Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3380,2,Mod(1,3380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3380, 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("3380.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3380 = 2^{2} \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3380.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: | \(26.9894358832\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - x^{8} - 19x^{7} + 16x^{6} + 106x^{5} - 87x^{4} - 153x^{3} + 149x^{2} - 26x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(0.715841\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3380.1 |
$q$-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 | ||||||||
\(3\) | −0.715841 | −0.413291 | −0.206645 | − | 0.978416i | \(-0.566255\pi\) | ||||
−0.206645 | + | 0.978416i | \(0.566255\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.76323 | 1.42237 | 0.711184 | − | 0.703006i | \(-0.248159\pi\) | ||||
0.711184 | + | 0.703006i | \(0.248159\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.48757 | −0.829191 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.96386 | −0.592126 | −0.296063 | − | 0.955168i | \(-0.595674\pi\) | ||||
−0.296063 | + | 0.955168i | \(0.595674\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.715841 | −0.184829 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.65737 | −1.37211 | −0.686057 | − | 0.727548i | \(-0.740660\pi\) | ||||
−0.686057 | + | 0.727548i | \(0.740660\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.336153 | 0.0771189 | 0.0385594 | − | 0.999256i | \(-0.487723\pi\) | ||||
0.0385594 | + | 0.999256i | \(0.487723\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.69387 | −0.587851 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.38546 | 0.288889 | 0.144444 | − | 0.989513i | \(-0.453861\pi\) | ||||
0.144444 | + | 0.989513i | \(0.453861\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.92823 | 0.755988 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.05504 | −0.195915 | −0.0979576 | − | 0.995191i | \(-0.531231\pi\) | ||||
−0.0979576 | + | 0.995191i | \(0.531231\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.97744 | 1.79200 | 0.896000 | − | 0.444053i | \(-0.146460\pi\) | ||||
0.896000 | + | 0.444053i | \(0.146460\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.40581 | 0.244720 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.76323 | 0.636102 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.428134 | −0.0703848 | −0.0351924 | − | 0.999381i | \(-0.511204\pi\) | ||||
−0.0351924 | + | 0.999381i | \(0.511204\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.99625 | 0.624110 | 0.312055 | − | 0.950064i | \(-0.398983\pi\) | ||||
0.312055 | + | 0.950064i | \(0.398983\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.41775 | 0.216205 | 0.108103 | − | 0.994140i | \(-0.465523\pi\) | ||||
0.108103 | + | 0.994140i | \(0.465523\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.48757 | −0.370825 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.5023 | 1.53192 | 0.765961 | − | 0.642887i | \(-0.222264\pi\) | ||||
0.765961 | + | 0.642887i | \(0.222264\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.16191 | 1.02313 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.04977 | 0.567082 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.428839 | −0.0589055 | −0.0294528 | − | 0.999566i | \(-0.509376\pi\) | ||||
−0.0294528 | + | 0.999566i | \(0.509376\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.96386 | −0.264807 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.240632 | −0.0318725 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.47905 | 1.10388 | 0.551939 | − | 0.833884i | \(-0.313888\pi\) | ||||
0.551939 | + | 0.833884i | \(0.313888\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.5518 | 1.60709 | 0.803545 | − | 0.595244i | \(-0.202945\pi\) | ||||
0.803545 | + | 0.595244i | \(0.202945\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −9.36131 | −1.17941 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.25232 | −1.00818 | −0.504091 | − | 0.863651i | \(-0.668172\pi\) | ||||
−0.504091 | + | 0.863651i | \(0.668172\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.991769 | −0.119395 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.6464 | −1.38218 | −0.691089 | − | 0.722770i | \(-0.742869\pi\) | ||||
−0.691089 | + | 0.722770i | \(0.742869\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.8433 | 1.26912 | 0.634558 | − | 0.772875i | \(-0.281182\pi\) | ||||
0.634558 | + | 0.772875i | \(0.281182\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.715841 | −0.0826582 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.39046 | −0.842221 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.33649 | 1.05044 | 0.525219 | − | 0.850967i | \(-0.323984\pi\) | ||||
0.525219 | + | 0.850967i | \(0.323984\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.65073 | 0.516748 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.2129 | −1.12102 | −0.560508 | − | 0.828149i | \(-0.689394\pi\) | ||||
−0.560508 | + | 0.828149i | \(0.689394\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.65737 | −0.613628 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.755237 | 0.0809699 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.45621 | −1.00236 | −0.501178 | − | 0.865344i | \(-0.667100\pi\) | ||||
−0.501178 | + | 0.865344i | \(0.667100\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.14225 | −0.740617 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.336153 | 0.0344886 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.8156 | 1.60583 | 0.802915 | − | 0.596094i | \(-0.203282\pi\) | ||||
0.802915 | + | 0.596094i | \(0.203282\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.88525 | 0.490986 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 17.5424 | 1.74554 | 0.872769 | − | 0.488133i | \(-0.162322\pi\) | ||||
0.872769 | + | 0.488133i | \(0.162322\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.760790 | −0.0749628 | −0.0374814 | − | 0.999297i | \(-0.511934\pi\) | ||||
−0.0374814 | + | 0.999297i | \(0.511934\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.69387 | −0.262895 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.38654 | −0.617410 | −0.308705 | − | 0.951158i | \(-0.599896\pi\) | ||||
−0.308705 | + | 0.951158i | \(0.599896\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.1620 | −1.16491 | −0.582456 | − | 0.812862i | \(-0.697908\pi\) | ||||
−0.582456 | + | 0.812862i | \(0.697908\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.306476 | 0.0290894 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 20.2283 | 1.90292 | 0.951459 | − | 0.307775i | \(-0.0995845\pi\) | ||||
0.951459 | + | 0.307775i | \(0.0995845\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.38546 | 0.129195 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −21.2900 | −1.95165 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.14325 | −0.649386 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.86068 | −0.257939 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.7363 | −1.48511 | −0.742555 | − | 0.669785i | \(-0.766386\pi\) | ||||
−0.742555 | + | 0.669785i | \(0.766386\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.01488 | −0.0893556 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.46690 | −0.302904 | −0.151452 | − | 0.988465i | \(-0.548395\pi\) | ||||
−0.151452 | + | 0.988465i | \(0.548395\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.26502 | 0.109691 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.92823 | 0.338088 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.22396 | 0.190006 | 0.0950029 | − | 0.995477i | \(-0.469714\pi\) | ||||
0.0950029 | + | 0.995477i | \(0.469714\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.90313 | 0.755154 | 0.377577 | − | 0.925978i | \(-0.376757\pi\) | ||||
0.377577 | + | 0.925978i | \(0.376757\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.51799 | −0.633129 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.05504 | −0.0876159 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.12678 | −0.422850 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.6217 | −1.27978 | −0.639892 | − | 0.768465i | \(-0.721021\pi\) | ||||
−0.639892 | + | 0.768465i | \(0.721021\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.21151 | 0.586864 | 0.293432 | − | 0.955980i | \(-0.405203\pi\) | ||||
0.293432 | + | 0.955980i | \(0.405203\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 14.0731 | 1.13774 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.97744 | 0.801407 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 21.1160 | 1.68524 | 0.842622 | − | 0.538506i | \(-0.181011\pi\) | ||||
0.842622 | + | 0.538506i | \(0.181011\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.306980 | 0.0243451 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.21381 | 0.410906 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.2476 | 0.880982 | 0.440491 | − | 0.897757i | \(-0.354804\pi\) | ||||
0.440491 | + | 0.897757i | \(0.354804\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.40581 | 0.109442 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.57105 | 0.121572 | 0.0607859 | − | 0.998151i | \(-0.480639\pi\) | ||||
0.0607859 | + | 0.998151i | \(0.480639\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.836206 | −0.0639462 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.92266 | −0.222206 | −0.111103 | − | 0.993809i | \(-0.535438\pi\) | ||||
−0.111103 | + | 0.993809i | \(0.535438\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.76323 | 0.284474 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.06965 | −0.456223 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.0344 | 0.750010 | 0.375005 | − | 0.927023i | \(-0.377641\pi\) | ||||
0.375005 | + | 0.927023i | \(0.377641\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 24.6169 | 1.82976 | 0.914879 | − | 0.403727i | \(-0.132286\pi\) | ||||
0.914879 | + | 0.403727i | \(0.132286\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.98507 | −0.664196 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.428134 | −0.0314771 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.1103 | 0.812464 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 14.7828 | 1.07529 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.01914 | 0.146100 | 0.0730498 | − | 0.997328i | \(-0.476727\pi\) | ||||
0.0730498 | + | 0.997328i | \(0.476727\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.31501 | −0.598527 | −0.299264 | − | 0.954170i | \(-0.596741\pi\) | ||||
−0.299264 | + | 0.954170i | \(0.596741\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.49617 | −0.605327 | −0.302664 | − | 0.953097i | \(-0.597876\pi\) | ||||
−0.302664 | + | 0.953097i | \(0.597876\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −19.0657 | −1.35153 | −0.675767 | − | 0.737115i | \(-0.736188\pi\) | ||||
−0.675767 | + | 0.737115i | \(0.736188\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.90734 | 0.416672 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.97034 | −0.278663 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.99625 | 0.279110 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.44643 | −0.239544 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.660158 | −0.0456641 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.2368 | 1.18663 | 0.593316 | − | 0.804970i | \(-0.297818\pi\) | ||||
0.593316 | + | 0.804970i | \(0.297818\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.33699 | 0.571241 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.41775 | 0.0966899 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 37.5474 | 2.54888 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.76210 | −0.524514 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.633842 | 0.0424452 | 0.0212226 | − | 0.999775i | \(-0.493244\pi\) | ||||
0.0212226 | + | 0.999775i | \(0.493244\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.48757 | −0.165838 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 13.9133 | 0.923459 | 0.461730 | − | 0.887021i | \(-0.347229\pi\) | ||||
0.461730 | + | 0.887021i | \(0.347229\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −21.7562 | −1.43769 | −0.718846 | − | 0.695169i | \(-0.755329\pi\) | ||||
−0.718846 | + | 0.695169i | \(0.755329\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.29039 | 0.348082 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.45256 | −0.619258 | −0.309629 | − | 0.950857i | \(-0.600205\pi\) | ||||
−0.309629 | + | 0.950857i | \(0.600205\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.5023 | 0.685096 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.68344 | −0.434136 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.50513 | 0.226728 | 0.113364 | − | 0.993554i | \(-0.463837\pi\) | ||||
0.113364 | + | 0.993554i | \(0.463837\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.2931 | 0.791870 | 0.395935 | − | 0.918279i | \(-0.370421\pi\) | ||||
0.395935 | + | 0.918279i | \(0.370421\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.1139 | −0.969555 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 7.16191 | 0.457557 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.31083 | 0.463305 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.89241 | −0.498164 | −0.249082 | − | 0.968482i | \(-0.580129\pi\) | ||||
−0.249082 | + | 0.968482i | \(0.580129\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.72085 | −0.171059 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.04977 | 0.253607 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.33042 | 0.270124 | 0.135062 | − | 0.990837i | \(-0.456877\pi\) | ||||
0.135062 | + | 0.990837i | \(0.456877\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.61117 | −0.100113 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.62448 | 0.162451 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 25.1235 | 1.54918 | 0.774592 | − | 0.632462i | \(-0.217955\pi\) | ||||
0.774592 | + | 0.632462i | \(0.217955\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.428839 | −0.0263434 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.76914 | 0.414265 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −32.0183 | −1.95219 | −0.976095 | − | 0.217345i | \(-0.930260\pi\) | ||||
−0.976095 | + | 0.217345i | \(0.930260\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.1300 | 0.736846 | 0.368423 | − | 0.929658i | \(-0.379898\pi\) | ||||
0.368423 | + | 0.929658i | \(0.379898\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.96386 | −0.118425 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.24396 | 0.194911 | 0.0974554 | − | 0.995240i | \(-0.468930\pi\) | ||||
0.0974554 | + | 0.995240i | \(0.468930\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −24.8196 | −1.48591 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.5156 | 0.865930 | 0.432965 | − | 0.901411i | \(-0.357467\pi\) | ||||
0.432965 | + | 0.901411i | \(0.357467\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −17.7093 | −1.05271 | −0.526353 | − | 0.850266i | \(-0.676441\pi\) | ||||
−0.526353 | + | 0.850266i | \(0.676441\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.240632 | −0.0142538 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 15.0388 | 0.887714 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.0058 | 0.882694 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11.3214 | −0.663674 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 21.7599 | 1.27123 | 0.635614 | − | 0.772007i | \(-0.280747\pi\) | ||||
0.635614 | + | 0.772007i | \(0.280747\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.47905 | 0.493670 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −7.71449 | −0.447640 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.33533 | 0.307523 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −12.5576 | −0.721415 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12.5518 | 0.718713 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.6875 | 0.609971 | 0.304985 | − | 0.952357i | \(-0.401348\pi\) | ||||
0.304985 | + | 0.952357i | \(0.401348\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.544604 | 0.0309814 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −26.4611 | −1.50047 | −0.750236 | − | 0.661170i | \(-0.770060\pi\) | ||||
−0.750236 | + | 0.661170i | \(0.770060\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.7056 | 1.11383 | 0.556914 | − | 0.830570i | \(-0.311985\pi\) | ||||
0.556914 | + | 0.830570i | \(0.311985\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −9.36131 | −0.527450 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.7487 | 0.603706 | 0.301853 | − | 0.953355i | \(-0.402395\pi\) | ||||
0.301853 | + | 0.953355i | \(0.402395\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.07194 | 0.116007 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.57174 | 0.255170 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.90174 | −0.105816 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.70608 | 0.481447 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 39.5227 | 2.17896 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.78709 | 0.208157 | 0.104079 | − | 0.994569i | \(-0.466811\pi\) | ||||
0.104079 | + | 0.994569i | \(0.466811\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.06502 | 0.0583625 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.25232 | −0.450872 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.9235 | 1.13978 | 0.569888 | − | 0.821722i | \(-0.306987\pi\) | ||||
0.569888 | + | 0.821722i | \(0.306987\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −14.4802 | −0.786458 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −19.5943 | −1.06109 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.609288 | 0.0328985 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.991769 | −0.0533951 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 21.8741 | 1.17426 | 0.587132 | − | 0.809491i | \(-0.300257\pi\) | ||||
0.587132 | + | 0.809491i | \(0.300257\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.94720 | 0.425404 | 0.212702 | − | 0.977117i | \(-0.431774\pi\) | ||||
0.212702 | + | 0.977117i | \(0.431774\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 21.3059 | 1.13400 | 0.567000 | − | 0.823718i | \(-0.308104\pi\) | ||||
0.567000 | + | 0.823718i | \(0.308104\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −11.6464 | −0.618128 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 15.2402 | 0.806599 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 15.0831 | 0.796054 | 0.398027 | − | 0.917374i | \(-0.369695\pi\) | ||||
0.398027 | + | 0.917374i | \(0.369695\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.8870 | −0.994053 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.11343 | 0.268385 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.8433 | 0.567566 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.7040 | −0.715344 | −0.357672 | − | 0.933847i | \(-0.616429\pi\) | ||||
−0.357672 | + | 0.933847i | \(0.616429\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9.94097 | −0.517506 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.61382 | −0.0837853 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.30720 | −0.171240 | −0.0856202 | − | 0.996328i | \(-0.527287\pi\) | ||||
−0.0856202 | + | 0.996328i | \(0.527287\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.715841 | −0.0369658 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −30.6788 | −1.57586 | −0.787931 | − | 0.615763i | \(-0.788848\pi\) | ||||
−0.787931 | + | 0.615763i | \(0.788848\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 11.9806 | 0.613783 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −18.6469 | −0.952812 | −0.476406 | − | 0.879226i | \(-0.658061\pi\) | ||||
−0.476406 | + | 0.879226i | \(0.658061\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.39046 | −0.376653 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.52676 | −0.179275 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 17.7486 | 0.899889 | 0.449944 | − | 0.893057i | \(-0.351444\pi\) | ||||
0.449944 | + | 0.893057i | \(0.351444\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.83806 | −0.396388 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.48174 | 0.125187 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9.33649 | 0.469770 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −36.9431 | −1.85412 | −0.927061 | − | 0.374911i | \(-0.877673\pi\) | ||||
−0.927061 | + | 0.374911i | \(0.877673\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.905554 | −0.0453344 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −17.6654 | −0.882167 | −0.441083 | − | 0.897466i | \(-0.645406\pi\) | ||||
−0.441083 | + | 0.897466i | \(0.645406\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.65073 | 0.231097 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.840796 | 0.0416767 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −29.2194 | −1.44481 | −0.722404 | − | 0.691471i | \(-0.756963\pi\) | ||||
−0.722404 | + | 0.691471i | \(0.756963\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.59200 | −0.0785277 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 31.9086 | 1.57012 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.2129 | −0.501333 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.37322 | −0.312098 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 22.7266 | 1.11027 | 0.555133 | − | 0.831762i | \(-0.312667\pi\) | ||||
0.555133 | + | 0.831762i | \(0.312667\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −34.8180 | −1.69692 | −0.848462 | − | 0.529256i | \(-0.822471\pi\) | ||||
−0.848462 | + | 0.529256i | \(0.822471\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −26.1253 | −1.27026 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.65737 | −0.274423 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 47.2352 | 2.28587 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −30.0595 | −1.44791 | −0.723957 | − | 0.689845i | \(-0.757679\pi\) | ||||
−0.723957 | + | 0.689845i | \(0.757679\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 27.8940 | 1.34050 | 0.670251 | − | 0.742135i | \(-0.266187\pi\) | ||||
0.670251 | + | 0.742135i | \(0.266187\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.755237 | 0.0362108 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.465727 | 0.0222788 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 20.2627 | 0.967087 | 0.483544 | − | 0.875320i | \(-0.339349\pi\) | ||||
0.483544 | + | 0.875320i | \(0.339349\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −17.8158 | −0.848369 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −34.5143 | −1.63983 | −0.819913 | − | 0.572489i | \(-0.805978\pi\) | ||||
−0.819913 | + | 0.572489i | \(0.805978\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.45621 | −0.448268 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 11.1827 | 0.528923 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.64277 | −0.124720 | −0.0623600 | − | 0.998054i | \(-0.519863\pi\) | ||||
−0.0623600 | + | 0.998054i | \(0.519863\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.84809 | −0.369552 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.16229 | −0.242546 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 35.0036 | 1.63740 | 0.818699 | − | 0.574223i | \(-0.194696\pi\) | ||||
0.818699 | + | 0.574223i | \(0.194696\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −22.2234 | −1.03730 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.16356 | 0.100767 | 0.0503836 | − | 0.998730i | \(-0.483956\pi\) | ||||
0.0503836 | + | 0.998730i | \(0.483956\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.59470 | −0.260008 | −0.130004 | − | 0.991513i | \(-0.541499\pi\) | ||||
−0.130004 | + | 0.991513i | \(0.541499\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −7.14225 | −0.331214 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 22.4990 | 1.04113 | 0.520565 | − | 0.853822i | \(-0.325721\pi\) | ||||
0.520565 | + | 0.853822i | \(0.325721\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −31.0554 | −1.43400 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −15.1157 | −0.696495 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.78427 | −0.128021 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.336153 | 0.0154238 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.06677 | 0.0488439 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −27.8803 | −1.27388 | −0.636941 | − | 0.770912i | \(-0.719801\pi\) | ||||
−0.636941 | + | 0.770912i | \(0.719801\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.73226 | −0.169824 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 15.8156 | 0.718149 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.0548 | 0.908771 | 0.454386 | − | 0.890805i | \(-0.349859\pi\) | ||||
0.454386 | + | 0.890805i | \(0.349859\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8.05151 | −0.364102 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −30.3986 | −1.37187 | −0.685935 | − | 0.727663i | \(-0.740607\pi\) | ||||
−0.685935 | + | 0.727663i | \(0.740607\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.96872 | 0.268818 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.88525 | 0.219575 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −43.8282 | −1.96596 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −21.0685 | −0.943154 | −0.471577 | − | 0.881825i | \(-0.656315\pi\) | ||||
−0.471577 | + | 0.881825i | \(0.656315\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.12462 | −0.0502445 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −25.8008 | −1.15040 | −0.575201 | − | 0.818012i | \(-0.695076\pi\) | ||||
−0.575201 | + | 0.818012i | \(0.695076\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17.5424 | 0.780629 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15.2047 | 0.673936 | 0.336968 | − | 0.941516i | \(-0.390599\pi\) | ||||
0.336968 | + | 0.941516i | \(0.390599\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 40.8060 | 1.80515 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.32049 | 0.0583009 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.760790 | −0.0335244 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −20.6251 | −0.907091 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.09216 | 0.0918355 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.0690 | 0.528754 | 0.264377 | − | 0.964419i | \(-0.414834\pi\) | ||||
0.264377 | + | 0.964419i | \(0.414834\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.6516 | 0.684397 | 0.342199 | − | 0.939628i | \(-0.388828\pi\) | ||||
0.342199 | + | 0.939628i | \(0.388828\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.69387 | −0.117570 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −56.4460 | −2.45883 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.0805 | −0.916543 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −21.0923 | −0.915326 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.38654 | −0.276114 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −7.18307 | −0.309972 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −14.0650 | −0.605822 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20.5902 | −0.885242 | −0.442621 | − | 0.896709i | \(-0.645951\pi\) | ||||
−0.442621 | + | 0.896709i | \(0.645951\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −17.6218 | −0.756222 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −12.1620 | −0.520965 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.8896 | −1.23523 | −0.617616 | − | 0.786480i | \(-0.711901\pi\) | ||||
−0.617616 | + | 0.786480i | \(0.711901\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −31.2235 | −1.33258 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.354654 | −0.0151088 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 35.1354 | 1.49411 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.306476 | 0.0130092 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 33.2861 | 1.41038 | 0.705189 | − | 0.709020i | \(-0.250862\pi\) | ||||
0.705189 | + | 0.709020i | \(0.250862\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.95319 | −0.335784 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −29.2175 | −1.23137 | −0.615686 | − | 0.787991i | \(-0.711121\pi\) | ||||
−0.615686 | + | 0.787991i | \(0.711121\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 20.2283 | 0.851011 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 17.5018 | 0.735006 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 29.3646 | 1.23103 | 0.615514 | − | 0.788126i | \(-0.288948\pi\) | ||||
0.615514 | + | 0.788126i | \(0.288948\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −34.0977 | −1.42694 | −0.713472 | − | 0.700683i | \(-0.752879\pi\) | ||||
−0.713472 | + | 0.700683i | \(0.752879\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.44538 | −0.0603816 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.38546 | 0.0577777 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.46819 | 0.269274 | 0.134637 | − | 0.990895i | \(-0.457013\pi\) | ||||
0.134637 | + | 0.990895i | \(0.457013\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.95222 | 0.247366 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −38.4336 | −1.59450 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.842180 | 0.0348795 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 17.0018 | 0.701738 | 0.350869 | − | 0.936425i | \(-0.385886\pi\) | ||||
0.350869 | + | 0.936425i | \(0.385886\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.35395 | 0.138197 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.08191 | 0.250176 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −10.2611 | −0.421375 | −0.210687 | − | 0.977553i | \(-0.567570\pi\) | ||||
−0.210687 | + | 0.977553i | \(0.567570\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −21.2900 | −0.872804 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 13.6480 | 0.558577 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10.9528 | −0.447520 | −0.223760 | − | 0.974644i | \(-0.571833\pi\) | ||||
−0.223760 | + | 0.974644i | \(0.571833\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.9210 | 0.731011 | 0.365506 | − | 0.930809i | \(-0.380896\pi\) | ||||
0.365506 | + | 0.930809i | \(0.380896\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 20.5282 | 0.835974 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.14325 | −0.290414 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.9922 | 0.446161 | 0.223081 | − | 0.974800i | \(-0.428389\pi\) | ||||
0.223081 | + | 0.974800i | \(0.428389\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.84213 | 0.115169 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.06699 | −0.0834850 | −0.0417425 | − | 0.999128i | \(-0.513291\pi\) | ||||
−0.0417425 | + | 0.999128i | \(0.513291\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.86068 | −0.115354 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 39.0188 | 1.57084 | 0.785420 | − | 0.618963i | \(-0.212447\pi\) | ||||
0.785420 | + | 0.618963i | \(0.212447\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15.8716 | −0.637935 | −0.318967 | − | 0.947766i | \(-0.603336\pi\) | ||||
−0.318967 | + | 0.947766i | \(0.603336\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.44240 | 0.218396 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −35.5859 | −1.42572 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.472568 | 0.0188726 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.42211 | 0.0965760 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.54118 | 0.260400 | 0.130200 | − | 0.991488i | \(-0.458438\pi\) | ||||
0.130200 | + | 0.991488i | \(0.458438\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −12.3388 | −0.490424 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −16.7363 | −0.664162 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 28.9713 | 1.14609 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −27.9790 | −1.10510 | −0.552552 | − | 0.833478i | \(-0.686346\pi\) | ||||
−0.552552 | + | 0.833478i | \(0.686346\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.570593 | 0.0225020 | 0.0112510 | − | 0.999937i | \(-0.496419\pi\) | ||||
0.0112510 | + | 0.999937i | \(0.496419\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.01488 | −0.0399610 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −35.4222 | −1.39259 | −0.696296 | − | 0.717755i | \(-0.745170\pi\) | ||||
−0.696296 | + | 0.717755i | \(0.745170\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −16.6517 | −0.653636 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −26.8780 | −1.05343 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −12.4879 | −0.488688 | −0.244344 | − | 0.969689i | \(-0.578573\pi\) | ||||
−0.244344 | + | 0.969689i | \(0.578573\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.46690 | −0.135463 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −26.9736 | −1.05234 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −48.6745 | −1.89609 | −0.948045 | − | 0.318135i | \(-0.896944\pi\) | ||||
−0.948045 | + | 0.318135i | \(0.896944\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.30190 | −0.128429 | −0.0642145 | − | 0.997936i | \(-0.520454\pi\) | ||||
−0.0642145 | + | 0.997936i | \(0.520454\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.26502 | 0.0490555 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.46171 | −0.0565976 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.453730 | −0.0175422 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −24.6499 | −0.951600 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.2607 | 0.935181 | 0.467590 | − | 0.883945i | \(-0.345122\pi\) | ||||
0.467590 | + | 0.883945i | \(0.345122\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.92823 | 0.151198 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 25.5400 | 0.981583 | 0.490791 | − | 0.871277i | \(-0.336708\pi\) | ||||
0.490791 | + | 0.871277i | \(0.336708\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 59.5177 | 2.28408 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.95972 | −0.381657 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −42.5536 | −1.62827 | −0.814133 | − | 0.580678i | \(-0.802788\pi\) | ||||
−0.814133 | + | 0.580678i | \(0.802788\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.22396 | 0.0849732 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 15.5740 | 0.594185 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.6314 | 0.632686 | 0.316343 | − | 0.948645i | \(-0.397545\pi\) | ||||
0.316343 | + | 0.948645i | \(0.397545\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 18.3843 | 0.698362 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.90313 | 0.337715 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −22.6083 | −0.856350 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6.76653 | 0.255934 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −17.5058 | −0.661185 | −0.330593 | − | 0.943774i | \(-0.607249\pi\) | ||||
−0.330593 | + | 0.943774i | \(0.607249\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.143919 | −0.00542800 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7.51799 | −0.283144 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 66.0163 | 2.48280 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.8149 | −0.631496 | −0.315748 | − | 0.948843i | \(-0.602255\pi\) | ||||
−0.315748 | + | 0.948843i | \(0.602255\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −23.2252 | −0.871013 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 13.8233 | 0.517688 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2.50911 | −0.0937046 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 30.3694 | 1.13259 | 0.566294 | − | 0.824203i | \(-0.308377\pi\) | ||||
0.566294 | + | 0.824203i | \(0.308377\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.86303 | −0.106625 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −8.79992 | −0.327273 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.05504 | −0.0391830 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.3641 | 0.532733 | 0.266367 | − | 0.963872i | \(-0.414177\pi\) | ||||
0.266367 | + | 0.963872i | \(0.414177\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3.13308 | −0.116040 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.02074 | −0.296658 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −45.8191 | −1.69237 | −0.846183 | − | 0.532892i | \(-0.821105\pi\) | ||||
−0.846183 | + | 0.532892i | \(0.821105\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.12678 | −0.189104 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 16.2064 | 0.596971 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.48314 | 0.201701 | 0.100850 | − | 0.994902i | \(-0.467844\pi\) | ||||
0.100850 | + | 0.994902i | \(0.467844\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 53.0367 | 1.94573 | 0.972864 | − | 0.231378i | \(-0.0743234\pi\) | ||||
0.972864 | + | 0.231378i | \(0.0743234\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15.6217 | −0.572337 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 25.4054 | 0.929535 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −24.0340 | −0.878184 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.975080 | 0.0355812 | 0.0177906 | − | 0.999842i | \(-0.494337\pi\) | ||||
0.0177906 | + | 0.999842i | \(0.494337\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.64971 | 0.205887 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.21151 | 0.262454 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 24.4113 | 0.887244 | 0.443622 | − | 0.896214i | \(-0.353693\pi\) | ||||
0.443622 | + | 0.896214i | \(0.353693\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.94770 | 0.0706969 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.66922 | −0.133009 | −0.0665046 | − | 0.997786i | \(-0.521185\pi\) | ||||
−0.0665046 | + | 0.997786i | \(0.521185\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −45.7686 | −1.65693 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 14.0731 | 0.508814 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 40.4300 | 1.45794 | 0.728972 | − | 0.684544i | \(-0.239999\pi\) | ||||
0.728972 | + | 0.684544i | \(0.239999\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.09989 | −0.111640 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −31.6144 | −1.13709 | −0.568546 | − | 0.822651i | \(-0.692494\pi\) | ||||
−0.568546 | + | 0.822651i | \(0.692494\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.97744 | 0.358400 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.15334 | 0.0413758 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.34335 | 0.0481306 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 22.8720 | 0.818424 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.14442 | −0.148109 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 21.1160 | 0.753664 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.11487 | 0.253618 | 0.126809 | − | 0.991927i | \(-0.459527\pi\) | ||||
0.126809 | + | 0.991927i | \(0.459527\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −17.9844 | −0.640263 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 76.1237 | 2.70665 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.306980 | 0.0108875 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −0.224720 | −0.00795999 | −0.00398000 | − | 0.999992i | \(-0.501267\pi\) | ||||
−0.00398000 | + | 0.999992i | \(0.501267\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −59.4155 | −2.10197 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 23.5230 | 0.831145 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −21.2948 | −0.751477 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.21381 | 0.183763 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 22.9200 | 0.806822 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.22088 | 0.218714 | 0.109357 | − | 0.994003i | \(-0.465121\pi\) | ||||
0.109357 | + | 0.994003i | \(0.465121\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 25.6039 | 0.899074 | 0.449537 | − | 0.893262i | \(-0.351589\pi\) | ||||
0.449537 | + | 0.893262i | \(0.351589\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.68316 | −0.304532 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 11.2476 | 0.393987 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.476582 | 0.0166735 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 42.9424 | 1.49870 | 0.749350 | − | 0.662174i | \(-0.230366\pi\) | ||||
0.749350 | + | 0.662174i | \(0.230366\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 45.1061 | 1.57230 | 0.786150 | − | 0.618036i | \(-0.212071\pi\) | ||||
0.786150 | + | 0.618036i | \(0.212071\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.40581 | 0.0489441 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10.5868 | 0.368139 | 0.184070 | − | 0.982913i | \(-0.441073\pi\) | ||||
0.184070 | + | 0.982913i | \(0.441073\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17.8655 | −0.620495 | −0.310247 | − | 0.950656i | \(-0.600412\pi\) | ||||
−0.310247 | + | 0.950656i | \(0.600412\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.32216 | −0.0805548 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −40.5175 | −1.40385 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.57105 | 0.0543685 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 39.1936 | 1.35473 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 10.2341 | 0.353320 | 0.176660 | − | 0.984272i | \(-0.443471\pi\) | ||||
0.176660 | + | 0.984272i | \(0.443471\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.8869 | −0.961617 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −10.3909 | −0.357881 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −26.8817 | −0.923666 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 12.6770 | 0.435074 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.593163 | −0.0203334 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −47.9341 | −1.64123 | −0.820616 | − | 0.571480i | \(-0.806369\pi\) | ||||
−0.820616 | + | 0.571480i | \(0.806369\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.836206 | −0.0285976 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −30.6992 | −1.04866 | −0.524332 | − | 0.851514i | \(-0.675685\pi\) | ||||
−0.524332 | + | 0.851514i | \(0.675685\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −55.0682 | −1.87890 | −0.939451 | − | 0.342685i | \(-0.888664\pi\) | ||||
−0.939451 | + | 0.342685i | \(0.888664\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −10.7654 | −0.366884 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −21.9551 | −0.747360 | −0.373680 | − | 0.927558i | \(-0.621904\pi\) | ||||
−0.373680 | + | 0.927558i | \(0.621904\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.92266 | −0.0993734 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −10.7418 | −0.364809 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −18.3356 | −0.621991 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −39.3424 | −1.33154 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.76323 | 0.127220 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.0497 | 0.373120 | 0.186560 | − | 0.982444i | \(-0.440266\pi\) | ||||
0.186560 | + | 0.982444i | \(0.440266\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −15.5766 | −0.525387 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 11.3150 | 0.381211 | 0.190606 | − | 0.981667i | \(-0.438955\pi\) | ||||
0.190606 | + | 0.981667i | \(0.438955\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 47.0917 | 1.58476 | 0.792381 | − | 0.610026i | \(-0.208841\pi\) | ||||
0.792381 | + | 0.610026i | \(0.208841\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.06965 | −0.204029 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −28.0464 | −0.941707 | −0.470853 | − | 0.882211i | \(-0.656054\pi\) | ||||
−0.470853 | + | 0.882211i | \(0.656054\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −62.9827 | −2.11237 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −9.13339 | −0.305980 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.53039 | 0.118140 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10.0344 | 0.335415 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −10.5265 | −0.351080 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.42610 | 0.0808250 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.81924 | −0.127096 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 24.6169 | 0.818293 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −40.2492 | −1.33645 | −0.668226 | − | 0.743958i | \(-0.732946\pi\) | ||||
−0.668226 | + | 0.743958i | \(0.732946\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −43.6381 | −1.44738 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.23171 | 0.0408085 | 0.0204042 | − | 0.999792i | \(-0.493505\pi\) | ||||
0.0204042 | + | 0.999792i | \(0.493505\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 20.0568 | 0.663783 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −8.98507 | −0.297037 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −13.0467 | −0.430841 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14.0110 | −0.462180 | −0.231090 | − | 0.972932i | \(-0.574229\pi\) | ||||
−0.231090 | + | 0.972932i | \(0.574229\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.65058 | −0.252095 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.428134 | −0.0140770 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.89252 | 0.0621585 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 24.7198 | 0.811029 | 0.405515 | − | 0.914089i | \(-0.367092\pi\) | ||||
0.405515 | + | 0.914089i | \(0.367092\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.40750 | 0.0789026 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 18.9419 | 0.620131 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 11.1103 | 0.363345 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 42.9404 | 1.40280 | 0.701401 | − | 0.712767i | \(-0.252558\pi\) | ||||
0.701401 | + | 0.712767i | \(0.252558\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −14.1061 | −0.460335 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −39.1437 | −1.27605 | −0.638024 | − | 0.770016i | \(-0.720248\pi\) | ||||
−0.638024 | + | 0.770016i | \(0.720248\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.53665 | 0.180298 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 14.7828 | 0.480885 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 17.0370 | 0.553627 | 0.276813 | − | 0.960924i | \(-0.410722\pi\) | ||||
0.276813 | + | 0.960924i | \(0.410722\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7.69434 | −0.249506 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.06939 | −0.164214 | −0.0821068 | − | 0.996624i | \(-0.526165\pi\) | ||||
−0.0821068 | + | 0.996624i | \(0.526165\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.01914 | 0.0653378 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.48318 | −0.0479444 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8.36928 | 0.270258 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 68.5493 | 2.21127 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 15.8870 | 0.511951 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −8.31501 | −0.267670 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −21.3805 | −0.687550 | −0.343775 | − | 0.939052i | \(-0.611706\pi\) | ||||
−0.343775 | + | 0.939052i | \(0.611706\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.36134 | 0.0437327 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.427629 | 0.0137233 | 0.00686164 | − | 0.999976i | \(-0.497816\pi\) | ||||
0.00686164 | + | 0.999976i | \(0.497816\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 33.5045 | 1.07411 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6.58761 | 0.210756 | 0.105378 | − | 0.994432i | \(-0.466395\pi\) | ||||
0.105378 | + | 0.994432i | \(0.466395\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18.5707 | 0.593522 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 30.2540 | 0.965934 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 45.4129 | 1.44844 | 0.724222 | − | 0.689566i | \(-0.242199\pi\) | ||||
0.724222 | + | 0.689566i | \(0.242199\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.49617 | −0.270711 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −28.2919 | −0.900542 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.96424 | 0.0624592 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 45.1183 | 1.43323 | 0.716614 | − | 0.697470i | \(-0.245691\pi\) | ||||
0.716614 | + | 0.697470i | \(0.245691\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.71095 | −0.0860295 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −19.0657 | −0.604425 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.3712 | 0.771844 | 0.385922 | − | 0.922531i | \(-0.373883\pi\) | ||||
0.385922 | + | 0.922531i | \(0.373883\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.68181 | −0.0532101 |
(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 | 3380.2.a.s.1.4 | yes | 9 | |
13.5 | odd | 4 | 3380.2.f.j.3041.7 | 18 | |||
13.8 | odd | 4 | 3380.2.f.j.3041.8 | 18 | |||
13.12 | even | 2 | 3380.2.a.r.1.4 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3380.2.a.r.1.4 | ✓ | 9 | 13.12 | even | 2 | ||
3380.2.a.s.1.4 | yes | 9 | 1.1 | even | 1 | trivial | |
3380.2.f.j.3041.7 | 18 | 13.5 | odd | 4 | |||
3380.2.f.j.3041.8 | 18 | 13.8 | odd | 4 |