Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6004,2,Mod(1,6004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6004, 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("6004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6004 = 2^{2} \cdot 19 \cdot 79 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6004.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: | \(47.9421813736\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 15x^{6} + 56x^{5} + 87x^{4} - 248x^{3} - 241x^{2} + 340x + 248 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{29}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(3.98766\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6004.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.98766 | 1.78333 | 0.891667 | − | 0.452691i | \(-0.149536\pi\) | ||||
0.891667 | + | 0.452691i | \(0.149536\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.872374 | 0.329726 | 0.164863 | − | 0.986316i | \(-0.447282\pi\) | ||||
0.164863 | + | 0.986316i | \(0.447282\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.00000 | −1.00000 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.27985 | −0.687402 | −0.343701 | − | 0.939079i | \(-0.611681\pi\) | ||||
−0.343701 | + | 0.939079i | \(0.611681\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.48344 | −0.688783 | −0.344392 | − | 0.938826i | \(-0.611915\pi\) | ||||
−0.344392 | + | 0.938826i | \(0.611915\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.54683 | 1.34530 | 0.672652 | − | 0.739959i | \(-0.265155\pi\) | ||||
0.672652 | + | 0.739959i | \(0.265155\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.94254 | −0.405047 | −0.202524 | − | 0.979277i | \(-0.564914\pi\) | ||||
−0.202524 | + | 0.979277i | \(0.564914\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 10.9014 | 2.18028 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.64516 | 1.23398 | 0.616988 | − | 0.786973i | \(-0.288353\pi\) | ||||
0.616988 | + | 0.786973i | \(0.288353\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.65034 | 1.01483 | 0.507416 | − | 0.861701i | \(-0.330601\pi\) | ||||
0.507416 | + | 0.861701i | \(0.330601\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.47873 | 0.588012 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.90214 | −1.13470 | −0.567352 | − | 0.823475i | \(-0.692032\pi\) | ||||
−0.567352 | + | 0.823475i | \(0.692032\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.55402 | −0.398871 | −0.199435 | − | 0.979911i | \(-0.563911\pi\) | ||||
−0.199435 | + | 0.979911i | \(0.563911\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.83331 | 0.584574 | 0.292287 | − | 0.956331i | \(-0.405584\pi\) | ||||
0.292287 | + | 0.956331i | \(0.405584\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −11.9630 | −1.78333 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.63462 | −0.530164 | −0.265082 | − | 0.964226i | \(-0.585399\pi\) | ||||
−0.265082 | + | 0.964226i | \(0.585399\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.23896 | −0.891281 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.39374 | 1.01561 | 0.507804 | − | 0.861472i | \(-0.330457\pi\) | ||||
0.507804 | + | 0.861472i | \(0.330457\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −9.09127 | −1.22587 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.04855 | 0.266699 | 0.133349 | − | 0.991069i | \(-0.457427\pi\) | ||||
0.133349 | + | 0.991069i | \(0.457427\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.17891 | 1.04720 | 0.523601 | − | 0.851964i | \(-0.324588\pi\) | ||||
0.523601 | + | 0.851964i | \(0.324588\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.61712 | −0.329726 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −9.90312 | −1.22833 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.55917 | 0.679161 | 0.339581 | − | 0.940577i | \(-0.389715\pi\) | ||||
0.339581 | + | 0.940577i | \(0.389715\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.39664 | −0.165751 | −0.0828753 | − | 0.996560i | \(-0.526410\pi\) | ||||
−0.0828753 | + | 0.996560i | \(0.526410\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.85774 | 0.334473 | 0.167237 | − | 0.985917i | \(-0.446516\pi\) | ||||
0.167237 | + | 0.985917i | \(0.446516\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.98888 | −0.226654 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.00000 | 0.112509 | ||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.801980 | −0.0880287 | −0.0440144 | − | 0.999031i | \(-0.514015\pi\) | ||||
−0.0440144 | + | 0.999031i | \(0.514015\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 22.1189 | 2.39913 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.75832 | 0.928381 | 0.464190 | − | 0.885736i | \(-0.346345\pi\) | ||||
0.464190 | + | 0.885736i | \(0.346345\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.16649 | −0.227110 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.98766 | 0.409125 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.744519 | 0.0755945 | 0.0377972 | − | 0.999285i | \(-0.487966\pi\) | ||||
0.0377972 | + | 0.999285i | \(0.487966\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.83956 | 0.687402 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.5768 | 1.15193 | 0.575966 | − | 0.817474i | \(-0.304626\pi\) | ||||
0.575966 | + | 0.817474i | \(0.304626\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.53366 | 0.742314 | 0.371157 | − | 0.928570i | \(-0.378961\pi\) | ||||
0.371157 | + | 0.928570i | \(0.378961\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.14032 | 0.206913 | 0.103456 | − | 0.994634i | \(-0.467010\pi\) | ||||
0.103456 | + | 0.994634i | \(0.467010\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.4799 | 1.38692 | 0.693460 | − | 0.720495i | \(-0.256085\pi\) | ||||
0.693460 | + | 0.720495i | \(0.256085\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.04557 | 0.756864 | 0.378432 | − | 0.925629i | \(-0.376463\pi\) | ||||
0.378432 | + | 0.925629i | \(0.376463\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.74618 | −0.722335 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 7.45033 | 0.688783 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.83891 | 0.443582 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.80227 | −0.527479 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 23.5328 | 2.10484 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.66732 | 0.591629 | 0.295815 | − | 0.955245i | \(-0.404409\pi\) | ||||
0.295815 | + | 0.955245i | \(0.404409\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.7110 | −1.02320 | −0.511598 | − | 0.859225i | \(-0.670946\pi\) | ||||
−0.511598 | + | 0.859225i | \(0.670946\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.872374 | 0.0756444 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 19.2910 | 1.64814 | 0.824071 | − | 0.566486i | \(-0.191698\pi\) | ||||
0.824071 | + | 0.566486i | \(0.191698\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.11435 | −0.688250 | −0.344125 | − | 0.938924i | \(-0.611824\pi\) | ||||
−0.344125 | + | 0.938924i | \(0.611824\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.66189 | 0.473471 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 26.4986 | 2.20059 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −11.2057 | −0.918004 | −0.459002 | − | 0.888435i | \(-0.651793\pi\) | ||||
−0.459002 | + | 0.888435i | \(0.651793\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.82671 | 0.636929 | 0.318464 | − | 0.947935i | \(-0.396833\pi\) | ||||
0.318464 | + | 0.947935i | \(0.396833\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −16.6405 | −1.34530 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 22.5316 | 1.80978 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.77306 | 0.700166 | 0.350083 | − | 0.936719i | \(-0.386153\pi\) | ||||
0.350083 | + | 0.936719i | \(0.386153\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.69462 | −0.133555 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.0618 | −1.25806 | −0.629030 | − | 0.777381i | \(-0.716548\pi\) | ||||
−0.629030 | + | 0.777381i | \(0.716548\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −20.5889 | −1.59321 | −0.796607 | − | 0.604498i | \(-0.793374\pi\) | ||||
−0.796607 | + | 0.604498i | \(0.793374\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.83251 | −0.525577 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.00000 | −0.229416 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.94682 | −0.680214 | −0.340107 | − | 0.940387i | \(-0.610463\pi\) | ||||
−0.340107 | + | 0.940387i | \(0.610463\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.51011 | 0.718897 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.47553 | −0.484004 | −0.242002 | − | 0.970276i | \(-0.577804\pi\) | ||||
−0.242002 | + | 0.970276i | \(0.577804\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.64865 | 0.419861 | 0.209930 | − | 0.977716i | \(-0.432676\pi\) | ||||
0.209930 | + | 0.977716i | \(0.432676\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −27.5234 | −2.02356 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.6460 | −0.924764 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 17.5415 | 1.26926 | 0.634628 | − | 0.772818i | \(-0.281153\pi\) | ||||
0.634628 | + | 0.772818i | \(0.281153\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.2859 | 0.884359 | 0.442179 | − | 0.896927i | \(-0.354206\pi\) | ||||
0.442179 | + | 0.896927i | \(0.354206\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.2090 | −0.869855 | −0.434928 | − | 0.900465i | \(-0.643226\pi\) | ||||
−0.434928 | + | 0.900465i | \(0.643226\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.321349 | 0.0227799 | 0.0113899 | − | 0.999935i | \(-0.496374\pi\) | ||||
0.0113899 | + | 0.999935i | \(0.496374\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.79707 | 0.406874 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10.1845 | −0.711320 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.82762 | 0.405047 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.27985 | −0.157701 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.9444 | 0.753442 | 0.376721 | − | 0.926327i | \(-0.377052\pi\) | ||||
0.376721 | + | 0.926327i | \(0.377052\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 15.2859 | 1.04249 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.92921 | 0.334617 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −13.7752 | −0.926623 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.9386 | −0.866430 | −0.433215 | − | 0.901291i | \(-0.642621\pi\) | ||||
−0.433215 | + | 0.901291i | \(0.642621\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −32.7042 | −2.18028 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.8651 | −0.787516 | −0.393758 | − | 0.919214i | \(-0.628825\pi\) | ||||
−0.393758 | + | 0.919214i | \(0.628825\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.23471 | 0.279837 | 0.139919 | − | 0.990163i | \(-0.455316\pi\) | ||||
0.139919 | + | 0.990163i | \(0.455316\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.179775 | 0.0117774 | 0.00588871 | − | 0.999983i | \(-0.498126\pi\) | ||||
0.00588871 | + | 0.999983i | \(0.498126\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −14.4936 | −0.945460 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.22256 | 0.273135 | 0.136567 | − | 0.990631i | \(-0.456393\pi\) | ||||
0.136567 | + | 0.990631i | \(0.456393\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.5055 | 0.805553 | 0.402776 | − | 0.915298i | \(-0.368045\pi\) | ||||
0.402776 | + | 0.915298i | \(0.368045\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −24.8789 | −1.58945 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.48344 | −0.158018 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.7232 | −0.803082 | −0.401541 | − | 0.915841i | \(-0.631525\pi\) | ||||
−0.401541 | + | 0.915841i | \(0.631525\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.42870 | 0.278430 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.0193 | 0.624988 | 0.312494 | − | 0.949920i | \(-0.398836\pi\) | ||||
0.312494 | + | 0.949920i | \(0.398836\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.02124 | −0.374142 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −19.9355 | −1.23398 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 14.8454 | 0.915409 | 0.457705 | − | 0.889104i | \(-0.348672\pi\) | ||||
0.457705 | + | 0.889104i | \(0.348672\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 29.4837 | 1.81117 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 18.3622 | 1.11956 | 0.559781 | − | 0.828641i | \(-0.310885\pi\) | ||||
0.559781 | + | 0.828641i | \(0.310885\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.0513 | −1.15729 | −0.578643 | − | 0.815581i | \(-0.696417\pi\) | ||||
−0.578643 | + | 0.815581i | \(0.696417\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −24.8536 | −1.49873 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.79884 | 0.108082 | 0.0540408 | − | 0.998539i | \(-0.482790\pi\) | ||||
0.0540408 | + | 0.998539i | \(0.482790\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −16.9510 | −1.01483 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.8457 | −0.646999 | −0.323499 | − | 0.946228i | \(-0.604859\pi\) | ||||
−0.323499 | + | 0.946228i | \(0.604859\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.02051 | −0.536213 | −0.268107 | − | 0.963389i | \(-0.586398\pi\) | ||||
−0.268107 | + | 0.963389i | \(0.586398\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.22806 | −0.131518 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.7673 | 0.809843 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.13503 | −0.416833 | −0.208416 | − | 0.978040i | \(-0.566831\pi\) | ||||
−0.208416 | + | 0.978040i | \(0.566831\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.16893 | 0.475613 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.82419 | 0.278990 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.34408 | 0.192750 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 32.6147 | 1.86751 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.8103 | 1.53014 | 0.765072 | − | 0.643945i | \(-0.222703\pi\) | ||||
0.765072 | + | 0.643945i | \(0.222703\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 31.0212 | 1.75905 | 0.879526 | − | 0.475851i | \(-0.157860\pi\) | ||||
0.879526 | + | 0.475851i | \(0.157860\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.3000 | 0.582192 | 0.291096 | − | 0.956694i | \(-0.405980\pi\) | ||||
0.291096 | + | 0.956694i | \(0.405980\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −10.4362 | −0.588012 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −22.6423 | −1.27172 | −0.635860 | − | 0.771804i | \(-0.719354\pi\) | ||||
−0.635860 | + | 0.771804i | \(0.719354\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −15.1500 | −0.848237 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.54683 | 0.308634 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −27.0730 | −1.50174 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.17075 | −0.174809 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 27.7124 | 1.52321 | 0.761605 | − | 0.648041i | \(-0.224412\pi\) | ||||
0.761605 | + | 0.648041i | \(0.224412\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 20.7064 | 1.13470 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 22.1681 | 1.21117 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.90426 | −0.158205 | −0.0791026 | − | 0.996866i | \(-0.525205\pi\) | ||||
−0.0791026 | + | 0.996866i | \(0.525205\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.8820 | −0.697597 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −11.5493 | −0.623605 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 24.0824 | 1.29281 | 0.646406 | − | 0.762993i | \(-0.276271\pi\) | ||||
0.646406 | + | 0.762993i | \(0.276271\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −23.1267 | −1.23794 | −0.618971 | − | 0.785414i | \(-0.712450\pi\) | ||||
−0.618971 | + | 0.785414i | \(0.712450\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.06998 | −0.323072 | −0.161536 | − | 0.986867i | \(-0.551645\pi\) | ||||
−0.161536 | + | 0.986867i | \(0.551645\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.56932 | −0.295589 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −28.3493 | −1.49622 | −0.748110 | − | 0.663575i | \(-0.769038\pi\) | ||||
−0.748110 | + | 0.663575i | \(0.769038\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11.3957 | 0.596477 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −25.1135 | −1.31091 | −0.655457 | − | 0.755232i | \(-0.727524\pi\) | ||||
−0.655457 | + | 0.755232i | \(0.727524\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 7.66205 | 0.398871 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.45011 | 0.334873 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.06942 | 0.0553726 | 0.0276863 | − | 0.999617i | \(-0.491186\pi\) | ||||
0.0276863 | + | 0.999617i | \(0.491186\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −16.5029 | −0.849942 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.6068 | 1.10987 | 0.554933 | − | 0.831895i | \(-0.312744\pi\) | ||||
0.554933 | + | 0.831895i | \(0.312744\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12.3609 | −0.631614 | −0.315807 | − | 0.948823i | \(-0.602275\pi\) | ||||
−0.315807 | + | 0.948823i | \(0.602275\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.93099 | −0.404201 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −11.4999 | −0.584574 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.82206 | −0.143084 | −0.0715422 | − | 0.997438i | \(-0.522792\pi\) | ||||
−0.0715422 | + | 0.997438i | \(0.522792\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.7749 | −0.544912 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.98766 | 0.200641 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.8720 | 0.796590 | 0.398295 | − | 0.917257i | \(-0.369602\pi\) | ||||
0.398295 | + | 0.917257i | \(0.369602\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.49385 | −0.224412 | −0.112206 | − | 0.993685i | \(-0.535792\pi\) | ||||
−0.112206 | + | 0.993685i | \(0.535792\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −14.0323 | −0.698999 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 35.8889 | 1.78333 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 15.7359 | 0.779998 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.09478 | 0.153027 | 0.0765134 | − | 0.997069i | \(-0.475621\pi\) | ||||
0.0765134 | + | 0.997069i | \(0.475621\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.78710 | 0.0879377 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.19802 | −0.156985 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14.3679 | −0.701917 | −0.350958 | − | 0.936391i | \(-0.614144\pi\) | ||||
−0.350958 | + | 0.936391i | \(0.614144\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.5319 | −0.562031 | −0.281016 | − | 0.959703i | \(-0.590671\pi\) | ||||
−0.281016 | + | 0.959703i | \(0.590671\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 10.9039 | 0.530164 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 60.4683 | 2.93314 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.13506 | 0.345290 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14.4239 | −0.694775 | −0.347387 | − | 0.937722i | \(-0.612931\pi\) | ||||
−0.347387 | + | 0.937722i | \(0.612931\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.445323 | −0.0214008 | −0.0107004 | − | 0.999943i | \(-0.503406\pi\) | ||||
−0.0107004 | + | 0.999943i | \(0.503406\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.94254 | −0.0929243 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −38.1363 | −1.82015 | −0.910073 | − | 0.414448i | \(-0.863975\pi\) | ||||
−0.910073 | + | 0.414448i | \(0.863975\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 18.7169 | 0.891281 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15.4816 | −0.735554 | −0.367777 | − | 0.929914i | \(-0.619881\pi\) | ||||
−0.367777 | + | 0.929914i | \(0.619881\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 34.9252 | 1.65561 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.87322 | 0.135596 | 0.0677978 | − | 0.997699i | \(-0.478403\pi\) | ||||
0.0677978 | + | 0.997699i | \(0.478403\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.82279 | 0.274184 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −8.63923 | −0.405013 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.7373 | −0.595824 | −0.297912 | − | 0.954593i | \(-0.596290\pi\) | ||||
−0.297912 | + | 0.954593i | \(0.596290\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 25.2623 | 1.17658 | 0.588290 | − | 0.808650i | \(-0.299801\pi\) | ||||
0.588290 | + | 0.808650i | \(0.299801\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.98300 | −0.138632 | −0.0693158 | − | 0.997595i | \(-0.522082\pi\) | ||||
−0.0693158 | + | 0.997595i | \(0.522082\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −26.1982 | −1.21231 | −0.606155 | − | 0.795347i | \(-0.707289\pi\) | ||||
−0.606155 | + | 0.795347i | \(0.707289\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.84968 | 0.223937 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.73939 | −0.401837 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10.9014 | 0.500191 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −22.1812 | −1.01561 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.146462 | −0.00669200 | −0.00334600 | − | 0.999994i | \(-0.501065\pi\) | ||||
−0.00334600 | + | 0.999994i | \(0.501065\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 17.1411 | 0.781565 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.96889 | 0.134810 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 21.1050 | 0.956361 | 0.478181 | − | 0.878262i | \(-0.341296\pi\) | ||||
0.478181 | + | 0.878262i | \(0.341296\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.6210 | −0.614706 | −0.307353 | − | 0.951596i | \(-0.599443\pi\) | ||||
−0.307353 | + | 0.951596i | \(0.599443\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 36.8596 | 1.66007 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 27.2738 | 1.22587 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.21839 | −0.0546523 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −30.0285 | −1.34426 | −0.672130 | − | 0.740434i | \(-0.734620\pi\) | ||||
−0.672130 | + | 0.740434i | \(0.734620\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −22.6193 | −1.00854 | −0.504272 | − | 0.863545i | \(-0.668239\pi\) | ||||
−0.504272 | + | 0.863545i | \(0.668239\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 46.1642 | 2.05428 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.93587 | −0.174454 | −0.0872271 | − | 0.996188i | \(-0.527801\pi\) | ||||
−0.0872271 | + | 0.996188i | \(0.527801\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.49302 | 0.110285 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 30.0417 | 1.32379 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.28641 | 0.364436 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 36.4829 | 1.59835 | 0.799173 | − | 0.601101i | \(-0.205271\pi\) | ||||
0.799173 | + | 0.601101i | \(0.205271\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.0284 | 0.613420 | 0.306710 | − | 0.951803i | \(-0.400772\pi\) | ||||
0.306710 | + | 0.951803i | \(0.400772\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 31.3415 | 1.36526 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.2265 | −0.835937 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.14566 | −0.266699 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.34276 | 0.274735 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.53487 | 0.368995 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 14.2239 | 0.612668 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.6015 | 0.885726 | 0.442863 | − | 0.896589i | \(-0.353963\pi\) | ||||
0.442863 | + | 0.896589i | \(0.353963\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 57.7408 | 2.47334 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.4113 | 0.445156 | 0.222578 | − | 0.974915i | \(-0.428553\pi\) | ||||
0.222578 | + | 0.974915i | \(0.428553\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −24.5367 | −1.04720 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.64516 | 0.283093 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.872374 | 0.0370971 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −11.3290 | −0.480024 | −0.240012 | − | 0.970770i | \(-0.577151\pi\) | ||||
−0.240012 | + | 0.970770i | \(0.577151\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.51981 | −0.402645 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 25.0048 | 1.05383 | 0.526914 | − | 0.849919i | \(-0.323349\pi\) | ||||
0.526914 | + | 0.849919i | \(0.323349\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 32.0830 | 1.34974 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7.85137 | 0.329726 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 21.0875 | 0.884033 | 0.442017 | − | 0.897007i | \(-0.354263\pi\) | ||||
0.442017 | + | 0.897007i | \(0.354263\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.55987 | 0.316371 | 0.158185 | − | 0.987409i | \(-0.449436\pi\) | ||||
0.158185 | + | 0.987409i | \(0.449436\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −21.1764 | −0.883118 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.2474 | 0.426604 | 0.213302 | − | 0.976986i | \(-0.431578\pi\) | ||||
0.213302 | + | 0.976986i | \(0.431578\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.699626 | −0.0290254 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −16.8566 | −0.698131 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 29.7094 | 1.22833 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −25.8692 | −1.06773 | −0.533867 | − | 0.845568i | \(-0.679262\pi\) | ||||
−0.533867 | + | 0.845568i | \(0.679262\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.65034 | 0.232818 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 16.5603 | 0.680052 | 0.340026 | − | 0.940416i | \(-0.389564\pi\) | ||||
0.340026 | + | 0.940416i | \(0.389564\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 19.2959 | 0.791055 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −45.5143 | −1.85966 | −0.929832 | − | 0.367984i | \(-0.880048\pi\) | ||||
−0.929832 | + | 0.367984i | \(0.880048\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.71450 | 0.151518 | 0.0757588 | − | 0.997126i | \(-0.475862\pi\) | ||||
0.0757588 | + | 0.997126i | \(0.475862\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −16.6775 | −0.679161 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −23.1375 | −0.940672 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13.2147 | −0.536366 | −0.268183 | − | 0.963368i | \(-0.586423\pi\) | ||||
−0.268183 | + | 0.963368i | \(0.586423\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.02638 | 0.365168 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17.5702 | 0.709652 | 0.354826 | − | 0.934932i | \(-0.384540\pi\) | ||||
0.354826 | + | 0.934932i | \(0.384540\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.46378 | 0.139447 | 0.0697233 | − | 0.997566i | \(-0.477788\pi\) | ||||
0.0697233 | + | 0.997566i | \(0.477788\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.0396 | 0.403527 | 0.201764 | − | 0.979434i | \(-0.435333\pi\) | ||||
0.201764 | + | 0.979434i | \(0.435333\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.64053 | 0.306112 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 39.3337 | 1.57335 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −38.2850 | −1.52652 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.4222 | −0.812997 | −0.406498 | − | 0.913651i | \(-0.633250\pi\) | ||||
−0.406498 | + | 0.913651i | \(0.633250\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 26.5870 | 1.05507 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.4941 | 0.613899 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.18992 | 0.165751 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.93322 | 0.194850 | 0.0974251 | − | 0.995243i | \(-0.468939\pi\) | ||||
0.0974251 | + | 0.995243i | \(0.468939\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 31.8777 | 1.25713 | 0.628566 | − | 0.777756i | \(-0.283642\pi\) | ||||
0.628566 | + | 0.777756i | \(0.283642\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.12314 | 0.0834694 | 0.0417347 | − | 0.999129i | \(-0.486712\pi\) | ||||
0.0417347 | + | 0.999129i | \(0.486712\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.67040 | −0.183329 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 30.5999 | 1.19747 | 0.598734 | − | 0.800948i | \(-0.295671\pi\) | ||||
0.598734 | + | 0.800948i | \(0.295671\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −46.6995 | −1.82470 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −8.57322 | −0.334473 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22.9880 | 0.895486 | 0.447743 | − | 0.894162i | \(-0.352228\pi\) | ||||
0.447743 | + | 0.894162i | \(0.352228\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.9218 | 0.619287 | 0.309644 | − | 0.950853i | \(-0.399790\pi\) | ||||
0.309644 | + | 0.950853i | \(0.399790\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.47873 | 0.134899 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12.9085 | −0.499819 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −18.6467 | −0.719848 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.7354 | −0.413820 | −0.206910 | − | 0.978360i | \(-0.566341\pi\) | ||||
−0.206910 | + | 0.978360i | \(0.566341\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −49.5312 | −1.90364 | −0.951820 | − | 0.306657i | \(-0.900789\pi\) | ||||
−0.951820 | + | 0.306657i | \(0.900789\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.649499 | 0.0249255 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.67031 | −0.216968 | −0.108484 | − | 0.994098i | \(-0.534600\pi\) | ||||
−0.108484 | + | 0.994098i | \(0.534600\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 76.9260 | 2.93919 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −18.3619 | −0.699534 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.95821 | −0.340786 | −0.170393 | − | 0.985376i | \(-0.554504\pi\) | ||||
−0.170393 | + | 0.985376i | \(0.554504\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.96665 | 0.226654 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −32.3573 | −1.22738 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −14.1667 | −0.536602 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −17.2560 | −0.651752 | −0.325876 | − | 0.945413i | \(-0.605659\pi\) | ||||
−0.325876 | + | 0.945413i | \(0.605659\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.90214 | −0.260319 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10.0993 | 0.379822 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.4533 | −0.392583 | −0.196291 | − | 0.980546i | \(-0.562890\pi\) | ||||
−0.196291 | + | 0.980546i | \(0.562890\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.00000 | −0.112509 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −10.9760 | −0.411055 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 22.5777 | 0.844357 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −39.8893 | −1.48762 | −0.743809 | − | 0.668392i | \(-0.766983\pi\) | ||||
−0.743809 | + | 0.668392i | \(0.766983\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.57217 | 0.244760 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 72.4416 | 2.69041 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24.0286 | 0.891170 | 0.445585 | − | 0.895240i | \(-0.352996\pi\) | ||||
0.445585 | + | 0.895240i | \(0.352996\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 21.2627 | 0.786430 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.99852 | 0.258496 | 0.129248 | − | 0.991612i | \(-0.458744\pi\) | ||||
0.129248 | + | 0.991612i | \(0.458744\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12.6741 | −0.466856 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.23781 | −0.155890 | −0.0779452 | − | 0.996958i | \(-0.524836\pi\) | ||||
−0.0779452 | + | 0.996958i | \(0.524836\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.34362 | 0.196038 | 0.0980192 | − | 0.995185i | \(-0.468749\pi\) | ||||
0.0980192 | + | 0.995185i | \(0.468749\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −44.6844 | −1.63711 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.40594 | 0.0880287 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.86716 | 0.0682246 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −48.2579 | −1.76095 | −0.880477 | − | 0.474089i | \(-0.842778\pi\) | ||||
−0.880477 | + | 0.474089i | \(0.842778\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 31.2102 | 1.13586 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.7924 | 0.392256 | 0.196128 | − | 0.980578i | \(-0.437163\pi\) | ||||
0.196128 | + | 0.980578i | \(0.437163\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −48.2148 | −1.74779 | −0.873893 | − | 0.486119i | \(-0.838412\pi\) | ||||
−0.873893 | + | 0.486119i | \(0.838412\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.6319 | 0.457304 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −66.3566 | −2.39913 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.08747 | −0.183698 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 26.5293 | 0.956671 | 0.478336 | − | 0.878177i | \(-0.341240\pi\) | ||||
0.478336 | + | 0.878177i | \(0.341240\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 19.0436 | 0.684950 | 0.342475 | − | 0.939527i | \(-0.388735\pi\) | ||||
0.342475 | + | 0.939527i | \(0.388735\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 61.5967 | 2.21262 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.55402 | −0.0915072 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.18413 | 0.113937 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 34.9839 | 1.24863 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.84495 | 0.101412 | 0.0507058 | − | 0.998714i | \(-0.483853\pi\) | ||||
0.0507058 | + | 0.998714i | \(0.483853\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.01875 | 0.249558 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −20.3119 | −0.721295 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.83860 | −0.100548 | −0.0502741 | − | 0.998735i | \(-0.516009\pi\) | ||||
−0.0502741 | + | 0.998735i | \(0.516009\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −20.1606 | −0.713232 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −26.2750 | −0.928381 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.51523 | −0.229917 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.75757 | −0.238173 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −40.7219 | −1.43171 | −0.715853 | − | 0.698251i | \(-0.753962\pi\) | ||||
−0.715853 | + | 0.698251i | \(0.753962\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.88322 | 0.241703 | 0.120851 | − | 0.992671i | \(-0.461438\pi\) | ||||
0.120851 | + | 0.992671i | \(0.461438\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −64.0491 | −2.24354 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.83331 | 0.134111 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.49948 | 0.227110 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20.0312 | 0.699093 | 0.349546 | − | 0.936919i | \(-0.386336\pi\) | ||||
0.349546 | + | 0.936919i | \(0.386336\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.22063 | 0.251695 | 0.125848 | − | 0.992050i | \(-0.459835\pi\) | ||||
0.125848 | + | 0.992050i | \(0.459835\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.92971 | −0.136649 | −0.0683247 | − | 0.997663i | \(-0.521765\pi\) | ||||
−0.0683247 | + | 0.997663i | \(0.521765\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −34.6915 | −1.20488 | −0.602442 | − | 0.798163i | \(-0.705806\pi\) | ||||
−0.602442 | + | 0.798163i | \(0.705806\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −34.6065 | −1.19904 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −82.1013 | −2.84123 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 46.9673 | 1.62149 | 0.810745 | − | 0.585400i | \(-0.199062\pi\) | ||||
0.810745 | + | 0.585400i | \(0.199062\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15.1582 | 0.522695 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −27.2457 | −0.937280 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.06175 | −0.173924 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 13.4077 | 0.459609 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −29.1513 | −0.998120 | −0.499060 | − | 0.866567i | \(-0.666321\pi\) | ||||
−0.499060 | + | 0.866567i | \(0.666321\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −11.9630 | −0.409125 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −54.9357 | −1.87657 | −0.938284 | − | 0.345867i | \(-0.887585\pi\) | ||||
−0.938284 | + | 0.345867i | \(0.887585\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15.8361 | −0.540322 | −0.270161 | − | 0.962815i | \(-0.587077\pi\) | ||||
−0.270161 | + | 0.962815i | \(0.587077\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 41.3913 | 1.40898 | 0.704489 | − | 0.709715i | \(-0.251176\pi\) | ||||
0.704489 | + | 0.709715i | \(0.251176\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −35.6769 | −1.21305 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.27985 | −0.0773387 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13.8059 | −0.467795 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.23356 | −0.0755945 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 20.5294 | 0.694021 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 28.2513 | 0.953980 | 0.476990 | − | 0.878909i | \(-0.341728\pi\) | ||||
0.476990 | + | 0.878909i | \(0.341728\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.20945 | −0.242893 | −0.121446 | − | 0.992598i | \(-0.538753\pi\) | ||||
−0.121446 | + | 0.992598i | \(0.538753\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −34.8519 | −1.17286 | −0.586429 | − | 0.810001i | \(-0.699467\pi\) | ||||
−0.586429 | + | 0.810001i | \(0.699467\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 14.5025 | 0.486947 | 0.243473 | − | 0.969908i | \(-0.421713\pi\) | ||||
0.243473 | + | 0.969908i | \(0.421713\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.81640 | 0.195076 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −20.5187 | −0.687402 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.63462 | −0.121628 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −25.8222 | −0.863141 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 37.5474 | 1.25228 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 41.0118 | 1.36630 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 22.5249 | 0.748752 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16.5530 | −0.549634 | −0.274817 | − | 0.961497i | \(-0.588617\pi\) | ||||
−0.274817 | + | 0.961497i | \(0.588617\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −34.7303 | −1.15193 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 33.4685 | 1.10886 | 0.554431 | − | 0.832230i | \(-0.312936\pi\) | ||||
0.554431 | + | 0.832230i | \(0.312936\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.82840 | 0.0605111 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −10.2164 | −0.337375 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −48.1504 | −1.58833 | −0.794167 | − | 0.607699i | \(-0.792093\pi\) | ||||
−0.794167 | + | 0.607699i | \(0.792093\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.46847 | 0.114166 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −75.2430 | −2.47398 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −22.6010 | −0.742314 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 31.9599 | 1.04857 | 0.524285 | − | 0.851543i | \(-0.324333\pi\) | ||||
0.524285 | + | 0.851543i | \(0.324333\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.23896 | −0.204474 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −50.4278 | −1.64916 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 29.0852 | 0.950172 | 0.475086 | − | 0.879939i | \(-0.342417\pi\) | ||||
0.475086 | + | 0.879939i | \(0.342417\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −33.3042 | −1.08569 | −0.542843 | − | 0.839834i | \(-0.682652\pi\) | ||||
−0.542843 | + | 0.839834i | \(0.682652\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.96128 | 0.161562 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.83837 | 0.0597391 | 0.0298695 | − | 0.999554i | \(-0.490491\pi\) | ||||
0.0298695 | + | 0.999554i | \(0.490491\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.09703 | −0.230379 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −14.3031 | −0.463323 | −0.231661 | − | 0.972797i | \(-0.574416\pi\) | ||||
−0.231661 | + | 0.972797i | \(0.574416\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 69.9494 | 2.26351 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 16.8290 | 0.543436 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.926384 | 0.0298834 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.42096 | −0.206913 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 48.9920 | 1.57711 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −44.2581 | −1.42325 | −0.711623 | − | 0.702562i | \(-0.752040\pi\) | ||||
−0.711623 | + | 0.702562i | \(0.752040\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.60977 | 0.180026 | 0.0900131 | − | 0.995941i | \(-0.471309\pi\) | ||||
0.0900131 | + | 0.995941i | \(0.471309\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.07875 | −0.226934 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −15.7298 | −0.503241 | −0.251620 | − | 0.967826i | \(-0.580963\pi\) | ||||
−0.251620 | + | 0.967826i | \(0.580963\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −19.9677 | −0.638170 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −43.4396 | −1.38692 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 23.2066 | 0.740177 | 0.370088 | − | 0.928997i | \(-0.379327\pi\) | ||||
0.370088 | + | 0.928997i | \(0.379327\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −48.6853 | −1.55124 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.44636 | −0.236780 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −39.6636 | −1.25996 | −0.629978 | − | 0.776613i | \(-0.716936\pi\) | ||||
−0.629978 | + | 0.776613i | \(0.716936\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.28143 | 0.0406241 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −16.3777 | −0.518688 | −0.259344 | − | 0.965785i | \(-0.583506\pi\) | ||||
−0.259344 | + | 0.965785i | \(0.583506\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 6004.2.a.d.1.8 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6004.2.a.d.1.8 | ✓ | 8 | 1.1 | even | 1 | trivial |