Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1078,2,Mod(1,1078)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1078, 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("1078.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1078 = 2 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1078.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: | \(8.60787333789\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 154) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1078.1 |
$q$-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 | ||||||||
\(3\) | 0.414214 | 0.239146 | 0.119573 | − | 0.992825i | \(-0.461847\pi\) | ||||
0.119573 | + | 0.992825i | \(0.461847\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.41421 | −1.52688 | −0.763441 | − | 0.645877i | \(-0.776492\pi\) | ||||
−0.763441 | + | 0.645877i | \(0.776492\pi\) | |||||||
\(6\) | 0.414214 | 0.169102 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.82843 | −0.942809 | ||||||||
\(10\) | −3.41421 | −1.07967 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0.414214 | 0.119573 | ||||||||
\(13\) | 1.82843 | 0.507114 | 0.253557 | − | 0.967320i | \(-0.418399\pi\) | ||||
0.253557 | + | 0.967320i | \(0.418399\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.41421 | −0.365148 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −7.65685 | −1.85706 | −0.928530 | − | 0.371257i | \(-0.878927\pi\) | ||||
−0.928530 | + | 0.371257i | \(0.878927\pi\) | |||||||
\(18\) | −2.82843 | −0.666667 | ||||||||
\(19\) | −3.41421 | −0.783274 | −0.391637 | − | 0.920120i | \(-0.628091\pi\) | ||||
−0.391637 | + | 0.920120i | \(0.628091\pi\) | |||||||
\(20\) | −3.41421 | −0.763441 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | 2.24264 | 0.467623 | 0.233811 | − | 0.972282i | \(-0.424880\pi\) | ||||
0.233811 | + | 0.972282i | \(0.424880\pi\) | |||||||
\(24\) | 0.414214 | 0.0845510 | ||||||||
\(25\) | 6.65685 | 1.33137 | ||||||||
\(26\) | 1.82843 | 0.358584 | ||||||||
\(27\) | −2.41421 | −0.464616 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.65685 | −1.60754 | −0.803769 | − | 0.594942i | \(-0.797175\pi\) | ||||
−0.803769 | + | 0.594942i | \(0.797175\pi\) | |||||||
\(30\) | −1.41421 | −0.258199 | ||||||||
\(31\) | −4.00000 | −0.718421 | −0.359211 | − | 0.933257i | \(-0.616954\pi\) | ||||
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0.414214 | 0.0721053 | ||||||||
\(34\) | −7.65685 | −1.31314 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.82843 | −0.471405 | ||||||||
\(37\) | −6.58579 | −1.08270 | −0.541348 | − | 0.840798i | \(-0.682086\pi\) | ||||
−0.541348 | + | 0.840798i | \(0.682086\pi\) | |||||||
\(38\) | −3.41421 | −0.553859 | ||||||||
\(39\) | 0.757359 | 0.121275 | ||||||||
\(40\) | −3.41421 | −0.539835 | ||||||||
\(41\) | −2.58579 | −0.403832 | −0.201916 | − | 0.979403i | \(-0.564717\pi\) | ||||
−0.201916 | + | 0.979403i | \(0.564717\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.65685 | 0.862662 | 0.431331 | − | 0.902194i | \(-0.358044\pi\) | ||||
0.431331 | + | 0.902194i | \(0.358044\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 9.65685 | 1.43956 | ||||||||
\(46\) | 2.24264 | 0.330659 | ||||||||
\(47\) | 6.48528 | 0.945976 | 0.472988 | − | 0.881069i | \(-0.343175\pi\) | ||||
0.472988 | + | 0.881069i | \(0.343175\pi\) | |||||||
\(48\) | 0.414214 | 0.0597866 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 6.65685 | 0.941421 | ||||||||
\(51\) | −3.17157 | −0.444109 | ||||||||
\(52\) | 1.82843 | 0.253557 | ||||||||
\(53\) | −11.8995 | −1.63452 | −0.817261 | − | 0.576268i | \(-0.804508\pi\) | ||||
−0.817261 | + | 0.576268i | \(0.804508\pi\) | |||||||
\(54\) | −2.41421 | −0.328533 | ||||||||
\(55\) | −3.41421 | −0.460372 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.41421 | −0.187317 | ||||||||
\(58\) | −8.65685 | −1.13670 | ||||||||
\(59\) | −8.41421 | −1.09544 | −0.547719 | − | 0.836663i | \(-0.684504\pi\) | ||||
−0.547719 | + | 0.836663i | \(0.684504\pi\) | |||||||
\(60\) | −1.41421 | −0.182574 | ||||||||
\(61\) | 6.17157 | 0.790189 | 0.395094 | − | 0.918640i | \(-0.370712\pi\) | ||||
0.395094 | + | 0.918640i | \(0.370712\pi\) | |||||||
\(62\) | −4.00000 | −0.508001 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −6.24264 | −0.774304 | ||||||||
\(66\) | 0.414214 | 0.0509862 | ||||||||
\(67\) | 11.2426 | 1.37351 | 0.686754 | − | 0.726890i | \(-0.259035\pi\) | ||||
0.686754 | + | 0.726890i | \(0.259035\pi\) | |||||||
\(68\) | −7.65685 | −0.928530 | ||||||||
\(69\) | 0.928932 | 0.111830 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.07107 | 0.364469 | 0.182234 | − | 0.983255i | \(-0.441667\pi\) | ||||
0.182234 | + | 0.983255i | \(0.441667\pi\) | |||||||
\(72\) | −2.82843 | −0.333333 | ||||||||
\(73\) | −6.58579 | −0.770808 | −0.385404 | − | 0.922748i | \(-0.625938\pi\) | ||||
−0.385404 | + | 0.922748i | \(0.625938\pi\) | |||||||
\(74\) | −6.58579 | −0.765582 | ||||||||
\(75\) | 2.75736 | 0.318392 | ||||||||
\(76\) | −3.41421 | −0.391637 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.757359 | 0.0857541 | ||||||||
\(79\) | −4.75736 | −0.535245 | −0.267622 | − | 0.963524i | \(-0.586238\pi\) | ||||
−0.267622 | + | 0.963524i | \(0.586238\pi\) | |||||||
\(80\) | −3.41421 | −0.381721 | ||||||||
\(81\) | 7.48528 | 0.831698 | ||||||||
\(82\) | −2.58579 | −0.285552 | ||||||||
\(83\) | 16.1421 | 1.77183 | 0.885915 | − | 0.463848i | \(-0.153532\pi\) | ||||
0.885915 | + | 0.463848i | \(0.153532\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 26.1421 | 2.83551 | ||||||||
\(86\) | 5.65685 | 0.609994 | ||||||||
\(87\) | −3.58579 | −0.384437 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | −4.48528 | −0.475439 | −0.237719 | − | 0.971334i | \(-0.576400\pi\) | ||||
−0.237719 | + | 0.971334i | \(0.576400\pi\) | |||||||
\(90\) | 9.65685 | 1.01792 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2.24264 | 0.233811 | ||||||||
\(93\) | −1.65685 | −0.171808 | ||||||||
\(94\) | 6.48528 | 0.668906 | ||||||||
\(95\) | 11.6569 | 1.19597 | ||||||||
\(96\) | 0.414214 | 0.0422755 | ||||||||
\(97\) | 1.82843 | 0.185649 | 0.0928243 | − | 0.995683i | \(-0.470411\pi\) | ||||
0.0928243 | + | 0.995683i | \(0.470411\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.82843 | −0.284268 | ||||||||
\(100\) | 6.65685 | 0.665685 | ||||||||
\(101\) | 11.8284 | 1.17697 | 0.588486 | − | 0.808507i | \(-0.299724\pi\) | ||||
0.588486 | + | 0.808507i | \(0.299724\pi\) | |||||||
\(102\) | −3.17157 | −0.314033 | ||||||||
\(103\) | 10.5858 | 1.04305 | 0.521524 | − | 0.853236i | \(-0.325364\pi\) | ||||
0.521524 | + | 0.853236i | \(0.325364\pi\) | |||||||
\(104\) | 1.82843 | 0.179292 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −11.8995 | −1.15578 | ||||||||
\(107\) | 11.0711 | 1.07028 | 0.535140 | − | 0.844763i | \(-0.320259\pi\) | ||||
0.535140 | + | 0.844763i | \(0.320259\pi\) | |||||||
\(108\) | −2.41421 | −0.232308 | ||||||||
\(109\) | −0.485281 | −0.0464815 | −0.0232408 | − | 0.999730i | \(-0.507398\pi\) | ||||
−0.0232408 | + | 0.999730i | \(0.507398\pi\) | |||||||
\(110\) | −3.41421 | −0.325532 | ||||||||
\(111\) | −2.72792 | −0.258923 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.8284 | −1.30087 | −0.650434 | − | 0.759562i | \(-0.725413\pi\) | ||||
−0.650434 | + | 0.759562i | \(0.725413\pi\) | |||||||
\(114\) | −1.41421 | −0.132453 | ||||||||
\(115\) | −7.65685 | −0.714005 | ||||||||
\(116\) | −8.65685 | −0.803769 | ||||||||
\(117\) | −5.17157 | −0.478112 | ||||||||
\(118\) | −8.41421 | −0.774591 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.41421 | −0.129099 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 6.17157 | 0.558748 | ||||||||
\(123\) | −1.07107 | −0.0965749 | ||||||||
\(124\) | −4.00000 | −0.359211 | ||||||||
\(125\) | −5.65685 | −0.505964 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.72792 | −0.863213 | −0.431607 | − | 0.902062i | \(-0.642053\pi\) | ||||
−0.431607 | + | 0.902062i | \(0.642053\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 2.34315 | 0.206302 | ||||||||
\(130\) | −6.24264 | −0.547516 | ||||||||
\(131\) | −3.41421 | −0.298301 | −0.149151 | − | 0.988814i | \(-0.547654\pi\) | ||||
−0.149151 | + | 0.988814i | \(0.547654\pi\) | |||||||
\(132\) | 0.414214 | 0.0360527 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 11.2426 | 0.971216 | ||||||||
\(135\) | 8.24264 | 0.709414 | ||||||||
\(136\) | −7.65685 | −0.656570 | ||||||||
\(137\) | −5.34315 | −0.456496 | −0.228248 | − | 0.973603i | \(-0.573300\pi\) | ||||
−0.228248 | + | 0.973603i | \(0.573300\pi\) | |||||||
\(138\) | 0.928932 | 0.0790760 | ||||||||
\(139\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.68629 | 0.226227 | ||||||||
\(142\) | 3.07107 | 0.257718 | ||||||||
\(143\) | 1.82843 | 0.152901 | ||||||||
\(144\) | −2.82843 | −0.235702 | ||||||||
\(145\) | 29.5563 | 2.45452 | ||||||||
\(146\) | −6.58579 | −0.545044 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.58579 | −0.541348 | ||||||||
\(149\) | 6.34315 | 0.519651 | 0.259825 | − | 0.965656i | \(-0.416335\pi\) | ||||
0.259825 | + | 0.965656i | \(0.416335\pi\) | |||||||
\(150\) | 2.75736 | 0.225137 | ||||||||
\(151\) | 9.72792 | 0.791647 | 0.395824 | − | 0.918327i | \(-0.370459\pi\) | ||||
0.395824 | + | 0.918327i | \(0.370459\pi\) | |||||||
\(152\) | −3.41421 | −0.276929 | ||||||||
\(153\) | 21.6569 | 1.75085 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 13.6569 | 1.09694 | ||||||||
\(156\) | 0.757359 | 0.0606373 | ||||||||
\(157\) | 6.34315 | 0.506238 | 0.253119 | − | 0.967435i | \(-0.418544\pi\) | ||||
0.253119 | + | 0.967435i | \(0.418544\pi\) | |||||||
\(158\) | −4.75736 | −0.378475 | ||||||||
\(159\) | −4.92893 | −0.390890 | ||||||||
\(160\) | −3.41421 | −0.269917 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 7.48528 | 0.588099 | ||||||||
\(163\) | −15.7279 | −1.23191 | −0.615953 | − | 0.787783i | \(-0.711229\pi\) | ||||
−0.615953 | + | 0.787783i | \(0.711229\pi\) | |||||||
\(164\) | −2.58579 | −0.201916 | ||||||||
\(165\) | −1.41421 | −0.110096 | ||||||||
\(166\) | 16.1421 | 1.25287 | ||||||||
\(167\) | −11.7279 | −0.907534 | −0.453767 | − | 0.891120i | \(-0.649920\pi\) | ||||
−0.453767 | + | 0.891120i | \(0.649920\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.65685 | −0.742835 | ||||||||
\(170\) | 26.1421 | 2.00501 | ||||||||
\(171\) | 9.65685 | 0.738478 | ||||||||
\(172\) | 5.65685 | 0.431331 | ||||||||
\(173\) | −4.17157 | −0.317159 | −0.158579 | − | 0.987346i | \(-0.550691\pi\) | ||||
−0.158579 | + | 0.987346i | \(0.550691\pi\) | |||||||
\(174\) | −3.58579 | −0.271838 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | −3.48528 | −0.261970 | ||||||||
\(178\) | −4.48528 | −0.336186 | ||||||||
\(179\) | −18.8995 | −1.41261 | −0.706307 | − | 0.707905i | \(-0.749640\pi\) | ||||
−0.706307 | + | 0.707905i | \(0.749640\pi\) | |||||||
\(180\) | 9.65685 | 0.719779 | ||||||||
\(181\) | 3.65685 | 0.271812 | 0.135906 | − | 0.990722i | \(-0.456606\pi\) | ||||
0.135906 | + | 0.990722i | \(0.456606\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.55635 | 0.188971 | ||||||||
\(184\) | 2.24264 | 0.165330 | ||||||||
\(185\) | 22.4853 | 1.65315 | ||||||||
\(186\) | −1.65685 | −0.121486 | ||||||||
\(187\) | −7.65685 | −0.559925 | ||||||||
\(188\) | 6.48528 | 0.472988 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 11.6569 | 0.845677 | ||||||||
\(191\) | −12.8284 | −0.928232 | −0.464116 | − | 0.885774i | \(-0.653628\pi\) | ||||
−0.464116 | + | 0.885774i | \(0.653628\pi\) | |||||||
\(192\) | 0.414214 | 0.0298933 | ||||||||
\(193\) | 2.10051 | 0.151198 | 0.0755988 | − | 0.997138i | \(-0.475913\pi\) | ||||
0.0755988 | + | 0.997138i | \(0.475913\pi\) | |||||||
\(194\) | 1.82843 | 0.131273 | ||||||||
\(195\) | −2.58579 | −0.185172 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −17.4853 | −1.24577 | −0.622887 | − | 0.782312i | \(-0.714041\pi\) | ||||
−0.622887 | + | 0.782312i | \(0.714041\pi\) | |||||||
\(198\) | −2.82843 | −0.201008 | ||||||||
\(199\) | 19.8995 | 1.41064 | 0.705319 | − | 0.708890i | \(-0.250804\pi\) | ||||
0.705319 | + | 0.708890i | \(0.250804\pi\) | |||||||
\(200\) | 6.65685 | 0.470711 | ||||||||
\(201\) | 4.65685 | 0.328469 | ||||||||
\(202\) | 11.8284 | 0.832245 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −3.17157 | −0.222055 | ||||||||
\(205\) | 8.82843 | 0.616604 | ||||||||
\(206\) | 10.5858 | 0.737547 | ||||||||
\(207\) | −6.34315 | −0.440879 | ||||||||
\(208\) | 1.82843 | 0.126779 | ||||||||
\(209\) | −3.41421 | −0.236166 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.58579 | 0.315699 | 0.157849 | − | 0.987463i | \(-0.449544\pi\) | ||||
0.157849 | + | 0.987463i | \(0.449544\pi\) | |||||||
\(212\) | −11.8995 | −0.817261 | ||||||||
\(213\) | 1.27208 | 0.0871613 | ||||||||
\(214\) | 11.0711 | 0.756803 | ||||||||
\(215\) | −19.3137 | −1.31718 | ||||||||
\(216\) | −2.41421 | −0.164266 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −0.485281 | −0.0328674 | ||||||||
\(219\) | −2.72792 | −0.184336 | ||||||||
\(220\) | −3.41421 | −0.230186 | ||||||||
\(221\) | −14.0000 | −0.941742 | ||||||||
\(222\) | −2.72792 | −0.183086 | ||||||||
\(223\) | 11.4142 | 0.764352 | 0.382176 | − | 0.924089i | \(-0.375175\pi\) | ||||
0.382176 | + | 0.924089i | \(0.375175\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −18.8284 | −1.25523 | ||||||||
\(226\) | −13.8284 | −0.919853 | ||||||||
\(227\) | −23.1716 | −1.53795 | −0.768976 | − | 0.639278i | \(-0.779233\pi\) | ||||
−0.768976 | + | 0.639278i | \(0.779233\pi\) | |||||||
\(228\) | −1.41421 | −0.0936586 | ||||||||
\(229\) | 0.686292 | 0.0453514 | 0.0226757 | − | 0.999743i | \(-0.492781\pi\) | ||||
0.0226757 | + | 0.999743i | \(0.492781\pi\) | |||||||
\(230\) | −7.65685 | −0.504878 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.65685 | −0.568350 | ||||||||
\(233\) | −1.41421 | −0.0926482 | −0.0463241 | − | 0.998926i | \(-0.514751\pi\) | ||||
−0.0463241 | + | 0.998926i | \(0.514751\pi\) | |||||||
\(234\) | −5.17157 | −0.338076 | ||||||||
\(235\) | −22.1421 | −1.44439 | ||||||||
\(236\) | −8.41421 | −0.547719 | ||||||||
\(237\) | −1.97056 | −0.128002 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −22.2132 | −1.43685 | −0.718426 | − | 0.695603i | \(-0.755137\pi\) | ||||
−0.718426 | + | 0.695603i | \(0.755137\pi\) | |||||||
\(240\) | −1.41421 | −0.0912871 | ||||||||
\(241\) | 3.75736 | 0.242033 | 0.121016 | − | 0.992651i | \(-0.461385\pi\) | ||||
0.121016 | + | 0.992651i | \(0.461385\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | 10.3431 | 0.663513 | ||||||||
\(244\) | 6.17157 | 0.395094 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.07107 | −0.0682888 | ||||||||
\(247\) | −6.24264 | −0.397210 | ||||||||
\(248\) | −4.00000 | −0.254000 | ||||||||
\(249\) | 6.68629 | 0.423727 | ||||||||
\(250\) | −5.65685 | −0.357771 | ||||||||
\(251\) | 2.14214 | 0.135210 | 0.0676052 | − | 0.997712i | \(-0.478464\pi\) | ||||
0.0676052 | + | 0.997712i | \(0.478464\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.24264 | 0.140994 | ||||||||
\(254\) | −9.72792 | −0.610384 | ||||||||
\(255\) | 10.8284 | 0.678102 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 3.14214 | 0.196001 | 0.0980005 | − | 0.995186i | \(-0.468755\pi\) | ||||
0.0980005 | + | 0.995186i | \(0.468755\pi\) | |||||||
\(258\) | 2.34315 | 0.145878 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −6.24264 | −0.387152 | ||||||||
\(261\) | 24.4853 | 1.51560 | ||||||||
\(262\) | −3.41421 | −0.210931 | ||||||||
\(263\) | 31.0416 | 1.91411 | 0.957054 | − | 0.289908i | \(-0.0936248\pi\) | ||||
0.957054 | + | 0.289908i | \(0.0936248\pi\) | |||||||
\(264\) | 0.414214 | 0.0254931 | ||||||||
\(265\) | 40.6274 | 2.49572 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.85786 | −0.113699 | ||||||||
\(268\) | 11.2426 | 0.686754 | ||||||||
\(269\) | 13.6569 | 0.832673 | 0.416337 | − | 0.909211i | \(-0.363314\pi\) | ||||
0.416337 | + | 0.909211i | \(0.363314\pi\) | |||||||
\(270\) | 8.24264 | 0.501631 | ||||||||
\(271\) | −26.5563 | −1.61318 | −0.806592 | − | 0.591109i | \(-0.798690\pi\) | ||||
−0.806592 | + | 0.591109i | \(0.798690\pi\) | |||||||
\(272\) | −7.65685 | −0.464265 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.34315 | −0.322791 | ||||||||
\(275\) | 6.65685 | 0.401423 | ||||||||
\(276\) | 0.928932 | 0.0559151 | ||||||||
\(277\) | −3.82843 | −0.230028 | −0.115014 | − | 0.993364i | \(-0.536691\pi\) | ||||
−0.115014 | + | 0.993364i | \(0.536691\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 11.3137 | 0.677334 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.7279 | −0.997904 | −0.498952 | − | 0.866630i | \(-0.666282\pi\) | ||||
−0.498952 | + | 0.866630i | \(0.666282\pi\) | |||||||
\(282\) | 2.68629 | 0.159966 | ||||||||
\(283\) | −20.5858 | −1.22370 | −0.611849 | − | 0.790975i | \(-0.709574\pi\) | ||||
−0.611849 | + | 0.790975i | \(0.709574\pi\) | |||||||
\(284\) | 3.07107 | 0.182234 | ||||||||
\(285\) | 4.82843 | 0.286011 | ||||||||
\(286\) | 1.82843 | 0.108117 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −2.82843 | −0.166667 | ||||||||
\(289\) | 41.6274 | 2.44867 | ||||||||
\(290\) | 29.5563 | 1.73561 | ||||||||
\(291\) | 0.757359 | 0.0443972 | ||||||||
\(292\) | −6.58579 | −0.385404 | ||||||||
\(293\) | −5.17157 | −0.302127 | −0.151063 | − | 0.988524i | \(-0.548270\pi\) | ||||
−0.151063 | + | 0.988524i | \(0.548270\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 28.7279 | 1.67260 | ||||||||
\(296\) | −6.58579 | −0.382791 | ||||||||
\(297\) | −2.41421 | −0.140087 | ||||||||
\(298\) | 6.34315 | 0.367449 | ||||||||
\(299\) | 4.10051 | 0.237138 | ||||||||
\(300\) | 2.75736 | 0.159196 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 9.72792 | 0.559779 | ||||||||
\(303\) | 4.89949 | 0.281469 | ||||||||
\(304\) | −3.41421 | −0.195819 | ||||||||
\(305\) | −21.0711 | −1.20653 | ||||||||
\(306\) | 21.6569 | 1.23804 | ||||||||
\(307\) | −9.89949 | −0.564994 | −0.282497 | − | 0.959268i | \(-0.591163\pi\) | ||||
−0.282497 | + | 0.959268i | \(0.591163\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.38478 | 0.249441 | ||||||||
\(310\) | 13.6569 | 0.775657 | ||||||||
\(311\) | −8.72792 | −0.494915 | −0.247458 | − | 0.968899i | \(-0.579595\pi\) | ||||
−0.247458 | + | 0.968899i | \(0.579595\pi\) | |||||||
\(312\) | 0.757359 | 0.0428770 | ||||||||
\(313\) | −9.34315 | −0.528106 | −0.264053 | − | 0.964508i | \(-0.585059\pi\) | ||||
−0.264053 | + | 0.964508i | \(0.585059\pi\) | |||||||
\(314\) | 6.34315 | 0.357964 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.75736 | −0.267622 | ||||||||
\(317\) | 31.3137 | 1.75875 | 0.879377 | − | 0.476127i | \(-0.157960\pi\) | ||||
0.879377 | + | 0.476127i | \(0.157960\pi\) | |||||||
\(318\) | −4.92893 | −0.276401 | ||||||||
\(319\) | −8.65685 | −0.484691 | ||||||||
\(320\) | −3.41421 | −0.190860 | ||||||||
\(321\) | 4.58579 | 0.255954 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 26.1421 | 1.45459 | ||||||||
\(324\) | 7.48528 | 0.415849 | ||||||||
\(325\) | 12.1716 | 0.675157 | ||||||||
\(326\) | −15.7279 | −0.871089 | ||||||||
\(327\) | −0.201010 | −0.0111159 | ||||||||
\(328\) | −2.58579 | −0.142776 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −1.41421 | −0.0778499 | ||||||||
\(331\) | −9.92893 | −0.545743 | −0.272872 | − | 0.962050i | \(-0.587973\pi\) | ||||
−0.272872 | + | 0.962050i | \(0.587973\pi\) | |||||||
\(332\) | 16.1421 | 0.885915 | ||||||||
\(333\) | 18.6274 | 1.02078 | ||||||||
\(334\) | −11.7279 | −0.641723 | ||||||||
\(335\) | −38.3848 | −2.09718 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −19.7574 | −1.07625 | −0.538126 | − | 0.842864i | \(-0.680868\pi\) | ||||
−0.538126 | + | 0.842864i | \(0.680868\pi\) | |||||||
\(338\) | −9.65685 | −0.525264 | ||||||||
\(339\) | −5.72792 | −0.311098 | ||||||||
\(340\) | 26.1421 | 1.41776 | ||||||||
\(341\) | −4.00000 | −0.216612 | ||||||||
\(342\) | 9.65685 | 0.522183 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 5.65685 | 0.304997 | ||||||||
\(345\) | −3.17157 | −0.170752 | ||||||||
\(346\) | −4.17157 | −0.224265 | ||||||||
\(347\) | 14.5858 | 0.783006 | 0.391503 | − | 0.920177i | \(-0.371955\pi\) | ||||
0.391503 | + | 0.920177i | \(0.371955\pi\) | |||||||
\(348\) | −3.58579 | −0.192218 | ||||||||
\(349\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.41421 | −0.235613 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | −25.3137 | −1.34731 | −0.673656 | − | 0.739045i | \(-0.735277\pi\) | ||||
−0.673656 | + | 0.739045i | \(0.735277\pi\) | |||||||
\(354\) | −3.48528 | −0.185241 | ||||||||
\(355\) | −10.4853 | −0.556501 | ||||||||
\(356\) | −4.48528 | −0.237719 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −18.8995 | −0.998869 | ||||||||
\(359\) | 10.7574 | 0.567752 | 0.283876 | − | 0.958861i | \(-0.408380\pi\) | ||||
0.283876 | + | 0.958861i | \(0.408380\pi\) | |||||||
\(360\) | 9.65685 | 0.508961 | ||||||||
\(361\) | −7.34315 | −0.386481 | ||||||||
\(362\) | 3.65685 | 0.192200 | ||||||||
\(363\) | 0.414214 | 0.0217406 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 22.4853 | 1.17693 | ||||||||
\(366\) | 2.55635 | 0.133623 | ||||||||
\(367\) | 14.7279 | 0.768791 | 0.384396 | − | 0.923168i | \(-0.374410\pi\) | ||||
0.384396 | + | 0.923168i | \(0.374410\pi\) | |||||||
\(368\) | 2.24264 | 0.116906 | ||||||||
\(369\) | 7.31371 | 0.380736 | ||||||||
\(370\) | 22.4853 | 1.16895 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −1.65685 | −0.0859039 | ||||||||
\(373\) | 13.9706 | 0.723368 | 0.361684 | − | 0.932301i | \(-0.382202\pi\) | ||||
0.361684 | + | 0.932301i | \(0.382202\pi\) | |||||||
\(374\) | −7.65685 | −0.395927 | ||||||||
\(375\) | −2.34315 | −0.121000 | ||||||||
\(376\) | 6.48528 | 0.334453 | ||||||||
\(377\) | −15.8284 | −0.815205 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −25.8701 | −1.32886 | −0.664428 | − | 0.747352i | \(-0.731325\pi\) | ||||
−0.664428 | + | 0.747352i | \(0.731325\pi\) | |||||||
\(380\) | 11.6569 | 0.597984 | ||||||||
\(381\) | −4.02944 | −0.206434 | ||||||||
\(382\) | −12.8284 | −0.656359 | ||||||||
\(383\) | 30.3848 | 1.55259 | 0.776295 | − | 0.630370i | \(-0.217097\pi\) | ||||
0.776295 | + | 0.630370i | \(0.217097\pi\) | |||||||
\(384\) | 0.414214 | 0.0211377 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.10051 | 0.106913 | ||||||||
\(387\) | −16.0000 | −0.813326 | ||||||||
\(388\) | 1.82843 | 0.0928243 | ||||||||
\(389\) | 2.72792 | 0.138311 | 0.0691556 | − | 0.997606i | \(-0.477970\pi\) | ||||
0.0691556 | + | 0.997606i | \(0.477970\pi\) | |||||||
\(390\) | −2.58579 | −0.130936 | ||||||||
\(391\) | −17.1716 | −0.868404 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.41421 | −0.0713376 | ||||||||
\(394\) | −17.4853 | −0.880896 | ||||||||
\(395\) | 16.2426 | 0.817256 | ||||||||
\(396\) | −2.82843 | −0.142134 | ||||||||
\(397\) | 22.0000 | 1.10415 | 0.552074 | − | 0.833795i | \(-0.313837\pi\) | ||||
0.552074 | + | 0.833795i | \(0.313837\pi\) | |||||||
\(398\) | 19.8995 | 0.997472 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 6.65685 | 0.332843 | ||||||||
\(401\) | −4.31371 | −0.215416 | −0.107708 | − | 0.994183i | \(-0.534351\pi\) | ||||
−0.107708 | + | 0.994183i | \(0.534351\pi\) | |||||||
\(402\) | 4.65685 | 0.232263 | ||||||||
\(403\) | −7.31371 | −0.364322 | ||||||||
\(404\) | 11.8284 | 0.588486 | ||||||||
\(405\) | −25.5563 | −1.26991 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.58579 | −0.326445 | ||||||||
\(408\) | −3.17157 | −0.157016 | ||||||||
\(409\) | −22.7279 | −1.12382 | −0.561912 | − | 0.827197i | \(-0.689934\pi\) | ||||
−0.561912 | + | 0.827197i | \(0.689934\pi\) | |||||||
\(410\) | 8.82843 | 0.436005 | ||||||||
\(411\) | −2.21320 | −0.109169 | ||||||||
\(412\) | 10.5858 | 0.521524 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −6.34315 | −0.311749 | ||||||||
\(415\) | −55.1127 | −2.70538 | ||||||||
\(416\) | 1.82843 | 0.0896460 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3.41421 | −0.166995 | ||||||||
\(419\) | 2.14214 | 0.104650 | 0.0523251 | − | 0.998630i | \(-0.483337\pi\) | ||||
0.0523251 | + | 0.998630i | \(0.483337\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.3137 | 1.13624 | 0.568120 | − | 0.822946i | \(-0.307671\pi\) | ||||
0.568120 | + | 0.822946i | \(0.307671\pi\) | |||||||
\(422\) | 4.58579 | 0.223233 | ||||||||
\(423\) | −18.3431 | −0.891874 | ||||||||
\(424\) | −11.8995 | −0.577891 | ||||||||
\(425\) | −50.9706 | −2.47244 | ||||||||
\(426\) | 1.27208 | 0.0616324 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 11.0711 | 0.535140 | ||||||||
\(429\) | 0.757359 | 0.0365657 | ||||||||
\(430\) | −19.3137 | −0.931390 | ||||||||
\(431\) | −20.4142 | −0.983318 | −0.491659 | − | 0.870788i | \(-0.663609\pi\) | ||||
−0.491659 | + | 0.870788i | \(0.663609\pi\) | |||||||
\(432\) | −2.41421 | −0.116154 | ||||||||
\(433\) | −2.14214 | −0.102944 | −0.0514722 | − | 0.998674i | \(-0.516391\pi\) | ||||
−0.0514722 | + | 0.998674i | \(0.516391\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 12.2426 | 0.586990 | ||||||||
\(436\) | −0.485281 | −0.0232408 | ||||||||
\(437\) | −7.65685 | −0.366277 | ||||||||
\(438\) | −2.72792 | −0.130345 | ||||||||
\(439\) | 9.38478 | 0.447911 | 0.223955 | − | 0.974599i | \(-0.428103\pi\) | ||||
0.223955 | + | 0.974599i | \(0.428103\pi\) | |||||||
\(440\) | −3.41421 | −0.162766 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −14.0000 | −0.665912 | ||||||||
\(443\) | −32.6274 | −1.55018 | −0.775088 | − | 0.631854i | \(-0.782294\pi\) | ||||
−0.775088 | + | 0.631854i | \(0.782294\pi\) | |||||||
\(444\) | −2.72792 | −0.129461 | ||||||||
\(445\) | 15.3137 | 0.725939 | ||||||||
\(446\) | 11.4142 | 0.540479 | ||||||||
\(447\) | 2.62742 | 0.124273 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 33.6569 | 1.58837 | 0.794183 | − | 0.607679i | \(-0.207899\pi\) | ||||
0.794183 | + | 0.607679i | \(0.207899\pi\) | |||||||
\(450\) | −18.8284 | −0.887581 | ||||||||
\(451\) | −2.58579 | −0.121760 | ||||||||
\(452\) | −13.8284 | −0.650434 | ||||||||
\(453\) | 4.02944 | 0.189319 | ||||||||
\(454\) | −23.1716 | −1.08750 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.41421 | −0.0662266 | ||||||||
\(457\) | −0.343146 | −0.0160517 | −0.00802584 | − | 0.999968i | \(-0.502555\pi\) | ||||
−0.00802584 | + | 0.999968i | \(0.502555\pi\) | |||||||
\(458\) | 0.686292 | 0.0320683 | ||||||||
\(459\) | 18.4853 | 0.862819 | ||||||||
\(460\) | −7.65685 | −0.357003 | ||||||||
\(461\) | 14.3137 | 0.666656 | 0.333328 | − | 0.942811i | \(-0.391828\pi\) | ||||
0.333328 | + | 0.942811i | \(0.391828\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.17157 | 0.333291 | 0.166646 | − | 0.986017i | \(-0.446706\pi\) | ||||
0.166646 | + | 0.986017i | \(0.446706\pi\) | |||||||
\(464\) | −8.65685 | −0.401884 | ||||||||
\(465\) | 5.65685 | 0.262330 | ||||||||
\(466\) | −1.41421 | −0.0655122 | ||||||||
\(467\) | −34.0000 | −1.57333 | −0.786666 | − | 0.617379i | \(-0.788195\pi\) | ||||
−0.786666 | + | 0.617379i | \(0.788195\pi\) | |||||||
\(468\) | −5.17157 | −0.239056 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −22.1421 | −1.02134 | ||||||||
\(471\) | 2.62742 | 0.121065 | ||||||||
\(472\) | −8.41421 | −0.387296 | ||||||||
\(473\) | 5.65685 | 0.260102 | ||||||||
\(474\) | −1.97056 | −0.0905109 | ||||||||
\(475\) | −22.7279 | −1.04283 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 33.6569 | 1.54104 | ||||||||
\(478\) | −22.2132 | −1.01601 | ||||||||
\(479\) | −26.0711 | −1.19122 | −0.595609 | − | 0.803275i | \(-0.703089\pi\) | ||||
−0.595609 | + | 0.803275i | \(0.703089\pi\) | |||||||
\(480\) | −1.41421 | −0.0645497 | ||||||||
\(481\) | −12.0416 | −0.549051 | ||||||||
\(482\) | 3.75736 | 0.171143 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −6.24264 | −0.283464 | ||||||||
\(486\) | 10.3431 | 0.469175 | ||||||||
\(487\) | 1.65685 | 0.0750792 | 0.0375396 | − | 0.999295i | \(-0.488048\pi\) | ||||
0.0375396 | + | 0.999295i | \(0.488048\pi\) | |||||||
\(488\) | 6.17157 | 0.279374 | ||||||||
\(489\) | −6.51472 | −0.294606 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 24.8284 | 1.12049 | 0.560246 | − | 0.828327i | \(-0.310707\pi\) | ||||
0.560246 | + | 0.828327i | \(0.310707\pi\) | |||||||
\(492\) | −1.07107 | −0.0482875 | ||||||||
\(493\) | 66.2843 | 2.98529 | ||||||||
\(494\) | −6.24264 | −0.280870 | ||||||||
\(495\) | 9.65685 | 0.434043 | ||||||||
\(496\) | −4.00000 | −0.179605 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 6.68629 | 0.299620 | ||||||||
\(499\) | −6.14214 | −0.274960 | −0.137480 | − | 0.990505i | \(-0.543900\pi\) | ||||
−0.137480 | + | 0.990505i | \(0.543900\pi\) | |||||||
\(500\) | −5.65685 | −0.252982 | ||||||||
\(501\) | −4.85786 | −0.217033 | ||||||||
\(502\) | 2.14214 | 0.0956082 | ||||||||
\(503\) | −38.2132 | −1.70384 | −0.851921 | − | 0.523670i | \(-0.824563\pi\) | ||||
−0.851921 | + | 0.523670i | \(0.824563\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −40.3848 | −1.79710 | ||||||||
\(506\) | 2.24264 | 0.0996975 | ||||||||
\(507\) | −4.00000 | −0.177646 | ||||||||
\(508\) | −9.72792 | −0.431607 | ||||||||
\(509\) | −13.3137 | −0.590120 | −0.295060 | − | 0.955479i | \(-0.595340\pi\) | ||||
−0.295060 | + | 0.955479i | \(0.595340\pi\) | |||||||
\(510\) | 10.8284 | 0.479491 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 8.24264 | 0.363921 | ||||||||
\(514\) | 3.14214 | 0.138594 | ||||||||
\(515\) | −36.1421 | −1.59261 | ||||||||
\(516\) | 2.34315 | 0.103151 | ||||||||
\(517\) | 6.48528 | 0.285222 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.72792 | −0.0758474 | ||||||||
\(520\) | −6.24264 | −0.273758 | ||||||||
\(521\) | 28.2843 | 1.23916 | 0.619578 | − | 0.784935i | \(-0.287304\pi\) | ||||
0.619578 | + | 0.784935i | \(0.287304\pi\) | |||||||
\(522\) | 24.4853 | 1.07169 | ||||||||
\(523\) | 12.7279 | 0.556553 | 0.278277 | − | 0.960501i | \(-0.410237\pi\) | ||||
0.278277 | + | 0.960501i | \(0.410237\pi\) | |||||||
\(524\) | −3.41421 | −0.149151 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 31.0416 | 1.35348 | ||||||||
\(527\) | 30.6274 | 1.33415 | ||||||||
\(528\) | 0.414214 | 0.0180263 | ||||||||
\(529\) | −17.9706 | −0.781329 | ||||||||
\(530\) | 40.6274 | 1.76474 | ||||||||
\(531\) | 23.7990 | 1.03279 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.72792 | −0.204789 | ||||||||
\(534\) | −1.85786 | −0.0803977 | ||||||||
\(535\) | −37.7990 | −1.63419 | ||||||||
\(536\) | 11.2426 | 0.485608 | ||||||||
\(537\) | −7.82843 | −0.337822 | ||||||||
\(538\) | 13.6569 | 0.588789 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 8.24264 | 0.354707 | ||||||||
\(541\) | −41.1421 | −1.76884 | −0.884419 | − | 0.466693i | \(-0.845445\pi\) | ||||
−0.884419 | + | 0.466693i | \(0.845445\pi\) | |||||||
\(542\) | −26.5563 | −1.14069 | ||||||||
\(543\) | 1.51472 | 0.0650028 | ||||||||
\(544\) | −7.65685 | −0.328285 | ||||||||
\(545\) | 1.65685 | 0.0709718 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18.8701 | −0.806825 | −0.403413 | − | 0.915018i | \(-0.632176\pi\) | ||||
−0.403413 | + | 0.915018i | \(0.632176\pi\) | |||||||
\(548\) | −5.34315 | −0.228248 | ||||||||
\(549\) | −17.4558 | −0.744997 | ||||||||
\(550\) | 6.65685 | 0.283849 | ||||||||
\(551\) | 29.5563 | 1.25914 | ||||||||
\(552\) | 0.928932 | 0.0395380 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −3.82843 | −0.162654 | ||||||||
\(555\) | 9.31371 | 0.395345 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 24.4853 | 1.03747 | 0.518737 | − | 0.854934i | \(-0.326402\pi\) | ||||
0.518737 | + | 0.854934i | \(0.326402\pi\) | |||||||
\(558\) | 11.3137 | 0.478947 | ||||||||
\(559\) | 10.3431 | 0.437468 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.17157 | −0.133904 | ||||||||
\(562\) | −16.7279 | −0.705625 | ||||||||
\(563\) | −5.07107 | −0.213720 | −0.106860 | − | 0.994274i | \(-0.534080\pi\) | ||||
−0.106860 | + | 0.994274i | \(0.534080\pi\) | |||||||
\(564\) | 2.68629 | 0.113113 | ||||||||
\(565\) | 47.2132 | 1.98627 | ||||||||
\(566\) | −20.5858 | −0.865285 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.07107 | 0.128859 | ||||||||
\(569\) | −4.00000 | −0.167689 | −0.0838444 | − | 0.996479i | \(-0.526720\pi\) | ||||
−0.0838444 | + | 0.996479i | \(0.526720\pi\) | |||||||
\(570\) | 4.82843 | 0.202241 | ||||||||
\(571\) | −10.3848 | −0.434589 | −0.217295 | − | 0.976106i | \(-0.569723\pi\) | ||||
−0.217295 | + | 0.976106i | \(0.569723\pi\) | |||||||
\(572\) | 1.82843 | 0.0764504 | ||||||||
\(573\) | −5.31371 | −0.221983 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 14.9289 | 0.622580 | ||||||||
\(576\) | −2.82843 | −0.117851 | ||||||||
\(577\) | −32.3137 | −1.34524 | −0.672619 | − | 0.739989i | \(-0.734831\pi\) | ||||
−0.672619 | + | 0.739989i | \(0.734831\pi\) | |||||||
\(578\) | 41.6274 | 1.73147 | ||||||||
\(579\) | 0.870058 | 0.0361584 | ||||||||
\(580\) | 29.5563 | 1.22726 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0.757359 | 0.0313936 | ||||||||
\(583\) | −11.8995 | −0.492827 | ||||||||
\(584\) | −6.58579 | −0.272522 | ||||||||
\(585\) | 17.6569 | 0.730021 | ||||||||
\(586\) | −5.17157 | −0.213636 | ||||||||
\(587\) | −44.8995 | −1.85320 | −0.926600 | − | 0.376048i | \(-0.877283\pi\) | ||||
−0.926600 | + | 0.376048i | \(0.877283\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13.6569 | 0.562721 | ||||||||
\(590\) | 28.7279 | 1.18271 | ||||||||
\(591\) | −7.24264 | −0.297922 | ||||||||
\(592\) | −6.58579 | −0.270674 | ||||||||
\(593\) | −35.6985 | −1.46596 | −0.732981 | − | 0.680250i | \(-0.761871\pi\) | ||||
−0.732981 | + | 0.680250i | \(0.761871\pi\) | |||||||
\(594\) | −2.41421 | −0.0990564 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.34315 | 0.259825 | ||||||||
\(597\) | 8.24264 | 0.337349 | ||||||||
\(598\) | 4.10051 | 0.167682 | ||||||||
\(599\) | −2.62742 | −0.107353 | −0.0536767 | − | 0.998558i | \(-0.517094\pi\) | ||||
−0.0536767 | + | 0.998558i | \(0.517094\pi\) | |||||||
\(600\) | 2.75736 | 0.112569 | ||||||||
\(601\) | −35.9411 | −1.46607 | −0.733035 | − | 0.680191i | \(-0.761897\pi\) | ||||
−0.733035 | + | 0.680191i | \(0.761897\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −31.7990 | −1.29495 | ||||||||
\(604\) | 9.72792 | 0.395824 | ||||||||
\(605\) | −3.41421 | −0.138808 | ||||||||
\(606\) | 4.89949 | 0.199028 | ||||||||
\(607\) | −9.02944 | −0.366494 | −0.183247 | − | 0.983067i | \(-0.558661\pi\) | ||||
−0.183247 | + | 0.983067i | \(0.558661\pi\) | |||||||
\(608\) | −3.41421 | −0.138465 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −21.0711 | −0.853143 | ||||||||
\(611\) | 11.8579 | 0.479718 | ||||||||
\(612\) | 21.6569 | 0.875426 | ||||||||
\(613\) | −16.6274 | −0.671575 | −0.335788 | − | 0.941938i | \(-0.609002\pi\) | ||||
−0.335788 | + | 0.941938i | \(0.609002\pi\) | |||||||
\(614\) | −9.89949 | −0.399511 | ||||||||
\(615\) | 3.65685 | 0.147459 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8.02944 | −0.323253 | −0.161626 | − | 0.986852i | \(-0.551674\pi\) | ||||
−0.161626 | + | 0.986852i | \(0.551674\pi\) | |||||||
\(618\) | 4.38478 | 0.176382 | ||||||||
\(619\) | 45.9411 | 1.84653 | 0.923265 | − | 0.384164i | \(-0.125510\pi\) | ||||
0.923265 | + | 0.384164i | \(0.125510\pi\) | |||||||
\(620\) | 13.6569 | 0.548472 | ||||||||
\(621\) | −5.41421 | −0.217265 | ||||||||
\(622\) | −8.72792 | −0.349958 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0.757359 | 0.0303186 | ||||||||
\(625\) | −13.9706 | −0.558823 | ||||||||
\(626\) | −9.34315 | −0.373427 | ||||||||
\(627\) | −1.41421 | −0.0564782 | ||||||||
\(628\) | 6.34315 | 0.253119 | ||||||||
\(629\) | 50.4264 | 2.01063 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 48.7279 | 1.93983 | 0.969914 | − | 0.243448i | \(-0.0782785\pi\) | ||||
0.969914 | + | 0.243448i | \(0.0782785\pi\) | |||||||
\(632\) | −4.75736 | −0.189238 | ||||||||
\(633\) | 1.89949 | 0.0754981 | ||||||||
\(634\) | 31.3137 | 1.24363 | ||||||||
\(635\) | 33.2132 | 1.31803 | ||||||||
\(636\) | −4.92893 | −0.195445 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −8.65685 | −0.342728 | ||||||||
\(639\) | −8.68629 | −0.343624 | ||||||||
\(640\) | −3.41421 | −0.134959 | ||||||||
\(641\) | −41.2843 | −1.63063 | −0.815315 | − | 0.579017i | \(-0.803436\pi\) | ||||
−0.815315 | + | 0.579017i | \(0.803436\pi\) | |||||||
\(642\) | 4.58579 | 0.180987 | ||||||||
\(643\) | 4.41421 | 0.174080 | 0.0870398 | − | 0.996205i | \(-0.472259\pi\) | ||||
0.0870398 | + | 0.996205i | \(0.472259\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.00000 | −0.315000 | ||||||||
\(646\) | 26.1421 | 1.02855 | ||||||||
\(647\) | −46.1838 | −1.81567 | −0.907836 | − | 0.419326i | \(-0.862266\pi\) | ||||
−0.907836 | + | 0.419326i | \(0.862266\pi\) | |||||||
\(648\) | 7.48528 | 0.294050 | ||||||||
\(649\) | −8.41421 | −0.330287 | ||||||||
\(650\) | 12.1716 | 0.477408 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −15.7279 | −0.615953 | ||||||||
\(653\) | 18.3848 | 0.719452 | 0.359726 | − | 0.933058i | \(-0.382870\pi\) | ||||
0.359726 | + | 0.933058i | \(0.382870\pi\) | |||||||
\(654\) | −0.201010 | −0.00786012 | ||||||||
\(655\) | 11.6569 | 0.455471 | ||||||||
\(656\) | −2.58579 | −0.100958 | ||||||||
\(657\) | 18.6274 | 0.726725 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12.0000 | −0.467454 | −0.233727 | − | 0.972302i | \(-0.575092\pi\) | ||||
−0.233727 | + | 0.972302i | \(0.575092\pi\) | |||||||
\(660\) | −1.41421 | −0.0550482 | ||||||||
\(661\) | −14.9706 | −0.582287 | −0.291144 | − | 0.956679i | \(-0.594036\pi\) | ||||
−0.291144 | + | 0.956679i | \(0.594036\pi\) | |||||||
\(662\) | −9.92893 | −0.385899 | ||||||||
\(663\) | −5.79899 | −0.225214 | ||||||||
\(664\) | 16.1421 | 0.626436 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 18.6274 | 0.721798 | ||||||||
\(667\) | −19.4142 | −0.751721 | ||||||||
\(668\) | −11.7279 | −0.453767 | ||||||||
\(669\) | 4.72792 | 0.182792 | ||||||||
\(670\) | −38.3848 | −1.48293 | ||||||||
\(671\) | 6.17157 | 0.238251 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25.5563 | −0.985125 | −0.492562 | − | 0.870277i | \(-0.663940\pi\) | ||||
−0.492562 | + | 0.870277i | \(0.663940\pi\) | |||||||
\(674\) | −19.7574 | −0.761025 | ||||||||
\(675\) | −16.0711 | −0.618576 | ||||||||
\(676\) | −9.65685 | −0.371417 | ||||||||
\(677\) | −12.6863 | −0.487574 | −0.243787 | − | 0.969829i | \(-0.578390\pi\) | ||||
−0.243787 | + | 0.969829i | \(0.578390\pi\) | |||||||
\(678\) | −5.72792 | −0.219980 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 26.1421 | 1.00251 | ||||||||
\(681\) | −9.59798 | −0.367795 | ||||||||
\(682\) | −4.00000 | −0.153168 | ||||||||
\(683\) | 16.4142 | 0.628072 | 0.314036 | − | 0.949411i | \(-0.398319\pi\) | ||||
0.314036 | + | 0.949411i | \(0.398319\pi\) | |||||||
\(684\) | 9.65685 | 0.369239 | ||||||||
\(685\) | 18.2426 | 0.697015 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.284271 | 0.0108456 | ||||||||
\(688\) | 5.65685 | 0.215666 | ||||||||
\(689\) | −21.7574 | −0.828889 | ||||||||
\(690\) | −3.17157 | −0.120740 | ||||||||
\(691\) | 13.9289 | 0.529882 | 0.264941 | − | 0.964265i | \(-0.414648\pi\) | ||||
0.264941 | + | 0.964265i | \(0.414648\pi\) | |||||||
\(692\) | −4.17157 | −0.158579 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 14.5858 | 0.553669 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −3.58579 | −0.135919 | ||||||||
\(697\) | 19.7990 | 0.749940 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.585786 | −0.0221565 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 36.1127 | 1.36396 | 0.681979 | − | 0.731372i | \(-0.261120\pi\) | ||||
0.681979 | + | 0.731372i | \(0.261120\pi\) | |||||||
\(702\) | −4.41421 | −0.166604 | ||||||||
\(703\) | 22.4853 | 0.848048 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | −9.17157 | −0.345421 | ||||||||
\(706\) | −25.3137 | −0.952694 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −3.48528 | −0.130985 | ||||||||
\(709\) | 36.0416 | 1.35357 | 0.676786 | − | 0.736180i | \(-0.263372\pi\) | ||||
0.676786 | + | 0.736180i | \(0.263372\pi\) | |||||||
\(710\) | −10.4853 | −0.393506 | ||||||||
\(711\) | 13.4558 | 0.504634 | ||||||||
\(712\) | −4.48528 | −0.168093 | ||||||||
\(713\) | −8.97056 | −0.335950 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.24264 | −0.233462 | ||||||||
\(716\) | −18.8995 | −0.706307 | ||||||||
\(717\) | −9.20101 | −0.343618 | ||||||||
\(718\) | 10.7574 | 0.401461 | ||||||||
\(719\) | −18.4853 | −0.689385 | −0.344692 | − | 0.938716i | \(-0.612017\pi\) | ||||
−0.344692 | + | 0.938716i | \(0.612017\pi\) | |||||||
\(720\) | 9.65685 | 0.359890 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −7.34315 | −0.273284 | ||||||||
\(723\) | 1.55635 | 0.0578812 | ||||||||
\(724\) | 3.65685 | 0.135906 | ||||||||
\(725\) | −57.6274 | −2.14023 | ||||||||
\(726\) | 0.414214 | 0.0153729 | ||||||||
\(727\) | −48.4264 | −1.79604 | −0.898018 | − | 0.439959i | \(-0.854993\pi\) | ||||
−0.898018 | + | 0.439959i | \(0.854993\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −18.1716 | −0.673021 | ||||||||
\(730\) | 22.4853 | 0.832218 | ||||||||
\(731\) | −43.3137 | −1.60202 | ||||||||
\(732\) | 2.55635 | 0.0944854 | ||||||||
\(733\) | −13.0000 | −0.480166 | −0.240083 | − | 0.970752i | \(-0.577175\pi\) | ||||
−0.240083 | + | 0.970752i | \(0.577175\pi\) | |||||||
\(734\) | 14.7279 | 0.543618 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.24264 | 0.0826648 | ||||||||
\(737\) | 11.2426 | 0.414128 | ||||||||
\(738\) | 7.31371 | 0.269221 | ||||||||
\(739\) | 32.4264 | 1.19282 | 0.596412 | − | 0.802678i | \(-0.296592\pi\) | ||||
0.596412 | + | 0.802678i | \(0.296592\pi\) | |||||||
\(740\) | 22.4853 | 0.826575 | ||||||||
\(741\) | −2.58579 | −0.0949912 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.31371 | 0.341687 | 0.170843 | − | 0.985298i | \(-0.445351\pi\) | ||||
0.170843 | + | 0.985298i | \(0.445351\pi\) | |||||||
\(744\) | −1.65685 | −0.0607432 | ||||||||
\(745\) | −21.6569 | −0.793446 | ||||||||
\(746\) | 13.9706 | 0.511499 | ||||||||
\(747\) | −45.6569 | −1.67050 | ||||||||
\(748\) | −7.65685 | −0.279962 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −2.34315 | −0.0855596 | ||||||||
\(751\) | 34.3431 | 1.25320 | 0.626600 | − | 0.779341i | \(-0.284446\pi\) | ||||
0.626600 | + | 0.779341i | \(0.284446\pi\) | |||||||
\(752\) | 6.48528 | 0.236494 | ||||||||
\(753\) | 0.887302 | 0.0323351 | ||||||||
\(754\) | −15.8284 | −0.576437 | ||||||||
\(755\) | −33.2132 | −1.20875 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.6569 | 0.714441 | 0.357220 | − | 0.934020i | \(-0.383725\pi\) | ||||
0.357220 | + | 0.934020i | \(0.383725\pi\) | |||||||
\(758\) | −25.8701 | −0.939643 | ||||||||
\(759\) | 0.928932 | 0.0337181 | ||||||||
\(760\) | 11.6569 | 0.422839 | ||||||||
\(761\) | −2.97056 | −0.107683 | −0.0538414 | − | 0.998549i | \(-0.517147\pi\) | ||||
−0.0538414 | + | 0.998549i | \(0.517147\pi\) | |||||||
\(762\) | −4.02944 | −0.145971 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −12.8284 | −0.464116 | ||||||||
\(765\) | −73.9411 | −2.67335 | ||||||||
\(766\) | 30.3848 | 1.09785 | ||||||||
\(767\) | −15.3848 | −0.555512 | ||||||||
\(768\) | 0.414214 | 0.0149466 | ||||||||
\(769\) | −10.9706 | −0.395609 | −0.197804 | − | 0.980242i | \(-0.563381\pi\) | ||||
−0.197804 | + | 0.980242i | \(0.563381\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.30152 | 0.0468729 | ||||||||
\(772\) | 2.10051 | 0.0755988 | ||||||||
\(773\) | 45.9411 | 1.65239 | 0.826194 | − | 0.563386i | \(-0.190502\pi\) | ||||
0.826194 | + | 0.563386i | \(0.190502\pi\) | |||||||
\(774\) | −16.0000 | −0.575108 | ||||||||
\(775\) | −26.6274 | −0.956485 | ||||||||
\(776\) | 1.82843 | 0.0656367 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.72792 | 0.0978007 | ||||||||
\(779\) | 8.82843 | 0.316311 | ||||||||
\(780\) | −2.58579 | −0.0925860 | ||||||||
\(781\) | 3.07107 | 0.109891 | ||||||||
\(782\) | −17.1716 | −0.614054 | ||||||||
\(783\) | 20.8995 | 0.746887 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −21.6569 | −0.772966 | ||||||||
\(786\) | −1.41421 | −0.0504433 | ||||||||
\(787\) | −17.5563 | −0.625816 | −0.312908 | − | 0.949783i | \(-0.601303\pi\) | ||||
−0.312908 | + | 0.949783i | \(0.601303\pi\) | |||||||
\(788\) | −17.4853 | −0.622887 | ||||||||
\(789\) | 12.8579 | 0.457752 | ||||||||
\(790\) | 16.2426 | 0.577887 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −2.82843 | −0.100504 | ||||||||
\(793\) | 11.2843 | 0.400716 | ||||||||
\(794\) | 22.0000 | 0.780751 | ||||||||
\(795\) | 16.8284 | 0.596843 | ||||||||
\(796\) | 19.8995 | 0.705319 | ||||||||
\(797\) | 3.65685 | 0.129532 | 0.0647662 | − | 0.997900i | \(-0.479370\pi\) | ||||
0.0647662 | + | 0.997900i | \(0.479370\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −49.6569 | −1.75673 | ||||||||
\(800\) | 6.65685 | 0.235355 | ||||||||
\(801\) | 12.6863 | 0.448248 | ||||||||
\(802\) | −4.31371 | −0.152322 | ||||||||
\(803\) | −6.58579 | −0.232407 | ||||||||
\(804\) | 4.65685 | 0.164235 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −7.31371 | −0.257614 | ||||||||
\(807\) | 5.65685 | 0.199131 | ||||||||
\(808\) | 11.8284 | 0.416123 | ||||||||
\(809\) | −1.37258 | −0.0482574 | −0.0241287 | − | 0.999709i | \(-0.507681\pi\) | ||||
−0.0241287 | + | 0.999709i | \(0.507681\pi\) | |||||||
\(810\) | −25.5563 | −0.897959 | ||||||||
\(811\) | 32.2843 | 1.13365 | 0.566827 | − | 0.823837i | \(-0.308171\pi\) | ||||
0.566827 | + | 0.823837i | \(0.308171\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −11.0000 | −0.385787 | ||||||||
\(814\) | −6.58579 | −0.230832 | ||||||||
\(815\) | 53.6985 | 1.88098 | ||||||||
\(816\) | −3.17157 | −0.111027 | ||||||||
\(817\) | −19.3137 | −0.675701 | ||||||||
\(818\) | −22.7279 | −0.794663 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 8.82843 | 0.308302 | ||||||||
\(821\) | −12.5147 | −0.436767 | −0.218383 | − | 0.975863i | \(-0.570078\pi\) | ||||
−0.218383 | + | 0.975863i | \(0.570078\pi\) | |||||||
\(822\) | −2.21320 | −0.0771943 | ||||||||
\(823\) | 7.45584 | 0.259894 | 0.129947 | − | 0.991521i | \(-0.458519\pi\) | ||||
0.129947 | + | 0.991521i | \(0.458519\pi\) | |||||||
\(824\) | 10.5858 | 0.368773 | ||||||||
\(825\) | 2.75736 | 0.0959989 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 49.3553 | 1.71625 | 0.858127 | − | 0.513438i | \(-0.171628\pi\) | ||||
0.858127 | + | 0.513438i | \(0.171628\pi\) | |||||||
\(828\) | −6.34315 | −0.220440 | ||||||||
\(829\) | 30.2426 | 1.05037 | 0.525185 | − | 0.850988i | \(-0.323996\pi\) | ||||
0.525185 | + | 0.850988i | \(0.323996\pi\) | |||||||
\(830\) | −55.1127 | −1.91299 | ||||||||
\(831\) | −1.58579 | −0.0550103 | ||||||||
\(832\) | 1.82843 | 0.0633893 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 40.0416 | 1.38570 | ||||||||
\(836\) | −3.41421 | −0.118083 | ||||||||
\(837\) | 9.65685 | 0.333790 | ||||||||
\(838\) | 2.14214 | 0.0739988 | ||||||||
\(839\) | −1.51472 | −0.0522939 | −0.0261469 | − | 0.999658i | \(-0.508324\pi\) | ||||
−0.0261469 | + | 0.999658i | \(0.508324\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 45.9411 | 1.58418 | ||||||||
\(842\) | 23.3137 | 0.803443 | ||||||||
\(843\) | −6.92893 | −0.238645 | ||||||||
\(844\) | 4.58579 | 0.157849 | ||||||||
\(845\) | 32.9706 | 1.13422 | ||||||||
\(846\) | −18.3431 | −0.630650 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −11.8995 | −0.408630 | ||||||||
\(849\) | −8.52691 | −0.292643 | ||||||||
\(850\) | −50.9706 | −1.74828 | ||||||||
\(851\) | −14.7696 | −0.506294 | ||||||||
\(852\) | 1.27208 | 0.0435807 | ||||||||
\(853\) | 14.0000 | 0.479351 | 0.239675 | − | 0.970853i | \(-0.422959\pi\) | ||||
0.239675 | + | 0.970853i | \(0.422959\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −32.9706 | −1.12757 | ||||||||
\(856\) | 11.0711 | 0.378401 | ||||||||
\(857\) | 10.6274 | 0.363026 | 0.181513 | − | 0.983389i | \(-0.441901\pi\) | ||||
0.181513 | + | 0.983389i | \(0.441901\pi\) | |||||||
\(858\) | 0.757359 | 0.0258558 | ||||||||
\(859\) | 19.7279 | 0.673108 | 0.336554 | − | 0.941664i | \(-0.390739\pi\) | ||||
0.336554 | + | 0.941664i | \(0.390739\pi\) | |||||||
\(860\) | −19.3137 | −0.658592 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −20.4142 | −0.695311 | ||||||||
\(863\) | −7.21320 | −0.245540 | −0.122770 | − | 0.992435i | \(-0.539178\pi\) | ||||
−0.122770 | + | 0.992435i | \(0.539178\pi\) | |||||||
\(864\) | −2.41421 | −0.0821332 | ||||||||
\(865\) | 14.2426 | 0.484264 | ||||||||
\(866\) | −2.14214 | −0.0727927 | ||||||||
\(867\) | 17.2426 | 0.585591 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.75736 | −0.161382 | ||||||||
\(870\) | 12.2426 | 0.415064 | ||||||||
\(871\) | 20.5563 | 0.696525 | ||||||||
\(872\) | −0.485281 | −0.0164337 | ||||||||
\(873\) | −5.17157 | −0.175031 | ||||||||
\(874\) | −7.65685 | −0.258997 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2.72792 | −0.0921679 | ||||||||
\(877\) | −25.6274 | −0.865376 | −0.432688 | − | 0.901544i | \(-0.642435\pi\) | ||||
−0.432688 | + | 0.901544i | \(0.642435\pi\) | |||||||
\(878\) | 9.38478 | 0.316721 | ||||||||
\(879\) | −2.14214 | −0.0722524 | ||||||||
\(880\) | −3.41421 | −0.115093 | ||||||||
\(881\) | −44.4558 | −1.49776 | −0.748878 | − | 0.662708i | \(-0.769407\pi\) | ||||
−0.748878 | + | 0.662708i | \(0.769407\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9.72792 | −0.327371 | −0.163685 | − | 0.986513i | \(-0.552338\pi\) | ||||
−0.163685 | + | 0.986513i | \(0.552338\pi\) | |||||||
\(884\) | −14.0000 | −0.470871 | ||||||||
\(885\) | 11.8995 | 0.399997 | ||||||||
\(886\) | −32.6274 | −1.09614 | ||||||||
\(887\) | −22.8995 | −0.768890 | −0.384445 | − | 0.923148i | \(-0.625607\pi\) | ||||
−0.384445 | + | 0.923148i | \(0.625607\pi\) | |||||||
\(888\) | −2.72792 | −0.0915431 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 15.3137 | 0.513317 | ||||||||
\(891\) | 7.48528 | 0.250766 | ||||||||
\(892\) | 11.4142 | 0.382176 | ||||||||
\(893\) | −22.1421 | −0.740958 | ||||||||
\(894\) | 2.62742 | 0.0878740 | ||||||||
\(895\) | 64.5269 | 2.15690 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.69848 | 0.0567108 | ||||||||
\(898\) | 33.6569 | 1.12314 | ||||||||
\(899\) | 34.6274 | 1.15489 | ||||||||
\(900\) | −18.8284 | −0.627614 | ||||||||
\(901\) | 91.1127 | 3.03540 | ||||||||
\(902\) | −2.58579 | −0.0860973 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −13.8284 | −0.459927 | ||||||||
\(905\) | −12.4853 | −0.415025 | ||||||||
\(906\) | 4.02944 | 0.133869 | ||||||||
\(907\) | 33.3137 | 1.10616 | 0.553082 | − | 0.833127i | \(-0.313452\pi\) | ||||
0.553082 | + | 0.833127i | \(0.313452\pi\) | |||||||
\(908\) | −23.1716 | −0.768976 | ||||||||
\(909\) | −33.4558 | −1.10966 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −13.5147 | −0.447763 | −0.223881 | − | 0.974616i | \(-0.571873\pi\) | ||||
−0.223881 | + | 0.974616i | \(0.571873\pi\) | |||||||
\(912\) | −1.41421 | −0.0468293 | ||||||||
\(913\) | 16.1421 | 0.534227 | ||||||||
\(914\) | −0.343146 | −0.0113503 | ||||||||
\(915\) | −8.72792 | −0.288536 | ||||||||
\(916\) | 0.686292 | 0.0226757 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 18.4853 | 0.610105 | ||||||||
\(919\) | −6.14214 | −0.202610 | −0.101305 | − | 0.994855i | \(-0.532302\pi\) | ||||
−0.101305 | + | 0.994855i | \(0.532302\pi\) | |||||||
\(920\) | −7.65685 | −0.252439 | ||||||||
\(921\) | −4.10051 | −0.135116 | ||||||||
\(922\) | 14.3137 | 0.471397 | ||||||||
\(923\) | 5.61522 | 0.184827 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −43.8406 | −1.44147 | ||||||||
\(926\) | 7.17157 | 0.235673 | ||||||||
\(927\) | −29.9411 | −0.983396 | ||||||||
\(928\) | −8.65685 | −0.284175 | ||||||||
\(929\) | 10.4558 | 0.343045 | 0.171523 | − | 0.985180i | \(-0.445131\pi\) | ||||
0.171523 | + | 0.985180i | \(0.445131\pi\) | |||||||
\(930\) | 5.65685 | 0.185496 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −1.41421 | −0.0463241 | ||||||||
\(933\) | −3.61522 | −0.118357 | ||||||||
\(934\) | −34.0000 | −1.11251 | ||||||||
\(935\) | 26.1421 | 0.854939 | ||||||||
\(936\) | −5.17157 | −0.169038 | ||||||||
\(937\) | −16.5858 | −0.541834 | −0.270917 | − | 0.962603i | \(-0.587327\pi\) | ||||
−0.270917 | + | 0.962603i | \(0.587327\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.87006 | −0.126295 | ||||||||
\(940\) | −22.1421 | −0.722197 | ||||||||
\(941\) | 13.3431 | 0.434974 | 0.217487 | − | 0.976063i | \(-0.430214\pi\) | ||||
0.217487 | + | 0.976063i | \(0.430214\pi\) | |||||||
\(942\) | 2.62742 | 0.0856059 | ||||||||
\(943\) | −5.79899 | −0.188841 | ||||||||
\(944\) | −8.41421 | −0.273859 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.65685 | 0.183920 | ||||||||
\(947\) | 29.1716 | 0.947949 | 0.473974 | − | 0.880539i | \(-0.342819\pi\) | ||||
0.473974 | + | 0.880539i | \(0.342819\pi\) | |||||||
\(948\) | −1.97056 | −0.0640009 | ||||||||
\(949\) | −12.0416 | −0.390888 | ||||||||
\(950\) | −22.7279 | −0.737391 | ||||||||
\(951\) | 12.9706 | 0.420599 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −25.5563 | −0.827851 | −0.413926 | − | 0.910311i | \(-0.635843\pi\) | ||||
−0.413926 | + | 0.910311i | \(0.635843\pi\) | |||||||
\(954\) | 33.6569 | 1.08968 | ||||||||
\(955\) | 43.7990 | 1.41730 | ||||||||
\(956\) | −22.2132 | −0.718426 | ||||||||
\(957\) | −3.58579 | −0.115912 | ||||||||
\(958\) | −26.0711 | −0.842318 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.41421 | −0.0456435 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | −12.0416 | −0.388238 | ||||||||
\(963\) | −31.3137 | −1.00907 | ||||||||
\(964\) | 3.75736 | 0.121016 | ||||||||
\(965\) | −7.17157 | −0.230861 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20.2843 | 0.652298 | 0.326149 | − | 0.945318i | \(-0.394249\pi\) | ||||
0.326149 | + | 0.945318i | \(0.394249\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | 10.8284 | 0.347859 | ||||||||
\(970\) | −6.24264 | −0.200439 | ||||||||
\(971\) | 47.7279 | 1.53166 | 0.765831 | − | 0.643042i | \(-0.222328\pi\) | ||||
0.765831 | + | 0.643042i | \(0.222328\pi\) | |||||||
\(972\) | 10.3431 | 0.331757 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 1.65685 | 0.0530890 | ||||||||
\(975\) | 5.04163 | 0.161461 | ||||||||
\(976\) | 6.17157 | 0.197547 | ||||||||
\(977\) | 40.0000 | 1.27971 | 0.639857 | − | 0.768494i | \(-0.278994\pi\) | ||||
0.639857 | + | 0.768494i | \(0.278994\pi\) | |||||||
\(978\) | −6.51472 | −0.208318 | ||||||||
\(979\) | −4.48528 | −0.143350 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.37258 | 0.0438232 | ||||||||
\(982\) | 24.8284 | 0.792307 | ||||||||
\(983\) | −52.4264 | −1.67214 | −0.836071 | − | 0.548621i | \(-0.815153\pi\) | ||||
−0.836071 | + | 0.548621i | \(0.815153\pi\) | |||||||
\(984\) | −1.07107 | −0.0341444 | ||||||||
\(985\) | 59.6985 | 1.90215 | ||||||||
\(986\) | 66.2843 | 2.11092 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −6.24264 | −0.198605 | ||||||||
\(989\) | 12.6863 | 0.403401 | ||||||||
\(990\) | 9.65685 | 0.306915 | ||||||||
\(991\) | −38.3848 | −1.21933 | −0.609666 | − | 0.792658i | \(-0.708697\pi\) | ||||
−0.609666 | + | 0.792658i | \(0.708697\pi\) | |||||||
\(992\) | −4.00000 | −0.127000 | ||||||||
\(993\) | −4.11270 | −0.130513 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −67.9411 | −2.15388 | ||||||||
\(996\) | 6.68629 | 0.211863 | ||||||||
\(997\) | 18.8284 | 0.596302 | 0.298151 | − | 0.954519i | \(-0.403630\pi\) | ||||
0.298151 | + | 0.954519i | \(0.403630\pi\) | |||||||
\(998\) | −6.14214 | −0.194426 | ||||||||
\(999\) | 15.8995 | 0.503038 |
(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 | 1078.2.a.t.1.2 | 2 | ||
3.2 | odd | 2 | 9702.2.a.cx.1.2 | 2 | |||
4.3 | odd | 2 | 8624.2.a.cc.1.1 | 2 | |||
7.2 | even | 3 | 154.2.e.e.67.1 | yes | 4 | ||
7.3 | odd | 6 | 1078.2.e.m.177.2 | 4 | |||
7.4 | even | 3 | 154.2.e.e.23.1 | ✓ | 4 | ||
7.5 | odd | 6 | 1078.2.e.m.67.2 | 4 | |||
7.6 | odd | 2 | 1078.2.a.x.1.1 | 2 | |||
21.2 | odd | 6 | 1386.2.k.t.991.1 | 4 | |||
21.11 | odd | 6 | 1386.2.k.t.793.1 | 4 | |||
21.20 | even | 2 | 9702.2.a.ch.1.1 | 2 | |||
28.11 | odd | 6 | 1232.2.q.f.177.2 | 4 | |||
28.23 | odd | 6 | 1232.2.q.f.529.2 | 4 | |||
28.27 | even | 2 | 8624.2.a.bh.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
154.2.e.e.23.1 | ✓ | 4 | 7.4 | even | 3 | ||
154.2.e.e.67.1 | yes | 4 | 7.2 | even | 3 | ||
1078.2.a.t.1.2 | 2 | 1.1 | even | 1 | trivial | ||
1078.2.a.x.1.1 | 2 | 7.6 | odd | 2 | |||
1078.2.e.m.67.2 | 4 | 7.5 | odd | 6 | |||
1078.2.e.m.177.2 | 4 | 7.3 | odd | 6 | |||
1232.2.q.f.177.2 | 4 | 28.11 | odd | 6 | |||
1232.2.q.f.529.2 | 4 | 28.23 | odd | 6 | |||
1386.2.k.t.793.1 | 4 | 21.11 | odd | 6 | |||
1386.2.k.t.991.1 | 4 | 21.2 | odd | 6 | |||
8624.2.a.bh.1.2 | 2 | 28.27 | even | 2 | |||
8624.2.a.cc.1.1 | 2 | 4.3 | odd | 2 | |||
9702.2.a.ch.1.1 | 2 | 21.20 | even | 2 | |||
9702.2.a.cx.1.2 | 2 | 3.2 | odd | 2 |