Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6160,2,Mod(1,6160)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6160, 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("6160.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6160 = 2^{4} \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6160.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: | \(49.1878476451\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.25488.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 9x^{2} - 6x + 6 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 3080) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.47535\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6160.1 |
$q$-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 | ||||||||
\(3\) | 0.732051 | 0.422650 | 0.211325 | − | 0.977416i | \(-0.432222\pi\) | ||||
0.211325 | + | 0.977416i | \(0.432222\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.46410 | −0.821367 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.08003 | −0.854247 | −0.427124 | − | 0.904193i | \(-0.640473\pi\) | ||||
−0.427124 | + | 0.904193i | \(0.640473\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.732051 | 0.189015 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.33477 | −0.808801 | −0.404401 | − | 0.914582i | \(-0.632520\pi\) | ||||
−0.404401 | + | 0.914582i | \(0.632520\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.76279 | 1.55149 | 0.775745 | − | 0.631046i | \(-0.217374\pi\) | ||||
0.775745 | + | 0.631046i | \(0.217374\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.732051 | 0.159747 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.34798 | −0.489588 | −0.244794 | − | 0.969575i | \(-0.578720\pi\) | ||||
−0.244794 | + | 0.969575i | \(0.578720\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.00000 | −0.769800 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.29869 | 0.612551 | 0.306275 | − | 0.951943i | \(-0.400917\pi\) | ||||
0.306275 | + | 0.951943i | \(0.400917\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.03074 | −1.44236 | −0.721182 | − | 0.692746i | \(-0.756401\pi\) | ||||
−0.721182 | + | 0.692746i | \(0.756401\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.732051 | −0.127434 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11.0175 | 1.81127 | 0.905635 | − | 0.424057i | \(-0.139394\pi\) | ||||
0.905635 | + | 0.424057i | \(0.139394\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.25474 | −0.361047 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.37872 | −0.996189 | −0.498094 | − | 0.867123i | \(-0.665967\pi\) | ||||
−0.498094 | + | 0.867123i | \(0.665967\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.16007 | 0.634404 | 0.317202 | − | 0.948358i | \(-0.397257\pi\) | ||||
0.317202 | + | 0.948358i | \(0.397257\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.46410 | −0.367327 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.7989 | −1.57518 | −0.787589 | − | 0.616201i | \(-0.788671\pi\) | ||||
−0.787589 | + | 0.616201i | \(0.788671\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.44122 | −0.341840 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.50805 | 0.893949 | 0.446975 | − | 0.894547i | \(-0.352501\pi\) | ||||
0.446975 | + | 0.894547i | \(0.352501\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.95071 | 0.655737 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.61593 | −0.731132 | −0.365566 | − | 0.930785i | \(-0.619125\pi\) | ||||
−0.365566 | + | 0.930785i | \(0.619125\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.54413 | 0.325743 | 0.162872 | − | 0.986647i | \(-0.447924\pi\) | ||||
0.162872 | + | 0.986647i | \(0.447924\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.46410 | −0.310448 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.08003 | −0.382031 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.414807 | 0.0506767 | 0.0253384 | − | 0.999679i | \(-0.491934\pi\) | ||||
0.0253384 | + | 0.999679i | \(0.491934\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.71884 | −0.206924 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.46410 | −0.648470 | −0.324235 | − | 0.945977i | \(-0.605107\pi\) | ||||
−0.324235 | + | 0.945977i | \(0.605107\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.49484 | −1.11129 | −0.555643 | − | 0.831421i | \(-0.687528\pi\) | ||||
−0.555643 | + | 0.831421i | \(0.687528\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.732051 | 0.0845299 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.11612 | −0.350591 | −0.175295 | − | 0.984516i | \(-0.556088\pi\) | ||||
−0.175295 | + | 0.984516i | \(0.556088\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.46410 | 0.496011 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −11.6242 | −1.27592 | −0.637959 | − | 0.770070i | \(-0.720221\pi\) | ||||
−0.637959 | + | 0.770070i | \(0.720221\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.33477 | −0.361707 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.41481 | 0.258894 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.46410 | −0.367194 | −0.183597 | − | 0.983002i | \(-0.558774\pi\) | ||||
−0.183597 | + | 0.983002i | \(0.558774\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.08003 | −0.322875 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.87891 | −0.609614 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.76279 | 0.693848 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.06682 | 0.819062 | 0.409531 | − | 0.912296i | \(-0.365692\pi\) | ||||
0.409531 | + | 0.912296i | \(0.365692\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.46410 | 0.247652 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −14.2855 | −1.42146 | −0.710729 | − | 0.703466i | \(-0.751635\pi\) | ||||
−0.710729 | + | 0.703466i | \(0.751635\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.56664 | 0.449964 | 0.224982 | − | 0.974363i | \(-0.427768\pi\) | ||||
0.224982 | + | 0.974363i | \(0.427768\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.732051 | 0.0714408 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −14.6735 | −1.41854 | −0.709269 | − | 0.704938i | \(-0.750975\pi\) | ||||
−0.709269 | + | 0.704938i | \(0.750975\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.9229 | −1.42935 | −0.714675 | − | 0.699457i | \(-0.753425\pi\) | ||||
−0.714675 | + | 0.699457i | \(0.753425\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.06539 | 0.765533 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.928203 | −0.0873180 | −0.0436590 | − | 0.999046i | \(-0.513902\pi\) | ||||
−0.0436590 | + | 0.999046i | \(0.513902\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.34798 | −0.218950 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 7.58951 | 0.701651 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.33477 | −0.305698 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.66955 | −0.421039 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.92820 | −0.614779 | −0.307389 | − | 0.951584i | \(-0.599455\pi\) | ||||
−0.307389 | + | 0.951584i | \(0.599455\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.04538 | 0.268131 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.86138 | 0.424741 | 0.212370 | − | 0.977189i | \(-0.431882\pi\) | ||||
0.212370 | + | 0.977189i | \(0.431882\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.76279 | 0.586408 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.00000 | −0.344265 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.74526 | 0.319979 | 0.159990 | − | 0.987119i | \(-0.448854\pi\) | ||||
0.159990 | + | 0.987119i | \(0.448854\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.2269 | −1.03707 | −0.518536 | − | 0.855056i | \(-0.673523\pi\) | ||||
−0.518536 | + | 0.855056i | \(0.673523\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.90533 | −0.665748 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.08003 | 0.257565 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.29869 | 0.273941 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.732051 | 0.0603785 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.06682 | −0.333167 | −0.166584 | − | 0.986027i | \(-0.553274\pi\) | ||||
−0.166584 | + | 0.986027i | \(0.553274\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.1322 | −1.31282 | −0.656411 | − | 0.754404i | \(-0.727926\pi\) | ||||
−0.656411 | + | 0.754404i | \(0.727926\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 8.21722 | 0.664323 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.03074 | −0.645044 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −23.2219 | −1.85331 | −0.926655 | − | 0.375912i | \(-0.877330\pi\) | ||||
−0.926655 | + | 0.375912i | \(0.877330\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.76422 | 0.377827 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.34798 | −0.185047 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.02288 | −0.550074 | −0.275037 | − | 0.961434i | \(-0.588690\pi\) | ||||
−0.275037 | + | 0.961434i | \(0.588690\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.732051 | −0.0569901 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −17.0883 | −1.32233 | −0.661165 | − | 0.750241i | \(-0.729938\pi\) | ||||
−0.661165 | + | 0.750241i | \(0.729938\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.51340 | −0.270261 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −16.6642 | −1.27434 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 23.7886 | 1.80861 | 0.904305 | − | 0.426887i | \(-0.140390\pi\) | ||||
0.904305 | + | 0.426887i | \(0.140390\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.11115 | −0.309013 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −18.4763 | −1.38098 | −0.690491 | − | 0.723341i | \(-0.742606\pi\) | ||||
−0.690491 | + | 0.723341i | \(0.742606\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 24.6860 | 1.83490 | 0.917449 | − | 0.397854i | \(-0.130245\pi\) | ||||
0.917449 | + | 0.397854i | \(0.130245\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.86244 | 0.137675 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 11.0175 | 0.810025 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.33477 | 0.243863 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.00000 | −0.290957 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.53627 | −0.400591 | −0.200295 | − | 0.979736i | \(-0.564190\pi\) | ||||
−0.200295 | + | 0.979736i | \(0.564190\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.23224 | 0.160680 | 0.0803400 | − | 0.996768i | \(-0.474399\pi\) | ||||
0.0803400 | + | 0.996768i | \(0.474399\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.25474 | −0.161465 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.8521 | −0.773181 | −0.386591 | − | 0.922251i | \(-0.626347\pi\) | ||||
−0.386591 | + | 0.922251i | \(0.626347\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.3020 | 1.43917 | 0.719584 | − | 0.694406i | \(-0.244333\pi\) | ||||
0.719584 | + | 0.694406i | \(0.244333\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.303660 | 0.0214185 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.29869 | 0.231522 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.37872 | −0.445509 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.78567 | 0.402132 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.76279 | −0.467792 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 28.6324 | 1.97114 | 0.985569 | − | 0.169274i | \(-0.0541423\pi\) | ||||
0.985569 | + | 0.169274i | \(0.0541423\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.00000 | −0.274075 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.16007 | 0.283714 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.03074 | −0.545162 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.95071 | −0.469685 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.2712 | 0.690917 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −15.1912 | −1.01728 | −0.508638 | − | 0.860980i | \(-0.669851\pi\) | ||||
−0.508638 | + | 0.860980i | \(0.669851\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.46410 | −0.164273 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.2215 | 0.678428 | 0.339214 | − | 0.940709i | \(-0.389839\pi\) | ||||
0.339214 | + | 0.940709i | \(0.389839\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −28.9136 | −1.91066 | −0.955332 | − | 0.295535i | \(-0.904502\pi\) | ||||
−0.955332 | + | 0.295535i | \(0.904502\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.732051 | −0.0481654 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4.00392 | −0.262305 | −0.131153 | − | 0.991362i | \(-0.541868\pi\) | ||||
−0.131153 | + | 0.991362i | \(0.541868\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.7989 | −0.704441 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.28116 | −0.148177 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −22.8964 | −1.48105 | −0.740524 | − | 0.672030i | \(-0.765422\pi\) | ||||
−0.740524 | + | 0.672030i | \(0.765422\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 21.8779 | 1.40928 | 0.704639 | − | 0.709566i | \(-0.251109\pi\) | ||||
0.704639 | + | 0.709566i | \(0.251109\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.2679 | 0.979439 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −20.8296 | −1.32536 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8.50948 | −0.539266 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.37375 | 0.0867102 | 0.0433551 | − | 0.999060i | \(-0.486195\pi\) | ||||
0.0433551 | + | 0.999060i | \(0.486195\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.34798 | 0.147616 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.44122 | −0.152875 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.62952 | 0.226403 | 0.113201 | − | 0.993572i | \(-0.463889\pi\) | ||||
0.113201 | + | 0.993572i | \(0.463889\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.0175 | 0.684596 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.12830 | −0.503129 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 24.8296 | 1.53106 | 0.765530 | − | 0.643400i | \(-0.222477\pi\) | ||||
0.765530 | + | 0.643400i | \(0.222477\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.50805 | 0.399786 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.53590 | −0.155194 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 20.1005 | 1.22555 | 0.612773 | − | 0.790259i | \(-0.290054\pi\) | ||||
0.612773 | + | 0.790259i | \(0.290054\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.49089 | 0.394294 | 0.197147 | − | 0.980374i | \(-0.436832\pi\) | ||||
0.197147 | + | 0.980374i | \(0.436832\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.25474 | −0.136463 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.00000 | −0.0603023 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 32.3327 | 1.94268 | 0.971342 | − | 0.237688i | \(-0.0763896\pi\) | ||||
0.971342 | + | 0.237688i | \(0.0763896\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 19.7886 | 1.18471 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.50911 | −0.209336 | −0.104668 | − | 0.994507i | \(-0.533378\pi\) | ||||
−0.104668 | + | 0.994507i | \(0.533378\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −21.1497 | −1.25722 | −0.628611 | − | 0.777720i | \(-0.716376\pi\) | ||||
−0.628611 | + | 0.777720i | \(0.716376\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.95071 | 0.293254 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.37872 | −0.376524 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.87928 | −0.345840 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.90533 | 0.346176 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 17.7046 | 1.03431 | 0.517156 | − | 0.855891i | \(-0.326991\pi\) | ||||
0.517156 | + | 0.855891i | \(0.326991\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.61593 | −0.326972 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.00000 | 0.232104 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.23186 | 0.418229 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.16007 | 0.239782 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −10.4577 | −0.600779 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.54413 | 0.145677 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −25.2669 | −1.44206 | −0.721030 | − | 0.692904i | \(-0.756331\pi\) | ||||
−0.721030 | + | 0.692904i | \(0.756331\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.34301 | 0.190177 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.0472 | 1.13677 | 0.568387 | − | 0.822762i | \(-0.307568\pi\) | ||||
0.568387 | + | 0.822762i | \(0.307568\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −22.2884 | −1.25981 | −0.629906 | − | 0.776671i | \(-0.716907\pi\) | ||||
−0.629906 | + | 0.776671i | \(0.716907\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.46410 | −0.138836 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.06682 | −0.228416 | −0.114208 | − | 0.993457i | \(-0.536433\pi\) | ||||
−0.114208 | + | 0.993457i | \(0.536433\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.29869 | −0.184691 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10.7417 | −0.599544 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −22.5524 | −1.25485 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.08003 | −0.170849 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −10.9243 | −0.604115 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −10.7989 | −0.595361 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.5749 | 0.691178 | 0.345589 | − | 0.938386i | \(-0.387679\pi\) | ||||
0.345589 | + | 0.938386i | \(0.387679\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −27.1483 | −1.48772 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.414807 | 0.0226633 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 28.5913 | 1.55747 | 0.778735 | − | 0.627353i | \(-0.215862\pi\) | ||||
0.778735 | + | 0.627353i | \(0.215862\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.679492 | −0.0369049 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.03074 | 0.434889 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.71884 | −0.0925394 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 19.9179 | 1.06925 | 0.534624 | − | 0.845090i | \(-0.320453\pi\) | ||||
0.534624 | + | 0.845090i | \(0.320453\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.1683 | 0.758412 | 0.379206 | − | 0.925312i | \(-0.376197\pi\) | ||||
0.379206 | + | 0.925312i | \(0.376197\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 12.3201 | 0.657600 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −13.4588 | −0.716337 | −0.358169 | − | 0.933657i | \(-0.616599\pi\) | ||||
−0.358169 | + | 0.933657i | \(0.616599\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.46410 | −0.290004 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.44122 | −0.129203 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 14.2308 | 0.751073 | 0.375537 | − | 0.926808i | \(-0.377458\pi\) | ||||
0.375537 | + | 0.926808i | \(0.377458\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 26.7353 | 1.40712 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.732051 | 0.0384227 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.49484 | −0.496983 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.3963 | −0.699279 | −0.349639 | − | 0.936884i | \(-0.613696\pi\) | ||||
−0.349639 | + | 0.936884i | \(0.613696\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 15.7178 | 0.818237 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.50805 | 0.337881 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 15.8789 | 0.822179 | 0.411089 | − | 0.911595i | \(-0.365148\pi\) | ||||
0.411089 | + | 0.911595i | \(0.365148\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.732051 | 0.0378029 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −10.1601 | −0.523270 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.6245 | −1.16214 | −0.581072 | − | 0.813852i | \(-0.697367\pi\) | ||||
−0.581072 | + | 0.813852i | \(0.697367\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.07180 | −0.259836 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10.9854 | −0.561326 | −0.280663 | − | 0.959806i | \(-0.590554\pi\) | ||||
−0.280663 | + | 0.959806i | \(0.590554\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.00000 | −0.0509647 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −10.2508 | −0.521079 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −22.6960 | −1.15073 | −0.575366 | − | 0.817896i | \(-0.695140\pi\) | ||||
−0.575366 | + | 0.817896i | \(0.695140\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.82999 | 0.395980 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.55878 | 0.179517 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.11612 | −0.156789 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.05321 | 0.0528591 | 0.0264295 | − | 0.999651i | \(-0.491586\pi\) | ||||
0.0264295 | + | 0.999651i | \(0.491586\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.95071 | 0.247845 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 19.7803 | 0.987782 | 0.493891 | − | 0.869524i | \(-0.335574\pi\) | ||||
0.493891 | + | 0.869524i | \(0.335574\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 24.7349 | 1.23214 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.46410 | 0.221823 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11.0175 | −0.546119 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.47731 | −0.419176 | −0.209588 | − | 0.977790i | \(-0.567212\pi\) | ||||
−0.209588 | + | 0.977790i | \(0.567212\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.74172 | 0.135239 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5.61593 | −0.276342 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −11.6242 | −0.570608 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.95071 | −0.438318 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13.1679 | −0.643295 | −0.321648 | − | 0.946859i | \(-0.604237\pi\) | ||||
−0.321648 | + | 0.946859i | \(0.604237\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.3162 | 0.990152 | 0.495076 | − | 0.868850i | \(-0.335140\pi\) | ||||
0.495076 | + | 0.868850i | \(0.335140\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 26.6095 | 1.29380 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.33477 | −0.161760 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.54413 | 0.123119 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.25474 | 0.108860 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.66849 | −0.0803684 | −0.0401842 | − | 0.999192i | \(-0.512794\pi\) | ||||
−0.0401842 | + | 0.999192i | \(0.512794\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.09324 | −0.292823 | −0.146411 | − | 0.989224i | \(-0.546772\pi\) | ||||
−0.146411 | + | 0.989224i | \(0.546772\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.41481 | 0.115781 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −15.8789 | −0.759591 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.02717 | 0.192206 | 0.0961031 | − | 0.995371i | \(-0.469362\pi\) | ||||
0.0961031 | + | 0.995371i | \(0.469362\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.46410 | −0.117338 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.15615 | 0.197465 | 0.0987323 | − | 0.995114i | \(-0.468521\pi\) | ||||
0.0987323 | + | 0.995114i | \(0.468521\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.46410 | −0.164214 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.97712 | −0.140813 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −22.5359 | −1.06353 | −0.531767 | − | 0.846890i | \(-0.678472\pi\) | ||||
−0.531767 | + | 0.846890i | \(0.678472\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.37872 | 0.300362 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −11.8096 | −0.554863 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.08003 | −0.144394 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.2279 | 0.525221 | 0.262611 | − | 0.964902i | \(-0.415417\pi\) | ||||
0.262611 | + | 0.964902i | \(0.415417\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 13.3391 | 0.622616 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −17.8482 | −0.831272 | −0.415636 | − | 0.909531i | \(-0.636441\pi\) | ||||
−0.415636 | + | 0.909531i | \(0.636441\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −23.4977 | −1.09203 | −0.546016 | − | 0.837775i | \(-0.683856\pi\) | ||||
−0.546016 | + | 0.837775i | \(0.683856\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.87891 | −0.272628 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −18.2576 | −0.844862 | −0.422431 | − | 0.906395i | \(-0.638823\pi\) | ||||
−0.422431 | + | 0.906395i | \(0.638823\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.414807 | 0.0191540 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −16.9996 | −0.783301 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.16007 | −0.191280 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.76279 | 0.310298 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −16.0365 | −0.734261 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 35.0062 | 1.59947 | 0.799736 | − | 0.600352i | \(-0.204973\pi\) | ||||
0.799736 | + | 0.600352i | \(0.204973\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −33.9344 | −1.54727 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.71884 | −0.0782100 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.06682 | 0.366296 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.20439 | 0.190519 | 0.0952595 | − | 0.995452i | \(-0.469632\pi\) | ||||
0.0952595 | + | 0.995452i | \(0.469632\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5.14110 | −0.232489 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −34.1355 | −1.54051 | −0.770257 | − | 0.637734i | \(-0.779872\pi\) | ||||
−0.770257 | + | 0.637734i | \(0.779872\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11.0004 | −0.495432 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.46410 | 0.110753 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.46410 | −0.245098 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −25.9053 | −1.15968 | −0.579841 | − | 0.814730i | \(-0.696885\pi\) | ||||
−0.579841 | + | 0.814730i | \(0.696885\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −12.5095 | −0.558882 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 22.7310 | 1.01353 | 0.506763 | − | 0.862085i | \(-0.330842\pi\) | ||||
0.506763 | + | 0.862085i | \(0.330842\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −14.2855 | −0.635695 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.57198 | −0.114226 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −12.6774 | −0.561915 | −0.280957 | − | 0.959720i | \(-0.590652\pi\) | ||||
−0.280957 | + | 0.959720i | \(0.590652\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.49484 | −0.420027 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −27.0512 | −1.19434 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.56664 | 0.201230 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.7989 | 0.474934 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 17.4144 | 0.764409 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −41.4270 | −1.81495 | −0.907475 | − | 0.420107i | \(-0.861993\pi\) | ||||
−0.907475 | + | 0.420107i | \(0.861993\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14.8032 | −0.647299 | −0.323649 | − | 0.946177i | \(-0.604910\pi\) | ||||
−0.323649 | + | 0.946177i | \(0.604910\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.732051 | 0.0319493 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 26.7807 | 1.16659 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.4870 | −0.760303 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 13.8382 | 0.600528 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 19.6467 | 0.850992 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14.6735 | −0.634389 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −13.5256 | −0.583672 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.9232 | 0.598606 | 0.299303 | − | 0.954158i | \(-0.403246\pi\) | ||||
0.299303 | + | 0.954158i | \(0.403246\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 18.0714 | 0.775519 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −14.9229 | −0.639225 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.73102 | 0.116770 | 0.0583851 | − | 0.998294i | \(-0.481405\pi\) | ||||
0.0583851 | + | 0.998294i | \(0.481405\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.26901 | −0.267555 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 22.3083 | 0.950367 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.11612 | −0.132511 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8.06539 | 0.342357 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15.6817 | 0.664456 | 0.332228 | − | 0.943199i | \(-0.392200\pi\) | ||||
0.332228 | + | 0.943199i | \(0.392200\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12.8131 | −0.541938 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.44122 | 0.103069 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.59700 | −0.151595 | −0.0757977 | − | 0.997123i | \(-0.524150\pi\) | ||||
−0.0757977 | + | 0.997123i | \(0.524150\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.928203 | −0.0390498 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.46410 | 0.187475 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 16.8453 | 0.706193 | 0.353097 | − | 0.935587i | \(-0.385129\pi\) | ||||
0.353097 | + | 0.935587i | \(0.385129\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.81352 | 0.159591 | 0.0797954 | − | 0.996811i | \(-0.474573\pi\) | ||||
0.0797954 | + | 0.996811i | \(0.474573\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.05283 | −0.169310 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.34798 | −0.0979176 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.06682 | −0.169304 | −0.0846521 | − | 0.996411i | \(-0.526978\pi\) | ||||
−0.0846521 | + | 0.996411i | \(0.526978\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.63411 | 0.0679114 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11.6242 | −0.482252 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.50805 | −0.269536 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 7.58951 | 0.313788 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −20.5456 | −0.848006 | −0.424003 | − | 0.905661i | \(-0.639375\pi\) | ||||
−0.424003 | + | 0.905661i | \(0.639375\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −54.3102 | −2.23781 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.94430 | −0.326785 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −42.5381 | −1.74683 | −0.873415 | − | 0.486976i | \(-0.838100\pi\) | ||||
−0.873415 | + | 0.486976i | \(0.838100\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.33477 | −0.136712 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 14.8621 | 0.608264 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 45.5421 | 1.86080 | 0.930399 | − | 0.366549i | \(-0.119461\pi\) | ||||
0.930399 | + | 0.366549i | \(0.119461\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.6831 | 0.680519 | 0.340260 | − | 0.940332i | \(-0.389485\pi\) | ||||
0.340260 | + | 0.940332i | \(0.389485\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.02213 | −0.0416242 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 37.7081 | 1.53053 | 0.765263 | − | 0.643717i | \(-0.222609\pi\) | ||||
0.765263 | + | 0.643717i | \(0.222609\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.41481 | 0.0978529 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 33.2609 | 1.34559 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 40.4577 | 1.63407 | 0.817035 | − | 0.576587i | \(-0.195616\pi\) | ||||
0.817035 | + | 0.576587i | \(0.195616\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4.66955 | −0.188294 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.1936 | 0.450639 | 0.225319 | − | 0.974285i | \(-0.427657\pi\) | ||||
0.225319 | + | 0.974285i | \(0.427657\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.1869 | 0.891766 | 0.445883 | − | 0.895091i | \(-0.352890\pi\) | ||||
0.445883 | + | 0.895091i | \(0.352890\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 9.39193 | 0.376885 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.46410 | −0.138786 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.95071 | −0.197712 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −36.7410 | −1.46496 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −29.6142 | −1.17892 | −0.589462 | − | 0.807796i | \(-0.700660\pi\) | ||||
−0.589462 | + | 0.807796i | \(0.700660\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 20.9604 | 0.833101 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.92820 | −0.274937 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.08003 | −0.122035 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 13.4641 | 0.532632 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.53236 | −0.376506 | −0.188253 | − | 0.982121i | \(-0.560282\pi\) | ||||
−0.188253 | + | 0.982121i | \(0.560282\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.3752 | 0.842955 | 0.421477 | − | 0.906839i | \(-0.361512\pi\) | ||||
0.421477 | + | 0.906839i | \(0.361512\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.04538 | 0.119912 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.03111 | 0.197794 | 0.0988968 | − | 0.995098i | \(-0.468469\pi\) | ||||
0.0988968 | + | 0.995098i | \(0.468469\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.61593 | 0.220445 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.87891 | −0.230413 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 30.9843 | 1.21251 | 0.606255 | − | 0.795270i | \(-0.292671\pi\) | ||||
0.606255 | + | 0.795270i | \(0.292671\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.86138 | 0.189950 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 23.3963 | 0.912775 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.87891 | −0.229010 | −0.114505 | − | 0.993423i | \(-0.536528\pi\) | ||||
−0.114505 | + | 0.993423i | \(0.536528\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −37.3548 | −1.45293 | −0.726467 | − | 0.687201i | \(-0.758839\pi\) | ||||
−0.726467 | + | 0.687201i | \(0.758839\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 7.51905 | 0.292016 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.76279 | 0.262250 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.74526 | −0.299898 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −11.1207 | −0.429952 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.54413 | −0.0982152 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.07646 | −0.118589 | −0.0592945 | − | 0.998241i | \(-0.518885\pi\) | ||||
−0.0592945 | + | 0.998241i | \(0.518885\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.00000 | −0.153960 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12.4123 | 0.477045 | 0.238523 | − | 0.971137i | \(-0.423337\pi\) | ||||
0.238523 | + | 0.971137i | \(0.423337\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.06682 | 0.309576 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.48269 | 0.286737 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.729163 | 0.0279006 | 0.0139503 | − | 0.999903i | \(-0.495559\pi\) | ||||
0.0139503 | + | 0.999903i | \(0.495559\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.74526 | 0.143099 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −21.1662 | −0.807542 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −20.0450 | −0.763654 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.63203 | 0.100127 | 0.0500635 | − | 0.998746i | \(-0.484058\pi\) | ||||
0.0500635 | + | 0.998746i | \(0.484058\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.46410 | 0.0936035 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −12.2269 | −0.463792 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 21.2716 | 0.805719 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.93107 | −0.110863 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 34.0297 | 1.28528 | 0.642642 | − | 0.766166i | \(-0.277838\pi\) | ||||
0.642642 | + | 0.766166i | \(0.277838\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 74.5092 | 2.81017 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7.90533 | −0.297732 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −14.2855 | −0.537261 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −26.5767 | −0.998110 | −0.499055 | − | 0.866570i | \(-0.666319\pi\) | ||||
−0.499055 | + | 0.866570i | \(0.666319\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.67843 | 0.287964 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 18.8560 | 0.706164 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.08003 | 0.115187 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −16.7614 | −0.625964 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.99214 | 0.335350 | 0.167675 | − | 0.985842i | \(-0.446374\pi\) | ||||
0.167675 | + | 0.985842i | \(0.446374\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.56664 | 0.170070 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 16.0157 | 0.595631 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.29869 | 0.122510 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 42.1702 | 1.56400 | 0.782002 | − | 0.623275i | \(-0.214198\pi\) | ||||
0.782002 | + | 0.623275i | \(0.214198\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.21539 | −0.0820515 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −13.8729 | −0.513107 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.79888 | 0.177251 | 0.0886253 | − | 0.996065i | \(-0.471753\pi\) | ||||
0.0886253 | + | 0.996065i | \(0.471753\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.732051 | 0.0270021 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.414807 | −0.0152796 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −51.1291 | −1.88081 | −0.940407 | − | 0.340050i | \(-0.889556\pi\) | ||||
−0.940407 | + | 0.340050i | \(0.889556\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −15.2483 | −0.560162 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 30.5417 | 1.12047 | 0.560233 | − | 0.828335i | \(-0.310712\pi\) | ||||
0.560233 | + | 0.828335i | \(0.310712\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.06682 | −0.148997 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 28.6431 | 1.04800 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −14.6735 | −0.536157 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 29.3977 | 1.07274 | 0.536369 | − | 0.843984i | \(-0.319796\pi\) | ||||
0.536369 | + | 0.843984i | \(0.319796\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.00565 | 0.0366480 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −16.1322 | −0.587111 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 43.8246 | 1.59283 | 0.796417 | − | 0.604748i | \(-0.206726\pi\) | ||||
0.796417 | + | 0.604748i | \(0.206726\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.71884 | 0.0623900 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −37.6721 | −1.36561 | −0.682806 | − | 0.730600i | \(-0.739240\pi\) | ||||
−0.682806 | + | 0.730600i | \(0.739240\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14.9229 | −0.540244 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 8.21722 | 0.297094 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 17.2973 | 0.624568 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −44.8061 | −1.61575 | −0.807874 | − | 0.589355i | \(-0.799382\pi\) | ||||
−0.807874 | + | 0.589355i | \(0.799382\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.65699 | 0.0956892 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −16.5631 | −0.595732 | −0.297866 | − | 0.954608i | \(-0.596275\pi\) | ||||
−0.297866 | + | 0.954608i | \(0.596275\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.03074 | −0.288473 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8.06539 | 0.289344 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −43.1379 | −1.54558 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.46410 | 0.195521 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −13.1947 | −0.471542 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −23.2219 | −0.828826 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −32.8911 | −1.17244 | −0.586220 | − | 0.810152i | \(-0.699385\pi\) | ||||
−0.586220 | + | 0.810152i | \(0.699385\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 18.1765 | 0.647102 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.928203 | −0.0330031 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.83602 | −0.278265 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.76422 | 0.168970 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −21.6778 | −0.767868 | −0.383934 | − | 0.923361i | \(-0.625431\pi\) | ||||
−0.383934 | + | 0.923361i | \(0.625431\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 36.0118 | 1.27401 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.53590 | 0.301601 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.49484 | 0.335066 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.34798 | −0.0827555 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 14.7146 | 0.517977 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −17.9443 | −0.630888 | −0.315444 | − | 0.948944i | \(-0.602153\pi\) | ||||
−0.315444 | + | 0.948944i | \(0.602153\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.51196 | 0.228666 | 0.114333 | − | 0.993442i | \(-0.463527\pi\) | ||||
0.114333 | + | 0.993442i | \(0.463527\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.75166 | 0.166648 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.02288 | −0.246001 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 28.1336 | 0.984272 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 7.58951 | 0.265199 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 31.0029 | 1.08201 | 0.541004 | − | 0.841020i | \(-0.318045\pi\) | ||||
0.541004 | + | 0.841020i | \(0.318045\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −32.1244 | −1.11979 | −0.559893 | − | 0.828565i | \(-0.689158\pi\) | ||||
−0.559893 | + | 0.828565i | \(0.689158\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.732051 | −0.0254867 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.31622 | 0.219636 | 0.109818 | − | 0.993952i | \(-0.464973\pi\) | ||||
0.109818 | + | 0.993952i | \(0.464973\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12.5398 | −0.435526 | −0.217763 | − | 0.976002i | \(-0.569876\pi\) | ||||
−0.217763 | + | 0.976002i | \(0.569876\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 23.6692 | 0.821074 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.33477 | −0.115543 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −17.0883 | −0.591364 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 32.1230 | 1.11033 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −17.4391 | −0.602066 | −0.301033 | − | 0.953614i | \(-0.597331\pi\) | ||||
−0.301033 | + | 0.953614i | \(0.597331\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.1187 | −0.624781 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.56884 | −0.0884757 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.51340 | −0.120865 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.00000 | 0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −15.4827 | −0.531364 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −25.8690 | −0.886777 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12.7539 | 0.436684 | 0.218342 | − | 0.975872i | \(-0.429935\pi\) | ||||
0.218342 | + | 0.975872i | \(0.429935\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −16.6642 | −0.569904 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 39.5357 | 1.35051 | 0.675256 | − | 0.737583i | \(-0.264033\pi\) | ||||
0.675256 | + | 0.737583i | \(0.264033\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.05286 | 0.240641 | 0.120320 | − | 0.992735i | \(-0.461608\pi\) | ||||
0.120320 | + | 0.992735i | \(0.461608\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.66955 | −0.159138 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −13.1962 | −0.449203 | −0.224602 | − | 0.974451i | \(-0.572108\pi\) | ||||
−0.224602 | + | 0.974451i | \(0.572108\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 23.7886 | 0.808835 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4.30393 | −0.146169 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.11612 | 0.105707 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.27762 | −0.0432905 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −19.8775 | −0.672751 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 25.9610 | 0.876642 | 0.438321 | − | 0.898819i | \(-0.355573\pi\) | ||||
0.438321 | + | 0.898819i | \(0.355573\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 12.9606 | 0.437152 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.05116 | 0.304941 | 0.152471 | − | 0.988308i | \(-0.451277\pi\) | ||||
0.152471 | + | 0.988308i | \(0.451277\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.22583 | 0.108558 | 0.0542790 | − | 0.998526i | \(-0.482714\pi\) | ||||
0.0542790 | + | 0.998526i | \(0.482714\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.11115 | −0.138195 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 22.4274 | 0.753037 | 0.376519 | − | 0.926409i | \(-0.377121\pi\) | ||||
0.376519 | + | 0.926409i | \(0.377121\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.92820 | −0.232364 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.46410 | −0.149553 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −73.0305 | −2.44387 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −18.4763 | −0.617594 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.29409 | 0.176765 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −26.4909 | −0.883521 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −21.7029 | −0.723027 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.04538 | 0.101344 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 24.6860 | 0.820591 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 39.7968 | 1.32143 | 0.660715 | − | 0.750637i | \(-0.270253\pi\) | ||||
0.660715 | + | 0.750637i | \(0.270253\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 35.2009 | 1.16754 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 13.7314 | 0.454942 | 0.227471 | − | 0.973785i | \(-0.426954\pi\) | ||||
0.227471 | + | 0.973785i | \(0.426954\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11.6242 | 0.384704 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.86244 | 0.0615702 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.86138 | 0.160537 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −37.7253 | −1.24444 | −0.622221 | − | 0.782841i | \(-0.713770\pi\) | ||||
−0.622221 | + | 0.782841i | \(0.713770\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −18.4967 | −0.609486 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 16.8296 | 0.553953 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11.0175 | 0.362254 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −11.2527 | −0.369586 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −6.32300 | −0.207451 | −0.103725 | − | 0.994606i | \(-0.533076\pi\) | ||||
−0.103725 | + | 0.994606i | \(0.533076\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.76279 | 0.221641 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 14.6756 | 0.480457 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.33477 | 0.109059 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.90536 | −0.160251 | −0.0801255 | − | 0.996785i | \(-0.525532\pi\) | ||||
−0.0801255 | + | 0.996785i | \(0.525532\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −16.3162 | −0.532460 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −21.7760 | −0.709877 | −0.354939 | − | 0.934890i | \(-0.615498\pi\) | ||||
−0.354939 | + | 0.934890i | \(0.615498\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 14.9771 | 0.487722 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.00000 | −0.130120 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −57.9569 | −1.88334 | −0.941672 | − | 0.336531i | \(-0.890746\pi\) | ||||
−0.941672 | + | 0.336531i | \(0.890746\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 29.2444 | 0.949314 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.97712 | −0.0965398 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.48057 | −0.177533 | −0.0887666 | − | 0.996052i | \(-0.528293\pi\) | ||||
−0.0887666 | + | 0.996052i | \(0.528293\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.53627 | −0.179150 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.41481 | −0.0780596 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.74526 | 0.120941 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 33.4928 | 1.08041 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 36.1569 | 1.16514 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.23224 | 0.0718583 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.46839 | 0.208009 | 0.104005 | − | 0.994577i | \(-0.466834\pi\) | ||||
0.104005 | + | 0.994577i | \(0.466834\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −16.5095 | −0.530361 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 25.1679 | 0.807677 | 0.403839 | − | 0.914830i | \(-0.367676\pi\) | ||||
0.403839 | + | 0.914830i | \(0.367676\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.2269 | −0.391976 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.25474 | −0.0722095 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 28.3209 | 0.906065 | 0.453033 | − | 0.891494i | \(-0.350342\pi\) | ||||
0.453033 | + | 0.891494i | \(0.350342\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.46410 | 0.110713 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 36.7714 | 1.17402 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 41.3348 | 1.31837 | 0.659187 | − | 0.751979i | \(-0.270900\pi\) | ||||
0.659187 | + | 0.751979i | \(0.270900\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10.8521 | −0.345777 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −7.90533 | −0.251629 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.76776 | −0.310597 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.11506 | −0.0671872 | −0.0335936 | − | 0.999436i | \(-0.510695\pi\) | ||||
−0.0335936 | + | 0.999436i | \(0.510695\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 9.20545 | 0.292126 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 20.3020 | 0.643615 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 23.5213 | 0.744926 | 0.372463 | − | 0.928047i | \(-0.378513\pi\) | ||||
0.372463 | + | 0.928047i | \(0.378513\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −44.0701 | −1.39432 |
(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 | 6160.2.a.bq.1.3 | 4 | ||
4.3 | odd | 2 | 3080.2.a.q.1.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3080.2.a.q.1.1 | ✓ | 4 | 4.3 | odd | 2 | ||
6160.2.a.bq.1.3 | 4 | 1.1 | even | 1 | trivial |