Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2601,2,Mod(1,2601)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2601, 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("2601.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2601 = 3^{2} \cdot 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2601.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: | \(20.7690895657\) |
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: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 867) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2601.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.41421 | −1.70711 | −0.853553 | − | 0.521005i | \(-0.825557\pi\) | ||||
−0.853553 | + | 0.521005i | \(0.825557\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.82843 | 1.91421 | ||||||||
\(5\) | −2.82843 | −1.26491 | −0.632456 | − | 0.774597i | \(-0.717953\pi\) | ||||
−0.632456 | + | 0.774597i | \(0.717953\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.00000 | −1.13389 | −0.566947 | − | 0.823754i | \(-0.691875\pi\) | ||||
−0.566947 | + | 0.823754i | \(0.691875\pi\) | |||||||
\(8\) | −4.41421 | −1.56066 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 6.82843 | 2.15934 | ||||||||
\(11\) | −0.828427 | −0.249780 | −0.124890 | − | 0.992171i | \(-0.539858\pi\) | ||||
−0.124890 | + | 0.992171i | \(0.539858\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.65685 | 1.84628 | 0.923140 | − | 0.384465i | \(-0.125614\pi\) | ||||
0.923140 | + | 0.384465i | \(0.125614\pi\) | |||||||
\(14\) | 7.24264 | 1.93568 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.00000 | 0.750000 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.00000 | −0.688247 | −0.344124 | − | 0.938924i | \(-0.611824\pi\) | ||||
−0.344124 | + | 0.938924i | \(0.611824\pi\) | |||||||
\(20\) | −10.8284 | −2.42131 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.00000 | 0.426401 | ||||||||
\(23\) | −2.82843 | −0.589768 | −0.294884 | − | 0.955533i | \(-0.595281\pi\) | ||||
−0.294884 | + | 0.955533i | \(0.595281\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.00000 | 0.600000 | ||||||||
\(26\) | −16.0711 | −3.15180 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −11.4853 | −2.17051 | ||||||||
\(29\) | −3.17157 | −0.588946 | −0.294473 | − | 0.955660i | \(-0.595144\pi\) | ||||
−0.294473 | + | 0.955660i | \(0.595144\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.65685 | 0.836396 | 0.418198 | − | 0.908356i | \(-0.362662\pi\) | ||||
0.418198 | + | 0.908356i | \(0.362662\pi\) | |||||||
\(32\) | 1.58579 | 0.280330 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 8.48528 | 1.43427 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.65685 | −1.09438 | −0.547190 | − | 0.837008i | \(-0.684303\pi\) | ||||
−0.547190 | + | 0.837008i | \(0.684303\pi\) | |||||||
\(38\) | 7.24264 | 1.17491 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 12.4853 | 1.97410 | ||||||||
\(41\) | 8.82843 | 1.37877 | 0.689384 | − | 0.724396i | \(-0.257881\pi\) | ||||
0.689384 | + | 0.724396i | \(0.257881\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.00000 | 0.457496 | 0.228748 | − | 0.973486i | \(-0.426537\pi\) | ||||
0.228748 | + | 0.973486i | \(0.426537\pi\) | |||||||
\(44\) | −3.17157 | −0.478133 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.82843 | 1.00680 | ||||||||
\(47\) | 9.65685 | 1.40860 | 0.704298 | − | 0.709904i | \(-0.251262\pi\) | ||||
0.704298 | + | 0.709904i | \(0.251262\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.00000 | 0.285714 | ||||||||
\(50\) | −7.24264 | −1.02426 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 25.4853 | 3.53417 | ||||||||
\(53\) | 1.65685 | 0.227586 | 0.113793 | − | 0.993504i | \(-0.463700\pi\) | ||||
0.113793 | + | 0.993504i | \(0.463700\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.34315 | 0.315950 | ||||||||
\(56\) | 13.2426 | 1.76962 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 7.65685 | 1.00539 | ||||||||
\(59\) | 8.82843 | 1.14936 | 0.574682 | − | 0.818377i | \(-0.305126\pi\) | ||||
0.574682 | + | 0.818377i | \(0.305126\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.65685 | 0.596249 | 0.298125 | − | 0.954527i | \(-0.403639\pi\) | ||||
0.298125 | + | 0.954527i | \(0.403639\pi\) | |||||||
\(62\) | −11.2426 | −1.42782 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −9.82843 | −1.22855 | ||||||||
\(65\) | −18.8284 | −2.33538 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.00000 | 0.122169 | 0.0610847 | − | 0.998133i | \(-0.480544\pi\) | ||||
0.0610847 | + | 0.998133i | \(0.480544\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −20.4853 | −2.44846 | ||||||||
\(71\) | −5.17157 | −0.613753 | −0.306876 | − | 0.951749i | \(-0.599284\pi\) | ||||
−0.306876 | + | 0.951749i | \(0.599284\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.65685 | 0.896167 | 0.448084 | − | 0.893992i | \(-0.352107\pi\) | ||||
0.448084 | + | 0.893992i | \(0.352107\pi\) | |||||||
\(74\) | 16.0711 | 1.86822 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −11.4853 | −1.31745 | ||||||||
\(77\) | 2.48528 | 0.283224 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.0000 | −1.35011 | −0.675053 | − | 0.737769i | \(-0.735879\pi\) | ||||
−0.675053 | + | 0.737769i | \(0.735879\pi\) | |||||||
\(80\) | −8.48528 | −0.948683 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −21.3137 | −2.35371 | ||||||||
\(83\) | −1.17157 | −0.128597 | −0.0642984 | − | 0.997931i | \(-0.520481\pi\) | ||||
−0.0642984 | + | 0.997931i | \(0.520481\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −7.24264 | −0.780994 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.65685 | 0.389822 | ||||||||
\(89\) | −5.31371 | −0.563252 | −0.281626 | − | 0.959524i | \(-0.590874\pi\) | ||||
−0.281626 | + | 0.959524i | \(0.590874\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −19.9706 | −2.09348 | ||||||||
\(92\) | −10.8284 | −1.12894 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −23.3137 | −2.40463 | ||||||||
\(95\) | 8.48528 | 0.870572 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.6569 | 1.08204 | 0.541020 | − | 0.841010i | \(-0.318038\pi\) | ||||
0.541020 | + | 0.841010i | \(0.318038\pi\) | |||||||
\(98\) | −4.82843 | −0.487745 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 11.4853 | 1.14853 | ||||||||
\(101\) | 11.6569 | 1.15990 | 0.579950 | − | 0.814652i | \(-0.303072\pi\) | ||||
0.579950 | + | 0.814652i | \(0.303072\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.0000 | −1.47799 | −0.738997 | − | 0.673709i | \(-0.764700\pi\) | ||||
−0.738997 | + | 0.673709i | \(0.764700\pi\) | |||||||
\(104\) | −29.3848 | −2.88141 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.00000 | −0.388514 | ||||||||
\(107\) | 6.00000 | 0.580042 | 0.290021 | − | 0.957020i | \(-0.406338\pi\) | ||||
0.290021 | + | 0.957020i | \(0.406338\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.65685 | 0.350263 | 0.175132 | − | 0.984545i | \(-0.443965\pi\) | ||||
0.175132 | + | 0.984545i | \(0.443965\pi\) | |||||||
\(110\) | −5.65685 | −0.539360 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −9.00000 | −0.850420 | ||||||||
\(113\) | 3.65685 | 0.344008 | 0.172004 | − | 0.985096i | \(-0.444976\pi\) | ||||
0.172004 | + | 0.985096i | \(0.444976\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.00000 | 0.746004 | ||||||||
\(116\) | −12.1421 | −1.12737 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −21.3137 | −1.96209 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.3137 | −0.937610 | ||||||||
\(122\) | −11.2426 | −1.01786 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 17.8284 | 1.60104 | ||||||||
\(125\) | 5.65685 | 0.505964 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.34315 | −0.119185 | −0.0595925 | − | 0.998223i | \(-0.518980\pi\) | ||||
−0.0595925 | + | 0.998223i | \(0.518980\pi\) | |||||||
\(128\) | 20.5563 | 1.81694 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 45.4558 | 3.98674 | ||||||||
\(131\) | −9.17157 | −0.801324 | −0.400662 | − | 0.916226i | \(-0.631220\pi\) | ||||
−0.400662 | + | 0.916226i | \(0.631220\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.00000 | 0.780399 | ||||||||
\(134\) | −2.41421 | −0.208556 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −17.7990 | −1.52067 | −0.760335 | − | 0.649531i | \(-0.774965\pi\) | ||||
−0.760335 | + | 0.649531i | \(0.774965\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.34315 | −0.453200 | −0.226600 | − | 0.973988i | \(-0.572761\pi\) | ||||
−0.226600 | + | 0.973988i | \(0.572761\pi\) | |||||||
\(140\) | 32.4853 | 2.74551 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 12.4853 | 1.04774 | ||||||||
\(143\) | −5.51472 | −0.461164 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.97056 | 0.744965 | ||||||||
\(146\) | −18.4853 | −1.52985 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −25.4853 | −2.09488 | ||||||||
\(149\) | −18.8284 | −1.54248 | −0.771242 | − | 0.636542i | \(-0.780364\pi\) | ||||
−0.771242 | + | 0.636542i | \(0.780364\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.00000 | 0.406894 | 0.203447 | − | 0.979086i | \(-0.434786\pi\) | ||||
0.203447 | + | 0.979086i | \(0.434786\pi\) | |||||||
\(152\) | 13.2426 | 1.07412 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −6.00000 | −0.483494 | ||||||||
\(155\) | −13.1716 | −1.05797 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.9706 | −1.43421 | −0.717104 | − | 0.696967i | \(-0.754533\pi\) | ||||
−0.717104 | + | 0.696967i | \(0.754533\pi\) | |||||||
\(158\) | 28.9706 | 2.30477 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −4.48528 | −0.354593 | ||||||||
\(161\) | 8.48528 | 0.668734 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.65685 | −0.129775 | −0.0648874 | − | 0.997893i | \(-0.520669\pi\) | ||||
−0.0648874 | + | 0.997893i | \(0.520669\pi\) | |||||||
\(164\) | 33.7990 | 2.63926 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.82843 | 0.219529 | ||||||||
\(167\) | 9.31371 | 0.720716 | 0.360358 | − | 0.932814i | \(-0.382654\pi\) | ||||
0.360358 | + | 0.932814i | \(0.382654\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 31.3137 | 2.40875 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 11.4853 | 0.875744 | ||||||||
\(173\) | 21.3137 | 1.62045 | 0.810226 | − | 0.586118i | \(-0.199345\pi\) | ||||
0.810226 | + | 0.586118i | \(0.199345\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.00000 | −0.680336 | ||||||||
\(176\) | −2.48528 | −0.187335 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 12.8284 | 0.961531 | ||||||||
\(179\) | −12.1421 | −0.907546 | −0.453773 | − | 0.891117i | \(-0.649922\pi\) | ||||
−0.453773 | + | 0.891117i | \(0.649922\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.9706 | −1.48440 | −0.742200 | − | 0.670178i | \(-0.766218\pi\) | ||||
−0.742200 | + | 0.670178i | \(0.766218\pi\) | |||||||
\(182\) | 48.2132 | 3.57380 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 12.4853 | 0.920427 | ||||||||
\(185\) | 18.8284 | 1.38429 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 36.9706 | 2.69636 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −20.4853 | −1.48616 | ||||||||
\(191\) | −26.1421 | −1.89158 | −0.945789 | − | 0.324781i | \(-0.894709\pi\) | ||||
−0.945789 | + | 0.324781i | \(0.894709\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.3137 | 0.742397 | 0.371198 | − | 0.928554i | \(-0.378947\pi\) | ||||
0.371198 | + | 0.928554i | \(0.378947\pi\) | |||||||
\(194\) | −25.7279 | −1.84716 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 7.65685 | 0.546918 | ||||||||
\(197\) | 2.34315 | 0.166942 | 0.0834711 | − | 0.996510i | \(-0.473399\pi\) | ||||
0.0834711 | + | 0.996510i | \(0.473399\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.00000 | −0.567105 | −0.283552 | − | 0.958957i | \(-0.591513\pi\) | ||||
−0.283552 | + | 0.958957i | \(0.591513\pi\) | |||||||
\(200\) | −13.2426 | −0.936396 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −28.1421 | −1.98007 | ||||||||
\(203\) | 9.51472 | 0.667802 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −24.9706 | −1.74402 | ||||||||
\(206\) | 36.2132 | 2.52309 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 19.9706 | 1.38471 | ||||||||
\(209\) | 2.48528 | 0.171911 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −21.9706 | −1.51252 | −0.756258 | − | 0.654274i | \(-0.772974\pi\) | ||||
−0.756258 | + | 0.654274i | \(0.772974\pi\) | |||||||
\(212\) | 6.34315 | 0.435649 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −14.4853 | −0.990193 | ||||||||
\(215\) | −8.48528 | −0.578691 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −13.9706 | −0.948384 | ||||||||
\(218\) | −8.82843 | −0.597937 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 8.97056 | 0.604795 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 26.6274 | 1.78310 | 0.891552 | − | 0.452919i | \(-0.149617\pi\) | ||||
0.891552 | + | 0.452919i | \(0.149617\pi\) | |||||||
\(224\) | −4.75736 | −0.317864 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −8.82843 | −0.587258 | ||||||||
\(227\) | −26.4853 | −1.75789 | −0.878945 | − | 0.476923i | \(-0.841752\pi\) | ||||
−0.878945 | + | 0.476923i | \(0.841752\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.9706 | 1.51794 | 0.758969 | − | 0.651127i | \(-0.225704\pi\) | ||||
0.758969 | + | 0.651127i | \(0.225704\pi\) | |||||||
\(230\) | −19.3137 | −1.27351 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 14.0000 | 0.919145 | ||||||||
\(233\) | −17.6569 | −1.15674 | −0.578369 | − | 0.815775i | \(-0.696311\pi\) | ||||
−0.578369 | + | 0.815775i | \(0.696311\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −27.3137 | −1.78175 | ||||||||
\(236\) | 33.7990 | 2.20013 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.34315 | 0.280935 | 0.140467 | − | 0.990085i | \(-0.455139\pi\) | ||||
0.140467 | + | 0.990085i | \(0.455139\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.00000 | −0.386494 | −0.193247 | − | 0.981150i | \(-0.561902\pi\) | ||||
−0.193247 | + | 0.981150i | \(0.561902\pi\) | |||||||
\(242\) | 24.8995 | 1.60060 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 17.8284 | 1.14135 | ||||||||
\(245\) | −5.65685 | −0.361403 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −19.9706 | −1.27070 | ||||||||
\(248\) | −20.5563 | −1.30533 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −13.6569 | −0.863735 | ||||||||
\(251\) | 4.82843 | 0.304768 | 0.152384 | − | 0.988321i | \(-0.451305\pi\) | ||||
0.152384 | + | 0.988321i | \(0.451305\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.34315 | 0.147312 | ||||||||
\(254\) | 3.24264 | 0.203461 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −29.9706 | −1.87316 | ||||||||
\(257\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 19.9706 | 1.24091 | ||||||||
\(260\) | −72.0833 | −4.47041 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 22.1421 | 1.36795 | ||||||||
\(263\) | −25.3137 | −1.56091 | −0.780455 | − | 0.625212i | \(-0.785013\pi\) | ||||
−0.780455 | + | 0.625212i | \(0.785013\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.68629 | −0.287877 | ||||||||
\(266\) | −21.7279 | −1.33222 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.82843 | 0.233858 | ||||||||
\(269\) | −5.17157 | −0.315316 | −0.157658 | − | 0.987494i | \(-0.550394\pi\) | ||||
−0.157658 | + | 0.987494i | \(0.550394\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −24.3137 | −1.47695 | −0.738476 | − | 0.674279i | \(-0.764454\pi\) | ||||
−0.738476 | + | 0.674279i | \(0.764454\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 42.9706 | 2.59595 | ||||||||
\(275\) | −2.48528 | −0.149868 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.97056 | −0.478905 | −0.239452 | − | 0.970908i | \(-0.576968\pi\) | ||||
−0.239452 | + | 0.970908i | \(0.576968\pi\) | |||||||
\(278\) | 12.8995 | 0.773660 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −37.4558 | −2.23841 | ||||||||
\(281\) | −3.17157 | −0.189200 | −0.0946001 | − | 0.995515i | \(-0.530157\pi\) | ||||
−0.0946001 | + | 0.995515i | \(0.530157\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.00000 | 0.178331 | 0.0891657 | − | 0.996017i | \(-0.471580\pi\) | ||||
0.0891657 | + | 0.996017i | \(0.471580\pi\) | |||||||
\(284\) | −19.7990 | −1.17485 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 13.3137 | 0.787256 | ||||||||
\(287\) | −26.4853 | −1.56338 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | −21.6569 | −1.27173 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 29.3137 | 1.71546 | ||||||||
\(293\) | −0.686292 | −0.0400936 | −0.0200468 | − | 0.999799i | \(-0.506382\pi\) | ||||
−0.0200468 | + | 0.999799i | \(0.506382\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −24.9706 | −1.45384 | ||||||||
\(296\) | 29.3848 | 1.70796 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 45.4558 | 2.63319 | ||||||||
\(299\) | −18.8284 | −1.08888 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.00000 | −0.518751 | ||||||||
\(302\) | −12.0711 | −0.694612 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −9.00000 | −0.516185 | ||||||||
\(305\) | −13.1716 | −0.754202 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.65685 | 0.551146 | 0.275573 | − | 0.961280i | \(-0.411132\pi\) | ||||
0.275573 | + | 0.961280i | \(0.411132\pi\) | |||||||
\(308\) | 9.51472 | 0.542151 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 31.7990 | 1.80606 | ||||||||
\(311\) | −22.9706 | −1.30254 | −0.651271 | − | 0.758846i | \(-0.725764\pi\) | ||||
−0.651271 | + | 0.758846i | \(0.725764\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.3431 | 0.754199 | 0.377100 | − | 0.926173i | \(-0.376921\pi\) | ||||
0.377100 | + | 0.926173i | \(0.376921\pi\) | |||||||
\(314\) | 43.3848 | 2.44834 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −45.9411 | −2.58439 | ||||||||
\(317\) | −20.4853 | −1.15057 | −0.575284 | − | 0.817954i | \(-0.695108\pi\) | ||||
−0.575284 | + | 0.817954i | \(0.695108\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.62742 | 0.147107 | ||||||||
\(320\) | 27.7990 | 1.55401 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −20.4853 | −1.14160 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 19.9706 | 1.10777 | ||||||||
\(326\) | 4.00000 | 0.221540 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −38.9706 | −2.15179 | ||||||||
\(329\) | −28.9706 | −1.59720 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.34315 | −0.403616 | −0.201808 | − | 0.979425i | \(-0.564682\pi\) | ||||
−0.201808 | + | 0.979425i | \(0.564682\pi\) | |||||||
\(332\) | −4.48528 | −0.246162 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −22.4853 | −1.23034 | ||||||||
\(335\) | −2.82843 | −0.154533 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.00000 | 0.108947 | 0.0544735 | − | 0.998515i | \(-0.482652\pi\) | ||||
0.0544735 | + | 0.998515i | \(0.482652\pi\) | |||||||
\(338\) | −75.5980 | −4.11199 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.85786 | −0.208915 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.0000 | 0.809924 | ||||||||
\(344\) | −13.2426 | −0.713995 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −51.4558 | −2.76628 | ||||||||
\(347\) | −15.7990 | −0.848134 | −0.424067 | − | 0.905631i | \(-0.639398\pi\) | ||||
−0.424067 | + | 0.905631i | \(0.639398\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −32.6274 | −1.74651 | −0.873253 | − | 0.487267i | \(-0.837994\pi\) | ||||
−0.873253 | + | 0.487267i | \(0.837994\pi\) | |||||||
\(350\) | 21.7279 | 1.16141 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.31371 | −0.0700209 | ||||||||
\(353\) | −11.3137 | −0.602168 | −0.301084 | − | 0.953598i | \(-0.597348\pi\) | ||||
−0.301084 | + | 0.953598i | \(0.597348\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 14.6274 | 0.776343 | ||||||||
\(356\) | −20.3431 | −1.07818 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 29.3137 | 1.54928 | ||||||||
\(359\) | −18.3431 | −0.968114 | −0.484057 | − | 0.875036i | \(-0.660837\pi\) | ||||
−0.484057 | + | 0.875036i | \(0.660837\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.0000 | −0.526316 | ||||||||
\(362\) | 48.2132 | 2.53403 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −76.4558 | −4.00738 | ||||||||
\(365\) | −21.6569 | −1.13357 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.3431 | 0.905305 | 0.452652 | − | 0.891687i | \(-0.350478\pi\) | ||||
0.452652 | + | 0.891687i | \(0.350478\pi\) | |||||||
\(368\) | −8.48528 | −0.442326 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −45.4558 | −2.36314 | ||||||||
\(371\) | −4.97056 | −0.258059 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 31.6569 | 1.63913 | 0.819565 | − | 0.572986i | \(-0.194215\pi\) | ||||
0.819565 | + | 0.572986i | \(0.194215\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −42.6274 | −2.19834 | ||||||||
\(377\) | −21.1127 | −1.08736 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.00000 | −0.154100 | −0.0770498 | − | 0.997027i | \(-0.524550\pi\) | ||||
−0.0770498 | + | 0.997027i | \(0.524550\pi\) | |||||||
\(380\) | 32.4853 | 1.66646 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 63.1127 | 3.22913 | ||||||||
\(383\) | 28.1421 | 1.43800 | 0.718998 | − | 0.695012i | \(-0.244601\pi\) | ||||
0.718998 | + | 0.695012i | \(0.244601\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.02944 | −0.358253 | ||||||||
\(386\) | −24.8995 | −1.26735 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 40.7990 | 2.07125 | ||||||||
\(389\) | −0.142136 | −0.00720656 | −0.00360328 | − | 0.999994i | \(-0.501147\pi\) | ||||
−0.00360328 | + | 0.999994i | \(0.501147\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −8.82843 | −0.445903 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −5.65685 | −0.284988 | ||||||||
\(395\) | 33.9411 | 1.70776 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.0000 | −1.10415 | −0.552074 | − | 0.833795i | \(-0.686163\pi\) | ||||
−0.552074 | + | 0.833795i | \(0.686163\pi\) | |||||||
\(398\) | 19.3137 | 0.968109 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 9.00000 | 0.450000 | ||||||||
\(401\) | 31.7990 | 1.58797 | 0.793983 | − | 0.607940i | \(-0.208004\pi\) | ||||
0.793983 | + | 0.607940i | \(0.208004\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 31.0000 | 1.54422 | ||||||||
\(404\) | 44.6274 | 2.22030 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −22.9706 | −1.14001 | ||||||||
\(407\) | 5.51472 | 0.273354 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.00000 | 0.247234 | 0.123617 | − | 0.992330i | \(-0.460551\pi\) | ||||
0.123617 | + | 0.992330i | \(0.460551\pi\) | |||||||
\(410\) | 60.2843 | 2.97723 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −57.4264 | −2.82920 | ||||||||
\(413\) | −26.4853 | −1.30326 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.31371 | 0.162664 | ||||||||
\(416\) | 10.5563 | 0.517568 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −6.00000 | −0.293470 | ||||||||
\(419\) | 22.1421 | 1.08171 | 0.540857 | − | 0.841115i | \(-0.318100\pi\) | ||||
0.540857 | + | 0.841115i | \(0.318100\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.6863 | 0.667029 | 0.333515 | − | 0.942745i | \(-0.391765\pi\) | ||||
0.333515 | + | 0.942745i | \(0.391765\pi\) | |||||||
\(422\) | 53.0416 | 2.58203 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −7.31371 | −0.355185 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13.9706 | −0.676083 | ||||||||
\(428\) | 22.9706 | 1.11032 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 20.4853 | 0.987888 | ||||||||
\(431\) | −40.9706 | −1.97348 | −0.986741 | − | 0.162301i | \(-0.948108\pi\) | ||||
−0.986741 | + | 0.162301i | \(0.948108\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.02944 | 0.0975285 | 0.0487643 | − | 0.998810i | \(-0.484472\pi\) | ||||
0.0487643 | + | 0.998810i | \(0.484472\pi\) | |||||||
\(434\) | 33.7279 | 1.61899 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 14.0000 | 0.670478 | ||||||||
\(437\) | 8.48528 | 0.405906 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −22.3137 | −1.06498 | −0.532488 | − | 0.846438i | \(-0.678743\pi\) | ||||
−0.532488 | + | 0.846438i | \(0.678743\pi\) | |||||||
\(440\) | −10.3431 | −0.493090 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −26.8284 | −1.27466 | −0.637329 | − | 0.770592i | \(-0.719961\pi\) | ||||
−0.637329 | + | 0.770592i | \(0.719961\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 15.0294 | 0.712464 | ||||||||
\(446\) | −64.2843 | −3.04395 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 29.4853 | 1.39305 | ||||||||
\(449\) | 1.02944 | 0.0485821 | 0.0242911 | − | 0.999705i | \(-0.492267\pi\) | ||||
0.0242911 | + | 0.999705i | \(0.492267\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.31371 | −0.344389 | ||||||||
\(452\) | 14.0000 | 0.658505 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 63.9411 | 3.00091 | ||||||||
\(455\) | 56.4853 | 2.64807 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.68629 | 0.125659 | 0.0628297 | − | 0.998024i | \(-0.479988\pi\) | ||||
0.0628297 | + | 0.998024i | \(0.479988\pi\) | |||||||
\(458\) | −55.4558 | −2.59128 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 30.6274 | 1.42801 | ||||||||
\(461\) | −16.6274 | −0.774416 | −0.387208 | − | 0.921992i | \(-0.626560\pi\) | ||||
−0.387208 | + | 0.921992i | \(0.626560\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.3137 | −0.479319 | −0.239659 | − | 0.970857i | \(-0.577036\pi\) | ||||
−0.239659 | + | 0.970857i | \(0.577036\pi\) | |||||||
\(464\) | −9.51472 | −0.441710 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 42.6274 | 1.97468 | ||||||||
\(467\) | 4.97056 | 0.230010 | 0.115005 | − | 0.993365i | \(-0.463312\pi\) | ||||
0.115005 | + | 0.993365i | \(0.463312\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.00000 | −0.138527 | ||||||||
\(470\) | 65.9411 | 3.04164 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −38.9706 | −1.79377 | ||||||||
\(473\) | −2.48528 | −0.114273 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9.00000 | −0.412948 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −10.4853 | −0.479586 | ||||||||
\(479\) | 12.1421 | 0.554788 | 0.277394 | − | 0.960756i | \(-0.410529\pi\) | ||||
0.277394 | + | 0.960756i | \(0.410529\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −44.3137 | −2.02053 | ||||||||
\(482\) | 14.4853 | 0.659786 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −39.4853 | −1.79479 | ||||||||
\(485\) | −30.1421 | −1.36868 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 33.9706 | 1.53935 | 0.769677 | − | 0.638434i | \(-0.220417\pi\) | ||||
0.769677 | + | 0.638434i | \(0.220417\pi\) | |||||||
\(488\) | −20.5563 | −0.930542 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 13.6569 | 0.616954 | ||||||||
\(491\) | 10.9706 | 0.495095 | 0.247547 | − | 0.968876i | \(-0.420375\pi\) | ||||
0.247547 | + | 0.968876i | \(0.420375\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 48.2132 | 2.16921 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 13.9706 | 0.627297 | ||||||||
\(497\) | 15.5147 | 0.695930 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 23.9706 | 1.07307 | 0.536535 | − | 0.843878i | \(-0.319733\pi\) | ||||
0.536535 | + | 0.843878i | \(0.319733\pi\) | |||||||
\(500\) | 21.6569 | 0.968524 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −11.6569 | −0.520271 | ||||||||
\(503\) | −24.1421 | −1.07644 | −0.538222 | − | 0.842803i | \(-0.680904\pi\) | ||||
−0.538222 | + | 0.842803i | \(0.680904\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −32.9706 | −1.46717 | ||||||||
\(506\) | −5.65685 | −0.251478 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −5.14214 | −0.228145 | ||||||||
\(509\) | −11.6569 | −0.516681 | −0.258340 | − | 0.966054i | \(-0.583176\pi\) | ||||
−0.258340 | + | 0.966054i | \(0.583176\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −22.9706 | −1.01616 | ||||||||
\(512\) | 31.2426 | 1.38074 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 42.4264 | 1.86953 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.00000 | −0.351840 | ||||||||
\(518\) | −48.2132 | −2.11837 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 83.1127 | 3.64473 | ||||||||
\(521\) | −18.1421 | −0.794821 | −0.397411 | − | 0.917641i | \(-0.630091\pi\) | ||||
−0.397411 | + | 0.917641i | \(0.630091\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.0000 | 0.699631 | 0.349816 | − | 0.936819i | \(-0.386244\pi\) | ||||
0.349816 | + | 0.936819i | \(0.386244\pi\) | |||||||
\(524\) | −35.1127 | −1.53391 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 61.1127 | 2.66464 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.0000 | −0.652174 | ||||||||
\(530\) | 11.3137 | 0.491436 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 34.4558 | 1.49385 | ||||||||
\(533\) | 58.7696 | 2.54559 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −16.9706 | −0.733701 | ||||||||
\(536\) | −4.41421 | −0.190665 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 12.4853 | 0.538279 | ||||||||
\(539\) | −1.65685 | −0.0713658 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −27.9411 | −1.20128 | −0.600641 | − | 0.799519i | \(-0.705088\pi\) | ||||
−0.600641 | + | 0.799519i | \(0.705088\pi\) | |||||||
\(542\) | 58.6985 | 2.52132 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10.3431 | −0.443052 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.00000 | −0.213785 | −0.106892 | − | 0.994271i | \(-0.534090\pi\) | ||||
−0.106892 | + | 0.994271i | \(0.534090\pi\) | |||||||
\(548\) | −68.1421 | −2.91089 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 6.00000 | 0.255841 | ||||||||
\(551\) | 9.51472 | 0.405341 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 36.0000 | 1.53088 | ||||||||
\(554\) | 19.2426 | 0.817541 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −20.4558 | −0.867521 | ||||||||
\(557\) | −21.6569 | −0.917630 | −0.458815 | − | 0.888532i | \(-0.651726\pi\) | ||||
−0.458815 | + | 0.888532i | \(0.651726\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 19.9706 | 0.844665 | ||||||||
\(560\) | 25.4558 | 1.07571 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 7.65685 | 0.322985 | ||||||||
\(563\) | −4.62742 | −0.195022 | −0.0975112 | − | 0.995234i | \(-0.531088\pi\) | ||||
−0.0975112 | + | 0.995234i | \(0.531088\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.3431 | −0.435139 | ||||||||
\(566\) | −7.24264 | −0.304431 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 22.8284 | 0.957860 | ||||||||
\(569\) | 16.3431 | 0.685140 | 0.342570 | − | 0.939492i | \(-0.388703\pi\) | ||||
0.342570 | + | 0.939492i | \(0.388703\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 30.9411 | 1.29485 | 0.647423 | − | 0.762131i | \(-0.275847\pi\) | ||||
0.647423 | + | 0.762131i | \(0.275847\pi\) | |||||||
\(572\) | −21.1127 | −0.882766 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 63.9411 | 2.66885 | ||||||||
\(575\) | −8.48528 | −0.353861 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13.9706 | −0.581602 | −0.290801 | − | 0.956784i | \(-0.593922\pi\) | ||||
−0.290801 | + | 0.956784i | \(0.593922\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 34.3431 | 1.42602 | ||||||||
\(581\) | 3.51472 | 0.145815 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.37258 | −0.0568466 | ||||||||
\(584\) | −33.7990 | −1.39861 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.65685 | 0.0684440 | ||||||||
\(587\) | 34.8284 | 1.43752 | 0.718762 | − | 0.695257i | \(-0.244709\pi\) | ||||
0.718762 | + | 0.695257i | \(0.244709\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13.9706 | −0.575647 | ||||||||
\(590\) | 60.2843 | 2.48186 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −19.9706 | −0.820785 | ||||||||
\(593\) | 32.8284 | 1.34810 | 0.674051 | − | 0.738685i | \(-0.264553\pi\) | ||||
0.674051 | + | 0.738685i | \(0.264553\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −72.0833 | −2.95265 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 45.4558 | 1.85883 | ||||||||
\(599\) | −20.8284 | −0.851026 | −0.425513 | − | 0.904952i | \(-0.639906\pi\) | ||||
−0.425513 | + | 0.904952i | \(0.639906\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.6569 | 0.679447 | 0.339724 | − | 0.940525i | \(-0.389666\pi\) | ||||
0.339724 | + | 0.940525i | \(0.389666\pi\) | |||||||
\(602\) | 21.7279 | 0.885564 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 19.1421 | 0.778882 | ||||||||
\(605\) | 29.1716 | 1.18599 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.0000 | −0.608831 | −0.304416 | − | 0.952539i | \(-0.598461\pi\) | ||||
−0.304416 | + | 0.952539i | \(0.598461\pi\) | |||||||
\(608\) | −4.75736 | −0.192936 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 31.7990 | 1.28750 | ||||||||
\(611\) | 64.2843 | 2.60066 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 31.0000 | 1.25208 | 0.626039 | − | 0.779792i | \(-0.284675\pi\) | ||||
0.626039 | + | 0.779792i | \(0.284675\pi\) | |||||||
\(614\) | −23.3137 | −0.940865 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −10.9706 | −0.442017 | ||||||||
\(617\) | −46.6274 | −1.87715 | −0.938575 | − | 0.345076i | \(-0.887853\pi\) | ||||
−0.938575 | + | 0.345076i | \(0.887853\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.00000 | −0.160774 | −0.0803868 | − | 0.996764i | \(-0.525616\pi\) | ||||
−0.0803868 | + | 0.996764i | \(0.525616\pi\) | |||||||
\(620\) | −50.4264 | −2.02517 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 55.4558 | 2.22358 | ||||||||
\(623\) | 15.9411 | 0.638668 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.0000 | −1.24000 | ||||||||
\(626\) | −32.2132 | −1.28750 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −68.7990 | −2.74538 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −33.9706 | −1.35235 | −0.676173 | − | 0.736743i | \(-0.736363\pi\) | ||||
−0.676173 | + | 0.736743i | \(0.736363\pi\) | |||||||
\(632\) | 52.9706 | 2.10706 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 49.4558 | 1.96414 | ||||||||
\(635\) | 3.79899 | 0.150758 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13.3137 | 0.527508 | ||||||||
\(638\) | −6.34315 | −0.251128 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −58.1421 | −2.29827 | ||||||||
\(641\) | 17.7990 | 0.703018 | 0.351509 | − | 0.936185i | \(-0.385669\pi\) | ||||
0.351509 | + | 0.936185i | \(0.385669\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24.6569 | −0.972371 | −0.486186 | − | 0.873856i | \(-0.661612\pi\) | ||||
−0.486186 | + | 0.873856i | \(0.661612\pi\) | |||||||
\(644\) | 32.4853 | 1.28010 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.02944 | 0.0404714 | 0.0202357 | − | 0.999795i | \(-0.493558\pi\) | ||||
0.0202357 | + | 0.999795i | \(0.493558\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.31371 | −0.287088 | ||||||||
\(650\) | −48.2132 | −1.89108 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6.34315 | −0.248417 | ||||||||
\(653\) | 41.2548 | 1.61443 | 0.807213 | − | 0.590260i | \(-0.200975\pi\) | ||||
0.807213 | + | 0.590260i | \(0.200975\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 25.9411 | 1.01360 | ||||||||
\(656\) | 26.4853 | 1.03408 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 69.9411 | 2.72659 | ||||||||
\(659\) | −14.2843 | −0.556436 | −0.278218 | − | 0.960518i | \(-0.589744\pi\) | ||||
−0.278218 | + | 0.960518i | \(0.589744\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.02944 | −0.156727 | −0.0783635 | − | 0.996925i | \(-0.524969\pi\) | ||||
−0.0783635 | + | 0.996925i | \(0.524969\pi\) | |||||||
\(662\) | 17.7279 | 0.689015 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5.17157 | 0.200696 | ||||||||
\(665\) | −25.4558 | −0.987135 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.97056 | 0.347342 | ||||||||
\(668\) | 35.6569 | 1.37961 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 6.82843 | 0.263805 | ||||||||
\(671\) | −3.85786 | −0.148931 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18.9411 | −0.730127 | −0.365063 | − | 0.930983i | \(-0.618953\pi\) | ||||
−0.365063 | + | 0.930983i | \(0.618953\pi\) | |||||||
\(674\) | −4.82843 | −0.185984 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 119.882 | 4.61086 | ||||||||
\(677\) | 26.4853 | 1.01791 | 0.508956 | − | 0.860793i | \(-0.330032\pi\) | ||||
0.508956 | + | 0.860793i | \(0.330032\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −31.9706 | −1.22692 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 9.31371 | 0.356640 | ||||||||
\(683\) | 0.343146 | 0.0131301 | 0.00656505 | − | 0.999978i | \(-0.497910\pi\) | ||||
0.00656505 | + | 0.999978i | \(0.497910\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 50.3431 | 1.92351 | ||||||||
\(686\) | −36.2132 | −1.38263 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 9.00000 | 0.343122 | ||||||||
\(689\) | 11.0294 | 0.420188 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −39.2843 | −1.49444 | −0.747222 | − | 0.664574i | \(-0.768613\pi\) | ||||
−0.747222 | + | 0.664574i | \(0.768613\pi\) | |||||||
\(692\) | 81.5980 | 3.10189 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 38.1421 | 1.44786 | ||||||||
\(695\) | 15.1127 | 0.573257 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 78.7696 | 2.98147 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −34.4558 | −1.30231 | ||||||||
\(701\) | 26.4853 | 1.00034 | 0.500168 | − | 0.865929i | \(-0.333272\pi\) | ||||
0.500168 | + | 0.865929i | \(0.333272\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 19.9706 | 0.753204 | ||||||||
\(704\) | 8.14214 | 0.306868 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 27.3137 | 1.02796 | ||||||||
\(707\) | −34.9706 | −1.31520 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18.0294 | −0.677110 | −0.338555 | − | 0.940947i | \(-0.609938\pi\) | ||||
−0.338555 | + | 0.940947i | \(0.609938\pi\) | |||||||
\(710\) | −35.3137 | −1.32530 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 23.4558 | 0.879045 | ||||||||
\(713\) | −13.1716 | −0.493279 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 15.5980 | 0.583331 | ||||||||
\(716\) | −46.4853 | −1.73724 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 44.2843 | 1.65267 | ||||||||
\(719\) | 4.62742 | 0.172574 | 0.0862868 | − | 0.996270i | \(-0.472500\pi\) | ||||
0.0862868 | + | 0.996270i | \(0.472500\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 45.0000 | 1.67589 | ||||||||
\(722\) | 24.1421 | 0.898477 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −76.4558 | −2.84146 | ||||||||
\(725\) | −9.51472 | −0.353368 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.00000 | 0.0370879 | 0.0185440 | − | 0.999828i | \(-0.494097\pi\) | ||||
0.0185440 | + | 0.999828i | \(0.494097\pi\) | |||||||
\(728\) | 88.1543 | 3.26722 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 52.2843 | 1.93513 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21.6274 | −0.798827 | −0.399413 | − | 0.916771i | \(-0.630786\pi\) | ||||
−0.399413 | + | 0.916771i | \(0.630786\pi\) | |||||||
\(734\) | −41.8701 | −1.54545 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.48528 | −0.165330 | ||||||||
\(737\) | −0.828427 | −0.0305155 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.0294 | −0.736795 | −0.368397 | − | 0.929668i | \(-0.620093\pi\) | ||||
−0.368397 | + | 0.929668i | \(0.620093\pi\) | |||||||
\(740\) | 72.0833 | 2.64983 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 12.0000 | 0.440534 | ||||||||
\(743\) | 20.8284 | 0.764121 | 0.382060 | − | 0.924137i | \(-0.375215\pi\) | ||||
0.382060 | + | 0.924137i | \(0.375215\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 53.2548 | 1.95111 | ||||||||
\(746\) | −76.4264 | −2.79817 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −18.0000 | −0.657706 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.00000 | −0.255434 | −0.127717 | − | 0.991811i | \(-0.540765\pi\) | ||||
−0.127717 | + | 0.991811i | \(0.540765\pi\) | |||||||
\(752\) | 28.9706 | 1.05645 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 50.9706 | 1.85624 | ||||||||
\(755\) | −14.1421 | −0.514685 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17.0000 | 0.617876 | 0.308938 | − | 0.951082i | \(-0.400027\pi\) | ||||
0.308938 | + | 0.951082i | \(0.400027\pi\) | |||||||
\(758\) | 7.24264 | 0.263065 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −37.4558 | −1.35867 | ||||||||
\(761\) | 43.1127 | 1.56283 | 0.781417 | − | 0.624009i | \(-0.214497\pi\) | ||||
0.781417 | + | 0.624009i | \(0.214497\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.9706 | −0.397161 | ||||||||
\(764\) | −100.083 | −3.62089 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −67.9411 | −2.45481 | ||||||||
\(767\) | 58.7696 | 2.12205 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.37258 | −0.121618 | −0.0608092 | − | 0.998149i | \(-0.519368\pi\) | ||||
−0.0608092 | + | 0.998149i | \(0.519368\pi\) | |||||||
\(770\) | 16.9706 | 0.611577 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 39.4853 | 1.42111 | ||||||||
\(773\) | −34.9706 | −1.25780 | −0.628902 | − | 0.777485i | \(-0.716495\pi\) | ||||
−0.628902 | + | 0.777485i | \(0.716495\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 13.9706 | 0.501837 | ||||||||
\(776\) | −47.0416 | −1.68870 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.343146 | 0.0123024 | ||||||||
\(779\) | −26.4853 | −0.948934 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.28427 | 0.153303 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 6.00000 | 0.214286 | ||||||||
\(785\) | 50.8284 | 1.81414 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 28.5980 | 1.01941 | 0.509704 | − | 0.860350i | \(-0.329755\pi\) | ||||
0.509704 | + | 0.860350i | \(0.329755\pi\) | |||||||
\(788\) | 8.97056 | 0.319563 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −81.9411 | −2.91533 | ||||||||
\(791\) | −10.9706 | −0.390068 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 31.0000 | 1.10084 | ||||||||
\(794\) | 53.1127 | 1.88490 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −30.6274 | −1.08556 | ||||||||
\(797\) | −26.6863 | −0.945277 | −0.472638 | − | 0.881256i | \(-0.656698\pi\) | ||||
−0.472638 | + | 0.881256i | \(0.656698\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 4.75736 | 0.168198 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −76.7696 | −2.71083 | ||||||||
\(803\) | −6.34315 | −0.223845 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −24.0000 | −0.845889 | ||||||||
\(806\) | −74.8406 | −2.63615 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −51.4558 | −1.81021 | ||||||||
\(809\) | 20.4853 | 0.720224 | 0.360112 | − | 0.932909i | \(-0.382738\pi\) | ||||
0.360112 | + | 0.932909i | \(0.382738\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.97056 | 0.0691958 | 0.0345979 | − | 0.999401i | \(-0.488985\pi\) | ||||
0.0345979 | + | 0.999401i | \(0.488985\pi\) | |||||||
\(812\) | 36.4264 | 1.27832 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −13.3137 | −0.466645 | ||||||||
\(815\) | 4.68629 | 0.164154 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.00000 | −0.314870 | ||||||||
\(818\) | −12.0711 | −0.422055 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −95.5980 | −3.33843 | ||||||||
\(821\) | 24.1421 | 0.842566 | 0.421283 | − | 0.906929i | \(-0.361580\pi\) | ||||
0.421283 | + | 0.906929i | \(0.361580\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27.2843 | 0.951070 | 0.475535 | − | 0.879697i | \(-0.342255\pi\) | ||||
0.475535 | + | 0.879697i | \(0.342255\pi\) | |||||||
\(824\) | 66.2132 | 2.30665 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 63.9411 | 2.22480 | ||||||||
\(827\) | −43.4558 | −1.51111 | −0.755554 | − | 0.655087i | \(-0.772632\pi\) | ||||
−0.755554 | + | 0.655087i | \(0.772632\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21.6274 | −0.751151 | −0.375576 | − | 0.926792i | \(-0.622555\pi\) | ||||
−0.375576 | + | 0.926792i | \(0.622555\pi\) | |||||||
\(830\) | −8.00000 | −0.277684 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −65.4264 | −2.26825 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −26.3431 | −0.911642 | ||||||||
\(836\) | 9.51472 | 0.329073 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −53.4558 | −1.84660 | ||||||||
\(839\) | 34.9706 | 1.20732 | 0.603659 | − | 0.797243i | \(-0.293709\pi\) | ||||
0.603659 | + | 0.797243i | \(0.293709\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.9411 | −0.653142 | ||||||||
\(842\) | −33.0416 | −1.13869 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −84.1127 | −2.89528 | ||||||||
\(845\) | −88.5685 | −3.04685 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 30.9411 | 1.06315 | ||||||||
\(848\) | 4.97056 | 0.170690 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 18.8284 | 0.645430 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.02944 | −0.274923 | −0.137461 | − | 0.990507i | \(-0.543894\pi\) | ||||
−0.137461 | + | 0.990507i | \(0.543894\pi\) | |||||||
\(854\) | 33.7279 | 1.15415 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −26.4853 | −0.905248 | ||||||||
\(857\) | 6.00000 | 0.204956 | 0.102478 | − | 0.994735i | \(-0.467323\pi\) | ||||
0.102478 | + | 0.994735i | \(0.467323\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.0294 | −0.342200 | −0.171100 | − | 0.985254i | \(-0.554732\pi\) | ||||
−0.171100 | + | 0.985254i | \(0.554732\pi\) | |||||||
\(860\) | −32.4853 | −1.10774 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 98.9117 | 3.36895 | ||||||||
\(863\) | 23.6569 | 0.805289 | 0.402644 | − | 0.915357i | \(-0.368091\pi\) | ||||
0.402644 | + | 0.915357i | \(0.368091\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −60.2843 | −2.04973 | ||||||||
\(866\) | −4.89949 | −0.166492 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −53.4853 | −1.81541 | ||||||||
\(869\) | 9.94113 | 0.337230 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.65685 | 0.225559 | ||||||||
\(872\) | −16.1421 | −0.546642 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −20.4853 | −0.692925 | ||||||||
\(875\) | −16.9706 | −0.573710 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −10.0000 | −0.337676 | −0.168838 | − | 0.985644i | \(-0.554001\pi\) | ||||
−0.168838 | + | 0.985644i | \(0.554001\pi\) | |||||||
\(878\) | 53.8701 | 1.81803 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 7.02944 | 0.236962 | ||||||||
\(881\) | 20.6274 | 0.694955 | 0.347478 | − | 0.937688i | \(-0.387038\pi\) | ||||
0.347478 | + | 0.937688i | \(0.387038\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33.9411 | 1.14221 | 0.571105 | − | 0.820877i | \(-0.306515\pi\) | ||||
0.571105 | + | 0.820877i | \(0.306515\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 64.7696 | 2.17598 | ||||||||
\(887\) | 7.31371 | 0.245570 | 0.122785 | − | 0.992433i | \(-0.460817\pi\) | ||||
0.122785 | + | 0.992433i | \(0.460817\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.02944 | 0.135143 | ||||||||
\(890\) | −36.2843 | −1.21625 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 101.941 | 3.41324 | ||||||||
\(893\) | −28.9706 | −0.969463 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 34.3431 | 1.14796 | ||||||||
\(896\) | −61.6690 | −2.06022 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2.48528 | −0.0829349 | ||||||||
\(899\) | −14.7696 | −0.492592 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 17.6569 | 0.587909 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −16.1421 | −0.536879 | ||||||||
\(905\) | 56.4853 | 1.87763 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.34315 | 0.0445984 | 0.0222992 | − | 0.999751i | \(-0.492901\pi\) | ||||
0.0222992 | + | 0.999751i | \(0.492901\pi\) | |||||||
\(908\) | −101.397 | −3.36498 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −136.368 | −4.52054 | ||||||||
\(911\) | 6.14214 | 0.203498 | 0.101749 | − | 0.994810i | \(-0.467556\pi\) | ||||
0.101749 | + | 0.994810i | \(0.467556\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.970563 | 0.0321209 | ||||||||
\(914\) | −6.48528 | −0.214514 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 87.9411 | 2.90566 | ||||||||
\(917\) | 27.5147 | 0.908616 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.02944 | 0.231880 | 0.115940 | − | 0.993256i | \(-0.463012\pi\) | ||||
0.115940 | + | 0.993256i | \(0.463012\pi\) | |||||||
\(920\) | −35.3137 | −1.16426 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 40.1421 | 1.32201 | ||||||||
\(923\) | −34.4264 | −1.13316 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −19.9706 | −0.656628 | ||||||||
\(926\) | 24.8995 | 0.818248 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −5.02944 | −0.165099 | ||||||||
\(929\) | −19.5980 | −0.642989 | −0.321494 | − | 0.946911i | \(-0.604185\pi\) | ||||
−0.321494 | + | 0.946911i | \(0.604185\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.00000 | −0.196642 | ||||||||
\(932\) | −67.5980 | −2.21425 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −12.0000 | −0.392652 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −17.9706 | −0.587073 | −0.293536 | − | 0.955948i | \(-0.594832\pi\) | ||||
−0.293536 | + | 0.955948i | \(0.594832\pi\) | |||||||
\(938\) | 7.24264 | 0.236481 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −104.569 | −3.41065 | ||||||||
\(941\) | 7.02944 | 0.229153 | 0.114577 | − | 0.993414i | \(-0.463449\pi\) | ||||
0.114577 | + | 0.993414i | \(0.463449\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −24.9706 | −0.813153 | ||||||||
\(944\) | 26.4853 | 0.862022 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.00000 | 0.195077 | ||||||||
\(947\) | 1.02944 | 0.0334522 | 0.0167261 | − | 0.999860i | \(-0.494676\pi\) | ||||
0.0167261 | + | 0.999860i | \(0.494676\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 50.9706 | 1.65457 | ||||||||
\(950\) | 21.7279 | 0.704947 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 31.1127 | 1.00784 | 0.503920 | − | 0.863751i | \(-0.331891\pi\) | ||||
0.503920 | + | 0.863751i | \(0.331891\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 73.9411 | 2.39268 | ||||||||
\(956\) | 16.6274 | 0.537769 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −29.3137 | −0.947083 | ||||||||
\(959\) | 53.3970 | 1.72428 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.31371 | −0.300442 | ||||||||
\(962\) | 106.983 | 3.44926 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −22.9706 | −0.739832 | ||||||||
\(965\) | −29.1716 | −0.939066 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −60.2843 | −1.93861 | −0.969306 | − | 0.245858i | \(-0.920930\pi\) | ||||
−0.969306 | + | 0.245858i | \(0.920930\pi\) | |||||||
\(968\) | 45.5269 | 1.46329 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 72.7696 | 2.33649 | ||||||||
\(971\) | 9.37258 | 0.300781 | 0.150390 | − | 0.988627i | \(-0.451947\pi\) | ||||
0.150390 | + | 0.988627i | \(0.451947\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16.0294 | 0.513880 | ||||||||
\(974\) | −82.0122 | −2.62784 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 13.9706 | 0.447187 | ||||||||
\(977\) | 37.1127 | 1.18734 | 0.593670 | − | 0.804708i | \(-0.297678\pi\) | ||||
0.593670 | + | 0.804708i | \(0.297678\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.40202 | 0.140689 | ||||||||
\(980\) | −21.6569 | −0.691803 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −26.4853 | −0.845179 | ||||||||
\(983\) | −6.34315 | −0.202315 | −0.101157 | − | 0.994870i | \(-0.532255\pi\) | ||||
−0.101157 | + | 0.994870i | \(0.532255\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.62742 | −0.211167 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −76.4558 | −2.43238 | ||||||||
\(989\) | −8.48528 | −0.269816 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −40.9706 | −1.30147 | −0.650736 | − | 0.759304i | \(-0.725540\pi\) | ||||
−0.650736 | + | 0.759304i | \(0.725540\pi\) | |||||||
\(992\) | 7.38478 | 0.234467 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −37.4558 | −1.18803 | ||||||||
\(995\) | 22.6274 | 0.717337 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 32.9411 | 1.04326 | 0.521628 | − | 0.853173i | \(-0.325325\pi\) | ||||
0.521628 | + | 0.853173i | \(0.325325\pi\) | |||||||
\(998\) | −57.8701 | −1.83184 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2601.2.a.m.1.1 | 2 | ||
3.2 | odd | 2 | 867.2.a.g.1.2 | ✓ | 2 | ||
17.16 | even | 2 | 2601.2.a.n.1.1 | 2 | |||
51.2 | odd | 8 | 867.2.e.b.616.2 | 4 | |||
51.5 | even | 16 | 867.2.h.a.688.2 | 8 | |||
51.8 | odd | 8 | 867.2.e.c.829.1 | 4 | |||
51.11 | even | 16 | 867.2.h.h.733.2 | 8 | |||
51.14 | even | 16 | 867.2.h.h.757.2 | 8 | |||
51.20 | even | 16 | 867.2.h.h.757.1 | 8 | |||
51.23 | even | 16 | 867.2.h.h.733.1 | 8 | |||
51.26 | odd | 8 | 867.2.e.b.829.1 | 4 | |||
51.29 | even | 16 | 867.2.h.a.688.1 | 8 | |||
51.32 | odd | 8 | 867.2.e.c.616.2 | 4 | |||
51.38 | odd | 4 | 867.2.d.b.577.2 | 4 | |||
51.41 | even | 16 | 867.2.h.a.712.2 | 8 | |||
51.44 | even | 16 | 867.2.h.a.712.1 | 8 | |||
51.47 | odd | 4 | 867.2.d.b.577.1 | 4 | |||
51.50 | odd | 2 | 867.2.a.h.1.2 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
867.2.a.g.1.2 | ✓ | 2 | 3.2 | odd | 2 | ||
867.2.a.h.1.2 | yes | 2 | 51.50 | odd | 2 | ||
867.2.d.b.577.1 | 4 | 51.47 | odd | 4 | |||
867.2.d.b.577.2 | 4 | 51.38 | odd | 4 | |||
867.2.e.b.616.2 | 4 | 51.2 | odd | 8 | |||
867.2.e.b.829.1 | 4 | 51.26 | odd | 8 | |||
867.2.e.c.616.2 | 4 | 51.32 | odd | 8 | |||
867.2.e.c.829.1 | 4 | 51.8 | odd | 8 | |||
867.2.h.a.688.1 | 8 | 51.29 | even | 16 | |||
867.2.h.a.688.2 | 8 | 51.5 | even | 16 | |||
867.2.h.a.712.1 | 8 | 51.44 | even | 16 | |||
867.2.h.a.712.2 | 8 | 51.41 | even | 16 | |||
867.2.h.h.733.1 | 8 | 51.23 | even | 16 | |||
867.2.h.h.733.2 | 8 | 51.11 | even | 16 | |||
867.2.h.h.757.1 | 8 | 51.20 | even | 16 | |||
867.2.h.h.757.2 | 8 | 51.14 | even | 16 | |||
2601.2.a.m.1.1 | 2 | 1.1 | even | 1 | trivial | ||
2601.2.a.n.1.1 | 2 | 17.16 | even | 2 |