Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6018,2,Mod(1,6018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6018, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6018.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: | \(48.0539719364\) |
Analytic rank: | \(0\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - 4 x^{10} - 27 x^{9} + 117 x^{8} + 200 x^{7} - 1023 x^{6} - 484 x^{5} + 3403 x^{4} + 562 x^{3} + \cdots + 1200 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(2.03178\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6018.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.03178 | 0.908640 | 0.454320 | − | 0.890839i | \(-0.349882\pi\) | ||||
0.454320 | + | 0.890839i | \(0.349882\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −2.78135 | −1.05125 | −0.525627 | − | 0.850715i | \(-0.676169\pi\) | ||||
−0.525627 | + | 0.850715i | \(0.676169\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.03178 | 0.642505 | ||||||||
\(11\) | 2.25439 | 0.679723 | 0.339861 | − | 0.940476i | \(-0.389620\pi\) | ||||
0.339861 | + | 0.940476i | \(0.389620\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −0.0372501 | −0.0103313 | −0.00516566 | − | 0.999987i | \(-0.501644\pi\) | ||||
−0.00516566 | + | 0.999987i | \(0.501644\pi\) | |||||||
\(14\) | −2.78135 | −0.743348 | ||||||||
\(15\) | −2.03178 | −0.524604 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −1.18098 | −0.270935 | −0.135468 | − | 0.990782i | \(-0.543254\pi\) | ||||
−0.135468 | + | 0.990782i | \(0.543254\pi\) | |||||||
\(20\) | 2.03178 | 0.454320 | ||||||||
\(21\) | 2.78135 | 0.606941 | ||||||||
\(22\) | 2.25439 | 0.480637 | ||||||||
\(23\) | −5.57535 | −1.16254 | −0.581270 | − | 0.813711i | \(-0.697444\pi\) | ||||
−0.581270 | + | 0.813711i | \(0.697444\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −0.871867 | −0.174373 | ||||||||
\(26\) | −0.0372501 | −0.00730535 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −2.78135 | −0.525627 | ||||||||
\(29\) | 9.92481 | 1.84299 | 0.921495 | − | 0.388389i | \(-0.126968\pi\) | ||||
0.921495 | + | 0.388389i | \(0.126968\pi\) | |||||||
\(30\) | −2.03178 | −0.370951 | ||||||||
\(31\) | −5.32991 | −0.957280 | −0.478640 | − | 0.878011i | \(-0.658870\pi\) | ||||
−0.478640 | + | 0.878011i | \(0.658870\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −2.25439 | −0.392438 | ||||||||
\(34\) | −1.00000 | −0.171499 | ||||||||
\(35\) | −5.65110 | −0.955211 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 10.1469 | 1.66815 | 0.834073 | − | 0.551654i | \(-0.186003\pi\) | ||||
0.834073 | + | 0.551654i | \(0.186003\pi\) | |||||||
\(38\) | −1.18098 | −0.191580 | ||||||||
\(39\) | 0.0372501 | 0.00596479 | ||||||||
\(40\) | 2.03178 | 0.321253 | ||||||||
\(41\) | 5.89015 | 0.919887 | 0.459944 | − | 0.887948i | \(-0.347870\pi\) | ||||
0.459944 | + | 0.887948i | \(0.347870\pi\) | |||||||
\(42\) | 2.78135 | 0.429172 | ||||||||
\(43\) | 0.151772 | 0.0231450 | 0.0115725 | − | 0.999933i | \(-0.496316\pi\) | ||||
0.0115725 | + | 0.999933i | \(0.496316\pi\) | |||||||
\(44\) | 2.25439 | 0.339861 | ||||||||
\(45\) | 2.03178 | 0.302880 | ||||||||
\(46\) | −5.57535 | −0.822040 | ||||||||
\(47\) | 10.2298 | 1.49216 | 0.746082 | − | 0.665854i | \(-0.231933\pi\) | ||||
0.746082 | + | 0.665854i | \(0.231933\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 0.735932 | 0.105133 | ||||||||
\(50\) | −0.871867 | −0.123301 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | −0.0372501 | −0.00516566 | ||||||||
\(53\) | 7.90996 | 1.08652 | 0.543258 | − | 0.839566i | \(-0.317190\pi\) | ||||
0.543258 | + | 0.839566i | \(0.317190\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 4.58042 | 0.617623 | ||||||||
\(56\) | −2.78135 | −0.371674 | ||||||||
\(57\) | 1.18098 | 0.156425 | ||||||||
\(58\) | 9.92481 | 1.30319 | ||||||||
\(59\) | −1.00000 | −0.130189 | ||||||||
\(60\) | −2.03178 | −0.262302 | ||||||||
\(61\) | −1.98880 | −0.254640 | −0.127320 | − | 0.991862i | \(-0.540638\pi\) | ||||
−0.127320 | + | 0.991862i | \(0.540638\pi\) | |||||||
\(62\) | −5.32991 | −0.676899 | ||||||||
\(63\) | −2.78135 | −0.350418 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.0756840 | −0.00938745 | ||||||||
\(66\) | −2.25439 | −0.277496 | ||||||||
\(67\) | 0.598471 | 0.0731149 | 0.0365575 | − | 0.999332i | \(-0.488361\pi\) | ||||
0.0365575 | + | 0.999332i | \(0.488361\pi\) | |||||||
\(68\) | −1.00000 | −0.121268 | ||||||||
\(69\) | 5.57535 | 0.671193 | ||||||||
\(70\) | −5.65110 | −0.675436 | ||||||||
\(71\) | 5.04374 | 0.598582 | 0.299291 | − | 0.954162i | \(-0.403250\pi\) | ||||
0.299291 | + | 0.954162i | \(0.403250\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 15.0296 | 1.75908 | 0.879539 | − | 0.475827i | \(-0.157851\pi\) | ||||
0.879539 | + | 0.475827i | \(0.157851\pi\) | |||||||
\(74\) | 10.1469 | 1.17956 | ||||||||
\(75\) | 0.871867 | 0.100675 | ||||||||
\(76\) | −1.18098 | −0.135468 | ||||||||
\(77\) | −6.27025 | −0.714561 | ||||||||
\(78\) | 0.0372501 | 0.00421774 | ||||||||
\(79\) | −16.6292 | −1.87093 | −0.935463 | − | 0.353424i | \(-0.885017\pi\) | ||||
−0.935463 | + | 0.353424i | \(0.885017\pi\) | |||||||
\(80\) | 2.03178 | 0.227160 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 5.89015 | 0.650459 | ||||||||
\(83\) | 12.2983 | 1.34991 | 0.674954 | − | 0.737859i | \(-0.264163\pi\) | ||||
0.674954 | + | 0.737859i | \(0.264163\pi\) | |||||||
\(84\) | 2.78135 | 0.303471 | ||||||||
\(85\) | −2.03178 | −0.220378 | ||||||||
\(86\) | 0.151772 | 0.0163660 | ||||||||
\(87\) | −9.92481 | −1.06405 | ||||||||
\(88\) | 2.25439 | 0.240318 | ||||||||
\(89\) | 3.69721 | 0.391903 | 0.195952 | − | 0.980614i | \(-0.437220\pi\) | ||||
0.195952 | + | 0.980614i | \(0.437220\pi\) | |||||||
\(90\) | 2.03178 | 0.214168 | ||||||||
\(91\) | 0.103606 | 0.0108608 | ||||||||
\(92\) | −5.57535 | −0.581270 | ||||||||
\(93\) | 5.32991 | 0.552686 | ||||||||
\(94\) | 10.2298 | 1.05512 | ||||||||
\(95\) | −2.39949 | −0.246183 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 6.58331 | 0.668434 | 0.334217 | − | 0.942496i | \(-0.391528\pi\) | ||||
0.334217 | + | 0.942496i | \(0.391528\pi\) | |||||||
\(98\) | 0.735932 | 0.0743403 | ||||||||
\(99\) | 2.25439 | 0.226574 | ||||||||
\(100\) | −0.871867 | −0.0871867 | ||||||||
\(101\) | −7.88892 | −0.784977 | −0.392489 | − | 0.919757i | \(-0.628386\pi\) | ||||
−0.392489 | + | 0.919757i | \(0.628386\pi\) | |||||||
\(102\) | 1.00000 | 0.0990148 | ||||||||
\(103\) | −1.85170 | −0.182453 | −0.0912266 | − | 0.995830i | \(-0.529079\pi\) | ||||
−0.0912266 | + | 0.995830i | \(0.529079\pi\) | |||||||
\(104\) | −0.0372501 | −0.00365267 | ||||||||
\(105\) | 5.65110 | 0.551491 | ||||||||
\(106\) | 7.90996 | 0.768283 | ||||||||
\(107\) | −13.1597 | −1.27219 | −0.636096 | − | 0.771610i | \(-0.719452\pi\) | ||||
−0.636096 | + | 0.771610i | \(0.719452\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 4.10644 | 0.393326 | 0.196663 | − | 0.980471i | \(-0.436990\pi\) | ||||
0.196663 | + | 0.980471i | \(0.436990\pi\) | |||||||
\(110\) | 4.58042 | 0.436726 | ||||||||
\(111\) | −10.1469 | −0.963104 | ||||||||
\(112\) | −2.78135 | −0.262813 | ||||||||
\(113\) | 9.23405 | 0.868666 | 0.434333 | − | 0.900752i | \(-0.356984\pi\) | ||||
0.434333 | + | 0.900752i | \(0.356984\pi\) | |||||||
\(114\) | 1.18098 | 0.110609 | ||||||||
\(115\) | −11.3279 | −1.05633 | ||||||||
\(116\) | 9.92481 | 0.921495 | ||||||||
\(117\) | −0.0372501 | −0.00344377 | ||||||||
\(118\) | −1.00000 | −0.0920575 | ||||||||
\(119\) | 2.78135 | 0.254966 | ||||||||
\(120\) | −2.03178 | −0.185475 | ||||||||
\(121\) | −5.91774 | −0.537977 | ||||||||
\(122\) | −1.98880 | −0.180058 | ||||||||
\(123\) | −5.89015 | −0.531097 | ||||||||
\(124\) | −5.32991 | −0.478640 | ||||||||
\(125\) | −11.9303 | −1.06708 | ||||||||
\(126\) | −2.78135 | −0.247783 | ||||||||
\(127\) | 12.9128 | 1.14583 | 0.572915 | − | 0.819615i | \(-0.305813\pi\) | ||||
0.572915 | + | 0.819615i | \(0.305813\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −0.151772 | −0.0133628 | ||||||||
\(130\) | −0.0756840 | −0.00663793 | ||||||||
\(131\) | 21.1277 | 1.84594 | 0.922968 | − | 0.384877i | \(-0.125756\pi\) | ||||
0.922968 | + | 0.384877i | \(0.125756\pi\) | |||||||
\(132\) | −2.25439 | −0.196219 | ||||||||
\(133\) | 3.28472 | 0.284822 | ||||||||
\(134\) | 0.598471 | 0.0517001 | ||||||||
\(135\) | −2.03178 | −0.174868 | ||||||||
\(136\) | −1.00000 | −0.0857493 | ||||||||
\(137\) | 3.61782 | 0.309091 | 0.154546 | − | 0.987986i | \(-0.450609\pi\) | ||||
0.154546 | + | 0.987986i | \(0.450609\pi\) | |||||||
\(138\) | 5.57535 | 0.474605 | ||||||||
\(139\) | −14.2864 | −1.21176 | −0.605880 | − | 0.795556i | \(-0.707179\pi\) | ||||
−0.605880 | + | 0.795556i | \(0.707179\pi\) | |||||||
\(140\) | −5.65110 | −0.477605 | ||||||||
\(141\) | −10.2298 | −0.861501 | ||||||||
\(142\) | 5.04374 | 0.423261 | ||||||||
\(143\) | −0.0839761 | −0.00702243 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 20.1650 | 1.67461 | ||||||||
\(146\) | 15.0296 | 1.24386 | ||||||||
\(147\) | −0.735932 | −0.0606986 | ||||||||
\(148\) | 10.1469 | 0.834073 | ||||||||
\(149\) | −1.51653 | −0.124239 | −0.0621193 | − | 0.998069i | \(-0.519786\pi\) | ||||
−0.0621193 | + | 0.998069i | \(0.519786\pi\) | |||||||
\(150\) | 0.871867 | 0.0711876 | ||||||||
\(151\) | 14.0352 | 1.14217 | 0.571086 | − | 0.820891i | \(-0.306522\pi\) | ||||
0.571086 | + | 0.820891i | \(0.306522\pi\) | |||||||
\(152\) | −1.18098 | −0.0957901 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | −6.27025 | −0.505271 | ||||||||
\(155\) | −10.8292 | −0.869823 | ||||||||
\(156\) | 0.0372501 | 0.00298239 | ||||||||
\(157\) | −13.0866 | −1.04442 | −0.522211 | − | 0.852816i | \(-0.674893\pi\) | ||||
−0.522211 | + | 0.852816i | \(0.674893\pi\) | |||||||
\(158\) | −16.6292 | −1.32294 | ||||||||
\(159\) | −7.90996 | −0.627301 | ||||||||
\(160\) | 2.03178 | 0.160626 | ||||||||
\(161\) | 15.5070 | 1.22212 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −9.34353 | −0.731842 | −0.365921 | − | 0.930646i | \(-0.619246\pi\) | ||||
−0.365921 | + | 0.930646i | \(0.619246\pi\) | |||||||
\(164\) | 5.89015 | 0.459944 | ||||||||
\(165\) | −4.58042 | −0.356585 | ||||||||
\(166\) | 12.2983 | 0.954530 | ||||||||
\(167\) | −3.48106 | −0.269372 | −0.134686 | − | 0.990888i | \(-0.543003\pi\) | ||||
−0.134686 | + | 0.990888i | \(0.543003\pi\) | |||||||
\(168\) | 2.78135 | 0.214586 | ||||||||
\(169\) | −12.9986 | −0.999893 | ||||||||
\(170\) | −2.03178 | −0.155830 | ||||||||
\(171\) | −1.18098 | −0.0903118 | ||||||||
\(172\) | 0.151772 | 0.0115725 | ||||||||
\(173\) | 5.45454 | 0.414701 | 0.207350 | − | 0.978267i | \(-0.433516\pi\) | ||||
0.207350 | + | 0.978267i | \(0.433516\pi\) | |||||||
\(174\) | −9.92481 | −0.752398 | ||||||||
\(175\) | 2.42497 | 0.183311 | ||||||||
\(176\) | 2.25439 | 0.169931 | ||||||||
\(177\) | 1.00000 | 0.0751646 | ||||||||
\(178\) | 3.69721 | 0.277117 | ||||||||
\(179\) | 19.3804 | 1.44856 | 0.724280 | − | 0.689506i | \(-0.242172\pi\) | ||||
0.724280 | + | 0.689506i | \(0.242172\pi\) | |||||||
\(180\) | 2.03178 | 0.151440 | ||||||||
\(181\) | −8.14477 | −0.605396 | −0.302698 | − | 0.953087i | \(-0.597887\pi\) | ||||
−0.302698 | + | 0.953087i | \(0.597887\pi\) | |||||||
\(182\) | 0.103606 | 0.00767977 | ||||||||
\(183\) | 1.98880 | 0.147017 | ||||||||
\(184\) | −5.57535 | −0.411020 | ||||||||
\(185\) | 20.6163 | 1.51574 | ||||||||
\(186\) | 5.32991 | 0.390808 | ||||||||
\(187\) | −2.25439 | −0.164857 | ||||||||
\(188\) | 10.2298 | 0.746082 | ||||||||
\(189\) | 2.78135 | 0.202314 | ||||||||
\(190\) | −2.39949 | −0.174077 | ||||||||
\(191\) | 18.5782 | 1.34427 | 0.672135 | − | 0.740429i | \(-0.265378\pi\) | ||||
0.672135 | + | 0.740429i | \(0.265378\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −1.64507 | −0.118414 | −0.0592072 | − | 0.998246i | \(-0.518857\pi\) | ||||
−0.0592072 | + | 0.998246i | \(0.518857\pi\) | |||||||
\(194\) | 6.58331 | 0.472654 | ||||||||
\(195\) | 0.0756840 | 0.00541985 | ||||||||
\(196\) | 0.735932 | 0.0525666 | ||||||||
\(197\) | 2.28114 | 0.162524 | 0.0812622 | − | 0.996693i | \(-0.474105\pi\) | ||||
0.0812622 | + | 0.996693i | \(0.474105\pi\) | |||||||
\(198\) | 2.25439 | 0.160212 | ||||||||
\(199\) | 19.6987 | 1.39640 | 0.698202 | − | 0.715901i | \(-0.253984\pi\) | ||||
0.698202 | + | 0.715901i | \(0.253984\pi\) | |||||||
\(200\) | −0.871867 | −0.0616503 | ||||||||
\(201\) | −0.598471 | −0.0422129 | ||||||||
\(202\) | −7.88892 | −0.555063 | ||||||||
\(203\) | −27.6044 | −1.93745 | ||||||||
\(204\) | 1.00000 | 0.0700140 | ||||||||
\(205\) | 11.9675 | 0.835847 | ||||||||
\(206\) | −1.85170 | −0.129014 | ||||||||
\(207\) | −5.57535 | −0.387513 | ||||||||
\(208\) | −0.0372501 | −0.00258283 | ||||||||
\(209\) | −2.66239 | −0.184161 | ||||||||
\(210\) | 5.65110 | 0.389963 | ||||||||
\(211\) | 22.3114 | 1.53598 | 0.767991 | − | 0.640461i | \(-0.221257\pi\) | ||||
0.767991 | + | 0.640461i | \(0.221257\pi\) | |||||||
\(212\) | 7.90996 | 0.543258 | ||||||||
\(213\) | −5.04374 | −0.345591 | ||||||||
\(214\) | −13.1597 | −0.899576 | ||||||||
\(215\) | 0.308368 | 0.0210305 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 14.8244 | 1.00634 | ||||||||
\(218\) | 4.10644 | 0.278123 | ||||||||
\(219\) | −15.0296 | −1.01560 | ||||||||
\(220\) | 4.58042 | 0.308812 | ||||||||
\(221\) | 0.0372501 | 0.00250571 | ||||||||
\(222\) | −10.1469 | −0.681018 | ||||||||
\(223\) | −10.3040 | −0.690008 | −0.345004 | − | 0.938601i | \(-0.612122\pi\) | ||||
−0.345004 | + | 0.938601i | \(0.612122\pi\) | |||||||
\(224\) | −2.78135 | −0.185837 | ||||||||
\(225\) | −0.871867 | −0.0581245 | ||||||||
\(226\) | 9.23405 | 0.614240 | ||||||||
\(227\) | 16.5140 | 1.09608 | 0.548038 | − | 0.836454i | \(-0.315375\pi\) | ||||
0.548038 | + | 0.836454i | \(0.315375\pi\) | |||||||
\(228\) | 1.18098 | 0.0782123 | ||||||||
\(229\) | 8.61010 | 0.568971 | 0.284486 | − | 0.958680i | \(-0.408177\pi\) | ||||
0.284486 | + | 0.958680i | \(0.408177\pi\) | |||||||
\(230\) | −11.3279 | −0.746938 | ||||||||
\(231\) | 6.27025 | 0.412552 | ||||||||
\(232\) | 9.92481 | 0.651596 | ||||||||
\(233\) | 6.17877 | 0.404785 | 0.202392 | − | 0.979305i | \(-0.435128\pi\) | ||||
0.202392 | + | 0.979305i | \(0.435128\pi\) | |||||||
\(234\) | −0.0372501 | −0.00243512 | ||||||||
\(235\) | 20.7846 | 1.35584 | ||||||||
\(236\) | −1.00000 | −0.0650945 | ||||||||
\(237\) | 16.6292 | 1.08018 | ||||||||
\(238\) | 2.78135 | 0.180288 | ||||||||
\(239\) | 22.5916 | 1.46133 | 0.730663 | − | 0.682738i | \(-0.239211\pi\) | ||||
0.730663 | + | 0.682738i | \(0.239211\pi\) | |||||||
\(240\) | −2.03178 | −0.131151 | ||||||||
\(241\) | −14.4275 | −0.929355 | −0.464677 | − | 0.885480i | \(-0.653830\pi\) | ||||
−0.464677 | + | 0.885480i | \(0.653830\pi\) | |||||||
\(242\) | −5.91774 | −0.380407 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −1.98880 | −0.127320 | ||||||||
\(245\) | 1.49525 | 0.0955281 | ||||||||
\(246\) | −5.89015 | −0.375542 | ||||||||
\(247\) | 0.0439916 | 0.00279912 | ||||||||
\(248\) | −5.32991 | −0.338449 | ||||||||
\(249\) | −12.2983 | −0.779370 | ||||||||
\(250\) | −11.9303 | −0.754541 | ||||||||
\(251\) | −27.5253 | −1.73738 | −0.868691 | − | 0.495354i | \(-0.835038\pi\) | ||||
−0.868691 | + | 0.495354i | \(0.835038\pi\) | |||||||
\(252\) | −2.78135 | −0.175209 | ||||||||
\(253\) | −12.5690 | −0.790205 | ||||||||
\(254\) | 12.9128 | 0.810223 | ||||||||
\(255\) | 2.03178 | 0.127235 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 24.7589 | 1.54441 | 0.772207 | − | 0.635371i | \(-0.219153\pi\) | ||||
0.772207 | + | 0.635371i | \(0.219153\pi\) | |||||||
\(258\) | −0.151772 | −0.00944892 | ||||||||
\(259\) | −28.2222 | −1.75364 | ||||||||
\(260\) | −0.0756840 | −0.00469372 | ||||||||
\(261\) | 9.92481 | 0.614330 | ||||||||
\(262\) | 21.1277 | 1.30527 | ||||||||
\(263\) | −10.5895 | −0.652978 | −0.326489 | − | 0.945201i | \(-0.605866\pi\) | ||||
−0.326489 | + | 0.945201i | \(0.605866\pi\) | |||||||
\(264\) | −2.25439 | −0.138748 | ||||||||
\(265\) | 16.0713 | 0.987252 | ||||||||
\(266\) | 3.28472 | 0.201399 | ||||||||
\(267\) | −3.69721 | −0.226265 | ||||||||
\(268\) | 0.598471 | 0.0365575 | ||||||||
\(269\) | 9.52384 | 0.580679 | 0.290339 | − | 0.956924i | \(-0.406232\pi\) | ||||
0.290339 | + | 0.956924i | \(0.406232\pi\) | |||||||
\(270\) | −2.03178 | −0.123650 | ||||||||
\(271\) | −1.40167 | −0.0851455 | −0.0425727 | − | 0.999093i | \(-0.513555\pi\) | ||||
−0.0425727 | + | 0.999093i | \(0.513555\pi\) | |||||||
\(272\) | −1.00000 | −0.0606339 | ||||||||
\(273\) | −0.103606 | −0.00627050 | ||||||||
\(274\) | 3.61782 | 0.218560 | ||||||||
\(275\) | −1.96552 | −0.118526 | ||||||||
\(276\) | 5.57535 | 0.335596 | ||||||||
\(277\) | −0.830252 | −0.0498850 | −0.0249425 | − | 0.999689i | \(-0.507940\pi\) | ||||
−0.0249425 | + | 0.999689i | \(0.507940\pi\) | |||||||
\(278\) | −14.2864 | −0.856843 | ||||||||
\(279\) | −5.32991 | −0.319093 | ||||||||
\(280\) | −5.65110 | −0.337718 | ||||||||
\(281\) | −14.6155 | −0.871888 | −0.435944 | − | 0.899974i | \(-0.643585\pi\) | ||||
−0.435944 | + | 0.899974i | \(0.643585\pi\) | |||||||
\(282\) | −10.2298 | −0.609174 | ||||||||
\(283\) | −25.6174 | −1.52280 | −0.761399 | − | 0.648283i | \(-0.775487\pi\) | ||||
−0.761399 | + | 0.648283i | \(0.775487\pi\) | |||||||
\(284\) | 5.04374 | 0.299291 | ||||||||
\(285\) | 2.39949 | 0.142134 | ||||||||
\(286\) | −0.0839761 | −0.00496561 | ||||||||
\(287\) | −16.3826 | −0.967035 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 20.1650 | 1.18413 | ||||||||
\(291\) | −6.58331 | −0.385920 | ||||||||
\(292\) | 15.0296 | 0.879539 | ||||||||
\(293\) | 1.15255 | 0.0673327 | 0.0336664 | − | 0.999433i | \(-0.489282\pi\) | ||||
0.0336664 | + | 0.999433i | \(0.489282\pi\) | |||||||
\(294\) | −0.735932 | −0.0429204 | ||||||||
\(295\) | −2.03178 | −0.118295 | ||||||||
\(296\) | 10.1469 | 0.589779 | ||||||||
\(297\) | −2.25439 | −0.130813 | ||||||||
\(298\) | −1.51653 | −0.0878500 | ||||||||
\(299\) | 0.207682 | 0.0120106 | ||||||||
\(300\) | 0.871867 | 0.0503373 | ||||||||
\(301\) | −0.422132 | −0.0243313 | ||||||||
\(302\) | 14.0352 | 0.807637 | ||||||||
\(303\) | 7.88892 | 0.453207 | ||||||||
\(304\) | −1.18098 | −0.0677339 | ||||||||
\(305\) | −4.04081 | −0.231376 | ||||||||
\(306\) | −1.00000 | −0.0571662 | ||||||||
\(307\) | −10.9773 | −0.626505 | −0.313253 | − | 0.949670i | \(-0.601419\pi\) | ||||
−0.313253 | + | 0.949670i | \(0.601419\pi\) | |||||||
\(308\) | −6.27025 | −0.357280 | ||||||||
\(309\) | 1.85170 | 0.105339 | ||||||||
\(310\) | −10.8292 | −0.615057 | ||||||||
\(311\) | 31.5873 | 1.79115 | 0.895575 | − | 0.444911i | \(-0.146765\pi\) | ||||
0.895575 | + | 0.444911i | \(0.146765\pi\) | |||||||
\(312\) | 0.0372501 | 0.00210887 | ||||||||
\(313\) | 21.7785 | 1.23099 | 0.615497 | − | 0.788140i | \(-0.288955\pi\) | ||||
0.615497 | + | 0.788140i | \(0.288955\pi\) | |||||||
\(314\) | −13.0866 | −0.738518 | ||||||||
\(315\) | −5.65110 | −0.318404 | ||||||||
\(316\) | −16.6292 | −0.935463 | ||||||||
\(317\) | 30.2537 | 1.69922 | 0.849610 | − | 0.527412i | \(-0.176838\pi\) | ||||
0.849610 | + | 0.527412i | \(0.176838\pi\) | |||||||
\(318\) | −7.90996 | −0.443568 | ||||||||
\(319\) | 22.3743 | 1.25272 | ||||||||
\(320\) | 2.03178 | 0.113580 | ||||||||
\(321\) | 13.1597 | 0.734501 | ||||||||
\(322\) | 15.5070 | 0.864172 | ||||||||
\(323\) | 1.18098 | 0.0657115 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0.0324771 | 0.00180151 | ||||||||
\(326\) | −9.34353 | −0.517490 | ||||||||
\(327\) | −4.10644 | −0.227087 | ||||||||
\(328\) | 5.89015 | 0.325229 | ||||||||
\(329\) | −28.4526 | −1.56864 | ||||||||
\(330\) | −4.58042 | −0.252144 | ||||||||
\(331\) | −12.9759 | −0.713218 | −0.356609 | − | 0.934254i | \(-0.616067\pi\) | ||||
−0.356609 | + | 0.934254i | \(0.616067\pi\) | |||||||
\(332\) | 12.2983 | 0.674954 | ||||||||
\(333\) | 10.1469 | 0.556049 | ||||||||
\(334\) | −3.48106 | −0.190475 | ||||||||
\(335\) | 1.21596 | 0.0664351 | ||||||||
\(336\) | 2.78135 | 0.151735 | ||||||||
\(337\) | −8.00664 | −0.436149 | −0.218075 | − | 0.975932i | \(-0.569978\pi\) | ||||
−0.218075 | + | 0.975932i | \(0.569978\pi\) | |||||||
\(338\) | −12.9986 | −0.707031 | ||||||||
\(339\) | −9.23405 | −0.501525 | ||||||||
\(340\) | −2.03178 | −0.110189 | ||||||||
\(341\) | −12.0157 | −0.650685 | ||||||||
\(342\) | −1.18098 | −0.0638601 | ||||||||
\(343\) | 17.4226 | 0.940732 | ||||||||
\(344\) | 0.151772 | 0.00818301 | ||||||||
\(345\) | 11.3279 | 0.609873 | ||||||||
\(346\) | 5.45454 | 0.293238 | ||||||||
\(347\) | 15.6248 | 0.838781 | 0.419390 | − | 0.907806i | \(-0.362244\pi\) | ||||
0.419390 | + | 0.907806i | \(0.362244\pi\) | |||||||
\(348\) | −9.92481 | −0.532026 | ||||||||
\(349\) | −33.0941 | −1.77148 | −0.885742 | − | 0.464177i | \(-0.846350\pi\) | ||||
−0.885742 | + | 0.464177i | \(0.846350\pi\) | |||||||
\(350\) | 2.42497 | 0.129620 | ||||||||
\(351\) | 0.0372501 | 0.00198826 | ||||||||
\(352\) | 2.25439 | 0.120159 | ||||||||
\(353\) | 3.84737 | 0.204775 | 0.102387 | − | 0.994745i | \(-0.467352\pi\) | ||||
0.102387 | + | 0.994745i | \(0.467352\pi\) | |||||||
\(354\) | 1.00000 | 0.0531494 | ||||||||
\(355\) | 10.2478 | 0.543895 | ||||||||
\(356\) | 3.69721 | 0.195952 | ||||||||
\(357\) | −2.78135 | −0.147205 | ||||||||
\(358\) | 19.3804 | 1.02429 | ||||||||
\(359\) | 23.7964 | 1.25593 | 0.627964 | − | 0.778242i | \(-0.283889\pi\) | ||||
0.627964 | + | 0.778242i | \(0.283889\pi\) | |||||||
\(360\) | 2.03178 | 0.107084 | ||||||||
\(361\) | −17.6053 | −0.926594 | ||||||||
\(362\) | −8.14477 | −0.428080 | ||||||||
\(363\) | 5.91774 | 0.310601 | ||||||||
\(364\) | 0.103606 | 0.00543042 | ||||||||
\(365\) | 30.5368 | 1.59837 | ||||||||
\(366\) | 1.98880 | 0.103956 | ||||||||
\(367\) | 14.3639 | 0.749789 | 0.374895 | − | 0.927067i | \(-0.377679\pi\) | ||||
0.374895 | + | 0.927067i | \(0.377679\pi\) | |||||||
\(368\) | −5.57535 | −0.290635 | ||||||||
\(369\) | 5.89015 | 0.306629 | ||||||||
\(370\) | 20.6163 | 1.07179 | ||||||||
\(371\) | −22.0004 | −1.14220 | ||||||||
\(372\) | 5.32991 | 0.276343 | ||||||||
\(373\) | 10.3434 | 0.535561 | 0.267780 | − | 0.963480i | \(-0.413710\pi\) | ||||
0.267780 | + | 0.963480i | \(0.413710\pi\) | |||||||
\(374\) | −2.25439 | −0.116572 | ||||||||
\(375\) | 11.9303 | 0.616080 | ||||||||
\(376\) | 10.2298 | 0.527560 | ||||||||
\(377\) | −0.369700 | −0.0190405 | ||||||||
\(378\) | 2.78135 | 0.143057 | ||||||||
\(379\) | 21.0732 | 1.08246 | 0.541230 | − | 0.840875i | \(-0.317959\pi\) | ||||
0.541230 | + | 0.840875i | \(0.317959\pi\) | |||||||
\(380\) | −2.39949 | −0.123091 | ||||||||
\(381\) | −12.9128 | −0.661545 | ||||||||
\(382\) | 18.5782 | 0.950542 | ||||||||
\(383\) | −27.4055 | −1.40036 | −0.700179 | − | 0.713967i | \(-0.746896\pi\) | ||||
−0.700179 | + | 0.713967i | \(0.746896\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −12.7398 | −0.649279 | ||||||||
\(386\) | −1.64507 | −0.0837316 | ||||||||
\(387\) | 0.151772 | 0.00771501 | ||||||||
\(388\) | 6.58331 | 0.334217 | ||||||||
\(389\) | −32.1966 | −1.63243 | −0.816215 | − | 0.577748i | \(-0.803932\pi\) | ||||
−0.816215 | + | 0.577748i | \(0.803932\pi\) | |||||||
\(390\) | 0.0756840 | 0.00383241 | ||||||||
\(391\) | 5.57535 | 0.281957 | ||||||||
\(392\) | 0.735932 | 0.0371702 | ||||||||
\(393\) | −21.1277 | −1.06575 | ||||||||
\(394\) | 2.28114 | 0.114922 | ||||||||
\(395\) | −33.7868 | −1.70000 | ||||||||
\(396\) | 2.25439 | 0.113287 | ||||||||
\(397\) | −7.03918 | −0.353286 | −0.176643 | − | 0.984275i | \(-0.556524\pi\) | ||||
−0.176643 | + | 0.984275i | \(0.556524\pi\) | |||||||
\(398\) | 19.6987 | 0.987407 | ||||||||
\(399\) | −3.28472 | −0.164442 | ||||||||
\(400\) | −0.871867 | −0.0435933 | ||||||||
\(401\) | −13.9264 | −0.695454 | −0.347727 | − | 0.937596i | \(-0.613046\pi\) | ||||
−0.347727 | + | 0.937596i | \(0.613046\pi\) | |||||||
\(402\) | −0.598471 | −0.0298490 | ||||||||
\(403\) | 0.198540 | 0.00988996 | ||||||||
\(404\) | −7.88892 | −0.392489 | ||||||||
\(405\) | 2.03178 | 0.100960 | ||||||||
\(406\) | −27.6044 | −1.36998 | ||||||||
\(407\) | 22.8751 | 1.13388 | ||||||||
\(408\) | 1.00000 | 0.0495074 | ||||||||
\(409\) | −28.4417 | −1.40635 | −0.703175 | − | 0.711016i | \(-0.748235\pi\) | ||||
−0.703175 | + | 0.711016i | \(0.748235\pi\) | |||||||
\(410\) | 11.9675 | 0.591033 | ||||||||
\(411\) | −3.61782 | −0.178454 | ||||||||
\(412\) | −1.85170 | −0.0912266 | ||||||||
\(413\) | 2.78135 | 0.136861 | ||||||||
\(414\) | −5.57535 | −0.274013 | ||||||||
\(415\) | 24.9874 | 1.22658 | ||||||||
\(416\) | −0.0372501 | −0.00182634 | ||||||||
\(417\) | 14.2864 | 0.699609 | ||||||||
\(418\) | −2.66239 | −0.130222 | ||||||||
\(419\) | −19.3607 | −0.945833 | −0.472917 | − | 0.881107i | \(-0.656799\pi\) | ||||
−0.472917 | + | 0.881107i | \(0.656799\pi\) | |||||||
\(420\) | 5.65110 | 0.275746 | ||||||||
\(421\) | 10.0335 | 0.489005 | 0.244503 | − | 0.969649i | \(-0.421375\pi\) | ||||
0.244503 | + | 0.969649i | \(0.421375\pi\) | |||||||
\(422\) | 22.3114 | 1.08610 | ||||||||
\(423\) | 10.2298 | 0.497388 | ||||||||
\(424\) | 7.90996 | 0.384142 | ||||||||
\(425\) | 0.871867 | 0.0422918 | ||||||||
\(426\) | −5.04374 | −0.244370 | ||||||||
\(427\) | 5.53157 | 0.267691 | ||||||||
\(428\) | −13.1597 | −0.636096 | ||||||||
\(429\) | 0.0839761 | 0.00405440 | ||||||||
\(430\) | 0.308368 | 0.0148708 | ||||||||
\(431\) | 33.6539 | 1.62105 | 0.810526 | − | 0.585703i | \(-0.199182\pi\) | ||||
0.810526 | + | 0.585703i | \(0.199182\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 25.9459 | 1.24688 | 0.623440 | − | 0.781871i | \(-0.285735\pi\) | ||||
0.623440 | + | 0.781871i | \(0.285735\pi\) | |||||||
\(434\) | 14.8244 | 0.711592 | ||||||||
\(435\) | −20.1650 | −0.966839 | ||||||||
\(436\) | 4.10644 | 0.196663 | ||||||||
\(437\) | 6.58437 | 0.314973 | ||||||||
\(438\) | −15.0296 | −0.718141 | ||||||||
\(439\) | 15.3049 | 0.730465 | 0.365233 | − | 0.930916i | \(-0.380989\pi\) | ||||
0.365233 | + | 0.930916i | \(0.380989\pi\) | |||||||
\(440\) | 4.58042 | 0.218363 | ||||||||
\(441\) | 0.735932 | 0.0350444 | ||||||||
\(442\) | 0.0372501 | 0.00177181 | ||||||||
\(443\) | 29.4490 | 1.39917 | 0.699583 | − | 0.714552i | \(-0.253369\pi\) | ||||
0.699583 | + | 0.714552i | \(0.253369\pi\) | |||||||
\(444\) | −10.1469 | −0.481552 | ||||||||
\(445\) | 7.51191 | 0.356099 | ||||||||
\(446\) | −10.3040 | −0.487910 | ||||||||
\(447\) | 1.51653 | 0.0717292 | ||||||||
\(448\) | −2.78135 | −0.131407 | ||||||||
\(449\) | 23.9846 | 1.13190 | 0.565952 | − | 0.824438i | \(-0.308509\pi\) | ||||
0.565952 | + | 0.824438i | \(0.308509\pi\) | |||||||
\(450\) | −0.871867 | −0.0411002 | ||||||||
\(451\) | 13.2787 | 0.625269 | ||||||||
\(452\) | 9.23405 | 0.434333 | ||||||||
\(453\) | −14.0352 | −0.659433 | ||||||||
\(454\) | 16.5140 | 0.775043 | ||||||||
\(455\) | 0.210504 | 0.00986859 | ||||||||
\(456\) | 1.18098 | 0.0553045 | ||||||||
\(457\) | 21.4907 | 1.00529 | 0.502646 | − | 0.864492i | \(-0.332360\pi\) | ||||
0.502646 | + | 0.864492i | \(0.332360\pi\) | |||||||
\(458\) | 8.61010 | 0.402324 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | −11.3279 | −0.528165 | ||||||||
\(461\) | −36.7596 | −1.71207 | −0.856033 | − | 0.516921i | \(-0.827078\pi\) | ||||
−0.856033 | + | 0.516921i | \(0.827078\pi\) | |||||||
\(462\) | 6.27025 | 0.291718 | ||||||||
\(463\) | −40.4962 | −1.88202 | −0.941010 | − | 0.338378i | \(-0.890122\pi\) | ||||
−0.941010 | + | 0.338378i | \(0.890122\pi\) | |||||||
\(464\) | 9.92481 | 0.460748 | ||||||||
\(465\) | 10.8292 | 0.502192 | ||||||||
\(466\) | 6.17877 | 0.286226 | ||||||||
\(467\) | −40.3215 | −1.86586 | −0.932929 | − | 0.360061i | \(-0.882756\pi\) | ||||
−0.932929 | + | 0.360061i | \(0.882756\pi\) | |||||||
\(468\) | −0.0372501 | −0.00172189 | ||||||||
\(469\) | −1.66456 | −0.0768623 | ||||||||
\(470\) | 20.7846 | 0.958724 | ||||||||
\(471\) | 13.0866 | 0.602997 | ||||||||
\(472\) | −1.00000 | −0.0460287 | ||||||||
\(473\) | 0.342153 | 0.0157322 | ||||||||
\(474\) | 16.6292 | 0.763802 | ||||||||
\(475\) | 1.02966 | 0.0472439 | ||||||||
\(476\) | 2.78135 | 0.127483 | ||||||||
\(477\) | 7.90996 | 0.362172 | ||||||||
\(478\) | 22.5916 | 1.03331 | ||||||||
\(479\) | −43.0779 | −1.96828 | −0.984140 | − | 0.177392i | \(-0.943234\pi\) | ||||
−0.984140 | + | 0.177392i | \(0.943234\pi\) | |||||||
\(480\) | −2.03178 | −0.0927377 | ||||||||
\(481\) | −0.377974 | −0.0172341 | ||||||||
\(482\) | −14.4275 | −0.657153 | ||||||||
\(483\) | −15.5070 | −0.705593 | ||||||||
\(484\) | −5.91774 | −0.268988 | ||||||||
\(485\) | 13.3758 | 0.607366 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 13.3110 | 0.603181 | 0.301590 | − | 0.953438i | \(-0.402483\pi\) | ||||
0.301590 | + | 0.953438i | \(0.402483\pi\) | |||||||
\(488\) | −1.98880 | −0.0900289 | ||||||||
\(489\) | 9.34353 | 0.422529 | ||||||||
\(490\) | 1.49525 | 0.0675486 | ||||||||
\(491\) | −25.7331 | −1.16132 | −0.580659 | − | 0.814147i | \(-0.697205\pi\) | ||||
−0.580659 | + | 0.814147i | \(0.697205\pi\) | |||||||
\(492\) | −5.89015 | −0.265549 | ||||||||
\(493\) | −9.92481 | −0.446991 | ||||||||
\(494\) | 0.0439916 | 0.00197928 | ||||||||
\(495\) | 4.58042 | 0.205874 | ||||||||
\(496\) | −5.32991 | −0.239320 | ||||||||
\(497\) | −14.0284 | −0.629261 | ||||||||
\(498\) | −12.2983 | −0.551098 | ||||||||
\(499\) | −17.7722 | −0.795595 | −0.397797 | − | 0.917473i | \(-0.630225\pi\) | ||||
−0.397797 | + | 0.917473i | \(0.630225\pi\) | |||||||
\(500\) | −11.9303 | −0.533541 | ||||||||
\(501\) | 3.48106 | 0.155522 | ||||||||
\(502\) | −27.5253 | −1.22852 | ||||||||
\(503\) | −43.0177 | −1.91806 | −0.959031 | − | 0.283300i | \(-0.908571\pi\) | ||||
−0.959031 | + | 0.283300i | \(0.908571\pi\) | |||||||
\(504\) | −2.78135 | −0.123891 | ||||||||
\(505\) | −16.0286 | −0.713262 | ||||||||
\(506\) | −12.5690 | −0.558759 | ||||||||
\(507\) | 12.9986 | 0.577289 | ||||||||
\(508\) | 12.9128 | 0.572915 | ||||||||
\(509\) | 10.5189 | 0.466240 | 0.233120 | − | 0.972448i | \(-0.425106\pi\) | ||||
0.233120 | + | 0.972448i | \(0.425106\pi\) | |||||||
\(510\) | 2.03178 | 0.0899688 | ||||||||
\(511\) | −41.8026 | −1.84924 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 1.18098 | 0.0521415 | ||||||||
\(514\) | 24.7589 | 1.09207 | ||||||||
\(515\) | −3.76224 | −0.165784 | ||||||||
\(516\) | −0.151772 | −0.00668140 | ||||||||
\(517\) | 23.0618 | 1.01426 | ||||||||
\(518\) | −28.2222 | −1.24001 | ||||||||
\(519\) | −5.45454 | −0.239428 | ||||||||
\(520\) | −0.0756840 | −0.00331896 | ||||||||
\(521\) | −6.03174 | −0.264255 | −0.132128 | − | 0.991233i | \(-0.542181\pi\) | ||||
−0.132128 | + | 0.991233i | \(0.542181\pi\) | |||||||
\(522\) | 9.92481 | 0.434397 | ||||||||
\(523\) | 22.3958 | 0.979298 | 0.489649 | − | 0.871920i | \(-0.337125\pi\) | ||||
0.489649 | + | 0.871920i | \(0.337125\pi\) | |||||||
\(524\) | 21.1277 | 0.922968 | ||||||||
\(525\) | −2.42497 | −0.105834 | ||||||||
\(526\) | −10.5895 | −0.461725 | ||||||||
\(527\) | 5.32991 | 0.232174 | ||||||||
\(528\) | −2.25439 | −0.0981096 | ||||||||
\(529\) | 8.08448 | 0.351499 | ||||||||
\(530\) | 16.0713 | 0.698093 | ||||||||
\(531\) | −1.00000 | −0.0433963 | ||||||||
\(532\) | 3.28472 | 0.142411 | ||||||||
\(533\) | −0.219409 | −0.00950365 | ||||||||
\(534\) | −3.69721 | −0.159994 | ||||||||
\(535\) | −26.7376 | −1.15597 | ||||||||
\(536\) | 0.598471 | 0.0258500 | ||||||||
\(537\) | −19.3804 | −0.836327 | ||||||||
\(538\) | 9.52384 | 0.410602 | ||||||||
\(539\) | 1.65907 | 0.0714614 | ||||||||
\(540\) | −2.03178 | −0.0874339 | ||||||||
\(541\) | −9.76691 | −0.419912 | −0.209956 | − | 0.977711i | \(-0.567332\pi\) | ||||
−0.209956 | + | 0.977711i | \(0.567332\pi\) | |||||||
\(542\) | −1.40167 | −0.0602069 | ||||||||
\(543\) | 8.14477 | 0.349526 | ||||||||
\(544\) | −1.00000 | −0.0428746 | ||||||||
\(545\) | 8.34339 | 0.357391 | ||||||||
\(546\) | −0.103606 | −0.00443392 | ||||||||
\(547\) | 29.3308 | 1.25409 | 0.627047 | − | 0.778981i | \(-0.284263\pi\) | ||||
0.627047 | + | 0.778981i | \(0.284263\pi\) | |||||||
\(548\) | 3.61782 | 0.154546 | ||||||||
\(549\) | −1.98880 | −0.0848801 | ||||||||
\(550\) | −1.96552 | −0.0838102 | ||||||||
\(551\) | −11.7210 | −0.499331 | ||||||||
\(552\) | 5.57535 | 0.237302 | ||||||||
\(553\) | 46.2516 | 1.96682 | ||||||||
\(554\) | −0.830252 | −0.0352740 | ||||||||
\(555\) | −20.6163 | −0.875115 | ||||||||
\(556\) | −14.2864 | −0.605880 | ||||||||
\(557\) | −35.9543 | −1.52343 | −0.761717 | − | 0.647910i | \(-0.775643\pi\) | ||||
−0.761717 | + | 0.647910i | \(0.775643\pi\) | |||||||
\(558\) | −5.32991 | −0.225633 | ||||||||
\(559\) | −0.00565353 | −0.000239119 0 | ||||||||
\(560\) | −5.65110 | −0.238803 | ||||||||
\(561\) | 2.25439 | 0.0951803 | ||||||||
\(562\) | −14.6155 | −0.616518 | ||||||||
\(563\) | 15.8750 | 0.669053 | 0.334526 | − | 0.942386i | \(-0.391424\pi\) | ||||
0.334526 | + | 0.942386i | \(0.391424\pi\) | |||||||
\(564\) | −10.2298 | −0.430751 | ||||||||
\(565\) | 18.7616 | 0.789305 | ||||||||
\(566\) | −25.6174 | −1.07678 | ||||||||
\(567\) | −2.78135 | −0.116806 | ||||||||
\(568\) | 5.04374 | 0.211631 | ||||||||
\(569\) | 3.60171 | 0.150992 | 0.0754958 | − | 0.997146i | \(-0.475946\pi\) | ||||
0.0754958 | + | 0.997146i | \(0.475946\pi\) | |||||||
\(570\) | 2.39949 | 0.100504 | ||||||||
\(571\) | −25.4611 | −1.06551 | −0.532757 | − | 0.846268i | \(-0.678844\pi\) | ||||
−0.532757 | + | 0.846268i | \(0.678844\pi\) | |||||||
\(572\) | −0.0839761 | −0.00351122 | ||||||||
\(573\) | −18.5782 | −0.776114 | ||||||||
\(574\) | −16.3826 | −0.683797 | ||||||||
\(575\) | 4.86096 | 0.202716 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 13.1523 | 0.547537 | 0.273769 | − | 0.961796i | \(-0.411730\pi\) | ||||
0.273769 | + | 0.961796i | \(0.411730\pi\) | |||||||
\(578\) | 1.00000 | 0.0415945 | ||||||||
\(579\) | 1.64507 | 0.0683666 | ||||||||
\(580\) | 20.1650 | 0.837307 | ||||||||
\(581\) | −34.2058 | −1.41910 | ||||||||
\(582\) | −6.58331 | −0.272887 | ||||||||
\(583\) | 17.8321 | 0.738530 | ||||||||
\(584\) | 15.0296 | 0.621928 | ||||||||
\(585\) | −0.0756840 | −0.00312915 | ||||||||
\(586\) | 1.15255 | 0.0476114 | ||||||||
\(587\) | 24.0351 | 0.992035 | 0.496017 | − | 0.868313i | \(-0.334795\pi\) | ||||
0.496017 | + | 0.868313i | \(0.334795\pi\) | |||||||
\(588\) | −0.735932 | −0.0303493 | ||||||||
\(589\) | 6.29451 | 0.259361 | ||||||||
\(590\) | −2.03178 | −0.0836471 | ||||||||
\(591\) | −2.28114 | −0.0938335 | ||||||||
\(592\) | 10.1469 | 0.417036 | ||||||||
\(593\) | 25.5162 | 1.04782 | 0.523912 | − | 0.851772i | \(-0.324472\pi\) | ||||
0.523912 | + | 0.851772i | \(0.324472\pi\) | |||||||
\(594\) | −2.25439 | −0.0924986 | ||||||||
\(595\) | 5.65110 | 0.231673 | ||||||||
\(596\) | −1.51653 | −0.0621193 | ||||||||
\(597\) | −19.6987 | −0.806214 | ||||||||
\(598\) | 0.207682 | 0.00849276 | ||||||||
\(599\) | −42.5275 | −1.73763 | −0.868813 | − | 0.495141i | \(-0.835116\pi\) | ||||
−0.868813 | + | 0.495141i | \(0.835116\pi\) | |||||||
\(600\) | 0.871867 | 0.0355938 | ||||||||
\(601\) | −6.32133 | −0.257853 | −0.128926 | − | 0.991654i | \(-0.541153\pi\) | ||||
−0.128926 | + | 0.991654i | \(0.541153\pi\) | |||||||
\(602\) | −0.422132 | −0.0172048 | ||||||||
\(603\) | 0.598471 | 0.0243716 | ||||||||
\(604\) | 14.0352 | 0.571086 | ||||||||
\(605\) | −12.0236 | −0.488827 | ||||||||
\(606\) | 7.88892 | 0.320466 | ||||||||
\(607\) | 27.4873 | 1.11567 | 0.557837 | − | 0.829950i | \(-0.311631\pi\) | ||||
0.557837 | + | 0.829950i | \(0.311631\pi\) | |||||||
\(608\) | −1.18098 | −0.0478951 | ||||||||
\(609\) | 27.6044 | 1.11859 | ||||||||
\(610\) | −4.04081 | −0.163608 | ||||||||
\(611\) | −0.381060 | −0.0154160 | ||||||||
\(612\) | −1.00000 | −0.0404226 | ||||||||
\(613\) | 22.7562 | 0.919115 | 0.459557 | − | 0.888148i | \(-0.348008\pi\) | ||||
0.459557 | + | 0.888148i | \(0.348008\pi\) | |||||||
\(614\) | −10.9773 | −0.443006 | ||||||||
\(615\) | −11.9675 | −0.482576 | ||||||||
\(616\) | −6.27025 | −0.252635 | ||||||||
\(617\) | −10.6856 | −0.430187 | −0.215093 | − | 0.976593i | \(-0.569006\pi\) | ||||
−0.215093 | + | 0.976593i | \(0.569006\pi\) | |||||||
\(618\) | 1.85170 | 0.0744862 | ||||||||
\(619\) | −4.76483 | −0.191515 | −0.0957574 | − | 0.995405i | \(-0.530527\pi\) | ||||
−0.0957574 | + | 0.995405i | \(0.530527\pi\) | |||||||
\(620\) | −10.8292 | −0.434911 | ||||||||
\(621\) | 5.57535 | 0.223731 | ||||||||
\(622\) | 31.5873 | 1.26653 | ||||||||
\(623\) | −10.2832 | −0.411989 | ||||||||
\(624\) | 0.0372501 | 0.00149120 | ||||||||
\(625\) | −19.8805 | −0.795221 | ||||||||
\(626\) | 21.7785 | 0.870444 | ||||||||
\(627\) | 2.66239 | 0.106325 | ||||||||
\(628\) | −13.0866 | −0.522211 | ||||||||
\(629\) | −10.1469 | −0.404585 | ||||||||
\(630\) | −5.65110 | −0.225145 | ||||||||
\(631\) | −26.9380 | −1.07239 | −0.536193 | − | 0.844095i | \(-0.680138\pi\) | ||||
−0.536193 | + | 0.844095i | \(0.680138\pi\) | |||||||
\(632\) | −16.6292 | −0.661472 | ||||||||
\(633\) | −22.3114 | −0.886799 | ||||||||
\(634\) | 30.2537 | 1.20153 | ||||||||
\(635\) | 26.2361 | 1.04115 | ||||||||
\(636\) | −7.90996 | −0.313650 | ||||||||
\(637\) | −0.0274135 | −0.00108616 | ||||||||
\(638\) | 22.3743 | 0.885809 | ||||||||
\(639\) | 5.04374 | 0.199527 | ||||||||
\(640\) | 2.03178 | 0.0803132 | ||||||||
\(641\) | −29.1739 | −1.15230 | −0.576151 | − | 0.817343i | \(-0.695446\pi\) | ||||
−0.576151 | + | 0.817343i | \(0.695446\pi\) | |||||||
\(642\) | 13.1597 | 0.519370 | ||||||||
\(643\) | −8.51754 | −0.335899 | −0.167949 | − | 0.985796i | \(-0.553715\pi\) | ||||
−0.167949 | + | 0.985796i | \(0.553715\pi\) | |||||||
\(644\) | 15.5070 | 0.611062 | ||||||||
\(645\) | −0.308368 | −0.0121420 | ||||||||
\(646\) | 1.18098 | 0.0464650 | ||||||||
\(647\) | −18.2072 | −0.715797 | −0.357899 | − | 0.933760i | \(-0.616507\pi\) | ||||
−0.357899 | + | 0.933760i | \(0.616507\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −2.25439 | −0.0884924 | ||||||||
\(650\) | 0.0324771 | 0.00127386 | ||||||||
\(651\) | −14.8244 | −0.581013 | ||||||||
\(652\) | −9.34353 | −0.365921 | ||||||||
\(653\) | 5.36556 | 0.209971 | 0.104985 | − | 0.994474i | \(-0.466520\pi\) | ||||
0.104985 | + | 0.994474i | \(0.466520\pi\) | |||||||
\(654\) | −4.10644 | −0.160575 | ||||||||
\(655\) | 42.9269 | 1.67729 | ||||||||
\(656\) | 5.89015 | 0.229972 | ||||||||
\(657\) | 15.0296 | 0.586359 | ||||||||
\(658\) | −28.4526 | −1.10920 | ||||||||
\(659\) | −41.6172 | −1.62118 | −0.810589 | − | 0.585616i | \(-0.800853\pi\) | ||||
−0.810589 | + | 0.585616i | \(0.800853\pi\) | |||||||
\(660\) | −4.58042 | −0.178293 | ||||||||
\(661\) | 17.5682 | 0.683326 | 0.341663 | − | 0.939823i | \(-0.389010\pi\) | ||||
0.341663 | + | 0.939823i | \(0.389010\pi\) | |||||||
\(662\) | −12.9759 | −0.504321 | ||||||||
\(663\) | −0.0372501 | −0.00144667 | ||||||||
\(664\) | 12.2983 | 0.477265 | ||||||||
\(665\) | 6.67384 | 0.258800 | ||||||||
\(666\) | 10.1469 | 0.393186 | ||||||||
\(667\) | −55.3342 | −2.14255 | ||||||||
\(668\) | −3.48106 | −0.134686 | ||||||||
\(669\) | 10.3040 | 0.398376 | ||||||||
\(670\) | 1.21596 | 0.0469767 | ||||||||
\(671\) | −4.48353 | −0.173085 | ||||||||
\(672\) | 2.78135 | 0.107293 | ||||||||
\(673\) | −0.545032 | −0.0210094 | −0.0105047 | − | 0.999945i | \(-0.503344\pi\) | ||||
−0.0105047 | + | 0.999945i | \(0.503344\pi\) | |||||||
\(674\) | −8.00664 | −0.308404 | ||||||||
\(675\) | 0.871867 | 0.0335582 | ||||||||
\(676\) | −12.9986 | −0.499947 | ||||||||
\(677\) | −18.0975 | −0.695544 | −0.347772 | − | 0.937579i | \(-0.613062\pi\) | ||||
−0.347772 | + | 0.937579i | \(0.613062\pi\) | |||||||
\(678\) | −9.23405 | −0.354632 | ||||||||
\(679\) | −18.3105 | −0.702693 | ||||||||
\(680\) | −2.03178 | −0.0779152 | ||||||||
\(681\) | −16.5140 | −0.632820 | ||||||||
\(682\) | −12.0157 | −0.460104 | ||||||||
\(683\) | 21.1621 | 0.809747 | 0.404873 | − | 0.914373i | \(-0.367316\pi\) | ||||
0.404873 | + | 0.914373i | \(0.367316\pi\) | |||||||
\(684\) | −1.18098 | −0.0451559 | ||||||||
\(685\) | 7.35062 | 0.280853 | ||||||||
\(686\) | 17.4226 | 0.665198 | ||||||||
\(687\) | −8.61010 | −0.328496 | ||||||||
\(688\) | 0.151772 | 0.00578626 | ||||||||
\(689\) | −0.294647 | −0.0112251 | ||||||||
\(690\) | 11.3279 | 0.431245 | ||||||||
\(691\) | 10.7258 | 0.408028 | 0.204014 | − | 0.978968i | \(-0.434601\pi\) | ||||
0.204014 | + | 0.978968i | \(0.434601\pi\) | |||||||
\(692\) | 5.45454 | 0.207350 | ||||||||
\(693\) | −6.27025 | −0.238187 | ||||||||
\(694\) | 15.6248 | 0.593108 | ||||||||
\(695\) | −29.0269 | −1.10105 | ||||||||
\(696\) | −9.92481 | −0.376199 | ||||||||
\(697\) | −5.89015 | −0.223105 | ||||||||
\(698\) | −33.0941 | −1.25263 | ||||||||
\(699\) | −6.17877 | −0.233703 | ||||||||
\(700\) | 2.42497 | 0.0916553 | ||||||||
\(701\) | 31.7060 | 1.19752 | 0.598760 | − | 0.800929i | \(-0.295660\pi\) | ||||
0.598760 | + | 0.800929i | \(0.295660\pi\) | |||||||
\(702\) | 0.0372501 | 0.00140591 | ||||||||
\(703\) | −11.9833 | −0.451960 | ||||||||
\(704\) | 2.25439 | 0.0849654 | ||||||||
\(705\) | −20.7846 | −0.782795 | ||||||||
\(706\) | 3.84737 | 0.144798 | ||||||||
\(707\) | 21.9419 | 0.825210 | ||||||||
\(708\) | 1.00000 | 0.0375823 | ||||||||
\(709\) | 42.0168 | 1.57797 | 0.788987 | − | 0.614410i | \(-0.210606\pi\) | ||||
0.788987 | + | 0.614410i | \(0.210606\pi\) | |||||||
\(710\) | 10.2478 | 0.384592 | ||||||||
\(711\) | −16.6292 | −0.623642 | ||||||||
\(712\) | 3.69721 | 0.138559 | ||||||||
\(713\) | 29.7161 | 1.11288 | ||||||||
\(714\) | −2.78135 | −0.104090 | ||||||||
\(715\) | −0.170621 | −0.00638087 | ||||||||
\(716\) | 19.3804 | 0.724280 | ||||||||
\(717\) | −22.5916 | −0.843697 | ||||||||
\(718\) | 23.7964 | 0.888075 | ||||||||
\(719\) | −43.4201 | −1.61930 | −0.809648 | − | 0.586916i | \(-0.800342\pi\) | ||||
−0.809648 | + | 0.586916i | \(0.800342\pi\) | |||||||
\(720\) | 2.03178 | 0.0757200 | ||||||||
\(721\) | 5.15023 | 0.191804 | ||||||||
\(722\) | −17.6053 | −0.655201 | ||||||||
\(723\) | 14.4275 | 0.536563 | ||||||||
\(724\) | −8.14477 | −0.302698 | ||||||||
\(725\) | −8.65311 | −0.321368 | ||||||||
\(726\) | 5.91774 | 0.219628 | ||||||||
\(727\) | −27.3644 | −1.01489 | −0.507445 | − | 0.861684i | \(-0.669410\pi\) | ||||
−0.507445 | + | 0.861684i | \(0.669410\pi\) | |||||||
\(728\) | 0.103606 | 0.00383988 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 30.5368 | 1.13022 | ||||||||
\(731\) | −0.151772 | −0.00561350 | ||||||||
\(732\) | 1.98880 | 0.0735083 | ||||||||
\(733\) | 8.54735 | 0.315704 | 0.157852 | − | 0.987463i | \(-0.449543\pi\) | ||||
0.157852 | + | 0.987463i | \(0.449543\pi\) | |||||||
\(734\) | 14.3639 | 0.530181 | ||||||||
\(735\) | −1.49525 | −0.0551532 | ||||||||
\(736\) | −5.57535 | −0.205510 | ||||||||
\(737\) | 1.34919 | 0.0496979 | ||||||||
\(738\) | 5.89015 | 0.216820 | ||||||||
\(739\) | −47.0170 | −1.72955 | −0.864773 | − | 0.502162i | \(-0.832538\pi\) | ||||
−0.864773 | + | 0.502162i | \(0.832538\pi\) | |||||||
\(740\) | 20.6163 | 0.757872 | ||||||||
\(741\) | −0.0439916 | −0.00161607 | ||||||||
\(742\) | −22.0004 | −0.807660 | ||||||||
\(743\) | 35.4503 | 1.30055 | 0.650273 | − | 0.759700i | \(-0.274654\pi\) | ||||
0.650273 | + | 0.759700i | \(0.274654\pi\) | |||||||
\(744\) | 5.32991 | 0.195404 | ||||||||
\(745\) | −3.08125 | −0.112888 | ||||||||
\(746\) | 10.3434 | 0.378699 | ||||||||
\(747\) | 12.2983 | 0.449970 | ||||||||
\(748\) | −2.25439 | −0.0824285 | ||||||||
\(749\) | 36.6017 | 1.33740 | ||||||||
\(750\) | 11.9303 | 0.435635 | ||||||||
\(751\) | −5.67770 | −0.207182 | −0.103591 | − | 0.994620i | \(-0.533033\pi\) | ||||
−0.103591 | + | 0.994620i | \(0.533033\pi\) | |||||||
\(752\) | 10.2298 | 0.373041 | ||||||||
\(753\) | 27.5253 | 1.00308 | ||||||||
\(754\) | −0.369700 | −0.0134637 | ||||||||
\(755\) | 28.5165 | 1.03782 | ||||||||
\(756\) | 2.78135 | 0.101157 | ||||||||
\(757\) | 13.7223 | 0.498745 | 0.249372 | − | 0.968408i | \(-0.419776\pi\) | ||||
0.249372 | + | 0.968408i | \(0.419776\pi\) | |||||||
\(758\) | 21.0732 | 0.765414 | ||||||||
\(759\) | 12.5690 | 0.456225 | ||||||||
\(760\) | −2.39949 | −0.0870387 | ||||||||
\(761\) | −5.71538 | −0.207182 | −0.103591 | − | 0.994620i | \(-0.533033\pi\) | ||||
−0.103591 | + | 0.994620i | \(0.533033\pi\) | |||||||
\(762\) | −12.9128 | −0.467783 | ||||||||
\(763\) | −11.4215 | −0.413485 | ||||||||
\(764\) | 18.5782 | 0.672135 | ||||||||
\(765\) | −2.03178 | −0.0734592 | ||||||||
\(766\) | −27.4055 | −0.990203 | ||||||||
\(767\) | 0.0372501 | 0.00134502 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 55.1363 | 1.98827 | 0.994133 | − | 0.108161i | \(-0.0344962\pi\) | ||||
0.994133 | + | 0.108161i | \(0.0344962\pi\) | |||||||
\(770\) | −12.7398 | −0.459109 | ||||||||
\(771\) | −24.7589 | −0.891668 | ||||||||
\(772\) | −1.64507 | −0.0592072 | ||||||||
\(773\) | −7.09370 | −0.255143 | −0.127571 | − | 0.991829i | \(-0.540718\pi\) | ||||
−0.127571 | + | 0.991829i | \(0.540718\pi\) | |||||||
\(774\) | 0.151772 | 0.00545534 | ||||||||
\(775\) | 4.64697 | 0.166924 | ||||||||
\(776\) | 6.58331 | 0.236327 | ||||||||
\(777\) | 28.2222 | 1.01247 | ||||||||
\(778\) | −32.1966 | −1.15430 | ||||||||
\(779\) | −6.95615 | −0.249230 | ||||||||
\(780\) | 0.0756840 | 0.00270992 | ||||||||
\(781\) | 11.3705 | 0.406870 | ||||||||
\(782\) | 5.57535 | 0.199374 | ||||||||
\(783\) | −9.92481 | −0.354684 | ||||||||
\(784\) | 0.735932 | 0.0262833 | ||||||||
\(785\) | −26.5890 | −0.949004 | ||||||||
\(786\) | −21.1277 | −0.753600 | ||||||||
\(787\) | −42.8679 | −1.52808 | −0.764038 | − | 0.645171i | \(-0.776786\pi\) | ||||
−0.764038 | + | 0.645171i | \(0.776786\pi\) | |||||||
\(788\) | 2.28114 | 0.0812622 | ||||||||
\(789\) | 10.5895 | 0.376997 | ||||||||
\(790\) | −33.7868 | −1.20208 | ||||||||
\(791\) | −25.6832 | −0.913188 | ||||||||
\(792\) | 2.25439 | 0.0801061 | ||||||||
\(793\) | 0.0740831 | 0.00263077 | ||||||||
\(794\) | −7.03918 | −0.249811 | ||||||||
\(795\) | −16.0713 | −0.569990 | ||||||||
\(796\) | 19.6987 | 0.698202 | ||||||||
\(797\) | −27.9382 | −0.989622 | −0.494811 | − | 0.869001i | \(-0.664763\pi\) | ||||
−0.494811 | + | 0.869001i | \(0.664763\pi\) | |||||||
\(798\) | −3.28472 | −0.116278 | ||||||||
\(799\) | −10.2298 | −0.361903 | ||||||||
\(800\) | −0.871867 | −0.0308251 | ||||||||
\(801\) | 3.69721 | 0.130634 | ||||||||
\(802\) | −13.9264 | −0.491760 | ||||||||
\(803\) | 33.8825 | 1.19569 | ||||||||
\(804\) | −0.598471 | −0.0211065 | ||||||||
\(805\) | 31.5068 | 1.11047 | ||||||||
\(806\) | 0.198540 | 0.00699326 | ||||||||
\(807\) | −9.52384 | −0.335255 | ||||||||
\(808\) | −7.88892 | −0.277531 | ||||||||
\(809\) | −54.0870 | −1.90160 | −0.950799 | − | 0.309807i | \(-0.899735\pi\) | ||||
−0.950799 | + | 0.309807i | \(0.899735\pi\) | |||||||
\(810\) | 2.03178 | 0.0713895 | ||||||||
\(811\) | 8.43451 | 0.296176 | 0.148088 | − | 0.988974i | \(-0.452688\pi\) | ||||
0.148088 | + | 0.988974i | \(0.452688\pi\) | |||||||
\(812\) | −27.6044 | −0.968725 | ||||||||
\(813\) | 1.40167 | 0.0491588 | ||||||||
\(814\) | 22.8751 | 0.801772 | ||||||||
\(815\) | −18.9840 | −0.664981 | ||||||||
\(816\) | 1.00000 | 0.0350070 | ||||||||
\(817\) | −0.179240 | −0.00627081 | ||||||||
\(818\) | −28.4417 | −0.994440 | ||||||||
\(819\) | 0.103606 | 0.00362028 | ||||||||
\(820\) | 11.9675 | 0.417923 | ||||||||
\(821\) | 14.1221 | 0.492866 | 0.246433 | − | 0.969160i | \(-0.420742\pi\) | ||||
0.246433 | + | 0.969160i | \(0.420742\pi\) | |||||||
\(822\) | −3.61782 | −0.126186 | ||||||||
\(823\) | 36.4697 | 1.27125 | 0.635626 | − | 0.771997i | \(-0.280742\pi\) | ||||
0.635626 | + | 0.771997i | \(0.280742\pi\) | |||||||
\(824\) | −1.85170 | −0.0645069 | ||||||||
\(825\) | 1.96552 | 0.0684308 | ||||||||
\(826\) | 2.78135 | 0.0967757 | ||||||||
\(827\) | 18.5680 | 0.645673 | 0.322836 | − | 0.946455i | \(-0.395364\pi\) | ||||
0.322836 | + | 0.946455i | \(0.395364\pi\) | |||||||
\(828\) | −5.57535 | −0.193757 | ||||||||
\(829\) | 16.4444 | 0.571137 | 0.285568 | − | 0.958358i | \(-0.407818\pi\) | ||||
0.285568 | + | 0.958358i | \(0.407818\pi\) | |||||||
\(830\) | 24.9874 | 0.867324 | ||||||||
\(831\) | 0.830252 | 0.0288011 | ||||||||
\(832\) | −0.0372501 | −0.00129141 | ||||||||
\(833\) | −0.735932 | −0.0254985 | ||||||||
\(834\) | 14.2864 | 0.494699 | ||||||||
\(835\) | −7.07275 | −0.244762 | ||||||||
\(836\) | −2.66239 | −0.0920805 | ||||||||
\(837\) | 5.32991 | 0.184229 | ||||||||
\(838\) | −19.3607 | −0.668805 | ||||||||
\(839\) | −47.0652 | −1.62487 | −0.812435 | − | 0.583052i | \(-0.801858\pi\) | ||||
−0.812435 | + | 0.583052i | \(0.801858\pi\) | |||||||
\(840\) | 5.65110 | 0.194982 | ||||||||
\(841\) | 69.5018 | 2.39661 | ||||||||
\(842\) | 10.0335 | 0.345779 | ||||||||
\(843\) | 14.6155 | 0.503385 | ||||||||
\(844\) | 22.3114 | 0.767991 | ||||||||
\(845\) | −26.4103 | −0.908543 | ||||||||
\(846\) | 10.2298 | 0.351707 | ||||||||
\(847\) | 16.4593 | 0.565550 | ||||||||
\(848\) | 7.90996 | 0.271629 | ||||||||
\(849\) | 25.6174 | 0.879188 | ||||||||
\(850\) | 0.871867 | 0.0299048 | ||||||||
\(851\) | −56.5727 | −1.93929 | ||||||||
\(852\) | −5.04374 | −0.172796 | ||||||||
\(853\) | 47.3699 | 1.62191 | 0.810957 | − | 0.585106i | \(-0.198947\pi\) | ||||
0.810957 | + | 0.585106i | \(0.198947\pi\) | |||||||
\(854\) | 5.53157 | 0.189286 | ||||||||
\(855\) | −2.39949 | −0.0820609 | ||||||||
\(856\) | −13.1597 | −0.449788 | ||||||||
\(857\) | 21.5791 | 0.737129 | 0.368565 | − | 0.929602i | \(-0.379849\pi\) | ||||
0.368565 | + | 0.929602i | \(0.379849\pi\) | |||||||
\(858\) | 0.0839761 | 0.00286690 | ||||||||
\(859\) | 6.07787 | 0.207374 | 0.103687 | − | 0.994610i | \(-0.466936\pi\) | ||||
0.103687 | + | 0.994610i | \(0.466936\pi\) | |||||||
\(860\) | 0.308368 | 0.0105153 | ||||||||
\(861\) | 16.3826 | 0.558318 | ||||||||
\(862\) | 33.6539 | 1.14626 | ||||||||
\(863\) | 0.0719156 | 0.00244803 | 0.00122402 | − | 0.999999i | \(-0.499610\pi\) | ||||
0.00122402 | + | 0.999999i | \(0.499610\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 11.0824 | 0.376814 | ||||||||
\(866\) | 25.9459 | 0.881677 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | 14.8244 | 0.503172 | ||||||||
\(869\) | −37.4885 | −1.27171 | ||||||||
\(870\) | −20.1650 | −0.683659 | ||||||||
\(871\) | −0.0222931 | −0.000755374 0 | ||||||||
\(872\) | 4.10644 | 0.139062 | ||||||||
\(873\) | 6.58331 | 0.222811 | ||||||||
\(874\) | 6.58437 | 0.222720 | ||||||||
\(875\) | 33.1825 | 1.12177 | ||||||||
\(876\) | −15.0296 | −0.507802 | ||||||||
\(877\) | 13.4348 | 0.453661 | 0.226831 | − | 0.973934i | \(-0.427164\pi\) | ||||
0.226831 | + | 0.973934i | \(0.427164\pi\) | |||||||
\(878\) | 15.3049 | 0.516517 | ||||||||
\(879\) | −1.15255 | −0.0388746 | ||||||||
\(880\) | 4.58042 | 0.154406 | ||||||||
\(881\) | 10.0121 | 0.337316 | 0.168658 | − | 0.985675i | \(-0.446057\pi\) | ||||
0.168658 | + | 0.985675i | \(0.446057\pi\) | |||||||
\(882\) | 0.735932 | 0.0247801 | ||||||||
\(883\) | −17.2750 | −0.581348 | −0.290674 | − | 0.956822i | \(-0.593880\pi\) | ||||
−0.290674 | + | 0.956822i | \(0.593880\pi\) | |||||||
\(884\) | 0.0372501 | 0.00125286 | ||||||||
\(885\) | 2.03178 | 0.0682976 | ||||||||
\(886\) | 29.4490 | 0.989359 | ||||||||
\(887\) | −10.2608 | −0.344523 | −0.172262 | − | 0.985051i | \(-0.555107\pi\) | ||||
−0.172262 | + | 0.985051i | \(0.555107\pi\) | |||||||
\(888\) | −10.1469 | −0.340509 | ||||||||
\(889\) | −35.9152 | −1.20456 | ||||||||
\(890\) | 7.51191 | 0.251800 | ||||||||
\(891\) | 2.25439 | 0.0755248 | ||||||||
\(892\) | −10.3040 | −0.345004 | ||||||||
\(893\) | −12.0811 | −0.404280 | ||||||||
\(894\) | 1.51653 | 0.0507202 | ||||||||
\(895\) | 39.3768 | 1.31622 | ||||||||
\(896\) | −2.78135 | −0.0929185 | ||||||||
\(897\) | −0.207682 | −0.00693431 | ||||||||
\(898\) | 23.9846 | 0.800377 | ||||||||
\(899\) | −52.8983 | −1.76426 | ||||||||
\(900\) | −0.871867 | −0.0290622 | ||||||||
\(901\) | −7.90996 | −0.263519 | ||||||||
\(902\) | 13.2787 | 0.442132 | ||||||||
\(903\) | 0.422132 | 0.0140477 | ||||||||
\(904\) | 9.23405 | 0.307120 | ||||||||
\(905\) | −16.5484 | −0.550087 | ||||||||
\(906\) | −14.0352 | −0.466289 | ||||||||
\(907\) | −5.63584 | −0.187135 | −0.0935675 | − | 0.995613i | \(-0.529827\pi\) | ||||
−0.0935675 | + | 0.995613i | \(0.529827\pi\) | |||||||
\(908\) | 16.5140 | 0.548038 | ||||||||
\(909\) | −7.88892 | −0.261659 | ||||||||
\(910\) | 0.210504 | 0.00697814 | ||||||||
\(911\) | 16.6569 | 0.551869 | 0.275934 | − | 0.961176i | \(-0.411013\pi\) | ||||
0.275934 | + | 0.961176i | \(0.411013\pi\) | |||||||
\(912\) | 1.18098 | 0.0391062 | ||||||||
\(913\) | 27.7250 | 0.917564 | ||||||||
\(914\) | 21.4907 | 0.710849 | ||||||||
\(915\) | 4.04081 | 0.133585 | ||||||||
\(916\) | 8.61010 | 0.284486 | ||||||||
\(917\) | −58.7636 | −1.94055 | ||||||||
\(918\) | 1.00000 | 0.0330049 | ||||||||
\(919\) | −21.4854 | −0.708738 | −0.354369 | − | 0.935106i | \(-0.615304\pi\) | ||||
−0.354369 | + | 0.935106i | \(0.615304\pi\) | |||||||
\(920\) | −11.3279 | −0.373469 | ||||||||
\(921\) | 10.9773 | 0.361713 | ||||||||
\(922\) | −36.7596 | −1.21061 | ||||||||
\(923\) | −0.187880 | −0.00618414 | ||||||||
\(924\) | 6.27025 | 0.206276 | ||||||||
\(925\) | −8.84678 | −0.290880 | ||||||||
\(926\) | −40.4962 | −1.33079 | ||||||||
\(927\) | −1.85170 | −0.0608177 | ||||||||
\(928\) | 9.92481 | 0.325798 | ||||||||
\(929\) | 14.2900 | 0.468840 | 0.234420 | − | 0.972135i | \(-0.424681\pi\) | ||||
0.234420 | + | 0.972135i | \(0.424681\pi\) | |||||||
\(930\) | 10.8292 | 0.355104 | ||||||||
\(931\) | −0.869121 | −0.0284843 | ||||||||
\(932\) | 6.17877 | 0.202392 | ||||||||
\(933\) | −31.5873 | −1.03412 | ||||||||
\(934\) | −40.3215 | −1.31936 | ||||||||
\(935\) | −4.58042 | −0.149796 | ||||||||
\(936\) | −0.0372501 | −0.00121756 | ||||||||
\(937\) | −2.17700 | −0.0711194 | −0.0355597 | − | 0.999368i | \(-0.511321\pi\) | ||||
−0.0355597 | + | 0.999368i | \(0.511321\pi\) | |||||||
\(938\) | −1.66456 | −0.0543498 | ||||||||
\(939\) | −21.7785 | −0.710714 | ||||||||
\(940\) | 20.7846 | 0.677920 | ||||||||
\(941\) | 29.2499 | 0.953518 | 0.476759 | − | 0.879034i | \(-0.341811\pi\) | ||||
0.476759 | + | 0.879034i | \(0.341811\pi\) | |||||||
\(942\) | 13.0866 | 0.426384 | ||||||||
\(943\) | −32.8396 | −1.06941 | ||||||||
\(944\) | −1.00000 | −0.0325472 | ||||||||
\(945\) | 5.65110 | 0.183830 | ||||||||
\(946\) | 0.342153 | 0.0111244 | ||||||||
\(947\) | −1.50415 | −0.0488783 | −0.0244392 | − | 0.999701i | \(-0.507780\pi\) | ||||
−0.0244392 | + | 0.999701i | \(0.507780\pi\) | |||||||
\(948\) | 16.6292 | 0.540090 | ||||||||
\(949\) | −0.559853 | −0.0181736 | ||||||||
\(950\) | 1.02966 | 0.0334065 | ||||||||
\(951\) | −30.2537 | −0.981045 | ||||||||
\(952\) | 2.78135 | 0.0901442 | ||||||||
\(953\) | 14.1942 | 0.459795 | 0.229898 | − | 0.973215i | \(-0.426161\pi\) | ||||
0.229898 | + | 0.973215i | \(0.426161\pi\) | |||||||
\(954\) | 7.90996 | 0.256094 | ||||||||
\(955\) | 37.7468 | 1.22146 | ||||||||
\(956\) | 22.5916 | 0.730663 | ||||||||
\(957\) | −22.3743 | −0.723260 | ||||||||
\(958\) | −43.0779 | −1.39178 | ||||||||
\(959\) | −10.0624 | −0.324933 | ||||||||
\(960\) | −2.03178 | −0.0655754 | ||||||||
\(961\) | −2.59208 | −0.0836156 | ||||||||
\(962\) | −0.377974 | −0.0121864 | ||||||||
\(963\) | −13.1597 | −0.424064 | ||||||||
\(964\) | −14.4275 | −0.464677 | ||||||||
\(965\) | −3.34241 | −0.107596 | ||||||||
\(966\) | −15.5070 | −0.498930 | ||||||||
\(967\) | −21.2194 | −0.682370 | −0.341185 | − | 0.939996i | \(-0.610828\pi\) | ||||
−0.341185 | + | 0.939996i | \(0.610828\pi\) | |||||||
\(968\) | −5.91774 | −0.190203 | ||||||||
\(969\) | −1.18098 | −0.0379385 | ||||||||
\(970\) | 13.3758 | 0.429472 | ||||||||
\(971\) | −22.6082 | −0.725533 | −0.362767 | − | 0.931880i | \(-0.618168\pi\) | ||||
−0.362767 | + | 0.931880i | \(0.618168\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 39.7356 | 1.27387 | ||||||||
\(974\) | 13.3110 | 0.426513 | ||||||||
\(975\) | −0.0324771 | −0.00104010 | ||||||||
\(976\) | −1.98880 | −0.0636601 | ||||||||
\(977\) | 21.9675 | 0.702803 | 0.351402 | − | 0.936225i | \(-0.385705\pi\) | ||||
0.351402 | + | 0.936225i | \(0.385705\pi\) | |||||||
\(978\) | 9.34353 | 0.298773 | ||||||||
\(979\) | 8.33493 | 0.266386 | ||||||||
\(980\) | 1.49525 | 0.0477641 | ||||||||
\(981\) | 4.10644 | 0.131109 | ||||||||
\(982\) | −25.7331 | −0.821176 | ||||||||
\(983\) | 19.0379 | 0.607213 | 0.303607 | − | 0.952797i | \(-0.401809\pi\) | ||||
0.303607 | + | 0.952797i | \(0.401809\pi\) | |||||||
\(984\) | −5.89015 | −0.187771 | ||||||||
\(985\) | 4.63477 | 0.147676 | ||||||||
\(986\) | −9.92481 | −0.316070 | ||||||||
\(987\) | 28.4526 | 0.905656 | ||||||||
\(988\) | 0.0439916 | 0.00139956 | ||||||||
\(989\) | −0.846182 | −0.0269070 | ||||||||
\(990\) | 4.58042 | 0.145575 | ||||||||
\(991\) | 11.3729 | 0.361272 | 0.180636 | − | 0.983550i | \(-0.442184\pi\) | ||||
0.180636 | + | 0.983550i | \(0.442184\pi\) | |||||||
\(992\) | −5.32991 | −0.169225 | ||||||||
\(993\) | 12.9759 | 0.411777 | ||||||||
\(994\) | −14.0284 | −0.444955 | ||||||||
\(995\) | 40.0235 | 1.26883 | ||||||||
\(996\) | −12.2983 | −0.389685 | ||||||||
\(997\) | 31.0414 | 0.983090 | 0.491545 | − | 0.870852i | \(-0.336432\pi\) | ||||
0.491545 | + | 0.870852i | \(0.336432\pi\) | |||||||
\(998\) | −17.7722 | −0.562571 | ||||||||
\(999\) | −10.1469 | −0.321035 |
(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 | 6018.2.a.z.1.7 | ✓ | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6018.2.a.z.1.7 | ✓ | 11 | 1.1 | even | 1 | trivial |