Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3525,2,Mod(1,3525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3525, 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("3525.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3525 = 3 \cdot 5^{2} \cdot 47 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3525.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: | \(28.1472667125\) |
Analytic rank: | \(0\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 3 x^{12} - 17 x^{11} + 51 x^{10} + 106 x^{9} - 316 x^{8} - 288 x^{7} + 852 x^{6} + 309 x^{5} - 923 x^{4} - 107 x^{3} + 293 x^{2} + 12 x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{29}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 705) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.57687\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3525.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.57687 | −1.82212 | −0.911060 | − | 0.412275i | \(-0.864734\pi\) | ||||
−0.911060 | + | 0.412275i | \(0.864734\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 4.64024 | 2.32012 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.57687 | 1.05200 | ||||||||
\(7\) | −1.51741 | −0.573525 | −0.286763 | − | 0.958002i | \(-0.592579\pi\) | ||||
−0.286763 | + | 0.958002i | \(0.592579\pi\) | |||||||
\(8\) | −6.80354 | −2.40541 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.409552 | −0.123485 | −0.0617423 | − | 0.998092i | \(-0.519666\pi\) | ||||
−0.0617423 | + | 0.998092i | \(0.519666\pi\) | |||||||
\(12\) | −4.64024 | −1.33952 | ||||||||
\(13\) | −1.70509 | −0.472907 | −0.236454 | − | 0.971643i | \(-0.575985\pi\) | ||||
−0.236454 | + | 0.971643i | \(0.575985\pi\) | |||||||
\(14\) | 3.91015 | 1.04503 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 8.25132 | 2.06283 | ||||||||
\(17\) | 3.62967 | 0.880325 | 0.440163 | − | 0.897918i | \(-0.354921\pi\) | ||||
0.440163 | + | 0.897918i | \(0.354921\pi\) | |||||||
\(18\) | −2.57687 | −0.607373 | ||||||||
\(19\) | −0.485553 | −0.111394 | −0.0556968 | − | 0.998448i | \(-0.517738\pi\) | ||||
−0.0556968 | + | 0.998448i | \(0.517738\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.51741 | 0.331125 | ||||||||
\(22\) | 1.05536 | 0.225004 | ||||||||
\(23\) | −7.71926 | −1.60958 | −0.804789 | − | 0.593562i | \(-0.797721\pi\) | ||||
−0.804789 | + | 0.593562i | \(0.797721\pi\) | |||||||
\(24\) | 6.80354 | 1.38877 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 4.39379 | 0.861693 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −7.04112 | −1.33065 | ||||||||
\(29\) | −1.53695 | −0.285405 | −0.142702 | − | 0.989766i | \(-0.545579\pi\) | ||||
−0.142702 | + | 0.989766i | \(0.545579\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.32311 | 0.776453 | 0.388226 | − | 0.921564i | \(-0.373088\pi\) | ||||
0.388226 | + | 0.921564i | \(0.373088\pi\) | |||||||
\(32\) | −7.65548 | −1.35331 | ||||||||
\(33\) | 0.409552 | 0.0712939 | ||||||||
\(34\) | −9.35318 | −1.60406 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.64024 | 0.773373 | ||||||||
\(37\) | 2.44384 | 0.401765 | 0.200883 | − | 0.979615i | \(-0.435619\pi\) | ||||
0.200883 | + | 0.979615i | \(0.435619\pi\) | |||||||
\(38\) | 1.25121 | 0.202972 | ||||||||
\(39\) | 1.70509 | 0.273033 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.76866 | −1.21326 | −0.606630 | − | 0.794984i | \(-0.707479\pi\) | ||||
−0.606630 | + | 0.794984i | \(0.707479\pi\) | |||||||
\(42\) | −3.91015 | −0.603349 | ||||||||
\(43\) | 7.59452 | 1.15815 | 0.579077 | − | 0.815273i | \(-0.303413\pi\) | ||||
0.579077 | + | 0.815273i | \(0.303413\pi\) | |||||||
\(44\) | −1.90042 | −0.286499 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 19.8915 | 2.93284 | ||||||||
\(47\) | −1.00000 | −0.145865 | ||||||||
\(48\) | −8.25132 | −1.19098 | ||||||||
\(49\) | −4.69748 | −0.671069 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.62967 | −0.508256 | ||||||||
\(52\) | −7.91202 | −1.09720 | ||||||||
\(53\) | −10.2033 | −1.40153 | −0.700765 | − | 0.713392i | \(-0.747158\pi\) | ||||
−0.700765 | + | 0.713392i | \(0.747158\pi\) | |||||||
\(54\) | 2.57687 | 0.350667 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 10.3237 | 1.37957 | ||||||||
\(57\) | 0.485553 | 0.0643131 | ||||||||
\(58\) | 3.96052 | 0.520042 | ||||||||
\(59\) | 0.118818 | 0.0154687 | 0.00773437 | − | 0.999970i | \(-0.497538\pi\) | ||||
0.00773437 | + | 0.999970i | \(0.497538\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.25962 | 0.289315 | 0.144658 | − | 0.989482i | \(-0.453792\pi\) | ||||
0.144658 | + | 0.989482i | \(0.453792\pi\) | |||||||
\(62\) | −11.1401 | −1.41479 | ||||||||
\(63\) | −1.51741 | −0.191175 | ||||||||
\(64\) | 3.22450 | 0.403063 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.05536 | −0.129906 | ||||||||
\(67\) | 15.7869 | 1.92868 | 0.964338 | − | 0.264675i | \(-0.0852648\pi\) | ||||
0.964338 | + | 0.264675i | \(0.0852648\pi\) | |||||||
\(68\) | 16.8426 | 2.04246 | ||||||||
\(69\) | 7.71926 | 0.929290 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.50172 | −1.12765 | −0.563824 | − | 0.825895i | \(-0.690670\pi\) | ||||
−0.563824 | + | 0.825895i | \(0.690670\pi\) | |||||||
\(72\) | −6.80354 | −0.801804 | ||||||||
\(73\) | −8.20986 | −0.960891 | −0.480446 | − | 0.877025i | \(-0.659525\pi\) | ||||
−0.480446 | + | 0.877025i | \(0.659525\pi\) | |||||||
\(74\) | −6.29745 | −0.732064 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.25308 | −0.258446 | ||||||||
\(77\) | 0.621456 | 0.0708215 | ||||||||
\(78\) | −4.39379 | −0.497499 | ||||||||
\(79\) | 13.2865 | 1.49485 | 0.747424 | − | 0.664348i | \(-0.231291\pi\) | ||||
0.747424 | + | 0.664348i | \(0.231291\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 20.0188 | 2.21071 | ||||||||
\(83\) | −6.59494 | −0.723889 | −0.361944 | − | 0.932200i | \(-0.617887\pi\) | ||||
−0.361944 | + | 0.932200i | \(0.617887\pi\) | |||||||
\(84\) | 7.04112 | 0.768249 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −19.5701 | −2.11029 | ||||||||
\(87\) | 1.53695 | 0.164779 | ||||||||
\(88\) | 2.78640 | 0.297031 | ||||||||
\(89\) | 17.7958 | 1.88635 | 0.943175 | − | 0.332296i | \(-0.107823\pi\) | ||||
0.943175 | + | 0.332296i | \(0.107823\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.58731 | 0.271224 | ||||||||
\(92\) | −35.8192 | −3.73441 | ||||||||
\(93\) | −4.32311 | −0.448285 | ||||||||
\(94\) | 2.57687 | 0.265783 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 7.65548 | 0.781335 | ||||||||
\(97\) | 5.61258 | 0.569872 | 0.284936 | − | 0.958547i | \(-0.408028\pi\) | ||||
0.284936 | + | 0.958547i | \(0.408028\pi\) | |||||||
\(98\) | 12.1048 | 1.22277 | ||||||||
\(99\) | −0.409552 | −0.0411615 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.93695 | 0.192734 | 0.0963671 | − | 0.995346i | \(-0.469278\pi\) | ||||
0.0963671 | + | 0.995346i | \(0.469278\pi\) | |||||||
\(102\) | 9.35318 | 0.926103 | ||||||||
\(103\) | 6.55151 | 0.645540 | 0.322770 | − | 0.946477i | \(-0.395386\pi\) | ||||
0.322770 | + | 0.946477i | \(0.395386\pi\) | |||||||
\(104\) | 11.6006 | 1.13754 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 26.2925 | 2.55376 | ||||||||
\(107\) | 0.241779 | 0.0233737 | 0.0116868 | − | 0.999932i | \(-0.496280\pi\) | ||||
0.0116868 | + | 0.999932i | \(0.496280\pi\) | |||||||
\(108\) | −4.64024 | −0.446507 | ||||||||
\(109\) | −3.75817 | −0.359968 | −0.179984 | − | 0.983670i | \(-0.557605\pi\) | ||||
−0.179984 | + | 0.983670i | \(0.557605\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.44384 | −0.231959 | ||||||||
\(112\) | −12.5206 | −1.18309 | ||||||||
\(113\) | 3.00612 | 0.282792 | 0.141396 | − | 0.989953i | \(-0.454841\pi\) | ||||
0.141396 | + | 0.989953i | \(0.454841\pi\) | |||||||
\(114\) | −1.25121 | −0.117186 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −7.13183 | −0.662173 | ||||||||
\(117\) | −1.70509 | −0.157636 | ||||||||
\(118\) | −0.306177 | −0.0281859 | ||||||||
\(119\) | −5.50769 | −0.504889 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.8323 | −0.984752 | ||||||||
\(122\) | −5.82275 | −0.527167 | ||||||||
\(123\) | 7.76866 | 0.700477 | ||||||||
\(124\) | 20.0602 | 1.80146 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 3.91015 | 0.348344 | ||||||||
\(127\) | 9.77663 | 0.867536 | 0.433768 | − | 0.901025i | \(-0.357184\pi\) | ||||
0.433768 | + | 0.901025i | \(0.357184\pi\) | |||||||
\(128\) | 7.00185 | 0.618882 | ||||||||
\(129\) | −7.59452 | −0.668661 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.07155 | −0.617844 | −0.308922 | − | 0.951087i | \(-0.599968\pi\) | ||||
−0.308922 | + | 0.951087i | \(0.599968\pi\) | |||||||
\(132\) | 1.90042 | 0.165410 | ||||||||
\(133\) | 0.736781 | 0.0638870 | ||||||||
\(134\) | −40.6807 | −3.51428 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −24.6946 | −2.11755 | ||||||||
\(137\) | −0.552072 | −0.0471667 | −0.0235833 | − | 0.999722i | \(-0.507508\pi\) | ||||
−0.0235833 | + | 0.999722i | \(0.507508\pi\) | |||||||
\(138\) | −19.8915 | −1.69328 | ||||||||
\(139\) | −3.52217 | −0.298746 | −0.149373 | − | 0.988781i | \(-0.547726\pi\) | ||||
−0.149373 | + | 0.988781i | \(0.547726\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.00000 | 0.0842152 | ||||||||
\(142\) | 24.4847 | 2.05471 | ||||||||
\(143\) | 0.698323 | 0.0583967 | ||||||||
\(144\) | 8.25132 | 0.687610 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 21.1557 | 1.75086 | ||||||||
\(147\) | 4.69748 | 0.387442 | ||||||||
\(148\) | 11.3400 | 0.932143 | ||||||||
\(149\) | −4.18581 | −0.342915 | −0.171458 | − | 0.985191i | \(-0.554848\pi\) | ||||
−0.171458 | + | 0.985191i | \(0.554848\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.9025 | −1.29413 | −0.647064 | − | 0.762436i | \(-0.724003\pi\) | ||||
−0.647064 | + | 0.762436i | \(0.724003\pi\) | |||||||
\(152\) | 3.30348 | 0.267948 | ||||||||
\(153\) | 3.62967 | 0.293442 | ||||||||
\(154\) | −1.60141 | −0.129045 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 7.91202 | 0.633469 | ||||||||
\(157\) | −13.1534 | −1.04976 | −0.524880 | − | 0.851177i | \(-0.675890\pi\) | ||||
−0.524880 | + | 0.851177i | \(0.675890\pi\) | |||||||
\(158\) | −34.2375 | −2.72379 | ||||||||
\(159\) | 10.2033 | 0.809174 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 11.7132 | 0.923133 | ||||||||
\(162\) | −2.57687 | −0.202458 | ||||||||
\(163\) | 2.82593 | 0.221344 | 0.110672 | − | 0.993857i | \(-0.464700\pi\) | ||||
0.110672 | + | 0.993857i | \(0.464700\pi\) | |||||||
\(164\) | −36.0484 | −2.81491 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 16.9943 | 1.31901 | ||||||||
\(167\) | 12.6036 | 0.975296 | 0.487648 | − | 0.873040i | \(-0.337855\pi\) | ||||
0.487648 | + | 0.873040i | \(0.337855\pi\) | |||||||
\(168\) | −10.3237 | −0.796492 | ||||||||
\(169\) | −10.0927 | −0.776359 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.485553 | −0.0371312 | ||||||||
\(172\) | 35.2404 | 2.68705 | ||||||||
\(173\) | −15.3764 | −1.16905 | −0.584524 | − | 0.811377i | \(-0.698719\pi\) | ||||
−0.584524 | + | 0.811377i | \(0.698719\pi\) | |||||||
\(174\) | −3.96052 | −0.300246 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.37935 | −0.254728 | ||||||||
\(177\) | −0.118818 | −0.00893088 | ||||||||
\(178\) | −45.8574 | −3.43715 | ||||||||
\(179\) | −24.2359 | −1.81147 | −0.905737 | − | 0.423840i | \(-0.860682\pi\) | ||||
−0.905737 | + | 0.423840i | \(0.860682\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.51402 | −0.558513 | −0.279257 | − | 0.960217i | \(-0.590088\pi\) | ||||
−0.279257 | + | 0.960217i | \(0.590088\pi\) | |||||||
\(182\) | −6.66716 | −0.494203 | ||||||||
\(183\) | −2.25962 | −0.167036 | ||||||||
\(184\) | 52.5183 | 3.87170 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 11.1401 | 0.816829 | ||||||||
\(187\) | −1.48654 | −0.108707 | ||||||||
\(188\) | −4.64024 | −0.338424 | ||||||||
\(189\) | 1.51741 | 0.110375 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.6707 | 1.06154 | 0.530768 | − | 0.847517i | \(-0.321903\pi\) | ||||
0.530768 | + | 0.847517i | \(0.321903\pi\) | |||||||
\(192\) | −3.22450 | −0.232709 | ||||||||
\(193\) | 4.00150 | 0.288034 | 0.144017 | − | 0.989575i | \(-0.453998\pi\) | ||||
0.144017 | + | 0.989575i | \(0.453998\pi\) | |||||||
\(194\) | −14.4629 | −1.03837 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −21.7974 | −1.55696 | ||||||||
\(197\) | −17.1433 | −1.22141 | −0.610704 | − | 0.791859i | \(-0.709114\pi\) | ||||
−0.610704 | + | 0.791859i | \(0.709114\pi\) | |||||||
\(198\) | 1.05536 | 0.0750012 | ||||||||
\(199\) | −12.0104 | −0.851392 | −0.425696 | − | 0.904866i | \(-0.639971\pi\) | ||||
−0.425696 | + | 0.904866i | \(0.639971\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −15.7869 | −1.11352 | ||||||||
\(202\) | −4.99127 | −0.351185 | ||||||||
\(203\) | 2.33218 | 0.163687 | ||||||||
\(204\) | −16.8426 | −1.17921 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −16.8824 | −1.17625 | ||||||||
\(207\) | −7.71926 | −0.536526 | ||||||||
\(208\) | −14.0693 | −0.975527 | ||||||||
\(209\) | 0.198859 | 0.0137554 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 26.1444 | 1.79986 | 0.899928 | − | 0.436039i | \(-0.143619\pi\) | ||||
0.899928 | + | 0.436039i | \(0.143619\pi\) | |||||||
\(212\) | −47.3457 | −3.25172 | ||||||||
\(213\) | 9.50172 | 0.651047 | ||||||||
\(214\) | −0.623032 | −0.0425896 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 6.80354 | 0.462922 | ||||||||
\(217\) | −6.55990 | −0.445315 | ||||||||
\(218\) | 9.68430 | 0.655904 | ||||||||
\(219\) | 8.20986 | 0.554771 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.18892 | −0.416312 | ||||||||
\(222\) | 6.29745 | 0.422657 | ||||||||
\(223\) | −8.60705 | −0.576371 | −0.288185 | − | 0.957575i | \(-0.593052\pi\) | ||||
−0.288185 | + | 0.957575i | \(0.593052\pi\) | |||||||
\(224\) | 11.6165 | 0.776158 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7.74636 | −0.515280 | ||||||||
\(227\) | 29.0547 | 1.92843 | 0.964214 | − | 0.265124i | \(-0.0854129\pi\) | ||||
0.964214 | + | 0.265124i | \(0.0854129\pi\) | |||||||
\(228\) | 2.25308 | 0.149214 | ||||||||
\(229\) | 5.27755 | 0.348750 | 0.174375 | − | 0.984679i | \(-0.444209\pi\) | ||||
0.174375 | + | 0.984679i | \(0.444209\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.621456 | −0.0408888 | ||||||||
\(232\) | 10.4567 | 0.686517 | ||||||||
\(233\) | 25.5165 | 1.67164 | 0.835821 | − | 0.549002i | \(-0.184992\pi\) | ||||
0.835821 | + | 0.549002i | \(0.184992\pi\) | |||||||
\(234\) | 4.39379 | 0.287231 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0.551342 | 0.0358893 | ||||||||
\(237\) | −13.2865 | −0.863051 | ||||||||
\(238\) | 14.1926 | 0.919968 | ||||||||
\(239\) | 23.0647 | 1.49193 | 0.745966 | − | 0.665984i | \(-0.231988\pi\) | ||||
0.745966 | + | 0.665984i | \(0.231988\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.2707 | −1.37017 | −0.685083 | − | 0.728465i | \(-0.740234\pi\) | ||||
−0.685083 | + | 0.728465i | \(0.740234\pi\) | |||||||
\(242\) | 27.9133 | 1.79433 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 10.4852 | 0.671246 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −20.0188 | −1.27635 | ||||||||
\(247\) | 0.827913 | 0.0526788 | ||||||||
\(248\) | −29.4124 | −1.86769 | ||||||||
\(249\) | 6.59494 | 0.417937 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.9282 | 1.19474 | 0.597370 | − | 0.801966i | \(-0.296213\pi\) | ||||
0.597370 | + | 0.801966i | \(0.296213\pi\) | |||||||
\(252\) | −7.04112 | −0.443549 | ||||||||
\(253\) | 3.16144 | 0.198758 | ||||||||
\(254\) | −25.1931 | −1.58075 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −24.4918 | −1.53074 | ||||||||
\(257\) | −21.7891 | −1.35916 | −0.679582 | − | 0.733599i | \(-0.737839\pi\) | ||||
−0.679582 | + | 0.733599i | \(0.737839\pi\) | |||||||
\(258\) | 19.5701 | 1.21838 | ||||||||
\(259\) | −3.70830 | −0.230423 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.53695 | −0.0951350 | ||||||||
\(262\) | 18.2224 | 1.12579 | ||||||||
\(263\) | 11.1448 | 0.687219 | 0.343610 | − | 0.939113i | \(-0.388350\pi\) | ||||
0.343610 | + | 0.939113i | \(0.388350\pi\) | |||||||
\(264\) | −2.78640 | −0.171491 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.89859 | −0.116410 | ||||||||
\(267\) | −17.7958 | −1.08908 | ||||||||
\(268\) | 73.2549 | 4.47475 | ||||||||
\(269\) | 25.8889 | 1.57848 | 0.789238 | − | 0.614088i | \(-0.210476\pi\) | ||||
0.789238 | + | 0.614088i | \(0.210476\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.7769 | 1.07987 | 0.539934 | − | 0.841707i | \(-0.318449\pi\) | ||||
0.539934 | + | 0.841707i | \(0.318449\pi\) | |||||||
\(272\) | 29.9496 | 1.81596 | ||||||||
\(273\) | −2.58731 | −0.156591 | ||||||||
\(274\) | 1.42261 | 0.0859433 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 35.8192 | 2.15606 | ||||||||
\(277\) | 23.2875 | 1.39921 | 0.699604 | − | 0.714531i | \(-0.253360\pi\) | ||||
0.699604 | + | 0.714531i | \(0.253360\pi\) | |||||||
\(278\) | 9.07615 | 0.544351 | ||||||||
\(279\) | 4.32311 | 0.258818 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.6599 | 1.11316 | 0.556578 | − | 0.830795i | \(-0.312114\pi\) | ||||
0.556578 | + | 0.830795i | \(0.312114\pi\) | |||||||
\(282\) | −2.57687 | −0.153450 | ||||||||
\(283\) | 25.1730 | 1.49638 | 0.748189 | − | 0.663486i | \(-0.230924\pi\) | ||||
0.748189 | + | 0.663486i | \(0.230924\pi\) | |||||||
\(284\) | −44.0902 | −2.61627 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.79949 | −0.106406 | ||||||||
\(287\) | 11.7882 | 0.695836 | ||||||||
\(288\) | −7.65548 | −0.451104 | ||||||||
\(289\) | −3.82546 | −0.225027 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.61258 | −0.329016 | ||||||||
\(292\) | −38.0957 | −2.22938 | ||||||||
\(293\) | −28.6924 | −1.67622 | −0.838112 | − | 0.545497i | \(-0.816341\pi\) | ||||
−0.838112 | + | 0.545497i | \(0.816341\pi\) | |||||||
\(294\) | −12.1048 | −0.705965 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −16.6268 | −0.966411 | ||||||||
\(297\) | 0.409552 | 0.0237646 | ||||||||
\(298\) | 10.7863 | 0.624833 | ||||||||
\(299\) | 13.1620 | 0.761180 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.5240 | −0.664231 | ||||||||
\(302\) | 40.9786 | 2.35806 | ||||||||
\(303\) | −1.93695 | −0.111275 | ||||||||
\(304\) | −4.00646 | −0.229786 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −9.35318 | −0.534686 | ||||||||
\(307\) | −8.58383 | −0.489905 | −0.244953 | − | 0.969535i | \(-0.578772\pi\) | ||||
−0.244953 | + | 0.969535i | \(0.578772\pi\) | |||||||
\(308\) | 2.88371 | 0.164314 | ||||||||
\(309\) | −6.55151 | −0.372703 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.5732 | 0.769664 | 0.384832 | − | 0.922987i | \(-0.374259\pi\) | ||||
0.384832 | + | 0.922987i | \(0.374259\pi\) | |||||||
\(312\) | −11.6006 | −0.656757 | ||||||||
\(313\) | 7.43322 | 0.420151 | 0.210075 | − | 0.977685i | \(-0.432629\pi\) | ||||
0.210075 | + | 0.977685i | \(0.432629\pi\) | |||||||
\(314\) | 33.8947 | 1.91279 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 61.6525 | 3.46822 | ||||||||
\(317\) | 16.1762 | 0.908543 | 0.454272 | − | 0.890863i | \(-0.349900\pi\) | ||||
0.454272 | + | 0.890863i | \(0.349900\pi\) | |||||||
\(318\) | −26.2925 | −1.47441 | ||||||||
\(319\) | 0.629462 | 0.0352431 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.241779 | −0.0134948 | ||||||||
\(322\) | −30.1835 | −1.68206 | ||||||||
\(323\) | −1.76240 | −0.0980626 | ||||||||
\(324\) | 4.64024 | 0.257791 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −7.28203 | −0.403315 | ||||||||
\(327\) | 3.75817 | 0.207827 | ||||||||
\(328\) | 52.8544 | 2.91839 | ||||||||
\(329\) | 1.51741 | 0.0836573 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23.9233 | 1.31494 | 0.657472 | − | 0.753479i | \(-0.271626\pi\) | ||||
0.657472 | + | 0.753479i | \(0.271626\pi\) | |||||||
\(332\) | −30.6021 | −1.67951 | ||||||||
\(333\) | 2.44384 | 0.133922 | ||||||||
\(334\) | −32.4778 | −1.77710 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 12.5206 | 0.683055 | ||||||||
\(337\) | 0.151324 | 0.00824317 | 0.00412158 | − | 0.999992i | \(-0.498688\pi\) | ||||
0.00412158 | + | 0.999992i | \(0.498688\pi\) | |||||||
\(338\) | 26.0074 | 1.41462 | ||||||||
\(339\) | −3.00612 | −0.163270 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.77054 | −0.0958799 | ||||||||
\(342\) | 1.25121 | 0.0676575 | ||||||||
\(343\) | 17.7498 | 0.958400 | ||||||||
\(344\) | −51.6696 | −2.78584 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 39.6230 | 2.13014 | ||||||||
\(347\) | 6.17087 | 0.331270 | 0.165635 | − | 0.986187i | \(-0.447033\pi\) | ||||
0.165635 | + | 0.986187i | \(0.447033\pi\) | |||||||
\(348\) | 7.13183 | 0.382306 | ||||||||
\(349\) | 27.4329 | 1.46845 | 0.734226 | − | 0.678905i | \(-0.237545\pi\) | ||||
0.734226 | + | 0.678905i | \(0.237545\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.70509 | 0.0910110 | ||||||||
\(352\) | 3.13532 | 0.167113 | ||||||||
\(353\) | 30.5374 | 1.62534 | 0.812671 | − | 0.582723i | \(-0.198013\pi\) | ||||
0.812671 | + | 0.582723i | \(0.198013\pi\) | |||||||
\(354\) | 0.306177 | 0.0162731 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 82.5767 | 4.37656 | ||||||||
\(357\) | 5.50769 | 0.291498 | ||||||||
\(358\) | 62.4526 | 3.30072 | ||||||||
\(359\) | −2.99142 | −0.157881 | −0.0789406 | − | 0.996879i | \(-0.525154\pi\) | ||||
−0.0789406 | + | 0.996879i | \(0.525154\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.7642 | −0.987591 | ||||||||
\(362\) | 19.3626 | 1.01768 | ||||||||
\(363\) | 10.8323 | 0.568547 | ||||||||
\(364\) | 12.0057 | 0.629272 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 5.82275 | 0.304360 | ||||||||
\(367\) | 5.64402 | 0.294615 | 0.147308 | − | 0.989091i | \(-0.452939\pi\) | ||||
0.147308 | + | 0.989091i | \(0.452939\pi\) | |||||||
\(368\) | −63.6941 | −3.32029 | ||||||||
\(369\) | −7.76866 | −0.404420 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 15.4825 | 0.803813 | ||||||||
\(372\) | −20.0602 | −1.04007 | ||||||||
\(373\) | −32.7211 | −1.69423 | −0.847116 | − | 0.531408i | \(-0.821663\pi\) | ||||
−0.847116 | + | 0.531408i | \(0.821663\pi\) | |||||||
\(374\) | 3.83062 | 0.198076 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.80354 | 0.350866 | ||||||||
\(377\) | 2.62064 | 0.134970 | ||||||||
\(378\) | −3.91015 | −0.201116 | ||||||||
\(379\) | −16.4931 | −0.847194 | −0.423597 | − | 0.905851i | \(-0.639233\pi\) | ||||
−0.423597 | + | 0.905851i | \(0.639233\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.77663 | −0.500872 | ||||||||
\(382\) | −37.8045 | −1.93425 | ||||||||
\(383\) | −11.3694 | −0.580950 | −0.290475 | − | 0.956883i | \(-0.593813\pi\) | ||||
−0.290475 | + | 0.956883i | \(0.593813\pi\) | |||||||
\(384\) | −7.00185 | −0.357312 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −10.3113 | −0.524833 | ||||||||
\(387\) | 7.59452 | 0.386051 | ||||||||
\(388\) | 26.0437 | 1.32217 | ||||||||
\(389\) | −4.34727 | −0.220415 | −0.110208 | − | 0.993909i | \(-0.535152\pi\) | ||||
−0.110208 | + | 0.993909i | \(0.535152\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −28.0184 | −1.41695 | ||||||||
\(392\) | 31.9595 | 1.61420 | ||||||||
\(393\) | 7.07155 | 0.356713 | ||||||||
\(394\) | 44.1759 | 2.22555 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.90042 | −0.0954996 | ||||||||
\(397\) | 23.3610 | 1.17245 | 0.586227 | − | 0.810147i | \(-0.300613\pi\) | ||||
0.586227 | + | 0.810147i | \(0.300613\pi\) | |||||||
\(398\) | 30.9491 | 1.55134 | ||||||||
\(399\) | −0.736781 | −0.0368852 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.43302 | −0.0715614 | −0.0357807 | − | 0.999360i | \(-0.511392\pi\) | ||||
−0.0357807 | + | 0.999360i | \(0.511392\pi\) | |||||||
\(402\) | 40.6807 | 2.02897 | ||||||||
\(403\) | −7.37129 | −0.367190 | ||||||||
\(404\) | 8.98793 | 0.447166 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −6.00972 | −0.298257 | ||||||||
\(407\) | −1.00088 | −0.0496118 | ||||||||
\(408\) | 24.6946 | 1.22257 | ||||||||
\(409\) | 10.2611 | 0.507378 | 0.253689 | − | 0.967286i | \(-0.418356\pi\) | ||||
0.253689 | + | 0.967286i | \(0.418356\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.552072 | 0.0272317 | ||||||||
\(412\) | 30.4006 | 1.49773 | ||||||||
\(413\) | −0.180295 | −0.00887171 | ||||||||
\(414\) | 19.8915 | 0.977614 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 13.0533 | 0.639990 | ||||||||
\(417\) | 3.52217 | 0.172481 | ||||||||
\(418\) | −0.512434 | −0.0250640 | ||||||||
\(419\) | 4.69348 | 0.229291 | 0.114646 | − | 0.993406i | \(-0.463427\pi\) | ||||
0.114646 | + | 0.993406i | \(0.463427\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.7878 | 0.769448 | 0.384724 | − | 0.923032i | \(-0.374297\pi\) | ||||
0.384724 | + | 0.923032i | \(0.374297\pi\) | |||||||
\(422\) | −67.3706 | −3.27955 | ||||||||
\(423\) | −1.00000 | −0.0486217 | ||||||||
\(424\) | 69.4185 | 3.37126 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −24.4847 | −1.18629 | ||||||||
\(427\) | −3.42877 | −0.165930 | ||||||||
\(428\) | 1.12191 | 0.0542297 | ||||||||
\(429\) | −0.698323 | −0.0337154 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.5978 | 0.751319 | 0.375659 | − | 0.926758i | \(-0.377416\pi\) | ||||
0.375659 | + | 0.926758i | \(0.377416\pi\) | |||||||
\(432\) | −8.25132 | −0.396992 | ||||||||
\(433\) | 31.9312 | 1.53452 | 0.767259 | − | 0.641338i | \(-0.221620\pi\) | ||||
0.767259 | + | 0.641338i | \(0.221620\pi\) | |||||||
\(434\) | 16.9040 | 0.811418 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −17.4388 | −0.835167 | ||||||||
\(437\) | 3.74811 | 0.179297 | ||||||||
\(438\) | −21.1557 | −1.01086 | ||||||||
\(439\) | 37.0698 | 1.76925 | 0.884623 | − | 0.466307i | \(-0.154416\pi\) | ||||
0.884623 | + | 0.466307i | \(0.154416\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.69748 | −0.223690 | ||||||||
\(442\) | 15.9480 | 0.758570 | ||||||||
\(443\) | 29.5069 | 1.40192 | 0.700958 | − | 0.713202i | \(-0.252756\pi\) | ||||
0.700958 | + | 0.713202i | \(0.252756\pi\) | |||||||
\(444\) | −11.3400 | −0.538173 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 22.1792 | 1.05022 | ||||||||
\(447\) | 4.18581 | 0.197982 | ||||||||
\(448\) | −4.89288 | −0.231167 | ||||||||
\(449\) | 7.79984 | 0.368097 | 0.184049 | − | 0.982917i | \(-0.441080\pi\) | ||||
0.184049 | + | 0.982917i | \(0.441080\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.18167 | 0.149819 | ||||||||
\(452\) | 13.9491 | 0.656110 | ||||||||
\(453\) | 15.9025 | 0.747165 | ||||||||
\(454\) | −74.8701 | −3.51383 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.30348 | −0.154700 | ||||||||
\(457\) | 21.6451 | 1.01252 | 0.506258 | − | 0.862382i | \(-0.331028\pi\) | ||||
0.506258 | + | 0.862382i | \(0.331028\pi\) | |||||||
\(458\) | −13.5995 | −0.635465 | ||||||||
\(459\) | −3.62967 | −0.169419 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −35.0177 | −1.63094 | −0.815469 | − | 0.578801i | \(-0.803521\pi\) | ||||
−0.815469 | + | 0.578801i | \(0.803521\pi\) | |||||||
\(462\) | 1.60141 | 0.0745043 | ||||||||
\(463\) | 13.1365 | 0.610503 | 0.305252 | − | 0.952272i | \(-0.401259\pi\) | ||||
0.305252 | + | 0.952272i | \(0.401259\pi\) | |||||||
\(464\) | −12.6819 | −0.588742 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −65.7526 | −3.04593 | ||||||||
\(467\) | 15.5109 | 0.717757 | 0.358878 | − | 0.933384i | \(-0.383159\pi\) | ||||
0.358878 | + | 0.933384i | \(0.383159\pi\) | |||||||
\(468\) | −7.91202 | −0.365733 | ||||||||
\(469\) | −23.9551 | −1.10614 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13.1534 | 0.606079 | ||||||||
\(472\) | −0.808380 | −0.0372087 | ||||||||
\(473\) | −3.11035 | −0.143014 | ||||||||
\(474\) | 34.2375 | 1.57258 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −25.5570 | −1.17140 | ||||||||
\(477\) | −10.2033 | −0.467177 | ||||||||
\(478\) | −59.4347 | −2.71848 | ||||||||
\(479\) | 18.6295 | 0.851204 | 0.425602 | − | 0.904910i | \(-0.360062\pi\) | ||||
0.425602 | + | 0.904910i | \(0.360062\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.16697 | −0.189998 | ||||||||
\(482\) | 54.8117 | 2.49661 | ||||||||
\(483\) | −11.7132 | −0.532971 | ||||||||
\(484\) | −50.2643 | −2.28474 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 2.57687 | 0.116889 | ||||||||
\(487\) | −36.0131 | −1.63191 | −0.815955 | − | 0.578115i | \(-0.803788\pi\) | ||||
−0.815955 | + | 0.578115i | \(0.803788\pi\) | |||||||
\(488\) | −15.3734 | −0.695923 | ||||||||
\(489\) | −2.82593 | −0.127793 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.0040 | 0.767379 | 0.383690 | − | 0.923462i | \(-0.374653\pi\) | ||||
0.383690 | + | 0.923462i | \(0.374653\pi\) | |||||||
\(492\) | 36.0484 | 1.62519 | ||||||||
\(493\) | −5.57864 | −0.251249 | ||||||||
\(494\) | −2.13342 | −0.0959871 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 35.6714 | 1.60169 | ||||||||
\(497\) | 14.4180 | 0.646734 | ||||||||
\(498\) | −16.9943 | −0.761531 | ||||||||
\(499\) | −20.0215 | −0.896283 | −0.448142 | − | 0.893963i | \(-0.647914\pi\) | ||||
−0.448142 | + | 0.893963i | \(0.647914\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −12.6036 | −0.563087 | ||||||||
\(502\) | −48.7755 | −2.17696 | ||||||||
\(503\) | −1.34377 | −0.0599159 | −0.0299579 | − | 0.999551i | \(-0.509537\pi\) | ||||
−0.0299579 | + | 0.999551i | \(0.509537\pi\) | |||||||
\(504\) | 10.3237 | 0.459855 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −8.14660 | −0.362161 | ||||||||
\(507\) | 10.0927 | 0.448231 | ||||||||
\(508\) | 45.3659 | 2.01279 | ||||||||
\(509\) | 37.6244 | 1.66767 | 0.833837 | − | 0.552011i | \(-0.186139\pi\) | ||||
0.833837 | + | 0.552011i | \(0.186139\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.4577 | 0.551095 | ||||||||
\(512\) | 49.1085 | 2.17031 | ||||||||
\(513\) | 0.485553 | 0.0214377 | ||||||||
\(514\) | 56.1475 | 2.47656 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −35.2404 | −1.55137 | ||||||||
\(517\) | 0.409552 | 0.0180121 | ||||||||
\(518\) | 9.55579 | 0.419857 | ||||||||
\(519\) | 15.3764 | 0.674950 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −23.1702 | −1.01510 | −0.507551 | − | 0.861621i | \(-0.669449\pi\) | ||||
−0.507551 | + | 0.861621i | \(0.669449\pi\) | |||||||
\(522\) | 3.96052 | 0.173347 | ||||||||
\(523\) | −41.1342 | −1.79867 | −0.899335 | − | 0.437259i | \(-0.855949\pi\) | ||||
−0.899335 | + | 0.437259i | \(0.855949\pi\) | |||||||
\(524\) | −32.8137 | −1.43347 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −28.7187 | −1.25220 | ||||||||
\(527\) | 15.6915 | 0.683531 | ||||||||
\(528\) | 3.37935 | 0.147067 | ||||||||
\(529\) | 36.5870 | 1.59074 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.118818 | 0.00515625 | ||||||||
\(532\) | 3.41884 | 0.148226 | ||||||||
\(533\) | 13.2463 | 0.573760 | ||||||||
\(534\) | 45.8574 | 1.98444 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −107.407 | −4.63926 | ||||||||
\(537\) | 24.2359 | 1.04586 | ||||||||
\(538\) | −66.7123 | −2.87617 | ||||||||
\(539\) | 1.92386 | 0.0828666 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.92870 | 0.340882 | 0.170441 | − | 0.985368i | \(-0.445481\pi\) | ||||
0.170441 | + | 0.985368i | \(0.445481\pi\) | |||||||
\(542\) | −45.8086 | −1.96765 | ||||||||
\(543\) | 7.51402 | 0.322458 | ||||||||
\(544\) | −27.7869 | −1.19135 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 6.66716 | 0.285328 | ||||||||
\(547\) | −18.6294 | −0.796537 | −0.398268 | − | 0.917269i | \(-0.630389\pi\) | ||||
−0.398268 | + | 0.917269i | \(0.630389\pi\) | |||||||
\(548\) | −2.56174 | −0.109432 | ||||||||
\(549\) | 2.25962 | 0.0964384 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.746273 | 0.0317923 | ||||||||
\(552\) | −52.5183 | −2.23533 | ||||||||
\(553\) | −20.1610 | −0.857333 | ||||||||
\(554\) | −60.0087 | −2.54952 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −16.3437 | −0.693127 | ||||||||
\(557\) | 13.1979 | 0.559214 | 0.279607 | − | 0.960115i | \(-0.409796\pi\) | ||||
0.279607 | + | 0.960115i | \(0.409796\pi\) | |||||||
\(558\) | −11.1401 | −0.471597 | ||||||||
\(559\) | −12.9494 | −0.547699 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.48654 | 0.0627618 | ||||||||
\(562\) | −48.0840 | −2.02830 | ||||||||
\(563\) | −6.28490 | −0.264877 | −0.132438 | − | 0.991191i | \(-0.542281\pi\) | ||||
−0.132438 | + | 0.991191i | \(0.542281\pi\) | |||||||
\(564\) | 4.64024 | 0.195389 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −64.8674 | −2.72658 | ||||||||
\(567\) | −1.51741 | −0.0637250 | ||||||||
\(568\) | 64.6453 | 2.71246 | ||||||||
\(569\) | −0.393539 | −0.0164980 | −0.00824900 | − | 0.999966i | \(-0.502626\pi\) | ||||
−0.00824900 | + | 0.999966i | \(0.502626\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.3529 | 1.10284 | 0.551418 | − | 0.834229i | \(-0.314087\pi\) | ||||
0.551418 | + | 0.834229i | \(0.314087\pi\) | |||||||
\(572\) | 3.24039 | 0.135487 | ||||||||
\(573\) | −14.6707 | −0.612879 | ||||||||
\(574\) | −30.3766 | −1.26790 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 3.22450 | 0.134354 | ||||||||
\(577\) | 29.8939 | 1.24450 | 0.622249 | − | 0.782819i | \(-0.286219\pi\) | ||||
0.622249 | + | 0.782819i | \(0.286219\pi\) | |||||||
\(578\) | 9.85770 | 0.410026 | ||||||||
\(579\) | −4.00150 | −0.166297 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.0072 | 0.415168 | ||||||||
\(582\) | 14.4629 | 0.599506 | ||||||||
\(583\) | 4.17878 | 0.173067 | ||||||||
\(584\) | 55.8561 | 2.31134 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 73.9363 | 3.05428 | ||||||||
\(587\) | 33.5669 | 1.38545 | 0.692727 | − | 0.721200i | \(-0.256409\pi\) | ||||
0.692727 | + | 0.721200i | \(0.256409\pi\) | |||||||
\(588\) | 21.7974 | 0.898911 | ||||||||
\(589\) | −2.09910 | −0.0864919 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 17.1433 | 0.705181 | ||||||||
\(592\) | 20.1649 | 0.828774 | ||||||||
\(593\) | 16.7068 | 0.686067 | 0.343033 | − | 0.939323i | \(-0.388546\pi\) | ||||
0.343033 | + | 0.939323i | \(0.388546\pi\) | |||||||
\(594\) | −1.05536 | −0.0433020 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −19.4232 | −0.795604 | ||||||||
\(597\) | 12.0104 | 0.491551 | ||||||||
\(598\) | −33.9168 | −1.38696 | ||||||||
\(599\) | −31.9754 | −1.30648 | −0.653241 | − | 0.757150i | \(-0.726591\pi\) | ||||
−0.653241 | + | 0.757150i | \(0.726591\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.4369 | 0.466520 | 0.233260 | − | 0.972414i | \(-0.425061\pi\) | ||||
0.233260 | + | 0.972414i | \(0.425061\pi\) | |||||||
\(602\) | 29.6957 | 1.21031 | ||||||||
\(603\) | 15.7869 | 0.642892 | ||||||||
\(604\) | −73.7914 | −3.00253 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 4.99127 | 0.202756 | ||||||||
\(607\) | 0.310562 | 0.0126053 | 0.00630266 | − | 0.999980i | \(-0.497994\pi\) | ||||
0.00630266 | + | 0.999980i | \(0.497994\pi\) | |||||||
\(608\) | 3.71715 | 0.150750 | ||||||||
\(609\) | −2.33218 | −0.0945047 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.70509 | 0.0689806 | ||||||||
\(612\) | 16.8426 | 0.680820 | ||||||||
\(613\) | 11.6310 | 0.469770 | 0.234885 | − | 0.972023i | \(-0.424529\pi\) | ||||
0.234885 | + | 0.972023i | \(0.424529\pi\) | |||||||
\(614\) | 22.1194 | 0.892665 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.22810 | −0.170355 | ||||||||
\(617\) | −13.0457 | −0.525199 | −0.262599 | − | 0.964905i | \(-0.584580\pi\) | ||||
−0.262599 | + | 0.964905i | \(0.584580\pi\) | |||||||
\(618\) | 16.8824 | 0.679108 | ||||||||
\(619\) | 23.8892 | 0.960190 | 0.480095 | − | 0.877217i | \(-0.340602\pi\) | ||||
0.480095 | + | 0.877217i | \(0.340602\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.71926 | 0.309763 | ||||||||
\(622\) | −34.9763 | −1.40242 | ||||||||
\(623\) | −27.0034 | −1.08187 | ||||||||
\(624\) | 14.0693 | 0.563221 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −19.1544 | −0.765565 | ||||||||
\(627\) | −0.198859 | −0.00794168 | ||||||||
\(628\) | −61.0351 | −2.43557 | ||||||||
\(629\) | 8.87035 | 0.353684 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.97907 | −0.158404 | −0.0792022 | − | 0.996859i | \(-0.525237\pi\) | ||||
−0.0792022 | + | 0.996859i | \(0.525237\pi\) | |||||||
\(632\) | −90.3952 | −3.59573 | ||||||||
\(633\) | −26.1444 | −1.03915 | ||||||||
\(634\) | −41.6838 | −1.65547 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 47.3457 | 1.87738 | ||||||||
\(637\) | 8.00963 | 0.317353 | ||||||||
\(638\) | −1.62204 | −0.0642172 | ||||||||
\(639\) | −9.50172 | −0.375882 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.7620 | 0.662060 | 0.331030 | − | 0.943620i | \(-0.392604\pi\) | ||||
0.331030 | + | 0.943620i | \(0.392604\pi\) | |||||||
\(642\) | 0.623032 | 0.0245891 | ||||||||
\(643\) | −1.13421 | −0.0447289 | −0.0223644 | − | 0.999750i | \(-0.507119\pi\) | ||||
−0.0223644 | + | 0.999750i | \(0.507119\pi\) | |||||||
\(644\) | 54.3522 | 2.14178 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.54147 | 0.178682 | ||||||||
\(647\) | −24.1301 | −0.948652 | −0.474326 | − | 0.880349i | \(-0.657308\pi\) | ||||
−0.474326 | + | 0.880349i | \(0.657308\pi\) | |||||||
\(648\) | −6.80354 | −0.267268 | ||||||||
\(649\) | −0.0486620 | −0.00191015 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.55990 | 0.257103 | ||||||||
\(652\) | 13.1130 | 0.513543 | ||||||||
\(653\) | 3.75913 | 0.147106 | 0.0735531 | − | 0.997291i | \(-0.476566\pi\) | ||||
0.0735531 | + | 0.997291i | \(0.476566\pi\) | |||||||
\(654\) | −9.68430 | −0.378686 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −64.1017 | −2.50275 | ||||||||
\(657\) | −8.20986 | −0.320297 | ||||||||
\(658\) | −3.91015 | −0.152434 | ||||||||
\(659\) | −10.4017 | −0.405193 | −0.202597 | − | 0.979262i | \(-0.564938\pi\) | ||||
−0.202597 | + | 0.979262i | \(0.564938\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.27614 | −0.283009 | −0.141505 | − | 0.989938i | \(-0.545194\pi\) | ||||
−0.141505 | + | 0.989938i | \(0.545194\pi\) | |||||||
\(662\) | −61.6472 | −2.39598 | ||||||||
\(663\) | 6.18892 | 0.240358 | ||||||||
\(664\) | 44.8689 | 1.74125 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −6.29745 | −0.244021 | ||||||||
\(667\) | 11.8641 | 0.459381 | ||||||||
\(668\) | 58.4837 | 2.26280 | ||||||||
\(669\) | 8.60705 | 0.332768 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.925434 | −0.0357260 | ||||||||
\(672\) | −11.6165 | −0.448115 | ||||||||
\(673\) | 31.4216 | 1.21121 | 0.605607 | − | 0.795764i | \(-0.292930\pi\) | ||||
0.605607 | + | 0.795764i | \(0.292930\pi\) | |||||||
\(674\) | −0.389943 | −0.0150200 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −46.8324 | −1.80124 | ||||||||
\(677\) | 19.6313 | 0.754493 | 0.377247 | − | 0.926113i | \(-0.376871\pi\) | ||||
0.377247 | + | 0.926113i | \(0.376871\pi\) | |||||||
\(678\) | 7.74636 | 0.297497 | ||||||||
\(679\) | −8.51657 | −0.326836 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −29.0547 | −1.11338 | ||||||||
\(682\) | 4.56244 | 0.174705 | ||||||||
\(683\) | −3.80221 | −0.145487 | −0.0727437 | − | 0.997351i | \(-0.523176\pi\) | ||||
−0.0727437 | + | 0.997351i | \(0.523176\pi\) | |||||||
\(684\) | −2.25308 | −0.0861488 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −45.7389 | −1.74632 | ||||||||
\(687\) | −5.27755 | −0.201351 | ||||||||
\(688\) | 62.6649 | 2.38908 | ||||||||
\(689\) | 17.3975 | 0.662794 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 47.0061 | 1.78819 | 0.894097 | − | 0.447873i | \(-0.147818\pi\) | ||||
0.894097 | + | 0.447873i | \(0.147818\pi\) | |||||||
\(692\) | −71.3502 | −2.71233 | ||||||||
\(693\) | 0.621456 | 0.0236072 | ||||||||
\(694\) | −15.9015 | −0.603613 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −10.4567 | −0.396361 | ||||||||
\(697\) | −28.1977 | −1.06806 | ||||||||
\(698\) | −70.6910 | −2.67569 | ||||||||
\(699\) | −25.5165 | −0.965123 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 37.4539 | 1.41461 | 0.707307 | − | 0.706906i | \(-0.249910\pi\) | ||||
0.707307 | + | 0.706906i | \(0.249910\pi\) | |||||||
\(702\) | −4.39379 | −0.165833 | ||||||||
\(703\) | −1.18662 | −0.0447541 | ||||||||
\(704\) | −1.32060 | −0.0497721 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −78.6907 | −2.96157 | ||||||||
\(707\) | −2.93914 | −0.110538 | ||||||||
\(708\) | −0.551342 | −0.0207207 | ||||||||
\(709\) | 34.7204 | 1.30395 | 0.651976 | − | 0.758240i | \(-0.273940\pi\) | ||||
0.651976 | + | 0.758240i | \(0.273940\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13.2865 | 0.498283 | ||||||||
\(712\) | −121.074 | −4.53745 | ||||||||
\(713\) | −33.3712 | −1.24976 | ||||||||
\(714\) | −14.1926 | −0.531144 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −112.460 | −4.20284 | ||||||||
\(717\) | −23.0647 | −0.861368 | ||||||||
\(718\) | 7.70850 | 0.287679 | ||||||||
\(719\) | −15.7765 | −0.588363 | −0.294181 | − | 0.955750i | \(-0.595047\pi\) | ||||
−0.294181 | + | 0.955750i | \(0.595047\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.94130 | −0.370233 | ||||||||
\(722\) | 48.3529 | 1.79951 | ||||||||
\(723\) | 21.2707 | 0.791066 | ||||||||
\(724\) | −34.8669 | −1.29582 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −27.9133 | −1.03596 | ||||||||
\(727\) | 9.80778 | 0.363750 | 0.181875 | − | 0.983322i | \(-0.441783\pi\) | ||||
0.181875 | + | 0.983322i | \(0.441783\pi\) | |||||||
\(728\) | −17.6029 | −0.652406 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 27.5657 | 1.01955 | ||||||||
\(732\) | −10.4852 | −0.387544 | ||||||||
\(733\) | −29.9733 | −1.10709 | −0.553544 | − | 0.832820i | \(-0.686725\pi\) | ||||
−0.553544 | + | 0.832820i | \(0.686725\pi\) | |||||||
\(734\) | −14.5439 | −0.536824 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 59.0947 | 2.17826 | ||||||||
\(737\) | −6.46555 | −0.238162 | ||||||||
\(738\) | 20.0188 | 0.736902 | ||||||||
\(739\) | 20.7720 | 0.764109 | 0.382055 | − | 0.924140i | \(-0.375217\pi\) | ||||
0.382055 | + | 0.924140i | \(0.375217\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.827913 | −0.0304141 | ||||||||
\(742\) | −39.8964 | −1.46464 | ||||||||
\(743\) | −30.5350 | −1.12022 | −0.560110 | − | 0.828418i | \(-0.689241\pi\) | ||||
−0.560110 | + | 0.828418i | \(0.689241\pi\) | |||||||
\(744\) | 29.4124 | 1.07831 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 84.3178 | 3.08709 | ||||||||
\(747\) | −6.59494 | −0.241296 | ||||||||
\(748\) | −6.89790 | −0.252212 | ||||||||
\(749\) | −0.366877 | −0.0134054 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −30.9000 | −1.12756 | −0.563779 | − | 0.825926i | \(-0.690653\pi\) | ||||
−0.563779 | + | 0.825926i | \(0.690653\pi\) | |||||||
\(752\) | −8.25132 | −0.300895 | ||||||||
\(753\) | −18.9282 | −0.689783 | ||||||||
\(754\) | −6.75305 | −0.245931 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 7.04112 | 0.256083 | ||||||||
\(757\) | −9.99773 | −0.363374 | −0.181687 | − | 0.983356i | \(-0.558156\pi\) | ||||
−0.181687 | + | 0.983356i | \(0.558156\pi\) | |||||||
\(758\) | 42.5005 | 1.54369 | ||||||||
\(759\) | −3.16144 | −0.114753 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18.0677 | 0.654953 | 0.327476 | − | 0.944859i | \(-0.393802\pi\) | ||||
0.327476 | + | 0.944859i | \(0.393802\pi\) | |||||||
\(762\) | 25.1931 | 0.912648 | ||||||||
\(763\) | 5.70267 | 0.206451 | ||||||||
\(764\) | 68.0757 | 2.46289 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 29.2975 | 1.05856 | ||||||||
\(767\) | −0.202595 | −0.00731528 | ||||||||
\(768\) | 24.4918 | 0.883773 | ||||||||
\(769\) | 5.15329 | 0.185832 | 0.0929162 | − | 0.995674i | \(-0.470381\pi\) | ||||
0.0929162 | + | 0.995674i | \(0.470381\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 21.7891 | 0.784714 | ||||||||
\(772\) | 18.5679 | 0.668273 | ||||||||
\(773\) | 16.5239 | 0.594322 | 0.297161 | − | 0.954827i | \(-0.403960\pi\) | ||||
0.297161 | + | 0.954827i | \(0.403960\pi\) | |||||||
\(774\) | −19.5701 | −0.703432 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −38.1854 | −1.37078 | ||||||||
\(777\) | 3.70830 | 0.133035 | ||||||||
\(778\) | 11.2023 | 0.401623 | ||||||||
\(779\) | 3.77210 | 0.135149 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.89145 | 0.139247 | ||||||||
\(782\) | 72.1997 | 2.58186 | ||||||||
\(783\) | 1.53695 | 0.0549262 | ||||||||
\(784\) | −38.7604 | −1.38430 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −18.2224 | −0.649973 | ||||||||
\(787\) | 2.05263 | 0.0731684 | 0.0365842 | − | 0.999331i | \(-0.488352\pi\) | ||||
0.0365842 | + | 0.999331i | \(0.488352\pi\) | |||||||
\(788\) | −79.5489 | −2.83381 | ||||||||
\(789\) | −11.1448 | −0.396766 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.56150 | −0.162188 | ||||||||
\(792\) | 2.78640 | 0.0990105 | ||||||||
\(793\) | −3.85286 | −0.136819 | ||||||||
\(794\) | −60.1981 | −2.13635 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −55.7309 | −1.97533 | ||||||||
\(797\) | −37.3883 | −1.32436 | −0.662180 | − | 0.749345i | \(-0.730369\pi\) | ||||
−0.662180 | + | 0.749345i | \(0.730369\pi\) | |||||||
\(798\) | 1.89859 | 0.0672092 | ||||||||
\(799\) | −3.62967 | −0.128409 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 17.7958 | 0.628783 | ||||||||
\(802\) | 3.69269 | 0.130393 | ||||||||
\(803\) | 3.36236 | 0.118655 | ||||||||
\(804\) | −73.2549 | −2.58350 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 18.9948 | 0.669064 | ||||||||
\(807\) | −25.8889 | −0.911333 | ||||||||
\(808\) | −13.1781 | −0.463605 | ||||||||
\(809\) | −23.1030 | −0.812257 | −0.406128 | − | 0.913816i | \(-0.633121\pi\) | ||||
−0.406128 | + | 0.913816i | \(0.633121\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −23.6977 | −0.832140 | −0.416070 | − | 0.909333i | \(-0.636593\pi\) | ||||
−0.416070 | + | 0.909333i | \(0.636593\pi\) | |||||||
\(812\) | 10.8219 | 0.379773 | ||||||||
\(813\) | −17.7769 | −0.623462 | ||||||||
\(814\) | 2.57914 | 0.0903986 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −29.9496 | −1.04845 | ||||||||
\(817\) | −3.68755 | −0.129011 | ||||||||
\(818\) | −26.4414 | −0.924503 | ||||||||
\(819\) | 2.58731 | 0.0904081 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 42.8599 | 1.49582 | 0.747911 | − | 0.663799i | \(-0.231057\pi\) | ||||
0.747911 | + | 0.663799i | \(0.231057\pi\) | |||||||
\(822\) | −1.42261 | −0.0496194 | ||||||||
\(823\) | −22.2558 | −0.775788 | −0.387894 | − | 0.921704i | \(-0.626797\pi\) | ||||
−0.387894 | + | 0.921704i | \(0.626797\pi\) | |||||||
\(824\) | −44.5735 | −1.55279 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.464595 | 0.0161653 | ||||||||
\(827\) | 25.8507 | 0.898917 | 0.449459 | − | 0.893301i | \(-0.351617\pi\) | ||||
0.449459 | + | 0.893301i | \(0.351617\pi\) | |||||||
\(828\) | −35.8192 | −1.24480 | ||||||||
\(829\) | −8.19269 | −0.284544 | −0.142272 | − | 0.989828i | \(-0.545441\pi\) | ||||
−0.142272 | + | 0.989828i | \(0.545441\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −23.2875 | −0.807833 | ||||||||
\(832\) | −5.49807 | −0.190611 | ||||||||
\(833\) | −17.0503 | −0.590759 | ||||||||
\(834\) | −9.07615 | −0.314281 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0.922755 | 0.0319141 | ||||||||
\(837\) | −4.32311 | −0.149428 | ||||||||
\(838\) | −12.0945 | −0.417796 | ||||||||
\(839\) | −13.6146 | −0.470027 | −0.235013 | − | 0.971992i | \(-0.575513\pi\) | ||||
−0.235013 | + | 0.971992i | \(0.575513\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.6378 | −0.918544 | ||||||||
\(842\) | −40.6829 | −1.40203 | ||||||||
\(843\) | −18.6599 | −0.642681 | ||||||||
\(844\) | 121.316 | 4.17588 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 2.57687 | 0.0885945 | ||||||||
\(847\) | 16.4369 | 0.564780 | ||||||||
\(848\) | −84.1907 | −2.89112 | ||||||||
\(849\) | −25.1730 | −0.863934 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −18.8647 | −0.646672 | ||||||||
\(852\) | 44.0902 | 1.51051 | ||||||||
\(853\) | −19.4589 | −0.666261 | −0.333130 | − | 0.942881i | \(-0.608105\pi\) | ||||
−0.333130 | + | 0.942881i | \(0.608105\pi\) | |||||||
\(854\) | 8.83547 | 0.302344 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.64495 | −0.0562233 | ||||||||
\(857\) | −18.3188 | −0.625758 | −0.312879 | − | 0.949793i | \(-0.601293\pi\) | ||||
−0.312879 | + | 0.949793i | \(0.601293\pi\) | |||||||
\(858\) | 1.79949 | 0.0614334 | ||||||||
\(859\) | −57.3781 | −1.95772 | −0.978858 | − | 0.204540i | \(-0.934430\pi\) | ||||
−0.978858 | + | 0.204540i | \(0.934430\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −11.7882 | −0.401741 | ||||||||
\(862\) | −40.1934 | −1.36899 | ||||||||
\(863\) | −18.0524 | −0.614510 | −0.307255 | − | 0.951627i | \(-0.599410\pi\) | ||||
−0.307255 | + | 0.951627i | \(0.599410\pi\) | |||||||
\(864\) | 7.65548 | 0.260445 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −82.2825 | −2.79607 | ||||||||
\(867\) | 3.82546 | 0.129919 | ||||||||
\(868\) | −30.4395 | −1.03318 | ||||||||
\(869\) | −5.44151 | −0.184591 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −26.9181 | −0.912084 | ||||||||
\(872\) | 25.5689 | 0.865871 | ||||||||
\(873\) | 5.61258 | 0.189957 | ||||||||
\(874\) | −9.65838 | −0.326700 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 38.0957 | 1.28713 | ||||||||
\(877\) | 14.4579 | 0.488209 | 0.244105 | − | 0.969749i | \(-0.421506\pi\) | ||||
0.244105 | + | 0.969749i | \(0.421506\pi\) | |||||||
\(878\) | −95.5240 | −3.22378 | ||||||||
\(879\) | 28.6924 | 0.967769 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 56.1913 | 1.89313 | 0.946567 | − | 0.322509i | \(-0.104526\pi\) | ||||
0.946567 | + | 0.322509i | \(0.104526\pi\) | |||||||
\(882\) | 12.1048 | 0.407589 | ||||||||
\(883\) | 41.7329 | 1.40443 | 0.702213 | − | 0.711967i | \(-0.252196\pi\) | ||||
0.702213 | + | 0.711967i | \(0.252196\pi\) | |||||||
\(884\) | −28.7181 | −0.965893 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −76.0354 | −2.55446 | ||||||||
\(887\) | −32.3399 | −1.08587 | −0.542933 | − | 0.839776i | \(-0.682686\pi\) | ||||
−0.542933 | + | 0.839776i | \(0.682686\pi\) | |||||||
\(888\) | 16.6268 | 0.557958 | ||||||||
\(889\) | −14.8351 | −0.497554 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.409552 | −0.0137205 | ||||||||
\(892\) | −39.9388 | −1.33725 | ||||||||
\(893\) | 0.485553 | 0.0162484 | ||||||||
\(894\) | −10.7863 | −0.360747 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −10.6246 | −0.354945 | ||||||||
\(897\) | −13.1620 | −0.439468 | ||||||||
\(898\) | −20.0991 | −0.670717 | ||||||||
\(899\) | −6.64441 | −0.221603 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −37.0347 | −1.23380 | ||||||||
\(902\) | −8.19874 | −0.272988 | ||||||||
\(903\) | 11.5240 | 0.383494 | ||||||||
\(904\) | −20.4522 | −0.680231 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −40.9786 | −1.36142 | ||||||||
\(907\) | −8.06590 | −0.267824 | −0.133912 | − | 0.990993i | \(-0.542754\pi\) | ||||
−0.133912 | + | 0.990993i | \(0.542754\pi\) | |||||||
\(908\) | 134.821 | 4.47418 | ||||||||
\(909\) | 1.93695 | 0.0642447 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.8121 | −0.358222 | −0.179111 | − | 0.983829i | \(-0.557322\pi\) | ||||
−0.179111 | + | 0.983829i | \(0.557322\pi\) | |||||||
\(912\) | 4.00646 | 0.132667 | ||||||||
\(913\) | 2.70097 | 0.0893891 | ||||||||
\(914\) | −55.7766 | −1.84493 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 24.4891 | 0.809142 | ||||||||
\(917\) | 10.7304 | 0.354349 | ||||||||
\(918\) | 9.35318 | 0.308701 | ||||||||
\(919\) | 46.7910 | 1.54349 | 0.771747 | − | 0.635930i | \(-0.219383\pi\) | ||||
0.771747 | + | 0.635930i | \(0.219383\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.58383 | 0.282847 | ||||||||
\(922\) | 90.2360 | 2.97176 | ||||||||
\(923\) | 16.2013 | 0.533272 | ||||||||
\(924\) | −2.88371 | −0.0948669 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −33.8509 | −1.11241 | ||||||||
\(927\) | 6.55151 | 0.215180 | ||||||||
\(928\) | 11.7661 | 0.386242 | ||||||||
\(929\) | −6.27773 | −0.205966 | −0.102983 | − | 0.994683i | \(-0.532839\pi\) | ||||
−0.102983 | + | 0.994683i | \(0.532839\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.28088 | 0.0747527 | ||||||||
\(932\) | 118.403 | 3.87841 | ||||||||
\(933\) | −13.5732 | −0.444366 | ||||||||
\(934\) | −39.9694 | −1.30784 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 11.6006 | 0.379179 | ||||||||
\(937\) | −23.1765 | −0.757145 | −0.378572 | − | 0.925572i | \(-0.623585\pi\) | ||||
−0.378572 | + | 0.925572i | \(0.623585\pi\) | |||||||
\(938\) | 61.7291 | 2.01553 | ||||||||
\(939\) | −7.43322 | −0.242574 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −46.6445 | −1.52057 | −0.760283 | − | 0.649592i | \(-0.774940\pi\) | ||||
−0.760283 | + | 0.649592i | \(0.774940\pi\) | |||||||
\(942\) | −33.8947 | −1.10435 | ||||||||
\(943\) | 59.9683 | 1.95284 | ||||||||
\(944\) | 0.980403 | 0.0319094 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.01496 | 0.260589 | ||||||||
\(947\) | −26.5370 | −0.862336 | −0.431168 | − | 0.902272i | \(-0.641898\pi\) | ||||
−0.431168 | + | 0.902272i | \(0.641898\pi\) | |||||||
\(948\) | −61.6525 | −2.00238 | ||||||||
\(949\) | 13.9986 | 0.454412 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −16.1762 | −0.524548 | ||||||||
\(952\) | 37.4718 | 1.21447 | ||||||||
\(953\) | 3.25613 | 0.105476 | 0.0527381 | − | 0.998608i | \(-0.483205\pi\) | ||||
0.0527381 | + | 0.998608i | \(0.483205\pi\) | |||||||
\(954\) | 26.2925 | 0.851252 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 107.026 | 3.46146 | ||||||||
\(957\) | −0.629462 | −0.0203476 | ||||||||
\(958\) | −48.0058 | −1.55100 | ||||||||
\(959\) | 0.837716 | 0.0270513 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.3108 | −0.397121 | ||||||||
\(962\) | 10.7377 | 0.346198 | ||||||||
\(963\) | 0.241779 | 0.00779122 | ||||||||
\(964\) | −98.7010 | −3.17895 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 30.1835 | 0.971137 | ||||||||
\(967\) | 57.0081 | 1.83326 | 0.916629 | − | 0.399739i | \(-0.130899\pi\) | ||||
0.916629 | + | 0.399739i | \(0.130899\pi\) | |||||||
\(968\) | 73.6977 | 2.36873 | ||||||||
\(969\) | 1.76240 | 0.0566165 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 48.7556 | 1.56464 | 0.782321 | − | 0.622876i | \(-0.214036\pi\) | ||||
0.782321 | + | 0.622876i | \(0.214036\pi\) | |||||||
\(972\) | −4.64024 | −0.148836 | ||||||||
\(973\) | 5.34456 | 0.171339 | ||||||||
\(974\) | 92.8010 | 2.97354 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 18.6449 | 0.596809 | ||||||||
\(977\) | −39.3330 | −1.25838 | −0.629188 | − | 0.777253i | \(-0.716612\pi\) | ||||
−0.629188 | + | 0.777253i | \(0.716612\pi\) | |||||||
\(978\) | 7.28203 | 0.232854 | ||||||||
\(979\) | −7.28830 | −0.232935 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.75817 | −0.119989 | ||||||||
\(982\) | −43.8170 | −1.39826 | ||||||||
\(983\) | −46.2193 | −1.47417 | −0.737083 | − | 0.675802i | \(-0.763797\pi\) | ||||
−0.737083 | + | 0.675802i | \(0.763797\pi\) | |||||||
\(984\) | −52.8544 | −1.68494 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 14.3754 | 0.457806 | ||||||||
\(987\) | −1.51741 | −0.0482995 | ||||||||
\(988\) | 3.84171 | 0.122221 | ||||||||
\(989\) | −58.6241 | −1.86414 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25.4629 | −0.808856 | −0.404428 | − | 0.914570i | \(-0.632529\pi\) | ||||
−0.404428 | + | 0.914570i | \(0.632529\pi\) | |||||||
\(992\) | −33.0955 | −1.05078 | ||||||||
\(993\) | −23.9233 | −0.759183 | ||||||||
\(994\) | −37.1532 | −1.17843 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 30.6021 | 0.969664 | ||||||||
\(997\) | 39.1066 | 1.23852 | 0.619260 | − | 0.785186i | \(-0.287433\pi\) | ||||
0.619260 | + | 0.785186i | \(0.287433\pi\) | |||||||
\(998\) | 51.5926 | 1.63314 | ||||||||
\(999\) | −2.44384 | −0.0773198 |
(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 | 3525.2.a.bh.1.3 | 13 | ||
5.2 | odd | 4 | 705.2.c.c.424.3 | ✓ | 26 | ||
5.3 | odd | 4 | 705.2.c.c.424.24 | yes | 26 | ||
5.4 | even | 2 | 3525.2.a.bi.1.11 | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
705.2.c.c.424.3 | ✓ | 26 | 5.2 | odd | 4 | ||
705.2.c.c.424.24 | yes | 26 | 5.3 | odd | 4 | ||
3525.2.a.bh.1.3 | 13 | 1.1 | even | 1 | trivial | ||
3525.2.a.bi.1.11 | 13 | 5.4 | even | 2 |