Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6240,2,Mod(1,6240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6240, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("6240.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6240 = 2^{5} \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6240.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: | \(49.8266508613\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.229.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 4x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.254102\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6240.1 |
$q$-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 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.681331 | 0.257519 | 0.128759 | − | 0.991676i | \(-0.458901\pi\) | ||||
0.128759 | + | 0.991676i | \(0.458901\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.18953 | 0.961681 | 0.480840 | − | 0.876808i | \(-0.340332\pi\) | ||||
0.480840 | + | 0.876808i | \(0.340332\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.69774 | 0.896833 | 0.448417 | − | 0.893825i | \(-0.351988\pi\) | ||||
0.448417 | + | 0.893825i | \(0.351988\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.87086 | 0.888037 | 0.444019 | − | 0.896018i | \(-0.353552\pi\) | ||||
0.444019 | + | 0.896018i | \(0.353552\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.681331 | −0.148679 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.04399 | 1.26026 | 0.630130 | − | 0.776490i | \(-0.283002\pi\) | ||||
0.630130 | + | 0.776490i | \(0.283002\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.85446 | 0.901450 | 0.450725 | − | 0.892663i | \(-0.351165\pi\) | ||||
0.450725 | + | 0.892663i | \(0.351165\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.00000 | −0.718421 | −0.359211 | − | 0.933257i | \(-0.616954\pi\) | ||||
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.18953 | −0.555227 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.681331 | −0.115166 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.18953 | 0.853154 | 0.426577 | − | 0.904451i | \(-0.359719\pi\) | ||||
0.426577 | + | 0.904451i | \(0.359719\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.18953 | 0.185774 | 0.0928870 | − | 0.995677i | \(-0.470390\pi\) | ||||
0.0928870 | + | 0.995677i | \(0.470390\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.37907 | 0.972799 | 0.486399 | − | 0.873737i | \(-0.338310\pi\) | ||||
0.486399 | + | 0.873737i | \(0.338310\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.7253 | −1.56445 | −0.782225 | − | 0.622997i | \(-0.785915\pi\) | ||||
−0.782225 | + | 0.622997i | \(0.785915\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.53579 | −0.933684 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.69774 | −0.517787 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.56860 | −1.03963 | −0.519814 | − | 0.854280i | \(-0.673999\pi\) | ||||
−0.519814 | + | 0.854280i | \(0.673999\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.18953 | −0.430077 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.87086 | −0.512709 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.01641 | −0.132325 | −0.0661624 | − | 0.997809i | \(-0.521076\pi\) | ||||
−0.0661624 | + | 0.997809i | \(0.521076\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.55220 | 0.838923 | 0.419461 | − | 0.907773i | \(-0.362219\pi\) | ||||
0.419461 | + | 0.907773i | \(0.362219\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.681331 | 0.0858396 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.00000 | −0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.04399 | −0.727611 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.82687 | −0.216810 | −0.108405 | − | 0.994107i | \(-0.534574\pi\) | ||||
−0.108405 | + | 0.994107i | \(0.534574\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.2171 | 1.19582 | 0.597912 | − | 0.801562i | \(-0.295997\pi\) | ||||
0.597912 | + | 0.801562i | \(0.295997\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.17313 | 0.247651 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.1731 | −1.14457 | −0.572283 | − | 0.820056i | \(-0.693942\pi\) | ||||
−0.572283 | + | 0.820056i | \(0.693942\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.72532 | −0.299143 | −0.149572 | − | 0.988751i | \(-0.547789\pi\) | ||||
−0.149572 | + | 0.988751i | \(0.547789\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.69774 | −0.401076 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.85446 | −0.520453 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.17313 | −0.442351 | −0.221175 | − | 0.975234i | \(-0.570989\pi\) | ||||
−0.221175 | + | 0.975234i | \(0.570989\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.681331 | 0.0714229 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.00000 | 0.414781 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.87086 | −0.397142 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.31867 | 0.540029 | 0.270015 | − | 0.962856i | \(-0.412971\pi\) | ||||
0.270015 | + | 0.962856i | \(0.412971\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.18953 | 0.320560 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.87086 | 0.186158 | 0.0930790 | − | 0.995659i | \(-0.470329\pi\) | ||||
0.0930790 | + | 0.995659i | \(0.470329\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −18.7253 | −1.84506 | −0.922530 | − | 0.385924i | \(-0.873883\pi\) | ||||
−0.922530 | + | 0.385924i | \(0.873883\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.681331 | 0.0664911 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.5522 | 1.21347 | 0.606733 | − | 0.794905i | \(-0.292480\pi\) | ||||
0.606733 | + | 0.794905i | \(0.292480\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.8873 | 1.42594 | 0.712971 | − | 0.701194i | \(-0.247349\pi\) | ||||
0.712971 | + | 0.701194i | \(0.247349\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.18953 | −0.492569 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.47539 | 0.232865 | 0.116433 | − | 0.993199i | \(-0.462854\pi\) | ||||
0.116433 | + | 0.993199i | \(0.462854\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.04399 | −0.563605 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.51938 | 0.230951 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.826873 | −0.0751702 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.18953 | −0.107257 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.4835 | 1.37393 | 0.686967 | − | 0.726688i | \(-0.258942\pi\) | ||||
0.686967 | + | 0.726688i | \(0.258942\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.37907 | −0.561646 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.21712 | 0.368451 | 0.184226 | − | 0.982884i | \(-0.441022\pi\) | ||||
0.184226 | + | 0.982884i | \(0.441022\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.63734 | 0.228686 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.7089 | 1.00036 | 0.500180 | − | 0.865921i | \(-0.333267\pi\) | ||||
0.500180 | + | 0.865921i | \(0.333267\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −20.2939 | −1.72131 | −0.860654 | − | 0.509190i | \(-0.829945\pi\) | ||||
−0.860654 | + | 0.509190i | \(0.829945\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.7253 | 0.903235 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.18953 | 0.266722 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.85446 | −0.403141 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.53579 | 0.539063 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.5358 | 1.10890 | 0.554448 | − | 0.832219i | \(-0.312930\pi\) | ||||
0.554448 | + | 0.832219i | \(0.312930\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.03281 | −0.490943 | −0.245472 | − | 0.969404i | \(-0.578943\pi\) | ||||
−0.245472 | + | 0.969404i | \(0.578943\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.69774 | 0.298944 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.00000 | 0.321288 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.4671 | −1.31421 | −0.657107 | − | 0.753797i | \(-0.728220\pi\) | ||||
−0.657107 | + | 0.753797i | \(0.728220\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.56860 | 0.600229 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.11796 | 0.324540 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.56860 | −0.436167 | −0.218083 | − | 0.975930i | \(-0.569980\pi\) | ||||
−0.218083 | + | 0.975930i | \(0.569980\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.18953 | 0.248305 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.01641 | 0.388181 | 0.194091 | − | 0.980984i | \(-0.437824\pi\) | ||||
0.194091 | + | 0.980984i | \(0.437824\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.87086 | 0.296012 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.01641 | 0.229333 | 0.114667 | − | 0.993404i | \(-0.463420\pi\) | ||||
0.114667 | + | 0.993404i | \(0.463420\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.681331 | 0.0515038 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.01641 | 0.0763978 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.129135 | 0.00965203 | 0.00482601 | − | 0.999988i | \(-0.498464\pi\) | ||||
0.00482601 | + | 0.999988i | \(0.498464\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.15672 | −0.531955 | −0.265977 | − | 0.963979i | \(-0.585695\pi\) | ||||
−0.265977 | + | 0.963979i | \(0.585695\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.55220 | −0.484352 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.18953 | −0.381542 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.7941 | 0.862467 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.681331 | −0.0495595 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.34625 | −0.314484 | −0.157242 | − | 0.987560i | \(-0.550260\pi\) | ||||
−0.157242 | + | 0.987560i | \(0.550260\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.7141 | 1.20311 | 0.601555 | − | 0.798831i | \(-0.294548\pi\) | ||||
0.601555 | + | 0.798831i | \(0.294548\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.00000 | 0.0716115 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.0164 | 0.784886 | 0.392443 | − | 0.919776i | \(-0.371630\pi\) | ||||
0.392443 | + | 0.919776i | \(0.371630\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.03281 | 0.144102 | 0.0720512 | − | 0.997401i | \(-0.477046\pi\) | ||||
0.0720512 | + | 0.997401i | \(0.477046\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.30749 | 0.232140 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.18953 | −0.0830807 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.04399 | 0.420086 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 12.3463 | 0.854008 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.7253 | −1.01373 | −0.506867 | − | 0.862025i | \(-0.669196\pi\) | ||||
−0.506867 | + | 0.862025i | \(0.669196\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.82687 | 0.125175 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.37907 | −0.435049 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.72532 | −0.185007 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −10.2171 | −0.690409 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.69774 | 0.248737 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.2335 | −1.15404 | −0.577021 | − | 0.816729i | \(-0.695785\pi\) | ||||
−0.577021 | + | 0.816729i | \(0.695785\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.4119 | 0.823806 | 0.411903 | − | 0.911228i | \(-0.364864\pi\) | ||||
0.411903 | + | 0.911228i | \(0.364864\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 25.6126 | 1.69253 | 0.846264 | − | 0.532764i | \(-0.178847\pi\) | ||||
0.846264 | + | 0.532764i | \(0.178847\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.17313 | −0.142981 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −13.4067 | −0.878299 | −0.439150 | − | 0.898414i | \(-0.644720\pi\) | ||||
−0.439150 | + | 0.898414i | \(0.644720\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.7253 | 0.699643 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 10.1731 | 0.660816 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.552195 | −0.0357185 | −0.0178593 | − | 0.999841i | \(-0.505685\pi\) | ||||
−0.0178593 | + | 0.999841i | \(0.505685\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.1372 | −1.10390 | −0.551952 | − | 0.833876i | \(-0.686117\pi\) | ||||
−0.551952 | + | 0.833876i | \(0.686117\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.53579 | 0.417556 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.87086 | 0.246297 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.72532 | 0.172710 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 22.5082 | 1.42071 | 0.710353 | − | 0.703846i | \(-0.248535\pi\) | ||||
0.710353 | + | 0.703846i | \(0.248535\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 19.2775 | 1.21197 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.69774 | 0.231561 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 30.7170 | 1.91607 | 0.958036 | − | 0.286646i | \(-0.0925405\pi\) | ||||
0.958036 | + | 0.286646i | \(0.0925405\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.53579 | 0.219703 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.85446 | 0.300483 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.5410 | 0.773312 | 0.386656 | − | 0.922224i | \(-0.373630\pi\) | ||||
0.386656 | + | 0.922224i | \(0.373630\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.56860 | 0.464936 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.17313 | 0.255391 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 22.6290 | 1.37971 | 0.689857 | − | 0.723945i | \(-0.257673\pi\) | ||||
0.689857 | + | 0.723945i | \(0.257673\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.4119 | −1.23993 | −0.619967 | − | 0.784628i | \(-0.712854\pi\) | ||||
−0.619967 | + | 0.784628i | \(0.712854\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.681331 | −0.0412360 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.18953 | 0.192336 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.12080 | −0.247595 | −0.123797 | − | 0.992308i | \(-0.539507\pi\) | ||||
−0.123797 | + | 0.992308i | \(0.539507\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.00000 | −0.239474 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −17.4835 | −1.04298 | −0.521488 | − | 0.853259i | \(-0.674623\pi\) | ||||
−0.521488 | + | 0.853259i | \(0.674623\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.87086 | 0.229290 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.810466 | 0.0478403 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.32674 | −0.195690 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.31867 | −0.311786 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.6373 | 0.738281 | 0.369141 | − | 0.929374i | \(-0.379652\pi\) | ||||
0.369141 | + | 0.929374i | \(0.379652\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.01641 | 0.0591775 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.18953 | −0.185076 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.04399 | 0.349533 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.34625 | 0.250514 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.87086 | −0.107478 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.55220 | −0.375178 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −24.0357 | −1.37179 | −0.685894 | − | 0.727702i | \(-0.740588\pi\) | ||||
−0.685894 | + | 0.727702i | \(0.740588\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 18.7253 | 1.06525 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −17.1044 | −0.969901 | −0.484951 | − | 0.874542i | \(-0.661162\pi\) | ||||
−0.484951 | + | 0.874542i | \(0.661162\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.7745 | 1.11772 | 0.558862 | − | 0.829261i | \(-0.311238\pi\) | ||||
0.558862 | + | 0.829261i | \(0.311238\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.681331 | −0.0383886 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.24186 | 0.294412 | 0.147206 | − | 0.989106i | \(-0.452972\pi\) | ||||
0.147206 | + | 0.989106i | \(0.452972\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 15.4835 | 0.866907 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.5522 | −0.700595 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 14.3134 | 0.796421 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.00000 | 0.0554700 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −14.8873 | −0.823268 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.30749 | −0.402875 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 26.6618 | 1.46547 | 0.732733 | − | 0.680516i | \(-0.238244\pi\) | ||||
0.732733 | + | 0.680516i | \(0.238244\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.18953 | 0.284385 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 26.4342 | 1.43996 | 0.719982 | − | 0.693992i | \(-0.244150\pi\) | ||||
0.719982 | + | 0.693992i | \(0.244150\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.47539 | −0.134445 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.7581 | −0.690892 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.22235 | −0.497960 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 6.04399 | 0.325398 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 24.2283 | 1.30064 | 0.650322 | − | 0.759659i | \(-0.274634\pi\) | ||||
0.650322 | + | 0.759659i | \(0.274634\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.97526 | −0.373377 | −0.186688 | − | 0.982419i | \(-0.559775\pi\) | ||||
−0.186688 | + | 0.982419i | \(0.559775\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.32985 | 0.283679 | 0.141840 | − | 0.989890i | \(-0.454698\pi\) | ||||
0.141840 | + | 0.989890i | \(0.454698\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.82687 | 0.0969603 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.51938 | −0.133340 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.72532 | −0.354949 | −0.177474 | − | 0.984125i | \(-0.556793\pi\) | ||||
−0.177474 | + | 0.984125i | \(0.556793\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.01641 | −0.211390 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.826873 | 0.0433996 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −10.2171 | −0.534788 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.34625 | 0.226873 | 0.113436 | − | 0.993545i | \(-0.463814\pi\) | ||||
0.113436 | + | 0.993545i | \(0.463814\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.18953 | 0.0619247 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.15672 | −0.267724 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −37.2252 | −1.92745 | −0.963724 | − | 0.266902i | \(-0.914000\pi\) | ||||
−0.963724 | + | 0.266902i | \(0.914000\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.85446 | 0.250017 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.45898 | −0.177676 | −0.0888380 | − | 0.996046i | \(-0.528315\pi\) | ||||
−0.0888380 | + | 0.996046i | \(0.528315\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −15.4835 | −0.793242 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −22.1208 | −1.13032 | −0.565160 | − | 0.824981i | \(-0.691186\pi\) | ||||
−0.565160 | + | 0.824981i | \(0.691186\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.17313 | −0.110753 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.37907 | 0.324266 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −27.0632 | −1.37216 | −0.686080 | − | 0.727526i | \(-0.740670\pi\) | ||||
−0.686080 | + | 0.727526i | \(0.740670\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 22.3491 | 1.13024 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.21712 | −0.212726 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 10.1731 | 0.511866 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 34.6402 | 1.73854 | 0.869270 | − | 0.494337i | \(-0.164589\pi\) | ||||
0.869270 | + | 0.494337i | \(0.164589\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.63734 | −0.132032 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 19.7745 | 0.987494 | 0.493747 | − | 0.869606i | \(-0.335627\pi\) | ||||
0.493747 | + | 0.869606i | \(0.335627\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.00000 | −0.199254 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16.5522 | 0.820462 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.32985 | 0.0657567 | 0.0328784 | − | 0.999459i | \(-0.489533\pi\) | ||||
0.0328784 | + | 0.999459i | \(0.489533\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11.7089 | −0.577558 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.692509 | −0.0340761 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.72532 | 0.133781 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 20.2939 | 0.993798 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 18.0796 | 0.883249 | 0.441624 | − | 0.897200i | \(-0.354402\pi\) | ||||
0.441624 | + | 0.897200i | \(0.354402\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.3215 | 1.13662 | 0.568310 | − | 0.822814i | \(-0.307597\pi\) | ||||
0.568310 | + | 0.822814i | \(0.307597\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −10.7253 | −0.521483 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.69774 | 0.179367 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.46421 | 0.216038 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.18953 | −0.153992 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 29.4506 | 1.41859 | 0.709294 | − | 0.704913i | \(-0.249014\pi\) | ||||
0.709294 | + | 0.704913i | \(0.249014\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.1924 | 0.730099 | 0.365049 | − | 0.930988i | \(-0.381052\pi\) | ||||
0.365049 | + | 0.930988i | \(0.381052\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.85446 | 0.232753 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 23.3955 | 1.11916 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.5850 | −0.696104 | −0.348052 | − | 0.937475i | \(-0.613157\pi\) | ||||
−0.348052 | + | 0.937475i | \(0.613157\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.53579 | −0.311228 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 30.3267 | 1.44087 | 0.720433 | − | 0.693524i | \(-0.243943\pi\) | ||||
0.720433 | + | 0.693524i | \(0.243943\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.17313 | 0.197825 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −13.5358 | −0.640221 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12.2388 | 0.577583 | 0.288791 | − | 0.957392i | \(-0.406747\pi\) | ||||
0.288791 | + | 0.957392i | \(0.406747\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.79406 | 0.178655 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.03281 | 0.283446 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.681331 | −0.0319413 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −21.4067 | −1.00136 | −0.500681 | − | 0.865632i | \(-0.666917\pi\) | ||||
−0.500681 | + | 0.865632i | \(0.666917\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.69774 | −0.172596 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.5194 | −0.583086 | −0.291543 | − | 0.956558i | \(-0.594169\pi\) | ||||
−0.291543 | + | 0.956558i | \(0.594169\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.69774 | 0.264796 | 0.132398 | − | 0.991197i | \(-0.457732\pi\) | ||||
0.132398 | + | 0.991197i | \(0.457732\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.00000 | −0.185496 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 31.2775 | 1.44735 | 0.723675 | − | 0.690140i | \(-0.242451\pi\) | ||||
0.723675 | + | 0.690140i | \(0.242451\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 16.4671 | 0.758762 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 20.3463 | 0.935522 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.87086 | 0.177607 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.56860 | −0.346542 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −17.6566 | −0.806750 | −0.403375 | − | 0.915035i | \(-0.632163\pi\) | ||||
−0.403375 | + | 0.915035i | \(0.632163\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.18953 | 0.236622 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.11796 | −0.187374 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5.31867 | −0.241508 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.93960 | −0.405092 | −0.202546 | − | 0.979273i | \(-0.564922\pi\) | ||||
−0.202546 | + | 0.979273i | \(0.564922\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.56860 | 0.251821 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.92008 | −0.312299 | −0.156150 | − | 0.987733i | \(-0.549908\pi\) | ||||
−0.156150 | + | 0.987733i | \(0.549908\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 17.9505 | 0.808450 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.18953 | −0.143359 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.24470 | −0.0558326 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.5798 | 0.786979 | 0.393490 | − | 0.919329i | \(-0.371268\pi\) | ||||
0.393490 | + | 0.919329i | \(0.371268\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.01641 | −0.224117 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 20.0245 | 0.892847 | 0.446424 | − | 0.894822i | \(-0.352697\pi\) | ||||
0.446424 | + | 0.894822i | \(0.352697\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.87086 | −0.0832524 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.865636 | −0.0383687 | −0.0191843 | − | 0.999816i | \(-0.506107\pi\) | ||||
−0.0191843 | + | 0.999816i | \(0.506107\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.96124 | 0.307947 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.87086 | −0.170903 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 18.7253 | 0.825136 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −34.2088 | −1.50450 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.01641 | −0.132406 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.4342 | 0.457132 | 0.228566 | − | 0.973528i | \(-0.426596\pi\) | ||||
0.228566 | + | 0.973528i | \(0.426596\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.92842 | −0.215505 | −0.107752 | − | 0.994178i | \(-0.534365\pi\) | ||||
−0.107752 | + | 0.994178i | \(0.534365\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.681331 | −0.0297357 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −14.7909 | −0.644304 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13.5298 | 0.588254 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.01641 | −0.0441083 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.18953 | 0.0515244 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.5522 | −0.542679 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.129135 | −0.00557260 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −20.8461 | −0.897906 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −33.2663 | −1.43023 | −0.715116 | − | 0.699006i | \(-0.753626\pi\) | ||||
−0.715116 | + | 0.699006i | \(0.753626\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7.15672 | 0.307124 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −14.8873 | −0.637701 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.45065 | −0.404080 | −0.202040 | − | 0.979377i | \(-0.564757\pi\) | ||||
−0.202040 | + | 0.979377i | \(0.564757\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.55220 | 0.279641 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 18.7909 | 0.800521 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.93126 | −0.294747 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.18953 | 0.220283 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 30.3463 | 1.28581 | 0.642906 | − | 0.765945i | \(-0.277729\pi\) | ||||
0.642906 | + | 0.765945i | \(0.277729\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.37907 | 0.269806 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −11.7941 | −0.497946 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −13.3983 | −0.564672 | −0.282336 | − | 0.959316i | \(-0.591109\pi\) | ||||
−0.282336 | + | 0.959316i | \(0.591109\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.47539 | −0.104140 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.681331 | 0.0286132 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.01641 | −0.126454 | −0.0632272 | − | 0.997999i | \(-0.520139\pi\) | ||||
−0.0632272 | + | 0.997999i | \(0.520139\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.6730 | −0.446651 | −0.223325 | − | 0.974744i | \(-0.571691\pi\) | ||||
−0.223325 | + | 0.974744i | \(0.571691\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.34625 | 0.181567 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.04399 | 0.252052 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 45.7529 | 1.90472 | 0.952359 | − | 0.304979i | \(-0.0986493\pi\) | ||||
0.952359 | + | 0.304979i | \(0.0986493\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −16.7141 | −0.694616 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.85685 | −0.0770349 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −24.1403 | −0.999790 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.00000 | −0.0413449 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −20.5878 | −0.849751 | −0.424876 | − | 0.905252i | \(-0.639682\pi\) | ||||
−0.424876 | + | 0.905252i | \(0.639682\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −15.4835 | −0.637985 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −11.0164 | −0.453154 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −21.8297 | −0.896439 | −0.448219 | − | 0.893924i | \(-0.647942\pi\) | ||||
−0.448219 | + | 0.893924i | \(0.647942\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.51938 | −0.103285 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.03281 | −0.0831975 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.51627 | −0.388824 | −0.194412 | − | 0.980920i | \(-0.562280\pi\) | ||||
−0.194412 | + | 0.980920i | \(0.562280\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.94767 | 0.405774 | 0.202887 | − | 0.979202i | \(-0.434968\pi\) | ||||
0.202887 | + | 0.979202i | \(0.434968\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.826873 | 0.0336172 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.6537 | −0.473011 | −0.236505 | − | 0.971630i | \(-0.576002\pi\) | ||||
−0.236505 | + | 0.971630i | \(0.576002\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.30749 | −0.134026 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −10.7253 | −0.433900 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −25.1895 | −1.01740 | −0.508698 | − | 0.860945i | \(-0.669873\pi\) | ||||
−0.508698 | + | 0.860945i | \(0.669873\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.18953 | 0.0479666 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18.4342 | −0.742134 | −0.371067 | − | 0.928606i | \(-0.621008\pi\) | ||||
−0.371067 | + | 0.928606i | \(0.621008\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21.9260 | 0.881282 | 0.440641 | − | 0.897683i | \(-0.354751\pi\) | ||||
0.440641 | + | 0.897683i | \(0.354751\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.04399 | −0.242537 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.84328 | −0.113914 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −12.3463 | −0.493062 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 19.1895 | 0.765137 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −29.1267 | −1.15952 | −0.579759 | − | 0.814788i | \(-0.696853\pi\) | ||||
−0.579759 | + | 0.814788i | \(0.696853\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 14.7253 | 0.585279 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −15.4835 | −0.614442 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.53579 | −0.258957 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.82687 | −0.0722700 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.27468 | −0.129342 | −0.0646710 | − | 0.997907i | \(-0.520600\pi\) | ||||
−0.0646710 | + | 0.997907i | \(0.520600\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −27.2775 | −1.07572 | −0.537860 | − | 0.843034i | \(-0.680767\pi\) | ||||
−0.537860 | + | 0.843034i | \(0.680767\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.37907 | 0.251176 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.43947 | 0.371104 | 0.185552 | − | 0.982634i | \(-0.440593\pi\) | ||||
0.185552 | + | 0.982634i | \(0.440593\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.24186 | −0.127254 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.72532 | 0.106814 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 37.6594 | 1.47373 | 0.736864 | − | 0.676041i | \(-0.236306\pi\) | ||||
0.736864 | + | 0.676041i | \(0.236306\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.21712 | −0.164776 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10.2171 | 0.398608 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.44258 | −0.0951493 | −0.0475746 | − | 0.998868i | \(-0.515149\pi\) | ||||
−0.0475746 | + | 0.998868i | \(0.515149\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −45.2007 | −1.75810 | −0.879052 | − | 0.476726i | \(-0.841823\pi\) | ||||
−0.879052 | + | 0.476726i | \(0.841823\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.69774 | −0.143608 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.63734 | −0.102272 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 29.3403 | 1.13606 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 17.2335 | 0.666287 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 20.8984 | 0.806776 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.6209 | 0.447954 | 0.223977 | − | 0.974594i | \(-0.428096\pi\) | ||||
0.223977 | + | 0.974594i | \(0.428096\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5.27752 | −0.202831 | −0.101416 | − | 0.994844i | \(-0.532337\pi\) | ||||
−0.101416 | + | 0.994844i | \(0.532337\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.62377 | 0.139068 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12.4119 | −0.475624 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −16.5878 | −0.634716 | −0.317358 | − | 0.948306i | \(-0.602796\pi\) | ||||
−0.317358 | + | 0.948306i | \(0.602796\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11.7089 | −0.447375 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −25.6126 | −0.977181 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7.56860 | −0.288341 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 45.5631 | 1.73330 | 0.866651 | − | 0.498915i | \(-0.166268\pi\) | ||||
0.866651 | + | 0.498915i | \(0.166268\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.17313 | 0.0825503 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 20.2939 | 0.769792 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.39858 | 0.166608 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 13.4067 | 0.507086 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.35432 | 0.0511521 | 0.0255760 | − | 0.999673i | \(-0.491858\pi\) | ||||
0.0255760 | + | 0.999673i | \(0.491858\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20.0880 | 0.757633 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −10.7253 | −0.403939 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.27468 | 0.0479392 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17.2887 | −0.649291 | −0.324645 | − | 0.945836i | \(-0.605245\pi\) | ||||
−0.324645 | + | 0.945836i | \(0.605245\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −10.1731 | −0.381522 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −24.1760 | −0.905397 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.18953 | −0.119282 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.552195 | 0.0206221 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 34.4671 | 1.28540 | 0.642702 | − | 0.766116i | \(-0.277813\pi\) | ||||
0.642702 | + | 0.766116i | \(0.277813\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.7581 | −0.475138 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 17.1372 | 0.637339 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.85446 | 0.180290 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −24.8461 | −0.921492 | −0.460746 | − | 0.887532i | \(-0.652418\pi\) | ||||
−0.460746 | + | 0.887532i | \(0.652418\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 23.5881 | 0.872438 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12.8433 | −0.474377 | −0.237189 | − | 0.971464i | \(-0.576226\pi\) | ||||
−0.237189 | + | 0.971464i | \(0.576226\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.53579 | −0.241076 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −23.2887 | −0.856689 | −0.428344 | − | 0.903616i | \(-0.640903\pi\) | ||||
−0.428344 | + | 0.903616i | \(0.640903\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.87086 | −0.142200 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14.8133 | 0.543448 | 0.271724 | − | 0.962375i | \(-0.412406\pi\) | ||||
0.271724 | + | 0.962375i | \(0.412406\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −13.5358 | −0.495913 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.72532 | −0.0997143 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.55220 | 0.312490 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.9313 | 0.690812 | 0.345406 | − | 0.938453i | \(-0.387741\pi\) | ||||
0.345406 | + | 0.938453i | \(0.387741\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −22.5082 | −0.820245 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.03281 | 0.219557 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 35.3460 | 1.28467 | 0.642336 | − | 0.766423i | \(-0.277965\pi\) | ||||
0.642336 | + | 0.766423i | \(0.277965\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −19.2775 | −0.699730 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.67610 | −0.350758 | −0.175379 | − | 0.984501i | \(-0.556115\pi\) | ||||
−0.175379 | + | 0.984501i | \(0.556115\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.1432 | 0.367207 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.69774 | −0.133692 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.01641 | −0.0367003 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 38.2416 | 1.37903 | 0.689514 | − | 0.724273i | \(-0.257824\pi\) | ||||
0.689514 | + | 0.724273i | \(0.257824\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −30.7170 | −1.10625 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0.571712 | 0.0205630 | 0.0102815 | − | 0.999947i | \(-0.496727\pi\) | ||||
0.0102815 | + | 0.999947i | \(0.496727\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.00000 | −0.143684 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.53579 | −0.126846 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.60453 | 0.164974 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.82687 | −0.208502 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.85446 | −0.173484 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 16.4671 | 0.587734 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26.4671 | 0.943449 | 0.471724 | − | 0.881746i | \(-0.343632\pi\) | ||||
0.471724 | + | 0.881746i | \(0.343632\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −12.5410 | −0.446472 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.68656 | 0.0599671 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.55220 | 0.232675 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −7.56860 | −0.268431 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6.46421 | −0.228974 | −0.114487 | − | 0.993425i | \(-0.536522\pi\) | ||||
−0.114487 | + | 0.993425i | \(0.536522\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −39.6594 | −1.40305 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.17313 | −0.147450 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 32.5878 | 1.15000 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.11796 | −0.145139 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −22.6290 | −0.796579 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 23.4506 | 0.824481 | 0.412240 | − | 0.911075i | \(-0.364746\pi\) | ||||
0.412240 | + | 0.911075i | \(0.364746\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.1455 | 0.602061 | 0.301031 | − | 0.953614i | \(-0.402669\pi\) | ||||
0.301031 | + | 0.953614i | \(0.402669\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 20.4119 | 0.715876 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.56860 | 0.195060 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 24.6925 | 0.863882 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.681331 | 0.0238076 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −38.2939 | −1.33647 | −0.668234 | − | 0.743952i | \(-0.732949\pi\) | ||||
−0.668234 | + | 0.743952i | \(0.732949\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −34.7253 | −1.21045 | −0.605224 | − | 0.796055i | \(-0.706917\pi\) | ||||
−0.605224 | + | 0.796055i | \(0.706917\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.18953 | −0.111045 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 44.7581 | 1.55639 | 0.778196 | − | 0.628021i | \(-0.216135\pi\) | ||||
0.778196 | + | 0.628021i | \(0.216135\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −10.8238 | −0.375925 | −0.187962 | − | 0.982176i | \(-0.560188\pi\) | ||||
−0.187962 | + | 0.982176i | \(0.560188\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.12080 | 0.142949 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −24.1676 | −0.837359 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.01641 | −0.173600 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.00000 | 0.138260 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.68940 | 0.127372 | 0.0636861 | − | 0.997970i | \(-0.479714\pi\) | ||||
0.0636861 | + | 0.997970i | \(0.479714\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.43424 | −0.187388 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 17.4835 | 0.602162 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.00000 | −0.0344010 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.563374 | −0.0193578 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 31.3655 | 1.07520 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.49702 | −0.290933 | −0.145466 | − | 0.989363i | \(-0.546468\pi\) | ||||
−0.145466 | + | 0.989363i | \(0.546468\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.87086 | −0.132381 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −42.5990 | −1.45516 | −0.727578 | − | 0.686025i | \(-0.759354\pi\) | ||||
−0.727578 | + | 0.686025i | \(0.759354\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20.5522 | −0.701232 | −0.350616 | − | 0.936519i | \(-0.614028\pi\) | ||||
−0.350616 | + | 0.936519i | \(0.614028\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.810466 | −0.0276206 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 47.5058 | 1.61712 | 0.808558 | − | 0.588416i | \(-0.200248\pi\) | ||||
0.808558 | + | 0.588416i | \(0.200248\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.01641 | −0.102561 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.32674 | 0.112982 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −32.4475 | −1.10071 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.31867 | 0.180010 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.681331 | −0.0230332 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.34030 | 0.247864 | 0.123932 | − | 0.992291i | \(-0.460449\pi\) | ||||
0.123932 | + | 0.992291i | \(0.460449\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −12.6373 | −0.426247 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −28.6373 | −0.964816 | −0.482408 | − | 0.875947i | \(-0.660238\pi\) | ||||
−0.482408 | + | 0.875947i | \(0.660238\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −20.0000 | −0.673054 | −0.336527 | − | 0.941674i | \(-0.609252\pi\) | ||||
−0.336527 | + | 0.941674i | \(0.609252\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.01641 | −0.0341661 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −44.7526 | −1.50265 | −0.751323 | − | 0.659934i | \(-0.770584\pi\) | ||||
−0.751323 | + | 0.659934i | \(0.770584\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.5494 | 0.353814 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.18953 | 0.106853 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −41.5163 | −1.38929 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.129135 | −0.00431652 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.04399 | −0.201803 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −19.4178 | −0.647621 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −27.9867 | −0.932372 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.34625 | −0.144634 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.15672 | 0.237897 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 50.4894 | 1.67647 | 0.838237 | − | 0.545307i | \(-0.183587\pi\) | ||||
0.838237 | + | 0.545307i | \(0.183587\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.87086 | 0.0620527 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.0552 | −0.333143 | −0.166571 | − | 0.986029i | \(-0.553270\pi\) | ||||
−0.166571 | + | 0.986029i | \(0.553270\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.69251 | −0.287680 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6.55220 | 0.216609 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.87325 | 0.0948832 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11.2119 | 0.369846 | 0.184923 | − | 0.982753i | \(-0.440796\pi\) | ||||
0.184923 | + | 0.982753i | \(0.440796\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 24.0357 | 0.792002 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.82687 | −0.0601322 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.18953 | 0.170631 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −18.7253 | −0.615020 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −26.9641 | −0.884663 | −0.442331 | − | 0.896852i | \(-0.645848\pi\) | ||||
−0.442331 | + | 0.896852i | \(0.645848\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −25.2992 | −0.829146 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 17.1044 | 0.559973 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −11.7941 | −0.385707 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 52.6207 | 1.71904 | 0.859521 | − | 0.511100i | \(-0.170762\pi\) | ||||
0.859521 | + | 0.511100i | \(0.170762\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −19.7745 | −0.645318 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −44.1565 | −1.43946 | −0.719730 | − | 0.694255i | \(-0.755734\pi\) | ||||
−0.719730 | + | 0.694255i | \(0.755734\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.18953 | 0.234123 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.681331 | 0.0221637 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8.51654 | 0.276750 | 0.138375 | − | 0.990380i | \(-0.455812\pi\) | ||||
0.138375 | + | 0.990380i | \(0.455812\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.2171 | 0.331662 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.24186 | −0.169979 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −9.57694 | −0.310228 | −0.155114 | − | 0.987897i | \(-0.549574\pi\) | ||||
−0.155114 | + | 0.987897i | \(0.549574\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.34625 | 0.140641 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −15.4835 | −0.500509 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.97764 | 0.257612 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12.5522 | 0.404489 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −16.7141 | −0.538047 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.26634 | 0.105038 | 0.0525192 | − | 0.998620i | \(-0.483275\pi\) | ||||
0.0525192 | + | 0.998620i | \(0.483275\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −14.3134 | −0.459814 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −46.0140 | −1.47666 | −0.738330 | − | 0.674440i | \(-0.764385\pi\) | ||||
−0.738330 | + | 0.674440i | \(0.764385\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −13.8269 | −0.443269 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.00000 | −0.0320256 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −32.7909 | −1.04908 | −0.524538 | − | 0.851387i | \(-0.675762\pi\) | ||||
−0.524538 | + | 0.851387i | \(0.675762\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −13.3103 | −0.425400 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.8873 | 0.475314 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 39.9177 | 1.27318 | 0.636588 | − | 0.771204i | \(-0.280345\pi\) | ||||
0.636588 | + | 0.771204i | \(0.280345\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.0164 | −0.351012 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 7.30749 | 0.232600 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 38.5550 | 1.22598 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −45.4863 | −1.44492 | −0.722460 | − | 0.691413i | \(-0.756989\pi\) | ||||
−0.722460 | + | 0.691413i | \(0.756989\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −26.6618 | −0.846087 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.03281 | −0.0644445 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 43.0221 | 1.36252 | 0.681262 | − | 0.732040i | \(-0.261432\pi\) | ||||
0.681262 | + | 0.732040i | \(0.261432\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.18953 | −0.164190 |
(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 | 6240.2.a.bw.1.3 | ✓ | 3 | |
4.3 | odd | 2 | 6240.2.a.cb.1.1 | yes | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6240.2.a.bw.1.3 | ✓ | 3 | 1.1 | even | 1 | trivial | |
6240.2.a.cb.1.1 | yes | 3 | 4.3 | odd | 2 |