Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2151,2,Mod(1,2151)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2151, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2151.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2151 = 3^{2} \cdot 239 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2151.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: | \(17.1758214748\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.8.2585660609.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} - 4x^{6} + 15x^{5} + x^{4} - 19x^{3} + 6x^{2} + 3x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 717) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-0.417244\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2151.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.711649 | 0.503212 | 0.251606 | − | 0.967830i | \(-0.419041\pi\) | ||||
0.251606 | + | 0.967830i | \(0.419041\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.49356 | −0.746778 | ||||||||
\(5\) | −0.309852 | −0.138570 | −0.0692849 | − | 0.997597i | \(-0.522072\pi\) | ||||
−0.0692849 | + | 0.997597i | \(0.522072\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.19834 | −1.58682 | −0.793412 | − | 0.608685i | \(-0.791697\pi\) | ||||
−0.793412 | + | 0.608685i | \(0.791697\pi\) | |||||||
\(8\) | −2.48618 | −0.878999 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.220506 | −0.0697300 | ||||||||
\(11\) | −1.06352 | −0.320664 | −0.160332 | − | 0.987063i | \(-0.551256\pi\) | ||||
−0.160332 | + | 0.987063i | \(0.551256\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.09563 | 0.858574 | 0.429287 | − | 0.903168i | \(-0.358765\pi\) | ||||
0.429287 | + | 0.903168i | \(0.358765\pi\) | |||||||
\(14\) | −2.98775 | −0.798509 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.21782 | 0.304455 | ||||||||
\(17\) | −1.63596 | −0.396780 | −0.198390 | − | 0.980123i | \(-0.563571\pi\) | ||||
−0.198390 | + | 0.980123i | \(0.563571\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.86500 | −1.34552 | −0.672761 | − | 0.739859i | \(-0.734892\pi\) | ||||
−0.672761 | + | 0.739859i | \(0.734892\pi\) | |||||||
\(20\) | 0.462781 | 0.103481 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.756853 | −0.161362 | ||||||||
\(23\) | 6.91896 | 1.44270 | 0.721351 | − | 0.692569i | \(-0.243521\pi\) | ||||
0.721351 | + | 0.692569i | \(0.243521\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.90399 | −0.980798 | ||||||||
\(26\) | 2.20300 | 0.432045 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 6.27046 | 1.18501 | ||||||||
\(29\) | 7.66121 | 1.42265 | 0.711326 | − | 0.702862i | \(-0.248095\pi\) | ||||
0.711326 | + | 0.702862i | \(0.248095\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.79991 | −1.04169 | −0.520847 | − | 0.853650i | \(-0.674384\pi\) | ||||
−0.520847 | + | 0.853650i | \(0.674384\pi\) | |||||||
\(32\) | 5.83903 | 1.03220 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.16423 | −0.199664 | ||||||||
\(35\) | 1.30086 | 0.219886 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.34450 | 0.714232 | 0.357116 | − | 0.934060i | \(-0.383760\pi\) | ||||
0.357116 | + | 0.934060i | \(0.383760\pi\) | |||||||
\(38\) | −4.17382 | −0.677083 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.770348 | 0.121803 | ||||||||
\(41\) | 11.0321 | 1.72292 | 0.861459 | − | 0.507827i | \(-0.169551\pi\) | ||||
0.861459 | + | 0.507827i | \(0.169551\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.61761 | −0.246684 | −0.123342 | − | 0.992364i | \(-0.539361\pi\) | ||||
−0.123342 | + | 0.992364i | \(0.539361\pi\) | |||||||
\(44\) | 1.58843 | 0.239465 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.92387 | 0.725985 | ||||||||
\(47\) | 4.79638 | 0.699624 | 0.349812 | − | 0.936820i | \(-0.386246\pi\) | ||||
0.349812 | + | 0.936820i | \(0.386246\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 10.6261 | 1.51801 | ||||||||
\(50\) | −3.48992 | −0.493549 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.62350 | −0.641164 | ||||||||
\(53\) | −8.64828 | −1.18793 | −0.593967 | − | 0.804490i | \(-0.702439\pi\) | ||||
−0.593967 | + | 0.804490i | \(0.702439\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.329534 | 0.0444343 | ||||||||
\(56\) | 10.4379 | 1.39482 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.45209 | 0.715895 | ||||||||
\(59\) | −4.12511 | −0.537044 | −0.268522 | − | 0.963274i | \(-0.586535\pi\) | ||||
−0.268522 | + | 0.963274i | \(0.586535\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.3840 | 1.45757 | 0.728783 | − | 0.684745i | \(-0.240086\pi\) | ||||
0.728783 | + | 0.684745i | \(0.240086\pi\) | |||||||
\(62\) | −4.12750 | −0.524193 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.71970 | 0.214962 | ||||||||
\(65\) | −0.959187 | −0.118972 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.9102 | −1.45506 | −0.727529 | − | 0.686077i | \(-0.759331\pi\) | ||||
−0.727529 | + | 0.686077i | \(0.759331\pi\) | |||||||
\(68\) | 2.44341 | 0.296306 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.925758 | 0.110649 | ||||||||
\(71\) | 7.05266 | 0.836997 | 0.418499 | − | 0.908217i | \(-0.362556\pi\) | ||||
0.418499 | + | 0.908217i | \(0.362556\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.39390 | 0.163144 | 0.0815720 | − | 0.996667i | \(-0.474006\pi\) | ||||
0.0815720 | + | 0.996667i | \(0.474006\pi\) | |||||||
\(74\) | 3.09176 | 0.359410 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 8.75970 | 1.00481 | ||||||||
\(77\) | 4.46502 | 0.508837 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.7555 | 1.43510 | 0.717551 | − | 0.696506i | \(-0.245263\pi\) | ||||
0.717551 | + | 0.696506i | \(0.245263\pi\) | |||||||
\(80\) | −0.377344 | −0.0421883 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 7.85095 | 0.866993 | ||||||||
\(83\) | 7.68673 | 0.843728 | 0.421864 | − | 0.906659i | \(-0.361376\pi\) | ||||
0.421864 | + | 0.906659i | \(0.361376\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.506906 | 0.0549817 | ||||||||
\(86\) | −1.15117 | −0.124134 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.64411 | 0.281863 | ||||||||
\(89\) | 9.42458 | 0.999004 | 0.499502 | − | 0.866313i | \(-0.333516\pi\) | ||||
0.499502 | + | 0.866313i | \(0.333516\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.9965 | −1.36241 | ||||||||
\(92\) | −10.3339 | −1.07738 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.41334 | 0.352059 | ||||||||
\(95\) | 1.81728 | 0.186449 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.84754 | −0.289124 | −0.144562 | − | 0.989496i | \(-0.546177\pi\) | ||||
−0.144562 | + | 0.989496i | \(0.546177\pi\) | |||||||
\(98\) | 7.56204 | 0.763881 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 7.32439 | 0.732439 | ||||||||
\(101\) | −8.99104 | −0.894642 | −0.447321 | − | 0.894373i | \(-0.647622\pi\) | ||||
−0.447321 | + | 0.894373i | \(0.647622\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.4683 | 1.72120 | 0.860601 | − | 0.509279i | \(-0.170088\pi\) | ||||
0.860601 | + | 0.509279i | \(0.170088\pi\) | |||||||
\(104\) | −7.69632 | −0.754686 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.15454 | −0.597782 | ||||||||
\(107\) | −3.92688 | −0.379626 | −0.189813 | − | 0.981820i | \(-0.560788\pi\) | ||||
−0.189813 | + | 0.981820i | \(0.560788\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 18.9932 | 1.81922 | 0.909608 | − | 0.415467i | \(-0.136382\pi\) | ||||
0.909608 | + | 0.415467i | \(0.136382\pi\) | |||||||
\(110\) | 0.234512 | 0.0223599 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −5.11283 | −0.483117 | ||||||||
\(113\) | 10.7573 | 1.01196 | 0.505980 | − | 0.862545i | \(-0.331131\pi\) | ||||
0.505980 | + | 0.862545i | \(0.331131\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.14385 | −0.199915 | ||||||||
\(116\) | −11.4425 | −1.06241 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.93563 | −0.270247 | ||||||||
\(119\) | 6.86834 | 0.629620 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.86892 | −0.897175 | ||||||||
\(122\) | 8.10138 | 0.733464 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 8.66249 | 0.777915 | ||||||||
\(125\) | 3.06877 | 0.274479 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.71405 | −0.773247 | −0.386624 | − | 0.922238i | \(-0.626359\pi\) | ||||
−0.386624 | + | 0.922238i | \(0.626359\pi\) | |||||||
\(128\) | −10.4542 | −0.924033 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.682604 | −0.0598683 | ||||||||
\(131\) | 8.70686 | 0.760722 | 0.380361 | − | 0.924838i | \(-0.375800\pi\) | ||||
0.380361 | + | 0.924838i | \(0.375800\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 24.6233 | 2.13511 | ||||||||
\(134\) | −8.47585 | −0.732202 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.06731 | 0.348769 | ||||||||
\(137\) | 16.3421 | 1.39620 | 0.698101 | − | 0.715999i | \(-0.254029\pi\) | ||||
0.698101 | + | 0.715999i | \(0.254029\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.8378 | −0.919247 | −0.459624 | − | 0.888114i | \(-0.652016\pi\) | ||||
−0.459624 | + | 0.888114i | \(0.652016\pi\) | |||||||
\(140\) | −1.94291 | −0.164206 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 5.01902 | 0.421187 | ||||||||
\(143\) | −3.29227 | −0.275313 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.37384 | −0.197137 | ||||||||
\(146\) | 0.991970 | 0.0820960 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.48876 | −0.533372 | ||||||||
\(149\) | −20.8899 | −1.71137 | −0.855684 | − | 0.517498i | \(-0.826863\pi\) | ||||
−0.855684 | + | 0.517498i | \(0.826863\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.1235 | −0.986597 | −0.493299 | − | 0.869860i | \(-0.664209\pi\) | ||||
−0.493299 | + | 0.869860i | \(0.664209\pi\) | |||||||
\(152\) | 14.5815 | 1.18271 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.17753 | 0.256053 | ||||||||
\(155\) | 1.79711 | 0.144347 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −21.1431 | −1.68740 | −0.843700 | − | 0.536815i | \(-0.819627\pi\) | ||||
−0.843700 | + | 0.536815i | \(0.819627\pi\) | |||||||
\(158\) | 9.07741 | 0.722160 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.80923 | −0.143032 | ||||||||
\(161\) | −29.0482 | −2.28932 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 19.6345 | 1.53790 | 0.768948 | − | 0.639311i | \(-0.220780\pi\) | ||||
0.768948 | + | 0.639311i | \(0.220780\pi\) | |||||||
\(164\) | −16.4770 | −1.28664 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.47025 | 0.424574 | ||||||||
\(167\) | −18.2792 | −1.41449 | −0.707243 | − | 0.706971i | \(-0.750061\pi\) | ||||
−0.707243 | + | 0.706971i | \(0.750061\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.41706 | −0.262851 | ||||||||
\(170\) | 0.360739 | 0.0276674 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.41600 | 0.184218 | ||||||||
\(173\) | 2.25763 | 0.171645 | 0.0858223 | − | 0.996310i | \(-0.472648\pi\) | ||||
0.0858223 | + | 0.996310i | \(0.472648\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 20.5886 | 1.55635 | ||||||||
\(176\) | −1.29518 | −0.0976278 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 6.70699 | 0.502710 | ||||||||
\(179\) | −24.3298 | −1.81849 | −0.909246 | − | 0.416258i | \(-0.863341\pi\) | ||||
−0.909246 | + | 0.416258i | \(0.863341\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.55124 | 0.115303 | 0.0576515 | − | 0.998337i | \(-0.481639\pi\) | ||||
0.0576515 | + | 0.998337i | \(0.481639\pi\) | |||||||
\(182\) | −9.24896 | −0.685579 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −17.2018 | −1.26813 | ||||||||
\(185\) | −1.34615 | −0.0989710 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.73988 | 0.127233 | ||||||||
\(188\) | −7.16366 | −0.522463 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.29326 | 0.0938233 | ||||||||
\(191\) | 1.96793 | 0.142394 | 0.0711972 | − | 0.997462i | \(-0.477318\pi\) | ||||
0.0711972 | + | 0.997462i | \(0.477318\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.01740 | 0.0732342 | 0.0366171 | − | 0.999329i | \(-0.488342\pi\) | ||||
0.0366171 | + | 0.999329i | \(0.488342\pi\) | |||||||
\(194\) | −2.02645 | −0.145491 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −15.8706 | −1.13362 | ||||||||
\(197\) | 15.1745 | 1.08114 | 0.540569 | − | 0.841299i | \(-0.318209\pi\) | ||||
0.540569 | + | 0.841299i | \(0.318209\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.06179 | −0.217045 | −0.108522 | − | 0.994094i | \(-0.534612\pi\) | ||||
−0.108522 | + | 0.994094i | \(0.534612\pi\) | |||||||
\(200\) | 12.1922 | 0.862121 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −6.39846 | −0.450194 | ||||||||
\(203\) | −32.1644 | −2.25750 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.41830 | −0.238745 | ||||||||
\(206\) | 12.4313 | 0.866129 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.76993 | 0.261398 | ||||||||
\(209\) | 6.23755 | 0.431460 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.3580 | 0.713074 | 0.356537 | − | 0.934281i | \(-0.383957\pi\) | ||||
0.356537 | + | 0.934281i | \(0.383957\pi\) | |||||||
\(212\) | 12.9167 | 0.887122 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.79456 | −0.191032 | ||||||||
\(215\) | 0.501220 | 0.0341829 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 24.3500 | 1.65299 | ||||||||
\(218\) | 13.5165 | 0.915451 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.492177 | −0.0331826 | ||||||||
\(221\) | −5.06435 | −0.340665 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.771196 | −0.0516431 | −0.0258216 | − | 0.999667i | \(-0.508220\pi\) | ||||
−0.0258216 | + | 0.999667i | \(0.508220\pi\) | |||||||
\(224\) | −24.5143 | −1.63793 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7.65541 | 0.509230 | ||||||||
\(227\) | 21.0118 | 1.39460 | 0.697302 | − | 0.716777i | \(-0.254384\pi\) | ||||
0.697302 | + | 0.716777i | \(0.254384\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 25.8503 | 1.70824 | 0.854119 | − | 0.520077i | \(-0.174097\pi\) | ||||
0.854119 | + | 0.520077i | \(0.174097\pi\) | |||||||
\(230\) | −1.52567 | −0.100600 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −19.0472 | −1.25051 | ||||||||
\(233\) | −17.9134 | −1.17354 | −0.586771 | − | 0.809753i | \(-0.699601\pi\) | ||||
−0.586771 | + | 0.809753i | \(0.699601\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.48617 | −0.0969467 | ||||||||
\(236\) | 6.16109 | 0.401053 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4.88785 | 0.316832 | ||||||||
\(239\) | −1.00000 | −0.0646846 | ||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.53136 | 0.613969 | 0.306984 | − | 0.951715i | \(-0.400680\pi\) | ||||
0.306984 | + | 0.951715i | \(0.400680\pi\) | |||||||
\(242\) | −7.02321 | −0.451469 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −17.0026 | −1.08848 | ||||||||
\(245\) | −3.29251 | −0.210351 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −18.1559 | −1.15523 | ||||||||
\(248\) | 14.4197 | 0.915649 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2.18389 | 0.138121 | ||||||||
\(251\) | 1.93621 | 0.122212 | 0.0611062 | − | 0.998131i | \(-0.480537\pi\) | ||||
0.0611062 | + | 0.998131i | \(0.480537\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.35846 | −0.462622 | ||||||||
\(254\) | −6.20135 | −0.389107 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −10.8791 | −0.679946 | ||||||||
\(257\) | 0.0592320 | 0.00369479 | 0.00184740 | − | 0.999998i | \(-0.499412\pi\) | ||||
0.00184740 | + | 0.999998i | \(0.499412\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −18.2397 | −1.13336 | ||||||||
\(260\) | 1.43260 | 0.0888460 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 6.19622 | 0.382804 | ||||||||
\(263\) | 24.0362 | 1.48213 | 0.741067 | − | 0.671431i | \(-0.234320\pi\) | ||||
0.741067 | + | 0.671431i | \(0.234320\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.67968 | 0.164612 | ||||||||
\(266\) | 17.5231 | 1.07441 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 17.7885 | 1.08661 | ||||||||
\(269\) | 15.8995 | 0.969407 | 0.484703 | − | 0.874679i | \(-0.338928\pi\) | ||||
0.484703 | + | 0.874679i | \(0.338928\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.308408 | −0.0187344 | −0.00936722 | − | 0.999956i | \(-0.502982\pi\) | ||||
−0.00936722 | + | 0.999956i | \(0.502982\pi\) | |||||||
\(272\) | −1.99231 | −0.120802 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11.6299 | 0.702585 | ||||||||
\(275\) | 5.21550 | 0.314506 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 16.9466 | 1.01822 | 0.509112 | − | 0.860700i | \(-0.329974\pi\) | ||||
0.509112 | + | 0.860700i | \(0.329974\pi\) | |||||||
\(278\) | −7.71268 | −0.462576 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.23419 | −0.193280 | ||||||||
\(281\) | 16.5825 | 0.989231 | 0.494615 | − | 0.869112i | \(-0.335309\pi\) | ||||
0.494615 | + | 0.869112i | \(0.335309\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.3402 | 0.674105 | 0.337052 | − | 0.941486i | \(-0.390570\pi\) | ||||
0.337052 | + | 0.941486i | \(0.390570\pi\) | |||||||
\(284\) | −10.5335 | −0.625051 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.34294 | −0.138541 | ||||||||
\(287\) | −46.3164 | −2.73397 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.3236 | −0.842566 | ||||||||
\(290\) | −1.68934 | −0.0992015 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.08187 | −0.121832 | ||||||||
\(293\) | −1.88336 | −0.110027 | −0.0550134 | − | 0.998486i | \(-0.517520\pi\) | ||||
−0.0550134 | + | 0.998486i | \(0.517520\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.27817 | 0.0744181 | ||||||||
\(296\) | −10.8012 | −0.627809 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −14.8663 | −0.861181 | ||||||||
\(299\) | 21.4186 | 1.23867 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.79130 | 0.391444 | ||||||||
\(302\) | −8.62768 | −0.496467 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −7.14252 | −0.409652 | ||||||||
\(305\) | −3.52734 | −0.201975 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.8785 | 1.24867 | 0.624335 | − | 0.781157i | \(-0.285370\pi\) | ||||
0.624335 | + | 0.781157i | \(0.285370\pi\) | |||||||
\(308\) | −6.66876 | −0.379988 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.27891 | 0.0726373 | ||||||||
\(311\) | 0.911901 | 0.0517092 | 0.0258546 | − | 0.999666i | \(-0.491769\pi\) | ||||
0.0258546 | + | 0.999666i | \(0.491769\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.29642 | −0.468941 | −0.234471 | − | 0.972123i | \(-0.575336\pi\) | ||||
−0.234471 | + | 0.972123i | \(0.575336\pi\) | |||||||
\(314\) | −15.0464 | −0.849119 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −19.0510 | −1.07170 | ||||||||
\(317\) | 7.20688 | 0.404779 | 0.202389 | − | 0.979305i | \(-0.435129\pi\) | ||||
0.202389 | + | 0.979305i | \(0.435129\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.14786 | −0.456193 | ||||||||
\(320\) | −0.532851 | −0.0297873 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −20.6721 | −1.15201 | ||||||||
\(323\) | 9.59493 | 0.533876 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −15.1810 | −0.842088 | ||||||||
\(326\) | 13.9729 | 0.773887 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −27.4277 | −1.51444 | ||||||||
\(329\) | −20.1368 | −1.11018 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.528456 | 0.0290466 | 0.0145233 | − | 0.999895i | \(-0.495377\pi\) | ||||
0.0145233 | + | 0.999895i | \(0.495377\pi\) | |||||||
\(332\) | −11.4806 | −0.630078 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −13.0084 | −0.711786 | ||||||||
\(335\) | 3.69038 | 0.201627 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.78750 | −0.533159 | −0.266579 | − | 0.963813i | \(-0.585893\pi\) | ||||
−0.266579 | + | 0.963813i | \(0.585893\pi\) | |||||||
\(338\) | −2.43174 | −0.132269 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.757093 | −0.0410591 | ||||||||
\(341\) | 6.16833 | 0.334034 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.2235 | −0.821994 | ||||||||
\(344\) | 4.02169 | 0.216835 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.60664 | 0.0863736 | ||||||||
\(347\) | 0.314769 | 0.0168977 | 0.00844885 | − | 0.999964i | \(-0.497311\pi\) | ||||
0.00844885 | + | 0.999964i | \(0.497311\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 31.7429 | 1.69916 | 0.849579 | − | 0.527461i | \(-0.176856\pi\) | ||||
0.849579 | + | 0.527461i | \(0.176856\pi\) | |||||||
\(350\) | 14.6519 | 0.783176 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −6.20993 | −0.330990 | ||||||||
\(353\) | 6.32810 | 0.336811 | 0.168405 | − | 0.985718i | \(-0.446138\pi\) | ||||
0.168405 | + | 0.985718i | \(0.446138\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.18528 | −0.115983 | ||||||||
\(356\) | −14.0761 | −0.746034 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −17.3143 | −0.915087 | ||||||||
\(359\) | 13.0530 | 0.688910 | 0.344455 | − | 0.938803i | \(-0.388064\pi\) | ||||
0.344455 | + | 0.938803i | \(0.388064\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.3982 | 0.810432 | ||||||||
\(362\) | 1.10394 | 0.0580219 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 19.4110 | 1.01742 | ||||||||
\(365\) | −0.431903 | −0.0226069 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −26.7594 | −1.39683 | −0.698415 | − | 0.715693i | \(-0.746111\pi\) | ||||
−0.698415 | + | 0.715693i | \(0.746111\pi\) | |||||||
\(368\) | 8.42606 | 0.439239 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.957987 | −0.0498033 | ||||||||
\(371\) | 36.3085 | 1.88504 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.1064 | −0.937512 | −0.468756 | − | 0.883328i | \(-0.655298\pi\) | ||||
−0.468756 | + | 0.883328i | \(0.655298\pi\) | |||||||
\(374\) | 1.23819 | 0.0640250 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −11.9247 | −0.614968 | ||||||||
\(377\) | 23.7163 | 1.22145 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −19.6799 | −1.01089 | −0.505445 | − | 0.862859i | \(-0.668672\pi\) | ||||
−0.505445 | + | 0.862859i | \(0.668672\pi\) | |||||||
\(380\) | −2.71421 | −0.139236 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.40048 | 0.0716546 | ||||||||
\(383\) | −1.56845 | −0.0801441 | −0.0400720 | − | 0.999197i | \(-0.512759\pi\) | ||||
−0.0400720 | + | 0.999197i | \(0.512759\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.38350 | −0.0705094 | ||||||||
\(386\) | 0.724033 | 0.0368523 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4.25297 | 0.215912 | ||||||||
\(389\) | 8.80566 | 0.446465 | 0.223232 | − | 0.974765i | \(-0.428339\pi\) | ||||
0.223232 | + | 0.974765i | \(0.428339\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.3192 | −0.572435 | ||||||||
\(392\) | −26.4184 | −1.33433 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 10.7989 | 0.544042 | ||||||||
\(395\) | −3.95230 | −0.198862 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.24404 | −0.313379 | −0.156690 | − | 0.987648i | \(-0.550082\pi\) | ||||
−0.156690 | + | 0.987648i | \(0.550082\pi\) | |||||||
\(398\) | −2.17892 | −0.109219 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −5.97219 | −0.298609 | ||||||||
\(401\) | 2.89416 | 0.144527 | 0.0722637 | − | 0.997386i | \(-0.476978\pi\) | ||||
0.0722637 | + | 0.997386i | \(0.476978\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −17.9544 | −0.894372 | ||||||||
\(404\) | 13.4286 | 0.668099 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −22.8898 | −1.13600 | ||||||||
\(407\) | −4.62047 | −0.229028 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.8662 | −0.586744 | −0.293372 | − | 0.955998i | \(-0.594777\pi\) | ||||
−0.293372 | + | 0.955998i | \(0.594777\pi\) | |||||||
\(410\) | −2.43263 | −0.120139 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −26.0899 | −1.28536 | ||||||||
\(413\) | 17.3186 | 0.852195 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.38175 | −0.116915 | ||||||||
\(416\) | 18.0755 | 0.886224 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 4.43894 | 0.217116 | ||||||||
\(419\) | −23.8835 | −1.16678 | −0.583392 | − | 0.812191i | \(-0.698275\pi\) | ||||
−0.583392 | + | 0.812191i | \(0.698275\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.4207 | 1.23893 | 0.619464 | − | 0.785025i | \(-0.287350\pi\) | ||||
0.619464 | + | 0.785025i | \(0.287350\pi\) | |||||||
\(422\) | 7.37126 | 0.358827 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 21.5012 | 1.04419 | ||||||||
\(425\) | 8.02276 | 0.389161 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −47.7938 | −2.31290 | ||||||||
\(428\) | 5.86501 | 0.283496 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.356693 | 0.0172013 | ||||||||
\(431\) | −33.8543 | −1.63071 | −0.815353 | − | 0.578965i | \(-0.803457\pi\) | ||||
−0.815353 | + | 0.578965i | \(0.803457\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.14549 | 0.439504 | 0.219752 | − | 0.975556i | \(-0.429475\pi\) | ||||
0.219752 | + | 0.975556i | \(0.429475\pi\) | |||||||
\(434\) | 17.3287 | 0.831802 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −28.3674 | −1.35855 | ||||||||
\(437\) | −40.5797 | −1.94119 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.56405 | −0.122376 | −0.0611878 | − | 0.998126i | \(-0.519489\pi\) | ||||
−0.0611878 | + | 0.998126i | \(0.519489\pi\) | |||||||
\(440\) | −0.819282 | −0.0390577 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.60404 | −0.171427 | ||||||||
\(443\) | −8.44657 | −0.401308 | −0.200654 | − | 0.979662i | \(-0.564307\pi\) | ||||
−0.200654 | + | 0.979662i | \(0.564307\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.92022 | −0.138432 | ||||||||
\(446\) | −0.548821 | −0.0259874 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −7.21987 | −0.341107 | ||||||||
\(449\) | 27.6378 | 1.30431 | 0.652153 | − | 0.758087i | \(-0.273866\pi\) | ||||
0.652153 | + | 0.758087i | \(0.273866\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.7328 | −0.552477 | ||||||||
\(452\) | −16.0666 | −0.755709 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 14.9530 | 0.701781 | ||||||||
\(455\) | 4.02700 | 0.188788 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −31.4026 | −1.46895 | −0.734476 | − | 0.678634i | \(-0.762572\pi\) | ||||
−0.734476 | + | 0.678634i | \(0.762572\pi\) | |||||||
\(458\) | 18.3964 | 0.859606 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.20196 | 0.149292 | ||||||||
\(461\) | −4.62584 | −0.215447 | −0.107723 | − | 0.994181i | \(-0.534356\pi\) | ||||
−0.107723 | + | 0.994181i | \(0.534356\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.3014 | −0.989962 | −0.494981 | − | 0.868904i | \(-0.664825\pi\) | ||||
−0.494981 | + | 0.868904i | \(0.664825\pi\) | |||||||
\(464\) | 9.32999 | 0.433134 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −12.7480 | −0.590540 | ||||||||
\(467\) | −18.5084 | −0.856466 | −0.428233 | − | 0.903668i | \(-0.640864\pi\) | ||||
−0.428233 | + | 0.903668i | \(0.640864\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 50.0029 | 2.30892 | ||||||||
\(470\) | −1.05763 | −0.0487847 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 10.2558 | 0.472061 | ||||||||
\(473\) | 1.72037 | 0.0791025 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 28.7619 | 1.31969 | ||||||||
\(476\) | −10.2583 | −0.470186 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −0.711649 | −0.0325501 | ||||||||
\(479\) | 28.3367 | 1.29473 | 0.647367 | − | 0.762178i | \(-0.275870\pi\) | ||||
0.647367 | + | 0.762178i | \(0.275870\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.4490 | 0.613221 | ||||||||
\(482\) | 6.78298 | 0.308956 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 14.7398 | 0.669990 | ||||||||
\(485\) | 0.882316 | 0.0400639 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 34.2775 | 1.55326 | 0.776631 | − | 0.629955i | \(-0.216927\pi\) | ||||
0.776631 | + | 0.629955i | \(0.216927\pi\) | |||||||
\(488\) | −28.3026 | −1.28120 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.34311 | −0.105851 | ||||||||
\(491\) | −29.8401 | −1.34666 | −0.673332 | − | 0.739340i | \(-0.735138\pi\) | ||||
−0.673332 | + | 0.739340i | \(0.735138\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.5335 | −0.564479 | ||||||||
\(494\) | −12.9206 | −0.581326 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.06326 | −0.317150 | ||||||||
\(497\) | −29.6095 | −1.32817 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.0147 | 0.672150 | 0.336075 | − | 0.941835i | \(-0.390900\pi\) | ||||
0.336075 | + | 0.941835i | \(0.390900\pi\) | |||||||
\(500\) | −4.58338 | −0.204975 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.37790 | 0.0614988 | ||||||||
\(503\) | 42.0242 | 1.87377 | 0.936883 | − | 0.349644i | \(-0.113697\pi\) | ||||
0.936883 | + | 0.349644i | \(0.113697\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.78589 | 0.123970 | ||||||||
\(506\) | −5.23664 | −0.232797 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 13.0149 | 0.577444 | ||||||||
\(509\) | 3.07761 | 0.136413 | 0.0682064 | − | 0.997671i | \(-0.478272\pi\) | ||||
0.0682064 | + | 0.997671i | \(0.478272\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.85208 | −0.258881 | ||||||||
\(512\) | 13.1664 | 0.581876 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0.0421524 | 0.00185926 | ||||||||
\(515\) | −5.41258 | −0.238507 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.10105 | −0.224344 | ||||||||
\(518\) | −12.9803 | −0.570320 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.38472 | 0.104577 | ||||||||
\(521\) | −24.5303 | −1.07469 | −0.537345 | − | 0.843363i | \(-0.680573\pi\) | ||||
−0.537345 | + | 0.843363i | \(0.680573\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 22.3722 | 0.978267 | 0.489133 | − | 0.872209i | \(-0.337313\pi\) | ||||
0.489133 | + | 0.872209i | \(0.337313\pi\) | |||||||
\(524\) | −13.0042 | −0.568090 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 17.1053 | 0.745827 | ||||||||
\(527\) | 9.48845 | 0.413323 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 24.8720 | 1.08139 | ||||||||
\(530\) | 1.90699 | 0.0828345 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −36.7762 | −1.59445 | ||||||||
\(533\) | 34.1512 | 1.47925 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.21675 | 0.0526047 | ||||||||
\(536\) | 29.6109 | 1.27899 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 11.3148 | 0.487817 | ||||||||
\(539\) | −11.3011 | −0.486771 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21.7122 | 0.933480 | 0.466740 | − | 0.884395i | \(-0.345428\pi\) | ||||
0.466740 | + | 0.884395i | \(0.345428\pi\) | |||||||
\(542\) | −0.219478 | −0.00942739 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −9.55245 | −0.409558 | ||||||||
\(545\) | −5.88507 | −0.252089 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20.9706 | 0.896638 | 0.448319 | − | 0.893874i | \(-0.352023\pi\) | ||||
0.448319 | + | 0.893874i | \(0.352023\pi\) | |||||||
\(548\) | −24.4079 | −1.04265 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3.71160 | 0.158263 | ||||||||
\(551\) | −44.9330 | −1.91421 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −53.5518 | −2.27725 | ||||||||
\(554\) | 12.0601 | 0.512383 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 16.1868 | 0.686474 | ||||||||
\(557\) | −21.7092 | −0.919848 | −0.459924 | − | 0.887958i | \(-0.652123\pi\) | ||||
−0.459924 | + | 0.887958i | \(0.652123\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.00754 | −0.211796 | ||||||||
\(560\) | 1.58422 | 0.0669455 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 11.8009 | 0.497792 | ||||||||
\(563\) | 37.4659 | 1.57900 | 0.789499 | − | 0.613752i | \(-0.210340\pi\) | ||||
0.789499 | + | 0.613752i | \(0.210340\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.33316 | −0.140227 | ||||||||
\(566\) | 8.07024 | 0.339217 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −17.5342 | −0.735720 | ||||||||
\(569\) | −20.9148 | −0.876792 | −0.438396 | − | 0.898782i | \(-0.644453\pi\) | ||||
−0.438396 | + | 0.898782i | \(0.644453\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 30.8439 | 1.29078 | 0.645388 | − | 0.763855i | \(-0.276696\pi\) | ||||
0.645388 | + | 0.763855i | \(0.276696\pi\) | |||||||
\(572\) | 4.91719 | 0.205598 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −32.9610 | −1.37576 | ||||||||
\(575\) | −33.9305 | −1.41500 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.04326 | 0.0850622 | 0.0425311 | − | 0.999095i | \(-0.486458\pi\) | ||||
0.0425311 | + | 0.999095i | \(0.486458\pi\) | |||||||
\(578\) | −10.1934 | −0.423989 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 3.54546 | 0.147217 | ||||||||
\(581\) | −32.2715 | −1.33885 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.19763 | 0.380927 | ||||||||
\(584\) | −3.46550 | −0.143403 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.34029 | −0.0553668 | ||||||||
\(587\) | −7.07648 | −0.292078 | −0.146039 | − | 0.989279i | \(-0.546652\pi\) | ||||
−0.146039 | + | 0.989279i | \(0.546652\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 34.0165 | 1.40162 | ||||||||
\(590\) | 0.909610 | 0.0374481 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 5.29083 | 0.217452 | ||||||||
\(593\) | 27.0220 | 1.10966 | 0.554831 | − | 0.831963i | \(-0.312783\pi\) | ||||
0.554831 | + | 0.831963i | \(0.312783\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.12817 | −0.0872463 | ||||||||
\(596\) | 31.2003 | 1.27801 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 15.2425 | 0.623312 | ||||||||
\(599\) | 30.4062 | 1.24236 | 0.621182 | − | 0.783666i | \(-0.286653\pi\) | ||||
0.621182 | + | 0.783666i | \(0.286653\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.96818 | −0.161865 | −0.0809327 | − | 0.996720i | \(-0.525790\pi\) | ||||
−0.0809327 | + | 0.996720i | \(0.525790\pi\) | |||||||
\(602\) | 4.83302 | 0.196979 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 18.1071 | 0.736769 | ||||||||
\(605\) | 3.05790 | 0.124321 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −43.1226 | −1.75029 | −0.875147 | − | 0.483858i | \(-0.839235\pi\) | ||||
−0.875147 | + | 0.483858i | \(0.839235\pi\) | |||||||
\(608\) | −34.2459 | −1.38885 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.51023 | −0.101636 | ||||||||
\(611\) | 14.8478 | 0.600679 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −26.0558 | −1.05238 | −0.526192 | − | 0.850366i | \(-0.676381\pi\) | ||||
−0.526192 | + | 0.850366i | \(0.676381\pi\) | |||||||
\(614\) | 15.5698 | 0.628345 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −11.1009 | −0.447267 | ||||||||
\(617\) | 39.3030 | 1.58228 | 0.791140 | − | 0.611635i | \(-0.209488\pi\) | ||||
0.791140 | + | 0.611635i | \(0.209488\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.28304 | 0.0515696 | 0.0257848 | − | 0.999668i | \(-0.491792\pi\) | ||||
0.0257848 | + | 0.999668i | \(0.491792\pi\) | |||||||
\(620\) | −2.68409 | −0.107796 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0.648953 | 0.0260207 | ||||||||
\(623\) | −39.5676 | −1.58524 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.5691 | 0.942764 | ||||||||
\(626\) | −5.90414 | −0.235977 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 31.5783 | 1.26011 | ||||||||
\(629\) | −7.10745 | −0.283393 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.5132 | 0.498142 | 0.249071 | − | 0.968485i | \(-0.419875\pi\) | ||||
0.249071 | + | 0.968485i | \(0.419875\pi\) | |||||||
\(632\) | −31.7124 | −1.26145 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 5.12877 | 0.203689 | ||||||||
\(635\) | 2.70006 | 0.107149 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 32.8944 | 1.30333 | ||||||||
\(638\) | −5.79842 | −0.229561 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3.23926 | 0.128043 | ||||||||
\(641\) | 7.80075 | 0.308111 | 0.154056 | − | 0.988062i | \(-0.450767\pi\) | ||||
0.154056 | + | 0.988062i | \(0.450767\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18.1134 | −0.714323 | −0.357162 | − | 0.934043i | \(-0.616255\pi\) | ||||
−0.357162 | + | 0.934043i | \(0.616255\pi\) | |||||||
\(644\) | 43.3851 | 1.70961 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.82822 | 0.268653 | ||||||||
\(647\) | 8.38465 | 0.329635 | 0.164817 | − | 0.986324i | \(-0.447297\pi\) | ||||
0.164817 | + | 0.986324i | \(0.447297\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.38714 | 0.172210 | ||||||||
\(650\) | −10.8035 | −0.423749 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −29.3253 | −1.14847 | ||||||||
\(653\) | −36.2780 | −1.41967 | −0.709834 | − | 0.704369i | \(-0.751230\pi\) | ||||
−0.709834 | + | 0.704369i | \(0.751230\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.69783 | −0.105413 | ||||||||
\(656\) | 13.4351 | 0.524552 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −14.3304 | −0.558655 | ||||||||
\(659\) | 41.1303 | 1.60221 | 0.801104 | − | 0.598525i | \(-0.204246\pi\) | ||||
0.801104 | + | 0.598525i | \(0.204246\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.1622 | −0.589740 | −0.294870 | − | 0.955537i | \(-0.595276\pi\) | ||||
−0.294870 | + | 0.955537i | \(0.595276\pi\) | |||||||
\(662\) | 0.376075 | 0.0146166 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −19.1106 | −0.741636 | ||||||||
\(665\) | −7.62956 | −0.295862 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 53.0076 | 2.05246 | ||||||||
\(668\) | 27.3010 | 1.05631 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2.62626 | 0.101461 | ||||||||
\(671\) | −12.1071 | −0.467388 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.6062 | 0.485932 | 0.242966 | − | 0.970035i | \(-0.421880\pi\) | ||||
0.242966 | + | 0.970035i | \(0.421880\pi\) | |||||||
\(674\) | −6.96526 | −0.268292 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.10357 | 0.196291 | ||||||||
\(677\) | −5.74831 | −0.220925 | −0.110463 | − | 0.993880i | \(-0.535233\pi\) | ||||
−0.110463 | + | 0.993880i | \(0.535233\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11.9550 | 0.458790 | ||||||||
\(680\) | −1.26026 | −0.0483289 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 4.38968 | 0.168090 | ||||||||
\(683\) | 36.0725 | 1.38028 | 0.690139 | − | 0.723677i | \(-0.257550\pi\) | ||||
0.690139 | + | 0.723677i | \(0.257550\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.06364 | −0.193472 | ||||||||
\(686\) | −10.8338 | −0.413637 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.96996 | −0.0751042 | ||||||||
\(689\) | −26.7719 | −1.01993 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21.3335 | −0.811566 | −0.405783 | − | 0.913969i | \(-0.633001\pi\) | ||||
−0.405783 | + | 0.913969i | \(0.633001\pi\) | |||||||
\(692\) | −3.37190 | −0.128180 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0.224005 | 0.00850312 | ||||||||
\(695\) | 3.35810 | 0.127380 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18.0481 | −0.683619 | ||||||||
\(698\) | 22.5898 | 0.855036 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −30.7503 | −1.16225 | ||||||||
\(701\) | −20.2170 | −0.763585 | −0.381792 | − | 0.924248i | \(-0.624693\pi\) | ||||
−0.381792 | + | 0.924248i | \(0.624693\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −25.4805 | −0.961015 | ||||||||
\(704\) | −1.82893 | −0.0689305 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.50339 | 0.169487 | ||||||||
\(707\) | 37.7475 | 1.41964 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 47.1596 | 1.77111 | 0.885557 | − | 0.464530i | \(-0.153777\pi\) | ||||
0.885557 | + | 0.464530i | \(0.153777\pi\) | |||||||
\(710\) | −1.55515 | −0.0583638 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −23.4313 | −0.878123 | ||||||||
\(713\) | −40.1293 | −1.50286 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.02012 | 0.0381501 | ||||||||
\(716\) | 36.3379 | 1.35801 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 9.28913 | 0.346667 | ||||||||
\(719\) | 37.6263 | 1.40322 | 0.701612 | − | 0.712560i | \(-0.252464\pi\) | ||||
0.701612 | + | 0.712560i | \(0.252464\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −73.3379 | −2.73125 | ||||||||
\(722\) | 10.9581 | 0.407819 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.31687 | −0.0861058 | ||||||||
\(725\) | −37.5705 | −1.39533 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.18124 | 0.192161 | 0.0960807 | − | 0.995374i | \(-0.469369\pi\) | ||||
0.0960807 | + | 0.995374i | \(0.469369\pi\) | |||||||
\(728\) | 32.3118 | 1.19755 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.307363 | −0.0113760 | ||||||||
\(731\) | 2.64636 | 0.0978791 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12.8952 | −0.476295 | −0.238148 | − | 0.971229i | \(-0.576540\pi\) | ||||
−0.238148 | + | 0.971229i | \(0.576540\pi\) | |||||||
\(734\) | −19.0433 | −0.702901 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 40.4000 | 1.48916 | ||||||||
\(737\) | 12.6667 | 0.466584 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.45746 | −0.347898 | −0.173949 | − | 0.984755i | \(-0.555653\pi\) | ||||
−0.173949 | + | 0.984755i | \(0.555653\pi\) | |||||||
\(740\) | 2.01055 | 0.0739093 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 25.8389 | 0.948575 | ||||||||
\(743\) | −22.0948 | −0.810581 | −0.405290 | − | 0.914188i | \(-0.632830\pi\) | ||||
−0.405290 | + | 0.914188i | \(0.632830\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.47277 | 0.237144 | ||||||||
\(746\) | −12.8854 | −0.471767 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.59861 | −0.0950147 | ||||||||
\(749\) | 16.4864 | 0.602399 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.6555 | 0.607769 | 0.303885 | − | 0.952709i | \(-0.401716\pi\) | ||||
0.303885 | + | 0.952709i | \(0.401716\pi\) | |||||||
\(752\) | 5.84113 | 0.213004 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 16.8777 | 0.614649 | ||||||||
\(755\) | 3.75649 | 0.136713 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25.3571 | 0.921619 | 0.460809 | − | 0.887499i | \(-0.347559\pi\) | ||||
0.460809 | + | 0.887499i | \(0.347559\pi\) | |||||||
\(758\) | −14.0052 | −0.508691 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.51809 | −0.163888 | ||||||||
\(761\) | −26.2708 | −0.952317 | −0.476158 | − | 0.879360i | \(-0.657971\pi\) | ||||
−0.476158 | + | 0.879360i | \(0.657971\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −79.7399 | −2.88678 | ||||||||
\(764\) | −2.93921 | −0.106337 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.11619 | −0.0403294 | ||||||||
\(767\) | −12.7698 | −0.461092 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 51.8160 | 1.86853 | 0.934267 | − | 0.356574i | \(-0.116055\pi\) | ||||
0.934267 | + | 0.356574i | \(0.116055\pi\) | |||||||
\(770\) | −0.984563 | −0.0354812 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.51955 | −0.0546897 | ||||||||
\(773\) | 34.0422 | 1.22441 | 0.612206 | − | 0.790698i | \(-0.290282\pi\) | ||||
0.612206 | + | 0.790698i | \(0.290282\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 28.4427 | 1.02169 | ||||||||
\(776\) | 7.07952 | 0.254140 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 6.26654 | 0.224666 | ||||||||
\(779\) | −64.7030 | −2.31823 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.50066 | −0.268395 | ||||||||
\(782\) | −8.05528 | −0.288056 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 12.9407 | 0.462167 | ||||||||
\(785\) | 6.55121 | 0.233823 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.27449 | −0.294954 | −0.147477 | − | 0.989065i | \(-0.547115\pi\) | ||||
−0.147477 | + | 0.989065i | \(0.547115\pi\) | |||||||
\(788\) | −22.6640 | −0.807371 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2.81265 | −0.100070 | ||||||||
\(791\) | −45.1628 | −1.60580 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 35.2406 | 1.25143 | ||||||||
\(794\) | −4.44356 | −0.157696 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.57296 | 0.162084 | ||||||||
\(797\) | 20.7719 | 0.735779 | 0.367890 | − | 0.929869i | \(-0.380080\pi\) | ||||
0.367890 | + | 0.929869i | \(0.380080\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.84670 | −0.277596 | ||||||||
\(800\) | −28.6346 | −1.01238 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.05963 | 0.0727279 | ||||||||
\(803\) | −1.48245 | −0.0523144 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.00062 | 0.317230 | ||||||||
\(806\) | −12.7772 | −0.450058 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 22.3534 | 0.786390 | ||||||||
\(809\) | −10.6449 | −0.374255 | −0.187127 | − | 0.982336i | \(-0.559918\pi\) | ||||
−0.187127 | + | 0.982336i | \(0.559918\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −46.7208 | −1.64059 | −0.820294 | − | 0.571942i | \(-0.806190\pi\) | ||||
−0.820294 | + | 0.571942i | \(0.806190\pi\) | |||||||
\(812\) | 48.0393 | 1.68585 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −3.28815 | −0.115250 | ||||||||
\(815\) | −6.08379 | −0.213106 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.48730 | 0.331919 | ||||||||
\(818\) | −8.44454 | −0.295256 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5.10542 | 0.178289 | ||||||||
\(821\) | 14.2115 | 0.495985 | 0.247992 | − | 0.968762i | \(-0.420229\pi\) | ||||
0.247992 | + | 0.968762i | \(0.420229\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.98657 | 0.313252 | 0.156626 | − | 0.987658i | \(-0.449938\pi\) | ||||
0.156626 | + | 0.987658i | \(0.449938\pi\) | |||||||
\(824\) | −43.4294 | −1.51294 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 12.3248 | 0.428834 | ||||||||
\(827\) | 48.3946 | 1.68285 | 0.841423 | − | 0.540378i | \(-0.181719\pi\) | ||||
0.841423 | + | 0.540378i | \(0.181719\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19.5661 | −0.679560 | −0.339780 | − | 0.940505i | \(-0.610353\pi\) | ||||
−0.339780 | + | 0.940505i | \(0.610353\pi\) | |||||||
\(830\) | −1.69497 | −0.0588331 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5.32355 | 0.184561 | ||||||||
\(833\) | −17.3839 | −0.602316 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.66383 | 0.196005 | ||||||||
\(836\) | −9.31613 | −0.322205 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −16.9966 | −0.587139 | ||||||||
\(839\) | 57.3202 | 1.97891 | 0.989456 | − | 0.144833i | \(-0.0462646\pi\) | ||||
0.989456 | + | 0.144833i | \(0.0462646\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.6942 | 1.02394 | ||||||||
\(842\) | 18.0906 | 0.623443 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −15.4702 | −0.532508 | ||||||||
\(845\) | 1.05878 | 0.0364232 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 41.4331 | 1.42366 | ||||||||
\(848\) | −10.5321 | −0.361673 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 5.70939 | 0.195830 | ||||||||
\(851\) | 30.0594 | 1.03042 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −25.5676 | −0.875417 | −0.437709 | − | 0.899117i | \(-0.644210\pi\) | ||||
−0.437709 | + | 0.899117i | \(0.644210\pi\) | |||||||
\(854\) | −34.0124 | −1.16388 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.76295 | 0.333691 | ||||||||
\(857\) | −20.0681 | −0.685514 | −0.342757 | − | 0.939424i | \(-0.611361\pi\) | ||||
−0.342757 | + | 0.939424i | \(0.611361\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.88891 | 0.303286 | 0.151643 | − | 0.988435i | \(-0.451544\pi\) | ||||
0.151643 | + | 0.988435i | \(0.451544\pi\) | |||||||
\(860\) | −0.748600 | −0.0255271 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −24.0924 | −0.820590 | ||||||||
\(863\) | −10.8293 | −0.368633 | −0.184316 | − | 0.982867i | \(-0.559007\pi\) | ||||
−0.184316 | + | 0.982867i | \(0.559007\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.699531 | −0.0237848 | ||||||||
\(866\) | 6.50838 | 0.221164 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −36.3681 | −1.23441 | ||||||||
\(869\) | −13.5657 | −0.460185 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −36.8695 | −1.24927 | ||||||||
\(872\) | −47.2206 | −1.59909 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −28.8785 | −0.976829 | ||||||||
\(875\) | −12.8837 | −0.435550 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −28.2847 | −0.955106 | −0.477553 | − | 0.878603i | \(-0.658476\pi\) | ||||
−0.477553 | + | 0.878603i | \(0.658476\pi\) | |||||||
\(878\) | −1.82471 | −0.0615808 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.401313 | 0.0135283 | ||||||||
\(881\) | 1.05729 | 0.0356210 | 0.0178105 | − | 0.999841i | \(-0.494330\pi\) | ||||
0.0178105 | + | 0.999841i | \(0.494330\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −46.6966 | −1.57147 | −0.785733 | − | 0.618566i | \(-0.787714\pi\) | ||||
−0.785733 | + | 0.618566i | \(0.787714\pi\) | |||||||
\(884\) | 7.56389 | 0.254401 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6.01099 | −0.201943 | ||||||||
\(887\) | 25.9247 | 0.870465 | 0.435232 | − | 0.900318i | \(-0.356666\pi\) | ||||
0.435232 | + | 0.900318i | \(0.356666\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 36.5846 | 1.22701 | ||||||||
\(890\) | −2.07817 | −0.0696605 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.15182 | 0.0385659 | ||||||||
\(893\) | −28.1307 | −0.941359 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.53862 | 0.251988 | ||||||||
\(896\) | 43.8905 | 1.46628 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 19.6684 | 0.656342 | ||||||||
\(899\) | −44.4344 | −1.48197 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14.1483 | 0.471348 | ||||||||
\(902\) | −8.34965 | −0.278013 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −26.7446 | −0.889512 | ||||||||
\(905\) | −0.480656 | −0.0159775 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −28.2503 | −0.938036 | −0.469018 | − | 0.883189i | \(-0.655392\pi\) | ||||
−0.469018 | + | 0.883189i | \(0.655392\pi\) | |||||||
\(908\) | −31.3823 | −1.04146 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2.86581 | 0.0950006 | ||||||||
\(911\) | 14.4287 | 0.478043 | 0.239021 | − | 0.971014i | \(-0.423173\pi\) | ||||
0.239021 | + | 0.971014i | \(0.423173\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.17500 | −0.270553 | ||||||||
\(914\) | −22.3476 | −0.739194 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −38.6089 | −1.27567 | ||||||||
\(917\) | −36.5544 | −1.20713 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.78663 | 0.289844 | 0.144922 | − | 0.989443i | \(-0.453707\pi\) | ||||
0.144922 | + | 0.989443i | \(0.453707\pi\) | |||||||
\(920\) | 5.33001 | 0.175725 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3.29197 | −0.108415 | ||||||||
\(923\) | 21.8325 | 0.718624 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −21.3054 | −0.700517 | ||||||||
\(926\) | −15.1591 | −0.498160 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 44.7341 | 1.46847 | ||||||||
\(929\) | 40.5112 | 1.32913 | 0.664565 | − | 0.747230i | \(-0.268617\pi\) | ||||
0.664565 | + | 0.747230i | \(0.268617\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −62.3220 | −2.04252 | ||||||||
\(932\) | 26.7546 | 0.876376 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −13.1715 | −0.430984 | ||||||||
\(935\) | −0.539106 | −0.0176306 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −9.15460 | −0.299068 | −0.149534 | − | 0.988757i | \(-0.547777\pi\) | ||||
−0.149534 | + | 0.988757i | \(0.547777\pi\) | |||||||
\(938\) | 35.5845 | 1.16188 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 2.21967 | 0.0723977 | ||||||||
\(941\) | 12.8924 | 0.420280 | 0.210140 | − | 0.977671i | \(-0.432608\pi\) | ||||
0.210140 | + | 0.977671i | \(0.432608\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 76.3304 | 2.48566 | ||||||||
\(944\) | −5.02365 | −0.163506 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.22430 | 0.0398053 | ||||||||
\(947\) | 56.1939 | 1.82606 | 0.913029 | − | 0.407895i | \(-0.133737\pi\) | ||||
0.913029 | + | 0.407895i | \(0.133737\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.31501 | 0.140071 | ||||||||
\(950\) | 20.4684 | 0.664082 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −17.0760 | −0.553435 | ||||||||
\(953\) | −27.2856 | −0.883868 | −0.441934 | − | 0.897048i | \(-0.645707\pi\) | ||||
−0.441934 | + | 0.897048i | \(0.645707\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.609767 | −0.0197316 | ||||||||
\(956\) | 1.49356 | 0.0483051 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 20.1657 | 0.651526 | ||||||||
\(959\) | −68.6099 | −2.21553 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.63896 | 0.0851278 | ||||||||
\(962\) | 9.57095 | 0.308580 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −14.2356 | −0.458498 | ||||||||
\(965\) | −0.315244 | −0.0101480 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −30.9244 | −0.994460 | −0.497230 | − | 0.867619i | \(-0.665650\pi\) | ||||
−0.497230 | + | 0.867619i | \(0.665650\pi\) | |||||||
\(968\) | 24.5360 | 0.788616 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.627899 | 0.0201606 | ||||||||
\(971\) | 15.5085 | 0.497692 | 0.248846 | − | 0.968543i | \(-0.419949\pi\) | ||||
0.248846 | + | 0.968543i | \(0.419949\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 45.5007 | 1.45868 | ||||||||
\(974\) | 24.3936 | 0.781620 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 13.8636 | 0.443764 | ||||||||
\(977\) | 57.5528 | 1.84128 | 0.920639 | − | 0.390416i | \(-0.127669\pi\) | ||||
0.920639 | + | 0.390416i | \(0.127669\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10.0232 | −0.320344 | ||||||||
\(980\) | 4.91755 | 0.157085 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −21.2357 | −0.677657 | ||||||||
\(983\) | 41.3072 | 1.31750 | 0.658748 | − | 0.752363i | \(-0.271086\pi\) | ||||
0.658748 | + | 0.752363i | \(0.271086\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.70185 | −0.149813 | ||||||||
\(986\) | −8.91944 | −0.284053 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 27.1168 | 0.862701 | ||||||||
\(989\) | −11.1922 | −0.355891 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.77458 | −0.0563713 | −0.0281857 | − | 0.999603i | \(-0.508973\pi\) | ||||
−0.0281857 | + | 0.999603i | \(0.508973\pi\) | |||||||
\(992\) | −33.8659 | −1.07524 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −21.0716 | −0.668350 | ||||||||
\(995\) | 0.948701 | 0.0300758 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 27.2945 | 0.864425 | 0.432212 | − | 0.901772i | \(-0.357733\pi\) | ||||
0.432212 | + | 0.901772i | \(0.357733\pi\) | |||||||
\(998\) | 10.6852 | 0.338234 | ||||||||
\(999\) | 0 | 0 |
(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 | 2151.2.a.g.1.4 | 8 | ||
3.2 | odd | 2 | 717.2.a.f.1.5 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
717.2.a.f.1.5 | ✓ | 8 | 3.2 | odd | 2 | ||
2151.2.a.g.1.4 | 8 | 1.1 | even | 1 | trivial |