Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5776,2,Mod(1,5776)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5776, 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("5776.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5776 = 2^{4} \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5776.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: | \(46.1215922075\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.20319417.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} - 9x^{4} + 19x^{3} + 27x^{2} - 27x - 27 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 76) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.812576\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5776.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.69196 | −1.55420 | −0.777102 | − | 0.629374i | \(-0.783311\pi\) | ||||
−0.777102 | + | 0.629374i | \(0.783311\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.28220 | −0.573419 | −0.286710 | − | 0.958018i | \(-0.592562\pi\) | ||||
−0.286710 | + | 0.958018i | \(0.592562\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.34467 | 1.26416 | 0.632082 | − | 0.774901i | \(-0.282200\pi\) | ||||
0.632082 | + | 0.774901i | \(0.282200\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.24666 | 1.41555 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.65641 | 1.70547 | 0.852736 | − | 0.522342i | \(-0.174941\pi\) | ||||
0.852736 | + | 0.522342i | \(0.174941\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.442077 | 0.122610 | 0.0613051 | − | 0.998119i | \(-0.480474\pi\) | ||||
0.0613051 | + | 0.998119i | \(0.480474\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.45165 | 0.891211 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.75211 | −1.15256 | −0.576278 | − | 0.817254i | \(-0.695495\pi\) | ||||
−0.576278 | + | 0.817254i | \(0.695495\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −9.00371 | −1.96477 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.67370 | 0.766020 | 0.383010 | − | 0.923744i | \(-0.374887\pi\) | ||||
0.383010 | + | 0.923744i | \(0.374887\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.35595 | −0.671190 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.35595 | −0.645853 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.01826 | −0.560476 | −0.280238 | − | 0.959931i | \(-0.590413\pi\) | ||||
−0.280238 | + | 0.959931i | \(0.590413\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.7825 | −1.93659 | −0.968293 | − | 0.249817i | \(-0.919629\pi\) | ||||
−0.968293 | + | 0.249817i | \(0.919629\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −15.2268 | −2.65065 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.28855 | −0.724896 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.81198 | 0.297888 | 0.148944 | − | 0.988846i | \(-0.452413\pi\) | ||||
0.148944 | + | 0.988846i | \(0.452413\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.19006 | −0.190561 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.03555 | −0.630247 | −0.315123 | − | 0.949051i | \(-0.602046\pi\) | ||||
−0.315123 | + | 0.949051i | \(0.602046\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.69288 | 0.410660 | 0.205330 | − | 0.978693i | \(-0.434173\pi\) | ||||
0.205330 | + | 0.978693i | \(0.434173\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.44508 | −0.811705 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.06741 | −0.885022 | −0.442511 | − | 0.896763i | \(-0.645912\pi\) | ||||
−0.442511 | + | 0.896763i | \(0.645912\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.18678 | 0.598112 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 12.7925 | 1.79131 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.63213 | −0.224191 | −0.112095 | − | 0.993697i | \(-0.535756\pi\) | ||||
−0.112095 | + | 0.993697i | \(0.535756\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.25268 | −0.977951 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.55249 | 1.11344 | 0.556720 | − | 0.830700i | \(-0.312060\pi\) | ||||
0.556720 | + | 0.830700i | \(0.312060\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.59561 | 0.332334 | 0.166167 | − | 0.986098i | \(-0.446861\pi\) | ||||
0.166167 | + | 0.986098i | \(0.446861\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 14.2036 | 1.78949 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.566834 | −0.0703071 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.03325 | −0.492740 | −0.246370 | − | 0.969176i | \(-0.579238\pi\) | ||||
−0.246370 | + | 0.969176i | \(0.579238\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −9.88947 | −1.19055 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.0941 | −1.31663 | −0.658316 | − | 0.752742i | \(-0.728731\pi\) | ||||
−0.658316 | + | 0.752742i | \(0.728731\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.36464 | −0.861966 | −0.430983 | − | 0.902360i | \(-0.641833\pi\) | ||||
−0.430983 | + | 0.902360i | \(0.641833\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 9.03409 | 1.04317 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 18.9188 | 2.15600 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.1592 | 1.14300 | 0.571502 | − | 0.820601i | \(-0.306361\pi\) | ||||
0.571502 | + | 0.820601i | \(0.306361\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.70588 | −0.411764 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.55683 | −0.500177 | −0.250089 | − | 0.968223i | \(-0.580460\pi\) | ||||
−0.250089 | + | 0.968223i | \(0.580460\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.09318 | 0.660898 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.12503 | 0.871095 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.9569 | −1.37343 | −0.686713 | − | 0.726929i | \(-0.740947\pi\) | ||||
−0.686713 | + | 0.726929i | \(0.740947\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.47860 | 0.154999 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 29.0260 | 3.00985 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.9018 | 1.20845 | 0.604224 | − | 0.796814i | \(-0.293483\pi\) | ||||
0.604224 | + | 0.796814i | \(0.293483\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 24.0208 | 2.41419 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.1962 | 1.01456 | 0.507279 | − | 0.861782i | \(-0.330651\pi\) | ||||
0.507279 | + | 0.861782i | \(0.330651\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.52677 | −0.446036 | −0.223018 | − | 0.974814i | \(-0.571591\pi\) | ||||
−0.223018 | + | 0.974814i | \(0.571591\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 11.5446 | 1.12664 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.27883 | 0.123629 | 0.0618146 | − | 0.998088i | \(-0.480311\pi\) | ||||
0.0618146 | + | 0.998088i | \(0.480311\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.42336 | −0.615246 | −0.307623 | − | 0.951508i | \(-0.599534\pi\) | ||||
−0.307623 | + | 0.951508i | \(0.599534\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.87778 | −0.462978 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.77037 | 0.166542 | 0.0832710 | − | 0.996527i | \(-0.473463\pi\) | ||||
0.0832710 | + | 0.996527i | \(0.473463\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.71044 | −0.439251 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.87735 | 0.173561 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −15.8942 | −1.45702 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 20.9950 | 1.90864 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 10.8635 | 0.979532 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.7140 | 0.958293 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.4819 | 1.19633 | 0.598165 | − | 0.801373i | \(-0.295897\pi\) | ||||
0.598165 | + | 0.801373i | \(0.295897\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.24912 | −0.638249 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.1327 | 0.885298 | 0.442649 | − | 0.896695i | \(-0.354039\pi\) | ||||
0.442649 | + | 0.896695i | \(0.354039\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.30302 | 0.370345 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.49669 | −0.298742 | −0.149371 | − | 0.988781i | \(-0.547725\pi\) | ||||
−0.149371 | + | 0.988781i | \(0.547725\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.6572 | −0.903933 | −0.451967 | − | 0.892035i | \(-0.649277\pi\) | ||||
−0.451967 | + | 0.892035i | \(0.649277\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 16.3332 | 1.37551 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.50057 | 0.209108 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.87002 | 0.321388 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −11.2707 | −0.929589 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.42125 | −0.689896 | −0.344948 | − | 0.938622i | \(-0.612103\pi\) | ||||
−0.344948 | + | 0.938622i | \(0.612103\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.3794 | −0.926039 | −0.463020 | − | 0.886348i | \(-0.653234\pi\) | ||||
−0.463020 | + | 0.886348i | \(0.653234\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −20.1806 | −1.63150 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 13.8253 | 1.11048 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.67602 | −0.373187 | −0.186593 | − | 0.982437i | \(-0.559745\pi\) | ||||
−0.186593 | + | 0.982437i | \(0.559745\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.39364 | 0.348438 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12.2873 | 0.968376 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.82998 | 0.143335 | 0.0716676 | − | 0.997429i | \(-0.477168\pi\) | ||||
0.0716676 | + | 0.997429i | \(0.477168\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 19.5239 | 1.51994 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −19.9744 | −1.54566 | −0.772832 | − | 0.634610i | \(-0.781161\pi\) | ||||
−0.772832 | + | 0.634610i | \(0.781161\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.8046 | −0.984967 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.67339 | 0.355311 | 0.177656 | − | 0.984093i | \(-0.443149\pi\) | ||||
0.177656 | + | 0.984093i | \(0.443149\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11.2245 | −0.848495 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −23.0230 | −1.73051 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.64250 | 0.571227 | 0.285613 | − | 0.958345i | \(-0.407803\pi\) | ||||
0.285613 | + | 0.958345i | \(0.407803\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.09446 | −0.452998 | −0.226499 | − | 0.974011i | \(-0.572728\pi\) | ||||
−0.226499 | + | 0.974011i | \(0.572728\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.98728 | −0.516515 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.32333 | −0.170815 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −26.8799 | −1.96565 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −11.2245 | −0.816465 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.93272 | −0.573992 | −0.286996 | − | 0.957932i | \(-0.592657\pi\) | ||||
−0.286996 | + | 0.957932i | \(0.592657\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.84941 | 0.493032 | 0.246516 | − | 0.969139i | \(-0.420714\pi\) | ||||
0.246516 | + | 0.969139i | \(0.420714\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.52589 | 0.109272 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −25.5509 | −1.82043 | −0.910213 | − | 0.414141i | \(-0.864082\pi\) | ||||
−0.910213 | + | 0.414141i | \(0.864082\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.62715 | 0.540675 | 0.270337 | − | 0.962766i | \(-0.412865\pi\) | ||||
0.270337 | + | 0.962766i | \(0.412865\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.8574 | 0.765819 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −10.0951 | −0.708534 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.17440 | 0.361396 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 15.6010 | 1.08434 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.4709 | 0.789690 | 0.394845 | − | 0.918748i | \(-0.370798\pi\) | ||||
0.394845 | + | 0.918748i | \(0.370798\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 29.8650 | 2.04632 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.45282 | −0.235480 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −36.0637 | −2.44816 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 19.8253 | 1.33967 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.10080 | −0.141315 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.79878 | −0.187420 | −0.0937102 | − | 0.995600i | \(-0.529873\pi\) | ||||
−0.0937102 | + | 0.995600i | \(0.529873\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −14.2516 | −0.950105 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.05837 | −0.402108 | −0.201054 | − | 0.979580i | \(-0.564437\pi\) | ||||
−0.201054 | + | 0.979580i | \(0.564437\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.97380 | −0.593005 | −0.296503 | − | 0.955032i | \(-0.595820\pi\) | ||||
−0.296503 | + | 0.955032i | \(0.595820\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −50.9287 | −3.35086 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.34058 | −0.480897 | −0.240449 | − | 0.970662i | \(-0.577295\pi\) | ||||
−0.240449 | + | 0.970662i | \(0.577295\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.77966 | 0.507489 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −27.3483 | −1.77646 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.1710 | 1.24007 | 0.620036 | − | 0.784574i | \(-0.287118\pi\) | ||||
0.620036 | + | 0.784574i | \(0.287118\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.1273 | 0.781191 | 0.390596 | − | 0.920562i | \(-0.372269\pi\) | ||||
0.390596 | + | 0.920562i | \(0.372269\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 20.0439 | 1.28582 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.36832 | −0.342969 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.2668 | 0.777378 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.6132 | −0.922379 | −0.461189 | − | 0.887302i | \(-0.652577\pi\) | ||||
−0.461189 | + | 0.887302i | \(0.652577\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 20.7800 | 1.30643 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −16.4026 | −1.02717 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.59119 | −0.161634 | −0.0808171 | − | 0.996729i | \(-0.525753\pi\) | ||||
−0.0808171 | + | 0.996729i | \(0.525753\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.06047 | 0.376579 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −12.8175 | −0.793383 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 23.0162 | 1.41924 | 0.709619 | − | 0.704585i | \(-0.248867\pi\) | ||||
0.709619 | + | 0.704585i | \(0.248867\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.09273 | 0.128555 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 34.8794 | 2.13459 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −26.1828 | −1.59639 | −0.798195 | − | 0.602399i | \(-0.794212\pi\) | ||||
−0.798195 | + | 0.602399i | \(0.794212\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.7762 | 0.897588 | 0.448794 | − | 0.893635i | \(-0.351854\pi\) | ||||
0.448794 | + | 0.893635i | \(0.351854\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.98034 | −0.240901 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −18.9826 | −1.14470 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.7470 | −0.886061 | −0.443030 | − | 0.896507i | \(-0.646097\pi\) | ||||
−0.443030 | + | 0.896507i | \(0.646097\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −45.7894 | −2.74134 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.9406 | −0.831624 | −0.415812 | − | 0.909451i | \(-0.636502\pi\) | ||||
−0.415812 | + | 0.909451i | \(0.636502\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 18.2889 | 1.08716 | 0.543580 | − | 0.839357i | \(-0.317068\pi\) | ||||
0.543580 | + | 0.839357i | \(0.317068\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −13.4976 | −0.796736 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.58253 | 0.328384 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −32.0393 | −1.87818 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −24.7475 | −1.44576 | −0.722882 | − | 0.690972i | \(-0.757183\pi\) | ||||
−0.722882 | + | 0.690972i | \(0.757183\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.9660 | −0.638468 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −18.9826 | −1.10148 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.62406 | 0.0939219 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.00677 | 0.519141 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −27.4477 | −1.57683 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.32810 | −0.190567 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −22.9330 | −1.30886 | −0.654429 | − | 0.756124i | \(-0.727091\pi\) | ||||
−0.654429 | + | 0.756124i | \(0.727091\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12.1859 | 0.693232 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −29.6666 | −1.68224 | −0.841119 | − | 0.540850i | \(-0.818103\pi\) | ||||
−0.841119 | + | 0.540850i | \(0.818103\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −20.7248 | −1.17143 | −0.585717 | − | 0.810516i | \(-0.699187\pi\) | ||||
−0.585717 | + | 0.810516i | \(0.699187\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −18.2120 | −1.02613 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 32.4136 | 1.82053 | 0.910264 | − | 0.414028i | \(-0.135879\pi\) | ||||
0.910264 | + | 0.414028i | \(0.135879\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −17.0725 | −0.955877 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.44256 | −0.192145 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.48359 | −0.0822948 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 17.2914 | 0.956218 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −20.2934 | −1.11881 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −21.2388 | −1.16739 | −0.583694 | − | 0.811974i | \(-0.698393\pi\) | ||||
−0.583694 | + | 0.811974i | \(0.698393\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.69486 | 0.421675 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.17146 | 0.282547 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.7668 | 0.640980 | 0.320490 | − | 0.947252i | \(-0.396153\pi\) | ||||
0.320490 | + | 0.947252i | \(0.396153\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.76575 | −0.258840 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −60.9900 | −3.30279 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.40926 | −0.508052 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 12.6803 | 0.682686 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −25.7460 | −1.38212 | −0.691059 | − | 0.722799i | \(-0.742855\pi\) | ||||
−0.691059 | + | 0.722799i | \(0.742855\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.1537 | 0.543517 | 0.271759 | − | 0.962365i | \(-0.412395\pi\) | ||||
0.271759 | + | 0.962365i | \(0.412395\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.48359 | −0.0791882 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.2411 | 0.811201 | 0.405600 | − | 0.914050i | \(-0.367062\pi\) | ||||
0.405600 | + | 0.914050i | \(0.367062\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 14.2250 | 0.754983 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 42.7866 | 2.26451 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 18.7653 | 0.990394 | 0.495197 | − | 0.868781i | \(-0.335096\pi\) | ||||
0.495197 | + | 0.868781i | \(0.335096\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −56.5178 | −2.96641 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.44298 | 0.494268 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.1097 | −0.632119 | −0.316060 | − | 0.948739i | \(-0.602360\pi\) | ||||
−0.316060 | + | 0.948739i | \(0.602360\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −17.1376 | −0.892147 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.45894 | −0.283414 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 33.1556 | 1.71673 | 0.858366 | − | 0.513038i | \(-0.171480\pi\) | ||||
0.858366 | + | 0.513038i | \(0.171480\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −28.8418 | −1.48938 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.33430 | −0.0687201 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −19.5956 | −1.00656 | −0.503280 | − | 0.864123i | \(-0.667874\pi\) | ||||
−0.503280 | + | 0.864123i | \(0.667874\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −36.2929 | −1.85934 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 25.0491 | 1.27995 | 0.639974 | − | 0.768396i | \(-0.278945\pi\) | ||||
0.639974 | + | 0.768396i | \(0.278945\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −24.2578 | −1.23629 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 11.4357 | 0.581310 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −16.5821 | −0.840745 | −0.420372 | − | 0.907352i | \(-0.638101\pi\) | ||||
−0.420372 | + | 0.907352i | \(0.638101\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −17.4578 | −0.882881 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −27.2768 | −1.37594 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −13.0262 | −0.655420 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 29.8911 | 1.50019 | 0.750095 | − | 0.661330i | \(-0.230008\pi\) | ||||
0.750095 | + | 0.661330i | \(0.230008\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −20.1885 | −1.00816 | −0.504082 | − | 0.863656i | \(-0.668169\pi\) | ||||
−0.504082 | + | 0.863656i | \(0.668169\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.76668 | −0.237445 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.75170 | 0.236114 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.2493 | 0.508039 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.9018 | 0.588508 | 0.294254 | − | 0.955727i | \(-0.404929\pi\) | ||||
0.294254 | + | 0.955727i | \(0.404929\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.41295 | 0.464306 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 28.6052 | 1.40757 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.84279 | 0.286811 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 28.6888 | 1.40490 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −17.0337 | −0.832151 | −0.416076 | − | 0.909330i | \(-0.636595\pi\) | ||||
−0.416076 | + | 0.909330i | \(0.636595\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.47848 | −0.267005 | −0.133502 | − | 0.991049i | \(-0.542622\pi\) | ||||
−0.133502 | + | 0.991049i | \(0.542622\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −25.7662 | −1.25279 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 15.9478 | 0.773584 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.68144 | 0.420124 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.73144 | −0.324997 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.293535 | 0.0141391 | 0.00706953 | − | 0.999975i | \(-0.497750\pi\) | ||||
0.00706953 | + | 0.999975i | \(0.497750\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −21.7700 | −1.04620 | −0.523101 | − | 0.852271i | \(-0.675225\pi\) | ||||
−0.523101 | + | 0.852271i | \(0.675225\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −10.4180 | −0.499503 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.6860 | −0.653199 | −0.326599 | − | 0.945163i | \(-0.605903\pi\) | ||||
−0.326599 | + | 0.945163i | \(0.605903\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 17.7798 | 0.846659 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.50161 | 0.451435 | 0.225718 | − | 0.974193i | \(-0.427527\pi\) | ||||
0.225718 | + | 0.974193i | \(0.427527\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 16.6134 | 0.787549 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 22.6697 | 1.07224 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −38.4822 | −1.81609 | −0.908043 | − | 0.418877i | \(-0.862424\pi\) | ||||
−0.908043 | + | 0.418877i | \(0.862424\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −22.8267 | −1.07487 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 30.6328 | 1.43925 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.89587 | −0.0888797 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.3537 | 0.577880 | 0.288940 | − | 0.957347i | \(-0.406697\pi\) | ||||
0.288940 | + | 0.957347i | \(0.406697\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 15.9478 | 0.744381 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.31110 | 0.154213 | 0.0771065 | − | 0.997023i | \(-0.475432\pi\) | ||||
0.0771065 | + | 0.997023i | \(0.475432\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.16441 | 0.193536 | 0.0967682 | − | 0.995307i | \(-0.469149\pi\) | ||||
0.0967682 | + | 0.995307i | \(0.469149\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −37.2172 | −1.72591 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −39.2187 | −1.81483 | −0.907413 | − | 0.420241i | \(-0.861946\pi\) | ||||
−0.907413 | + | 0.420241i | \(0.861946\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13.4899 | −0.622905 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.5877 | 0.580009 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 15.2320 | 0.700369 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.93111 | −0.317354 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.42103 | 0.339075 | 0.169538 | − | 0.985524i | \(-0.445773\pi\) | ||||
0.169538 | + | 0.985524i | \(0.445773\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.801035 | 0.0365241 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −33.0770 | −1.50505 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −15.2606 | −0.692948 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 32.6140 | 1.47788 | 0.738940 | − | 0.673771i | \(-0.235327\pi\) | ||||
0.738940 | + | 0.673771i | \(0.235327\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.92624 | −0.222772 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 24.1272 | 1.08885 | 0.544423 | − | 0.838811i | \(-0.316749\pi\) | ||||
0.544423 | + | 0.838811i | \(0.316749\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 14.3431 | 0.645980 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −30.7996 | −1.38434 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −37.1062 | −1.66444 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.1228 | −0.766521 | −0.383260 | − | 0.923640i | \(-0.625199\pi\) | ||||
−0.383260 | + | 0.923640i | \(0.625199\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 53.7703 | 2.40228 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −25.0649 | −1.11759 | −0.558794 | − | 0.829306i | \(-0.688736\pi\) | ||||
−0.558794 | + | 0.829306i | \(0.688736\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.0736 | −0.581767 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 34.4694 | 1.53084 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 13.0588 | 0.578822 | 0.289411 | − | 0.957205i | \(-0.406541\pi\) | ||||
0.289411 | + | 0.957205i | \(0.406541\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −24.6323 | −1.08967 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.80425 | 0.255766 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −34.3198 | −1.50938 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −12.5806 | −0.552226 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19.1979 | −0.841076 | −0.420538 | − | 0.907275i | \(-0.638159\pi\) | ||||
−0.420538 | + | 0.907275i | \(0.638159\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 42.2288 | 1.84654 | 0.923269 | − | 0.384154i | \(-0.125507\pi\) | ||||
0.923269 | + | 0.384154i | \(0.125507\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 30.2160 | 1.31873 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 51.2394 | 2.23202 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.50390 | −0.413213 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 36.3195 | 1.57613 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.78402 | −0.0772747 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.63972 | −0.0708914 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −20.5733 | −0.887804 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 23.6822 | 1.02006 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.908031 | 0.0390393 | 0.0195197 | − | 0.999809i | \(-0.493786\pi\) | ||||
0.0195197 | + | 0.999809i | \(0.493786\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 16.4060 | 0.704051 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.23606 | 0.352794 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 34.6089 | 1.47977 | 0.739885 | − | 0.672734i | \(-0.234880\pi\) | ||||
0.739885 | + | 0.672734i | \(0.234880\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 11.0227 | 0.470436 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 33.9792 | 1.44494 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.25431 | 0.265481 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.26969 | 0.308027 | 0.154013 | − | 0.988069i | \(-0.450780\pi\) | ||||
0.154013 | + | 0.988069i | \(0.450780\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.19046 | 0.0503511 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 72.3596 | 3.05503 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.45317 | −0.103389 | −0.0516944 | − | 0.998663i | \(-0.516462\pi\) | ||||
−0.0516944 | + | 0.998663i | \(0.516462\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.26997 | −0.0954984 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −12.3949 | −0.520538 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −18.1326 | −0.760159 | −0.380080 | − | 0.924954i | \(-0.624103\pi\) | ||||
−0.380080 | + | 0.924954i | \(0.624103\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 25.1171 | 1.05112 | 0.525560 | − | 0.850757i | \(-0.323856\pi\) | ||||
0.525560 | + | 0.850757i | \(0.323856\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 21.3546 | 0.892101 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −12.3288 | −0.514145 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −20.6753 | −0.860722 | −0.430361 | − | 0.902657i | \(-0.641614\pi\) | ||||
−0.430361 | + | 0.902657i | \(0.641614\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −18.4384 | −0.766272 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −15.2411 | −0.632307 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.23201 | −0.382351 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.40715 | −0.0995233 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 25.0153 | 1.03249 | 0.516247 | − | 0.856440i | \(-0.327329\pi\) | ||||
0.516247 | + | 0.856440i | \(0.327329\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 68.7820 | 2.82931 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −37.4535 | −1.53803 | −0.769016 | − | 0.639229i | \(-0.779253\pi\) | ||||
−0.769016 | + | 0.639229i | \(0.779253\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 20.3796 | 0.835483 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −20.5320 | −0.840319 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −41.9168 | −1.71267 | −0.856336 | − | 0.516419i | \(-0.827265\pi\) | ||||
−0.856336 | + | 0.516419i | \(0.827265\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24.3133 | 0.991760 | 0.495880 | − | 0.868391i | \(-0.334846\pi\) | ||||
0.495880 | + | 0.868391i | \(0.334846\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −17.1278 | −0.697500 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −26.9199 | −1.09445 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −19.2612 | −0.781790 | −0.390895 | − | 0.920435i | \(-0.627834\pi\) | ||||
−0.390895 | + | 0.920435i | \(0.627834\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 27.1755 | 1.10121 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.68226 | −0.108513 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.0959 | 0.650108 | 0.325054 | − | 0.945695i | \(-0.394618\pi\) | ||||
0.325054 | + | 0.945695i | \(0.394618\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −13.9293 | −0.561683 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23.0188 | 0.926700 | 0.463350 | − | 0.886175i | \(-0.346647\pi\) | ||||
0.463350 | + | 0.886175i | \(0.346647\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.28899 | −0.132196 | −0.0660979 | − | 0.997813i | \(-0.521055\pi\) | ||||
−0.0660979 | + | 0.997813i | \(0.521055\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −12.3288 | −0.494737 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −43.3364 | −1.73624 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.04216 | 0.121686 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8.61072 | −0.343332 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −42.0411 | −1.67363 | −0.836816 | − | 0.547485i | \(-0.815585\pi\) | ||||
−0.836816 | + | 0.547485i | \(0.815585\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −30.8792 | −1.22734 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −17.2866 | −0.685999 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.85088 | 0.0733346 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −47.1130 | −1.86376 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18.8123 | −0.743042 | −0.371521 | − | 0.928424i | \(-0.621164\pi\) | ||||
−0.371521 | + | 0.928424i | \(0.621164\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15.8236 | −0.624021 | −0.312010 | − | 0.950079i | \(-0.601002\pi\) | ||||
−0.312010 | + | 0.950079i | \(0.601002\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9.29485 | 0.365984 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.04659 | 0.316344 | 0.158172 | − | 0.987412i | \(-0.449440\pi\) | ||||
0.158172 | + | 0.987412i | \(0.449440\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 48.3764 | 1.89894 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 97.0821 | 3.80495 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −41.3583 | −1.61848 | −0.809238 | − | 0.587481i | \(-0.800120\pi\) | ||||
−0.809238 | + | 0.587481i | \(0.800120\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12.9922 | −0.507647 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −31.2751 | −1.22016 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.67610 | 0.0652915 | 0.0326457 | − | 0.999467i | \(-0.489607\pi\) | ||||
0.0326457 | + | 0.999467i | \(0.489607\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.1120 | −0.432207 | −0.216104 | − | 0.976370i | \(-0.569335\pi\) | ||||
−0.216104 | + | 0.976370i | \(0.569335\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.65527 | 0.219632 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −11.0882 | −0.429336 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7.53421 | 0.291290 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 14.6818 | 0.566786 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 50.1601 | 1.93353 | 0.966764 | − | 0.255669i | \(-0.0822959\pi\) | ||||
0.966764 | + | 0.255669i | \(0.0822959\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 11.2624 | 0.433490 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −24.5938 | −0.945218 | −0.472609 | − | 0.881272i | \(-0.656688\pi\) | ||||
−0.472609 | + | 0.881272i | \(0.656688\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 39.8076 | 1.52768 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 16.3089 | 0.624958 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 40.1865 | 1.53769 | 0.768846 | − | 0.639434i | \(-0.220831\pi\) | ||||
0.768846 | + | 0.639434i | \(0.220831\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.48347 | 0.171305 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 24.1571 | 0.921651 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.721529 | −0.0274881 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.38100 | 0.356870 | 0.178435 | − | 0.983952i | \(-0.442897\pi\) | ||||
0.178435 | + | 0.983952i | \(0.442897\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 80.3417 | 3.05193 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 13.6647 | 0.518333 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19.1774 | 0.726394 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 19.7605 | 0.747413 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −37.1748 | −1.40407 | −0.702036 | − | 0.712141i | \(-0.747726\pi\) | ||||
−0.702036 | + | 0.712141i | \(0.747726\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −20.9425 | −0.788741 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 34.1028 | 1.28257 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −31.2732 | −1.17449 | −0.587246 | − | 0.809409i | \(-0.699788\pi\) | ||||
−0.587246 | + | 0.809409i | \(0.699788\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 43.1428 | 1.61798 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −39.6115 | −1.48346 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.20625 | −0.119907 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −51.6077 | −1.92732 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −26.0486 | −0.971450 | −0.485725 | − | 0.874112i | \(-0.661444\pi\) | ||||
−0.485725 | + | 0.874112i | \(0.661444\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.1405 | −0.563863 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −32.6463 | −1.21413 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 10.1291 | 0.376186 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.07973 | 0.0771328 | 0.0385664 | − | 0.999256i | \(-0.487721\pi\) | ||||
0.0385664 | + | 0.999256i | \(0.487721\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −42.8399 | −1.58666 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.7968 | −0.473308 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.92827 | −0.255901 | −0.127951 | − | 0.991781i | \(-0.540840\pi\) | ||||
−0.127951 | + | 0.991781i | \(0.540840\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 14.4513 | 0.533044 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −22.8137 | −0.840355 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17.3210 | −0.637165 | −0.318582 | − | 0.947895i | \(-0.603207\pi\) | ||||
−0.318582 | + | 0.947895i | \(0.603207\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 52.1550 | 1.91338 | 0.956690 | − | 0.291108i | \(-0.0940239\pi\) | ||||
0.956690 | + | 0.291108i | \(0.0940239\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.7978 | 0.395600 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −19.3513 | −0.708027 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.27726 | 0.156288 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.6198 | 0.424013 | 0.212006 | − | 0.977268i | \(-0.432000\pi\) | ||||
0.212006 | + | 0.977268i | \(0.432000\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 39.3382 | 1.43357 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 14.5907 | 0.531009 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −27.2620 | −0.990856 | −0.495428 | − | 0.868649i | \(-0.664989\pi\) | ||||
−0.495428 | + | 0.868649i | \(0.664989\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −55.9389 | −2.03045 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 32.8211 | 1.18976 | 0.594882 | − | 0.803813i | \(-0.297199\pi\) | ||||
0.594882 | + | 0.803813i | \(0.297199\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −21.4840 | −0.777772 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 25.8756 | 0.935535 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.78086 | 0.136519 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.45229 | 0.0884319 | 0.0442159 | − | 0.999022i | \(-0.485921\pi\) | ||||
0.0442159 | + | 0.999022i | \(0.485921\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.97539 | 0.251213 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −9.70810 | −0.349176 | −0.174588 | − | 0.984642i | \(-0.555859\pi\) | ||||
−0.174588 | + | 0.984642i | \(0.555859\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 36.1854 | 1.29982 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −16.3145 | −0.585281 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −62.7530 | −2.24548 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 10.1291 | 0.361985 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.99561 | 0.213993 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 32.4028 | 1.15503 | 0.577517 | − | 0.816379i | \(-0.304022\pi\) | ||||
0.577517 | + | 0.816379i | \(0.304022\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −61.9587 | −2.20579 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.92128 | 0.210536 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.14746 | 0.0407475 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.63354 | −0.199801 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 14.1556 | 0.501417 | 0.250708 | − | 0.968063i | \(-0.419336\pi\) | ||||
0.250708 | + | 0.968063i | \(0.419336\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 28.8330 | 1.02004 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −55.0234 | −1.94416 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −41.6574 | −1.47006 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −15.7548 | −0.555285 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 70.4830 | 2.48112 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4.19788 | −0.147589 | −0.0737947 | − | 0.997273i | \(-0.523511\pi\) | ||||
−0.0737947 | + | 0.997273i | \(0.523511\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 45.6564 | 1.60321 | 0.801607 | − | 0.597852i | \(-0.203979\pi\) | ||||
0.801607 | + | 0.597852i | \(0.203979\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −39.7769 | −1.39504 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.34641 | −0.0821912 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.27911 | 0.219410 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.15692 | 0.145078 | 0.0725388 | − | 0.997366i | \(-0.476890\pi\) | ||||
0.0725388 | + | 0.997366i | \(0.476890\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 46.3619 | 1.61607 | 0.808037 | − | 0.589131i | \(-0.200530\pi\) | ||||
0.808037 | + | 0.589131i | \(0.200530\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 51.1005 | 1.77909 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −30.5080 | −1.06087 | −0.530434 | − | 0.847726i | \(-0.677971\pi\) | ||||
−0.530434 | + | 0.847726i | \(0.677971\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.28342 | −0.252964 | −0.126482 | − | 0.991969i | \(-0.540369\pi\) | ||||
−0.126482 | + | 0.991969i | \(0.540369\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 39.6983 | 1.37712 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −19.8961 | −0.689357 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 25.6113 | 0.886314 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 36.1854 | 1.25075 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −13.2993 | −0.459144 | −0.229572 | − | 0.973292i | \(-0.573733\pi\) | ||||
−0.229572 | + | 0.973292i | \(0.573733\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.8901 | −0.685866 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 37.5274 | 1.29251 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 16.4181 | 0.564799 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 70.2213 | 2.41283 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −49.2330 | −1.68967 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.65668 | 0.228188 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.3649 | 0.560323 | 0.280161 | − | 0.959953i | \(-0.409612\pi\) | ||||
0.280161 | + | 0.959953i | \(0.409612\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −28.6087 | −0.977255 | −0.488628 | − | 0.872492i | \(-0.662502\pi\) | ||||
−0.488628 | + | 0.872492i | \(0.662502\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.40768 | 0.184508 | 0.0922538 | − | 0.995736i | \(-0.470593\pi\) | ||||
0.0922538 | + | 0.995736i | \(0.470593\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 36.3349 | 1.23829 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −42.0613 | −1.43178 | −0.715892 | − | 0.698211i | \(-0.753980\pi\) | ||||
−0.715892 | + | 0.698211i | \(0.753980\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.99224 | −0.203742 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −15.0280 | −0.510376 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 57.4648 | 1.94936 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.78301 | −0.0604150 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 50.5430 | 1.71062 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 35.8349 | 1.21144 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11.7349 | −0.396259 | −0.198129 | − | 0.980176i | \(-0.563487\pi\) | ||||
−0.198129 | + | 0.980176i | \(0.563487\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 66.6193 | 2.24701 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 23.5318 | 0.792806 | 0.396403 | − | 0.918077i | \(-0.370258\pi\) | ||||
0.396403 | + | 0.918077i | \(0.370258\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.56204 | 0.119872 | 0.0599361 | − | 0.998202i | \(-0.480910\pi\) | ||||
0.0599361 | + | 0.998202i | \(0.480910\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 29.5202 | 0.992310 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −24.5918 | −0.825711 | −0.412856 | − | 0.910796i | \(-0.635469\pi\) | ||||
−0.412856 | + | 0.910796i | \(0.635469\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 45.0926 | 1.51236 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −20.9620 | −0.702253 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.79924 | −0.327553 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.37191 | −0.145974 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 32.5442 | 1.08541 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.75607 | 0.258392 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −24.2459 | −0.806852 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.81434 | 0.259758 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.96372 | 0.0984088 | 0.0492044 | − | 0.998789i | \(-0.484331\pi\) | ||||
0.0492044 | + | 0.998789i | \(0.484331\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 43.2997 | 1.43616 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31.6411 | 1.04832 | 0.524158 | − | 0.851621i | \(-0.324380\pi\) | ||||
0.524158 | + | 0.851621i | \(0.324380\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −25.7753 | −0.853039 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 8.95912 | 0.296179 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 33.8905 | 1.11916 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −39.8066 | −1.31310 | −0.656549 | − | 0.754284i | \(-0.727984\pi\) | ||||
−0.656549 | + | 0.754284i | \(0.727984\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 61.7349 | 2.03423 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.90447 | −0.161433 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.08092 | −0.199939 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −19.2237 | −0.631388 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.42005 | −0.0793992 | −0.0396996 | − | 0.999212i | \(-0.512640\pi\) | ||||
−0.0396996 | + | 0.999212i | \(0.512640\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 79.8613 | 2.61454 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 34.4655 | 1.12714 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.8154 | 0.483997 | 0.241999 | − | 0.970277i | \(-0.422197\pi\) | ||||
0.241999 | + | 0.970277i | \(0.422197\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 55.7903 | 1.82065 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14.7737 | −0.481610 | −0.240805 | − | 0.970573i | \(-0.577411\pi\) | ||||
−0.240805 | + | 0.970573i | \(0.577411\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −14.8254 | −0.482782 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 14.3921 | 0.468177 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −50.0448 | −1.62624 | −0.813119 | − | 0.582097i | \(-0.802232\pi\) | ||||
−0.813119 | + | 0.582097i | \(0.802232\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.25574 | −0.105686 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −87.2561 | −2.82947 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.78937 | −0.187536 | −0.0937680 | − | 0.995594i | \(-0.529891\pi\) | ||||
−0.0937680 | + | 0.995594i | \(0.529891\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10.1714 | 0.329138 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 45.9585 | 1.48563 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −11.6952 | −0.377659 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 85.2613 | 2.75037 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.43076 | 0.175004 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −8.78235 | −0.282714 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −31.7279 | −1.02030 | −0.510151 | − | 0.860085i | \(-0.670410\pi\) | ||||
−0.510151 | + | 0.860085i | \(0.670410\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.01674 | −0.289361 | −0.144680 | − | 0.989478i | \(-0.546215\pi\) | ||||
−0.144680 | + | 0.989478i | \(0.546215\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −35.6448 | −1.14272 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.99377 | 0.127903 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 42.4099 | 1.35681 | 0.678407 | − | 0.734686i | \(-0.262671\pi\) | ||||
0.678407 | + | 0.734686i | \(0.262671\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −73.2894 | −2.34234 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −27.2778 | −0.870913 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −50.7523 | −1.61875 | −0.809374 | − | 0.587294i | \(-0.800193\pi\) | ||||
−0.809374 | + | 0.587294i | \(0.800193\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 32.7615 | 1.04387 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 54.6292 | 1.73887 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.89283 | 0.314574 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10.0696 | −0.319871 | −0.159936 | − | 0.987127i | \(-0.551129\pi\) | ||||
−0.159936 | + | 0.987127i | \(0.551129\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 57.1739 | 1.81436 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.77957 | −0.310033 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −32.7409 | −1.03692 | −0.518458 | − | 0.855103i | \(-0.673494\pi\) | ||||
−0.518458 | + | 0.855103i | \(0.673494\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.08092 | −0.192392 |
(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 | 5776.2.a.by.1.1 | 6 | ||
4.3 | odd | 2 | 1444.2.a.g.1.6 | 6 | |||
19.2 | odd | 18 | 304.2.u.e.289.2 | 12 | |||
19.10 | odd | 18 | 304.2.u.e.81.2 | 12 | |||
19.18 | odd | 2 | 5776.2.a.bw.1.6 | 6 | |||
76.7 | odd | 6 | 1444.2.e.h.429.1 | 12 | |||
76.11 | odd | 6 | 1444.2.e.h.653.1 | 12 | |||
76.27 | even | 6 | 1444.2.e.g.653.6 | 12 | |||
76.31 | even | 6 | 1444.2.e.g.429.6 | 12 | |||
76.59 | even | 18 | 76.2.i.a.61.1 | yes | 12 | ||
76.67 | even | 18 | 76.2.i.a.5.1 | ✓ | 12 | ||
76.75 | even | 2 | 1444.2.a.h.1.1 | 6 | |||
228.59 | odd | 18 | 684.2.bo.c.289.2 | 12 | |||
228.143 | odd | 18 | 684.2.bo.c.613.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.2.i.a.5.1 | ✓ | 12 | 76.67 | even | 18 | ||
76.2.i.a.61.1 | yes | 12 | 76.59 | even | 18 | ||
304.2.u.e.81.2 | 12 | 19.10 | odd | 18 | |||
304.2.u.e.289.2 | 12 | 19.2 | odd | 18 | |||
684.2.bo.c.289.2 | 12 | 228.59 | odd | 18 | |||
684.2.bo.c.613.2 | 12 | 228.143 | odd | 18 | |||
1444.2.a.g.1.6 | 6 | 4.3 | odd | 2 | |||
1444.2.a.h.1.1 | 6 | 76.75 | even | 2 | |||
1444.2.e.g.429.6 | 12 | 76.31 | even | 6 | |||
1444.2.e.g.653.6 | 12 | 76.27 | even | 6 | |||
1444.2.e.h.429.1 | 12 | 76.7 | odd | 6 | |||
1444.2.e.h.653.1 | 12 | 76.11 | odd | 6 | |||
5776.2.a.bw.1.6 | 6 | 19.18 | odd | 2 | |||
5776.2.a.by.1.1 | 6 | 1.1 | even | 1 | trivial |