Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1575,2,Mod(1,1575)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1575, 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("1575.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1575.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(12.5764383184\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{13}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 525) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.30278\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1575.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.30278 | −0.921201 | −0.460601 | − | 0.887607i | \(-0.652366\pi\) | ||||
−0.460601 | + | 0.887607i | \(0.652366\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.302776 | −0.151388 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 3.00000 | 1.06066 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.00000 | 0.904534 | 0.452267 | − | 0.891883i | \(-0.350615\pi\) | ||||
0.452267 | + | 0.891883i | \(0.350615\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.60555 | −1.27735 | −0.638675 | − | 0.769477i | \(-0.720517\pi\) | ||||
−0.638675 | + | 0.769477i | \(0.720517\pi\) | |||||||
\(14\) | 1.30278 | 0.348181 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.30278 | −0.825694 | ||||||||
\(17\) | −2.60555 | −0.631939 | −0.315970 | − | 0.948769i | \(-0.602330\pi\) | ||||
−0.315970 | + | 0.948769i | \(0.602330\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.605551 | −0.138923 | −0.0694615 | − | 0.997585i | \(-0.522128\pi\) | ||||
−0.0694615 | + | 0.997585i | \(0.522128\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.90833 | −0.833258 | ||||||||
\(23\) | 8.21110 | 1.71213 | 0.856067 | − | 0.516865i | \(-0.172901\pi\) | ||||
0.856067 | + | 0.516865i | \(0.172901\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 6.00000 | 1.17670 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.302776 | 0.0572192 | ||||||||
\(29\) | 0.394449 | 0.0732473 | 0.0366236 | − | 0.999329i | \(-0.488340\pi\) | ||||
0.0366236 | + | 0.999329i | \(0.488340\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.21110 | 1.29515 | 0.647576 | − | 0.762001i | \(-0.275783\pi\) | ||||
0.647576 | + | 0.762001i | \(0.275783\pi\) | |||||||
\(32\) | −1.69722 | −0.300030 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.39445 | 0.582143 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.2111 | −1.67869 | −0.839347 | − | 0.543595i | \(-0.817063\pi\) | ||||
−0.839347 | + | 0.543595i | \(0.817063\pi\) | |||||||
\(38\) | 0.788897 | 0.127976 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.39445 | −0.365150 | −0.182575 | − | 0.983192i | \(-0.558443\pi\) | ||||
−0.182575 | + | 0.983192i | \(0.558443\pi\) | |||||||
\(44\) | −0.908327 | −0.136935 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −10.6972 | −1.57722 | ||||||||
\(47\) | 3.39445 | 0.495131 | 0.247566 | − | 0.968871i | \(-0.420369\pi\) | ||||
0.247566 | + | 0.968871i | \(0.420369\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.39445 | 0.193375 | ||||||||
\(53\) | −11.2111 | −1.53996 | −0.769982 | − | 0.638066i | \(-0.779735\pi\) | ||||
−0.769982 | + | 0.638066i | \(0.779735\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.00000 | −0.400892 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.513878 | −0.0674755 | ||||||||
\(59\) | 3.39445 | 0.441920 | 0.220960 | − | 0.975283i | \(-0.429081\pi\) | ||||
0.220960 | + | 0.975283i | \(0.429081\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.2111 | 1.69151 | 0.845754 | − | 0.533573i | \(-0.179151\pi\) | ||||
0.845754 | + | 0.533573i | \(0.179151\pi\) | |||||||
\(62\) | −9.39445 | −1.19310 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.81665 | 1.10208 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.39445 | −1.02555 | −0.512773 | − | 0.858524i | \(-0.671382\pi\) | ||||
−0.512773 | + | 0.858524i | \(0.671382\pi\) | |||||||
\(68\) | 0.788897 | 0.0956679 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.00000 | 0.356034 | 0.178017 | − | 0.984027i | \(-0.443032\pi\) | ||||
0.178017 | + | 0.984027i | \(0.443032\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.60555 | 0.773121 | 0.386561 | − | 0.922264i | \(-0.373663\pi\) | ||||
0.386561 | + | 0.922264i | \(0.373663\pi\) | |||||||
\(74\) | 13.3028 | 1.54642 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.183346 | 0.0210312 | ||||||||
\(77\) | −3.00000 | −0.341882 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.81665 | 0.766933 | 0.383467 | − | 0.923555i | \(-0.374730\pi\) | ||||
0.383467 | + | 0.923555i | \(0.374730\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.2111 | 1.23058 | 0.615289 | − | 0.788301i | \(-0.289039\pi\) | ||||
0.615289 | + | 0.788301i | \(0.289039\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 3.11943 | 0.336377 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 9.00000 | 0.959403 | ||||||||
\(89\) | 13.8167 | 1.46456 | 0.732281 | − | 0.681002i | \(-0.238456\pi\) | ||||
0.732281 | + | 0.681002i | \(0.238456\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.60555 | 0.482793 | ||||||||
\(92\) | −2.48612 | −0.259196 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.42221 | −0.456116 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.2111 | 1.54445 | 0.772227 | − | 0.635347i | \(-0.219143\pi\) | ||||
0.772227 | + | 0.635347i | \(0.219143\pi\) | |||||||
\(98\) | −1.30278 | −0.131600 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.39445 | −0.934783 | −0.467391 | − | 0.884051i | \(-0.654806\pi\) | ||||
−0.467391 | + | 0.884051i | \(0.654806\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.8167 | 1.75553 | 0.877764 | − | 0.479094i | \(-0.159035\pi\) | ||||
0.877764 | + | 0.479094i | \(0.159035\pi\) | |||||||
\(104\) | −13.8167 | −1.35483 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 14.6056 | 1.41862 | ||||||||
\(107\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.2111 | −1.16961 | −0.584806 | − | 0.811173i | \(-0.698829\pi\) | ||||
−0.584806 | + | 0.811173i | \(0.698829\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.30278 | 0.312083 | ||||||||
\(113\) | 10.8167 | 1.01755 | 0.508773 | − | 0.860901i | \(-0.330099\pi\) | ||||
0.508773 | + | 0.860901i | \(0.330099\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.119429 | −0.0110887 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.42221 | −0.407097 | ||||||||
\(119\) | 2.60555 | 0.238850 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.00000 | −0.181818 | ||||||||
\(122\) | −17.2111 | −1.55822 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.18335 | −0.196070 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.81665 | 0.782352 | 0.391176 | − | 0.920316i | \(-0.372068\pi\) | ||||
0.391176 | + | 0.920316i | \(0.372068\pi\) | |||||||
\(128\) | −8.09167 | −0.715210 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.6056 | 1.27609 | 0.638046 | − | 0.769998i | \(-0.279743\pi\) | ||||
0.638046 | + | 0.769998i | \(0.279743\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.605551 | 0.0525080 | ||||||||
\(134\) | 10.9361 | 0.944734 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7.81665 | −0.670273 | ||||||||
\(137\) | 11.2111 | 0.957829 | 0.478915 | − | 0.877862i | \(-0.341030\pi\) | ||||
0.478915 | + | 0.877862i | \(0.341030\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −17.0278 | −1.44428 | −0.722138 | − | 0.691749i | \(-0.756840\pi\) | ||||
−0.722138 | + | 0.691749i | \(0.756840\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.90833 | −0.327980 | ||||||||
\(143\) | −13.8167 | −1.15541 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −8.60555 | −0.712200 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.09167 | 0.254134 | ||||||||
\(149\) | 23.6056 | 1.93384 | 0.966921 | − | 0.255076i | \(-0.0821004\pi\) | ||||
0.966921 | + | 0.255076i | \(0.0821004\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.8167 | −1.20576 | −0.602881 | − | 0.797831i | \(-0.705981\pi\) | ||||
−0.602881 | + | 0.797831i | \(0.705981\pi\) | |||||||
\(152\) | −1.81665 | −0.147350 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.90833 | 0.314942 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.4222 | 1.15102 | 0.575509 | − | 0.817796i | \(-0.304804\pi\) | ||||
0.575509 | + | 0.817796i | \(0.304804\pi\) | |||||||
\(158\) | −8.88057 | −0.706500 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.21110 | −0.647126 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.78890 | −0.218443 | −0.109222 | − | 0.994017i | \(-0.534836\pi\) | ||||
−0.109222 | + | 0.994017i | \(0.534836\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −14.6056 | −1.13361 | ||||||||
\(167\) | 19.0278 | 1.47241 | 0.736206 | − | 0.676758i | \(-0.236615\pi\) | ||||
0.736206 | + | 0.676758i | \(0.236615\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.21110 | 0.631623 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.724981 | 0.0552793 | ||||||||
\(173\) | 13.8167 | 1.05046 | 0.525230 | − | 0.850960i | \(-0.323979\pi\) | ||||
0.525230 | + | 0.850960i | \(0.323979\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −9.90833 | −0.746868 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −18.0000 | −1.34916 | ||||||||
\(179\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.39445 | 0.400966 | 0.200483 | − | 0.979697i | \(-0.435749\pi\) | ||||
0.200483 | + | 0.979697i | \(0.435749\pi\) | |||||||
\(182\) | −6.00000 | −0.444750 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 24.6333 | 1.81599 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.81665 | −0.571610 | ||||||||
\(188\) | −1.02776 | −0.0749568 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 17.2111 | 1.24535 | 0.622676 | − | 0.782480i | \(-0.286046\pi\) | ||||
0.622676 | + | 0.782480i | \(0.286046\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.21110 | 0.447085 | 0.223542 | − | 0.974694i | \(-0.428238\pi\) | ||||
0.223542 | + | 0.974694i | \(0.428238\pi\) | |||||||
\(194\) | −19.8167 | −1.42275 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.302776 | −0.0216268 | ||||||||
\(197\) | −4.81665 | −0.343172 | −0.171586 | − | 0.985169i | \(-0.554889\pi\) | ||||
−0.171586 | + | 0.985169i | \(0.554889\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.00000 | 0.567105 | 0.283552 | − | 0.958957i | \(-0.408487\pi\) | ||||
0.283552 | + | 0.958957i | \(0.408487\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 12.2389 | 0.861123 | ||||||||
\(203\) | −0.394449 | −0.0276849 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −23.2111 | −1.61719 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 15.2111 | 1.05470 | ||||||||
\(209\) | −1.81665 | −0.125661 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.42221 | −0.166751 | −0.0833757 | − | 0.996518i | \(-0.526570\pi\) | ||||
−0.0833757 | + | 0.996518i | \(0.526570\pi\) | |||||||
\(212\) | 3.39445 | 0.233132 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.21110 | −0.489522 | ||||||||
\(218\) | 15.9083 | 1.07745 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.0000 | 0.807207 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −22.6056 | −1.51378 | −0.756890 | − | 0.653542i | \(-0.773282\pi\) | ||||
−0.756890 | + | 0.653542i | \(0.773282\pi\) | |||||||
\(224\) | 1.69722 | 0.113401 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −14.0917 | −0.937364 | ||||||||
\(227\) | 15.3944 | 1.02177 | 0.510883 | − | 0.859650i | \(-0.329319\pi\) | ||||
0.510883 | + | 0.859650i | \(0.329319\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.21110 | 0.476523 | 0.238262 | − | 0.971201i | \(-0.423422\pi\) | ||||
0.238262 | + | 0.971201i | \(0.423422\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.18335 | 0.0776905 | ||||||||
\(233\) | −22.8167 | −1.49477 | −0.747384 | − | 0.664392i | \(-0.768691\pi\) | ||||
−0.747384 | + | 0.664392i | \(0.768691\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.02776 | −0.0669012 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.39445 | −0.220029 | ||||||||
\(239\) | −29.2111 | −1.88951 | −0.944755 | − | 0.327779i | \(-0.893700\pi\) | ||||
−0.944755 | + | 0.327779i | \(0.893700\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.6056 | 1.06966 | 0.534829 | − | 0.844960i | \(-0.320376\pi\) | ||||
0.534829 | + | 0.844960i | \(0.320376\pi\) | |||||||
\(242\) | 2.60555 | 0.167491 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −4.00000 | −0.256074 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.78890 | 0.177453 | ||||||||
\(248\) | 21.6333 | 1.37372 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.81665 | −0.493383 | −0.246691 | − | 0.969094i | \(-0.579343\pi\) | ||||
−0.246691 | + | 0.969094i | \(0.579343\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 24.6333 | 1.54868 | ||||||||
\(254\) | −11.4861 | −0.720703 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −7.09167 | −0.443230 | ||||||||
\(257\) | 21.6333 | 1.34945 | 0.674724 | − | 0.738070i | \(-0.264263\pi\) | ||||
0.674724 | + | 0.738070i | \(0.264263\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.2111 | 0.634487 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −19.0278 | −1.17554 | ||||||||
\(263\) | −20.2111 | −1.24627 | −0.623135 | − | 0.782114i | \(-0.714141\pi\) | ||||
−0.623135 | + | 0.782114i | \(0.714141\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.788897 | −0.0483704 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.54163 | 0.155255 | ||||||||
\(269\) | −11.2111 | −0.683553 | −0.341776 | − | 0.939781i | \(-0.611029\pi\) | ||||
−0.341776 | + | 0.939781i | \(0.611029\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.3944 | −1.17813 | −0.589064 | − | 0.808086i | \(-0.700504\pi\) | ||||
−0.589064 | + | 0.808086i | \(0.700504\pi\) | |||||||
\(272\) | 8.60555 | 0.521788 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −14.6056 | −0.882354 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.0000 | 0.600842 | 0.300421 | − | 0.953807i | \(-0.402873\pi\) | ||||
0.300421 | + | 0.953807i | \(0.402873\pi\) | |||||||
\(278\) | 22.1833 | 1.33047 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.8167 | 1.36113 | 0.680564 | − | 0.732689i | \(-0.261735\pi\) | ||||
0.680564 | + | 0.732689i | \(0.261735\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −29.6333 | −1.76152 | −0.880759 | − | 0.473565i | \(-0.842967\pi\) | ||||
−0.880759 | + | 0.473565i | \(0.842967\pi\) | |||||||
\(284\) | −0.908327 | −0.0538993 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 18.0000 | 1.06436 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.2111 | −0.600653 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.00000 | −0.117041 | ||||||||
\(293\) | 3.39445 | 0.198306 | 0.0991529 | − | 0.995072i | \(-0.468387\pi\) | ||||
0.0991529 | + | 0.995072i | \(0.468387\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −30.6333 | −1.78052 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −30.7527 | −1.78146 | ||||||||
\(299\) | −37.8167 | −2.18699 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.39445 | 0.138014 | ||||||||
\(302\) | 19.3028 | 1.11075 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.00000 | 0.114708 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.39445 | 0.0795854 | 0.0397927 | − | 0.999208i | \(-0.487330\pi\) | ||||
0.0397927 | + | 0.999208i | \(0.487330\pi\) | |||||||
\(308\) | 0.908327 | 0.0517567 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.81665 | 0.443242 | 0.221621 | − | 0.975133i | \(-0.428865\pi\) | ||||
0.221621 | + | 0.975133i | \(0.428865\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.18335 | 0.123410 | 0.0617050 | − | 0.998094i | \(-0.480346\pi\) | ||||
0.0617050 | + | 0.998094i | \(0.480346\pi\) | |||||||
\(314\) | −18.7889 | −1.06032 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.06392 | −0.116104 | ||||||||
\(317\) | −23.6056 | −1.32582 | −0.662910 | − | 0.748699i | \(-0.730679\pi\) | ||||
−0.662910 | + | 0.748699i | \(0.730679\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.18335 | 0.0662547 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 10.6972 | 0.596133 | ||||||||
\(323\) | 1.57779 | 0.0877909 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 3.63331 | 0.201230 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.39445 | −0.187142 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 29.2389 | 1.60711 | 0.803557 | − | 0.595228i | \(-0.202938\pi\) | ||||
0.803557 | + | 0.595228i | \(0.202938\pi\) | |||||||
\(332\) | −3.39445 | −0.186295 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −24.7889 | −1.35639 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.21110 | −0.392814 | −0.196407 | − | 0.980522i | \(-0.562927\pi\) | ||||
−0.196407 | + | 0.980522i | \(0.562927\pi\) | |||||||
\(338\) | −10.6972 | −0.581852 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 21.6333 | 1.17151 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −7.18335 | −0.387300 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −18.0000 | −0.967686 | ||||||||
\(347\) | 15.7889 | 0.847592 | 0.423796 | − | 0.905758i | \(-0.360697\pi\) | ||||
0.423796 | + | 0.905758i | \(0.360697\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −33.4500 | −1.79054 | −0.895268 | − | 0.445529i | \(-0.853016\pi\) | ||||
−0.895268 | + | 0.445529i | \(0.853016\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −5.09167 | −0.271387 | ||||||||
\(353\) | −30.0000 | −1.59674 | −0.798369 | − | 0.602168i | \(-0.794304\pi\) | ||||
−0.798369 | + | 0.602168i | \(0.794304\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −4.18335 | −0.221717 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 18.6333 | 0.983428 | 0.491714 | − | 0.870757i | \(-0.336370\pi\) | ||||
0.491714 | + | 0.870757i | \(0.336370\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.6333 | −0.980700 | ||||||||
\(362\) | −7.02776 | −0.369371 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.39445 | −0.0730890 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.4222 | 0.752833 | 0.376416 | − | 0.926451i | \(-0.377156\pi\) | ||||
0.376416 | + | 0.926451i | \(0.377156\pi\) | |||||||
\(368\) | −27.1194 | −1.41370 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11.2111 | 0.582051 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.00000 | 0.0517780 | 0.0258890 | − | 0.999665i | \(-0.491758\pi\) | ||||
0.0258890 | + | 0.999665i | \(0.491758\pi\) | |||||||
\(374\) | 10.1833 | 0.526568 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10.1833 | 0.525166 | ||||||||
\(377\) | −1.81665 | −0.0935624 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.81665 | 0.350148 | 0.175074 | − | 0.984555i | \(-0.443984\pi\) | ||||
0.175074 | + | 0.984555i | \(0.443984\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −22.4222 | −1.14722 | ||||||||
\(383\) | 24.2389 | 1.23855 | 0.619274 | − | 0.785175i | \(-0.287427\pi\) | ||||
0.619274 | + | 0.785175i | \(0.287427\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −8.09167 | −0.411855 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4.60555 | −0.233811 | ||||||||
\(389\) | 7.18335 | 0.364210 | 0.182105 | − | 0.983279i | \(-0.441709\pi\) | ||||
0.182105 | + | 0.983279i | \(0.441709\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −21.3944 | −1.08196 | ||||||||
\(392\) | 3.00000 | 0.151523 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6.27502 | 0.316131 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.00000 | −0.100377 | −0.0501886 | − | 0.998740i | \(-0.515982\pi\) | ||||
−0.0501886 | + | 0.998740i | \(0.515982\pi\) | |||||||
\(398\) | −10.4222 | −0.522418 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.81665 | −0.240532 | −0.120266 | − | 0.992742i | \(-0.538375\pi\) | ||||
−0.120266 | + | 0.992742i | \(0.538375\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −33.2111 | −1.65436 | ||||||||
\(404\) | 2.84441 | 0.141515 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.513878 | 0.0255033 | ||||||||
\(407\) | −30.6333 | −1.51844 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.81665 | 0.485402 | 0.242701 | − | 0.970101i | \(-0.421967\pi\) | ||||
0.242701 | + | 0.970101i | \(0.421967\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −5.39445 | −0.265765 | ||||||||
\(413\) | −3.39445 | −0.167030 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 7.81665 | 0.383243 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.36669 | 0.115759 | ||||||||
\(419\) | −6.00000 | −0.293119 | −0.146560 | − | 0.989202i | \(-0.546820\pi\) | ||||
−0.146560 | + | 0.989202i | \(0.546820\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.21110 | 0.205237 | 0.102618 | − | 0.994721i | \(-0.467278\pi\) | ||||
0.102618 | + | 0.994721i | \(0.467278\pi\) | |||||||
\(422\) | 3.15559 | 0.153612 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −33.6333 | −1.63338 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13.2111 | −0.639330 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −34.4222 | −1.65806 | −0.829030 | − | 0.559205i | \(-0.811107\pi\) | ||||
−0.829030 | + | 0.559205i | \(0.811107\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 22.7889 | 1.09516 | 0.547582 | − | 0.836752i | \(-0.315548\pi\) | ||||
0.547582 | + | 0.836752i | \(0.315548\pi\) | |||||||
\(434\) | 9.39445 | 0.450948 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.69722 | 0.177065 | ||||||||
\(437\) | −4.97224 | −0.237855 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.605551 | −0.0289014 | −0.0144507 | − | 0.999896i | \(-0.504600\pi\) | ||||
−0.0144507 | + | 0.999896i | \(0.504600\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −15.6333 | −0.743601 | ||||||||
\(443\) | −27.6333 | −1.31290 | −0.656449 | − | 0.754370i | \(-0.727942\pi\) | ||||
−0.656449 | + | 0.754370i | \(0.727942\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 29.4500 | 1.39450 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −8.81665 | −0.416548 | ||||||||
\(449\) | 13.1833 | 0.622161 | 0.311080 | − | 0.950384i | \(-0.399309\pi\) | ||||
0.311080 | + | 0.950384i | \(0.399309\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −3.27502 | −0.154044 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −20.0555 | −0.941252 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.2111 | 0.851879 | 0.425940 | − | 0.904752i | \(-0.359944\pi\) | ||||
0.425940 | + | 0.904752i | \(0.359944\pi\) | |||||||
\(458\) | −9.39445 | −0.438974 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −24.2389 | −1.12892 | −0.564458 | − | 0.825462i | \(-0.690915\pi\) | ||||
−0.564458 | + | 0.825462i | \(0.690915\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.78890 | −0.129611 | −0.0648055 | − | 0.997898i | \(-0.520643\pi\) | ||||
−0.0648055 | + | 0.997898i | \(0.520643\pi\) | |||||||
\(464\) | −1.30278 | −0.0604798 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 29.7250 | 1.37698 | ||||||||
\(467\) | 28.4222 | 1.31522 | 0.657611 | − | 0.753357i | \(-0.271567\pi\) | ||||
0.657611 | + | 0.753357i | \(0.271567\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.39445 | 0.387620 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 10.1833 | 0.468727 | ||||||||
\(473\) | −7.18335 | −0.330291 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −0.788897 | −0.0361591 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 38.0555 | 1.74062 | ||||||||
\(479\) | −27.3944 | −1.25168 | −0.625842 | − | 0.779950i | \(-0.715245\pi\) | ||||
−0.625842 | + | 0.779950i | \(0.715245\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 47.0278 | 2.14428 | ||||||||
\(482\) | −21.6333 | −0.985370 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.605551 | 0.0275251 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.816654 | −0.0370061 | −0.0185031 | − | 0.999829i | \(-0.505890\pi\) | ||||
−0.0185031 | + | 0.999829i | \(0.505890\pi\) | |||||||
\(488\) | 39.6333 | 1.79412 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.00000 | 0.135388 | 0.0676941 | − | 0.997706i | \(-0.478436\pi\) | ||||
0.0676941 | + | 0.997706i | \(0.478436\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.02776 | −0.0462878 | ||||||||
\(494\) | −3.63331 | −0.163470 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −23.8167 | −1.06940 | ||||||||
\(497\) | −3.00000 | −0.134568 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −28.0000 | −1.25345 | −0.626726 | − | 0.779240i | \(-0.715605\pi\) | ||||
−0.626726 | + | 0.779240i | \(0.715605\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 10.1833 | 0.454505 | ||||||||
\(503\) | −23.2111 | −1.03493 | −0.517466 | − | 0.855704i | \(-0.673125\pi\) | ||||
−0.517466 | + | 0.855704i | \(0.673125\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −32.0917 | −1.42665 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.66947 | −0.118438 | ||||||||
\(509\) | −8.60555 | −0.381434 | −0.190717 | − | 0.981645i | \(-0.561081\pi\) | ||||
−0.190717 | + | 0.981645i | \(0.561081\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.60555 | −0.292212 | ||||||||
\(512\) | 25.4222 | 1.12351 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −28.1833 | −1.24311 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.1833 | 0.447863 | ||||||||
\(518\) | −13.3028 | −0.584490 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.57779 | 0.331989 | 0.165995 | − | 0.986127i | \(-0.446917\pi\) | ||||
0.165995 | + | 0.986127i | \(0.446917\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.0000 | 0.699631 | 0.349816 | − | 0.936819i | \(-0.386244\pi\) | ||||
0.349816 | + | 0.936819i | \(0.386244\pi\) | |||||||
\(524\) | −4.42221 | −0.193185 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 26.3305 | 1.14807 | ||||||||
\(527\) | −18.7889 | −0.818457 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 44.4222 | 1.93140 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.183346 | −0.00794906 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −25.1833 | −1.08775 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 14.6056 | 0.629690 | ||||||||
\(539\) | 3.00000 | 0.129219 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.57779 | −0.110828 | −0.0554140 | − | 0.998463i | \(-0.517648\pi\) | ||||
−0.0554140 | + | 0.998463i | \(0.517648\pi\) | |||||||
\(542\) | 25.2666 | 1.08529 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.42221 | 0.189600 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.3944 | 0.957517 | 0.478759 | − | 0.877947i | \(-0.341087\pi\) | ||||
0.478759 | + | 0.877947i | \(0.341087\pi\) | |||||||
\(548\) | −3.39445 | −0.145004 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.238859 | −0.0101757 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.81665 | −0.289874 | ||||||||
\(554\) | −13.0278 | −0.553496 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.15559 | 0.218646 | ||||||||
\(557\) | −39.2389 | −1.66260 | −0.831302 | − | 0.555821i | \(-0.812404\pi\) | ||||
−0.831302 | + | 0.555821i | \(0.812404\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11.0278 | 0.466424 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −29.7250 | −1.25387 | ||||||||
\(563\) | 0.788897 | 0.0332481 | 0.0166240 | − | 0.999862i | \(-0.494708\pi\) | ||||
0.0166240 | + | 0.999862i | \(0.494708\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 38.6056 | 1.62271 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9.00000 | 0.377632 | ||||||||
\(569\) | 22.8167 | 0.956524 | 0.478262 | − | 0.878217i | \(-0.341267\pi\) | ||||
0.478262 | + | 0.878217i | \(0.341267\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.60555 | 0.0671902 | 0.0335951 | − | 0.999436i | \(-0.489304\pi\) | ||||
0.0335951 | + | 0.999436i | \(0.489304\pi\) | |||||||
\(572\) | 4.18335 | 0.174914 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23.3944 | −0.973924 | −0.486962 | − | 0.873423i | \(-0.661895\pi\) | ||||
−0.486962 | + | 0.873423i | \(0.661895\pi\) | |||||||
\(578\) | 13.3028 | 0.553323 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11.2111 | −0.465115 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −33.6333 | −1.39295 | ||||||||
\(584\) | 19.8167 | 0.820019 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.42221 | −0.182680 | ||||||||
\(587\) | 16.1833 | 0.667958 | 0.333979 | − | 0.942580i | \(-0.391609\pi\) | ||||
0.333979 | + | 0.942580i | \(0.391609\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.36669 | −0.179926 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 33.7250 | 1.38609 | ||||||||
\(593\) | −15.6333 | −0.641983 | −0.320991 | − | 0.947082i | \(-0.604016\pi\) | ||||
−0.320991 | + | 0.947082i | \(0.604016\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −7.14719 | −0.292760 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 49.2666 | 2.01466 | ||||||||
\(599\) | −20.2111 | −0.825803 | −0.412902 | − | 0.910776i | \(-0.635485\pi\) | ||||
−0.412902 | + | 0.910776i | \(0.635485\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.78890 | 0.113761 | 0.0568807 | − | 0.998381i | \(-0.481885\pi\) | ||||
0.0568807 | + | 0.998381i | \(0.481885\pi\) | |||||||
\(602\) | −3.11943 | −0.127138 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4.48612 | 0.182538 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.18335 | 0.0886193 | 0.0443096 | − | 0.999018i | \(-0.485891\pi\) | ||||
0.0443096 | + | 0.999018i | \(0.485891\pi\) | |||||||
\(608\) | 1.02776 | 0.0416810 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −15.6333 | −0.632456 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20.5778 | 0.831129 | 0.415565 | − | 0.909564i | \(-0.363584\pi\) | ||||
0.415565 | + | 0.909564i | \(0.363584\pi\) | |||||||
\(614\) | −1.81665 | −0.0733142 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −9.00000 | −0.362620 | ||||||||
\(617\) | 1.18335 | 0.0476397 | 0.0238199 | − | 0.999716i | \(-0.492417\pi\) | ||||
0.0238199 | + | 0.999716i | \(0.492417\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.60555 | 0.185113 | 0.0925564 | − | 0.995707i | \(-0.470496\pi\) | ||||
0.0925564 | + | 0.995707i | \(0.470496\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −10.1833 | −0.408315 | ||||||||
\(623\) | −13.8167 | −0.553553 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −2.84441 | −0.113685 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −4.36669 | −0.174250 | ||||||||
\(629\) | 26.6056 | 1.06083 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.0278 | −0.558436 | −0.279218 | − | 0.960228i | \(-0.590075\pi\) | ||||
−0.279218 | + | 0.960228i | \(0.590075\pi\) | |||||||
\(632\) | 20.4500 | 0.813456 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 30.7527 | 1.22135 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.60555 | −0.182479 | ||||||||
\(638\) | −1.54163 | −0.0610339 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.18335 | −0.0467394 | −0.0233697 | − | 0.999727i | \(-0.507439\pi\) | ||||
−0.0233697 | + | 0.999727i | \(0.507439\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.57779 | −0.377711 | −0.188856 | − | 0.982005i | \(-0.560478\pi\) | ||||
−0.188856 | + | 0.982005i | \(0.560478\pi\) | |||||||
\(644\) | 2.48612 | 0.0979669 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.05551 | −0.0808731 | ||||||||
\(647\) | 6.00000 | 0.235884 | 0.117942 | − | 0.993020i | \(-0.462370\pi\) | ||||
0.117942 | + | 0.993020i | \(0.462370\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.1833 | 0.399731 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.844410 | 0.0330697 | ||||||||
\(653\) | 11.2111 | 0.438724 | 0.219362 | − | 0.975643i | \(-0.429602\pi\) | ||||
0.219362 | + | 0.975643i | \(0.429602\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 4.42221 | 0.172396 | ||||||||
\(659\) | 12.0000 | 0.467454 | 0.233727 | − | 0.972302i | \(-0.424908\pi\) | ||||
0.233727 | + | 0.972302i | \(0.424908\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −41.8167 | −1.62648 | −0.813240 | − | 0.581929i | \(-0.802298\pi\) | ||||
−0.813240 | + | 0.581929i | \(0.802298\pi\) | |||||||
\(662\) | −38.0917 | −1.48047 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 33.6333 | 1.30523 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.23886 | 0.125409 | ||||||||
\(668\) | −5.76114 | −0.222905 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 39.6333 | 1.53003 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.0000 | 0.385472 | 0.192736 | − | 0.981251i | \(-0.438264\pi\) | ||||
0.192736 | + | 0.981251i | \(0.438264\pi\) | |||||||
\(674\) | 9.39445 | 0.361861 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.48612 | −0.0956201 | ||||||||
\(677\) | −23.2111 | −0.892075 | −0.446038 | − | 0.895014i | \(-0.647165\pi\) | ||||
−0.446038 | + | 0.895014i | \(0.647165\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15.2111 | −0.583749 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −28.1833 | −1.07920 | ||||||||
\(683\) | 24.6333 | 0.942567 | 0.471284 | − | 0.881982i | \(-0.343791\pi\) | ||||
0.471284 | + | 0.881982i | \(0.343791\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.30278 | 0.0497402 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 7.90833 | 0.301502 | ||||||||
\(689\) | 51.6333 | 1.96707 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 26.7889 | 1.01910 | 0.509549 | − | 0.860442i | \(-0.329812\pi\) | ||||
0.509549 | + | 0.860442i | \(0.329812\pi\) | |||||||
\(692\) | −4.18335 | −0.159027 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −20.5694 | −0.780803 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 43.5778 | 1.64944 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 35.2111 | 1.32990 | 0.664952 | − | 0.746886i | \(-0.268452\pi\) | ||||
0.664952 | + | 0.746886i | \(0.268452\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.18335 | 0.233209 | ||||||||
\(704\) | 26.4500 | 0.996870 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 39.0833 | 1.47092 | ||||||||
\(707\) | 9.39445 | 0.353315 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22.8444 | 0.857940 | 0.428970 | − | 0.903319i | \(-0.358877\pi\) | ||||
0.428970 | + | 0.903319i | \(0.358877\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 41.4500 | 1.55340 | ||||||||
\(713\) | 59.2111 | 2.21747 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −24.2750 | −0.905936 | ||||||||
\(719\) | −41.2111 | −1.53691 | −0.768457 | − | 0.639901i | \(-0.778975\pi\) | ||||
−0.768457 | + | 0.639901i | \(0.778975\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17.8167 | −0.663527 | ||||||||
\(722\) | 24.2750 | 0.903423 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.63331 | −0.0607014 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 30.6056 | 1.13510 | 0.567549 | − | 0.823340i | \(-0.307892\pi\) | ||||
0.567549 | + | 0.823340i | \(0.307892\pi\) | |||||||
\(728\) | 13.8167 | 0.512079 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.23886 | 0.230753 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −20.0000 | −0.738717 | −0.369358 | − | 0.929287i | \(-0.620423\pi\) | ||||
−0.369358 | + | 0.929287i | \(0.620423\pi\) | |||||||
\(734\) | −18.7889 | −0.693511 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −13.9361 | −0.513691 | ||||||||
\(737\) | −25.1833 | −0.927640 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24.8167 | 0.912895 | 0.456448 | − | 0.889750i | \(-0.349122\pi\) | ||||
0.456448 | + | 0.889750i | \(0.349122\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −14.6056 | −0.536187 | ||||||||
\(743\) | 15.6333 | 0.573530 | 0.286765 | − | 0.958001i | \(-0.407420\pi\) | ||||
0.286765 | + | 0.958001i | \(0.407420\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.30278 | −0.0476980 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.36669 | 0.0865348 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −43.6333 | −1.59220 | −0.796101 | − | 0.605164i | \(-0.793108\pi\) | ||||
−0.796101 | + | 0.605164i | \(0.793108\pi\) | |||||||
\(752\) | −11.2111 | −0.408827 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.36669 | 0.0861899 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −41.0000 | −1.49017 | −0.745085 | − | 0.666969i | \(-0.767591\pi\) | ||||
−0.745085 | + | 0.666969i | \(0.767591\pi\) | |||||||
\(758\) | −8.88057 | −0.322557 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15.6333 | −0.566707 | −0.283353 | − | 0.959016i | \(-0.591447\pi\) | ||||
−0.283353 | + | 0.959016i | \(0.591447\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.2111 | 0.442072 | ||||||||
\(764\) | −5.21110 | −0.188531 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −31.5778 | −1.14095 | ||||||||
\(767\) | −15.6333 | −0.564486 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.6333 | 0.419508 | 0.209754 | − | 0.977754i | \(-0.432734\pi\) | ||||
0.209754 | + | 0.977754i | \(0.432734\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.88057 | −0.0676832 | ||||||||
\(773\) | 6.00000 | 0.215805 | 0.107903 | − | 0.994161i | \(-0.465587\pi\) | ||||
0.107903 | + | 0.994161i | \(0.465587\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 45.6333 | 1.63814 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −9.35829 | −0.335511 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.00000 | 0.322045 | ||||||||
\(782\) | 27.8722 | 0.996707 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.30278 | −0.117956 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 22.2389 | 0.792730 | 0.396365 | − | 0.918093i | \(-0.370272\pi\) | ||||
0.396365 | + | 0.918093i | \(0.370272\pi\) | |||||||
\(788\) | 1.45837 | 0.0519521 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.8167 | −0.384596 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −60.8444 | −2.16065 | ||||||||
\(794\) | 2.60555 | 0.0924676 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.42221 | −0.0858528 | ||||||||
\(797\) | 35.4500 | 1.25570 | 0.627851 | − | 0.778334i | \(-0.283935\pi\) | ||||
0.627851 | + | 0.778334i | \(0.283935\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.84441 | −0.312893 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 6.27502 | 0.221579 | ||||||||
\(803\) | 19.8167 | 0.699315 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 43.2666 | 1.52400 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −28.1833 | −0.991487 | ||||||||
\(809\) | 32.4500 | 1.14088 | 0.570440 | − | 0.821339i | \(-0.306773\pi\) | ||||
0.570440 | + | 0.821339i | \(0.306773\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −42.8444 | −1.50447 | −0.752235 | − | 0.658894i | \(-0.771024\pi\) | ||||
−0.752235 | + | 0.658894i | \(0.771024\pi\) | |||||||
\(812\) | 0.119429 | 0.00419115 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 39.9083 | 1.39879 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.44996 | 0.0507277 | ||||||||
\(818\) | −12.7889 | −0.447153 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 37.2666 | 1.30061 | 0.650307 | − | 0.759672i | \(-0.274640\pi\) | ||||
0.650307 | + | 0.759672i | \(0.274640\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.18335 | −0.110964 | −0.0554822 | − | 0.998460i | \(-0.517670\pi\) | ||||
−0.0554822 | + | 0.998460i | \(0.517670\pi\) | |||||||
\(824\) | 53.4500 | 1.86202 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.42221 | 0.153868 | ||||||||
\(827\) | 12.6333 | 0.439303 | 0.219652 | − | 0.975578i | \(-0.429508\pi\) | ||||
0.219652 | + | 0.975578i | \(0.429508\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 50.2389 | 1.74487 | 0.872434 | − | 0.488732i | \(-0.162540\pi\) | ||||
0.872434 | + | 0.488732i | \(0.162540\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −40.6056 | −1.40774 | ||||||||
\(833\) | −2.60555 | −0.0902770 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0.550039 | 0.0190235 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 7.81665 | 0.270022 | ||||||||
\(839\) | 43.8167 | 1.51272 | 0.756359 | − | 0.654156i | \(-0.226976\pi\) | ||||
0.756359 | + | 0.654156i | \(0.226976\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.8444 | −0.994635 | ||||||||
\(842\) | −5.48612 | −0.189064 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0.733385 | 0.0252441 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.00000 | 0.0687208 | ||||||||
\(848\) | 37.0278 | 1.27154 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −83.8444 | −2.87415 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.2111 | 0.726254 | 0.363127 | − | 0.931740i | \(-0.381709\pi\) | ||||
0.363127 | + | 0.931740i | \(0.381709\pi\) | |||||||
\(854\) | 17.2111 | 0.588952 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −15.6333 | −0.534024 | −0.267012 | − | 0.963693i | \(-0.586036\pi\) | ||||
−0.267012 | + | 0.963693i | \(0.586036\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.36669 | −0.217229 | −0.108614 | − | 0.994084i | \(-0.534641\pi\) | ||||
−0.108614 | + | 0.994084i | \(0.534641\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 44.8444 | 1.52741 | ||||||||
\(863\) | 48.6333 | 1.65550 | 0.827749 | − | 0.561099i | \(-0.189621\pi\) | ||||
0.827749 | + | 0.561099i | \(0.189621\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −29.6888 | −1.00887 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.18335 | 0.0741076 | ||||||||
\(869\) | 20.4500 | 0.693717 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 38.6611 | 1.30998 | ||||||||
\(872\) | −36.6333 | −1.24056 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 6.47772 | 0.219112 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 22.0000 | 0.742887 | 0.371444 | − | 0.928456i | \(-0.378863\pi\) | ||||
0.371444 | + | 0.928456i | \(0.378863\pi\) | |||||||
\(878\) | 0.788897 | 0.0266240 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.63331 | 0.324554 | 0.162277 | − | 0.986745i | \(-0.448116\pi\) | ||||
0.162277 | + | 0.986745i | \(0.448116\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.39445 | −0.282496 | −0.141248 | − | 0.989974i | \(-0.545111\pi\) | ||||
−0.141248 | + | 0.989974i | \(0.545111\pi\) | |||||||
\(884\) | −3.63331 | −0.122201 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 36.0000 | 1.20944 | ||||||||
\(887\) | −29.2111 | −0.980813 | −0.490406 | − | 0.871494i | \(-0.663152\pi\) | ||||
−0.490406 | + | 0.871494i | \(0.663152\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.81665 | −0.295701 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 6.84441 | 0.229168 | ||||||||
\(893\) | −2.05551 | −0.0687851 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 8.09167 | 0.270324 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −17.1749 | −0.573135 | ||||||||
\(899\) | 2.84441 | 0.0948664 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 29.2111 | 0.973163 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 32.4500 | 1.07927 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.21110 | −0.0402140 | −0.0201070 | − | 0.999798i | \(-0.506401\pi\) | ||||
−0.0201070 | + | 0.999798i | \(0.506401\pi\) | |||||||
\(908\) | −4.66106 | −0.154683 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15.0000 | −0.496972 | −0.248486 | − | 0.968635i | \(-0.579933\pi\) | ||||
−0.248486 | + | 0.968635i | \(0.579933\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 33.6333 | 1.11310 | ||||||||
\(914\) | −23.7250 | −0.784753 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.18335 | −0.0721398 | ||||||||
\(917\) | −14.6056 | −0.482318 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10.3944 | −0.342881 | −0.171441 | − | 0.985194i | \(-0.554842\pi\) | ||||
−0.171441 | + | 0.985194i | \(0.554842\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 31.5778 | 1.03996 | ||||||||
\(923\) | −13.8167 | −0.454781 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 3.63331 | 0.119398 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.669468 | −0.0219764 | ||||||||
\(929\) | −30.2389 | −0.992105 | −0.496052 | − | 0.868293i | \(-0.665218\pi\) | ||||
−0.496052 | + | 0.868293i | \(0.665218\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.605551 | −0.0198461 | ||||||||
\(932\) | 6.90833 | 0.226290 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −37.0278 | −1.21159 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −44.4777 | −1.45302 | −0.726512 | − | 0.687154i | \(-0.758860\pi\) | ||||
−0.726512 | + | 0.687154i | \(0.758860\pi\) | |||||||
\(938\) | −10.9361 | −0.357076 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6.00000 | −0.195594 | −0.0977972 | − | 0.995206i | \(-0.531180\pi\) | ||||
−0.0977972 | + | 0.995206i | \(0.531180\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −11.2111 | −0.364890 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 9.35829 | 0.304264 | ||||||||
\(947\) | 56.8444 | 1.84720 | 0.923598 | − | 0.383363i | \(-0.125234\pi\) | ||||
0.923598 | + | 0.383363i | \(0.125234\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −30.4222 | −0.987547 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 7.81665 | 0.253339 | ||||||||
\(953\) | −6.39445 | −0.207137 | −0.103568 | − | 0.994622i | \(-0.533026\pi\) | ||||
−0.103568 | + | 0.994622i | \(0.533026\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 8.84441 | 0.286049 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 35.6888 | 1.15305 | ||||||||
\(959\) | −11.2111 | −0.362025 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 21.0000 | 0.677419 | ||||||||
\(962\) | −61.2666 | −1.97531 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −5.02776 | −0.161933 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −16.8444 | −0.541680 | −0.270840 | − | 0.962624i | \(-0.587301\pi\) | ||||
−0.270840 | + | 0.962624i | \(0.587301\pi\) | |||||||
\(968\) | −6.00000 | −0.192847 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 39.8722 | 1.27956 | 0.639779 | − | 0.768559i | \(-0.279026\pi\) | ||||
0.639779 | + | 0.768559i | \(0.279026\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 17.0278 | 0.545885 | ||||||||
\(974\) | 1.06392 | 0.0340901 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −43.6333 | −1.39667 | ||||||||
\(977\) | 34.0278 | 1.08864 | 0.544322 | − | 0.838876i | \(-0.316787\pi\) | ||||
0.544322 | + | 0.838876i | \(0.316787\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 41.4500 | 1.32475 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −3.90833 | −0.124720 | ||||||||
\(983\) | −32.0555 | −1.02241 | −0.511206 | − | 0.859458i | \(-0.670801\pi\) | ||||
−0.511206 | + | 0.859458i | \(0.670801\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1.33894 | 0.0426404 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.844410 | −0.0268643 | ||||||||
\(989\) | −19.6611 | −0.625185 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.97224 | 0.316779 | 0.158389 | − | 0.987377i | \(-0.449370\pi\) | ||||
0.158389 | + | 0.987377i | \(0.449370\pi\) | |||||||
\(992\) | −12.2389 | −0.388584 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 3.90833 | 0.123965 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −49.4500 | −1.56610 | −0.783048 | − | 0.621961i | \(-0.786336\pi\) | ||||
−0.783048 | + | 0.621961i | \(0.786336\pi\) | |||||||
\(998\) | 36.4777 | 1.15468 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1575.2.a.t.1.1 | 2 | ||
3.2 | odd | 2 | 525.2.a.f.1.2 | ✓ | 2 | ||
5.2 | odd | 4 | 1575.2.d.g.1324.2 | 4 | |||
5.3 | odd | 4 | 1575.2.d.g.1324.3 | 4 | |||
5.4 | even | 2 | 1575.2.a.o.1.2 | 2 | |||
12.11 | even | 2 | 8400.2.a.df.1.1 | 2 | |||
15.2 | even | 4 | 525.2.d.d.274.3 | 4 | |||
15.8 | even | 4 | 525.2.d.d.274.2 | 4 | |||
15.14 | odd | 2 | 525.2.a.h.1.1 | yes | 2 | ||
21.20 | even | 2 | 3675.2.a.w.1.2 | 2 | |||
60.59 | even | 2 | 8400.2.a.cw.1.2 | 2 | |||
105.104 | even | 2 | 3675.2.a.bb.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
525.2.a.f.1.2 | ✓ | 2 | 3.2 | odd | 2 | ||
525.2.a.h.1.1 | yes | 2 | 15.14 | odd | 2 | ||
525.2.d.d.274.2 | 4 | 15.8 | even | 4 | |||
525.2.d.d.274.3 | 4 | 15.2 | even | 4 | |||
1575.2.a.o.1.2 | 2 | 5.4 | even | 2 | |||
1575.2.a.t.1.1 | 2 | 1.1 | even | 1 | trivial | ||
1575.2.d.g.1324.2 | 4 | 5.2 | odd | 4 | |||
1575.2.d.g.1324.3 | 4 | 5.3 | odd | 4 | |||
3675.2.a.w.1.2 | 2 | 21.20 | even | 2 | |||
3675.2.a.bb.1.1 | 2 | 105.104 | even | 2 | |||
8400.2.a.cw.1.2 | 2 | 60.59 | even | 2 | |||
8400.2.a.df.1.1 | 2 | 12.11 | even | 2 |