Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4598,2,Mod(1,4598)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4598, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4598.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4598 = 2 \cdot 11^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4598.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: | \(36.7152148494\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.33452.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 8x^{2} + 7x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.79836\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4598.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −2.79836 | −1.61563 | −0.807816 | − | 0.589434i | \(-0.799351\pi\) | ||||
−0.807816 | + | 0.589434i | \(0.799351\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.116104 | 0.0519234 | 0.0259617 | − | 0.999663i | \(-0.491735\pi\) | ||||
0.0259617 | + | 0.999663i | \(0.491735\pi\) | |||||||
\(6\) | −2.79836 | −1.14242 | ||||||||
\(7\) | −2.35735 | −0.890995 | −0.445498 | − | 0.895283i | \(-0.646973\pi\) | ||||
−0.445498 | + | 0.895283i | \(0.646973\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 4.83081 | 1.61027 | ||||||||
\(10\) | 0.116104 | 0.0367154 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −2.79836 | −0.807816 | ||||||||
\(13\) | −2.88390 | −0.799849 | −0.399924 | − | 0.916548i | \(-0.630964\pi\) | ||||
−0.399924 | + | 0.916548i | \(0.630964\pi\) | |||||||
\(14\) | −2.35735 | −0.630029 | ||||||||
\(15\) | −0.324902 | −0.0838892 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.91446 | −0.706861 | −0.353431 | − | 0.935461i | \(-0.614985\pi\) | ||||
−0.353431 | + | 0.935461i | \(0.614985\pi\) | |||||||
\(18\) | 4.83081 | 1.13863 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0.116104 | 0.0259617 | ||||||||
\(21\) | 6.59672 | 1.43952 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.44101 | −0.300471 | −0.150235 | − | 0.988650i | \(-0.548003\pi\) | ||||
−0.150235 | + | 0.988650i | \(0.548003\pi\) | |||||||
\(24\) | −2.79836 | −0.571212 | ||||||||
\(25\) | −4.98652 | −0.997304 | ||||||||
\(26\) | −2.88390 | −0.565578 | ||||||||
\(27\) | −5.12326 | −0.985972 | ||||||||
\(28\) | −2.35735 | −0.445498 | ||||||||
\(29\) | −5.15383 | −0.957042 | −0.478521 | − | 0.878076i | \(-0.658827\pi\) | ||||
−0.478521 | + | 0.878076i | \(0.658827\pi\) | |||||||
\(30\) | −0.324902 | −0.0593186 | ||||||||
\(31\) | 8.32490 | 1.49520 | 0.747598 | − | 0.664151i | \(-0.231207\pi\) | ||||
0.747598 | + | 0.664151i | \(0.231207\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.91446 | −0.499826 | ||||||||
\(35\) | −0.273699 | −0.0462636 | ||||||||
\(36\) | 4.83081 | 0.805135 | ||||||||
\(37\) | 10.5436 | 1.73336 | 0.866681 | − | 0.498863i | \(-0.166249\pi\) | ||||
0.866681 | + | 0.498863i | \(0.166249\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | 8.07017 | 1.29226 | ||||||||
\(40\) | 0.116104 | 0.0183577 | ||||||||
\(41\) | −9.98652 | −1.55963 | −0.779816 | − | 0.626009i | \(-0.784687\pi\) | ||||
−0.779816 | + | 0.626009i | \(0.784687\pi\) | |||||||
\(42\) | 6.59672 | 1.01790 | ||||||||
\(43\) | 2.76591 | 0.421797 | 0.210898 | − | 0.977508i | \(-0.432361\pi\) | ||||
0.210898 | + | 0.977508i | \(0.432361\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.560878 | 0.0836107 | ||||||||
\(46\) | −1.44101 | −0.212465 | ||||||||
\(47\) | 4.23221 | 0.617331 | 0.308666 | − | 0.951171i | \(-0.400118\pi\) | ||||
0.308666 | + | 0.951171i | \(0.400118\pi\) | |||||||
\(48\) | −2.79836 | −0.403908 | ||||||||
\(49\) | −1.44289 | −0.206127 | ||||||||
\(50\) | −4.98652 | −0.705200 | ||||||||
\(51\) | 8.15571 | 1.14203 | ||||||||
\(52\) | −2.88390 | −0.399924 | ||||||||
\(53\) | 5.56427 | 0.764311 | 0.382155 | − | 0.924098i | \(-0.375182\pi\) | ||||
0.382155 | + | 0.924098i | \(0.375182\pi\) | |||||||
\(54\) | −5.12326 | −0.697187 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.35735 | −0.315014 | ||||||||
\(57\) | 2.79836 | 0.370652 | ||||||||
\(58\) | −5.15383 | −0.676731 | ||||||||
\(59\) | −8.51118 | −1.10806 | −0.554031 | − | 0.832496i | \(-0.686911\pi\) | ||||
−0.554031 | + | 0.832496i | \(0.686911\pi\) | |||||||
\(60\) | −0.324902 | −0.0419446 | ||||||||
\(61\) | −2.71470 | −0.347582 | −0.173791 | − | 0.984783i | \(-0.555602\pi\) | ||||
−0.173791 | + | 0.984783i | \(0.555602\pi\) | |||||||
\(62\) | 8.32490 | 1.05726 | ||||||||
\(63\) | −11.3879 | −1.43474 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.334833 | −0.0415309 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.41044 | 0.416651 | 0.208326 | − | 0.978060i | \(-0.433199\pi\) | ||||
0.208326 | + | 0.978060i | \(0.433199\pi\) | |||||||
\(68\) | −2.91446 | −0.353431 | ||||||||
\(69\) | 4.03245 | 0.485450 | ||||||||
\(70\) | −0.273699 | −0.0327133 | ||||||||
\(71\) | −1.16919 | −0.138757 | −0.0693787 | − | 0.997590i | \(-0.522102\pi\) | ||||
−0.0693787 | + | 0.997590i | \(0.522102\pi\) | |||||||
\(72\) | 4.83081 | 0.569316 | ||||||||
\(73\) | 1.31775 | 0.154231 | 0.0771153 | − | 0.997022i | \(-0.475429\pi\) | ||||
0.0771153 | + | 0.997022i | \(0.475429\pi\) | |||||||
\(74\) | 10.5436 | 1.22567 | ||||||||
\(75\) | 13.9541 | 1.61128 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 8.07017 | 0.913767 | ||||||||
\(79\) | 1.93510 | 0.217716 | 0.108858 | − | 0.994057i | \(-0.465281\pi\) | ||||
0.108858 | + | 0.994057i | \(0.465281\pi\) | |||||||
\(80\) | 0.116104 | 0.0129809 | ||||||||
\(81\) | −0.155711 | −0.0173012 | ||||||||
\(82\) | −9.98652 | −1.10283 | ||||||||
\(83\) | −4.05120 | −0.444677 | −0.222339 | − | 0.974970i | \(-0.571369\pi\) | ||||
−0.222339 | + | 0.974970i | \(0.571369\pi\) | |||||||
\(84\) | 6.59672 | 0.719761 | ||||||||
\(85\) | −0.338382 | −0.0367027 | ||||||||
\(86\) | 2.76591 | 0.298255 | ||||||||
\(87\) | 14.4223 | 1.54623 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.25833 | −0.981382 | −0.490691 | − | 0.871334i | \(-0.663256\pi\) | ||||
−0.490691 | + | 0.871334i | \(0.663256\pi\) | |||||||
\(90\) | 0.560878 | 0.0591217 | ||||||||
\(91\) | 6.79836 | 0.712662 | ||||||||
\(92\) | −1.44101 | −0.150235 | ||||||||
\(93\) | −23.2961 | −2.41569 | ||||||||
\(94\) | 4.23221 | 0.436519 | ||||||||
\(95\) | −0.116104 | −0.0119121 | ||||||||
\(96\) | −2.79836 | −0.285606 | ||||||||
\(97\) | 8.71094 | 0.884462 | 0.442231 | − | 0.896901i | \(-0.354187\pi\) | ||||
0.442231 | + | 0.896901i | \(0.354187\pi\) | |||||||
\(98\) | −1.44289 | −0.145754 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.98652 | −0.498652 | ||||||||
\(101\) | 7.83269 | 0.779382 | 0.389691 | − | 0.920946i | \(-0.372582\pi\) | ||||
0.389691 | + | 0.920946i | \(0.372582\pi\) | |||||||
\(102\) | 8.15571 | 0.807536 | ||||||||
\(103\) | −1.94503 | −0.191649 | −0.0958247 | − | 0.995398i | \(-0.530549\pi\) | ||||
−0.0958247 | + | 0.995398i | \(0.530549\pi\) | |||||||
\(104\) | −2.88390 | −0.282789 | ||||||||
\(105\) | 0.765907 | 0.0747449 | ||||||||
\(106\) | 5.56427 | 0.540449 | ||||||||
\(107\) | 6.57331 | 0.635465 | 0.317733 | − | 0.948180i | \(-0.397079\pi\) | ||||
0.317733 | + | 0.948180i | \(0.397079\pi\) | |||||||
\(108\) | −5.12326 | −0.492986 | ||||||||
\(109\) | −3.02341 | −0.289590 | −0.144795 | − | 0.989462i | \(-0.546252\pi\) | ||||
−0.144795 | + | 0.989462i | \(0.546252\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −29.5049 | −2.80048 | ||||||||
\(112\) | −2.35735 | −0.222749 | ||||||||
\(113\) | −0.478728 | −0.0450350 | −0.0225175 | − | 0.999746i | \(-0.507168\pi\) | ||||
−0.0225175 | + | 0.999746i | \(0.507168\pi\) | |||||||
\(114\) | 2.79836 | 0.262090 | ||||||||
\(115\) | −0.167307 | −0.0156015 | ||||||||
\(116\) | −5.15383 | −0.478521 | ||||||||
\(117\) | −13.9315 | −1.28797 | ||||||||
\(118\) | −8.51118 | −0.783518 | ||||||||
\(119\) | 6.87042 | 0.629810 | ||||||||
\(120\) | −0.324902 | −0.0296593 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −2.71470 | −0.245778 | ||||||||
\(123\) | 27.9459 | 2.51979 | ||||||||
\(124\) | 8.32490 | 0.747598 | ||||||||
\(125\) | −1.15948 | −0.103707 | ||||||||
\(126\) | −11.3879 | −1.01452 | ||||||||
\(127\) | 11.3645 | 1.00844 | 0.504219 | − | 0.863576i | \(-0.331781\pi\) | ||||
0.504219 | + | 0.863576i | \(0.331781\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −7.74000 | −0.681469 | ||||||||
\(130\) | −0.334833 | −0.0293668 | ||||||||
\(131\) | 19.6481 | 1.71667 | 0.858333 | − | 0.513093i | \(-0.171500\pi\) | ||||
0.858333 | + | 0.513093i | \(0.171500\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.35735 | 0.204408 | ||||||||
\(134\) | 3.41044 | 0.294617 | ||||||||
\(135\) | −0.594833 | −0.0511951 | ||||||||
\(136\) | −2.91446 | −0.249913 | ||||||||
\(137\) | −5.18101 | −0.442643 | −0.221322 | − | 0.975201i | \(-0.571037\pi\) | ||||
−0.221322 | + | 0.975201i | \(0.571037\pi\) | |||||||
\(138\) | 4.03245 | 0.343265 | ||||||||
\(139\) | −21.5598 | −1.82868 | −0.914340 | − | 0.404947i | \(-0.867290\pi\) | ||||
−0.914340 | + | 0.404947i | \(0.867290\pi\) | |||||||
\(140\) | −0.273699 | −0.0231318 | ||||||||
\(141\) | −11.8432 | −0.997380 | ||||||||
\(142\) | −1.16919 | −0.0981163 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 4.83081 | 0.402567 | ||||||||
\(145\) | −0.598382 | −0.0496929 | ||||||||
\(146\) | 1.31775 | 0.109057 | ||||||||
\(147\) | 4.03772 | 0.333026 | ||||||||
\(148\) | 10.5436 | 0.866681 | ||||||||
\(149\) | 14.4518 | 1.18393 | 0.591967 | − | 0.805962i | \(-0.298351\pi\) | ||||
0.591967 | + | 0.805962i | \(0.298351\pi\) | |||||||
\(150\) | 13.9541 | 1.13934 | ||||||||
\(151\) | 23.3987 | 1.90416 | 0.952079 | − | 0.305853i | \(-0.0989415\pi\) | ||||
0.952079 | + | 0.305853i | \(0.0989415\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | −14.0792 | −1.13824 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.966557 | 0.0776357 | ||||||||
\(156\) | 8.07017 | 0.646131 | ||||||||
\(157\) | 19.0773 | 1.52254 | 0.761268 | − | 0.648437i | \(-0.224577\pi\) | ||||
0.761268 | + | 0.648437i | \(0.224577\pi\) | |||||||
\(158\) | 1.93510 | 0.153948 | ||||||||
\(159\) | −15.5708 | −1.23485 | ||||||||
\(160\) | 0.116104 | 0.00917885 | ||||||||
\(161\) | 3.39696 | 0.267718 | ||||||||
\(162\) | −0.155711 | −0.0122338 | ||||||||
\(163\) | 14.2465 | 1.11587 | 0.557937 | − | 0.829883i | \(-0.311593\pi\) | ||||
0.557937 | + | 0.829883i | \(0.311593\pi\) | |||||||
\(164\) | −9.98652 | −0.779816 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.05120 | −0.314434 | ||||||||
\(167\) | 8.77584 | 0.679095 | 0.339547 | − | 0.940589i | \(-0.389726\pi\) | ||||
0.339547 | + | 0.940589i | \(0.389726\pi\) | |||||||
\(168\) | 6.59672 | 0.508948 | ||||||||
\(169\) | −4.68315 | −0.360242 | ||||||||
\(170\) | −0.338382 | −0.0259527 | ||||||||
\(171\) | −4.83081 | −0.369421 | ||||||||
\(172\) | 2.76591 | 0.210898 | ||||||||
\(173\) | −2.93321 | −0.223008 | −0.111504 | − | 0.993764i | \(-0.535567\pi\) | ||||
−0.111504 | + | 0.993764i | \(0.535567\pi\) | |||||||
\(174\) | 14.4223 | 1.09335 | ||||||||
\(175\) | 11.7550 | 0.888593 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 23.8173 | 1.79022 | ||||||||
\(178\) | −9.25833 | −0.693942 | ||||||||
\(179\) | 7.27182 | 0.543521 | 0.271760 | − | 0.962365i | \(-0.412394\pi\) | ||||
0.271760 | + | 0.962365i | \(0.412394\pi\) | |||||||
\(180\) | 0.560878 | 0.0418054 | ||||||||
\(181\) | 15.7408 | 1.17001 | 0.585003 | − | 0.811031i | \(-0.301093\pi\) | ||||
0.585003 | + | 0.811031i | \(0.301093\pi\) | |||||||
\(182\) | 6.79836 | 0.503928 | ||||||||
\(183\) | 7.59672 | 0.561565 | ||||||||
\(184\) | −1.44101 | −0.106232 | ||||||||
\(185\) | 1.22416 | 0.0900021 | ||||||||
\(186\) | −23.2961 | −1.70815 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 4.23221 | 0.308666 | ||||||||
\(189\) | 12.0773 | 0.878496 | ||||||||
\(190\) | −0.116104 | −0.00842309 | ||||||||
\(191\) | 24.2998 | 1.75827 | 0.879137 | − | 0.476569i | \(-0.158120\pi\) | ||||
0.879137 | + | 0.476569i | \(0.158120\pi\) | |||||||
\(192\) | −2.79836 | −0.201954 | ||||||||
\(193\) | 10.9100 | 0.785321 | 0.392660 | − | 0.919684i | \(-0.371555\pi\) | ||||
0.392660 | + | 0.919684i | \(0.371555\pi\) | |||||||
\(194\) | 8.71094 | 0.625409 | ||||||||
\(195\) | 0.936982 | 0.0670987 | ||||||||
\(196\) | −1.44289 | −0.103064 | ||||||||
\(197\) | 3.53558 | 0.251900 | 0.125950 | − | 0.992037i | \(-0.459802\pi\) | ||||
0.125950 | + | 0.992037i | \(0.459802\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.09081 | 0.431766 | 0.215883 | − | 0.976419i | \(-0.430737\pi\) | ||||
0.215883 | + | 0.976419i | \(0.430737\pi\) | |||||||
\(200\) | −4.98652 | −0.352600 | ||||||||
\(201\) | −9.54363 | −0.673156 | ||||||||
\(202\) | 7.83269 | 0.551106 | ||||||||
\(203\) | 12.1494 | 0.852720 | ||||||||
\(204\) | 8.15571 | 0.571014 | ||||||||
\(205\) | −1.15948 | −0.0809815 | ||||||||
\(206\) | −1.94503 | −0.135517 | ||||||||
\(207\) | −6.96122 | −0.483839 | ||||||||
\(208\) | −2.88390 | −0.199962 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0.765907 | 0.0528526 | ||||||||
\(211\) | −23.5851 | −1.62367 | −0.811833 | − | 0.583889i | \(-0.801530\pi\) | ||||
−0.811833 | + | 0.583889i | \(0.801530\pi\) | |||||||
\(212\) | 5.56427 | 0.382155 | ||||||||
\(213\) | 3.27182 | 0.224181 | ||||||||
\(214\) | 6.57331 | 0.449342 | ||||||||
\(215\) | 0.321134 | 0.0219011 | ||||||||
\(216\) | −5.12326 | −0.348594 | ||||||||
\(217\) | −19.6247 | −1.33221 | ||||||||
\(218\) | −3.02341 | −0.204771 | ||||||||
\(219\) | −3.68753 | −0.249180 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.40501 | 0.565382 | ||||||||
\(222\) | −29.5049 | −1.98024 | ||||||||
\(223\) | 1.82893 | 0.122474 | 0.0612369 | − | 0.998123i | \(-0.480495\pi\) | ||||
0.0612369 | + | 0.998123i | \(0.480495\pi\) | |||||||
\(224\) | −2.35735 | −0.157507 | ||||||||
\(225\) | −24.0889 | −1.60593 | ||||||||
\(226\) | −0.478728 | −0.0318445 | ||||||||
\(227\) | −8.91169 | −0.591489 | −0.295745 | − | 0.955267i | \(-0.595568\pi\) | ||||
−0.295745 | + | 0.955267i | \(0.595568\pi\) | |||||||
\(228\) | 2.79836 | 0.185326 | ||||||||
\(229\) | −9.45720 | −0.624949 | −0.312475 | − | 0.949926i | \(-0.601158\pi\) | ||||
−0.312475 | + | 0.949926i | \(0.601158\pi\) | |||||||
\(230\) | −0.167307 | −0.0110319 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.15383 | −0.338365 | ||||||||
\(233\) | 17.4294 | 1.14184 | 0.570919 | − | 0.821006i | \(-0.306587\pi\) | ||||
0.570919 | + | 0.821006i | \(0.306587\pi\) | |||||||
\(234\) | −13.9315 | −0.910734 | ||||||||
\(235\) | 0.491378 | 0.0320540 | ||||||||
\(236\) | −8.51118 | −0.554031 | ||||||||
\(237\) | −5.41510 | −0.351748 | ||||||||
\(238\) | 6.87042 | 0.445343 | ||||||||
\(239\) | 25.0036 | 1.61735 | 0.808674 | − | 0.588256i | \(-0.200185\pi\) | ||||
0.808674 | + | 0.588256i | \(0.200185\pi\) | |||||||
\(240\) | −0.324902 | −0.0209723 | ||||||||
\(241\) | −1.94503 | −0.125290 | −0.0626452 | − | 0.998036i | \(-0.519954\pi\) | ||||
−0.0626452 | + | 0.998036i | \(0.519954\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.8055 | 1.01392 | ||||||||
\(244\) | −2.71470 | −0.173791 | ||||||||
\(245\) | −0.167526 | −0.0107028 | ||||||||
\(246\) | 27.9459 | 1.78176 | ||||||||
\(247\) | 2.88390 | 0.183498 | ||||||||
\(248\) | 8.32490 | 0.528632 | ||||||||
\(249\) | 11.3367 | 0.718435 | ||||||||
\(250\) | −1.15948 | −0.0733318 | ||||||||
\(251\) | −12.6048 | −0.795606 | −0.397803 | − | 0.917471i | \(-0.630227\pi\) | ||||
−0.397803 | + | 0.917471i | \(0.630227\pi\) | |||||||
\(252\) | −11.3879 | −0.717371 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 11.3645 | 0.713073 | ||||||||
\(255\) | 0.946913 | 0.0592980 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −2.53986 | −0.158432 | −0.0792161 | − | 0.996857i | \(-0.525242\pi\) | ||||
−0.0792161 | + | 0.996857i | \(0.525242\pi\) | |||||||
\(258\) | −7.74000 | −0.481871 | ||||||||
\(259\) | −24.8551 | −1.54442 | ||||||||
\(260\) | −0.334833 | −0.0207654 | ||||||||
\(261\) | −24.8972 | −1.54110 | ||||||||
\(262\) | 19.6481 | 1.21387 | ||||||||
\(263\) | 31.0972 | 1.91753 | 0.958767 | − | 0.284192i | \(-0.0917252\pi\) | ||||
0.958767 | + | 0.284192i | \(0.0917252\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.646035 | 0.0396856 | ||||||||
\(266\) | 2.35735 | 0.144539 | ||||||||
\(267\) | 25.9081 | 1.58555 | ||||||||
\(268\) | 3.41044 | 0.208326 | ||||||||
\(269\) | −21.4294 | −1.30657 | −0.653287 | − | 0.757110i | \(-0.726611\pi\) | ||||
−0.653287 | + | 0.757110i | \(0.726611\pi\) | |||||||
\(270\) | −0.594833 | −0.0362004 | ||||||||
\(271\) | 18.0152 | 1.09435 | 0.547173 | − | 0.837020i | \(-0.315704\pi\) | ||||
0.547173 | + | 0.837020i | \(0.315704\pi\) | |||||||
\(272\) | −2.91446 | −0.176715 | ||||||||
\(273\) | −19.0242 | −1.15140 | ||||||||
\(274\) | −5.18101 | −0.312996 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 4.03245 | 0.242725 | ||||||||
\(277\) | −27.1522 | −1.63142 | −0.815708 | − | 0.578464i | \(-0.803652\pi\) | ||||
−0.815708 | + | 0.578464i | \(0.803652\pi\) | |||||||
\(278\) | −21.5598 | −1.29307 | ||||||||
\(279\) | 40.2160 | 2.40767 | ||||||||
\(280\) | −0.273699 | −0.0163566 | ||||||||
\(281\) | −16.1810 | −0.965278 | −0.482639 | − | 0.875819i | \(-0.660322\pi\) | ||||
−0.482639 | + | 0.875819i | \(0.660322\pi\) | |||||||
\(282\) | −11.8432 | −0.705254 | ||||||||
\(283\) | 23.8947 | 1.42039 | 0.710195 | − | 0.704005i | \(-0.248607\pi\) | ||||
0.710195 | + | 0.704005i | \(0.248607\pi\) | |||||||
\(284\) | −1.16919 | −0.0693787 | ||||||||
\(285\) | 0.324902 | 0.0192455 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 23.5417 | 1.38963 | ||||||||
\(288\) | 4.83081 | 0.284658 | ||||||||
\(289\) | −8.50591 | −0.500348 | ||||||||
\(290\) | −0.598382 | −0.0351382 | ||||||||
\(291\) | −24.3763 | −1.42897 | ||||||||
\(292\) | 1.31775 | 0.0771153 | ||||||||
\(293\) | −5.58052 | −0.326018 | −0.163009 | − | 0.986625i | \(-0.552120\pi\) | ||||
−0.163009 | + | 0.986625i | \(0.552120\pi\) | |||||||
\(294\) | 4.03772 | 0.235485 | ||||||||
\(295\) | −0.988185 | −0.0575343 | ||||||||
\(296\) | 10.5436 | 0.612836 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 14.4518 | 0.837168 | ||||||||
\(299\) | 4.15571 | 0.240331 | ||||||||
\(300\) | 13.9541 | 0.805639 | ||||||||
\(301\) | −6.52022 | −0.375819 | ||||||||
\(302\) | 23.3987 | 1.34644 | ||||||||
\(303\) | −21.9187 | −1.25920 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | −0.315189 | −0.0180477 | ||||||||
\(306\) | −14.0792 | −0.804855 | ||||||||
\(307\) | 1.22416 | 0.0698666 | 0.0349333 | − | 0.999390i | \(-0.488878\pi\) | ||||
0.0349333 | + | 0.999390i | \(0.488878\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.44289 | 0.309635 | ||||||||
\(310\) | 0.966557 | 0.0548968 | ||||||||
\(311\) | 28.1663 | 1.59716 | 0.798581 | − | 0.601888i | \(-0.205584\pi\) | ||||
0.798581 | + | 0.601888i | \(0.205584\pi\) | |||||||
\(312\) | 8.07017 | 0.456884 | ||||||||
\(313\) | 33.4796 | 1.89238 | 0.946188 | − | 0.323617i | \(-0.104899\pi\) | ||||
0.946188 | + | 0.323617i | \(0.104899\pi\) | |||||||
\(314\) | 19.0773 | 1.07660 | ||||||||
\(315\) | −1.32219 | −0.0744968 | ||||||||
\(316\) | 1.93510 | 0.108858 | ||||||||
\(317\) | 14.4644 | 0.812399 | 0.406200 | − | 0.913784i | \(-0.366854\pi\) | ||||
0.406200 | + | 0.913784i | \(0.366854\pi\) | |||||||
\(318\) | −15.5708 | −0.873168 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0.116104 | 0.00649043 | ||||||||
\(321\) | −18.3945 | −1.02668 | ||||||||
\(322\) | 3.39696 | 0.189305 | ||||||||
\(323\) | 2.91446 | 0.162165 | ||||||||
\(324\) | −0.155711 | −0.00865059 | ||||||||
\(325\) | 14.3806 | 0.797692 | ||||||||
\(326\) | 14.2465 | 0.789042 | ||||||||
\(327\) | 8.46059 | 0.467872 | ||||||||
\(328\) | −9.98652 | −0.551413 | ||||||||
\(329\) | −9.97681 | −0.550039 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.36895 | −0.295104 | −0.147552 | − | 0.989054i | \(-0.547139\pi\) | ||||
−0.147552 | + | 0.989054i | \(0.547139\pi\) | |||||||
\(332\) | −4.05120 | −0.222339 | ||||||||
\(333\) | 50.9343 | 2.79118 | ||||||||
\(334\) | 8.77584 | 0.480193 | ||||||||
\(335\) | 0.395967 | 0.0216340 | ||||||||
\(336\) | 6.59672 | 0.359880 | ||||||||
\(337\) | −29.2373 | −1.59266 | −0.796329 | − | 0.604864i | \(-0.793228\pi\) | ||||
−0.796329 | + | 0.604864i | \(0.793228\pi\) | |||||||
\(338\) | −4.68315 | −0.254730 | ||||||||
\(339\) | 1.33965 | 0.0727600 | ||||||||
\(340\) | −0.338382 | −0.0183513 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −4.83081 | −0.261220 | ||||||||
\(343\) | 19.9029 | 1.07465 | ||||||||
\(344\) | 2.76591 | 0.149128 | ||||||||
\(345\) | 0.468185 | 0.0252062 | ||||||||
\(346\) | −2.93321 | −0.157691 | ||||||||
\(347\) | −26.6983 | −1.43324 | −0.716620 | − | 0.697464i | \(-0.754312\pi\) | ||||
−0.716620 | + | 0.697464i | \(0.754312\pi\) | |||||||
\(348\) | 14.4223 | 0.773114 | ||||||||
\(349\) | 9.89006 | 0.529403 | 0.264701 | − | 0.964330i | \(-0.414727\pi\) | ||||
0.264701 | + | 0.964330i | \(0.414727\pi\) | |||||||
\(350\) | 11.7550 | 0.628330 | ||||||||
\(351\) | 14.7749 | 0.788628 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 34.4402 | 1.83307 | 0.916533 | − | 0.399960i | \(-0.130976\pi\) | ||||
0.916533 | + | 0.399960i | \(0.130976\pi\) | |||||||
\(354\) | 23.8173 | 1.26588 | ||||||||
\(355\) | −0.135748 | −0.00720476 | ||||||||
\(356\) | −9.25833 | −0.490691 | ||||||||
\(357\) | −19.2259 | −1.01754 | ||||||||
\(358\) | 7.27182 | 0.384327 | ||||||||
\(359\) | 18.2006 | 0.960590 | 0.480295 | − | 0.877107i | \(-0.340530\pi\) | ||||
0.480295 | + | 0.877107i | \(0.340530\pi\) | |||||||
\(360\) | 0.560878 | 0.0295609 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 15.7408 | 0.827320 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 6.79836 | 0.356331 | ||||||||
\(365\) | 0.152996 | 0.00800818 | ||||||||
\(366\) | 7.59672 | 0.397087 | ||||||||
\(367\) | −8.77961 | −0.458292 | −0.229146 | − | 0.973392i | \(-0.573593\pi\) | ||||
−0.229146 | + | 0.973392i | \(0.573593\pi\) | |||||||
\(368\) | −1.44101 | −0.0751176 | ||||||||
\(369\) | −48.2430 | −2.51143 | ||||||||
\(370\) | 1.22416 | 0.0636411 | ||||||||
\(371\) | −13.1169 | −0.680997 | ||||||||
\(372\) | −23.2961 | −1.20784 | ||||||||
\(373\) | −36.2449 | −1.87669 | −0.938344 | − | 0.345704i | \(-0.887640\pi\) | ||||
−0.938344 | + | 0.345704i | \(0.887640\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.24464 | 0.167552 | ||||||||
\(376\) | 4.23221 | 0.218259 | ||||||||
\(377\) | 14.8631 | 0.765489 | ||||||||
\(378\) | 12.0773 | 0.621191 | ||||||||
\(379\) | 21.2124 | 1.08961 | 0.544804 | − | 0.838563i | \(-0.316604\pi\) | ||||
0.544804 | + | 0.838563i | \(0.316604\pi\) | |||||||
\(380\) | −0.116104 | −0.00595603 | ||||||||
\(381\) | −31.8020 | −1.62926 | ||||||||
\(382\) | 24.2998 | 1.24329 | ||||||||
\(383\) | −13.4808 | −0.688838 | −0.344419 | − | 0.938816i | \(-0.611924\pi\) | ||||
−0.344419 | + | 0.938816i | \(0.611924\pi\) | |||||||
\(384\) | −2.79836 | −0.142803 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 10.9100 | 0.555305 | ||||||||
\(387\) | 13.3616 | 0.679207 | ||||||||
\(388\) | 8.71094 | 0.442231 | ||||||||
\(389\) | −5.06679 | −0.256896 | −0.128448 | − | 0.991716i | \(-0.541000\pi\) | ||||
−0.128448 | + | 0.991716i | \(0.541000\pi\) | |||||||
\(390\) | 0.936982 | 0.0474459 | ||||||||
\(391\) | 4.19976 | 0.212391 | ||||||||
\(392\) | −1.44289 | −0.0728769 | ||||||||
\(393\) | −54.9825 | −2.77350 | ||||||||
\(394\) | 3.53558 | 0.178120 | ||||||||
\(395\) | 0.224673 | 0.0113045 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.76862 | 0.289519 | 0.144759 | − | 0.989467i | \(-0.453759\pi\) | ||||
0.144759 | + | 0.989467i | \(0.453759\pi\) | |||||||
\(398\) | 6.09081 | 0.305305 | ||||||||
\(399\) | −6.59672 | −0.330249 | ||||||||
\(400\) | −4.98652 | −0.249326 | ||||||||
\(401\) | 18.9431 | 0.945976 | 0.472988 | − | 0.881069i | \(-0.343175\pi\) | ||||
0.472988 | + | 0.881069i | \(0.343175\pi\) | |||||||
\(402\) | −9.54363 | −0.475993 | ||||||||
\(403\) | −24.0081 | −1.19593 | ||||||||
\(404\) | 7.83269 | 0.389691 | ||||||||
\(405\) | −0.0180787 | −0.000898337 0 | ||||||||
\(406\) | 12.1494 | 0.602964 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 8.15571 | 0.403768 | ||||||||
\(409\) | −28.7314 | −1.42068 | −0.710338 | − | 0.703860i | \(-0.751458\pi\) | ||||
−0.710338 | + | 0.703860i | \(0.751458\pi\) | |||||||
\(410\) | −1.15948 | −0.0572626 | ||||||||
\(411\) | 14.4983 | 0.715149 | ||||||||
\(412\) | −1.94503 | −0.0958247 | ||||||||
\(413\) | 20.0638 | 0.987277 | ||||||||
\(414\) | −6.96122 | −0.342126 | ||||||||
\(415\) | −0.470362 | −0.0230892 | ||||||||
\(416\) | −2.88390 | −0.141395 | ||||||||
\(417\) | 60.3321 | 2.95448 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −32.9954 | −1.61193 | −0.805965 | − | 0.591963i | \(-0.798353\pi\) | ||||
−0.805965 | + | 0.591963i | \(0.798353\pi\) | |||||||
\(420\) | 0.765907 | 0.0373725 | ||||||||
\(421\) | 21.1197 | 1.02931 | 0.514656 | − | 0.857397i | \(-0.327920\pi\) | ||||
0.514656 | + | 0.857397i | \(0.327920\pi\) | |||||||
\(422\) | −23.5851 | −1.14811 | ||||||||
\(423\) | 20.4450 | 0.994070 | ||||||||
\(424\) | 5.56427 | 0.270225 | ||||||||
\(425\) | 14.5330 | 0.704955 | ||||||||
\(426\) | 3.27182 | 0.158520 | ||||||||
\(427\) | 6.39952 | 0.309694 | ||||||||
\(428\) | 6.57331 | 0.317733 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.321134 | 0.0154865 | ||||||||
\(431\) | −38.9916 | −1.87816 | −0.939080 | − | 0.343698i | \(-0.888320\pi\) | ||||
−0.939080 | + | 0.343698i | \(0.888320\pi\) | |||||||
\(432\) | −5.12326 | −0.246493 | ||||||||
\(433\) | 15.8146 | 0.760002 | 0.380001 | − | 0.924986i | \(-0.375924\pi\) | ||||
0.380001 | + | 0.924986i | \(0.375924\pi\) | |||||||
\(434\) | −19.6247 | −0.942017 | ||||||||
\(435\) | 1.67449 | 0.0802855 | ||||||||
\(436\) | −3.02341 | −0.144795 | ||||||||
\(437\) | 1.44101 | 0.0689327 | ||||||||
\(438\) | −3.68753 | −0.176197 | ||||||||
\(439\) | 14.6697 | 0.700145 | 0.350072 | − | 0.936723i | \(-0.386157\pi\) | ||||
0.350072 | + | 0.936723i | \(0.386157\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.97032 | −0.331920 | ||||||||
\(442\) | 8.40501 | 0.399785 | ||||||||
\(443\) | 18.4375 | 0.875990 | 0.437995 | − | 0.898977i | \(-0.355689\pi\) | ||||
0.437995 | + | 0.898977i | \(0.355689\pi\) | |||||||
\(444\) | −29.5049 | −1.40024 | ||||||||
\(445\) | −1.07493 | −0.0509567 | ||||||||
\(446\) | 1.82893 | 0.0866021 | ||||||||
\(447\) | −40.4412 | −1.91280 | ||||||||
\(448\) | −2.35735 | −0.111374 | ||||||||
\(449\) | 26.6266 | 1.25659 | 0.628294 | − | 0.777976i | \(-0.283754\pi\) | ||||
0.628294 | + | 0.777976i | \(0.283754\pi\) | |||||||
\(450\) | −24.0889 | −1.13556 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −0.478728 | −0.0225175 | ||||||||
\(453\) | −65.4779 | −3.07642 | ||||||||
\(454\) | −8.91169 | −0.418246 | ||||||||
\(455\) | 0.789319 | 0.0370038 | ||||||||
\(456\) | 2.79836 | 0.131045 | ||||||||
\(457\) | −5.75520 | −0.269217 | −0.134609 | − | 0.990899i | \(-0.542978\pi\) | ||||
−0.134609 | + | 0.990899i | \(0.542978\pi\) | |||||||
\(458\) | −9.45720 | −0.441906 | ||||||||
\(459\) | 14.9315 | 0.696945 | ||||||||
\(460\) | −0.167307 | −0.00780073 | ||||||||
\(461\) | −18.3114 | −0.852848 | −0.426424 | − | 0.904523i | \(-0.640227\pi\) | ||||
−0.426424 | + | 0.904523i | \(0.640227\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.12176 | 0.0521324 | 0.0260662 | − | 0.999660i | \(-0.491702\pi\) | ||||
0.0260662 | + | 0.999660i | \(0.491702\pi\) | |||||||
\(464\) | −5.15383 | −0.239260 | ||||||||
\(465\) | −2.70477 | −0.125431 | ||||||||
\(466\) | 17.4294 | 0.807402 | ||||||||
\(467\) | −19.1053 | −0.884090 | −0.442045 | − | 0.896993i | \(-0.645747\pi\) | ||||
−0.442045 | + | 0.896993i | \(0.645747\pi\) | |||||||
\(468\) | −13.9315 | −0.643986 | ||||||||
\(469\) | −8.03961 | −0.371235 | ||||||||
\(470\) | 0.491378 | 0.0226656 | ||||||||
\(471\) | −53.3852 | −2.45986 | ||||||||
\(472\) | −8.51118 | −0.391759 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −5.41510 | −0.248724 | ||||||||
\(475\) | 4.98652 | 0.228797 | ||||||||
\(476\) | 6.87042 | 0.314905 | ||||||||
\(477\) | 26.8799 | 1.23075 | ||||||||
\(478\) | 25.0036 | 1.14364 | ||||||||
\(479\) | −16.7568 | −0.765638 | −0.382819 | − | 0.923823i | \(-0.625047\pi\) | ||||
−0.382819 | + | 0.923823i | \(0.625047\pi\) | |||||||
\(480\) | −0.324902 | −0.0148297 | ||||||||
\(481\) | −30.4067 | −1.38643 | ||||||||
\(482\) | −1.94503 | −0.0885937 | ||||||||
\(483\) | −9.50591 | −0.432534 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.01138 | 0.0459243 | ||||||||
\(486\) | 15.8055 | 0.716953 | ||||||||
\(487\) | −1.61042 | −0.0729749 | −0.0364874 | − | 0.999334i | \(-0.511617\pi\) | ||||
−0.0364874 | + | 0.999334i | \(0.511617\pi\) | |||||||
\(488\) | −2.71470 | −0.122889 | ||||||||
\(489\) | −39.8669 | −1.80284 | ||||||||
\(490\) | −0.167526 | −0.00756804 | ||||||||
\(491\) | 0.200650 | 0.00905520 | 0.00452760 | − | 0.999990i | \(-0.498559\pi\) | ||||
0.00452760 | + | 0.999990i | \(0.498559\pi\) | |||||||
\(492\) | 27.9459 | 1.25990 | ||||||||
\(493\) | 15.0206 | 0.676495 | ||||||||
\(494\) | 2.88390 | 0.129753 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.32490 | 0.373799 | ||||||||
\(497\) | 2.75619 | 0.123632 | ||||||||
\(498\) | 11.3367 | 0.508010 | ||||||||
\(499\) | −22.9954 | −1.02942 | −0.514708 | − | 0.857366i | \(-0.672100\pi\) | ||||
−0.514708 | + | 0.857366i | \(0.672100\pi\) | |||||||
\(500\) | −1.15948 | −0.0518534 | ||||||||
\(501\) | −24.5579 | −1.09717 | ||||||||
\(502\) | −12.6048 | −0.562578 | ||||||||
\(503\) | 19.3795 | 0.864089 | 0.432044 | − | 0.901852i | \(-0.357792\pi\) | ||||
0.432044 | + | 0.901852i | \(0.357792\pi\) | |||||||
\(504\) | −11.3879 | −0.507258 | ||||||||
\(505\) | 0.909410 | 0.0404682 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 13.1051 | 0.582019 | ||||||||
\(508\) | 11.3645 | 0.504219 | ||||||||
\(509\) | −20.0485 | −0.888633 | −0.444317 | − | 0.895870i | \(-0.646554\pi\) | ||||
−0.444317 | + | 0.895870i | \(0.646554\pi\) | |||||||
\(510\) | 0.946913 | 0.0419300 | ||||||||
\(511\) | −3.10639 | −0.137419 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 5.12326 | 0.226197 | ||||||||
\(514\) | −2.53986 | −0.112029 | ||||||||
\(515\) | −0.225826 | −0.00995110 | ||||||||
\(516\) | −7.74000 | −0.340735 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −24.8551 | −1.09207 | ||||||||
\(519\) | 8.20819 | 0.360299 | ||||||||
\(520\) | −0.334833 | −0.0146834 | ||||||||
\(521\) | −37.7371 | −1.65329 | −0.826645 | − | 0.562723i | \(-0.809754\pi\) | ||||
−0.826645 | + | 0.562723i | \(0.809754\pi\) | |||||||
\(522\) | −24.8972 | −1.08972 | ||||||||
\(523\) | 19.3222 | 0.844900 | 0.422450 | − | 0.906386i | \(-0.361170\pi\) | ||||
0.422450 | + | 0.906386i | \(0.361170\pi\) | |||||||
\(524\) | 19.6481 | 0.858333 | ||||||||
\(525\) | −32.8947 | −1.43564 | ||||||||
\(526\) | 31.0972 | 1.35590 | ||||||||
\(527\) | −24.2626 | −1.05690 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.9235 | −0.909717 | ||||||||
\(530\) | 0.646035 | 0.0280620 | ||||||||
\(531\) | −41.1159 | −1.78428 | ||||||||
\(532\) | 2.35735 | 0.102204 | ||||||||
\(533\) | 28.8001 | 1.24747 | ||||||||
\(534\) | 25.9081 | 1.12115 | ||||||||
\(535\) | 0.763189 | 0.0329956 | ||||||||
\(536\) | 3.41044 | 0.147309 | ||||||||
\(537\) | −20.3491 | −0.878130 | ||||||||
\(538\) | −21.4294 | −0.923887 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −0.594833 | −0.0255975 | ||||||||
\(541\) | −36.4375 | −1.56657 | −0.783284 | − | 0.621664i | \(-0.786457\pi\) | ||||
−0.783284 | + | 0.621664i | \(0.786457\pi\) | |||||||
\(542\) | 18.0152 | 0.773819 | ||||||||
\(543\) | −44.0485 | −1.89030 | ||||||||
\(544\) | −2.91446 | −0.124957 | ||||||||
\(545\) | −0.351031 | −0.0150365 | ||||||||
\(546\) | −19.0242 | −0.814162 | ||||||||
\(547\) | −0.362012 | −0.0154785 | −0.00773926 | − | 0.999970i | \(-0.502464\pi\) | ||||
−0.00773926 | + | 0.999970i | \(0.502464\pi\) | |||||||
\(548\) | −5.18101 | −0.221322 | ||||||||
\(549\) | −13.1142 | −0.559701 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.15383 | 0.219560 | ||||||||
\(552\) | 4.03245 | 0.171633 | ||||||||
\(553\) | −4.56171 | −0.193984 | ||||||||
\(554\) | −27.1522 | −1.15358 | ||||||||
\(555\) | −3.42564 | −0.145410 | ||||||||
\(556\) | −21.5598 | −0.914340 | ||||||||
\(557\) | −16.2646 | −0.689153 | −0.344577 | − | 0.938758i | \(-0.611978\pi\) | ||||
−0.344577 | + | 0.938758i | \(0.611978\pi\) | |||||||
\(558\) | 40.2160 | 1.70248 | ||||||||
\(559\) | −7.97659 | −0.337374 | ||||||||
\(560\) | −0.273699 | −0.0115659 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −16.1810 | −0.682555 | ||||||||
\(563\) | 27.4256 | 1.15585 | 0.577926 | − | 0.816089i | \(-0.303862\pi\) | ||||
0.577926 | + | 0.816089i | \(0.303862\pi\) | |||||||
\(564\) | −11.8432 | −0.498690 | ||||||||
\(565\) | −0.0555824 | −0.00233837 | ||||||||
\(566\) | 23.8947 | 1.00437 | ||||||||
\(567\) | 0.367065 | 0.0154153 | ||||||||
\(568\) | −1.16919 | −0.0490582 | ||||||||
\(569\) | 29.5183 | 1.23747 | 0.618736 | − | 0.785599i | \(-0.287645\pi\) | ||||
0.618736 | + | 0.785599i | \(0.287645\pi\) | |||||||
\(570\) | 0.324902 | 0.0136086 | ||||||||
\(571\) | −11.2449 | −0.470583 | −0.235291 | − | 0.971925i | \(-0.575604\pi\) | ||||
−0.235291 | + | 0.971925i | \(0.575604\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −67.9996 | −2.84072 | ||||||||
\(574\) | 23.5417 | 0.982614 | ||||||||
\(575\) | 7.18560 | 0.299660 | ||||||||
\(576\) | 4.83081 | 0.201284 | ||||||||
\(577\) | 3.62933 | 0.151091 | 0.0755455 | − | 0.997142i | \(-0.475930\pi\) | ||||
0.0755455 | + | 0.997142i | \(0.475930\pi\) | |||||||
\(578\) | −8.50591 | −0.353799 | ||||||||
\(579\) | −30.5301 | −1.26879 | ||||||||
\(580\) | −0.598382 | −0.0248464 | ||||||||
\(581\) | 9.55011 | 0.396205 | ||||||||
\(582\) | −24.3763 | −1.01043 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 1.31775 | 0.0545287 | ||||||||
\(585\) | −1.61751 | −0.0668759 | ||||||||
\(586\) | −5.58052 | −0.230529 | ||||||||
\(587\) | 3.55545 | 0.146749 | 0.0733745 | − | 0.997304i | \(-0.476623\pi\) | ||||
0.0733745 | + | 0.997304i | \(0.476623\pi\) | |||||||
\(588\) | 4.03772 | 0.166513 | ||||||||
\(589\) | −8.32490 | −0.343022 | ||||||||
\(590\) | −0.988185 | −0.0406829 | ||||||||
\(591\) | −9.89383 | −0.406978 | ||||||||
\(592\) | 10.5436 | 0.433341 | ||||||||
\(593\) | −40.0017 | −1.64267 | −0.821336 | − | 0.570445i | \(-0.806771\pi\) | ||||
−0.821336 | + | 0.570445i | \(0.806771\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.797685 | 0.0327019 | ||||||||
\(596\) | 14.4518 | 0.591967 | ||||||||
\(597\) | −17.0443 | −0.697575 | ||||||||
\(598\) | 4.15571 | 0.169940 | ||||||||
\(599\) | 5.82276 | 0.237912 | 0.118956 | − | 0.992900i | \(-0.462045\pi\) | ||||
0.118956 | + | 0.992900i | \(0.462045\pi\) | |||||||
\(600\) | 13.9541 | 0.569672 | ||||||||
\(601\) | 38.8791 | 1.58591 | 0.792955 | − | 0.609280i | \(-0.208541\pi\) | ||||
0.792955 | + | 0.609280i | \(0.208541\pi\) | |||||||
\(602\) | −6.52022 | −0.265744 | ||||||||
\(603\) | 16.4752 | 0.670921 | ||||||||
\(604\) | 23.3987 | 0.952079 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −21.9187 | −0.890386 | ||||||||
\(607\) | −5.26210 | −0.213582 | −0.106791 | − | 0.994281i | \(-0.534058\pi\) | ||||
−0.106791 | + | 0.994281i | \(0.534058\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | −33.9983 | −1.37768 | ||||||||
\(610\) | −0.315189 | −0.0127616 | ||||||||
\(611\) | −12.2052 | −0.493771 | ||||||||
\(612\) | −14.0792 | −0.569118 | ||||||||
\(613\) | 41.7855 | 1.68770 | 0.843851 | − | 0.536577i | \(-0.180283\pi\) | ||||
0.843851 | + | 0.536577i | \(0.180283\pi\) | |||||||
\(614\) | 1.22416 | 0.0494031 | ||||||||
\(615\) | 3.24464 | 0.130836 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.7661 | 0.755496 | 0.377748 | − | 0.925908i | \(-0.376699\pi\) | ||||
0.377748 | + | 0.925908i | \(0.376699\pi\) | |||||||
\(618\) | 5.44289 | 0.218945 | ||||||||
\(619\) | −26.7901 | −1.07679 | −0.538394 | − | 0.842694i | \(-0.680969\pi\) | ||||
−0.538394 | + | 0.842694i | \(0.680969\pi\) | |||||||
\(620\) | 0.966557 | 0.0388179 | ||||||||
\(621\) | 7.38265 | 0.296255 | ||||||||
\(622\) | 28.1663 | 1.12936 | ||||||||
\(623\) | 21.8252 | 0.874406 | ||||||||
\(624\) | 8.07017 | 0.323065 | ||||||||
\(625\) | 24.7980 | 0.991919 | ||||||||
\(626\) | 33.4796 | 1.33811 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 19.0773 | 0.761268 | ||||||||
\(629\) | −30.7290 | −1.22525 | ||||||||
\(630\) | −1.32219 | −0.0526772 | ||||||||
\(631\) | 10.0038 | 0.398244 | 0.199122 | − | 0.979975i | \(-0.436191\pi\) | ||||
0.199122 | + | 0.979975i | \(0.436191\pi\) | |||||||
\(632\) | 1.93510 | 0.0769741 | ||||||||
\(633\) | 65.9996 | 2.62325 | ||||||||
\(634\) | 14.4644 | 0.574453 | ||||||||
\(635\) | 1.31947 | 0.0523615 | ||||||||
\(636\) | −15.5708 | −0.617423 | ||||||||
\(637\) | 4.16114 | 0.164871 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.64814 | −0.223437 | ||||||||
\(640\) | 0.116104 | 0.00458943 | ||||||||
\(641\) | −17.8470 | −0.704914 | −0.352457 | − | 0.935828i | \(-0.614654\pi\) | ||||
−0.352457 | + | 0.935828i | \(0.614654\pi\) | |||||||
\(642\) | −18.3945 | −0.725972 | ||||||||
\(643\) | 37.1053 | 1.46329 | 0.731646 | − | 0.681685i | \(-0.238752\pi\) | ||||
0.731646 | + | 0.681685i | \(0.238752\pi\) | |||||||
\(644\) | 3.39696 | 0.133859 | ||||||||
\(645\) | −0.898648 | −0.0353842 | ||||||||
\(646\) | 2.91446 | 0.114668 | ||||||||
\(647\) | 28.7099 | 1.12870 | 0.564351 | − | 0.825535i | \(-0.309126\pi\) | ||||
0.564351 | + | 0.825535i | \(0.309126\pi\) | |||||||
\(648\) | −0.155711 | −0.00611689 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 14.3806 | 0.564054 | ||||||||
\(651\) | 54.9170 | 2.15237 | ||||||||
\(652\) | 14.2465 | 0.557937 | ||||||||
\(653\) | −23.2212 | −0.908717 | −0.454358 | − | 0.890819i | \(-0.650131\pi\) | ||||
−0.454358 | + | 0.890819i | \(0.650131\pi\) | |||||||
\(654\) | 8.46059 | 0.330835 | ||||||||
\(655\) | 2.28123 | 0.0891352 | ||||||||
\(656\) | −9.98652 | −0.389908 | ||||||||
\(657\) | 6.36578 | 0.248353 | ||||||||
\(658\) | −9.97681 | −0.388936 | ||||||||
\(659\) | −9.79370 | −0.381508 | −0.190754 | − | 0.981638i | \(-0.561093\pi\) | ||||
−0.190754 | + | 0.981638i | \(0.561093\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.9368 | 1.00883 | 0.504413 | − | 0.863463i | \(-0.331709\pi\) | ||||
0.504413 | + | 0.863463i | \(0.331709\pi\) | |||||||
\(662\) | −5.36895 | −0.208670 | ||||||||
\(663\) | −23.5202 | −0.913450 | ||||||||
\(664\) | −4.05120 | −0.157217 | ||||||||
\(665\) | 0.273699 | 0.0106136 | ||||||||
\(666\) | 50.9343 | 1.97366 | ||||||||
\(667\) | 7.42669 | 0.287563 | ||||||||
\(668\) | 8.77584 | 0.339547 | ||||||||
\(669\) | −5.11799 | −0.197873 | ||||||||
\(670\) | 0.395967 | 0.0152975 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 6.59672 | 0.254474 | ||||||||
\(673\) | 16.0695 | 0.619434 | 0.309717 | − | 0.950829i | \(-0.399766\pi\) | ||||
0.309717 | + | 0.950829i | \(0.399766\pi\) | |||||||
\(674\) | −29.2373 | −1.12618 | ||||||||
\(675\) | 25.5472 | 0.983314 | ||||||||
\(676\) | −4.68315 | −0.180121 | ||||||||
\(677\) | −18.9254 | −0.727362 | −0.363681 | − | 0.931524i | \(-0.618480\pi\) | ||||
−0.363681 | + | 0.931524i | \(0.618480\pi\) | |||||||
\(678\) | 1.33965 | 0.0514491 | ||||||||
\(679\) | −20.5347 | −0.788051 | ||||||||
\(680\) | −0.338382 | −0.0129763 | ||||||||
\(681\) | 24.9381 | 0.955630 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 24.8175 | 0.949617 | 0.474809 | − | 0.880089i | \(-0.342517\pi\) | ||||
0.474809 | + | 0.880089i | \(0.342517\pi\) | |||||||
\(684\) | −4.83081 | −0.184711 | ||||||||
\(685\) | −0.601537 | −0.0229836 | ||||||||
\(686\) | 19.9029 | 0.759895 | ||||||||
\(687\) | 26.4646 | 1.00969 | ||||||||
\(688\) | 2.76591 | 0.105449 | ||||||||
\(689\) | −16.0468 | −0.611333 | ||||||||
\(690\) | 0.468185 | 0.0178235 | ||||||||
\(691\) | −0.761528 | −0.0289699 | −0.0144849 | − | 0.999895i | \(-0.504611\pi\) | ||||
−0.0144849 | + | 0.999895i | \(0.504611\pi\) | |||||||
\(692\) | −2.93321 | −0.111504 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −26.6983 | −1.01345 | ||||||||
\(695\) | −2.50319 | −0.0949514 | ||||||||
\(696\) | 14.4223 | 0.546674 | ||||||||
\(697\) | 29.1053 | 1.10244 | ||||||||
\(698\) | 9.89006 | 0.374344 | ||||||||
\(699\) | −48.7737 | −1.84479 | ||||||||
\(700\) | 11.7550 | 0.444297 | ||||||||
\(701\) | 37.8593 | 1.42993 | 0.714964 | − | 0.699162i | \(-0.246443\pi\) | ||||
0.714964 | + | 0.699162i | \(0.246443\pi\) | |||||||
\(702\) | 14.7749 | 0.557644 | ||||||||
\(703\) | −10.5436 | −0.397661 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.37505 | −0.0517874 | ||||||||
\(706\) | 34.4402 | 1.29617 | ||||||||
\(707\) | −18.4644 | −0.694426 | ||||||||
\(708\) | 23.8173 | 0.895110 | ||||||||
\(709\) | 10.3898 | 0.390197 | 0.195099 | − | 0.980784i | \(-0.437497\pi\) | ||||
0.195099 | + | 0.980784i | \(0.437497\pi\) | |||||||
\(710\) | −0.135748 | −0.00509454 | ||||||||
\(711\) | 9.34809 | 0.350581 | ||||||||
\(712\) | −9.25833 | −0.346971 | ||||||||
\(713\) | −11.9962 | −0.449262 | ||||||||
\(714\) | −19.2259 | −0.719511 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 7.27182 | 0.271760 | ||||||||
\(717\) | −69.9690 | −2.61304 | ||||||||
\(718\) | 18.2006 | 0.679240 | ||||||||
\(719\) | −49.0175 | −1.82805 | −0.914023 | − | 0.405663i | \(-0.867041\pi\) | ||||
−0.914023 | + | 0.405663i | \(0.867041\pi\) | |||||||
\(720\) | 0.560878 | 0.0209027 | ||||||||
\(721\) | 4.58512 | 0.170759 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | 5.44289 | 0.202423 | ||||||||
\(724\) | 15.7408 | 0.585003 | ||||||||
\(725\) | 25.6997 | 0.954461 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.39418 | −0.200059 | −0.100030 | − | 0.994984i | \(-0.531894\pi\) | ||||
−0.100030 | + | 0.994984i | \(0.531894\pi\) | |||||||
\(728\) | 6.79836 | 0.251964 | ||||||||
\(729\) | −43.7624 | −1.62083 | ||||||||
\(730\) | 0.152996 | 0.00566264 | ||||||||
\(731\) | −8.06113 | −0.298152 | ||||||||
\(732\) | 7.59672 | 0.280783 | ||||||||
\(733\) | −19.9693 | −0.737582 | −0.368791 | − | 0.929512i | \(-0.620228\pi\) | ||||
−0.368791 | + | 0.929512i | \(0.620228\pi\) | |||||||
\(734\) | −8.77961 | −0.324061 | ||||||||
\(735\) | 0.468797 | 0.0172918 | ||||||||
\(736\) | −1.44101 | −0.0531162 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −48.2430 | −1.77585 | ||||||||
\(739\) | 48.7027 | 1.79156 | 0.895778 | − | 0.444501i | \(-0.146619\pi\) | ||||
0.895778 | + | 0.444501i | \(0.146619\pi\) | |||||||
\(740\) | 1.22416 | 0.0450011 | ||||||||
\(741\) | −8.07017 | −0.296465 | ||||||||
\(742\) | −13.1169 | −0.481538 | ||||||||
\(743\) | −37.5929 | −1.37915 | −0.689576 | − | 0.724214i | \(-0.742203\pi\) | ||||
−0.689576 | + | 0.724214i | \(0.742203\pi\) | |||||||
\(744\) | −23.2961 | −0.854075 | ||||||||
\(745\) | 1.67791 | 0.0614740 | ||||||||
\(746\) | −36.2449 | −1.32702 | ||||||||
\(747\) | −19.5706 | −0.716050 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −15.4956 | −0.566197 | ||||||||
\(750\) | 3.24464 | 0.118477 | ||||||||
\(751\) | −26.4442 | −0.964964 | −0.482482 | − | 0.875906i | \(-0.660265\pi\) | ||||
−0.482482 | + | 0.875906i | \(0.660265\pi\) | |||||||
\(752\) | 4.23221 | 0.154333 | ||||||||
\(753\) | 35.2726 | 1.28541 | ||||||||
\(754\) | 14.8631 | 0.541282 | ||||||||
\(755\) | 2.71669 | 0.0988704 | ||||||||
\(756\) | 12.0773 | 0.439248 | ||||||||
\(757\) | 49.7039 | 1.80652 | 0.903260 | − | 0.429093i | \(-0.141167\pi\) | ||||
0.903260 | + | 0.429093i | \(0.141167\pi\) | |||||||
\(758\) | 21.2124 | 0.770469 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.116104 | −0.00421155 | ||||||||
\(761\) | −7.24019 | −0.262457 | −0.131228 | − | 0.991352i | \(-0.541892\pi\) | ||||
−0.131228 | + | 0.991352i | \(0.541892\pi\) | |||||||
\(762\) | −31.8020 | −1.15206 | ||||||||
\(763\) | 7.12725 | 0.258024 | ||||||||
\(764\) | 24.2998 | 0.879137 | ||||||||
\(765\) | −1.63466 | −0.0591012 | ||||||||
\(766\) | −13.4808 | −0.487082 | ||||||||
\(767\) | 24.5454 | 0.886281 | ||||||||
\(768\) | −2.79836 | −0.100977 | ||||||||
\(769\) | 31.5373 | 1.13726 | 0.568632 | − | 0.822592i | \(-0.307473\pi\) | ||||
0.568632 | + | 0.822592i | \(0.307473\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.10744 | 0.255968 | ||||||||
\(772\) | 10.9100 | 0.392660 | ||||||||
\(773\) | −36.0430 | −1.29638 | −0.648188 | − | 0.761480i | \(-0.724473\pi\) | ||||
−0.648188 | + | 0.761480i | \(0.724473\pi\) | |||||||
\(774\) | 13.3616 | 0.480272 | ||||||||
\(775\) | −41.5123 | −1.49117 | ||||||||
\(776\) | 8.71094 | 0.312704 | ||||||||
\(777\) | 69.5533 | 2.49521 | ||||||||
\(778\) | −5.06679 | −0.181653 | ||||||||
\(779\) | 9.98652 | 0.357804 | ||||||||
\(780\) | 0.936982 | 0.0335493 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 4.19976 | 0.150183 | ||||||||
\(783\) | 26.4044 | 0.943616 | ||||||||
\(784\) | −1.44289 | −0.0515318 | ||||||||
\(785\) | 2.21496 | 0.0790553 | ||||||||
\(786\) | −54.9825 | −1.96116 | ||||||||
\(787\) | −24.5894 | −0.876517 | −0.438259 | − | 0.898849i | \(-0.644405\pi\) | ||||
−0.438259 | + | 0.898849i | \(0.644405\pi\) | |||||||
\(788\) | 3.53558 | 0.125950 | ||||||||
\(789\) | −87.0211 | −3.09803 | ||||||||
\(790\) | 0.224673 | 0.00799352 | ||||||||
\(791\) | 1.12853 | 0.0401260 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.82893 | 0.278013 | ||||||||
\(794\) | 5.76862 | 0.204721 | ||||||||
\(795\) | −1.80784 | −0.0641174 | ||||||||
\(796\) | 6.09081 | 0.215883 | ||||||||
\(797\) | −39.0060 | −1.38166 | −0.690832 | − | 0.723016i | \(-0.742755\pi\) | ||||
−0.690832 | + | 0.723016i | \(0.742755\pi\) | |||||||
\(798\) | −6.59672 | −0.233521 | ||||||||
\(799\) | −12.3346 | −0.436367 | ||||||||
\(800\) | −4.98652 | −0.176300 | ||||||||
\(801\) | −44.7252 | −1.58029 | ||||||||
\(802\) | 18.9431 | 0.668906 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −9.54363 | −0.336578 | ||||||||
\(805\) | 0.394402 | 0.0139008 | ||||||||
\(806\) | −24.0081 | −0.845651 | ||||||||
\(807\) | 59.9672 | 2.11094 | ||||||||
\(808\) | 7.83269 | 0.275553 | ||||||||
\(809\) | 37.8563 | 1.33096 | 0.665478 | − | 0.746418i | \(-0.268228\pi\) | ||||
0.665478 | + | 0.746418i | \(0.268228\pi\) | |||||||
\(810\) | −0.0180787 | −0.000635220 0 | ||||||||
\(811\) | −37.2754 | −1.30891 | −0.654457 | − | 0.756099i | \(-0.727103\pi\) | ||||
−0.654457 | + | 0.756099i | \(0.727103\pi\) | |||||||
\(812\) | 12.1494 | 0.426360 | ||||||||
\(813\) | −50.4130 | −1.76806 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.65408 | 0.0579400 | ||||||||
\(816\) | 8.15571 | 0.285507 | ||||||||
\(817\) | −2.76591 | −0.0967669 | ||||||||
\(818\) | −28.7314 | −1.00457 | ||||||||
\(819\) | 32.8416 | 1.14758 | ||||||||
\(820\) | −1.15948 | −0.0404907 | ||||||||
\(821\) | −1.94263 | −0.0677984 | −0.0338992 | − | 0.999425i | \(-0.510793\pi\) | ||||
−0.0338992 | + | 0.999425i | \(0.510793\pi\) | |||||||
\(822\) | 14.4983 | 0.505687 | ||||||||
\(823\) | 29.1781 | 1.01708 | 0.508542 | − | 0.861037i | \(-0.330185\pi\) | ||||
0.508542 | + | 0.861037i | \(0.330185\pi\) | |||||||
\(824\) | −1.94503 | −0.0677583 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 20.0638 | 0.698111 | ||||||||
\(827\) | 4.87930 | 0.169670 | 0.0848349 | − | 0.996395i | \(-0.472964\pi\) | ||||
0.0848349 | + | 0.996395i | \(0.472964\pi\) | |||||||
\(828\) | −6.96122 | −0.241919 | ||||||||
\(829\) | 15.4007 | 0.534889 | 0.267445 | − | 0.963573i | \(-0.413821\pi\) | ||||
0.267445 | + | 0.963573i | \(0.413821\pi\) | |||||||
\(830\) | −0.470362 | −0.0163265 | ||||||||
\(831\) | 75.9815 | 2.63577 | ||||||||
\(832\) | −2.88390 | −0.0999811 | ||||||||
\(833\) | 4.20525 | 0.145703 | ||||||||
\(834\) | 60.3321 | 2.08913 | ||||||||
\(835\) | 1.01891 | 0.0352609 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −42.6506 | −1.47422 | ||||||||
\(838\) | −32.9954 | −1.13981 | ||||||||
\(839\) | −0.435061 | −0.0150200 | −0.00750999 | − | 0.999972i | \(-0.502391\pi\) | ||||
−0.00750999 | + | 0.999972i | \(0.502391\pi\) | |||||||
\(840\) | 0.765907 | 0.0264263 | ||||||||
\(841\) | −2.43807 | −0.0840713 | ||||||||
\(842\) | 21.1197 | 0.727833 | ||||||||
\(843\) | 45.2803 | 1.55953 | ||||||||
\(844\) | −23.5851 | −0.811833 | ||||||||
\(845\) | −0.543734 | −0.0187050 | ||||||||
\(846\) | 20.4450 | 0.702913 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 5.56427 | 0.191078 | ||||||||
\(849\) | −66.8658 | −2.29483 | ||||||||
\(850\) | 14.5330 | 0.498479 | ||||||||
\(851\) | −15.1934 | −0.520824 | ||||||||
\(852\) | 3.27182 | 0.112091 | ||||||||
\(853\) | −30.7594 | −1.05318 | −0.526591 | − | 0.850119i | \(-0.676530\pi\) | ||||
−0.526591 | + | 0.850119i | \(0.676530\pi\) | |||||||
\(854\) | 6.39952 | 0.218987 | ||||||||
\(855\) | −0.560878 | −0.0191816 | ||||||||
\(856\) | 6.57331 | 0.224671 | ||||||||
\(857\) | −19.0071 | −0.649270 | −0.324635 | − | 0.945839i | \(-0.605241\pi\) | ||||
−0.324635 | + | 0.945839i | \(0.605241\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −40.7564 | −1.39059 | −0.695295 | − | 0.718724i | \(-0.744726\pi\) | ||||
−0.695295 | + | 0.718724i | \(0.744726\pi\) | |||||||
\(860\) | 0.321134 | 0.0109506 | ||||||||
\(861\) | −65.8782 | −2.24512 | ||||||||
\(862\) | −38.9916 | −1.32806 | ||||||||
\(863\) | −40.9208 | −1.39296 | −0.696480 | − | 0.717576i | \(-0.745251\pi\) | ||||
−0.696480 | + | 0.717576i | \(0.745251\pi\) | |||||||
\(864\) | −5.12326 | −0.174297 | ||||||||
\(865\) | −0.340559 | −0.0115794 | ||||||||
\(866\) | 15.8146 | 0.537402 | ||||||||
\(867\) | 23.8026 | 0.808378 | ||||||||
\(868\) | −19.6247 | −0.666107 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 1.67449 | 0.0567704 | ||||||||
\(871\) | −9.83535 | −0.333258 | ||||||||
\(872\) | −3.02341 | −0.102386 | ||||||||
\(873\) | 42.0809 | 1.42422 | ||||||||
\(874\) | 1.44101 | 0.0487428 | ||||||||
\(875\) | 2.73330 | 0.0924024 | ||||||||
\(876\) | −3.68753 | −0.124590 | ||||||||
\(877\) | 41.0999 | 1.38785 | 0.693923 | − | 0.720050i | \(-0.255881\pi\) | ||||
0.693923 | + | 0.720050i | \(0.255881\pi\) | |||||||
\(878\) | 14.6697 | 0.495077 | ||||||||
\(879\) | 15.6163 | 0.526725 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −28.0388 | −0.944650 | −0.472325 | − | 0.881424i | \(-0.656585\pi\) | ||||
−0.472325 | + | 0.881424i | \(0.656585\pi\) | |||||||
\(882\) | −6.97032 | −0.234703 | ||||||||
\(883\) | −9.46358 | −0.318475 | −0.159237 | − | 0.987240i | \(-0.550904\pi\) | ||||
−0.159237 | + | 0.987240i | \(0.550904\pi\) | |||||||
\(884\) | 8.40501 | 0.282691 | ||||||||
\(885\) | 2.76530 | 0.0929544 | ||||||||
\(886\) | 18.4375 | 0.619418 | ||||||||
\(887\) | −11.8774 | −0.398804 | −0.199402 | − | 0.979918i | \(-0.563900\pi\) | ||||
−0.199402 | + | 0.979918i | \(0.563900\pi\) | |||||||
\(888\) | −29.5049 | −0.990118 | ||||||||
\(889\) | −26.7901 | −0.898513 | ||||||||
\(890\) | −1.07493 | −0.0360318 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.82893 | 0.0612369 | ||||||||
\(893\) | −4.23221 | −0.141625 | ||||||||
\(894\) | −40.4412 | −1.35256 | ||||||||
\(895\) | 0.844289 | 0.0282215 | ||||||||
\(896\) | −2.35735 | −0.0787536 | ||||||||
\(897\) | −11.6292 | −0.388287 | ||||||||
\(898\) | 26.6266 | 0.888541 | ||||||||
\(899\) | −42.9051 | −1.43097 | ||||||||
\(900\) | −24.0889 | −0.802964 | ||||||||
\(901\) | −16.2168 | −0.540261 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 18.2459 | 0.607186 | ||||||||
\(904\) | −0.478728 | −0.0159223 | ||||||||
\(905\) | 1.82758 | 0.0607508 | ||||||||
\(906\) | −65.4779 | −2.17536 | ||||||||
\(907\) | 36.1192 | 1.19932 | 0.599659 | − | 0.800256i | \(-0.295303\pi\) | ||||
0.599659 | + | 0.800256i | \(0.295303\pi\) | |||||||
\(908\) | −8.91169 | −0.295745 | ||||||||
\(909\) | 37.8382 | 1.25502 | ||||||||
\(910\) | 0.789319 | 0.0261657 | ||||||||
\(911\) | 27.7855 | 0.920576 | 0.460288 | − | 0.887770i | \(-0.347746\pi\) | ||||
0.460288 | + | 0.887770i | \(0.347746\pi\) | |||||||
\(912\) | 2.79836 | 0.0926629 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −5.75520 | −0.190365 | ||||||||
\(915\) | 0.882012 | 0.0291584 | ||||||||
\(916\) | −9.45720 | −0.312475 | ||||||||
\(917\) | −46.3176 | −1.52954 | ||||||||
\(918\) | 14.9315 | 0.492815 | ||||||||
\(919\) | −46.5464 | −1.53542 | −0.767712 | − | 0.640795i | \(-0.778605\pi\) | ||||
−0.767712 | + | 0.640795i | \(0.778605\pi\) | |||||||
\(920\) | −0.167307 | −0.00551595 | ||||||||
\(921\) | −3.42564 | −0.112879 | ||||||||
\(922\) | −18.3114 | −0.603055 | ||||||||
\(923\) | 3.37182 | 0.110985 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −52.5760 | −1.72869 | ||||||||
\(926\) | 1.12176 | 0.0368632 | ||||||||
\(927\) | −9.39607 | −0.308607 | ||||||||
\(928\) | −5.15383 | −0.169183 | ||||||||
\(929\) | 28.6551 | 0.940144 | 0.470072 | − | 0.882628i | \(-0.344228\pi\) | ||||
0.470072 | + | 0.882628i | \(0.344228\pi\) | |||||||
\(930\) | −2.70477 | −0.0886930 | ||||||||
\(931\) | 1.44289 | 0.0472888 | ||||||||
\(932\) | 17.4294 | 0.570919 | ||||||||
\(933\) | −78.8193 | −2.58043 | ||||||||
\(934\) | −19.1053 | −0.625146 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −13.9315 | −0.455367 | ||||||||
\(937\) | −37.8593 | −1.23681 | −0.618404 | − | 0.785860i | \(-0.712221\pi\) | ||||
−0.618404 | + | 0.785860i | \(0.712221\pi\) | |||||||
\(938\) | −8.03961 | −0.262502 | ||||||||
\(939\) | −93.6878 | −3.05739 | ||||||||
\(940\) | 0.491378 | 0.0160270 | ||||||||
\(941\) | −4.46036 | −0.145403 | −0.0727017 | − | 0.997354i | \(-0.523162\pi\) | ||||
−0.0727017 | + | 0.997354i | \(0.523162\pi\) | |||||||
\(942\) | −53.3852 | −1.73938 | ||||||||
\(943\) | 14.3906 | 0.468624 | ||||||||
\(944\) | −8.51118 | −0.277015 | ||||||||
\(945\) | 1.40223 | 0.0456146 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 29.2314 | 0.949892 | 0.474946 | − | 0.880015i | \(-0.342468\pi\) | ||||
0.474946 | + | 0.880015i | \(0.342468\pi\) | |||||||
\(948\) | −5.41510 | −0.175874 | ||||||||
\(949\) | −3.80024 | −0.123361 | ||||||||
\(950\) | 4.98652 | 0.161784 | ||||||||
\(951\) | −40.4765 | −1.31254 | ||||||||
\(952\) | 6.87042 | 0.222671 | ||||||||
\(953\) | −5.00428 | −0.162105 | −0.0810523 | − | 0.996710i | \(-0.525828\pi\) | ||||
−0.0810523 | + | 0.996710i | \(0.525828\pi\) | |||||||
\(954\) | 26.8799 | 0.870269 | ||||||||
\(955\) | 2.82132 | 0.0912956 | ||||||||
\(956\) | 25.0036 | 0.808674 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −16.7568 | −0.541388 | ||||||||
\(959\) | 12.2135 | 0.394393 | ||||||||
\(960\) | −0.324902 | −0.0104862 | ||||||||
\(961\) | 38.3040 | 1.23561 | ||||||||
\(962\) | −30.4067 | −0.980352 | ||||||||
\(963\) | 31.7544 | 1.02327 | ||||||||
\(964\) | −1.94503 | −0.0626452 | ||||||||
\(965\) | 1.26670 | 0.0407765 | ||||||||
\(966\) | −9.50591 | −0.305848 | ||||||||
\(967\) | 33.5154 | 1.07778 | 0.538891 | − | 0.842375i | \(-0.318843\pi\) | ||||
0.538891 | + | 0.842375i | \(0.318843\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.15571 | −0.261999 | ||||||||
\(970\) | 1.01138 | 0.0324734 | ||||||||
\(971\) | 55.5902 | 1.78398 | 0.891988 | − | 0.452060i | \(-0.149311\pi\) | ||||
0.891988 | + | 0.452060i | \(0.149311\pi\) | |||||||
\(972\) | 15.8055 | 0.506962 | ||||||||
\(973\) | 50.8241 | 1.62935 | ||||||||
\(974\) | −1.61042 | −0.0516010 | ||||||||
\(975\) | −40.2421 | −1.28878 | ||||||||
\(976\) | −2.71470 | −0.0868956 | ||||||||
\(977\) | 55.0510 | 1.76124 | 0.880618 | − | 0.473826i | \(-0.157127\pi\) | ||||
0.880618 | + | 0.473826i | \(0.157127\pi\) | |||||||
\(978\) | −39.8669 | −1.27480 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −0.167526 | −0.00535141 | ||||||||
\(981\) | −14.6055 | −0.466318 | ||||||||
\(982\) | 0.200650 | 0.00640299 | ||||||||
\(983\) | −42.1648 | −1.34485 | −0.672424 | − | 0.740166i | \(-0.734747\pi\) | ||||
−0.672424 | + | 0.740166i | \(0.734747\pi\) | |||||||
\(984\) | 27.9459 | 0.890881 | ||||||||
\(985\) | 0.410497 | 0.0130795 | ||||||||
\(986\) | 15.0206 | 0.478354 | ||||||||
\(987\) | 27.9187 | 0.888661 | ||||||||
\(988\) | 2.88390 | 0.0917489 | ||||||||
\(989\) | −3.98569 | −0.126738 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −50.2222 | −1.59536 | −0.797680 | − | 0.603081i | \(-0.793940\pi\) | ||||
−0.797680 | + | 0.603081i | \(0.793940\pi\) | |||||||
\(992\) | 8.32490 | 0.264316 | ||||||||
\(993\) | 15.0242 | 0.476780 | ||||||||
\(994\) | 2.75619 | 0.0874212 | ||||||||
\(995\) | 0.707169 | 0.0224188 | ||||||||
\(996\) | 11.3367 | 0.359218 | ||||||||
\(997\) | 41.3157 | 1.30848 | 0.654241 | − | 0.756286i | \(-0.272988\pi\) | ||||
0.654241 | + | 0.756286i | \(0.272988\pi\) | |||||||
\(998\) | −22.9954 | −0.727907 | ||||||||
\(999\) | −54.0178 | −1.70905 |
(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 | 4598.2.a.bu.1.1 | yes | 4 | |
11.10 | odd | 2 | 4598.2.a.br.1.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4598.2.a.br.1.1 | ✓ | 4 | 11.10 | odd | 2 | ||
4598.2.a.bu.1.1 | yes | 4 | 1.1 | even | 1 | trivial |