Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6036,2,Mod(1,6036)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6036, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6036.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6036 = 2^{2} \cdot 3 \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6036.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: | \(48.1977026600\) |
Analytic rank: | \(1\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - 4 x^{14} - 27 x^{13} + 106 x^{12} + 266 x^{11} - 1004 x^{10} - 1105 x^{9} + 4076 x^{8} + \cdots - 44 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Root | \(1.33620\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6036.1 |
$q$-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 | ||||||||
\(5\) | 0.336200 | 0.150353 | 0.0751766 | − | 0.997170i | \(-0.476048\pi\) | ||||
0.0751766 | + | 0.997170i | \(0.476048\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.568501 | 0.214873 | 0.107437 | − | 0.994212i | \(-0.465736\pi\) | ||||
0.107437 | + | 0.994212i | \(0.465736\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.54286 | 1.67123 | 0.835617 | − | 0.549312i | \(-0.185110\pi\) | ||||
0.835617 | + | 0.549312i | \(0.185110\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.92976 | −1.64462 | −0.822310 | − | 0.569040i | \(-0.807315\pi\) | ||||
−0.822310 | + | 0.569040i | \(0.807315\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.336200 | 0.0868064 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.0480914 | 0.0116639 | 0.00583194 | − | 0.999983i | \(-0.498144\pi\) | ||||
0.00583194 | + | 0.999983i | \(0.498144\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.03166 | −0.695510 | −0.347755 | − | 0.937585i | \(-0.613056\pi\) | ||||
−0.347755 | + | 0.937585i | \(0.613056\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.568501 | 0.124057 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.32774 | −1.11091 | −0.555455 | − | 0.831546i | \(-0.687456\pi\) | ||||
−0.555455 | + | 0.831546i | \(0.687456\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.88697 | −0.977394 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.918207 | 0.170507 | 0.0852534 | − | 0.996359i | \(-0.472830\pi\) | ||||
0.0852534 | + | 0.996359i | \(0.472830\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.65025 | −1.55363 | −0.776815 | − | 0.629729i | \(-0.783166\pi\) | ||||
−0.776815 | + | 0.629729i | \(0.783166\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.54286 | 0.964888 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.191130 | 0.0323069 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.04634 | −0.994012 | −0.497006 | − | 0.867747i | \(-0.665567\pi\) | ||||
−0.497006 | + | 0.867747i | \(0.665567\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.92976 | −0.949521 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.72602 | 0.269559 | 0.134780 | − | 0.990876i | \(-0.456967\pi\) | ||||
0.134780 | + | 0.990876i | \(0.456967\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.69093 | −1.02036 | −0.510179 | − | 0.860068i | \(-0.670421\pi\) | ||||
−0.510179 | + | 0.860068i | \(0.670421\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.336200 | 0.0501177 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.136711 | −0.0199413 | −0.00997066 | − | 0.999950i | \(-0.503174\pi\) | ||||
−0.00997066 | + | 0.999950i | \(0.503174\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.67681 | −0.953829 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.0480914 | 0.00673414 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.99811 | −0.274462 | −0.137231 | − | 0.990539i | \(-0.543820\pi\) | ||||
−0.137231 | + | 0.990539i | \(0.543820\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.86351 | 0.251275 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.03166 | −0.401553 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −11.7881 | −1.53468 | −0.767338 | − | 0.641242i | \(-0.778419\pi\) | ||||
−0.767338 | + | 0.641242i | \(0.778419\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.84008 | 0.875782 | 0.437891 | − | 0.899028i | \(-0.355726\pi\) | ||||
0.437891 | + | 0.899028i | \(0.355726\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.568501 | 0.0716244 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.99358 | −0.247274 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.26008 | 0.886960 | 0.443480 | − | 0.896284i | \(-0.353744\pi\) | ||||
0.443480 | + | 0.896284i | \(0.353744\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.32774 | −0.641385 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.1144 | 1.43772 | 0.718858 | − | 0.695157i | \(-0.244665\pi\) | ||||
0.718858 | + | 0.695157i | \(0.244665\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.77178 | −0.675536 | −0.337768 | − | 0.941229i | \(-0.609672\pi\) | ||||
−0.337768 | + | 0.941229i | \(0.609672\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.88697 | −0.564299 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.15112 | 0.359104 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.6180 | −1.75717 | −0.878583 | − | 0.477590i | \(-0.841510\pi\) | ||||
−0.878583 | + | 0.477590i | \(0.841510\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.52142 | −0.606054 | −0.303027 | − | 0.952982i | \(-0.597997\pi\) | ||||
−0.303027 | + | 0.952982i | \(0.597997\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.0161683 | 0.00175370 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.918207 | 0.0984422 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.27474 | −0.771121 | −0.385561 | − | 0.922683i | \(-0.625992\pi\) | ||||
−0.385561 | + | 0.922683i | \(0.625992\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.37108 | −0.353385 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.65025 | −0.896989 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.01924 | −0.104572 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.99135 | 0.709864 | 0.354932 | − | 0.934892i | \(-0.384504\pi\) | ||||
0.354932 | + | 0.934892i | \(0.384504\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.54286 | 0.557078 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.90051 | −0.189108 | −0.0945538 | − | 0.995520i | \(-0.530142\pi\) | ||||
−0.0945538 | + | 0.995520i | \(0.530142\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.87606 | 0.480452 | 0.240226 | − | 0.970717i | \(-0.422778\pi\) | ||||
0.240226 | + | 0.970717i | \(0.422778\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.191130 | 0.0186524 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.45469 | 0.140630 | 0.0703149 | − | 0.997525i | \(-0.477600\pi\) | ||||
0.0703149 | + | 0.997525i | \(0.477600\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.07174 | 0.294219 | 0.147110 | − | 0.989120i | \(-0.453003\pi\) | ||||
0.147110 | + | 0.989120i | \(0.453003\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.04634 | −0.573893 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.1872 | 1.52277 | 0.761384 | − | 0.648301i | \(-0.224520\pi\) | ||||
0.761384 | + | 0.648301i | \(0.224520\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.79119 | −0.167029 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.92976 | −0.548206 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.0273400 | 0.00250626 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 19.7233 | 1.79302 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.72602 | 0.155630 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.32400 | −0.297307 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.483648 | −0.0429168 | −0.0214584 | − | 0.999770i | \(-0.506831\pi\) | ||||
−0.0214584 | + | 0.999770i | \(0.506831\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.69093 | −0.589104 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.65627 | 0.494190 | 0.247095 | − | 0.968991i | \(-0.420524\pi\) | ||||
0.247095 | + | 0.968991i | \(0.420524\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.72350 | −0.149446 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.336200 | 0.0289355 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.57562 | 0.647229 | 0.323615 | − | 0.946189i | \(-0.395102\pi\) | ||||
0.323615 | + | 0.946189i | \(0.395102\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.55882 | −0.810769 | −0.405384 | − | 0.914146i | \(-0.632862\pi\) | ||||
−0.405384 | + | 0.914146i | \(0.632862\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.136711 | −0.0115131 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −32.8678 | −2.74854 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.308701 | 0.0256362 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.67681 | −0.550694 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.79959 | −0.557044 | −0.278522 | − | 0.960430i | \(-0.589845\pi\) | ||||
−0.278522 | + | 0.960430i | \(0.589845\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.77057 | −0.469603 | −0.234801 | − | 0.972043i | \(-0.575444\pi\) | ||||
−0.234801 | + | 0.972043i | \(0.575444\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.0480914 | 0.00388796 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.90821 | −0.233593 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.7887 | 1.49950 | 0.749750 | − | 0.661722i | \(-0.230174\pi\) | ||||
0.749750 | + | 0.661722i | \(0.230174\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.99811 | −0.158461 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.02883 | −0.238705 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.77830 | −0.530918 | −0.265459 | − | 0.964122i | \(-0.585523\pi\) | ||||
−0.265459 | + | 0.964122i | \(0.585523\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.86351 | 0.145074 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.2654 | 0.949128 | 0.474564 | − | 0.880221i | \(-0.342606\pi\) | ||||
0.474564 | + | 0.880221i | \(0.342606\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 22.1620 | 1.70477 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.03166 | −0.231837 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −19.8113 | −1.50623 | −0.753113 | − | 0.657891i | \(-0.771449\pi\) | ||||
−0.753113 | + | 0.657891i | \(0.771449\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.77825 | −0.210016 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −11.7881 | −0.886046 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.16149 | 0.684762 | 0.342381 | − | 0.939561i | \(-0.388767\pi\) | ||||
0.342381 | + | 0.939561i | \(0.388767\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.84269 | −0.359954 | −0.179977 | − | 0.983671i | \(-0.557602\pi\) | ||||
−0.179977 | + | 0.983671i | \(0.557602\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.84008 | 0.505633 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.03278 | −0.149453 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.266564 | 0.0194931 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.568501 | 0.0413524 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.7260 | −1.13790 | −0.568948 | − | 0.822373i | \(-0.692650\pi\) | ||||
−0.568948 | + | 0.822373i | \(0.692650\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.40289 | 0.460890 | 0.230445 | − | 0.973085i | \(-0.425982\pi\) | ||||
0.230445 | + | 0.973085i | \(0.425982\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.99358 | −0.142764 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 21.5420 | 1.53481 | 0.767404 | − | 0.641164i | \(-0.221548\pi\) | ||||
0.767404 | + | 0.641164i | \(0.221548\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.7287 | 0.760540 | 0.380270 | − | 0.924876i | \(-0.375831\pi\) | ||||
0.380270 | + | 0.924876i | \(0.375831\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.26008 | 0.512086 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.522002 | 0.0366374 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.580289 | 0.0405291 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.32774 | −0.370304 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −16.8040 | −1.16236 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.5669 | 1.27820 | 0.639098 | − | 0.769125i | \(-0.279308\pi\) | ||||
0.639098 | + | 0.769125i | \(0.279308\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 12.1144 | 0.830066 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.24949 | −0.153414 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.91768 | −0.333834 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.77178 | −0.390021 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.285170 | −0.0191826 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.2813 | −0.889382 | −0.444691 | − | 0.895684i | \(-0.646686\pi\) | ||||
−0.444691 | + | 0.895684i | \(0.646686\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.88697 | −0.325798 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.03830 | −0.400776 | −0.200388 | − | 0.979717i | \(-0.564220\pi\) | ||||
−0.200388 | + | 0.979717i | \(0.564220\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.52759 | −0.431356 | −0.215678 | − | 0.976465i | \(-0.569196\pi\) | ||||
−0.215678 | + | 0.976465i | \(0.569196\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.15112 | 0.207329 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.2938 | 1.19847 | 0.599234 | − | 0.800574i | \(-0.295472\pi\) | ||||
0.599234 | + | 0.800574i | \(0.295472\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.0459622 | −0.00299824 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −15.6180 | −1.01450 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.30923 | 0.537480 | 0.268740 | − | 0.963213i | \(-0.413393\pi\) | ||||
0.268740 | + | 0.963213i | \(0.413393\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.796935 | 0.0513351 | 0.0256676 | − | 0.999671i | \(-0.491829\pi\) | ||||
0.0256676 | + | 0.999671i | \(0.491829\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.24474 | −0.143411 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 17.9770 | 1.14385 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.52142 | −0.349906 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.06101 | −0.571926 | −0.285963 | − | 0.958241i | \(-0.592313\pi\) | ||||
−0.285963 | + | 0.958241i | \(0.592313\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −29.5309 | −1.85659 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.0161683 | 0.00101250 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.10088 | 0.505319 | 0.252660 | − | 0.967555i | \(-0.418695\pi\) | ||||
0.252660 | + | 0.967555i | \(0.418695\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.43735 | −0.213587 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.918207 | 0.0568356 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −23.8160 | −1.46856 | −0.734278 | − | 0.678848i | \(-0.762479\pi\) | ||||
−0.734278 | + | 0.678848i | \(0.762479\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.671766 | −0.0412662 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.27474 | −0.445207 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −30.4623 | −1.85732 | −0.928661 | − | 0.370929i | \(-0.879039\pi\) | ||||
−0.928661 | + | 0.370929i | \(0.879039\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.18720 | 0.254354 | 0.127177 | − | 0.991880i | \(-0.459408\pi\) | ||||
0.127177 | + | 0.991880i | \(0.459408\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.37108 | −0.204027 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −27.0878 | −1.63345 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −27.5699 | −1.65652 | −0.828259 | − | 0.560346i | \(-0.810668\pi\) | ||||
−0.828259 | + | 0.560346i | \(0.810668\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −8.65025 | −0.517877 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.1734 | −0.964823 | −0.482411 | − | 0.875945i | \(-0.660239\pi\) | ||||
−0.482411 | + | 0.875945i | \(0.660239\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 25.6248 | 1.52323 | 0.761617 | − | 0.648027i | \(-0.224406\pi\) | ||||
0.761617 | + | 0.648027i | \(0.224406\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.01924 | −0.0603747 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.981246 | 0.0579211 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9977 | −0.999864 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.99135 | 0.409840 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 18.2763 | 1.06771 | 0.533857 | − | 0.845575i | \(-0.320742\pi\) | ||||
0.533857 | + | 0.845575i | \(0.320742\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.96315 | −0.230744 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.54286 | 0.321629 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 31.5922 | 1.82703 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.80380 | −0.219248 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.90051 | −0.109181 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.29963 | 0.131677 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.44082 | 0.367597 | 0.183799 | − | 0.982964i | \(-0.441161\pi\) | ||||
0.183799 | + | 0.982964i | \(0.441161\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.87606 | 0.277389 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −19.9197 | −1.12954 | −0.564771 | − | 0.825247i | \(-0.691036\pi\) | ||||
−0.564771 | + | 0.825247i | \(0.691036\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.71046 | 0.153204 | 0.0766021 | − | 0.997062i | \(-0.475593\pi\) | ||||
0.0766021 | + | 0.997062i | \(0.475593\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.191130 | 0.0107690 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −18.1488 | −1.01934 | −0.509669 | − | 0.860371i | \(-0.670232\pi\) | ||||
−0.509669 | + | 0.860371i | \(0.670232\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.08949 | 0.284957 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.45469 | 0.0811926 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.145797 | −0.00811234 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 28.9786 | 1.60744 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.07174 | 0.169867 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.0777203 | −0.00428486 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.42591 | −0.188305 | −0.0941527 | − | 0.995558i | \(-0.530014\pi\) | ||||
−0.0941527 | + | 0.995558i | \(0.530014\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.04634 | −0.331337 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.44084 | 0.133357 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.8658 | 0.646370 | 0.323185 | − | 0.946336i | \(-0.395246\pi\) | ||||
0.323185 | + | 0.946336i | \(0.395246\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 16.1872 | 0.879171 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −47.9471 | −2.59648 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.77528 | −0.419826 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.79119 | −0.0964342 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.195187 | 0.0104782 | 0.00523910 | − | 0.999986i | \(-0.498332\pi\) | ||||
0.00523910 | + | 0.999986i | \(0.498332\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.1755 | −0.865856 | −0.432928 | − | 0.901428i | \(-0.642520\pi\) | ||||
−0.432928 | + | 0.901428i | \(0.642520\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.92976 | −0.316507 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.38986 | 0.233649 | 0.116824 | − | 0.993153i | \(-0.462729\pi\) | ||||
0.116824 | + | 0.993153i | \(0.462729\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.07286 | 0.216165 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.0273400 | 0.00144699 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12.9668 | 0.684361 | 0.342180 | − | 0.939634i | \(-0.388835\pi\) | ||||
0.342180 | + | 0.939634i | \(0.388835\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.80906 | −0.516266 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 19.7233 | 1.03520 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.94047 | −0.101569 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.1768 | 0.740024 | 0.370012 | − | 0.929027i | \(-0.379354\pi\) | ||||
0.370012 | + | 0.929027i | \(0.379354\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.72602 | 0.0898531 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.13593 | −0.0589746 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.89627 | −0.201741 | −0.100871 | − | 0.994900i | \(-0.532163\pi\) | ||||
−0.100871 | + | 0.994900i | \(0.532163\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.32400 | −0.171651 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.44475 | −0.280419 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.0492 | −0.618926 | −0.309463 | − | 0.950911i | \(-0.600149\pi\) | ||||
−0.309463 | + | 0.950911i | \(0.600149\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.483648 | −0.0247781 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.80286 | 0.143220 | 0.0716099 | − | 0.997433i | \(-0.477186\pi\) | ||||
0.0716099 | + | 0.997433i | \(0.477186\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.05941 | 0.0539924 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.69093 | −0.340119 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −25.5777 | −1.29684 | −0.648420 | − | 0.761283i | \(-0.724570\pi\) | ||||
−0.648420 | + | 0.761283i | \(0.724570\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.256219 | −0.0129575 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.65627 | 0.285321 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.25078 | −0.264195 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.22753 | 0.262362 | 0.131181 | − | 0.991358i | \(-0.458123\pi\) | ||||
0.131181 | + | 0.991358i | \(0.458123\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.72350 | −0.0862830 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 19.0644 | 0.952030 | 0.476015 | − | 0.879437i | \(-0.342081\pi\) | ||||
0.476015 | + | 0.879437i | \(0.342081\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 51.2939 | 2.55513 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.336200 | 0.0167059 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −33.5140 | −1.66123 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.0060 | −0.840893 | −0.420447 | − | 0.907317i | \(-0.638127\pi\) | ||||
−0.420447 | + | 0.907317i | \(0.638127\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.57562 | 0.373678 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.70154 | −0.329761 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.85630 | −0.0911222 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9.55882 | −0.468098 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −17.3133 | −0.845812 | −0.422906 | − | 0.906173i | \(-0.638990\pi\) | ||||
−0.422906 | + | 0.906173i | \(0.638990\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.1150 | 0.785395 | 0.392697 | − | 0.919668i | \(-0.371542\pi\) | ||||
0.392697 | + | 0.919668i | \(0.371542\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.136711 | −0.00664711 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.235021 | −0.0114002 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.88859 | 0.188182 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −32.8678 | −1.58687 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.73736 | 0.0836859 | 0.0418429 | − | 0.999124i | \(-0.486677\pi\) | ||||
0.0418429 | + | 0.999124i | \(0.486677\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 32.3803 | 1.55610 | 0.778049 | − | 0.628204i | \(-0.216210\pi\) | ||||
0.778049 | + | 0.628204i | \(0.216210\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.308701 | 0.0148011 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 16.1519 | 0.772649 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11.0108 | −0.525516 | −0.262758 | − | 0.964862i | \(-0.584632\pi\) | ||||
−0.262758 | + | 0.964862i | \(0.584632\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.67681 | −0.317943 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 33.8002 | 1.60590 | 0.802948 | − | 0.596050i | \(-0.203264\pi\) | ||||
0.802948 | + | 0.596050i | \(0.203264\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.44577 | −0.115940 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6.79959 | −0.321609 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −21.1168 | −0.996564 | −0.498282 | − | 0.867015i | \(-0.666035\pi\) | ||||
−0.498282 | + | 0.867015i | \(0.666035\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.56710 | 0.450497 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.77057 | −0.271125 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.13336 | −0.0531325 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.9348 | −0.605063 | −0.302532 | − | 0.953139i | \(-0.597832\pi\) | ||||
−0.302532 | + | 0.953139i | \(0.597832\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.0480914 | 0.00224471 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −35.9572 | −1.67470 | −0.837348 | − | 0.546671i | \(-0.815895\pi\) | ||||
−0.837348 | + | 0.546671i | \(0.815895\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.51016 | 0.116657 | 0.0583286 | − | 0.998297i | \(-0.481423\pi\) | ||||
0.0583286 | + | 0.998297i | \(0.481423\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.90821 | −0.134865 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14.7440 | 0.682273 | 0.341136 | − | 0.940014i | \(-0.389188\pi\) | ||||
0.341136 | + | 0.940014i | \(0.389188\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.12736 | 0.190584 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 18.7887 | 0.865736 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −37.0869 | −1.70526 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 14.8156 | 0.679787 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.99811 | −0.0914873 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −11.2343 | −0.513307 | −0.256653 | − | 0.966503i | \(-0.582620\pi\) | ||||
−0.256653 | + | 0.966503i | \(0.582620\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 35.8533 | 1.63477 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.02883 | −0.137816 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.35049 | 0.106730 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19.0292 | 0.862297 | 0.431149 | − | 0.902281i | \(-0.358108\pi\) | ||||
0.431149 | + | 0.902281i | \(0.358108\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.77830 | −0.306525 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.513681 | −0.0231821 | −0.0115911 | − | 0.999933i | \(-0.503690\pi\) | ||||
−0.0115911 | + | 0.999933i | \(0.503690\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.0441579 | 0.00198877 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.86351 | 0.0837585 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.88706 | 0.308927 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.45555 | 0.378522 | 0.189261 | − | 0.981927i | \(-0.439391\pi\) | ||||
0.189261 | + | 0.981927i | \(0.439391\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12.2654 | 0.547979 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.00000 | −0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.638951 | −0.0284329 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 22.1620 | 0.984251 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 23.5281 | 1.04286 | 0.521432 | − | 0.853293i | \(-0.325398\pi\) | ||||
0.521432 | + | 0.853293i | \(0.325398\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.28126 | −0.145155 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.03166 | −0.133851 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.63933 | 0.0722375 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.757769 | −0.0333266 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −19.8113 | −0.869620 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21.2294 | −0.930077 | −0.465038 | − | 0.885291i | \(-0.653959\pi\) | ||||
−0.465038 | + | 0.885291i | \(0.653959\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.27776 | 0.405688 | 0.202844 | − | 0.979211i | \(-0.434982\pi\) | ||||
0.202844 | + | 0.979211i | \(0.434982\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.77825 | −0.121253 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.416002 | −0.0181213 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.38483 | 0.234123 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −11.7881 | −0.511559 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10.2349 | −0.443323 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.489065 | 0.0211441 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.16149 | 0.395347 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −37.0086 | −1.59407 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −37.5396 | −1.61396 | −0.806978 | − | 0.590582i | \(-0.798898\pi\) | ||||
−0.806978 | + | 0.590582i | \(0.798898\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4.84269 | −0.207820 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.03272 | 0.0442368 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.44448 | 0.403817 | 0.201908 | − | 0.979404i | \(-0.435286\pi\) | ||||
0.201908 | + | 0.979404i | \(0.435286\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.84008 | 0.291927 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.78369 | −0.118589 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.87887 | −0.377568 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.03278 | −0.0862866 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 21.0390 | 0.891449 | 0.445725 | − | 0.895170i | \(-0.352946\pi\) | ||||
0.445725 | + | 0.895170i | \(0.352946\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 39.6756 | 1.67810 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.266564 | 0.0112543 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 13.5991 | 0.573135 | 0.286567 | − | 0.958060i | \(-0.407486\pi\) | ||||
0.286567 | + | 0.958060i | \(0.407486\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.44215 | 0.228953 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.568501 | 0.0238748 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −12.3332 | −0.517036 | −0.258518 | − | 0.966006i | \(-0.583234\pi\) | ||||
−0.258518 | + | 0.966006i | \(0.583234\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 34.3361 | 1.43692 | 0.718460 | − | 0.695568i | \(-0.244847\pi\) | ||||
0.718460 | + | 0.695568i | \(0.244847\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −15.7260 | −0.656965 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 26.0365 | 1.08580 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −41.7402 | −1.73767 | −0.868834 | − | 0.495103i | \(-0.835130\pi\) | ||||
−0.868834 | + | 0.495103i | \(0.835130\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.40289 | 0.266095 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.13893 | −0.130225 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.0753 | −0.458690 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.99358 | −0.0824246 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −17.9306 | −0.740075 | −0.370037 | − | 0.929017i | \(-0.620655\pi\) | ||||
−0.370037 | + | 0.929017i | \(0.620655\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 26.2246 | 1.08056 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 21.5420 | 0.886121 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 30.8101 | 1.26522 | 0.632610 | − | 0.774471i | \(-0.281984\pi\) | ||||
0.632610 | + | 0.774471i | \(0.281984\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.00919171 | 0.000376823 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 10.7287 | 0.439098 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 29.1427 | 1.19074 | 0.595370 | − | 0.803452i | \(-0.297005\pi\) | ||||
0.595370 | + | 0.803452i | \(0.297005\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25.7001 | 1.04833 | 0.524165 | − | 0.851617i | \(-0.324377\pi\) | ||||
0.524165 | + | 0.851617i | \(0.324377\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.26008 | 0.295653 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.63096 | 0.269587 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −23.2341 | −0.943044 | −0.471522 | − | 0.881854i | \(-0.656295\pi\) | ||||
−0.471522 | + | 0.881854i | \(0.656295\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.522002 | 0.0211526 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.810662 | 0.0327959 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −32.6732 | −1.31966 | −0.659828 | − | 0.751416i | \(-0.729371\pi\) | ||||
−0.659828 | + | 0.751416i | \(0.729371\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.580289 | 0.0233995 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.49927 | 0.261651 | 0.130825 | − | 0.991405i | \(-0.458237\pi\) | ||||
0.130825 | + | 0.991405i | \(0.458237\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19.3608 | 0.778177 | 0.389088 | − | 0.921200i | \(-0.372790\pi\) | ||||
0.389088 | + | 0.921200i | \(0.372790\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.32774 | −0.213795 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.13570 | −0.165693 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.3173 | 0.932693 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −16.8040 | −0.671089 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.290777 | −0.0115940 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −38.1142 | −1.51730 | −0.758651 | − | 0.651497i | \(-0.774141\pi\) | ||||
−0.758651 | + | 0.651497i | \(0.774141\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 18.5669 | 0.737967 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.162603 | −0.00645268 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 39.5919 | 1.56869 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12.1144 | 0.479239 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11.7450 | −0.463898 | −0.231949 | − | 0.972728i | \(-0.574510\pi\) | ||||
−0.231949 | + | 0.972728i | \(0.574510\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.4611 | −0.412545 | −0.206273 | − | 0.978495i | \(-0.566133\pi\) | ||||
−0.206273 | + | 0.978495i | \(0.566133\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.24949 | −0.0885736 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −35.0039 | −1.37615 | −0.688073 | − | 0.725641i | \(-0.741543\pi\) | ||||
−0.688073 | + | 0.725641i | \(0.741543\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −65.3396 | −2.56480 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.91768 | −0.192739 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 38.5534 | 1.50871 | 0.754356 | − | 0.656466i | \(-0.227949\pi\) | ||||
0.754356 | + | 0.656466i | \(0.227949\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.90164 | 0.0743031 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.77178 | −0.225179 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −24.5841 | −0.957660 | −0.478830 | − | 0.877908i | \(-0.658939\pi\) | ||||
−0.478830 | + | 0.877908i | \(0.658939\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −41.6360 | −1.61945 | −0.809726 | − | 0.586809i | \(-0.800384\pi\) | ||||
−0.809726 | + | 0.586809i | \(0.800384\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.285170 | −0.0110751 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.579441 | −0.0224698 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.89197 | −0.189418 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −13.2813 | −0.513485 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 37.9136 | 1.46364 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −27.7634 | −1.07020 | −0.535101 | − | 0.844788i | \(-0.679726\pi\) | ||||
−0.535101 | + | 0.844788i | \(0.679726\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.88697 | −0.188100 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 25.0836 | 0.964041 | 0.482021 | − | 0.876160i | \(-0.339903\pi\) | ||||
0.482021 | + | 0.876160i | \(0.339903\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.97459 | 0.152531 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.03830 | −0.231388 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.102814 | 0.00393405 | 0.00196703 | − | 0.999998i | \(-0.499374\pi\) | ||||
0.00196703 | + | 0.999998i | \(0.499374\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.54692 | 0.0973130 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.52759 | −0.249043 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 11.8483 | 0.451386 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.49770 | 0.361310 | 0.180655 | − | 0.983547i | \(-0.442178\pi\) | ||||
0.180655 | + | 0.983547i | \(0.442178\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.15112 | 0.119701 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.21368 | −0.121902 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.0830068 | 0.00314411 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 18.2938 | 0.691936 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14.4454 | −0.545594 | −0.272797 | − | 0.962072i | \(-0.587949\pi\) | ||||
−0.272797 | + | 0.962072i | \(0.587949\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18.3304 | 0.691345 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.0459622 | −0.00173104 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.08044 | −0.0406342 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22.7137 | 0.853032 | 0.426516 | − | 0.904480i | \(-0.359741\pi\) | ||||
0.426516 | + | 0.904480i | \(0.359741\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −15.6180 | −0.585722 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 46.0863 | 1.72594 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11.0502 | −0.413252 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8.30923 | 0.310314 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 18.8282 | 0.702172 | 0.351086 | − | 0.936343i | \(-0.385812\pi\) | ||||
0.351086 | + | 0.936343i | \(0.385812\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.77205 | 0.103236 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.796935 | 0.0296383 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.48725 | −0.166652 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11.6081 | −0.430520 | −0.215260 | − | 0.976557i | \(-0.569060\pi\) | ||||
−0.215260 | + | 0.976557i | \(0.569060\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.321776 | −0.0119013 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.5798 | 0.760131 | 0.380066 | − | 0.924959i | \(-0.375901\pi\) | ||||
0.380066 | + | 0.924959i | \(0.375901\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.24474 | −0.0827985 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 40.2416 | 1.48232 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15.0843 | −0.554885 | −0.277443 | − | 0.960742i | \(-0.589487\pi\) | ||||
−0.277443 | + | 0.960742i | \(0.589487\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 17.9770 | 0.660401 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 30.1216 | 1.10506 | 0.552528 | − | 0.833495i | \(-0.313663\pi\) | ||||
0.552528 | + | 0.833495i | \(0.313663\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.28602 | −0.0837533 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.52142 | −0.202018 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.826991 | 0.0302176 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.93111 | 0.289410 | 0.144705 | − | 0.989475i | \(-0.453777\pi\) | ||||
0.144705 | + | 0.989475i | \(0.453777\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −9.06101 | −0.330202 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.94007 | −0.0706062 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18.2385 | 0.662890 | 0.331445 | − | 0.943475i | \(-0.392464\pi\) | ||||
0.331445 | + | 0.943475i | \(0.392464\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −29.5309 | −1.07190 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.01903 | 0.109440 | 0.0547199 | − | 0.998502i | \(-0.482573\pi\) | ||||
0.0547199 | + | 0.998502i | \(0.482573\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.74629 | 0.0632198 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.0161683 | 0.000584567 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 69.9005 | 2.52396 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −47.4452 | −1.71092 | −0.855460 | − | 0.517870i | \(-0.826725\pi\) | ||||
−0.855460 | + | 0.517870i | \(0.826725\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.10088 | 0.291746 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 26.0581 | 0.937247 | 0.468623 | − | 0.883398i | \(-0.344750\pi\) | ||||
0.468623 | + | 0.883398i | \(0.344750\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 42.2735 | 1.51851 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.43735 | −0.123314 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.23271 | −0.187481 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 67.1485 | 2.40276 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.918207 | 0.0328141 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.31675 | 0.225454 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.0940 | 0.466750 | 0.233375 | − | 0.972387i | \(-0.425023\pi\) | ||||
0.233375 | + | 0.972387i | \(0.425023\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −23.8160 | −0.847872 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.20247 | 0.327202 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −40.5600 | −1.44033 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.671766 | −0.0238251 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −51.0395 | −1.80791 | −0.903957 | − | 0.427624i | \(-0.859351\pi\) | ||||
−0.903957 | + | 0.427624i | \(0.859351\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.00657462 | −0.000232593 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.27474 | −0.257040 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −31.9921 | −1.12898 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.01829 | −0.0358901 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −30.4623 | −1.07233 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.43758 | 0.0857007 | 0.0428504 | − | 0.999082i | \(-0.486356\pi\) | ||||
0.0428504 | + | 0.999082i | \(0.486356\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18.8617 | −0.662323 | −0.331161 | − | 0.943574i | \(-0.607440\pi\) | ||||
−0.331161 | + | 0.943574i | \(0.607440\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.18720 | 0.146851 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.27886 | −0.0798251 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 20.2846 | 0.709669 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.37108 | −0.117795 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −28.5856 | −0.997644 | −0.498822 | − | 0.866704i | \(-0.666234\pi\) | ||||
−0.498822 | + | 0.866704i | \(0.666234\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.65296 | −0.0924762 | −0.0462381 | − | 0.998930i | \(-0.514723\pi\) | ||||
−0.0462381 | + | 0.998930i | \(0.514723\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −27.0878 | −0.943075 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 24.9577 | 0.867864 | 0.433932 | − | 0.900946i | \(-0.357126\pi\) | ||||
0.433932 | + | 0.900946i | \(0.357126\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −36.7438 | −1.27617 | −0.638083 | − | 0.769967i | \(-0.720272\pi\) | ||||
−0.638083 | + | 0.769967i | \(0.720272\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −27.5699 | −0.956391 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.321097 | −0.0111253 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.12364 | 0.142704 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.65025 | −0.298996 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 25.2911 | 0.873146 | 0.436573 | − | 0.899669i | \(-0.356192\pi\) | ||||
0.436573 | + | 0.899669i | \(0.356192\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.1569 | −0.970927 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −16.1734 | −0.557041 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7.45088 | 0.256318 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11.2127 | 0.385273 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 25.6248 | 0.879440 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 32.2133 | 1.10426 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.6684 | 0.570714 | 0.285357 | − | 0.958421i | \(-0.407888\pi\) | ||||
0.285357 | + | 0.958421i | \(0.407888\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.01924 | −0.0348574 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.14969 | 0.141751 | 0.0708754 | − | 0.997485i | \(-0.477421\pi\) | ||||
0.0708754 | + | 0.997485i | \(0.477421\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 39.5949 | 1.35096 | 0.675480 | − | 0.737379i | \(-0.263937\pi\) | ||||
0.675480 | + | 0.737379i | \(0.263937\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.981246 | 0.0334408 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −13.5820 | −0.462335 | −0.231168 | − | 0.972914i | \(-0.574255\pi\) | ||||
−0.231168 | + | 0.972914i | \(0.574255\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.66056 | −0.226466 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16.9977 | −0.577272 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −86.5685 | −2.93664 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −43.0505 | −1.45871 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.99135 | 0.236621 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.88970 | −0.0638834 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 49.0070 | 1.65485 | 0.827424 | − | 0.561578i | \(-0.189805\pi\) | ||||
0.827424 | + | 0.561578i | \(0.189805\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 18.2763 | 0.616445 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.55703 | −0.119839 | −0.0599197 | − | 0.998203i | \(-0.519084\pi\) | ||||
−0.0599197 | + | 0.998203i | \(0.519084\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 36.9287 | 1.24275 | 0.621375 | − | 0.783513i | \(-0.286574\pi\) | ||||
0.621375 | + | 0.783513i | \(0.286574\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.96315 | −0.133220 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −13.5282 | −0.454232 | −0.227116 | − | 0.973868i | \(-0.572930\pi\) | ||||
−0.227116 | + | 0.973868i | \(0.572930\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.274955 | −0.00922168 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.54286 | 0.185693 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.414460 | 0.0138694 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.08009 | 0.102956 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 31.5922 | 1.05483 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7.94272 | −0.264905 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.0960921 | −0.00320129 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.80380 | −0.126583 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.62811 | −0.0541202 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −21.0281 | −0.698227 | −0.349113 | − | 0.937080i | \(-0.613517\pi\) | ||||
−0.349113 | + | 0.937080i | \(0.613517\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.90051 | −0.0630359 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26.3558 | 0.873207 | 0.436603 | − | 0.899654i | \(-0.356181\pi\) | ||||
0.436603 | + | 0.899654i | \(0.356181\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −30.6044 | −1.01286 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.29963 | 0.0760235 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.21560 | 0.106188 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −39.9002 | −1.31619 | −0.658093 | − | 0.752937i | \(-0.728637\pi\) | ||||
−0.658093 | + | 0.752937i | \(0.728637\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.44082 | 0.212232 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −71.8355 | −2.36450 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 29.5483 | 0.971541 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.87606 | 0.160151 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −31.7964 | −1.04320 | −0.521602 | − | 0.853189i | \(-0.674666\pi\) | ||||
−0.521602 | + | 0.853189i | \(0.674666\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 20.2418 | 0.663398 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −19.9197 | −0.652142 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.0896187 | 0.00293085 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16.9699 | 0.554381 | 0.277191 | − | 0.960815i | \(-0.410597\pi\) | ||||
0.277191 | + | 0.960815i | \(0.410597\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.71046 | 0.0884525 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 18.9142 | 0.616584 | 0.308292 | − | 0.951292i | \(-0.400243\pi\) | ||||
0.308292 | + | 0.951292i | \(0.400243\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.19580 | −0.299456 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.191130 | 0.00621746 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −14.6973 | −0.477600 | −0.238800 | − | 0.971069i | \(-0.576754\pi\) | ||||
−0.238800 | + | 0.971069i | \(0.576754\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 34.2253 | 1.11100 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −18.1488 | −0.588515 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −18.2332 | −0.590630 | −0.295315 | − | 0.955400i | \(-0.595425\pi\) | ||||
−0.295315 | + | 0.955400i | \(0.595425\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.28710 | −0.171086 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.08949 | 0.164520 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.30675 | 0.139072 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 43.8268 | 1.41377 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.45469 | 0.0468766 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.15265 | 0.0692963 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24.0153 | 0.772280 | 0.386140 | − | 0.922440i | \(-0.373808\pi\) | ||||
0.386140 | + | 0.922440i | \(0.373808\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.145797 | −0.00468366 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −56.5272 | −1.81404 | −0.907021 | − | 0.421085i | \(-0.861650\pi\) | ||||
−0.907021 | + | 0.421085i | \(0.861650\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.43420 | −0.174213 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 28.9786 | 0.928057 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −30.6477 | −0.980506 | −0.490253 | − | 0.871580i | \(-0.663096\pi\) | ||||
−0.490253 | + | 0.871580i | \(0.663096\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −40.3229 | −1.28872 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.07174 | 0.0980730 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −29.3932 | −0.937498 | −0.468749 | − | 0.883331i | \(-0.655295\pi\) | ||||
−0.468749 | + | 0.883331i | \(0.655295\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.24243 | 0.230763 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.0777203 | −0.00247386 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 35.6476 | 1.13353 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.5125 | 0.619836 | 0.309918 | − | 0.950763i | \(-0.399698\pi\) | ||||
0.309918 | + | 0.950763i | \(0.399698\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3.42591 | −0.108718 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.60700 | 0.114350 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −51.0617 | −1.61714 | −0.808570 | − | 0.588401i | \(-0.799758\pi\) | ||||
−0.808570 | + | 0.588401i | \(0.799758\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.04634 | −0.191298 |
(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 | 6036.2.a.g.1.11 | ✓ | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6036.2.a.g.1.11 | ✓ | 15 | 1.1 | even | 1 | trivial |