Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1875,2,Mod(1,1875)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1875, 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("1875.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1875 = 3 \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1875.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: | \(14.9719503790\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.5125.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 6x^{2} + 7x + 11 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 75) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.12233\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1875.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.12233 | −1.50072 | −0.750358 | − | 0.661031i | \(-0.770119\pi\) | ||||
−0.750358 | + | 0.661031i | \(0.770119\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 2.50430 | 1.25215 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.12233 | 0.866439 | ||||||||
\(7\) | −4.35840 | −1.64732 | −0.823660 | − | 0.567083i | \(-0.808072\pi\) | ||||
−0.823660 | + | 0.567083i | \(0.808072\pi\) | |||||||
\(8\) | −1.07029 | −0.378405 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.57991 | −0.476360 | −0.238180 | − | 0.971221i | \(-0.576551\pi\) | ||||
−0.238180 | + | 0.971221i | \(0.576551\pi\) | |||||||
\(12\) | −2.50430 | −0.722929 | ||||||||
\(13\) | −1.19794 | −0.332249 | −0.166124 | − | 0.986105i | \(-0.553125\pi\) | ||||
−0.166124 | + | 0.986105i | \(0.553125\pi\) | |||||||
\(14\) | 9.24998 | 2.47216 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.73708 | −0.684271 | ||||||||
\(17\) | 1.12233 | 0.272206 | 0.136103 | − | 0.990695i | \(-0.456542\pi\) | ||||
0.136103 | + | 0.990695i | \(0.456542\pi\) | |||||||
\(18\) | −2.12233 | −0.500239 | ||||||||
\(19\) | 7.67867 | 1.76161 | 0.880804 | − | 0.473480i | \(-0.157002\pi\) | ||||
0.880804 | + | 0.473480i | \(0.157002\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.35840 | 0.951081 | ||||||||
\(22\) | 3.35309 | 0.714881 | ||||||||
\(23\) | 2.32027 | 0.483810 | 0.241905 | − | 0.970300i | \(-0.422228\pi\) | ||||
0.241905 | + | 0.970300i | \(0.422228\pi\) | |||||||
\(24\) | 1.07029 | 0.218472 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.54243 | 0.498611 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −10.9147 | −2.06269 | ||||||||
\(29\) | −5.50430 | −1.02212 | −0.511061 | − | 0.859544i | \(-0.670748\pi\) | ||||
−0.511061 | + | 0.859544i | \(0.670748\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.80206 | 0.862475 | 0.431238 | − | 0.902238i | \(-0.358077\pi\) | ||||
0.431238 | + | 0.902238i | \(0.358077\pi\) | |||||||
\(32\) | 7.94959 | 1.40530 | ||||||||
\(33\) | 1.57991 | 0.275026 | ||||||||
\(34\) | −2.38197 | −0.408504 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.50430 | 0.417383 | ||||||||
\(37\) | 6.37232 | 1.04760 | 0.523801 | − | 0.851841i | \(-0.324514\pi\) | ||||
0.523801 | + | 0.851841i | \(0.324514\pi\) | |||||||
\(38\) | −16.2967 | −2.64368 | ||||||||
\(39\) | 1.19794 | 0.191824 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.47214 | −1.16695 | −0.583476 | − | 0.812131i | \(-0.698308\pi\) | ||||
−0.583476 | + | 0.812131i | \(0.698308\pi\) | |||||||
\(42\) | −9.24998 | −1.42730 | ||||||||
\(43\) | 1.24998 | 0.190620 | 0.0953102 | − | 0.995448i | \(-0.469616\pi\) | ||||
0.0953102 | + | 0.995448i | \(0.469616\pi\) | |||||||
\(44\) | −3.95656 | −0.596473 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.92439 | −0.726062 | ||||||||
\(47\) | −4.12765 | −0.602079 | −0.301040 | − | 0.953612i | \(-0.597334\pi\) | ||||
−0.301040 | + | 0.953612i | \(0.597334\pi\) | |||||||
\(48\) | 2.73708 | 0.395064 | ||||||||
\(49\) | 11.9957 | 1.71367 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.12233 | −0.157158 | ||||||||
\(52\) | −3.00000 | −0.416025 | ||||||||
\(53\) | −3.74568 | −0.514509 | −0.257254 | − | 0.966344i | \(-0.582818\pi\) | ||||
−0.257254 | + | 0.966344i | \(0.582818\pi\) | |||||||
\(54\) | 2.12233 | 0.288813 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.66476 | 0.623355 | ||||||||
\(57\) | −7.67867 | −1.01707 | ||||||||
\(58\) | 11.6820 | 1.53392 | ||||||||
\(59\) | 9.15613 | 1.19203 | 0.596013 | − | 0.802975i | \(-0.296751\pi\) | ||||
0.596013 | + | 0.802975i | \(0.296751\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.39588 | 0.178724 | 0.0893620 | − | 0.995999i | \(-0.471517\pi\) | ||||
0.0893620 | + | 0.995999i | \(0.471517\pi\) | |||||||
\(62\) | −10.1916 | −1.29433 | ||||||||
\(63\) | −4.35840 | −0.549107 | ||||||||
\(64\) | −11.3975 | −1.42469 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3.35309 | −0.412736 | ||||||||
\(67\) | 3.86270 | 0.471904 | 0.235952 | − | 0.971765i | \(-0.424179\pi\) | ||||
0.235952 | + | 0.971765i | \(0.424179\pi\) | |||||||
\(68\) | 2.81066 | 0.340843 | ||||||||
\(69\) | −2.32027 | −0.279328 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.6051 | −1.25859 | −0.629297 | − | 0.777165i | \(-0.716657\pi\) | ||||
−0.629297 | + | 0.777165i | \(0.716657\pi\) | |||||||
\(72\) | −1.07029 | −0.126135 | ||||||||
\(73\) | −4.99672 | −0.584821 | −0.292411 | − | 0.956293i | \(-0.594457\pi\) | ||||
−0.292411 | + | 0.956293i | \(0.594457\pi\) | |||||||
\(74\) | −13.5242 | −1.57215 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 19.2297 | 2.20580 | ||||||||
\(77\) | 6.88586 | 0.784717 | ||||||||
\(78\) | −2.54243 | −0.287873 | ||||||||
\(79\) | 14.5531 | 1.63735 | 0.818673 | − | 0.574259i | \(-0.194710\pi\) | ||||
0.818673 | + | 0.574259i | \(0.194710\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 15.8584 | 1.75126 | ||||||||
\(83\) | 8.73603 | 0.958904 | 0.479452 | − | 0.877568i | \(-0.340835\pi\) | ||||
0.479452 | + | 0.877568i | \(0.340835\pi\) | |||||||
\(84\) | 10.9147 | 1.19090 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.65288 | −0.286067 | ||||||||
\(87\) | 5.50430 | 0.590123 | ||||||||
\(88\) | 1.69096 | 0.180257 | ||||||||
\(89\) | −10.0381 | −1.06404 | −0.532020 | − | 0.846732i | \(-0.678567\pi\) | ||||
−0.532020 | + | 0.846732i | \(0.678567\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.22110 | 0.547320 | ||||||||
\(92\) | 5.81066 | 0.605803 | ||||||||
\(93\) | −4.80206 | −0.497950 | ||||||||
\(94\) | 8.76025 | 0.903550 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −7.94959 | −0.811351 | ||||||||
\(97\) | 7.49996 | 0.761506 | 0.380753 | − | 0.924677i | \(-0.375665\pi\) | ||||
0.380753 | + | 0.924677i | \(0.375665\pi\) | |||||||
\(98\) | −25.4588 | −2.57173 | ||||||||
\(99\) | −1.57991 | −0.158787 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.51821 | −0.648586 | −0.324293 | − | 0.945957i | \(-0.605126\pi\) | ||||
−0.324293 | + | 0.945957i | \(0.605126\pi\) | |||||||
\(102\) | 2.38197 | 0.235850 | ||||||||
\(103\) | −8.04876 | −0.793068 | −0.396534 | − | 0.918020i | \(-0.629787\pi\) | ||||
−0.396534 | + | 0.918020i | \(0.629787\pi\) | |||||||
\(104\) | 1.28215 | 0.125725 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.94959 | 0.772132 | ||||||||
\(107\) | −9.47745 | −0.916220 | −0.458110 | − | 0.888896i | \(-0.651473\pi\) | ||||
−0.458110 | + | 0.888896i | \(0.651473\pi\) | |||||||
\(108\) | −2.50430 | −0.240976 | ||||||||
\(109\) | −11.6657 | −1.11738 | −0.558688 | − | 0.829378i | \(-0.688695\pi\) | ||||
−0.558688 | + | 0.829378i | \(0.688695\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.37232 | −0.604833 | ||||||||
\(112\) | 11.9293 | 1.12721 | ||||||||
\(113\) | 14.9254 | 1.40406 | 0.702030 | − | 0.712147i | \(-0.252277\pi\) | ||||
0.702030 | + | 0.712147i | \(0.252277\pi\) | |||||||
\(114\) | 16.2967 | 1.52633 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −13.7844 | −1.27985 | ||||||||
\(117\) | −1.19794 | −0.110750 | ||||||||
\(118\) | −19.4324 | −1.78889 | ||||||||
\(119\) | −4.89158 | −0.448410 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.50390 | −0.773082 | ||||||||
\(122\) | −2.96252 | −0.268214 | ||||||||
\(123\) | 7.47214 | 0.673740 | ||||||||
\(124\) | 12.0258 | 1.07995 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 9.24998 | 0.824054 | ||||||||
\(127\) | 16.9957 | 1.50812 | 0.754061 | − | 0.656805i | \(-0.228092\pi\) | ||||
0.754061 | + | 0.656805i | \(0.228092\pi\) | |||||||
\(128\) | 8.29014 | 0.732752 | ||||||||
\(129\) | −1.24998 | −0.110055 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.328872 | −0.0287337 | −0.0143669 | − | 0.999897i | \(-0.504573\pi\) | ||||
−0.0143669 | + | 0.999897i | \(0.504573\pi\) | |||||||
\(132\) | 3.95656 | 0.344374 | ||||||||
\(133\) | −33.4667 | −2.90194 | ||||||||
\(134\) | −8.19794 | −0.708194 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.20122 | −0.103004 | ||||||||
\(137\) | −4.56271 | −0.389818 | −0.194909 | − | 0.980821i | \(-0.562441\pi\) | ||||
−0.194909 | + | 0.980821i | \(0.562441\pi\) | |||||||
\(138\) | 4.92439 | 0.419192 | ||||||||
\(139\) | −4.73400 | −0.401533 | −0.200766 | − | 0.979639i | \(-0.564343\pi\) | ||||
−0.200766 | + | 0.979639i | \(0.564343\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.12765 | 0.347611 | ||||||||
\(142\) | 22.5076 | 1.88879 | ||||||||
\(143\) | 1.89263 | 0.158270 | ||||||||
\(144\) | −2.73708 | −0.228090 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 10.6047 | 0.877651 | ||||||||
\(147\) | −11.9957 | −0.989386 | ||||||||
\(148\) | 15.9582 | 1.31175 | ||||||||
\(149\) | 4.67644 | 0.383109 | 0.191555 | − | 0.981482i | \(-0.438647\pi\) | ||||
0.191555 | + | 0.981482i | \(0.438647\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.54178 | −0.532362 | −0.266181 | − | 0.963923i | \(-0.585762\pi\) | ||||
−0.266181 | + | 0.963923i | \(0.585762\pi\) | |||||||
\(152\) | −8.21842 | −0.666602 | ||||||||
\(153\) | 1.12233 | 0.0907353 | ||||||||
\(154\) | −14.6141 | −1.17764 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 3.00000 | 0.240192 | ||||||||
\(157\) | −3.99404 | −0.318759 | −0.159379 | − | 0.987217i | \(-0.550949\pi\) | ||||
−0.159379 | + | 0.987217i | \(0.550949\pi\) | |||||||
\(158\) | −30.8864 | −2.45719 | ||||||||
\(159\) | 3.74568 | 0.297052 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.1127 | −0.796991 | ||||||||
\(162\) | −2.12233 | −0.166746 | ||||||||
\(163\) | −4.80141 | −0.376075 | −0.188038 | − | 0.982162i | \(-0.560213\pi\) | ||||
−0.188038 | + | 0.982162i | \(0.560213\pi\) | |||||||
\(164\) | −18.7125 | −1.46120 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −18.5408 | −1.43904 | ||||||||
\(167\) | −23.6600 | −1.83087 | −0.915434 | − | 0.402469i | \(-0.868152\pi\) | ||||
−0.915434 | + | 0.402469i | \(0.868152\pi\) | |||||||
\(168\) | −4.66476 | −0.359894 | ||||||||
\(169\) | −11.5649 | −0.889611 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.67867 | 0.587203 | ||||||||
\(172\) | 3.13033 | 0.238685 | ||||||||
\(173\) | −14.5043 | −1.10274 | −0.551371 | − | 0.834260i | \(-0.685895\pi\) | ||||
−0.551371 | + | 0.834260i | \(0.685895\pi\) | |||||||
\(174\) | −11.6820 | −0.885607 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.32433 | 0.325959 | ||||||||
\(177\) | −9.15613 | −0.688217 | ||||||||
\(178\) | 21.3043 | 1.59682 | ||||||||
\(179\) | 0.796746 | 0.0595516 | 0.0297758 | − | 0.999557i | \(-0.490521\pi\) | ||||
0.0297758 | + | 0.999557i | \(0.490521\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.2185 | −1.05685 | −0.528425 | − | 0.848980i | \(-0.677217\pi\) | ||||
−0.528425 | + | 0.848980i | \(0.677217\pi\) | |||||||
\(182\) | −11.0809 | −0.821372 | ||||||||
\(183\) | −1.39588 | −0.103186 | ||||||||
\(184\) | −2.48337 | −0.183076 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 10.1916 | 0.747282 | ||||||||
\(187\) | −1.77318 | −0.129668 | ||||||||
\(188\) | −10.3369 | −0.753894 | ||||||||
\(189\) | 4.35840 | 0.317027 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.3697 | −0.750324 | −0.375162 | − | 0.926959i | \(-0.622413\pi\) | ||||
−0.375162 | + | 0.926959i | \(0.622413\pi\) | |||||||
\(192\) | 11.3975 | 0.822544 | ||||||||
\(193\) | −4.34712 | −0.312913 | −0.156456 | − | 0.987685i | \(-0.550007\pi\) | ||||
−0.156456 | + | 0.987685i | \(0.550007\pi\) | |||||||
\(194\) | −15.9174 | −1.14280 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 30.0407 | 2.14577 | ||||||||
\(197\) | −1.87990 | −0.133937 | −0.0669686 | − | 0.997755i | \(-0.521333\pi\) | ||||
−0.0669686 | + | 0.997755i | \(0.521333\pi\) | |||||||
\(198\) | 3.35309 | 0.238294 | ||||||||
\(199\) | 4.26028 | 0.302003 | 0.151002 | − | 0.988534i | \(-0.451750\pi\) | ||||
0.151002 | + | 0.988534i | \(0.451750\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.86270 | −0.272454 | ||||||||
\(202\) | 13.8338 | 0.973344 | ||||||||
\(203\) | 23.9899 | 1.68376 | ||||||||
\(204\) | −2.81066 | −0.196786 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 17.0821 | 1.19017 | ||||||||
\(207\) | 2.32027 | 0.161270 | ||||||||
\(208\) | 3.27886 | 0.227348 | ||||||||
\(209\) | −12.1316 | −0.839159 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.29671 | −0.640012 | −0.320006 | − | 0.947416i | \(-0.603685\pi\) | ||||
−0.320006 | + | 0.947416i | \(0.603685\pi\) | |||||||
\(212\) | −9.38031 | −0.644242 | ||||||||
\(213\) | 10.6051 | 0.726649 | ||||||||
\(214\) | 20.1143 | 1.37499 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.07029 | 0.0728241 | ||||||||
\(217\) | −20.9293 | −1.42077 | ||||||||
\(218\) | 24.7586 | 1.67686 | ||||||||
\(219\) | 4.99672 | 0.337647 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.34449 | −0.0904400 | ||||||||
\(222\) | 13.5242 | 0.907683 | ||||||||
\(223\) | 3.39758 | 0.227519 | 0.113759 | − | 0.993508i | \(-0.463711\pi\) | ||||
0.113759 | + | 0.993508i | \(0.463711\pi\) | |||||||
\(224\) | −34.6475 | −2.31498 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −31.6766 | −2.10710 | ||||||||
\(227\) | −26.7973 | −1.77860 | −0.889300 | − | 0.457324i | \(-0.848808\pi\) | ||||
−0.889300 | + | 0.457324i | \(0.848808\pi\) | |||||||
\(228\) | −19.2297 | −1.27352 | ||||||||
\(229\) | −1.18200 | −0.0781085 | −0.0390543 | − | 0.999237i | \(-0.512435\pi\) | ||||
−0.0390543 | + | 0.999237i | \(0.512435\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.88586 | −0.453057 | ||||||||
\(232\) | 5.89121 | 0.386777 | ||||||||
\(233\) | −7.09483 | −0.464798 | −0.232399 | − | 0.972621i | \(-0.574658\pi\) | ||||
−0.232399 | + | 0.972621i | \(0.574658\pi\) | |||||||
\(234\) | 2.54243 | 0.166204 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 22.9297 | 1.49260 | ||||||||
\(237\) | −14.5531 | −0.945323 | ||||||||
\(238\) | 10.3816 | 0.672937 | ||||||||
\(239\) | 0.0427926 | 0.00276802 | 0.00138401 | − | 0.999999i | \(-0.499559\pi\) | ||||
0.00138401 | + | 0.999999i | \(0.499559\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.7711 | −0.758242 | −0.379121 | − | 0.925347i | \(-0.623774\pi\) | ||||
−0.379121 | + | 0.925347i | \(0.623774\pi\) | |||||||
\(242\) | 18.0481 | 1.16018 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 3.49570 | 0.223789 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −15.8584 | −1.01109 | ||||||||
\(247\) | −9.19859 | −0.585292 | ||||||||
\(248\) | −5.13961 | −0.326365 | ||||||||
\(249\) | −8.73603 | −0.553623 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.4764 | 1.10310 | 0.551550 | − | 0.834142i | \(-0.314036\pi\) | ||||
0.551550 | + | 0.834142i | \(0.314036\pi\) | |||||||
\(252\) | −10.9147 | −0.687564 | ||||||||
\(253\) | −3.66581 | −0.230468 | ||||||||
\(254\) | −36.0705 | −2.26326 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5.20057 | 0.325036 | ||||||||
\(257\) | −15.4671 | −0.964814 | −0.482407 | − | 0.875947i | \(-0.660237\pi\) | ||||
−0.482407 | + | 0.875947i | \(0.660237\pi\) | |||||||
\(258\) | 2.65288 | 0.165161 | ||||||||
\(259\) | −27.7731 | −1.72574 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.50430 | −0.340708 | ||||||||
\(262\) | 0.697977 | 0.0431211 | ||||||||
\(263\) | −1.44759 | −0.0892624 | −0.0446312 | − | 0.999004i | \(-0.514211\pi\) | ||||
−0.0446312 | + | 0.999004i | \(0.514211\pi\) | |||||||
\(264\) | −1.69096 | −0.104071 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 71.0276 | 4.35498 | ||||||||
\(267\) | 10.0381 | 0.614323 | ||||||||
\(268\) | 9.67336 | 0.590895 | ||||||||
\(269\) | −8.70617 | −0.530825 | −0.265412 | − | 0.964135i | \(-0.585508\pi\) | ||||
−0.265412 | + | 0.964135i | \(0.585508\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −28.6338 | −1.73938 | −0.869689 | − | 0.493600i | \(-0.835681\pi\) | ||||
−0.869689 | + | 0.493600i | \(0.835681\pi\) | |||||||
\(272\) | −3.07192 | −0.186263 | ||||||||
\(273\) | −5.22110 | −0.315995 | ||||||||
\(274\) | 9.68359 | 0.585007 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −5.81066 | −0.349761 | ||||||||
\(277\) | −5.30210 | −0.318572 | −0.159286 | − | 0.987232i | \(-0.550919\pi\) | ||||
−0.159286 | + | 0.987232i | \(0.550919\pi\) | |||||||
\(278\) | 10.0471 | 0.602587 | ||||||||
\(279\) | 4.80206 | 0.287492 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.0832 | −1.43668 | −0.718342 | − | 0.695691i | \(-0.755098\pi\) | ||||
−0.718342 | + | 0.695691i | \(0.755098\pi\) | |||||||
\(282\) | −8.76025 | −0.521665 | ||||||||
\(283\) | 27.1143 | 1.61178 | 0.805889 | − | 0.592066i | \(-0.201688\pi\) | ||||
0.805889 | + | 0.592066i | \(0.201688\pi\) | |||||||
\(284\) | −26.5583 | −1.57595 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.01680 | −0.237518 | ||||||||
\(287\) | 32.5666 | 1.92234 | ||||||||
\(288\) | 7.94959 | 0.468434 | ||||||||
\(289\) | −15.7404 | −0.925904 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.49996 | −0.439656 | ||||||||
\(292\) | −12.5133 | −0.732284 | ||||||||
\(293\) | 20.3016 | 1.18603 | 0.593017 | − | 0.805190i | \(-0.297937\pi\) | ||||
0.593017 | + | 0.805190i | \(0.297937\pi\) | |||||||
\(294\) | 25.4588 | 1.48479 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −6.82024 | −0.396418 | ||||||||
\(297\) | 1.57991 | 0.0916754 | ||||||||
\(298\) | −9.92497 | −0.574938 | ||||||||
\(299\) | −2.77955 | −0.160745 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.44792 | −0.314013 | ||||||||
\(302\) | 13.8838 | 0.798925 | ||||||||
\(303\) | 6.51821 | 0.374462 | ||||||||
\(304\) | −21.0172 | −1.20542 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −2.38197 | −0.136168 | ||||||||
\(307\) | 2.51330 | 0.143442 | 0.0717208 | − | 0.997425i | \(-0.477151\pi\) | ||||
0.0717208 | + | 0.997425i | \(0.477151\pi\) | |||||||
\(308\) | 17.2443 | 0.982583 | ||||||||
\(309\) | 8.04876 | 0.457878 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.82417 | 0.273554 | 0.136777 | − | 0.990602i | \(-0.456326\pi\) | ||||
0.136777 | + | 0.990602i | \(0.456326\pi\) | |||||||
\(312\) | −1.28215 | −0.0725872 | ||||||||
\(313\) | 5.98812 | 0.338468 | 0.169234 | − | 0.985576i | \(-0.445871\pi\) | ||||
0.169234 | + | 0.985576i | \(0.445871\pi\) | |||||||
\(314\) | 8.47668 | 0.478366 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 36.4452 | 2.05020 | ||||||||
\(317\) | −17.3531 | −0.974646 | −0.487323 | − | 0.873222i | \(-0.662027\pi\) | ||||
−0.487323 | + | 0.873222i | \(0.662027\pi\) | |||||||
\(318\) | −7.94959 | −0.445791 | ||||||||
\(319\) | 8.69627 | 0.486898 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.47745 | 0.528980 | ||||||||
\(322\) | 21.4625 | 1.19606 | ||||||||
\(323\) | 8.61803 | 0.479520 | ||||||||
\(324\) | 2.50430 | 0.139128 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 10.1902 | 0.564383 | ||||||||
\(327\) | 11.6657 | 0.645117 | ||||||||
\(328\) | 7.99737 | 0.441581 | ||||||||
\(329\) | 17.9899 | 0.991818 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.3355 | 1.11774 | 0.558870 | − | 0.829255i | \(-0.311235\pi\) | ||||
0.558870 | + | 0.829255i | \(0.311235\pi\) | |||||||
\(332\) | 21.8776 | 1.20069 | ||||||||
\(333\) | 6.37232 | 0.349201 | ||||||||
\(334\) | 50.2145 | 2.74761 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −11.9293 | −0.650797 | ||||||||
\(337\) | −34.2571 | −1.86610 | −0.933052 | − | 0.359741i | \(-0.882865\pi\) | ||||
−0.933052 | + | 0.359741i | \(0.882865\pi\) | |||||||
\(338\) | 24.5447 | 1.33505 | ||||||||
\(339\) | −14.9254 | −0.810635 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.58680 | −0.410848 | ||||||||
\(342\) | −16.2967 | −0.881225 | ||||||||
\(343\) | −21.7731 | −1.17564 | ||||||||
\(344\) | −1.33784 | −0.0721318 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 30.7830 | 1.65490 | ||||||||
\(347\) | 0.0493616 | 0.00264987 | 0.00132494 | − | 0.999999i | \(-0.499578\pi\) | ||||
0.00132494 | + | 0.999999i | \(0.499578\pi\) | |||||||
\(348\) | 13.7844 | 0.738922 | ||||||||
\(349\) | −7.47437 | −0.400094 | −0.200047 | − | 0.979786i | \(-0.564109\pi\) | ||||
−0.200047 | + | 0.979786i | \(0.564109\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.19794 | 0.0639413 | ||||||||
\(352\) | −12.5596 | −0.669429 | ||||||||
\(353\) | 18.5650 | 0.988115 | 0.494057 | − | 0.869429i | \(-0.335513\pi\) | ||||
0.494057 | + | 0.869429i | \(0.335513\pi\) | |||||||
\(354\) | 19.4324 | 1.03282 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −25.1385 | −1.33234 | ||||||||
\(357\) | 4.89158 | 0.258890 | ||||||||
\(358\) | −1.69096 | −0.0893700 | ||||||||
\(359\) | 10.6044 | 0.559681 | 0.279841 | − | 0.960046i | \(-0.409718\pi\) | ||||
0.279841 | + | 0.960046i | \(0.409718\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 39.9620 | 2.10327 | ||||||||
\(362\) | 30.1763 | 1.58603 | ||||||||
\(363\) | 8.50390 | 0.446339 | ||||||||
\(364\) | 13.0752 | 0.685327 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2.96252 | 0.154854 | ||||||||
\(367\) | 11.6176 | 0.606435 | 0.303218 | − | 0.952921i | \(-0.401939\pi\) | ||||
0.303218 | + | 0.952921i | \(0.401939\pi\) | |||||||
\(368\) | −6.35078 | −0.331057 | ||||||||
\(369\) | −7.47214 | −0.388984 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 16.3252 | 0.847561 | ||||||||
\(372\) | −12.0258 | −0.623509 | ||||||||
\(373\) | 23.1272 | 1.19748 | 0.598742 | − | 0.800942i | \(-0.295668\pi\) | ||||
0.598742 | + | 0.800942i | \(0.295668\pi\) | |||||||
\(374\) | 3.76328 | 0.194595 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.41779 | 0.227830 | ||||||||
\(377\) | 6.59382 | 0.339599 | ||||||||
\(378\) | −9.24998 | −0.475768 | ||||||||
\(379\) | 24.8912 | 1.27857 | 0.639287 | − | 0.768968i | \(-0.279230\pi\) | ||||
0.639287 | + | 0.768968i | \(0.279230\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −16.9957 | −0.870714 | ||||||||
\(382\) | 22.0079 | 1.12602 | ||||||||
\(383\) | 15.7221 | 0.803363 | 0.401681 | − | 0.915780i | \(-0.368426\pi\) | ||||
0.401681 | + | 0.915780i | \(0.368426\pi\) | |||||||
\(384\) | −8.29014 | −0.423054 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 9.22604 | 0.469593 | ||||||||
\(387\) | 1.24998 | 0.0635401 | ||||||||
\(388\) | 18.7822 | 0.953519 | ||||||||
\(389\) | −8.50633 | −0.431288 | −0.215644 | − | 0.976472i | \(-0.569185\pi\) | ||||
−0.215644 | + | 0.976472i | \(0.569185\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.60412 | 0.131696 | ||||||||
\(392\) | −12.8389 | −0.648460 | ||||||||
\(393\) | 0.328872 | 0.0165894 | ||||||||
\(394\) | 3.98977 | 0.201002 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −3.95656 | −0.198824 | ||||||||
\(397\) | −26.2549 | −1.31770 | −0.658848 | − | 0.752276i | \(-0.728956\pi\) | ||||
−0.658848 | + | 0.752276i | \(0.728956\pi\) | |||||||
\(398\) | −9.04174 | −0.453222 | ||||||||
\(399\) | 33.4667 | 1.67543 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −25.2815 | −1.26250 | −0.631250 | − | 0.775579i | \(-0.717458\pi\) | ||||
−0.631250 | + | 0.775579i | \(0.717458\pi\) | |||||||
\(402\) | 8.19794 | 0.408876 | ||||||||
\(403\) | −5.75258 | −0.286556 | ||||||||
\(404\) | −16.3236 | −0.812127 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −50.9147 | −2.52685 | ||||||||
\(407\) | −10.0677 | −0.499035 | ||||||||
\(408\) | 1.20122 | 0.0594695 | ||||||||
\(409\) | 33.7932 | 1.67097 | 0.835483 | − | 0.549517i | \(-0.185188\pi\) | ||||
0.835483 | + | 0.549517i | \(0.185188\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.56271 | 0.225062 | ||||||||
\(412\) | −20.1565 | −0.993039 | ||||||||
\(413\) | −39.9061 | −1.96365 | ||||||||
\(414\) | −4.92439 | −0.242021 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −9.52313 | −0.466910 | ||||||||
\(417\) | 4.73400 | 0.231825 | ||||||||
\(418\) | 25.7473 | 1.25934 | ||||||||
\(419\) | 7.93332 | 0.387568 | 0.193784 | − | 0.981044i | \(-0.437924\pi\) | ||||
0.193784 | + | 0.981044i | \(0.437924\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.48795 | 0.364941 | 0.182470 | − | 0.983211i | \(-0.441591\pi\) | ||||
0.182470 | + | 0.983211i | \(0.441591\pi\) | |||||||
\(422\) | 19.7307 | 0.960476 | ||||||||
\(423\) | −4.12765 | −0.200693 | ||||||||
\(424\) | 4.00897 | 0.194693 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −22.5076 | −1.09049 | ||||||||
\(427\) | −6.08380 | −0.294416 | ||||||||
\(428\) | −23.7344 | −1.14724 | ||||||||
\(429\) | −1.89263 | −0.0913771 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 23.3470 | 1.12459 | 0.562294 | − | 0.826937i | \(-0.309919\pi\) | ||||
0.562294 | + | 0.826937i | \(0.309919\pi\) | |||||||
\(432\) | 2.73708 | 0.131688 | ||||||||
\(433\) | 3.35677 | 0.161316 | 0.0806581 | − | 0.996742i | \(-0.474298\pi\) | ||||
0.0806581 | + | 0.996742i | \(0.474298\pi\) | |||||||
\(434\) | 44.4190 | 2.13218 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −29.2145 | −1.39912 | ||||||||
\(437\) | 17.8166 | 0.852285 | ||||||||
\(438\) | −10.6047 | −0.506712 | ||||||||
\(439\) | −9.48402 | −0.452648 | −0.226324 | − | 0.974052i | \(-0.572671\pi\) | ||||
−0.226324 | + | 0.974052i | \(0.572671\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 11.9957 | 0.571222 | ||||||||
\(442\) | 2.85345 | 0.135725 | ||||||||
\(443\) | −9.65446 | −0.458697 | −0.229349 | − | 0.973344i | \(-0.573660\pi\) | ||||
−0.229349 | + | 0.973344i | \(0.573660\pi\) | |||||||
\(444\) | −15.9582 | −0.757342 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −7.21080 | −0.341441 | ||||||||
\(447\) | −4.67644 | −0.221188 | ||||||||
\(448\) | 49.6749 | 2.34692 | ||||||||
\(449\) | 31.5260 | 1.48780 | 0.743902 | − | 0.668289i | \(-0.232973\pi\) | ||||
0.743902 | + | 0.668289i | \(0.232973\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.8053 | 0.555888 | ||||||||
\(452\) | 37.3776 | 1.75809 | ||||||||
\(453\) | 6.54178 | 0.307360 | ||||||||
\(454\) | 56.8729 | 2.66918 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 8.21842 | 0.384863 | ||||||||
\(457\) | 9.94467 | 0.465192 | 0.232596 | − | 0.972573i | \(-0.425278\pi\) | ||||
0.232596 | + | 0.972573i | \(0.425278\pi\) | |||||||
\(458\) | 2.50859 | 0.117219 | ||||||||
\(459\) | −1.12233 | −0.0523860 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −23.6836 | −1.10305 | −0.551527 | − | 0.834157i | \(-0.685955\pi\) | ||||
−0.551527 | + | 0.834157i | \(0.685955\pi\) | |||||||
\(462\) | 14.6141 | 0.679909 | ||||||||
\(463\) | −27.6504 | −1.28502 | −0.642511 | − | 0.766277i | \(-0.722107\pi\) | ||||
−0.642511 | + | 0.766277i | \(0.722107\pi\) | |||||||
\(464\) | 15.0657 | 0.699409 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 15.0576 | 0.697530 | ||||||||
\(467\) | −4.35840 | −0.201683 | −0.100841 | − | 0.994903i | \(-0.532153\pi\) | ||||
−0.100841 | + | 0.994903i | \(0.532153\pi\) | |||||||
\(468\) | −3.00000 | −0.138675 | ||||||||
\(469\) | −16.8352 | −0.777377 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.99404 | 0.184035 | ||||||||
\(472\) | −9.79973 | −0.451069 | ||||||||
\(473\) | −1.97485 | −0.0908038 | ||||||||
\(474\) | 30.8864 | 1.41866 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −12.2500 | −0.561477 | ||||||||
\(477\) | −3.74568 | −0.171503 | ||||||||
\(478\) | −0.0908201 | −0.00415401 | ||||||||
\(479\) | 12.8143 | 0.585499 | 0.292750 | − | 0.956189i | \(-0.405430\pi\) | ||||
0.292750 | + | 0.956189i | \(0.405430\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.63365 | −0.348064 | ||||||||
\(482\) | 24.9822 | 1.13791 | ||||||||
\(483\) | 10.1127 | 0.460143 | ||||||||
\(484\) | −21.2963 | −0.968014 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 2.12233 | 0.0962710 | ||||||||
\(487\) | 6.92209 | 0.313670 | 0.156835 | − | 0.987625i | \(-0.449871\pi\) | ||||
0.156835 | + | 0.987625i | \(0.449871\pi\) | |||||||
\(488\) | −1.49400 | −0.0676301 | ||||||||
\(489\) | 4.80141 | 0.217127 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 26.8161 | 1.21020 | 0.605098 | − | 0.796151i | \(-0.293134\pi\) | ||||
0.605098 | + | 0.796151i | \(0.293134\pi\) | |||||||
\(492\) | 18.7125 | 0.843623 | ||||||||
\(493\) | −6.17766 | −0.278228 | ||||||||
\(494\) | 19.5225 | 0.878358 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −13.1436 | −0.590167 | ||||||||
\(497\) | 46.2213 | 2.07331 | ||||||||
\(498\) | 18.5408 | 0.830832 | ||||||||
\(499\) | 2.75460 | 0.123313 | 0.0616565 | − | 0.998097i | \(-0.480362\pi\) | ||||
0.0616565 | + | 0.998097i | \(0.480362\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 23.6600 | 1.05705 | ||||||||
\(502\) | −37.0907 | −1.65544 | ||||||||
\(503\) | −15.7102 | −0.700483 | −0.350241 | − | 0.936659i | \(-0.613900\pi\) | ||||
−0.350241 | + | 0.936659i | \(0.613900\pi\) | |||||||
\(504\) | 4.66476 | 0.207785 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 7.78008 | 0.345867 | ||||||||
\(507\) | 11.5649 | 0.513617 | ||||||||
\(508\) | 42.5622 | 1.88839 | ||||||||
\(509\) | −41.0884 | −1.82121 | −0.910606 | − | 0.413277i | \(-0.864384\pi\) | ||||
−0.910606 | + | 0.413277i | \(0.864384\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 21.7777 | 0.963388 | ||||||||
\(512\) | −27.6176 | −1.22054 | ||||||||
\(513\) | −7.67867 | −0.339022 | ||||||||
\(514\) | 32.8264 | 1.44791 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −3.13033 | −0.137805 | ||||||||
\(517\) | 6.52129 | 0.286806 | ||||||||
\(518\) | 58.9438 | 2.58984 | ||||||||
\(519\) | 14.5043 | 0.636668 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 36.1710 | 1.58468 | 0.792341 | − | 0.610079i | \(-0.208862\pi\) | ||||
0.792341 | + | 0.610079i | \(0.208862\pi\) | |||||||
\(522\) | 11.6820 | 0.511305 | ||||||||
\(523\) | −28.0490 | −1.22650 | −0.613248 | − | 0.789891i | \(-0.710137\pi\) | ||||
−0.613248 | + | 0.789891i | \(0.710137\pi\) | |||||||
\(524\) | −0.823595 | −0.0359789 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.07228 | 0.133958 | ||||||||
\(527\) | 5.38951 | 0.234771 | ||||||||
\(528\) | −4.32433 | −0.188192 | ||||||||
\(529\) | −17.6163 | −0.765927 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.15613 | 0.397342 | ||||||||
\(532\) | −83.8108 | −3.63366 | ||||||||
\(533\) | 8.95117 | 0.387718 | ||||||||
\(534\) | −21.3043 | −0.921925 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −4.13422 | −0.178571 | ||||||||
\(537\) | −0.796746 | −0.0343821 | ||||||||
\(538\) | 18.4774 | 0.796617 | ||||||||
\(539\) | −18.9520 | −0.816321 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.45822 | 0.148681 | 0.0743403 | − | 0.997233i | \(-0.476315\pi\) | ||||
0.0743403 | + | 0.997233i | \(0.476315\pi\) | |||||||
\(542\) | 60.7704 | 2.61031 | ||||||||
\(543\) | 14.2185 | 0.610173 | ||||||||
\(544\) | 8.92209 | 0.382531 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 11.0809 | 0.474220 | ||||||||
\(547\) | −13.9635 | −0.597034 | −0.298517 | − | 0.954404i | \(-0.596492\pi\) | ||||
−0.298517 | + | 0.954404i | \(0.596492\pi\) | |||||||
\(548\) | −11.4264 | −0.488111 | ||||||||
\(549\) | 1.39588 | 0.0595747 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −42.2657 | −1.80058 | ||||||||
\(552\) | 2.48337 | 0.105699 | ||||||||
\(553\) | −63.4281 | −2.69724 | ||||||||
\(554\) | 11.2528 | 0.478086 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −11.8554 | −0.502779 | ||||||||
\(557\) | 6.59585 | 0.279475 | 0.139738 | − | 0.990189i | \(-0.455374\pi\) | ||||
0.139738 | + | 0.990189i | \(0.455374\pi\) | |||||||
\(558\) | −10.1916 | −0.431444 | ||||||||
\(559\) | −1.49740 | −0.0633334 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.77318 | 0.0748638 | ||||||||
\(562\) | 51.1126 | 2.15605 | ||||||||
\(563\) | 16.0218 | 0.675238 | 0.337619 | − | 0.941283i | \(-0.390379\pi\) | ||||
0.337619 | + | 0.941283i | \(0.390379\pi\) | |||||||
\(564\) | 10.3369 | 0.435261 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −57.5456 | −2.41882 | ||||||||
\(567\) | −4.35840 | −0.183036 | ||||||||
\(568\) | 11.3505 | 0.476258 | ||||||||
\(569\) | 23.0914 | 0.968042 | 0.484021 | − | 0.875056i | \(-0.339176\pi\) | ||||
0.484021 | + | 0.875056i | \(0.339176\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −34.0102 | −1.42328 | −0.711640 | − | 0.702544i | \(-0.752047\pi\) | ||||
−0.711640 | + | 0.702544i | \(0.752047\pi\) | |||||||
\(572\) | 4.73972 | 0.198178 | ||||||||
\(573\) | 10.3697 | 0.433200 | ||||||||
\(574\) | −69.1171 | −2.88489 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −11.3975 | −0.474896 | ||||||||
\(577\) | 6.46727 | 0.269236 | 0.134618 | − | 0.990898i | \(-0.457019\pi\) | ||||
0.134618 | + | 0.990898i | \(0.457019\pi\) | |||||||
\(578\) | 33.4063 | 1.38952 | ||||||||
\(579\) | 4.34712 | 0.180660 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −38.0751 | −1.57962 | ||||||||
\(582\) | 15.9174 | 0.659798 | ||||||||
\(583\) | 5.91782 | 0.245091 | ||||||||
\(584\) | 5.34794 | 0.221299 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −43.0868 | −1.77990 | ||||||||
\(587\) | −38.5012 | −1.58911 | −0.794557 | − | 0.607189i | \(-0.792297\pi\) | ||||
−0.794557 | + | 0.607189i | \(0.792297\pi\) | |||||||
\(588\) | −30.0407 | −1.23886 | ||||||||
\(589\) | 36.8735 | 1.51934 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.87990 | 0.0773287 | ||||||||
\(592\) | −17.4416 | −0.716843 | ||||||||
\(593\) | −4.93069 | −0.202479 | −0.101240 | − | 0.994862i | \(-0.532281\pi\) | ||||
−0.101240 | + | 0.994862i | \(0.532281\pi\) | |||||||
\(594\) | −3.35309 | −0.137579 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 11.7112 | 0.479710 | ||||||||
\(597\) | −4.26028 | −0.174362 | ||||||||
\(598\) | 5.89913 | 0.241233 | ||||||||
\(599\) | −35.0268 | −1.43116 | −0.715578 | − | 0.698533i | \(-0.753836\pi\) | ||||
−0.715578 | + | 0.698533i | \(0.753836\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.90570 | −0.200108 | −0.100054 | − | 0.994982i | \(-0.531901\pi\) | ||||
−0.100054 | + | 0.994982i | \(0.531901\pi\) | |||||||
\(602\) | 11.5623 | 0.471244 | ||||||||
\(603\) | 3.86270 | 0.157301 | ||||||||
\(604\) | −16.3826 | −0.666597 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −13.8338 | −0.561961 | ||||||||
\(607\) | −48.6955 | −1.97649 | −0.988244 | − | 0.152884i | \(-0.951144\pi\) | ||||
−0.988244 | + | 0.152884i | \(0.951144\pi\) | |||||||
\(608\) | 61.0423 | 2.47559 | ||||||||
\(609\) | −23.9899 | −0.972122 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.94467 | 0.200040 | ||||||||
\(612\) | 2.81066 | 0.113614 | ||||||||
\(613\) | −17.2139 | −0.695262 | −0.347631 | − | 0.937631i | \(-0.613014\pi\) | ||||
−0.347631 | + | 0.937631i | \(0.613014\pi\) | |||||||
\(614\) | −5.33406 | −0.215265 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7.36988 | −0.296941 | ||||||||
\(617\) | 31.6092 | 1.27254 | 0.636268 | − | 0.771468i | \(-0.280477\pi\) | ||||
0.636268 | + | 0.771468i | \(0.280477\pi\) | |||||||
\(618\) | −17.0821 | −0.687145 | ||||||||
\(619\) | −22.8196 | −0.917198 | −0.458599 | − | 0.888643i | \(-0.651649\pi\) | ||||
−0.458599 | + | 0.888643i | \(0.651649\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.32027 | −0.0931094 | ||||||||
\(622\) | −10.2385 | −0.410526 | ||||||||
\(623\) | 43.7502 | 1.75281 | ||||||||
\(624\) | −3.27886 | −0.131259 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −12.7088 | −0.507945 | ||||||||
\(627\) | 12.1316 | 0.484489 | ||||||||
\(628\) | −10.0023 | −0.399134 | ||||||||
\(629\) | 7.15186 | 0.285163 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 38.0499 | 1.51474 | 0.757372 | − | 0.652984i | \(-0.226483\pi\) | ||||
0.757372 | + | 0.652984i | \(0.226483\pi\) | |||||||
\(632\) | −15.5760 | −0.619581 | ||||||||
\(633\) | 9.29671 | 0.369511 | ||||||||
\(634\) | 36.8290 | 1.46267 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 9.38031 | 0.371953 | ||||||||
\(637\) | −14.3701 | −0.569363 | ||||||||
\(638\) | −18.4564 | −0.730696 | ||||||||
\(639\) | −10.6051 | −0.419531 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 26.5108 | 1.04711 | 0.523557 | − | 0.851991i | \(-0.324605\pi\) | ||||
0.523557 | + | 0.851991i | \(0.324605\pi\) | |||||||
\(642\) | −20.1143 | −0.793849 | ||||||||
\(643\) | 36.0014 | 1.41976 | 0.709879 | − | 0.704324i | \(-0.248750\pi\) | ||||
0.709879 | + | 0.704324i | \(0.248750\pi\) | |||||||
\(644\) | −25.3252 | −0.997952 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −18.2903 | −0.719624 | ||||||||
\(647\) | −41.7840 | −1.64270 | −0.821349 | − | 0.570426i | \(-0.806778\pi\) | ||||
−0.821349 | + | 0.570426i | \(0.806778\pi\) | |||||||
\(648\) | −1.07029 | −0.0420450 | ||||||||
\(649\) | −14.4658 | −0.567833 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 20.9293 | 0.820284 | ||||||||
\(652\) | −12.0242 | −0.470903 | ||||||||
\(653\) | −21.4404 | −0.839027 | −0.419513 | − | 0.907749i | \(-0.637799\pi\) | ||||
−0.419513 | + | 0.907749i | \(0.637799\pi\) | |||||||
\(654\) | −24.7586 | −0.968137 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 20.4519 | 0.798511 | ||||||||
\(657\) | −4.99672 | −0.194940 | ||||||||
\(658\) | −38.1807 | −1.48844 | ||||||||
\(659\) | −16.8319 | −0.655678 | −0.327839 | − | 0.944734i | \(-0.606320\pi\) | ||||
−0.327839 | + | 0.944734i | \(0.606320\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.03846 | 0.0792868 | 0.0396434 | − | 0.999214i | \(-0.487378\pi\) | ||||
0.0396434 | + | 0.999214i | \(0.487378\pi\) | |||||||
\(662\) | −43.1587 | −1.67741 | ||||||||
\(663\) | 1.34449 | 0.0522156 | ||||||||
\(664\) | −9.35010 | −0.362854 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −13.5242 | −0.524051 | ||||||||
\(667\) | −12.7715 | −0.494514 | ||||||||
\(668\) | −59.2518 | −2.29252 | ||||||||
\(669\) | −3.39758 | −0.131358 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.20536 | −0.0851369 | ||||||||
\(672\) | 34.6475 | 1.33656 | ||||||||
\(673\) | −35.3776 | −1.36371 | −0.681854 | − | 0.731489i | \(-0.738826\pi\) | ||||
−0.681854 | + | 0.731489i | \(0.738826\pi\) | |||||||
\(674\) | 72.7050 | 2.80049 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −28.9621 | −1.11393 | ||||||||
\(677\) | −44.4173 | −1.70710 | −0.853548 | − | 0.521014i | \(-0.825554\pi\) | ||||
−0.853548 | + | 0.521014i | \(0.825554\pi\) | |||||||
\(678\) | 31.6766 | 1.21653 | ||||||||
\(679\) | −32.6879 | −1.25444 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 26.7973 | 1.02688 | ||||||||
\(682\) | 16.1017 | 0.616567 | ||||||||
\(683\) | −42.4952 | −1.62603 | −0.813016 | − | 0.582241i | \(-0.802176\pi\) | ||||
−0.813016 | + | 0.582241i | \(0.802176\pi\) | |||||||
\(684\) | 19.2297 | 0.735266 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 46.2098 | 1.76430 | ||||||||
\(687\) | 1.18200 | 0.0450960 | ||||||||
\(688\) | −3.42130 | −0.130436 | ||||||||
\(689\) | 4.48710 | 0.170945 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.0808 | 1.06825 | 0.534123 | − | 0.845407i | \(-0.320642\pi\) | ||||
0.534123 | + | 0.845407i | \(0.320642\pi\) | |||||||
\(692\) | −36.3231 | −1.38080 | ||||||||
\(693\) | 6.88586 | 0.261572 | ||||||||
\(694\) | −0.104762 | −0.00397671 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −5.89121 | −0.223306 | ||||||||
\(697\) | −8.38623 | −0.317651 | ||||||||
\(698\) | 15.8631 | 0.600427 | ||||||||
\(699\) | 7.09483 | 0.268351 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 46.4314 | 1.75369 | 0.876845 | − | 0.480772i | \(-0.159644\pi\) | ||||
0.876845 | + | 0.480772i | \(0.159644\pi\) | |||||||
\(702\) | −2.54243 | −0.0959578 | ||||||||
\(703\) | 48.9309 | 1.84547 | ||||||||
\(704\) | 18.0070 | 0.678664 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −39.4011 | −1.48288 | ||||||||
\(707\) | 28.4090 | 1.06843 | ||||||||
\(708\) | −22.9297 | −0.861750 | ||||||||
\(709\) | 48.6331 | 1.82646 | 0.913228 | − | 0.407450i | \(-0.133582\pi\) | ||||
0.913228 | + | 0.407450i | \(0.133582\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 14.5531 | 0.545782 | ||||||||
\(712\) | 10.7437 | 0.402638 | ||||||||
\(713\) | 11.1421 | 0.417275 | ||||||||
\(714\) | −10.3816 | −0.388520 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.99529 | 0.0745675 | ||||||||
\(717\) | −0.0427926 | −0.00159812 | ||||||||
\(718\) | −22.5062 | −0.839923 | ||||||||
\(719\) | −21.1954 | −0.790456 | −0.395228 | − | 0.918583i | \(-0.629334\pi\) | ||||
−0.395228 | + | 0.918583i | \(0.629334\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 35.0797 | 1.30644 | ||||||||
\(722\) | −84.8128 | −3.15641 | ||||||||
\(723\) | 11.7711 | 0.437771 | ||||||||
\(724\) | −35.6073 | −1.32333 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −18.0481 | −0.669828 | ||||||||
\(727\) | −13.5911 | −0.504066 | −0.252033 | − | 0.967719i | \(-0.581099\pi\) | ||||
−0.252033 | + | 0.967719i | \(0.581099\pi\) | |||||||
\(728\) | −5.58810 | −0.207109 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.40290 | 0.0518880 | ||||||||
\(732\) | −3.49570 | −0.129205 | ||||||||
\(733\) | −18.6531 | −0.688967 | −0.344484 | − | 0.938792i | \(-0.611946\pi\) | ||||
−0.344484 | + | 0.938792i | \(0.611946\pi\) | |||||||
\(734\) | −24.6565 | −0.910088 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 18.4452 | 0.679900 | ||||||||
\(737\) | −6.10270 | −0.224796 | ||||||||
\(738\) | 15.8584 | 0.583754 | ||||||||
\(739\) | 26.4452 | 0.972803 | 0.486401 | − | 0.873735i | \(-0.338309\pi\) | ||||
0.486401 | + | 0.873735i | \(0.338309\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.19859 | 0.337919 | ||||||||
\(742\) | −34.6475 | −1.27195 | ||||||||
\(743\) | 29.0191 | 1.06461 | 0.532304 | − | 0.846553i | \(-0.321326\pi\) | ||||
0.532304 | + | 0.846553i | \(0.321326\pi\) | |||||||
\(744\) | 5.13961 | 0.188427 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −49.0837 | −1.79708 | ||||||||
\(747\) | 8.73603 | 0.319635 | ||||||||
\(748\) | −4.44058 | −0.162364 | ||||||||
\(749\) | 41.3065 | 1.50931 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.9489 | 0.581985 | 0.290992 | − | 0.956725i | \(-0.406015\pi\) | ||||
0.290992 | + | 0.956725i | \(0.406015\pi\) | |||||||
\(752\) | 11.2977 | 0.411985 | ||||||||
\(753\) | −17.4764 | −0.636875 | ||||||||
\(754\) | −13.9943 | −0.509642 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 10.9147 | 0.396965 | ||||||||
\(757\) | 16.4183 | 0.596734 | 0.298367 | − | 0.954451i | \(-0.403558\pi\) | ||||
0.298367 | + | 0.954451i | \(0.403558\pi\) | |||||||
\(758\) | −52.8274 | −1.91878 | ||||||||
\(759\) | 3.66581 | 0.133061 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −49.2715 | −1.78609 | −0.893045 | − | 0.449967i | \(-0.851436\pi\) | ||||
−0.893045 | + | 0.449967i | \(0.851436\pi\) | |||||||
\(762\) | 36.0705 | 1.30670 | ||||||||
\(763\) | 50.8440 | 1.84068 | ||||||||
\(764\) | −25.9688 | −0.939518 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −33.3676 | −1.20562 | ||||||||
\(767\) | −10.9685 | −0.396049 | ||||||||
\(768\) | −5.20057 | −0.187660 | ||||||||
\(769\) | 49.4236 | 1.78226 | 0.891129 | − | 0.453749i | \(-0.149914\pi\) | ||||
0.891129 | + | 0.453749i | \(0.149914\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15.4671 | 0.557036 | ||||||||
\(772\) | −10.8865 | −0.391814 | ||||||||
\(773\) | −25.9084 | −0.931860 | −0.465930 | − | 0.884822i | \(-0.654280\pi\) | ||||
−0.465930 | + | 0.884822i | \(0.654280\pi\) | |||||||
\(774\) | −2.65288 | −0.0953557 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −8.02715 | −0.288158 | ||||||||
\(777\) | 27.7731 | 0.996355 | ||||||||
\(778\) | 18.0533 | 0.647241 | ||||||||
\(779\) | −57.3761 | −2.05571 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.7551 | 0.599543 | ||||||||
\(782\) | −5.52681 | −0.197638 | ||||||||
\(783\) | 5.50430 | 0.196708 | ||||||||
\(784\) | −32.8331 | −1.17261 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −0.697977 | −0.0248960 | ||||||||
\(787\) | −30.7155 | −1.09489 | −0.547444 | − | 0.836842i | \(-0.684399\pi\) | ||||
−0.547444 | + | 0.836842i | \(0.684399\pi\) | |||||||
\(788\) | −4.70783 | −0.167710 | ||||||||
\(789\) | 1.44759 | 0.0515357 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −65.0508 | −2.31294 | ||||||||
\(792\) | 1.69096 | 0.0600857 | ||||||||
\(793\) | −1.67218 | −0.0593808 | ||||||||
\(794\) | 55.7216 | 1.97749 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 10.6690 | 0.378154 | ||||||||
\(797\) | 33.7141 | 1.19421 | 0.597107 | − | 0.802161i | \(-0.296317\pi\) | ||||
0.597107 | + | 0.802161i | \(0.296317\pi\) | |||||||
\(798\) | −71.0276 | −2.51435 | ||||||||
\(799\) | −4.63260 | −0.163890 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10.0381 | −0.354680 | ||||||||
\(802\) | 53.6559 | 1.89465 | ||||||||
\(803\) | 7.89434 | 0.278585 | ||||||||
\(804\) | −9.67336 | −0.341153 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 12.2089 | 0.430040 | ||||||||
\(807\) | 8.70617 | 0.306472 | ||||||||
\(808\) | 6.97639 | 0.245429 | ||||||||
\(809\) | −0.923014 | −0.0324514 | −0.0162257 | − | 0.999868i | \(-0.505165\pi\) | ||||
−0.0162257 | + | 0.999868i | \(0.505165\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26.7815 | 0.940424 | 0.470212 | − | 0.882553i | \(-0.344177\pi\) | ||||
0.470212 | + | 0.882553i | \(0.344177\pi\) | |||||||
\(812\) | 60.0780 | 2.10832 | ||||||||
\(813\) | 28.6338 | 1.00423 | ||||||||
\(814\) | 21.3669 | 0.748910 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 3.07192 | 0.107539 | ||||||||
\(817\) | 9.59820 | 0.335799 | ||||||||
\(818\) | −71.7204 | −2.50765 | ||||||||
\(819\) | 5.22110 | 0.182440 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −36.8489 | −1.28604 | −0.643018 | − | 0.765851i | \(-0.722318\pi\) | ||||
−0.643018 | + | 0.765851i | \(0.722318\pi\) | |||||||
\(822\) | −9.68359 | −0.337754 | ||||||||
\(823\) | −20.4262 | −0.712012 | −0.356006 | − | 0.934484i | \(-0.615862\pi\) | ||||
−0.356006 | + | 0.934484i | \(0.615862\pi\) | |||||||
\(824\) | 8.61452 | 0.300101 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 84.6940 | 2.94688 | ||||||||
\(827\) | −4.33017 | −0.150575 | −0.0752874 | − | 0.997162i | \(-0.523987\pi\) | ||||
−0.0752874 | + | 0.997162i | \(0.523987\pi\) | |||||||
\(828\) | 5.81066 | 0.201934 | ||||||||
\(829\) | −0.614348 | −0.0213372 | −0.0106686 | − | 0.999943i | \(-0.503396\pi\) | ||||
−0.0106686 | + | 0.999943i | \(0.503396\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.30210 | 0.183928 | ||||||||
\(832\) | 13.6535 | 0.473351 | ||||||||
\(833\) | 13.4631 | 0.466470 | ||||||||
\(834\) | −10.0471 | −0.347904 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −30.3811 | −1.05075 | ||||||||
\(837\) | −4.80206 | −0.165983 | ||||||||
\(838\) | −16.8372 | −0.581630 | ||||||||
\(839\) | 5.39981 | 0.186422 | 0.0932111 | − | 0.995646i | \(-0.470287\pi\) | ||||
0.0932111 | + | 0.995646i | \(0.470287\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.29731 | 0.0447349 | ||||||||
\(842\) | −15.8919 | −0.547672 | ||||||||
\(843\) | 24.0832 | 0.829469 | ||||||||
\(844\) | −23.2817 | −0.801391 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 8.76025 | 0.301183 | ||||||||
\(847\) | 37.0634 | 1.27351 | ||||||||
\(848\) | 10.2522 | 0.352063 | ||||||||
\(849\) | −27.1143 | −0.930561 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 14.7855 | 0.506841 | ||||||||
\(852\) | 26.5583 | 0.909874 | ||||||||
\(853\) | 39.7935 | 1.36250 | 0.681252 | − | 0.732049i | \(-0.261436\pi\) | ||||
0.681252 | + | 0.732049i | \(0.261436\pi\) | |||||||
\(854\) | 12.9119 | 0.441835 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 10.1436 | 0.346702 | ||||||||
\(857\) | 42.8643 | 1.46422 | 0.732109 | − | 0.681188i | \(-0.238536\pi\) | ||||
0.732109 | + | 0.681188i | \(0.238536\pi\) | |||||||
\(858\) | 4.01680 | 0.137131 | ||||||||
\(859\) | −4.56494 | −0.155754 | −0.0778769 | − | 0.996963i | \(-0.524814\pi\) | ||||
−0.0778769 | + | 0.996963i | \(0.524814\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −32.5666 | −1.10987 | ||||||||
\(862\) | −49.5502 | −1.68769 | ||||||||
\(863\) | 37.6273 | 1.28085 | 0.640424 | − | 0.768022i | \(-0.278759\pi\) | ||||
0.640424 | + | 0.768022i | \(0.278759\pi\) | |||||||
\(864\) | −7.94959 | −0.270450 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −7.12419 | −0.242090 | ||||||||
\(867\) | 15.7404 | 0.534571 | ||||||||
\(868\) | −52.4133 | −1.77902 | ||||||||
\(869\) | −22.9925 | −0.779966 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.62728 | −0.156790 | ||||||||
\(872\) | 12.4857 | 0.422821 | ||||||||
\(873\) | 7.49996 | 0.253835 | ||||||||
\(874\) | −37.8128 | −1.27904 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 12.5133 | 0.422784 | ||||||||
\(877\) | −52.4041 | −1.76956 | −0.884781 | − | 0.466008i | \(-0.845692\pi\) | ||||
−0.884781 | + | 0.466008i | \(0.845692\pi\) | |||||||
\(878\) | 20.1283 | 0.679296 | ||||||||
\(879\) | −20.3016 | −0.684757 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.93778 | −0.267430 | −0.133715 | − | 0.991020i | \(-0.542691\pi\) | ||||
−0.133715 | + | 0.991020i | \(0.542691\pi\) | |||||||
\(882\) | −25.4588 | −0.857242 | ||||||||
\(883\) | −31.6919 | −1.06652 | −0.533259 | − | 0.845952i | \(-0.679033\pi\) | ||||
−0.533259 | + | 0.845952i | \(0.679033\pi\) | |||||||
\(884\) | −3.36700 | −0.113244 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 20.4900 | 0.688374 | ||||||||
\(887\) | −2.82104 | −0.0947213 | −0.0473606 | − | 0.998878i | \(-0.515081\pi\) | ||||
−0.0473606 | + | 0.998878i | \(0.515081\pi\) | |||||||
\(888\) | 6.82024 | 0.228872 | ||||||||
\(889\) | −74.0739 | −2.48436 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.57991 | −0.0529288 | ||||||||
\(892\) | 8.50856 | 0.284888 | ||||||||
\(893\) | −31.6949 | −1.06063 | ||||||||
\(894\) | 9.92497 | 0.331941 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −36.1318 | −1.20708 | ||||||||
\(897\) | 2.77955 | 0.0928064 | ||||||||
\(898\) | −66.9087 | −2.23277 | ||||||||
\(899\) | −26.4320 | −0.881556 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.20390 | −0.140052 | ||||||||
\(902\) | −25.0547 | −0.834231 | ||||||||
\(903\) | 5.44792 | 0.181295 | ||||||||
\(904\) | −15.9745 | −0.531304 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −13.8838 | −0.461259 | ||||||||
\(907\) | 44.1799 | 1.46697 | 0.733485 | − | 0.679705i | \(-0.237892\pi\) | ||||
0.733485 | + | 0.679705i | \(0.237892\pi\) | |||||||
\(908\) | −67.1085 | −2.22707 | ||||||||
\(909\) | −6.51821 | −0.216195 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −34.5260 | −1.14390 | −0.571949 | − | 0.820289i | \(-0.693812\pi\) | ||||
−0.571949 | + | 0.820289i | \(0.693812\pi\) | |||||||
\(912\) | 21.0172 | 0.695948 | ||||||||
\(913\) | −13.8021 | −0.456783 | ||||||||
\(914\) | −21.1059 | −0.698122 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.96007 | −0.0978036 | ||||||||
\(917\) | 1.43336 | 0.0473336 | ||||||||
\(918\) | 2.38197 | 0.0786166 | ||||||||
\(919\) | −0.531075 | −0.0175185 | −0.00875927 | − | 0.999962i | \(-0.502788\pi\) | ||||
−0.00875927 | + | 0.999962i | \(0.502788\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.51330 | −0.0828161 | ||||||||
\(922\) | 50.2645 | 1.65537 | ||||||||
\(923\) | 12.7043 | 0.418166 | ||||||||
\(924\) | −17.2443 | −0.567295 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 58.6833 | 1.92845 | ||||||||
\(927\) | −8.04876 | −0.264356 | ||||||||
\(928\) | −43.7569 | −1.43639 | ||||||||
\(929\) | 46.1961 | 1.51565 | 0.757823 | − | 0.652460i | \(-0.226263\pi\) | ||||
0.757823 | + | 0.652460i | \(0.226263\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 92.1108 | 3.01881 | ||||||||
\(932\) | −17.7676 | −0.581997 | ||||||||
\(933\) | −4.82417 | −0.157936 | ||||||||
\(934\) | 9.24998 | 0.302669 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.28215 | 0.0419082 | ||||||||
\(937\) | 30.1220 | 0.984042 | 0.492021 | − | 0.870583i | \(-0.336258\pi\) | ||||
0.492021 | + | 0.870583i | \(0.336258\pi\) | |||||||
\(938\) | 35.7299 | 1.16662 | ||||||||
\(939\) | −5.98812 | −0.195415 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 57.0783 | 1.86070 | 0.930350 | − | 0.366672i | \(-0.119503\pi\) | ||||
0.930350 | + | 0.366672i | \(0.119503\pi\) | |||||||
\(942\) | −8.47668 | −0.276185 | ||||||||
\(943\) | −17.3374 | −0.564583 | ||||||||
\(944\) | −25.0611 | −0.815668 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.19130 | 0.136271 | ||||||||
\(947\) | 41.1250 | 1.33638 | 0.668192 | − | 0.743989i | \(-0.267069\pi\) | ||||
0.668192 | + | 0.743989i | \(0.267069\pi\) | |||||||
\(948\) | −36.4452 | −1.18369 | ||||||||
\(949\) | 5.98576 | 0.194306 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 17.3531 | 0.562712 | ||||||||
\(952\) | 5.23542 | 0.169681 | ||||||||
\(953\) | −34.8143 | −1.12775 | −0.563873 | − | 0.825861i | \(-0.690689\pi\) | ||||
−0.563873 | + | 0.825861i | \(0.690689\pi\) | |||||||
\(954\) | 7.94959 | 0.257377 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0.107165 | 0.00346598 | ||||||||
\(957\) | −8.69627 | −0.281111 | ||||||||
\(958\) | −27.1962 | −0.878668 | ||||||||
\(959\) | 19.8861 | 0.642156 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.94022 | −0.256136 | ||||||||
\(962\) | 16.2012 | 0.522346 | ||||||||
\(963\) | −9.47745 | −0.305407 | ||||||||
\(964\) | −29.4783 | −0.949432 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −21.4625 | −0.690544 | ||||||||
\(967\) | 37.2697 | 1.19851 | 0.599257 | − | 0.800557i | \(-0.295463\pi\) | ||||
0.599257 | + | 0.800557i | \(0.295463\pi\) | |||||||
\(968\) | 9.10165 | 0.292538 | ||||||||
\(969\) | −8.61803 | −0.276851 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −26.0092 | −0.834677 | −0.417338 | − | 0.908751i | \(-0.637037\pi\) | ||||
−0.417338 | + | 0.908751i | \(0.637037\pi\) | |||||||
\(972\) | −2.50430 | −0.0803254 | ||||||||
\(973\) | 20.6327 | 0.661453 | ||||||||
\(974\) | −14.6910 | −0.470729 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.82064 | −0.122296 | ||||||||
\(977\) | −0.458579 | −0.0146712 | −0.00733561 | − | 0.999973i | \(-0.502335\pi\) | ||||
−0.00733561 | + | 0.999973i | \(0.502335\pi\) | |||||||
\(978\) | −10.1902 | −0.325846 | ||||||||
\(979\) | 15.8593 | 0.506865 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11.6657 | −0.372458 | ||||||||
\(982\) | −56.9128 | −1.81616 | ||||||||
\(983\) | −8.94565 | −0.285322 | −0.142661 | − | 0.989772i | \(-0.545566\pi\) | ||||
−0.142661 | + | 0.989772i | \(0.545566\pi\) | |||||||
\(984\) | −7.99737 | −0.254947 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 13.1111 | 0.417541 | ||||||||
\(987\) | −17.9899 | −0.572626 | ||||||||
\(988\) | −23.0360 | −0.732874 | ||||||||
\(989\) | 2.90030 | 0.0922241 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −56.5337 | −1.79585 | −0.897926 | − | 0.440147i | \(-0.854926\pi\) | ||||
−0.897926 | + | 0.440147i | \(0.854926\pi\) | |||||||
\(992\) | 38.1744 | 1.21204 | ||||||||
\(993\) | −20.3355 | −0.645327 | ||||||||
\(994\) | −98.0970 | −3.11145 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −21.8776 | −0.693219 | ||||||||
\(997\) | −39.6114 | −1.25451 | −0.627253 | − | 0.778816i | \(-0.715821\pi\) | ||||
−0.627253 | + | 0.778816i | \(0.715821\pi\) | |||||||
\(998\) | −5.84619 | −0.185058 | ||||||||
\(999\) | −6.37232 | −0.201611 |
(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 | 1875.2.a.e.1.2 | 4 | ||
3.2 | odd | 2 | 5625.2.a.n.1.3 | 4 | |||
5.2 | odd | 4 | 1875.2.b.c.1249.2 | 8 | |||
5.3 | odd | 4 | 1875.2.b.c.1249.7 | 8 | |||
5.4 | even | 2 | 1875.2.a.h.1.3 | 4 | |||
15.14 | odd | 2 | 5625.2.a.i.1.2 | 4 | |||
25.2 | odd | 20 | 375.2.i.b.274.1 | 16 | |||
25.9 | even | 10 | 75.2.g.b.31.2 | ✓ | 8 | ||
25.11 | even | 5 | 375.2.g.b.226.1 | 8 | |||
25.12 | odd | 20 | 375.2.i.b.349.4 | 16 | |||
25.13 | odd | 20 | 375.2.i.b.349.1 | 16 | |||
25.14 | even | 10 | 75.2.g.b.46.2 | yes | 8 | ||
25.16 | even | 5 | 375.2.g.b.151.1 | 8 | |||
25.23 | odd | 20 | 375.2.i.b.274.4 | 16 | |||
75.14 | odd | 10 | 225.2.h.c.46.1 | 8 | |||
75.59 | odd | 10 | 225.2.h.c.181.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.2.g.b.31.2 | ✓ | 8 | 25.9 | even | 10 | ||
75.2.g.b.46.2 | yes | 8 | 25.14 | even | 10 | ||
225.2.h.c.46.1 | 8 | 75.14 | odd | 10 | |||
225.2.h.c.181.1 | 8 | 75.59 | odd | 10 | |||
375.2.g.b.151.1 | 8 | 25.16 | even | 5 | |||
375.2.g.b.226.1 | 8 | 25.11 | even | 5 | |||
375.2.i.b.274.1 | 16 | 25.2 | odd | 20 | |||
375.2.i.b.274.4 | 16 | 25.23 | odd | 20 | |||
375.2.i.b.349.1 | 16 | 25.13 | odd | 20 | |||
375.2.i.b.349.4 | 16 | 25.12 | odd | 20 | |||
1875.2.a.e.1.2 | 4 | 1.1 | even | 1 | trivial | ||
1875.2.a.h.1.3 | 4 | 5.4 | even | 2 | |||
1875.2.b.c.1249.2 | 8 | 5.2 | odd | 4 | |||
1875.2.b.c.1249.7 | 8 | 5.3 | odd | 4 | |||
5625.2.a.i.1.2 | 4 | 15.14 | odd | 2 | |||
5625.2.a.n.1.3 | 4 | 3.2 | odd | 2 |