Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1925,2,Mod(1,1925)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1925, 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("1925.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1925 = 5^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1925.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: | \(15.3712023891\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 385) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(0.311108\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1925.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.21432 | −0.858654 | −0.429327 | − | 0.903149i | \(-0.641249\pi\) | ||||
−0.429327 | + | 0.903149i | \(0.641249\pi\) | |||||||
\(3\) | 0.688892 | 0.397732 | 0.198866 | − | 0.980027i | \(-0.436274\pi\) | ||||
0.198866 | + | 0.980027i | \(0.436274\pi\) | |||||||
\(4\) | −0.525428 | −0.262714 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.836535 | −0.341514 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 3.06668 | 1.08423 | ||||||||
\(9\) | −2.52543 | −0.841809 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −0.361963 | −0.104490 | ||||||||
\(13\) | 3.73975 | 1.03722 | 0.518610 | − | 0.855011i | \(-0.326450\pi\) | ||||
0.518610 | + | 0.855011i | \(0.326450\pi\) | |||||||
\(14\) | −1.21432 | −0.324541 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.67307 | −0.668268 | ||||||||
\(17\) | −0.0666765 | −0.0161714 | −0.00808572 | − | 0.999967i | \(-0.502574\pi\) | ||||
−0.00808572 | + | 0.999967i | \(0.502574\pi\) | |||||||
\(18\) | 3.06668 | 0.722823 | ||||||||
\(19\) | 6.42864 | 1.47483 | 0.737416 | − | 0.675439i | \(-0.236046\pi\) | ||||
0.737416 | + | 0.675439i | \(0.236046\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.688892 | 0.150329 | ||||||||
\(22\) | 1.21432 | 0.258894 | ||||||||
\(23\) | 1.09679 | 0.228696 | 0.114348 | − | 0.993441i | \(-0.463522\pi\) | ||||
0.114348 | + | 0.993441i | \(0.463522\pi\) | |||||||
\(24\) | 2.11261 | 0.431235 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −4.54125 | −0.890612 | ||||||||
\(27\) | −3.80642 | −0.732547 | ||||||||
\(28\) | −0.525428 | −0.0992965 | ||||||||
\(29\) | −7.80642 | −1.44962 | −0.724808 | − | 0.688951i | \(-0.758072\pi\) | ||||
−0.724808 | + | 0.688951i | \(0.758072\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.59210 | −1.00437 | −0.502186 | − | 0.864760i | \(-0.667471\pi\) | ||||
−0.502186 | + | 0.864760i | \(0.667471\pi\) | |||||||
\(32\) | −2.88739 | −0.510423 | ||||||||
\(33\) | −0.688892 | −0.119921 | ||||||||
\(34\) | 0.0809666 | 0.0138857 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.32693 | 0.221155 | ||||||||
\(37\) | −1.33185 | −0.218955 | −0.109478 | − | 0.993989i | \(-0.534918\pi\) | ||||
−0.109478 | + | 0.993989i | \(0.534918\pi\) | |||||||
\(38\) | −7.80642 | −1.26637 | ||||||||
\(39\) | 2.57628 | 0.412535 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.64296 | 1.03746 | 0.518728 | − | 0.854939i | \(-0.326406\pi\) | ||||
0.518728 | + | 0.854939i | \(0.326406\pi\) | |||||||
\(42\) | −0.836535 | −0.129080 | ||||||||
\(43\) | 11.7605 | 1.79346 | 0.896729 | − | 0.442580i | \(-0.145937\pi\) | ||||
0.896729 | + | 0.442580i | \(0.145937\pi\) | |||||||
\(44\) | 0.525428 | 0.0792112 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.33185 | −0.196371 | ||||||||
\(47\) | 2.26025 | 0.329692 | 0.164846 | − | 0.986319i | \(-0.447287\pi\) | ||||
0.164846 | + | 0.986319i | \(0.447287\pi\) | |||||||
\(48\) | −1.84146 | −0.265792 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.0459330 | −0.00643190 | ||||||||
\(52\) | −1.96497 | −0.272492 | ||||||||
\(53\) | 1.71900 | 0.236123 | 0.118062 | − | 0.993006i | \(-0.462332\pi\) | ||||
0.118062 | + | 0.993006i | \(0.462332\pi\) | |||||||
\(54\) | 4.62222 | 0.629004 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.06668 | 0.409802 | ||||||||
\(57\) | 4.42864 | 0.586588 | ||||||||
\(58\) | 9.47949 | 1.24472 | ||||||||
\(59\) | 2.54125 | 0.330842 | 0.165421 | − | 0.986223i | \(-0.447102\pi\) | ||||
0.165421 | + | 0.986223i | \(0.447102\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.4494 | 1.85005 | 0.925027 | − | 0.379901i | \(-0.124042\pi\) | ||||
0.925027 | + | 0.379901i | \(0.124042\pi\) | |||||||
\(62\) | 6.79060 | 0.862407 | ||||||||
\(63\) | −2.52543 | −0.318174 | ||||||||
\(64\) | 8.85236 | 1.10654 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.836535 | 0.102970 | ||||||||
\(67\) | −10.3827 | −1.26845 | −0.634225 | − | 0.773149i | \(-0.718681\pi\) | ||||
−0.634225 | + | 0.773149i | \(0.718681\pi\) | |||||||
\(68\) | 0.0350337 | 0.00424846 | ||||||||
\(69\) | 0.755569 | 0.0909598 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.5620 | −1.49083 | −0.745417 | − | 0.666598i | \(-0.767750\pi\) | ||||
−0.745417 | + | 0.666598i | \(0.767750\pi\) | |||||||
\(72\) | −7.74467 | −0.912718 | ||||||||
\(73\) | −1.17775 | −0.137846 | −0.0689229 | − | 0.997622i | \(-0.521956\pi\) | ||||
−0.0689229 | + | 0.997622i | \(0.521956\pi\) | |||||||
\(74\) | 1.61729 | 0.188007 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.37778 | −0.387458 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | −3.12843 | −0.354225 | ||||||||
\(79\) | −8.51606 | −0.958132 | −0.479066 | − | 0.877779i | \(-0.659024\pi\) | ||||
−0.479066 | + | 0.877779i | \(0.659024\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.95407 | 0.550452 | ||||||||
\(82\) | −8.06668 | −0.890815 | ||||||||
\(83\) | 12.1017 | 1.32834 | 0.664168 | − | 0.747584i | \(-0.268786\pi\) | ||||
0.664168 | + | 0.747584i | \(0.268786\pi\) | |||||||
\(84\) | −0.361963 | −0.0394934 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −14.2810 | −1.53996 | ||||||||
\(87\) | −5.37778 | −0.576559 | ||||||||
\(88\) | −3.06668 | −0.326909 | ||||||||
\(89\) | 15.6128 | 1.65496 | 0.827479 | − | 0.561496i | \(-0.189774\pi\) | ||||
0.827479 | + | 0.561496i | \(0.189774\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.73975 | 0.392032 | ||||||||
\(92\) | −0.576283 | −0.0600816 | ||||||||
\(93\) | −3.85236 | −0.399471 | ||||||||
\(94\) | −2.74467 | −0.283091 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.98910 | −0.203012 | ||||||||
\(97\) | 13.4193 | 1.36252 | 0.681260 | − | 0.732041i | \(-0.261432\pi\) | ||||
0.681260 | + | 0.732041i | \(0.261432\pi\) | |||||||
\(98\) | −1.21432 | −0.122665 | ||||||||
\(99\) | 2.52543 | 0.253815 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.44938 | −0.840745 | −0.420373 | − | 0.907352i | \(-0.638101\pi\) | ||||
−0.420373 | + | 0.907352i | \(0.638101\pi\) | |||||||
\(102\) | 0.0557773 | 0.00552277 | ||||||||
\(103\) | 9.54617 | 0.940612 | 0.470306 | − | 0.882503i | \(-0.344144\pi\) | ||||
0.470306 | + | 0.882503i | \(0.344144\pi\) | |||||||
\(104\) | 11.4686 | 1.12459 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.08742 | −0.202748 | ||||||||
\(107\) | 8.56199 | 0.827719 | 0.413860 | − | 0.910341i | \(-0.364180\pi\) | ||||
0.413860 | + | 0.910341i | \(0.364180\pi\) | |||||||
\(108\) | 2.00000 | 0.192450 | ||||||||
\(109\) | −6.99063 | −0.669581 | −0.334791 | − | 0.942293i | \(-0.608666\pi\) | ||||
−0.334791 | + | 0.942293i | \(0.608666\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.917502 | −0.0870854 | ||||||||
\(112\) | −2.67307 | −0.252581 | ||||||||
\(113\) | 1.57136 | 0.147821 | 0.0739106 | − | 0.997265i | \(-0.476452\pi\) | ||||
0.0739106 | + | 0.997265i | \(0.476452\pi\) | |||||||
\(114\) | −5.37778 | −0.503676 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 4.10171 | 0.380834 | ||||||||
\(117\) | −9.44446 | −0.873141 | ||||||||
\(118\) | −3.08589 | −0.284079 | ||||||||
\(119\) | −0.0666765 | −0.00611223 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −17.5462 | −1.58856 | ||||||||
\(123\) | 4.57628 | 0.412630 | ||||||||
\(124\) | 2.93825 | 0.263862 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 3.06668 | 0.273201 | ||||||||
\(127\) | 13.3778 | 1.18709 | 0.593543 | − | 0.804802i | \(-0.297729\pi\) | ||||
0.593543 | + | 0.804802i | \(0.297729\pi\) | |||||||
\(128\) | −4.97481 | −0.439715 | ||||||||
\(129\) | 8.10171 | 0.713316 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.75557 | −0.240755 | −0.120378 | − | 0.992728i | \(-0.538411\pi\) | ||||
−0.120378 | + | 0.992728i | \(0.538411\pi\) | |||||||
\(132\) | 0.361963 | 0.0315048 | ||||||||
\(133\) | 6.42864 | 0.557434 | ||||||||
\(134\) | 12.6079 | 1.08916 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.204475 | −0.0175336 | ||||||||
\(137\) | 17.8938 | 1.52877 | 0.764387 | − | 0.644758i | \(-0.223042\pi\) | ||||
0.764387 | + | 0.644758i | \(0.223042\pi\) | |||||||
\(138\) | −0.917502 | −0.0781030 | ||||||||
\(139\) | −3.86665 | −0.327965 | −0.163982 | − | 0.986463i | \(-0.552434\pi\) | ||||
−0.163982 | + | 0.986463i | \(0.552434\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.55707 | 0.131129 | ||||||||
\(142\) | 15.2543 | 1.28011 | ||||||||
\(143\) | −3.73975 | −0.312733 | ||||||||
\(144\) | 6.75065 | 0.562554 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.43017 | 0.118362 | ||||||||
\(147\) | 0.688892 | 0.0568189 | ||||||||
\(148\) | 0.699791 | 0.0575225 | ||||||||
\(149\) | 4.88892 | 0.400516 | 0.200258 | − | 0.979743i | \(-0.435822\pi\) | ||||
0.200258 | + | 0.979743i | \(0.435822\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 22.1891 | 1.80573 | 0.902863 | − | 0.429929i | \(-0.141461\pi\) | ||||
0.902863 | + | 0.429929i | \(0.141461\pi\) | |||||||
\(152\) | 19.7146 | 1.59906 | ||||||||
\(153\) | 0.168387 | 0.0136133 | ||||||||
\(154\) | 1.21432 | 0.0978527 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.35365 | −0.108379 | ||||||||
\(157\) | 4.81579 | 0.384342 | 0.192171 | − | 0.981361i | \(-0.438447\pi\) | ||||
0.192171 | + | 0.981361i | \(0.438447\pi\) | |||||||
\(158\) | 10.3412 | 0.822703 | ||||||||
\(159\) | 1.18421 | 0.0939138 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.09679 | 0.0864390 | ||||||||
\(162\) | −6.01582 | −0.472648 | ||||||||
\(163\) | −6.08742 | −0.476804 | −0.238402 | − | 0.971167i | \(-0.576624\pi\) | ||||
−0.238402 | + | 0.971167i | \(0.576624\pi\) | |||||||
\(164\) | −3.49039 | −0.272554 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −14.6953 | −1.14058 | ||||||||
\(167\) | 3.67307 | 0.284231 | 0.142115 | − | 0.989850i | \(-0.454610\pi\) | ||||
0.142115 | + | 0.989850i | \(0.454610\pi\) | |||||||
\(168\) | 2.11261 | 0.162991 | ||||||||
\(169\) | 0.985710 | 0.0758238 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −16.2351 | −1.24153 | ||||||||
\(172\) | −6.17929 | −0.471166 | ||||||||
\(173\) | 0.628669 | 0.0477968 | 0.0238984 | − | 0.999714i | \(-0.492392\pi\) | ||||
0.0238984 | + | 0.999714i | \(0.492392\pi\) | |||||||
\(174\) | 6.53035 | 0.495065 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.67307 | 0.201490 | ||||||||
\(177\) | 1.75065 | 0.131587 | ||||||||
\(178\) | −18.9590 | −1.42104 | ||||||||
\(179\) | −7.70471 | −0.575877 | −0.287939 | − | 0.957649i | \(-0.592970\pi\) | ||||
−0.287939 | + | 0.957649i | \(0.592970\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.9175 | 0.811492 | 0.405746 | − | 0.913986i | \(-0.367012\pi\) | ||||
0.405746 | + | 0.913986i | \(0.367012\pi\) | |||||||
\(182\) | −4.54125 | −0.336620 | ||||||||
\(183\) | 9.95407 | 0.735826 | ||||||||
\(184\) | 3.36349 | 0.247960 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 4.67799 | 0.343007 | ||||||||
\(187\) | 0.0666765 | 0.00487587 | ||||||||
\(188\) | −1.18760 | −0.0866146 | ||||||||
\(189\) | −3.80642 | −0.276877 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.9175 | −0.789963 | −0.394981 | − | 0.918689i | \(-0.629249\pi\) | ||||
−0.394981 | + | 0.918689i | \(0.629249\pi\) | |||||||
\(192\) | 6.09832 | 0.440108 | ||||||||
\(193\) | −11.7003 | −0.842204 | −0.421102 | − | 0.907013i | \(-0.638357\pi\) | ||||
−0.421102 | + | 0.907013i | \(0.638357\pi\) | |||||||
\(194\) | −16.2953 | −1.16993 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.525428 | −0.0375305 | ||||||||
\(197\) | −10.8430 | −0.772531 | −0.386265 | − | 0.922388i | \(-0.626235\pi\) | ||||
−0.386265 | + | 0.922388i | \(0.626235\pi\) | |||||||
\(198\) | −3.06668 | −0.217939 | ||||||||
\(199\) | 2.08097 | 0.147516 | 0.0737579 | − | 0.997276i | \(-0.476501\pi\) | ||||
0.0737579 | + | 0.997276i | \(0.476501\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.15257 | −0.504503 | ||||||||
\(202\) | 10.2603 | 0.721909 | ||||||||
\(203\) | −7.80642 | −0.547904 | ||||||||
\(204\) | 0.0241344 | 0.00168975 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −11.5921 | −0.807660 | ||||||||
\(207\) | −2.76986 | −0.192518 | ||||||||
\(208\) | −9.99661 | −0.693140 | ||||||||
\(209\) | −6.42864 | −0.444678 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.0923 | 1.58974 | 0.794871 | − | 0.606778i | \(-0.207538\pi\) | ||||
0.794871 | + | 0.606778i | \(0.207538\pi\) | |||||||
\(212\) | −0.903212 | −0.0620328 | ||||||||
\(213\) | −8.65386 | −0.592953 | ||||||||
\(214\) | −10.3970 | −0.710724 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −11.6731 | −0.794252 | ||||||||
\(217\) | −5.59210 | −0.379617 | ||||||||
\(218\) | 8.48886 | 0.574938 | ||||||||
\(219\) | −0.811346 | −0.0548257 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.249353 | −0.0167733 | ||||||||
\(222\) | 1.11414 | 0.0747762 | ||||||||
\(223\) | 21.5462 | 1.44284 | 0.721419 | − | 0.692499i | \(-0.243490\pi\) | ||||
0.721419 | + | 0.692499i | \(0.243490\pi\) | |||||||
\(224\) | −2.88739 | −0.192922 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.90813 | −0.126927 | ||||||||
\(227\) | 27.2257 | 1.80703 | 0.903516 | − | 0.428553i | \(-0.140977\pi\) | ||||
0.903516 | + | 0.428553i | \(0.140977\pi\) | |||||||
\(228\) | −2.32693 | −0.154105 | ||||||||
\(229\) | 25.0005 | 1.65208 | 0.826039 | − | 0.563613i | \(-0.190589\pi\) | ||||
0.826039 | + | 0.563613i | \(0.190589\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.688892 | −0.0453258 | ||||||||
\(232\) | −23.9398 | −1.57172 | ||||||||
\(233\) | 3.65878 | 0.239695 | 0.119847 | − | 0.992792i | \(-0.461759\pi\) | ||||
0.119847 | + | 0.992792i | \(0.461759\pi\) | |||||||
\(234\) | 11.4686 | 0.749726 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.33524 | −0.0869169 | ||||||||
\(237\) | −5.86665 | −0.381080 | ||||||||
\(238\) | 0.0809666 | 0.00524829 | ||||||||
\(239\) | 14.7052 | 0.951200 | 0.475600 | − | 0.879662i | \(-0.342231\pi\) | ||||
0.475600 | + | 0.879662i | \(0.342231\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.6938 | 0.882096 | 0.441048 | − | 0.897483i | \(-0.354607\pi\) | ||||
0.441048 | + | 0.897483i | \(0.354607\pi\) | |||||||
\(242\) | −1.21432 | −0.0780594 | ||||||||
\(243\) | 14.8321 | 0.951479 | ||||||||
\(244\) | −7.59210 | −0.486035 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −5.55707 | −0.354306 | ||||||||
\(247\) | 24.0415 | 1.52972 | ||||||||
\(248\) | −17.1492 | −1.08897 | ||||||||
\(249\) | 8.33677 | 0.528322 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.0114 | −0.695032 | −0.347516 | − | 0.937674i | \(-0.612975\pi\) | ||||
−0.347516 | + | 0.937674i | \(0.612975\pi\) | |||||||
\(252\) | 1.32693 | 0.0835887 | ||||||||
\(253\) | −1.09679 | −0.0689545 | ||||||||
\(254\) | −16.2449 | −1.01930 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −11.6637 | −0.728981 | ||||||||
\(257\) | 15.9496 | 0.994910 | 0.497455 | − | 0.867490i | \(-0.334268\pi\) | ||||
0.497455 | + | 0.867490i | \(0.334268\pi\) | |||||||
\(258\) | −9.83807 | −0.612491 | ||||||||
\(259\) | −1.33185 | −0.0827572 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 19.7146 | 1.22030 | ||||||||
\(262\) | 3.34614 | 0.206725 | ||||||||
\(263\) | 5.11108 | 0.315163 | 0.157581 | − | 0.987506i | \(-0.449630\pi\) | ||||
0.157581 | + | 0.987506i | \(0.449630\pi\) | |||||||
\(264\) | −2.11261 | −0.130022 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −7.80642 | −0.478643 | ||||||||
\(267\) | 10.7556 | 0.658230 | ||||||||
\(268\) | 5.45536 | 0.333239 | ||||||||
\(269\) | −18.2351 | −1.11181 | −0.555906 | − | 0.831245i | \(-0.687628\pi\) | ||||
−0.555906 | + | 0.831245i | \(0.687628\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.23506 | 0.378753 | 0.189377 | − | 0.981905i | \(-0.439353\pi\) | ||||
0.189377 | + | 0.981905i | \(0.439353\pi\) | |||||||
\(272\) | 0.178231 | 0.0108068 | ||||||||
\(273\) | 2.57628 | 0.155924 | ||||||||
\(274\) | −21.7288 | −1.31269 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.396997 | −0.0238964 | ||||||||
\(277\) | −6.32248 | −0.379881 | −0.189941 | − | 0.981796i | \(-0.560830\pi\) | ||||
−0.189941 | + | 0.981796i | \(0.560830\pi\) | |||||||
\(278\) | 4.69535 | 0.281608 | ||||||||
\(279\) | 14.1225 | 0.845489 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −25.2257 | −1.50484 | −0.752419 | − | 0.658684i | \(-0.771113\pi\) | ||||
−0.752419 | + | 0.658684i | \(0.771113\pi\) | |||||||
\(282\) | −1.89078 | −0.112594 | ||||||||
\(283\) | −13.4193 | −0.797693 | −0.398846 | − | 0.917018i | \(-0.630589\pi\) | ||||
−0.398846 | + | 0.917018i | \(0.630589\pi\) | |||||||
\(284\) | 6.60042 | 0.391663 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.54125 | 0.268530 | ||||||||
\(287\) | 6.64296 | 0.392121 | ||||||||
\(288\) | 7.29190 | 0.429679 | ||||||||
\(289\) | −16.9956 | −0.999738 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.24443 | 0.541918 | ||||||||
\(292\) | 0.618825 | 0.0362140 | ||||||||
\(293\) | −17.6064 | −1.02858 | −0.514288 | − | 0.857617i | \(-0.671944\pi\) | ||||
−0.514288 | + | 0.857617i | \(0.671944\pi\) | |||||||
\(294\) | −0.836535 | −0.0487877 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −4.08436 | −0.237398 | ||||||||
\(297\) | 3.80642 | 0.220871 | ||||||||
\(298\) | −5.93671 | −0.343905 | ||||||||
\(299\) | 4.10171 | 0.237208 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.7605 | 0.677863 | ||||||||
\(302\) | −26.9447 | −1.55049 | ||||||||
\(303\) | −5.82071 | −0.334391 | ||||||||
\(304\) | −17.1842 | −0.985582 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.204475 | −0.0116891 | ||||||||
\(307\) | −26.3368 | −1.50312 | −0.751560 | − | 0.659665i | \(-0.770698\pi\) | ||||
−0.751560 | + | 0.659665i | \(0.770698\pi\) | |||||||
\(308\) | 0.525428 | 0.0299390 | ||||||||
\(309\) | 6.57628 | 0.374112 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.96052 | 0.337990 | 0.168995 | − | 0.985617i | \(-0.445948\pi\) | ||||
0.168995 | + | 0.985617i | \(0.445948\pi\) | |||||||
\(312\) | 7.90063 | 0.447285 | ||||||||
\(313\) | 5.52098 | 0.312064 | 0.156032 | − | 0.987752i | \(-0.450130\pi\) | ||||
0.156032 | + | 0.987752i | \(0.450130\pi\) | |||||||
\(314\) | −5.84791 | −0.330017 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.47457 | 0.251714 | ||||||||
\(317\) | 15.7146 | 0.882618 | 0.441309 | − | 0.897355i | \(-0.354514\pi\) | ||||
0.441309 | + | 0.897355i | \(0.354514\pi\) | |||||||
\(318\) | −1.43801 | −0.0806395 | ||||||||
\(319\) | 7.80642 | 0.437076 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.89829 | 0.329210 | ||||||||
\(322\) | −1.33185 | −0.0742212 | ||||||||
\(323\) | −0.428639 | −0.0238501 | ||||||||
\(324\) | −2.60300 | −0.144611 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 7.39207 | 0.409409 | ||||||||
\(327\) | −4.81579 | −0.266314 | ||||||||
\(328\) | 20.3718 | 1.12484 | ||||||||
\(329\) | 2.26025 | 0.124612 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.2351 | 1.00229 | 0.501145 | − | 0.865363i | \(-0.332912\pi\) | ||||
0.501145 | + | 0.865363i | \(0.332912\pi\) | |||||||
\(332\) | −6.35857 | −0.348972 | ||||||||
\(333\) | 3.36349 | 0.184318 | ||||||||
\(334\) | −4.46028 | −0.244056 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.84146 | −0.100460 | ||||||||
\(337\) | −32.2908 | −1.75899 | −0.879497 | − | 0.475904i | \(-0.842121\pi\) | ||||
−0.879497 | + | 0.475904i | \(0.842121\pi\) | |||||||
\(338\) | −1.19697 | −0.0651064 | ||||||||
\(339\) | 1.08250 | 0.0587932 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.59210 | 0.302829 | ||||||||
\(342\) | 19.7146 | 1.06604 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 36.0656 | 1.94453 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.763405 | −0.0410409 | ||||||||
\(347\) | −22.6909 | −1.21811 | −0.609056 | − | 0.793127i | \(-0.708451\pi\) | ||||
−0.609056 | + | 0.793127i | \(0.708451\pi\) | |||||||
\(348\) | 2.82564 | 0.151470 | ||||||||
\(349\) | 16.9097 | 0.905154 | 0.452577 | − | 0.891725i | \(-0.350505\pi\) | ||||
0.452577 | + | 0.891725i | \(0.350505\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −14.2351 | −0.759811 | ||||||||
\(352\) | 2.88739 | 0.153898 | ||||||||
\(353\) | −24.3970 | −1.29852 | −0.649261 | − | 0.760566i | \(-0.724922\pi\) | ||||
−0.649261 | + | 0.760566i | \(0.724922\pi\) | |||||||
\(354\) | −2.12584 | −0.112987 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −8.20342 | −0.434780 | ||||||||
\(357\) | −0.0459330 | −0.00243103 | ||||||||
\(358\) | 9.35599 | 0.494479 | ||||||||
\(359\) | −32.8113 | −1.73172 | −0.865858 | − | 0.500289i | \(-0.833227\pi\) | ||||
−0.865858 | + | 0.500289i | \(0.833227\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 22.3274 | 1.17513 | ||||||||
\(362\) | −13.2573 | −0.696790 | ||||||||
\(363\) | 0.688892 | 0.0361575 | ||||||||
\(364\) | −1.96497 | −0.102992 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −12.0874 | −0.631820 | ||||||||
\(367\) | 6.94269 | 0.362406 | 0.181203 | − | 0.983446i | \(-0.442001\pi\) | ||||
0.181203 | + | 0.983446i | \(0.442001\pi\) | |||||||
\(368\) | −2.93179 | −0.152830 | ||||||||
\(369\) | −16.7763 | −0.873340 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.71900 | 0.0892462 | ||||||||
\(372\) | 2.02413 | 0.104946 | ||||||||
\(373\) | −36.9733 | −1.91440 | −0.957202 | − | 0.289421i | \(-0.906537\pi\) | ||||
−0.957202 | + | 0.289421i | \(0.906537\pi\) | |||||||
\(374\) | −0.0809666 | −0.00418669 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.93146 | 0.357463 | ||||||||
\(377\) | −29.1941 | −1.50357 | ||||||||
\(378\) | 4.62222 | 0.237741 | ||||||||
\(379\) | −23.6414 | −1.21438 | −0.607189 | − | 0.794557i | \(-0.707703\pi\) | ||||
−0.607189 | + | 0.794557i | \(0.707703\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.21585 | 0.472142 | ||||||||
\(382\) | 13.2573 | 0.678304 | ||||||||
\(383\) | −13.7210 | −0.701111 | −0.350555 | − | 0.936542i | \(-0.614007\pi\) | ||||
−0.350555 | + | 0.936542i | \(0.614007\pi\) | |||||||
\(384\) | −3.42711 | −0.174889 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 14.2079 | 0.723161 | ||||||||
\(387\) | −29.7003 | −1.50975 | ||||||||
\(388\) | −7.05086 | −0.357953 | ||||||||
\(389\) | −15.5526 | −0.788549 | −0.394275 | − | 0.918993i | \(-0.629004\pi\) | ||||
−0.394275 | + | 0.918993i | \(0.629004\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.0731300 | −0.00369835 | ||||||||
\(392\) | 3.06668 | 0.154891 | ||||||||
\(393\) | −1.89829 | −0.0957561 | ||||||||
\(394\) | 13.1669 | 0.663337 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.32693 | −0.0666807 | ||||||||
\(397\) | 0.253799 | 0.0127378 | 0.00636891 | − | 0.999980i | \(-0.497973\pi\) | ||||
0.00636891 | + | 0.999980i | \(0.497973\pi\) | |||||||
\(398\) | −2.52696 | −0.126665 | ||||||||
\(399\) | 4.42864 | 0.221709 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 20.3684 | 1.01715 | 0.508575 | − | 0.861018i | \(-0.330172\pi\) | ||||
0.508575 | + | 0.861018i | \(0.330172\pi\) | |||||||
\(402\) | 8.68550 | 0.433193 | ||||||||
\(403\) | −20.9131 | −1.04175 | ||||||||
\(404\) | 4.43954 | 0.220875 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 9.47949 | 0.470459 | ||||||||
\(407\) | 1.33185 | 0.0660174 | ||||||||
\(408\) | −0.140862 | −0.00697368 | ||||||||
\(409\) | 12.1225 | 0.599417 | 0.299708 | − | 0.954031i | \(-0.403111\pi\) | ||||
0.299708 | + | 0.954031i | \(0.403111\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.3269 | 0.608043 | ||||||||
\(412\) | −5.01582 | −0.247112 | ||||||||
\(413\) | 2.54125 | 0.125047 | ||||||||
\(414\) | 3.36349 | 0.165307 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −10.7981 | −0.529421 | ||||||||
\(417\) | −2.66370 | −0.130442 | ||||||||
\(418\) | 7.80642 | 0.381825 | ||||||||
\(419\) | −21.4400 | −1.04741 | −0.523707 | − | 0.851899i | \(-0.675451\pi\) | ||||
−0.523707 | + | 0.851899i | \(0.675451\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.8622 | 1.45539 | 0.727697 | − | 0.685898i | \(-0.240591\pi\) | ||||
0.727697 | + | 0.685898i | \(0.240591\pi\) | |||||||
\(422\) | −28.0415 | −1.36504 | ||||||||
\(423\) | −5.70810 | −0.277538 | ||||||||
\(424\) | 5.27163 | 0.256013 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 10.5086 | 0.509141 | ||||||||
\(427\) | 14.4494 | 0.699255 | ||||||||
\(428\) | −4.49871 | −0.217453 | ||||||||
\(429\) | −2.57628 | −0.124384 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −19.6588 | −0.946930 | −0.473465 | − | 0.880813i | \(-0.656997\pi\) | ||||
−0.473465 | + | 0.880813i | \(0.656997\pi\) | |||||||
\(432\) | 10.1748 | 0.489537 | ||||||||
\(433\) | 32.9719 | 1.58453 | 0.792264 | − | 0.610178i | \(-0.208902\pi\) | ||||
0.792264 | + | 0.610178i | \(0.208902\pi\) | |||||||
\(434\) | 6.79060 | 0.325959 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.67307 | 0.175908 | ||||||||
\(437\) | 7.05086 | 0.337288 | ||||||||
\(438\) | 0.985233 | 0.0470763 | ||||||||
\(439\) | −0.815792 | −0.0389356 | −0.0194678 | − | 0.999810i | \(-0.506197\pi\) | ||||
−0.0194678 | + | 0.999810i | \(0.506197\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.52543 | −0.120258 | ||||||||
\(442\) | 0.302795 | 0.0144025 | ||||||||
\(443\) | −24.9763 | −1.18666 | −0.593331 | − | 0.804959i | \(-0.702187\pi\) | ||||
−0.593331 | + | 0.804959i | \(0.702187\pi\) | |||||||
\(444\) | 0.482081 | 0.0228785 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −26.1639 | −1.23890 | ||||||||
\(447\) | 3.36794 | 0.159298 | ||||||||
\(448\) | 8.85236 | 0.418235 | ||||||||
\(449\) | 0.414349 | 0.0195544 | 0.00977718 | − | 0.999952i | \(-0.496888\pi\) | ||||
0.00977718 | + | 0.999952i | \(0.496888\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.64296 | −0.312805 | ||||||||
\(452\) | −0.825636 | −0.0388347 | ||||||||
\(453\) | 15.2859 | 0.718195 | ||||||||
\(454\) | −33.0607 | −1.55162 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 13.5812 | 0.635998 | ||||||||
\(457\) | −9.33185 | −0.436526 | −0.218263 | − | 0.975890i | \(-0.570039\pi\) | ||||
−0.218263 | + | 0.975890i | \(0.570039\pi\) | |||||||
\(458\) | −30.3586 | −1.41856 | ||||||||
\(459\) | 0.253799 | 0.0118463 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 29.9891 | 1.39673 | 0.698366 | − | 0.715741i | \(-0.253911\pi\) | ||||
0.698366 | + | 0.715741i | \(0.253911\pi\) | |||||||
\(462\) | 0.836535 | 0.0389191 | ||||||||
\(463\) | 31.5353 | 1.46557 | 0.732784 | − | 0.680461i | \(-0.238220\pi\) | ||||
0.732784 | + | 0.680461i | \(0.238220\pi\) | |||||||
\(464\) | 20.8671 | 0.968732 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.44293 | −0.205815 | ||||||||
\(467\) | 5.67952 | 0.262817 | 0.131409 | − | 0.991328i | \(-0.458050\pi\) | ||||
0.131409 | + | 0.991328i | \(0.458050\pi\) | |||||||
\(468\) | 4.96238 | 0.229386 | ||||||||
\(469\) | −10.3827 | −0.479429 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.31756 | 0.152865 | ||||||||
\(472\) | 7.79319 | 0.358711 | ||||||||
\(473\) | −11.7605 | −0.540748 | ||||||||
\(474\) | 7.12399 | 0.327215 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.0350337 | 0.00160577 | ||||||||
\(477\) | −4.34122 | −0.198771 | ||||||||
\(478\) | −17.8568 | −0.816751 | ||||||||
\(479\) | −39.4608 | −1.80301 | −0.901504 | − | 0.432771i | \(-0.857536\pi\) | ||||
−0.901504 | + | 0.432771i | \(0.857536\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.98079 | −0.227104 | ||||||||
\(482\) | −16.6287 | −0.757415 | ||||||||
\(483\) | 0.755569 | 0.0343796 | ||||||||
\(484\) | −0.525428 | −0.0238831 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −18.0109 | −0.816991 | ||||||||
\(487\) | 3.19850 | 0.144938 | 0.0724689 | − | 0.997371i | \(-0.476912\pi\) | ||||
0.0724689 | + | 0.997371i | \(0.476912\pi\) | |||||||
\(488\) | 44.3116 | 2.00589 | ||||||||
\(489\) | −4.19358 | −0.189640 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 26.3511 | 1.18921 | 0.594603 | − | 0.804019i | \(-0.297309\pi\) | ||||
0.594603 | + | 0.804019i | \(0.297309\pi\) | |||||||
\(492\) | −2.40451 | −0.108403 | ||||||||
\(493\) | 0.520505 | 0.0234424 | ||||||||
\(494\) | −29.1941 | −1.31350 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 14.9481 | 0.671189 | ||||||||
\(497\) | −12.5620 | −0.563482 | ||||||||
\(498\) | −10.1235 | −0.453645 | ||||||||
\(499\) | 3.52987 | 0.158019 | 0.0790094 | − | 0.996874i | \(-0.474824\pi\) | ||||
0.0790094 | + | 0.996874i | \(0.474824\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.53035 | 0.113048 | ||||||||
\(502\) | 13.3713 | 0.596792 | ||||||||
\(503\) | −22.7368 | −1.01379 | −0.506893 | − | 0.862009i | \(-0.669206\pi\) | ||||
−0.506893 | + | 0.862009i | \(0.669206\pi\) | |||||||
\(504\) | −7.74467 | −0.344975 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.33185 | 0.0592080 | ||||||||
\(507\) | 0.679048 | 0.0301576 | ||||||||
\(508\) | −7.02906 | −0.311864 | ||||||||
\(509\) | −36.2351 | −1.60609 | −0.803045 | − | 0.595918i | \(-0.796788\pi\) | ||||
−0.803045 | + | 0.595918i | \(0.796788\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.17775 | −0.0521008 | ||||||||
\(512\) | 24.1131 | 1.06566 | ||||||||
\(513\) | −24.4701 | −1.08038 | ||||||||
\(514\) | −19.3679 | −0.854283 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −4.25686 | −0.187398 | ||||||||
\(517\) | −2.26025 | −0.0994058 | ||||||||
\(518\) | 1.61729 | 0.0710598 | ||||||||
\(519\) | 0.433085 | 0.0190103 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.79706 | −0.297784 | −0.148892 | − | 0.988853i | \(-0.547571\pi\) | ||||
−0.148892 | + | 0.988853i | \(0.547571\pi\) | |||||||
\(522\) | −23.9398 | −1.04782 | ||||||||
\(523\) | −34.0701 | −1.48978 | −0.744890 | − | 0.667187i | \(-0.767498\pi\) | ||||
−0.744890 | + | 0.667187i | \(0.767498\pi\) | |||||||
\(524\) | 1.44785 | 0.0632497 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.20648 | −0.270616 | ||||||||
\(527\) | 0.372862 | 0.0162421 | ||||||||
\(528\) | 1.84146 | 0.0801392 | ||||||||
\(529\) | −21.7971 | −0.947698 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.41774 | −0.278506 | ||||||||
\(532\) | −3.37778 | −0.146446 | ||||||||
\(533\) | 24.8430 | 1.07607 | ||||||||
\(534\) | −13.0607 | −0.565192 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −31.8404 | −1.37530 | ||||||||
\(537\) | −5.30772 | −0.229045 | ||||||||
\(538\) | 22.1432 | 0.954661 | ||||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −27.1941 | −1.16916 | −0.584582 | − | 0.811335i | \(-0.698741\pi\) | ||||
−0.584582 | + | 0.811335i | \(0.698741\pi\) | |||||||
\(542\) | −7.57136 | −0.325218 | ||||||||
\(543\) | 7.52098 | 0.322756 | ||||||||
\(544\) | 0.192521 | 0.00825428 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −3.12843 | −0.133884 | ||||||||
\(547\) | 40.2449 | 1.72075 | 0.860374 | − | 0.509663i | \(-0.170230\pi\) | ||||
0.860374 | + | 0.509663i | \(0.170230\pi\) | |||||||
\(548\) | −9.40192 | −0.401630 | ||||||||
\(549\) | −36.4909 | −1.55739 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −50.1847 | −2.13794 | ||||||||
\(552\) | 2.31708 | 0.0986217 | ||||||||
\(553\) | −8.51606 | −0.362140 | ||||||||
\(554\) | 7.67752 | 0.326186 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.03164 | 0.0861608 | ||||||||
\(557\) | 7.09679 | 0.300701 | 0.150350 | − | 0.988633i | \(-0.451960\pi\) | ||||
0.150350 | + | 0.988633i | \(0.451960\pi\) | |||||||
\(558\) | −17.1492 | −0.725982 | ||||||||
\(559\) | 43.9813 | 1.86021 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.0459330 | 0.00193929 | ||||||||
\(562\) | 30.6321 | 1.29214 | ||||||||
\(563\) | 18.7971 | 0.792201 | 0.396101 | − | 0.918207i | \(-0.370363\pi\) | ||||
0.396101 | + | 0.918207i | \(0.370363\pi\) | |||||||
\(564\) | −0.818128 | −0.0344494 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 16.2953 | 0.684942 | ||||||||
\(567\) | 4.95407 | 0.208051 | ||||||||
\(568\) | −38.5236 | −1.61641 | ||||||||
\(569\) | −0.0316429 | −0.00132654 | −0.000663269 | − | 1.00000i | \(-0.500211\pi\) | ||||
−0.000663269 | 1.00000i | \(0.500211\pi\) | ||||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.0503787 | 0.00210828 | 0.00105414 | − | 0.999999i | \(-0.499664\pi\) | ||||
0.00105414 | + | 0.999999i | \(0.499664\pi\) | |||||||
\(572\) | 1.96497 | 0.0821594 | ||||||||
\(573\) | −7.52098 | −0.314194 | ||||||||
\(574\) | −8.06668 | −0.336697 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −22.3560 | −0.931499 | ||||||||
\(577\) | 13.6316 | 0.567490 | 0.283745 | − | 0.958900i | \(-0.408423\pi\) | ||||
0.283745 | + | 0.958900i | \(0.408423\pi\) | |||||||
\(578\) | 20.6380 | 0.858429 | ||||||||
\(579\) | −8.06022 | −0.334971 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.1017 | 0.502064 | ||||||||
\(582\) | −11.2257 | −0.465320 | ||||||||
\(583\) | −1.71900 | −0.0711939 | ||||||||
\(584\) | −3.61179 | −0.149457 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 21.3798 | 0.883191 | ||||||||
\(587\) | −1.63804 | −0.0676090 | −0.0338045 | − | 0.999428i | \(-0.510762\pi\) | ||||
−0.0338045 | + | 0.999428i | \(0.510762\pi\) | |||||||
\(588\) | −0.361963 | −0.0149271 | ||||||||
\(589\) | −35.9496 | −1.48128 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.46965 | −0.307260 | ||||||||
\(592\) | 3.56013 | 0.146321 | ||||||||
\(593\) | −8.46367 | −0.347561 | −0.173781 | − | 0.984784i | \(-0.555598\pi\) | ||||
−0.173781 | + | 0.984784i | \(0.555598\pi\) | |||||||
\(594\) | −4.62222 | −0.189652 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.56877 | −0.105221 | ||||||||
\(597\) | 1.43356 | 0.0586718 | ||||||||
\(598\) | −4.98079 | −0.203680 | ||||||||
\(599\) | −26.9590 | −1.10151 | −0.550757 | − | 0.834665i | \(-0.685661\pi\) | ||||
−0.550757 | + | 0.834665i | \(0.685661\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.4909 | −0.672677 | −0.336338 | − | 0.941741i | \(-0.609189\pi\) | ||||
−0.336338 | + | 0.941741i | \(0.609189\pi\) | |||||||
\(602\) | −14.2810 | −0.582050 | ||||||||
\(603\) | 26.2208 | 1.06779 | ||||||||
\(604\) | −11.6588 | −0.474389 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 7.06821 | 0.287126 | ||||||||
\(607\) | −19.5526 | −0.793617 | −0.396808 | − | 0.917902i | \(-0.629882\pi\) | ||||
−0.396808 | + | 0.917902i | \(0.629882\pi\) | |||||||
\(608\) | −18.5620 | −0.752788 | ||||||||
\(609\) | −5.37778 | −0.217919 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.45277 | 0.341963 | ||||||||
\(612\) | −0.0884751 | −0.00357639 | ||||||||
\(613\) | 39.5955 | 1.59925 | 0.799623 | − | 0.600502i | \(-0.205032\pi\) | ||||
0.799623 | + | 0.600502i | \(0.205032\pi\) | |||||||
\(614\) | 31.9813 | 1.29066 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.06668 | −0.123560 | ||||||||
\(617\) | −23.1669 | −0.932662 | −0.466331 | − | 0.884610i | \(-0.654425\pi\) | ||||
−0.466331 | + | 0.884610i | \(0.654425\pi\) | |||||||
\(618\) | −7.98571 | −0.321232 | ||||||||
\(619\) | 3.43017 | 0.137870 | 0.0689351 | − | 0.997621i | \(-0.478040\pi\) | ||||
0.0689351 | + | 0.997621i | \(0.478040\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.17484 | −0.167531 | ||||||||
\(622\) | −7.23798 | −0.290216 | ||||||||
\(623\) | 15.6128 | 0.625516 | ||||||||
\(624\) | −6.88659 | −0.275684 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −6.70424 | −0.267955 | ||||||||
\(627\) | −4.42864 | −0.176863 | ||||||||
\(628\) | −2.53035 | −0.100972 | ||||||||
\(629\) | 0.0888033 | 0.00354082 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.9590 | 0.436270 | 0.218135 | − | 0.975919i | \(-0.430003\pi\) | ||||
0.218135 | + | 0.975919i | \(0.430003\pi\) | |||||||
\(632\) | −26.1160 | −1.03884 | ||||||||
\(633\) | 15.9081 | 0.632292 | ||||||||
\(634\) | −19.0825 | −0.757863 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.622216 | −0.0246725 | ||||||||
\(637\) | 3.73975 | 0.148174 | ||||||||
\(638\) | −9.47949 | −0.375297 | ||||||||
\(639\) | 31.7244 | 1.25500 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −14.9862 | −0.591919 | −0.295959 | − | 0.955201i | \(-0.595639\pi\) | ||||
−0.295959 | + | 0.955201i | \(0.595639\pi\) | |||||||
\(642\) | −7.16241 | −0.282678 | ||||||||
\(643\) | 14.4222 | 0.568755 | 0.284378 | − | 0.958712i | \(-0.408213\pi\) | ||||
0.284378 | + | 0.958712i | \(0.408213\pi\) | |||||||
\(644\) | −0.576283 | −0.0227087 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.520505 | 0.0204790 | ||||||||
\(647\) | 33.7309 | 1.32610 | 0.663048 | − | 0.748577i | \(-0.269262\pi\) | ||||
0.663048 | + | 0.748577i | \(0.269262\pi\) | |||||||
\(648\) | 15.1925 | 0.596819 | ||||||||
\(649\) | −2.54125 | −0.0997527 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.85236 | −0.150986 | ||||||||
\(652\) | 3.19850 | 0.125263 | ||||||||
\(653\) | −36.7971 | −1.43998 | −0.719990 | − | 0.693984i | \(-0.755854\pi\) | ||||
−0.719990 | + | 0.693984i | \(0.755854\pi\) | |||||||
\(654\) | 5.84791 | 0.228671 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −17.7571 | −0.693298 | ||||||||
\(657\) | 2.97433 | 0.116040 | ||||||||
\(658\) | −2.74467 | −0.106998 | ||||||||
\(659\) | 3.79213 | 0.147721 | 0.0738603 | − | 0.997269i | \(-0.476468\pi\) | ||||
0.0738603 | + | 0.997269i | \(0.476468\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −35.2543 | −1.37123 | −0.685616 | − | 0.727963i | \(-0.740467\pi\) | ||||
−0.685616 | + | 0.727963i | \(0.740467\pi\) | |||||||
\(662\) | −22.1432 | −0.860620 | ||||||||
\(663\) | −0.171778 | −0.00667129 | ||||||||
\(664\) | 37.1120 | 1.44023 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.08436 | −0.158266 | ||||||||
\(667\) | −8.56199 | −0.331522 | ||||||||
\(668\) | −1.92993 | −0.0746713 | ||||||||
\(669\) | 14.8430 | 0.573863 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −14.4494 | −0.557812 | ||||||||
\(672\) | −1.98910 | −0.0767312 | ||||||||
\(673\) | 35.1383 | 1.35448 | 0.677240 | − | 0.735762i | \(-0.263176\pi\) | ||||
0.677240 | + | 0.735762i | \(0.263176\pi\) | |||||||
\(674\) | 39.2114 | 1.51037 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.517919 | −0.0199200 | ||||||||
\(677\) | −23.1907 | −0.891290 | −0.445645 | − | 0.895210i | \(-0.647026\pi\) | ||||
−0.445645 | + | 0.895210i | \(0.647026\pi\) | |||||||
\(678\) | −1.31450 | −0.0504830 | ||||||||
\(679\) | 13.4193 | 0.514984 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 18.7556 | 0.718715 | ||||||||
\(682\) | −6.79060 | −0.260026 | ||||||||
\(683\) | 7.74758 | 0.296453 | 0.148227 | − | 0.988953i | \(-0.452644\pi\) | ||||
0.148227 | + | 0.988953i | \(0.452644\pi\) | |||||||
\(684\) | 8.53035 | 0.326166 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.21432 | −0.0463629 | ||||||||
\(687\) | 17.2226 | 0.657084 | ||||||||
\(688\) | −31.4366 | −1.19851 | ||||||||
\(689\) | 6.42864 | 0.244912 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.7763 | −0.562117 | −0.281059 | − | 0.959691i | \(-0.590686\pi\) | ||||
−0.281059 | + | 0.959691i | \(0.590686\pi\) | |||||||
\(692\) | −0.330320 | −0.0125569 | ||||||||
\(693\) | 2.52543 | 0.0959331 | ||||||||
\(694\) | 27.5540 | 1.04594 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −16.4919 | −0.625125 | ||||||||
\(697\) | −0.442930 | −0.0167772 | ||||||||
\(698\) | −20.5337 | −0.777214 | ||||||||
\(699\) | 2.52051 | 0.0953343 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19.8765 | −0.750725 | −0.375362 | − | 0.926878i | \(-0.622482\pi\) | ||||
−0.375362 | + | 0.926878i | \(0.622482\pi\) | |||||||
\(702\) | 17.2859 | 0.652415 | ||||||||
\(703\) | −8.56199 | −0.322922 | ||||||||
\(704\) | −8.85236 | −0.333636 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 29.6258 | 1.11498 | ||||||||
\(707\) | −8.44938 | −0.317772 | ||||||||
\(708\) | −0.919838 | −0.0345696 | ||||||||
\(709\) | 0.368416 | 0.0138362 | 0.00691808 | − | 0.999976i | \(-0.497798\pi\) | ||||
0.00691808 | + | 0.999976i | \(0.497798\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 21.5067 | 0.806564 | ||||||||
\(712\) | 47.8796 | 1.79436 | ||||||||
\(713\) | −6.13335 | −0.229696 | ||||||||
\(714\) | 0.0557773 | 0.00208741 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4.04827 | 0.151291 | ||||||||
\(717\) | 10.1303 | 0.378323 | ||||||||
\(718\) | 39.8435 | 1.48694 | ||||||||
\(719\) | −5.86865 | −0.218864 | −0.109432 | − | 0.993994i | \(-0.534903\pi\) | ||||
−0.109432 | + | 0.993994i | \(0.534903\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.54617 | 0.355518 | ||||||||
\(722\) | −27.1126 | −1.00903 | ||||||||
\(723\) | 9.43356 | 0.350838 | ||||||||
\(724\) | −5.73636 | −0.213190 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −0.836535 | −0.0310467 | ||||||||
\(727\) | −1.19066 | −0.0441592 | −0.0220796 | − | 0.999756i | \(-0.507029\pi\) | ||||
−0.0220796 | + | 0.999756i | \(0.507029\pi\) | |||||||
\(728\) | 11.4686 | 0.425054 | ||||||||
\(729\) | −4.64449 | −0.172018 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.784149 | −0.0290028 | ||||||||
\(732\) | −5.23014 | −0.193312 | ||||||||
\(733\) | −19.6795 | −0.726880 | −0.363440 | − | 0.931618i | \(-0.618398\pi\) | ||||
−0.363440 | + | 0.931618i | \(0.618398\pi\) | |||||||
\(734\) | −8.43065 | −0.311181 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.16686 | −0.116732 | ||||||||
\(737\) | 10.3827 | 0.382452 | ||||||||
\(738\) | 20.3718 | 0.749897 | ||||||||
\(739\) | 27.1427 | 0.998461 | 0.499231 | − | 0.866469i | \(-0.333616\pi\) | ||||
0.499231 | + | 0.866469i | \(0.333616\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 16.5620 | 0.608420 | ||||||||
\(742\) | −2.08742 | −0.0766316 | ||||||||
\(743\) | 31.0509 | 1.13915 | 0.569573 | − | 0.821941i | \(-0.307109\pi\) | ||||
0.569573 | + | 0.821941i | \(0.307109\pi\) | |||||||
\(744\) | −11.8139 | −0.433120 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 44.8974 | 1.64381 | ||||||||
\(747\) | −30.5620 | −1.11820 | ||||||||
\(748\) | −0.0350337 | −0.00128096 | ||||||||
\(749\) | 8.56199 | 0.312848 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −35.8292 | −1.30743 | −0.653713 | − | 0.756743i | \(-0.726789\pi\) | ||||
−0.653713 | + | 0.756743i | \(0.726789\pi\) | |||||||
\(752\) | −6.04182 | −0.220322 | ||||||||
\(753\) | −7.58565 | −0.276436 | ||||||||
\(754\) | 35.4509 | 1.29105 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.00000 | 0.0727393 | ||||||||
\(757\) | 1.15563 | 0.0420020 | 0.0210010 | − | 0.999779i | \(-0.493315\pi\) | ||||
0.0210010 | + | 0.999779i | \(0.493315\pi\) | |||||||
\(758\) | 28.7083 | 1.04273 | ||||||||
\(759\) | −0.755569 | −0.0274254 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 36.5640 | 1.32544 | 0.662722 | − | 0.748866i | \(-0.269401\pi\) | ||||
0.662722 | + | 0.748866i | \(0.269401\pi\) | |||||||
\(762\) | −11.1910 | −0.405407 | ||||||||
\(763\) | −6.99063 | −0.253078 | ||||||||
\(764\) | 5.73636 | 0.207534 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 16.6617 | 0.602012 | ||||||||
\(767\) | 9.50363 | 0.343156 | ||||||||
\(768\) | −8.03503 | −0.289939 | ||||||||
\(769\) | −38.7545 | −1.39752 | −0.698762 | − | 0.715354i | \(-0.746265\pi\) | ||||
−0.698762 | + | 0.715354i | \(0.746265\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.9876 | 0.395708 | ||||||||
\(772\) | 6.14764 | 0.221259 | ||||||||
\(773\) | −55.3372 | −1.99034 | −0.995171 | − | 0.0981537i | \(-0.968706\pi\) | ||||
−0.995171 | + | 0.0981537i | \(0.968706\pi\) | |||||||
\(774\) | 36.0656 | 1.29635 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 41.1526 | 1.47729 | ||||||||
\(777\) | −0.917502 | −0.0329152 | ||||||||
\(778\) | 18.8859 | 0.677091 | ||||||||
\(779\) | 42.7052 | 1.53007 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.5620 | 0.449503 | ||||||||
\(782\) | 0.0888033 | 0.00317560 | ||||||||
\(783\) | 29.7146 | 1.06191 | ||||||||
\(784\) | −2.67307 | −0.0954668 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 2.30513 | 0.0822213 | ||||||||
\(787\) | 13.6731 | 0.487392 | 0.243696 | − | 0.969852i | \(-0.421640\pi\) | ||||
0.243696 | + | 0.969852i | \(0.421640\pi\) | |||||||
\(788\) | 5.69721 | 0.202955 | ||||||||
\(789\) | 3.52098 | 0.125350 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.57136 | 0.0558711 | ||||||||
\(792\) | 7.74467 | 0.275195 | ||||||||
\(793\) | 54.0370 | 1.91891 | ||||||||
\(794\) | −0.308193 | −0.0109374 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.09340 | −0.0387544 | ||||||||
\(797\) | −17.8765 | −0.633218 | −0.316609 | − | 0.948556i | \(-0.602544\pi\) | ||||
−0.316609 | + | 0.948556i | \(0.602544\pi\) | |||||||
\(798\) | −5.37778 | −0.190372 | ||||||||
\(799\) | −0.150706 | −0.00533159 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −39.4291 | −1.39316 | ||||||||
\(802\) | −24.7338 | −0.873380 | ||||||||
\(803\) | 1.17775 | 0.0415621 | ||||||||
\(804\) | 3.75815 | 0.132540 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 25.3951 | 0.894506 | ||||||||
\(807\) | −12.5620 | −0.442203 | ||||||||
\(808\) | −25.9115 | −0.911564 | ||||||||
\(809\) | 14.6450 | 0.514890 | 0.257445 | − | 0.966293i | \(-0.417119\pi\) | ||||
0.257445 | + | 0.966293i | \(0.417119\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30.2667 | 1.06281 | 0.531404 | − | 0.847119i | \(-0.321665\pi\) | ||||
0.531404 | + | 0.847119i | \(0.321665\pi\) | |||||||
\(812\) | 4.10171 | 0.143942 | ||||||||
\(813\) | 4.29529 | 0.150642 | ||||||||
\(814\) | −1.61729 | −0.0566861 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0.122782 | 0.00429823 | ||||||||
\(817\) | 75.6040 | 2.64505 | ||||||||
\(818\) | −14.7205 | −0.514691 | ||||||||
\(819\) | −9.44446 | −0.330016 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.4286 | 0.363962 | 0.181981 | − | 0.983302i | \(-0.441749\pi\) | ||||
0.181981 | + | 0.983302i | \(0.441749\pi\) | |||||||
\(822\) | −14.9688 | −0.522098 | ||||||||
\(823\) | −4.28100 | −0.149226 | −0.0746131 | − | 0.997213i | \(-0.523772\pi\) | ||||
−0.0746131 | + | 0.997213i | \(0.523772\pi\) | |||||||
\(824\) | 29.2750 | 1.01984 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.08589 | −0.107372 | ||||||||
\(827\) | 13.8336 | 0.481042 | 0.240521 | − | 0.970644i | \(-0.422682\pi\) | ||||
0.240521 | + | 0.970644i | \(0.422682\pi\) | |||||||
\(828\) | 1.45536 | 0.0505773 | ||||||||
\(829\) | 10.8573 | 0.377089 | 0.188544 | − | 0.982065i | \(-0.439623\pi\) | ||||
0.188544 | + | 0.982065i | \(0.439623\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.35551 | −0.151091 | ||||||||
\(832\) | 33.1056 | 1.14773 | ||||||||
\(833\) | −0.0666765 | −0.00231021 | ||||||||
\(834\) | 3.23459 | 0.112005 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 3.37778 | 0.116823 | ||||||||
\(837\) | 21.2859 | 0.735749 | ||||||||
\(838\) | 26.0350 | 0.899365 | ||||||||
\(839\) | 52.4820 | 1.81188 | 0.905940 | − | 0.423407i | \(-0.139166\pi\) | ||||
0.905940 | + | 0.423407i | \(0.139166\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 31.9403 | 1.10139 | ||||||||
\(842\) | −36.2623 | −1.24968 | ||||||||
\(843\) | −17.3778 | −0.598523 | ||||||||
\(844\) | −12.1334 | −0.417647 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 6.93146 | 0.238309 | ||||||||
\(847\) | 1.00000 | 0.0343604 | ||||||||
\(848\) | −4.59502 | −0.157794 | ||||||||
\(849\) | −9.24443 | −0.317268 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.46076 | −0.0500742 | ||||||||
\(852\) | 4.54698 | 0.155777 | ||||||||
\(853\) | −9.89184 | −0.338690 | −0.169345 | − | 0.985557i | \(-0.554165\pi\) | ||||
−0.169345 | + | 0.985557i | \(0.554165\pi\) | |||||||
\(854\) | −17.5462 | −0.600418 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 26.2569 | 0.897441 | ||||||||
\(857\) | 3.58766 | 0.122552 | 0.0612760 | − | 0.998121i | \(-0.480483\pi\) | ||||
0.0612760 | + | 0.998121i | \(0.480483\pi\) | |||||||
\(858\) | 3.12843 | 0.106803 | ||||||||
\(859\) | −17.2050 | −0.587025 | −0.293513 | − | 0.955955i | \(-0.594824\pi\) | ||||
−0.293513 | + | 0.955955i | \(0.594824\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.57628 | 0.155959 | ||||||||
\(862\) | 23.8720 | 0.813085 | ||||||||
\(863\) | −15.0781 | −0.513263 | −0.256631 | − | 0.966509i | \(-0.582613\pi\) | ||||
−0.256631 | + | 0.966509i | \(0.582613\pi\) | |||||||
\(864\) | 10.9906 | 0.373909 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −40.0384 | −1.36056 | ||||||||
\(867\) | −11.7081 | −0.397628 | ||||||||
\(868\) | 2.93825 | 0.0997306 | ||||||||
\(869\) | 8.51606 | 0.288888 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −38.8287 | −1.31566 | ||||||||
\(872\) | −21.4380 | −0.725983 | ||||||||
\(873\) | −33.8894 | −1.14698 | ||||||||
\(874\) | −8.56199 | −0.289614 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.426304 | 0.0144035 | ||||||||
\(877\) | 31.4750 | 1.06284 | 0.531418 | − | 0.847109i | \(-0.321659\pi\) | ||||
0.531418 | + | 0.847109i | \(0.321659\pi\) | |||||||
\(878\) | 0.990632 | 0.0334322 | ||||||||
\(879\) | −12.1289 | −0.409098 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −47.1209 | −1.58754 | −0.793772 | − | 0.608215i | \(-0.791886\pi\) | ||||
−0.793772 | + | 0.608215i | \(0.791886\pi\) | |||||||
\(882\) | 3.06668 | 0.103260 | ||||||||
\(883\) | −33.8118 | −1.13786 | −0.568929 | − | 0.822386i | \(-0.692642\pi\) | ||||
−0.568929 | + | 0.822386i | \(0.692642\pi\) | |||||||
\(884\) | 0.131017 | 0.00440658 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 30.3293 | 1.01893 | ||||||||
\(887\) | 31.6258 | 1.06189 | 0.530944 | − | 0.847407i | \(-0.321837\pi\) | ||||
0.530944 | + | 0.847407i | \(0.321837\pi\) | |||||||
\(888\) | −2.81368 | −0.0944210 | ||||||||
\(889\) | 13.3778 | 0.448676 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.95407 | −0.165967 | ||||||||
\(892\) | −11.3210 | −0.379054 | ||||||||
\(893\) | 14.5303 | 0.486240 | ||||||||
\(894\) | −4.08976 | −0.136782 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −4.97481 | −0.166197 | ||||||||
\(897\) | 2.82564 | 0.0943452 | ||||||||
\(898\) | −0.503153 | −0.0167904 | ||||||||
\(899\) | 43.6543 | 1.45595 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.114617 | −0.00381845 | ||||||||
\(902\) | 8.06668 | 0.268591 | ||||||||
\(903\) | 8.10171 | 0.269608 | ||||||||
\(904\) | 4.81885 | 0.160273 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −18.5620 | −0.616681 | ||||||||
\(907\) | 46.8943 | 1.55710 | 0.778550 | − | 0.627582i | \(-0.215955\pi\) | ||||
0.778550 | + | 0.627582i | \(0.215955\pi\) | |||||||
\(908\) | −14.3051 | −0.474732 | ||||||||
\(909\) | 21.3383 | 0.707747 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −28.5620 | −0.946301 | −0.473151 | − | 0.880982i | \(-0.656883\pi\) | ||||
−0.473151 | + | 0.880982i | \(0.656883\pi\) | |||||||
\(912\) | −11.8381 | −0.391998 | ||||||||
\(913\) | −12.1017 | −0.400508 | ||||||||
\(914\) | 11.3319 | 0.374824 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −13.1359 | −0.434024 | ||||||||
\(917\) | −2.75557 | −0.0909969 | ||||||||
\(918\) | −0.308193 | −0.0101719 | ||||||||
\(919\) | 30.3555 | 1.00134 | 0.500668 | − | 0.865639i | \(-0.333088\pi\) | ||||
0.500668 | + | 0.865639i | \(0.333088\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −18.1432 | −0.597839 | ||||||||
\(922\) | −36.4164 | −1.19931 | ||||||||
\(923\) | −46.9787 | −1.54632 | ||||||||
\(924\) | 0.361963 | 0.0119077 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −38.2939 | −1.25842 | ||||||||
\(927\) | −24.1082 | −0.791816 | ||||||||
\(928\) | 22.5402 | 0.739918 | ||||||||
\(929\) | 2.71408 | 0.0890461 | 0.0445231 | − | 0.999008i | \(-0.485823\pi\) | ||||
0.0445231 | + | 0.999008i | \(0.485823\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.42864 | 0.210690 | ||||||||
\(932\) | −1.92242 | −0.0629711 | ||||||||
\(933\) | 4.10616 | 0.134430 | ||||||||
\(934\) | −6.89676 | −0.225669 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −28.9631 | −0.946689 | ||||||||
\(937\) | −13.7081 | −0.447824 | −0.223912 | − | 0.974609i | \(-0.571883\pi\) | ||||
−0.223912 | + | 0.974609i | \(0.571883\pi\) | |||||||
\(938\) | 12.6079 | 0.411663 | ||||||||
\(939\) | 3.80336 | 0.124118 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −21.1635 | −0.689909 | −0.344955 | − | 0.938619i | \(-0.612106\pi\) | ||||
−0.344955 | + | 0.938619i | \(0.612106\pi\) | |||||||
\(942\) | −4.02858 | −0.131258 | ||||||||
\(943\) | 7.28592 | 0.237262 | ||||||||
\(944\) | −6.79294 | −0.221091 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 14.2810 | 0.464315 | ||||||||
\(947\) | 14.8746 | 0.483361 | 0.241680 | − | 0.970356i | \(-0.422301\pi\) | ||||
0.241680 | + | 0.970356i | \(0.422301\pi\) | |||||||
\(948\) | 3.08250 | 0.100115 | ||||||||
\(949\) | −4.40451 | −0.142976 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10.8256 | 0.351045 | ||||||||
\(952\) | −0.204475 | −0.00662709 | ||||||||
\(953\) | −35.0968 | −1.13690 | −0.568448 | − | 0.822719i | \(-0.692456\pi\) | ||||
−0.568448 | + | 0.822719i | \(0.692456\pi\) | |||||||
\(954\) | 5.27163 | 0.170675 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −7.72651 | −0.249893 | ||||||||
\(957\) | 5.37778 | 0.173839 | ||||||||
\(958\) | 47.9180 | 1.54816 | ||||||||
\(959\) | 17.8938 | 0.577822 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.271628 | 0.00876221 | ||||||||
\(962\) | 6.04827 | 0.195004 | ||||||||
\(963\) | −21.6227 | −0.696782 | ||||||||
\(964\) | −7.19511 | −0.231739 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −0.917502 | −0.0295201 | ||||||||
\(967\) | 53.0879 | 1.70719 | 0.853596 | − | 0.520936i | \(-0.174417\pi\) | ||||
0.853596 | + | 0.520936i | \(0.174417\pi\) | |||||||
\(968\) | 3.06668 | 0.0985667 | ||||||||
\(969\) | −0.295286 | −0.00948597 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.4400 | 0.688043 | 0.344021 | − | 0.938962i | \(-0.388211\pi\) | ||||
0.344021 | + | 0.938962i | \(0.388211\pi\) | |||||||
\(972\) | −7.79319 | −0.249967 | ||||||||
\(973\) | −3.86665 | −0.123959 | ||||||||
\(974\) | −3.88400 | −0.124451 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −38.6242 | −1.23633 | ||||||||
\(977\) | 54.0415 | 1.72894 | 0.864470 | − | 0.502684i | \(-0.167654\pi\) | ||||
0.864470 | + | 0.502684i | \(0.167654\pi\) | |||||||
\(978\) | 5.09234 | 0.162835 | ||||||||
\(979\) | −15.6128 | −0.498989 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 17.6543 | 0.563660 | ||||||||
\(982\) | −31.9986 | −1.02112 | ||||||||
\(983\) | 38.3432 | 1.22296 | 0.611480 | − | 0.791260i | \(-0.290575\pi\) | ||||
0.611480 | + | 0.791260i | \(0.290575\pi\) | |||||||
\(984\) | 14.0340 | 0.447387 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −0.632060 | −0.0201289 | ||||||||
\(987\) | 1.55707 | 0.0495621 | ||||||||
\(988\) | −12.6321 | −0.401879 | ||||||||
\(989\) | 12.8988 | 0.410157 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 51.6543 | 1.64085 | 0.820427 | − | 0.571751i | \(-0.193736\pi\) | ||||
0.820427 | + | 0.571751i | \(0.193736\pi\) | |||||||
\(992\) | 16.1466 | 0.512655 | ||||||||
\(993\) | 12.5620 | 0.398643 | ||||||||
\(994\) | 15.2543 | 0.483836 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −4.38037 | −0.138797 | ||||||||
\(997\) | −41.4445 | −1.31256 | −0.656280 | − | 0.754518i | \(-0.727871\pi\) | ||||
−0.656280 | + | 0.754518i | \(0.727871\pi\) | |||||||
\(998\) | −4.28639 | −0.135683 | ||||||||
\(999\) | 5.06959 | 0.160395 |
(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 | 1925.2.a.v.1.1 | 3 | ||
5.2 | odd | 4 | 1925.2.b.n.1849.3 | 6 | |||
5.3 | odd | 4 | 1925.2.b.n.1849.4 | 6 | |||
5.4 | even | 2 | 385.2.a.f.1.3 | ✓ | 3 | ||
15.14 | odd | 2 | 3465.2.a.bh.1.1 | 3 | |||
20.19 | odd | 2 | 6160.2.a.bn.1.2 | 3 | |||
35.34 | odd | 2 | 2695.2.a.g.1.3 | 3 | |||
55.54 | odd | 2 | 4235.2.a.q.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
385.2.a.f.1.3 | ✓ | 3 | 5.4 | even | 2 | ||
1925.2.a.v.1.1 | 3 | 1.1 | even | 1 | trivial | ||
1925.2.b.n.1849.3 | 6 | 5.2 | odd | 4 | |||
1925.2.b.n.1849.4 | 6 | 5.3 | odd | 4 | |||
2695.2.a.g.1.3 | 3 | 35.34 | odd | 2 | |||
3465.2.a.bh.1.1 | 3 | 15.14 | odd | 2 | |||
4235.2.a.q.1.1 | 3 | 55.54 | odd | 2 | |||
6160.2.a.bn.1.2 | 3 | 20.19 | odd | 2 |