Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1805,2,Mod(1,1805)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1805, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1805.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1805 = 5 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1805.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: | \(14.4129975648\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.361.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 6x + 7 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 95) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.22188\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1805.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.28514 | 1.61584 | 0.807920 | − | 0.589292i | \(-0.200593\pi\) | ||||
0.807920 | + | 0.589292i | \(0.200593\pi\) | |||||||
\(3\) | −2.50702 | −1.44743 | −0.723714 | − | 0.690100i | \(-0.757566\pi\) | ||||
−0.723714 | + | 0.690100i | \(0.757566\pi\) | |||||||
\(4\) | 3.22188 | 1.61094 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −5.72889 | −2.33881 | ||||||||
\(7\) | 3.50702 | 1.32553 | 0.662764 | − | 0.748828i | \(-0.269383\pi\) | ||||
0.662764 | + | 0.748828i | \(0.269383\pi\) | |||||||
\(8\) | 2.79216 | 0.987178 | ||||||||
\(9\) | 3.28514 | 1.09505 | ||||||||
\(10\) | −2.28514 | −0.722626 | ||||||||
\(11\) | −4.50702 | −1.35892 | −0.679459 | − | 0.733714i | \(-0.737785\pi\) | ||||
−0.679459 | + | 0.733714i | \(0.737785\pi\) | |||||||
\(12\) | −8.07730 | −2.33172 | ||||||||
\(13\) | −5.00000 | −1.38675 | −0.693375 | − | 0.720577i | \(-0.743877\pi\) | ||||
−0.693375 | + | 0.720577i | \(0.743877\pi\) | |||||||
\(14\) | 8.01404 | 2.14184 | ||||||||
\(15\) | 2.50702 | 0.647309 | ||||||||
\(16\) | −0.0632663 | −0.0158166 | ||||||||
\(17\) | 0.158610 | 0.0384685 | 0.0192343 | − | 0.999815i | \(-0.493877\pi\) | ||||
0.0192343 | + | 0.999815i | \(0.493877\pi\) | |||||||
\(18\) | 7.50702 | 1.76942 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | −3.22188 | −0.720433 | ||||||||
\(21\) | −8.79216 | −1.91861 | ||||||||
\(22\) | −10.2992 | −2.19579 | ||||||||
\(23\) | 1.15861 | 0.241587 | 0.120793 | − | 0.992678i | \(-0.461456\pi\) | ||||
0.120793 | + | 0.992678i | \(0.461456\pi\) | |||||||
\(24\) | −7.00000 | −1.42887 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −11.4257 | −2.24077 | ||||||||
\(27\) | −0.714858 | −0.137574 | ||||||||
\(28\) | 11.2992 | 2.13534 | ||||||||
\(29\) | −3.50702 | −0.651237 | −0.325619 | − | 0.945501i | \(-0.605573\pi\) | ||||
−0.325619 | + | 0.945501i | \(0.605573\pi\) | |||||||
\(30\) | 5.72889 | 1.04595 | ||||||||
\(31\) | −2.28514 | −0.410424 | −0.205212 | − | 0.978718i | \(-0.565788\pi\) | ||||
−0.205212 | + | 0.978718i | \(0.565788\pi\) | |||||||
\(32\) | −5.72889 | −1.01274 | ||||||||
\(33\) | 11.2992 | 1.96693 | ||||||||
\(34\) | 0.362446 | 0.0621590 | ||||||||
\(35\) | −3.50702 | −0.592794 | ||||||||
\(36\) | 10.5843 | 1.76405 | ||||||||
\(37\) | −10.9648 | −1.80260 | −0.901302 | − | 0.433192i | \(-0.857387\pi\) | ||||
−0.901302 | + | 0.433192i | \(0.857387\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 12.5351 | 2.00722 | ||||||||
\(40\) | −2.79216 | −0.441479 | ||||||||
\(41\) | 6.07730 | 0.949115 | 0.474558 | − | 0.880224i | \(-0.342608\pi\) | ||||
0.474558 | + | 0.880224i | \(0.342608\pi\) | |||||||
\(42\) | −20.0913 | −3.10016 | ||||||||
\(43\) | −3.34841 | −0.510628 | −0.255314 | − | 0.966858i | \(-0.582179\pi\) | ||||
−0.255314 | + | 0.966858i | \(0.582179\pi\) | |||||||
\(44\) | −14.5211 | −2.18913 | ||||||||
\(45\) | −3.28514 | −0.489720 | ||||||||
\(46\) | 2.64759 | 0.390366 | ||||||||
\(47\) | 3.06327 | 0.446823 | 0.223412 | − | 0.974724i | \(-0.428281\pi\) | ||||
0.223412 | + | 0.974724i | \(0.428281\pi\) | |||||||
\(48\) | 0.158610 | 0.0228934 | ||||||||
\(49\) | 5.29918 | 0.757026 | ||||||||
\(50\) | 2.28514 | 0.323168 | ||||||||
\(51\) | −0.397638 | −0.0556804 | ||||||||
\(52\) | −16.1094 | −2.23397 | ||||||||
\(53\) | −5.74293 | −0.788852 | −0.394426 | − | 0.918928i | \(-0.629057\pi\) | ||||
−0.394426 | + | 0.918928i | \(0.629057\pi\) | |||||||
\(54\) | −1.63355 | −0.222298 | ||||||||
\(55\) | 4.50702 | 0.607726 | ||||||||
\(56\) | 9.79216 | 1.30853 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −8.01404 | −1.05229 | ||||||||
\(59\) | 3.06327 | 0.398803 | 0.199402 | − | 0.979918i | \(-0.436100\pi\) | ||||
0.199402 | + | 0.979918i | \(0.436100\pi\) | |||||||
\(60\) | 8.07730 | 1.04278 | ||||||||
\(61\) | −0.873467 | −0.111836 | −0.0559180 | − | 0.998435i | \(-0.517809\pi\) | ||||
−0.0559180 | + | 0.998435i | \(0.517809\pi\) | |||||||
\(62\) | −5.22188 | −0.663179 | ||||||||
\(63\) | 11.5211 | 1.45152 | ||||||||
\(64\) | −12.9648 | −1.62060 | ||||||||
\(65\) | 5.00000 | 0.620174 | ||||||||
\(66\) | 25.8202 | 3.17825 | ||||||||
\(67\) | −8.44375 | −1.03157 | −0.515784 | − | 0.856719i | \(-0.672499\pi\) | ||||
−0.515784 | + | 0.856719i | \(0.672499\pi\) | |||||||
\(68\) | 0.511021 | 0.0619704 | ||||||||
\(69\) | −2.90466 | −0.349680 | ||||||||
\(70\) | −8.01404 | −0.957861 | ||||||||
\(71\) | −16.2359 | −1.92685 | −0.963424 | − | 0.267981i | \(-0.913644\pi\) | ||||
−0.963424 | + | 0.267981i | \(0.913644\pi\) | |||||||
\(72\) | 9.17265 | 1.08101 | ||||||||
\(73\) | −7.15861 | −0.837852 | −0.418926 | − | 0.908020i | \(-0.637593\pi\) | ||||
−0.418926 | + | 0.908020i | \(0.637593\pi\) | |||||||
\(74\) | −25.0561 | −2.91272 | ||||||||
\(75\) | −2.50702 | −0.289486 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −15.8062 | −1.80128 | ||||||||
\(78\) | 28.6445 | 3.24335 | ||||||||
\(79\) | −10.1265 | −1.13932 | −0.569662 | − | 0.821879i | \(-0.692926\pi\) | ||||
−0.569662 | + | 0.821879i | \(0.692926\pi\) | |||||||
\(80\) | 0.0632663 | 0.00707339 | ||||||||
\(81\) | −8.06327 | −0.895918 | ||||||||
\(82\) | 13.8875 | 1.53362 | ||||||||
\(83\) | 4.85543 | 0.532952 | 0.266476 | − | 0.963841i | \(-0.414141\pi\) | ||||
0.266476 | + | 0.963841i | \(0.414141\pi\) | |||||||
\(84\) | −28.3273 | −3.09076 | ||||||||
\(85\) | −0.158610 | −0.0172037 | ||||||||
\(86\) | −7.65159 | −0.825092 | ||||||||
\(87\) | 8.79216 | 0.942619 | ||||||||
\(88\) | −12.5843 | −1.34149 | ||||||||
\(89\) | −1.11250 | −0.117924 | −0.0589621 | − | 0.998260i | \(-0.518779\pi\) | ||||
−0.0589621 | + | 0.998260i | \(0.518779\pi\) | |||||||
\(90\) | −7.50702 | −0.791309 | ||||||||
\(91\) | −17.5351 | −1.83818 | ||||||||
\(92\) | 3.73290 | 0.389181 | ||||||||
\(93\) | 5.72889 | 0.594059 | ||||||||
\(94\) | 7.00000 | 0.721995 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 14.3624 | 1.46586 | ||||||||
\(97\) | 1.61951 | 0.164437 | 0.0822184 | − | 0.996614i | \(-0.473800\pi\) | ||||
0.0822184 | + | 0.996614i | \(0.473800\pi\) | |||||||
\(98\) | 12.1094 | 1.22323 | ||||||||
\(99\) | −14.8062 | −1.48808 | ||||||||
\(100\) | 3.22188 | 0.322188 | ||||||||
\(101\) | 12.3132 | 1.22521 | 0.612605 | − | 0.790389i | \(-0.290121\pi\) | ||||
0.612605 | + | 0.790389i | \(0.290121\pi\) | |||||||
\(102\) | −0.908659 | −0.0899707 | ||||||||
\(103\) | 10.6164 | 1.04606 | 0.523032 | − | 0.852313i | \(-0.324801\pi\) | ||||
0.523032 | + | 0.852313i | \(0.324801\pi\) | |||||||
\(104\) | −13.9608 | −1.36897 | ||||||||
\(105\) | 8.79216 | 0.858027 | ||||||||
\(106\) | −13.1234 | −1.27466 | ||||||||
\(107\) | −2.17265 | −0.210038 | −0.105019 | − | 0.994470i | \(-0.533490\pi\) | ||||
−0.105019 | + | 0.994470i | \(0.533490\pi\) | |||||||
\(108\) | −2.30318 | −0.221624 | ||||||||
\(109\) | 15.8202 | 1.51530 | 0.757652 | − | 0.652659i | \(-0.226347\pi\) | ||||
0.757652 | + | 0.652659i | \(0.226347\pi\) | |||||||
\(110\) | 10.2992 | 0.981988 | ||||||||
\(111\) | 27.4890 | 2.60914 | ||||||||
\(112\) | −0.221876 | −0.0209653 | ||||||||
\(113\) | 9.83828 | 0.925507 | 0.462754 | − | 0.886487i | \(-0.346861\pi\) | ||||
0.462754 | + | 0.886487i | \(0.346861\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.15861 | −0.108041 | ||||||||
\(116\) | −11.2992 | −1.04910 | ||||||||
\(117\) | −16.4257 | −1.51856 | ||||||||
\(118\) | 7.00000 | 0.644402 | ||||||||
\(119\) | 0.556248 | 0.0509911 | ||||||||
\(120\) | 7.00000 | 0.639010 | ||||||||
\(121\) | 9.31322 | 0.846656 | ||||||||
\(122\) | −1.99600 | −0.180709 | ||||||||
\(123\) | −15.2359 | −1.37378 | ||||||||
\(124\) | −7.36245 | −0.661167 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 26.3273 | 2.34542 | ||||||||
\(127\) | 15.7109 | 1.39411 | 0.697056 | − | 0.717016i | \(-0.254493\pi\) | ||||
0.697056 | + | 0.717016i | \(0.254493\pi\) | |||||||
\(128\) | −18.1686 | −1.60590 | ||||||||
\(129\) | 8.39452 | 0.739097 | ||||||||
\(130\) | 11.4257 | 1.00210 | ||||||||
\(131\) | −11.5351 | −1.00783 | −0.503913 | − | 0.863754i | \(-0.668107\pi\) | ||||
−0.503913 | + | 0.863754i | \(0.668107\pi\) | |||||||
\(132\) | 36.4046 | 3.16861 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −19.2952 | −1.66685 | ||||||||
\(135\) | 0.714858 | 0.0615251 | ||||||||
\(136\) | 0.442864 | 0.0379753 | ||||||||
\(137\) | 0.109381 | 0.00934503 | 0.00467252 | − | 0.999989i | \(-0.498513\pi\) | ||||
0.00467252 | + | 0.999989i | \(0.498513\pi\) | |||||||
\(138\) | −6.63755 | −0.565026 | ||||||||
\(139\) | 1.44375 | 0.122457 | 0.0612287 | − | 0.998124i | \(-0.480498\pi\) | ||||
0.0612287 | + | 0.998124i | \(0.480498\pi\) | |||||||
\(140\) | −11.2992 | −0.954955 | ||||||||
\(141\) | −7.67967 | −0.646745 | ||||||||
\(142\) | −37.1014 | −3.11348 | ||||||||
\(143\) | 22.5351 | 1.88448 | ||||||||
\(144\) | −0.207839 | −0.0173199 | ||||||||
\(145\) | 3.50702 | 0.291242 | ||||||||
\(146\) | −16.3584 | −1.35383 | ||||||||
\(147\) | −13.2851 | −1.09574 | ||||||||
\(148\) | −35.3273 | −2.90388 | ||||||||
\(149\) | 1.72889 | 0.141637 | 0.0708183 | − | 0.997489i | \(-0.477439\pi\) | ||||
0.0708183 | + | 0.997489i | \(0.477439\pi\) | |||||||
\(150\) | −5.72889 | −0.467762 | ||||||||
\(151\) | −20.1406 | −1.63902 | −0.819508 | − | 0.573068i | \(-0.805753\pi\) | ||||
−0.819508 | + | 0.573068i | \(0.805753\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.521056 | 0.0421249 | ||||||||
\(154\) | −36.1194 | −2.91059 | ||||||||
\(155\) | 2.28514 | 0.183547 | ||||||||
\(156\) | 40.3865 | 3.23351 | ||||||||
\(157\) | 3.77812 | 0.301527 | 0.150764 | − | 0.988570i | \(-0.451827\pi\) | ||||
0.150764 | + | 0.988570i | \(0.451827\pi\) | |||||||
\(158\) | −23.1406 | −1.84096 | ||||||||
\(159\) | 14.3976 | 1.14181 | ||||||||
\(160\) | 5.72889 | 0.452909 | ||||||||
\(161\) | 4.06327 | 0.320230 | ||||||||
\(162\) | −18.4257 | −1.44766 | ||||||||
\(163\) | −1.61640 | −0.126606 | −0.0633031 | − | 0.997994i | \(-0.520163\pi\) | ||||
−0.0633031 | + | 0.997994i | \(0.520163\pi\) | |||||||
\(164\) | 19.5803 | 1.52897 | ||||||||
\(165\) | −11.2992 | −0.879640 | ||||||||
\(166\) | 11.0953 | 0.861166 | ||||||||
\(167\) | 6.49298 | 0.502442 | 0.251221 | − | 0.967930i | \(-0.419168\pi\) | ||||
0.251221 | + | 0.967930i | \(0.419168\pi\) | |||||||
\(168\) | −24.5491 | −1.89401 | ||||||||
\(169\) | 12.0000 | 0.923077 | ||||||||
\(170\) | −0.362446 | −0.0277983 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −10.7882 | −0.822589 | ||||||||
\(173\) | 8.52106 | 0.647844 | 0.323922 | − | 0.946084i | \(-0.394998\pi\) | ||||
0.323922 | + | 0.946084i | \(0.394998\pi\) | |||||||
\(174\) | 20.0913 | 1.52312 | ||||||||
\(175\) | 3.50702 | 0.265106 | ||||||||
\(176\) | 0.285142 | 0.0214934 | ||||||||
\(177\) | −7.67967 | −0.577239 | ||||||||
\(178\) | −2.54221 | −0.190547 | ||||||||
\(179\) | −10.2711 | −0.767698 | −0.383849 | − | 0.923396i | \(-0.625402\pi\) | ||||
−0.383849 | + | 0.923396i | \(0.625402\pi\) | |||||||
\(180\) | −10.5843 | −0.788909 | ||||||||
\(181\) | 12.2671 | 0.911807 | 0.455903 | − | 0.890029i | \(-0.349316\pi\) | ||||
0.455903 | + | 0.890029i | \(0.349316\pi\) | |||||||
\(182\) | −40.0702 | −2.97020 | ||||||||
\(183\) | 2.18980 | 0.161875 | ||||||||
\(184\) | 3.23503 | 0.238489 | ||||||||
\(185\) | 10.9648 | 0.806149 | ||||||||
\(186\) | 13.0913 | 0.959904 | ||||||||
\(187\) | −0.714858 | −0.0522756 | ||||||||
\(188\) | 9.86946 | 0.719805 | ||||||||
\(189\) | −2.50702 | −0.182359 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.71085 | 0.413223 | 0.206611 | − | 0.978423i | \(-0.433756\pi\) | ||||
0.206611 | + | 0.978423i | \(0.433756\pi\) | |||||||
\(192\) | 32.5030 | 2.34570 | ||||||||
\(193\) | −10.1586 | −0.731233 | −0.365616 | − | 0.930766i | \(-0.619142\pi\) | ||||
−0.365616 | + | 0.930766i | \(0.619142\pi\) | |||||||
\(194\) | 3.70082 | 0.265703 | ||||||||
\(195\) | −12.5351 | −0.897657 | ||||||||
\(196\) | 17.0733 | 1.21952 | ||||||||
\(197\) | 16.2038 | 1.15448 | 0.577238 | − | 0.816576i | \(-0.304131\pi\) | ||||
0.577238 | + | 0.816576i | \(0.304131\pi\) | |||||||
\(198\) | −33.8343 | −2.40450 | ||||||||
\(199\) | 0.334372 | 0.0237030 | 0.0118515 | − | 0.999930i | \(-0.496227\pi\) | ||||
0.0118515 | + | 0.999930i | \(0.496227\pi\) | |||||||
\(200\) | 2.79216 | 0.197436 | ||||||||
\(201\) | 21.1686 | 1.49312 | ||||||||
\(202\) | 28.1375 | 1.97974 | ||||||||
\(203\) | −12.2992 | −0.863233 | ||||||||
\(204\) | −1.28114 | −0.0896977 | ||||||||
\(205\) | −6.07730 | −0.424457 | ||||||||
\(206\) | 24.2600 | 1.69027 | ||||||||
\(207\) | 3.80620 | 0.264549 | ||||||||
\(208\) | 0.316332 | 0.0219336 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 20.0913 | 1.38643 | ||||||||
\(211\) | 2.02807 | 0.139618 | 0.0698092 | − | 0.997560i | \(-0.477761\pi\) | ||||
0.0698092 | + | 0.997560i | \(0.477761\pi\) | |||||||
\(212\) | −18.5030 | −1.27079 | ||||||||
\(213\) | 40.7037 | 2.78897 | ||||||||
\(214\) | −4.96481 | −0.339387 | ||||||||
\(215\) | 3.34841 | 0.228360 | ||||||||
\(216\) | −1.99600 | −0.135810 | ||||||||
\(217\) | −8.01404 | −0.544028 | ||||||||
\(218\) | 36.1515 | 2.44849 | ||||||||
\(219\) | 17.9468 | 1.21273 | ||||||||
\(220\) | 14.5211 | 0.979009 | ||||||||
\(221\) | −0.793049 | −0.0533463 | ||||||||
\(222\) | 62.8162 | 4.21595 | ||||||||
\(223\) | −19.2319 | −1.28786 | −0.643932 | − | 0.765083i | \(-0.722698\pi\) | ||||
−0.643932 | + | 0.765083i | \(0.722698\pi\) | |||||||
\(224\) | −20.0913 | −1.34241 | ||||||||
\(225\) | 3.28514 | 0.219009 | ||||||||
\(226\) | 22.4819 | 1.49547 | ||||||||
\(227\) | 4.00000 | 0.265489 | 0.132745 | − | 0.991150i | \(-0.457621\pi\) | ||||
0.132745 | + | 0.991150i | \(0.457621\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.9788 | −0.857666 | −0.428833 | − | 0.903384i | \(-0.641075\pi\) | ||||
−0.428833 | + | 0.903384i | \(0.641075\pi\) | |||||||
\(230\) | −2.64759 | −0.174577 | ||||||||
\(231\) | 39.6264 | 2.60723 | ||||||||
\(232\) | −9.79216 | −0.642887 | ||||||||
\(233\) | 27.0733 | 1.77363 | 0.886815 | − | 0.462124i | \(-0.152912\pi\) | ||||
0.886815 | + | 0.462124i | \(0.152912\pi\) | |||||||
\(234\) | −37.5351 | −2.45375 | ||||||||
\(235\) | −3.06327 | −0.199825 | ||||||||
\(236\) | 9.86946 | 0.642447 | ||||||||
\(237\) | 25.3874 | 1.64909 | ||||||||
\(238\) | 1.27111 | 0.0823935 | ||||||||
\(239\) | 20.0602 | 1.29758 | 0.648792 | − | 0.760966i | \(-0.275275\pi\) | ||||
0.648792 | + | 0.760966i | \(0.275275\pi\) | |||||||
\(240\) | −0.158610 | −0.0102382 | ||||||||
\(241\) | −21.5843 | −1.39037 | −0.695184 | − | 0.718832i | \(-0.744677\pi\) | ||||
−0.695184 | + | 0.718832i | \(0.744677\pi\) | |||||||
\(242\) | 21.2820 | 1.36806 | ||||||||
\(243\) | 22.3593 | 1.43435 | ||||||||
\(244\) | −2.81420 | −0.180161 | ||||||||
\(245\) | −5.29918 | −0.338552 | ||||||||
\(246\) | −34.8162 | −2.21980 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −6.38049 | −0.405161 | ||||||||
\(249\) | −12.1726 | −0.771410 | ||||||||
\(250\) | −2.28514 | −0.144525 | ||||||||
\(251\) | −7.26799 | −0.458752 | −0.229376 | − | 0.973338i | \(-0.573668\pi\) | ||||
−0.229376 | + | 0.973338i | \(0.573668\pi\) | |||||||
\(252\) | 37.1194 | 2.33830 | ||||||||
\(253\) | −5.22188 | −0.328297 | ||||||||
\(254\) | 35.9015 | 2.25266 | ||||||||
\(255\) | 0.397638 | 0.0249010 | ||||||||
\(256\) | −15.5883 | −0.974270 | ||||||||
\(257\) | 15.0773 | 0.940496 | 0.470248 | − | 0.882534i | \(-0.344164\pi\) | ||||
0.470248 | + | 0.882534i | \(0.344164\pi\) | |||||||
\(258\) | 19.1827 | 1.19426 | ||||||||
\(259\) | −38.4538 | −2.38940 | ||||||||
\(260\) | 16.1094 | 0.999061 | ||||||||
\(261\) | −11.5211 | −0.713135 | ||||||||
\(262\) | −26.3593 | −1.62848 | ||||||||
\(263\) | 20.1546 | 1.24279 | 0.621393 | − | 0.783499i | \(-0.286567\pi\) | ||||
0.621393 | + | 0.783499i | \(0.286567\pi\) | |||||||
\(264\) | 31.5491 | 1.94171 | ||||||||
\(265\) | 5.74293 | 0.352786 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.78905 | 0.170687 | ||||||||
\(268\) | −27.2047 | −1.66179 | ||||||||
\(269\) | −7.72489 | −0.470995 | −0.235497 | − | 0.971875i | \(-0.575672\pi\) | ||||
−0.235497 | + | 0.971875i | \(0.575672\pi\) | |||||||
\(270\) | 1.63355 | 0.0994148 | ||||||||
\(271\) | −5.28514 | −0.321050 | −0.160525 | − | 0.987032i | \(-0.551319\pi\) | ||||
−0.160525 | + | 0.987032i | \(0.551319\pi\) | |||||||
\(272\) | −0.0100347 | −0.000608441 0 | ||||||||
\(273\) | 43.9608 | 2.66063 | ||||||||
\(274\) | 0.249951 | 0.0151001 | ||||||||
\(275\) | −4.50702 | −0.271783 | ||||||||
\(276\) | −9.35844 | −0.563312 | ||||||||
\(277\) | 30.6264 | 1.84016 | 0.920082 | − | 0.391726i | \(-0.128122\pi\) | ||||
0.920082 | + | 0.391726i | \(0.128122\pi\) | |||||||
\(278\) | 3.29918 | 0.197872 | ||||||||
\(279\) | −7.50702 | −0.449433 | ||||||||
\(280\) | −9.79216 | −0.585194 | ||||||||
\(281\) | 13.3624 | 0.797137 | 0.398568 | − | 0.917139i | \(-0.369507\pi\) | ||||
0.398568 | + | 0.917139i | \(0.369507\pi\) | |||||||
\(282\) | −17.5491 | −1.04504 | ||||||||
\(283\) | 4.09534 | 0.243443 | 0.121721 | − | 0.992564i | \(-0.461159\pi\) | ||||
0.121721 | + | 0.992564i | \(0.461159\pi\) | |||||||
\(284\) | −52.3101 | −3.10403 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 51.4959 | 3.04502 | ||||||||
\(287\) | 21.3132 | 1.25808 | ||||||||
\(288\) | −18.8202 | −1.10899 | ||||||||
\(289\) | −16.9748 | −0.998520 | ||||||||
\(290\) | 8.01404 | 0.470600 | ||||||||
\(291\) | −4.06015 | −0.238010 | ||||||||
\(292\) | −23.0642 | −1.34973 | ||||||||
\(293\) | 12.1726 | 0.711134 | 0.355567 | − | 0.934651i | \(-0.384288\pi\) | ||||
0.355567 | + | 0.934651i | \(0.384288\pi\) | |||||||
\(294\) | −30.3584 | −1.77054 | ||||||||
\(295\) | −3.06327 | −0.178350 | ||||||||
\(296\) | −30.6155 | −1.77949 | ||||||||
\(297\) | 3.22188 | 0.186952 | ||||||||
\(298\) | 3.95077 | 0.228862 | ||||||||
\(299\) | −5.79305 | −0.335021 | ||||||||
\(300\) | −8.07730 | −0.466343 | ||||||||
\(301\) | −11.7429 | −0.676851 | ||||||||
\(302\) | −46.0241 | −2.64839 | ||||||||
\(303\) | −30.8695 | −1.77340 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.873467 | 0.0500146 | ||||||||
\(306\) | 1.19069 | 0.0680670 | ||||||||
\(307\) | 24.5351 | 1.40029 | 0.700146 | − | 0.714000i | \(-0.253118\pi\) | ||||
0.700146 | + | 0.714000i | \(0.253118\pi\) | |||||||
\(308\) | −50.9256 | −2.90176 | ||||||||
\(309\) | −26.6155 | −1.51410 | ||||||||
\(310\) | 5.22188 | 0.296583 | ||||||||
\(311\) | −10.2038 | −0.578606 | −0.289303 | − | 0.957238i | \(-0.593424\pi\) | ||||
−0.289303 | + | 0.957238i | \(0.593424\pi\) | |||||||
\(312\) | 35.0000 | 1.98148 | ||||||||
\(313\) | −31.9820 | −1.80773 | −0.903864 | − | 0.427821i | \(-0.859281\pi\) | ||||
−0.903864 | + | 0.427821i | \(0.859281\pi\) | |||||||
\(314\) | 8.63355 | 0.487219 | ||||||||
\(315\) | −11.5211 | −0.649138 | ||||||||
\(316\) | −32.6264 | −1.83538 | ||||||||
\(317\) | 2.23591 | 0.125581 | 0.0627907 | − | 0.998027i | \(-0.480000\pi\) | ||||
0.0627907 | + | 0.998027i | \(0.480000\pi\) | |||||||
\(318\) | 32.9007 | 1.84498 | ||||||||
\(319\) | 15.8062 | 0.884977 | ||||||||
\(320\) | 12.9648 | 0.724755 | ||||||||
\(321\) | 5.44687 | 0.304014 | ||||||||
\(322\) | 9.28514 | 0.517441 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −25.9788 | −1.44327 | ||||||||
\(325\) | −5.00000 | −0.277350 | ||||||||
\(326\) | −3.69370 | −0.204575 | ||||||||
\(327\) | −39.6616 | −2.19329 | ||||||||
\(328\) | 16.9688 | 0.936946 | ||||||||
\(329\) | 10.7429 | 0.592277 | ||||||||
\(330\) | −25.8202 | −1.42136 | ||||||||
\(331\) | −10.0913 | −0.554670 | −0.277335 | − | 0.960773i | \(-0.589451\pi\) | ||||
−0.277335 | + | 0.960773i | \(0.589451\pi\) | |||||||
\(332\) | 15.6436 | 0.858553 | ||||||||
\(333\) | −36.0210 | −1.97394 | ||||||||
\(334\) | 14.8374 | 0.811866 | ||||||||
\(335\) | 8.44375 | 0.461331 | ||||||||
\(336\) | 0.556248 | 0.0303458 | ||||||||
\(337\) | 5.61240 | 0.305727 | 0.152863 | − | 0.988247i | \(-0.451151\pi\) | ||||
0.152863 | + | 0.988247i | \(0.451151\pi\) | |||||||
\(338\) | 27.4217 | 1.49154 | ||||||||
\(339\) | −24.6647 | −1.33960 | ||||||||
\(340\) | −0.511021 | −0.0277140 | ||||||||
\(341\) | 10.2992 | 0.557732 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5.96481 | −0.322069 | ||||||||
\(344\) | −9.34930 | −0.504080 | ||||||||
\(345\) | 2.90466 | 0.156381 | ||||||||
\(346\) | 19.4718 | 1.04681 | ||||||||
\(347\) | 5.47494 | 0.293910 | 0.146955 | − | 0.989143i | \(-0.453053\pi\) | ||||
0.146955 | + | 0.989143i | \(0.453053\pi\) | |||||||
\(348\) | 28.3273 | 1.51850 | ||||||||
\(349\) | −18.8202 | −1.00742 | −0.503712 | − | 0.863872i | \(-0.668033\pi\) | ||||
−0.503712 | + | 0.863872i | \(0.668033\pi\) | |||||||
\(350\) | 8.01404 | 0.428368 | ||||||||
\(351\) | 3.57429 | 0.190781 | ||||||||
\(352\) | 25.8202 | 1.37622 | ||||||||
\(353\) | −12.7008 | −0.675996 | −0.337998 | − | 0.941147i | \(-0.609750\pi\) | ||||
−0.337998 | + | 0.941147i | \(0.609750\pi\) | |||||||
\(354\) | −17.5491 | −0.932726 | ||||||||
\(355\) | 16.2359 | 0.861713 | ||||||||
\(356\) | −3.58432 | −0.189969 | ||||||||
\(357\) | −1.39452 | −0.0738060 | ||||||||
\(358\) | −23.4709 | −1.24048 | ||||||||
\(359\) | −11.0804 | −0.584802 | −0.292401 | − | 0.956296i | \(-0.594454\pi\) | ||||
−0.292401 | + | 0.956296i | \(0.594454\pi\) | |||||||
\(360\) | −9.17265 | −0.483441 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 28.0321 | 1.47333 | ||||||||
\(363\) | −23.3484 | −1.22547 | ||||||||
\(364\) | −56.4959 | −2.96119 | ||||||||
\(365\) | 7.15861 | 0.374699 | ||||||||
\(366\) | 5.00400 | 0.261563 | ||||||||
\(367\) | −20.6405 | −1.07742 | −0.538712 | − | 0.842490i | \(-0.681089\pi\) | ||||
−0.538712 | + | 0.842490i | \(0.681089\pi\) | |||||||
\(368\) | −0.0733010 | −0.00382108 | ||||||||
\(369\) | 19.9648 | 1.03933 | ||||||||
\(370\) | 25.0561 | 1.30261 | ||||||||
\(371\) | −20.1406 | −1.04565 | ||||||||
\(372\) | 18.4578 | 0.956992 | ||||||||
\(373\) | 4.55313 | 0.235752 | 0.117876 | − | 0.993028i | \(-0.462391\pi\) | ||||
0.117876 | + | 0.993028i | \(0.462391\pi\) | |||||||
\(374\) | −1.63355 | −0.0844689 | ||||||||
\(375\) | 2.50702 | 0.129462 | ||||||||
\(376\) | 8.55313 | 0.441094 | ||||||||
\(377\) | 17.5351 | 0.903103 | ||||||||
\(378\) | −5.72889 | −0.294663 | ||||||||
\(379\) | −19.9187 | −1.02315 | −0.511577 | − | 0.859237i | \(-0.670939\pi\) | ||||
−0.511577 | + | 0.859237i | \(0.670939\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −39.3874 | −2.01788 | ||||||||
\(382\) | 13.0501 | 0.667702 | ||||||||
\(383\) | −19.9748 | −1.02067 | −0.510333 | − | 0.859977i | \(-0.670478\pi\) | ||||
−0.510333 | + | 0.859977i | \(0.670478\pi\) | |||||||
\(384\) | 45.5491 | 2.32442 | ||||||||
\(385\) | 15.8062 | 0.805558 | ||||||||
\(386\) | −23.2139 | −1.18155 | ||||||||
\(387\) | −11.0000 | −0.559161 | ||||||||
\(388\) | 5.21787 | 0.264897 | ||||||||
\(389\) | 13.8022 | 0.699799 | 0.349900 | − | 0.936787i | \(-0.386216\pi\) | ||||
0.349900 | + | 0.936787i | \(0.386216\pi\) | |||||||
\(390\) | −28.6445 | −1.45047 | ||||||||
\(391\) | 0.183767 | 0.00929349 | ||||||||
\(392\) | 14.7962 | 0.747319 | ||||||||
\(393\) | 28.9187 | 1.45876 | ||||||||
\(394\) | 37.0281 | 1.86545 | ||||||||
\(395\) | 10.1265 | 0.509521 | ||||||||
\(396\) | −47.7037 | −2.39720 | ||||||||
\(397\) | −16.5491 | −0.830577 | −0.415289 | − | 0.909690i | \(-0.636319\pi\) | ||||
−0.415289 | + | 0.909690i | \(0.636319\pi\) | |||||||
\(398\) | 0.764087 | 0.0383002 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.0632663 | −0.00316332 | ||||||||
\(401\) | 8.52506 | 0.425721 | 0.212861 | − | 0.977083i | \(-0.431722\pi\) | ||||
0.212861 | + | 0.977083i | \(0.431722\pi\) | |||||||
\(402\) | 48.3734 | 2.41264 | ||||||||
\(403\) | 11.4257 | 0.569155 | ||||||||
\(404\) | 39.6717 | 1.97374 | ||||||||
\(405\) | 8.06327 | 0.400667 | ||||||||
\(406\) | −28.1054 | −1.39485 | ||||||||
\(407\) | 49.4186 | 2.44959 | ||||||||
\(408\) | −1.11027 | −0.0549665 | ||||||||
\(409\) | −11.5663 | −0.571916 | −0.285958 | − | 0.958242i | \(-0.592312\pi\) | ||||
−0.285958 | + | 0.958242i | \(0.592312\pi\) | |||||||
\(410\) | −13.8875 | −0.685855 | ||||||||
\(411\) | −0.274220 | −0.0135263 | ||||||||
\(412\) | 34.2047 | 1.68515 | ||||||||
\(413\) | 10.7429 | 0.528625 | ||||||||
\(414\) | 8.69771 | 0.427469 | ||||||||
\(415\) | −4.85543 | −0.238344 | ||||||||
\(416\) | 28.6445 | 1.40441 | ||||||||
\(417\) | −3.61951 | −0.177248 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −21.7149 | −1.06084 | −0.530420 | − | 0.847735i | \(-0.677966\pi\) | ||||
−0.530420 | + | 0.847735i | \(0.677966\pi\) | |||||||
\(420\) | 28.3273 | 1.38223 | ||||||||
\(421\) | −6.92270 | −0.337392 | −0.168696 | − | 0.985668i | \(-0.553956\pi\) | ||||
−0.168696 | + | 0.985668i | \(0.553956\pi\) | |||||||
\(422\) | 4.63444 | 0.225601 | ||||||||
\(423\) | 10.0633 | 0.489293 | ||||||||
\(424\) | −16.0352 | −0.778738 | ||||||||
\(425\) | 0.158610 | 0.00769371 | ||||||||
\(426\) | 93.0138 | 4.50654 | ||||||||
\(427\) | −3.06327 | −0.148242 | ||||||||
\(428\) | −7.00000 | −0.338358 | ||||||||
\(429\) | −56.4959 | −2.72765 | ||||||||
\(430\) | 7.65159 | 0.368992 | ||||||||
\(431\) | −27.9788 | −1.34769 | −0.673847 | − | 0.738871i | \(-0.735359\pi\) | ||||
−0.673847 | + | 0.738871i | \(0.735359\pi\) | |||||||
\(432\) | 0.0452264 | 0.00217596 | ||||||||
\(433\) | 6.25395 | 0.300546 | 0.150273 | − | 0.988645i | \(-0.451985\pi\) | ||||
0.150273 | + | 0.988645i | \(0.451985\pi\) | |||||||
\(434\) | −18.3132 | −0.879063 | ||||||||
\(435\) | −8.79216 | −0.421552 | ||||||||
\(436\) | 50.9708 | 2.44106 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 41.0109 | 1.95958 | ||||||||
\(439\) | 31.1976 | 1.48898 | 0.744490 | − | 0.667633i | \(-0.232693\pi\) | ||||
0.744490 | + | 0.667633i | \(0.232693\pi\) | |||||||
\(440\) | 12.5843 | 0.599934 | ||||||||
\(441\) | 17.4086 | 0.828979 | ||||||||
\(442\) | −1.81223 | −0.0861990 | ||||||||
\(443\) | −32.7037 | −1.55380 | −0.776901 | − | 0.629623i | \(-0.783209\pi\) | ||||
−0.776901 | + | 0.629623i | \(0.783209\pi\) | |||||||
\(444\) | 88.5661 | 4.20316 | ||||||||
\(445\) | 1.11250 | 0.0527373 | ||||||||
\(446\) | −43.9477 | −2.08098 | ||||||||
\(447\) | −4.33437 | −0.205009 | ||||||||
\(448\) | −45.4678 | −2.14815 | ||||||||
\(449\) | 25.6304 | 1.20958 | 0.604788 | − | 0.796387i | \(-0.293258\pi\) | ||||
0.604788 | + | 0.796387i | \(0.293258\pi\) | |||||||
\(450\) | 7.50702 | 0.353884 | ||||||||
\(451\) | −27.3905 | −1.28977 | ||||||||
\(452\) | 31.6977 | 1.49093 | ||||||||
\(453\) | 50.4928 | 2.37236 | ||||||||
\(454\) | 9.14057 | 0.428988 | ||||||||
\(455\) | 17.5351 | 0.822058 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 33.1646 | 1.55138 | 0.775688 | − | 0.631116i | \(-0.217403\pi\) | ||||
0.775688 | + | 0.631116i | \(0.217403\pi\) | |||||||
\(458\) | −29.6585 | −1.38585 | ||||||||
\(459\) | −0.113383 | −0.00529229 | ||||||||
\(460\) | −3.73290 | −0.174047 | ||||||||
\(461\) | 2.17576 | 0.101335 | 0.0506677 | − | 0.998716i | \(-0.483865\pi\) | ||||
0.0506677 | + | 0.998716i | \(0.483865\pi\) | |||||||
\(462\) | 90.5520 | 4.21286 | ||||||||
\(463\) | −6.20072 | −0.288172 | −0.144086 | − | 0.989565i | \(-0.546024\pi\) | ||||
−0.144086 | + | 0.989565i | \(0.546024\pi\) | |||||||
\(464\) | 0.221876 | 0.0103003 | ||||||||
\(465\) | −5.72889 | −0.265671 | ||||||||
\(466\) | 61.8664 | 2.86590 | ||||||||
\(467\) | −17.1546 | −0.793821 | −0.396910 | − | 0.917857i | \(-0.629918\pi\) | ||||
−0.396910 | + | 0.917857i | \(0.629918\pi\) | |||||||
\(468\) | −52.9216 | −2.44630 | ||||||||
\(469\) | −29.6124 | −1.36737 | ||||||||
\(470\) | −7.00000 | −0.322886 | ||||||||
\(471\) | −9.47183 | −0.436439 | ||||||||
\(472\) | 8.55313 | 0.393690 | ||||||||
\(473\) | 15.0913 | 0.693901 | ||||||||
\(474\) | 58.0138 | 2.66466 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.79216 | 0.0821436 | ||||||||
\(477\) | −18.8664 | −0.863831 | ||||||||
\(478\) | 45.8403 | 2.09669 | ||||||||
\(479\) | −35.7781 | −1.63474 | −0.817372 | − | 0.576110i | \(-0.804570\pi\) | ||||
−0.817372 | + | 0.576110i | \(0.804570\pi\) | |||||||
\(480\) | −14.3624 | −0.655553 | ||||||||
\(481\) | 54.8240 | 2.49976 | ||||||||
\(482\) | −49.3233 | −2.24661 | ||||||||
\(483\) | −10.1867 | −0.463510 | ||||||||
\(484\) | 30.0060 | 1.36391 | ||||||||
\(485\) | −1.61951 | −0.0735383 | ||||||||
\(486\) | 51.0943 | 2.31768 | ||||||||
\(487\) | −23.7149 | −1.07462 | −0.537311 | − | 0.843384i | \(-0.680560\pi\) | ||||
−0.537311 | + | 0.843384i | \(0.680560\pi\) | |||||||
\(488\) | −2.43886 | −0.110402 | ||||||||
\(489\) | 4.05234 | 0.183253 | ||||||||
\(490\) | −12.1094 | −0.547046 | ||||||||
\(491\) | −39.1867 | −1.76847 | −0.884235 | − | 0.467042i | \(-0.845320\pi\) | ||||
−0.884235 | + | 0.467042i | \(0.845320\pi\) | |||||||
\(492\) | −49.0882 | −2.21307 | ||||||||
\(493\) | −0.556248 | −0.0250521 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 14.8062 | 0.665489 | ||||||||
\(496\) | 0.144573 | 0.00649150 | ||||||||
\(497\) | −56.9397 | −2.55409 | ||||||||
\(498\) | −27.8162 | −1.24648 | ||||||||
\(499\) | −9.37648 | −0.419749 | −0.209875 | − | 0.977728i | \(-0.567306\pi\) | ||||
−0.209875 | + | 0.977728i | \(0.567306\pi\) | |||||||
\(500\) | −3.22188 | −0.144087 | ||||||||
\(501\) | −16.2780 | −0.727249 | ||||||||
\(502\) | −16.6084 | −0.741269 | ||||||||
\(503\) | 13.4930 | 0.601622 | 0.300811 | − | 0.953684i | \(-0.402743\pi\) | ||||
0.300811 | + | 0.953684i | \(0.402743\pi\) | |||||||
\(504\) | 32.1686 | 1.43291 | ||||||||
\(505\) | −12.3132 | −0.547931 | ||||||||
\(506\) | −11.9327 | −0.530475 | ||||||||
\(507\) | −30.0842 | −1.33609 | ||||||||
\(508\) | 50.6184 | 2.24583 | ||||||||
\(509\) | 25.7069 | 1.13944 | 0.569718 | − | 0.821840i | \(-0.307052\pi\) | ||||
0.569718 | + | 0.821840i | \(0.307052\pi\) | |||||||
\(510\) | 0.908659 | 0.0402361 | ||||||||
\(511\) | −25.1054 | −1.11060 | ||||||||
\(512\) | 0.715746 | 0.0316318 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 34.4538 | 1.51969 | ||||||||
\(515\) | −10.6164 | −0.467814 | ||||||||
\(516\) | 27.0461 | 1.19064 | ||||||||
\(517\) | −13.8062 | −0.607196 | ||||||||
\(518\) | −87.8724 | −3.86089 | ||||||||
\(519\) | −21.3624 | −0.937707 | ||||||||
\(520\) | 13.9608 | 0.612222 | ||||||||
\(521\) | −37.7358 | −1.65324 | −0.826618 | − | 0.562763i | \(-0.809738\pi\) | ||||
−0.826618 | + | 0.562763i | \(0.809738\pi\) | |||||||
\(522\) | −26.3273 | −1.15231 | ||||||||
\(523\) | 38.4006 | 1.67914 | 0.839570 | − | 0.543252i | \(-0.182807\pi\) | ||||
0.839570 | + | 0.543252i | \(0.182807\pi\) | |||||||
\(524\) | −37.1646 | −1.62354 | ||||||||
\(525\) | −8.79216 | −0.383721 | ||||||||
\(526\) | 46.0561 | 2.00814 | ||||||||
\(527\) | −0.362446 | −0.0157884 | ||||||||
\(528\) | −0.714858 | −0.0311102 | ||||||||
\(529\) | −21.6576 | −0.941636 | ||||||||
\(530\) | 13.1234 | 0.570045 | ||||||||
\(531\) | 10.0633 | 0.436709 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −30.3865 | −1.31619 | ||||||||
\(534\) | 6.37337 | 0.275803 | ||||||||
\(535\) | 2.17265 | 0.0939317 | ||||||||
\(536\) | −23.5763 | −1.01834 | ||||||||
\(537\) | 25.7499 | 1.11119 | ||||||||
\(538\) | −17.6525 | −0.761052 | ||||||||
\(539\) | −23.8835 | −1.02874 | ||||||||
\(540\) | 2.30318 | 0.0991132 | ||||||||
\(541\) | −12.8062 | −0.550581 | −0.275291 | − | 0.961361i | \(-0.588774\pi\) | ||||
−0.275291 | + | 0.961361i | \(0.588774\pi\) | |||||||
\(542\) | −12.0773 | −0.518765 | ||||||||
\(543\) | −30.7539 | −1.31977 | ||||||||
\(544\) | −0.908659 | −0.0389584 | ||||||||
\(545\) | −15.8202 | −0.677664 | ||||||||
\(546\) | 100.457 | 4.29915 | ||||||||
\(547\) | −18.2571 | −0.780616 | −0.390308 | − | 0.920684i | \(-0.627631\pi\) | ||||
−0.390308 | + | 0.920684i | \(0.627631\pi\) | |||||||
\(548\) | 0.352411 | 0.0150543 | ||||||||
\(549\) | −2.86946 | −0.122466 | ||||||||
\(550\) | −10.2992 | −0.439159 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −8.11027 | −0.345196 | ||||||||
\(553\) | −35.5139 | −1.51021 | ||||||||
\(554\) | 69.9858 | 2.97341 | ||||||||
\(555\) | −27.4890 | −1.16684 | ||||||||
\(556\) | 4.65159 | 0.197271 | ||||||||
\(557\) | 14.9047 | 0.631531 | 0.315765 | − | 0.948837i | \(-0.397739\pi\) | ||||
0.315765 | + | 0.948837i | \(0.397739\pi\) | |||||||
\(558\) | −17.1546 | −0.726212 | ||||||||
\(559\) | 16.7420 | 0.708113 | ||||||||
\(560\) | 0.221876 | 0.00937598 | ||||||||
\(561\) | 1.79216 | 0.0756651 | ||||||||
\(562\) | 30.5351 | 1.28805 | ||||||||
\(563\) | 45.7810 | 1.92944 | 0.964720 | − | 0.263276i | \(-0.0848031\pi\) | ||||
0.964720 | + | 0.263276i | \(0.0848031\pi\) | |||||||
\(564\) | −24.7429 | −1.04187 | ||||||||
\(565\) | −9.83828 | −0.413899 | ||||||||
\(566\) | 9.35844 | 0.393365 | ||||||||
\(567\) | −28.2780 | −1.18757 | ||||||||
\(568\) | −45.3333 | −1.90214 | ||||||||
\(569\) | 0.379598 | 0.0159136 | 0.00795679 | − | 0.999968i | \(-0.497467\pi\) | ||||
0.00795679 | + | 0.999968i | \(0.497467\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.8514 | −0.663361 | −0.331681 | − | 0.943392i | \(-0.607616\pi\) | ||||
−0.331681 | + | 0.943392i | \(0.607616\pi\) | |||||||
\(572\) | 72.6053 | 3.03578 | ||||||||
\(573\) | −14.3172 | −0.598110 | ||||||||
\(574\) | 48.7037 | 2.03285 | ||||||||
\(575\) | 1.15861 | 0.0483174 | ||||||||
\(576\) | −42.5912 | −1.77464 | ||||||||
\(577\) | −19.2350 | −0.800765 | −0.400382 | − | 0.916348i | \(-0.631123\pi\) | ||||
−0.400382 | + | 0.916348i | \(0.631123\pi\) | |||||||
\(578\) | −38.7899 | −1.61345 | ||||||||
\(579\) | 25.4678 | 1.05841 | ||||||||
\(580\) | 11.2992 | 0.469173 | ||||||||
\(581\) | 17.0281 | 0.706444 | ||||||||
\(582\) | −9.27803 | −0.384587 | ||||||||
\(583\) | 25.8835 | 1.07199 | ||||||||
\(584\) | −19.9880 | −0.827109 | ||||||||
\(585\) | 16.4257 | 0.679120 | ||||||||
\(586\) | 27.8162 | 1.14908 | ||||||||
\(587\) | 40.8483 | 1.68599 | 0.842995 | − | 0.537921i | \(-0.180790\pi\) | ||||
0.842995 | + | 0.537921i | \(0.180790\pi\) | |||||||
\(588\) | −42.8031 | −1.76517 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −7.00000 | −0.288185 | ||||||||
\(591\) | −40.6233 | −1.67102 | ||||||||
\(592\) | 0.693703 | 0.0285110 | ||||||||
\(593\) | −14.2468 | −0.585047 | −0.292524 | − | 0.956258i | \(-0.594495\pi\) | ||||
−0.292524 | + | 0.956258i | \(0.594495\pi\) | |||||||
\(594\) | 7.36245 | 0.302085 | ||||||||
\(595\) | −0.556248 | −0.0228039 | ||||||||
\(596\) | 5.57028 | 0.228168 | ||||||||
\(597\) | −0.838276 | −0.0343083 | ||||||||
\(598\) | −13.2379 | −0.541340 | ||||||||
\(599\) | −15.8514 | −0.647672 | −0.323836 | − | 0.946113i | \(-0.604973\pi\) | ||||
−0.323836 | + | 0.946113i | \(0.604973\pi\) | |||||||
\(600\) | −7.00000 | −0.285774 | ||||||||
\(601\) | 16.4718 | 0.671900 | 0.335950 | − | 0.941880i | \(-0.390943\pi\) | ||||
0.335950 | + | 0.941880i | \(0.390943\pi\) | |||||||
\(602\) | −26.8343 | −1.09368 | ||||||||
\(603\) | −27.7389 | −1.12962 | ||||||||
\(604\) | −64.8904 | −2.64035 | ||||||||
\(605\) | −9.31322 | −0.378636 | ||||||||
\(606\) | −70.5411 | −2.86554 | ||||||||
\(607\) | −10.3914 | −0.421774 | −0.210887 | − | 0.977510i | \(-0.567635\pi\) | ||||
−0.210887 | + | 0.977510i | \(0.567635\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 30.8343 | 1.24947 | ||||||||
\(610\) | 1.99600 | 0.0808156 | ||||||||
\(611\) | −15.3163 | −0.619632 | ||||||||
\(612\) | 1.67878 | 0.0678606 | ||||||||
\(613\) | −21.7850 | −0.879890 | −0.439945 | − | 0.898025i | \(-0.645002\pi\) | ||||
−0.439945 | + | 0.898025i | \(0.645002\pi\) | |||||||
\(614\) | 56.0662 | 2.26265 | ||||||||
\(615\) | 15.2359 | 0.614371 | ||||||||
\(616\) | −44.1335 | −1.77819 | ||||||||
\(617\) | −42.7710 | −1.72190 | −0.860948 | − | 0.508693i | \(-0.830129\pi\) | ||||
−0.860948 | + | 0.508693i | \(0.830129\pi\) | |||||||
\(618\) | −60.8202 | −2.44655 | ||||||||
\(619\) | 28.7882 | 1.15709 | 0.578547 | − | 0.815649i | \(-0.303620\pi\) | ||||
0.578547 | + | 0.815649i | \(0.303620\pi\) | |||||||
\(620\) | 7.36245 | 0.295683 | ||||||||
\(621\) | −0.828241 | −0.0332362 | ||||||||
\(622\) | −23.3172 | −0.934935 | ||||||||
\(623\) | −3.90154 | −0.156312 | ||||||||
\(624\) | −0.793049 | −0.0317474 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −73.0833 | −2.92100 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 12.1726 | 0.485742 | ||||||||
\(629\) | −1.73913 | −0.0693435 | ||||||||
\(630\) | −26.3273 | −1.04890 | ||||||||
\(631\) | −19.3874 | −0.771800 | −0.385900 | − | 0.922541i | \(-0.626109\pi\) | ||||
−0.385900 | + | 0.922541i | \(0.626109\pi\) | |||||||
\(632\) | −28.2749 | −1.12472 | ||||||||
\(633\) | −5.08442 | −0.202088 | ||||||||
\(634\) | 5.10938 | 0.202919 | ||||||||
\(635\) | −15.7109 | −0.623466 | ||||||||
\(636\) | 46.3874 | 1.83938 | ||||||||
\(637\) | −26.4959 | −1.04981 | ||||||||
\(638\) | 36.1194 | 1.42998 | ||||||||
\(639\) | −53.3373 | −2.10999 | ||||||||
\(640\) | 18.1686 | 0.718179 | ||||||||
\(641\) | 40.6866 | 1.60702 | 0.803512 | − | 0.595289i | \(-0.202962\pi\) | ||||
0.803512 | + | 0.595289i | \(0.202962\pi\) | |||||||
\(642\) | 12.4469 | 0.491239 | ||||||||
\(643\) | −34.1054 | −1.34498 | −0.672492 | − | 0.740104i | \(-0.734776\pi\) | ||||
−0.672492 | + | 0.740104i | \(0.734776\pi\) | |||||||
\(644\) | 13.0913 | 0.515871 | ||||||||
\(645\) | −8.39452 | −0.330534 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −48.0029 | −1.88719 | −0.943595 | − | 0.331103i | \(-0.892579\pi\) | ||||
−0.943595 | + | 0.331103i | \(0.892579\pi\) | |||||||
\(648\) | −22.5139 | −0.884431 | ||||||||
\(649\) | −13.8062 | −0.541941 | ||||||||
\(650\) | −11.4257 | −0.448153 | ||||||||
\(651\) | 20.0913 | 0.787442 | ||||||||
\(652\) | −5.20784 | −0.203955 | ||||||||
\(653\) | 3.90866 | 0.152958 | 0.0764788 | − | 0.997071i | \(-0.475632\pi\) | ||||
0.0764788 | + | 0.997071i | \(0.475632\pi\) | |||||||
\(654\) | −90.6325 | −3.54401 | ||||||||
\(655\) | 11.5351 | 0.450713 | ||||||||
\(656\) | −0.384489 | −0.0150118 | ||||||||
\(657\) | −23.5171 | −0.917488 | ||||||||
\(658\) | 24.5491 | 0.957025 | ||||||||
\(659\) | 13.0882 | 0.509845 | 0.254922 | − | 0.966961i | \(-0.417950\pi\) | ||||
0.254922 | + | 0.966961i | \(0.417950\pi\) | |||||||
\(660\) | −36.4046 | −1.41705 | ||||||||
\(661\) | −23.9428 | −0.931266 | −0.465633 | − | 0.884978i | \(-0.654173\pi\) | ||||
−0.465633 | + | 0.884978i | \(0.654173\pi\) | |||||||
\(662\) | −23.0602 | −0.896258 | ||||||||
\(663\) | 1.98819 | 0.0772149 | ||||||||
\(664\) | 13.5571 | 0.526119 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −82.3130 | −3.18956 | ||||||||
\(667\) | −4.06327 | −0.157330 | ||||||||
\(668\) | 20.9196 | 0.809403 | ||||||||
\(669\) | 48.2148 | 1.86409 | ||||||||
\(670\) | 19.2952 | 0.745438 | ||||||||
\(671\) | 3.93673 | 0.151976 | ||||||||
\(672\) | 50.3694 | 1.94304 | ||||||||
\(673\) | −11.3304 | −0.436754 | −0.218377 | − | 0.975865i | \(-0.570076\pi\) | ||||
−0.218377 | + | 0.975865i | \(0.570076\pi\) | |||||||
\(674\) | 12.8251 | 0.494005 | ||||||||
\(675\) | −0.714858 | −0.0275149 | ||||||||
\(676\) | 38.6625 | 1.48702 | ||||||||
\(677\) | 8.90466 | 0.342234 | 0.171117 | − | 0.985251i | \(-0.445262\pi\) | ||||
0.171117 | + | 0.985251i | \(0.445262\pi\) | |||||||
\(678\) | −56.3624 | −2.16459 | ||||||||
\(679\) | 5.67967 | 0.217966 | ||||||||
\(680\) | −0.442864 | −0.0169831 | ||||||||
\(681\) | −10.0281 | −0.384277 | ||||||||
\(682\) | 23.5351 | 0.901205 | ||||||||
\(683\) | −26.6977 | −1.02156 | −0.510780 | − | 0.859712i | \(-0.670643\pi\) | ||||
−0.510780 | + | 0.859712i | \(0.670643\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.109381 | −0.00417923 | ||||||||
\(686\) | −13.6304 | −0.520412 | ||||||||
\(687\) | 32.5382 | 1.24141 | ||||||||
\(688\) | 0.211842 | 0.00807638 | ||||||||
\(689\) | 28.7147 | 1.09394 | ||||||||
\(690\) | 6.63755 | 0.252687 | ||||||||
\(691\) | 35.9708 | 1.36840 | 0.684198 | − | 0.729297i | \(-0.260153\pi\) | ||||
0.684198 | + | 0.729297i | \(0.260153\pi\) | |||||||
\(692\) | 27.4538 | 1.04364 | ||||||||
\(693\) | −51.9256 | −1.97249 | ||||||||
\(694\) | 12.5110 | 0.474912 | ||||||||
\(695\) | −1.44375 | −0.0547646 | ||||||||
\(696\) | 24.5491 | 0.930532 | ||||||||
\(697\) | 0.963920 | 0.0365111 | ||||||||
\(698\) | −43.0069 | −1.62784 | ||||||||
\(699\) | −67.8733 | −2.56720 | ||||||||
\(700\) | 11.2992 | 0.427069 | ||||||||
\(701\) | 2.45087 | 0.0925681 | 0.0462840 | − | 0.998928i | \(-0.485262\pi\) | ||||
0.0462840 | + | 0.998928i | \(0.485262\pi\) | |||||||
\(702\) | 8.16776 | 0.308272 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 58.4326 | 2.20226 | ||||||||
\(705\) | 7.67967 | 0.289233 | ||||||||
\(706\) | −29.0232 | −1.09230 | ||||||||
\(707\) | 43.1827 | 1.62405 | ||||||||
\(708\) | −24.7429 | −0.929896 | ||||||||
\(709\) | −50.2881 | −1.88861 | −0.944304 | − | 0.329075i | \(-0.893263\pi\) | ||||
−0.944304 | + | 0.329075i | \(0.893263\pi\) | |||||||
\(710\) | 37.1014 | 1.39239 | ||||||||
\(711\) | −33.2671 | −1.24761 | ||||||||
\(712\) | −3.10627 | −0.116412 | ||||||||
\(713\) | −2.64759 | −0.0991530 | ||||||||
\(714\) | −3.18668 | −0.119259 | ||||||||
\(715\) | −22.5351 | −0.842765 | ||||||||
\(716\) | −33.0922 | −1.23671 | ||||||||
\(717\) | −50.2912 | −1.87816 | ||||||||
\(718\) | −25.3203 | −0.944946 | ||||||||
\(719\) | −48.0983 | −1.79376 | −0.896881 | − | 0.442271i | \(-0.854173\pi\) | ||||
−0.896881 | + | 0.442271i | \(0.854173\pi\) | |||||||
\(720\) | 0.207839 | 0.00774570 | ||||||||
\(721\) | 37.2319 | 1.38659 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 54.1123 | 2.01246 | ||||||||
\(724\) | 39.5231 | 1.46886 | ||||||||
\(725\) | −3.50702 | −0.130247 | ||||||||
\(726\) | −53.3544 | −1.98017 | ||||||||
\(727\) | −16.6797 | −0.618615 | −0.309307 | − | 0.950962i | \(-0.600097\pi\) | ||||
−0.309307 | + | 0.950962i | \(0.600097\pi\) | |||||||
\(728\) | −48.9608 | −1.81461 | ||||||||
\(729\) | −31.8655 | −1.18020 | ||||||||
\(730\) | 16.3584 | 0.605453 | ||||||||
\(731\) | −0.531091 | −0.0196431 | ||||||||
\(732\) | 7.05526 | 0.260770 | ||||||||
\(733\) | −4.13365 | −0.152680 | −0.0763399 | − | 0.997082i | \(-0.524323\pi\) | ||||
−0.0763399 | + | 0.997082i | \(0.524323\pi\) | |||||||
\(734\) | −47.1664 | −1.74094 | ||||||||
\(735\) | 13.2851 | 0.490030 | ||||||||
\(736\) | −6.63755 | −0.244663 | ||||||||
\(737\) | 38.0561 | 1.40182 | ||||||||
\(738\) | 45.6224 | 1.67938 | ||||||||
\(739\) | 46.9740 | 1.72796 | 0.863982 | − | 0.503522i | \(-0.167963\pi\) | ||||
0.863982 | + | 0.503522i | \(0.167963\pi\) | |||||||
\(740\) | 35.3273 | 1.29866 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −46.0241 | −1.68960 | ||||||||
\(743\) | 41.2139 | 1.51199 | 0.755995 | − | 0.654577i | \(-0.227153\pi\) | ||||
0.755995 | + | 0.654577i | \(0.227153\pi\) | |||||||
\(744\) | 15.9960 | 0.586442 | ||||||||
\(745\) | −1.72889 | −0.0633418 | ||||||||
\(746\) | 10.4046 | 0.380938 | ||||||||
\(747\) | 15.9508 | 0.583608 | ||||||||
\(748\) | −2.30318 | −0.0842127 | ||||||||
\(749\) | −7.61951 | −0.278411 | ||||||||
\(750\) | 5.72889 | 0.209190 | ||||||||
\(751\) | 5.97885 | 0.218171 | 0.109086 | − | 0.994032i | \(-0.465208\pi\) | ||||
0.109086 | + | 0.994032i | \(0.465208\pi\) | |||||||
\(752\) | −0.193802 | −0.00706722 | ||||||||
\(753\) | 18.2210 | 0.664010 | ||||||||
\(754\) | 40.0702 | 1.45927 | ||||||||
\(755\) | 20.1406 | 0.732990 | ||||||||
\(756\) | −8.07730 | −0.293769 | ||||||||
\(757\) | 36.3936 | 1.32275 | 0.661375 | − | 0.750056i | \(-0.269973\pi\) | ||||
0.661375 | + | 0.750056i | \(0.269973\pi\) | |||||||
\(758\) | −45.5171 | −1.65325 | ||||||||
\(759\) | 13.0913 | 0.475186 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.71397 | −0.0983813 | −0.0491907 | − | 0.998789i | \(-0.515664\pi\) | ||||
−0.0491907 | + | 0.998789i | \(0.515664\pi\) | |||||||
\(762\) | −90.0058 | −3.26057 | ||||||||
\(763\) | 55.4819 | 2.00858 | ||||||||
\(764\) | 18.3997 | 0.665677 | ||||||||
\(765\) | −0.521056 | −0.0188388 | ||||||||
\(766\) | −45.6454 | −1.64923 | ||||||||
\(767\) | −15.3163 | −0.553041 | ||||||||
\(768\) | 39.0802 | 1.41019 | ||||||||
\(769\) | 39.7991 | 1.43519 | 0.717596 | − | 0.696460i | \(-0.245243\pi\) | ||||
0.717596 | + | 0.696460i | \(0.245243\pi\) | |||||||
\(770\) | 36.1194 | 1.30165 | ||||||||
\(771\) | −37.7991 | −1.36130 | ||||||||
\(772\) | −32.7298 | −1.17797 | ||||||||
\(773\) | 44.9748 | 1.61763 | 0.808816 | − | 0.588061i | \(-0.200109\pi\) | ||||
0.808816 | + | 0.588061i | \(0.200109\pi\) | |||||||
\(774\) | −25.1366 | −0.903515 | ||||||||
\(775\) | −2.28514 | −0.0820847 | ||||||||
\(776\) | 4.52194 | 0.162328 | ||||||||
\(777\) | 96.4044 | 3.45849 | ||||||||
\(778\) | 31.5400 | 1.13076 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −40.3865 | −1.44607 | ||||||||
\(781\) | 73.1756 | 2.61843 | ||||||||
\(782\) | 0.419934 | 0.0150168 | ||||||||
\(783\) | 2.50702 | 0.0895935 | ||||||||
\(784\) | −0.335260 | −0.0119736 | ||||||||
\(785\) | −3.77812 | −0.134847 | ||||||||
\(786\) | 66.0833 | 2.35711 | ||||||||
\(787\) | −17.7149 | −0.631466 | −0.315733 | − | 0.948848i | \(-0.602250\pi\) | ||||
−0.315733 | + | 0.948848i | \(0.602250\pi\) | |||||||
\(788\) | 52.2068 | 1.85979 | ||||||||
\(789\) | −50.5280 | −1.79884 | ||||||||
\(790\) | 23.1406 | 0.823305 | ||||||||
\(791\) | 34.5030 | 1.22679 | ||||||||
\(792\) | −41.3413 | −1.46900 | ||||||||
\(793\) | 4.36734 | 0.155089 | ||||||||
\(794\) | −37.8171 | −1.34208 | ||||||||
\(795\) | −14.3976 | −0.510632 | ||||||||
\(796\) | 1.07730 | 0.0381840 | ||||||||
\(797\) | 25.4930 | 0.903008 | 0.451504 | − | 0.892269i | \(-0.350888\pi\) | ||||
0.451504 | + | 0.892269i | \(0.350888\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.485864 | 0.0171886 | ||||||||
\(800\) | −5.72889 | −0.202547 | ||||||||
\(801\) | −3.65471 | −0.129133 | ||||||||
\(802\) | 19.4810 | 0.687897 | ||||||||
\(803\) | 32.2640 | 1.13857 | ||||||||
\(804\) | 68.2028 | 2.40533 | ||||||||
\(805\) | −4.06327 | −0.143211 | ||||||||
\(806\) | 26.1094 | 0.919664 | ||||||||
\(807\) | 19.3664 | 0.681731 | ||||||||
\(808\) | 34.3805 | 1.20950 | ||||||||
\(809\) | −20.4678 | −0.719610 | −0.359805 | − | 0.933027i | \(-0.617157\pi\) | ||||
−0.359805 | + | 0.933027i | \(0.617157\pi\) | |||||||
\(810\) | 18.4257 | 0.647414 | ||||||||
\(811\) | −22.9015 | −0.804182 | −0.402091 | − | 0.915600i | \(-0.631716\pi\) | ||||
−0.402091 | + | 0.915600i | \(0.631716\pi\) | |||||||
\(812\) | −39.6264 | −1.39062 | ||||||||
\(813\) | 13.2500 | 0.464696 | ||||||||
\(814\) | 112.929 | 3.95814 | ||||||||
\(815\) | 1.61640 | 0.0566200 | ||||||||
\(816\) | 0.0251571 | 0.000880674 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −26.4306 | −0.924124 | ||||||||
\(819\) | −57.6053 | −2.01289 | ||||||||
\(820\) | −19.5803 | −0.683774 | ||||||||
\(821\) | 30.7218 | 1.07220 | 0.536099 | − | 0.844155i | \(-0.319897\pi\) | ||||
0.536099 | + | 0.844155i | \(0.319897\pi\) | |||||||
\(822\) | −0.626631 | −0.0218563 | ||||||||
\(823\) | 4.19692 | 0.146295 | 0.0731476 | − | 0.997321i | \(-0.476696\pi\) | ||||
0.0731476 | + | 0.997321i | \(0.476696\pi\) | |||||||
\(824\) | 29.6427 | 1.03265 | ||||||||
\(825\) | 11.2992 | 0.393387 | ||||||||
\(826\) | 24.5491 | 0.854173 | ||||||||
\(827\) | −21.3304 | −0.741730 | −0.370865 | − | 0.928687i | \(-0.620939\pi\) | ||||
−0.370865 | + | 0.928687i | \(0.620939\pi\) | |||||||
\(828\) | 12.2631 | 0.426172 | ||||||||
\(829\) | 34.0390 | 1.18222 | 0.591112 | − | 0.806590i | \(-0.298689\pi\) | ||||
0.591112 | + | 0.806590i | \(0.298689\pi\) | |||||||
\(830\) | −11.0953 | −0.385125 | ||||||||
\(831\) | −76.7810 | −2.66350 | ||||||||
\(832\) | 64.8240 | 2.24737 | ||||||||
\(833\) | 0.840502 | 0.0291217 | ||||||||
\(834\) | −8.27111 | −0.286405 | ||||||||
\(835\) | −6.49298 | −0.224699 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.63355 | 0.0564638 | ||||||||
\(838\) | −49.6215 | −1.71415 | ||||||||
\(839\) | 10.4117 | 0.359451 | 0.179725 | − | 0.983717i | \(-0.442479\pi\) | ||||
0.179725 | + | 0.983717i | \(0.442479\pi\) | |||||||
\(840\) | 24.5491 | 0.847025 | ||||||||
\(841\) | −16.7008 | −0.575890 | ||||||||
\(842\) | −15.8193 | −0.545171 | ||||||||
\(843\) | −33.4999 | −1.15380 | ||||||||
\(844\) | 6.53421 | 0.224917 | ||||||||
\(845\) | −12.0000 | −0.412813 | ||||||||
\(846\) | 22.9960 | 0.790619 | ||||||||
\(847\) | 32.6616 | 1.12227 | ||||||||
\(848\) | 0.363334 | 0.0124769 | ||||||||
\(849\) | −10.2671 | −0.352366 | ||||||||
\(850\) | 0.362446 | 0.0124318 | ||||||||
\(851\) | −12.7039 | −0.435485 | ||||||||
\(852\) | 131.142 | 4.49286 | ||||||||
\(853\) | −13.1305 | −0.449581 | −0.224790 | − | 0.974407i | \(-0.572170\pi\) | ||||
−0.224790 | + | 0.974407i | \(0.572170\pi\) | |||||||
\(854\) | −7.00000 | −0.239535 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.06638 | −0.207345 | ||||||||
\(857\) | −43.2459 | −1.47725 | −0.738627 | − | 0.674115i | \(-0.764525\pi\) | ||||
−0.738627 | + | 0.674115i | \(0.764525\pi\) | |||||||
\(858\) | −129.101 | −4.40744 | ||||||||
\(859\) | 31.4687 | 1.07370 | 0.536849 | − | 0.843678i | \(-0.319614\pi\) | ||||
0.536849 | + | 0.843678i | \(0.319614\pi\) | |||||||
\(860\) | 10.7882 | 0.367873 | ||||||||
\(861\) | −53.4326 | −1.82098 | ||||||||
\(862\) | −63.9356 | −2.17766 | ||||||||
\(863\) | −23.7842 | −0.809622 | −0.404811 | − | 0.914400i | \(-0.632663\pi\) | ||||
−0.404811 | + | 0.914400i | \(0.632663\pi\) | |||||||
\(864\) | 4.09534 | 0.139326 | ||||||||
\(865\) | −8.52106 | −0.289725 | ||||||||
\(866\) | 14.2912 | 0.485634 | ||||||||
\(867\) | 42.5562 | 1.44529 | ||||||||
\(868\) | −25.8202 | −0.876396 | ||||||||
\(869\) | 45.6405 | 1.54825 | ||||||||
\(870\) | −20.0913 | −0.681160 | ||||||||
\(871\) | 42.2188 | 1.43053 | ||||||||
\(872\) | 44.1726 | 1.49587 | ||||||||
\(873\) | 5.32033 | 0.180066 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.50702 | −0.118559 | ||||||||
\(876\) | 57.8223 | 1.95363 | ||||||||
\(877\) | −38.1695 | −1.28889 | −0.644447 | − | 0.764649i | \(-0.722912\pi\) | ||||
−0.644447 | + | 0.764649i | \(0.722912\pi\) | |||||||
\(878\) | 71.2910 | 2.40595 | ||||||||
\(879\) | −30.5171 | −1.02931 | ||||||||
\(880\) | −0.285142 | −0.00961215 | ||||||||
\(881\) | 5.49209 | 0.185033 | 0.0925167 | − | 0.995711i | \(-0.470509\pi\) | ||||
0.0925167 | + | 0.995711i | \(0.470509\pi\) | |||||||
\(882\) | 39.7810 | 1.33950 | ||||||||
\(883\) | −34.2983 | −1.15423 | −0.577115 | − | 0.816663i | \(-0.695821\pi\) | ||||
−0.577115 | + | 0.816663i | \(0.695821\pi\) | |||||||
\(884\) | −2.55511 | −0.0859375 | ||||||||
\(885\) | 7.67967 | 0.258149 | ||||||||
\(886\) | −74.7327 | −2.51069 | ||||||||
\(887\) | −37.5171 | −1.25970 | −0.629850 | − | 0.776717i | \(-0.716884\pi\) | ||||
−0.629850 | + | 0.776717i | \(0.716884\pi\) | |||||||
\(888\) | 76.7537 | 2.57568 | ||||||||
\(889\) | 55.0983 | 1.84794 | ||||||||
\(890\) | 2.54221 | 0.0852151 | ||||||||
\(891\) | 36.3413 | 1.21748 | ||||||||
\(892\) | −61.9628 | −2.07467 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −9.90466 | −0.331261 | ||||||||
\(895\) | 10.2711 | 0.343325 | ||||||||
\(896\) | −63.7178 | −2.12866 | ||||||||
\(897\) | 14.5233 | 0.484918 | ||||||||
\(898\) | 58.5692 | 1.95448 | ||||||||
\(899\) | 8.01404 | 0.267283 | ||||||||
\(900\) | 10.5843 | 0.352811 | ||||||||
\(901\) | −0.910886 | −0.0303460 | ||||||||
\(902\) | −62.5912 | −2.08406 | ||||||||
\(903\) | 29.4397 | 0.979694 | ||||||||
\(904\) | 27.4701 | 0.913640 | ||||||||
\(905\) | −12.2671 | −0.407772 | ||||||||
\(906\) | 115.383 | 3.83335 | ||||||||
\(907\) | −22.2531 | −0.738901 | −0.369450 | − | 0.929250i | \(-0.620454\pi\) | ||||
−0.369450 | + | 0.929250i | \(0.620454\pi\) | |||||||
\(908\) | 12.8875 | 0.427687 | ||||||||
\(909\) | 40.4507 | 1.34166 | ||||||||
\(910\) | 40.0702 | 1.32831 | ||||||||
\(911\) | 10.0421 | 0.332710 | 0.166355 | − | 0.986066i | \(-0.446800\pi\) | ||||
0.166355 | + | 0.986066i | \(0.446800\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −21.8835 | −0.724238 | ||||||||
\(914\) | 75.7859 | 2.50678 | ||||||||
\(915\) | −2.18980 | −0.0723925 | ||||||||
\(916\) | −41.8162 | −1.38165 | ||||||||
\(917\) | −40.4538 | −1.33590 | ||||||||
\(918\) | −0.259097 | −0.00855149 | ||||||||
\(919\) | 6.06104 | 0.199935 | 0.0999676 | − | 0.994991i | \(-0.468126\pi\) | ||||
0.0999676 | + | 0.994991i | \(0.468126\pi\) | |||||||
\(920\) | −3.23503 | −0.106656 | ||||||||
\(921\) | −61.5099 | −2.02682 | ||||||||
\(922\) | 4.97193 | 0.163742 | ||||||||
\(923\) | 81.1796 | 2.67206 | ||||||||
\(924\) | 127.671 | 4.20008 | ||||||||
\(925\) | −10.9648 | −0.360521 | ||||||||
\(926\) | −14.1695 | −0.465640 | ||||||||
\(927\) | 34.8764 | 1.14549 | ||||||||
\(928\) | 20.0913 | 0.659531 | ||||||||
\(929\) | −51.8764 | −1.70201 | −0.851004 | − | 0.525158i | \(-0.824006\pi\) | ||||
−0.851004 | + | 0.525158i | \(0.824006\pi\) | |||||||
\(930\) | −13.0913 | −0.429282 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 87.2268 | 2.85721 | ||||||||
\(933\) | 25.5812 | 0.837491 | ||||||||
\(934\) | −39.2007 | −1.28269 | ||||||||
\(935\) | 0.714858 | 0.0233783 | ||||||||
\(936\) | −45.8632 | −1.49909 | ||||||||
\(937\) | 25.1998 | 0.823243 | 0.411621 | − | 0.911355i | \(-0.364963\pi\) | ||||
0.411621 | + | 0.911355i | \(0.364963\pi\) | |||||||
\(938\) | −67.6685 | −2.20946 | ||||||||
\(939\) | 80.1794 | 2.61655 | ||||||||
\(940\) | −9.86946 | −0.321906 | ||||||||
\(941\) | −1.93585 | −0.0631068 | −0.0315534 | − | 0.999502i | \(-0.510045\pi\) | ||||
−0.0315534 | + | 0.999502i | \(0.510045\pi\) | |||||||
\(942\) | −21.6445 | −0.705215 | ||||||||
\(943\) | 7.04122 | 0.229294 | ||||||||
\(944\) | −0.193802 | −0.00630770 | ||||||||
\(945\) | 2.50702 | 0.0815533 | ||||||||
\(946\) | 34.4859 | 1.12123 | ||||||||
\(947\) | 31.3624 | 1.01914 | 0.509571 | − | 0.860428i | \(-0.329804\pi\) | ||||
0.509571 | + | 0.860428i | \(0.329804\pi\) | |||||||
\(948\) | 81.7951 | 2.65658 | ||||||||
\(949\) | 35.7930 | 1.16189 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.60548 | −0.181770 | ||||||||
\(952\) | 1.55313 | 0.0503373 | ||||||||
\(953\) | 52.9085 | 1.71387 | 0.856937 | − | 0.515422i | \(-0.172365\pi\) | ||||
0.856937 | + | 0.515422i | \(0.172365\pi\) | |||||||
\(954\) | −43.1123 | −1.39581 | ||||||||
\(955\) | −5.71085 | −0.184799 | ||||||||
\(956\) | 64.6313 | 2.09033 | ||||||||
\(957\) | −39.6264 | −1.28094 | ||||||||
\(958\) | −81.7581 | −2.64148 | ||||||||
\(959\) | 0.383601 | 0.0123871 | ||||||||
\(960\) | −32.5030 | −1.04903 | ||||||||
\(961\) | −25.7781 | −0.831552 | ||||||||
\(962\) | 125.281 | 4.03921 | ||||||||
\(963\) | −7.13746 | −0.230001 | ||||||||
\(964\) | −69.5420 | −2.23980 | ||||||||
\(965\) | 10.1586 | 0.327017 | ||||||||
\(966\) | −23.2780 | −0.748958 | ||||||||
\(967\) | −60.0281 | −1.93037 | −0.965186 | − | 0.261563i | \(-0.915762\pi\) | ||||
−0.965186 | + | 0.261563i | \(0.915762\pi\) | |||||||
\(968\) | 26.0040 | 0.835800 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −3.70082 | −0.118826 | ||||||||
\(971\) | 1.75005 | 0.0561618 | 0.0280809 | − | 0.999606i | \(-0.491060\pi\) | ||||
0.0280809 | + | 0.999606i | \(0.491060\pi\) | |||||||
\(972\) | 72.0390 | 2.31065 | ||||||||
\(973\) | 5.06327 | 0.162321 | ||||||||
\(974\) | −54.1918 | −1.73642 | ||||||||
\(975\) | 12.5351 | 0.401444 | ||||||||
\(976\) | 0.0552611 | 0.00176886 | ||||||||
\(977\) | 5.47583 | 0.175187 | 0.0875937 | − | 0.996156i | \(-0.472082\pi\) | ||||
0.0875937 | + | 0.996156i | \(0.472082\pi\) | |||||||
\(978\) | 9.26018 | 0.296108 | ||||||||
\(979\) | 5.01404 | 0.160249 | ||||||||
\(980\) | −17.0733 | −0.545387 | ||||||||
\(981\) | 51.9717 | 1.65933 | ||||||||
\(982\) | −89.5472 | −2.85756 | ||||||||
\(983\) | 5.05926 | 0.161365 | 0.0806827 | − | 0.996740i | \(-0.474290\pi\) | ||||
0.0806827 | + | 0.996740i | \(0.474290\pi\) | |||||||
\(984\) | −42.5411 | −1.35616 | ||||||||
\(985\) | −16.2038 | −0.516297 | ||||||||
\(986\) | −1.27111 | −0.0404802 | ||||||||
\(987\) | −26.9327 | −0.857278 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.87950 | −0.123361 | ||||||||
\(990\) | 33.8343 | 1.07532 | ||||||||
\(991\) | 0.0984581 | 0.00312762 | 0.00156381 | − | 0.999999i | \(-0.499502\pi\) | ||||
0.00156381 | + | 0.999999i | \(0.499502\pi\) | |||||||
\(992\) | 13.0913 | 0.415650 | ||||||||
\(993\) | 25.2992 | 0.802845 | ||||||||
\(994\) | −130.115 | −4.12700 | ||||||||
\(995\) | −0.334372 | −0.0106003 | ||||||||
\(996\) | −39.2188 | −1.24269 | ||||||||
\(997\) | 18.3593 | 0.581446 | 0.290723 | − | 0.956807i | \(-0.406104\pi\) | ||||
0.290723 | + | 0.956807i | \(0.406104\pi\) | |||||||
\(998\) | −21.4266 | −0.678247 | ||||||||
\(999\) | 7.83828 | 0.247992 |
(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 | 1805.2.a.h.1.3 | 3 | ||
5.4 | even | 2 | 9025.2.a.z.1.1 | 3 | |||
19.7 | even | 3 | 95.2.e.b.11.1 | ✓ | 6 | ||
19.11 | even | 3 | 95.2.e.b.26.1 | yes | 6 | ||
19.18 | odd | 2 | 1805.2.a.g.1.1 | 3 | |||
57.11 | odd | 6 | 855.2.k.g.406.3 | 6 | |||
57.26 | odd | 6 | 855.2.k.g.676.3 | 6 | |||
76.7 | odd | 6 | 1520.2.q.j.961.1 | 6 | |||
76.11 | odd | 6 | 1520.2.q.j.881.1 | 6 | |||
95.7 | odd | 12 | 475.2.j.b.49.2 | 12 | |||
95.49 | even | 6 | 475.2.e.d.26.3 | 6 | |||
95.64 | even | 6 | 475.2.e.d.201.3 | 6 | |||
95.68 | odd | 12 | 475.2.j.b.349.2 | 12 | |||
95.83 | odd | 12 | 475.2.j.b.49.5 | 12 | |||
95.87 | odd | 12 | 475.2.j.b.349.5 | 12 | |||
95.94 | odd | 2 | 9025.2.a.ba.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.e.b.11.1 | ✓ | 6 | 19.7 | even | 3 | ||
95.2.e.b.26.1 | yes | 6 | 19.11 | even | 3 | ||
475.2.e.d.26.3 | 6 | 95.49 | even | 6 | |||
475.2.e.d.201.3 | 6 | 95.64 | even | 6 | |||
475.2.j.b.49.2 | 12 | 95.7 | odd | 12 | |||
475.2.j.b.49.5 | 12 | 95.83 | odd | 12 | |||
475.2.j.b.349.2 | 12 | 95.68 | odd | 12 | |||
475.2.j.b.349.5 | 12 | 95.87 | odd | 12 | |||
855.2.k.g.406.3 | 6 | 57.11 | odd | 6 | |||
855.2.k.g.676.3 | 6 | 57.26 | odd | 6 | |||
1520.2.q.j.881.1 | 6 | 76.11 | odd | 6 | |||
1520.2.q.j.961.1 | 6 | 76.7 | odd | 6 | |||
1805.2.a.g.1.1 | 3 | 19.18 | odd | 2 | |||
1805.2.a.h.1.3 | 3 | 1.1 | even | 1 | trivial | ||
9025.2.a.z.1.1 | 3 | 5.4 | even | 2 | |||
9025.2.a.ba.1.3 | 3 | 95.94 | odd | 2 |