Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4600,2,Mod(1,4600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4600, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("4600.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4600 = 2^{3} \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4600.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: | \(36.7311849298\) |
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: | \( x^{8} - 3x^{7} - 13x^{6} + 38x^{5} + 41x^{4} - 123x^{3} + 15x^{2} + 32x - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 920) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.54092\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4600.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.54092 | −1.46700 | −0.733499 | − | 0.679690i | \(-0.762114\pi\) | ||||
−0.733499 | + | 0.679690i | \(0.762114\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.780573 | −0.295029 | −0.147514 | − | 0.989060i | \(-0.547127\pi\) | ||||
−0.147514 | + | 0.989060i | \(0.547127\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.45626 | 1.15209 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.16287 | 1.55666 | 0.778332 | − | 0.627853i | \(-0.216066\pi\) | ||||
0.778332 | + | 0.627853i | \(0.216066\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.34898 | −0.928839 | −0.464419 | − | 0.885615i | \(-0.653737\pi\) | ||||
−0.464419 | + | 0.885615i | \(0.653737\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.62869 | 1.60769 | 0.803847 | − | 0.594836i | \(-0.202783\pi\) | ||||
0.803847 | + | 0.594836i | \(0.202783\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.40858 | 1.47023 | 0.735114 | − | 0.677943i | \(-0.237128\pi\) | ||||
0.735114 | + | 0.677943i | \(0.237128\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.98337 | 0.432807 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.15931 | −0.223109 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.0877744 | −0.0162993 | −0.00814965 | − | 0.999967i | \(-0.502594\pi\) | ||||
−0.00814965 | + | 0.999967i | \(0.502594\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.29521 | 0.591837 | 0.295918 | − | 0.955213i | \(-0.404374\pi\) | ||||
0.295918 | + | 0.955213i | \(0.404374\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −13.1184 | −2.28362 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.68291 | 0.769865 | 0.384933 | − | 0.922945i | \(-0.374225\pi\) | ||||
0.384933 | + | 0.922945i | \(0.374225\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 8.50947 | 1.36261 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.75800 | −0.899249 | −0.449624 | − | 0.893218i | \(-0.648442\pi\) | ||||
−0.449624 | + | 0.893218i | \(0.648442\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.62914 | −0.400940 | −0.200470 | − | 0.979700i | \(-0.564247\pi\) | ||||
−0.200470 | + | 0.979700i | \(0.564247\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.13068 | −0.748387 | −0.374193 | − | 0.927351i | \(-0.622080\pi\) | ||||
−0.374193 | + | 0.927351i | \(0.622080\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.39071 | −0.912958 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −16.8429 | −2.35848 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.80399 | −1.20932 | −0.604660 | − | 0.796483i | \(-0.706691\pi\) | ||||
−0.604660 | + | 0.796483i | \(0.706691\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −16.2837 | −2.15682 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.98687 | 0.388858 | 0.194429 | − | 0.980917i | \(-0.437715\pi\) | ||||
0.194429 | + | 0.980917i | \(0.437715\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.05559 | −0.263191 | −0.131596 | − | 0.991303i | \(-0.542010\pi\) | ||||
−0.131596 | + | 0.991303i | \(0.542010\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.69786 | −0.339898 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.60245 | 0.440109 | 0.220054 | − | 0.975488i | \(-0.429376\pi\) | ||||
0.220054 | + | 0.975488i | \(0.429376\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.54092 | 0.305890 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.5286 | 1.36819 | 0.684096 | − | 0.729392i | \(-0.260197\pi\) | ||||
0.684096 | + | 0.729392i | \(0.260197\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.4673 | 1.22510 | 0.612551 | − | 0.790431i | \(-0.290143\pi\) | ||||
0.612551 | + | 0.790431i | \(0.290143\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.03000 | −0.459261 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.43878 | 0.386893 | 0.193447 | − | 0.981111i | \(-0.438033\pi\) | ||||
0.193447 | + | 0.981111i | \(0.438033\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.42306 | −0.824785 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.62938 | −0.398376 | −0.199188 | − | 0.979961i | \(-0.563830\pi\) | ||||
−0.199188 | + | 0.979961i | \(0.563830\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.223028 | 0.0239111 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.3109 | 1.51695 | 0.758477 | − | 0.651700i | \(-0.225944\pi\) | ||||
0.758477 | + | 0.651700i | \(0.225944\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.61412 | 0.274034 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.37284 | −0.868223 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.427584 | 0.0434146 | 0.0217073 | − | 0.999764i | \(-0.493090\pi\) | ||||
0.0217073 | + | 0.999764i | \(0.493090\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 17.8442 | 1.79341 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.99434 | −0.795467 | −0.397733 | − | 0.917501i | \(-0.630203\pi\) | ||||
−0.397733 | + | 0.917501i | \(0.630203\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.7780 | 1.06199 | 0.530993 | − | 0.847376i | \(-0.321819\pi\) | ||||
0.530993 | + | 0.847376i | \(0.321819\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.1623 | 1.46580 | 0.732898 | − | 0.680339i | \(-0.238167\pi\) | ||||
0.732898 | + | 0.680339i | \(0.238167\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −16.5127 | −1.58163 | −0.790816 | − | 0.612054i | \(-0.790344\pi\) | ||||
−0.790816 | + | 0.612054i | \(0.790344\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −11.8989 | −1.12939 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.5233 | −1.36623 | −0.683117 | − | 0.730309i | \(-0.739376\pi\) | ||||
−0.683117 | + | 0.730309i | \(0.739376\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −11.5749 | −1.07010 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.17418 | −0.474316 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 15.6552 | 1.42320 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 14.6306 | 1.31920 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.4865 | −1.46294 | −0.731471 | − | 0.681873i | \(-0.761166\pi\) | ||||
−0.731471 | + | 0.681873i | \(0.761166\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.68042 | 0.588178 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.94157 | 0.431747 | 0.215874 | − | 0.976421i | \(-0.430740\pi\) | ||||
0.215874 | + | 0.976421i | \(0.430740\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.00236 | −0.433760 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 17.9516 | 1.53371 | 0.766854 | − | 0.641821i | \(-0.221821\pi\) | ||||
0.766854 | + | 0.641821i | \(0.221821\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −17.4812 | −1.48274 | −0.741368 | − | 0.671099i | \(-0.765823\pi\) | ||||
−0.741368 | + | 0.671099i | \(0.765823\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 13.0366 | 1.09788 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −17.2903 | −1.44589 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 16.2382 | 1.33931 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −22.0079 | −1.80295 | −0.901477 | − | 0.432827i | \(-0.857516\pi\) | ||||
−0.901477 | + | 0.432827i | \(0.857516\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.40875 | 0.602916 | 0.301458 | − | 0.953480i | \(-0.402527\pi\) | ||||
0.301458 | + | 0.953480i | \(0.402527\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 22.9104 | 1.85220 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.19240 | 0.414399 | 0.207199 | − | 0.978299i | \(-0.433565\pi\) | ||||
0.207199 | + | 0.978299i | \(0.433565\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 22.3702 | 1.77407 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.780573 | 0.0615178 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.5618 | 0.905588 | 0.452794 | − | 0.891615i | \(-0.350427\pi\) | ||||
0.452794 | + | 0.891615i | \(0.350427\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −19.4882 | −1.50804 | −0.754019 | − | 0.656852i | \(-0.771888\pi\) | ||||
−0.754019 | + | 0.656852i | \(0.771888\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.78436 | −0.137258 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 22.1497 | 1.69383 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −18.9062 | −1.43741 | −0.718706 | − | 0.695314i | \(-0.755265\pi\) | ||||
−0.718706 | + | 0.695314i | \(0.755265\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −7.58939 | −0.570454 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 16.5404 | 1.23628 | 0.618142 | − | 0.786066i | \(-0.287886\pi\) | ||||
0.618142 | + | 0.786066i | \(0.287886\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.51586 | 0.409990 | 0.204995 | − | 0.978763i | \(-0.434282\pi\) | ||||
0.204995 | + | 0.978763i | \(0.434282\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.22308 | 0.386101 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 34.2231 | 2.50264 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.904924 | 0.0658235 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 24.0346 | 1.73909 | 0.869543 | − | 0.493858i | \(-0.164414\pi\) | ||||
0.869543 | + | 0.493858i | \(0.164414\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.2163 | 1.09530 | 0.547648 | − | 0.836709i | \(-0.315523\pi\) | ||||
0.547648 | + | 0.836709i | \(0.315523\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.82490 | −0.628748 | −0.314374 | − | 0.949299i | \(-0.601795\pi\) | ||||
−0.314374 | + | 0.949299i | \(0.601795\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.3228 | 1.08620 | 0.543101 | − | 0.839668i | \(-0.317250\pi\) | ||||
0.543101 | + | 0.839668i | \(0.317250\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.15352 | −0.645639 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.0685144 | 0.00480877 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.45626 | −0.240226 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 33.0866 | 2.28865 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.67170 | 0.321613 | 0.160806 | − | 0.986986i | \(-0.448591\pi\) | ||||
0.160806 | + | 0.986986i | \(0.448591\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −29.2932 | −2.00714 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.57215 | −0.174609 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −26.5965 | −1.79722 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −22.1993 | −1.49329 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.7813 | 1.39162 | 0.695810 | − | 0.718226i | \(-0.255046\pi\) | ||||
0.695810 | + | 0.718226i | \(0.255046\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −13.7696 | −0.913920 | −0.456960 | − | 0.889487i | \(-0.651062\pi\) | ||||
−0.456960 | + | 0.889487i | \(0.651062\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.6065 | 1.22955 | 0.614777 | − | 0.788701i | \(-0.289246\pi\) | ||||
0.614777 | + | 0.788701i | \(0.289246\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 10.2399 | 0.673735 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.451458 | 0.0295760 | 0.0147880 | − | 0.999891i | \(-0.495293\pi\) | ||||
0.0147880 | + | 0.999891i | \(0.495293\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.73766 | −0.567572 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.5522 | 0.811937 | 0.405969 | − | 0.913887i | \(-0.366934\pi\) | ||||
0.405969 | + | 0.913887i | \(0.366934\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.7582 | 1.07949 | 0.539745 | − | 0.841828i | \(-0.318521\pi\) | ||||
0.539745 | + | 0.841828i | \(0.318521\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 22.3393 | 1.43307 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −21.4622 | −1.36561 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 9.22194 | 0.584417 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.77866 | −0.427865 | −0.213933 | − | 0.976848i | \(-0.568627\pi\) | ||||
−0.213933 | + | 0.976848i | \(0.568627\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.16287 | −0.324587 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.18182 | 0.447990 | 0.223995 | − | 0.974590i | \(-0.428090\pi\) | ||||
0.223995 | + | 0.974590i | \(0.428090\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.65535 | −0.227133 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.303371 | −0.0187782 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 18.2061 | 1.12264 | 0.561318 | − | 0.827600i | \(-0.310294\pi\) | ||||
0.561318 | + | 0.827600i | \(0.310294\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −36.3628 | −2.22537 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.56736 | −0.339448 | −0.169724 | − | 0.985492i | \(-0.554288\pi\) | ||||
−0.169724 | + | 0.985492i | \(0.554288\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.85908 | 0.234422 | 0.117211 | − | 0.993107i | \(-0.462605\pi\) | ||||
0.117211 | + | 0.993107i | \(0.462605\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6.64226 | −0.402008 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.01542 | −0.361431 | −0.180716 | − | 0.983535i | \(-0.557841\pi\) | ||||
−0.180716 | + | 0.983535i | \(0.557841\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 11.3891 | 0.681846 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.8891 | −1.00752 | −0.503761 | − | 0.863843i | \(-0.668051\pi\) | ||||
−0.503761 | + | 0.863843i | \(0.668051\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.62178 | 0.0964047 | 0.0482023 | − | 0.998838i | \(-0.484651\pi\) | ||||
0.0482023 | + | 0.998838i | \(0.484651\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.49454 | 0.265304 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 26.9395 | 1.58468 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.08645 | −0.0636891 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 28.3659 | 1.65716 | 0.828578 | − | 0.559874i | \(-0.189151\pi\) | ||||
0.828578 | + | 0.559874i | \(0.189151\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.98535 | −0.347305 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.34898 | 0.193676 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.05223 | 0.118289 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 20.3130 | 1.16695 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.54137 | −0.316262 | −0.158131 | − | 0.987418i | \(-0.550547\pi\) | ||||
−0.158131 | + | 0.987418i | \(0.550547\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −27.3860 | −1.55793 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.09153 | 0.515533 | 0.257767 | − | 0.966207i | \(-0.417013\pi\) | ||||
0.257767 | + | 0.966207i | \(0.417013\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.6354 | 1.39248 | 0.696238 | − | 0.717811i | \(-0.254856\pi\) | ||||
0.696238 | + | 0.717811i | \(0.254856\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 23.3406 | 1.31094 | 0.655469 | − | 0.755222i | \(-0.272471\pi\) | ||||
0.655469 | + | 0.755222i | \(0.272471\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.453168 | −0.0253725 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −38.5262 | −2.15032 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 42.4805 | 2.36368 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 41.9575 | 2.32025 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.00487 | 0.220796 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.6239 | 1.35345 | 0.676725 | − | 0.736236i | \(-0.263399\pi\) | ||||
0.676725 | + | 0.736236i | \(0.263399\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 16.1853 | 0.886950 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.9958 | −0.816875 | −0.408438 | − | 0.912786i | \(-0.633926\pi\) | ||||
−0.408438 | + | 0.912786i | \(0.633926\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 36.9024 | 2.00426 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 17.0127 | 0.921290 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.4524 | 0.564378 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8.76366 | 0.470458 | 0.235229 | − | 0.971940i | \(-0.424416\pi\) | ||||
0.235229 | + | 0.971940i | \(0.424416\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 33.1731 | 1.77572 | 0.887859 | − | 0.460116i | \(-0.152192\pi\) | ||||
0.887859 | + | 0.460116i | \(0.152192\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.88249 | 0.207232 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 23.8513 | 1.26948 | 0.634738 | − | 0.772727i | \(-0.281108\pi\) | ||||
0.634738 | + | 0.772727i | \(0.281108\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 13.1472 | 0.695821 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.53298 | −0.450353 | −0.225177 | − | 0.974318i | \(-0.572296\pi\) | ||||
−0.225177 | + | 0.974318i | \(0.572296\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 22.0699 | 1.16157 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −39.7786 | −2.08783 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 23.3388 | 1.21828 | 0.609138 | − | 0.793064i | \(-0.291515\pi\) | ||||
0.609138 | + | 0.793064i | \(0.291515\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −19.9011 | −1.03601 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.87216 | 0.356785 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −26.3073 | −1.36214 | −0.681070 | − | 0.732218i | \(-0.738485\pi\) | ||||
−0.681070 | + | 0.732218i | \(0.738485\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.293955 | 0.0151394 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −33.0601 | −1.69818 | −0.849091 | − | 0.528246i | \(-0.822850\pi\) | ||||
−0.849091 | + | 0.528246i | \(0.822850\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 41.8908 | 2.14613 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −23.7177 | −1.21192 | −0.605958 | − | 0.795496i | \(-0.707210\pi\) | ||||
−0.605958 | + | 0.795496i | \(0.707210\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −9.08697 | −0.461917 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.39287 | 0.222728 | 0.111364 | − | 0.993780i | \(-0.464478\pi\) | ||||
0.111364 | + | 0.993780i | \(0.464478\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.62869 | −0.335227 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −12.5561 | −0.633372 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.668437 | −0.0335479 | −0.0167740 | − | 0.999859i | \(-0.505340\pi\) | ||||
−0.0167740 | + | 0.999859i | \(0.505340\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 12.7106 | 0.636325 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.1310 | 0.555857 | 0.277928 | − | 0.960602i | \(-0.410352\pi\) | ||||
0.277928 | + | 0.960602i | \(0.410352\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −11.0356 | −0.549721 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 24.1772 | 1.19842 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.7667 | −0.878506 | −0.439253 | − | 0.898364i | \(-0.644757\pi\) | ||||
−0.439253 | + | 0.898364i | \(0.644757\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −45.6135 | −2.24995 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.33147 | −0.114724 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 44.4182 | 2.17517 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −37.4277 | −1.82846 | −0.914231 | − | 0.405194i | \(-0.867204\pi\) | ||||
−0.914231 | + | 0.405194i | \(0.867204\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −27.0798 | −1.31979 | −0.659895 | − | 0.751358i | \(-0.729399\pi\) | ||||
−0.659895 | + | 0.751358i | \(0.729399\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −17.7329 | −0.862205 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.60454 | 0.0776490 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 43.9333 | 2.12112 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −33.3003 | −1.60402 | −0.802009 | − | 0.597312i | \(-0.796235\pi\) | ||||
−0.802009 | + | 0.597312i | \(0.796235\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.71773 | −0.130606 | −0.0653028 | − | 0.997865i | \(-0.520801\pi\) | ||||
−0.0653028 | + | 0.997865i | \(0.520801\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.40858 | −0.306564 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16.7478 | −0.799331 | −0.399665 | − | 0.916661i | \(-0.630874\pi\) | ||||
−0.399665 | + | 0.916661i | \(0.630874\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −22.0879 | −1.05181 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11.6392 | −0.552993 | −0.276497 | − | 0.961015i | \(-0.589173\pi\) | ||||
−0.276497 | + | 0.961015i | \(0.589173\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 55.9201 | 2.64493 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.4132 | 0.491430 | 0.245715 | − | 0.969342i | \(-0.420977\pi\) | ||||
0.245715 | + | 0.969342i | \(0.420977\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −29.7278 | −1.39983 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −18.8250 | −0.884476 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.66798 | 0.311915 | 0.155957 | − | 0.987764i | \(-0.450154\pi\) | ||||
0.155957 | + | 0.987764i | \(0.450154\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.68469 | −0.358690 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.1142 | −0.471064 | −0.235532 | − | 0.971867i | \(-0.575683\pi\) | ||||
−0.235532 | + | 0.971867i | \(0.575683\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 25.4957 | 1.18489 | 0.592443 | − | 0.805612i | \(-0.298164\pi\) | ||||
0.592443 | + | 0.805612i | \(0.298164\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9.17713 | −0.424667 | −0.212334 | − | 0.977197i | \(-0.568106\pi\) | ||||
−0.212334 | + | 0.977197i | \(0.568106\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.81197 | −0.129845 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −13.1935 | −0.607922 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −13.5739 | −0.624128 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −30.4288 | −1.39324 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −22.6115 | −1.03315 | −0.516574 | − | 0.856243i | \(-0.672793\pi\) | ||||
−0.516574 | + | 0.856243i | \(0.672793\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.6829 | −0.715081 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.98337 | −0.0902465 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.32242 | −0.286496 | −0.143248 | − | 0.989687i | \(-0.545755\pi\) | ||||
−0.143248 | + | 0.989687i | \(0.545755\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −29.3775 | −1.32850 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.5410 | 0.927002 | 0.463501 | − | 0.886096i | \(-0.346593\pi\) | ||||
0.463501 | + | 0.886096i | \(0.346593\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.581830 | −0.0262043 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8.99891 | −0.403656 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −33.1588 | −1.48439 | −0.742196 | − | 0.670183i | \(-0.766216\pi\) | ||||
−0.742196 | + | 0.670183i | \(0.766216\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 49.5178 | 2.21229 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16.9045 | 0.753736 | 0.376868 | − | 0.926267i | \(-0.377001\pi\) | ||||
0.376868 | + | 0.926267i | \(0.377001\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.53391 | 0.201358 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 28.6358 | 1.26926 | 0.634631 | − | 0.772816i | \(-0.281152\pi\) | ||||
0.634631 | + | 0.772816i | \(0.281152\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.17048 | −0.361441 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7.42951 | −0.328021 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −26.4890 | −1.16499 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 48.0391 | 2.10868 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 38.4207 | 1.68324 | 0.841622 | − | 0.540068i | \(-0.181601\pi\) | ||||
0.841622 | + | 0.540068i | \(0.181601\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 38.6386 | 1.68955 | 0.844773 | − | 0.535124i | \(-0.179735\pi\) | ||||
0.844773 | + | 0.535124i | \(0.179735\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 21.8429 | 0.951492 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.3234 | 0.447997 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 19.2834 | 0.835257 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −42.0277 | −1.81363 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −32.9944 | −1.42117 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.42943 | 0.190436 | 0.0952180 | − | 0.995456i | \(-0.469645\pi\) | ||||
0.0952180 | + | 0.995456i | \(0.469645\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −14.0153 | −0.601455 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.1695 | 1.20444 | 0.602220 | − | 0.798330i | \(-0.294283\pi\) | ||||
0.602220 | + | 0.798330i | \(0.294283\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.10464 | −0.303219 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.562509 | −0.0239637 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.68422 | −0.114145 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −12.1942 | −0.516687 | −0.258343 | − | 0.966053i | \(-0.583177\pi\) | ||||
−0.258343 | + | 0.966053i | \(0.583177\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.80492 | 0.372409 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −86.9579 | −3.67137 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15.8362 | −0.667415 | −0.333708 | − | 0.942677i | \(-0.608300\pi\) | ||||
−0.333708 | + | 0.942677i | \(0.608300\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5.79424 | 0.243335 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0.674355 | 0.0282704 | 0.0141352 | − | 0.999900i | \(-0.495500\pi\) | ||||
0.0141352 | + | 0.999900i | \(0.495500\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −39.9107 | −1.67021 | −0.835105 | − | 0.550090i | \(-0.814593\pi\) | ||||
−0.835105 | + | 0.550090i | \(0.814593\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −61.0700 | −2.55124 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.727423 | 0.0302830 | 0.0151415 | − | 0.999885i | \(-0.495180\pi\) | ||||
0.0151415 | + | 0.999885i | \(0.495180\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −38.6635 | −1.60680 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.83299 | 0.117532 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −45.4538 | −1.88251 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 38.4075 | 1.58525 | 0.792623 | − | 0.609712i | \(-0.208715\pi\) | ||||
0.792623 | + | 0.609712i | \(0.208715\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 21.1176 | 0.870135 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 22.4233 | 0.922373 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9.65052 | 0.396299 | 0.198150 | − | 0.980172i | \(-0.436507\pi\) | ||||
0.198150 | + | 0.980172i | \(0.436507\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −38.9338 | −1.59346 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 35.5951 | 1.45438 | 0.727189 | − | 0.686437i | \(-0.240826\pi\) | ||||
0.727189 | + | 0.686437i | \(0.240826\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.48461 | −0.101349 | −0.0506747 | − | 0.998715i | \(-0.516137\pi\) | ||||
−0.0506747 | + | 0.998715i | \(0.516137\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 12.4510 | 0.507043 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.0165 | −0.609500 | −0.304750 | − | 0.952432i | \(-0.598573\pi\) | ||||
−0.304750 | + | 0.952432i | \(0.598573\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.174089 | −0.00705445 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 17.1825 | 0.695131 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.41556 | 0.178343 | 0.0891714 | − | 0.996016i | \(-0.471578\pi\) | ||||
0.0891714 | + | 0.996016i | \(0.471578\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.0132 | 0.443373 | 0.221686 | − | 0.975118i | \(-0.428844\pi\) | ||||
0.221686 | + | 0.975118i | \(0.428844\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 28.9235 | 1.16253 | 0.581267 | − | 0.813713i | \(-0.302557\pi\) | ||||
0.581267 | + | 0.813713i | \(0.302557\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.15931 | 0.0465214 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −11.1707 | −0.447545 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −84.0704 | −3.35745 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 31.0415 | 1.23771 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.6238 | −0.542357 | −0.271178 | − | 0.962529i | \(-0.587413\pi\) | ||||
−0.271178 | + | 0.962529i | \(0.587413\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −11.8704 | −0.471806 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 21.4023 | 0.847991 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 39.8458 | 1.57627 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −28.1924 | −1.11353 | −0.556766 | − | 0.830670i | \(-0.687958\pi\) | ||||
−0.556766 | + | 0.830670i | \(0.687958\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18.5514 | −0.731596 | −0.365798 | − | 0.930694i | \(-0.619204\pi\) | ||||
−0.365798 | + | 0.930694i | \(0.619204\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 13.6338 | 0.535999 | 0.268000 | − | 0.963419i | \(-0.413637\pi\) | ||||
0.268000 | + | 0.963419i | \(0.413637\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15.4208 | 0.605320 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.53562 | 0.256151 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 37.6196 | 1.47217 | 0.736084 | − | 0.676890i | \(-0.236673\pi\) | ||||
0.736084 | + | 0.676890i | \(0.236673\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 36.1776 | 1.41142 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11.7947 | 0.459455 | 0.229727 | − | 0.973255i | \(-0.426217\pi\) | ||||
0.229727 | + | 0.973255i | \(0.426217\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.49839 | −0.252758 | −0.126379 | − | 0.991982i | \(-0.540336\pi\) | ||||
−0.126379 | + | 0.991982i | \(0.540336\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 56.4066 | 2.19065 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.0877744 | 0.00339864 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −52.8036 | −2.04150 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10.6127 | −0.409700 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −45.7524 | −1.76362 | −0.881812 | − | 0.471601i | \(-0.843676\pi\) | ||||
−0.881812 | + | 0.471601i | \(0.843676\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 25.3462 | 0.974133 | 0.487066 | − | 0.873365i | \(-0.338067\pi\) | ||||
0.487066 | + | 0.873365i | \(0.338067\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.333760 | −0.0128085 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 34.9874 | 1.34072 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −24.3192 | −0.930548 | −0.465274 | − | 0.885167i | \(-0.654044\pi\) | ||||
−0.465274 | + | 0.885167i | \(0.654044\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −47.2776 | −1.80375 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 29.4843 | 1.12326 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.4950 | 0.513374 | 0.256687 | − | 0.966495i | \(-0.417369\pi\) | ||||
0.256687 | + | 0.966495i | \(0.417369\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −13.9287 | −0.529107 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −38.1680 | −1.44572 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.14712 | −0.0433879 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25.8467 | 0.976217 | 0.488109 | − | 0.872783i | \(-0.337687\pi\) | ||||
0.488109 | + | 0.872783i | \(0.337687\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 30.0108 | 1.13188 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.24017 | 0.234686 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −44.9373 | −1.68766 | −0.843828 | − | 0.536613i | \(-0.819704\pi\) | ||||
−0.843828 | + | 0.536613i | \(0.819704\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 11.8853 | 0.445734 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.29521 | −0.123406 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −31.8942 | −1.19111 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 25.2188 | 0.940502 | 0.470251 | − | 0.882533i | \(-0.344163\pi\) | ||||
0.470251 | + | 0.882533i | \(0.344163\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.41300 | −0.313317 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −42.5812 | −1.58361 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18.6009 | 0.689868 | 0.344934 | − | 0.938627i | \(-0.387901\pi\) | ||||
0.344934 | + | 0.938627i | \(0.387901\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −34.4931 | −1.27752 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −17.4277 | −0.644588 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −30.0268 | −1.10907 | −0.554533 | − | 0.832162i | \(-0.687103\pi\) | ||||
−0.554533 | + | 0.832162i | \(0.687103\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 18.5990 | 0.685101 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −21.5513 | −0.792779 | −0.396389 | − | 0.918082i | \(-0.629737\pi\) | ||||
−0.396389 | + | 0.918082i | \(0.629737\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 54.5336 | 2.00334 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −0.818910 | −0.0300429 | −0.0150215 | − | 0.999887i | \(-0.504782\pi\) | ||||
−0.0150215 | + | 0.999887i | \(0.504782\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −12.5441 | −0.458963 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11.8353 | −0.432452 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −40.9390 | −1.49388 | −0.746942 | − | 0.664889i | \(-0.768479\pi\) | ||||
−0.746942 | + | 0.664889i | \(0.768479\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 17.2240 | 0.627678 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.99781 | −0.217994 | −0.108997 | − | 0.994042i | \(-0.534764\pi\) | ||||
−0.108997 | + | 0.994042i | \(0.534764\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 13.1184 | 0.476168 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 35.9456 | 1.30303 | 0.651513 | − | 0.758637i | \(-0.274135\pi\) | ||||
0.651513 | + | 0.758637i | \(0.274135\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.8894 | 0.466627 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −10.0030 | −0.361186 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −52.5292 | −1.89425 | −0.947126 | − | 0.320861i | \(-0.896028\pi\) | ||||
−0.947126 | + | 0.320861i | \(0.896028\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.2484 | −0.657201 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 10.2492 | 0.368638 | 0.184319 | − | 0.982866i | \(-0.440992\pi\) | ||||
0.184319 | + | 0.982866i | \(0.440992\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 9.28794 | 0.333203 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −36.9006 | −1.32210 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 59.5206 | 2.12982 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.101758 | 0.00363652 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 24.2959 | 0.866057 | 0.433028 | − | 0.901380i | \(-0.357445\pi\) | ||||
0.433028 | + | 0.901380i | \(0.357445\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −46.2602 | −1.64691 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11.3365 | 0.403079 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.88412 | 0.244462 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12.7075 | 0.450122 | 0.225061 | − | 0.974345i | \(-0.427742\pi\) | ||||
0.225061 | + | 0.974345i | \(0.427742\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −34.0097 | −1.20318 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 49.4622 | 1.74766 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 54.0412 | 1.90707 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 14.1462 | 0.497970 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 39.2057 | 1.37840 | 0.689200 | − | 0.724571i | \(-0.257962\pi\) | ||||
0.689200 | + | 0.724571i | \(0.257962\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8.34215 | −0.292932 | −0.146466 | − | 0.989216i | \(-0.546790\pi\) | ||||
−0.146466 | + | 0.989216i | \(0.546790\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −9.80560 | −0.343897 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16.8490 | −0.589473 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 9.03507 | 0.315711 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −44.1654 | −1.54138 | −0.770691 | − | 0.637209i | \(-0.780089\pi\) | ||||
−0.770691 | + | 0.637209i | \(0.780089\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 28.3933 | 0.989727 | 0.494863 | − | 0.868971i | \(-0.335218\pi\) | ||||
0.494863 | + | 0.868971i | \(0.335218\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −25.1333 | −0.873970 | −0.436985 | − | 0.899469i | \(-0.643954\pi\) | ||||
−0.436985 | + | 0.899469i | \(0.643954\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.477200 | 0.0165739 | 0.00828693 | − | 0.999966i | \(-0.497362\pi\) | ||||
0.00828693 | + | 0.999966i | \(0.497362\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 15.2847 | 0.530219 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −42.3620 | −1.46776 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.82016 | −0.132044 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −18.7742 | −0.648159 | −0.324079 | − | 0.946030i | \(-0.605055\pi\) | ||||
−0.324079 | + | 0.946030i | \(0.605055\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9923 | −0.999734 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 42.9139 | 1.47803 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −12.2200 | −0.419885 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.12080 | −0.141426 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.68291 | −0.160528 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.41061 | 0.0482983 | 0.0241492 | − | 0.999708i | \(-0.492312\pi\) | ||||
0.0241492 | + | 0.999708i | \(0.492312\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 34.0802 | 1.16416 | 0.582079 | − | 0.813132i | \(-0.302239\pi\) | ||||
0.582079 | + | 0.813132i | \(0.302239\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.81779 | 0.0961418 | 0.0480709 | − | 0.998844i | \(-0.484693\pi\) | ||||
0.0480709 | + | 0.998844i | \(0.484693\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −11.4203 | −0.389201 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −43.8527 | −1.49276 | −0.746382 | − | 0.665517i | \(-0.768211\pi\) | ||||
−0.746382 | + | 0.665517i | \(0.768211\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −68.4511 | −2.32472 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17.7540 | 0.602263 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.0645 | −0.408790 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.47784 | 0.0500173 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.803651 | −0.0271374 | −0.0135687 | − | 0.999908i | \(-0.504319\pi\) | ||||
−0.0135687 | + | 0.999908i | \(0.504319\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −72.0754 | −2.43104 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 51.3971 | 1.73161 | 0.865806 | − | 0.500379i | \(-0.166806\pi\) | ||||
0.865806 | + | 0.500379i | \(0.166806\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.7742 | 0.901024 | 0.450512 | − | 0.892770i | \(-0.351241\pi\) | ||||
0.450512 | + | 0.892770i | \(0.351241\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.02598 | 0.101602 | 0.0508012 | − | 0.998709i | \(-0.483822\pi\) | ||||
0.0508012 | + | 0.998709i | \(0.483822\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12.8689 | 0.431610 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −38.3243 | −1.28391 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −32.8804 | −1.10030 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8.50947 | −0.284123 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.289235 | −0.00964652 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −58.3589 | −1.94422 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.21456 | −0.173530 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −36.1018 | −1.19874 | −0.599370 | − | 0.800472i | \(-0.704582\pi\) | ||||
−0.599370 | + | 0.800472i | \(0.704582\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −27.6305 | −0.916446 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 55.7984 | 1.84868 | 0.924342 | − | 0.381566i | \(-0.124615\pi\) | ||||
0.924342 | + | 0.381566i | \(0.124615\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −18.7380 | −0.620137 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.85726 | −0.127378 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −38.9936 | −1.28628 | −0.643141 | − | 0.765748i | \(-0.722369\pi\) | ||||
−0.643141 | + | 0.765748i | \(0.722369\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 14.0801 | 0.463957 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −38.6090 | −1.27083 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 37.2515 | 1.22350 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −51.1409 | −1.67788 | −0.838939 | − | 0.544226i | \(-0.816823\pi\) | ||||
−0.838939 | + | 0.544226i | \(0.816823\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −40.9553 | −1.34226 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −23.1008 | −0.756287 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 45.7344 | 1.49408 | 0.747039 | − | 0.664780i | \(-0.231475\pi\) | ||||
0.747039 | + | 0.664780i | \(0.231475\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −62.5965 | −2.04276 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 46.9452 | 1.53037 | 0.765184 | − | 0.643811i | \(-0.222648\pi\) | ||||
0.765184 | + | 0.643811i | \(0.222648\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.75800 | 0.187506 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 27.3471 | 0.888660 | 0.444330 | − | 0.895863i | \(-0.353442\pi\) | ||||
0.444330 | + | 0.895863i | \(0.353442\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −35.0547 | −1.13792 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −59.3065 | −1.92314 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 39.4077 | 1.27654 | 0.638270 | − | 0.769813i | \(-0.279650\pi\) | ||||
0.638270 | + | 0.769813i | \(0.279650\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.15146 | 0.0372215 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −14.0125 | −0.452488 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.1416 | −0.649730 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 52.4048 | 1.68872 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.59634 | −0.179966 | −0.0899831 | − | 0.995943i | \(-0.528681\pi\) | ||||
−0.0899831 | + | 0.995943i | \(0.528681\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −107.939 | −3.46751 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19.2387 | −0.617398 | −0.308699 | − | 0.951160i | \(-0.599894\pi\) | ||||
−0.308699 | + | 0.951160i | \(0.599894\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 13.6453 | 0.437450 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 41.1594 | 1.31681 | 0.658403 | − | 0.752666i | \(-0.271232\pi\) | ||||
0.658403 | + | 0.752666i | \(0.271232\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 73.8854 | 2.36139 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −57.0722 | −1.82218 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −53.9616 | −1.72111 | −0.860554 | − | 0.509359i | \(-0.829883\pi\) | ||||
−0.860554 | + | 0.509359i | \(0.829883\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −10.1760 | −0.323907 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.62914 | 0.0836017 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 50.4344 | 1.60210 | 0.801051 | − | 0.598597i | \(-0.204275\pi\) | ||||
0.801051 | + | 0.598597i | \(0.204275\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −62.5672 | −1.98551 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −44.7163 | −1.41618 | −0.708090 | − | 0.706122i | \(-0.750443\pi\) | ||||
−0.708090 | + | 0.706122i | \(0.750443\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.42893 | −0.171764 |
(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 | 4600.2.a.bk.1.1 | 8 | ||
4.3 | odd | 2 | 9200.2.a.dd.1.8 | 8 | |||
5.2 | odd | 4 | 920.2.e.c.369.14 | yes | 16 | ||
5.3 | odd | 4 | 920.2.e.c.369.3 | ✓ | 16 | ||
5.4 | even | 2 | 4600.2.a.bj.1.8 | 8 | |||
20.3 | even | 4 | 1840.2.e.h.369.14 | 16 | |||
20.7 | even | 4 | 1840.2.e.h.369.3 | 16 | |||
20.19 | odd | 2 | 9200.2.a.de.1.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
920.2.e.c.369.3 | ✓ | 16 | 5.3 | odd | 4 | ||
920.2.e.c.369.14 | yes | 16 | 5.2 | odd | 4 | ||
1840.2.e.h.369.3 | 16 | 20.7 | even | 4 | |||
1840.2.e.h.369.14 | 16 | 20.3 | even | 4 | |||
4600.2.a.bj.1.8 | 8 | 5.4 | even | 2 | |||
4600.2.a.bk.1.1 | 8 | 1.1 | even | 1 | trivial | ||
9200.2.a.dd.1.8 | 8 | 4.3 | odd | 2 | |||
9200.2.a.de.1.1 | 8 | 20.19 | odd | 2 |