Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7440,2,Mod(1,7440)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7440, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7440.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7440 = 2^{4} \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7440.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: | \(59.4086991038\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{3} - x^{2} - 3x + 1 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 465) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.311108\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7440.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.688892 | −0.260377 | −0.130188 | − | 0.991489i | \(-0.541558\pi\) | ||||
−0.130188 | + | 0.991489i | \(0.541558\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.00000 | −0.603023 | −0.301511 | − | 0.953463i | \(-0.597491\pi\) | ||||
−0.301511 | + | 0.953463i | \(0.597491\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.73975 | 1.03722 | 0.518610 | − | 0.855011i | \(-0.326450\pi\) | ||||
0.518610 | + | 0.855011i | \(0.326450\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.28100 | 0.553223 | 0.276611 | − | 0.960982i | \(-0.410789\pi\) | ||||
0.276611 | + | 0.960982i | \(0.410789\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.688892 | 0.150329 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.90321 | −0.605362 | −0.302681 | − | 0.953092i | \(-0.597882\pi\) | ||||
−0.302681 | + | 0.953092i | \(0.597882\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.02074 | −0.746633 | −0.373317 | − | 0.927704i | \(-0.621780\pi\) | ||||
−0.373317 | + | 0.927704i | \(0.621780\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.00000 | −0.179605 | ||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.00000 | 0.348155 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.688892 | −0.116444 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.79060 | −1.44517 | −0.722583 | − | 0.691284i | \(-0.757045\pi\) | ||||
−0.722583 | + | 0.691284i | \(0.757045\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.73975 | −0.598839 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.75557 | 0.430348 | 0.215174 | − | 0.976576i | \(-0.430968\pi\) | ||||
0.215174 | + | 0.976576i | \(0.430968\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.05086 | −0.160254 | −0.0801270 | − | 0.996785i | \(-0.525533\pi\) | ||||
−0.0801270 | + | 0.996785i | \(0.525533\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.70964 | −0.686971 | −0.343485 | − | 0.939158i | \(-0.611608\pi\) | ||||
−0.343485 | + | 0.939158i | \(0.611608\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.52543 | −0.932204 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.28100 | −0.319403 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.14764 | 0.295001 | 0.147501 | − | 0.989062i | \(-0.452877\pi\) | ||||
0.147501 | + | 0.989062i | \(0.452877\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.00000 | −0.269680 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.44938 | 0.839638 | 0.419819 | − | 0.907608i | \(-0.362094\pi\) | ||||
0.419819 | + | 0.907608i | \(0.362094\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.05086 | −0.646696 | −0.323348 | − | 0.946280i | \(-0.604808\pi\) | ||||
−0.323348 | + | 0.946280i | \(0.604808\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.688892 | −0.0867923 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.73975 | 0.463859 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.44446 | 0.665147 | 0.332573 | − | 0.943077i | \(-0.392083\pi\) | ||||
0.332573 | + | 0.943077i | \(0.392083\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.90321 | 0.349506 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.96989 | −1.06453 | −0.532265 | − | 0.846578i | \(-0.678659\pi\) | ||||
−0.532265 | + | 0.846578i | \(0.678659\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.92396 | −1.04447 | −0.522235 | − | 0.852802i | \(-0.674902\pi\) | ||||
−0.522235 | + | 0.852802i | \(0.674902\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.37778 | 0.157013 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.38271 | 0.943128 | 0.471564 | − | 0.881832i | \(-0.343690\pi\) | ||||
0.471564 | + | 0.881832i | \(0.343690\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.5161 | 1.15429 | 0.577144 | − | 0.816643i | \(-0.304167\pi\) | ||||
0.577144 | + | 0.816643i | \(0.304167\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.28100 | 0.247409 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.02074 | 0.431069 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.5002 | 1.43102 | 0.715511 | − | 0.698601i | \(-0.246194\pi\) | ||||
0.715511 | + | 0.698601i | \(0.246194\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.57628 | −0.270068 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.00000 | 0.103695 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.0000 | −1.21842 | −0.609208 | − | 0.793011i | \(-0.708512\pi\) | ||||
−0.609208 | + | 0.793011i | \(0.708512\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.00000 | −0.201008 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.29529 | 0.825412 | 0.412706 | − | 0.910864i | \(-0.364584\pi\) | ||||
0.412706 | + | 0.910864i | \(0.364584\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.98418 | −0.294040 | −0.147020 | − | 0.989134i | \(-0.546968\pi\) | ||||
−0.147020 | + | 0.989134i | \(0.546968\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.688892 | 0.0672290 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.52543 | −0.147469 | −0.0737343 | − | 0.997278i | \(-0.523492\pi\) | ||||
−0.0737343 | + | 0.997278i | \(0.523492\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.76049 | 0.360190 | 0.180095 | − | 0.983649i | \(-0.442360\pi\) | ||||
0.180095 | + | 0.983649i | \(0.442360\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.79060 | 0.834367 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.18421 | −0.863978 | −0.431989 | − | 0.901879i | \(-0.642188\pi\) | ||||
−0.431989 | + | 0.901879i | \(0.642188\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.90321 | −0.270726 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.73975 | 0.345740 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.57136 | −0.144046 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.75557 | −0.248461 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.4795 | 1.01864 | 0.509320 | − | 0.860577i | \(-0.329897\pi\) | ||||
0.509320 | + | 0.860577i | \(0.329897\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.05086 | 0.0925226 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.0716 | −1.14207 | −0.571035 | − | 0.820925i | \(-0.693458\pi\) | ||||
−0.571035 | + | 0.820925i | \(0.693458\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.1383 | −0.951607 | −0.475804 | − | 0.879552i | \(-0.657843\pi\) | ||||
−0.475804 | + | 0.879552i | \(0.657843\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.2351 | −0.868127 | −0.434063 | − | 0.900882i | \(-0.642921\pi\) | ||||
−0.434063 | + | 0.900882i | \(0.642921\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.70964 | 0.396623 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −7.47949 | −0.625467 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.02074 | −0.333905 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.52543 | 0.538208 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.51114 | −0.123797 | −0.0618986 | − | 0.998082i | \(-0.519716\pi\) | ||||
−0.0618986 | + | 0.998082i | \(0.519716\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.76049 | 0.143267 | 0.0716334 | − | 0.997431i | \(-0.477179\pi\) | ||||
0.0716334 | + | 0.997431i | \(0.477179\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.28100 | 0.184408 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.00000 | −0.0803219 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.43801 | −0.274383 | −0.137191 | − | 0.990545i | \(-0.543808\pi\) | ||||
−0.137191 | + | 0.990545i | \(0.543808\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.14764 | −0.170319 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.00000 | 0.157622 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.5970 | 0.830023 | 0.415012 | − | 0.909816i | \(-0.363778\pi\) | ||||
0.415012 | + | 0.909816i | \(0.363778\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.00000 | 0.155700 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 20.0415 | 1.55086 | 0.775428 | − | 0.631435i | \(-0.217534\pi\) | ||||
0.775428 | + | 0.631435i | \(0.217534\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.985710 | 0.0758238 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −18.8988 | −1.43685 | −0.718423 | − | 0.695606i | \(-0.755136\pi\) | ||||
−0.718423 | + | 0.695606i | \(0.755136\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.688892 | −0.0520754 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.44938 | −0.484765 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −16.2953 | −1.21797 | −0.608983 | − | 0.793183i | \(-0.708422\pi\) | ||||
−0.608983 | + | 0.793183i | \(0.708422\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.70471 | −0.126710 | −0.0633552 | − | 0.997991i | \(-0.520180\pi\) | ||||
−0.0633552 | + | 0.997991i | \(0.520180\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.05086 | 0.373370 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.79060 | −0.646298 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.56199 | −0.333606 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.688892 | 0.0501095 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.53188 | 0.255558 | 0.127779 | − | 0.991803i | \(-0.459215\pi\) | ||||
0.127779 | + | 0.991803i | \(0.459215\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.4193 | 1.25387 | 0.626933 | − | 0.779073i | \(-0.284310\pi\) | ||||
0.626933 | + | 0.779073i | \(0.284310\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.73975 | −0.267809 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.0143 | 0.713489 | 0.356744 | − | 0.934202i | \(-0.383887\pi\) | ||||
0.356744 | + | 0.934202i | \(0.383887\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −27.1798 | −1.92672 | −0.963361 | − | 0.268208i | \(-0.913569\pi\) | ||||
−0.963361 | + | 0.268208i | \(0.913569\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.44446 | −0.384023 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.76986 | 0.194406 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.75557 | 0.192457 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.90321 | −0.201787 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.93978 | 0.133540 | 0.0667699 | − | 0.997768i | \(-0.478731\pi\) | ||||
0.0667699 | + | 0.997768i | \(0.478731\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.96989 | 0.614607 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.05086 | −0.0716677 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.688892 | 0.0467650 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.92396 | 0.603025 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.53035 | 0.573813 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −23.5526 | −1.57720 | −0.788600 | − | 0.614906i | \(-0.789194\pi\) | ||||
−0.788600 | + | 0.614906i | \(0.789194\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −19.8020 | −1.31430 | −0.657152 | − | 0.753758i | \(-0.728239\pi\) | ||||
−0.657152 | + | 0.753758i | \(0.728239\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −24.4099 | −1.61305 | −0.806526 | − | 0.591199i | \(-0.798655\pi\) | ||||
−0.806526 | + | 0.591199i | \(0.798655\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.37778 | −0.0906516 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.13828 | 0.205595 | 0.102798 | − | 0.994702i | \(-0.467221\pi\) | ||||
0.102798 | + | 0.994702i | \(0.467221\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.70964 | −0.307223 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.38271 | −0.544515 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.81579 | −0.440877 | −0.220438 | − | 0.975401i | \(-0.570749\pi\) | ||||
−0.220438 | + | 0.975401i | \(0.570749\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.0923 | 1.10101 | 0.550507 | − | 0.834830i | \(-0.314434\pi\) | ||||
0.550507 | + | 0.834830i | \(0.314434\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.52543 | −0.416894 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −10.5161 | −0.666428 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −16.1748 | −1.02095 | −0.510473 | − | 0.859894i | \(-0.670530\pi\) | ||||
−0.510473 | + | 0.859894i | \(0.670530\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.80642 | 0.365047 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.28100 | −0.142842 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 19.0464 | 1.18808 | 0.594041 | − | 0.804435i | \(-0.297532\pi\) | ||||
0.594041 | + | 0.804435i | \(0.297532\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.05578 | 0.376288 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.02074 | −0.248878 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.23506 | 0.384470 | 0.192235 | − | 0.981349i | \(-0.438426\pi\) | ||||
0.192235 | + | 0.981349i | \(0.438426\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.14764 | 0.131929 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −13.5002 | −0.826201 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 20.8365 | 1.27043 | 0.635213 | − | 0.772337i | \(-0.280912\pi\) | ||||
0.635213 | + | 0.772337i | \(0.280912\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.62222 | −0.402271 | −0.201135 | − | 0.979563i | \(-0.564463\pi\) | ||||
−0.201135 | + | 0.979563i | \(0.564463\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.57628 | 0.155924 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.00000 | −0.120605 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.79060 | 0.287839 | 0.143920 | − | 0.989589i | \(-0.454029\pi\) | ||||
0.143920 | + | 0.989589i | \(0.454029\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.00000 | −0.0598684 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.8256 | −1.24235 | −0.621177 | − | 0.783671i | \(-0.713345\pi\) | ||||
−0.621177 | + | 0.783671i | \(0.713345\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.8731 | 0.705783 | 0.352891 | − | 0.935664i | \(-0.385199\pi\) | ||||
0.352891 | + | 0.935664i | \(0.385199\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.89829 | −0.112053 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.7971 | −0.693944 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.0000 | 0.703452 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −18.0143 | −1.05241 | −0.526203 | − | 0.850359i | \(-0.676385\pi\) | ||||
−0.526203 | + | 0.850359i | \(0.676385\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.44938 | 0.375498 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.00000 | 0.116052 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10.8573 | −0.627893 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.723926 | 0.0417264 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8.29529 | −0.476552 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.05086 | −0.289211 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.9240 | −0.623463 | −0.311732 | − | 0.950170i | \(-0.600909\pi\) | ||||
−0.311732 | + | 0.950170i | \(0.600909\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.98418 | 0.169764 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.10324 | −0.289378 | −0.144689 | − | 0.989477i | \(-0.546218\pi\) | ||||
−0.144689 | + | 0.989477i | \(0.546218\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −22.1082 | −1.24963 | −0.624814 | − | 0.780774i | \(-0.714825\pi\) | ||||
−0.624814 | + | 0.780774i | \(0.714825\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.688892 | −0.0388147 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.06515 | −0.0598245 | −0.0299123 | − | 0.999553i | \(-0.509523\pi\) | ||||
−0.0299123 | + | 0.999553i | \(0.509523\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.04149 | 0.450237 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.52543 | 0.0851411 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.73975 | 0.207444 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.76049 | −0.207956 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.24443 | 0.178871 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.9447 | 1.37108 | 0.685542 | − | 0.728033i | \(-0.259565\pi\) | ||||
0.685542 | + | 0.728033i | \(0.259565\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8.79060 | −0.481722 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.44446 | 0.297463 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.453829 | 0.0247216 | 0.0123608 | − | 0.999924i | \(-0.496065\pi\) | ||||
0.0123608 | + | 0.999924i | \(0.496065\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9.18421 | 0.498818 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.00000 | 0.108306 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.31756 | 0.503101 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.90321 | 0.156304 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 29.7560 | 1.59739 | 0.798694 | − | 0.601737i | \(-0.205525\pi\) | ||||
0.798694 | + | 0.601737i | \(0.205525\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.65878 | −0.517023 | −0.258511 | − | 0.966008i | \(-0.583232\pi\) | ||||
−0.258511 | + | 0.966008i | \(0.583232\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.73975 | −0.199613 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −16.8617 | −0.897459 | −0.448730 | − | 0.893668i | \(-0.648123\pi\) | ||||
−0.448730 | + | 0.893668i | \(0.648123\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.96989 | −0.476072 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.57136 | 0.0831652 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.64296 | −0.456158 | −0.228079 | − | 0.973643i | \(-0.573244\pi\) | ||||
−0.228079 | + | 0.973643i | \(0.573244\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.0000 | −1.00000 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.00000 | 0.367405 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.92396 | −0.467101 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.95899 | −0.363256 | −0.181628 | − | 0.983367i | \(-0.558137\pi\) | ||||
−0.181628 | + | 0.983367i | \(0.558137\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.75557 | 0.143449 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.47949 | −0.0768115 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 21.0005 | 1.08736 | 0.543682 | − | 0.839291i | \(-0.317030\pi\) | ||||
0.543682 | + | 0.839291i | \(0.317030\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −15.0366 | −0.774422 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −29.7146 | −1.52633 | −0.763167 | − | 0.646201i | \(-0.776357\pi\) | ||||
−0.763167 | + | 0.646201i | \(0.776357\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −11.4795 | −0.588112 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.05578 | −0.207241 | −0.103620 | − | 0.994617i | \(-0.533043\pi\) | ||||
−0.103620 | + | 0.994617i | \(0.533043\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.37778 | 0.0702184 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.05086 | −0.0534180 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.9985 | −0.557644 | −0.278822 | − | 0.960343i | \(-0.589944\pi\) | ||||
−0.278822 | + | 0.960343i | \(0.589944\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.62222 | −0.334900 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 13.0716 | 0.659375 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.38271 | 0.421780 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.193576 | 0.00971531 | 0.00485765 | − | 0.999988i | \(-0.498454\pi\) | ||||
0.00485765 | + | 0.999988i | \(0.498454\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −38.6242 | −1.92880 | −0.964401 | − | 0.264445i | \(-0.914811\pi\) | ||||
−0.964401 | + | 0.264445i | \(0.914811\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.73975 | −0.186290 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 17.5812 | 0.871468 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.94914 | 0.145826 | 0.0729129 | − | 0.997338i | \(-0.476770\pi\) | ||||
0.0729129 | + | 0.997338i | \(0.476770\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.1383 | 0.549411 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.44293 | −0.218622 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.5161 | 0.516213 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 10.2351 | 0.501213 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 26.0020 | 1.27028 | 0.635141 | − | 0.772397i | \(-0.280942\pi\) | ||||
0.635141 | + | 0.772397i | \(0.280942\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.0143 | −0.975437 | −0.487718 | − | 0.873001i | \(-0.662171\pi\) | ||||
−0.487718 | + | 0.873001i | \(0.662171\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.70964 | −0.228990 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.28100 | 0.110645 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.47949 | 0.168385 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 7.47949 | 0.361113 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.77631 | 0.133730 | 0.0668651 | − | 0.997762i | \(-0.478700\pi\) | ||||
0.0668651 | + | 0.997762i | \(0.478700\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −30.7590 | −1.47818 | −0.739091 | − | 0.673606i | \(-0.764744\pi\) | ||||
−0.739091 | + | 0.673606i | \(0.764744\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.02074 | 0.192780 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −26.8385 | −1.28093 | −0.640467 | − | 0.767986i | \(-0.721259\pi\) | ||||
−0.640467 | + | 0.767986i | \(0.721259\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.52543 | −0.310735 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11.7190 | 0.556787 | 0.278393 | − | 0.960467i | \(-0.410198\pi\) | ||||
0.278393 | + | 0.960467i | \(0.410198\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.5002 | 0.639973 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.51114 | 0.0714743 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 33.8084 | 1.59552 | 0.797759 | − | 0.602976i | \(-0.206019\pi\) | ||||
0.797759 | + | 0.602976i | \(0.206019\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.51114 | −0.259509 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.76049 | −0.0827151 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.57628 | −0.120778 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.61930 | 0.262860 | 0.131430 | − | 0.991325i | \(-0.458043\pi\) | ||||
0.131430 | + | 0.991325i | \(0.458043\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.28100 | −0.106468 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.93825 | −0.136848 | −0.0684239 | − | 0.997656i | \(-0.521797\pi\) | ||||
−0.0684239 | + | 0.997656i | \(0.521797\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.61285 | 0.0749554 | 0.0374777 | − | 0.999297i | \(-0.488068\pi\) | ||||
0.0374777 | + | 0.999297i | \(0.488068\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.00000 | 0.0463739 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11.5857 | 0.536120 | 0.268060 | − | 0.963402i | \(-0.413617\pi\) | ||||
0.268060 | + | 0.963402i | \(0.413617\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.75065 | −0.173189 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.43801 | 0.158415 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.10171 | 0.0966367 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.14764 | 0.0983338 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −26.0020 | −1.18806 | −0.594031 | − | 0.804442i | \(-0.702464\pi\) | ||||
−0.594031 | + | 0.804442i | \(0.702464\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −32.8746 | −1.49895 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.00000 | −0.0910032 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −12.0000 | −0.544892 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −40.8988 | −1.85330 | −0.926650 | − | 0.375925i | \(-0.877325\pi\) | ||||
−0.926650 | + | 0.375925i | \(0.877325\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −10.5970 | −0.479214 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16.6953 | −0.753450 | −0.376725 | − | 0.926325i | \(-0.622950\pi\) | ||||
−0.376725 | + | 0.926325i | \(0.622950\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.17130 | −0.413055 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.00000 | −0.0898933 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.17929 | 0.277179 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 26.3684 | 1.18041 | 0.590206 | − | 0.807253i | \(-0.299046\pi\) | ||||
0.590206 | + | 0.807253i | \(0.299046\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −20.0415 | −0.895388 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.47505 | 0.422472 | 0.211236 | − | 0.977435i | \(-0.432251\pi\) | ||||
0.211236 | + | 0.977435i | \(0.432251\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.29529 | 0.369135 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.985710 | −0.0437769 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 21.9003 | 0.970714 | 0.485357 | − | 0.874316i | \(-0.338690\pi\) | ||||
0.485357 | + | 0.874316i | \(0.338690\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.14764 | 0.271956 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.98418 | −0.131499 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.41927 | 0.414259 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 18.8988 | 0.829564 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −36.2034 | −1.58610 | −0.793050 | − | 0.609156i | \(-0.791508\pi\) | ||||
−0.793050 | + | 0.609156i | \(0.791508\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.7971 | 0.647030 | 0.323515 | − | 0.946223i | \(-0.395135\pi\) | ||||
0.323515 | + | 0.946223i | \(0.395135\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.688892 | 0.0300657 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.28100 | −0.0993618 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.5714 | −0.633537 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.44938 | 0.279879 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.3051 | 0.446365 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.52543 | −0.0659500 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 16.2953 | 0.703194 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 13.0509 | 0.562140 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −41.9956 | −1.80553 | −0.902765 | − | 0.430134i | \(-0.858466\pi\) | ||||
−0.902765 | + | 0.430134i | \(0.858466\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.70471 | 0.0731563 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.76049 | 0.161082 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 34.8004 | 1.48796 | 0.743980 | − | 0.668202i | \(-0.232936\pi\) | ||||
0.743980 | + | 0.668202i | \(0.232936\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.05086 | −0.215565 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.77478 | −0.245569 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8.79060 | 0.373140 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 26.3096 | 1.11477 | 0.557386 | − | 0.830253i | \(-0.311804\pi\) | ||||
0.557386 | + | 0.830253i | \(0.311804\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.92993 | −0.166218 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.56199 | 0.192607 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 31.8306 | 1.34150 | 0.670749 | − | 0.741684i | \(-0.265973\pi\) | ||||
0.670749 | + | 0.741684i | \(0.265973\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.18421 | −0.386383 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.688892 | −0.0289308 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 23.6622 | 0.991970 | 0.495985 | − | 0.868331i | \(-0.334807\pi\) | ||||
0.495985 | + | 0.868331i | \(0.334807\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18.8889 | −0.790477 | −0.395238 | − | 0.918579i | \(-0.629338\pi\) | ||||
−0.395238 | + | 0.918579i | \(0.629338\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.53188 | −0.147546 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.90321 | −0.121072 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.11108 | 0.0462548 | 0.0231274 | − | 0.999733i | \(-0.492638\pi\) | ||||
0.0231274 | + | 0.999733i | \(0.492638\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −17.4193 | −0.723920 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.24443 | −0.300550 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.29529 | −0.177893 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.73975 | 0.154620 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 17.3778 | 0.717258 | 0.358629 | − | 0.933480i | \(-0.383244\pi\) | ||||
0.358629 | + | 0.933480i | \(0.383244\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −10.0143 | −0.411933 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −37.1753 | −1.52661 | −0.763304 | − | 0.646040i | \(-0.776424\pi\) | ||||
−0.763304 | + | 0.646040i | \(0.776424\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.57136 | −0.0644195 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 27.1798 | 1.11239 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −15.6207 | −0.638244 | −0.319122 | − | 0.947714i | \(-0.603388\pi\) | ||||
−0.319122 | + | 0.947714i | \(0.603388\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −26.7239 | −1.09009 | −0.545046 | − | 0.838406i | \(-0.683488\pi\) | ||||
−0.545046 | + | 0.838406i | \(0.683488\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.44446 | 0.221716 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.00000 | −0.284590 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.3936 | −0.584218 | −0.292109 | − | 0.956385i | \(-0.594357\pi\) | ||||
−0.292109 | + | 0.956385i | \(0.594357\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.76986 | −0.112240 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −17.6128 | −0.712540 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.09526 | 0.246185 | 0.123093 | − | 0.992395i | \(-0.460719\pi\) | ||||
0.123093 | + | 0.992395i | \(0.460719\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.75557 | −0.111115 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.34614 | 0.0541936 | 0.0270968 | − | 0.999633i | \(-0.491374\pi\) | ||||
0.0270968 | + | 0.999633i | \(0.491374\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.71900 | −0.229866 | −0.114933 | − | 0.993373i | \(-0.536665\pi\) | ||||
−0.114933 | + | 0.993373i | \(0.536665\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.90321 | 0.116502 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9.30021 | −0.372605 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −20.0513 | −0.799499 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −37.3274 | −1.48598 | −0.742990 | − | 0.669302i | \(-0.766593\pi\) | ||||
−0.742990 | + | 0.669302i | \(0.766593\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.93978 | −0.0770992 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 11.4795 | 0.455550 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −24.4035 | −0.966900 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.96989 | −0.354843 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 36.1323 | 1.42714 | 0.713570 | − | 0.700584i | \(-0.247077\pi\) | ||||
0.713570 | + | 0.700584i | \(0.247077\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.10123 | 0.122301 | 0.0611504 | − | 0.998129i | \(-0.480523\pi\) | ||||
0.0611504 | + | 0.998129i | \(0.480523\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.05086 | 0.0413774 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −29.6227 | −1.16459 | −0.582294 | − | 0.812978i | \(-0.697845\pi\) | ||||
−0.582294 | + | 0.812978i | \(0.697845\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12.8988 | −0.506321 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.688892 | −0.0269998 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −25.2114 | −0.986599 | −0.493299 | − | 0.869860i | \(-0.664209\pi\) | ||||
−0.493299 | + | 0.869860i | \(0.664209\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −13.0716 | −0.510750 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −8.92396 | −0.348157 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −40.6242 | −1.58250 | −0.791248 | − | 0.611496i | \(-0.790568\pi\) | ||||
−0.791248 | + | 0.611496i | \(0.790568\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −38.7783 | −1.50830 | −0.754151 | − | 0.656701i | \(-0.771951\pi\) | ||||
−0.754151 | + | 0.656701i | \(0.771951\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −8.53035 | −0.331291 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.6731 | 0.451983 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 23.5526 | 0.910597 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.1017 | 0.389972 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 40.1813 | 1.54888 | 0.774438 | − | 0.632650i | \(-0.218033\pi\) | ||||
0.774438 | + | 0.632650i | \(0.218033\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10.6811 | 0.410506 | 0.205253 | − | 0.978709i | \(-0.434198\pi\) | ||||
0.205253 | + | 0.978709i | \(0.434198\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.26671 | 0.317247 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 19.8020 | 0.758813 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −31.6271 | −1.21018 | −0.605089 | − | 0.796158i | \(-0.706863\pi\) | ||||
−0.605089 | + | 0.796158i | \(0.706863\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11.1383 | −0.425572 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 24.4099 | 0.931296 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.03164 | 0.305981 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.6508 | −0.405175 | −0.202588 | − | 0.979264i | \(-0.564935\pi\) | ||||
−0.202588 | + | 0.979264i | \(0.564935\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.37778 | 0.0523377 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −10.2351 | −0.388238 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.28544 | 0.238078 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.13828 | −0.118700 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 39.3590 | 1.48657 | 0.743285 | − | 0.668974i | \(-0.233266\pi\) | ||||
0.743285 | + | 0.668974i | \(0.233266\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.70964 | 0.177375 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.71456 | −0.214918 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 20.1847 | 0.758052 | 0.379026 | − | 0.925386i | \(-0.376259\pi\) | ||||
0.379026 | + | 0.925386i | \(0.376259\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.38271 | 0.314376 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.90321 | 0.108726 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.47949 | −0.279717 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.81579 | 0.254540 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −24.1017 | −0.898842 | −0.449421 | − | 0.893320i | \(-0.648370\pi\) | ||||
−0.449421 | + | 0.893320i | \(0.648370\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.05578 | 0.0765611 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −17.0923 | −0.635671 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.02074 | −0.149327 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.1180 | 0.523608 | 0.261804 | − | 0.965121i | \(-0.415683\pi\) | ||||
0.261804 | + | 0.965121i | \(0.415683\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.39700 | −0.0886561 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −23.1240 | −0.854104 | −0.427052 | − | 0.904227i | \(-0.640448\pi\) | ||||
−0.427052 | + | 0.904227i | \(0.640448\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6.52543 | 0.240694 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −10.8889 | −0.401099 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.128907 | 0.00474193 | 0.00237097 | − | 0.999997i | \(-0.499245\pi\) | ||||
0.00237097 | + | 0.999997i | \(0.499245\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −28.0129 | −1.02769 | −0.513847 | − | 0.857882i | \(-0.671780\pi\) | ||||
−0.513847 | + | 0.857882i | \(0.671780\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.51114 | −0.0553638 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 10.5161 | 0.384763 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.05086 | 0.0383974 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.56247 | 0.129996 | 0.0649982 | − | 0.997885i | \(-0.479296\pi\) | ||||
0.0649982 | + | 0.997885i | \(0.479296\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 16.1748 | 0.589444 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.76049 | 0.0640708 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 27.0573 | 0.983415 | 0.491707 | − | 0.870761i | \(-0.336373\pi\) | ||||
0.491707 | + | 0.870761i | \(0.336373\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5.80642 | −0.210760 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13.1447 | 0.476496 | 0.238248 | − | 0.971204i | \(-0.423427\pi\) | ||||
0.238248 | + | 0.971204i | \(0.423427\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.59057 | −0.0937850 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.28100 | 0.0824696 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 24.1191 | 0.870889 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 25.7418 | 0.928271 | 0.464136 | − | 0.885764i | \(-0.346365\pi\) | ||||
0.464136 | + | 0.885764i | \(0.346365\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −19.0464 | −0.685940 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 50.3007 | 1.80919 | 0.904595 | − | 0.426272i | \(-0.140173\pi\) | ||||
0.904595 | + | 0.426272i | \(0.140173\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.00000 | −0.0359211 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6.05578 | −0.217250 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 17.9398 | 0.641936 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.02074 | 0.143690 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.43801 | −0.122708 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.70519 | −0.310307 | −0.155153 | − | 0.987890i | \(-0.549587\pi\) | ||||
−0.155153 | + | 0.987890i | \(0.549587\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.23506 | −0.221974 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.32693 | 0.224960 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −18.8889 | −0.670765 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.14764 | −0.0761691 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 39.0464 | 1.38309 | 0.691547 | − | 0.722331i | \(-0.256929\pi\) | ||||
0.691547 | + | 0.722331i | \(0.256929\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.7427 | −0.380048 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 13.5002 | 0.477007 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 17.8479 | 0.629839 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.00000 | 0.0704907 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −20.8365 | −0.733481 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −24.0435 | −0.845324 | −0.422662 | − | 0.906287i | \(-0.638904\pi\) | ||||
−0.422662 | + | 0.906287i | \(0.638904\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −45.5812 | −1.60057 | −0.800286 | − | 0.599618i | \(-0.795319\pi\) | ||||
−0.800286 | + | 0.599618i | \(0.795319\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.62222 | 0.232251 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10.5970 | 0.371198 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.57628 | −0.0900226 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −32.2054 | −1.12398 | −0.561989 | − | 0.827145i | \(-0.689964\pi\) | ||||
−0.561989 | + | 0.827145i | \(0.689964\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −33.1052 | −1.15398 | −0.576988 | − | 0.816752i | \(-0.695772\pi\) | ||||
−0.576988 | + | 0.816752i | \(0.695772\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.00000 | 0.0696311 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.147643 | 0.00513406 | 0.00256703 | − | 0.999997i | \(-0.499183\pi\) | ||||
0.00256703 | + | 0.999997i | \(0.499183\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.9175 | −0.726495 | −0.363247 | − | 0.931693i | \(-0.618332\pi\) | ||||
−0.363247 | + | 0.931693i | \(0.618332\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.79060 | −0.166184 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −14.8845 | −0.515717 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 20.0415 | 0.693564 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.00000 | 0.0345651 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 42.9066 | 1.48130 | 0.740650 | − | 0.671891i | \(-0.234518\pi\) | ||||
0.740650 | + | 0.671891i | \(0.234518\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.8336 | −0.442539 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 20.8256 | 0.717273 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.985710 | 0.0339095 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.82225 | 0.165694 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −11.8731 | −0.407484 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 25.5210 | 0.874848 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −49.2226 | −1.68535 | −0.842675 | − | 0.538422i | \(-0.819021\pi\) | ||||
−0.842675 | + | 0.538422i | \(0.819021\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 34.2449 | 1.16978 | 0.584892 | − | 0.811111i | \(-0.301137\pi\) | ||||
0.584892 | + | 0.811111i | \(0.301137\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14.5718 | −0.497185 | −0.248592 | − | 0.968608i | \(-0.579968\pi\) | ||||
−0.248592 | + | 0.968608i | \(0.579968\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.89829 | 0.0646935 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −44.6164 | −1.51876 | −0.759380 | − | 0.650648i | \(-0.774497\pi\) | ||||
−0.759380 | + | 0.650648i | \(0.774497\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18.8988 | −0.642577 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 11.7971 | 0.400649 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −16.7654 | −0.568728 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20.3609 | 0.689903 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −12.0000 | −0.406138 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.688892 | −0.0232888 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.05038 | 0.271842 | 0.135921 | − | 0.990720i | \(-0.456601\pi\) | ||||
0.135921 | + | 0.990720i | \(0.456601\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 18.0143 | 0.607607 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −28.7130 | −0.967366 | −0.483683 | − | 0.875243i | \(-0.660701\pi\) | ||||
−0.483683 | + | 0.875243i | \(0.660701\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.4197 | 0.889095 | 0.444548 | − | 0.895755i | \(-0.353364\pi\) | ||||
0.444548 | + | 0.895755i | \(0.353364\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.44938 | −0.216794 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 44.7926 | 1.50399 | 0.751994 | − | 0.659170i | \(-0.229092\pi\) | ||||
0.751994 | + | 0.659170i | \(0.229092\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.90813 | −0.265230 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.00000 | −0.0670025 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −16.2953 | −0.544691 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 10.8573 | 0.362514 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.02074 | 0.134099 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.89877 | 0.163202 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.723926 | −0.0240907 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.70471 | −0.0566666 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.21924 | −0.239711 | −0.119855 | − | 0.992791i | \(-0.538243\pi\) | ||||
−0.119855 | + | 0.992791i | \(0.538243\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8.29529 | 0.275137 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −21.1052 | −0.699248 | −0.349624 | − | 0.936890i | \(-0.613691\pi\) | ||||
−0.349624 | + | 0.936890i | \(0.613691\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −21.0321 | −0.696062 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.05086 | 0.166976 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9.00492 | 0.297369 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16.4415 | −0.542357 | −0.271178 | − | 0.962529i | \(-0.587413\pi\) | ||||
−0.271178 | + | 0.962529i | \(0.587413\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.9240 | 0.359957 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −33.5451 | −1.10415 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.79060 | −0.289033 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.98418 | −0.0980133 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.26470 | 0.205538 | 0.102769 | − | 0.994705i | \(-0.467230\pi\) | ||||
0.102769 | + | 0.994705i | \(0.467230\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5.10324 | 0.167073 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.56199 | −0.149193 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 37.1437 | 1.21343 | 0.606715 | − | 0.794919i | \(-0.292487\pi\) | ||||
0.606715 | + | 0.794919i | \(0.292487\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 22.1082 | 0.721473 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 39.1318 | 1.27566 | 0.637830 | − | 0.770177i | \(-0.279832\pi\) | ||||
0.637830 | + | 0.770177i | \(0.279832\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.00000 | −0.260516 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.688892 | 0.0224097 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 53.0968 | 1.72541 | 0.862707 | − | 0.505704i | \(-0.168767\pi\) | ||||
0.862707 | + | 0.505704i | \(0.168767\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −33.3733 | −1.08334 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.06515 | 0.0345397 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6.57628 | −0.213027 | −0.106513 | − | 0.994311i | \(-0.533969\pi\) | ||||
−0.106513 | + | 0.994311i | \(0.533969\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.53188 | 0.114289 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8.04149 | −0.259944 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.67307 | 0.247776 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.52543 | −0.0491562 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 17.4193 | 0.560746 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −54.2449 | −1.74440 | −0.872199 | − | 0.489151i | \(-0.837307\pi\) | ||||
−0.872199 | + | 0.489151i | \(0.837307\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 42.8879 | 1.37634 | 0.688169 | − | 0.725551i | \(-0.258415\pi\) | ||||
0.688169 | + | 0.725551i | \(0.258415\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.05086 | 0.226040 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.73975 | −0.119768 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 11.6316 | 0.372127 | 0.186064 | − | 0.982538i | \(-0.440427\pi\) | ||||
0.186064 | + | 0.982538i | \(0.440427\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −27.0005 | −0.862939 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.76049 | 0.120063 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 30.3595 | 0.968318 | 0.484159 | − | 0.874980i | \(-0.339126\pi\) | ||||
0.484159 | + | 0.874980i | \(0.339126\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.0143 | 0.319082 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.24443 | −0.103271 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.05086 | 0.0970115 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −42.5589 | −1.35193 | −0.675964 | − | 0.736934i | \(-0.736273\pi\) | ||||
−0.675964 | + | 0.736934i | \(0.736273\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −24.9447 | −0.791596 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −27.1798 | −0.861656 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −33.5339 | −1.06203 | −0.531014 | − | 0.847363i | \(-0.678189\pi\) | ||||
−0.531014 | + | 0.847363i | \(0.678189\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8.79060 | 0.278122 |
(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 | 7440.2.a.bp.1.2 | 3 | ||
4.3 | odd | 2 | 465.2.a.f.1.2 | ✓ | 3 | ||
12.11 | even | 2 | 1395.2.a.i.1.2 | 3 | |||
20.3 | even | 4 | 2325.2.c.o.1024.3 | 6 | |||
20.7 | even | 4 | 2325.2.c.o.1024.4 | 6 | |||
20.19 | odd | 2 | 2325.2.a.q.1.2 | 3 | |||
60.59 | even | 2 | 6975.2.a.be.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
465.2.a.f.1.2 | ✓ | 3 | 4.3 | odd | 2 | ||
1395.2.a.i.1.2 | 3 | 12.11 | even | 2 | |||
2325.2.a.q.1.2 | 3 | 20.19 | odd | 2 | |||
2325.2.c.o.1024.3 | 6 | 20.3 | even | 4 | |||
2325.2.c.o.1024.4 | 6 | 20.7 | even | 4 | |||
6975.2.a.be.1.2 | 3 | 60.59 | even | 2 | |||
7440.2.a.bp.1.2 | 3 | 1.1 | even | 1 | trivial |