Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4005,2,Mod(1,4005)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4005, 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("4005.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4005 = 3^{2} \cdot 5 \cdot 89 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4005.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: | \(31.9800860095\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.725.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 3x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 445) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.477260\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4005.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.77222 | −1.25315 | −0.626575 | − | 0.779361i | \(-0.715544\pi\) | ||||
−0.626575 | + | 0.779361i | \(0.715544\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.14077 | 0.570387 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.19059 | −1.20593 | −0.602964 | − | 0.797768i | \(-0.706014\pi\) | ||||
−0.602964 | + | 0.797768i | \(0.706014\pi\) | |||||||
\(8\) | 1.52274 | 0.538370 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.77222 | −0.560426 | ||||||||
\(11\) | 2.70504 | 0.815599 | 0.407800 | − | 0.913071i | \(-0.366296\pi\) | ||||
0.407800 | + | 0.913071i | \(0.366296\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.03640 | 0.564795 | 0.282398 | − | 0.959297i | \(-0.408870\pi\) | ||||
0.282398 | + | 0.959297i | \(0.408870\pi\) | |||||||
\(14\) | 5.65443 | 1.51121 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.98018 | −1.24505 | ||||||||
\(17\) | −2.67180 | −0.648008 | −0.324004 | − | 0.946056i | \(-0.605029\pi\) | ||||
−0.324004 | + | 0.946056i | \(0.605029\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.45989 | 0.334921 | 0.167461 | − | 0.985879i | \(-0.446443\pi\) | ||||
0.167461 | + | 0.985879i | \(0.446443\pi\) | |||||||
\(20\) | 1.14077 | 0.255085 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.79393 | −1.02207 | ||||||||
\(23\) | 5.62632 | 1.17317 | 0.586585 | − | 0.809888i | \(-0.300472\pi\) | ||||
0.586585 | + | 0.809888i | \(0.300472\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −3.60895 | −0.707774 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.63974 | −0.687846 | ||||||||
\(29\) | −3.44007 | −0.638805 | −0.319403 | − | 0.947619i | \(-0.603482\pi\) | ||||
−0.319403 | + | 0.947619i | \(0.603482\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.62237 | −1.54862 | −0.774312 | − | 0.632805i | \(-0.781904\pi\) | ||||
−0.774312 | + | 0.632805i | \(0.781904\pi\) | |||||||
\(32\) | 5.78051 | 1.02186 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.73503 | 0.812052 | ||||||||
\(35\) | −3.19059 | −0.539308 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.46573 | 1.55616 | 0.778079 | − | 0.628167i | \(-0.216195\pi\) | ||||
0.778079 | + | 0.628167i | \(0.216195\pi\) | |||||||
\(38\) | −2.58725 | −0.419707 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.52274 | 0.240766 | ||||||||
\(41\) | 10.1119 | 1.57921 | 0.789605 | − | 0.613616i | \(-0.210286\pi\) | ||||
0.789605 | + | 0.613616i | \(0.210286\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.51878 | 0.384111 | 0.192055 | − | 0.981384i | \(-0.438485\pi\) | ||||
0.192055 | + | 0.981384i | \(0.438485\pi\) | |||||||
\(44\) | 3.08584 | 0.465207 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −9.97110 | −1.47016 | ||||||||
\(47\) | −1.05810 | −0.154340 | −0.0771702 | − | 0.997018i | \(-0.524588\pi\) | ||||
−0.0771702 | + | 0.997018i | \(0.524588\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.17985 | 0.454265 | ||||||||
\(50\) | −1.77222 | −0.250630 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.32307 | 0.322152 | ||||||||
\(53\) | 1.72802 | 0.237362 | 0.118681 | − | 0.992932i | \(-0.462133\pi\) | ||||
0.118681 | + | 0.992932i | \(0.462133\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.70504 | 0.364747 | ||||||||
\(56\) | −4.85844 | −0.649236 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 6.09657 | 0.800519 | ||||||||
\(59\) | 3.39934 | 0.442556 | 0.221278 | − | 0.975211i | \(-0.428977\pi\) | ||||
0.221278 | + | 0.975211i | \(0.428977\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14.9071 | −1.90866 | −0.954328 | − | 0.298760i | \(-0.903427\pi\) | ||||
−0.954328 | + | 0.298760i | \(0.903427\pi\) | |||||||
\(62\) | 15.2808 | 1.94066 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.283993 | −0.0354992 | ||||||||
\(65\) | 2.03640 | 0.252584 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.16888 | −0.264971 | −0.132486 | − | 0.991185i | \(-0.542296\pi\) | ||||
−0.132486 | + | 0.991185i | \(0.542296\pi\) | |||||||
\(68\) | −3.04793 | −0.369615 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 5.65443 | 0.675834 | ||||||||
\(71\) | −6.88221 | −0.816768 | −0.408384 | − | 0.912810i | \(-0.633908\pi\) | ||||
−0.408384 | + | 0.912810i | \(0.633908\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.79954 | −1.02991 | −0.514954 | − | 0.857218i | \(-0.672191\pi\) | ||||
−0.514954 | + | 0.857218i | \(0.672191\pi\) | |||||||
\(74\) | −16.7754 | −1.95010 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.66540 | 0.191035 | ||||||||
\(77\) | −8.63066 | −0.983555 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.97939 | 0.672734 | 0.336367 | − | 0.941731i | \(-0.390802\pi\) | ||||
0.336367 | + | 0.941731i | \(0.390802\pi\) | |||||||
\(80\) | −4.98018 | −0.556801 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −17.9205 | −1.97899 | ||||||||
\(83\) | 7.29685 | 0.800933 | 0.400467 | − | 0.916311i | \(-0.368848\pi\) | ||||
0.400467 | + | 0.916311i | \(0.368848\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.67180 | −0.289798 | ||||||||
\(86\) | −4.46385 | −0.481349 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.11907 | 0.439094 | ||||||||
\(89\) | 1.00000 | 0.106000 | ||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.49731 | −0.681103 | ||||||||
\(92\) | 6.41837 | 0.669161 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.87520 | 0.193412 | ||||||||
\(95\) | 1.45989 | 0.149781 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.6505 | 1.58907 | 0.794533 | − | 0.607222i | \(-0.207716\pi\) | ||||
0.794533 | + | 0.607222i | \(0.207716\pi\) | |||||||
\(98\) | −5.63541 | −0.569262 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.14077 | 0.114077 | ||||||||
\(101\) | −17.0561 | −1.69715 | −0.848575 | − | 0.529075i | \(-0.822539\pi\) | ||||
−0.848575 | + | 0.529075i | \(0.822539\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.69162 | 0.659345 | 0.329673 | − | 0.944095i | \(-0.393062\pi\) | ||||
0.329673 | + | 0.944095i | \(0.393062\pi\) | |||||||
\(104\) | 3.10091 | 0.304069 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.06244 | −0.297450 | ||||||||
\(107\) | 15.9256 | 1.53959 | 0.769794 | − | 0.638292i | \(-0.220359\pi\) | ||||
0.769794 | + | 0.638292i | \(0.220359\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.65443 | −0.158466 | −0.0792330 | − | 0.996856i | \(-0.525247\pi\) | ||||
−0.0792330 | + | 0.996856i | \(0.525247\pi\) | |||||||
\(110\) | −4.79393 | −0.457083 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 15.8897 | 1.50144 | ||||||||
\(113\) | 2.74388 | 0.258123 | 0.129061 | − | 0.991637i | \(-0.458804\pi\) | ||||
0.129061 | + | 0.991637i | \(0.458804\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.62632 | 0.524657 | ||||||||
\(116\) | −3.92434 | −0.364366 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −6.02438 | −0.554590 | ||||||||
\(119\) | 8.52463 | 0.781451 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.68277 | −0.334798 | ||||||||
\(122\) | 26.4187 | 2.39183 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −9.83617 | −0.883314 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.0122478 | −0.00108681 | −0.000543407 | − | 1.00000i | \(-0.500173\pi\) | ||||
−0.000543407 | 1.00000i | \(0.500173\pi\) | ||||||||
\(128\) | −11.0577 | −0.977374 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.60895 | −0.316526 | ||||||||
\(131\) | 18.4349 | 1.61067 | 0.805334 | − | 0.592821i | \(-0.201986\pi\) | ||||
0.805334 | + | 0.592821i | \(0.201986\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.65790 | −0.403891 | ||||||||
\(134\) | 3.84374 | 0.332049 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.06846 | −0.348868 | ||||||||
\(137\) | −17.8348 | −1.52373 | −0.761864 | − | 0.647737i | \(-0.775715\pi\) | ||||
−0.761864 | + | 0.647737i | \(0.775715\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.69547 | −0.652721 | −0.326361 | − | 0.945245i | \(-0.605822\pi\) | ||||
−0.326361 | + | 0.945245i | \(0.605822\pi\) | |||||||
\(140\) | −3.63974 | −0.307614 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 12.1968 | 1.02353 | ||||||||
\(143\) | 5.50854 | 0.460647 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.44007 | −0.285682 | ||||||||
\(146\) | 15.5947 | 1.29063 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 10.7983 | 0.887612 | ||||||||
\(149\) | 16.0825 | 1.31753 | 0.658764 | − | 0.752349i | \(-0.271079\pi\) | ||||
0.658764 | + | 0.752349i | \(0.271079\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.01304 | −0.245198 | −0.122599 | − | 0.992456i | \(-0.539123\pi\) | ||||
−0.122599 | + | 0.992456i | \(0.539123\pi\) | |||||||
\(152\) | 2.22303 | 0.180312 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 15.2955 | 1.23254 | ||||||||
\(155\) | −8.62237 | −0.692565 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.7128 | −0.854972 | −0.427486 | − | 0.904022i | \(-0.640601\pi\) | ||||
−0.427486 | + | 0.904022i | \(0.640601\pi\) | |||||||
\(158\) | −10.5968 | −0.843037 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 5.78051 | 0.456990 | ||||||||
\(161\) | −17.9513 | −1.41476 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.55250 | −0.121601 | −0.0608007 | − | 0.998150i | \(-0.519365\pi\) | ||||
−0.0608007 | + | 0.998150i | \(0.519365\pi\) | |||||||
\(164\) | 11.5354 | 0.900761 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −12.9316 | −1.00369 | ||||||||
\(167\) | 12.8252 | 0.992444 | 0.496222 | − | 0.868196i | \(-0.334720\pi\) | ||||
0.496222 | + | 0.868196i | \(0.334720\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.85308 | −0.681006 | ||||||||
\(170\) | 4.73503 | 0.363161 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.87336 | 0.219092 | ||||||||
\(173\) | 14.9094 | 1.13354 | 0.566770 | − | 0.823876i | \(-0.308193\pi\) | ||||
0.566770 | + | 0.823876i | \(0.308193\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.19059 | −0.241186 | ||||||||
\(176\) | −13.4716 | −1.01546 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.77222 | −0.132834 | ||||||||
\(179\) | 20.1349 | 1.50495 | 0.752475 | − | 0.658621i | \(-0.228860\pi\) | ||||
0.752475 | + | 0.658621i | \(0.228860\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.51916 | −0.335907 | −0.167953 | − | 0.985795i | \(-0.553716\pi\) | ||||
−0.167953 | + | 0.985795i | \(0.553716\pi\) | |||||||
\(182\) | 11.5147 | 0.853525 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 8.56743 | 0.631599 | ||||||||
\(185\) | 9.46573 | 0.695935 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.22733 | −0.528515 | ||||||||
\(188\) | −1.20706 | −0.0880338 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.58725 | −0.187699 | ||||||||
\(191\) | −9.55425 | −0.691321 | −0.345661 | − | 0.938360i | \(-0.612345\pi\) | ||||
−0.345661 | + | 0.938360i | \(0.612345\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 24.9743 | 1.79769 | 0.898844 | − | 0.438270i | \(-0.144408\pi\) | ||||
0.898844 | + | 0.438270i | \(0.144408\pi\) | |||||||
\(194\) | −27.7361 | −1.99134 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.62749 | 0.259107 | ||||||||
\(197\) | −11.1011 | −0.790923 | −0.395462 | − | 0.918482i | \(-0.629415\pi\) | ||||
−0.395462 | + | 0.918482i | \(0.629415\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.82995 | −0.555050 | −0.277525 | − | 0.960718i | \(-0.589514\pi\) | ||||
−0.277525 | + | 0.960718i | \(0.589514\pi\) | |||||||
\(200\) | 1.52274 | 0.107674 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 30.2273 | 2.12679 | ||||||||
\(203\) | 10.9758 | 0.770354 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.1119 | 0.706244 | ||||||||
\(206\) | −11.8590 | −0.826259 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −10.1416 | −0.703196 | ||||||||
\(209\) | 3.94905 | 0.273162 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.5375 | 1.41386 | 0.706929 | − | 0.707284i | \(-0.250080\pi\) | ||||
0.706929 | + | 0.707284i | \(0.250080\pi\) | |||||||
\(212\) | 1.97128 | 0.135388 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −28.2238 | −1.92934 | ||||||||
\(215\) | 2.51878 | 0.171780 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 27.5104 | 1.86753 | ||||||||
\(218\) | 2.93202 | 0.198582 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.08584 | 0.208047 | ||||||||
\(221\) | −5.44086 | −0.365992 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.16530 | −0.278929 | −0.139465 | − | 0.990227i | \(-0.544538\pi\) | ||||
−0.139465 | + | 0.990227i | \(0.544538\pi\) | |||||||
\(224\) | −18.4432 | −1.23229 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.86277 | −0.323467 | ||||||||
\(227\) | 7.69980 | 0.511054 | 0.255527 | − | 0.966802i | \(-0.417751\pi\) | ||||
0.255527 | + | 0.966802i | \(0.417751\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.206071 | 0.0136176 | 0.00680879 | − | 0.999977i | \(-0.497833\pi\) | ||||
0.00680879 | + | 0.999977i | \(0.497833\pi\) | |||||||
\(230\) | −9.97110 | −0.657475 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.23833 | −0.343913 | ||||||||
\(233\) | −15.9391 | −1.04421 | −0.522104 | − | 0.852882i | \(-0.674853\pi\) | ||||
−0.522104 | + | 0.852882i | \(0.674853\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.05810 | −0.0690231 | ||||||||
\(236\) | 3.87788 | 0.252428 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −15.1075 | −0.979276 | ||||||||
\(239\) | −16.9216 | −1.09457 | −0.547284 | − | 0.836947i | \(-0.684338\pi\) | ||||
−0.547284 | + | 0.836947i | \(0.684338\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.84197 | 0.247483 | 0.123741 | − | 0.992315i | \(-0.460511\pi\) | ||||
0.123741 | + | 0.992315i | \(0.460511\pi\) | |||||||
\(242\) | 6.52670 | 0.419552 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −17.0056 | −1.08867 | ||||||||
\(245\) | 3.17985 | 0.203153 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.97291 | 0.189162 | ||||||||
\(248\) | −13.1296 | −0.833732 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.77222 | −0.112085 | ||||||||
\(251\) | 1.25626 | 0.0792946 | 0.0396473 | − | 0.999214i | \(-0.487377\pi\) | ||||
0.0396473 | + | 0.999214i | \(0.487377\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 15.2194 | 0.956837 | ||||||||
\(254\) | 0.0217058 | 0.00136194 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 20.1647 | 1.26030 | ||||||||
\(257\) | −6.84313 | −0.426863 | −0.213431 | − | 0.976958i | \(-0.568464\pi\) | ||||
−0.213431 | + | 0.976958i | \(0.568464\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −30.2013 | −1.87661 | ||||||||
\(260\) | 2.32307 | 0.144071 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −32.6708 | −2.01841 | ||||||||
\(263\) | 4.38743 | 0.270541 | 0.135270 | − | 0.990809i | \(-0.456810\pi\) | ||||
0.135270 | + | 0.990809i | \(0.456810\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.72802 | 0.106152 | ||||||||
\(266\) | 8.25484 | 0.506137 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.47420 | −0.151136 | ||||||||
\(269\) | 25.5807 | 1.55968 | 0.779840 | − | 0.625978i | \(-0.215300\pi\) | ||||
0.779840 | + | 0.625978i | \(0.215300\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.2568 | 0.866036 | 0.433018 | − | 0.901385i | \(-0.357449\pi\) | ||||
0.433018 | + | 0.901385i | \(0.357449\pi\) | |||||||
\(272\) | 13.3061 | 0.806799 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 31.6072 | 1.90946 | ||||||||
\(275\) | 2.70504 | 0.163120 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.43597 | 0.566952 | 0.283476 | − | 0.958979i | \(-0.408512\pi\) | ||||
0.283476 | + | 0.958979i | \(0.408512\pi\) | |||||||
\(278\) | 13.6381 | 0.817958 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −4.85844 | −0.290347 | ||||||||
\(281\) | 20.3543 | 1.21423 | 0.607117 | − | 0.794612i | \(-0.292326\pi\) | ||||
0.607117 | + | 0.794612i | \(0.292326\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.77106 | 0.283610 | 0.141805 | − | 0.989895i | \(-0.454709\pi\) | ||||
0.141805 | + | 0.989895i | \(0.454709\pi\) | |||||||
\(284\) | −7.85105 | −0.465874 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −9.76235 | −0.577260 | ||||||||
\(287\) | −32.2628 | −1.90441 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.86146 | −0.580086 | ||||||||
\(290\) | 6.09657 | 0.358003 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −10.0383 | −0.587446 | ||||||||
\(293\) | −12.5065 | −0.730636 | −0.365318 | − | 0.930883i | \(-0.619040\pi\) | ||||
−0.365318 | + | 0.930883i | \(0.619040\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.39934 | 0.197917 | ||||||||
\(296\) | 14.4139 | 0.837788 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −28.5018 | −1.65106 | ||||||||
\(299\) | 11.4574 | 0.662601 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.03640 | −0.463210 | ||||||||
\(302\) | 5.33977 | 0.307270 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −7.27051 | −0.416992 | ||||||||
\(305\) | −14.9071 | −0.853577 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.9679 | 0.911334 | 0.455667 | − | 0.890150i | \(-0.349401\pi\) | ||||
0.455667 | + | 0.890150i | \(0.349401\pi\) | |||||||
\(308\) | −9.84563 | −0.561007 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 15.2808 | 0.867889 | ||||||||
\(311\) | 17.7230 | 1.00498 | 0.502490 | − | 0.864583i | \(-0.332417\pi\) | ||||
0.502490 | + | 0.864583i | \(0.332417\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.8006 | 1.11920 | 0.559599 | − | 0.828763i | \(-0.310955\pi\) | ||||
0.559599 | + | 0.828763i | \(0.310955\pi\) | |||||||
\(314\) | 18.9854 | 1.07141 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.82114 | 0.383719 | ||||||||
\(317\) | 1.15759 | 0.0650167 | 0.0325083 | − | 0.999471i | \(-0.489650\pi\) | ||||
0.0325083 | + | 0.999471i | \(0.489650\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.30552 | −0.521009 | ||||||||
\(320\) | −0.283993 | −0.0158757 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 31.8137 | 1.77291 | ||||||||
\(323\) | −3.90054 | −0.217032 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.03640 | 0.112959 | ||||||||
\(326\) | 2.75138 | 0.152385 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 15.3978 | 0.850199 | ||||||||
\(329\) | 3.37598 | 0.186124 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.88134 | −0.103408 | −0.0517040 | − | 0.998662i | \(-0.516465\pi\) | ||||
−0.0517040 | + | 0.998662i | \(0.516465\pi\) | |||||||
\(332\) | 8.32406 | 0.456842 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −22.7291 | −1.24368 | ||||||||
\(335\) | −2.16888 | −0.118499 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.86868 | 0.101794 | 0.0508969 | − | 0.998704i | \(-0.483792\pi\) | ||||
0.0508969 | + | 0.998704i | \(0.483792\pi\) | |||||||
\(338\) | 15.6896 | 0.853403 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3.04793 | −0.165297 | ||||||||
\(341\) | −23.3238 | −1.26306 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.1885 | 0.658118 | ||||||||
\(344\) | 3.83545 | 0.206794 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −26.4228 | −1.42050 | ||||||||
\(347\) | 9.65267 | 0.518182 | 0.259091 | − | 0.965853i | \(-0.416577\pi\) | ||||
0.259091 | + | 0.965853i | \(0.416577\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 34.0970 | 1.82517 | 0.912585 | − | 0.408886i | \(-0.134083\pi\) | ||||
0.912585 | + | 0.408886i | \(0.134083\pi\) | |||||||
\(350\) | 5.65443 | 0.302242 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 15.6365 | 0.833428 | ||||||||
\(353\) | 36.9671 | 1.96756 | 0.983779 | − | 0.179382i | \(-0.0574099\pi\) | ||||
0.983779 | + | 0.179382i | \(0.0574099\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.88221 | −0.365270 | ||||||||
\(356\) | 1.14077 | 0.0604609 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −35.6835 | −1.88593 | ||||||||
\(359\) | −1.00561 | −0.0530742 | −0.0265371 | − | 0.999648i | \(-0.508448\pi\) | ||||
−0.0265371 | + | 0.999648i | \(0.508448\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.8687 | −0.887828 | ||||||||
\(362\) | 8.00896 | 0.420942 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −7.41196 | −0.388492 | ||||||||
\(365\) | −8.79954 | −0.460589 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.09416 | 0.213713 | 0.106857 | − | 0.994274i | \(-0.465921\pi\) | ||||
0.106857 | + | 0.994274i | \(0.465921\pi\) | |||||||
\(368\) | −28.0201 | −1.46065 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −16.7754 | −0.872111 | ||||||||
\(371\) | −5.51340 | −0.286242 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.86807 | 0.355615 | 0.177808 | − | 0.984065i | \(-0.443099\pi\) | ||||
0.177808 | + | 0.984065i | \(0.443099\pi\) | |||||||
\(374\) | 12.8084 | 0.662309 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.61122 | −0.0830923 | ||||||||
\(377\) | −7.00536 | −0.360794 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.27864 | −0.0656791 | −0.0328396 | − | 0.999461i | \(-0.510455\pi\) | ||||
−0.0328396 | + | 0.999461i | \(0.510455\pi\) | |||||||
\(380\) | 1.66540 | 0.0854333 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 16.9323 | 0.866330 | ||||||||
\(383\) | 19.8336 | 1.01345 | 0.506726 | − | 0.862107i | \(-0.330856\pi\) | ||||
0.506726 | + | 0.862107i | \(0.330856\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.63066 | −0.439859 | ||||||||
\(386\) | −44.2600 | −2.25277 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 17.8537 | 0.906382 | ||||||||
\(389\) | −13.9074 | −0.705132 | −0.352566 | − | 0.935787i | \(-0.614691\pi\) | ||||
−0.352566 | + | 0.935787i | \(0.614691\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −15.0324 | −0.760223 | ||||||||
\(392\) | 4.84209 | 0.244562 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 19.6737 | 0.991146 | ||||||||
\(395\) | 5.97939 | 0.300856 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.27223 | −0.114040 | −0.0570201 | − | 0.998373i | \(-0.518160\pi\) | ||||
−0.0570201 | + | 0.998373i | \(0.518160\pi\) | |||||||
\(398\) | 13.8764 | 0.695562 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.98018 | −0.249009 | ||||||||
\(401\) | 20.7709 | 1.03725 | 0.518624 | − | 0.855002i | \(-0.326444\pi\) | ||||
0.518624 | + | 0.855002i | \(0.326444\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −17.5586 | −0.874655 | ||||||||
\(404\) | −19.4572 | −0.968032 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −19.4517 | −0.965369 | ||||||||
\(407\) | 25.6052 | 1.26920 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 37.1089 | 1.83492 | 0.917458 | − | 0.397833i | \(-0.130238\pi\) | ||||
0.917458 | + | 0.397833i | \(0.130238\pi\) | |||||||
\(410\) | −17.9205 | −0.885030 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 7.63363 | 0.376082 | ||||||||
\(413\) | −10.8459 | −0.533691 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.29685 | 0.358188 | ||||||||
\(416\) | 11.7714 | 0.577142 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −6.99860 | −0.342313 | ||||||||
\(419\) | −28.9496 | −1.41428 | −0.707139 | − | 0.707074i | \(-0.750015\pi\) | ||||
−0.707139 | + | 0.707074i | \(0.750015\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 34.0480 | 1.65940 | 0.829699 | − | 0.558211i | \(-0.188512\pi\) | ||||
0.829699 | + | 0.558211i | \(0.188512\pi\) | |||||||
\(422\) | −36.3970 | −1.77178 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.63133 | 0.127789 | ||||||||
\(425\) | −2.67180 | −0.129602 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 47.5624 | 2.30170 | ||||||||
\(428\) | 18.1675 | 0.878161 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4.46385 | −0.215266 | ||||||||
\(431\) | −15.7133 | −0.756881 | −0.378441 | − | 0.925626i | \(-0.623540\pi\) | ||||
−0.378441 | + | 0.925626i | \(0.623540\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −22.0260 | −1.05850 | −0.529251 | − | 0.848465i | \(-0.677527\pi\) | ||||
−0.529251 | + | 0.848465i | \(0.677527\pi\) | |||||||
\(434\) | −48.7546 | −2.34030 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.88733 | −0.0903869 | ||||||||
\(437\) | 8.21381 | 0.392920 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 32.5888 | 1.55538 | 0.777690 | − | 0.628648i | \(-0.216391\pi\) | ||||
0.777690 | + | 0.628648i | \(0.216391\pi\) | |||||||
\(440\) | 4.11907 | 0.196369 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 9.64242 | 0.458643 | ||||||||
\(443\) | −33.3935 | −1.58657 | −0.793287 | − | 0.608849i | \(-0.791632\pi\) | ||||
−0.793287 | + | 0.608849i | \(0.791632\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.00000 | 0.0474045 | ||||||||
\(446\) | 7.38184 | 0.349540 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.906106 | 0.0428095 | ||||||||
\(449\) | 2.89521 | 0.136634 | 0.0683168 | − | 0.997664i | \(-0.478237\pi\) | ||||
0.0683168 | + | 0.997664i | \(0.478237\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 27.3530 | 1.28800 | ||||||||
\(452\) | 3.13015 | 0.147230 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −13.6458 | −0.640427 | ||||||||
\(455\) | −6.49731 | −0.304599 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.5490 | 0.867686 | 0.433843 | − | 0.900988i | \(-0.357157\pi\) | ||||
0.433843 | + | 0.900988i | \(0.357157\pi\) | |||||||
\(458\) | −0.365204 | −0.0170649 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 6.41837 | 0.299258 | ||||||||
\(461\) | −20.3168 | −0.946248 | −0.473124 | − | 0.880996i | \(-0.656874\pi\) | ||||
−0.473124 | + | 0.880996i | \(0.656874\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.0650 | 0.932499 | 0.466250 | − | 0.884653i | \(-0.345605\pi\) | ||||
0.466250 | + | 0.884653i | \(0.345605\pi\) | |||||||
\(464\) | 17.1322 | 0.795342 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 28.2477 | 1.30855 | ||||||||
\(467\) | 35.1654 | 1.62726 | 0.813631 | − | 0.581382i | \(-0.197488\pi\) | ||||
0.813631 | + | 0.581382i | \(0.197488\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.92001 | 0.319536 | ||||||||
\(470\) | 1.87520 | 0.0864964 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5.17631 | 0.238259 | ||||||||
\(473\) | 6.81340 | 0.313281 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.45989 | 0.0669843 | ||||||||
\(476\) | 9.72467 | 0.445730 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 29.9888 | 1.37166 | ||||||||
\(479\) | 36.9126 | 1.68658 | 0.843290 | − | 0.537458i | \(-0.180615\pi\) | ||||
0.843290 | + | 0.537458i | \(0.180615\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 19.2760 | 0.878910 | ||||||||
\(482\) | −6.80882 | −0.310133 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.20121 | −0.190964 | ||||||||
\(485\) | 15.6505 | 0.710652 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13.4262 | −0.608400 | −0.304200 | − | 0.952608i | \(-0.598389\pi\) | ||||
−0.304200 | + | 0.952608i | \(0.598389\pi\) | |||||||
\(488\) | −22.6996 | −1.02756 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −5.63541 | −0.254582 | ||||||||
\(491\) | 29.1214 | 1.31423 | 0.657115 | − | 0.753791i | \(-0.271777\pi\) | ||||
0.657115 | + | 0.753791i | \(0.271777\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.19120 | 0.413951 | ||||||||
\(494\) | −5.26867 | −0.237049 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 42.9410 | 1.92811 | ||||||||
\(497\) | 21.9583 | 0.984964 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.11813 | 0.273885 | 0.136943 | − | 0.990579i | \(-0.456272\pi\) | ||||
0.136943 | + | 0.990579i | \(0.456272\pi\) | |||||||
\(500\) | 1.14077 | 0.0510170 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2.22638 | −0.0993681 | ||||||||
\(503\) | 16.6291 | 0.741456 | 0.370728 | − | 0.928742i | \(-0.379108\pi\) | ||||
0.370728 | + | 0.928742i | \(0.379108\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17.0561 | −0.758989 | ||||||||
\(506\) | −26.9722 | −1.19906 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.0139719 | −0.000619905 0 | ||||||||
\(509\) | 6.47859 | 0.287159 | 0.143579 | − | 0.989639i | \(-0.454139\pi\) | ||||
0.143579 | + | 0.989639i | \(0.454139\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 28.0757 | 1.24200 | ||||||||
\(512\) | −13.6210 | −0.601967 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 12.1276 | 0.534924 | ||||||||
\(515\) | 6.69162 | 0.294868 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.86221 | −0.125880 | ||||||||
\(518\) | 53.5234 | 2.35168 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 3.10091 | 0.135984 | ||||||||
\(521\) | −22.4933 | −0.985449 | −0.492724 | − | 0.870185i | \(-0.663999\pi\) | ||||
−0.492724 | + | 0.870185i | \(0.663999\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.1820 | 0.620134 | 0.310067 | − | 0.950715i | \(-0.399648\pi\) | ||||
0.310067 | + | 0.950715i | \(0.399648\pi\) | |||||||
\(524\) | 21.0301 | 0.918705 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.77551 | −0.339028 | ||||||||
\(527\) | 23.0373 | 1.00352 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.65553 | 0.376327 | ||||||||
\(530\) | −3.06244 | −0.133024 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −5.31361 | −0.230374 | ||||||||
\(533\) | 20.5918 | 0.891930 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15.9256 | 0.688525 | ||||||||
\(536\) | −3.30264 | −0.142652 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −45.3346 | −1.95452 | ||||||||
\(539\) | 8.60162 | 0.370498 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −35.2225 | −1.51433 | −0.757166 | − | 0.653222i | \(-0.773417\pi\) | ||||
−0.757166 | + | 0.653222i | \(0.773417\pi\) | |||||||
\(542\) | −25.2661 | −1.08527 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −15.4444 | −0.662173 | ||||||||
\(545\) | −1.65443 | −0.0708681 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.43480 | −0.0613477 | −0.0306739 | − | 0.999529i | \(-0.509765\pi\) | ||||
−0.0306739 | + | 0.999529i | \(0.509765\pi\) | |||||||
\(548\) | −20.3454 | −0.869114 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4.79393 | −0.204414 | ||||||||
\(551\) | −5.02212 | −0.213949 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −19.0778 | −0.811270 | ||||||||
\(554\) | −16.7226 | −0.710477 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8.77879 | −0.372304 | ||||||||
\(557\) | 0.533965 | 0.0226248 | 0.0113124 | − | 0.999936i | \(-0.496399\pi\) | ||||
0.0113124 | + | 0.999936i | \(0.496399\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.12925 | 0.216944 | ||||||||
\(560\) | 15.8897 | 0.671463 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −36.0723 | −1.52162 | ||||||||
\(563\) | 36.0788 | 1.52054 | 0.760270 | − | 0.649607i | \(-0.225067\pi\) | ||||
0.760270 | + | 0.649607i | \(0.225067\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.74388 | 0.115436 | ||||||||
\(566\) | −8.45537 | −0.355406 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −10.4798 | −0.439723 | ||||||||
\(569\) | 39.9398 | 1.67436 | 0.837181 | − | 0.546925i | \(-0.184202\pi\) | ||||
0.837181 | + | 0.546925i | \(0.184202\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −34.5619 | −1.44637 | −0.723184 | − | 0.690655i | \(-0.757322\pi\) | ||||
−0.723184 | + | 0.690655i | \(0.757322\pi\) | |||||||
\(572\) | 6.28399 | 0.262747 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 57.1769 | 2.38652 | ||||||||
\(575\) | 5.62632 | 0.234634 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 46.3225 | 1.92843 | 0.964215 | − | 0.265122i | \(-0.0854121\pi\) | ||||
0.964215 | + | 0.265122i | \(0.0854121\pi\) | |||||||
\(578\) | 17.4767 | 0.726935 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −3.92434 | −0.162949 | ||||||||
\(581\) | −23.2812 | −0.965869 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.67436 | 0.193592 | ||||||||
\(584\) | −13.3994 | −0.554472 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 22.1642 | 0.915597 | ||||||||
\(587\) | −14.1115 | −0.582445 | −0.291223 | − | 0.956655i | \(-0.594062\pi\) | ||||
−0.291223 | + | 0.956655i | \(0.594062\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12.5877 | −0.518667 | ||||||||
\(590\) | −6.02438 | −0.248020 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −47.1411 | −1.93749 | ||||||||
\(593\) | 46.5842 | 1.91298 | 0.956491 | − | 0.291760i | \(-0.0942410\pi\) | ||||
0.956491 | + | 0.291760i | \(0.0942410\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.52463 | 0.349476 | ||||||||
\(596\) | 18.3465 | 0.751501 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −20.3051 | −0.830339 | ||||||||
\(599\) | 4.68560 | 0.191448 | 0.0957241 | − | 0.995408i | \(-0.469483\pi\) | ||||
0.0957241 | + | 0.995408i | \(0.469483\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −29.7661 | −1.21419 | −0.607093 | − | 0.794631i | \(-0.707664\pi\) | ||||
−0.607093 | + | 0.794631i | \(0.707664\pi\) | |||||||
\(602\) | 14.2423 | 0.580472 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3.43720 | −0.139857 | ||||||||
\(605\) | −3.68277 | −0.149726 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.61468 | 0.349659 | 0.174829 | − | 0.984599i | \(-0.444063\pi\) | ||||
0.174829 | + | 0.984599i | \(0.444063\pi\) | |||||||
\(608\) | 8.43890 | 0.342243 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 26.4187 | 1.06966 | ||||||||
\(611\) | −2.15472 | −0.0871708 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16.8722 | −0.681463 | −0.340731 | − | 0.940161i | \(-0.610675\pi\) | ||||
−0.340731 | + | 0.940161i | \(0.610675\pi\) | |||||||
\(614\) | −28.2986 | −1.14204 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −13.1422 | −0.529516 | ||||||||
\(617\) | −0.826593 | −0.0332774 | −0.0166387 | − | 0.999862i | \(-0.505297\pi\) | ||||
−0.0166387 | + | 0.999862i | \(0.505297\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.92336 | −0.318467 | −0.159233 | − | 0.987241i | \(-0.550902\pi\) | ||||
−0.159233 | + | 0.987241i | \(0.550902\pi\) | |||||||
\(620\) | −9.83617 | −0.395030 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −31.4091 | −1.25939 | ||||||||
\(623\) | −3.19059 | −0.127828 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −35.0911 | −1.40252 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −12.2209 | −0.487665 | ||||||||
\(629\) | −25.2906 | −1.00840 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 36.1596 | 1.43949 | 0.719745 | − | 0.694238i | \(-0.244259\pi\) | ||||
0.719745 | + | 0.694238i | \(0.244259\pi\) | |||||||
\(632\) | 9.10506 | 0.362180 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −2.05151 | −0.0814757 | ||||||||
\(635\) | −0.0122478 | −0.000486038 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.47545 | 0.256567 | ||||||||
\(638\) | 16.4915 | 0.652903 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −11.0577 | −0.437095 | ||||||||
\(641\) | 17.4184 | 0.687984 | 0.343992 | − | 0.938973i | \(-0.388221\pi\) | ||||
0.343992 | + | 0.938973i | \(0.388221\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −42.1096 | −1.66064 | −0.830321 | − | 0.557286i | \(-0.811843\pi\) | ||||
−0.830321 | + | 0.557286i | \(0.811843\pi\) | |||||||
\(644\) | −20.4784 | −0.806960 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.91262 | 0.271973 | ||||||||
\(647\) | 21.0971 | 0.829413 | 0.414707 | − | 0.909955i | \(-0.363884\pi\) | ||||
0.414707 | + | 0.909955i | \(0.363884\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.19533 | 0.360948 | ||||||||
\(650\) | −3.60895 | −0.141555 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.77106 | −0.0693599 | ||||||||
\(653\) | 28.2222 | 1.10442 | 0.552210 | − | 0.833705i | \(-0.313785\pi\) | ||||
0.552210 | + | 0.833705i | \(0.313785\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18.4349 | 0.720313 | ||||||||
\(656\) | −50.3590 | −1.96619 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −5.98298 | −0.233241 | ||||||||
\(659\) | −33.8928 | −1.32028 | −0.660138 | − | 0.751144i | \(-0.729502\pi\) | ||||
−0.660138 | + | 0.751144i | \(0.729502\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.46911 | −0.212724 | −0.106362 | − | 0.994327i | \(-0.533920\pi\) | ||||
−0.106362 | + | 0.994327i | \(0.533920\pi\) | |||||||
\(662\) | 3.33416 | 0.129586 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 11.1112 | 0.431198 | ||||||||
\(665\) | −4.65790 | −0.180626 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −19.3550 | −0.749427 | ||||||||
\(668\) | 14.6307 | 0.566077 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 3.84374 | 0.148497 | ||||||||
\(671\) | −40.3242 | −1.55670 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −40.9495 | −1.57849 | −0.789244 | − | 0.614080i | \(-0.789527\pi\) | ||||
−0.789244 | + | 0.614080i | \(0.789527\pi\) | |||||||
\(674\) | −3.31172 | −0.127563 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −10.0994 | −0.388437 | ||||||||
\(677\) | −12.1363 | −0.466437 | −0.233219 | − | 0.972424i | \(-0.574926\pi\) | ||||
−0.233219 | + | 0.972424i | \(0.574926\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −49.9342 | −1.91630 | ||||||||
\(680\) | −4.06846 | −0.156018 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 41.3350 | 1.58280 | ||||||||
\(683\) | 12.9361 | 0.494986 | 0.247493 | − | 0.968890i | \(-0.420393\pi\) | ||||
0.247493 | + | 0.968890i | \(0.420393\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −17.8348 | −0.681432 | ||||||||
\(686\) | −21.6008 | −0.824721 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −12.5440 | −0.478236 | ||||||||
\(689\) | 3.51894 | 0.134061 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.09541 | −0.231880 | −0.115940 | − | 0.993256i | \(-0.536988\pi\) | ||||
−0.115940 | + | 0.993256i | \(0.536988\pi\) | |||||||
\(692\) | 17.0082 | 0.646556 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −17.1067 | −0.649361 | ||||||||
\(695\) | −7.69547 | −0.291906 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −27.0170 | −1.02334 | ||||||||
\(698\) | −60.4275 | −2.28721 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3.63974 | −0.137569 | ||||||||
\(701\) | −24.9250 | −0.941403 | −0.470701 | − | 0.882293i | \(-0.655999\pi\) | ||||
−0.470701 | + | 0.882293i | \(0.655999\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.8189 | 0.521190 | ||||||||
\(704\) | −0.768213 | −0.0289531 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −65.5139 | −2.46565 | ||||||||
\(707\) | 54.4191 | 2.04664 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −48.1319 | −1.80763 | −0.903816 | − | 0.427921i | \(-0.859246\pi\) | ||||
−0.903816 | + | 0.427921i | \(0.859246\pi\) | |||||||
\(710\) | 12.1968 | 0.457738 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.52274 | 0.0570671 | ||||||||
\(713\) | −48.5122 | −1.81680 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.50854 | 0.206008 | ||||||||
\(716\) | 22.9693 | 0.858404 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.78217 | 0.0665100 | ||||||||
\(719\) | −16.3018 | −0.607954 | −0.303977 | − | 0.952679i | \(-0.598315\pi\) | ||||
−0.303977 | + | 0.952679i | \(0.598315\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −21.3502 | −0.795123 | ||||||||
\(722\) | 29.8951 | 1.11258 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −5.15534 | −0.191597 | ||||||||
\(725\) | −3.44007 | −0.127761 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 44.8912 | 1.66492 | 0.832462 | − | 0.554083i | \(-0.186931\pi\) | ||||
0.832462 | + | 0.554083i | \(0.186931\pi\) | |||||||
\(728\) | −9.89371 | −0.366685 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 15.5947 | 0.577188 | ||||||||
\(731\) | −6.72970 | −0.248907 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.45088 | 0.275204 | 0.137602 | − | 0.990488i | \(-0.456060\pi\) | ||||
0.137602 | + | 0.990488i | \(0.456060\pi\) | |||||||
\(734\) | −7.25576 | −0.267815 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 32.5230 | 1.19882 | ||||||||
\(737\) | −5.86691 | −0.216110 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.2444 | 0.413633 | 0.206817 | − | 0.978380i | \(-0.433690\pi\) | ||||
0.206817 | + | 0.978380i | \(0.433690\pi\) | |||||||
\(740\) | 10.7983 | 0.396952 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 9.77098 | 0.358704 | ||||||||
\(743\) | −2.94251 | −0.107950 | −0.0539750 | − | 0.998542i | \(-0.517189\pi\) | ||||
−0.0539750 | + | 0.998542i | \(0.517189\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 16.0825 | 0.589217 | ||||||||
\(746\) | −12.1718 | −0.445640 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −8.24475 | −0.301458 | ||||||||
\(749\) | −50.8121 | −1.85663 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.0559 | 0.476416 | 0.238208 | − | 0.971214i | \(-0.423440\pi\) | ||||
0.238208 | + | 0.971214i | \(0.423440\pi\) | |||||||
\(752\) | 5.26956 | 0.192161 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 12.4151 | 0.452130 | ||||||||
\(755\) | −3.01304 | −0.109656 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16.1988 | −0.588754 | −0.294377 | − | 0.955689i | \(-0.595112\pi\) | ||||
−0.294377 | + | 0.955689i | \(0.595112\pi\) | |||||||
\(758\) | 2.26603 | 0.0823059 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.22303 | 0.0806378 | ||||||||
\(761\) | −23.7871 | −0.862282 | −0.431141 | − | 0.902285i | \(-0.641889\pi\) | ||||
−0.431141 | + | 0.902285i | \(0.641889\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.27861 | 0.191099 | ||||||||
\(764\) | −10.8992 | −0.394321 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −35.1496 | −1.27001 | ||||||||
\(767\) | 6.92241 | 0.249954 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −20.9770 | −0.756451 | −0.378225 | − | 0.925714i | \(-0.623466\pi\) | ||||
−0.378225 | + | 0.925714i | \(0.623466\pi\) | |||||||
\(770\) | 15.2955 | 0.551210 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 28.4900 | 1.02538 | ||||||||
\(773\) | 16.6061 | 0.597280 | 0.298640 | − | 0.954366i | \(-0.403467\pi\) | ||||
0.298640 | + | 0.954366i | \(0.403467\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.62237 | −0.309725 | ||||||||
\(776\) | 23.8316 | 0.855505 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 24.6470 | 0.883637 | ||||||||
\(779\) | 14.7622 | 0.528911 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.6166 | −0.666156 | ||||||||
\(782\) | 26.6408 | 0.952674 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −15.8362 | −0.565580 | ||||||||
\(785\) | −10.7128 | −0.382355 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −50.6611 | −1.80587 | −0.902937 | − | 0.429773i | \(-0.858593\pi\) | ||||
−0.902937 | + | 0.429773i | \(0.858593\pi\) | |||||||
\(788\) | −12.6639 | −0.451132 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −10.5968 | −0.377018 | ||||||||
\(791\) | −8.75460 | −0.311278 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −30.3568 | −1.07800 | ||||||||
\(794\) | 4.02691 | 0.142910 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8.93220 | −0.316594 | ||||||||
\(797\) | 47.4446 | 1.68057 | 0.840287 | − | 0.542142i | \(-0.182386\pi\) | ||||
0.840287 | + | 0.542142i | \(0.182386\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.82705 | 0.100014 | ||||||||
\(800\) | 5.78051 | 0.204372 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −36.8106 | −1.29983 | ||||||||
\(803\) | −23.8031 | −0.839993 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −17.9513 | −0.632700 | ||||||||
\(806\) | 31.1177 | 1.09607 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −25.9721 | −0.913695 | ||||||||
\(809\) | −27.5792 | −0.969631 | −0.484816 | − | 0.874616i | \(-0.661113\pi\) | ||||
−0.484816 | + | 0.874616i | \(0.661113\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.4096 | 0.400645 | 0.200322 | − | 0.979730i | \(-0.435801\pi\) | ||||
0.200322 | + | 0.979730i | \(0.435801\pi\) | |||||||
\(812\) | 12.5210 | 0.439400 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −45.3781 | −1.59050 | ||||||||
\(815\) | −1.55250 | −0.0543818 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.67714 | 0.128647 | ||||||||
\(818\) | −65.7652 | −2.29943 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 11.5354 | 0.402832 | ||||||||
\(821\) | −28.7824 | −1.00451 | −0.502257 | − | 0.864719i | \(-0.667497\pi\) | ||||
−0.502257 | + | 0.864719i | \(0.667497\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 52.5379 | 1.83136 | 0.915679 | − | 0.401911i | \(-0.131654\pi\) | ||||
0.915679 | + | 0.401911i | \(0.131654\pi\) | |||||||
\(824\) | 10.1896 | 0.354972 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 19.2213 | 0.668796 | ||||||||
\(827\) | −51.6561 | −1.79626 | −0.898129 | − | 0.439732i | \(-0.855073\pi\) | ||||
−0.898129 | + | 0.439732i | \(0.855073\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −44.4506 | −1.54383 | −0.771917 | − | 0.635723i | \(-0.780702\pi\) | ||||
−0.771917 | + | 0.635723i | \(0.780702\pi\) | |||||||
\(830\) | −12.9316 | −0.448864 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −0.578324 | −0.0200498 | ||||||||
\(833\) | −8.49594 | −0.294367 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.8252 | 0.443834 | ||||||||
\(836\) | 4.50498 | 0.155808 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 51.3051 | 1.77230 | ||||||||
\(839\) | 24.5071 | 0.846078 | 0.423039 | − | 0.906111i | \(-0.360963\pi\) | ||||
0.423039 | + | 0.906111i | \(0.360963\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.1659 | −0.591928 | ||||||||
\(842\) | −60.3406 | −2.07948 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 23.4286 | 0.806447 | ||||||||
\(845\) | −8.85308 | −0.304555 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11.7502 | 0.403742 | ||||||||
\(848\) | −8.60586 | −0.295526 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4.73503 | 0.162410 | ||||||||
\(851\) | 53.2573 | 1.82564 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.76300 | −0.265800 | −0.132900 | − | 0.991129i | \(-0.542429\pi\) | ||||
−0.132900 | + | 0.991129i | \(0.542429\pi\) | |||||||
\(854\) | −84.2911 | −2.88438 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 24.2506 | 0.828868 | ||||||||
\(857\) | 6.72226 | 0.229628 | 0.114814 | − | 0.993387i | \(-0.463373\pi\) | ||||
0.114814 | + | 0.993387i | \(0.463373\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.13678 | 0.209384 | 0.104692 | − | 0.994505i | \(-0.466614\pi\) | ||||
0.104692 | + | 0.994505i | \(0.466614\pi\) | |||||||
\(860\) | 2.87336 | 0.0979808 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 27.8474 | 0.948486 | ||||||||
\(863\) | 7.96255 | 0.271048 | 0.135524 | − | 0.990774i | \(-0.456728\pi\) | ||||
0.135524 | + | 0.990774i | \(0.456728\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14.9094 | 0.506934 | ||||||||
\(866\) | 39.0350 | 1.32646 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 31.3832 | 1.06521 | ||||||||
\(869\) | 16.1745 | 0.548682 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.41671 | −0.149654 | ||||||||
\(872\) | −2.51927 | −0.0853133 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −14.5567 | −0.492388 | ||||||||
\(875\) | −3.19059 | −0.107862 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.78873 | 0.127936 | 0.0639681 | − | 0.997952i | \(-0.479624\pi\) | ||||
0.0639681 | + | 0.997952i | \(0.479624\pi\) | |||||||
\(878\) | −57.7547 | −1.94913 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −13.4716 | −0.454127 | ||||||||
\(881\) | 35.4998 | 1.19602 | 0.598009 | − | 0.801490i | \(-0.295959\pi\) | ||||
0.598009 | + | 0.801490i | \(0.295959\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −22.4461 | −0.755371 | −0.377685 | − | 0.925934i | \(-0.623280\pi\) | ||||
−0.377685 | + | 0.925934i | \(0.623280\pi\) | |||||||
\(884\) | −6.20679 | −0.208757 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 59.1807 | 1.98822 | ||||||||
\(887\) | 25.8592 | 0.868267 | 0.434133 | − | 0.900849i | \(-0.357055\pi\) | ||||
0.434133 | + | 0.900849i | \(0.357055\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.0390776 | 0.00131062 | ||||||||
\(890\) | −1.77222 | −0.0594050 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4.75167 | −0.159098 | ||||||||
\(893\) | −1.54471 | −0.0516919 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20.1349 | 0.673034 | ||||||||
\(896\) | 35.2807 | 1.17864 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −5.13096 | −0.171222 | ||||||||
\(899\) | 29.6616 | 0.989268 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.61694 | −0.153812 | ||||||||
\(902\) | −48.4756 | −1.61406 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4.17822 | 0.138965 | ||||||||
\(905\) | −4.51916 | −0.150222 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −45.8976 | −1.52400 | −0.762002 | − | 0.647575i | \(-0.775783\pi\) | ||||
−0.762002 | + | 0.647575i | \(0.775783\pi\) | |||||||
\(908\) | 8.78373 | 0.291498 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 11.5147 | 0.381708 | ||||||||
\(911\) | −50.0150 | −1.65707 | −0.828536 | − | 0.559936i | \(-0.810826\pi\) | ||||
−0.828536 | + | 0.559936i | \(0.810826\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 19.7383 | 0.653241 | ||||||||
\(914\) | −32.8730 | −1.08734 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.235081 | 0.00776729 | ||||||||
\(917\) | −58.8183 | −1.94235 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −40.9072 | −1.34940 | −0.674702 | − | 0.738090i | \(-0.735728\pi\) | ||||
−0.674702 | + | 0.738090i | \(0.735728\pi\) | |||||||
\(920\) | 8.56743 | 0.282460 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 36.0059 | 1.18579 | ||||||||
\(923\) | −14.0149 | −0.461307 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.46573 | 0.311231 | ||||||||
\(926\) | −35.5596 | −1.16856 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −19.8854 | −0.652769 | ||||||||
\(929\) | −22.6729 | −0.743874 | −0.371937 | − | 0.928258i | \(-0.621306\pi\) | ||||
−0.371937 | + | 0.928258i | \(0.621306\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.64223 | 0.152143 | ||||||||
\(932\) | −18.1830 | −0.595603 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −62.3210 | −2.03920 | ||||||||
\(935\) | −7.22733 | −0.236359 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −38.5330 | −1.25882 | −0.629409 | − | 0.777074i | \(-0.716703\pi\) | ||||
−0.629409 | + | 0.777074i | \(0.716703\pi\) | |||||||
\(938\) | −12.2638 | −0.400427 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.20706 | −0.0393699 | ||||||||
\(941\) | −4.39678 | −0.143331 | −0.0716655 | − | 0.997429i | \(-0.522831\pi\) | ||||
−0.0716655 | + | 0.997429i | \(0.522831\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 56.8927 | 1.85268 | ||||||||
\(944\) | −16.9293 | −0.551003 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −12.0749 | −0.392588 | ||||||||
\(947\) | −5.70322 | −0.185330 | −0.0926649 | − | 0.995697i | \(-0.529539\pi\) | ||||
−0.0926649 | + | 0.995697i | \(0.529539\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −17.9194 | −0.581688 | ||||||||
\(950\) | −2.58725 | −0.0839414 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 12.9808 | 0.420710 | ||||||||
\(953\) | 24.8332 | 0.804426 | 0.402213 | − | 0.915546i | \(-0.368241\pi\) | ||||
0.402213 | + | 0.915546i | \(0.368241\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9.55425 | −0.309168 | ||||||||
\(956\) | −19.3037 | −0.624327 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −65.4174 | −2.11354 | ||||||||
\(959\) | 56.9034 | 1.83751 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 43.3452 | 1.39823 | ||||||||
\(962\) | −34.1614 | −1.10141 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 4.38281 | 0.141161 | ||||||||
\(965\) | 24.9743 | 0.803950 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 43.4590 | 1.39755 | 0.698774 | − | 0.715343i | \(-0.253730\pi\) | ||||
0.698774 | + | 0.715343i | \(0.253730\pi\) | |||||||
\(968\) | −5.60791 | −0.180245 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −27.7361 | −0.890554 | ||||||||
\(971\) | 35.4713 | 1.13833 | 0.569165 | − | 0.822223i | \(-0.307267\pi\) | ||||
0.569165 | + | 0.822223i | \(0.307267\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 24.5531 | 0.787135 | ||||||||
\(974\) | 23.7942 | 0.762417 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 74.2400 | 2.37636 | ||||||||
\(977\) | −7.14406 | −0.228559 | −0.114279 | − | 0.993449i | \(-0.536456\pi\) | ||||
−0.114279 | + | 0.993449i | \(0.536456\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.70504 | 0.0864534 | ||||||||
\(980\) | 3.62749 | 0.115876 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −51.6096 | −1.64693 | ||||||||
\(983\) | 14.0179 | 0.447100 | 0.223550 | − | 0.974692i | \(-0.428235\pi\) | ||||
0.223550 | + | 0.974692i | \(0.428235\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.1011 | −0.353712 | ||||||||
\(986\) | −16.2889 | −0.518743 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.39142 | 0.107896 | ||||||||
\(989\) | 14.1715 | 0.450627 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25.6111 | −0.813565 | −0.406782 | − | 0.913525i | \(-0.633349\pi\) | ||||
−0.406782 | + | 0.913525i | \(0.633349\pi\) | |||||||
\(992\) | −49.8417 | −1.58248 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −38.9150 | −1.23431 | ||||||||
\(995\) | −7.82995 | −0.248226 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −27.3942 | −0.867582 | −0.433791 | − | 0.901013i | \(-0.642824\pi\) | ||||
−0.433791 | + | 0.901013i | \(0.642824\pi\) | |||||||
\(998\) | −10.8427 | −0.343220 | ||||||||
\(999\) | 0 | 0 |
(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 | 4005.2.a.l.1.1 | 4 | ||
3.2 | odd | 2 | 445.2.a.d.1.4 | ✓ | 4 | ||
12.11 | even | 2 | 7120.2.a.bc.1.3 | 4 | |||
15.14 | odd | 2 | 2225.2.a.i.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
445.2.a.d.1.4 | ✓ | 4 | 3.2 | odd | 2 | ||
2225.2.a.i.1.1 | 4 | 15.14 | odd | 2 | |||
4005.2.a.l.1.1 | 4 | 1.1 | even | 1 | trivial | ||
7120.2.a.bc.1.3 | 4 | 12.11 | even | 2 |