Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8004,2,Mod(1,8004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8004, 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("8004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8004 = 2^{2} \cdot 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8004.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: | \(63.9122617778\) |
Analytic rank: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - x^{8} - 17x^{7} + 4x^{6} + 75x^{5} + x^{4} - 118x^{3} - 26x^{2} + 60x + 24 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(-1.91513\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8004.1 |
$q$-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 | ||||||||
\(5\) | 1.91513 | 0.856473 | 0.428236 | − | 0.903667i | \(-0.359135\pi\) | ||||
0.428236 | + | 0.903667i | \(0.359135\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.97719 | −1.12527 | −0.562636 | − | 0.826705i | \(-0.690213\pi\) | ||||
−0.562636 | + | 0.826705i | \(0.690213\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.04500 | 0.616592 | 0.308296 | − | 0.951290i | \(-0.400241\pi\) | ||||
0.308296 | + | 0.951290i | \(0.400241\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.36883 | 0.379645 | 0.189822 | − | 0.981818i | \(-0.439209\pi\) | ||||
0.189822 | + | 0.981818i | \(0.439209\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.91513 | 0.494485 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.26690 | −1.51995 | −0.759974 | − | 0.649954i | \(-0.774788\pi\) | ||||
−0.759974 | + | 0.649954i | \(0.774788\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.09894 | −0.481530 | −0.240765 | − | 0.970583i | \(-0.577398\pi\) | ||||
−0.240765 | + | 0.970583i | \(0.577398\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.97719 | −0.649676 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.33227 | −0.266455 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.34340 | 0.241282 | 0.120641 | − | 0.992696i | \(-0.461505\pi\) | ||||
0.120641 | + | 0.992696i | \(0.461505\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.04500 | 0.355990 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.70171 | −0.963765 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.21257 | −0.856942 | −0.428471 | − | 0.903556i | \(-0.640948\pi\) | ||||
−0.428471 | + | 0.903556i | \(0.640948\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.36883 | 0.219188 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.87339 | 1.22962 | 0.614808 | − | 0.788677i | \(-0.289233\pi\) | ||||
0.614808 | + | 0.788677i | \(0.289233\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.58152 | −0.241180 | −0.120590 | − | 0.992702i | \(-0.538479\pi\) | ||||
−0.120590 | + | 0.992702i | \(0.538479\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.91513 | 0.285491 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.90675 | 0.569858 | 0.284929 | − | 0.958549i | \(-0.408030\pi\) | ||||
0.284929 | + | 0.958549i | \(0.408030\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.86366 | 0.266237 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.26690 | −0.877542 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.86566 | −1.35515 | −0.677576 | − | 0.735453i | \(-0.736970\pi\) | ||||
−0.677576 | + | 0.735453i | \(0.736970\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.91645 | 0.528094 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.09894 | −0.278012 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.00323 | −0.260799 | −0.130399 | − | 0.991462i | \(-0.541626\pi\) | ||||
−0.130399 | + | 0.991462i | \(0.541626\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.80143 | −1.25494 | −0.627472 | − | 0.778639i | \(-0.715910\pi\) | ||||
−0.627472 | + | 0.778639i | \(0.715910\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.97719 | −0.375091 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.62148 | 0.325155 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.45384 | 0.299784 | 0.149892 | − | 0.988702i | \(-0.452107\pi\) | ||||
0.149892 | + | 0.988702i | \(0.452107\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.65971 | −1.02772 | −0.513859 | − | 0.857875i | \(-0.671785\pi\) | ||||
−0.513859 | + | 0.857875i | \(0.671785\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.2737 | 1.67061 | 0.835303 | − | 0.549790i | \(-0.185292\pi\) | ||||
0.835303 | + | 0.549790i | \(0.185292\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.33227 | −0.153838 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.08837 | −0.693834 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.878902 | 0.0988842 | 0.0494421 | − | 0.998777i | \(-0.484256\pi\) | ||||
0.0494421 | + | 0.998777i | \(0.484256\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −13.3255 | −1.46266 | −0.731330 | − | 0.682024i | \(-0.761100\pi\) | ||||
−0.731330 | + | 0.682024i | \(0.761100\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −12.0019 | −1.30179 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.00000 | −0.107211 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.49647 | −0.582624 | −0.291312 | − | 0.956628i | \(-0.594092\pi\) | ||||
−0.291312 | + | 0.956628i | \(0.594092\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.07526 | −0.427203 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.34340 | 0.139304 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.01975 | −0.412418 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.26837 | −0.839525 | −0.419763 | − | 0.907634i | \(-0.637887\pi\) | ||||
−0.419763 | + | 0.907634i | \(0.637887\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.04500 | 0.205531 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.3712 | 1.03197 | 0.515985 | − | 0.856597i | \(-0.327426\pi\) | ||||
0.515985 | + | 0.856597i | \(0.327426\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.930722 | 0.0917067 | 0.0458534 | − | 0.998948i | \(-0.485399\pi\) | ||||
0.0458534 | + | 0.998948i | \(0.485399\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.70171 | −0.556430 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −15.1650 | −1.46606 | −0.733028 | − | 0.680199i | \(-0.761893\pi\) | ||||
−0.733028 | + | 0.680199i | \(0.761893\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.05050 | −0.100619 | −0.0503096 | − | 0.998734i | \(-0.516021\pi\) | ||||
−0.0503096 | + | 0.998734i | \(0.516021\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.21257 | −0.494756 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.6446 | −1.00136 | −0.500678 | − | 0.865633i | \(-0.666916\pi\) | ||||
−0.500678 | + | 0.865633i | \(0.666916\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.91513 | −0.178587 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.36883 | 0.126548 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 18.6578 | 1.71035 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.81796 | −0.619814 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 7.87339 | 0.709920 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.1271 | −1.08468 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.98416 | 0.885951 | 0.442976 | − | 0.896534i | \(-0.353923\pi\) | ||||
0.442976 | + | 0.896534i | \(0.353923\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.58152 | −0.139245 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.00561 | 0.524713 | 0.262356 | − | 0.964971i | \(-0.415500\pi\) | ||||
0.262356 | + | 0.964971i | \(0.415500\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.24895 | 0.541853 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.91513 | 0.164828 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.4401 | 1.06283 | 0.531413 | − | 0.847113i | \(-0.321661\pi\) | ||||
0.531413 | + | 0.847113i | \(0.321661\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −22.9607 | −1.94750 | −0.973750 | − | 0.227622i | \(-0.926905\pi\) | ||||
−0.973750 | + | 0.227622i | \(0.926905\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.90675 | 0.329008 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.79926 | 0.234086 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.91513 | −0.159043 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.86366 | 0.153712 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −14.9121 | −1.22165 | −0.610823 | − | 0.791767i | \(-0.709161\pi\) | ||||
−0.610823 | + | 0.791767i | \(0.709161\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.53402 | −0.124837 | −0.0624185 | − | 0.998050i | \(-0.519881\pi\) | ||||
−0.0624185 | + | 0.998050i | \(0.519881\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.26690 | −0.506649 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.57279 | 0.206651 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.66353 | 0.771234 | 0.385617 | − | 0.922659i | \(-0.373989\pi\) | ||||
0.385617 | + | 0.922659i | \(0.373989\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.86566 | −0.782398 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.97719 | 0.234635 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.9447 | 1.01391 | 0.506953 | − | 0.861974i | \(-0.330772\pi\) | ||||
0.506953 | + | 0.861974i | \(0.330772\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.91645 | 0.304895 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.50077 | 0.425663 | 0.212831 | − | 0.977089i | \(-0.431732\pi\) | ||||
0.212831 | + | 0.977089i | \(0.431732\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.1263 | −0.855870 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.09894 | −0.160510 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.96116 | −0.757333 | −0.378666 | − | 0.925533i | \(-0.623617\pi\) | ||||
−0.378666 | + | 0.925533i | \(0.623617\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.96643 | 0.299834 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.00323 | −0.150572 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −13.0081 | −0.972274 | −0.486137 | − | 0.873883i | \(-0.661594\pi\) | ||||
−0.486137 | + | 0.873883i | \(0.661594\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.81020 | 0.729186 | 0.364593 | − | 0.931167i | \(-0.381208\pi\) | ||||
0.364593 | + | 0.931167i | \(0.381208\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.80143 | −0.724543 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −9.98276 | −0.733947 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.8158 | −0.937188 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.97719 | −0.216559 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.75152 | 0.416166 | 0.208083 | − | 0.978111i | \(-0.433278\pi\) | ||||
0.208083 | + | 0.978111i | \(0.433278\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.3988 | 0.820502 | 0.410251 | − | 0.911973i | \(-0.365441\pi\) | ||||
0.410251 | + | 0.911973i | \(0.365441\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.62148 | 0.187728 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 17.2757 | 1.23084 | 0.615422 | − | 0.788198i | \(-0.288986\pi\) | ||||
0.615422 | + | 0.788198i | \(0.288986\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.9978 | −0.779613 | −0.389807 | − | 0.920897i | \(-0.627458\pi\) | ||||
−0.389807 | + | 0.920897i | \(0.627458\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.45384 | 0.173081 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.97719 | 0.208958 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 15.0786 | 1.05313 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.29235 | −0.296908 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.49631 | −0.378382 | −0.189191 | − | 0.981940i | \(-0.560586\pi\) | ||||
−0.189191 | + | 0.981940i | \(0.560586\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −8.65971 | −0.593353 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.02882 | −0.206564 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.99955 | −0.271507 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 14.2737 | 0.964525 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.57831 | −0.577040 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.8557 | 1.39660 | 0.698300 | − | 0.715806i | \(-0.253940\pi\) | ||||
0.698300 | + | 0.715806i | \(0.253940\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.33227 | −0.0888183 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.4917 | 0.829101 | 0.414550 | − | 0.910026i | \(-0.363939\pi\) | ||||
0.414550 | + | 0.910026i | \(0.363939\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −28.0229 | −1.85180 | −0.925902 | − | 0.377764i | \(-0.876693\pi\) | ||||
−0.925902 | + | 0.377764i | \(0.876693\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.08837 | −0.400585 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.2804 | −0.804518 | −0.402259 | − | 0.915526i | \(-0.631775\pi\) | ||||
−0.402259 | + | 0.915526i | \(0.631775\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.48194 | 0.488068 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.878902 | 0.0570908 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.94247 | 0.578440 | 0.289220 | − | 0.957263i | \(-0.406604\pi\) | ||||
0.289220 | + | 0.957263i | \(0.406604\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.940096 | −0.0605569 | −0.0302785 | − | 0.999542i | \(-0.509639\pi\) | ||||
−0.0302785 | + | 0.999542i | \(0.509639\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.56915 | 0.228025 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.87309 | −0.182810 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −13.3255 | −0.844467 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.5996 | 1.17400 | 0.586998 | − | 0.809588i | \(-0.300310\pi\) | ||||
0.586998 | + | 0.809588i | \(0.300310\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.04500 | −0.128568 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −12.0019 | −0.751591 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.55236 | 0.159212 | 0.0796058 | − | 0.996826i | \(-0.474634\pi\) | ||||
0.0796058 | + | 0.996826i | \(0.474634\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 15.5188 | 0.964293 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.00000 | −0.0618984 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 21.8897 | 1.34978 | 0.674889 | − | 0.737920i | \(-0.264192\pi\) | ||||
0.674889 | + | 0.737920i | \(0.264192\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −18.8940 | −1.16065 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.49647 | −0.336378 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −24.3149 | −1.48251 | −0.741254 | − | 0.671225i | \(-0.765769\pi\) | ||||
−0.741254 | + | 0.671225i | \(0.765769\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.46398 | 0.210422 | 0.105211 | − | 0.994450i | \(-0.466448\pi\) | ||||
0.105211 | + | 0.994450i | \(0.466448\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.07526 | −0.246646 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.72451 | −0.164294 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.3852 | 1.22483 | 0.612413 | − | 0.790538i | \(-0.290199\pi\) | ||||
0.612413 | + | 0.790538i | \(0.290199\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.34340 | 0.0804272 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.4489 | −0.981260 | −0.490630 | − | 0.871368i | \(-0.663233\pi\) | ||||
−0.490630 | + | 0.871368i | \(0.663233\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.85058 | −0.347781 | −0.173891 | − | 0.984765i | \(-0.555634\pi\) | ||||
−0.173891 | + | 0.984765i | \(0.555634\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.01975 | −0.238109 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −23.4406 | −1.38365 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 22.2741 | 1.31024 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.26837 | −0.484700 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −32.9715 | −1.92621 | −0.963107 | − | 0.269120i | \(-0.913267\pi\) | ||||
−0.963107 | + | 0.269120i | \(0.913267\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.83645 | −0.223367 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.04500 | 0.118663 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.36883 | −0.0791614 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.70849 | 0.271393 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 10.3712 | 0.595809 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −18.7710 | −1.07483 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.75728 | −0.271512 | −0.135756 | − | 0.990742i | \(-0.543346\pi\) | ||||
−0.135756 | + | 0.990742i | \(0.543346\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.930722 | 0.0529469 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.7276 | −0.608305 | −0.304153 | − | 0.952623i | \(-0.598373\pi\) | ||||
−0.304153 | + | 0.952623i | \(0.598373\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 23.2780 | 1.31575 | 0.657876 | − | 0.753127i | \(-0.271455\pi\) | ||||
0.657876 | + | 0.753127i | \(0.271455\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5.70171 | −0.321255 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −26.6155 | −1.49488 | −0.747438 | − | 0.664332i | \(-0.768716\pi\) | ||||
−0.747438 | + | 0.664332i | \(0.768716\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.04500 | −0.114498 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −15.1650 | −0.846427 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.1539 | 0.731901 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.82365 | −0.101158 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.05050 | −0.0580925 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −11.6311 | −0.641245 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.55686 | −0.305432 | −0.152716 | − | 0.988270i | \(-0.548802\pi\) | ||||
−0.152716 | + | 0.988270i | \(0.548802\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5.21257 | −0.285647 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.69942 | 0.256757 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.0060 | −0.980851 | −0.490426 | − | 0.871483i | \(-0.663159\pi\) | ||||
−0.490426 | + | 0.871483i | \(0.663159\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −10.6446 | −0.578134 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.74726 | 0.148772 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.2919 | 0.825683 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.91513 | −0.103107 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 17.1964 | 0.923150 | 0.461575 | − | 0.887101i | \(-0.347284\pi\) | ||||
0.461575 | + | 0.887101i | \(0.347284\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −20.4351 | −1.09387 | −0.546934 | − | 0.837176i | \(-0.684205\pi\) | ||||
−0.546934 | + | 0.837176i | \(0.684205\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.36883 | 0.0730626 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.80347 | −0.362112 | −0.181056 | − | 0.983473i | \(-0.557952\pi\) | ||||
−0.181056 | + | 0.983473i | \(0.557952\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −16.5845 | −0.880212 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 18.6578 | 0.987474 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −16.6516 | −0.878836 | −0.439418 | − | 0.898283i | \(-0.644815\pi\) | ||||
−0.439418 | + | 0.898283i | \(0.644815\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.5944 | −0.768128 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6.81796 | −0.357850 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 27.3359 | 1.43083 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.95943 | −0.415479 | −0.207740 | − | 0.978184i | \(-0.566611\pi\) | ||||
−0.207740 | + | 0.978184i | \(0.566611\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 7.87339 | 0.409872 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 29.3719 | 1.52492 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 25.8613 | 1.33905 | 0.669523 | − | 0.742791i | \(-0.266499\pi\) | ||||
0.669523 | + | 0.742791i | \(0.266499\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −12.1271 | −0.626242 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.36883 | −0.0704982 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −28.2449 | −1.45084 | −0.725422 | − | 0.688304i | \(-0.758355\pi\) | ||||
−0.725422 | + | 0.688304i | \(0.758355\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.98416 | 0.511504 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −36.8460 | −1.88274 | −0.941372 | − | 0.337370i | \(-0.890463\pi\) | ||||
−0.941372 | + | 0.337370i | \(0.890463\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −11.6600 | −0.594250 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.58152 | −0.0803933 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 28.9688 | 1.46878 | 0.734389 | − | 0.678729i | \(-0.237469\pi\) | ||||
0.734389 | + | 0.678729i | \(0.237469\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.26690 | 0.316931 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.00561 | 0.302943 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.68321 | 0.0846916 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.14013 | 0.458730 | 0.229365 | − | 0.973340i | \(-0.426335\pi\) | ||||
0.229365 | + | 0.973340i | \(0.426335\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6.24895 | 0.312839 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.4623 | −0.772150 | −0.386075 | − | 0.922467i | \(-0.626169\pi\) | ||||
−0.386075 | + | 0.922467i | \(0.626169\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.83888 | 0.0916013 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.91513 | 0.0951636 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.6597 | −0.528384 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −22.2649 | −1.10093 | −0.550463 | − | 0.834859i | \(-0.685549\pi\) | ||||
−0.550463 | + | 0.834859i | \(0.685549\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.4401 | 0.613623 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.96400 | 0.293469 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −25.5200 | −1.25273 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −22.9607 | −1.12439 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.87683 | 0.189395 | 0.0946977 | − | 0.995506i | \(-0.469812\pi\) | ||||
0.0946977 | + | 0.995506i | \(0.469812\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.50411 | −0.170780 | −0.0853900 | − | 0.996348i | \(-0.527214\pi\) | ||||
−0.0853900 | + | 0.996348i | \(0.527214\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.90675 | 0.189953 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 8.34923 | 0.404997 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 29.1807 | 1.41215 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.79926 | 0.135150 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 35.8991 | 1.72920 | 0.864599 | − | 0.502462i | \(-0.167572\pi\) | ||||
0.864599 | + | 0.502462i | \(0.167572\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −33.9905 | −1.63348 | −0.816740 | − | 0.577006i | \(-0.804221\pi\) | ||||
−0.816740 | + | 0.577006i | \(0.804221\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.91513 | −0.0918235 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.09894 | 0.100406 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.28540 | 0.299986 | 0.149993 | − | 0.988687i | \(-0.452075\pi\) | ||||
0.149993 | + | 0.988687i | \(0.452075\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.86366 | 0.0887457 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 36.9811 | 1.75702 | 0.878512 | − | 0.477721i | \(-0.158537\pi\) | ||||
0.878512 | + | 0.477721i | \(0.158537\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.5265 | −0.499002 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −14.9121 | −0.705318 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.78344 | −0.0841658 | −0.0420829 | − | 0.999114i | \(-0.513399\pi\) | ||||
−0.0420829 | + | 0.999114i | \(0.513399\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.1011 | 0.758172 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.53402 | −0.0720747 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −7.80466 | −0.365888 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.05415 | 0.329979 | 0.164990 | − | 0.986295i | \(-0.447241\pi\) | ||||
0.164990 | + | 0.986295i | \(0.447241\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.26690 | −0.292514 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −32.5834 | −1.51756 | −0.758781 | − | 0.651346i | \(-0.774205\pi\) | ||||
−0.758781 | + | 0.651346i | \(0.774205\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.39669 | −0.204331 | −0.102166 | − | 0.994767i | \(-0.532577\pi\) | ||||
−0.102166 | + | 0.994767i | \(0.532577\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.57279 | 0.119310 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17.9704 | 0.831571 | 0.415786 | − | 0.909463i | \(-0.363507\pi\) | ||||
0.415786 | + | 0.909463i | \(0.363507\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.30555 | −0.337339 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.66353 | 0.445272 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.23422 | −0.148710 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.79637 | 0.128306 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.86566 | −0.451717 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12.4889 | 0.570633 | 0.285316 | − | 0.958433i | \(-0.407901\pi\) | ||||
0.285316 | + | 0.958433i | \(0.407901\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.13512 | −0.325333 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.97719 | 0.135467 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −15.8350 | −0.719030 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −41.0747 | −1.86127 | −0.930637 | − | 0.365944i | \(-0.880746\pi\) | ||||
−0.930637 | + | 0.365944i | \(0.880746\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 12.9447 | 0.585379 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.4708 | 0.788448 | 0.394224 | − | 0.919014i | \(-0.371013\pi\) | ||||
0.394224 | + | 0.919014i | \(0.371013\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.26690 | 0.282247 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.91645 | 0.176031 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 25.7816 | 1.15646 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.5429 | 0.740563 | 0.370281 | − | 0.928920i | \(-0.379261\pi\) | ||||
0.370281 | + | 0.928920i | \(0.379261\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.50077 | 0.245756 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 28.5878 | 1.27467 | 0.637334 | − | 0.770587i | \(-0.280037\pi\) | ||||
0.637334 | + | 0.770587i | \(0.280037\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 19.8622 | 0.883855 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −11.1263 | −0.494137 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −43.6303 | −1.93388 | −0.966940 | − | 0.255004i | \(-0.917923\pi\) | ||||
−0.966940 | + | 0.255004i | \(0.917923\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −42.4954 | −1.87989 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.09894 | −0.0926706 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.78245 | 0.0785443 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.98932 | 0.351370 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9.96116 | −0.437246 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.35339 | 0.146915 | 0.0734573 | − | 0.997298i | \(-0.476597\pi\) | ||||
0.0734573 | + | 0.997298i | \(0.476597\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 23.9658 | 1.04795 | 0.523976 | − | 0.851733i | \(-0.324448\pi\) | ||||
0.523976 | + | 0.851733i | \(0.324448\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.96643 | 0.173109 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.41895 | −0.366735 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.00323 | −0.0869328 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.7773 | 0.466817 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −29.0429 | −1.25564 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −13.0081 | −0.561342 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.81119 | 0.164160 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.93074 | 0.168996 | 0.0844978 | − | 0.996424i | \(-0.473071\pi\) | ||||
0.0844978 | + | 0.996424i | \(0.473071\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9.81020 | 0.420996 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.01184 | −0.0861776 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 36.3389 | 1.55374 | 0.776869 | − | 0.629662i | \(-0.216807\pi\) | ||||
0.776869 | + | 0.629662i | \(0.216807\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9.80143 | −0.418315 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.09894 | 0.0894180 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.61666 | −0.111272 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −9.98276 | −0.423745 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −23.2713 | −0.986035 | −0.493018 | − | 0.870019i | \(-0.664106\pi\) | ||||
−0.493018 | + | 0.870019i | \(0.664106\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.16483 | −0.0915626 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12.8158 | −0.541086 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 26.3970 | 1.11250 | 0.556251 | − | 0.831015i | \(-0.312239\pi\) | ||||
0.556251 | + | 0.831015i | \(0.312239\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −20.3857 | −0.857635 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.97719 | −0.125030 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 24.0833 | 1.00962 | 0.504811 | − | 0.863230i | \(-0.331562\pi\) | ||||
0.504811 | + | 0.863230i | \(0.331562\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.0239 | 0.503185 | 0.251592 | − | 0.967833i | \(-0.419046\pi\) | ||||
0.251592 | + | 0.967833i | \(0.419046\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5.75152 | 0.240273 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.33227 | 0.0555597 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −41.9631 | −1.74695 | −0.873473 | − | 0.486873i | \(-0.838137\pi\) | ||||
−0.873473 | + | 0.486873i | \(0.838137\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 11.3988 | 0.473717 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 39.6724 | 1.64589 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −20.1753 | −0.835576 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.62148 | 0.108385 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.05295 | −0.249832 | −0.124916 | − | 0.992167i | \(-0.539866\pi\) | ||||
−0.124916 | + | 0.992167i | \(0.539866\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.81972 | −0.116184 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 17.2757 | 0.710628 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13.5815 | 0.557726 | 0.278863 | − | 0.960331i | \(-0.410042\pi\) | ||||
0.278863 | + | 0.960331i | \(0.410042\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 35.7321 | 1.46487 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −10.9978 | −0.450110 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 34.9387 | 1.42756 | 0.713778 | − | 0.700372i | \(-0.246982\pi\) | ||||
0.713778 | + | 0.700372i | \(0.246982\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.53774 | −0.185098 | −0.0925491 | − | 0.995708i | \(-0.529502\pi\) | ||||
−0.0925491 | + | 0.995708i | \(0.529502\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.45384 | 0.0999281 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −13.0573 | −0.530854 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −37.1037 | −1.50599 | −0.752996 | − | 0.658025i | \(-0.771392\pi\) | ||||
−0.752996 | + | 0.658025i | \(0.771392\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.97719 | 0.120642 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.34767 | 0.216344 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.2866 | 0.657811 | 0.328906 | − | 0.944363i | \(-0.393320\pi\) | ||||
0.328906 | + | 0.944363i | \(0.393320\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 15.0786 | 0.608027 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.9355 | 0.681799 | 0.340899 | − | 0.940100i | \(-0.389268\pi\) | ||||
0.340899 | + | 0.940100i | \(0.389268\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −41.7152 | −1.67668 | −0.838338 | − | 0.545151i | \(-0.816472\pi\) | ||||
−0.838338 | + | 0.545151i | \(0.816472\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 16.3640 | 0.655611 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16.5637 | −0.662547 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.29235 | −0.171420 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 32.6667 | 1.30251 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.9485 | 0.515472 | 0.257736 | − | 0.966215i | \(-0.417024\pi\) | ||||
0.257736 | + | 0.966215i | \(0.417024\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.49631 | −0.218459 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 19.1210 | 0.758793 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.55103 | 0.101076 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.65971 | −0.342573 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22.2148 | −0.877431 | −0.438716 | − | 0.898626i | \(-0.644566\pi\) | ||||
−0.438716 | + | 0.898626i | \(0.644566\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.67998 | −0.381741 | −0.190871 | − | 0.981615i | \(-0.561131\pi\) | ||||
−0.190871 | + | 0.981615i | \(0.561131\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.02882 | −0.119260 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 36.9496 | 1.45264 | 0.726320 | − | 0.687357i | \(-0.241229\pi\) | ||||
0.726320 | + | 0.687357i | \(0.241229\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.09662 | −0.160806 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.99955 | −0.156755 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 46.7622 | 1.82995 | 0.914973 | − | 0.403515i | \(-0.132212\pi\) | ||||
0.914973 | + | 0.403515i | \(0.132212\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11.5015 | 0.449402 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 14.2737 | 0.556869 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19.2858 | 0.751267 | 0.375633 | − | 0.926768i | \(-0.377425\pi\) | ||||
0.375633 | + | 0.926768i | \(0.377425\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −29.0834 | −1.13121 | −0.565607 | − | 0.824675i | \(-0.691358\pi\) | ||||
−0.565607 | + | 0.824675i | \(0.691358\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −8.57831 | −0.333154 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 11.9676 | 0.464082 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 20.8557 | 0.806327 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −20.0440 | −0.773789 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 30.0182 | 1.15712 | 0.578558 | − | 0.815641i | \(-0.303616\pi\) | ||||
0.578558 | + | 0.815641i | \(0.303616\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.33227 | −0.0512792 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 45.6725 | 1.75534 | 0.877669 | − | 0.479267i | \(-0.159097\pi\) | ||||
0.877669 | + | 0.479267i | \(0.159097\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 24.6165 | 0.944694 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.4917 | 0.478682 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −16.7995 | −0.642816 | −0.321408 | − | 0.946941i | \(-0.604156\pi\) | ||||
−0.321408 | + | 0.946941i | \(0.604156\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 23.8243 | 0.910282 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −28.0229 | −1.06914 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −13.5044 | −0.514476 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 40.6370 | 1.54591 | 0.772953 | − | 0.634463i | \(-0.218779\pi\) | ||||
0.772953 | + | 0.634463i | \(0.218779\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6.08837 | −0.231278 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −43.9727 | −1.66798 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −49.3418 | −1.86895 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −12.2804 | −0.464488 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −24.8484 | −0.938513 | −0.469256 | − | 0.883062i | \(-0.655478\pi\) | ||||
−0.469256 | + | 0.883062i | \(0.655478\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.9409 | 0.412644 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7.48194 | 0.281786 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −30.8770 | −1.16125 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 39.6290 | 1.48830 | 0.744150 | − | 0.668012i | \(-0.232855\pi\) | ||||
0.744150 | + | 0.668012i | \(0.232855\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.878902 | 0.0329614 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.34340 | −0.0503107 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.36095 | 0.200488 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8.94247 | 0.333963 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 17.5417 | 0.654197 | 0.327098 | − | 0.944990i | \(-0.393929\pi\) | ||||
0.327098 | + | 0.944990i | \(0.393929\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.77094 | −0.103195 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.940096 | −0.0349626 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.33227 | 0.0494794 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.6238 | 0.653631 | 0.326815 | − | 0.945088i | \(-0.394024\pi\) | ||||
0.326815 | + | 0.945088i | \(0.394024\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.91125 | 0.366581 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 29.7967 | 1.10057 | 0.550284 | − | 0.834978i | \(-0.314520\pi\) | ||||
0.550284 | + | 0.834978i | \(0.314520\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.56915 | 0.131650 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.01811 | 0.184845 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −44.6690 | −1.64318 | −0.821588 | − | 0.570082i | \(-0.806911\pi\) | ||||
−0.821588 | + | 0.570082i | \(0.806911\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.87309 | −0.105546 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 30.2257 | 1.10887 | 0.554436 | − | 0.832226i | \(-0.312934\pi\) | ||||
0.554436 | + | 0.832226i | \(0.312934\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −28.5586 | −1.04631 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −13.3255 | −0.487553 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 45.1491 | 1.64971 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.702893 | −0.0256489 | −0.0128245 | − | 0.999918i | \(-0.504082\pi\) | ||||
−0.0128245 | + | 0.999918i | \(0.504082\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 18.5996 | 0.677807 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.93785 | −0.106919 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21.2356 | 0.771820 | 0.385910 | − | 0.922537i | \(-0.373888\pi\) | ||||
0.385910 | + | 0.922537i | \(0.373888\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.04500 | −0.0742290 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.2752 | 0.771227 | 0.385613 | − | 0.922660i | \(-0.373990\pi\) | ||||
0.385613 | + | 0.922660i | \(0.373990\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.12753 | 0.113224 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −12.0019 | −0.433931 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.74208 | −0.0990107 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −0.507069 | −0.0182854 | −0.00914268 | − | 0.999958i | \(-0.502910\pi\) | ||||
−0.00914268 | + | 0.999958i | \(0.502910\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.55236 | 0.0919209 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 17.7540 | 0.638565 | 0.319283 | − | 0.947660i | \(-0.396558\pi\) | ||||
0.319283 | + | 0.947660i | \(0.396558\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.78978 | −0.0642906 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 15.5188 | 0.556735 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −16.5258 | −0.592098 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17.7091 | −0.633683 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.00000 | −0.0357371 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 18.5069 | 0.660541 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −27.1313 | −0.967127 | −0.483563 | − | 0.875309i | \(-0.660658\pi\) | ||||
−0.483563 | + | 0.875309i | \(0.660658\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 21.8897 | 0.779294 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 31.6909 | 1.12680 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −13.4165 | −0.476433 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −18.8940 | −0.670102 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0.564690 | 0.0200023 | 0.0100012 | − | 0.999950i | \(-0.496816\pi\) | ||||
0.0100012 | + | 0.999950i | \(0.496816\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −24.4832 | −0.866154 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.49647 | −0.194208 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 29.1897 | 1.03008 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.70171 | 0.200959 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −24.3149 | −0.855926 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −13.6861 | −0.481177 | −0.240588 | − | 0.970627i | \(-0.577340\pi\) | ||||
−0.240588 | + | 0.970627i | \(0.577340\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19.4358 | −0.682483 | −0.341241 | − | 0.939976i | \(-0.610847\pi\) | ||||
−0.341241 | + | 0.939976i | \(0.610847\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.46398 | 0.121487 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 24.7908 | 0.868382 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.31952 | 0.116135 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.07526 | −0.142401 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −18.3709 | −0.641148 | −0.320574 | − | 0.947223i | \(-0.603876\pi\) | ||||
−0.320574 | + | 0.947223i | \(0.603876\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −23.1554 | −0.807147 | −0.403574 | − | 0.914947i | \(-0.632232\pi\) | ||||
−0.403574 | + | 0.914947i | \(0.632232\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.72451 | −0.0948551 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −57.0284 | −1.98307 | −0.991536 | − | 0.129832i | \(-0.958556\pi\) | ||||
−0.991536 | + | 0.129832i | \(0.958556\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −56.2996 | −1.95536 | −0.977682 | − | 0.210089i | \(-0.932625\pi\) | ||||
−0.977682 | + | 0.210089i | \(0.932625\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 20.3852 | 0.707154 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −11.6794 | −0.404667 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.5347 | 0.364568 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.34340 | 0.0464347 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −55.4700 | −1.91504 | −0.957519 | − | 0.288371i | \(-0.906886\pi\) | ||||
−0.957519 | + | 0.288371i | \(0.906886\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −16.4489 | −0.566531 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −21.3083 | −0.733029 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 20.2984 | 0.697460 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5.85058 | −0.200792 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.21257 | 0.178685 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −22.7217 | −0.777977 | −0.388988 | − | 0.921243i | \(-0.627175\pi\) | ||||
−0.388988 | + | 0.921243i | \(0.627175\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.01975 | −0.137473 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −40.9883 | −1.40014 | −0.700068 | − | 0.714077i | \(-0.746847\pi\) | ||||
−0.700068 | + | 0.714077i | \(0.746847\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −50.0067 | −1.70621 | −0.853104 | − | 0.521741i | \(-0.825283\pi\) | ||||
−0.853104 | + | 0.521741i | \(0.825283\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −23.4406 | −0.798853 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 20.8350 | 0.709232 | 0.354616 | − | 0.935012i | \(-0.384612\pi\) | ||||
0.354616 | + | 0.935012i | \(0.384612\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19.0769 | −0.648635 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 22.2741 | 0.756468 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.79736 | 0.0609712 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.35888 | 0.113811 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8.26837 | −0.279842 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 36.1048 | 1.22056 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.70605 | −0.260215 | −0.130107 | − | 0.991500i | \(-0.541532\pi\) | ||||
−0.130107 | + | 0.991500i | \(0.541532\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −32.9715 | −1.11210 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −48.1678 | −1.62281 | −0.811407 | − | 0.584482i | \(-0.801298\pi\) | ||||
−0.811407 | + | 0.584482i | \(0.801298\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.7355 | 0.394932 | 0.197466 | − | 0.980310i | \(-0.436729\pi\) | ||||
0.197466 | + | 0.980310i | \(0.436729\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.83645 | −0.128961 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 29.9496 | 1.00561 | 0.502804 | − | 0.864400i | \(-0.332302\pi\) | ||||
0.502804 | + | 0.864400i | \(0.332302\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −29.7248 | −0.996936 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.04500 | 0.0685102 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8.20004 | −0.274404 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −24.9123 | −0.832726 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.36883 | −0.0457038 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.34340 | −0.0448049 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 61.8271 | 2.05976 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.70849 | 0.156689 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 18.7878 | 0.624528 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −54.0361 | −1.79424 | −0.897120 | − | 0.441786i | \(-0.854345\pi\) | ||||
−0.897120 | + | 0.441786i | \(0.854345\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10.3712 | 0.343990 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.74195 | −0.190239 | −0.0951197 | − | 0.995466i | \(-0.530323\pi\) | ||||
−0.0951197 | + | 0.995466i | \(0.530323\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −27.2506 | −0.901864 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −18.7710 | −0.620551 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −17.8799 | −0.590445 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −37.0026 | −1.22060 | −0.610302 | − | 0.792169i | \(-0.708952\pi\) | ||||
−0.610302 | + | 0.792169i | \(0.708952\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.75728 | −0.156758 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −11.8536 | −0.390168 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.94458 | 0.228336 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.930722 | 0.0305689 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.62066 | 0.184408 | 0.0922040 | − | 0.995740i | \(-0.470609\pi\) | ||||
0.0922040 | + | 0.995740i | \(0.470609\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.91172 | −0.128201 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −10.7276 | −0.351205 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −24.5440 | −0.802675 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −18.5337 | −0.605471 | −0.302736 | − | 0.953075i | \(-0.597900\pi\) | ||||
−0.302736 | + | 0.953075i | \(0.597900\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 23.2780 | 0.759649 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 39.7857 | 1.29698 | 0.648489 | − | 0.761224i | \(-0.275401\pi\) | ||||
0.648489 | + | 0.761224i | \(0.275401\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.87339 | −0.256393 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5.70171 | −0.185477 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 48.2941 | 1.56935 | 0.784673 | − | 0.619910i | \(-0.212831\pi\) | ||||
0.784673 | + | 0.619910i | \(0.212831\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 19.5382 | 0.634237 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −26.6155 | −0.863067 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.78374 | −0.0577809 | −0.0288905 | − | 0.999583i | \(-0.509197\pi\) | ||||
−0.0288905 | + | 0.999583i | \(0.509197\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 11.0149 | 0.356434 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.04500 | −0.0661056 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −37.0364 | −1.19597 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.1953 | −0.941783 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −15.1650 | −0.488685 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 21.8302 | 0.702737 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.8378 | 0.412836 | 0.206418 | − | 0.978464i | \(-0.433819\pi\) | ||||
0.206418 | + | 0.978464i | \(0.433819\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 13.1539 | 0.422563 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 42.7856 | 1.37306 | 0.686528 | − | 0.727103i | \(-0.259134\pi\) | ||||
0.686528 | + | 0.727103i | \(0.259134\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 68.3583 | 2.19147 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.82365 | −0.0584037 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 48.2828 | 1.54470 | 0.772351 | − | 0.635195i | \(-0.219080\pi\) | ||||
0.772351 | + | 0.635195i | \(0.219080\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −11.2403 | −0.359242 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.05050 | −0.0335397 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −18.0755 | −0.576520 | −0.288260 | − | 0.957552i | \(-0.593077\pi\) | ||||
−0.288260 | + | 0.957552i | \(0.593077\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 33.0852 | 1.05418 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −11.6311 | −0.370223 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.58152 | 0.0502895 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −59.8805 | −1.90217 | −0.951084 | − | 0.308932i | \(-0.900028\pi\) | ||||
−0.951084 | + | 0.308932i | \(0.900028\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −5.55686 | −0.176342 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −21.0622 | −0.667717 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.18469 | 0.0375195 | 0.0187598 | − | 0.999824i | \(-0.494028\pi\) | ||||
0.0187598 | + | 0.999824i | \(0.494028\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.21257 | −0.164919 |
(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 | 8004.2.a.f.1.8 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8004.2.a.f.1.8 | ✓ | 9 | 1.1 | even | 1 | trivial |