Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7800,2,Mod(1,7800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7800, 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("7800.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7800 = 2^{3} \cdot 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7800.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: | \(62.2833135766\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.17009\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7800.1 |
$q$-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 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.24846 | −1.22780 | −0.613902 | − | 0.789382i | \(-0.710401\pi\) | ||||
−0.613902 | + | 0.789382i | \(0.710401\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.460811 | −0.138940 | −0.0694699 | − | 0.997584i | \(-0.522131\pi\) | ||||
−0.0694699 | + | 0.997584i | \(0.522131\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.26180 | −1.03364 | −0.516819 | − | 0.856095i | \(-0.672884\pi\) | ||||
−0.516819 | + | 0.856095i | \(0.672884\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.70928 | 0.392135 | 0.196067 | − | 0.980590i | \(-0.437183\pi\) | ||||
0.196067 | + | 0.980590i | \(0.437183\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.24846 | −0.708873 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.38962 | 1.74936 | 0.874678 | − | 0.484704i | \(-0.161073\pi\) | ||||
0.874678 | + | 0.484704i | \(0.161073\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.34017 | 0.620255 | 0.310127 | − | 0.950695i | \(-0.399628\pi\) | ||||
0.310127 | + | 0.950695i | \(0.399628\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.87936 | −1.41518 | −0.707588 | − | 0.706626i | \(-0.750217\pi\) | ||||
−0.707588 | + | 0.706626i | \(0.750217\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.460811 | −0.0802169 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.46800 | 1.22773 | 0.613866 | − | 0.789410i | \(-0.289614\pi\) | ||||
0.613866 | + | 0.789410i | \(0.289614\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.78765 | −1.37240 | −0.686200 | − | 0.727413i | \(-0.740723\pi\) | ||||
−0.686200 | + | 0.727413i | \(0.740723\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.89269 | −0.593630 | −0.296815 | − | 0.954935i | \(-0.595924\pi\) | ||||
−0.296815 | + | 0.954935i | \(0.595924\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.751536 | 0.109623 | 0.0548114 | − | 0.998497i | \(-0.482544\pi\) | ||||
0.0548114 | + | 0.998497i | \(0.482544\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.55252 | 0.507503 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.26180 | −0.596771 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.70928 | −1.19631 | −0.598155 | − | 0.801380i | \(-0.704099\pi\) | ||||
−0.598155 | + | 0.801380i | \(0.704099\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.70928 | 0.226399 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.27513 | −0.426385 | −0.213193 | − | 0.977010i | \(-0.568386\pi\) | ||||
−0.213193 | + | 0.977010i | \(0.568386\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.07838 | −1.03433 | −0.517165 | − | 0.855886i | \(-0.673013\pi\) | ||||
−0.517165 | + | 0.855886i | \(0.673013\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.24846 | −0.409268 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.95774 | 0.605684 | 0.302842 | − | 0.953041i | \(-0.402065\pi\) | ||||
0.302842 | + | 0.953041i | \(0.402065\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.38962 | 1.00999 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.23287 | 0.977061 | 0.488531 | − | 0.872547i | \(-0.337533\pi\) | ||||
0.488531 | + | 0.872547i | \(0.337533\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.8082 | 1.61612 | 0.808062 | − | 0.589097i | \(-0.200517\pi\) | ||||
0.808062 | + | 0.589097i | \(0.200517\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.49693 | 0.170591 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.2062 | −1.37331 | −0.686653 | − | 0.726986i | \(-0.740921\pi\) | ||||
−0.686653 | + | 0.726986i | \(0.740921\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.40522 | 0.812828 | 0.406414 | − | 0.913689i | \(-0.366779\pi\) | ||||
0.406414 | + | 0.913689i | \(0.366779\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.34017 | 0.358104 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.44521 | −1.00119 | −0.500595 | − | 0.865681i | \(-0.666886\pi\) | ||||
−0.500595 | + | 0.865681i | \(0.666886\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.24846 | −0.340532 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.87936 | −0.817052 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.49693 | −0.253525 | −0.126762 | − | 0.991933i | \(-0.540459\pi\) | ||||
−0.126762 | + | 0.991933i | \(0.540459\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.460811 | −0.0463133 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.72979 | 0.769143 | 0.384572 | − | 0.923095i | \(-0.374349\pi\) | ||||
0.384572 | + | 0.923095i | \(0.374349\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.89269 | −0.186493 | −0.0932463 | − | 0.995643i | \(-0.529724\pi\) | ||||
−0.0932463 | + | 0.995643i | \(0.529724\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.17727 | 0.693853 | 0.346927 | − | 0.937892i | \(-0.387225\pi\) | ||||
0.346927 | + | 0.937892i | \(0.387225\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.2267 | −1.07533 | −0.537663 | − | 0.843160i | \(-0.680693\pi\) | ||||
−0.537663 | + | 0.843160i | \(0.680693\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.46800 | 0.708831 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −17.9155 | −1.68535 | −0.842673 | − | 0.538425i | \(-0.819019\pi\) | ||||
−0.842673 | + | 0.538425i | \(0.819019\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 13.8443 | 1.26910 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.7877 | −0.980696 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −8.78765 | −0.792356 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.2267 | −0.996211 | −0.498105 | − | 0.867117i | \(-0.665971\pi\) | ||||
−0.498105 | + | 0.867117i | \(0.665971\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.89269 | −0.342732 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.4947 | −1.17903 | −0.589517 | − | 0.807756i | \(-0.700682\pi\) | ||||
−0.589517 | + | 0.807756i | \(0.700682\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.55252 | −0.481465 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.65983 | 0.141809 | 0.0709043 | − | 0.997483i | \(-0.477412\pi\) | ||||
0.0709043 | + | 0.997483i | \(0.477412\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.6803 | 1.24517 | 0.622585 | − | 0.782552i | \(-0.286082\pi\) | ||||
0.622585 | + | 0.782552i | \(0.286082\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.751536 | 0.0632907 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.460811 | −0.0385350 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.55252 | 0.293007 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.1834 | 0.834258 | 0.417129 | − | 0.908847i | \(-0.363036\pi\) | ||||
0.417129 | + | 0.908847i | \(0.363036\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.34736 | 0.109647 | 0.0548233 | − | 0.998496i | \(-0.482540\pi\) | ||||
0.0548233 | + | 0.998496i | \(0.482540\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.26180 | −0.344546 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.9649 | −1.51357 | −0.756783 | − | 0.653666i | \(-0.773230\pi\) | ||||
−0.756783 | + | 0.653666i | \(0.773230\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.70928 | −0.690690 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −27.2534 | −2.14787 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.07611 | 0.475918 | 0.237959 | − | 0.971275i | \(-0.423522\pi\) | ||||
0.237959 | + | 0.971275i | \(0.423522\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −16.1483 | −1.24960 | −0.624798 | − | 0.780786i | \(-0.714819\pi\) | ||||
−0.624798 | + | 0.780786i | \(0.714819\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.70928 | 0.130712 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −22.3112 | −1.69629 | −0.848146 | − | 0.529762i | \(-0.822281\pi\) | ||||
−0.848146 | + | 0.529762i | \(0.822281\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.27513 | −0.246174 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.52586 | −0.711996 | −0.355998 | − | 0.934487i | \(-0.615859\pi\) | ||||
−0.355998 | + | 0.934487i | \(0.615859\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.5730 | −1.45485 | −0.727426 | − | 0.686186i | \(-0.759284\pi\) | ||||
−0.727426 | + | 0.686186i | \(0.759284\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.07838 | −0.597171 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.96388 | 0.143613 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.24846 | −0.236291 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.52359 | −0.327316 | −0.163658 | − | 0.986517i | \(-0.552329\pi\) | ||||
−0.163658 | + | 0.986517i | \(0.552329\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.38962 | 0.315972 | 0.157986 | − | 0.987441i | \(-0.449500\pi\) | ||||
0.157986 | + | 0.987441i | \(0.449500\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.6309 | 0.757420 | 0.378710 | − | 0.925515i | \(-0.376368\pi\) | ||||
0.378710 | + | 0.925515i | \(0.376368\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17.7321 | −1.25699 | −0.628496 | − | 0.777813i | \(-0.716329\pi\) | ||||
−0.628496 | + | 0.777813i | \(0.716329\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.95774 | 0.349692 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −10.8504 | −0.761551 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.38962 | 0.583119 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.787653 | −0.0544831 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.9132 | 1.02667 | 0.513334 | − | 0.858189i | \(-0.328410\pi\) | ||||
0.513334 | + | 0.858189i | \(0.328410\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.23287 | 0.564107 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 25.5958 | 1.73756 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 13.8082 | 0.933070 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.26180 | −0.286679 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.5464 | 1.37589 | 0.687944 | − | 0.725764i | \(-0.258514\pi\) | ||||
0.687944 | + | 0.725764i | \(0.258514\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 21.6381 | 1.43617 | 0.718085 | − | 0.695955i | \(-0.245019\pi\) | ||||
0.718085 | + | 0.695955i | \(0.245019\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.3607 | 1.27939 | 0.639695 | − | 0.768629i | \(-0.279061\pi\) | ||||
0.639695 | + | 0.768629i | \(0.279061\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.49693 | 0.0984907 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −24.0722 | −1.57702 | −0.788512 | − | 0.615019i | \(-0.789148\pi\) | ||||
−0.788512 | + | 0.615019i | \(0.789148\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −12.2062 | −0.792878 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −14.2423 | −0.921259 | −0.460630 | − | 0.887592i | \(-0.652376\pi\) | ||||
−0.460630 | + | 0.887592i | \(0.652376\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −28.3896 | −1.82874 | −0.914368 | − | 0.404884i | \(-0.867312\pi\) | ||||
−0.914368 | + | 0.404884i | \(0.867312\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.70928 | 0.108759 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.40522 | 0.469287 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.41628 | 0.278753 | 0.139377 | − | 0.990239i | \(-0.455490\pi\) | ||||
0.139377 | + | 0.990239i | \(0.455490\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.86603 | −0.243055 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.34244 | −0.520387 | −0.260194 | − | 0.965556i | \(-0.583786\pi\) | ||||
−0.260194 | + | 0.965556i | \(0.583786\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −24.2595 | −1.50741 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.34017 | 0.206752 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.95055 | −0.490252 | −0.245126 | − | 0.969491i | \(-0.578829\pi\) | ||||
−0.245126 | + | 0.969491i | \(0.578829\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9.44521 | −0.578038 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.41855 | −0.391346 | −0.195673 | − | 0.980669i | \(-0.562689\pi\) | ||||
−0.195673 | + | 0.980669i | \(0.562689\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.9555 | −1.09072 | −0.545359 | − | 0.838203i | \(-0.683607\pi\) | ||||
−0.545359 | + | 0.838203i | \(0.683607\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.24846 | −0.196606 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.86991 | 0.112352 | 0.0561759 | − | 0.998421i | \(-0.482109\pi\) | ||||
0.0561759 | + | 0.998421i | \(0.482109\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.87936 | −0.471725 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.77924 | 0.404416 | 0.202208 | − | 0.979343i | \(-0.435188\pi\) | ||||
0.202208 | + | 0.979343i | \(0.435188\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.73206 | −0.578511 | −0.289256 | − | 0.957252i | \(-0.593408\pi\) | ||||
−0.289256 | + | 0.957252i | \(0.593408\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 28.5464 | 1.68504 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.16290 | 0.0684058 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.49693 | −0.146373 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −26.9939 | −1.57700 | −0.788499 | − | 0.615036i | \(-0.789141\pi\) | ||||
−0.788499 | + | 0.615036i | \(0.789141\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.460811 | −0.0267390 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.38962 | 0.485184 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.6453 | 0.728861 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.72979 | 0.444065 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.95055 | 0.453762 | 0.226881 | − | 0.973922i | \(-0.427147\pi\) | ||||
0.226881 | + | 0.973922i | \(0.427147\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.89269 | −0.107672 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −16.2557 | −0.921773 | −0.460887 | − | 0.887459i | \(-0.652469\pi\) | ||||
−0.460887 | + | 0.887459i | \(0.652469\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.4885 | −0.649369 | −0.324685 | − | 0.945822i | \(-0.605258\pi\) | ||||
−0.324685 | + | 0.945822i | \(0.605258\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.18568 | −0.403588 | −0.201794 | − | 0.979428i | \(-0.564677\pi\) | ||||
−0.201794 | + | 0.979428i | \(0.564677\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.53919 | −0.0861780 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.17727 | 0.400596 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.28458 | −0.405325 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −11.2267 | −0.620839 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.44134 | −0.134595 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.49466 | −0.521874 | −0.260937 | − | 0.965356i | \(-0.584031\pi\) | ||||
−0.260937 | + | 0.965356i | \(0.584031\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.46800 | 0.409244 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.10731 | 0.169266 | 0.0846329 | − | 0.996412i | \(-0.473028\pi\) | ||||
0.0846329 | + | 0.996412i | \(0.473028\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −17.9155 | −0.973035 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.63090 | 0.196624 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.1990 | 0.604690 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.99386 | 0.375450 | 0.187725 | − | 0.982222i | \(-0.439889\pi\) | ||||
0.187725 | + | 0.982222i | \(0.439889\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.52586 | 0.295792 | 0.147896 | − | 0.989003i | \(-0.452750\pi\) | ||||
0.147896 | + | 0.989003i | \(0.452750\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 24.3051 | 1.29363 | 0.646815 | − | 0.762647i | \(-0.276101\pi\) | ||||
0.646815 | + | 0.762647i | \(0.276101\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 13.8443 | 0.732717 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −30.9493 | −1.63344 | −0.816722 | − | 0.577032i | \(-0.804211\pi\) | ||||
−0.816722 | + | 0.577032i | \(0.804211\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.0784 | −0.846230 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10.7877 | −0.566205 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 28.1978 | 1.47191 | 0.735956 | − | 0.677029i | \(-0.236733\pi\) | ||||
0.735956 | + | 0.677029i | \(0.236733\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.78765 | −0.457467 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 28.2918 | 1.46884 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −21.6719 | −1.12213 | −0.561065 | − | 0.827772i | \(-0.689608\pi\) | ||||
−0.561065 | + | 0.827772i | \(0.689608\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.34017 | 0.172028 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.1350 | −0.828800 | −0.414400 | − | 0.910095i | \(-0.636009\pi\) | ||||
−0.414400 | + | 0.910095i | \(0.636009\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −11.2267 | −0.575162 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −29.3256 | −1.49847 | −0.749235 | − | 0.662305i | \(-0.769578\pi\) | ||||
−0.749235 | + | 0.662305i | \(0.769578\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.89269 | −0.197877 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.39803 | −0.324393 | −0.162197 | − | 0.986758i | \(-0.551858\pi\) | ||||
−0.162197 | + | 0.986758i | \(0.551858\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −35.7548 | −1.80820 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −13.4947 | −0.680716 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −29.4863 | −1.47987 | −0.739936 | − | 0.672677i | \(-0.765144\pi\) | ||||
−0.739936 | + | 0.672677i | \(0.765144\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5.55252 | −0.277974 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.99159 | 0.498956 | 0.249478 | − | 0.968380i | \(-0.419741\pi\) | ||||
0.249478 | + | 0.968380i | \(0.419741\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.87936 | −0.392499 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.44134 | −0.170581 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 31.8225 | 1.57352 | 0.786762 | − | 0.617257i | \(-0.211756\pi\) | ||||
0.786762 | + | 0.617257i | \(0.211756\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.65983 | 0.0818732 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 10.6391 | 0.523517 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 14.6803 | 0.718900 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.37525 | −0.116038 | −0.0580192 | − | 0.998315i | \(-0.518478\pi\) | ||||
−0.0580192 | + | 0.998315i | \(0.518478\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.3090 | 0.697377 | 0.348688 | − | 0.937239i | \(-0.386627\pi\) | ||||
0.348688 | + | 0.937239i | \(0.386627\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.751536 | 0.0365409 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 26.2423 | 1.26995 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.460811 | −0.0222482 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −17.5402 | −0.844883 | −0.422442 | − | 0.906390i | \(-0.638827\pi\) | ||||
−0.422442 | + | 0.906390i | \(0.638827\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 35.0082 | 1.68239 | 0.841194 | − | 0.540733i | \(-0.181853\pi\) | ||||
0.841194 | + | 0.540733i | \(0.181853\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 14.3402 | 0.685984 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.7610 | −0.513594 | −0.256797 | − | 0.966465i | \(-0.582667\pi\) | ||||
−0.256797 | + | 0.966465i | \(0.582667\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.55252 | 0.169168 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 37.6658 | 1.78956 | 0.894778 | − | 0.446511i | \(-0.147334\pi\) | ||||
0.894778 | + | 0.446511i | \(0.147334\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.1834 | 0.481659 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 31.9299 | 1.50686 | 0.753432 | − | 0.657526i | \(-0.228397\pi\) | ||||
0.753432 | + | 0.657526i | \(0.228397\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.04945 | 0.190681 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.34736 | 0.0633045 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.2579 | 0.713735 | 0.356868 | − | 0.934155i | \(-0.383845\pi\) | ||||
0.356868 | + | 0.934155i | \(0.383845\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.26180 | −0.198924 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.73206 | 0.266969 | 0.133484 | − | 0.991051i | \(-0.457383\pi\) | ||||
0.133484 | + | 0.991051i | \(0.457383\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.6959 | −0.636505 | −0.318252 | − | 0.948006i | \(-0.603096\pi\) | ||||
−0.318252 | + | 0.948006i | \(0.603096\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −21.6430 | −1.00152 | −0.500759 | − | 0.865586i | \(-0.666946\pi\) | ||||
−0.500759 | + | 0.865586i | \(0.666946\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16.1050 | −0.743662 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −18.9649 | −0.873858 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.79380 | 0.0824788 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.70928 | −0.398770 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −13.1990 | −0.603078 | −0.301539 | − | 0.953454i | \(-0.597500\pi\) | ||||
−0.301539 | + | 0.953454i | \(0.597500\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.46800 | 0.340511 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −27.2534 | −1.24007 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.51867 | 0.204760 | 0.102380 | − | 0.994745i | \(-0.467354\pi\) | ||||
0.102380 | + | 0.994745i | \(0.467354\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.07611 | 0.274771 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.15061 | −0.232444 | −0.116222 | − | 0.993223i | \(-0.537078\pi\) | ||||
−0.116222 | + | 0.993223i | \(0.537078\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −14.2351 | −0.641118 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −26.7442 | −1.19964 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.3991 | 0.555059 | 0.277529 | − | 0.960717i | \(-0.410484\pi\) | ||||
0.277529 | + | 0.960717i | \(0.410484\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −16.1483 | −0.721455 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18.6042 | 0.829522 | 0.414761 | − | 0.909930i | \(-0.363865\pi\) | ||||
0.414761 | + | 0.909930i | \(0.363865\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.0761103 | −0.00337353 | −0.00168677 | − | 0.999999i | \(-0.500537\pi\) | ||||
−0.00168677 | + | 0.999999i | \(0.500537\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −44.8554 | −1.98428 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.70928 | 0.0754664 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.346316 | −0.0152310 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −22.3112 | −0.979355 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.8432 | −0.694105 | −0.347053 | − | 0.937846i | \(-0.612817\pi\) | ||||
−0.347053 | + | 0.937846i | \(0.612817\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.97334 | 0.173742 | 0.0868710 | − | 0.996220i | \(-0.472313\pi\) | ||||
0.0868710 | + | 0.996220i | \(0.472313\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 33.5802 | 1.46278 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 47.3857 | 2.06025 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.27513 | −0.142128 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.78765 | −0.380636 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9.52586 | −0.411071 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.63704 | −0.0705123 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −42.2739 | −1.81750 | −0.908749 | − | 0.417344i | \(-0.862961\pi\) | ||||
−0.908749 | + | 0.417344i | \(0.862961\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −19.5730 | −0.839959 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 37.6781 | 1.61100 | 0.805499 | − | 0.592597i | \(-0.201897\pi\) | ||||
0.805499 | + | 0.592597i | \(0.201897\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8.07838 | −0.344777 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.70928 | 0.243223 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 39.6514 | 1.68615 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.33630 | 0.183735 | 0.0918674 | − | 0.995771i | \(-0.470716\pi\) | ||||
0.0918674 | + | 0.995771i | \(0.470716\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.89269 | −0.164643 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.96388 | 0.0829152 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18.0183 | −0.759379 | −0.379689 | − | 0.925114i | \(-0.623969\pi\) | ||||
−0.379689 | + | 0.925114i | \(0.623969\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.24846 | −0.136423 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −41.9854 | −1.76012 | −0.880061 | − | 0.474861i | \(-0.842498\pi\) | ||||
−0.880061 | + | 0.474861i | \(0.842498\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 39.6925 | 1.66108 | 0.830539 | − | 0.556961i | \(-0.188033\pi\) | ||||
0.830539 | + | 0.556961i | \(0.188033\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.52359 | −0.188976 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23.8043 | −0.990986 | −0.495493 | − | 0.868612i | \(-0.665013\pi\) | ||||
−0.495493 | + | 0.868612i | \(0.665013\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.38962 | 0.182426 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −24.0556 | −0.997994 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.01333 | 0.166215 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.87936 | −0.0775696 | −0.0387848 | − | 0.999248i | \(-0.512349\pi\) | ||||
−0.0387848 | + | 0.999248i | \(0.512349\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13.4680 | −0.554939 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 10.6309 | 0.437297 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.10504 | 0.0453785 | 0.0226893 | − | 0.999743i | \(-0.492777\pi\) | ||||
0.0226893 | + | 0.999743i | \(0.492777\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −17.7321 | −0.725725 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 26.4885 | 1.08229 | 0.541146 | − | 0.840929i | \(-0.317991\pi\) | ||||
0.541146 | + | 0.840929i | \(0.317991\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.43680 | −0.344144 | −0.172072 | − | 0.985084i | \(-0.555046\pi\) | ||||
−0.172072 | + | 0.985084i | \(0.555046\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.95774 | 0.201895 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 31.0784 | 1.26143 | 0.630716 | − | 0.776014i | \(-0.282761\pi\) | ||||
0.630716 | + | 0.776014i | \(0.282761\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −10.8504 | −0.439682 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.751536 | 0.0304039 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.47027 | 0.180552 | 0.0902762 | − | 0.995917i | \(-0.471225\pi\) | ||||
0.0902762 | + | 0.995917i | \(0.471225\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.60197 | 0.386561 | 0.193280 | − | 0.981144i | \(-0.438087\pi\) | ||||
0.193280 | + | 0.981144i | \(0.438087\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15.8348 | 0.636456 | 0.318228 | − | 0.948014i | \(-0.396912\pi\) | ||||
0.318228 | + | 0.948014i | \(0.396912\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.38962 | 0.336664 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 30.6824 | 1.22927 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.787653 | −0.0314558 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −31.8271 | −1.26903 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.88655 | 0.274149 | 0.137075 | − | 0.990561i | \(-0.456230\pi\) | ||||
0.137075 | + | 0.990561i | \(0.456230\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 14.9132 | 0.592747 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.55252 | 0.140756 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.23287 | 0.325687 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.73820 | −0.0686550 | −0.0343275 | − | 0.999411i | \(-0.510929\pi\) | ||||
−0.0343275 | + | 0.999411i | \(0.510929\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.4536 | 0.451687 | 0.225843 | − | 0.974164i | \(-0.427486\pi\) | ||||
0.225843 | + | 0.974164i | \(0.427486\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 23.9688 | 0.942311 | 0.471155 | − | 0.882050i | \(-0.343837\pi\) | ||||
0.471155 | + | 0.882050i | \(0.343837\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.50921 | 0.0592419 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 25.5958 | 1.00318 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 25.2967 | 0.989936 | 0.494968 | − | 0.868911i | \(-0.335180\pi\) | ||||
0.494968 | + | 0.868911i | \(0.335180\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 13.8082 | 0.538708 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 40.4040 | 1.57392 | 0.786958 | − | 0.617006i | \(-0.211655\pi\) | ||||
0.786958 | + | 0.617006i | \(0.211655\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.160631 | 0.00624783 | 0.00312391 | − | 0.999995i | \(-0.499006\pi\) | ||||
0.00312391 | + | 0.999995i | \(0.499006\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.26180 | −0.165514 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 28.0228 | 1.08505 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 20.5464 | 0.794369 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.72261 | 0.143710 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.89723 | 0.188774 | 0.0943871 | − | 0.995536i | \(-0.469911\pi\) | ||||
0.0943871 | + | 0.995536i | \(0.469911\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14.7792 | −0.568012 | −0.284006 | − | 0.958822i | \(-0.591664\pi\) | ||||
−0.284006 | + | 0.958822i | \(0.591664\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.11118 | 0.311279 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 21.6381 | 0.829173 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 22.2462 | 0.851227 | 0.425614 | − | 0.904905i | \(-0.360058\pi\) | ||||
0.425614 | + | 0.904905i | \(0.360058\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 19.3607 | 0.738656 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8.70928 | −0.331797 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13.6732 | −0.520151 | −0.260076 | − | 0.965588i | \(-0.583748\pi\) | ||||
−0.260076 | + | 0.965588i | \(0.583748\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.49693 | 0.0568636 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 37.4512 | 1.41856 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −24.0722 | −0.910496 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.34632 | −0.239697 | −0.119849 | − | 0.992792i | \(-0.538241\pi\) | ||||
−0.119849 | + | 0.992792i | \(0.538241\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.7649 | 0.481436 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −25.1100 | −0.944357 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 41.5136 | 1.55907 | 0.779537 | − | 0.626356i | \(-0.215454\pi\) | ||||
0.779537 | + | 0.626356i | \(0.215454\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −12.2062 | −0.457768 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −66.1049 | −2.47565 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −14.2423 | −0.531889 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −46.9854 | −1.75226 | −0.876131 | − | 0.482074i | \(-0.839884\pi\) | ||||
−0.876131 | + | 0.482074i | \(0.839884\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.14834 | 0.228976 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −28.3896 | −1.05582 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 48.7754 | 1.80898 | 0.904489 | − | 0.426497i | \(-0.140252\pi\) | ||||
0.904489 | + | 0.426497i | \(0.140252\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 16.5899 | 0.613598 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 46.6225 | 1.72204 | 0.861020 | − | 0.508570i | \(-0.169826\pi\) | ||||
0.861020 | + | 0.508570i | \(0.169826\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.28458 | −0.0841536 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23.6837 | 0.871217 | 0.435609 | − | 0.900136i | \(-0.356533\pi\) | ||||
0.435609 | + | 0.900136i | \(0.356533\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.70928 | 0.0627918 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −12.9044 | −0.473417 | −0.236709 | − | 0.971581i | \(-0.576069\pi\) | ||||
−0.236709 | + | 0.971581i | \(0.576069\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7.40522 | 0.270943 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −23.3151 | −0.851916 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.17501 | −0.298310 | −0.149155 | − | 0.988814i | \(-0.547655\pi\) | ||||
−0.149155 | + | 0.988814i | \(0.547655\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.41628 | 0.160938 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.83096 | 0.175584 | 0.0877921 | − | 0.996139i | \(-0.472019\pi\) | ||||
0.0877921 | + | 0.996139i | \(0.472019\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.86603 | −0.140328 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −41.4413 | −1.50225 | −0.751124 | − | 0.660162i | \(-0.770488\pi\) | ||||
−0.751124 | + | 0.660162i | \(0.770488\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 36.4696 | 1.32029 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.27513 | −0.118258 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −18.1711 | −0.655268 | −0.327634 | − | 0.944805i | \(-0.606251\pi\) | ||||
−0.327634 | + | 0.944805i | \(0.606251\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.34244 | −0.300446 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −23.6598 | −0.850985 | −0.425492 | − | 0.904962i | \(-0.639899\pi\) | ||||
−0.425492 | + | 0.904962i | \(0.639899\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −24.2595 | −0.870306 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −15.0205 | −0.538166 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.79380 | −0.135753 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.34017 | 0.119368 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 39.2089 | 1.39764 | 0.698822 | − | 0.715295i | \(-0.253708\pi\) | ||||
0.698822 | + | 0.715295i | \(0.253708\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −7.95055 | −0.283047 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 58.1978 | 2.06928 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.07838 | −0.286872 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −40.7998 | −1.44520 | −0.722601 | − | 0.691266i | \(-0.757054\pi\) | ||||
−0.722601 | + | 0.691266i | \(0.757054\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.20289 | −0.113310 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.44521 | −0.333730 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.36296 | −0.224544 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.41855 | −0.225944 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 13.0205 | 0.457777 | 0.228889 | − | 0.973453i | \(-0.426491\pi\) | ||||
0.228889 | + | 0.973453i | \(0.426491\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −47.2628 | −1.65962 | −0.829811 | − | 0.558044i | \(-0.811552\pi\) | ||||
−0.829811 | + | 0.558044i | \(0.811552\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −17.9555 | −0.629726 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.65368 | −0.232783 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.24846 | −0.113511 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −43.4512 | −1.51646 | −0.758228 | − | 0.651989i | \(-0.773935\pi\) | ||||
−0.758228 | + | 0.651989i | \(0.773935\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 36.7936 | 1.28254 | 0.641272 | − | 0.767313i | \(-0.278407\pi\) | ||||
0.641272 | + | 0.767313i | \(0.278407\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 24.5018 | 0.852013 | 0.426006 | − | 0.904720i | \(-0.359920\pi\) | ||||
0.426006 | + | 0.904720i | \(0.359920\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 40.4908 | 1.40630 | 0.703152 | − | 0.711040i | \(-0.251776\pi\) | ||||
0.703152 | + | 0.711040i | \(0.251776\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.86991 | 0.0648663 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −15.1401 | −0.524574 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.87936 | −0.272351 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −25.4245 | −0.877752 | −0.438876 | − | 0.898548i | \(-0.644623\pi\) | ||||
−0.438876 | + | 0.898548i | \(0.644623\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.8432 | −0.615284 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6.77924 | 0.233490 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 35.0433 | 1.20410 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −9.73206 | −0.334003 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 62.6537 | 2.14774 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21.1917 | −0.725588 | −0.362794 | − | 0.931869i | \(-0.618177\pi\) | ||||
−0.362794 | + | 0.931869i | \(0.618177\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −18.3135 | −0.625578 | −0.312789 | − | 0.949823i | \(-0.601263\pi\) | ||||
−0.312789 | + | 0.949823i | \(0.601263\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.8865 | 0.576162 | 0.288081 | − | 0.957606i | \(-0.406983\pi\) | ||||
0.288081 | + | 0.957606i | \(0.406983\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 28.5464 | 0.972858 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 10.0095 | 0.340726 | 0.170363 | − | 0.985381i | \(-0.445506\pi\) | ||||
0.170363 | + | 0.985381i | \(0.445506\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.16290 | 0.0394941 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.62475 | 0.190807 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.95774 | 0.167987 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.49693 | −0.0845082 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −38.7070 | −1.30704 | −0.653521 | − | 0.756908i | \(-0.726709\pi\) | ||||
−0.653521 | + | 0.756908i | \(0.726709\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −26.9939 | −0.910480 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −41.9998 | −1.41501 | −0.707505 | − | 0.706708i | \(-0.750179\pi\) | ||||
−0.707505 | + | 0.706708i | \(0.750179\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.4846 | 0.891279 | 0.445640 | − | 0.895212i | \(-0.352976\pi\) | ||||
0.445640 | + | 0.895212i | \(0.352976\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −43.9916 | −1.47709 | −0.738547 | − | 0.674203i | \(-0.764487\pi\) | ||||
−0.738547 | + | 0.674203i | \(0.764487\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 36.4696 | 1.22315 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.460811 | −0.0154378 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.28458 | 0.0429869 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.38962 | 0.280121 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −26.3184 | −0.877769 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 37.1171 | 1.23655 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 12.6453 | 0.420808 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −29.1917 | −0.969293 | −0.484646 | − | 0.874710i | \(-0.661052\pi\) | ||||
−0.484646 | + | 0.874710i | \(0.661052\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.72979 | 0.256381 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 38.6453 | 1.28038 | 0.640188 | − | 0.768219i | \(-0.278857\pi\) | ||||
0.640188 | + | 0.768219i | \(0.278857\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.41241 | −0.112934 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 43.8369 | 1.44762 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.3857 | 0.804412 | 0.402206 | − | 0.915549i | \(-0.368244\pi\) | ||||
0.402206 | + | 0.915549i | \(0.368244\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.95055 | 0.261980 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8.23287 | 0.270988 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.89269 | −0.0621642 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −7.14608 | −0.234455 | −0.117228 | − | 0.993105i | \(-0.537401\pi\) | ||||
−0.117228 | + | 0.993105i | \(0.537401\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.07223 | 0.199009 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −16.2557 | −0.532186 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −9.76487 | −0.319004 | −0.159502 | − | 0.987198i | \(-0.550989\pi\) | ||||
−0.159502 | + | 0.987198i | \(0.550989\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −11.4885 | −0.374914 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 32.6453 | 1.06421 | 0.532103 | − | 0.846680i | \(-0.321402\pi\) | ||||
0.532103 | + | 0.846680i | \(0.321402\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −73.7251 | −2.40082 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −30.8466 | −1.00238 | −0.501189 | − | 0.865338i | \(-0.667104\pi\) | ||||
−0.501189 | + | 0.865338i | \(0.667104\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 13.8082 | 0.448232 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7.18568 | −0.233012 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −35.6596 | −1.15513 | −0.577565 | − | 0.816345i | \(-0.695997\pi\) | ||||
−0.577565 | + | 0.816345i | \(0.695997\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.53919 | −0.0497549 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.39189 | −0.174113 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 31.0843 | 1.00272 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.17727 | 0.231284 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −31.4112 | −1.01012 | −0.505058 | − | 0.863086i | \(-0.668529\pi\) | ||||
−0.505058 | + | 0.863086i | \(0.668529\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7.28458 | −0.234014 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −24.0722 | −0.772515 | −0.386257 | − | 0.922391i | \(-0.626232\pi\) | ||||
−0.386257 | + | 0.922391i | \(0.626232\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −47.6886 | −1.52883 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 9.99547 | 0.319783 | 0.159892 | − | 0.987135i | \(-0.448886\pi\) | ||||
0.159892 | + | 0.987135i | \(0.448886\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.35246 | 0.139105 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11.2267 | −0.358442 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −25.4112 | −0.810491 | −0.405245 | − | 0.914208i | \(-0.632814\pi\) | ||||
−0.405245 | + | 0.914208i | \(0.632814\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.44134 | −0.0777086 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −32.6582 | −1.03847 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 38.0638 | 1.20914 | 0.604569 | − | 0.796553i | \(-0.293346\pi\) | ||||
0.604569 | + | 0.796553i | \(0.293346\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −9.49466 | −0.301304 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −28.5441 | −0.904001 | −0.452001 | − | 0.892018i | \(-0.649289\pi\) | ||||
−0.452001 | + | 0.892018i | \(0.649289\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.46800 | 0.236277 |
(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 | 7800.2.a.bo.1.1 | yes | 3 | |
5.4 | even | 2 | 7800.2.a.bl.1.3 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7800.2.a.bl.1.3 | ✓ | 3 | 5.4 | even | 2 | ||
7800.2.a.bo.1.1 | yes | 3 | 1.1 | even | 1 | trivial |