Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6040,2,Mod(1,6040)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6040, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6040.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6040 = 2^{3} \cdot 5 \cdot 151 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6040.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.2296428209\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} - 18 x^{10} + 54 x^{9} + 110 x^{8} - 335 x^{7} - 258 x^{6} + 825 x^{5} + 168 x^{4} - 669 x^{3} + 39 x^{2} + 106 x - 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Root | \(2.45327\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6040.1 |
$q$-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 | ||||||||
\(3\) | 2.45327 | 1.41640 | 0.708198 | − | 0.706014i | \(-0.249508\pi\) | ||||
0.708198 | + | 0.706014i | \(0.249508\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.17952 | −1.20175 | −0.600874 | − | 0.799344i | \(-0.705181\pi\) | ||||
−0.600874 | + | 0.799344i | \(0.705181\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.01854 | 1.00618 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.84859 | −0.557371 | −0.278685 | − | 0.960382i | \(-0.589899\pi\) | ||||
−0.278685 | + | 0.960382i | \(0.589899\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.347557 | 0.0963950 | 0.0481975 | − | 0.998838i | \(-0.484652\pi\) | ||||
0.0481975 | + | 0.998838i | \(0.484652\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.45327 | −0.633432 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.562260 | 0.136368 | 0.0681841 | − | 0.997673i | \(-0.478279\pi\) | ||||
0.0681841 | + | 0.997673i | \(0.478279\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.75513 | −0.861486 | −0.430743 | − | 0.902475i | \(-0.641748\pi\) | ||||
−0.430743 | + | 0.902475i | \(0.641748\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −7.80023 | −1.70215 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.184488 | 0.0384684 | 0.0192342 | − | 0.999815i | \(-0.493877\pi\) | ||||
0.0192342 | + | 0.999815i | \(0.493877\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.0454727 | 0.00875123 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.03672 | −0.192514 | −0.0962568 | − | 0.995357i | \(-0.530687\pi\) | ||||
−0.0962568 | + | 0.995357i | \(0.530687\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.93218 | 1.42466 | 0.712330 | − | 0.701844i | \(-0.247640\pi\) | ||||
0.712330 | + | 0.701844i | \(0.247640\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.53509 | −0.789458 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.17952 | 0.537438 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.09134 | 0.179416 | 0.0897078 | − | 0.995968i | \(-0.471407\pi\) | ||||
0.0897078 | + | 0.995968i | \(0.471407\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.852651 | 0.136533 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.61724 | 0.564918 | 0.282459 | − | 0.959279i | \(-0.408850\pi\) | ||||
0.282459 | + | 0.959279i | \(0.408850\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.30386 | 0.351335 | 0.175667 | − | 0.984450i | \(-0.443792\pi\) | ||||
0.175667 | + | 0.984450i | \(0.443792\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.01854 | −0.449977 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.03471 | 1.31785 | 0.658924 | − | 0.752210i | \(-0.271012\pi\) | ||||
0.658924 | + | 0.752210i | \(0.271012\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.10938 | 0.444197 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.37938 | 0.193151 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.80091 | 1.07154 | 0.535769 | − | 0.844365i | \(-0.320022\pi\) | ||||
0.535769 | + | 0.844365i | \(0.320022\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.84859 | 0.249264 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −9.21235 | −1.22021 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.62811 | 0.732718 | 0.366359 | − | 0.930474i | \(-0.380604\pi\) | ||||
0.366359 | + | 0.930474i | \(0.380604\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.83177 | 0.618645 | 0.309323 | − | 0.950957i | \(-0.399898\pi\) | ||||
0.309323 | + | 0.950957i | \(0.399898\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −9.59751 | −1.20917 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.347557 | −0.0431091 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.2531 | 1.61912 | 0.809562 | − | 0.587035i | \(-0.199705\pi\) | ||||
0.809562 | + | 0.587035i | \(0.199705\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.452599 | 0.0544865 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.6606 | 1.38386 | 0.691928 | − | 0.721966i | \(-0.256761\pi\) | ||||
0.691928 | + | 0.721966i | \(0.256761\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.05704 | 0.591882 | 0.295941 | − | 0.955206i | \(-0.404367\pi\) | ||||
0.295941 | + | 0.955206i | \(0.404367\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.45327 | 0.283279 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.87764 | 0.669819 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.3678 | 1.16647 | 0.583236 | − | 0.812303i | \(-0.301786\pi\) | ||||
0.583236 | + | 0.812303i | \(0.301786\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.94405 | −0.993783 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.27862 | 0.798933 | 0.399466 | − | 0.916748i | \(-0.369195\pi\) | ||||
0.399466 | + | 0.916748i | \(0.369195\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.562260 | −0.0609857 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.54335 | −0.272676 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.70193 | −0.710403 | −0.355201 | − | 0.934790i | \(-0.615588\pi\) | ||||
−0.355201 | + | 0.934790i | \(0.615588\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.10507 | −0.115842 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 19.4598 | 2.01788 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.75513 | 0.385268 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.3155 | −1.45352 | −0.726761 | − | 0.686891i | \(-0.758975\pi\) | ||||
−0.726761 | + | 0.686891i | \(0.758975\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.58003 | −0.560815 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.9624 | 1.28980 | 0.644901 | − | 0.764266i | \(-0.276898\pi\) | ||||
0.644901 | + | 0.764266i | \(0.276898\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.78787 | 0.471763 | 0.235881 | − | 0.971782i | \(-0.424202\pi\) | ||||
0.235881 | + | 0.971782i | \(0.424202\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 7.80023 | 0.761225 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −14.6953 | −1.42065 | −0.710326 | − | 0.703873i | \(-0.751453\pi\) | ||||
−0.710326 | + | 0.703873i | \(0.751453\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.8774 | 1.42500 | 0.712498 | − | 0.701674i | \(-0.247564\pi\) | ||||
0.712498 | + | 0.701674i | \(0.247564\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.67736 | 0.254124 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.478687 | −0.0450311 | −0.0225155 | − | 0.999746i | \(-0.507168\pi\) | ||||
−0.0225155 | + | 0.999746i | \(0.507168\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.184488 | −0.0172036 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.04911 | 0.0969905 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.78772 | −0.163880 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.58272 | −0.689338 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.87407 | 0.800148 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.41528 | 0.746735 | 0.373368 | − | 0.927683i | \(-0.378203\pi\) | ||||
0.373368 | + | 0.927683i | \(0.378203\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.65198 | 0.497629 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.2435 | −0.982345 | −0.491172 | − | 0.871062i | \(-0.663432\pi\) | ||||
−0.491172 | + | 0.871062i | \(0.663432\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.9395 | 1.03529 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.0454727 | −0.00391367 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −19.9335 | −1.70303 | −0.851515 | − | 0.524330i | \(-0.824316\pi\) | ||||
−0.851515 | + | 0.524330i | \(0.824316\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.66713 | 0.480679 | 0.240340 | − | 0.970689i | \(-0.422741\pi\) | ||||
0.240340 | + | 0.970689i | \(0.422741\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 22.1646 | 1.86659 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.642490 | −0.0537277 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.03672 | 0.0860947 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.62814 | 0.629159 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.45349 | −0.610613 | −0.305307 | − | 0.952254i | \(-0.598759\pi\) | ||||
−0.305307 | + | 0.952254i | \(0.598759\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.00000 | 0.0813788 | ||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.69720 | 0.137211 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.93218 | −0.637128 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.31268 | −0.423998 | −0.211999 | − | 0.977270i | \(-0.567997\pi\) | ||||
−0.211999 | + | 0.977270i | \(0.567997\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 19.1377 | 1.51772 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.586584 | −0.0462293 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.537088 | 0.0420680 | 0.0210340 | − | 0.999779i | \(-0.493304\pi\) | ||||
0.0210340 | + | 0.999779i | \(0.493304\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.53509 | 0.353056 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −21.3038 | −1.64854 | −0.824270 | − | 0.566196i | \(-0.808414\pi\) | ||||
−0.824270 | + | 0.566196i | \(0.808414\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.8792 | −0.990708 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −11.3350 | −0.866809 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.0816 | 0.918544 | 0.459272 | − | 0.888296i | \(-0.348110\pi\) | ||||
0.459272 | + | 0.888296i | \(0.348110\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.17952 | −0.240349 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 13.8073 | 1.03782 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.4481 | 0.780924 | 0.390462 | − | 0.920619i | \(-0.372315\pi\) | ||||
0.390462 | + | 0.920619i | \(0.372315\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.0088 | −1.26426 | −0.632128 | − | 0.774864i | \(-0.717818\pi\) | ||||
−0.632128 | + | 0.774864i | \(0.717818\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.8536 | 0.876247 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.09134 | −0.0802371 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.03939 | −0.0760076 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.144582 | −0.0105168 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.10005 | −0.151955 | −0.0759773 | − | 0.997110i | \(-0.524208\pi\) | ||||
−0.0759773 | + | 0.997110i | \(0.524208\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.6532 | 0.838818 | 0.419409 | − | 0.907797i | \(-0.362237\pi\) | ||||
0.419409 | + | 0.907797i | \(0.362237\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.852651 | −0.0610596 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.46171 | 0.531624 | 0.265812 | − | 0.964025i | \(-0.414360\pi\) | ||||
0.265812 | + | 0.964025i | \(0.414360\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.3841 | −0.877884 | −0.438942 | − | 0.898515i | \(-0.644647\pi\) | ||||
−0.438942 | + | 0.898515i | \(0.644647\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 32.5134 | 2.29332 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.29627 | 0.231353 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.61724 | −0.252639 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.556884 | 0.0387061 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.94170 | 0.480167 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.5045 | −1.41159 | −0.705794 | − | 0.708417i | \(-0.749410\pi\) | ||||
−0.705794 | + | 0.708417i | \(0.749410\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 28.6066 | 1.96009 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.30386 | −0.157122 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −25.2205 | −1.71208 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 12.4063 | 0.838340 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.195418 | 0.0131452 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.1235 | −0.878817 | −0.439408 | − | 0.898287i | \(-0.644812\pi\) | ||||
−0.439408 | + | 0.898287i | \(0.644812\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.01854 | 0.201236 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.9641 | 1.12595 | 0.562974 | − | 0.826475i | \(-0.309657\pi\) | ||||
0.562974 | + | 0.826475i | \(0.309657\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.9238 | −0.721864 | −0.360932 | − | 0.932592i | \(-0.617541\pi\) | ||||
−0.360932 | + | 0.932592i | \(0.617541\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 14.4194 | 0.948729 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 23.6513 | 1.54945 | 0.774724 | − | 0.632300i | \(-0.217889\pi\) | ||||
0.774724 | + | 0.632300i | \(0.217889\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.03471 | −0.589359 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 25.4351 | 1.65219 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 23.1090 | 1.49480 | 0.747399 | − | 0.664375i | \(-0.231302\pi\) | ||||
0.747399 | + | 0.664375i | \(0.231302\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.56228 | 0.551545 | 0.275772 | − | 0.961223i | \(-0.411066\pi\) | ||||
0.275772 | + | 0.961223i | \(0.411066\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −22.0786 | −1.41634 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.10938 | −0.198651 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.30512 | −0.0830429 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 17.8564 | 1.13161 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.57051 | 0.288488 | 0.144244 | − | 0.989542i | \(-0.453925\pi\) | ||||
0.144244 | + | 0.989542i | \(0.453925\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.341043 | −0.0214412 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.37938 | −0.0863799 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.9860 | 0.685285 | 0.342643 | − | 0.939466i | \(-0.388678\pi\) | ||||
0.342643 | + | 0.939466i | \(0.388678\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.46995 | −0.215612 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.12937 | −0.193703 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.5717 | −0.651880 | −0.325940 | − | 0.945391i | \(-0.605681\pi\) | ||||
−0.325940 | + | 0.945391i | \(0.605681\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.80091 | −0.479206 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −16.4416 | −1.00621 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.38232 | 0.145252 | 0.0726262 | − | 0.997359i | \(-0.476862\pi\) | ||||
0.0726262 | + | 0.997359i | \(0.476862\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.9765 | 0.727519 | 0.363759 | − | 0.931493i | \(-0.381493\pi\) | ||||
0.363759 | + | 0.931493i | \(0.381493\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.71103 | −0.164079 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.84859 | −0.111474 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.8588 | 0.652441 | 0.326220 | − | 0.945294i | \(-0.394225\pi\) | ||||
0.326220 | + | 0.945294i | \(0.394225\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 23.9436 | 1.43346 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.4058 | 1.33662 | 0.668310 | − | 0.743883i | \(-0.267018\pi\) | ||||
0.668310 | + | 0.743883i | \(0.267018\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.2818 | 0.908408 | 0.454204 | − | 0.890898i | \(-0.349924\pi\) | ||||
0.454204 | + | 0.890898i | \(0.349924\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 9.21235 | 0.545692 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −11.5011 | −0.678889 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.6839 | −0.981404 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −35.1198 | −2.05876 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.2760 | 0.658748 | 0.329374 | − | 0.944200i | \(-0.393162\pi\) | ||||
0.329374 | + | 0.944200i | \(0.393162\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.62811 | −0.327681 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.0840604 | −0.00487768 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.0641201 | 0.00370816 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.32517 | −0.422216 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 31.8002 | 1.82687 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.83177 | −0.276667 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.82435 | 0.389486 | 0.194743 | − | 0.980854i | \(-0.437613\pi\) | ||||
0.194743 | + | 0.980854i | \(0.437613\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11.7459 | 0.668203 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −14.0236 | −0.795207 | −0.397604 | − | 0.917557i | \(-0.630158\pi\) | ||||
−0.397604 | + | 0.917557i | \(0.630158\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 18.9323 | 1.07011 | 0.535057 | − | 0.844816i | \(-0.320290\pi\) | ||||
0.535057 | + | 0.844816i | \(0.320290\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 9.59751 | 0.540758 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −27.1834 | −1.52677 | −0.763387 | − | 0.645941i | \(-0.776465\pi\) | ||||
−0.763387 | + | 0.645941i | \(0.776465\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.91647 | 0.107301 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −36.0516 | −2.01221 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.11136 | −0.117479 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.347557 | 0.0192790 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 36.4983 | 2.01836 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −28.7261 | −1.58372 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 31.0143 | 1.70470 | 0.852350 | − | 0.522972i | \(-0.175177\pi\) | ||||
0.852350 | + | 0.522972i | \(0.175177\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.29426 | 0.180524 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −13.2531 | −0.724094 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.11446 | 0.496496 | 0.248248 | − | 0.968696i | \(-0.420145\pi\) | ||||
0.248248 | + | 0.968696i | \(0.420145\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.17435 | −0.0637818 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −14.6633 | −0.794064 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.3703 | 0.667935 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.452599 | −0.0243671 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.683614 | 0.0366983 | 0.0183492 | − | 0.999832i | \(-0.494159\pi\) | ||||
0.0183492 | + | 0.999832i | \(0.494159\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.92961 | 0.103290 | 0.0516448 | − | 0.998666i | \(-0.483554\pi\) | ||||
0.0516448 | + | 0.998666i | \(0.483554\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.0158044 | 0.000843574 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.76551 | −0.253642 | −0.126821 | − | 0.991926i | \(-0.540477\pi\) | ||||
−0.126821 | + | 0.991926i | \(0.540477\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −11.6606 | −0.618879 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.38576 | −0.232119 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.0594328 | 0.00313674 | 0.00156837 | − | 0.999999i | \(-0.499501\pi\) | ||||
0.00156837 | + | 0.999999i | \(0.499501\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.89900 | −0.257842 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −18.6025 | −0.976375 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.05704 | −0.264698 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 25.5393 | 1.33314 | 0.666570 | − | 0.745443i | \(-0.267762\pi\) | ||||
0.666570 | + | 0.745443i | \(0.267762\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10.9188 | 0.568409 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −24.8032 | −1.28772 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.4093 | 0.953198 | 0.476599 | − | 0.879121i | \(-0.341869\pi\) | ||||
0.476599 | + | 0.879121i | \(0.341869\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.45327 | −0.126686 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.360318 | −0.0185573 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.54292 | −0.387454 | −0.193727 | − | 0.981056i | \(-0.562058\pi\) | ||||
−0.193727 | + | 0.981056i | \(0.562058\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 20.6450 | 1.05767 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.60748 | 0.184333 | 0.0921667 | − | 0.995744i | \(-0.470621\pi\) | ||||
0.0921667 | + | 0.995744i | \(0.470621\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.87764 | −0.299552 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.95427 | 0.353505 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.80568 | −0.192956 | −0.0964778 | − | 0.995335i | \(-0.530758\pi\) | ||||
−0.0964778 | + | 0.995335i | \(0.530758\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.103730 | 0.00524587 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −27.5832 | −1.39139 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −10.3678 | −0.521662 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.33774 | −0.117328 | −0.0586639 | − | 0.998278i | \(-0.518684\pi\) | ||||
−0.0586639 | + | 0.998278i | \(0.518684\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 29.2909 | 1.46638 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.8370 | −0.940675 | −0.470338 | − | 0.882487i | \(-0.655868\pi\) | ||||
−0.470338 | + | 0.882487i | \(0.655868\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.75688 | 0.137330 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 8.94405 | 0.444433 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.01745 | −0.100001 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.85637 | 0.0917916 | 0.0458958 | − | 0.998946i | \(-0.485386\pi\) | ||||
0.0458958 | + | 0.998946i | \(0.485386\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −48.9022 | −2.41217 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −17.8947 | −0.880542 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.27862 | −0.357293 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13.9030 | 0.680832 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.1243 | 0.738868 | 0.369434 | − | 0.929257i | \(-0.379552\pi\) | ||||
0.369434 | + | 0.929257i | \(0.379552\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.0385 | −0.489246 | −0.244623 | − | 0.969618i | \(-0.578664\pi\) | ||||
−0.244623 | + | 0.969618i | \(0.578664\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 27.2716 | 1.32599 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.562260 | 0.0272736 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −15.3627 | −0.743455 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.57620 | −0.0760998 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.0366 | 0.772454 | 0.386227 | − | 0.922404i | \(-0.373778\pi\) | ||||
0.386227 | + | 0.922404i | \(0.373778\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −24.2093 | −1.16342 | −0.581711 | − | 0.813395i | \(-0.697617\pi\) | ||||
−0.581711 | + | 0.813395i | \(0.697617\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.54335 | 0.121944 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.692776 | −0.0331400 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.0185 | 0.716796 | 0.358398 | − | 0.933569i | \(-0.383323\pi\) | ||||
0.358398 | + | 0.933569i | \(0.383323\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9.38577 | 0.446941 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13.0636 | 0.620669 | 0.310334 | − | 0.950627i | \(-0.399559\pi\) | ||||
0.310334 | + | 0.950627i | \(0.399559\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.70193 | 0.317702 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −18.2854 | −0.864871 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 27.0002 | 1.27422 | 0.637109 | − | 0.770774i | \(-0.280130\pi\) | ||||
0.637109 | + | 0.770774i | \(0.280130\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.68680 | −0.314869 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.45327 | 0.115265 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.10507 | 0.0518063 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −23.5842 | −1.10322 | −0.551612 | − | 0.834101i | \(-0.685987\pi\) | ||||
−0.551612 | + | 0.834101i | \(0.685987\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.0255675 | 0.00119339 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −28.3311 | −1.31951 | −0.659755 | − | 0.751480i | \(-0.729340\pi\) | ||||
−0.659755 | + | 0.751480i | \(0.729340\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.0551 | 0.746145 | 0.373073 | − | 0.927802i | \(-0.378304\pi\) | ||||
0.373073 | + | 0.927802i | \(0.378304\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −19.4598 | −0.902425 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −39.6316 | −1.83393 | −0.916967 | − | 0.398963i | \(-0.869370\pi\) | ||||
−0.916967 | + | 0.398963i | \(0.869370\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −42.1385 | −1.94578 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −13.0334 | −0.600550 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.25888 | −0.195824 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.75513 | −0.172297 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 23.5473 | 1.07816 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 31.8513 | 1.45532 | 0.727662 | − | 0.685936i | \(-0.240607\pi\) | ||||
0.727662 | + | 0.685936i | \(0.240607\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.379304 | 0.0172948 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.43905 | −0.0654790 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 14.3155 | 0.650034 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −25.7700 | −1.16775 | −0.583875 | − | 0.811844i | \(-0.698464\pi\) | ||||
−0.583875 | + | 0.811844i | \(0.698464\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.31762 | 0.0595850 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.01715 | −0.0459032 | −0.0229516 | − | 0.999737i | \(-0.507306\pi\) | ||||
−0.0229516 | + | 0.999737i | \(0.507306\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.582905 | −0.0262527 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.58003 | 0.250804 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −37.0751 | −1.66305 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.88659 | −0.397818 | −0.198909 | − | 0.980018i | \(-0.563740\pi\) | ||||
−0.198909 | + | 0.980018i | \(0.563740\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −52.2641 | −2.33499 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −26.3462 | −1.17472 | −0.587359 | − | 0.809326i | \(-0.699832\pi\) | ||||
−0.587359 | + | 0.809326i | \(0.699832\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.9624 | −0.576817 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −31.5962 | −1.40324 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 24.8057 | 1.09949 | 0.549746 | − | 0.835332i | \(-0.314724\pi\) | ||||
0.549746 | + | 0.835332i | \(0.314724\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16.0790 | −0.711293 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.170756 | −0.00753906 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.78787 | −0.210979 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −16.7015 | −0.734530 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 29.6393 | 1.30102 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.22150 | 0.272569 | 0.136284 | − | 0.990670i | \(-0.456484\pi\) | ||||
0.136284 | + | 0.990670i | \(0.456484\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.99802 | 0.0873672 | 0.0436836 | − | 0.999045i | \(-0.486091\pi\) | ||||
0.0436836 | + | 0.999045i | \(0.486091\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −7.80023 | −0.340430 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.45995 | 0.194278 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9660 | −0.998520 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 16.9887 | 0.737245 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.25720 | 0.0544553 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14.6953 | 0.635335 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 25.6319 | 1.10610 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.74796 | −0.247582 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.2836 | −0.485118 | −0.242559 | − | 0.970137i | \(-0.577987\pi\) | ||||
−0.242559 | + | 0.970137i | \(0.577987\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −41.7272 | −1.79069 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −14.8774 | −0.637277 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.89315 | 0.251973 | 0.125987 | − | 0.992032i | \(-0.459790\pi\) | ||||
0.125987 | + | 0.992032i | \(0.459790\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 14.5849 | 0.622468 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.89301 | 0.165848 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −32.9648 | −1.40181 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.67736 | −0.113648 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 34.3228 | 1.45431 | 0.727153 | − | 0.686476i | \(-0.240843\pi\) | ||||
0.727153 | + | 0.686476i | \(0.240843\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.800721 | 0.0338669 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.54990 | −0.107657 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 28.8583 | 1.21623 | 0.608117 | − | 0.793847i | \(-0.291925\pi\) | ||||
0.608117 | + | 0.793847i | \(0.291925\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.478687 | 0.0201385 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 28.4378 | 1.19428 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −17.9690 | −0.753300 | −0.376650 | − | 0.926356i | \(-0.622924\pi\) | ||||
−0.376650 | + | 0.926356i | \(0.622924\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.1563 | 0.550573 | 0.275286 | − | 0.961362i | \(-0.411227\pi\) | ||||
0.275286 | + | 0.961362i | \(0.411227\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.15200 | −0.215228 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.184488 | 0.00769368 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.0147 | 0.708329 | 0.354165 | − | 0.935183i | \(-0.384765\pi\) | ||||
0.354165 | + | 0.935183i | \(0.384765\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 28.5885 | 1.18810 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −23.1426 | −0.960115 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −14.4207 | −0.597244 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.04911 | −0.0433755 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 31.7045 | 1.30859 | 0.654293 | − | 0.756241i | \(-0.272966\pi\) | ||||
0.654293 | + | 0.756241i | \(0.272966\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −29.7863 | −1.22733 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 18.3056 | 0.752991 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −15.3419 | −0.630018 | −0.315009 | − | 0.949089i | \(-0.602008\pi\) | ||||
−0.315009 | + | 0.949089i | \(0.602008\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.78772 | 0.0732894 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −30.3815 | −1.24343 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7.89873 | 0.322733 | 0.161367 | − | 0.986895i | \(-0.448410\pi\) | ||||
0.161367 | + | 0.986895i | \(0.448410\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.83231 | 0.278696 | 0.139348 | − | 0.990243i | \(-0.455499\pi\) | ||||
0.139348 | + | 0.990243i | \(0.455499\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 40.0049 | 1.62913 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.58272 | 0.308281 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.6498 | 0.594618 | 0.297309 | − | 0.954781i | \(-0.403911\pi\) | ||||
0.297309 | + | 0.954781i | \(0.403911\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 8.08664 | 0.327687 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.14008 | 0.127034 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.41504 | 0.137932 | 0.0689660 | − | 0.997619i | \(-0.478030\pi\) | ||||
0.0689660 | + | 0.997619i | \(0.478030\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8.87407 | −0.357837 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 24.8508 | 1.00046 | 0.500228 | − | 0.865894i | \(-0.333250\pi\) | ||||
0.500228 | + | 0.865894i | \(0.333250\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −29.0389 | −1.16717 | −0.583586 | − | 0.812051i | \(-0.698351\pi\) | ||||
−0.583586 | + | 0.812051i | \(0.698351\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.00838917 | 0.000336646 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 21.3089 | 0.853725 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 17.0299 | 0.680107 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.613619 | 0.0244666 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.76540 | 0.110089 | 0.0550445 | − | 0.998484i | \(-0.482470\pi\) | ||||
0.0550445 | + | 0.998484i | \(0.482470\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −50.3031 | −1.99937 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.41528 | −0.333950 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.08069 | 0.0428183 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 35.1979 | 1.39241 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.291889 | 0.0115289 | 0.00576446 | − | 0.999983i | \(-0.498165\pi\) | ||||
0.00576446 | + | 0.999983i | \(0.498165\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.09175 | −0.319108 | −0.159554 | − | 0.987189i | \(-0.551006\pi\) | ||||
−0.159554 | + | 0.987189i | \(0.551006\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.65198 | −0.222547 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12.4961 | −0.491273 | −0.245636 | − | 0.969362i | \(-0.578997\pi\) | ||||
−0.245636 | + | 0.969362i | \(0.578997\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.4041 | −0.408395 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −61.8728 | −2.42499 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8.17861 | −0.320054 | −0.160027 | − | 0.987113i | \(-0.551158\pi\) | ||||
−0.160027 | + | 0.987113i | \(0.551158\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11.2435 | 0.439318 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 15.2649 | 0.595539 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 45.2257 | 1.76174 | 0.880871 | − | 0.473357i | \(-0.156958\pi\) | ||||
0.880871 | + | 0.473357i | \(0.156958\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.4453 | 0.873021 | 0.436511 | − | 0.899699i | \(-0.356214\pi\) | ||||
0.436511 | + | 0.899699i | \(0.356214\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.479412 | 0.0186188 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −11.9395 | −0.462995 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.191262 | −0.00740569 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −32.1956 | −1.24475 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.93197 | −0.344815 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.59172 | −0.254092 | −0.127046 | − | 0.991897i | \(-0.540550\pi\) | ||||
−0.127046 | + | 0.991897i | \(0.540550\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.0454727 | 0.00175025 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.28244 | 0.241454 | 0.120727 | − | 0.992686i | \(-0.461477\pi\) | ||||
0.120727 | + | 0.992686i | \(0.461477\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 45.5166 | 1.74677 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 41.6176 | 1.59479 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −46.6355 | −1.78446 | −0.892230 | − | 0.451582i | \(-0.850860\pi\) | ||||
−0.892230 | + | 0.451582i | \(0.850860\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 19.9335 | 0.761618 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −26.7990 | −1.02245 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.71126 | 0.103291 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.9584 | 0.759254 | 0.379627 | − | 0.925140i | \(-0.376052\pi\) | ||||
0.379627 | + | 0.925140i | \(0.376052\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 17.7419 | 0.673957 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.66713 | −0.214966 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.03383 | 0.0770369 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 58.0230 | 2.19463 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −35.9484 | −1.35775 | −0.678876 | − | 0.734253i | \(-0.737533\pi\) | ||||
−0.678876 | + | 0.734253i | \(0.737533\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.09813 | −0.154564 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −22.1646 | −0.834766 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −41.2141 | −1.55002 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −49.6979 | −1.86644 | −0.933221 | − | 0.359303i | \(-0.883015\pi\) | ||||
−0.933221 | + | 0.359303i | \(0.883015\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 31.2957 | 1.17368 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.46339 | 0.0548044 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.642490 | 0.0240278 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 56.6927 | 2.11723 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 13.6081 | 0.507496 | 0.253748 | − | 0.967270i | \(-0.418337\pi\) | ||||
0.253748 | + | 0.967270i | \(0.418337\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.2231 | −0.566940 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 21.0056 | 0.781206 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.03672 | −0.0385027 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −41.0886 | −1.52389 | −0.761945 | − | 0.647642i | \(-0.775755\pi\) | ||||
−0.761945 | + | 0.647642i | \(0.775755\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.3326 | −1.01232 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.29537 | 0.0479109 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.94145 | 0.0717090 | 0.0358545 | − | 0.999357i | \(-0.488585\pi\) | ||||
0.0358545 | + | 0.999357i | \(0.488585\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −7.62814 | −0.281368 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −24.4995 | −0.902452 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10.3848 | 0.382011 | 0.191005 | − | 0.981589i | \(-0.438825\pi\) | ||||
0.191005 | + | 0.981589i | \(0.438825\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.20182 | −0.117622 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −11.8130 | −0.433378 | −0.216689 | − | 0.976241i | \(-0.569526\pi\) | ||||
−0.216689 | + | 0.976241i | \(0.569526\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.45349 | 0.273075 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 21.9708 | 0.803869 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 46.7242 | 1.70727 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.7633 | 0.392760 | 0.196380 | − | 0.980528i | \(-0.437081\pi\) | ||||
0.196380 | + | 0.980528i | \(0.437081\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 11.2127 | 0.408613 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.00000 | −0.0363937 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −50.8259 | −1.84730 | −0.923649 | − | 0.383240i | \(-0.874808\pi\) | ||||
−0.923649 | + | 0.383240i | \(0.874808\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.836670 | −0.0303692 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −22.4407 | −0.813475 | −0.406737 | − | 0.913545i | \(-0.633334\pi\) | ||||
−0.406737 | + | 0.913545i | \(0.633334\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −47.3030 | −1.71248 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.69720 | −0.0613625 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.95609 | 0.0706303 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10.5434 | −0.380205 | −0.190102 | − | 0.981764i | \(-0.560882\pi\) | ||||
−0.190102 | + | 0.981764i | \(0.560882\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 26.9515 | 0.970635 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −23.0253 | −0.828162 | −0.414081 | − | 0.910240i | \(-0.635897\pi\) | ||||
−0.414081 | + | 0.910240i | \(0.635897\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.93218 | 0.284932 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8.51273 | −0.305392 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −13.5832 | −0.486669 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −21.5556 | −0.771321 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.0471424 | −0.00168473 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.31268 | 0.189618 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.4695 | 0.729659 | 0.364830 | − | 0.931074i | \(-0.381127\pi\) | ||||
0.364830 | + | 0.931074i | \(0.381127\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −25.9353 | −0.923320 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.52200 | 0.0541160 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.67932 | 0.0596343 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −19.1377 | −0.678746 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 17.9438 | 0.635602 | 0.317801 | − | 0.948157i | \(-0.397056\pi\) | ||||
0.317801 | + | 0.948157i | \(0.397056\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.07986 | 0.179712 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −20.2300 | −0.714792 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.34840 | −0.329898 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.586584 | 0.0206744 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.84447 | 0.205735 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 24.7656 | 0.870713 | 0.435356 | − | 0.900258i | \(-0.356622\pi\) | ||||
0.435356 | + | 0.900258i | \(0.356622\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.01277 | 0.246252 | 0.123126 | − | 0.992391i | \(-0.460708\pi\) | ||||
0.123126 | + | 0.992391i | \(0.460708\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 29.3815 | 1.03045 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.537088 | −0.0188134 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.65128 | −0.302670 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.33568 | −0.116558 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 31.6819 | 1.10571 | 0.552853 | − | 0.833279i | \(-0.313539\pi\) | ||||
0.552853 | + | 0.833279i | \(0.313539\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.56321 | −0.333352 | −0.166676 | − | 0.986012i | \(-0.553303\pi\) | ||||
−0.166676 | + | 0.986012i | \(0.553303\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.53509 | −0.157892 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 11.1021 | 0.386058 | 0.193029 | − | 0.981193i | \(-0.438169\pi\) | ||||
0.193029 | + | 0.981193i | \(0.438169\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.3884 | −0.395534 | −0.197767 | − | 0.980249i | \(-0.563369\pi\) | ||||
−0.197767 | + | 0.980249i | \(0.563369\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 26.6395 | 0.924115 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.74828 | 0.0605743 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 21.3038 | 0.737250 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.360698 | 0.0124675 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 11.6880 | 0.403515 | 0.201757 | − | 0.979436i | \(-0.435335\pi\) | ||||
0.201757 | + | 0.979436i | \(0.435335\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.9252 | −0.962939 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 54.9675 | 1.89318 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.8792 | 0.443058 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 24.1094 | 0.828410 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 37.4904 | 1.28667 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.201340 | 0.00690183 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 35.2687 | 1.20758 | 0.603789 | − | 0.797144i | \(-0.293657\pi\) | ||||
0.603789 | + | 0.797144i | \(0.293657\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 11.3350 | 0.387649 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −16.4026 | −0.560303 | −0.280152 | − | 0.959956i | \(-0.590385\pi\) | ||||
−0.280152 | + | 0.959956i | \(0.590385\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21.4579 | 0.732135 | 0.366067 | − | 0.930588i | \(-0.380704\pi\) | ||||
0.366067 | + | 0.930588i | \(0.380704\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −28.2153 | −0.961576 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 13.5031 | 0.459652 | 0.229826 | − | 0.973232i | \(-0.426184\pi\) | ||||
0.229826 | + | 0.973232i | \(0.426184\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12.0816 | −0.410785 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −40.9300 | −1.39006 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −19.1659 | −0.650158 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.60621 | 0.156075 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −43.2119 | −1.46250 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.17952 | 0.107488 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15.8614 | −0.535600 | −0.267800 | − | 0.963475i | \(-0.586297\pi\) | ||||
−0.267800 | + | 0.963475i | \(0.586297\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 27.6630 | 0.933048 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.3293 | 0.415386 | 0.207693 | − | 0.978194i | \(-0.433404\pi\) | ||||
0.207693 | + | 0.978194i | \(0.433404\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.0825 | 0.608523 | 0.304262 | − | 0.952588i | \(-0.401590\pi\) | ||||
0.304262 | + | 0.952588i | \(0.401590\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −13.8073 | −0.464127 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.49410 | 0.184474 | 0.0922368 | − | 0.995737i | \(-0.470598\pi\) | ||||
0.0922368 | + | 0.995737i | \(0.470598\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −26.7566 | −0.897387 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 16.5339 | 0.553906 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −33.9265 | −1.13531 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −10.4481 | −0.349240 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.157304 | 0.00525222 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −8.22343 | −0.274267 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.38614 | 0.146124 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −17.9706 | −0.598025 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 17.0088 | 0.565392 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 26.0553 | 0.865152 | 0.432576 | − | 0.901598i | \(-0.357605\pi\) | ||||
0.432576 | + | 0.901598i | \(0.357605\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 39.1273 | 1.29777 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16.3194 | −0.540686 | −0.270343 | − | 0.962764i | \(-0.587137\pi\) | ||||
−0.270343 | + | 0.962764i | \(0.587137\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13.4552 | −0.445302 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −11.8536 | −0.391869 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 35.7488 | 1.18053 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26.2762 | 0.866773 | 0.433387 | − | 0.901208i | \(-0.357318\pi\) | ||||
0.433387 | + | 0.901208i | \(0.357318\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 16.7420 | 0.551667 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.05272 | 0.133397 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.09134 | 0.0358831 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 14.4524 | 0.474678 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −46.7450 | −1.53365 | −0.766826 | − | 0.641855i | \(-0.778165\pi\) | ||||
−0.766826 | + | 0.641855i | \(0.778165\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −11.6761 | −0.382669 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −34.4038 | −1.12633 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.03939 | 0.0339917 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −27.4327 | −0.896188 | −0.448094 | − | 0.893986i | \(-0.647897\pi\) | ||||
−0.448094 | + | 0.893986i | \(0.647897\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 46.4460 | 1.51571 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.51900 | 0.212513 | 0.106257 | − | 0.994339i | \(-0.466113\pi\) | ||||
0.106257 | + | 0.994339i | \(0.466113\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.667338 | 0.0217315 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.144582 | 0.00470324 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 43.7858 | 1.42285 | 0.711424 | − | 0.702763i | \(-0.248051\pi\) | ||||
0.711424 | + | 0.702763i | \(0.248051\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.75761 | 0.0570545 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −66.6883 | −2.16252 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 59.0036 | 1.91131 | 0.955657 | − | 0.294483i | \(-0.0951473\pi\) | ||||
0.955657 | + | 0.294483i | \(0.0951473\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.10005 | 0.0679561 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.70161 | 0.151981 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 63.3789 | 2.04661 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 31.9194 | 1.02966 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −44.3584 | −1.42943 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −11.6532 | −0.375131 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 39.4813 | 1.26963 | 0.634817 | − | 0.772663i | \(-0.281076\pi\) | ||||
0.634817 | + | 0.772663i | \(0.281076\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.17974 | −0.166397 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −30.8018 | −0.988475 | −0.494238 | − | 0.869327i | \(-0.664553\pi\) | ||||
−0.494238 | + | 0.869327i | \(0.664553\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −18.0188 | −0.577655 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.852651 | 0.0273067 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −34.0177 | −1.08832 | −0.544161 | − | 0.838981i | \(-0.683152\pi\) | ||||
−0.544161 | + | 0.838981i | \(0.683152\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.3891 | 0.395958 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 44.9079 | 1.43380 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 28.6619 | 0.914172 | 0.457086 | − | 0.889423i | \(-0.348893\pi\) | ||||
0.457086 | + | 0.889423i | \(0.348893\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.46171 | −0.237750 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −70.4728 | −2.24317 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.425034 | 0.0135153 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.9754 | −0.443942 | −0.221971 | − | 0.975053i | \(-0.571249\pi\) | ||||
−0.221971 | + | 0.975053i | \(0.571249\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 76.0865 | 2.41453 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 12.3841 | 0.392602 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.75327 | −0.0555266 | −0.0277633 | − | 0.999615i | \(-0.508838\pi\) | ||||
−0.0277633 | + | 0.999615i | \(0.508838\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.0496263 | 0.00157011 |
(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 | 6040.2.a.m.1.11 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6040.2.a.m.1.11 | ✓ | 12 | 1.1 | even | 1 | trivial |