Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5445,2,Mod(1,5445)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5445, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5445.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5445 = 3^{2} \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5445.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: | \(43.4785439006\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 3x^{6} + 22x^{5} - 3x^{4} - 32x^{3} + 9x^{2} + 8x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 495) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-1.39491\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5445.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.39491 | 1.69346 | 0.846729 | − | 0.532025i | \(-0.178569\pi\) | ||||
0.846729 | + | 0.532025i | \(0.178569\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.73560 | 1.86780 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.96984 | 0.744531 | 0.372266 | − | 0.928126i | \(-0.378581\pi\) | ||||
0.372266 | + | 0.928126i | \(0.378581\pi\) | |||||||
\(8\) | 4.15660 | 1.46958 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.39491 | 0.757337 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.92022 | 0.809923 | 0.404961 | − | 0.914334i | \(-0.367285\pi\) | ||||
0.404961 | + | 0.914334i | \(0.367285\pi\) | |||||||
\(14\) | 4.71760 | 1.26083 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.48350 | 0.620875 | ||||||||
\(17\) | 6.62030 | 1.60566 | 0.802829 | − | 0.596210i | \(-0.203327\pi\) | ||||
0.802829 | + | 0.596210i | \(0.203327\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.56013 | −0.816750 | −0.408375 | − | 0.912814i | \(-0.633904\pi\) | ||||
−0.408375 | + | 0.912814i | \(0.633904\pi\) | |||||||
\(20\) | 3.73560 | 0.835305 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.78918 | −0.581585 | −0.290792 | − | 0.956786i | \(-0.593919\pi\) | ||||
−0.290792 | + | 0.956786i | \(0.593919\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 6.99366 | 1.37157 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 7.35855 | 1.39063 | ||||||||
\(29\) | 3.51753 | 0.653188 | 0.326594 | − | 0.945165i | \(-0.394099\pi\) | ||||
0.326594 | + | 0.945165i | \(0.394099\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.11992 | 1.45838 | 0.729191 | − | 0.684311i | \(-0.239897\pi\) | ||||
0.729191 | + | 0.684311i | \(0.239897\pi\) | |||||||
\(32\) | −2.36545 | −0.418156 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 15.8550 | 2.71911 | ||||||||
\(35\) | 1.96984 | 0.332964 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.42991 | 0.728273 | 0.364137 | − | 0.931346i | \(-0.381364\pi\) | ||||
0.364137 | + | 0.931346i | \(0.381364\pi\) | |||||||
\(38\) | −8.52619 | −1.38313 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.15660 | 0.657217 | ||||||||
\(41\) | −7.07811 | −1.10542 | −0.552708 | − | 0.833375i | \(-0.686405\pi\) | ||||
−0.552708 | + | 0.833375i | \(0.686405\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.8914 | −1.66092 | −0.830462 | − | 0.557075i | \(-0.811924\pi\) | ||||
−0.830462 | + | 0.557075i | \(0.811924\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.67984 | −0.984889 | ||||||||
\(47\) | 0.0271524 | 0.00396059 | 0.00198029 | − | 0.999998i | \(-0.499370\pi\) | ||||
0.00198029 | + | 0.999998i | \(0.499370\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.11971 | −0.445673 | ||||||||
\(50\) | 2.39491 | 0.338692 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 10.9088 | 1.51277 | ||||||||
\(53\) | −4.10948 | −0.564481 | −0.282240 | − | 0.959344i | \(-0.591078\pi\) | ||||
−0.282240 | + | 0.959344i | \(0.591078\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 8.18786 | 1.09415 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 8.42417 | 1.10615 | ||||||||
\(59\) | 9.51441 | 1.23867 | 0.619335 | − | 0.785127i | \(-0.287402\pi\) | ||||
0.619335 | + | 0.785127i | \(0.287402\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.10231 | 0.397210 | 0.198605 | − | 0.980080i | \(-0.436359\pi\) | ||||
0.198605 | + | 0.980080i | \(0.436359\pi\) | |||||||
\(62\) | 19.4465 | 2.46971 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −10.6320 | −1.32900 | ||||||||
\(65\) | 2.92022 | 0.362209 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.58295 | 0.193388 | 0.0966939 | − | 0.995314i | \(-0.469173\pi\) | ||||
0.0966939 | + | 0.995314i | \(0.469173\pi\) | |||||||
\(68\) | 24.7308 | 2.99905 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 4.71760 | 0.563861 | ||||||||
\(71\) | 6.05837 | 0.718997 | 0.359498 | − | 0.933146i | \(-0.382948\pi\) | ||||
0.359498 | + | 0.933146i | \(0.382948\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.37292 | −0.277729 | −0.138864 | − | 0.990311i | \(-0.544345\pi\) | ||||
−0.138864 | + | 0.990311i | \(0.544345\pi\) | |||||||
\(74\) | 10.6092 | 1.23330 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −13.2992 | −1.52552 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.5389 | −1.41074 | −0.705369 | − | 0.708840i | \(-0.749219\pi\) | ||||
−0.705369 | + | 0.708840i | \(0.749219\pi\) | |||||||
\(80\) | 2.48350 | 0.277664 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −16.9515 | −1.87197 | ||||||||
\(83\) | 5.04333 | 0.553577 | 0.276789 | − | 0.960931i | \(-0.410730\pi\) | ||||
0.276789 | + | 0.960931i | \(0.410730\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.62030 | 0.718072 | ||||||||
\(86\) | −26.0840 | −2.81271 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.0573 | −1.27807 | −0.639035 | − | 0.769177i | \(-0.720666\pi\) | ||||
−0.639035 | + | 0.769177i | \(0.720666\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.75238 | 0.603013 | ||||||||
\(92\) | −10.4193 | −1.08628 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.0650277 | 0.00670709 | ||||||||
\(95\) | −3.56013 | −0.365262 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.4097 | 1.05694 | 0.528470 | − | 0.848952i | \(-0.322766\pi\) | ||||
0.528470 | + | 0.848952i | \(0.322766\pi\) | |||||||
\(98\) | −7.47144 | −0.754729 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.73560 | 0.373560 | ||||||||
\(101\) | 17.2166 | 1.71311 | 0.856556 | − | 0.516054i | \(-0.172600\pi\) | ||||
0.856556 | + | 0.516054i | \(0.172600\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.66999 | 0.657213 | 0.328607 | − | 0.944467i | \(-0.393421\pi\) | ||||
0.328607 | + | 0.944467i | \(0.393421\pi\) | |||||||
\(104\) | 12.1382 | 1.19025 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.84185 | −0.955925 | ||||||||
\(107\) | 9.61908 | 0.929912 | 0.464956 | − | 0.885334i | \(-0.346070\pi\) | ||||
0.464956 | + | 0.885334i | \(0.346070\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −19.2602 | −1.84480 | −0.922398 | − | 0.386240i | \(-0.873773\pi\) | ||||
−0.922398 | + | 0.386240i | \(0.873773\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.89211 | 0.462261 | ||||||||
\(113\) | 3.56283 | 0.335163 | 0.167582 | − | 0.985858i | \(-0.446404\pi\) | ||||
0.167582 | + | 0.985858i | \(0.446404\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.78918 | −0.260093 | ||||||||
\(116\) | 13.1401 | 1.22003 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 22.7862 | 2.09764 | ||||||||
\(119\) | 13.0410 | 1.19546 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 7.42975 | 0.672658 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 30.3328 | 2.72396 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.3179 | 1.71419 | 0.857094 | − | 0.515159i | \(-0.172267\pi\) | ||||
0.857094 | + | 0.515159i | \(0.172267\pi\) | |||||||
\(128\) | −20.7319 | −1.83246 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 6.99366 | 0.613385 | ||||||||
\(131\) | 13.9027 | 1.21468 | 0.607341 | − | 0.794441i | \(-0.292236\pi\) | ||||
0.607341 | + | 0.794441i | \(0.292236\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.01290 | −0.608096 | ||||||||
\(134\) | 3.79102 | 0.327494 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 27.5180 | 2.35964 | ||||||||
\(137\) | −22.7270 | −1.94169 | −0.970847 | − | 0.239699i | \(-0.922951\pi\) | ||||
−0.970847 | + | 0.239699i | \(0.922951\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.7100 | 1.07804 | 0.539022 | − | 0.842291i | \(-0.318794\pi\) | ||||
0.539022 | + | 0.842291i | \(0.318794\pi\) | |||||||
\(140\) | 7.35855 | 0.621911 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 14.5093 | 1.21759 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.51753 | 0.292115 | ||||||||
\(146\) | −5.68292 | −0.470322 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 16.5484 | 1.36027 | ||||||||
\(149\) | −4.30274 | −0.352494 | −0.176247 | − | 0.984346i | \(-0.556396\pi\) | ||||
−0.176247 | + | 0.984346i | \(0.556396\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.5844 | 1.43100 | 0.715499 | − | 0.698614i | \(-0.246199\pi\) | ||||
0.715499 | + | 0.698614i | \(0.246199\pi\) | |||||||
\(152\) | −14.7980 | −1.20028 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.11992 | 0.652208 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −23.8112 | −1.90034 | −0.950172 | − | 0.311726i | \(-0.899093\pi\) | ||||
−0.950172 | + | 0.311726i | \(0.899093\pi\) | |||||||
\(158\) | −30.0296 | −2.38903 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.36545 | −0.187005 | ||||||||
\(161\) | −5.49425 | −0.433008 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −19.8452 | −1.55440 | −0.777198 | − | 0.629256i | \(-0.783360\pi\) | ||||
−0.777198 | + | 0.629256i | \(0.783360\pi\) | |||||||
\(164\) | −26.4410 | −2.06469 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 12.0783 | 0.937460 | ||||||||
\(167\) | −14.4760 | −1.12019 | −0.560094 | − | 0.828429i | \(-0.689235\pi\) | ||||
−0.560094 | + | 0.828429i | \(0.689235\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.47232 | −0.344025 | ||||||||
\(170\) | 15.8550 | 1.21602 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −40.6859 | −3.10227 | ||||||||
\(173\) | 4.31904 | 0.328371 | 0.164185 | − | 0.986429i | \(-0.447500\pi\) | ||||
0.164185 | + | 0.986429i | \(0.447500\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.96984 | 0.148906 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −28.8761 | −2.16436 | ||||||||
\(179\) | −7.45911 | −0.557520 | −0.278760 | − | 0.960361i | \(-0.589923\pi\) | ||||
−0.278760 | + | 0.960361i | \(0.589923\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.4634 | −1.52104 | −0.760518 | − | 0.649317i | \(-0.775055\pi\) | ||||
−0.760518 | + | 0.649317i | \(0.775055\pi\) | |||||||
\(182\) | 13.7764 | 1.02118 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −11.5935 | −0.854686 | ||||||||
\(185\) | 4.42991 | 0.325694 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0.101431 | 0.00739759 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −8.52619 | −0.618555 | ||||||||
\(191\) | 6.55174 | 0.474067 | 0.237034 | − | 0.971501i | \(-0.423825\pi\) | ||||
0.237034 | + | 0.971501i | \(0.423825\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.82579 | −0.491331 | −0.245665 | − | 0.969355i | \(-0.579006\pi\) | ||||
−0.245665 | + | 0.969355i | \(0.579006\pi\) | |||||||
\(194\) | 24.9302 | 1.78988 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −11.6540 | −0.832428 | ||||||||
\(197\) | 3.45091 | 0.245867 | 0.122934 | − | 0.992415i | \(-0.460770\pi\) | ||||
0.122934 | + | 0.992415i | \(0.460770\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.6742 | −0.756671 | −0.378336 | − | 0.925668i | \(-0.623504\pi\) | ||||
−0.378336 | + | 0.925668i | \(0.623504\pi\) | |||||||
\(200\) | 4.15660 | 0.293916 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 41.2321 | 2.90108 | ||||||||
\(203\) | 6.92898 | 0.486319 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.07811 | −0.494357 | ||||||||
\(206\) | 15.9740 | 1.11296 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 7.25237 | 0.502861 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.37923 | −0.0949503 | −0.0474752 | − | 0.998872i | \(-0.515117\pi\) | ||||
−0.0474752 | + | 0.998872i | \(0.515117\pi\) | |||||||
\(212\) | −15.3514 | −1.05434 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 23.0368 | 1.57477 | ||||||||
\(215\) | −10.8914 | −0.742788 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 15.9950 | 1.08581 | ||||||||
\(218\) | −46.1266 | −3.12408 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 19.3327 | 1.30046 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.1038 | 0.810531 | 0.405265 | − | 0.914199i | \(-0.367179\pi\) | ||||
0.405265 | + | 0.914199i | \(0.367179\pi\) | |||||||
\(224\) | −4.65956 | −0.311330 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.53267 | 0.567585 | ||||||||
\(227\) | −17.3320 | −1.15037 | −0.575183 | − | 0.818025i | \(-0.695069\pi\) | ||||
−0.575183 | + | 0.818025i | \(0.695069\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.837178 | −0.0553223 | −0.0276611 | − | 0.999617i | \(-0.508806\pi\) | ||||
−0.0276611 | + | 0.999617i | \(0.508806\pi\) | |||||||
\(230\) | −6.67984 | −0.440456 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 14.6210 | 0.959914 | ||||||||
\(233\) | −19.0481 | −1.24788 | −0.623941 | − | 0.781471i | \(-0.714470\pi\) | ||||
−0.623941 | + | 0.781471i | \(0.714470\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.0271524 | 0.00177123 | ||||||||
\(236\) | 35.5420 | 2.31359 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 31.2319 | 2.02446 | ||||||||
\(239\) | 25.7936 | 1.66845 | 0.834223 | − | 0.551427i | \(-0.185916\pi\) | ||||
0.834223 | + | 0.551427i | \(0.185916\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.0680 | −1.09944 | −0.549722 | − | 0.835348i | \(-0.685266\pi\) | ||||
−0.549722 | + | 0.835348i | \(0.685266\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 11.5890 | 0.741908 | ||||||||
\(245\) | −3.11971 | −0.199311 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10.3964 | −0.661504 | ||||||||
\(248\) | 33.7513 | 2.14321 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2.39491 | 0.151467 | ||||||||
\(251\) | −10.3166 | −0.651177 | −0.325589 | − | 0.945512i | \(-0.605562\pi\) | ||||
−0.325589 | + | 0.945512i | \(0.605562\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 46.2647 | 2.90291 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −28.3869 | −1.77418 | ||||||||
\(257\) | −11.2636 | −0.702604 | −0.351302 | − | 0.936262i | \(-0.614261\pi\) | ||||
−0.351302 | + | 0.936262i | \(0.614261\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.72624 | 0.542222 | ||||||||
\(260\) | 10.9088 | 0.676533 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 33.2957 | 2.05701 | ||||||||
\(263\) | 5.15082 | 0.317613 | 0.158806 | − | 0.987310i | \(-0.449235\pi\) | ||||
0.158806 | + | 0.987310i | \(0.449235\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.10948 | −0.252444 | ||||||||
\(266\) | −16.7953 | −1.02978 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5.91326 | 0.361210 | ||||||||
\(269\) | 23.1522 | 1.41161 | 0.705806 | − | 0.708405i | \(-0.250585\pi\) | ||||
0.705806 | + | 0.708405i | \(0.250585\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.1449 | 0.798498 | 0.399249 | − | 0.916843i | \(-0.369271\pi\) | ||||
0.399249 | + | 0.916843i | \(0.369271\pi\) | |||||||
\(272\) | 16.4415 | 0.996913 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −54.4290 | −3.28818 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.3489 | 0.621807 | 0.310903 | − | 0.950442i | \(-0.399368\pi\) | ||||
0.310903 | + | 0.950442i | \(0.399368\pi\) | |||||||
\(278\) | 30.4392 | 1.82562 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 8.18786 | 0.489319 | ||||||||
\(281\) | 0.387020 | 0.0230877 | 0.0115438 | − | 0.999933i | \(-0.496325\pi\) | ||||
0.0115438 | + | 0.999933i | \(0.496325\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.5253 | −0.863442 | −0.431721 | − | 0.902007i | \(-0.642094\pi\) | ||||
−0.431721 | + | 0.902007i | \(0.642094\pi\) | |||||||
\(284\) | 22.6317 | 1.34294 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −13.9428 | −0.823016 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 26.8283 | 1.57814 | ||||||||
\(290\) | 8.42417 | 0.494684 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −8.86426 | −0.518742 | ||||||||
\(293\) | −14.8176 | −0.865652 | −0.432826 | − | 0.901478i | \(-0.642483\pi\) | ||||
−0.432826 | + | 0.901478i | \(0.642483\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.51441 | 0.553950 | ||||||||
\(296\) | 18.4134 | 1.07026 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −10.3047 | −0.596934 | ||||||||
\(299\) | −8.14502 | −0.471039 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −21.4544 | −1.23661 | ||||||||
\(302\) | 42.1131 | 2.42334 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −8.84158 | −0.507100 | ||||||||
\(305\) | 3.10231 | 0.177638 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 32.3539 | 1.84653 | 0.923266 | − | 0.384161i | \(-0.125509\pi\) | ||||
0.923266 | + | 0.384161i | \(0.125509\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 19.4465 | 1.10449 | ||||||||
\(311\) | 1.76355 | 0.100002 | 0.0500008 | − | 0.998749i | \(-0.484078\pi\) | ||||
0.0500008 | + | 0.998749i | \(0.484078\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −26.1735 | −1.47941 | −0.739706 | − | 0.672930i | \(-0.765036\pi\) | ||||
−0.739706 | + | 0.672930i | \(0.765036\pi\) | |||||||
\(314\) | −57.0258 | −3.21815 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −46.8404 | −2.63498 | ||||||||
\(317\) | 10.3755 | 0.582744 | 0.291372 | − | 0.956610i | \(-0.405888\pi\) | ||||
0.291372 | + | 0.956610i | \(0.405888\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −10.6320 | −0.594349 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −13.1582 | −0.733281 | ||||||||
\(323\) | −23.5691 | −1.31142 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.92022 | 0.161985 | ||||||||
\(326\) | −47.5275 | −2.63230 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −29.4209 | −1.62450 | ||||||||
\(329\) | 0.0534861 | 0.00294878 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.22380 | 0.506986 | 0.253493 | − | 0.967337i | \(-0.418421\pi\) | ||||
0.253493 | + | 0.967337i | \(0.418421\pi\) | |||||||
\(332\) | 18.8399 | 1.03397 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −34.6688 | −1.89699 | ||||||||
\(335\) | 1.58295 | 0.0864857 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 28.5372 | 1.55452 | 0.777261 | − | 0.629178i | \(-0.216608\pi\) | ||||
0.777261 | + | 0.629178i | \(0.216608\pi\) | |||||||
\(338\) | −10.7108 | −0.582592 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 24.7308 | 1.34121 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.9343 | −1.07635 | ||||||||
\(344\) | −45.2713 | −2.44086 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 10.3437 | 0.556082 | ||||||||
\(347\) | −10.1698 | −0.545945 | −0.272972 | − | 0.962022i | \(-0.588007\pi\) | ||||
−0.272972 | + | 0.962022i | \(0.588007\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −23.7174 | −1.26957 | −0.634783 | − | 0.772691i | \(-0.718910\pi\) | ||||
−0.634783 | + | 0.772691i | \(0.718910\pi\) | |||||||
\(350\) | 4.71760 | 0.252166 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 14.1383 | 0.752504 | 0.376252 | − | 0.926517i | \(-0.377213\pi\) | ||||
0.376252 | + | 0.926517i | \(0.377213\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.05837 | 0.321545 | ||||||||
\(356\) | −45.0412 | −2.38718 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −17.8639 | −0.944137 | ||||||||
\(359\) | 24.0330 | 1.26841 | 0.634207 | − | 0.773163i | \(-0.281327\pi\) | ||||
0.634207 | + | 0.773163i | \(0.281327\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.32548 | −0.332920 | ||||||||
\(362\) | −49.0081 | −2.57581 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 21.4886 | 1.12631 | ||||||||
\(365\) | −2.37292 | −0.124204 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.79705 | −0.0938055 | −0.0469027 | − | 0.998899i | \(-0.514935\pi\) | ||||
−0.0469027 | + | 0.998899i | \(0.514935\pi\) | |||||||
\(368\) | −6.92694 | −0.361091 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 10.6092 | 0.551549 | ||||||||
\(371\) | −8.09504 | −0.420274 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.87802 | −0.356131 | −0.178065 | − | 0.984019i | \(-0.556984\pi\) | ||||
−0.178065 | + | 0.984019i | \(0.556984\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.112862 | 0.00582041 | ||||||||
\(377\) | 10.2719 | 0.529032 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.53329 | −0.181493 | −0.0907465 | − | 0.995874i | \(-0.528925\pi\) | ||||
−0.0907465 | + | 0.995874i | \(0.528925\pi\) | |||||||
\(380\) | −13.2992 | −0.682235 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 15.6908 | 0.802813 | ||||||||
\(383\) | 1.90335 | 0.0972564 | 0.0486282 | − | 0.998817i | \(-0.484515\pi\) | ||||
0.0486282 | + | 0.998817i | \(0.484515\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −16.3472 | −0.832048 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 38.8863 | 1.97415 | ||||||||
\(389\) | 7.02219 | 0.356039 | 0.178020 | − | 0.984027i | \(-0.443031\pi\) | ||||
0.178020 | + | 0.984027i | \(0.443031\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.4652 | −0.933826 | ||||||||
\(392\) | −12.9674 | −0.654953 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 8.26463 | 0.416366 | ||||||||
\(395\) | −12.5389 | −0.630902 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.5149 | −0.628104 | −0.314052 | − | 0.949406i | \(-0.601687\pi\) | ||||
−0.314052 | + | 0.949406i | \(0.601687\pi\) | |||||||
\(398\) | −25.5637 | −1.28139 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.48350 | 0.124175 | ||||||||
\(401\) | −27.3284 | −1.36472 | −0.682358 | − | 0.731018i | \(-0.739045\pi\) | ||||
−0.682358 | + | 0.731018i | \(0.739045\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 23.7120 | 1.18118 | ||||||||
\(404\) | 64.3142 | 3.19975 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 16.5943 | 0.823561 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.5990 | −0.573531 | −0.286766 | − | 0.958001i | \(-0.592580\pi\) | ||||
−0.286766 | + | 0.958001i | \(0.592580\pi\) | |||||||
\(410\) | −16.9515 | −0.837172 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 24.9164 | 1.22754 | ||||||||
\(413\) | 18.7419 | 0.922229 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.04333 | 0.247567 | ||||||||
\(416\) | −6.90762 | −0.338674 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.07542 | −0.443363 | −0.221682 | − | 0.975119i | \(-0.571155\pi\) | ||||
−0.221682 | + | 0.975119i | \(0.571155\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.5151 | 0.902372 | 0.451186 | − | 0.892430i | \(-0.351001\pi\) | ||||
0.451186 | + | 0.892430i | \(0.351001\pi\) | |||||||
\(422\) | −3.30314 | −0.160794 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −17.0815 | −0.829551 | ||||||||
\(425\) | 6.62030 | 0.321132 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.11106 | 0.295735 | ||||||||
\(428\) | 35.9330 | 1.73689 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −26.0840 | −1.25788 | ||||||||
\(431\) | 24.7913 | 1.19415 | 0.597077 | − | 0.802184i | \(-0.296329\pi\) | ||||
0.597077 | + | 0.802184i | \(0.296329\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −35.3858 | −1.70053 | −0.850267 | − | 0.526352i | \(-0.823559\pi\) | ||||
−0.850267 | + | 0.526352i | \(0.823559\pi\) | |||||||
\(434\) | 38.3066 | 1.83877 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −71.9485 | −3.44571 | ||||||||
\(437\) | 9.92985 | 0.475009 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.2916 | −0.491192 | −0.245596 | − | 0.969372i | \(-0.578984\pi\) | ||||
−0.245596 | + | 0.969372i | \(0.578984\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 46.3001 | 2.20227 | ||||||||
\(443\) | −35.8502 | −1.70330 | −0.851648 | − | 0.524114i | \(-0.824397\pi\) | ||||
−0.851648 | + | 0.524114i | \(0.824397\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12.0573 | −0.571571 | ||||||||
\(446\) | 28.9875 | 1.37260 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −20.9435 | −0.989485 | ||||||||
\(449\) | 26.8436 | 1.26683 | 0.633414 | − | 0.773813i | \(-0.281653\pi\) | ||||
0.633414 | + | 0.773813i | \(0.281653\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 13.3093 | 0.626017 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −41.5086 | −1.94810 | ||||||||
\(455\) | 5.75238 | 0.269676 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −19.6380 | −0.918627 | −0.459314 | − | 0.888274i | \(-0.651905\pi\) | ||||
−0.459314 | + | 0.888274i | \(0.651905\pi\) | |||||||
\(458\) | −2.00497 | −0.0936860 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −10.4193 | −0.485801 | ||||||||
\(461\) | −19.5626 | −0.911122 | −0.455561 | − | 0.890205i | \(-0.650561\pi\) | ||||
−0.455561 | + | 0.890205i | \(0.650561\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.7474 | −0.685371 | −0.342686 | − | 0.939450i | \(-0.611337\pi\) | ||||
−0.342686 | + | 0.939450i | \(0.611337\pi\) | |||||||
\(464\) | 8.73578 | 0.405549 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −45.6185 | −2.11324 | ||||||||
\(467\) | 10.3049 | 0.476854 | 0.238427 | − | 0.971160i | \(-0.423368\pi\) | ||||
0.238427 | + | 0.971160i | \(0.423368\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.11816 | 0.143983 | ||||||||
\(470\) | 0.0650277 | 0.00299950 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 39.5476 | 1.82033 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.56013 | −0.163350 | ||||||||
\(476\) | 48.7158 | 2.23288 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 61.7733 | 2.82544 | ||||||||
\(479\) | 11.3976 | 0.520768 | 0.260384 | − | 0.965505i | \(-0.416151\pi\) | ||||
0.260384 | + | 0.965505i | \(0.416151\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.9363 | 0.589845 | ||||||||
\(482\) | −40.8762 | −1.86186 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.4097 | 0.472678 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −34.6435 | −1.56984 | −0.784922 | − | 0.619594i | \(-0.787297\pi\) | ||||
−0.784922 | + | 0.619594i | \(0.787297\pi\) | |||||||
\(488\) | 12.8951 | 0.583732 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −7.47144 | −0.337525 | ||||||||
\(491\) | 36.6153 | 1.65242 | 0.826212 | − | 0.563360i | \(-0.190491\pi\) | ||||
0.826212 | + | 0.563360i | \(0.190491\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 23.2871 | 1.04880 | ||||||||
\(494\) | −24.8983 | −1.12023 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 20.1658 | 0.905473 | ||||||||
\(497\) | 11.9341 | 0.535315 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −21.3515 | −0.955824 | −0.477912 | − | 0.878408i | \(-0.658606\pi\) | ||||
−0.477912 | + | 0.878408i | \(0.658606\pi\) | |||||||
\(500\) | 3.73560 | 0.167061 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −24.7073 | −1.10274 | ||||||||
\(503\) | −11.6575 | −0.519783 | −0.259891 | − | 0.965638i | \(-0.583687\pi\) | ||||
−0.259891 | + | 0.965638i | \(0.583687\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17.2166 | 0.766127 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 72.1640 | 3.20176 | ||||||||
\(509\) | −29.3434 | −1.30062 | −0.650311 | − | 0.759668i | \(-0.725361\pi\) | ||||
−0.650311 | + | 0.759668i | \(0.725361\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.67427 | −0.206778 | ||||||||
\(512\) | −26.5205 | −1.17205 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −26.9753 | −1.18983 | ||||||||
\(515\) | 6.66999 | 0.293915 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 20.8986 | 0.918230 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 12.1382 | 0.532295 | ||||||||
\(521\) | −4.00057 | −0.175268 | −0.0876340 | − | 0.996153i | \(-0.527931\pi\) | ||||
−0.0876340 | + | 0.996153i | \(0.527931\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.44571 | −0.194397 | −0.0971986 | − | 0.995265i | \(-0.530988\pi\) | ||||
−0.0971986 | + | 0.995265i | \(0.530988\pi\) | |||||||
\(524\) | 51.9348 | 2.26878 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 12.3357 | 0.537864 | ||||||||
\(527\) | 53.7563 | 2.34166 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.2205 | −0.661759 | ||||||||
\(530\) | −9.84185 | −0.427502 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −26.1974 | −1.13580 | ||||||||
\(533\) | −20.6696 | −0.895301 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.61908 | 0.415869 | ||||||||
\(536\) | 6.57969 | 0.284199 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 55.4474 | 2.39051 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.1859 | −0.566905 | −0.283452 | − | 0.958986i | \(-0.591480\pi\) | ||||
−0.283452 | + | 0.958986i | \(0.591480\pi\) | |||||||
\(542\) | 31.4810 | 1.35222 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −15.6599 | −0.671415 | ||||||||
\(545\) | −19.2602 | −0.825018 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.86825 | 0.0798806 | 0.0399403 | − | 0.999202i | \(-0.487283\pi\) | ||||
0.0399403 | + | 0.999202i | \(0.487283\pi\) | |||||||
\(548\) | −84.8988 | −3.62670 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.5229 | −0.533491 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −24.6997 | −1.05034 | ||||||||
\(554\) | 24.7848 | 1.05300 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 47.4793 | 2.01357 | ||||||||
\(557\) | −13.5209 | −0.572900 | −0.286450 | − | 0.958095i | \(-0.592475\pi\) | ||||
−0.286450 | + | 0.958095i | \(0.592475\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −31.8053 | −1.34522 | ||||||||
\(560\) | 4.89211 | 0.206729 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.926879 | 0.0390980 | ||||||||
\(563\) | 30.5720 | 1.28846 | 0.644228 | − | 0.764833i | \(-0.277179\pi\) | ||||
0.644228 | + | 0.764833i | \(0.277179\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.56283 | 0.149890 | ||||||||
\(566\) | −34.7869 | −1.46220 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 25.1823 | 1.05662 | ||||||||
\(569\) | −36.4840 | −1.52949 | −0.764745 | − | 0.644333i | \(-0.777135\pi\) | ||||
−0.764745 | + | 0.644333i | \(0.777135\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.9929 | −0.836679 | −0.418339 | − | 0.908291i | \(-0.637388\pi\) | ||||
−0.418339 | + | 0.908291i | \(0.637388\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −33.3917 | −1.39374 | ||||||||
\(575\) | −2.78918 | −0.116317 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −31.1211 | −1.29559 | −0.647794 | − | 0.761816i | \(-0.724308\pi\) | ||||
−0.647794 | + | 0.761816i | \(0.724308\pi\) | |||||||
\(578\) | 64.2514 | 2.67251 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 13.1401 | 0.545612 | ||||||||
\(581\) | 9.93458 | 0.412156 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −9.86327 | −0.408145 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −35.4868 | −1.46594 | ||||||||
\(587\) | 31.9068 | 1.31693 | 0.658467 | − | 0.752610i | \(-0.271205\pi\) | ||||
0.658467 | + | 0.752610i | \(0.271205\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −28.9080 | −1.19113 | ||||||||
\(590\) | 22.7862 | 0.938091 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 11.0017 | 0.452167 | ||||||||
\(593\) | 34.5829 | 1.42015 | 0.710074 | − | 0.704127i | \(-0.248662\pi\) | ||||
0.710074 | + | 0.704127i | \(0.248662\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13.0410 | 0.534627 | ||||||||
\(596\) | −16.0733 | −0.658388 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −19.5066 | −0.797684 | ||||||||
\(599\) | 17.7818 | 0.726543 | 0.363271 | − | 0.931683i | \(-0.381660\pi\) | ||||
0.363271 | + | 0.931683i | \(0.381660\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14.8208 | −0.604554 | −0.302277 | − | 0.953220i | \(-0.597747\pi\) | ||||
−0.302277 | + | 0.953220i | \(0.597747\pi\) | |||||||
\(602\) | −51.3813 | −2.09415 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 65.6883 | 2.67282 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13.8034 | −0.560264 | −0.280132 | − | 0.959962i | \(-0.590378\pi\) | ||||
−0.280132 | + | 0.959962i | \(0.590378\pi\) | |||||||
\(608\) | 8.42129 | 0.341528 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7.42975 | 0.300822 | ||||||||
\(611\) | 0.0792910 | 0.00320777 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.4951 | 0.908570 | 0.454285 | − | 0.890856i | \(-0.349895\pi\) | ||||
0.454285 | + | 0.890856i | \(0.349895\pi\) | |||||||
\(614\) | 77.4846 | 3.12702 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10.6195 | 0.427525 | 0.213762 | − | 0.976886i | \(-0.431428\pi\) | ||||
0.213762 | + | 0.976886i | \(0.431428\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.63250 | −0.105809 | −0.0529046 | − | 0.998600i | \(-0.516848\pi\) | ||||
−0.0529046 | + | 0.998600i | \(0.516848\pi\) | |||||||
\(620\) | 30.3328 | 1.21819 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 4.22354 | 0.169349 | ||||||||
\(623\) | −23.7510 | −0.951563 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −62.6832 | −2.50532 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −88.9493 | −3.54946 | ||||||||
\(629\) | 29.3273 | 1.16936 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.1315 | 0.960660 | 0.480330 | − | 0.877088i | \(-0.340517\pi\) | ||||
0.480330 | + | 0.877088i | \(0.340517\pi\) | |||||||
\(632\) | −52.1193 | −2.07320 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 24.8483 | 0.986852 | ||||||||
\(635\) | 19.3179 | 0.766608 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9.11024 | −0.360961 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −20.7319 | −0.819500 | ||||||||
\(641\) | −45.7507 | −1.80705 | −0.903523 | − | 0.428540i | \(-0.859028\pi\) | ||||
−0.903523 | + | 0.428540i | \(0.859028\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.60925 | −0.260643 | −0.130322 | − | 0.991472i | \(-0.541601\pi\) | ||||
−0.130322 | + | 0.991472i | \(0.541601\pi\) | |||||||
\(644\) | −20.5243 | −0.808772 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −56.4459 | −2.22083 | ||||||||
\(647\) | −1.86148 | −0.0731824 | −0.0365912 | − | 0.999330i | \(-0.511650\pi\) | ||||
−0.0365912 | + | 0.999330i | \(0.511650\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 6.99366 | 0.274314 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −74.1337 | −2.90330 | ||||||||
\(653\) | 31.9277 | 1.24943 | 0.624713 | − | 0.780854i | \(-0.285216\pi\) | ||||
0.624713 | + | 0.780854i | \(0.285216\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13.9027 | 0.543223 | ||||||||
\(656\) | −17.5785 | −0.686325 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.128094 | 0.00499364 | ||||||||
\(659\) | −8.36924 | −0.326019 | −0.163010 | − | 0.986624i | \(-0.552120\pi\) | ||||
−0.163010 | + | 0.986624i | \(0.552120\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −34.0773 | −1.32545 | −0.662726 | − | 0.748862i | \(-0.730601\pi\) | ||||
−0.662726 | + | 0.748862i | \(0.730601\pi\) | |||||||
\(662\) | 22.0902 | 0.858559 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 20.9631 | 0.813527 | ||||||||
\(665\) | −7.01290 | −0.271949 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.81102 | −0.379884 | ||||||||
\(668\) | −54.0766 | −2.09228 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 3.79102 | 0.146460 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.06786 | −0.0797103 | −0.0398551 | − | 0.999205i | \(-0.512690\pi\) | ||||
−0.0398551 | + | 0.999205i | \(0.512690\pi\) | |||||||
\(674\) | 68.3441 | 2.63252 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −16.7068 | −0.642569 | ||||||||
\(677\) | 18.0905 | 0.695275 | 0.347637 | − | 0.937629i | \(-0.386984\pi\) | ||||
0.347637 | + | 0.937629i | \(0.386984\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 20.5054 | 0.786925 | ||||||||
\(680\) | 27.5180 | 1.05527 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −47.3828 | −1.81305 | −0.906526 | − | 0.422149i | \(-0.861276\pi\) | ||||
−0.906526 | + | 0.422149i | \(0.861276\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −22.7270 | −0.868352 | ||||||||
\(686\) | −47.7408 | −1.82275 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −27.0488 | −1.03123 | ||||||||
\(689\) | −12.0006 | −0.457186 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.8475 | 0.602869 | 0.301435 | − | 0.953487i | \(-0.402535\pi\) | ||||
0.301435 | + | 0.953487i | \(0.402535\pi\) | |||||||
\(692\) | 16.1342 | 0.613331 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −24.3558 | −0.924534 | ||||||||
\(695\) | 12.7100 | 0.482116 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −46.8592 | −1.77492 | ||||||||
\(698\) | −56.8012 | −2.14996 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 7.35855 | 0.278127 | ||||||||
\(701\) | 26.3059 | 0.993560 | 0.496780 | − | 0.867876i | \(-0.334516\pi\) | ||||
0.496780 | + | 0.867876i | \(0.334516\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −15.7711 | −0.594817 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 33.8599 | 1.27433 | ||||||||
\(707\) | 33.9139 | 1.27547 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 30.8329 | 1.15795 | 0.578977 | − | 0.815344i | \(-0.303452\pi\) | ||||
0.578977 | + | 0.815344i | \(0.303452\pi\) | |||||||
\(710\) | 14.5093 | 0.544523 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −50.1174 | −1.87823 | ||||||||
\(713\) | −22.6479 | −0.848172 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −27.8643 | −1.04134 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 57.5569 | 2.14801 | ||||||||
\(719\) | 47.2434 | 1.76188 | 0.880940 | − | 0.473228i | \(-0.156911\pi\) | ||||
0.880940 | + | 0.473228i | \(0.156911\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13.1388 | 0.489316 | ||||||||
\(722\) | −15.1490 | −0.563786 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −76.4432 | −2.84099 | ||||||||
\(725\) | 3.51753 | 0.130638 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −24.4299 | −0.906054 | −0.453027 | − | 0.891497i | \(-0.649656\pi\) | ||||
−0.453027 | + | 0.891497i | \(0.649656\pi\) | |||||||
\(728\) | 23.9104 | 0.886177 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −5.68292 | −0.210334 | ||||||||
\(731\) | −72.1043 | −2.66688 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 27.9875 | 1.03374 | 0.516870 | − | 0.856064i | \(-0.327097\pi\) | ||||
0.516870 | + | 0.856064i | \(0.327097\pi\) | |||||||
\(734\) | −4.30379 | −0.158856 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.59766 | 0.243193 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.70533 | −0.0995172 | −0.0497586 | − | 0.998761i | \(-0.515845\pi\) | ||||
−0.0497586 | + | 0.998761i | \(0.515845\pi\) | |||||||
\(740\) | 16.5484 | 0.608331 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −19.3869 | −0.711716 | ||||||||
\(743\) | 4.14414 | 0.152034 | 0.0760168 | − | 0.997107i | \(-0.475780\pi\) | ||||
0.0760168 | + | 0.997107i | \(0.475780\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.30274 | −0.157640 | ||||||||
\(746\) | −16.4723 | −0.603092 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 18.9481 | 0.692348 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −44.4316 | −1.62133 | −0.810666 | − | 0.585508i | \(-0.800895\pi\) | ||||
−0.810666 | + | 0.585508i | \(0.800895\pi\) | |||||||
\(752\) | 0.0674331 | 0.00245903 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 24.6004 | 0.895894 | ||||||||
\(755\) | 17.5844 | 0.639962 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29.9901 | 1.09001 | 0.545004 | − | 0.838433i | \(-0.316528\pi\) | ||||
0.545004 | + | 0.838433i | \(0.316528\pi\) | |||||||
\(758\) | −8.46192 | −0.307351 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −14.7980 | −0.536782 | ||||||||
\(761\) | 39.8420 | 1.44427 | 0.722135 | − | 0.691752i | \(-0.243161\pi\) | ||||
0.722135 | + | 0.691752i | \(0.243161\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −37.9397 | −1.37351 | ||||||||
\(764\) | 24.4747 | 0.885462 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4.55834 | 0.164700 | ||||||||
\(767\) | 27.7841 | 1.00323 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.5304 | 0.740346 | 0.370173 | − | 0.928963i | \(-0.379298\pi\) | ||||
0.370173 | + | 0.928963i | \(0.379298\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −25.4984 | −0.917708 | ||||||||
\(773\) | 16.3315 | 0.587401 | 0.293701 | − | 0.955897i | \(-0.405113\pi\) | ||||
0.293701 | + | 0.955897i | \(0.405113\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.11992 | 0.291676 | ||||||||
\(776\) | 43.2688 | 1.55326 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 16.8175 | 0.602938 | ||||||||
\(779\) | 25.1990 | 0.902848 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −44.2225 | −1.58139 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −7.74781 | −0.276708 | ||||||||
\(785\) | −23.8112 | −0.849860 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.38766 | −0.263342 | −0.131671 | − | 0.991293i | \(-0.542034\pi\) | ||||
−0.131671 | + | 0.991293i | \(0.542034\pi\) | |||||||
\(788\) | 12.8912 | 0.459231 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −30.0296 | −1.06841 | ||||||||
\(791\) | 7.01823 | 0.249539 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.05941 | 0.321709 | ||||||||
\(794\) | −29.9720 | −1.06367 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −39.8744 | −1.41331 | ||||||||
\(797\) | 23.1554 | 0.820207 | 0.410104 | − | 0.912039i | \(-0.365492\pi\) | ||||
0.410104 | + | 0.912039i | \(0.365492\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.179757 | 0.00635935 | ||||||||
\(800\) | −2.36545 | −0.0836311 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −65.4491 | −2.31109 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.49425 | −0.193647 | ||||||||
\(806\) | 56.7880 | 2.00027 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 71.5624 | 2.51756 | ||||||||
\(809\) | −14.9484 | −0.525559 | −0.262779 | − | 0.964856i | \(-0.584639\pi\) | ||||
−0.262779 | + | 0.964856i | \(0.584639\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −25.1135 | −0.881855 | −0.440927 | − | 0.897543i | \(-0.645350\pi\) | ||||
−0.440927 | + | 0.897543i | \(0.645350\pi\) | |||||||
\(812\) | 25.8839 | 0.908347 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −19.8452 | −0.695147 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 38.7748 | 1.35656 | ||||||||
\(818\) | −27.7785 | −0.971251 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −26.4410 | −0.923359 | ||||||||
\(821\) | −13.1035 | −0.457315 | −0.228657 | − | 0.973507i | \(-0.573434\pi\) | ||||
−0.228657 | + | 0.973507i | \(0.573434\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.5741 | −0.717169 | −0.358584 | − | 0.933497i | \(-0.616741\pi\) | ||||
−0.358584 | + | 0.933497i | \(0.616741\pi\) | |||||||
\(824\) | 27.7245 | 0.965828 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 44.8852 | 1.56176 | ||||||||
\(827\) | 12.6343 | 0.439338 | 0.219669 | − | 0.975574i | \(-0.429502\pi\) | ||||
0.219669 | + | 0.975574i | \(0.429502\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.78876 | 0.270515 | 0.135257 | − | 0.990810i | \(-0.456814\pi\) | ||||
0.135257 | + | 0.990810i | \(0.456814\pi\) | |||||||
\(830\) | 12.0783 | 0.419245 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −31.0479 | −1.07639 | ||||||||
\(833\) | −20.6534 | −0.715599 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.4760 | −0.500963 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −21.7348 | −0.750817 | ||||||||
\(839\) | 30.5522 | 1.05478 | 0.527389 | − | 0.849624i | \(-0.323171\pi\) | ||||
0.527389 | + | 0.849624i | \(0.323171\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.6270 | −0.573345 | ||||||||
\(842\) | 44.3421 | 1.52813 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −5.15226 | −0.177348 | ||||||||
\(845\) | −4.47232 | −0.153853 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −10.2059 | −0.350472 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 15.8550 | 0.543823 | ||||||||
\(851\) | −12.3558 | −0.423553 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 25.6737 | 0.879051 | 0.439525 | − | 0.898230i | \(-0.355147\pi\) | ||||
0.439525 | + | 0.898230i | \(0.355147\pi\) | |||||||
\(854\) | 14.6354 | 0.500815 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 39.9827 | 1.36658 | ||||||||
\(857\) | 14.7370 | 0.503407 | 0.251703 | − | 0.967804i | \(-0.419009\pi\) | ||||
0.251703 | + | 0.967804i | \(0.419009\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.68741 | −0.0575738 | −0.0287869 | − | 0.999586i | \(-0.509164\pi\) | ||||
−0.0287869 | + | 0.999586i | \(0.509164\pi\) | |||||||
\(860\) | −40.6859 | −1.38738 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 59.3729 | 2.02225 | ||||||||
\(863\) | −13.1473 | −0.447538 | −0.223769 | − | 0.974642i | \(-0.571836\pi\) | ||||
−0.223769 | + | 0.974642i | \(0.571836\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.31904 | 0.146852 | ||||||||
\(866\) | −84.7458 | −2.87978 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 59.7509 | 2.02808 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.62255 | 0.156629 | ||||||||
\(872\) | −80.0572 | −2.71108 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 23.7811 | 0.804408 | ||||||||
\(875\) | 1.96984 | 0.0665929 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −46.9492 | −1.58536 | −0.792681 | − | 0.609637i | \(-0.791315\pi\) | ||||
−0.792681 | + | 0.609637i | \(0.791315\pi\) | |||||||
\(878\) | −24.6475 | −0.831813 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −14.1843 | −0.477880 | −0.238940 | − | 0.971034i | \(-0.576800\pi\) | ||||
−0.238940 | + | 0.971034i | \(0.576800\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10.3899 | −0.349647 | −0.174824 | − | 0.984600i | \(-0.555936\pi\) | ||||
−0.174824 | + | 0.984600i | \(0.555936\pi\) | |||||||
\(884\) | 72.2193 | 2.42900 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −85.8581 | −2.88446 | ||||||||
\(887\) | 3.84764 | 0.129191 | 0.0645955 | − | 0.997912i | \(-0.479424\pi\) | ||||
0.0645955 | + | 0.997912i | \(0.479424\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 38.0533 | 1.27627 | ||||||||
\(890\) | −28.8761 | −0.967931 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 45.2150 | 1.51391 | ||||||||
\(893\) | −0.0966662 | −0.00323481 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.45911 | −0.249331 | ||||||||
\(896\) | −40.8386 | −1.36432 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 64.2881 | 2.14532 | ||||||||
\(899\) | 28.5621 | 0.952598 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −27.2060 | −0.906363 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 14.8093 | 0.492550 | ||||||||
\(905\) | −20.4634 | −0.680228 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.20437 | 0.0399904 | 0.0199952 | − | 0.999800i | \(-0.493635\pi\) | ||||
0.0199952 | + | 0.999800i | \(0.493635\pi\) | |||||||
\(908\) | −64.7455 | −2.14865 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 13.7764 | 0.456684 | ||||||||
\(911\) | −38.9307 | −1.28983 | −0.644915 | − | 0.764254i | \(-0.723107\pi\) | ||||
−0.644915 | + | 0.764254i | \(0.723107\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −47.0313 | −1.55566 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.12736 | −0.103331 | ||||||||
\(917\) | 27.3861 | 0.904369 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9.56757 | −0.315605 | −0.157802 | − | 0.987471i | \(-0.550441\pi\) | ||||
−0.157802 | + | 0.987471i | \(0.550441\pi\) | |||||||
\(920\) | −11.5935 | −0.382227 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −46.8507 | −1.54295 | ||||||||
\(923\) | 17.6918 | 0.582332 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.42991 | 0.145655 | ||||||||
\(926\) | −35.3188 | −1.16065 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −8.32052 | −0.273134 | ||||||||
\(929\) | 6.45603 | 0.211816 | 0.105908 | − | 0.994376i | \(-0.466225\pi\) | ||||
0.105908 | + | 0.994376i | \(0.466225\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.1066 | 0.364003 | ||||||||
\(932\) | −71.1561 | −2.33079 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 24.6793 | 0.807532 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.478554 | 0.0156337 | 0.00781684 | − | 0.999969i | \(-0.497512\pi\) | ||||
0.00781684 | + | 0.999969i | \(0.497512\pi\) | |||||||
\(938\) | 7.46772 | 0.243830 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.101431 | 0.00330830 | ||||||||
\(941\) | −18.3345 | −0.597689 | −0.298845 | − | 0.954302i | \(-0.596601\pi\) | ||||
−0.298845 | + | 0.954302i | \(0.596601\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 19.7421 | 0.642893 | ||||||||
\(944\) | 23.6290 | 0.769060 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 23.6619 | 0.768908 | 0.384454 | − | 0.923144i | \(-0.374390\pi\) | ||||
0.384454 | + | 0.923144i | \(0.374390\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.92943 | −0.224939 | ||||||||
\(950\) | −8.52619 | −0.276626 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 54.2061 | 1.75683 | ||||||||
\(953\) | −19.5111 | −0.632026 | −0.316013 | − | 0.948755i | \(-0.602344\pi\) | ||||
−0.316013 | + | 0.948755i | \(0.602344\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.55174 | 0.212009 | ||||||||
\(956\) | 96.3544 | 3.11632 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 27.2962 | 0.881899 | ||||||||
\(959\) | −44.7686 | −1.44565 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 34.9332 | 1.12688 | ||||||||
\(962\) | 30.9813 | 0.998878 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −63.7591 | −2.05354 | ||||||||
\(965\) | −6.82579 | −0.219730 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.3686 | −0.429905 | −0.214953 | − | 0.976624i | \(-0.568960\pi\) | ||||
−0.214953 | + | 0.976624i | \(0.568960\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 24.9302 | 0.800461 | ||||||||
\(971\) | −55.6001 | −1.78429 | −0.892146 | − | 0.451747i | \(-0.850801\pi\) | ||||
−0.892146 | + | 0.451747i | \(0.850801\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 25.0366 | 0.802638 | ||||||||
\(974\) | −82.9680 | −2.65847 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.70458 | 0.246618 | ||||||||
\(977\) | 42.9068 | 1.37271 | 0.686355 | − | 0.727267i | \(-0.259210\pi\) | ||||
0.686355 | + | 0.727267i | \(0.259210\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −11.6540 | −0.372273 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 87.6903 | 2.79831 | ||||||||
\(983\) | −34.5788 | −1.10289 | −0.551446 | − | 0.834211i | \(-0.685924\pi\) | ||||
−0.551446 | + | 0.834211i | \(0.685924\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.45091 | 0.109955 | ||||||||
\(986\) | 55.7705 | 1.77609 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −38.8366 | −1.23556 | ||||||||
\(989\) | 30.3781 | 0.965968 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 15.5839 | 0.495038 | 0.247519 | − | 0.968883i | \(-0.420385\pi\) | ||||
0.247519 | + | 0.968883i | \(0.420385\pi\) | |||||||
\(992\) | −19.2072 | −0.609830 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 28.5810 | 0.906534 | ||||||||
\(995\) | −10.6742 | −0.338394 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.04074 | 0.127972 | 0.0639858 | − | 0.997951i | \(-0.479619\pi\) | ||||
0.0639858 | + | 0.997951i | \(0.479619\pi\) | |||||||
\(998\) | −51.1349 | −1.61865 | ||||||||
\(999\) | 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 | 5445.2.a.cd.1.7 | 8 | ||
3.2 | odd | 2 | 5445.2.a.ca.1.2 | 8 | |||
11.5 | even | 5 | 495.2.n.g.91.1 | ✓ | 16 | ||
11.9 | even | 5 | 495.2.n.g.136.1 | yes | 16 | ||
11.10 | odd | 2 | 5445.2.a.cb.1.2 | 8 | |||
33.5 | odd | 10 | 495.2.n.h.91.4 | yes | 16 | ||
33.20 | odd | 10 | 495.2.n.h.136.4 | yes | 16 | ||
33.32 | even | 2 | 5445.2.a.cc.1.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
495.2.n.g.91.1 | ✓ | 16 | 11.5 | even | 5 | ||
495.2.n.g.136.1 | yes | 16 | 11.9 | even | 5 | ||
495.2.n.h.91.4 | yes | 16 | 33.5 | odd | 10 | ||
495.2.n.h.136.4 | yes | 16 | 33.20 | odd | 10 | ||
5445.2.a.ca.1.2 | 8 | 3.2 | odd | 2 | |||
5445.2.a.cb.1.2 | 8 | 11.10 | odd | 2 | |||
5445.2.a.cc.1.7 | 8 | 33.32 | even | 2 | |||
5445.2.a.cd.1.7 | 8 | 1.1 | even | 1 | trivial |