Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1932,2,Mod(1,1932)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1932, 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("1932.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1932 = 2^{2} \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1932.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: | \(15.4270976705\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1932.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.618034 | 0.276393 | 0.138197 | − | 0.990405i | \(-0.455869\pi\) | ||||
0.138197 | + | 0.990405i | \(0.455869\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.00000 | −0.904534 | −0.452267 | − | 0.891883i | \(-0.649385\pi\) | ||||
−0.452267 | + | 0.891883i | \(0.649385\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.61803 | −0.448762 | −0.224381 | − | 0.974502i | \(-0.572036\pi\) | ||||
−0.224381 | + | 0.974502i | \(0.572036\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.618034 | 0.159576 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.70820 | −1.62698 | −0.813489 | − | 0.581580i | \(-0.802435\pi\) | ||||
−0.813489 | + | 0.581580i | \(0.802435\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.236068 | 0.0541577 | 0.0270789 | − | 0.999633i | \(-0.491379\pi\) | ||||
0.0270789 | + | 0.999633i | \(0.491379\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.61803 | −0.923607 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.23607 | −1.15801 | −0.579004 | − | 0.815324i | \(-0.696559\pi\) | ||||
−0.579004 | + | 0.815324i | \(0.696559\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.00000 | −0.538816 | −0.269408 | − | 0.963026i | \(-0.586828\pi\) | ||||
−0.269408 | + | 0.963026i | \(0.586828\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.00000 | −0.522233 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.618034 | −0.104467 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.527864 | 0.0867803 | 0.0433902 | − | 0.999058i | \(-0.486184\pi\) | ||||
0.0433902 | + | 0.999058i | \(0.486184\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.61803 | −0.259093 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.94427 | 0.928339 | 0.464170 | − | 0.885746i | \(-0.346353\pi\) | ||||
0.464170 | + | 0.885746i | \(0.346353\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.09017 | 0.318748 | 0.159374 | − | 0.987218i | \(-0.449052\pi\) | ||||
0.159374 | + | 0.987218i | \(0.449052\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.618034 | 0.0921311 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.76393 | −0.694891 | −0.347445 | − | 0.937700i | \(-0.612951\pi\) | ||||
−0.347445 | + | 0.937700i | \(0.612951\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.70820 | −0.939336 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.32624 | 0.868976 | 0.434488 | − | 0.900678i | \(-0.356929\pi\) | ||||
0.434488 | + | 0.900678i | \(0.356929\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.85410 | −0.250007 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.236068 | 0.0312680 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.38197 | −0.961050 | −0.480525 | − | 0.876981i | \(-0.659554\pi\) | ||||
−0.480525 | + | 0.876981i | \(0.659554\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.854102 | −0.109357 | −0.0546783 | − | 0.998504i | \(-0.517413\pi\) | ||||
−0.0546783 | + | 0.998504i | \(0.517413\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.00000 | −0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.5623 | −1.65690 | −0.828450 | − | 0.560063i | \(-0.810777\pi\) | ||||
−0.828450 | + | 0.560063i | \(0.810777\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.38197 | −0.282687 | −0.141344 | − | 0.989961i | \(-0.545142\pi\) | ||||
−0.141344 | + | 0.989961i | \(0.545142\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.23607 | 0.729877 | 0.364938 | − | 0.931032i | \(-0.381090\pi\) | ||||
0.364938 | + | 0.931032i | \(0.381090\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.61803 | −0.533245 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.00000 | 0.341882 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.70820 | 0.754732 | 0.377366 | − | 0.926064i | \(-0.376830\pi\) | ||||
0.377366 | + | 0.926064i | \(0.376830\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.47214 | 0.161588 | 0.0807940 | − | 0.996731i | \(-0.474254\pi\) | ||||
0.0807940 | + | 0.996731i | \(0.474254\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.14590 | −0.449686 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.23607 | −0.668577 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.79837 | 0.826626 | 0.413313 | − | 0.910589i | \(-0.364372\pi\) | ||||
0.413313 | + | 0.910589i | \(0.364372\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.61803 | 0.169616 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.00000 | −0.311086 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.145898 | 0.0149688 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.4164 | 1.46376 | 0.731882 | − | 0.681431i | \(-0.238642\pi\) | ||||
0.731882 | + | 0.681431i | \(0.238642\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.00000 | −0.301511 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.3262 | −1.02750 | −0.513750 | − | 0.857940i | \(-0.671744\pi\) | ||||
−0.513750 | + | 0.857940i | \(0.671744\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.41641 | −0.730760 | −0.365380 | − | 0.930858i | \(-0.619061\pi\) | ||||
−0.365380 | + | 0.930858i | \(0.619061\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.618034 | −0.0603139 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.38197 | 0.810315 | 0.405158 | − | 0.914247i | \(-0.367217\pi\) | ||||
0.405158 | + | 0.914247i | \(0.367217\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.09017 | 0.870680 | 0.435340 | − | 0.900266i | \(-0.356628\pi\) | ||||
0.435340 | + | 0.900266i | \(0.356628\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.527864 | 0.0501026 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.3262 | −1.15955 | −0.579777 | − | 0.814775i | \(-0.696861\pi\) | ||||
−0.579777 | + | 0.814775i | \(0.696861\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.618034 | −0.0576320 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.61803 | −0.149587 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.70820 | 0.614940 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.00000 | −0.181818 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.94427 | 0.535977 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.94427 | −0.531672 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.5623 | −1.29220 | −0.646098 | − | 0.763255i | \(-0.723600\pi\) | ||||
−0.646098 | + | 0.763255i | \(0.723600\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.09017 | 0.184029 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.9443 | −1.04358 | −0.521788 | − | 0.853075i | \(-0.674735\pi\) | ||||
−0.521788 | + | 0.853075i | \(0.674735\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.236068 | −0.0204697 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.618034 | 0.0531919 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.00000 | −0.768922 | −0.384461 | − | 0.923141i | \(-0.625613\pi\) | ||||
−0.384461 | + | 0.923141i | \(0.625613\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.145898 | 0.0123749 | 0.00618745 | − | 0.999981i | \(-0.498030\pi\) | ||||
0.00618745 | + | 0.999981i | \(0.498030\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.76393 | −0.401195 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.85410 | 0.405920 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.85410 | −0.320066 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.23607 | 0.265109 | 0.132555 | − | 0.991176i | \(-0.457682\pi\) | ||||
0.132555 | + | 0.991176i | \(0.457682\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 21.1246 | 1.71910 | 0.859548 | − | 0.511055i | \(-0.170745\pi\) | ||||
0.859548 | + | 0.511055i | \(0.170745\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.70820 | −0.542326 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.85410 | −0.148925 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.2361 | 1.05635 | 0.528177 | − | 0.849135i | \(-0.322876\pi\) | ||||
0.528177 | + | 0.849135i | \(0.322876\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.32624 | 0.501703 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.00000 | 0.0788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.14590 | 0.324732 | 0.162366 | − | 0.986731i | \(-0.448088\pi\) | ||||
0.162366 | + | 0.986731i | \(0.448088\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.85410 | −0.144342 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −19.4721 | −1.50680 | −0.753400 | − | 0.657563i | \(-0.771587\pi\) | ||||
−0.753400 | + | 0.657563i | \(0.771587\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.3820 | −0.798613 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.236068 | 0.0180526 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.52786 | 0.344247 | 0.172124 | − | 0.985075i | \(-0.444937\pi\) | ||||
0.172124 | + | 0.985075i | \(0.444937\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.61803 | 0.349091 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −7.38197 | −0.554863 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −18.0344 | −1.34796 | −0.673979 | − | 0.738751i | \(-0.735416\pi\) | ||||
−0.673979 | + | 0.738751i | \(0.735416\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.52786 | 0.633871 | 0.316936 | − | 0.948447i | \(-0.397346\pi\) | ||||
0.316936 | + | 0.948447i | \(0.397346\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.854102 | −0.0631370 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.326238 | 0.0239855 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 20.1246 | 1.47166 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.6525 | 0.770786 | 0.385393 | − | 0.922753i | \(-0.374066\pi\) | ||||
0.385393 | + | 0.922753i | \(0.374066\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.70820 | 0.554849 | 0.277424 | − | 0.960747i | \(-0.410519\pi\) | ||||
0.277424 | + | 0.960747i | \(0.410519\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.00000 | −0.0716115 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.61803 | 0.257774 | 0.128887 | − | 0.991659i | \(-0.458860\pi\) | ||||
0.128887 | + | 0.991659i | \(0.458860\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.43769 | 0.172804 | 0.0864018 | − | 0.996260i | \(-0.472463\pi\) | ||||
0.0864018 | + | 0.996260i | \(0.472463\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −13.5623 | −0.956611 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.23607 | 0.437686 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.67376 | 0.256587 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.708204 | −0.0489875 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.1246 | 0.972378 | 0.486189 | − | 0.873854i | \(-0.338387\pi\) | ||||
0.486189 | + | 0.873854i | \(0.338387\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.38197 | −0.163210 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.29180 | 0.0880998 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.00000 | 0.203653 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.23607 | 0.421394 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.8541 | 0.730126 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.7984 | −0.857043 | −0.428521 | − | 0.903532i | \(-0.640965\pi\) | ||||
−0.428521 | + | 0.903532i | \(0.640965\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.61803 | −0.307869 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −29.4508 | −1.95472 | −0.977361 | − | 0.211580i | \(-0.932139\pi\) | ||||
−0.977361 | + | 0.211580i | \(0.932139\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.27051 | −0.612613 | −0.306306 | − | 0.951933i | \(-0.599093\pi\) | ||||
−0.306306 | + | 0.951933i | \(0.599093\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.00000 | 0.197386 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.909830 | −0.0596049 | −0.0298025 | − | 0.999556i | \(-0.509488\pi\) | ||||
−0.0298025 | + | 0.999556i | \(0.509488\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.94427 | −0.192063 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.70820 | 0.435745 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.3820 | −0.994977 | −0.497488 | − | 0.867471i | \(-0.665744\pi\) | ||||
−0.497488 | + | 0.867471i | \(0.665744\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 21.0000 | 1.35273 | 0.676364 | − | 0.736567i | \(-0.263554\pi\) | ||||
0.676364 | + | 0.736567i | \(0.263554\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.618034 | 0.0394847 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.381966 | −0.0243039 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.47214 | 0.0932928 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.65248 | 0.546139 | 0.273070 | − | 0.961994i | \(-0.411961\pi\) | ||||
0.273070 | + | 0.961994i | \(0.411961\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.00000 | 0.188608 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.14590 | −0.259626 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −14.6525 | −0.913996 | −0.456998 | − | 0.889468i | \(-0.651075\pi\) | ||||
−0.456998 | + | 0.889468i | \(0.651075\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.527864 | −0.0327999 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.23607 | −0.386003 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.18034 | −0.442759 | −0.221379 | − | 0.975188i | \(-0.571056\pi\) | ||||
−0.221379 | + | 0.975188i | \(0.571056\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.90983 | 0.240179 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.79837 | 0.477253 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.79837 | 0.109649 | 0.0548244 | − | 0.998496i | \(-0.482540\pi\) | ||||
0.0548244 | + | 0.998496i | \(0.482540\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.18034 | 0.0717005 | 0.0358503 | − | 0.999357i | \(-0.488586\pi\) | ||||
0.0358503 | + | 0.999357i | \(0.488586\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.61803 | 0.0979279 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 13.8541 | 0.835434 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.03444 | −0.302490 | −0.151245 | − | 0.988496i | \(-0.548328\pi\) | ||||
−0.151245 | + | 0.988496i | \(0.548328\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.00000 | −0.179605 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −17.2361 | −1.02822 | −0.514109 | − | 0.857725i | \(-0.671877\pi\) | ||||
−0.514109 | + | 0.857725i | \(0.671877\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.14590 | −0.484223 | −0.242112 | − | 0.970248i | \(-0.577840\pi\) | ||||
−0.242112 | + | 0.970248i | \(0.577840\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.145898 | 0.00864225 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.94427 | −0.350879 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 28.0000 | 1.64706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 14.4164 | 0.845105 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 16.9443 | 0.989895 | 0.494947 | − | 0.868923i | \(-0.335187\pi\) | ||||
0.494947 | + | 0.868923i | \(0.335187\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.56231 | −0.265628 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.00000 | −0.174078 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.61803 | 0.0935733 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.09017 | −0.120475 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −10.3262 | −0.593227 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.527864 | −0.0302254 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.58359 | −0.0903804 | −0.0451902 | − | 0.998978i | \(-0.514389\pi\) | ||||
−0.0451902 | + | 0.998978i | \(0.514389\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.41641 | −0.421905 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 18.2705 | 1.03603 | 0.518013 | − | 0.855373i | \(-0.326672\pi\) | ||||
0.518013 | + | 0.855373i | \(0.326672\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 26.4721 | 1.49629 | 0.748147 | − | 0.663533i | \(-0.230944\pi\) | ||||
0.748147 | + | 0.663533i | \(0.230944\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.618034 | −0.0348223 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.38197 | 0.189950 | 0.0949751 | − | 0.995480i | \(-0.469723\pi\) | ||||
0.0949751 | + | 0.995480i | \(0.469723\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 18.7082 | 1.04746 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8.38197 | 0.467836 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.58359 | −0.0881134 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.47214 | 0.414480 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 9.09017 | 0.502688 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.76393 | 0.262644 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −27.8885 | −1.53289 | −0.766447 | − | 0.642308i | \(-0.777977\pi\) | ||||
−0.766447 | + | 0.642308i | \(0.777977\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.527864 | 0.0289268 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.38197 | −0.457956 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.3820 | −0.565542 | −0.282771 | − | 0.959187i | \(-0.591254\pi\) | ||||
−0.282771 | + | 0.959187i | \(0.591254\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −12.3262 | −0.669469 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.00000 | 0.487377 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.618034 | −0.0332738 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.52786 | −0.243068 | −0.121534 | − | 0.992587i | \(-0.538781\pi\) | ||||
−0.121534 | + | 0.992587i | \(0.538781\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.8541 | 1.06277 | 0.531383 | − | 0.847132i | \(-0.321673\pi\) | ||||
0.531383 | + | 0.847132i | \(0.321673\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.61803 | −0.0863643 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −15.0000 | −0.798369 | −0.399185 | − | 0.916871i | \(-0.630707\pi\) | ||||
−0.399185 | + | 0.916871i | \(0.630707\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.47214 | −0.0781329 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.70820 | 0.355036 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.03444 | −0.107374 | −0.0536869 | − | 0.998558i | \(-0.517097\pi\) | ||||
−0.0536869 | + | 0.998558i | \(0.517097\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9443 | −0.997067 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.00000 | −0.104973 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.85410 | 0.201733 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.20163 | −0.323722 | −0.161861 | − | 0.986814i | \(-0.551750\pi\) | ||||
−0.161861 | + | 0.986814i | \(0.551750\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.94427 | 0.309446 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.32624 | −0.328442 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 28.8885 | 1.49579 | 0.747896 | − | 0.663816i | \(-0.231064\pi\) | ||||
0.747896 | + | 0.663816i | \(0.231064\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.94427 | −0.306961 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.0902 | 0.519670 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.52786 | −0.283947 | −0.141974 | − | 0.989870i | \(-0.545345\pi\) | ||||
−0.141974 | + | 0.989870i | \(0.545345\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −14.5623 | −0.746050 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 29.9443 | 1.53008 | 0.765040 | − | 0.643982i | \(-0.222719\pi\) | ||||
0.765040 | + | 0.643982i | \(0.222719\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.85410 | 0.0944938 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.09017 | 0.106249 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.65248 | 0.489400 | 0.244700 | − | 0.969599i | \(-0.421311\pi\) | ||||
0.244700 | + | 0.969599i | \(0.421311\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.70820 | 0.339248 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −11.9443 | −0.602509 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.14590 | 0.208603 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 25.1246 | 1.26097 | 0.630484 | − | 0.776202i | \(-0.282856\pi\) | ||||
0.630484 | + | 0.776202i | \(0.282856\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.236068 | −0.0118182 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −11.7639 | −0.587463 | −0.293731 | − | 0.955888i | \(-0.594897\pi\) | ||||
−0.293731 | + | 0.955888i | \(0.594897\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.85410 | 0.241800 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.618034 | 0.0307104 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.58359 | −0.0784957 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.58359 | 0.473878 | 0.236939 | − | 0.971525i | \(-0.423856\pi\) | ||||
0.236939 | + | 0.971525i | \(0.423856\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.00000 | −0.443937 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.38197 | 0.363243 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.909830 | 0.0446618 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.145898 | 0.00714466 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −24.2148 | −1.18297 | −0.591485 | − | 0.806316i | \(-0.701458\pi\) | ||||
−0.591485 | + | 0.806316i | \(0.701458\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.6180 | −0.761176 | −0.380588 | − | 0.924745i | \(-0.624278\pi\) | ||||
−0.380588 | + | 0.924745i | \(0.624278\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.76393 | −0.231630 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 30.9787 | 1.50269 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.854102 | 0.0413329 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.85410 | 0.234358 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 25.1459 | 1.21124 | 0.605618 | − | 0.795756i | \(-0.292926\pi\) | ||||
0.605618 | + | 0.795756i | \(0.292926\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 27.7082 | 1.33157 | 0.665786 | − | 0.746143i | \(-0.268097\pi\) | ||||
0.665786 | + | 0.746143i | \(0.268097\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.85410 | −0.184790 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.236068 | −0.0112927 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 30.8885 | 1.47423 | 0.737115 | − | 0.675767i | \(-0.236188\pi\) | ||||
0.737115 | + | 0.675767i | \(0.236188\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −19.4164 | −0.922501 | −0.461251 | − | 0.887270i | \(-0.652599\pi\) | ||||
−0.461251 | + | 0.887270i | \(0.652599\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.81966 | 0.228474 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.23607 | 0.153061 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.909830 | 0.0429375 | 0.0214688 | − | 0.999770i | \(-0.493166\pi\) | ||||
0.0214688 | + | 0.999770i | \(0.493166\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −17.8328 | −0.839714 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 21.1246 | 0.992521 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.00000 | 0.0468807 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.97871 | −0.326450 | −0.163225 | − | 0.986589i | \(-0.552190\pi\) | ||||
−0.163225 | + | 0.986589i | \(0.552190\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.70820 | −0.313112 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.20163 | 0.335413 | 0.167707 | − | 0.985837i | \(-0.446364\pi\) | ||||
0.167707 | + | 0.985837i | \(0.446364\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −37.8328 | −1.75824 | −0.879120 | − | 0.476600i | \(-0.841869\pi\) | ||||
−0.879120 | + | 0.476600i | \(0.841869\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.85410 | −0.0859819 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −24.8885 | −1.15170 | −0.575852 | − | 0.817554i | \(-0.695330\pi\) | ||||
−0.575852 | + | 0.817554i | \(0.695330\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.5623 | 0.626249 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13.2361 | 0.609886 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.27051 | −0.288318 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.09017 | −0.0500204 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.32624 | 0.289659 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13.7639 | 0.628890 | 0.314445 | − | 0.949276i | \(-0.398182\pi\) | ||||
0.314445 | + | 0.949276i | \(0.398182\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.854102 | −0.0389437 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.00000 | 0.0455016 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.90983 | 0.404575 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −29.0000 | −1.31412 | −0.657058 | − | 0.753840i | \(-0.728199\pi\) | ||||
−0.657058 | + | 0.753840i | \(0.728199\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.14590 | 0.187484 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.09017 | 0.274846 | 0.137423 | − | 0.990512i | \(-0.456118\pi\) | ||||
0.137423 | + | 0.990512i | \(0.456118\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 41.8328 | 1.88406 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.85410 | −0.0833357 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.38197 | 0.106846 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 34.5066 | 1.54473 | 0.772363 | − | 0.635181i | \(-0.219075\pi\) | ||||
0.772363 | + | 0.635181i | \(0.219075\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −19.4721 | −0.869951 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 40.2148 | 1.79309 | 0.896544 | − | 0.442954i | \(-0.146070\pi\) | ||||
0.896544 | + | 0.442954i | \(0.146070\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.38197 | −0.283994 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −10.3820 | −0.461079 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.7639 | 0.743048 | 0.371524 | − | 0.928423i | \(-0.378835\pi\) | ||||
0.371524 | + | 0.928423i | \(0.378835\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.23607 | −0.275867 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.236068 | 0.0104227 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.58359 | −0.201977 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14.2918 | 0.628552 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.52786 | 0.198751 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −22.3607 | −0.979639 | −0.489820 | − | 0.871824i | \(-0.662937\pi\) | ||||
−0.489820 | + | 0.871824i | \(0.662937\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18.0000 | 0.787085 | 0.393543 | − | 0.919306i | \(-0.371249\pi\) | ||||
0.393543 | + | 0.919306i | \(0.371249\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.61803 | 0.201548 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 20.1246 | 0.876642 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.38197 | −0.320350 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9.61803 | −0.416603 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.18034 | 0.223966 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −18.0344 | −0.778244 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.00000 | −0.129219 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 37.1246 | 1.59611 | 0.798056 | − | 0.602583i | \(-0.205862\pi\) | ||||
0.798056 | + | 0.602583i | \(0.205862\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.52786 | 0.365966 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.61803 | 0.240650 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.8541 | −0.763386 | −0.381693 | − | 0.924289i | \(-0.624659\pi\) | ||||
−0.381693 | + | 0.924289i | \(0.624659\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.854102 | −0.0364522 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.47214 | −0.0627151 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.70820 | −0.285262 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.326238 | 0.0138480 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 18.7639 | 0.795053 | 0.397527 | − | 0.917591i | \(-0.369869\pi\) | ||||
0.397527 | + | 0.917591i | \(0.369869\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.38197 | −0.143042 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 20.1246 | 0.849662 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −28.3820 | −1.19616 | −0.598079 | − | 0.801437i | \(-0.704069\pi\) | ||||
−0.598079 | + | 0.801437i | \(0.704069\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.61803 | −0.320493 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.58359 | −0.192154 | −0.0960771 | − | 0.995374i | \(-0.530630\pi\) | ||||
−0.0960771 | + | 0.995374i | \(0.530630\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.708204 | 0.0296374 | 0.0148187 | − | 0.999890i | \(-0.495283\pi\) | ||||
0.0148187 | + | 0.999890i | \(0.495283\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10.6525 | 0.445014 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.61803 | 0.192585 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 37.7771 | 1.57268 | 0.786340 | − | 0.617794i | \(-0.211973\pi\) | ||||
0.786340 | + | 0.617794i | \(0.211973\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.70820 | 0.320342 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.47214 | −0.0610745 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −18.9787 | −0.786018 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.00000 | −0.0413449 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22.3820 | 0.923803 | 0.461901 | − | 0.886931i | \(-0.347167\pi\) | ||||
0.461901 | + | 0.886931i | \(0.347167\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.708204 | −0.0291810 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.61803 | 0.148826 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −24.6525 | −1.01236 | −0.506178 | − | 0.862429i | \(-0.668942\pi\) | ||||
−0.506178 | + | 0.862429i | \(0.668942\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.14590 | 0.169965 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.43769 | 0.0997682 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.74265 | −0.357215 | −0.178607 | − | 0.983920i | \(-0.557159\pi\) | ||||
−0.178607 | + | 0.983920i | \(0.557159\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.20163 | 0.212179 | 0.106089 | − | 0.994357i | \(-0.466167\pi\) | ||||
0.106089 | + | 0.994357i | \(0.466167\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −13.5623 | −0.552300 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.23607 | −0.0502533 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.56231 | −0.185178 | −0.0925891 | − | 0.995704i | \(-0.529514\pi\) | ||||
−0.0925891 | + | 0.995704i | \(0.529514\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6.23607 | 0.252698 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.70820 | 0.311841 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.29180 | −0.375292 | −0.187646 | − | 0.982237i | \(-0.560086\pi\) | ||||
−0.187646 | + | 0.982237i | \(0.560086\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.67376 | 0.148140 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22.8541 | 0.920072 | 0.460036 | − | 0.887900i | \(-0.347837\pi\) | ||||
0.460036 | + | 0.887900i | \(0.347837\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −31.1459 | −1.25186 | −0.625930 | − | 0.779880i | \(-0.715280\pi\) | ||||
−0.625930 | + | 0.779880i | \(0.715280\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7.79837 | −0.312435 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.4164 | 0.776656 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.708204 | −0.0282829 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.54102 | −0.141190 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −40.7771 | −1.62331 | −0.811655 | − | 0.584137i | \(-0.801433\pi\) | ||||
−0.811655 | + | 0.584137i | \(0.801433\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 14.1246 | 0.561403 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −9.00000 | −0.357154 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.61803 | −0.0641088 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.38197 | −0.0942291 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −24.6738 | −0.974555 | −0.487278 | − | 0.873247i | \(-0.662010\pi\) | ||||
−0.487278 | + | 0.873247i | \(0.662010\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.32624 | 0.288919 | 0.144459 | − | 0.989511i | \(-0.453856\pi\) | ||||
0.144459 | + | 0.989511i | \(0.453856\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.29180 | 0.0508644 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 26.3951 | 1.03770 | 0.518850 | − | 0.854866i | \(-0.326360\pi\) | ||||
0.518850 | + | 0.854866i | \(0.326360\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 22.1459 | 0.869303 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.00000 | 0.117579 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −25.8541 | −1.01175 | −0.505875 | − | 0.862607i | \(-0.668830\pi\) | ||||
−0.505875 | + | 0.862607i | \(0.668830\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.38197 | −0.288437 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.23607 | 0.243292 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22.3050 | 0.868878 | 0.434439 | − | 0.900701i | \(-0.356947\pi\) | ||||
0.434439 | + | 0.900701i | \(0.356947\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −28.7771 | −1.11930 | −0.559649 | − | 0.828729i | \(-0.689064\pi\) | ||||
−0.559649 | + | 0.828729i | \(0.689064\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 10.8541 | 0.421538 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.145898 | −0.00565768 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.23607 | 0.241462 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −12.7984 | −0.494814 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.56231 | 0.0989167 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −44.3050 | −1.70783 | −0.853915 | − | 0.520412i | \(-0.825778\pi\) | ||||
−0.853915 | + | 0.520412i | \(0.825778\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.61803 | −0.177748 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0.0901699 | 0.00346551 | 0.00173276 | − | 0.999998i | \(-0.499448\pi\) | ||||
0.00173276 | + | 0.999998i | \(0.499448\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −14.4164 | −0.553251 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −29.4508 | −1.12856 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9.00000 | −0.344375 | −0.172188 | − | 0.985064i | \(-0.555084\pi\) | ||||
−0.172188 | + | 0.985064i | \(0.555084\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.56231 | −0.212525 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −9.27051 | −0.353692 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −10.2361 | −0.389963 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.6180 | 0.746305 | 0.373153 | − | 0.927770i | \(-0.378277\pi\) | ||||
0.373153 | + | 0.927770i | \(0.378277\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.00000 | 0.113961 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.0901699 | 0.00342034 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −39.8754 | −1.51039 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.909830 | −0.0344129 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.0902 | 0.494409 | 0.247204 | − | 0.968963i | \(-0.420488\pi\) | ||||
0.247204 | + | 0.968963i | \(0.420488\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.124612 | 0.00469982 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.94427 | −0.110888 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10.3262 | 0.388358 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.0901699 | 0.00338640 | 0.00169320 | − | 0.999999i | \(-0.499461\pi\) | ||||
0.00169320 | + | 0.999999i | \(0.499461\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.70820 | 0.251577 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.00000 | 0.112351 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.00000 | 0.112194 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −15.3820 | −0.574450 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.65248 | −0.136214 | −0.0681072 | − | 0.997678i | \(-0.521696\pi\) | ||||
−0.0681072 | + | 0.997678i | \(0.521696\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.41641 | 0.276201 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 21.0000 | 0.780998 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 28.7984 | 1.06954 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19.2918 | −0.715493 | −0.357747 | − | 0.933819i | \(-0.616455\pi\) | ||||
−0.357747 | + | 0.933819i | \(0.616455\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −14.0213 | −0.518596 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.59675 | −0.0589772 | −0.0294886 | − | 0.999565i | \(-0.509388\pi\) | ||||
−0.0294886 | + | 0.999565i | \(0.509388\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.618034 | 0.0227965 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 40.6869 | 1.49872 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.2918 | 0.562518 | 0.281259 | − | 0.959632i | \(-0.409248\pi\) | ||||
0.281259 | + | 0.959632i | \(0.409248\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.381966 | −0.0140319 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −22.6180 | −0.829775 | −0.414888 | − | 0.909873i | \(-0.636179\pi\) | ||||
−0.414888 | + | 0.909873i | \(0.636179\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.00000 | 0.0732743 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.47214 | 0.0538626 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8.38197 | −0.306270 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.72949 | 0.172582 | 0.0862908 | − | 0.996270i | \(-0.472499\pi\) | ||||
0.0862908 | + | 0.996270i | \(0.472499\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.65248 | 0.315314 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 13.0557 | 0.475147 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.52786 | −0.309950 | −0.154975 | − | 0.987918i | \(-0.549530\pi\) | ||||
−0.154975 | + | 0.987918i | \(0.549530\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.00000 | 0.108893 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17.5279 | −0.635385 | −0.317692 | − | 0.948194i | \(-0.602908\pi\) | ||||
−0.317692 | + | 0.948194i | \(0.602908\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.09017 | −0.329086 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.14590 | −0.149895 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 11.9443 | 0.431283 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −35.1246 | −1.26663 | −0.633313 | − | 0.773896i | \(-0.718305\pi\) | ||||
−0.633313 | + | 0.773896i | \(0.718305\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14.6525 | −0.527696 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −33.9443 | −1.22089 | −0.610445 | − | 0.792058i | \(-0.709009\pi\) | ||||
−0.610445 | + | 0.792058i | \(0.709009\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 13.8541 | 0.497654 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.527864 | −0.0189370 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.40325 | 0.0502767 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.14590 | 0.255700 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.23607 | −0.222859 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.18034 | 0.291969 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.9098 | 0.460186 | 0.230093 | − | 0.973169i | \(-0.426097\pi\) | ||||
0.230093 | + | 0.973169i | \(0.426097\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −7.18034 | −0.255627 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 12.3262 | 0.438271 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.38197 | 0.0490751 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.90983 | 0.138667 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 44.1803 | 1.56495 | 0.782474 | − | 0.622683i | \(-0.213957\pi\) | ||||
0.782474 | + | 0.622683i | \(0.213957\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 31.9574 | 1.13057 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.79837 | 0.275542 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −18.7082 | −0.660198 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.618034 | 0.0217828 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.79837 | 0.0633058 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.21478 | 0.323974 | 0.161987 | − | 0.986793i | \(-0.448210\pi\) | ||||
0.161987 | + | 0.986793i | \(0.448210\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −27.2918 | −0.958345 | −0.479172 | − | 0.877721i | \(-0.659063\pi\) | ||||
−0.479172 | + | 0.877721i | \(0.659063\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.18034 | 0.0413963 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.56231 | 0.0897537 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.493422 | 0.0172627 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.61803 | 0.0565387 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −38.2918 | −1.33639 | −0.668196 | − | 0.743985i | \(-0.732933\pi\) | ||||
−0.668196 | + | 0.743985i | \(0.732933\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −39.0902 | −1.36260 | −0.681299 | − | 0.732005i | \(-0.738585\pi\) | ||||
−0.681299 | + | 0.732005i | \(0.738585\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 13.8541 | 0.482338 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −13.9230 | −0.484150 | −0.242075 | − | 0.970258i | \(-0.577828\pi\) | ||||
−0.242075 | + | 0.970258i | \(0.577828\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.00000 | 0.243120 | 0.121560 | − | 0.992584i | \(-0.461210\pi\) | ||||
0.121560 | + | 0.992584i | \(0.461210\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.03444 | −0.174643 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.70820 | −0.232425 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12.0344 | −0.416469 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.00000 | −0.103695 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0.0901699 | 0.00311301 | 0.00155651 | − | 0.999999i | \(-0.499505\pi\) | ||||
0.00155651 | + | 0.999999i | \(0.499505\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.88854 | 0.340984 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −17.2361 | −0.593642 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.41641 | −0.220731 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.00000 | 0.0687208 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −8.14590 | −0.279566 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.527864 | −0.0180949 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.7082 | 0.537839 | 0.268919 | − | 0.963163i | \(-0.413333\pi\) | ||||
0.268919 | + | 0.963163i | \(0.413333\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.145898 | 0.00498961 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10.1803 | 0.347754 | 0.173877 | − | 0.984767i | \(-0.444371\pi\) | ||||
0.173877 | + | 0.984767i | \(0.444371\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 27.3050 | 0.931633 | 0.465816 | − | 0.884881i | \(-0.345761\pi\) | ||||
0.465816 | + | 0.884881i | \(0.345761\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.94427 | −0.202580 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 19.3475 | 0.658597 | 0.329299 | − | 0.944226i | \(-0.393188\pi\) | ||||
0.329299 | + | 0.944226i | \(0.393188\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.79837 | 0.0951476 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 28.0000 | 0.950930 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −20.1246 | −0.682681 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 21.9443 | 0.743553 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 14.4164 | 0.487921 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5.94427 | 0.200953 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.4164 | 0.790716 | 0.395358 | − | 0.918527i | \(-0.370621\pi\) | ||||
0.395358 | + | 0.918527i | \(0.370621\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 16.9443 | 0.571516 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.70820 | 0.124933 | 0.0624663 | − | 0.998047i | \(-0.480103\pi\) | ||||
0.0624663 | + | 0.998047i | \(0.480103\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −37.3262 | −1.25613 | −0.628064 | − | 0.778162i | \(-0.716152\pi\) | ||||
−0.628064 | + | 0.778162i | \(0.716152\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.56231 | −0.153360 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 30.2705 | 1.01638 | 0.508192 | − | 0.861244i | \(-0.330314\pi\) | ||||
0.508192 | + | 0.861244i | \(0.330314\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 14.5623 | 0.488404 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.00000 | −0.100504 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.12461 | −0.0376337 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −11.1459 | −0.372566 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.61803 | 0.0540246 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 18.7082 | 0.623954 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −42.4377 | −1.41380 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.09017 | −0.0695565 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.27051 | 0.175198 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −32.4377 | −1.07708 | −0.538538 | − | 0.842601i | \(-0.681023\pi\) | ||||
−0.538538 | + | 0.842601i | \(0.681023\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −10.3262 | −0.342500 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −56.1803 | −1.86134 | −0.930669 | − | 0.365863i | \(-0.880774\pi\) | ||||
−0.930669 | + | 0.365863i | \(0.880774\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.41641 | −0.146162 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.527864 | −0.0174506 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 11.9443 | 0.394435 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 36.3050 | 1.19759 | 0.598795 | − | 0.800902i | \(-0.295646\pi\) | ||||
0.598795 | + | 0.800902i | \(0.295646\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.58359 | −0.0521811 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.85410 | 0.126859 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.43769 | −0.0801509 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7.41641 | −0.243587 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −36.0344 | −1.18225 | −0.591126 | − | 0.806579i | \(-0.701316\pi\) | ||||
−0.591126 | + | 0.806579i | \(0.701316\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.236068 | 0.00773682 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 18.2705 | 0.598150 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 12.4377 | 0.406756 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −40.7082 | −1.32988 | −0.664940 | − | 0.746897i | \(-0.731543\pi\) | ||||
−0.664940 | + | 0.746897i | \(0.731543\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 26.4721 | 0.863886 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −36.0000 | −1.17357 | −0.586783 | − | 0.809744i | \(-0.699606\pi\) | ||||
−0.586783 | + | 0.809744i | \(0.699606\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.94427 | −0.193572 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.618034 | −0.0201046 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −55.3050 | −1.79717 | −0.898585 | − | 0.438800i | \(-0.855404\pi\) | ||||
−0.898585 | + | 0.438800i | \(0.855404\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10.0902 | −0.327541 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.38197 | 0.109668 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −30.0902 | −0.974716 | −0.487358 | − | 0.873202i | \(-0.662039\pi\) | ||||
−0.487358 | + | 0.873202i | \(0.662039\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.58359 | 0.213040 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 18.7082 | 0.604750 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.00000 | 0.290625 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.0000 | −0.709677 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.38197 | 0.270105 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.76393 | 0.153356 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −54.0000 | −1.73652 | −0.868261 | − | 0.496107i | \(-0.834762\pi\) | ||||
−0.868261 | + | 0.496107i | \(0.834762\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.58359 | −0.0508723 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 19.7984 | 0.635360 | 0.317680 | − | 0.948198i | \(-0.397096\pi\) | ||||
0.317680 | + | 0.948198i | \(0.397096\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.145898 | −0.00467728 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 7.47214 | 0.239300 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −59.2837 | −1.89665 | −0.948326 | − | 0.317297i | \(-0.897225\pi\) | ||||
−0.948326 | + | 0.317297i | \(0.897225\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −23.3951 | −0.747711 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.09017 | 0.290227 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −45.4721 | −1.45034 | −0.725168 | − | 0.688572i | \(-0.758238\pi\) | ||||
−0.725168 | + | 0.688572i | \(0.758238\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.23607 | 0.0712470 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4.76393 | 0.151638 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.09017 | −0.0664635 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −59.6869 | −1.89602 | −0.948009 | − | 0.318244i | \(-0.896907\pi\) | ||||
−0.948009 | + | 0.318244i | \(0.896907\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −27.8885 | −0.885016 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.50658 | 0.0477617 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −15.4721 | −0.490007 | −0.245004 | − | 0.969522i | \(-0.578789\pi\) | ||||
−0.245004 | + | 0.969522i | \(0.578789\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.527864 | 0.0167009 |
(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 | 1932.2.a.g.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 5796.2.a.l.1.1 | 2 | |||
4.3 | odd | 2 | 7728.2.a.ba.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1932.2.a.g.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
5796.2.a.l.1.1 | 2 | 3.2 | odd | 2 | |||
7728.2.a.ba.1.2 | 2 | 4.3 | odd | 2 |