Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.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: | \(63.8883066572\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | 7.7.118870813.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 9x^{5} - 3x^{4} + 20x^{3} + 7x^{2} - 13x - 4 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2667) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(1.20244\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.24280 | 0.878791 | 0.439396 | − | 0.898294i | \(-0.355193\pi\) | ||||
0.439396 | + | 0.898294i | \(0.355193\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.455452 | −0.227726 | ||||||||
\(5\) | 3.33400 | 1.49101 | 0.745506 | − | 0.666499i | \(-0.232208\pi\) | ||||
0.745506 | + | 0.666499i | \(0.232208\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −3.05163 | −1.07891 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 4.14349 | 1.31029 | ||||||||
\(11\) | −2.90717 | −0.876544 | −0.438272 | − | 0.898842i | \(-0.644409\pi\) | ||||
−0.438272 | + | 0.898842i | \(0.644409\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.59254 | −1.27374 | −0.636871 | − | 0.770970i | \(-0.719772\pi\) | ||||
−0.636871 | + | 0.770970i | \(0.719772\pi\) | |||||||
\(14\) | 1.24280 | 0.332152 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.88166 | −0.720415 | ||||||||
\(17\) | 5.29249 | 1.28362 | 0.641809 | − | 0.766865i | \(-0.278184\pi\) | ||||
0.641809 | + | 0.766865i | \(0.278184\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.86822 | 0.428600 | 0.214300 | − | 0.976768i | \(-0.431253\pi\) | ||||
0.214300 | + | 0.976768i | \(0.431253\pi\) | |||||||
\(20\) | −1.51848 | −0.339542 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.61302 | −0.770299 | ||||||||
\(23\) | −5.03184 | −1.04921 | −0.524606 | − | 0.851345i | \(-0.675787\pi\) | ||||
−0.524606 | + | 0.851345i | \(0.675787\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.11557 | 1.22311 | ||||||||
\(26\) | −5.70761 | −1.11935 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.455452 | −0.0860724 | ||||||||
\(29\) | −3.69938 | −0.686957 | −0.343478 | − | 0.939161i | \(-0.611605\pi\) | ||||
−0.343478 | + | 0.939161i | \(0.611605\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.968597 | 0.173965 | 0.0869826 | − | 0.996210i | \(-0.472278\pi\) | ||||
0.0869826 | + | 0.996210i | \(0.472278\pi\) | |||||||
\(32\) | 2.52194 | 0.445821 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.57750 | 1.12803 | ||||||||
\(35\) | 3.33400 | 0.563549 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.5381 | −1.73246 | −0.866230 | − | 0.499645i | \(-0.833464\pi\) | ||||
−0.866230 | + | 0.499645i | \(0.833464\pi\) | |||||||
\(38\) | 2.32183 | 0.376650 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −10.1741 | −1.60867 | ||||||||
\(41\) | −11.5606 | −1.80546 | −0.902731 | − | 0.430205i | \(-0.858441\pi\) | ||||
−0.902731 | + | 0.430205i | \(0.858441\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.54868 | 0.388670 | 0.194335 | − | 0.980935i | \(-0.437745\pi\) | ||||
0.194335 | + | 0.980935i | \(0.437745\pi\) | |||||||
\(44\) | 1.32408 | 0.199612 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.25356 | −0.922038 | ||||||||
\(47\) | −7.34702 | −1.07167 | −0.535837 | − | 0.844322i | \(-0.680004\pi\) | ||||
−0.535837 | + | 0.844322i | \(0.680004\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 7.60043 | 1.07486 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.09168 | 0.290064 | ||||||||
\(53\) | 11.2837 | 1.54993 | 0.774966 | − | 0.632003i | \(-0.217767\pi\) | ||||
0.774966 | + | 0.632003i | \(0.217767\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −9.69250 | −1.30694 | ||||||||
\(56\) | −3.05163 | −0.407791 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.59758 | −0.603691 | ||||||||
\(59\) | 13.3410 | 1.73685 | 0.868425 | − | 0.495820i | \(-0.165132\pi\) | ||||
0.868425 | + | 0.495820i | \(0.165132\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.666722 | 0.0853651 | 0.0426825 | − | 0.999089i | \(-0.486410\pi\) | ||||
0.0426825 | + | 0.999089i | \(0.486410\pi\) | |||||||
\(62\) | 1.20377 | 0.152879 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.89758 | 1.11220 | ||||||||
\(65\) | −15.3116 | −1.89916 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −14.0335 | −1.71447 | −0.857233 | − | 0.514929i | \(-0.827818\pi\) | ||||
−0.857233 | + | 0.514929i | \(0.827818\pi\) | |||||||
\(68\) | −2.41048 | −0.292313 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 4.14349 | 0.495242 | ||||||||
\(71\) | −9.88541 | −1.17318 | −0.586591 | − | 0.809883i | \(-0.699530\pi\) | ||||
−0.586591 | + | 0.809883i | \(0.699530\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.57222 | −0.301056 | −0.150528 | − | 0.988606i | \(-0.548097\pi\) | ||||
−0.150528 | + | 0.988606i | \(0.548097\pi\) | |||||||
\(74\) | −13.0968 | −1.52247 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.850887 | −0.0976034 | ||||||||
\(77\) | −2.90717 | −0.331302 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.5706 | 1.63932 | 0.819661 | − | 0.572849i | \(-0.194162\pi\) | ||||
0.819661 | + | 0.572849i | \(0.194162\pi\) | |||||||
\(80\) | −9.60746 | −1.07415 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −14.3675 | −1.58662 | ||||||||
\(83\) | −0.493442 | −0.0541623 | −0.0270811 | − | 0.999633i | \(-0.508621\pi\) | ||||
−0.0270811 | + | 0.999633i | \(0.508621\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 17.6452 | 1.91389 | ||||||||
\(86\) | 3.16749 | 0.341560 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 8.87160 | 0.945716 | ||||||||
\(89\) | −12.1652 | −1.28951 | −0.644754 | − | 0.764390i | \(-0.723040\pi\) | ||||
−0.644754 | + | 0.764390i | \(0.723040\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.59254 | −0.481429 | ||||||||
\(92\) | 2.29176 | 0.238933 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −9.13087 | −0.941777 | ||||||||
\(95\) | 6.22866 | 0.639047 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.7006 | −1.49262 | −0.746312 | − | 0.665596i | \(-0.768177\pi\) | ||||
−0.746312 | + | 0.665596i | \(0.768177\pi\) | |||||||
\(98\) | 1.24280 | 0.125542 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.78535 | −0.278535 | ||||||||
\(101\) | 7.69701 | 0.765881 | 0.382941 | − | 0.923773i | \(-0.374911\pi\) | ||||
0.382941 | + | 0.923773i | \(0.374911\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −18.0952 | −1.78297 | −0.891486 | − | 0.453048i | \(-0.850337\pi\) | ||||
−0.891486 | + | 0.453048i | \(0.850337\pi\) | |||||||
\(104\) | 14.0148 | 1.37426 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 14.0233 | 1.36207 | ||||||||
\(107\) | 2.30658 | 0.222986 | 0.111493 | − | 0.993765i | \(-0.464437\pi\) | ||||
0.111493 | + | 0.993765i | \(0.464437\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.892079 | −0.0854457 | −0.0427228 | − | 0.999087i | \(-0.513603\pi\) | ||||
−0.0427228 | + | 0.999087i | \(0.513603\pi\) | |||||||
\(110\) | −12.0458 | −1.14852 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.88166 | −0.272291 | ||||||||
\(113\) | −4.35699 | −0.409872 | −0.204936 | − | 0.978775i | \(-0.565699\pi\) | ||||
−0.204936 | + | 0.978775i | \(0.565699\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −16.7762 | −1.56439 | ||||||||
\(116\) | 1.68489 | 0.156438 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 16.5802 | 1.52633 | ||||||||
\(119\) | 5.29249 | 0.485162 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.54838 | −0.231671 | ||||||||
\(122\) | 0.828601 | 0.0750181 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.441150 | −0.0396164 | ||||||||
\(125\) | 3.71933 | 0.332667 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00000 | −0.0887357 | ||||||||
\(128\) | 6.01402 | 0.531569 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −19.0292 | −1.66897 | ||||||||
\(131\) | −8.71812 | −0.761706 | −0.380853 | − | 0.924636i | \(-0.624370\pi\) | ||||
−0.380853 | + | 0.924636i | \(0.624370\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.86822 | 0.161996 | ||||||||
\(134\) | −17.4408 | −1.50666 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −16.1507 | −1.38491 | ||||||||
\(137\) | 4.66285 | 0.398374 | 0.199187 | − | 0.979962i | \(-0.436170\pi\) | ||||
0.199187 | + | 0.979962i | \(0.436170\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −19.7441 | −1.67467 | −0.837334 | − | 0.546691i | \(-0.815887\pi\) | ||||
−0.837334 | + | 0.546691i | \(0.815887\pi\) | |||||||
\(140\) | −1.51848 | −0.128335 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −12.2856 | −1.03098 | ||||||||
\(143\) | 13.3513 | 1.11649 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −12.3337 | −1.02426 | ||||||||
\(146\) | −3.19675 | −0.264565 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.79962 | 0.394526 | ||||||||
\(149\) | 5.49864 | 0.450467 | 0.225233 | − | 0.974305i | \(-0.427686\pi\) | ||||
0.225233 | + | 0.974305i | \(0.427686\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.8169 | −0.961645 | −0.480822 | − | 0.876818i | \(-0.659662\pi\) | ||||
−0.480822 | + | 0.876818i | \(0.659662\pi\) | |||||||
\(152\) | −5.70113 | −0.462423 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.61302 | −0.291146 | ||||||||
\(155\) | 3.22931 | 0.259384 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.77762 | 0.301487 | 0.150744 | − | 0.988573i | \(-0.451833\pi\) | ||||
0.150744 | + | 0.988573i | \(0.451833\pi\) | |||||||
\(158\) | 18.1083 | 1.44062 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 8.40817 | 0.664724 | ||||||||
\(161\) | −5.03184 | −0.396565 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −20.0111 | −1.56739 | −0.783694 | − | 0.621147i | \(-0.786667\pi\) | ||||
−0.783694 | + | 0.621147i | \(0.786667\pi\) | |||||||
\(164\) | 5.26530 | 0.411151 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.613249 | −0.0475973 | ||||||||
\(167\) | 16.4295 | 1.27135 | 0.635675 | − | 0.771957i | \(-0.280722\pi\) | ||||
0.635675 | + | 0.771957i | \(0.280722\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.09145 | 0.622419 | ||||||||
\(170\) | 21.9294 | 1.68191 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.16080 | −0.0885103 | ||||||||
\(173\) | 16.2436 | 1.23498 | 0.617489 | − | 0.786580i | \(-0.288150\pi\) | ||||
0.617489 | + | 0.786580i | \(0.288150\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.11557 | 0.462294 | ||||||||
\(176\) | 8.37746 | 0.631475 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −15.1189 | −1.13321 | ||||||||
\(179\) | 4.00381 | 0.299259 | 0.149630 | − | 0.988742i | \(-0.452192\pi\) | ||||
0.149630 | + | 0.988742i | \(0.452192\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −24.4061 | −1.81409 | −0.907044 | − | 0.421035i | \(-0.861667\pi\) | ||||
−0.907044 | + | 0.421035i | \(0.861667\pi\) | |||||||
\(182\) | −5.70761 | −0.423076 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 15.3553 | 1.13201 | ||||||||
\(185\) | −35.1342 | −2.58312 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −15.3862 | −1.12515 | ||||||||
\(188\) | 3.34622 | 0.244048 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 7.74097 | 0.561589 | ||||||||
\(191\) | 22.5671 | 1.63290 | 0.816450 | − | 0.577416i | \(-0.195939\pi\) | ||||
0.816450 | + | 0.577416i | \(0.195939\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.7333 | 1.49242 | 0.746208 | − | 0.665713i | \(-0.231873\pi\) | ||||
0.746208 | + | 0.665713i | \(0.231873\pi\) | |||||||
\(194\) | −18.2699 | −1.31170 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.455452 | −0.0325323 | ||||||||
\(197\) | 3.77768 | 0.269148 | 0.134574 | − | 0.990904i | \(-0.457033\pi\) | ||||
0.134574 | + | 0.990904i | \(0.457033\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.73569 | −0.690145 | −0.345072 | − | 0.938576i | \(-0.612146\pi\) | ||||
−0.345072 | + | 0.938576i | \(0.612146\pi\) | |||||||
\(200\) | −18.6625 | −1.31964 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 9.56583 | 0.673050 | ||||||||
\(203\) | −3.69938 | −0.259645 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −38.5431 | −2.69196 | ||||||||
\(206\) | −22.4887 | −1.56686 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 13.2341 | 0.917623 | ||||||||
\(209\) | −5.43124 | −0.375687 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.66669 | 0.321268 | 0.160634 | − | 0.987014i | \(-0.448646\pi\) | ||||
0.160634 | + | 0.987014i | \(0.448646\pi\) | |||||||
\(212\) | −5.13918 | −0.352960 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.86662 | 0.195958 | ||||||||
\(215\) | 8.49730 | 0.579511 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.968597 | 0.0657527 | ||||||||
\(218\) | −1.10867 | −0.0750889 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4.41447 | 0.297624 | ||||||||
\(221\) | −24.3060 | −1.63500 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.37863 | 0.360180 | 0.180090 | − | 0.983650i | \(-0.442361\pi\) | ||||
0.180090 | + | 0.983650i | \(0.442361\pi\) | |||||||
\(224\) | 2.52194 | 0.168504 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.41486 | −0.360191 | ||||||||
\(227\) | 11.5084 | 0.763837 | 0.381918 | − | 0.924196i | \(-0.375264\pi\) | ||||
0.381918 | + | 0.924196i | \(0.375264\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.87862 | −0.124142 | −0.0620712 | − | 0.998072i | \(-0.519771\pi\) | ||||
−0.0620712 | + | 0.998072i | \(0.519771\pi\) | |||||||
\(230\) | −20.8494 | −1.37477 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 11.2891 | 0.741168 | ||||||||
\(233\) | −13.5663 | −0.888755 | −0.444378 | − | 0.895840i | \(-0.646575\pi\) | ||||
−0.444378 | + | 0.895840i | \(0.646575\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −24.4950 | −1.59788 | ||||||||
\(236\) | −6.07619 | −0.395526 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 6.57750 | 0.426356 | ||||||||
\(239\) | −22.4619 | −1.45294 | −0.726468 | − | 0.687200i | \(-0.758840\pi\) | ||||
−0.726468 | + | 0.687200i | \(0.758840\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.0289 | 0.774848 | 0.387424 | − | 0.921902i | \(-0.373365\pi\) | ||||
0.387424 | + | 0.921902i | \(0.373365\pi\) | |||||||
\(242\) | −3.16712 | −0.203590 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −0.303660 | −0.0194399 | ||||||||
\(245\) | 3.33400 | 0.213002 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.57990 | −0.545926 | ||||||||
\(248\) | −2.95580 | −0.187694 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 4.62237 | 0.292345 | ||||||||
\(251\) | −5.27452 | −0.332924 | −0.166462 | − | 0.986048i | \(-0.553234\pi\) | ||||
−0.166462 | + | 0.986048i | \(0.553234\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 14.6284 | 0.919680 | ||||||||
\(254\) | −1.24280 | −0.0779801 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −10.3210 | −0.645060 | ||||||||
\(257\) | 28.6479 | 1.78701 | 0.893504 | − | 0.449055i | \(-0.148239\pi\) | ||||
0.893504 | + | 0.449055i | \(0.148239\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.5381 | −0.654808 | ||||||||
\(260\) | 6.97368 | 0.432489 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −10.8349 | −0.669380 | ||||||||
\(263\) | 6.33902 | 0.390881 | 0.195440 | − | 0.980716i | \(-0.437386\pi\) | ||||
0.195440 | + | 0.980716i | \(0.437386\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 37.6198 | 2.31097 | ||||||||
\(266\) | 2.32183 | 0.142360 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6.39159 | 0.390429 | ||||||||
\(269\) | −1.26346 | −0.0770348 | −0.0385174 | − | 0.999258i | \(-0.512264\pi\) | ||||
−0.0385174 | + | 0.999258i | \(0.512264\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.15641 | −0.313230 | −0.156615 | − | 0.987660i | \(-0.550058\pi\) | ||||
−0.156615 | + | 0.987660i | \(0.550058\pi\) | |||||||
\(272\) | −15.2512 | −0.924737 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.79498 | 0.350087 | ||||||||
\(275\) | −17.7790 | −1.07211 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.77471 | 0.166716 | 0.0833580 | − | 0.996520i | \(-0.473435\pi\) | ||||
0.0833580 | + | 0.996520i | \(0.473435\pi\) | |||||||
\(278\) | −24.5379 | −1.47168 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −10.1741 | −0.608022 | ||||||||
\(281\) | −5.01385 | −0.299101 | −0.149551 | − | 0.988754i | \(-0.547783\pi\) | ||||
−0.149551 | + | 0.988754i | \(0.547783\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.84064 | −0.525521 | −0.262761 | − | 0.964861i | \(-0.584633\pi\) | ||||
−0.262761 | + | 0.964861i | \(0.584633\pi\) | |||||||
\(284\) | 4.50233 | 0.267164 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 16.5930 | 0.981162 | ||||||||
\(287\) | −11.5606 | −0.682401 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.0105 | 0.647674 | ||||||||
\(290\) | −15.3283 | −0.900111 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.17152 | 0.0685583 | ||||||||
\(293\) | 16.5617 | 0.967545 | 0.483772 | − | 0.875194i | \(-0.339266\pi\) | ||||
0.483772 | + | 0.875194i | \(0.339266\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 44.4789 | 2.58966 | ||||||||
\(296\) | 32.1585 | 1.86918 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6.83371 | 0.395866 | ||||||||
\(299\) | 23.1089 | 1.33643 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.54868 | 0.146903 | ||||||||
\(302\) | −14.6860 | −0.845085 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −5.38358 | −0.308770 | ||||||||
\(305\) | 2.22285 | 0.127280 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −23.4209 | −1.33670 | −0.668352 | − | 0.743845i | \(-0.733000\pi\) | ||||
−0.668352 | + | 0.743845i | \(0.733000\pi\) | |||||||
\(308\) | 1.32408 | 0.0754462 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4.01338 | 0.227944 | ||||||||
\(311\) | 19.5726 | 1.10986 | 0.554929 | − | 0.831898i | \(-0.312745\pi\) | ||||
0.554929 | + | 0.831898i | \(0.312745\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.10217 | 0.288392 | 0.144196 | − | 0.989549i | \(-0.453940\pi\) | ||||
0.144196 | + | 0.989549i | \(0.453940\pi\) | |||||||
\(314\) | 4.69483 | 0.264944 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.63622 | −0.373316 | ||||||||
\(317\) | 19.6691 | 1.10472 | 0.552362 | − | 0.833604i | \(-0.313727\pi\) | ||||
0.552362 | + | 0.833604i | \(0.313727\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.7547 | 0.602148 | ||||||||
\(320\) | 29.6646 | 1.65830 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −6.25356 | −0.348497 | ||||||||
\(323\) | 9.88756 | 0.550158 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −28.0860 | −1.55793 | ||||||||
\(326\) | −24.8697 | −1.37741 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 35.2787 | 1.94794 | ||||||||
\(329\) | −7.34702 | −0.405055 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.1305 | 0.831648 | 0.415824 | − | 0.909445i | \(-0.363493\pi\) | ||||
0.415824 | + | 0.909445i | \(0.363493\pi\) | |||||||
\(332\) | 0.224739 | 0.0123342 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 20.4185 | 1.11725 | ||||||||
\(335\) | −46.7877 | −2.55629 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.21235 | −0.392882 | −0.196441 | − | 0.980516i | \(-0.562938\pi\) | ||||
−0.196441 | + | 0.980516i | \(0.562938\pi\) | |||||||
\(338\) | 10.0560 | 0.546977 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −8.03654 | −0.435842 | ||||||||
\(341\) | −2.81587 | −0.152488 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −7.77763 | −0.419342 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 20.1875 | 1.08529 | ||||||||
\(347\) | −28.7813 | −1.54506 | −0.772531 | − | 0.634977i | \(-0.781010\pi\) | ||||
−0.772531 | + | 0.634977i | \(0.781010\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −28.8201 | −1.54270 | −0.771352 | − | 0.636409i | \(-0.780419\pi\) | ||||
−0.771352 | + | 0.636409i | \(0.780419\pi\) | |||||||
\(350\) | 7.60043 | 0.406260 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −7.33171 | −0.390782 | ||||||||
\(353\) | −26.6489 | −1.41838 | −0.709188 | − | 0.705019i | \(-0.750938\pi\) | ||||
−0.709188 | + | 0.705019i | \(0.750938\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −32.9580 | −1.74923 | ||||||||
\(356\) | 5.54066 | 0.293655 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.97593 | 0.262986 | ||||||||
\(359\) | 14.4278 | 0.761469 | 0.380734 | − | 0.924684i | \(-0.375671\pi\) | ||||
0.380734 | + | 0.924684i | \(0.375671\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.5097 | −0.816302 | ||||||||
\(362\) | −30.3318 | −1.59421 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.09168 | 0.109634 | ||||||||
\(365\) | −8.57580 | −0.448878 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.35795 | −0.436282 | −0.218141 | − | 0.975917i | \(-0.569999\pi\) | ||||
−0.218141 | + | 0.975917i | \(0.569999\pi\) | |||||||
\(368\) | 14.5000 | 0.755867 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −43.6647 | −2.27002 | ||||||||
\(371\) | 11.2837 | 0.585819 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 30.3153 | 1.56966 | 0.784832 | − | 0.619708i | \(-0.212749\pi\) | ||||
0.784832 | + | 0.619708i | \(0.212749\pi\) | |||||||
\(374\) | −19.1219 | −0.988769 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 22.4204 | 1.15624 | ||||||||
\(377\) | 16.9895 | 0.875006 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.57847 | 0.132447 | 0.0662235 | − | 0.997805i | \(-0.478905\pi\) | ||||
0.0662235 | + | 0.997805i | \(0.478905\pi\) | |||||||
\(380\) | −2.83686 | −0.145528 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 28.0464 | 1.43498 | ||||||||
\(383\) | 14.6277 | 0.747438 | 0.373719 | − | 0.927542i | \(-0.378082\pi\) | ||||
0.373719 | + | 0.927542i | \(0.378082\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.69250 | −0.493976 | ||||||||
\(386\) | 25.7673 | 1.31152 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 6.69544 | 0.339909 | ||||||||
\(389\) | −19.5586 | −0.991663 | −0.495831 | − | 0.868419i | \(-0.665137\pi\) | ||||
−0.495831 | + | 0.868419i | \(0.665137\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −26.6310 | −1.34679 | ||||||||
\(392\) | −3.05163 | −0.154131 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 4.69489 | 0.236525 | ||||||||
\(395\) | 48.5784 | 2.44425 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.35455 | −0.419303 | −0.209651 | − | 0.977776i | \(-0.567233\pi\) | ||||
−0.209651 | + | 0.977776i | \(0.567233\pi\) | |||||||
\(398\) | −12.0995 | −0.606493 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −17.6230 | −0.881150 | ||||||||
\(401\) | −7.25894 | −0.362494 | −0.181247 | − | 0.983438i | \(-0.558013\pi\) | ||||
−0.181247 | + | 0.983438i | \(0.558013\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.44832 | −0.221587 | ||||||||
\(404\) | −3.50562 | −0.174411 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.59758 | −0.228174 | ||||||||
\(407\) | 30.6361 | 1.51858 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.46320 | 0.418478 | 0.209239 | − | 0.977864i | \(-0.432901\pi\) | ||||
0.209239 | + | 0.977864i | \(0.432901\pi\) | |||||||
\(410\) | −47.9013 | −2.36567 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 8.24150 | 0.406029 | ||||||||
\(413\) | 13.3410 | 0.656468 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.64514 | −0.0807566 | ||||||||
\(416\) | −11.5821 | −0.567861 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −6.74994 | −0.330150 | ||||||||
\(419\) | −26.7971 | −1.30912 | −0.654561 | − | 0.756009i | \(-0.727146\pi\) | ||||
−0.654561 | + | 0.756009i | \(0.727146\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.1261 | 0.688463 | 0.344231 | − | 0.938885i | \(-0.388140\pi\) | ||||
0.344231 | + | 0.938885i | \(0.388140\pi\) | |||||||
\(422\) | 5.79976 | 0.282328 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −34.4336 | −1.67225 | ||||||||
\(425\) | 32.3666 | 1.57001 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.666722 | 0.0322650 | ||||||||
\(428\) | −1.05054 | −0.0507797 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 10.5604 | 0.509269 | ||||||||
\(431\) | 16.6128 | 0.800211 | 0.400105 | − | 0.916469i | \(-0.368974\pi\) | ||||
0.400105 | + | 0.916469i | \(0.368974\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.5878 | 1.18161 | 0.590807 | − | 0.806813i | \(-0.298810\pi\) | ||||
0.590807 | + | 0.806813i | \(0.298810\pi\) | |||||||
\(434\) | 1.20377 | 0.0577829 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.406300 | 0.0194582 | ||||||||
\(437\) | −9.40061 | −0.449692 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −38.1271 | −1.81971 | −0.909853 | − | 0.414930i | \(-0.863806\pi\) | ||||
−0.909853 | + | 0.414930i | \(0.863806\pi\) | |||||||
\(440\) | 29.5780 | 1.41007 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −30.2074 | −1.43682 | ||||||||
\(443\) | −22.7120 | −1.07908 | −0.539541 | − | 0.841959i | \(-0.681402\pi\) | ||||
−0.539541 | + | 0.841959i | \(0.681402\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −40.5588 | −1.92267 | ||||||||
\(446\) | 6.68455 | 0.316523 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 8.89758 | 0.420371 | ||||||||
\(449\) | 29.0754 | 1.37215 | 0.686075 | − | 0.727531i | \(-0.259332\pi\) | ||||
0.686075 | + | 0.727531i | \(0.259332\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 33.6086 | 1.58257 | ||||||||
\(452\) | 1.98440 | 0.0933385 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 14.3026 | 0.671253 | ||||||||
\(455\) | −15.3116 | −0.717817 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 25.5196 | 1.19376 | 0.596879 | − | 0.802332i | \(-0.296407\pi\) | ||||
0.596879 | + | 0.802332i | \(0.296407\pi\) | |||||||
\(458\) | −2.33474 | −0.109095 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 7.64075 | 0.356252 | ||||||||
\(461\) | 10.8134 | 0.503631 | 0.251815 | − | 0.967775i | \(-0.418972\pi\) | ||||
0.251815 | + | 0.967775i | \(0.418972\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.98793 | 0.278283 | 0.139141 | − | 0.990273i | \(-0.455566\pi\) | ||||
0.139141 | + | 0.990273i | \(0.455566\pi\) | |||||||
\(464\) | 10.6603 | 0.494894 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −16.8601 | −0.781030 | ||||||||
\(467\) | −41.9564 | −1.94151 | −0.970755 | − | 0.240074i | \(-0.922828\pi\) | ||||
−0.970755 | + | 0.240074i | \(0.922828\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.0335 | −0.648007 | ||||||||
\(470\) | −30.4423 | −1.40420 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −40.7118 | −1.87391 | ||||||||
\(473\) | −7.40943 | −0.340686 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 11.4253 | 0.524227 | ||||||||
\(476\) | −2.41048 | −0.110484 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −27.9156 | −1.27683 | ||||||||
\(479\) | 9.65088 | 0.440960 | 0.220480 | − | 0.975392i | \(-0.429238\pi\) | ||||
0.220480 | + | 0.975392i | \(0.429238\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 48.3969 | 2.20671 | ||||||||
\(482\) | 14.9495 | 0.680930 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.16067 | 0.0527575 | ||||||||
\(485\) | −49.0120 | −2.22552 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −17.7189 | −0.802920 | −0.401460 | − | 0.915877i | \(-0.631497\pi\) | ||||
−0.401460 | + | 0.915877i | \(0.631497\pi\) | |||||||
\(488\) | −2.03459 | −0.0921016 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 4.14349 | 0.187184 | ||||||||
\(491\) | 4.97599 | 0.224563 | 0.112282 | − | 0.993676i | \(-0.464184\pi\) | ||||
0.112282 | + | 0.993676i | \(0.464184\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −19.5789 | −0.881790 | ||||||||
\(494\) | −10.6631 | −0.479755 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.79117 | −0.125327 | ||||||||
\(497\) | −9.88541 | −0.443421 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 44.0654 | 1.97264 | 0.986318 | − | 0.164851i | \(-0.0527143\pi\) | ||||
0.986318 | + | 0.164851i | \(0.0527143\pi\) | |||||||
\(500\) | −1.69398 | −0.0757569 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −6.55516 | −0.292571 | ||||||||
\(503\) | −5.31840 | −0.237136 | −0.118568 | − | 0.992946i | \(-0.537830\pi\) | ||||
−0.118568 | + | 0.992946i | \(0.537830\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 25.6619 | 1.14194 | ||||||||
\(506\) | 18.1802 | 0.808207 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.455452 | 0.0202074 | ||||||||
\(509\) | −10.4607 | −0.463661 | −0.231830 | − | 0.972756i | \(-0.574471\pi\) | ||||
−0.231830 | + | 0.972756i | \(0.574471\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.57222 | −0.113788 | ||||||||
\(512\) | −24.8549 | −1.09844 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 35.6036 | 1.57041 | ||||||||
\(515\) | −60.3294 | −2.65843 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 21.3590 | 0.939369 | ||||||||
\(518\) | −13.0968 | −0.575440 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 46.7252 | 2.04904 | ||||||||
\(521\) | −35.6052 | −1.55989 | −0.779947 | − | 0.625846i | \(-0.784754\pi\) | ||||
−0.779947 | + | 0.625846i | \(0.784754\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 23.5608 | 1.03024 | 0.515120 | − | 0.857118i | \(-0.327747\pi\) | ||||
0.515120 | + | 0.857118i | \(0.327747\pi\) | |||||||
\(524\) | 3.97069 | 0.173460 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7.87813 | 0.343503 | ||||||||
\(527\) | 5.12629 | 0.223305 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.31943 | 0.100845 | ||||||||
\(530\) | 46.7538 | 2.03086 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.850887 | −0.0368906 | ||||||||
\(533\) | 53.0926 | 2.29969 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.69015 | 0.332474 | ||||||||
\(536\) | 42.8251 | 1.84976 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1.57023 | −0.0676975 | ||||||||
\(539\) | −2.90717 | −0.125221 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.71667 | 0.331765 | 0.165883 | − | 0.986145i | \(-0.446953\pi\) | ||||
0.165883 | + | 0.986145i | \(0.446953\pi\) | |||||||
\(542\) | −6.40838 | −0.275264 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 13.3474 | 0.572263 | ||||||||
\(545\) | −2.97419 | −0.127400 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.9737 | −0.682987 | −0.341494 | − | 0.939884i | \(-0.610933\pi\) | ||||
−0.341494 | + | 0.939884i | \(0.610933\pi\) | |||||||
\(548\) | −2.12370 | −0.0907201 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −22.0957 | −0.942164 | ||||||||
\(551\) | −6.91126 | −0.294430 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.5706 | 0.619605 | ||||||||
\(554\) | 3.44840 | 0.146509 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 8.99247 | 0.381366 | ||||||||
\(557\) | −0.464136 | −0.0196661 | −0.00983304 | − | 0.999952i | \(-0.503130\pi\) | ||||
−0.00983304 | + | 0.999952i | \(0.503130\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11.7049 | −0.495065 | ||||||||
\(560\) | −9.60746 | −0.405989 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6.23121 | −0.262848 | ||||||||
\(563\) | −35.9885 | −1.51673 | −0.758367 | − | 0.651828i | \(-0.774002\pi\) | ||||
−0.758367 | + | 0.651828i | \(0.774002\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −14.5262 | −0.611123 | ||||||||
\(566\) | −10.9871 | −0.461824 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 30.1666 | 1.26576 | ||||||||
\(569\) | 11.1032 | 0.465469 | 0.232735 | − | 0.972540i | \(-0.425233\pi\) | ||||
0.232735 | + | 0.972540i | \(0.425233\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.2214 | 0.427753 | 0.213877 | − | 0.976861i | \(-0.431391\pi\) | ||||
0.213877 | + | 0.976861i | \(0.431391\pi\) | |||||||
\(572\) | −6.08088 | −0.254254 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −14.3675 | −0.599688 | ||||||||
\(575\) | −30.7726 | −1.28331 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.4490 | 0.434999 | 0.217500 | − | 0.976060i | \(-0.430210\pi\) | ||||
0.217500 | + | 0.976060i | \(0.430210\pi\) | |||||||
\(578\) | 13.6838 | 0.569170 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 5.61742 | 0.233251 | ||||||||
\(581\) | −0.493442 | −0.0204714 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −32.8035 | −1.35858 | ||||||||
\(584\) | 7.84948 | 0.324814 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 20.5829 | 0.850270 | ||||||||
\(587\) | −37.8825 | −1.56358 | −0.781789 | − | 0.623543i | \(-0.785693\pi\) | ||||
−0.781789 | + | 0.623543i | \(0.785693\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.80956 | 0.0745615 | ||||||||
\(590\) | 55.2783 | 2.27577 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 30.3673 | 1.24809 | ||||||||
\(593\) | 43.2711 | 1.77693 | 0.888466 | − | 0.458942i | \(-0.151772\pi\) | ||||
0.888466 | + | 0.458942i | \(0.151772\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 17.6452 | 0.723382 | ||||||||
\(596\) | −2.50437 | −0.102583 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 28.7198 | 1.17444 | ||||||||
\(599\) | 28.8279 | 1.17787 | 0.588937 | − | 0.808179i | \(-0.299547\pi\) | ||||
0.588937 | + | 0.808179i | \(0.299547\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 29.8137 | 1.21612 | 0.608062 | − | 0.793889i | \(-0.291947\pi\) | ||||
0.608062 | + | 0.793889i | \(0.291947\pi\) | |||||||
\(602\) | 3.16749 | 0.129097 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 5.38203 | 0.218992 | ||||||||
\(605\) | −8.49630 | −0.345424 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.0035 | −0.608974 | −0.304487 | − | 0.952516i | \(-0.598485\pi\) | ||||
−0.304487 | + | 0.952516i | \(0.598485\pi\) | |||||||
\(608\) | 4.71156 | 0.191079 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.76256 | 0.111853 | ||||||||
\(611\) | 33.7415 | 1.36504 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.68365 | −0.229561 | −0.114780 | − | 0.993391i | \(-0.536616\pi\) | ||||
−0.114780 | + | 0.993391i | \(0.536616\pi\) | |||||||
\(614\) | −29.1075 | −1.17468 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 8.87160 | 0.357447 | ||||||||
\(617\) | −13.5363 | −0.544952 | −0.272476 | − | 0.962163i | \(-0.587842\pi\) | ||||
−0.272476 | + | 0.962163i | \(0.587842\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −27.0321 | −1.08651 | −0.543256 | − | 0.839567i | \(-0.682809\pi\) | ||||
−0.543256 | + | 0.839567i | \(0.682809\pi\) | |||||||
\(620\) | −1.47079 | −0.0590685 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 24.3247 | 0.975334 | ||||||||
\(623\) | −12.1652 | −0.487388 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −18.1776 | −0.727105 | ||||||||
\(626\) | 6.34097 | 0.253436 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.72053 | −0.0686565 | ||||||||
\(629\) | −55.7730 | −2.22382 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.75817 | 0.109801 | 0.0549004 | − | 0.998492i | \(-0.482516\pi\) | ||||
0.0549004 | + | 0.998492i | \(0.482516\pi\) | |||||||
\(632\) | −44.4641 | −1.76869 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 24.4447 | 0.970822 | ||||||||
\(635\) | −3.33400 | −0.132306 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.59254 | −0.181963 | ||||||||
\(638\) | 13.3659 | 0.529162 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 20.0507 | 0.792575 | ||||||||
\(641\) | 10.2155 | 0.403489 | 0.201744 | − | 0.979438i | \(-0.435339\pi\) | ||||
0.201744 | + | 0.979438i | \(0.435339\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −25.3762 | −1.00074 | −0.500370 | − | 0.865812i | \(-0.666803\pi\) | ||||
−0.500370 | + | 0.865812i | \(0.666803\pi\) | |||||||
\(644\) | 2.29176 | 0.0903081 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 12.2882 | 0.483474 | ||||||||
\(647\) | 22.1567 | 0.871068 | 0.435534 | − | 0.900172i | \(-0.356560\pi\) | ||||
0.435534 | + | 0.900172i | \(0.356560\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −38.7845 | −1.52243 | ||||||||
\(650\) | −34.9053 | −1.36910 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9.11409 | 0.356935 | ||||||||
\(653\) | 9.65817 | 0.377954 | 0.188977 | − | 0.981982i | \(-0.439483\pi\) | ||||
0.188977 | + | 0.981982i | \(0.439483\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −29.0662 | −1.13571 | ||||||||
\(656\) | 33.3137 | 1.30068 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −9.13087 | −0.355958 | ||||||||
\(659\) | 14.6717 | 0.571527 | 0.285764 | − | 0.958300i | \(-0.407753\pi\) | ||||
0.285764 | + | 0.958300i | \(0.407753\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 33.3172 | 1.29589 | 0.647945 | − | 0.761687i | \(-0.275629\pi\) | ||||
0.647945 | + | 0.761687i | \(0.275629\pi\) | |||||||
\(662\) | 18.8042 | 0.730845 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.50580 | 0.0584365 | ||||||||
\(665\) | 6.22866 | 0.241537 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18.6147 | 0.720763 | ||||||||
\(668\) | −7.48283 | −0.289519 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −58.1477 | −2.24644 | ||||||||
\(671\) | −1.93827 | −0.0748262 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.32670 | 0.0511404 | 0.0255702 | − | 0.999673i | \(-0.491860\pi\) | ||||
0.0255702 | + | 0.999673i | \(0.491860\pi\) | |||||||
\(674\) | −8.96350 | −0.345261 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.68527 | −0.141741 | ||||||||
\(677\) | −11.9106 | −0.457761 | −0.228881 | − | 0.973454i | \(-0.573507\pi\) | ||||
−0.228881 | + | 0.973454i | \(0.573507\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −14.7006 | −0.564159 | ||||||||
\(680\) | −53.8466 | −2.06492 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3.49956 | −0.134005 | ||||||||
\(683\) | 6.04534 | 0.231318 | 0.115659 | − | 0.993289i | \(-0.463102\pi\) | ||||
0.115659 | + | 0.993289i | \(0.463102\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15.5459 | 0.593980 | ||||||||
\(686\) | 1.24280 | 0.0474503 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −7.34442 | −0.280003 | ||||||||
\(689\) | −51.8208 | −1.97421 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −26.4623 | −1.00667 | −0.503336 | − | 0.864090i | \(-0.667894\pi\) | ||||
−0.503336 | + | 0.864090i | \(0.667894\pi\) | |||||||
\(692\) | −7.39818 | −0.281237 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −35.7694 | −1.35779 | ||||||||
\(695\) | −65.8267 | −2.49695 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −61.1844 | −2.31752 | ||||||||
\(698\) | −35.8176 | −1.35571 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.78535 | −0.105276 | ||||||||
\(701\) | −27.8873 | −1.05329 | −0.526645 | − | 0.850085i | \(-0.676550\pi\) | ||||
−0.526645 | + | 0.850085i | \(0.676550\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −19.6876 | −0.742532 | ||||||||
\(704\) | −25.8668 | −0.974890 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −33.1192 | −1.24646 | ||||||||
\(707\) | 7.69701 | 0.289476 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −21.7892 | −0.818312 | −0.409156 | − | 0.912465i | \(-0.634177\pi\) | ||||
−0.409156 | + | 0.912465i | \(0.634177\pi\) | |||||||
\(710\) | −40.9601 | −1.53721 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 37.1237 | 1.39127 | ||||||||
\(713\) | −4.87383 | −0.182526 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 44.5132 | 1.66470 | ||||||||
\(716\) | −1.82355 | −0.0681491 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 17.9308 | 0.669172 | ||||||||
\(719\) | −0.503768 | −0.0187874 | −0.00939368 | − | 0.999956i | \(-0.502990\pi\) | ||||
−0.00939368 | + | 0.999956i | \(0.502990\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −18.0952 | −0.673900 | ||||||||
\(722\) | −19.2755 | −0.717359 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 11.1158 | 0.413115 | ||||||||
\(725\) | −22.6238 | −0.840227 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23.4153 | 0.868427 | 0.434213 | − | 0.900810i | \(-0.357026\pi\) | ||||
0.434213 | + | 0.900810i | \(0.357026\pi\) | |||||||
\(728\) | 14.0148 | 0.519421 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −10.6580 | −0.394470 | ||||||||
\(731\) | 13.4889 | 0.498903 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 52.3311 | 1.93289 | 0.966446 | − | 0.256871i | \(-0.0826915\pi\) | ||||
0.966446 | + | 0.256871i | \(0.0826915\pi\) | |||||||
\(734\) | −10.3872 | −0.383400 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −12.6900 | −0.467760 | ||||||||
\(737\) | 40.7978 | 1.50280 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −11.4312 | −0.420504 | −0.210252 | − | 0.977647i | \(-0.567429\pi\) | ||||
−0.210252 | + | 0.977647i | \(0.567429\pi\) | |||||||
\(740\) | 16.0020 | 0.588243 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 14.0233 | 0.514813 | ||||||||
\(743\) | −33.8238 | −1.24087 | −0.620437 | − | 0.784256i | \(-0.713045\pi\) | ||||
−0.620437 | + | 0.784256i | \(0.713045\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 18.3325 | 0.671651 | ||||||||
\(746\) | 37.6758 | 1.37941 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 7.00766 | 0.256225 | ||||||||
\(749\) | 2.30658 | 0.0842807 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −50.0895 | −1.82779 | −0.913896 | − | 0.405949i | \(-0.866941\pi\) | ||||
−0.913896 | + | 0.405949i | \(0.866941\pi\) | |||||||
\(752\) | 21.1716 | 0.772049 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 21.1146 | 0.768947 | ||||||||
\(755\) | −39.3975 | −1.43382 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16.9391 | 0.615663 | 0.307831 | − | 0.951441i | \(-0.400397\pi\) | ||||
0.307831 | + | 0.951441i | \(0.400397\pi\) | |||||||
\(758\) | 3.20451 | 0.116393 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −19.0076 | −0.689478 | ||||||||
\(761\) | 32.7577 | 1.18747 | 0.593734 | − | 0.804662i | \(-0.297653\pi\) | ||||
0.593734 | + | 0.804662i | \(0.297653\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.892079 | −0.0322954 | ||||||||
\(764\) | −10.2783 | −0.371854 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 18.1792 | 0.656842 | ||||||||
\(767\) | −61.2691 | −2.21230 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 47.6458 | 1.71815 | 0.859075 | − | 0.511850i | \(-0.171040\pi\) | ||||
0.859075 | + | 0.511850i | \(0.171040\pi\) | |||||||
\(770\) | −12.0458 | −0.434101 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −9.44303 | −0.339862 | ||||||||
\(773\) | 47.1769 | 1.69683 | 0.848417 | − | 0.529328i | \(-0.177556\pi\) | ||||
0.848417 | + | 0.529328i | \(0.177556\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.92353 | 0.212779 | ||||||||
\(776\) | 44.8609 | 1.61041 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −24.3075 | −0.871464 | ||||||||
\(779\) | −21.5978 | −0.773821 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 28.7385 | 1.02835 | ||||||||
\(782\) | −33.0969 | −1.18354 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.88166 | −0.102916 | ||||||||
\(785\) | 12.5946 | 0.449521 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15.6611 | −0.558257 | −0.279129 | − | 0.960254i | \(-0.590046\pi\) | ||||
−0.279129 | + | 0.960254i | \(0.590046\pi\) | |||||||
\(788\) | −1.72055 | −0.0612921 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 60.3732 | 2.14798 | ||||||||
\(791\) | −4.35699 | −0.154917 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.06195 | −0.108733 | ||||||||
\(794\) | −10.3830 | −0.368479 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.43414 | 0.157164 | ||||||||
\(797\) | 2.11085 | 0.0747702 | 0.0373851 | − | 0.999301i | \(-0.488097\pi\) | ||||
0.0373851 | + | 0.999301i | \(0.488097\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −38.8841 | −1.37562 | ||||||||
\(800\) | 15.4231 | 0.545290 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −9.02139 | −0.318556 | ||||||||
\(803\) | 7.47788 | 0.263889 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −16.7762 | −0.591282 | ||||||||
\(806\) | −5.52837 | −0.194729 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −23.4884 | −0.826321 | ||||||||
\(809\) | 10.8674 | 0.382079 | 0.191039 | − | 0.981582i | \(-0.438814\pi\) | ||||
0.191039 | + | 0.981582i | \(0.438814\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −46.4996 | −1.63282 | −0.816411 | − | 0.577472i | \(-0.804039\pi\) | ||||
−0.816411 | + | 0.577472i | \(0.804039\pi\) | |||||||
\(812\) | 1.68489 | 0.0591280 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 38.0746 | 1.33451 | ||||||||
\(815\) | −66.7170 | −2.33699 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.76150 | 0.166584 | ||||||||
\(818\) | 10.5181 | 0.367755 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 17.5545 | 0.613031 | ||||||||
\(821\) | 26.4225 | 0.922152 | 0.461076 | − | 0.887361i | \(-0.347464\pi\) | ||||
0.461076 | + | 0.887361i | \(0.347464\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −26.4500 | −0.921989 | −0.460995 | − | 0.887403i | \(-0.652507\pi\) | ||||
−0.460995 | + | 0.887403i | \(0.652507\pi\) | |||||||
\(824\) | 55.2199 | 1.92368 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 16.5802 | 0.576898 | ||||||||
\(827\) | −31.2695 | −1.08735 | −0.543673 | − | 0.839297i | \(-0.682967\pi\) | ||||
−0.543673 | + | 0.839297i | \(0.682967\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −52.6203 | −1.82758 | −0.913790 | − | 0.406187i | \(-0.866858\pi\) | ||||
−0.913790 | + | 0.406187i | \(0.866858\pi\) | |||||||
\(830\) | −2.04457 | −0.0709682 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −40.8625 | −1.41665 | ||||||||
\(833\) | 5.29249 | 0.183374 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 54.7758 | 1.89560 | ||||||||
\(836\) | 2.47367 | 0.0855537 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −33.3033 | −1.15044 | ||||||||
\(839\) | 29.2755 | 1.01070 | 0.505352 | − | 0.862913i | \(-0.331363\pi\) | ||||
0.505352 | + | 0.862913i | \(0.331363\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.3146 | −0.528090 | ||||||||
\(842\) | 17.5559 | 0.605015 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.12546 | −0.0731612 | ||||||||
\(845\) | 26.9769 | 0.928034 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.54838 | −0.0875633 | ||||||||
\(848\) | −32.5157 | −1.11659 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 40.2252 | 1.37971 | ||||||||
\(851\) | 53.0263 | 1.81772 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −22.4780 | −0.769631 | −0.384816 | − | 0.922994i | \(-0.625735\pi\) | ||||
−0.384816 | + | 0.922994i | \(0.625735\pi\) | |||||||
\(854\) | 0.828601 | 0.0283542 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.03884 | −0.240583 | ||||||||
\(857\) | 35.5634 | 1.21482 | 0.607412 | − | 0.794387i | \(-0.292208\pi\) | ||||
0.607412 | + | 0.794387i | \(0.292208\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 38.2979 | 1.30671 | 0.653354 | − | 0.757053i | \(-0.273361\pi\) | ||||
0.653354 | + | 0.757053i | \(0.273361\pi\) | |||||||
\(860\) | −3.87011 | −0.131970 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 20.6464 | 0.703218 | ||||||||
\(863\) | −47.7198 | −1.62440 | −0.812201 | − | 0.583378i | \(-0.801730\pi\) | ||||
−0.812201 | + | 0.583378i | \(0.801730\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 54.1562 | 1.84137 | ||||||||
\(866\) | 30.5577 | 1.03839 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −0.441150 | −0.0149736 | ||||||||
\(869\) | −42.3592 | −1.43694 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 64.4495 | 2.18379 | ||||||||
\(872\) | 2.72230 | 0.0921886 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −11.6831 | −0.395185 | ||||||||
\(875\) | 3.71933 | 0.125736 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.9916 | −0.708837 | −0.354418 | − | 0.935087i | \(-0.615321\pi\) | ||||
−0.354418 | + | 0.935087i | \(0.615321\pi\) | |||||||
\(878\) | −47.3843 | −1.59914 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 27.9305 | 0.941536 | ||||||||
\(881\) | 47.8891 | 1.61343 | 0.806713 | − | 0.590943i | \(-0.201244\pi\) | ||||
0.806713 | + | 0.590943i | \(0.201244\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10.1634 | 0.342026 | 0.171013 | − | 0.985269i | \(-0.445296\pi\) | ||||
0.171013 | + | 0.985269i | \(0.445296\pi\) | |||||||
\(884\) | 11.0702 | 0.372332 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −28.2265 | −0.948287 | ||||||||
\(887\) | 49.2135 | 1.65243 | 0.826213 | − | 0.563357i | \(-0.190490\pi\) | ||||
0.826213 | + | 0.563357i | \(0.190490\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.00000 | −0.0335389 | ||||||||
\(890\) | −50.4064 | −1.68963 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.44971 | −0.0820223 | ||||||||
\(893\) | −13.7259 | −0.459319 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13.3487 | 0.446199 | ||||||||
\(896\) | 6.01402 | 0.200914 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 36.1348 | 1.20583 | ||||||||
\(899\) | −3.58320 | −0.119507 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 59.7188 | 1.98952 | ||||||||
\(902\) | 41.7687 | 1.39075 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 13.2959 | 0.442216 | ||||||||
\(905\) | −81.3699 | −2.70483 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 50.4233 | 1.67428 | 0.837139 | − | 0.546991i | \(-0.184227\pi\) | ||||
0.837139 | + | 0.546991i | \(0.184227\pi\) | |||||||
\(908\) | −5.24151 | −0.173946 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −19.0292 | −0.630811 | ||||||||
\(911\) | −19.4045 | −0.642899 | −0.321449 | − | 0.946927i | \(-0.604170\pi\) | ||||
−0.321449 | + | 0.946927i | \(0.604170\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.43452 | 0.0474756 | ||||||||
\(914\) | 31.7157 | 1.04906 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.855620 | 0.0282705 | ||||||||
\(917\) | −8.71812 | −0.287898 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −38.9767 | −1.28572 | −0.642861 | − | 0.765983i | \(-0.722253\pi\) | ||||
−0.642861 | + | 0.765983i | \(0.722253\pi\) | |||||||
\(920\) | 51.1947 | 1.68784 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 13.4389 | 0.442586 | ||||||||
\(923\) | 45.3992 | 1.49433 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −64.4468 | −2.11900 | ||||||||
\(926\) | 7.44179 | 0.244552 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −9.32962 | −0.306260 | ||||||||
\(929\) | 2.48794 | 0.0816266 | 0.0408133 | − | 0.999167i | \(-0.487005\pi\) | ||||
0.0408133 | + | 0.999167i | \(0.487005\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.86822 | 0.0612286 | ||||||||
\(932\) | 6.17878 | 0.202393 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −52.1433 | −1.70618 | ||||||||
\(935\) | −51.2975 | −1.67761 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 42.9656 | 1.40362 | 0.701812 | − | 0.712362i | \(-0.252375\pi\) | ||||
0.701812 | + | 0.712362i | \(0.252375\pi\) | |||||||
\(938\) | −17.4408 | −0.569463 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 11.1563 | 0.363878 | ||||||||
\(941\) | −49.3601 | −1.60909 | −0.804547 | − | 0.593889i | \(-0.797592\pi\) | ||||
−0.804547 | + | 0.593889i | \(0.797592\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 58.1711 | 1.89431 | ||||||||
\(944\) | −38.4442 | −1.25125 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.20843 | −0.299392 | ||||||||
\(947\) | 7.03435 | 0.228586 | 0.114293 | − | 0.993447i | \(-0.463540\pi\) | ||||
0.114293 | + | 0.993447i | \(0.463540\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11.8130 | 0.383468 | ||||||||
\(950\) | 14.1993 | 0.460686 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −16.1507 | −0.523448 | ||||||||
\(953\) | −12.7667 | −0.413553 | −0.206777 | − | 0.978388i | \(-0.566297\pi\) | ||||
−0.206777 | + | 0.978388i | \(0.566297\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 75.2389 | 2.43467 | ||||||||
\(956\) | 10.2303 | 0.330872 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 11.9941 | 0.387512 | ||||||||
\(959\) | 4.66285 | 0.150571 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.0618 | −0.969736 | ||||||||
\(962\) | 60.1476 | 1.93924 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −5.47858 | −0.176453 | ||||||||
\(965\) | 69.1249 | 2.22521 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 53.8825 | 1.73274 | 0.866372 | − | 0.499400i | \(-0.166446\pi\) | ||||
0.866372 | + | 0.499400i | \(0.166446\pi\) | |||||||
\(968\) | 7.77671 | 0.249953 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −60.9120 | −1.95577 | ||||||||
\(971\) | 55.2100 | 1.77177 | 0.885887 | − | 0.463901i | \(-0.153551\pi\) | ||||
0.885887 | + | 0.463901i | \(0.153551\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −19.7441 | −0.632965 | ||||||||
\(974\) | −22.0210 | −0.705599 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.92127 | −0.0614982 | ||||||||
\(977\) | 38.3352 | 1.22645 | 0.613226 | − | 0.789908i | \(-0.289872\pi\) | ||||
0.613226 | + | 0.789908i | \(0.289872\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 35.3662 | 1.13031 | ||||||||
\(980\) | −1.51848 | −0.0485060 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 6.18415 | 0.197344 | ||||||||
\(983\) | 19.8976 | 0.634635 | 0.317317 | − | 0.948319i | \(-0.397218\pi\) | ||||
0.317317 | + | 0.948319i | \(0.397218\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.5948 | 0.401303 | ||||||||
\(986\) | −24.3326 | −0.774909 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.90774 | 0.124322 | ||||||||
\(989\) | −12.8245 | −0.407797 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.55649 | 0.176508 | 0.0882538 | − | 0.996098i | \(-0.471871\pi\) | ||||
0.0882538 | + | 0.996098i | \(0.471871\pi\) | |||||||
\(992\) | 2.44275 | 0.0775573 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −12.2856 | −0.389675 | ||||||||
\(995\) | −32.4588 | −1.02901 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.32640 | 0.137019 | 0.0685093 | − | 0.997650i | \(-0.478176\pi\) | ||||
0.0685093 | + | 0.997650i | \(0.478176\pi\) | |||||||
\(998\) | 54.7644 | 1.73354 | ||||||||
\(999\) | 0 | 0 |
(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 | 8001.2.a.l.1.5 | 7 | ||
3.2 | odd | 2 | 2667.2.a.j.1.3 | ✓ | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2667.2.a.j.1.3 | ✓ | 7 | 3.2 | odd | 2 | ||
8001.2.a.l.1.5 | 7 | 1.1 | even | 1 | trivial |