0.473972\pi\) | |||||||
\(314\) | −17.4034 | −0.982132 | ||||||||
\(315\) | 0.286208 | 0.0161260 | ||||||||
\(316\) | 2.93362 | 0.165029 | ||||||||
\(317\) | −5.01208 | −0.281507 | −0.140753 | − | 0.990045i | \(-0.544952\pi\) | ||||
−0.140753 | + | 0.990045i | \(0.544952\pi\) | |||||||
\(318\) | 12.3720 | 0.693785 | ||||||||
\(319\) | 0.396125 | 0.0221787 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 22.4155 | 1.25111 | ||||||||
\(322\) | −1.33944 | −0.0746439 | ||||||||
\(323\) | 3.20775 | 0.178484 | ||||||||
\(324\) | −2.57673 | −0.143152 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −9.16852 | −0.507797 | ||||||||
\(327\) | 8.39911 | 0.464472 | ||||||||
\(328\) | 8.96615 | 0.495073 | ||||||||
\(329\) | −0.283815 | −0.0156472 | ||||||||
\(330\) | −1.38404 | −0.0761891 | ||||||||
\(331\) | 24.0194 | 1.32022 | 0.660112 | − | 0.751167i | \(-0.270509\pi\) | ||||
0.660112 | + | 0.751167i | \(0.270509\pi\) | |||||||
\(332\) | −15.6625 | −0.859590 | ||||||||
\(333\) | 3.20775 | 0.175784 | ||||||||
\(334\) | 7.36227 | 0.402846 | ||||||||
\(335\) | 3.87263 | 0.211584 | ||||||||
\(336\) | 0.246980 | 0.0134738 | ||||||||
\(337\) | 28.5133 | 1.55322 | 0.776610 | − | 0.629981i | \(-0.216938\pi\) | ||||
0.776610 | + | 0.629981i | \(0.216938\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.83579 | −0.154019 | ||||||||
\(340\) | 6.49396 | 0.352184 | ||||||||
\(341\) | 6.96376 | 0.377108 | ||||||||
\(342\) | 0.713792 | 0.0385974 | ||||||||
\(343\) | 2.76510 | 0.149301 | ||||||||
\(344\) | −5.65279 | −0.304778 | ||||||||
\(345\) | 8.43296 | 0.454015 | ||||||||
\(346\) | 8.59179 | 0.461898 | ||||||||
\(347\) | −25.1987 | −1.35273 | −0.676367 | − | 0.736565i | \(-0.736447\pi\) | ||||
−0.676367 | + | 0.736565i | \(0.736447\pi\) | |||||||
\(348\) | 0.445042 | 0.0238567 | ||||||||
\(349\) | 16.4155 | 0.878702 | 0.439351 | − | 0.898316i | \(-0.355209\pi\) | ||||
0.439351 | + | 0.898316i | \(0.355209\pi\) | |||||||
\(350\) | 0.198062 | 0.0105869 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.10992 | 0.0591587 | ||||||||
\(353\) | 1.10992 | 0.0590749 | 0.0295374 | − | 0.999564i | \(-0.490597\pi\) | ||||
0.0295374 | + | 0.999564i | \(0.490597\pi\) | |||||||
\(354\) | −5.75600 | −0.305928 | ||||||||
\(355\) | −13.6039 | −0.722019 | ||||||||
\(356\) | 17.0804 | 0.905258 | ||||||||
\(357\) | 1.60388 | 0.0848861 | ||||||||
\(358\) | 0.659498 | 0.0348555 | ||||||||
\(359\) | 36.7633 | 1.94029 | 0.970146 | − | 0.242520i | \(-0.0779740\pi\) | ||||
0.970146 | + | 0.242520i | \(0.0779740\pi\) | |||||||
\(360\) | 1.44504 | 0.0761604 | ||||||||
\(361\) | −18.7560 | −0.987158 | ||||||||
\(362\) | 20.4101 | 1.07273 | ||||||||
\(363\) | 12.1806 | 0.639316 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.591794 | −0.0309759 | ||||||||
\(366\) | 6.86294 | 0.358731 | ||||||||
\(367\) | 7.09485 | 0.370348 | 0.185174 | − | 0.982706i | \(-0.440715\pi\) | ||||
0.185174 | + | 0.982706i | \(0.440715\pi\) | |||||||
\(368\) | −6.76271 | −0.352531 | ||||||||
\(369\) | 12.9565 | 0.674486 | ||||||||
\(370\) | 2.21983 | 0.115404 | ||||||||
\(371\) | −1.96508 | −0.102022 | ||||||||
\(372\) | 7.82371 | 0.405640 | ||||||||
\(373\) | 26.8901 | 1.39232 | 0.696158 | − | 0.717889i | \(-0.254891\pi\) | ||||
0.696158 | + | 0.717889i | \(0.254891\pi\) | |||||||
\(374\) | 7.20775 | 0.372704 | ||||||||
\(375\) | −1.24698 | −0.0643937 | ||||||||
\(376\) | −1.43296 | −0.0738993 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 1.09783 | 0.0564665 | ||||||||
\(379\) | 8.46980 | 0.435064 | 0.217532 | − | 0.976053i | \(-0.430199\pi\) | ||||
0.217532 | + | 0.976053i | \(0.430199\pi\) | |||||||
\(380\) | 0.493959 | 0.0253396 | ||||||||
\(381\) | −17.1806 | −0.880189 | ||||||||
\(382\) | −12.7332 | −0.651486 | ||||||||
\(383\) | −4.79656 | −0.245093 | −0.122546 | − | 0.992463i | \(-0.539106\pi\) | ||||
−0.122546 | + | 0.992463i | \(0.539106\pi\) | |||||||
\(384\) | 1.24698 | 0.0636347 | ||||||||
\(385\) | 0.219833 | 0.0112037 | ||||||||
\(386\) | 8.68963 | 0.442290 | ||||||||
\(387\) | −8.16852 | −0.415229 | ||||||||
\(388\) | −13.5797 | −0.689405 | ||||||||
\(389\) | 29.2131 | 1.48116 | 0.740582 | − | 0.671966i | \(-0.234550\pi\) | ||||
0.740582 | + | 0.671966i | \(0.234550\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −43.9168 | −2.22097 | ||||||||
\(392\) | 6.96077 | 0.351572 | ||||||||
\(393\) | 24.0737 | 1.21436 | ||||||||
\(394\) | 5.28621 | 0.266315 | ||||||||
\(395\) | 2.93362 | 0.147607 | ||||||||
\(396\) | 1.60388 | 0.0805978 | ||||||||
\(397\) | −22.6112 | −1.13482 | −0.567411 | − | 0.823435i | \(-0.692055\pi\) | ||||
−0.567411 | + | 0.823435i | \(0.692055\pi\) | |||||||
\(398\) | 10.9444 | 0.548592 | ||||||||
\(399\) | 0.121998 | 0.00610753 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 10.5894 | 0.528809 | 0.264405 | − | 0.964412i | \(-0.414825\pi\) | ||||
0.264405 | + | 0.964412i | \(0.414825\pi\) | |||||||
\(402\) | 4.82908 | 0.240853 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −5.55496 | −0.276369 | ||||||||
\(405\) | −2.57673 | −0.128039 | ||||||||
\(406\) | −0.0706876 | −0.00350817 | ||||||||
\(407\) | 2.46383 | 0.122127 | ||||||||
\(408\) | 8.09783 | 0.400903 | ||||||||
\(409\) | 11.7127 | 0.579157 | 0.289579 | − | 0.957154i | \(-0.406485\pi\) | ||||
0.289579 | + | 0.957154i | \(0.406485\pi\) | |||||||
\(410\) | 8.96615 | 0.442806 | ||||||||
\(411\) | 24.3612 | 1.20165 | ||||||||
\(412\) | −4.39373 | −0.216464 | ||||||||
\(413\) | 0.914247 | 0.0449871 | ||||||||
\(414\) | −9.77240 | −0.480287 | ||||||||
\(415\) | −15.6625 | −0.768841 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 22.9638 | 1.12454 | ||||||||
\(418\) | 0.548253 | 0.0268159 | ||||||||
\(419\) | 21.3250 | 1.04179 | 0.520896 | − | 0.853620i | \(-0.325598\pi\) | ||||
0.520896 | + | 0.853620i | \(0.325598\pi\) | |||||||
\(420\) | 0.246980 | 0.0120514 | ||||||||
\(421\) | 22.1457 | 1.07931 | 0.539657 | − | 0.841885i | \(-0.318554\pi\) | ||||
0.539657 | + | 0.841885i | \(0.318554\pi\) | |||||||
\(422\) | −3.30559 | −0.160913 | ||||||||
\(423\) | −2.07069 | −0.100680 | ||||||||
\(424\) | −9.92154 | −0.481833 | ||||||||
\(425\) | 6.49396 | 0.315003 | ||||||||
\(426\) | −16.9638 | −0.821897 | ||||||||
\(427\) | −1.09006 | −0.0527519 | ||||||||
\(428\) | −17.9758 | −0.868895 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −5.65279 | −0.272602 | ||||||||
\(431\) | −36.8068 | −1.77292 | −0.886462 | − | 0.462802i | \(-0.846844\pi\) | ||||
−0.886462 | + | 0.462802i | \(0.846844\pi\) | |||||||
\(432\) | 5.54288 | 0.266682 | ||||||||
\(433\) | 2.08708 | 0.100299 | 0.0501494 | − | 0.998742i | \(-0.484030\pi\) | ||||
0.0501494 | + | 0.998742i | \(0.484030\pi\) | |||||||
\(434\) | −1.24267 | −0.0596500 | ||||||||
\(435\) | 0.445042 | 0.0213381 | ||||||||
\(436\) | −6.73556 | −0.322575 | ||||||||
\(437\) | −3.34050 | −0.159798 | ||||||||
\(438\) | −0.737955 | −0.0352608 | ||||||||
\(439\) | 9.95646 | 0.475196 | 0.237598 | − | 0.971364i | \(-0.423640\pi\) | ||||
0.237598 | + | 0.971364i | \(0.423640\pi\) | |||||||
\(440\) | 1.10992 | 0.0529132 | ||||||||
\(441\) | 10.0586 | 0.478981 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15.3884 | −0.731123 | −0.365561 | − | 0.930787i | \(-0.619123\pi\) | ||||
−0.365561 | + | 0.930787i | \(0.619123\pi\) | |||||||
\(444\) | 2.76809 | 0.131368 | ||||||||
\(445\) | 17.0804 | 0.809687 | ||||||||
\(446\) | −16.6310 | −0.787502 | ||||||||
\(447\) | 21.5308 | 1.01837 | ||||||||
\(448\) | −0.198062 | −0.00935756 | ||||||||
\(449\) | −8.18060 | −0.386067 | −0.193033 | − | 0.981192i | \(-0.561833\pi\) | ||||
−0.193033 | + | 0.981192i | \(0.561833\pi\) | |||||||
\(450\) | 1.44504 | 0.0681199 | ||||||||
\(451\) | 9.95167 | 0.468606 | ||||||||
\(452\) | 2.27413 | 0.106966 | ||||||||
\(453\) | 4.95779 | 0.232937 | ||||||||
\(454\) | −10.8616 | −0.509761 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.615957 | 0.0288448 | ||||||||
\(457\) | −16.0737 | −0.751895 | −0.375947 | − | 0.926641i | \(-0.622683\pi\) | ||||
−0.375947 | + | 0.926641i | \(0.622683\pi\) | |||||||
\(458\) | −23.3991 | −1.09337 | ||||||||
\(459\) | 35.9952 | 1.68011 | ||||||||
\(460\) | −6.76271 | −0.315313 | ||||||||
\(461\) | −27.5308 | −1.28224 | −0.641118 | − | 0.767442i | \(-0.721529\pi\) | ||||
−0.641118 | + | 0.767442i | \(0.721529\pi\) | |||||||
\(462\) | 0.274127 | 0.0127535 | ||||||||
\(463\) | 10.6595 | 0.495389 | 0.247694 | − | 0.968838i | \(-0.420327\pi\) | ||||
0.247694 | + | 0.968838i | \(0.420327\pi\) | |||||||
\(464\) | −0.356896 | −0.0165685 | ||||||||
\(465\) | 7.82371 | 0.362816 | ||||||||
\(466\) | −14.3913 | −0.666666 | ||||||||
\(467\) | −10.7976 | −0.499655 | −0.249827 | − | 0.968290i | \(-0.580374\pi\) | ||||
−0.249827 | + | 0.968290i | \(0.580374\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.767021 | −0.0354177 | ||||||||
\(470\) | −1.43296 | −0.0660975 | ||||||||
\(471\) | −21.7017 | −0.999962 | ||||||||
\(472\) | 4.61596 | 0.212467 | ||||||||
\(473\) | −6.27413 | −0.288485 | ||||||||
\(474\) | 3.65817 | 0.168025 | ||||||||
\(475\) | 0.493959 | 0.0226644 | ||||||||
\(476\) | −1.28621 | −0.0589533 | ||||||||
\(477\) | −14.3370 | −0.656448 | ||||||||
\(478\) | 3.56033 | 0.162846 | ||||||||
\(479\) | −9.08575 | −0.415139 | −0.207569 | − | 0.978220i | \(-0.566555\pi\) | ||||
−0.207569 | + | 0.978220i | \(0.566555\pi\) | |||||||
\(480\) | 1.24698 | 0.0569166 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −29.1890 | −1.32952 | ||||||||
\(483\) | −1.67025 | −0.0759991 | ||||||||
\(484\) | −9.76809 | −0.444004 | ||||||||
\(485\) | −13.5797 | −0.616623 | ||||||||
\(486\) | 13.4155 | 0.608540 | ||||||||
\(487\) | 40.8471 | 1.85096 | 0.925480 | − | 0.378796i | \(-0.123662\pi\) | ||||
0.925480 | + | 0.378796i | \(0.123662\pi\) | |||||||
\(488\) | −5.50365 | −0.249138 | ||||||||
\(489\) | −11.4330 | −0.517016 | ||||||||
\(490\) | 6.96077 | 0.314456 | ||||||||
\(491\) | 29.0944 | 1.31301 | 0.656505 | − | 0.754321i | \(-0.272034\pi\) | ||||
0.656505 | + | 0.754321i | \(0.272034\pi\) | |||||||
\(492\) | 11.1806 | 0.504061 | ||||||||
\(493\) | −2.31767 | −0.104382 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.60388 | 0.0720888 | ||||||||
\(496\) | −6.27413 | −0.281717 | ||||||||
\(497\) | 2.69441 | 0.120861 | ||||||||
\(498\) | −19.5308 | −0.875196 | ||||||||
\(499\) | −16.2150 | −0.725885 | −0.362943 | − | 0.931812i | \(-0.618228\pi\) | ||||
−0.362943 | + | 0.931812i | \(0.618228\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 9.18060 | 0.410159 | ||||||||
\(502\) | 29.3599 | 1.31040 | ||||||||
\(503\) | −1.49502 | −0.0666598 | −0.0333299 | − | 0.999444i | \(-0.510611\pi\) | ||||
−0.0333299 | + | 0.999444i | \(0.510611\pi\) | |||||||
\(504\) | −0.286208 | −0.0127487 | ||||||||
\(505\) | −5.55496 | −0.247192 | ||||||||
\(506\) | −7.50604 | −0.333684 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 13.7778 | 0.611290 | ||||||||
\(509\) | 4.63102 | 0.205266 | 0.102633 | − | 0.994719i | \(-0.467273\pi\) | ||||
0.102633 | + | 0.994719i | \(0.467273\pi\) | |||||||
\(510\) | 8.09783 | 0.358578 | ||||||||
\(511\) | 0.117212 | 0.00518516 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 2.73795 | 0.120884 | ||||||||
\(514\) | −21.5362 | −0.949920 | ||||||||
\(515\) | −4.39373 | −0.193611 | ||||||||
\(516\) | −7.04892 | −0.310311 | ||||||||
\(517\) | −1.59047 | −0.0699486 | ||||||||
\(518\) | −0.439665 | −0.0193178 | ||||||||
\(519\) | 10.7138 | 0.470283 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.23729 | −0.404693 | −0.202347 | − | 0.979314i | \(-0.564857\pi\) | ||||
−0.202347 | + | 0.979314i | \(0.564857\pi\) | |||||||
\(522\) | −0.515729 | −0.0225729 | ||||||||
\(523\) | −2.88471 | −0.126139 | −0.0630697 | − | 0.998009i | \(-0.520089\pi\) | ||||
−0.0630697 | + | 0.998009i | \(0.520089\pi\) | |||||||
\(524\) | −19.3056 | −0.843368 | ||||||||
\(525\) | 0.246980 | 0.0107791 | ||||||||
\(526\) | 6.57002 | 0.286467 | ||||||||
\(527\) | −40.7439 | −1.77483 | ||||||||
\(528\) | 1.38404 | 0.0602327 | ||||||||
\(529\) | 22.7342 | 0.988445 | ||||||||
\(530\) | −9.92154 | −0.430964 | ||||||||
\(531\) | 6.67025 | 0.289464 | ||||||||
\(532\) | −0.0978347 | −0.00424167 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 21.2989 | 0.921693 | ||||||||
\(535\) | −17.9758 | −0.777163 | ||||||||
\(536\) | −3.87263 | −0.167272 | ||||||||
\(537\) | 0.822380 | 0.0354883 | ||||||||
\(538\) | −7.36898 | −0.317699 | ||||||||
\(539\) | 7.72587 | 0.332777 | ||||||||
\(540\) | 5.54288 | 0.238527 | ||||||||
\(541\) | −28.2301 | −1.21371 | −0.606854 | − | 0.794814i | \(-0.707569\pi\) | ||||
−0.606854 | + | 0.794814i | \(0.707569\pi\) | |||||||
\(542\) | 15.5797 | 0.669206 | ||||||||
\(543\) | 25.4510 | 1.09221 | ||||||||
\(544\) | −6.49396 | −0.278426 | ||||||||
\(545\) | −6.73556 | −0.288520 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 37.8756 | 1.61944 | 0.809722 | − | 0.586814i | \(-0.199618\pi\) | ||||
0.809722 | + | 0.586814i | \(0.199618\pi\) | |||||||
\(548\) | −19.5362 | −0.834544 | ||||||||
\(549\) | −7.95300 | −0.339426 | ||||||||
\(550\) | 1.10992 | 0.0473270 | ||||||||
\(551\) | −0.176292 | −0.00751029 | ||||||||
\(552\) | −8.43296 | −0.358931 | ||||||||
\(553\) | −0.581040 | −0.0247083 | ||||||||
\(554\) | 13.9952 | 0.594600 | ||||||||
\(555\) | 2.76809 | 0.117499 | ||||||||
\(556\) | −18.4155 | −0.780991 | ||||||||
\(557\) | 41.2030 | 1.74583 | 0.872913 | − | 0.487876i | \(-0.162228\pi\) | ||||
0.872913 | + | 0.487876i | \(0.162228\pi\) | |||||||
\(558\) | −9.06638 | −0.383810 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −0.198062 | −0.00836966 | ||||||||
\(561\) | 8.98792 | 0.379470 | ||||||||
\(562\) | 13.3341 | 0.562463 | ||||||||
\(563\) | 8.00836 | 0.337512 | 0.168756 | − | 0.985658i | \(-0.446025\pi\) | ||||
0.168756 | + | 0.985658i | \(0.446025\pi\) | |||||||
\(564\) | −1.78687 | −0.0752409 | ||||||||
\(565\) | 2.27413 | 0.0956732 | ||||||||
\(566\) | 20.7289 | 0.871299 | ||||||||
\(567\) | 0.510353 | 0.0214328 | ||||||||
\(568\) | 13.6039 | 0.570806 | ||||||||
\(569\) | 43.1377 | 1.80842 | 0.904212 | − | 0.427083i | \(-0.140459\pi\) | ||||
0.904212 | + | 0.427083i | \(0.140459\pi\) | |||||||
\(570\) | 0.615957 | 0.0257996 | ||||||||
\(571\) | −8.98792 | −0.376133 | −0.188066 | − | 0.982156i | \(-0.560222\pi\) | ||||
−0.188066 | + | 0.982156i | \(0.560222\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −15.8780 | −0.663313 | ||||||||
\(574\) | −1.77586 | −0.0741228 | ||||||||
\(575\) | −6.76271 | −0.282024 | ||||||||
\(576\) | −1.44504 | −0.0602101 | ||||||||
\(577\) | −1.03624 | −0.0431394 | −0.0215697 | − | 0.999767i | \(-0.506866\pi\) | ||||
−0.0215697 | + | 0.999767i | \(0.506866\pi\) | |||||||
\(578\) | −25.1715 | −1.04700 | ||||||||
\(579\) | 10.8358 | 0.450320 | ||||||||
\(580\) | −0.356896 | −0.0148193 | ||||||||
\(581\) | 3.10215 | 0.128699 | ||||||||
\(582\) | −16.9336 | −0.701921 | ||||||||
\(583\) | −11.0121 | −0.456074 | ||||||||
\(584\) | 0.591794 | 0.0244886 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 16.3913 | 0.677120 | ||||||||
\(587\) | −3.70410 | −0.152885 | −0.0764423 | − | 0.997074i | \(-0.524356\pi\) | ||||
−0.0764423 | + | 0.997074i | \(0.524356\pi\) | |||||||
\(588\) | 8.67994 | 0.357955 | ||||||||
\(589\) | −3.09916 | −0.127699 | ||||||||
\(590\) | 4.61596 | 0.190036 | ||||||||
\(591\) | 6.59179 | 0.271150 | ||||||||
\(592\) | −2.21983 | −0.0912346 | ||||||||
\(593\) | 12.2064 | 0.501258 | 0.250629 | − | 0.968083i | \(-0.419363\pi\) | ||||
0.250629 | + | 0.968083i | \(0.419363\pi\) | |||||||
\(594\) | 6.15213 | 0.252425 | ||||||||
\(595\) | −1.28621 | −0.0527294 | ||||||||
\(596\) | −17.2664 | −0.707258 | ||||||||
\(597\) | 13.6474 | 0.558552 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −31.5013 | −1.28711 | −0.643553 | − | 0.765401i | \(-0.722540\pi\) | ||||
−0.643553 | + | 0.765401i | \(0.722540\pi\) | |||||||
\(600\) | 1.24698 | 0.0509077 | ||||||||
\(601\) | 19.6907 | 0.803200 | 0.401600 | − | 0.915815i | \(-0.368454\pi\) | ||||
0.401600 | + | 0.915815i | \(0.368454\pi\) | |||||||
\(602\) | 1.11960 | 0.0456317 | ||||||||
\(603\) | −5.59611 | −0.227891 | ||||||||
\(604\) | −3.97584 | −0.161775 | ||||||||
\(605\) | −9.76809 | −0.397129 | ||||||||
\(606\) | −6.92692 | −0.281387 | ||||||||
\(607\) | −31.0562 | −1.26053 | −0.630266 | − | 0.776379i | \(-0.717054\pi\) | ||||
−0.630266 | + | 0.776379i | \(0.717054\pi\) | |||||||
\(608\) | −0.493959 | −0.0200327 | ||||||||
\(609\) | −0.0881460 | −0.00357186 | ||||||||
\(610\) | −5.50365 | −0.222836 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −9.38404 | −0.379327 | ||||||||
\(613\) | 18.3720 | 0.742037 | 0.371018 | − | 0.928626i | \(-0.379009\pi\) | ||||
0.371018 | + | 0.928626i | \(0.379009\pi\) | |||||||
\(614\) | −6.94869 | −0.280426 | ||||||||
\(615\) | 11.1806 | 0.450845 | ||||||||
\(616\) | −0.219833 | −0.00885730 | ||||||||
\(617\) | −9.27545 | −0.373416 | −0.186708 | − | 0.982415i | \(-0.559782\pi\) | ||||
−0.186708 | + | 0.982415i | \(0.559782\pi\) | |||||||
\(618\) | −5.47889 | −0.220393 | ||||||||
\(619\) | −14.9095 | −0.599262 | −0.299631 | − | 0.954055i | \(-0.596864\pi\) | ||||
−0.299631 | + | 0.954055i | \(0.596864\pi\) | |||||||
\(620\) | −6.27413 | −0.251975 | ||||||||
\(621\) | −37.4849 | −1.50422 | ||||||||
\(622\) | 24.3612 | 0.976795 | ||||||||
\(623\) | −3.38298 | −0.135536 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −2.89008 | −0.115511 | ||||||||
\(627\) | 0.683661 | 0.0273028 | ||||||||
\(628\) | 17.4034 | 0.694472 | ||||||||
\(629\) | −14.4155 | −0.574784 | ||||||||
\(630\) | −0.286208 | −0.0114028 | ||||||||
\(631\) | 30.0823 | 1.19756 | 0.598779 | − | 0.800915i | \(-0.295653\pi\) | ||||
0.598779 | + | 0.800915i | \(0.295653\pi\) | |||||||
\(632\) | −2.93362 | −0.116693 | ||||||||
\(633\) | −4.12200 | −0.163835 | ||||||||
\(634\) | 5.01208 | 0.199055 | ||||||||
\(635\) | 13.7778 | 0.546754 | ||||||||
\(636\) | −12.3720 | −0.490580 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −0.396125 | −0.0156827 | ||||||||
\(639\) | 19.6582 | 0.777665 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 12.1787 | 0.481029 | 0.240515 | − | 0.970646i | \(-0.422684\pi\) | ||||
0.240515 | + | 0.970646i | \(0.422684\pi\) | |||||||
\(642\) | −22.4155 | −0.884669 | ||||||||
\(643\) | −3.36467 | −0.132689 | −0.0663447 | − | 0.997797i | \(-0.521134\pi\) | ||||
−0.0663447 | + | 0.997797i | \(0.521134\pi\) | |||||||
\(644\) | 1.33944 | 0.0527812 | ||||||||
\(645\) | −7.04892 | −0.277551 | ||||||||
\(646\) | −3.20775 | −0.126207 | ||||||||
\(647\) | 28.3913 | 1.11618 | 0.558089 | − | 0.829781i | \(-0.311535\pi\) | ||||
0.558089 | + | 0.829781i | \(0.311535\pi\) | |||||||
\(648\) | 2.57673 | 0.101223 | ||||||||
\(649\) | 5.12333 | 0.201108 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.54958 | −0.0607329 | ||||||||
\(652\) | 9.16852 | 0.359067 | ||||||||
\(653\) | −25.6823 | −1.00503 | −0.502514 | − | 0.864569i | \(-0.667591\pi\) | ||||
−0.502514 | + | 0.864569i | \(0.667591\pi\) | |||||||
\(654\) | −8.39911 | −0.328431 | ||||||||
\(655\) | −19.3056 | −0.754332 | ||||||||
\(656\) | −8.96615 | −0.350069 | ||||||||
\(657\) | 0.855167 | 0.0333632 | ||||||||
\(658\) | 0.283815 | 0.0110643 | ||||||||
\(659\) | −5.26205 | −0.204980 | −0.102490 | − | 0.994734i | \(-0.532681\pi\) | ||||
−0.102490 | + | 0.994734i | \(0.532681\pi\) | |||||||
\(660\) | 1.38404 | 0.0538738 | ||||||||
\(661\) | −32.9476 | −1.28151 | −0.640757 | − | 0.767744i | \(-0.721379\pi\) | ||||
−0.640757 | + | 0.767744i | \(0.721379\pi\) | |||||||
\(662\) | −24.0194 | −0.933540 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 15.6625 | 0.607822 | ||||||||
\(665\) | −0.0978347 | −0.00379387 | ||||||||
\(666\) | −3.20775 | −0.124298 | ||||||||
\(667\) | 2.41358 | 0.0934543 | ||||||||
\(668\) | −7.36227 | −0.284855 | ||||||||
\(669\) | −20.7385 | −0.801799 | ||||||||
\(670\) | −3.87263 | −0.149613 | ||||||||
\(671\) | −6.10859 | −0.235819 | ||||||||
\(672\) | −0.246980 | −0.00952745 | ||||||||
\(673\) | 20.1655 | 0.777324 | 0.388662 | − | 0.921380i | \(-0.372937\pi\) | ||||
0.388662 | + | 0.921380i | \(0.372937\pi\) | |||||||
\(674\) | −28.5133 | −1.09829 | ||||||||
\(675\) | 5.54288 | 0.213345 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 46.4590 | 1.78557 | 0.892783 | − | 0.450487i | \(-0.148750\pi\) | ||||
0.892783 | + | 0.450487i | \(0.148750\pi\) | |||||||
\(678\) | 2.83579 | 0.108908 | ||||||||
\(679\) | 2.68963 | 0.103218 | ||||||||
\(680\) | −6.49396 | −0.249032 | ||||||||
\(681\) | −13.5442 | −0.519015 | ||||||||
\(682\) | −6.96376 | −0.266656 | ||||||||
\(683\) | −27.0911 | −1.03661 | −0.518307 | − | 0.855195i | \(-0.673437\pi\) | ||||
−0.518307 | + | 0.855195i | \(0.673437\pi\) | |||||||
\(684\) | −0.713792 | −0.0272925 | ||||||||
\(685\) | −19.5362 | −0.746439 | ||||||||
\(686\) | −2.76510 | −0.105572 | ||||||||
\(687\) | −29.1782 | −1.11322 | ||||||||
\(688\) | 5.65279 | 0.215511 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −8.43296 | −0.321037 | ||||||||
\(691\) | −3.47112 | −0.132048 | −0.0660239 | − | 0.997818i | \(-0.521031\pi\) | ||||
−0.0660239 | + | 0.997818i | \(0.521031\pi\) | |||||||
\(692\) | −8.59179 | −0.326611 | ||||||||
\(693\) | −0.317667 | −0.0120672 | ||||||||
\(694\) | 25.1987 | 0.956528 | ||||||||
\(695\) | −18.4155 | −0.698540 | ||||||||
\(696\) | −0.445042 | −0.0168693 | ||||||||
\(697\) | −58.2258 | −2.20546 | ||||||||
\(698\) | −16.4155 | −0.621336 | ||||||||
\(699\) | −17.9457 | −0.678769 | ||||||||
\(700\) | −0.198062 | −0.00748605 | ||||||||
\(701\) | 8.07606 | 0.305029 | 0.152514 | − | 0.988301i | \(-0.451263\pi\) | ||||
0.152514 | + | 0.988301i | \(0.451263\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.09651 | −0.0413555 | ||||||||
\(704\) | −1.10992 | −0.0418315 | ||||||||
\(705\) | −1.78687 | −0.0672975 | ||||||||
\(706\) | −1.10992 | −0.0417722 | ||||||||
\(707\) | 1.10023 | 0.0413783 | ||||||||
\(708\) | 5.75600 | 0.216324 | ||||||||
\(709\) | 20.5157 | 0.770484 | 0.385242 | − | 0.922816i | \(-0.374118\pi\) | ||||
0.385242 | + | 0.922816i | \(0.374118\pi\) | |||||||
\(710\) | 13.6039 | 0.510544 | ||||||||
\(711\) | −4.23921 | −0.158983 | ||||||||
\(712\) | −17.0804 | −0.640114 | ||||||||
\(713\) | 42.4301 | 1.58902 | ||||||||
\(714\) | −1.60388 | −0.0600235 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −0.659498 | −0.0246466 | ||||||||
\(717\) | 4.43967 | 0.165802 | ||||||||
\(718\) | −36.7633 | −1.37199 | ||||||||
\(719\) | 52.4650 | 1.95661 | 0.978307 | − | 0.207159i | \(-0.0664216\pi\) | ||||
0.978307 | + | 0.207159i | \(0.0664216\pi\) | |||||||
\(720\) | −1.44504 | −0.0538535 | ||||||||
\(721\) | 0.870232 | 0.0324091 | ||||||||
\(722\) | 18.7560 | 0.698026 | ||||||||
\(723\) | −36.3980 | −1.35366 | ||||||||
\(724\) | −20.4101 | −0.758536 | ||||||||
\(725\) | −0.356896 | −0.0132548 | ||||||||
\(726\) | −12.1806 | −0.452065 | ||||||||
\(727\) | 4.11397 | 0.152579 | 0.0762893 | − | 0.997086i | \(-0.475693\pi\) | ||||
0.0762893 | + | 0.997086i | \(0.475693\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 24.4590 | 0.905890 | ||||||||
\(730\) | 0.591794 | 0.0219033 | ||||||||
\(731\) | 36.7090 | 1.35773 | ||||||||
\(732\) | −6.86294 | −0.253661 | ||||||||
\(733\) | 20.9336 | 0.773201 | 0.386601 | − | 0.922247i | \(-0.373649\pi\) | ||||
0.386601 | + | 0.922247i | \(0.373649\pi\) | |||||||
\(734\) | −7.09485 | −0.261876 | ||||||||
\(735\) | 8.67994 | 0.320164 | ||||||||
\(736\) | 6.76271 | 0.249277 | ||||||||
\(737\) | −4.29829 | −0.158330 | ||||||||
\(738\) | −12.9565 | −0.476934 | ||||||||
\(739\) | 25.8297 | 0.950160 | 0.475080 | − | 0.879943i | \(-0.342419\pi\) | ||||
0.475080 | + | 0.879943i | \(0.342419\pi\) | |||||||
\(740\) | −2.21983 | −0.0816027 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.96508 | 0.0721405 | ||||||||
\(743\) | −52.0411 | −1.90920 | −0.954602 | − | 0.297883i | \(-0.903719\pi\) | ||||
−0.954602 | + | 0.297883i | \(0.903719\pi\) | |||||||
\(744\) | −7.82371 | −0.286831 | ||||||||
\(745\) | −17.2664 | −0.632590 | ||||||||
\(746\) | −26.8901 | −0.984516 | ||||||||
\(747\) | 22.6329 | 0.828096 | ||||||||
\(748\) | −7.20775 | −0.263541 | ||||||||
\(749\) | 3.56033 | 0.130092 | ||||||||
\(750\) | 1.24698 | 0.0455333 | ||||||||
\(751\) | 7.89738 | 0.288179 | 0.144090 | − | 0.989565i | \(-0.453975\pi\) | ||||
0.144090 | + | 0.989565i | \(0.453975\pi\) | |||||||
\(752\) | 1.43296 | 0.0522547 | ||||||||
\(753\) | 36.6112 | 1.33419 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.97584 | −0.144696 | ||||||||
\(756\) | −1.09783 | −0.0399279 | ||||||||
\(757\) | −16.1366 | −0.586494 | −0.293247 | − | 0.956037i | \(-0.594736\pi\) | ||||
−0.293247 | + | 0.956037i | \(0.594736\pi\) | |||||||
\(758\) | −8.46980 | −0.307637 | ||||||||
\(759\) | −9.35988 | −0.339742 | ||||||||
\(760\) | −0.493959 | −0.0179178 | ||||||||
\(761\) | 32.4064 | 1.17473 | 0.587366 | − | 0.809322i | \(-0.300165\pi\) | ||||
0.587366 | + | 0.809322i | \(0.300165\pi\) | |||||||
\(762\) | 17.1806 | 0.622388 | ||||||||
\(763\) | 1.33406 | 0.0482962 | ||||||||
\(764\) | 12.7332 | 0.460670 | ||||||||
\(765\) | −9.38404 | −0.339281 | ||||||||
\(766\) | 4.79656 | 0.173307 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.24698 | −0.0449965 | ||||||||
\(769\) | 5.44935 | 0.196509 | 0.0982544 | − | 0.995161i | \(-0.468674\pi\) | ||||
0.0982544 | + | 0.995161i | \(0.468674\pi\) | |||||||
\(770\) | −0.219833 | −0.00792221 | ||||||||
\(771\) | −26.8552 | −0.967165 | ||||||||
\(772\) | −8.68963 | −0.312747 | ||||||||
\(773\) | −35.0616 | −1.26108 | −0.630539 | − | 0.776158i | \(-0.717166\pi\) | ||||
−0.630539 | + | 0.776158i | \(0.717166\pi\) | |||||||
\(774\) | 8.16852 | 0.293611 | ||||||||
\(775\) | −6.27413 | −0.225373 | ||||||||
\(776\) | 13.5797 | 0.487483 | ||||||||
\(777\) | −0.548253 | −0.0196685 | ||||||||
\(778\) | −29.2131 | −1.04734 | ||||||||
\(779\) | −4.42891 | −0.158682 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.0992 | 0.540291 | ||||||||
\(782\) | 43.9168 | 1.57046 | ||||||||
\(783\) | −1.97823 | −0.0706962 | ||||||||
\(784\) | −6.96077 | −0.248599 | ||||||||
\(785\) | 17.4034 | 0.621155 | ||||||||
\(786\) | −24.0737 | −0.858679 | ||||||||
\(787\) | 40.2344 | 1.43420 | 0.717101 | − | 0.696969i | \(-0.245469\pi\) | ||||
0.717101 | + | 0.696969i | \(0.245469\pi\) | |||||||
\(788\) | −5.28621 | −0.188313 | ||||||||
\(789\) | 8.19269 | 0.291667 | ||||||||
\(790\) | −2.93362 | −0.104374 | ||||||||
\(791\) | −0.450419 | −0.0160150 | ||||||||
\(792\) | −1.60388 | −0.0569912 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 22.6112 | 0.802440 | ||||||||
\(795\) | −12.3720 | −0.438788 | ||||||||
\(796\) | −10.9444 | −0.387913 | ||||||||
\(797\) | −2.73317 | −0.0968138 | −0.0484069 | − | 0.998828i | \(-0.515414\pi\) | ||||
−0.0484069 | + | 0.998828i | \(0.515414\pi\) | |||||||
\(798\) | −0.121998 | −0.00431868 | ||||||||
\(799\) | 9.30559 | 0.329208 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | −24.6819 | −0.872091 | ||||||||
\(802\) | −10.5894 | −0.373925 | ||||||||
\(803\) | 0.656842 | 0.0231794 | ||||||||
\(804\) | −4.82908 | −0.170309 | ||||||||
\(805\) | 1.33944 | 0.0472090 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −9.18896 | −0.323467 | ||||||||
\(808\) | 5.55496 | 0.195423 | ||||||||
\(809\) | −36.4782 | −1.28250 | −0.641252 | − | 0.767330i | \(-0.721585\pi\) | ||||
−0.641252 | + | 0.767330i | \(0.721585\pi\) | |||||||
\(810\) | 2.57673 | 0.0905370 | ||||||||
\(811\) | 3.51679 | 0.123491 | 0.0617457 | − | 0.998092i | \(-0.480333\pi\) | ||||
0.0617457 | + | 0.998092i | \(0.480333\pi\) | |||||||
\(812\) | 0.0706876 | 0.00248065 | ||||||||
\(813\) | 19.4276 | 0.681355 | ||||||||
\(814\) | −2.46383 | −0.0863571 | ||||||||
\(815\) | 9.16852 | 0.321159 | ||||||||
\(816\) | −8.09783 | −0.283481 | ||||||||
\(817\) | 2.79225 | 0.0976884 | ||||||||
\(818\) | −11.7127 | −0.409526 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −8.96615 | −0.313111 | ||||||||
\(821\) | 29.3980 | 1.02600 | 0.512999 | − | 0.858389i | \(-0.328534\pi\) | ||||
0.512999 | + | 0.858389i | \(0.328534\pi\) | |||||||
\(822\) | −24.3612 | −0.849695 | ||||||||
\(823\) | 53.7318 | 1.87297 | 0.936487 | − | 0.350702i | \(-0.114057\pi\) | ||||
0.936487 | + | 0.350702i | \(0.114057\pi\) | |||||||
\(824\) | 4.39373 | 0.153063 | ||||||||
\(825\) | 1.38404 | 0.0481862 | ||||||||
\(826\) | −0.914247 | −0.0318107 | ||||||||
\(827\) | −47.3099 | −1.64513 | −0.822563 | − | 0.568674i | \(-0.807457\pi\) | ||||
−0.822563 | + | 0.568674i | \(0.807457\pi\) | |||||||
\(828\) | 9.77240 | 0.339614 | ||||||||
\(829\) | −49.3749 | −1.71486 | −0.857431 | − | 0.514598i | \(-0.827941\pi\) | ||||
−0.857431 | + | 0.514598i | \(0.827941\pi\) | |||||||
\(830\) | 15.6625 | 0.543653 | ||||||||
\(831\) | 17.4517 | 0.605394 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −45.2030 | −1.56619 | ||||||||
\(834\) | −22.9638 | −0.795170 | ||||||||
\(835\) | −7.36227 | −0.254782 | ||||||||
\(836\) | −0.548253 | −0.0189617 | ||||||||
\(837\) | −34.7767 | −1.20206 | ||||||||
\(838\) | −21.3250 | −0.736659 | ||||||||
\(839\) | 10.6219 | 0.366710 | 0.183355 | − | 0.983047i | \(-0.441304\pi\) | ||||
0.183355 | + | 0.983047i | \(0.441304\pi\) | |||||||
\(840\) | −0.246980 | −0.00852161 | ||||||||
\(841\) | −28.8726 | −0.995608 | ||||||||
\(842\) | −22.1457 | −0.763191 | ||||||||
\(843\) | 16.6273 | 0.572675 | ||||||||
\(844\) | 3.30559 | 0.113783 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 2.07069 | 0.0711917 | ||||||||
\(847\) | 1.93469 | 0.0664767 | ||||||||
\(848\) | 9.92154 | 0.340707 | ||||||||
\(849\) | 25.8485 | 0.887117 | ||||||||
\(850\) | −6.49396 | −0.222741 | ||||||||
\(851\) | 15.0121 | 0.514608 | ||||||||
\(852\) | 16.9638 | 0.581169 | ||||||||
\(853\) | 11.4625 | 0.392469 | 0.196234 | − | 0.980557i | \(-0.437129\pi\) | ||||
0.196234 | + | 0.980557i | \(0.437129\pi\) | |||||||
\(854\) | 1.09006 | 0.0373013 | ||||||||
\(855\) | −0.713792 | −0.0244112 | ||||||||
\(856\) | 17.9758 | 0.614401 | ||||||||
\(857\) | −19.4819 | −0.665488 | −0.332744 | − | 0.943017i | \(-0.607975\pi\) | ||||
−0.332744 | + | 0.943017i | \(0.607975\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −23.1448 | −0.789692 | −0.394846 | − | 0.918747i | \(-0.629202\pi\) | ||||
−0.394846 | + | 0.918747i | \(0.629202\pi\) | |||||||
\(860\) | 5.65279 | 0.192759 | ||||||||
\(861\) | −2.21446 | −0.0754684 | ||||||||
\(862\) | 36.8068 | 1.25365 | ||||||||
\(863\) | −38.9681 | −1.32649 | −0.663244 | − | 0.748403i | \(-0.730821\pi\) | ||||
−0.663244 | + | 0.748403i | \(0.730821\pi\) | |||||||
\(864\) | −5.54288 | −0.188572 | ||||||||
\(865\) | −8.59179 | −0.292130 | ||||||||
\(866\) | −2.08708 | −0.0709219 | ||||||||
\(867\) | −31.3884 | −1.06600 | ||||||||
\(868\) | 1.24267 | 0.0421789 | ||||||||
\(869\) | −3.25608 | −0.110455 | ||||||||
\(870\) | −0.445042 | −0.0150883 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 6.73556 | 0.228095 | ||||||||
\(873\) | 19.6233 | 0.664146 | ||||||||
\(874\) | 3.34050 | 0.112994 | ||||||||
\(875\) | −0.198062 | −0.00669573 | ||||||||
\(876\) | 0.737955 | 0.0249332 | ||||||||
\(877\) | −28.2064 | −0.952463 | −0.476232 | − | 0.879320i | \(-0.657998\pi\) | ||||
−0.476232 | + | 0.879320i | \(0.657998\pi\) | |||||||
\(878\) | −9.95646 | −0.336014 | ||||||||
\(879\) | 20.4397 | 0.689413 | ||||||||
\(880\) | −1.10992 | −0.0374153 | ||||||||
\(881\) | −21.2948 | −0.717441 | −0.358721 | − | 0.933445i | \(-0.616787\pi\) | ||||
−0.358721 | + | 0.933445i | \(0.616787\pi\) | |||||||
\(882\) | −10.0586 | −0.338691 | ||||||||
\(883\) | −46.8068 | −1.57518 | −0.787588 | − | 0.616202i | \(-0.788670\pi\) | ||||
−0.787588 | + | 0.616202i | \(0.788670\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.75600 | 0.193486 | ||||||||
\(886\) | 15.3884 | 0.516982 | ||||||||
\(887\) | 1.62565 | 0.0545838 | 0.0272919 | − | 0.999628i | \(-0.491312\pi\) | ||||
0.0272919 | + | 0.999628i | \(0.491312\pi\) | |||||||
\(888\) | −2.76809 | −0.0928909 | ||||||||
\(889\) | −2.72886 | −0.0915229 | ||||||||
\(890\) | −17.0804 | −0.572536 | ||||||||
\(891\) | 2.85995 | 0.0958120 | ||||||||
\(892\) | 16.6310 | 0.556848 | ||||||||
\(893\) | 0.707824 | 0.0236864 | ||||||||
\(894\) | −21.5308 | −0.720098 | ||||||||
\(895\) | −0.659498 | −0.0220446 | ||||||||
\(896\) | 0.198062 | 0.00661680 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 8.18060 | 0.272990 | ||||||||
\(899\) | 2.23921 | 0.0746818 | ||||||||
\(900\) | −1.44504 | −0.0481681 | ||||||||
\(901\) | 64.4301 | 2.14648 | ||||||||
\(902\) | −9.95167 | −0.331354 | ||||||||
\(903\) | 1.39612 | 0.0464601 | ||||||||
\(904\) | −2.27413 | −0.0756363 | ||||||||
\(905\) | −20.4101 | −0.678456 | ||||||||
\(906\) | −4.95779 | −0.164711 | ||||||||
\(907\) | −28.8442 | −0.957754 | −0.478877 | − | 0.877882i | \(-0.658956\pi\) | ||||
−0.478877 | + | 0.877882i | \(0.658956\pi\) | |||||||
\(908\) | 10.8616 | 0.360455 | ||||||||
\(909\) | 8.02715 | 0.266244 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11.5254 | 0.381854 | 0.190927 | − | 0.981604i | \(-0.438851\pi\) | ||||
0.190927 | + | 0.981604i | \(0.438851\pi\) | |||||||
\(912\) | −0.615957 | −0.0203964 | ||||||||
\(913\) | 17.3840 | 0.575328 | ||||||||
\(914\) | 16.0737 | 0.531670 | ||||||||
\(915\) | −6.86294 | −0.226882 | ||||||||
\(916\) | 23.3991 | 0.773128 | ||||||||
\(917\) | 3.82371 | 0.126270 | ||||||||
\(918\) | −35.9952 | −1.18802 | ||||||||
\(919\) | 8.28275 | 0.273223 | 0.136611 | − | 0.990625i | \(-0.456379\pi\) | ||||
0.136611 | + | 0.990625i | \(0.456379\pi\) | |||||||
\(920\) | 6.76271 | 0.222960 | ||||||||
\(921\) | −8.66487 | −0.285517 | ||||||||
\(922\) | 27.5308 | 0.906678 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −0.274127 | −0.00901811 | ||||||||
\(925\) | −2.21983 | −0.0729876 | ||||||||
\(926\) | −10.6595 | −0.350293 | ||||||||
\(927\) | 6.34913 | 0.208533 | ||||||||
\(928\) | 0.356896 | 0.0117157 | ||||||||
\(929\) | −25.3846 | −0.832843 | −0.416421 | − | 0.909172i | \(-0.636716\pi\) | ||||
−0.416421 | + | 0.909172i | \(0.636716\pi\) | |||||||
\(930\) | −7.82371 | −0.256549 | ||||||||
\(931\) | −3.43834 | −0.112687 | ||||||||
\(932\) | 14.3913 | 0.471404 | ||||||||
\(933\) | 30.3779 | 0.994529 | ||||||||
\(934\) | 10.7976 | 0.353309 | ||||||||
\(935\) | −7.20775 | −0.235719 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −21.4819 | −0.701782 | −0.350891 | − | 0.936416i | \(-0.614121\pi\) | ||||
−0.350891 | + | 0.936416i | \(0.614121\pi\) | |||||||
\(938\) | 0.767021 | 0.0250441 | ||||||||
\(939\) | −3.60388 | −0.117608 | ||||||||
\(940\) | 1.43296 | 0.0467380 | ||||||||
\(941\) | −12.1148 | −0.394932 | −0.197466 | − | 0.980310i | \(-0.563271\pi\) | ||||
−0.197466 | + | 0.980310i | \(0.563271\pi\) | |||||||
\(942\) | 21.7017 | 0.707080 | ||||||||
\(943\) | 60.6355 | 1.97456 | ||||||||
\(944\) | −4.61596 | −0.150237 | ||||||||
\(945\) | −1.09783 | −0.0357126 | ||||||||
\(946\) | 6.27413 | 0.203989 | ||||||||
\(947\) | 23.4553 | 0.762196 | 0.381098 | − | 0.924535i | \(-0.375546\pi\) | ||||
0.381098 | + | 0.924535i | \(0.375546\pi\) | |||||||
\(948\) | −3.65817 | −0.118812 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −0.493959 | −0.0160262 | ||||||||
\(951\) | 6.24996 | 0.202669 | ||||||||
\(952\) | 1.28621 | 0.0416862 | ||||||||
\(953\) | −42.5086 | −1.37699 | −0.688494 | − | 0.725242i | \(-0.741728\pi\) | ||||
−0.688494 | + | 0.725242i | \(0.741728\pi\) | |||||||
\(954\) | 14.3370 | 0.464179 | ||||||||
\(955\) | 12.7332 | 0.412036 | ||||||||
\(956\) | −3.56033 | −0.115149 | ||||||||
\(957\) | −0.493959 | −0.0159674 | ||||||||
\(958\) | 9.08575 | 0.293547 | ||||||||
\(959\) | 3.86938 | 0.124949 | ||||||||
\(960\) | −1.24698 | −0.0402461 | ||||||||
\(961\) | 8.36467 | 0.269828 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 25.9758 | 0.837060 | ||||||||
\(964\) | 29.1890 | 0.940113 | ||||||||
\(965\) | −8.68963 | −0.279729 | ||||||||
\(966\) | 1.67025 | 0.0537395 | ||||||||
\(967\) | 24.7827 | 0.796957 | 0.398479 | − | 0.917178i | \(-0.369538\pi\) | ||||
0.398479 | + | 0.917178i | \(0.369538\pi\) | |||||||
\(968\) | 9.76809 | 0.313958 | ||||||||
\(969\) | −4.00000 | −0.128499 | ||||||||
\(970\) | 13.5797 | 0.436018 | ||||||||
\(971\) | −46.1124 | −1.47982 | −0.739909 | − | 0.672707i | \(-0.765132\pi\) | ||||
−0.739909 | + | 0.672707i | \(0.765132\pi\) | |||||||
\(972\) | −13.4155 | −0.430302 | ||||||||
\(973\) | 3.64742 | 0.116931 | ||||||||
\(974\) | −40.8471 | −1.30883 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.50365 | 0.176167 | ||||||||
\(977\) | −14.3827 | −0.460144 | −0.230072 | − | 0.973174i | \(-0.573896\pi\) | ||||
−0.230072 | + | 0.973174i | \(0.573896\pi\) | |||||||
\(978\) | 11.4330 | 0.365586 | ||||||||
\(979\) | −18.9578 | −0.605894 | ||||||||
\(980\) | −6.96077 | −0.222354 | ||||||||
\(981\) | 9.73317 | 0.310756 | ||||||||
\(982\) | −29.0944 | −0.928439 | ||||||||
\(983\) | 9.73615 | 0.310535 | 0.155268 | − | 0.987872i | \(-0.450376\pi\) | ||||
0.155268 | + | 0.987872i | \(0.450376\pi\) | |||||||
\(984\) | −11.1806 | −0.356425 | ||||||||
\(985\) | −5.28621 | −0.168433 | ||||||||
\(986\) | 2.31767 | 0.0738096 | ||||||||
\(987\) | 0.353912 | 0.0112651 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −38.2282 | −1.21559 | ||||||||
\(990\) | −1.60388 | −0.0509745 | ||||||||
\(991\) | −25.7948 | −0.819398 | −0.409699 | − | 0.912221i | \(-0.634366\pi\) | ||||
−0.409699 | + | 0.912221i | \(0.634366\pi\) | |||||||
\(992\) | 6.27413 | 0.199204 | ||||||||
\(993\) | −29.9517 | −0.950488 | ||||||||
\(994\) | −2.69441 | −0.0854616 | ||||||||
\(995\) | −10.9444 | −0.346960 | ||||||||
\(996\) | 19.5308 | 0.618857 | ||||||||
\(997\) | 29.8974 | 0.946860 | 0.473430 | − | 0.880832i | \(-0.343016\pi\) | ||||
0.473430 | + | 0.880832i | \(0.343016\pi\) | |||||||
\(998\) | 16.2150 | 0.513278 | ||||||||
\(999\) | −12.3043 | −0.389289 |
(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 | 1690.2.a.q.1.1 | ✓ | 3 | |
5.4 | even | 2 | 8450.2.a.bz.1.3 | 3 | |||
13.2 | odd | 12 | 1690.2.l.l.1161.3 | 12 | |||
13.3 | even | 3 | 1690.2.e.q.191.3 | 6 | |||
13.4 | even | 6 | 1690.2.e.o.991.3 | 6 | |||
13.5 | odd | 4 | 1690.2.d.j.1351.4 | 6 | |||
13.6 | odd | 12 | 1690.2.l.l.361.6 | 12 | |||
13.7 | odd | 12 | 1690.2.l.l.361.3 | 12 | |||
13.8 | odd | 4 | 1690.2.d.j.1351.1 | 6 | |||
13.9 | even | 3 | 1690.2.e.q.991.3 | 6 | |||
13.10 | even | 6 | 1690.2.e.o.191.3 | 6 | |||
13.11 | odd | 12 | 1690.2.l.l.1161.6 | 12 | |||
13.12 | even | 2 | 1690.2.a.s.1.1 | yes | 3 | ||
65.64 | even | 2 | 8450.2.a.bo.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1690.2.a.q.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
1690.2.a.s.1.1 | yes | 3 | 13.12 | even | 2 | ||
1690.2.d.j.1351.1 | 6 | 13.8 | odd | 4 | |||
1690.2.d.j.1351.4 | 6 | 13.5 | odd | 4 | |||
1690.2.e.o.191.3 | 6 | 13.10 | even | 6 | |||
1690.2.e.o.991.3 | 6 | 13.4 | even | 6 | |||
1690.2.e.q.191.3 | 6 | 13.3 | even | 3 | |||
1690.2.e.q.991.3 | 6 | 13.9 | even | 3 | |||
1690.2.l.l.361.3 | 12 | 13.7 | odd | 12 | |||
1690.2.l.l.361.6 | 12 | 13.6 | odd | 12 | |||
1690.2.l.l.1161.3 | 12 | 13.2 | odd | 12 | |||
1690.2.l.l.1161.6 | 12 | 13.11 | odd | 12 | |||
8450.2.a.bo.1.3 | 3 | 65.64 | even | 2 | |||
8450.2.a.bz.1.3 | 3 | 5.4 | even | 2 |