Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1450,2,Mod(1,1450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1450, 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("1450.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1450 = 2 \cdot 5^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1450.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: | \(11.5783082931\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 290) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1450.1 |
$q$-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 | ||||||||
\(3\) | −2.61803 | −1.51152 | −0.755761 | − | 0.654847i | \(-0.772733\pi\) | ||||
−0.755761 | + | 0.654847i | \(0.772733\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.61803 | −1.06881 | ||||||||
\(7\) | −0.381966 | −0.144370 | −0.0721848 | − | 0.997391i | \(-0.522997\pi\) | ||||
−0.0721848 | + | 0.997391i | \(0.522997\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 3.85410 | 1.28470 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.00000 | 0.603023 | 0.301511 | − | 0.953463i | \(-0.402509\pi\) | ||||
0.301511 | + | 0.953463i | \(0.402509\pi\) | |||||||
\(12\) | −2.61803 | −0.755761 | ||||||||
\(13\) | −2.61803 | −0.726112 | −0.363056 | − | 0.931767i | \(-0.618267\pi\) | ||||
−0.363056 | + | 0.931767i | \(0.618267\pi\) | |||||||
\(14\) | −0.381966 | −0.102085 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.61803 | −1.36257 | −0.681287 | − | 0.732017i | \(-0.738579\pi\) | ||||
−0.681287 | + | 0.732017i | \(0.738579\pi\) | |||||||
\(18\) | 3.85410 | 0.908421 | ||||||||
\(19\) | −2.00000 | −0.458831 | −0.229416 | − | 0.973329i | \(-0.573682\pi\) | ||||
−0.229416 | + | 0.973329i | \(0.573682\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 2.00000 | 0.426401 | ||||||||
\(23\) | 1.85410 | 0.386607 | 0.193303 | − | 0.981139i | \(-0.438080\pi\) | ||||
0.193303 | + | 0.981139i | \(0.438080\pi\) | |||||||
\(24\) | −2.61803 | −0.534404 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.61803 | −0.513439 | ||||||||
\(27\) | −2.23607 | −0.430331 | ||||||||
\(28\) | −0.381966 | −0.0721848 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.85410 | 0.512612 | 0.256306 | − | 0.966596i | \(-0.417495\pi\) | ||||
0.256306 | + | 0.966596i | \(0.417495\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −5.23607 | −0.911482 | ||||||||
\(34\) | −5.61803 | −0.963485 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.85410 | 0.642350 | ||||||||
\(37\) | 8.94427 | 1.47043 | 0.735215 | − | 0.677834i | \(-0.237081\pi\) | ||||
0.735215 | + | 0.677834i | \(0.237081\pi\) | |||||||
\(38\) | −2.00000 | −0.324443 | ||||||||
\(39\) | 6.85410 | 1.09753 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.70820 | −0.891472 | −0.445736 | − | 0.895165i | \(-0.647058\pi\) | ||||
−0.445736 | + | 0.895165i | \(0.647058\pi\) | |||||||
\(42\) | 1.00000 | 0.154303 | ||||||||
\(43\) | −5.61803 | −0.856742 | −0.428371 | − | 0.903603i | \(-0.640912\pi\) | ||||
−0.428371 | + | 0.903603i | \(0.640912\pi\) | |||||||
\(44\) | 2.00000 | 0.301511 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.85410 | 0.273372 | ||||||||
\(47\) | −10.4721 | −1.52752 | −0.763759 | − | 0.645501i | \(-0.776648\pi\) | ||||
−0.763759 | + | 0.645501i | \(0.776648\pi\) | |||||||
\(48\) | −2.61803 | −0.377881 | ||||||||
\(49\) | −6.85410 | −0.979157 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 14.7082 | 2.05956 | ||||||||
\(52\) | −2.61803 | −0.363056 | ||||||||
\(53\) | −11.6180 | −1.59586 | −0.797930 | − | 0.602750i | \(-0.794071\pi\) | ||||
−0.797930 | + | 0.602750i | \(0.794071\pi\) | |||||||
\(54\) | −2.23607 | −0.304290 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.381966 | −0.0510424 | ||||||||
\(57\) | 5.23607 | 0.693534 | ||||||||
\(58\) | −1.00000 | −0.131306 | ||||||||
\(59\) | −3.85410 | −0.501761 | −0.250881 | − | 0.968018i | \(-0.580720\pi\) | ||||
−0.250881 | + | 0.968018i | \(0.580720\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.14590 | −0.530828 | −0.265414 | − | 0.964135i | \(-0.585509\pi\) | ||||
−0.265414 | + | 0.964135i | \(0.585509\pi\) | |||||||
\(62\) | 2.85410 | 0.362471 | ||||||||
\(63\) | −1.47214 | −0.185472 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −5.23607 | −0.644515 | ||||||||
\(67\) | −8.94427 | −1.09272 | −0.546358 | − | 0.837552i | \(-0.683986\pi\) | ||||
−0.546358 | + | 0.837552i | \(0.683986\pi\) | |||||||
\(68\) | −5.61803 | −0.681287 | ||||||||
\(69\) | −4.85410 | −0.584365 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.70820 | 0.914796 | 0.457398 | − | 0.889262i | \(-0.348782\pi\) | ||||
0.457398 | + | 0.889262i | \(0.348782\pi\) | |||||||
\(72\) | 3.85410 | 0.454210 | ||||||||
\(73\) | −14.5623 | −1.70439 | −0.852194 | − | 0.523225i | \(-0.824729\pi\) | ||||
−0.852194 | + | 0.523225i | \(0.824729\pi\) | |||||||
\(74\) | 8.94427 | 1.03975 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.00000 | −0.229416 | ||||||||
\(77\) | −0.763932 | −0.0870581 | ||||||||
\(78\) | 6.85410 | 0.776074 | ||||||||
\(79\) | −13.5623 | −1.52588 | −0.762939 | − | 0.646470i | \(-0.776245\pi\) | ||||
−0.762939 | + | 0.646470i | \(0.776245\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.70820 | −0.634245 | ||||||||
\(82\) | −5.70820 | −0.630366 | ||||||||
\(83\) | 2.94427 | 0.323176 | 0.161588 | − | 0.986858i | \(-0.448338\pi\) | ||||
0.161588 | + | 0.986858i | \(0.448338\pi\) | |||||||
\(84\) | 1.00000 | 0.109109 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −5.61803 | −0.605808 | ||||||||
\(87\) | 2.61803 | 0.280683 | ||||||||
\(88\) | 2.00000 | 0.213201 | ||||||||
\(89\) | 2.00000 | 0.212000 | 0.106000 | − | 0.994366i | \(-0.466196\pi\) | ||||
0.106000 | + | 0.994366i | \(0.466196\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.00000 | 0.104828 | ||||||||
\(92\) | 1.85410 | 0.193303 | ||||||||
\(93\) | −7.47214 | −0.774824 | ||||||||
\(94\) | −10.4721 | −1.08012 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.61803 | −0.267202 | ||||||||
\(97\) | −13.8541 | −1.40667 | −0.703335 | − | 0.710858i | \(-0.748307\pi\) | ||||
−0.703335 | + | 0.710858i | \(0.748307\pi\) | |||||||
\(98\) | −6.85410 | −0.692369 | ||||||||
\(99\) | 7.70820 | 0.774704 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.14590 | 0.412532 | 0.206266 | − | 0.978496i | \(-0.433869\pi\) | ||||
0.206266 | + | 0.978496i | \(0.433869\pi\) | |||||||
\(102\) | 14.7082 | 1.45633 | ||||||||
\(103\) | 19.4164 | 1.91316 | 0.956578 | − | 0.291477i | \(-0.0941468\pi\) | ||||
0.956578 | + | 0.291477i | \(0.0941468\pi\) | |||||||
\(104\) | −2.61803 | −0.256719 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −11.6180 | −1.12844 | ||||||||
\(107\) | −8.18034 | −0.790823 | −0.395412 | − | 0.918504i | \(-0.629398\pi\) | ||||
−0.395412 | + | 0.918504i | \(0.629398\pi\) | |||||||
\(108\) | −2.23607 | −0.215166 | ||||||||
\(109\) | −7.41641 | −0.710363 | −0.355182 | − | 0.934797i | \(-0.615581\pi\) | ||||
−0.355182 | + | 0.934797i | \(0.615581\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −23.4164 | −2.22259 | ||||||||
\(112\) | −0.381966 | −0.0360924 | ||||||||
\(113\) | 7.09017 | 0.666987 | 0.333494 | − | 0.942752i | \(-0.391772\pi\) | ||||
0.333494 | + | 0.942752i | \(0.391772\pi\) | |||||||
\(114\) | 5.23607 | 0.490403 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.00000 | −0.0928477 | ||||||||
\(117\) | −10.0902 | −0.932837 | ||||||||
\(118\) | −3.85410 | −0.354799 | ||||||||
\(119\) | 2.14590 | 0.196714 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | −4.14590 | −0.375352 | ||||||||
\(123\) | 14.9443 | 1.34748 | ||||||||
\(124\) | 2.85410 | 0.256306 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.47214 | −0.131148 | ||||||||
\(127\) | 21.7082 | 1.92629 | 0.963146 | − | 0.268980i | \(-0.0866865\pi\) | ||||
0.963146 | + | 0.268980i | \(0.0866865\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 14.7082 | 1.29499 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.41641 | −0.473234 | −0.236617 | − | 0.971603i | \(-0.576039\pi\) | ||||
−0.236617 | + | 0.971603i | \(0.576039\pi\) | |||||||
\(132\) | −5.23607 | −0.455741 | ||||||||
\(133\) | 0.763932 | 0.0662413 | ||||||||
\(134\) | −8.94427 | −0.772667 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.61803 | −0.481742 | ||||||||
\(137\) | −1.85410 | −0.158407 | −0.0792033 | − | 0.996858i | \(-0.525238\pi\) | ||||
−0.0792033 | + | 0.996858i | \(0.525238\pi\) | |||||||
\(138\) | −4.85410 | −0.413209 | ||||||||
\(139\) | 14.5623 | 1.23516 | 0.617579 | − | 0.786509i | \(-0.288113\pi\) | ||||
0.617579 | + | 0.786509i | \(0.288113\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 27.4164 | 2.30888 | ||||||||
\(142\) | 7.70820 | 0.646858 | ||||||||
\(143\) | −5.23607 | −0.437862 | ||||||||
\(144\) | 3.85410 | 0.321175 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −14.5623 | −1.20519 | ||||||||
\(147\) | 17.9443 | 1.48002 | ||||||||
\(148\) | 8.94427 | 0.735215 | ||||||||
\(149\) | 5.41641 | 0.443729 | 0.221865 | − | 0.975077i | \(-0.428786\pi\) | ||||
0.221865 | + | 0.975077i | \(0.428786\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.7082 | 1.44107 | 0.720537 | − | 0.693417i | \(-0.243896\pi\) | ||||
0.720537 | + | 0.693417i | \(0.243896\pi\) | |||||||
\(152\) | −2.00000 | −0.162221 | ||||||||
\(153\) | −21.6525 | −1.75050 | ||||||||
\(154\) | −0.763932 | −0.0615594 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 6.85410 | 0.548767 | ||||||||
\(157\) | 3.70820 | 0.295947 | 0.147973 | − | 0.988991i | \(-0.452725\pi\) | ||||
0.147973 | + | 0.988991i | \(0.452725\pi\) | |||||||
\(158\) | −13.5623 | −1.07896 | ||||||||
\(159\) | 30.4164 | 2.41218 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.708204 | −0.0558143 | ||||||||
\(162\) | −5.70820 | −0.448479 | ||||||||
\(163\) | 19.4164 | 1.52081 | 0.760405 | − | 0.649449i | \(-0.225000\pi\) | ||||
0.760405 | + | 0.649449i | \(0.225000\pi\) | |||||||
\(164\) | −5.70820 | −0.445736 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.94427 | 0.228520 | ||||||||
\(167\) | −0.381966 | −0.0295574 | −0.0147787 | − | 0.999891i | \(-0.504704\pi\) | ||||
−0.0147787 | + | 0.999891i | \(0.504704\pi\) | |||||||
\(168\) | 1.00000 | 0.0771517 | ||||||||
\(169\) | −6.14590 | −0.472761 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.70820 | −0.589461 | ||||||||
\(172\) | −5.61803 | −0.428371 | ||||||||
\(173\) | 20.5066 | 1.55909 | 0.779543 | − | 0.626349i | \(-0.215451\pi\) | ||||
0.779543 | + | 0.626349i | \(0.215451\pi\) | |||||||
\(174\) | 2.61803 | 0.198473 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.00000 | 0.150756 | ||||||||
\(177\) | 10.0902 | 0.758424 | ||||||||
\(178\) | 2.00000 | 0.149906 | ||||||||
\(179\) | 15.8541 | 1.18499 | 0.592496 | − | 0.805574i | \(-0.298143\pi\) | ||||
0.592496 | + | 0.805574i | \(0.298143\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.0000 | −0.743294 | −0.371647 | − | 0.928374i | \(-0.621207\pi\) | ||||
−0.371647 | + | 0.928374i | \(0.621207\pi\) | |||||||
\(182\) | 1.00000 | 0.0741249 | ||||||||
\(183\) | 10.8541 | 0.802358 | ||||||||
\(184\) | 1.85410 | 0.136686 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −7.47214 | −0.547884 | ||||||||
\(187\) | −11.2361 | −0.821663 | ||||||||
\(188\) | −10.4721 | −0.763759 | ||||||||
\(189\) | 0.854102 | 0.0621268 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.2705 | −0.743148 | −0.371574 | − | 0.928403i | \(-0.621182\pi\) | ||||
−0.371574 | + | 0.928403i | \(0.621182\pi\) | |||||||
\(192\) | −2.61803 | −0.188940 | ||||||||
\(193\) | −17.5623 | −1.26416 | −0.632081 | − | 0.774902i | \(-0.717799\pi\) | ||||
−0.632081 | + | 0.774902i | \(0.717799\pi\) | |||||||
\(194\) | −13.8541 | −0.994667 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.85410 | −0.489579 | ||||||||
\(197\) | −11.6180 | −0.827751 | −0.413875 | − | 0.910334i | \(-0.635825\pi\) | ||||
−0.413875 | + | 0.910334i | \(0.635825\pi\) | |||||||
\(198\) | 7.70820 | 0.547798 | ||||||||
\(199\) | −21.1246 | −1.49748 | −0.748742 | − | 0.662862i | \(-0.769342\pi\) | ||||
−0.748742 | + | 0.662862i | \(0.769342\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 23.4164 | 1.65167 | ||||||||
\(202\) | 4.14590 | 0.291704 | ||||||||
\(203\) | 0.381966 | 0.0268088 | ||||||||
\(204\) | 14.7082 | 1.02978 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 19.4164 | 1.35281 | ||||||||
\(207\) | 7.14590 | 0.496674 | ||||||||
\(208\) | −2.61803 | −0.181528 | ||||||||
\(209\) | −4.00000 | −0.276686 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.4164 | 1.06131 | 0.530655 | − | 0.847588i | \(-0.321946\pi\) | ||||
0.530655 | + | 0.847588i | \(0.321946\pi\) | |||||||
\(212\) | −11.6180 | −0.797930 | ||||||||
\(213\) | −20.1803 | −1.38273 | ||||||||
\(214\) | −8.18034 | −0.559197 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.23607 | −0.152145 | ||||||||
\(217\) | −1.09017 | −0.0740056 | ||||||||
\(218\) | −7.41641 | −0.502303 | ||||||||
\(219\) | 38.1246 | 2.57622 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 14.7082 | 0.989381 | ||||||||
\(222\) | −23.4164 | −1.57161 | ||||||||
\(223\) | 6.43769 | 0.431100 | 0.215550 | − | 0.976493i | \(-0.430846\pi\) | ||||
0.215550 | + | 0.976493i | \(0.430846\pi\) | |||||||
\(224\) | −0.381966 | −0.0255212 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7.09017 | 0.471631 | ||||||||
\(227\) | −7.52786 | −0.499642 | −0.249821 | − | 0.968292i | \(-0.580372\pi\) | ||||
−0.249821 | + | 0.968292i | \(0.580372\pi\) | |||||||
\(228\) | 5.23607 | 0.346767 | ||||||||
\(229\) | −14.8541 | −0.981587 | −0.490793 | − | 0.871276i | \(-0.663293\pi\) | ||||
−0.490793 | + | 0.871276i | \(0.663293\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.00000 | 0.131590 | ||||||||
\(232\) | −1.00000 | −0.0656532 | ||||||||
\(233\) | 6.76393 | 0.443120 | 0.221560 | − | 0.975147i | \(-0.428885\pi\) | ||||
0.221560 | + | 0.975147i | \(0.428885\pi\) | |||||||
\(234\) | −10.0902 | −0.659615 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −3.85410 | −0.250881 | ||||||||
\(237\) | 35.5066 | 2.30640 | ||||||||
\(238\) | 2.14590 | 0.139098 | ||||||||
\(239\) | −7.70820 | −0.498602 | −0.249301 | − | 0.968426i | \(-0.580201\pi\) | ||||
−0.249301 | + | 0.968426i | \(0.580201\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.14590 | −0.138229 | −0.0691147 | − | 0.997609i | \(-0.522017\pi\) | ||||
−0.0691147 | + | 0.997609i | \(0.522017\pi\) | |||||||
\(242\) | −7.00000 | −0.449977 | ||||||||
\(243\) | 21.6525 | 1.38901 | ||||||||
\(244\) | −4.14590 | −0.265414 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 14.9443 | 0.952812 | ||||||||
\(247\) | 5.23607 | 0.333163 | ||||||||
\(248\) | 2.85410 | 0.181236 | ||||||||
\(249\) | −7.70820 | −0.488488 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.1246 | 0.702179 | 0.351090 | − | 0.936342i | \(-0.385811\pi\) | ||||
0.351090 | + | 0.936342i | \(0.385811\pi\) | |||||||
\(252\) | −1.47214 | −0.0927358 | ||||||||
\(253\) | 3.70820 | 0.233133 | ||||||||
\(254\) | 21.7082 | 1.36209 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −15.7082 | −0.979851 | −0.489925 | − | 0.871764i | \(-0.662976\pi\) | ||||
−0.489925 | + | 0.871764i | \(0.662976\pi\) | |||||||
\(258\) | 14.7082 | 0.915693 | ||||||||
\(259\) | −3.41641 | −0.212285 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.85410 | −0.238563 | ||||||||
\(262\) | −5.41641 | −0.334627 | ||||||||
\(263\) | −27.5967 | −1.70169 | −0.850844 | − | 0.525418i | \(-0.823909\pi\) | ||||
−0.850844 | + | 0.525418i | \(0.823909\pi\) | |||||||
\(264\) | −5.23607 | −0.322258 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.763932 | 0.0468397 | ||||||||
\(267\) | −5.23607 | −0.320442 | ||||||||
\(268\) | −8.94427 | −0.546358 | ||||||||
\(269\) | −30.2705 | −1.84563 | −0.922813 | − | 0.385249i | \(-0.874116\pi\) | ||||
−0.922813 | + | 0.385249i | \(0.874116\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.41641 | −0.207532 | −0.103766 | − | 0.994602i | \(-0.533089\pi\) | ||||
−0.103766 | + | 0.994602i | \(0.533089\pi\) | |||||||
\(272\) | −5.61803 | −0.340643 | ||||||||
\(273\) | −2.61803 | −0.158451 | ||||||||
\(274\) | −1.85410 | −0.112010 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −4.85410 | −0.292183 | ||||||||
\(277\) | 30.0000 | 1.80253 | 0.901263 | − | 0.433273i | \(-0.142641\pi\) | ||||
0.901263 | + | 0.433273i | \(0.142641\pi\) | |||||||
\(278\) | 14.5623 | 0.873389 | ||||||||
\(279\) | 11.0000 | 0.658553 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.56231 | 0.152854 | 0.0764272 | − | 0.997075i | \(-0.475649\pi\) | ||||
0.0764272 | + | 0.997075i | \(0.475649\pi\) | |||||||
\(282\) | 27.4164 | 1.63262 | ||||||||
\(283\) | 11.2361 | 0.667915 | 0.333957 | − | 0.942588i | \(-0.391616\pi\) | ||||
0.333957 | + | 0.942588i | \(0.391616\pi\) | |||||||
\(284\) | 7.70820 | 0.457398 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5.23607 | −0.309615 | ||||||||
\(287\) | 2.18034 | 0.128701 | ||||||||
\(288\) | 3.85410 | 0.227105 | ||||||||
\(289\) | 14.5623 | 0.856606 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 36.2705 | 2.12621 | ||||||||
\(292\) | −14.5623 | −0.852194 | ||||||||
\(293\) | −7.41641 | −0.433271 | −0.216636 | − | 0.976253i | \(-0.569508\pi\) | ||||
−0.216636 | + | 0.976253i | \(0.569508\pi\) | |||||||
\(294\) | 17.9443 | 1.04653 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 8.94427 | 0.519875 | ||||||||
\(297\) | −4.47214 | −0.259500 | ||||||||
\(298\) | 5.41641 | 0.313764 | ||||||||
\(299\) | −4.85410 | −0.280720 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.14590 | 0.123688 | ||||||||
\(302\) | 17.7082 | 1.01899 | ||||||||
\(303\) | −10.8541 | −0.623552 | ||||||||
\(304\) | −2.00000 | −0.114708 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −21.6525 | −1.23779 | ||||||||
\(307\) | 24.0000 | 1.36975 | 0.684876 | − | 0.728659i | \(-0.259856\pi\) | ||||
0.684876 | + | 0.728659i | \(0.259856\pi\) | |||||||
\(308\) | −0.763932 | −0.0435291 | ||||||||
\(309\) | −50.8328 | −2.89178 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −14.4377 | −0.818687 | −0.409343 | − | 0.912380i | \(-0.634242\pi\) | ||||
−0.409343 | + | 0.912380i | \(0.634242\pi\) | |||||||
\(312\) | 6.85410 | 0.388037 | ||||||||
\(313\) | 17.2361 | 0.974240 | 0.487120 | − | 0.873335i | \(-0.338047\pi\) | ||||
0.487120 | + | 0.873335i | \(0.338047\pi\) | |||||||
\(314\) | 3.70820 | 0.209266 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −13.5623 | −0.762939 | ||||||||
\(317\) | −2.18034 | −0.122460 | −0.0612300 | − | 0.998124i | \(-0.519502\pi\) | ||||
−0.0612300 | + | 0.998124i | \(0.519502\pi\) | |||||||
\(318\) | 30.4164 | 1.70567 | ||||||||
\(319\) | −2.00000 | −0.111979 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 21.4164 | 1.19535 | ||||||||
\(322\) | −0.708204 | −0.0394667 | ||||||||
\(323\) | 11.2361 | 0.625192 | ||||||||
\(324\) | −5.70820 | −0.317122 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 19.4164 | 1.07538 | ||||||||
\(327\) | 19.4164 | 1.07373 | ||||||||
\(328\) | −5.70820 | −0.315183 | ||||||||
\(329\) | 4.00000 | 0.220527 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.1246 | −0.721394 | −0.360697 | − | 0.932683i | \(-0.617461\pi\) | ||||
−0.360697 | + | 0.932683i | \(0.617461\pi\) | |||||||
\(332\) | 2.94427 | 0.161588 | ||||||||
\(333\) | 34.4721 | 1.88906 | ||||||||
\(334\) | −0.381966 | −0.0209003 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.00000 | 0.0545545 | ||||||||
\(337\) | −6.38197 | −0.347648 | −0.173824 | − | 0.984777i | \(-0.555612\pi\) | ||||
−0.173824 | + | 0.984777i | \(0.555612\pi\) | |||||||
\(338\) | −6.14590 | −0.334293 | ||||||||
\(339\) | −18.5623 | −1.00817 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.70820 | 0.309117 | ||||||||
\(342\) | −7.70820 | −0.416812 | ||||||||
\(343\) | 5.29180 | 0.285730 | ||||||||
\(344\) | −5.61803 | −0.302904 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 20.5066 | 1.10244 | ||||||||
\(347\) | 6.00000 | 0.322097 | 0.161048 | − | 0.986947i | \(-0.448512\pi\) | ||||
0.161048 | + | 0.986947i | \(0.448512\pi\) | |||||||
\(348\) | 2.61803 | 0.140341 | ||||||||
\(349\) | 28.8328 | 1.54339 | 0.771693 | − | 0.635996i | \(-0.219410\pi\) | ||||
0.771693 | + | 0.635996i | \(0.219410\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.85410 | 0.312469 | ||||||||
\(352\) | 2.00000 | 0.106600 | ||||||||
\(353\) | 20.9443 | 1.11475 | 0.557376 | − | 0.830260i | \(-0.311808\pi\) | ||||
0.557376 | + | 0.830260i | \(0.311808\pi\) | |||||||
\(354\) | 10.0902 | 0.536286 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2.00000 | 0.106000 | ||||||||
\(357\) | −5.61803 | −0.297338 | ||||||||
\(358\) | 15.8541 | 0.837915 | ||||||||
\(359\) | −33.2705 | −1.75595 | −0.877975 | − | 0.478706i | \(-0.841106\pi\) | ||||
−0.877975 | + | 0.478706i | \(0.841106\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | −10.0000 | −0.525588 | ||||||||
\(363\) | 18.3262 | 0.961878 | ||||||||
\(364\) | 1.00000 | 0.0524142 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 10.8541 | 0.567353 | ||||||||
\(367\) | 5.12461 | 0.267503 | 0.133751 | − | 0.991015i | \(-0.457298\pi\) | ||||
0.133751 | + | 0.991015i | \(0.457298\pi\) | |||||||
\(368\) | 1.85410 | 0.0966517 | ||||||||
\(369\) | −22.0000 | −1.14527 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.43769 | 0.230394 | ||||||||
\(372\) | −7.47214 | −0.387412 | ||||||||
\(373\) | 18.2705 | 0.946011 | 0.473006 | − | 0.881059i | \(-0.343169\pi\) | ||||
0.473006 | + | 0.881059i | \(0.343169\pi\) | |||||||
\(374\) | −11.2361 | −0.581003 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −10.4721 | −0.540059 | ||||||||
\(377\) | 2.61803 | 0.134836 | ||||||||
\(378\) | 0.854102 | 0.0439303 | ||||||||
\(379\) | 26.0000 | 1.33553 | 0.667765 | − | 0.744372i | \(-0.267251\pi\) | ||||
0.667765 | + | 0.744372i | \(0.267251\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −56.8328 | −2.91163 | ||||||||
\(382\) | −10.2705 | −0.525485 | ||||||||
\(383\) | 1.14590 | 0.0585527 | 0.0292763 | − | 0.999571i | \(-0.490680\pi\) | ||||
0.0292763 | + | 0.999571i | \(0.490680\pi\) | |||||||
\(384\) | −2.61803 | −0.133601 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −17.5623 | −0.893898 | ||||||||
\(387\) | −21.6525 | −1.10066 | ||||||||
\(388\) | −13.8541 | −0.703335 | ||||||||
\(389\) | 32.8328 | 1.66469 | 0.832345 | − | 0.554258i | \(-0.186998\pi\) | ||||
0.832345 | + | 0.554258i | \(0.186998\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.4164 | −0.526780 | ||||||||
\(392\) | −6.85410 | −0.346184 | ||||||||
\(393\) | 14.1803 | 0.715304 | ||||||||
\(394\) | −11.6180 | −0.585308 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 7.70820 | 0.387352 | ||||||||
\(397\) | 31.0344 | 1.55757 | 0.778787 | − | 0.627288i | \(-0.215835\pi\) | ||||
0.778787 | + | 0.627288i | \(0.215835\pi\) | |||||||
\(398\) | −21.1246 | −1.05888 | ||||||||
\(399\) | −2.00000 | −0.100125 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −24.9787 | −1.24738 | −0.623689 | − | 0.781673i | \(-0.714367\pi\) | ||||
−0.623689 | + | 0.781673i | \(0.714367\pi\) | |||||||
\(402\) | 23.4164 | 1.16790 | ||||||||
\(403\) | −7.47214 | −0.372214 | ||||||||
\(404\) | 4.14590 | 0.206266 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.381966 | 0.0189567 | ||||||||
\(407\) | 17.8885 | 0.886702 | ||||||||
\(408\) | 14.7082 | 0.728165 | ||||||||
\(409\) | 33.1246 | 1.63791 | 0.818953 | − | 0.573860i | \(-0.194555\pi\) | ||||
0.818953 | + | 0.573860i | \(0.194555\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.85410 | 0.239435 | ||||||||
\(412\) | 19.4164 | 0.956578 | ||||||||
\(413\) | 1.47214 | 0.0724391 | ||||||||
\(414\) | 7.14590 | 0.351202 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.61803 | −0.128360 | ||||||||
\(417\) | −38.1246 | −1.86697 | ||||||||
\(418\) | −4.00000 | −0.195646 | ||||||||
\(419\) | −15.1459 | −0.739926 | −0.369963 | − | 0.929047i | \(-0.620630\pi\) | ||||
−0.369963 | + | 0.929047i | \(0.620630\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.0000 | −0.487370 | −0.243685 | − | 0.969854i | \(-0.578356\pi\) | ||||
−0.243685 | + | 0.969854i | \(0.578356\pi\) | |||||||
\(422\) | 15.4164 | 0.750459 | ||||||||
\(423\) | −40.3607 | −1.96240 | ||||||||
\(424\) | −11.6180 | −0.564222 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −20.1803 | −0.977741 | ||||||||
\(427\) | 1.58359 | 0.0766354 | ||||||||
\(428\) | −8.18034 | −0.395412 | ||||||||
\(429\) | 13.7082 | 0.661838 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.58359 | −0.317120 | −0.158560 | − | 0.987349i | \(-0.550685\pi\) | ||||
−0.158560 | + | 0.987349i | \(0.550685\pi\) | |||||||
\(432\) | −2.23607 | −0.107583 | ||||||||
\(433\) | 7.52786 | 0.361766 | 0.180883 | − | 0.983505i | \(-0.442104\pi\) | ||||
0.180883 | + | 0.983505i | \(0.442104\pi\) | |||||||
\(434\) | −1.09017 | −0.0523298 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7.41641 | −0.355182 | ||||||||
\(437\) | −3.70820 | −0.177387 | ||||||||
\(438\) | 38.1246 | 1.82166 | ||||||||
\(439\) | 3.12461 | 0.149130 | 0.0745648 | − | 0.997216i | \(-0.476243\pi\) | ||||
0.0745648 | + | 0.997216i | \(0.476243\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −26.4164 | −1.25792 | ||||||||
\(442\) | 14.7082 | 0.699598 | ||||||||
\(443\) | 13.0902 | 0.621933 | 0.310966 | − | 0.950421i | \(-0.399347\pi\) | ||||
0.310966 | + | 0.950421i | \(0.399347\pi\) | |||||||
\(444\) | −23.4164 | −1.11129 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 6.43769 | 0.304834 | ||||||||
\(447\) | −14.1803 | −0.670707 | ||||||||
\(448\) | −0.381966 | −0.0180462 | ||||||||
\(449\) | −31.4164 | −1.48263 | −0.741316 | − | 0.671156i | \(-0.765798\pi\) | ||||
−0.741316 | + | 0.671156i | \(0.765798\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.4164 | −0.537578 | ||||||||
\(452\) | 7.09017 | 0.333494 | ||||||||
\(453\) | −46.3607 | −2.17821 | ||||||||
\(454\) | −7.52786 | −0.353300 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 5.23607 | 0.245201 | ||||||||
\(457\) | 27.7082 | 1.29614 | 0.648068 | − | 0.761583i | \(-0.275577\pi\) | ||||
0.648068 | + | 0.761583i | \(0.275577\pi\) | |||||||
\(458\) | −14.8541 | −0.694087 | ||||||||
\(459\) | 12.5623 | 0.586358 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −30.8541 | −1.43702 | −0.718509 | − | 0.695517i | \(-0.755175\pi\) | ||||
−0.718509 | + | 0.695517i | \(0.755175\pi\) | |||||||
\(462\) | 2.00000 | 0.0930484 | ||||||||
\(463\) | −17.8885 | −0.831351 | −0.415676 | − | 0.909513i | \(-0.636455\pi\) | ||||
−0.415676 | + | 0.909513i | \(0.636455\pi\) | |||||||
\(464\) | −1.00000 | −0.0464238 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.76393 | 0.313333 | ||||||||
\(467\) | −10.2016 | −0.472075 | −0.236037 | − | 0.971744i | \(-0.575849\pi\) | ||||
−0.236037 | + | 0.971744i | \(0.575849\pi\) | |||||||
\(468\) | −10.0902 | −0.466418 | ||||||||
\(469\) | 3.41641 | 0.157755 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.70820 | −0.447330 | ||||||||
\(472\) | −3.85410 | −0.177399 | ||||||||
\(473\) | −11.2361 | −0.516635 | ||||||||
\(474\) | 35.5066 | 1.63087 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2.14590 | 0.0983571 | ||||||||
\(477\) | −44.7771 | −2.05020 | ||||||||
\(478\) | −7.70820 | −0.352565 | ||||||||
\(479\) | 27.9787 | 1.27838 | 0.639190 | − | 0.769049i | \(-0.279270\pi\) | ||||
0.639190 | + | 0.769049i | \(0.279270\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −23.4164 | −1.06770 | ||||||||
\(482\) | −2.14590 | −0.0977430 | ||||||||
\(483\) | 1.85410 | 0.0843646 | ||||||||
\(484\) | −7.00000 | −0.318182 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 21.6525 | 0.982176 | ||||||||
\(487\) | −18.4377 | −0.835492 | −0.417746 | − | 0.908564i | \(-0.637180\pi\) | ||||
−0.417746 | + | 0.908564i | \(0.637180\pi\) | |||||||
\(488\) | −4.14590 | −0.187676 | ||||||||
\(489\) | −50.8328 | −2.29874 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.7082 | −0.889419 | −0.444709 | − | 0.895675i | \(-0.646693\pi\) | ||||
−0.444709 | + | 0.895675i | \(0.646693\pi\) | |||||||
\(492\) | 14.9443 | 0.673740 | ||||||||
\(493\) | 5.61803 | 0.253024 | ||||||||
\(494\) | 5.23607 | 0.235582 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.85410 | 0.128153 | ||||||||
\(497\) | −2.94427 | −0.132069 | ||||||||
\(498\) | −7.70820 | −0.345413 | ||||||||
\(499\) | 8.43769 | 0.377723 | 0.188862 | − | 0.982004i | \(-0.439520\pi\) | ||||
0.188862 | + | 0.982004i | \(0.439520\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.00000 | 0.0446767 | ||||||||
\(502\) | 11.1246 | 0.496516 | ||||||||
\(503\) | −15.0557 | −0.671302 | −0.335651 | − | 0.941986i | \(-0.608956\pi\) | ||||
−0.335651 | + | 0.941986i | \(0.608956\pi\) | |||||||
\(504\) | −1.47214 | −0.0655741 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.70820 | 0.164850 | ||||||||
\(507\) | 16.0902 | 0.714590 | ||||||||
\(508\) | 21.7082 | 0.963146 | ||||||||
\(509\) | 19.1246 | 0.847684 | 0.423842 | − | 0.905736i | \(-0.360681\pi\) | ||||
0.423842 | + | 0.905736i | \(0.360681\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.56231 | 0.246062 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 4.47214 | 0.197450 | ||||||||
\(514\) | −15.7082 | −0.692859 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 14.7082 | 0.647493 | ||||||||
\(517\) | −20.9443 | −0.921128 | ||||||||
\(518\) | −3.41641 | −0.150108 | ||||||||
\(519\) | −53.6869 | −2.35659 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 37.3951 | 1.63831 | 0.819155 | − | 0.573572i | \(-0.194443\pi\) | ||||
0.819155 | + | 0.573572i | \(0.194443\pi\) | |||||||
\(522\) | −3.85410 | −0.168689 | ||||||||
\(523\) | −29.1246 | −1.27353 | −0.636765 | − | 0.771058i | \(-0.719728\pi\) | ||||
−0.636765 | + | 0.771058i | \(0.719728\pi\) | |||||||
\(524\) | −5.41641 | −0.236617 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −27.5967 | −1.20328 | ||||||||
\(527\) | −16.0344 | −0.698471 | ||||||||
\(528\) | −5.23607 | −0.227871 | ||||||||
\(529\) | −19.5623 | −0.850535 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −14.8541 | −0.644613 | ||||||||
\(532\) | 0.763932 | 0.0331207 | ||||||||
\(533\) | 14.9443 | 0.647308 | ||||||||
\(534\) | −5.23607 | −0.226587 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −8.94427 | −0.386334 | ||||||||
\(537\) | −41.5066 | −1.79114 | ||||||||
\(538\) | −30.2705 | −1.30505 | ||||||||
\(539\) | −13.7082 | −0.590454 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.43769 | −0.319771 | −0.159886 | − | 0.987136i | \(-0.551113\pi\) | ||||
−0.159886 | + | 0.987136i | \(0.551113\pi\) | |||||||
\(542\) | −3.41641 | −0.146747 | ||||||||
\(543\) | 26.1803 | 1.12351 | ||||||||
\(544\) | −5.61803 | −0.240871 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −2.61803 | −0.112042 | ||||||||
\(547\) | −38.8328 | −1.66037 | −0.830186 | − | 0.557487i | \(-0.811766\pi\) | ||||
−0.830186 | + | 0.557487i | \(0.811766\pi\) | |||||||
\(548\) | −1.85410 | −0.0792033 | ||||||||
\(549\) | −15.9787 | −0.681955 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.00000 | 0.0852029 | ||||||||
\(552\) | −4.85410 | −0.206604 | ||||||||
\(553\) | 5.18034 | 0.220290 | ||||||||
\(554\) | 30.0000 | 1.27458 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 14.5623 | 0.617579 | ||||||||
\(557\) | −16.7984 | −0.711770 | −0.355885 | − | 0.934530i | \(-0.615821\pi\) | ||||
−0.355885 | + | 0.934530i | \(0.615821\pi\) | |||||||
\(558\) | 11.0000 | 0.465667 | ||||||||
\(559\) | 14.7082 | 0.622091 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 29.4164 | 1.24196 | ||||||||
\(562\) | 2.56231 | 0.108084 | ||||||||
\(563\) | −17.6738 | −0.744860 | −0.372430 | − | 0.928060i | \(-0.621475\pi\) | ||||
−0.372430 | + | 0.928060i | \(0.621475\pi\) | |||||||
\(564\) | 27.4164 | 1.15444 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 11.2361 | 0.472287 | ||||||||
\(567\) | 2.18034 | 0.0915657 | ||||||||
\(568\) | 7.70820 | 0.323429 | ||||||||
\(569\) | 12.0000 | 0.503066 | 0.251533 | − | 0.967849i | \(-0.419065\pi\) | ||||
0.251533 | + | 0.967849i | \(0.419065\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.145898 | −0.00610564 | −0.00305282 | − | 0.999995i | \(-0.500972\pi\) | ||||
−0.00305282 | + | 0.999995i | \(0.500972\pi\) | |||||||
\(572\) | −5.23607 | −0.218931 | ||||||||
\(573\) | 26.8885 | 1.12329 | ||||||||
\(574\) | 2.18034 | 0.0910056 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 3.85410 | 0.160588 | ||||||||
\(577\) | −1.03444 | −0.0430644 | −0.0215322 | − | 0.999768i | \(-0.506854\pi\) | ||||
−0.0215322 | + | 0.999768i | \(0.506854\pi\) | |||||||
\(578\) | 14.5623 | 0.605712 | ||||||||
\(579\) | 45.9787 | 1.91081 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.12461 | −0.0466568 | ||||||||
\(582\) | 36.2705 | 1.50346 | ||||||||
\(583\) | −23.2361 | −0.962340 | ||||||||
\(584\) | −14.5623 | −0.602593 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.41641 | −0.306369 | ||||||||
\(587\) | 18.6525 | 0.769870 | 0.384935 | − | 0.922944i | \(-0.374224\pi\) | ||||
0.384935 | + | 0.922944i | \(0.374224\pi\) | |||||||
\(588\) | 17.9443 | 0.740009 | ||||||||
\(589\) | −5.70820 | −0.235202 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 30.4164 | 1.25116 | ||||||||
\(592\) | 8.94427 | 0.367607 | ||||||||
\(593\) | 19.3050 | 0.792759 | 0.396380 | − | 0.918087i | \(-0.370266\pi\) | ||||
0.396380 | + | 0.918087i | \(0.370266\pi\) | |||||||
\(594\) | −4.47214 | −0.183494 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5.41641 | 0.221865 | ||||||||
\(597\) | 55.3050 | 2.26348 | ||||||||
\(598\) | −4.85410 | −0.198499 | ||||||||
\(599\) | 3.43769 | 0.140460 | 0.0702302 | − | 0.997531i | \(-0.477627\pi\) | ||||
0.0702302 | + | 0.997531i | \(0.477627\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.70820 | −0.314424 | −0.157212 | − | 0.987565i | \(-0.550251\pi\) | ||||
−0.157212 | + | 0.987565i | \(0.550251\pi\) | |||||||
\(602\) | 2.14590 | 0.0874603 | ||||||||
\(603\) | −34.4721 | −1.40381 | ||||||||
\(604\) | 17.7082 | 0.720537 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −10.8541 | −0.440918 | ||||||||
\(607\) | −5.23607 | −0.212525 | −0.106263 | − | 0.994338i | \(-0.533888\pi\) | ||||
−0.106263 | + | 0.994338i | \(0.533888\pi\) | |||||||
\(608\) | −2.00000 | −0.0811107 | ||||||||
\(609\) | −1.00000 | −0.0405220 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 27.4164 | 1.10915 | ||||||||
\(612\) | −21.6525 | −0.875249 | ||||||||
\(613\) | 28.7426 | 1.16090 | 0.580452 | − | 0.814294i | \(-0.302876\pi\) | ||||
0.580452 | + | 0.814294i | \(0.302876\pi\) | |||||||
\(614\) | 24.0000 | 0.968561 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.763932 | −0.0307797 | ||||||||
\(617\) | −30.3820 | −1.22313 | −0.611566 | − | 0.791193i | \(-0.709460\pi\) | ||||
−0.611566 | + | 0.791193i | \(0.709460\pi\) | |||||||
\(618\) | −50.8328 | −2.04480 | ||||||||
\(619\) | 19.4164 | 0.780411 | 0.390206 | − | 0.920728i | \(-0.372404\pi\) | ||||
0.390206 | + | 0.920728i | \(0.372404\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.14590 | −0.166369 | ||||||||
\(622\) | −14.4377 | −0.578899 | ||||||||
\(623\) | −0.763932 | −0.0306063 | ||||||||
\(624\) | 6.85410 | 0.274384 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 17.2361 | 0.688892 | ||||||||
\(627\) | 10.4721 | 0.418217 | ||||||||
\(628\) | 3.70820 | 0.147973 | ||||||||
\(629\) | −50.2492 | −2.00357 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.8328 | 0.749723 | 0.374861 | − | 0.927081i | \(-0.377690\pi\) | ||||
0.374861 | + | 0.927081i | \(0.377690\pi\) | |||||||
\(632\) | −13.5623 | −0.539480 | ||||||||
\(633\) | −40.3607 | −1.60419 | ||||||||
\(634\) | −2.18034 | −0.0865924 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 30.4164 | 1.20609 | ||||||||
\(637\) | 17.9443 | 0.710978 | ||||||||
\(638\) | −2.00000 | −0.0791808 | ||||||||
\(639\) | 29.7082 | 1.17524 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13.7082 | 0.541442 | 0.270721 | − | 0.962658i | \(-0.412738\pi\) | ||||
0.270721 | + | 0.962658i | \(0.412738\pi\) | |||||||
\(642\) | 21.4164 | 0.845238 | ||||||||
\(643\) | 43.4164 | 1.71218 | 0.856088 | − | 0.516830i | \(-0.172888\pi\) | ||||
0.856088 | + | 0.516830i | \(0.172888\pi\) | |||||||
\(644\) | −0.708204 | −0.0279071 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 11.2361 | 0.442077 | ||||||||
\(647\) | −22.4721 | −0.883471 | −0.441735 | − | 0.897145i | \(-0.645637\pi\) | ||||
−0.441735 | + | 0.897145i | \(0.645637\pi\) | |||||||
\(648\) | −5.70820 | −0.224239 | ||||||||
\(649\) | −7.70820 | −0.302573 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.85410 | 0.111861 | ||||||||
\(652\) | 19.4164 | 0.760405 | ||||||||
\(653\) | 25.3050 | 0.990259 | 0.495130 | − | 0.868819i | \(-0.335121\pi\) | ||||
0.495130 | + | 0.868819i | \(0.335121\pi\) | |||||||
\(654\) | 19.4164 | 0.759242 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −5.70820 | −0.222868 | ||||||||
\(657\) | −56.1246 | −2.18963 | ||||||||
\(658\) | 4.00000 | 0.155936 | ||||||||
\(659\) | −26.5410 | −1.03389 | −0.516946 | − | 0.856018i | \(-0.672931\pi\) | ||||
−0.516946 | + | 0.856018i | \(0.672931\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24.8328 | −0.965885 | −0.482942 | − | 0.875652i | \(-0.660432\pi\) | ||||
−0.482942 | + | 0.875652i | \(0.660432\pi\) | |||||||
\(662\) | −13.1246 | −0.510103 | ||||||||
\(663\) | −38.5066 | −1.49547 | ||||||||
\(664\) | 2.94427 | 0.114260 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 34.4721 | 1.33577 | ||||||||
\(667\) | −1.85410 | −0.0717911 | ||||||||
\(668\) | −0.381966 | −0.0147787 | ||||||||
\(669\) | −16.8541 | −0.651617 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.29180 | −0.320101 | ||||||||
\(672\) | 1.00000 | 0.0385758 | ||||||||
\(673\) | −9.05573 | −0.349073 | −0.174536 | − | 0.984651i | \(-0.555843\pi\) | ||||
−0.174536 | + | 0.984651i | \(0.555843\pi\) | |||||||
\(674\) | −6.38197 | −0.245824 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.14590 | −0.236381 | ||||||||
\(677\) | −15.0557 | −0.578639 | −0.289319 | − | 0.957233i | \(-0.593429\pi\) | ||||
−0.289319 | + | 0.957233i | \(0.593429\pi\) | |||||||
\(678\) | −18.5623 | −0.712881 | ||||||||
\(679\) | 5.29180 | 0.203080 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 19.7082 | 0.755220 | ||||||||
\(682\) | 5.70820 | 0.218578 | ||||||||
\(683\) | −47.7771 | −1.82814 | −0.914070 | − | 0.405557i | \(-0.867078\pi\) | ||||
−0.914070 | + | 0.405557i | \(0.867078\pi\) | |||||||
\(684\) | −7.70820 | −0.294731 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 5.29180 | 0.202042 | ||||||||
\(687\) | 38.8885 | 1.48369 | ||||||||
\(688\) | −5.61803 | −0.214186 | ||||||||
\(689\) | 30.4164 | 1.15877 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.56231 | 0.249642 | 0.124821 | − | 0.992179i | \(-0.460164\pi\) | ||||
0.124821 | + | 0.992179i | \(0.460164\pi\) | |||||||
\(692\) | 20.5066 | 0.779543 | ||||||||
\(693\) | −2.94427 | −0.111844 | ||||||||
\(694\) | 6.00000 | 0.227757 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 2.61803 | 0.0992363 | ||||||||
\(697\) | 32.0689 | 1.21470 | ||||||||
\(698\) | 28.8328 | 1.09134 | ||||||||
\(699\) | −17.7082 | −0.669786 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 31.1246 | 1.17556 | 0.587780 | − | 0.809021i | \(-0.300002\pi\) | ||||
0.587780 | + | 0.809021i | \(0.300002\pi\) | |||||||
\(702\) | 5.85410 | 0.220949 | ||||||||
\(703\) | −17.8885 | −0.674679 | ||||||||
\(704\) | 2.00000 | 0.0753778 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 20.9443 | 0.788248 | ||||||||
\(707\) | −1.58359 | −0.0595571 | ||||||||
\(708\) | 10.0902 | 0.379212 | ||||||||
\(709\) | 25.7082 | 0.965492 | 0.482746 | − | 0.875760i | \(-0.339639\pi\) | ||||
0.482746 | + | 0.875760i | \(0.339639\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −52.2705 | −1.96030 | ||||||||
\(712\) | 2.00000 | 0.0749532 | ||||||||
\(713\) | 5.29180 | 0.198179 | ||||||||
\(714\) | −5.61803 | −0.210250 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 15.8541 | 0.592496 | ||||||||
\(717\) | 20.1803 | 0.753649 | ||||||||
\(718\) | −33.2705 | −1.24164 | ||||||||
\(719\) | 21.7082 | 0.809579 | 0.404790 | − | 0.914410i | \(-0.367345\pi\) | ||||
0.404790 | + | 0.914410i | \(0.367345\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.41641 | −0.276201 | ||||||||
\(722\) | −15.0000 | −0.558242 | ||||||||
\(723\) | 5.61803 | 0.208937 | ||||||||
\(724\) | −10.0000 | −0.371647 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 18.3262 | 0.680150 | ||||||||
\(727\) | 15.0557 | 0.558386 | 0.279193 | − | 0.960235i | \(-0.409933\pi\) | ||||
0.279193 | + | 0.960235i | \(0.409933\pi\) | |||||||
\(728\) | 1.00000 | 0.0370625 | ||||||||
\(729\) | −39.5623 | −1.46527 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 31.5623 | 1.16737 | ||||||||
\(732\) | 10.8541 | 0.401179 | ||||||||
\(733\) | −12.0000 | −0.443230 | −0.221615 | − | 0.975134i | \(-0.571133\pi\) | ||||
−0.221615 | + | 0.975134i | \(0.571133\pi\) | |||||||
\(734\) | 5.12461 | 0.189153 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.85410 | 0.0683431 | ||||||||
\(737\) | −17.8885 | −0.658933 | ||||||||
\(738\) | −22.0000 | −0.809831 | ||||||||
\(739\) | 41.7082 | 1.53426 | 0.767131 | − | 0.641491i | \(-0.221684\pi\) | ||||
0.767131 | + | 0.641491i | \(0.221684\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −13.7082 | −0.503583 | ||||||||
\(742\) | 4.43769 | 0.162913 | ||||||||
\(743\) | −1.41641 | −0.0519630 | −0.0259815 | − | 0.999662i | \(-0.508271\pi\) | ||||
−0.0259815 | + | 0.999662i | \(0.508271\pi\) | |||||||
\(744\) | −7.47214 | −0.273942 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 18.2705 | 0.668931 | ||||||||
\(747\) | 11.3475 | 0.415184 | ||||||||
\(748\) | −11.2361 | −0.410831 | ||||||||
\(749\) | 3.12461 | 0.114171 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.00000 | −0.145962 | −0.0729810 | − | 0.997333i | \(-0.523251\pi\) | ||||
−0.0729810 | + | 0.997333i | \(0.523251\pi\) | |||||||
\(752\) | −10.4721 | −0.381880 | ||||||||
\(753\) | −29.1246 | −1.06136 | ||||||||
\(754\) | 2.61803 | 0.0953432 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.854102 | 0.0310634 | ||||||||
\(757\) | 26.0689 | 0.947490 | 0.473745 | − | 0.880662i | \(-0.342902\pi\) | ||||
0.473745 | + | 0.880662i | \(0.342902\pi\) | |||||||
\(758\) | 26.0000 | 0.944363 | ||||||||
\(759\) | −9.70820 | −0.352385 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.14590 | −0.114039 | −0.0570194 | − | 0.998373i | \(-0.518160\pi\) | ||||
−0.0570194 | + | 0.998373i | \(0.518160\pi\) | |||||||
\(762\) | −56.8328 | −2.05884 | ||||||||
\(763\) | 2.83282 | 0.102555 | ||||||||
\(764\) | −10.2705 | −0.371574 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.14590 | 0.0414030 | ||||||||
\(767\) | 10.0902 | 0.364335 | ||||||||
\(768\) | −2.61803 | −0.0944702 | ||||||||
\(769\) | −45.4164 | −1.63776 | −0.818879 | − | 0.573967i | \(-0.805404\pi\) | ||||
−0.818879 | + | 0.573967i | \(0.805404\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 41.1246 | 1.48107 | ||||||||
\(772\) | −17.5623 | −0.632081 | ||||||||
\(773\) | −11.2361 | −0.404133 | −0.202067 | − | 0.979372i | \(-0.564766\pi\) | ||||
−0.202067 | + | 0.979372i | \(0.564766\pi\) | |||||||
\(774\) | −21.6525 | −0.778282 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −13.8541 | −0.497333 | ||||||||
\(777\) | 8.94427 | 0.320874 | ||||||||
\(778\) | 32.8328 | 1.17711 | ||||||||
\(779\) | 11.4164 | 0.409035 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.4164 | 0.551642 | ||||||||
\(782\) | −10.4164 | −0.372490 | ||||||||
\(783\) | 2.23607 | 0.0799106 | ||||||||
\(784\) | −6.85410 | −0.244789 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 14.1803 | 0.505796 | ||||||||
\(787\) | −29.7771 | −1.06144 | −0.530719 | − | 0.847548i | \(-0.678078\pi\) | ||||
−0.530719 | + | 0.847548i | \(0.678078\pi\) | |||||||
\(788\) | −11.6180 | −0.413875 | ||||||||
\(789\) | 72.2492 | 2.57214 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.70820 | −0.0962926 | ||||||||
\(792\) | 7.70820 | 0.273899 | ||||||||
\(793\) | 10.8541 | 0.385440 | ||||||||
\(794\) | 31.0344 | 1.10137 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −21.1246 | −0.748742 | ||||||||
\(797\) | 30.7639 | 1.08971 | 0.544857 | − | 0.838529i | \(-0.316584\pi\) | ||||
0.544857 | + | 0.838529i | \(0.316584\pi\) | |||||||
\(798\) | −2.00000 | −0.0707992 | ||||||||
\(799\) | 58.8328 | 2.08136 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.70820 | 0.272356 | ||||||||
\(802\) | −24.9787 | −0.882029 | ||||||||
\(803\) | −29.1246 | −1.02779 | ||||||||
\(804\) | 23.4164 | 0.825833 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −7.47214 | −0.263195 | ||||||||
\(807\) | 79.2492 | 2.78970 | ||||||||
\(808\) | 4.14590 | 0.145852 | ||||||||
\(809\) | −12.5836 | −0.442416 | −0.221208 | − | 0.975227i | \(-0.571000\pi\) | ||||
−0.221208 | + | 0.975227i | \(0.571000\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −25.3951 | −0.891743 | −0.445872 | − | 0.895097i | \(-0.647106\pi\) | ||||
−0.445872 | + | 0.895097i | \(0.647106\pi\) | |||||||
\(812\) | 0.381966 | 0.0134044 | ||||||||
\(813\) | 8.94427 | 0.313689 | ||||||||
\(814\) | 17.8885 | 0.626993 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 14.7082 | 0.514890 | ||||||||
\(817\) | 11.2361 | 0.393100 | ||||||||
\(818\) | 33.1246 | 1.15817 | ||||||||
\(819\) | 3.85410 | 0.134673 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8.00000 | −0.279202 | −0.139601 | − | 0.990208i | \(-0.544582\pi\) | ||||
−0.139601 | + | 0.990208i | \(0.544582\pi\) | |||||||
\(822\) | 4.85410 | 0.169306 | ||||||||
\(823\) | −0.763932 | −0.0266290 | −0.0133145 | − | 0.999911i | \(-0.504238\pi\) | ||||
−0.0133145 | + | 0.999911i | \(0.504238\pi\) | |||||||
\(824\) | 19.4164 | 0.676403 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.47214 | 0.0512222 | ||||||||
\(827\) | −49.7984 | −1.73166 | −0.865830 | − | 0.500339i | \(-0.833209\pi\) | ||||
−0.865830 | + | 0.500339i | \(0.833209\pi\) | |||||||
\(828\) | 7.14590 | 0.248337 | ||||||||
\(829\) | −34.2705 | −1.19026 | −0.595132 | − | 0.803628i | \(-0.702900\pi\) | ||||
−0.595132 | + | 0.803628i | \(0.702900\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −78.5410 | −2.72456 | ||||||||
\(832\) | −2.61803 | −0.0907640 | ||||||||
\(833\) | 38.5066 | 1.33417 | ||||||||
\(834\) | −38.1246 | −1.32015 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −4.00000 | −0.138343 | ||||||||
\(837\) | −6.38197 | −0.220593 | ||||||||
\(838\) | −15.1459 | −0.523206 | ||||||||
\(839\) | 14.8328 | 0.512086 | 0.256043 | − | 0.966665i | \(-0.417581\pi\) | ||||
0.256043 | + | 0.966665i | \(0.417581\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −10.0000 | −0.344623 | ||||||||
\(843\) | −6.70820 | −0.231043 | ||||||||
\(844\) | 15.4164 | 0.530655 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −40.3607 | −1.38763 | ||||||||
\(847\) | 2.67376 | 0.0918716 | ||||||||
\(848\) | −11.6180 | −0.398965 | ||||||||
\(849\) | −29.4164 | −1.00957 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 16.5836 | 0.568478 | ||||||||
\(852\) | −20.1803 | −0.691367 | ||||||||
\(853\) | −44.8328 | −1.53505 | −0.767523 | − | 0.641021i | \(-0.778511\pi\) | ||||
−0.767523 | + | 0.641021i | \(0.778511\pi\) | |||||||
\(854\) | 1.58359 | 0.0541894 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8.18034 | −0.279598 | ||||||||
\(857\) | −44.1803 | −1.50917 | −0.754586 | − | 0.656201i | \(-0.772162\pi\) | ||||
−0.754586 | + | 0.656201i | \(0.772162\pi\) | |||||||
\(858\) | 13.7082 | 0.467990 | ||||||||
\(859\) | 14.2918 | 0.487630 | 0.243815 | − | 0.969822i | \(-0.421601\pi\) | ||||
0.243815 | + | 0.969822i | \(0.421601\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.70820 | −0.194535 | ||||||||
\(862\) | −6.58359 | −0.224238 | ||||||||
\(863\) | 33.9230 | 1.15475 | 0.577376 | − | 0.816478i | \(-0.304077\pi\) | ||||
0.577376 | + | 0.816478i | \(0.304077\pi\) | |||||||
\(864\) | −2.23607 | −0.0760726 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 7.52786 | 0.255807 | ||||||||
\(867\) | −38.1246 | −1.29478 | ||||||||
\(868\) | −1.09017 | −0.0370028 | ||||||||
\(869\) | −27.1246 | −0.920139 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 23.4164 | 0.793435 | ||||||||
\(872\) | −7.41641 | −0.251151 | ||||||||
\(873\) | −53.3951 | −1.80715 | ||||||||
\(874\) | −3.70820 | −0.125432 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 38.1246 | 1.28811 | ||||||||
\(877\) | 8.72949 | 0.294774 | 0.147387 | − | 0.989079i | \(-0.452914\pi\) | ||||
0.147387 | + | 0.989079i | \(0.452914\pi\) | |||||||
\(878\) | 3.12461 | 0.105451 | ||||||||
\(879\) | 19.4164 | 0.654899 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −41.4164 | −1.39535 | −0.697677 | − | 0.716412i | \(-0.745783\pi\) | ||||
−0.697677 | + | 0.716412i | \(0.745783\pi\) | |||||||
\(882\) | −26.4164 | −0.889487 | ||||||||
\(883\) | 20.2918 | 0.682873 | 0.341437 | − | 0.939905i | \(-0.389087\pi\) | ||||
0.341437 | + | 0.939905i | \(0.389087\pi\) | |||||||
\(884\) | 14.7082 | 0.494690 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 13.0902 | 0.439773 | ||||||||
\(887\) | −24.0000 | −0.805841 | −0.402921 | − | 0.915235i | \(-0.632005\pi\) | ||||
−0.402921 | + | 0.915235i | \(0.632005\pi\) | |||||||
\(888\) | −23.4164 | −0.785803 | ||||||||
\(889\) | −8.29180 | −0.278098 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −11.4164 | −0.382464 | ||||||||
\(892\) | 6.43769 | 0.215550 | ||||||||
\(893\) | 20.9443 | 0.700873 | ||||||||
\(894\) | −14.1803 | −0.474262 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.381966 | −0.0127606 | ||||||||
\(897\) | 12.7082 | 0.424315 | ||||||||
\(898\) | −31.4164 | −1.04838 | ||||||||
\(899\) | −2.85410 | −0.0951896 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 65.2705 | 2.17448 | ||||||||
\(902\) | −11.4164 | −0.380125 | ||||||||
\(903\) | −5.61803 | −0.186956 | ||||||||
\(904\) | 7.09017 | 0.235816 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −46.3607 | −1.54023 | ||||||||
\(907\) | −34.7426 | −1.15361 | −0.576805 | − | 0.816882i | \(-0.695701\pi\) | ||||
−0.576805 | + | 0.816882i | \(0.695701\pi\) | |||||||
\(908\) | −7.52786 | −0.249821 | ||||||||
\(909\) | 15.9787 | 0.529980 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.14590 | 0.203623 | 0.101811 | − | 0.994804i | \(-0.467536\pi\) | ||||
0.101811 | + | 0.994804i | \(0.467536\pi\) | |||||||
\(912\) | 5.23607 | 0.173384 | ||||||||
\(913\) | 5.88854 | 0.194882 | ||||||||
\(914\) | 27.7082 | 0.916506 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −14.8541 | −0.490793 | ||||||||
\(917\) | 2.06888 | 0.0683206 | ||||||||
\(918\) | 12.5623 | 0.414618 | ||||||||
\(919\) | 14.5410 | 0.479664 | 0.239832 | − | 0.970814i | \(-0.422908\pi\) | ||||
0.239832 | + | 0.970814i | \(0.422908\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −62.8328 | −2.07041 | ||||||||
\(922\) | −30.8541 | −1.01613 | ||||||||
\(923\) | −20.1803 | −0.664244 | ||||||||
\(924\) | 2.00000 | 0.0657952 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −17.8885 | −0.587854 | ||||||||
\(927\) | 74.8328 | 2.45783 | ||||||||
\(928\) | −1.00000 | −0.0328266 | ||||||||
\(929\) | 40.8541 | 1.34038 | 0.670190 | − | 0.742190i | \(-0.266213\pi\) | ||||
0.670190 | + | 0.742190i | \(0.266213\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13.7082 | 0.449268 | ||||||||
\(932\) | 6.76393 | 0.221560 | ||||||||
\(933\) | 37.7984 | 1.23746 | ||||||||
\(934\) | −10.2016 | −0.333807 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −10.0902 | −0.329808 | ||||||||
\(937\) | 14.0689 | 0.459610 | 0.229805 | − | 0.973237i | \(-0.426191\pi\) | ||||
0.229805 | + | 0.973237i | \(0.426191\pi\) | |||||||
\(938\) | 3.41641 | 0.111550 | ||||||||
\(939\) | −45.1246 | −1.47259 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.29180 | −0.270305 | −0.135152 | − | 0.990825i | \(-0.543152\pi\) | ||||
−0.135152 | + | 0.990825i | \(0.543152\pi\) | |||||||
\(942\) | −9.70820 | −0.316310 | ||||||||
\(943\) | −10.5836 | −0.344649 | ||||||||
\(944\) | −3.85410 | −0.125440 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −11.2361 | −0.365316 | ||||||||
\(947\) | 9.15905 | 0.297629 | 0.148815 | − | 0.988865i | \(-0.452454\pi\) | ||||
0.148815 | + | 0.988865i | \(0.452454\pi\) | |||||||
\(948\) | 35.5066 | 1.15320 | ||||||||
\(949\) | 38.1246 | 1.23758 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.70820 | 0.185101 | ||||||||
\(952\) | 2.14590 | 0.0695490 | ||||||||
\(953\) | −50.8328 | −1.64664 | −0.823318 | − | 0.567580i | \(-0.807880\pi\) | ||||
−0.823318 | + | 0.567580i | \(0.807880\pi\) | |||||||
\(954\) | −44.7771 | −1.44971 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −7.70820 | −0.249301 | ||||||||
\(957\) | 5.23607 | 0.169258 | ||||||||
\(958\) | 27.9787 | 0.903951 | ||||||||
\(959\) | 0.708204 | 0.0228691 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.8541 | −0.737229 | ||||||||
\(962\) | −23.4164 | −0.754975 | ||||||||
\(963\) | −31.5279 | −1.01597 | ||||||||
\(964\) | −2.14590 | −0.0691147 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.85410 | 0.0596548 | ||||||||
\(967\) | −20.2918 | −0.652540 | −0.326270 | − | 0.945277i | \(-0.605792\pi\) | ||||
−0.326270 | + | 0.945277i | \(0.605792\pi\) | |||||||
\(968\) | −7.00000 | −0.224989 | ||||||||
\(969\) | −29.4164 | −0.944991 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11.7082 | −0.375734 | −0.187867 | − | 0.982194i | \(-0.560157\pi\) | ||||
−0.187867 | + | 0.982194i | \(0.560157\pi\) | |||||||
\(972\) | 21.6525 | 0.694503 | ||||||||
\(973\) | −5.56231 | −0.178319 | ||||||||
\(974\) | −18.4377 | −0.590782 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.14590 | −0.132707 | ||||||||
\(977\) | 50.9443 | 1.62985 | 0.814926 | − | 0.579565i | \(-0.196778\pi\) | ||||
0.814926 | + | 0.579565i | \(0.196778\pi\) | |||||||
\(978\) | −50.8328 | −1.62545 | ||||||||
\(979\) | 4.00000 | 0.127841 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −28.5836 | −0.912604 | ||||||||
\(982\) | −19.7082 | −0.628914 | ||||||||
\(983\) | −45.5967 | −1.45431 | −0.727155 | − | 0.686473i | \(-0.759158\pi\) | ||||
−0.727155 | + | 0.686473i | \(0.759158\pi\) | |||||||
\(984\) | 14.9443 | 0.476406 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 5.61803 | 0.178915 | ||||||||
\(987\) | −10.4721 | −0.333332 | ||||||||
\(988\) | 5.23607 | 0.166582 | ||||||||
\(989\) | −10.4164 | −0.331223 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −14.5836 | −0.463263 | −0.231632 | − | 0.972804i | \(-0.574406\pi\) | ||||
−0.231632 | + | 0.972804i | \(0.574406\pi\) | |||||||
\(992\) | 2.85410 | 0.0906178 | ||||||||
\(993\) | 34.3607 | 1.09040 | ||||||||
\(994\) | −2.94427 | −0.0933866 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −7.70820 | −0.244244 | ||||||||
\(997\) | 23.1246 | 0.732364 | 0.366182 | − | 0.930543i | \(-0.380665\pi\) | ||||
0.366182 | + | 0.930543i | \(0.380665\pi\) | |||||||
\(998\) | 8.43769 | 0.267091 | ||||||||
\(999\) | −20.0000 | −0.632772 |
(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 | 1450.2.a.l.1.1 | 2 | ||
5.2 | odd | 4 | 290.2.b.a.59.4 | yes | 4 | ||
5.3 | odd | 4 | 290.2.b.a.59.1 | ✓ | 4 | ||
5.4 | even | 2 | 1450.2.a.k.1.2 | 2 | |||
15.2 | even | 4 | 2610.2.e.e.2089.1 | 4 | |||
15.8 | even | 4 | 2610.2.e.e.2089.4 | 4 | |||
20.3 | even | 4 | 2320.2.d.d.929.4 | 4 | |||
20.7 | even | 4 | 2320.2.d.d.929.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
290.2.b.a.59.1 | ✓ | 4 | 5.3 | odd | 4 | ||
290.2.b.a.59.4 | yes | 4 | 5.2 | odd | 4 | ||
1450.2.a.k.1.2 | 2 | 5.4 | even | 2 | |||
1450.2.a.l.1.1 | 2 | 1.1 | even | 1 | trivial | ||
2320.2.d.d.929.1 | 4 | 20.7 | even | 4 | |||
2320.2.d.d.929.4 | 4 | 20.3 | even | 4 | |||
2610.2.e.e.2089.1 | 4 | 15.2 | even | 4 | |||
2610.2.e.e.2089.4 | 4 | 15.8 | even | 4 |