Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1521,2,Mod(1,1521)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1521, 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("1521.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1521 = 3^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1521.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: | \(12.1452461474\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.1997632.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 8x^{4} + 19x^{2} - 13 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(1.09456\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1521.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.45945 | 1.73910 | 0.869549 | − | 0.493847i | \(-0.164410\pi\) | ||||
0.869549 | + | 0.493847i | \(0.164410\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.04892 | 2.02446 | ||||||||
\(5\) | −3.33722 | −1.49245 | −0.746226 | − | 0.665693i | \(-0.768136\pi\) | ||||
−0.746226 | + | 0.665693i | \(0.768136\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.69202 | −1.39545 | −0.697726 | − | 0.716364i | \(-0.745805\pi\) | ||||
−0.697726 | + | 0.716364i | \(0.745805\pi\) | |||||||
\(8\) | 5.03922 | 1.78163 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −8.20775 | −2.59552 | ||||||||
\(11\) | 0.270334 | 0.0815088 | 0.0407544 | − | 0.999169i | \(-0.487024\pi\) | ||||
0.0407544 | + | 0.999169i | \(0.487024\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −9.08036 | −2.42683 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.29590 | 1.07397 | ||||||||
\(17\) | −4.04114 | −0.980120 | −0.490060 | − | 0.871689i | \(-0.663025\pi\) | ||||
−0.490060 | + | 0.871689i | \(0.663025\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.15883 | −1.64235 | −0.821175 | − | 0.570677i | \(-0.806681\pi\) | ||||
−0.821175 | + | 0.570677i | \(0.806681\pi\) | |||||||
\(20\) | −13.5121 | −3.02141 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.664874 | 0.141752 | ||||||||
\(23\) | −2.79656 | −0.583122 | −0.291561 | − | 0.956552i | \(-0.594175\pi\) | ||||
−0.291561 | + | 0.956552i | \(0.594175\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.13706 | 1.22741 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −14.9487 | −2.82504 | ||||||||
\(29\) | 7.83578 | 1.45507 | 0.727533 | − | 0.686072i | \(-0.240667\pi\) | ||||
0.727533 | + | 0.686072i | \(0.240667\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.14914 | −0.385998 | −0.192999 | − | 0.981199i | \(-0.561821\pi\) | ||||
−0.192999 | + | 0.981199i | \(0.561821\pi\) | |||||||
\(32\) | 0.487125 | 0.0861124 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −9.93900 | −1.70452 | ||||||||
\(35\) | 12.3211 | 2.08265 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.37867 | −0.719848 | −0.359924 | − | 0.932982i | \(-0.617197\pi\) | ||||
−0.359924 | + | 0.932982i | \(0.617197\pi\) | |||||||
\(38\) | −17.6068 | −2.85620 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −16.8170 | −2.65900 | ||||||||
\(41\) | 7.61898 | 1.18989 | 0.594943 | − | 0.803768i | \(-0.297175\pi\) | ||||
0.594943 | + | 0.803768i | \(0.297175\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.89008 | −0.593232 | −0.296616 | − | 0.954997i | \(-0.595858\pi\) | ||||
−0.296616 | + | 0.954997i | \(0.595858\pi\) | |||||||
\(44\) | 1.09456 | 0.165011 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.87800 | −1.01411 | ||||||||
\(47\) | −0.877769 | −0.128036 | −0.0640179 | − | 0.997949i | \(-0.520391\pi\) | ||||
−0.0640179 | + | 0.997949i | \(0.520391\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.63102 | 0.947289 | ||||||||
\(50\) | 15.0938 | 2.13459 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.83770 | 0.939230 | 0.469615 | − | 0.882871i | \(-0.344393\pi\) | ||||
0.469615 | + | 0.882871i | \(0.344393\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.902165 | −0.121648 | ||||||||
\(56\) | −18.6049 | −2.48619 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 19.2717 | 2.53050 | ||||||||
\(59\) | −3.40399 | −0.443162 | −0.221581 | − | 0.975142i | \(-0.571122\pi\) | ||||
−0.221581 | + | 0.975142i | \(0.571122\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.06100 | 0.391921 | 0.195960 | − | 0.980612i | \(-0.437218\pi\) | ||||
0.195960 | + | 0.980612i | \(0.437218\pi\) | |||||||
\(62\) | −5.28572 | −0.671288 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.39373 | −0.924216 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.00969 | 0.612031 | 0.306015 | − | 0.952027i | \(-0.401004\pi\) | ||||
0.306015 | + | 0.952027i | \(0.401004\pi\) | |||||||
\(68\) | −16.3622 | −1.98421 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 30.3032 | 3.62192 | ||||||||
\(71\) | 7.59516 | 0.901379 | 0.450690 | − | 0.892681i | \(-0.351178\pi\) | ||||
0.450690 | + | 0.892681i | \(0.351178\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.405813 | 0.0474968 | 0.0237484 | − | 0.999718i | \(-0.492440\pi\) | ||||
0.0237484 | + | 0.999718i | \(0.492440\pi\) | |||||||
\(74\) | −10.7691 | −1.25189 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −28.9855 | −3.32487 | ||||||||
\(77\) | −0.998079 | −0.113742 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.3937 | −1.39440 | −0.697202 | − | 0.716875i | \(-0.745572\pi\) | ||||
−0.697202 | + | 0.716875i | \(0.745572\pi\) | |||||||
\(80\) | −14.3364 | −1.60285 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 18.7385 | 2.06933 | ||||||||
\(83\) | −6.98772 | −0.767002 | −0.383501 | − | 0.923540i | \(-0.625282\pi\) | ||||
−0.383501 | + | 0.923540i | \(0.625282\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 13.4862 | 1.46278 | ||||||||
\(86\) | −9.56748 | −1.03169 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.36227 | 0.145219 | ||||||||
\(89\) | −13.3918 | −1.41953 | −0.709766 | − | 0.704438i | \(-0.751199\pi\) | ||||
−0.709766 | + | 0.704438i | \(0.751199\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −11.3230 | −1.18051 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.15883 | −0.222667 | ||||||||
\(95\) | 23.8906 | 2.45113 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.9758 | 1.11443 | 0.557214 | − | 0.830369i | \(-0.311870\pi\) | ||||
0.557214 | + | 0.830369i | \(0.311870\pi\) | |||||||
\(98\) | 16.3087 | 1.64743 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 24.8485 | 2.48485 | ||||||||
\(101\) | −17.3603 | −1.72742 | −0.863708 | − | 0.503992i | \(-0.831864\pi\) | ||||
−0.863708 | + | 0.503992i | \(0.831864\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.71379 | −0.661530 | −0.330765 | − | 0.943713i | \(-0.607307\pi\) | ||||
−0.330765 | + | 0.943713i | \(0.607307\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 16.8170 | 1.63341 | ||||||||
\(107\) | 5.72991 | 0.553931 | 0.276966 | − | 0.960880i | \(-0.410671\pi\) | ||||
0.276966 | + | 0.960880i | \(0.410671\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.8509 | −1.03932 | −0.519662 | − | 0.854372i | \(-0.673942\pi\) | ||||
−0.519662 | + | 0.854372i | \(0.673942\pi\) | |||||||
\(110\) | −2.21883 | −0.211558 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −15.8605 | −1.49868 | ||||||||
\(113\) | 7.52839 | 0.708211 | 0.354106 | − | 0.935205i | \(-0.384785\pi\) | ||||
0.354106 | + | 0.935205i | \(0.384785\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.33273 | 0.870282 | ||||||||
\(116\) | 31.7264 | 2.94572 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −8.37196 | −0.770702 | ||||||||
\(119\) | 14.9200 | 1.36771 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9269 | −0.993356 | ||||||||
\(122\) | 7.52839 | 0.681588 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −8.70171 | −0.781437 | ||||||||
\(125\) | −3.79463 | −0.339402 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.79225 | 0.336508 | 0.168254 | − | 0.985744i | \(-0.446187\pi\) | ||||
0.168254 | + | 0.985744i | \(0.446187\pi\) | |||||||
\(128\) | −19.1588 | −1.69341 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.8103 | 1.29398 | 0.646990 | − | 0.762499i | \(-0.276028\pi\) | ||||
0.646990 | + | 0.762499i | \(0.276028\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 26.4306 | 2.29182 | ||||||||
\(134\) | 12.3211 | 1.06438 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −20.3642 | −1.74622 | ||||||||
\(137\) | 21.3479 | 1.82388 | 0.911938 | − | 0.410328i | \(-0.134586\pi\) | ||||
0.911938 | + | 0.410328i | \(0.134586\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.63102 | −0.562436 | −0.281218 | − | 0.959644i | \(-0.590738\pi\) | ||||
−0.281218 | + | 0.959644i | \(0.590738\pi\) | |||||||
\(140\) | 49.8871 | 4.21623 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 18.6799 | 1.56759 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −26.1497 | −2.17162 | ||||||||
\(146\) | 0.998079 | 0.0826016 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −17.7289 | −1.45730 | ||||||||
\(149\) | −17.2294 | −1.41149 | −0.705744 | − | 0.708467i | \(-0.749387\pi\) | ||||
−0.705744 | + | 0.708467i | \(0.749387\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −20.2838 | −1.65067 | −0.825337 | − | 0.564641i | \(-0.809015\pi\) | ||||
−0.825337 | + | 0.564641i | \(0.809015\pi\) | |||||||
\(152\) | −36.0749 | −2.92606 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.45473 | −0.197808 | ||||||||
\(155\) | 7.17218 | 0.576083 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.86592 | 0.627769 | 0.313884 | − | 0.949461i | \(-0.398370\pi\) | ||||
0.313884 | + | 0.949461i | \(0.398370\pi\) | |||||||
\(158\) | −30.4818 | −2.42500 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.62565 | −0.128519 | ||||||||
\(161\) | 10.3249 | 0.813720 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.5700 | 0.827908 | 0.413954 | − | 0.910298i | \(-0.364147\pi\) | ||||
0.413954 | + | 0.910298i | \(0.364147\pi\) | |||||||
\(164\) | 30.8486 | 2.40887 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −17.1860 | −1.33389 | ||||||||
\(167\) | 17.6439 | 1.36532 | 0.682662 | − | 0.730734i | \(-0.260822\pi\) | ||||
0.682662 | + | 0.730734i | \(0.260822\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 33.1687 | 2.54392 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −15.7506 | −1.20097 | ||||||||
\(173\) | 3.35045 | 0.254730 | 0.127365 | − | 0.991856i | \(-0.459348\pi\) | ||||
0.127365 | + | 0.991856i | \(0.459348\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −22.6582 | −1.71280 | ||||||||
\(176\) | 1.16133 | 0.0875383 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −32.9366 | −2.46870 | ||||||||
\(179\) | 20.9573 | 1.56642 | 0.783210 | − | 0.621757i | \(-0.213581\pi\) | ||||
0.783210 | + | 0.621757i | \(0.213581\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.770479 | −0.0572692 | −0.0286346 | − | 0.999590i | \(-0.509116\pi\) | ||||
−0.0286346 | + | 0.999590i | \(0.509116\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −14.0925 | −1.03891 | ||||||||
\(185\) | 14.6126 | 1.07434 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.09246 | −0.0798884 | ||||||||
\(188\) | −3.55401 | −0.259203 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 58.7579 | 4.26275 | ||||||||
\(191\) | 4.28765 | 0.310243 | 0.155122 | − | 0.987895i | \(-0.450423\pi\) | ||||
0.155122 | + | 0.987895i | \(0.450423\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21.1957 | 1.52570 | 0.762849 | − | 0.646577i | \(-0.223800\pi\) | ||||
0.762849 | + | 0.646577i | \(0.223800\pi\) | |||||||
\(194\) | 26.9946 | 1.93810 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 26.8485 | 1.91775 | ||||||||
\(197\) | 8.74326 | 0.622931 | 0.311466 | − | 0.950257i | \(-0.399180\pi\) | ||||
0.311466 | + | 0.950257i | \(0.399180\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.47219 | −0.458801 | −0.229401 | − | 0.973332i | \(-0.573677\pi\) | ||||
−0.229401 | + | 0.973332i | \(0.573677\pi\) | |||||||
\(200\) | 30.9260 | 2.18680 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −42.6969 | −3.00415 | ||||||||
\(203\) | −28.9298 | −2.03048 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −25.4263 | −1.77585 | ||||||||
\(206\) | −16.5123 | −1.15046 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.93528 | −0.133866 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.1793 | −1.25151 | −0.625756 | − | 0.780018i | \(-0.715210\pi\) | ||||
−0.625756 | + | 0.780018i | \(0.715210\pi\) | |||||||
\(212\) | 27.6853 | 1.90143 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 14.0925 | 0.963341 | ||||||||
\(215\) | 12.9821 | 0.885371 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.93469 | 0.538642 | ||||||||
\(218\) | −26.6872 | −1.80748 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3.65279 | −0.246271 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.92931 | −0.330091 | −0.165046 | − | 0.986286i | \(-0.552777\pi\) | ||||
−0.165046 | + | 0.986286i | \(0.552777\pi\) | |||||||
\(224\) | −1.79848 | −0.120166 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 18.5157 | 1.23165 | ||||||||
\(227\) | −20.9143 | −1.38813 | −0.694067 | − | 0.719911i | \(-0.744183\pi\) | ||||
−0.694067 | + | 0.719911i | \(0.744183\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.686645 | −0.0453748 | −0.0226874 | − | 0.999743i | \(-0.507222\pi\) | ||||
−0.0226874 | + | 0.999743i | \(0.507222\pi\) | |||||||
\(230\) | 22.9534 | 1.51350 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 39.4862 | 2.59240 | ||||||||
\(233\) | −16.1157 | −1.05578 | −0.527889 | − | 0.849314i | \(-0.677016\pi\) | ||||
−0.527889 | + | 0.849314i | \(0.677016\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.92931 | 0.191087 | ||||||||
\(236\) | −13.7825 | −0.897163 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 36.6950 | 2.37858 | ||||||||
\(239\) | −23.7406 | −1.53565 | −0.767826 | − | 0.640658i | \(-0.778662\pi\) | ||||
−0.767826 | + | 0.640658i | \(0.778662\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.30798 | −0.599580 | −0.299790 | − | 0.954005i | \(-0.596917\pi\) | ||||
−0.299790 | + | 0.954005i | \(0.596917\pi\) | |||||||
\(242\) | −26.8743 | −1.72754 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 12.3937 | 0.793427 | ||||||||
\(245\) | −22.1292 | −1.41378 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −10.8300 | −0.687706 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −9.33273 | −0.590254 | ||||||||
\(251\) | 2.04498 | 0.129078 | 0.0645391 | − | 0.997915i | \(-0.479442\pi\) | ||||
0.0645391 | + | 0.997915i | \(0.479442\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.756004 | −0.0475296 | ||||||||
\(254\) | 9.32686 | 0.585220 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −32.3327 | −2.02080 | ||||||||
\(257\) | −10.7691 | −0.671760 | −0.335880 | − | 0.941905i | \(-0.609034\pi\) | ||||
−0.335880 | + | 0.941905i | \(0.609034\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 16.1661 | 1.00451 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 36.4252 | 2.25036 | ||||||||
\(263\) | −14.3661 | −0.885851 | −0.442925 | − | 0.896558i | \(-0.646059\pi\) | ||||
−0.442925 | + | 0.896558i | \(0.646059\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −22.8189 | −1.40176 | ||||||||
\(266\) | 65.0048 | 3.98570 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 20.2838 | 1.23903 | ||||||||
\(269\) | −21.0941 | −1.28613 | −0.643064 | − | 0.765812i | \(-0.722337\pi\) | ||||
−0.643064 | + | 0.765812i | \(0.722337\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −24.2567 | −1.47349 | −0.736744 | − | 0.676172i | \(-0.763638\pi\) | ||||
−0.736744 | + | 0.676172i | \(0.763638\pi\) | |||||||
\(272\) | −17.3603 | −1.05262 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 52.5042 | 3.17190 | ||||||||
\(275\) | 1.65906 | 0.100045 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −25.3207 | −1.52137 | −0.760685 | − | 0.649121i | \(-0.775137\pi\) | ||||
−0.760685 | + | 0.649121i | \(0.775137\pi\) | |||||||
\(278\) | −16.3087 | −0.978131 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 62.0887 | 3.71051 | ||||||||
\(281\) | 6.60768 | 0.394181 | 0.197091 | − | 0.980385i | \(-0.436851\pi\) | ||||
0.197091 | + | 0.980385i | \(0.436851\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 23.3002 | 1.38505 | 0.692527 | − | 0.721392i | \(-0.256497\pi\) | ||||
0.692527 | + | 0.721392i | \(0.256497\pi\) | |||||||
\(284\) | 30.7522 | 1.82480 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −28.1295 | −1.66043 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.669186 | −0.0393639 | ||||||||
\(290\) | −64.3141 | −3.77665 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.64310 | 0.0961554 | ||||||||
\(293\) | −6.98183 | −0.407883 | −0.203942 | − | 0.978983i | \(-0.565375\pi\) | ||||
−0.203942 | + | 0.978983i | \(0.565375\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.3599 | 0.661398 | ||||||||
\(296\) | −22.0651 | −1.28251 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −42.3749 | −2.45471 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 14.3623 | 0.827828 | ||||||||
\(302\) | −49.8871 | −2.87068 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −30.7536 | −1.76384 | ||||||||
\(305\) | −10.2152 | −0.584923 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −29.0103 | −1.65570 | −0.827852 | − | 0.560946i | \(-0.810437\pi\) | ||||
−0.827852 | + | 0.560946i | \(0.810437\pi\) | |||||||
\(308\) | −4.04114 | −0.230265 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 17.6396 | 1.00186 | ||||||||
\(311\) | 2.90626 | 0.164799 | 0.0823995 | − | 0.996599i | \(-0.473742\pi\) | ||||
0.0823995 | + | 0.996599i | \(0.473742\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −25.1239 | −1.42009 | −0.710044 | − | 0.704157i | \(-0.751325\pi\) | ||||
−0.710044 | + | 0.704157i | \(0.751325\pi\) | |||||||
\(314\) | 19.3459 | 1.09175 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −50.1812 | −2.82291 | ||||||||
\(317\) | 5.44309 | 0.305714 | 0.152857 | − | 0.988248i | \(-0.451153\pi\) | ||||
0.152857 | + | 0.988248i | \(0.451153\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.11828 | 0.118601 | ||||||||
\(320\) | 24.6745 | 1.37935 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 25.3937 | 1.41514 | ||||||||
\(323\) | 28.9298 | 1.60970 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 25.9965 | 1.43981 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 38.3937 | 2.11994 | ||||||||
\(329\) | 3.24074 | 0.178668 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −26.4306 | −1.45276 | −0.726378 | − | 0.687296i | \(-0.758798\pi\) | ||||
−0.726378 | + | 0.687296i | \(0.758798\pi\) | |||||||
\(332\) | −28.2927 | −1.55276 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 43.3943 | 2.37443 | ||||||||
\(335\) | −16.7185 | −0.913427 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.86161 | 0.210355 | 0.105178 | − | 0.994453i | \(-0.466459\pi\) | ||||
0.105178 | + | 0.994453i | \(0.466459\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 54.6045 | 2.96134 | ||||||||
\(341\) | −0.580987 | −0.0314622 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.36227 | 0.0735558 | ||||||||
\(344\) | −19.6030 | −1.05692 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8.24027 | 0.443000 | ||||||||
\(347\) | 25.1961 | 1.35260 | 0.676299 | − | 0.736628i | \(-0.263583\pi\) | ||||
0.676299 | + | 0.736628i | \(0.263583\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.5918 | −0.888138 | −0.444069 | − | 0.895993i | \(-0.646466\pi\) | ||||
−0.444069 | + | 0.895993i | \(0.646466\pi\) | |||||||
\(350\) | −55.7267 | −2.97872 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.131687 | 0.00701892 | ||||||||
\(353\) | 11.9840 | 0.637844 | 0.318922 | − | 0.947781i | \(-0.396679\pi\) | ||||
0.318922 | + | 0.947781i | \(0.396679\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −25.3467 | −1.34526 | ||||||||
\(356\) | −54.2224 | −2.87378 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 51.5435 | 2.72416 | ||||||||
\(359\) | 10.7097 | 0.565236 | 0.282618 | − | 0.959232i | \(-0.408797\pi\) | ||||
0.282618 | + | 0.959232i | \(0.408797\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 32.2489 | 1.69731 | ||||||||
\(362\) | −1.89496 | −0.0995968 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.35429 | −0.0708868 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −18.1497 | −0.947409 | −0.473704 | − | 0.880684i | \(-0.657083\pi\) | ||||
−0.473704 | + | 0.880684i | \(0.657083\pi\) | |||||||
\(368\) | −12.0137 | −0.626258 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 35.9390 | 1.86838 | ||||||||
\(371\) | −25.2449 | −1.31065 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.45473 | −0.127101 | −0.0635506 | − | 0.997979i | \(-0.520242\pi\) | ||||
−0.0635506 | + | 0.997979i | \(0.520242\pi\) | |||||||
\(374\) | −2.68685 | −0.138934 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.42327 | −0.228113 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.5080 | 1.00206 | 0.501028 | − | 0.865431i | \(-0.332955\pi\) | ||||
0.501028 | + | 0.865431i | \(0.332955\pi\) | |||||||
\(380\) | 96.7312 | 4.96221 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 10.5453 | 0.539543 | ||||||||
\(383\) | 23.0961 | 1.18016 | 0.590078 | − | 0.807346i | \(-0.299097\pi\) | ||||
0.590078 | + | 0.807346i | \(0.299097\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.33081 | 0.169754 | ||||||||
\(386\) | 52.1298 | 2.65334 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 44.4403 | 2.25611 | ||||||||
\(389\) | −21.6480 | −1.09760 | −0.548798 | − | 0.835955i | \(-0.684914\pi\) | ||||
−0.548798 | + | 0.835955i | \(0.684914\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.3013 | 0.571530 | ||||||||
\(392\) | 33.4152 | 1.68772 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 21.5036 | 1.08334 | ||||||||
\(395\) | 41.3607 | 2.08108 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 24.7627 | 1.24280 | 0.621402 | − | 0.783492i | \(-0.286563\pi\) | ||||
0.621402 | + | 0.783492i | \(0.286563\pi\) | |||||||
\(398\) | −15.9181 | −0.797900 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 26.3642 | 1.31821 | ||||||||
\(401\) | 7.35454 | 0.367268 | 0.183634 | − | 0.982995i | \(-0.441214\pi\) | ||||
0.183634 | + | 0.982995i | \(0.441214\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −70.2905 | −3.49708 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −71.1517 | −3.53120 | ||||||||
\(407\) | −1.18370 | −0.0586740 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.3588 | 0.858338 | 0.429169 | − | 0.903224i | \(-0.358806\pi\) | ||||
0.429169 | + | 0.903224i | \(0.358806\pi\) | |||||||
\(410\) | −62.5347 | −3.08837 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −27.1836 | −1.33924 | ||||||||
\(413\) | 12.5676 | 0.618412 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 23.3196 | 1.14471 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −4.75973 | −0.232806 | ||||||||
\(419\) | 0.998079 | 0.0487594 | 0.0243797 | − | 0.999703i | \(-0.492239\pi\) | ||||
0.0243797 | + | 0.999703i | \(0.492239\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.786872 | 0.0383498 | 0.0191749 | − | 0.999816i | \(-0.493896\pi\) | ||||
0.0191749 | + | 0.999816i | \(0.493896\pi\) | |||||||
\(422\) | −44.7111 | −2.17650 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 34.4566 | 1.67336 | ||||||||
\(425\) | −24.8007 | −1.20301 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11.3013 | −0.546907 | ||||||||
\(428\) | 23.1999 | 1.12141 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 31.9288 | 1.53975 | ||||||||
\(431\) | −26.5478 | −1.27876 | −0.639380 | − | 0.768891i | \(-0.720809\pi\) | ||||
−0.639380 | + | 0.768891i | \(0.720809\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.1118 | 1.15874 | 0.579370 | − | 0.815064i | \(-0.303298\pi\) | ||||
0.579370 | + | 0.815064i | \(0.303298\pi\) | |||||||
\(434\) | 19.5150 | 0.936750 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −43.9342 | −2.10407 | ||||||||
\(437\) | 20.0201 | 0.957690 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.27844 | 0.251926 | 0.125963 | − | 0.992035i | \(-0.459798\pi\) | ||||
0.125963 | + | 0.992035i | \(0.459798\pi\) | |||||||
\(440\) | −4.54621 | −0.216732 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.63809 | −0.362897 | −0.181448 | − | 0.983400i | \(-0.558079\pi\) | ||||
−0.181448 | + | 0.983400i | \(0.558079\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 44.6915 | 2.11858 | ||||||||
\(446\) | −12.1234 | −0.574061 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 27.2978 | 1.28970 | ||||||||
\(449\) | −33.3616 | −1.57443 | −0.787216 | − | 0.616677i | \(-0.788479\pi\) | ||||
−0.787216 | + | 0.616677i | \(0.788479\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.05967 | 0.0969861 | ||||||||
\(452\) | 30.4818 | 1.43374 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −51.4379 | −2.41410 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −20.7342 | −0.969907 | −0.484953 | − | 0.874540i | \(-0.661163\pi\) | ||||
−0.484953 | + | 0.874540i | \(0.661163\pi\) | |||||||
\(458\) | −1.68877 | −0.0789111 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 37.7875 | 1.76185 | ||||||||
\(461\) | 34.5897 | 1.61100 | 0.805502 | − | 0.592593i | \(-0.201896\pi\) | ||||
0.805502 | + | 0.592593i | \(0.201896\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.0508 | 0.978315 | 0.489158 | − | 0.872195i | \(-0.337304\pi\) | ||||
0.489158 | + | 0.872195i | \(0.337304\pi\) | |||||||
\(464\) | 33.6617 | 1.56270 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −39.6359 | −1.83610 | ||||||||
\(467\) | −14.0587 | −0.650559 | −0.325279 | − | 0.945618i | \(-0.605458\pi\) | ||||
−0.325279 | + | 0.945618i | \(0.605458\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −18.4959 | −0.854060 | ||||||||
\(470\) | 7.20451 | 0.332319 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −17.1535 | −0.789552 | ||||||||
\(473\) | −1.05162 | −0.0483536 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −43.9342 | −2.01584 | ||||||||
\(476\) | 60.4098 | 2.76888 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −58.3889 | −2.67065 | ||||||||
\(479\) | −28.3118 | −1.29360 | −0.646800 | − | 0.762660i | \(-0.723893\pi\) | ||||
−0.646800 | + | 0.762660i | \(0.723893\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −22.8926 | −1.04273 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −44.2422 | −2.01101 | ||||||||
\(485\) | −36.6288 | −1.66323 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18.7211 | −0.848333 | −0.424167 | − | 0.905584i | \(-0.639433\pi\) | ||||
−0.424167 | + | 0.905584i | \(0.639433\pi\) | |||||||
\(488\) | 15.4250 | 0.698259 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −54.4258 | −2.45871 | ||||||||
\(491\) | 22.7828 | 1.02818 | 0.514088 | − | 0.857738i | \(-0.328131\pi\) | ||||
0.514088 | + | 0.857738i | \(0.328131\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −31.6655 | −1.42614 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −9.23251 | −0.414552 | ||||||||
\(497\) | −28.0415 | −1.25783 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.84787 | −0.172254 | −0.0861272 | − | 0.996284i | \(-0.527449\pi\) | ||||
−0.0861272 | + | 0.996284i | \(0.527449\pi\) | |||||||
\(500\) | −15.3642 | −0.687106 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5.02954 | 0.224479 | ||||||||
\(503\) | −21.8456 | −0.974049 | −0.487025 | − | 0.873388i | \(-0.661918\pi\) | ||||
−0.487025 | + | 0.873388i | \(0.661918\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 57.9353 | 2.57809 | ||||||||
\(506\) | −1.85936 | −0.0826586 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 15.3545 | 0.681246 | ||||||||
\(509\) | −9.29715 | −0.412089 | −0.206044 | − | 0.978543i | \(-0.566059\pi\) | ||||
−0.206044 | + | 0.978543i | \(0.566059\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.49827 | −0.0662796 | ||||||||
\(512\) | −41.2033 | −1.82095 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −26.4862 | −1.16826 | ||||||||
\(515\) | 22.4054 | 0.987301 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.237291 | −0.0104360 | ||||||||
\(518\) | 39.7599 | 1.74695 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.5440 | 0.812428 | 0.406214 | − | 0.913778i | \(-0.366849\pi\) | ||||
0.406214 | + | 0.913778i | \(0.366849\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 27.8635 | 1.21839 | 0.609193 | − | 0.793022i | \(-0.291493\pi\) | ||||
0.609193 | + | 0.793022i | \(0.291493\pi\) | |||||||
\(524\) | 59.9656 | 2.61961 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −35.3327 | −1.54058 | ||||||||
\(527\) | 8.68500 | 0.378324 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.1793 | −0.659969 | ||||||||
\(530\) | −56.1221 | −2.43779 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 107.015 | 4.63970 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −19.1220 | −0.826716 | ||||||||
\(536\) | 25.2449 | 1.09041 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −51.8799 | −2.23670 | ||||||||
\(539\) | 1.79259 | 0.0772124 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.2228 | 0.740467 | 0.370233 | − | 0.928939i | \(-0.379278\pi\) | ||||
0.370233 | + | 0.928939i | \(0.379278\pi\) | |||||||
\(542\) | −59.6582 | −2.56254 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.96854 | −0.0844005 | ||||||||
\(545\) | 36.2117 | 1.55114 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.01400 | 0.214383 | 0.107192 | − | 0.994238i | \(-0.465814\pi\) | ||||
0.107192 | + | 0.994238i | \(0.465814\pi\) | |||||||
\(548\) | 86.4360 | 3.69236 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 4.08038 | 0.173988 | ||||||||
\(551\) | −56.0950 | −2.38973 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 45.7579 | 1.94582 | ||||||||
\(554\) | −62.2750 | −2.64581 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −26.8485 | −1.13863 | ||||||||
\(557\) | 22.2660 | 0.943441 | 0.471720 | − | 0.881748i | \(-0.343633\pi\) | ||||
0.471720 | + | 0.881748i | \(0.343633\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 52.9302 | 2.23671 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 16.2513 | 0.685519 | ||||||||
\(563\) | −16.2254 | −0.683821 | −0.341910 | − | 0.939733i | \(-0.611074\pi\) | ||||
−0.341910 | + | 0.939733i | \(0.611074\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −25.1239 | −1.05697 | ||||||||
\(566\) | 57.3058 | 2.40874 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 38.2737 | 1.60593 | ||||||||
\(569\) | −7.33071 | −0.307319 | −0.153660 | − | 0.988124i | \(-0.549106\pi\) | ||||
−0.153660 | + | 0.988124i | \(0.549106\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 25.2825 | 1.05804 | 0.529020 | − | 0.848610i | \(-0.322560\pi\) | ||||
0.529020 | + | 0.848610i | \(0.322560\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −69.1831 | −2.88765 | ||||||||
\(575\) | −17.1626 | −0.715732 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.26742 | −0.177655 | −0.0888275 | − | 0.996047i | \(-0.528312\pi\) | ||||
−0.0888275 | + | 0.996047i | \(0.528312\pi\) | |||||||
\(578\) | −1.64583 | −0.0684576 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −105.878 | −4.39635 | ||||||||
\(581\) | 25.7988 | 1.07032 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.84846 | 0.0765555 | ||||||||
\(584\) | 2.04498 | 0.0846219 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −17.1715 | −0.709348 | ||||||||
\(587\) | −27.4579 | −1.13331 | −0.566654 | − | 0.823956i | \(-0.691762\pi\) | ||||
−0.566654 | + | 0.823956i | \(0.691762\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 15.3854 | 0.633943 | ||||||||
\(590\) | 27.9391 | 1.15023 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −18.8103 | −0.773099 | ||||||||
\(593\) | 1.16721 | 0.0479317 | 0.0239658 | − | 0.999713i | \(-0.492371\pi\) | ||||
0.0239658 | + | 0.999713i | \(0.492371\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −49.7913 | −2.04124 | ||||||||
\(596\) | −69.7604 | −2.85750 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.197682 | −0.00807706 | −0.00403853 | − | 0.999992i | \(-0.501286\pi\) | ||||
−0.00403853 | + | 0.999992i | \(0.501286\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.6340 | 0.841679 | 0.420839 | − | 0.907135i | \(-0.361736\pi\) | ||||
0.420839 | + | 0.907135i | \(0.361736\pi\) | |||||||
\(602\) | 35.3234 | 1.43967 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −82.1275 | −3.34172 | ||||||||
\(605\) | 36.4656 | 1.48254 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.8159 | 0.885482 | 0.442741 | − | 0.896650i | \(-0.354006\pi\) | ||||
0.442741 | + | 0.896650i | \(0.354006\pi\) | |||||||
\(608\) | −3.48725 | −0.141427 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −25.1239 | −1.01724 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −26.1299 | −1.05538 | −0.527688 | − | 0.849438i | \(-0.676941\pi\) | ||||
−0.527688 | + | 0.849438i | \(0.676941\pi\) | |||||||
\(614\) | −71.3495 | −2.87943 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5.02954 | −0.202646 | ||||||||
\(617\) | −1.84141 | −0.0741326 | −0.0370663 | − | 0.999313i | \(-0.511801\pi\) | ||||
−0.0370663 | + | 0.999313i | \(0.511801\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.77000 | 0.312303 | 0.156151 | − | 0.987733i | \(-0.450091\pi\) | ||||
0.156151 | + | 0.987733i | \(0.450091\pi\) | |||||||
\(620\) | 29.0396 | 1.16626 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 7.14782 | 0.286601 | ||||||||
\(623\) | 49.4429 | 1.98089 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −18.0218 | −0.720871 | ||||||||
\(626\) | −61.7911 | −2.46967 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 31.8485 | 1.27089 | ||||||||
\(629\) | 17.6948 | 0.705538 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.1468 | −0.762220 | −0.381110 | − | 0.924530i | \(-0.624458\pi\) | ||||
−0.381110 | + | 0.924530i | \(0.624458\pi\) | |||||||
\(632\) | −62.4547 | −2.48432 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 13.3870 | 0.531667 | ||||||||
\(635\) | −12.6556 | −0.502222 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 5.20981 | 0.206258 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 63.9372 | 2.52734 | ||||||||
\(641\) | −24.9496 | −0.985450 | −0.492725 | − | 0.870185i | \(-0.663999\pi\) | ||||
−0.492725 | + | 0.870185i | \(0.663999\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 42.4161 | 1.67273 | 0.836364 | − | 0.548175i | \(-0.184677\pi\) | ||||
0.836364 | + | 0.548175i | \(0.184677\pi\) | |||||||
\(644\) | 41.8048 | 1.64734 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 71.1517 | 2.79942 | ||||||||
\(647\) | 9.05326 | 0.355921 | 0.177960 | − | 0.984038i | \(-0.443050\pi\) | ||||
0.177960 | + | 0.984038i | \(0.443050\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.920215 | −0.0361216 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 42.7972 | 1.67607 | ||||||||
\(653\) | 1.57907 | 0.0617936 | 0.0308968 | − | 0.999523i | \(-0.490164\pi\) | ||||
0.0308968 | + | 0.999523i | \(0.490164\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −49.4252 | −1.93120 | ||||||||
\(656\) | 32.7304 | 1.27791 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 7.97046 | 0.310721 | ||||||||
\(659\) | −43.1591 | −1.68124 | −0.840621 | − | 0.541624i | \(-0.817809\pi\) | ||||
−0.840621 | + | 0.541624i | \(0.817809\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.64848 | −0.180805 | −0.0904025 | − | 0.995905i | \(-0.528815\pi\) | ||||
−0.0904025 | + | 0.995905i | \(0.528815\pi\) | |||||||
\(662\) | −65.0048 | −2.52648 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −35.2127 | −1.36652 | ||||||||
\(665\) | −88.2047 | −3.42043 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −21.9132 | −0.848482 | ||||||||
\(668\) | 71.4386 | 2.76404 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −41.1183 | −1.58854 | ||||||||
\(671\) | 0.827492 | 0.0319450 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.52243 | −0.174327 | −0.0871635 | − | 0.996194i | \(-0.527780\pi\) | ||||
−0.0871635 | + | 0.996194i | \(0.527780\pi\) | |||||||
\(674\) | 9.49745 | 0.365828 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −32.1706 | −1.23642 | −0.618208 | − | 0.786014i | \(-0.712141\pi\) | ||||
−0.618208 | + | 0.786014i | \(0.712141\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −40.5230 | −1.55513 | ||||||||
\(680\) | 67.9599 | 2.60614 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.42891 | −0.0547158 | ||||||||
\(683\) | −32.2241 | −1.23302 | −0.616511 | − | 0.787346i | \(-0.711454\pi\) | ||||
−0.616511 | + | 0.787346i | \(0.711454\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −71.2428 | −2.72205 | ||||||||
\(686\) | 3.35045 | 0.127921 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −16.7114 | −0.637116 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14.7482 | 0.561049 | 0.280525 | − | 0.959847i | \(-0.409492\pi\) | ||||
0.280525 | + | 0.959847i | \(0.409492\pi\) | |||||||
\(692\) | 13.5657 | 0.515690 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 61.9687 | 2.35230 | ||||||||
\(695\) | 22.1292 | 0.839409 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −30.7894 | −1.16623 | ||||||||
\(698\) | −40.8068 | −1.54456 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −91.7411 | −3.46749 | ||||||||
\(701\) | 41.5583 | 1.56964 | 0.784818 | − | 0.619726i | \(-0.212756\pi\) | ||||
0.784818 | + | 0.619726i | \(0.212756\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 31.3461 | 1.18224 | ||||||||
\(704\) | −1.99878 | −0.0753318 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 29.4741 | 1.10927 | ||||||||
\(707\) | 64.0947 | 2.41053 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 40.6034 | 1.52489 | 0.762446 | − | 0.647051i | \(-0.223998\pi\) | ||||
0.762446 | + | 0.647051i | \(0.223998\pi\) | |||||||
\(710\) | −62.3391 | −2.33955 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −67.4844 | −2.52908 | ||||||||
\(713\) | 6.01020 | 0.225084 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 84.8543 | 3.17115 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 26.3400 | 0.983001 | ||||||||
\(719\) | −42.1881 | −1.57335 | −0.786676 | − | 0.617366i | \(-0.788200\pi\) | ||||
−0.786676 | + | 0.617366i | \(0.788200\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 24.7875 | 0.923133 | ||||||||
\(722\) | 79.3147 | 2.95179 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −3.11960 | −0.115939 | ||||||||
\(725\) | 48.0886 | 1.78597 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −29.1661 | −1.08171 | −0.540856 | − | 0.841115i | \(-0.681900\pi\) | ||||
−0.540856 | + | 0.841115i | \(0.681900\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −3.33081 | −0.123279 | ||||||||
\(731\) | 15.7204 | 0.581439 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 47.7622 | 1.76414 | 0.882069 | − | 0.471120i | \(-0.156150\pi\) | ||||
0.882069 | + | 0.471120i | \(0.156150\pi\) | |||||||
\(734\) | −44.6385 | −1.64764 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.36227 | −0.0502140 | ||||||||
\(737\) | 1.35429 | 0.0498859 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −28.7157 | −1.05632 | −0.528162 | − | 0.849143i | \(-0.677119\pi\) | ||||
−0.528162 | + | 0.849143i | \(0.677119\pi\) | |||||||
\(740\) | 59.1652 | 2.17495 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −62.0887 | −2.27935 | ||||||||
\(743\) | 2.76684 | 0.101506 | 0.0507528 | − | 0.998711i | \(-0.483838\pi\) | ||||
0.0507528 | + | 0.998711i | \(0.483838\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 57.4984 | 2.10658 | ||||||||
\(746\) | −6.03730 | −0.221041 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −4.42327 | −0.161731 | ||||||||
\(749\) | −21.1550 | −0.772985 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 31.6980 | 1.15668 | 0.578338 | − | 0.815797i | \(-0.303701\pi\) | ||||
0.578338 | + | 0.815797i | \(0.303701\pi\) | |||||||
\(752\) | −3.77081 | −0.137507 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 67.6916 | 2.46355 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12.5138 | −0.454822 | −0.227411 | − | 0.973799i | \(-0.573026\pi\) | ||||
−0.227411 | + | 0.973799i | \(0.573026\pi\) | |||||||
\(758\) | 47.9789 | 1.74267 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 120.390 | 4.36701 | ||||||||
\(761\) | −0.883654 | −0.0320324 | −0.0160162 | − | 0.999872i | \(-0.505098\pi\) | ||||
−0.0160162 | + | 0.999872i | \(0.505098\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 40.0616 | 1.45033 | ||||||||
\(764\) | 17.3603 | 0.628074 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 56.8039 | 2.05241 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 29.9866 | 1.08134 | 0.540672 | − | 0.841233i | \(-0.318170\pi\) | ||||
0.540672 | + | 0.841233i | \(0.318170\pi\) | |||||||
\(770\) | 8.19199 | 0.295219 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 85.8195 | 3.08871 | ||||||||
\(773\) | 6.54825 | 0.235524 | 0.117762 | − | 0.993042i | \(-0.462428\pi\) | ||||
0.117762 | + | 0.993042i | \(0.462428\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −13.1894 | −0.473779 | ||||||||
\(776\) | 55.3096 | 1.98550 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −53.2422 | −1.90883 | ||||||||
\(779\) | −54.5430 | −1.95421 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.05323 | 0.0734703 | ||||||||
\(782\) | 27.7950 | 0.993946 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 28.4862 | 1.01736 | ||||||||
\(785\) | −26.2503 | −0.936915 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −29.6055 | −1.05532 | −0.527662 | − | 0.849455i | \(-0.676931\pi\) | ||||
−0.527662 | + | 0.849455i | \(0.676931\pi\) | |||||||
\(788\) | 35.4007 | 1.26110 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 101.725 | 3.61920 | ||||||||
\(791\) | −27.7950 | −0.988275 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 60.9028 | 2.16136 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −26.2054 | −0.928824 | ||||||||
\(797\) | 30.2353 | 1.07099 | 0.535495 | − | 0.844538i | \(-0.320125\pi\) | ||||
0.535495 | + | 0.844538i | \(0.320125\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.54719 | 0.125491 | ||||||||
\(800\) | 2.98952 | 0.105695 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 18.0881 | 0.638715 | ||||||||
\(803\) | 0.109705 | 0.00387141 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −34.4566 | −1.21444 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −87.4825 | −3.07762 | ||||||||
\(809\) | 4.37562 | 0.153839 | 0.0769193 | − | 0.997037i | \(-0.475492\pi\) | ||||
0.0769193 | + | 0.997037i | \(0.475492\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 46.9643 | 1.64914 | 0.824571 | − | 0.565759i | \(-0.191417\pi\) | ||||
0.824571 | + | 0.565759i | \(0.191417\pi\) | |||||||
\(812\) | −117.135 | −4.11062 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2.91126 | −0.102040 | ||||||||
\(815\) | −35.2745 | −1.23561 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 27.8485 | 0.974294 | ||||||||
\(818\) | 42.6932 | 1.49273 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −102.949 | −3.59513 | ||||||||
\(821\) | −9.00037 | −0.314115 | −0.157058 | − | 0.987589i | \(-0.550201\pi\) | ||||
−0.157058 | + | 0.987589i | \(0.550201\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −44.3226 | −1.54499 | −0.772494 | − | 0.635022i | \(-0.780991\pi\) | ||||
−0.772494 | + | 0.635022i | \(0.780991\pi\) | |||||||
\(824\) | −33.8323 | −1.17860 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 30.9095 | 1.07548 | ||||||||
\(827\) | 32.7568 | 1.13907 | 0.569533 | − | 0.821968i | \(-0.307124\pi\) | ||||
0.569533 | + | 0.821968i | \(0.307124\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.2765 | −0.391650 | −0.195825 | − | 0.980639i | \(-0.562738\pi\) | ||||
−0.195825 | + | 0.980639i | \(0.562738\pi\) | |||||||
\(830\) | 57.3535 | 1.99077 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −26.7969 | −0.928457 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −58.8816 | −2.03768 | ||||||||
\(836\) | −7.83578 | −0.271006 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2.45473 | 0.0847973 | ||||||||
\(839\) | 36.1311 | 1.24738 | 0.623692 | − | 0.781670i | \(-0.285632\pi\) | ||||
0.623692 | + | 0.781670i | \(0.285632\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 32.3994 | 1.11722 | ||||||||
\(842\) | 1.93528 | 0.0666940 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −73.6064 | −2.53364 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 40.3424 | 1.38618 | ||||||||
\(848\) | 29.3740 | 1.00871 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −60.9963 | −2.09216 | ||||||||
\(851\) | 12.2452 | 0.419760 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.2597 | 0.625199 | 0.312599 | − | 0.949885i | \(-0.398800\pi\) | ||||
0.312599 | + | 0.949885i | \(0.398800\pi\) | |||||||
\(854\) | −27.7950 | −0.951124 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 28.8743 | 0.986903 | ||||||||
\(857\) | 7.58927 | 0.259245 | 0.129622 | − | 0.991563i | \(-0.458624\pi\) | ||||
0.129622 | + | 0.991563i | \(0.458624\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.05536 | −0.206606 | −0.103303 | − | 0.994650i | \(-0.532941\pi\) | ||||
−0.103303 | + | 0.994650i | \(0.532941\pi\) | |||||||
\(860\) | 52.5634 | 1.79240 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −65.2930 | −2.22389 | ||||||||
\(863\) | 12.6905 | 0.431991 | 0.215995 | − | 0.976394i | \(-0.430700\pi\) | ||||
0.215995 | + | 0.976394i | \(0.430700\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.1812 | −0.380172 | ||||||||
\(866\) | 59.3020 | 2.01516 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 32.1269 | 1.09046 | ||||||||
\(869\) | −3.35045 | −0.113656 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −54.6798 | −1.85169 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 49.2385 | 1.66552 | ||||||||
\(875\) | 14.0099 | 0.473620 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13.7004 | 0.462629 | 0.231315 | − | 0.972879i | \(-0.425697\pi\) | ||||
0.231315 | + | 0.972879i | \(0.425697\pi\) | |||||||
\(878\) | 12.9821 | 0.438124 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −3.87561 | −0.130647 | ||||||||
\(881\) | 23.5832 | 0.794540 | 0.397270 | − | 0.917702i | \(-0.369958\pi\) | ||||
0.397270 | + | 0.917702i | \(0.369958\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 42.1661 | 1.41900 | 0.709502 | − | 0.704704i | \(-0.248920\pi\) | ||||
0.709502 | + | 0.704704i | \(0.248920\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −18.7855 | −0.631113 | ||||||||
\(887\) | −50.0239 | −1.67964 | −0.839820 | − | 0.542866i | \(-0.817339\pi\) | ||||
−0.839820 | + | 0.542866i | \(0.817339\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −14.0011 | −0.469581 | ||||||||
\(890\) | 109.917 | 3.68442 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −19.9584 | −0.668256 | ||||||||
\(893\) | 6.28380 | 0.210279 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −69.9391 | −2.33781 | ||||||||
\(896\) | 70.7347 | 2.36308 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −82.0514 | −2.73809 | ||||||||
\(899\) | −16.8402 | −0.561653 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −27.6321 | −0.920558 | ||||||||
\(902\) | 5.06567 | 0.168668 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 37.9372 | 1.26177 | ||||||||
\(905\) | 2.57126 | 0.0854716 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14.3375 | 0.476069 | 0.238035 | − | 0.971257i | \(-0.423497\pi\) | ||||
0.238035 | + | 0.971257i | \(0.423497\pi\) | |||||||
\(908\) | −84.6804 | −2.81022 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −50.2433 | −1.66464 | −0.832318 | − | 0.554298i | \(-0.812987\pi\) | ||||
−0.832318 | + | 0.554298i | \(0.812987\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.88902 | −0.0625174 | ||||||||
\(914\) | −50.9949 | −1.68676 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.78017 | −0.0918593 | ||||||||
\(917\) | −54.6798 | −1.80569 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 45.9077 | 1.51435 | 0.757177 | − | 0.653210i | \(-0.226578\pi\) | ||||
0.757177 | + | 0.653210i | \(0.226578\pi\) | |||||||
\(920\) | 47.0297 | 1.55052 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 85.0719 | 2.80169 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −26.8722 | −0.883551 | ||||||||
\(926\) | 51.7736 | 1.70139 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.81700 | 0.125299 | ||||||||
\(929\) | 29.3561 | 0.963142 | 0.481571 | − | 0.876407i | \(-0.340066\pi\) | ||||
0.481571 | + | 0.876407i | \(0.340066\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −47.4704 | −1.55578 | ||||||||
\(932\) | −65.2513 | −2.13738 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −34.5767 | −1.13139 | ||||||||
\(935\) | 3.64578 | 0.119230 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.54719 | 0.115882 | 0.0579408 | − | 0.998320i | \(-0.481547\pi\) | ||||
0.0579408 | + | 0.998320i | \(0.481547\pi\) | |||||||
\(938\) | −45.4898 | −1.48529 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 11.8605 | 0.386848 | ||||||||
\(941\) | −3.58845 | −0.116980 | −0.0584900 | − | 0.998288i | \(-0.518629\pi\) | ||||
−0.0584900 | + | 0.998288i | \(0.518629\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −21.3069 | −0.693849 | ||||||||
\(944\) | −14.6232 | −0.475944 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.58642 | −0.0840917 | ||||||||
\(947\) | 8.84562 | 0.287444 | 0.143722 | − | 0.989618i | \(-0.454093\pi\) | ||||
0.143722 | + | 0.989618i | \(0.454093\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −108.054 | −3.50574 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 75.1850 | 2.43676 | ||||||||
\(953\) | 49.0867 | 1.59008 | 0.795038 | − | 0.606560i | \(-0.207451\pi\) | ||||
0.795038 | + | 0.606560i | \(0.207451\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −14.3088 | −0.463023 | ||||||||
\(956\) | −96.1238 | −3.10886 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −69.6316 | −2.24970 | ||||||||
\(959\) | −78.8170 | −2.54513 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.3812 | −0.851006 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −37.6872 | −1.21382 | ||||||||
\(965\) | −70.7347 | −2.27703 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 37.9014 | 1.21883 | 0.609414 | − | 0.792852i | \(-0.291405\pi\) | ||||
0.609414 | + | 0.792852i | \(0.291405\pi\) | |||||||
\(968\) | −55.0631 | −1.76980 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −90.0869 | −2.89252 | ||||||||
\(971\) | 8.58735 | 0.275581 | 0.137791 | − | 0.990461i | \(-0.456000\pi\) | ||||
0.137791 | + | 0.990461i | \(0.456000\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 24.4819 | 0.784853 | ||||||||
\(974\) | −46.0437 | −1.47533 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 13.1497 | 0.420913 | ||||||||
\(977\) | 48.0469 | 1.53716 | 0.768578 | − | 0.639756i | \(-0.220965\pi\) | ||||
0.768578 | + | 0.639756i | \(0.220965\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.62027 | −0.115704 | ||||||||
\(980\) | −89.5993 | −2.86215 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 56.0334 | 1.78810 | ||||||||
\(983\) | 29.1110 | 0.928498 | 0.464249 | − | 0.885705i | \(-0.346324\pi\) | ||||
0.464249 | + | 0.885705i | \(0.346324\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −29.1782 | −0.929695 | ||||||||
\(986\) | −77.8798 | −2.48020 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 10.8788 | 0.345927 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −33.1094 | −1.05176 | −0.525878 | − | 0.850560i | \(-0.676263\pi\) | ||||
−0.525878 | + | 0.850560i | \(0.676263\pi\) | |||||||
\(992\) | −1.04690 | −0.0332392 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −68.9667 | −2.18749 | ||||||||
\(995\) | 21.5991 | 0.684739 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −45.3661 | −1.43676 | −0.718380 | − | 0.695651i | \(-0.755116\pi\) | ||||
−0.718380 | + | 0.695651i | \(0.755116\pi\) | |||||||
\(998\) | −9.46366 | −0.299567 | ||||||||
\(999\) | 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 | 1521.2.a.v.1.6 | yes | 6 | |
3.2 | odd | 2 | inner | 1521.2.a.v.1.1 | ✓ | 6 | |
13.5 | odd | 4 | 1521.2.b.n.1351.1 | 12 | |||
13.8 | odd | 4 | 1521.2.b.n.1351.12 | 12 | |||
13.12 | even | 2 | 1521.2.a.w.1.1 | yes | 6 | ||
39.5 | even | 4 | 1521.2.b.n.1351.11 | 12 | |||
39.8 | even | 4 | 1521.2.b.n.1351.2 | 12 | |||
39.38 | odd | 2 | 1521.2.a.w.1.6 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1521.2.a.v.1.1 | ✓ | 6 | 3.2 | odd | 2 | inner | |
1521.2.a.v.1.6 | yes | 6 | 1.1 | even | 1 | trivial | |
1521.2.a.w.1.1 | yes | 6 | 13.12 | even | 2 | ||
1521.2.a.w.1.6 | yes | 6 | 39.38 | odd | 2 | ||
1521.2.b.n.1351.1 | 12 | 13.5 | odd | 4 | |||
1521.2.b.n.1351.2 | 12 | 39.8 | even | 4 | |||
1521.2.b.n.1351.11 | 12 | 39.5 | even | 4 | |||
1521.2.b.n.1351.12 | 12 | 13.8 | odd | 4 |