Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8008,2,Mod(1,8008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("8008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8008.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: | \(63.9442019386\) |
Analytic rank: | \(1\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 3 x^{13} - 27 x^{12} + 78 x^{11} + 273 x^{10} - 750 x^{9} - 1306 x^{8} + 3378 x^{7} + \cdots - 128 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(3.38813\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8008.1 |
$q$-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 | ||||||||
\(3\) | −3.38813 | −1.95614 | −0.978070 | − | 0.208278i | \(-0.933214\pi\) | ||||
−0.978070 | + | 0.208278i | \(0.933214\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.16385 | −1.86213 | −0.931065 | − | 0.364853i | \(-0.881119\pi\) | ||||
−0.931065 | + | 0.364853i | \(0.881119\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 8.47945 | 2.82648 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 14.1077 | 3.64259 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.56251 | −1.10657 | −0.553285 | − | 0.832992i | \(-0.686626\pi\) | ||||
−0.553285 | + | 0.832992i | \(0.686626\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.578129 | −0.132632 | −0.0663159 | − | 0.997799i | \(-0.521125\pi\) | ||||
−0.0663159 | + | 0.997799i | \(0.521125\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.38813 | −0.739351 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.33270 | −1.32046 | −0.660230 | − | 0.751064i | \(-0.729541\pi\) | ||||
−0.660230 | + | 0.751064i | \(0.729541\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 12.3376 | 2.46753 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −18.5651 | −3.57285 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.97225 | 0.551933 | 0.275967 | − | 0.961167i | \(-0.411002\pi\) | ||||
0.275967 | + | 0.961167i | \(0.411002\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.14700 | 0.924429 | 0.462214 | − | 0.886768i | \(-0.347055\pi\) | ||||
0.462214 | + | 0.886768i | \(0.347055\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.38813 | 0.589798 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.16385 | −0.703819 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.64891 | 0.599878 | 0.299939 | − | 0.953958i | \(-0.403034\pi\) | ||||
0.299939 | + | 0.953958i | \(0.403034\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.38813 | 0.542535 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.27358 | −1.29212 | −0.646058 | − | 0.763288i | \(-0.723584\pi\) | ||||
−0.646058 | + | 0.763288i | \(0.723584\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.1989 | −1.55532 | −0.777660 | − | 0.628685i | \(-0.783594\pi\) | ||||
−0.777660 | + | 0.628685i | \(0.783594\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −35.3071 | −5.26328 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.73854 | −0.545322 | −0.272661 | − | 0.962110i | \(-0.587904\pi\) | ||||
−0.272661 | + | 0.962110i | \(0.587904\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 15.4584 | 2.16461 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.91971 | −1.08786 | −0.543928 | − | 0.839132i | \(-0.683063\pi\) | ||||
−0.543928 | + | 0.839132i | \(0.683063\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.16385 | 0.561453 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.95878 | 0.259446 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 14.8556 | 1.93404 | 0.967020 | − | 0.254701i | \(-0.0819771\pi\) | ||||
0.967020 | + | 0.254701i | \(0.0819771\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.44437 | −0.312970 | −0.156485 | − | 0.987680i | \(-0.550016\pi\) | ||||
−0.156485 | + | 0.987680i | \(0.550016\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 8.47945 | 1.06831 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.16385 | 0.516462 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.18087 | −0.144266 | −0.0721332 | − | 0.997395i | \(-0.522981\pi\) | ||||
−0.0721332 | + | 0.997395i | \(0.522981\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 21.4560 | 2.58300 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.4792 | 1.59969 | 0.799844 | − | 0.600208i | \(-0.204916\pi\) | ||||
0.799844 | + | 0.600208i | \(0.204916\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.09880 | 0.128605 | 0.0643024 | − | 0.997930i | \(-0.479518\pi\) | ||||
0.0643024 | + | 0.997930i | \(0.479518\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −41.8016 | −4.82683 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.93914 | 1.11824 | 0.559120 | − | 0.829087i | \(-0.311139\pi\) | ||||
0.559120 | + | 0.829087i | \(0.311139\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 37.4627 | 4.16252 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −15.7239 | −1.72592 | −0.862960 | − | 0.505272i | \(-0.831392\pi\) | ||||
−0.862960 | + | 0.505272i | \(0.831392\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 18.9976 | 2.06058 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −10.0704 | −1.07966 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.11272 | 0.859947 | 0.429973 | − | 0.902842i | \(-0.358523\pi\) | ||||
0.429973 | + | 0.902842i | \(0.358523\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | −0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −17.4387 | −1.80831 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.40724 | 0.246978 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.1163 | 1.02715 | 0.513575 | − | 0.858045i | \(-0.328321\pi\) | ||||
0.513575 | + | 0.858045i | \(0.328321\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.47945 | −0.852216 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.5130 | 1.24509 | 0.622544 | − | 0.782585i | \(-0.286099\pi\) | ||||
0.622544 | + | 0.782585i | \(0.286099\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.10720 | −0.601760 | −0.300880 | − | 0.953662i | \(-0.597280\pi\) | ||||
−0.300880 | + | 0.953662i | \(0.597280\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 14.1077 | 1.37677 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.32012 | 0.417642 | 0.208821 | − | 0.977954i | \(-0.433037\pi\) | ||||
0.208821 | + | 0.977954i | \(0.433037\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.94475 | 0.473621 | 0.236810 | − | 0.971556i | \(-0.423898\pi\) | ||||
0.236810 | + | 0.971556i | \(0.423898\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −12.3630 | −1.17344 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.5510 | 1.27477 | 0.637385 | − | 0.770545i | \(-0.280016\pi\) | ||||
0.637385 | + | 0.770545i | \(0.280016\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 26.3684 | 2.45887 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −8.47945 | −0.783925 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.56251 | −0.418244 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 28.0320 | 2.52756 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −30.5529 | −2.73273 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.22621 | −0.463751 | −0.231875 | − | 0.972745i | \(-0.574486\pi\) | ||||
−0.231875 | + | 0.972745i | \(0.574486\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 34.5553 | 3.04242 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.90049 | 0.690269 | 0.345135 | − | 0.938553i | \(-0.387833\pi\) | ||||
0.345135 | + | 0.938553i | \(0.387833\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.578129 | −0.0501301 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 77.3022 | 6.65312 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.1583 | 1.03876 | 0.519379 | − | 0.854544i | \(-0.326163\pi\) | ||||
0.519379 | + | 0.854544i | \(0.326163\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.65024 | 0.479247 | 0.239624 | − | 0.970866i | \(-0.422976\pi\) | ||||
0.239624 | + | 0.970866i | \(0.422976\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.6667 | 1.06673 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.00000 | 0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −12.3760 | −1.02777 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.38813 | −0.279448 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.36077 | −0.684941 | −0.342470 | − | 0.939529i | \(-0.611264\pi\) | ||||
−0.342470 | + | 0.939529i | \(0.611264\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.72322 | 0.140233 | 0.0701167 | − | 0.997539i | \(-0.477663\pi\) | ||||
0.0701167 | + | 0.997539i | \(0.477663\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −38.6875 | −3.12770 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −21.4313 | −1.72141 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.6885 | 1.65112 | 0.825561 | − | 0.564312i | \(-0.190859\pi\) | ||||
0.825561 | + | 0.564312i | \(0.190859\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 26.8330 | 2.12800 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.33270 | −0.499087 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.82463 | −0.377894 | −0.188947 | − | 0.981987i | \(-0.560507\pi\) | ||||
−0.188947 | + | 0.981987i | \(0.560507\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −14.1077 | −1.09828 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.413591 | −0.0320046 | −0.0160023 | − | 0.999872i | \(-0.505094\pi\) | ||||
−0.0160023 | + | 0.999872i | \(0.505094\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.90221 | −0.374882 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.38148 | −0.485175 | −0.242588 | − | 0.970129i | \(-0.577996\pi\) | ||||
−0.242588 | + | 0.970129i | \(0.577996\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 12.3376 | 0.932638 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −50.3329 | −3.78325 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −21.3150 | −1.59316 | −0.796580 | − | 0.604533i | \(-0.793360\pi\) | ||||
−0.796580 | + | 0.604533i | \(0.793360\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.9922 | −0.817044 | −0.408522 | − | 0.912749i | \(-0.633956\pi\) | ||||
−0.408522 | + | 0.912749i | \(0.633956\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.28186 | 0.612212 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −15.1935 | −1.11705 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.56251 | 0.333644 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −18.5651 | −1.35041 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.4677 | −1.04684 | −0.523422 | − | 0.852074i | \(-0.675345\pi\) | ||||
−0.523422 | + | 0.852074i | \(0.675345\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.8784 | 1.28692 | 0.643459 | − | 0.765481i | \(-0.277499\pi\) | ||||
0.643459 | + | 0.765481i | \(0.277499\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −14.1077 | −1.01027 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.7107 | 0.976844 | 0.488422 | − | 0.872608i | \(-0.337573\pi\) | ||||
0.488422 | + | 0.872608i | \(0.337573\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.64030 | −0.116277 | −0.0581387 | − | 0.998309i | \(-0.518517\pi\) | ||||
−0.0581387 | + | 0.998309i | \(0.518517\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.00095 | 0.282205 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.97225 | 0.208611 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 34.4500 | 2.40609 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −53.6978 | −3.73226 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.578129 | 0.0399900 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 25.1395 | 1.73068 | 0.865338 | − | 0.501188i | \(-0.167104\pi\) | ||||
0.865338 | + | 0.501188i | \(0.167104\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −45.6694 | −3.12921 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 42.4668 | 2.89621 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.14700 | 0.349401 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.72288 | −0.251569 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.56251 | 0.306907 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.50169 | 0.301456 | 0.150728 | − | 0.988575i | \(-0.451838\pi\) | ||||
0.150728 | + | 0.988575i | \(0.451838\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 104.616 | 6.97443 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.91855 | 0.459201 | 0.229600 | − | 0.973285i | \(-0.426258\pi\) | ||||
0.229600 | + | 0.973285i | \(0.426258\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.2406 | 1.46970 | 0.734851 | − | 0.678229i | \(-0.237252\pi\) | ||||
0.734851 | + | 0.678229i | \(0.237252\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.38813 | 0.222923 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4.54086 | −0.297482 | −0.148741 | − | 0.988876i | \(-0.547522\pi\) | ||||
−0.148741 | + | 0.988876i | \(0.547522\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 15.5667 | 1.01546 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −33.6751 | −2.18743 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −23.6439 | −1.52940 | −0.764700 | − | 0.644387i | \(-0.777113\pi\) | ||||
−0.764700 | + | 0.644387i | \(0.777113\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.5134 | 1.19255 | 0.596277 | − | 0.802779i | \(-0.296646\pi\) | ||||
0.596277 | + | 0.802779i | \(0.296646\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −71.2332 | −4.56961 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.16385 | −0.266019 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.578129 | 0.0367855 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 53.2746 | 3.37614 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.345313 | 0.0217960 | 0.0108980 | − | 0.999941i | \(-0.496531\pi\) | ||||
0.0108980 | + | 0.999941i | \(0.496531\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.33270 | 0.398134 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −64.3664 | −4.03078 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.59696 | 0.411507 | 0.205754 | − | 0.978604i | \(-0.434035\pi\) | ||||
0.205754 | + | 0.978604i | \(0.434035\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.64891 | 0.226732 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 25.2030 | 1.56003 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 18.8188 | 1.16042 | 0.580210 | − | 0.814467i | \(-0.302971\pi\) | ||||
0.580210 | + | 0.814467i | \(0.302971\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 32.9765 | 2.02573 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −27.4870 | −1.68218 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −18.8982 | −1.15224 | −0.576121 | − | 0.817364i | \(-0.695434\pi\) | ||||
−0.576121 | + | 0.817364i | \(0.695434\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −30.2005 | −1.83455 | −0.917274 | − | 0.398257i | \(-0.869615\pi\) | ||||
−0.917274 | + | 0.398257i | \(0.869615\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.38813 | 0.205059 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −12.3376 | −0.743988 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.0964 | 1.32764 | 0.663821 | − | 0.747892i | \(-0.268934\pi\) | ||||
0.663821 | + | 0.747892i | \(0.268934\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 43.6437 | 2.61288 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −28.1117 | −1.67700 | −0.838500 | − | 0.544901i | \(-0.816567\pi\) | ||||
−0.838500 | + | 0.544901i | \(0.816567\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.10241 | −0.422194 | −0.211097 | − | 0.977465i | \(-0.567704\pi\) | ||||
−0.211097 | + | 0.977465i | \(0.567704\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −8.15606 | −0.483123 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.27358 | −0.488374 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.81647 | 0.224499 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −34.2752 | −2.00925 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.05751 | −0.412304 | −0.206152 | − | 0.978520i | \(-0.566094\pi\) | ||||
−0.206152 | + | 0.978520i | \(0.566094\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −61.8567 | −3.60143 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 18.5651 | 1.07726 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.33270 | 0.366230 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.1989 | −0.587856 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −42.3956 | −2.43556 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 10.1780 | 0.582790 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.77610 | 0.557951 | 0.278976 | − | 0.960298i | \(-0.410005\pi\) | ||||
0.278976 | + | 0.960298i | \(0.410005\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 20.6920 | 1.17713 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.63596 | −0.149472 | −0.0747358 | − | 0.997203i | \(-0.523811\pi\) | ||||
−0.0747358 | + | 0.997203i | \(0.523811\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.11565 | 0.176107 | 0.0880534 | − | 0.996116i | \(-0.471935\pi\) | ||||
0.0880534 | + | 0.996116i | \(0.471935\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −35.3071 | −1.98933 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 26.3543 | 1.48020 | 0.740102 | − | 0.672495i | \(-0.234777\pi\) | ||||
0.740102 | + | 0.672495i | \(0.234777\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.97225 | −0.166414 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −14.6371 | −0.816966 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.63772 | 0.146767 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −12.3376 | −0.684369 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −16.7535 | −0.926469 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.73854 | −0.206113 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −32.3193 | −1.77643 | −0.888215 | − | 0.459428i | \(-0.848054\pi\) | ||||
−0.888215 | + | 0.459428i | \(0.848054\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 30.9408 | 1.69554 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.91697 | 0.268643 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 24.9855 | 1.36105 | 0.680525 | − | 0.732725i | \(-0.261752\pi\) | ||||
0.680525 | + | 0.732725i | \(0.261752\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −45.9126 | −2.49363 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.14700 | −0.278726 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −89.3397 | −4.80989 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.828424 | 0.0444721 | 0.0222361 | − | 0.999753i | \(-0.492921\pi\) | ||||
0.0222361 | + | 0.999753i | \(0.492921\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.41117 | −0.0755381 | −0.0377691 | − | 0.999286i | \(-0.512025\pi\) | ||||
−0.0377691 | + | 0.999286i | \(0.512025\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 18.5651 | 0.990931 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.0527 | 0.694725 | 0.347363 | − | 0.937731i | \(-0.387077\pi\) | ||||
0.347363 | + | 0.937731i | \(0.387077\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −56.1254 | −2.97883 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 15.4584 | 0.818144 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.03934 | −0.213188 | −0.106594 | − | 0.994303i | \(-0.533995\pi\) | ||||
−0.106594 | + | 0.994303i | \(0.533995\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.6658 | −0.982409 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.38813 | −0.177831 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.57524 | −0.239479 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −25.1989 | −1.31537 | −0.657686 | − | 0.753292i | \(-0.728465\pi\) | ||||
−0.657686 | + | 0.753292i | \(0.728465\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −70.1554 | −3.65214 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.91971 | −0.411171 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.8836 | −0.563530 | −0.281765 | − | 0.959483i | \(-0.590920\pi\) | ||||
−0.281765 | + | 0.959483i | \(0.590920\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 103.517 | 5.34560 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.97225 | −0.153079 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.232332 | −0.0119341 | −0.00596706 | − | 0.999982i | \(-0.501899\pi\) | ||||
−0.00596706 | + | 0.999982i | \(0.501899\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 17.7071 | 0.907162 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −34.9499 | −1.78586 | −0.892928 | − | 0.450200i | \(-0.851353\pi\) | ||||
−0.892928 | + | 0.450200i | \(0.851353\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.16385 | 0.212209 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −86.4812 | −4.39608 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.22161 | 0.163342 | 0.0816710 | − | 0.996659i | \(-0.473974\pi\) | ||||
0.0816710 | + | 0.996659i | \(0.473974\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 28.8930 | 1.46118 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −26.7679 | −1.35026 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −41.3851 | −2.08231 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.31581 | −0.266793 | −0.133396 | − | 0.991063i | \(-0.542588\pi\) | ||||
−0.133396 | + | 0.991063i | \(0.542588\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.95878 | 0.0980615 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.24669 | −0.0622566 | −0.0311283 | − | 0.999515i | \(-0.509910\pi\) | ||||
−0.0311283 | + | 0.999515i | \(0.509910\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.14700 | −0.256390 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −155.989 | −7.75115 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.64891 | −0.180870 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.8690 | 0.784670 | 0.392335 | − | 0.919822i | \(-0.371667\pi\) | ||||
0.392335 | + | 0.919822i | \(0.371667\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −41.1941 | −2.03195 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 14.8556 | 0.730998 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 65.4719 | 3.21389 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −19.1438 | −0.937474 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 11.4891 | 0.561282 | 0.280641 | − | 0.959813i | \(-0.409453\pi\) | ||||
0.280641 | + | 0.959813i | \(0.409453\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −22.7327 | −1.10792 | −0.553962 | − | 0.832542i | \(-0.686885\pi\) | ||||
−0.553962 | + | 0.832542i | \(0.686885\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −31.7008 | −1.54134 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −56.2906 | −2.73050 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.44437 | −0.118291 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.38813 | −0.163581 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 26.4519 | 1.27414 | 0.637071 | − | 0.770805i | \(-0.280146\pi\) | ||||
0.637071 | + | 0.770805i | \(0.280146\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −27.1072 | −1.30269 | −0.651344 | − | 0.758782i | \(-0.725795\pi\) | ||||
−0.651344 | + | 0.758782i | \(0.725795\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 41.9316 | 2.01046 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.66112 | 0.175135 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.9418 | 0.904043 | 0.452022 | − | 0.892007i | \(-0.350703\pi\) | ||||
0.452022 | + | 0.892007i | \(0.350703\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.47945 | 0.403783 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −34.3524 | −1.63213 | −0.816065 | − | 0.577960i | \(-0.803849\pi\) | ||||
−0.816065 | + | 0.577960i | \(0.803849\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −33.7802 | −1.60133 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 28.3274 | 1.33984 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11.5809 | −0.546535 | −0.273267 | − | 0.961938i | \(-0.588104\pi\) | ||||
−0.273267 | + | 0.961938i | \(0.588104\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.27358 | 0.389588 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.83849 | −0.274316 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.16385 | 0.195204 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.5678 | 0.728230 | 0.364115 | − | 0.931354i | \(-0.381372\pi\) | ||||
0.364115 | + | 0.931354i | \(0.381372\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 84.7034 | 3.95361 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.2297 | 0.616169 | 0.308084 | − | 0.951359i | \(-0.400312\pi\) | ||||
0.308084 | + | 0.951359i | \(0.400312\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −23.1636 | −1.07651 | −0.538253 | − | 0.842783i | \(-0.680915\pi\) | ||||
−0.538253 | + | 0.842783i | \(0.680915\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 72.6122 | 3.36731 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −22.0130 | −1.01864 | −0.509319 | − | 0.860578i | \(-0.670103\pi\) | ||||
−0.509319 | + | 0.860578i | \(0.670103\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.18087 | −0.0545276 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −70.0954 | −3.22983 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10.1989 | 0.468947 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.13275 | −0.327273 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −67.1547 | −3.07480 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.80906 | −0.219731 | −0.109866 | − | 0.993946i | \(-0.535042\pi\) | ||||
−0.109866 | + | 0.993946i | \(0.535042\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.64891 | −0.166376 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 21.4560 | 0.976284 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −42.1226 | −1.91269 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.4710 | 0.746373 | 0.373187 | − | 0.927756i | \(-0.378265\pi\) | ||||
0.373187 | + | 0.927756i | \(0.378265\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 16.3465 | 0.739213 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.1439 | −0.818825 | −0.409412 | − | 0.912349i | \(-0.634266\pi\) | ||||
−0.409412 | + | 0.912349i | \(0.634266\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −13.5609 | −0.610753 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 35.3071 | 1.58694 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 13.4792 | 0.604625 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.6272 | −0.744334 | −0.372167 | − | 0.928166i | \(-0.621385\pi\) | ||||
−0.372167 | + | 0.928166i | \(0.621385\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.40130 | 0.0626055 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −31.8164 | −1.41862 | −0.709311 | − | 0.704896i | \(-0.750994\pi\) | ||||
−0.709311 | + | 0.704896i | \(0.750994\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −52.1021 | −2.31851 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.38813 | −0.150472 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 24.8265 | 1.10042 | 0.550209 | − | 0.835027i | \(-0.314548\pi\) | ||||
0.550209 | + | 0.835027i | \(0.314548\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.09880 | 0.0486081 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 10.7330 | 0.473874 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 25.4295 | 1.12056 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.73854 | 0.164421 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 21.6213 | 0.949071 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20.2143 | 0.885605 | 0.442803 | − | 0.896619i | \(-0.353984\pi\) | ||||
0.442803 | + | 0.896619i | \(0.353984\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 32.5433 | 1.42302 | 0.711509 | − | 0.702677i | \(-0.248012\pi\) | ||||
0.711509 | + | 0.702677i | \(0.248012\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −41.8016 | −1.82437 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −23.4832 | −1.02295 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.1031 | 0.743614 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 125.968 | 5.46653 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.27358 | 0.358369 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −17.9883 | −0.777704 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 72.2181 | 3.11644 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.876603 | 0.0376881 | 0.0188440 | − | 0.999822i | \(-0.494001\pi\) | ||||
0.0188440 | + | 0.999822i | \(0.494001\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 37.2430 | 1.59825 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −20.5892 | −0.881944 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.7936 | −0.461502 | −0.230751 | − | 0.973013i | \(-0.574118\pi\) | ||||
−0.230751 | + | 0.973013i | \(0.574118\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −20.7269 | −0.884603 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.71834 | −0.0732039 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.93914 | 0.422655 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 51.4777 | 2.18511 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 28.3459 | 1.20105 | 0.600526 | − | 0.799605i | \(-0.294958\pi\) | ||||
0.600526 | + | 0.799605i | \(0.294958\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10.1989 | 0.431368 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −15.4584 | −0.652653 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 18.2804 | 0.770428 | 0.385214 | − | 0.922827i | \(-0.374128\pi\) | ||||
0.385214 | + | 0.922827i | \(0.374128\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −56.4243 | −2.37379 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 37.4627 | 1.57328 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −29.4714 | −1.23551 | −0.617753 | − | 0.786372i | \(-0.711957\pi\) | ||||
−0.617753 | + | 0.786372i | \(0.711957\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −45.3596 | −1.89824 | −0.949120 | − | 0.314915i | \(-0.898024\pi\) | ||||
−0.949120 | + | 0.314915i | \(0.898024\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 49.0184 | 2.04777 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −78.1306 | −3.25827 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14.8665 | −0.618901 | −0.309450 | − | 0.950916i | \(-0.600145\pi\) | ||||
−0.309450 | + | 0.950916i | \(0.600145\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −60.5745 | −2.51739 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −15.7239 | −0.652337 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.91971 | 0.328001 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 35.3071 | 1.45977 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 19.3463 | 0.798509 | 0.399254 | − | 0.916840i | \(-0.369269\pi\) | ||||
0.399254 | + | 0.916840i | \(0.369269\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.97563 | −0.122609 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −46.4535 | −1.91084 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −11.1479 | −0.457789 | −0.228895 | − | 0.973451i | \(-0.573511\pi\) | ||||
−0.228895 | + | 0.973451i | \(0.573511\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 18.9976 | 0.778826 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.55754 | 0.227455 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 13.1330 | 0.536601 | 0.268301 | − | 0.963335i | \(-0.413538\pi\) | ||||
0.268301 | + | 0.963335i | \(0.413538\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −27.5749 | −1.12480 | −0.562401 | − | 0.826864i | \(-0.690122\pi\) | ||||
−0.562401 | + | 0.826864i | \(0.690122\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10.0131 | −0.407767 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.16385 | −0.169285 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 33.5137 | 1.36028 | 0.680140 | − | 0.733082i | \(-0.261919\pi\) | ||||
0.680140 | + | 0.733082i | \(0.261919\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −10.0704 | −0.408073 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.73854 | 0.151245 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 40.8801 | 1.65113 | 0.825566 | − | 0.564305i | \(-0.190856\pi\) | ||||
0.825566 | + | 0.564305i | \(0.190856\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −116.721 | −4.70665 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −24.4563 | −0.984572 | −0.492286 | − | 0.870433i | \(-0.663839\pi\) | ||||
−0.492286 | + | 0.870433i | \(0.663839\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.8443 | 0.435870 | 0.217935 | − | 0.975963i | \(-0.430068\pi\) | ||||
0.217935 | + | 0.975963i | \(0.430068\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 117.567 | 4.71781 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.11272 | 0.325029 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 65.5293 | 2.62117 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.95878 | −0.0782260 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −16.6482 | −0.663807 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24.5019 | −0.975405 | −0.487702 | − | 0.873010i | \(-0.662165\pi\) | ||||
−0.487702 | + | 0.873010i | \(0.662165\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −85.1761 | −3.38544 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 21.7611 | 0.863565 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00000 | −0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 114.296 | 4.52149 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −36.0544 | −1.42406 | −0.712031 | − | 0.702148i | \(-0.752225\pi\) | ||||
−0.712031 | + | 0.702148i | \(0.752225\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −40.1974 | −1.58523 | −0.792616 | − | 0.609721i | \(-0.791281\pi\) | ||||
−0.792616 | + | 0.609721i | \(0.791281\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −143.883 | −5.66539 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 25.7746 | 1.01330 | 0.506652 | − | 0.862151i | \(-0.330883\pi\) | ||||
0.506652 | + | 0.862151i | \(0.330883\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −14.8556 | −0.583135 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −17.4387 | −0.683477 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 23.7994 | 0.931341 | 0.465671 | − | 0.884958i | \(-0.345813\pi\) | ||||
0.465671 | + | 0.884958i | \(0.345813\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −32.8965 | −1.28537 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9.31722 | 0.363499 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11.0585 | 0.430780 | 0.215390 | − | 0.976528i | \(-0.430898\pi\) | ||||
0.215390 | + | 0.976528i | \(0.430898\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.20167 | 0.357904 | 0.178952 | − | 0.983858i | \(-0.442729\pi\) | ||||
0.178952 | + | 0.983858i | \(0.442729\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −15.4584 | −0.600354 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.40724 | 0.0933488 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −18.8224 | −0.728806 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −15.2523 | −0.589689 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.44437 | 0.0943639 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 26.7574 | 1.03142 | 0.515711 | − | 0.856762i | \(-0.327528\pi\) | ||||
0.515711 | + | 0.856762i | \(0.327528\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −229.049 | −8.81612 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 46.1583 | 1.77401 | 0.887004 | − | 0.461761i | \(-0.152782\pi\) | ||||
0.887004 | + | 0.461761i | \(0.152782\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.1163 | 0.388226 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −23.4410 | −0.898260 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 23.2642 | 0.890179 | 0.445090 | − | 0.895486i | \(-0.353172\pi\) | ||||
0.445090 | + | 0.895486i | \(0.353172\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −50.6255 | −1.93430 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −75.3542 | −2.87494 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.91971 | 0.301717 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.09564 | −0.117764 | −0.0588819 | − | 0.998265i | \(-0.518754\pi\) | ||||
−0.0588819 | + | 0.998265i | \(0.518754\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −8.47945 | −0.322107 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −23.5267 | −0.892420 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 37.7483 | 1.42982 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 15.3850 | 0.581916 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 31.7833 | 1.20044 | 0.600220 | − | 0.799835i | \(-0.295080\pi\) | ||||
0.600220 | + | 0.799835i | \(0.295080\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.10954 | −0.0795629 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −52.7422 | −1.98638 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12.5130 | 0.470599 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −37.4506 | −1.40649 | −0.703244 | − | 0.710948i | \(-0.748266\pi\) | ||||
−0.703244 | + | 0.710948i | \(0.748266\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 84.2784 | 3.16069 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −32.5944 | −1.22067 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.16385 | −0.155719 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 80.1088 | 2.99172 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 29.0398 | 1.08300 | 0.541500 | − | 0.840700i | \(-0.317856\pi\) | ||||
0.541500 | + | 0.840700i | \(0.317856\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.10720 | −0.227444 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −62.7259 | −2.33280 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 36.6706 | 1.36191 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.5015 | 0.649094 | 0.324547 | − | 0.945870i | \(-0.394788\pi\) | ||||
0.324547 | + | 0.945870i | \(0.394788\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 128.960 | 4.77628 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 46.5326 | 1.72107 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −30.7054 | −1.13413 | −0.567066 | − | 0.823673i | \(-0.691921\pi\) | ||||
−0.567066 | + | 0.823673i | \(0.691921\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 14.1077 | 0.520370 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.18087 | 0.0434980 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15.9903 | −0.588211 | −0.294106 | − | 0.955773i | \(-0.595022\pi\) | ||||
−0.294106 | + | 0.955773i | \(0.595022\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.95878 | −0.0719575 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 35.6528 | 1.30798 | 0.653988 | − | 0.756505i | \(-0.273095\pi\) | ||||
0.653988 | + | 0.756505i | \(0.273095\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 34.8130 | 1.27545 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −133.330 | −4.87828 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.32012 | 0.157854 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.26334 | 0.265043 | 0.132521 | − | 0.991180i | \(-0.457693\pi\) | ||||
0.132521 | + | 0.991180i | \(0.457693\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.16997 | −0.0426359 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7.17522 | −0.261133 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 48.8018 | 1.77373 | 0.886865 | − | 0.462028i | \(-0.152878\pi\) | ||||
0.886865 | + | 0.462028i | \(0.152878\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −21.4560 | −0.778805 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −37.9565 | −1.37592 | −0.687961 | − | 0.725748i | \(-0.741494\pi\) | ||||
−0.687961 | + | 0.725748i | \(0.741494\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.94475 | 0.179012 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 161.089 | 5.82419 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −14.8556 | −0.536406 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −52.9477 | −1.90934 | −0.954672 | − | 0.297660i | \(-0.903794\pi\) | ||||
−0.954672 | + | 0.297660i | \(0.903794\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −22.3514 | −0.804965 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −35.4012 | −1.27329 | −0.636647 | − | 0.771155i | \(-0.719679\pi\) | ||||
−0.636647 | + | 0.771155i | \(0.719679\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 63.5019 | 2.28105 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −12.3630 | −0.443520 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.78320 | 0.171376 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.4792 | −0.482324 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −55.1801 | −1.97198 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −86.1438 | −3.07461 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.57573 | −0.234400 | −0.117200 | − | 0.993108i | \(-0.537392\pi\) | ||||
−0.117200 | + | 0.993108i | \(0.537392\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −63.7607 | −2.26994 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13.5510 | 0.481818 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.44437 | 0.0868022 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −111.729 | −3.96261 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 37.3458 | 1.32286 | 0.661429 | − | 0.750008i | \(-0.269950\pi\) | ||||
0.661429 | + | 0.750008i | \(0.269950\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 17.0571 | 0.603438 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 68.7914 | 2.43062 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.09880 | −0.0387758 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 26.3684 | 0.929365 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 64.0295 | 2.25395 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0.109808 | 0.00386065 | 0.00193032 | − | 0.999998i | \(-0.499386\pi\) | ||||
0.00193032 | + | 0.999998i | \(0.499386\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 37.4524 | 1.31513 | 0.657566 | − | 0.753397i | \(-0.271586\pi\) | ||||
0.657566 | + | 0.753397i | \(0.271586\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 102.323 | 3.58863 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 20.0890 | 0.703688 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.89629 | 0.206285 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −8.47945 | −0.296296 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −52.5790 | −1.83502 | −0.917510 | − | 0.397712i | \(-0.869804\pi\) | ||||
−0.917510 | + | 0.397712i | \(0.869804\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −44.9995 | −1.56858 | −0.784292 | − | 0.620392i | \(-0.786973\pi\) | ||||
−0.784292 | + | 0.620392i | \(0.786973\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 41.8016 | 1.45534 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −23.4245 | −0.814550 | −0.407275 | − | 0.913306i | \(-0.633521\pi\) | ||||
−0.407275 | + | 0.913306i | \(0.633521\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.98216 | −0.207769 | −0.103885 | − | 0.994589i | \(-0.533127\pi\) | ||||
−0.103885 | + | 0.994589i | \(0.533127\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −74.8654 | −2.59705 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.56251 | −0.158082 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.72213 | 0.0595968 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −95.5545 | −3.30285 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 20.9921 | 0.724728 | 0.362364 | − | 0.932037i | \(-0.381970\pi\) | ||||
0.362364 | + | 0.932037i | \(0.381970\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.1657 | −0.695370 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 95.2460 | 3.28045 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.16385 | −0.143241 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.00000 | 0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 24.0639 | 0.825871 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −23.1075 | −0.792114 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.9772 | 0.375853 | 0.187926 | − | 0.982183i | \(-0.439823\pi\) | ||||
0.187926 | + | 0.982183i | \(0.439823\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 20.4121 | 0.698078 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10.1129 | 0.345449 | 0.172725 | − | 0.984970i | \(-0.444743\pi\) | ||||
0.172725 | + | 0.984970i | \(0.444743\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −25.4516 | −0.868396 | −0.434198 | − | 0.900817i | \(-0.642968\pi\) | ||||
−0.434198 | + | 0.900817i | \(0.642968\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 28.0320 | 0.955328 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0.579248 | 0.0197178 | 0.00985892 | − | 0.999951i | \(-0.496862\pi\) | ||||
0.00985892 | + | 0.999951i | \(0.496862\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 26.5715 | 0.903460 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −12.9307 | −0.439150 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.93914 | −0.337162 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.18087 | 0.0400123 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 85.7803 | 2.90322 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −30.5529 | −1.03288 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.5639 | 0.626860 | 0.313430 | − | 0.949611i | \(-0.398522\pi\) | ||||
0.313430 | + | 0.949611i | \(0.398522\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 23.9118 | 0.806525 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 11.8188 | 0.398187 | 0.199094 | − | 0.979980i | \(-0.436200\pi\) | ||||
0.199094 | + | 0.979980i | \(0.436200\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 41.9213 | 1.41076 | 0.705382 | − | 0.708827i | \(-0.250775\pi\) | ||||
0.705382 | + | 0.708827i | \(0.250775\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 209.579 | 7.04491 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 18.8509 | 0.632950 | 0.316475 | − | 0.948601i | \(-0.397501\pi\) | ||||
0.316475 | + | 0.948601i | \(0.397501\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.22621 | −0.175281 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −37.4627 | −1.25505 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.16136 | 0.0723271 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 88.7526 | 2.96667 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −21.4560 | −0.716396 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 15.2982 | 0.510223 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 36.1337 | 1.20379 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 34.5553 | 1.14993 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 45.7699 | 1.52144 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −47.6986 | −1.58381 | −0.791903 | − | 0.610647i | \(-0.790910\pi\) | ||||
−0.791903 | + | 0.610647i | \(0.790910\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 106.103 | 3.51922 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18.1443 | −0.601148 | −0.300574 | − | 0.953758i | \(-0.597178\pi\) | ||||
−0.300574 | + | 0.953758i | \(0.597178\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15.7239 | 0.520385 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −34.4844 | −1.14002 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.90049 | 0.260897 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.8502 | 0.687786 | 0.343893 | − | 0.939009i | \(-0.388254\pi\) | ||||
0.343893 | + | 0.939009i | \(0.388254\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −33.1227 | −1.09143 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −13.4792 | −0.443674 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 45.0190 | 1.48022 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −51.7857 | −1.70086 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 22.6593 | 0.743429 | 0.371714 | − | 0.928347i | \(-0.378770\pi\) | ||||
0.371714 | + | 0.928347i | \(0.378770\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.578129 | −0.0189474 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.93099 | 0.292387 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −18.9976 | −0.621288 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.69027 | −0.0878873 | −0.0439437 | − | 0.999034i | \(-0.513992\pi\) | ||||
−0.0439437 | + | 0.999034i | \(0.513992\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −10.5562 | −0.344489 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −35.6464 | −1.16204 | −0.581020 | − | 0.813889i | \(-0.697346\pi\) | ||||
−0.581020 | + | 0.813889i | \(0.697346\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 52.3941 | 1.70619 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 77.3022 | 2.51464 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 11.8507 | 0.385097 | 0.192548 | − | 0.981287i | \(-0.438325\pi\) | ||||
0.192548 | + | 0.981287i | \(0.438325\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.09880 | −0.0356686 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −89.2918 | −2.89549 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −30.4931 | −0.987768 | −0.493884 | − | 0.869528i | \(-0.664423\pi\) | ||||
−0.493884 | + | 0.869528i | \(0.664423\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 60.2412 | 1.94936 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 10.0704 | 0.325529 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 12.1583 | 0.392613 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.50839 | −0.145432 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 36.6322 | 1.18046 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −74.4431 | −2.39641 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.05417 | 0.259005 | 0.129502 | − | 0.991579i | \(-0.458662\pi\) | ||||
0.129502 | + | 0.991579i | \(0.458662\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.93694 | −0.287096 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 40.5052 | 1.29987 | 0.649936 | − | 0.759989i | \(-0.274796\pi\) | ||||
0.649936 | + | 0.759989i | \(0.274796\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.65024 | 0.181138 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 41.8016 | 1.33872 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −15.4470 | −0.494194 | −0.247097 | − | 0.968991i | \(-0.579477\pi\) | ||||
−0.247097 | + | 0.968991i | \(0.579477\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.11272 | −0.259284 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 41.9287 | 1.33868 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.70663 | 0.0544332 | 0.0272166 | − | 0.999630i | \(-0.491336\pi\) | ||||
0.0272166 | + | 0.999630i | \(0.491336\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −57.0891 | −1.81901 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 12.6667 | 0.403185 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 64.5867 | 2.05374 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.0360 | 0.858828 | 0.429414 | − | 0.903108i | \(-0.358720\pi\) | ||||
0.429414 | + | 0.903108i | \(0.358720\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 109.502 | 3.47494 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.82995 | 0.216524 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −60.0098 | −1.90053 | −0.950265 | − | 0.311441i | \(-0.899188\pi\) | ||||
−0.950265 | + | 0.311441i | \(0.899188\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −67.7424 | −2.14327 |
(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 | 8008.2.a.y.1.1 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8008.2.a.y.1.1 | ✓ | 14 | 1.1 | even | 1 | trivial |