Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8752,2,Mod(1,8752)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8752, 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("8752.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8752 = 2^{4} \cdot 547 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8752.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: | \(69.8850718490\) |
Analytic rank: | \(1\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 4 x^{17} - 18 x^{16} + 84 x^{15} + 116 x^{14} - 708 x^{13} - 282 x^{12} + 3104 x^{11} + \cdots + 328 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 547) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Root | \(2.72204\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8752.1 |
$q$-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 | ||||||||
\(3\) | 1.76734 | 1.02037 | 0.510187 | − | 0.860063i | \(-0.329576\pi\) | ||||
0.510187 | + | 0.860063i | \(0.329576\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.469688 | 0.210051 | 0.105025 | − | 0.994470i | \(-0.466508\pi\) | ||||
0.105025 | + | 0.994470i | \(0.466508\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.03831 | −0.392445 | −0.196222 | − | 0.980559i | \(-0.562867\pi\) | ||||
−0.196222 | + | 0.980559i | \(0.562867\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.123492 | 0.0411640 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.84194 | 0.555366 | 0.277683 | − | 0.960673i | \(-0.410434\pi\) | ||||
0.277683 | + | 0.960673i | \(0.410434\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.700934 | −0.194404 | −0.0972021 | − | 0.995265i | \(-0.530989\pi\) | ||||
−0.0972021 | + | 0.995265i | \(0.530989\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.830099 | 0.214331 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.793975 | 0.192567 | 0.0962837 | − | 0.995354i | \(-0.469304\pi\) | ||||
0.0962837 | + | 0.995354i | \(0.469304\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.65845 | −0.839306 | −0.419653 | − | 0.907685i | \(-0.637848\pi\) | ||||
−0.419653 | + | 0.907685i | \(0.637848\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.83505 | −0.400441 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.65159 | 0.761409 | 0.380704 | − | 0.924697i | \(-0.375682\pi\) | ||||
0.380704 | + | 0.924697i | \(0.375682\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.77939 | −0.955879 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.08377 | −0.978372 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.52848 | 1.02661 | 0.513307 | − | 0.858205i | \(-0.328420\pi\) | ||||
0.513307 | + | 0.858205i | \(0.328420\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.13605 | −1.10207 | −0.551034 | − | 0.834483i | \(-0.685766\pi\) | ||||
−0.551034 | + | 0.834483i | \(0.685766\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.25534 | 0.566681 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.487683 | −0.0824334 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.73114 | −0.448997 | −0.224498 | − | 0.974474i | \(-0.572074\pi\) | ||||
−0.224498 | + | 0.974474i | \(0.572074\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.23879 | −0.198365 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.69220 | −1.51367 | −0.756833 | − | 0.653608i | \(-0.773255\pi\) | ||||
−0.756833 | + | 0.653608i | \(0.773255\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.25340 | 0.648638 | 0.324319 | − | 0.945948i | \(-0.394865\pi\) | ||||
0.324319 | + | 0.945948i | \(0.394865\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.0580027 | 0.00864653 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.21084 | 0.760078 | 0.380039 | − | 0.924970i | \(-0.375910\pi\) | ||||
0.380039 | + | 0.924970i | \(0.375910\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.92191 | −0.845987 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.40322 | 0.196491 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.01107 | −0.963044 | −0.481522 | − | 0.876434i | \(-0.659916\pi\) | ||||
−0.481522 | + | 0.876434i | \(0.659916\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.865138 | 0.116655 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.46572 | −0.856406 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.98691 | −0.909619 | −0.454809 | − | 0.890589i | \(-0.650293\pi\) | ||||
−0.454809 | + | 0.890589i | \(0.650293\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.87686 | −0.496381 | −0.248191 | − | 0.968711i | \(-0.579836\pi\) | ||||
−0.248191 | + | 0.968711i | \(0.579836\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.128223 | −0.0161546 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.329220 | −0.0408348 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.10753 | 0.623984 | 0.311992 | − | 0.950085i | \(-0.399004\pi\) | ||||
0.311992 | + | 0.950085i | \(0.399004\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.45360 | 0.776922 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.33192 | −0.158070 | −0.0790350 | − | 0.996872i | \(-0.525184\pi\) | ||||
−0.0790350 | + | 0.996872i | \(0.525184\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.83377 | −0.916874 | −0.458437 | − | 0.888727i | \(-0.651591\pi\) | ||||
−0.458437 | + | 0.888727i | \(0.651591\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −8.44681 | −0.975354 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.91251 | −0.217950 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.36166 | −0.490726 | −0.245363 | − | 0.969431i | \(-0.578907\pi\) | ||||
−0.245363 | + | 0.969431i | \(0.578907\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.35523 | −1.03947 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.3348 | 1.46368 | 0.731842 | − | 0.681475i | \(-0.238661\pi\) | ||||
0.731842 | + | 0.681475i | \(0.238661\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.372921 | 0.0404489 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.77071 | 1.04753 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.208861 | −0.0221393 | −0.0110696 | − | 0.999939i | \(-0.503524\pi\) | ||||
−0.0110696 | + | 0.999939i | \(0.503524\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.727788 | 0.0762929 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −10.8445 | −1.12452 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.71833 | −0.176297 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.08809 | 0.313549 | 0.156774 | − | 0.987634i | \(-0.449890\pi\) | ||||
0.156774 | + | 0.987634i | \(0.449890\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.227465 | 0.0228611 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.00261 | −0.796290 | −0.398145 | − | 0.917323i | \(-0.630346\pi\) | ||||
−0.398145 | + | 0.917323i | \(0.630346\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.26470 | 0.321681 | 0.160840 | − | 0.986980i | \(-0.448580\pi\) | ||||
0.160840 | + | 0.986980i | \(0.448580\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.861901 | −0.0841129 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 18.4884 | 1.78735 | 0.893673 | − | 0.448719i | \(-0.148120\pi\) | ||||
0.893673 | + | 0.448719i | \(0.148120\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −18.6769 | −1.78893 | −0.894463 | − | 0.447141i | \(-0.852442\pi\) | ||||
−0.894463 | + | 0.447141i | \(0.852442\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.82686 | −0.458145 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.85874 | 0.739288 | 0.369644 | − | 0.929173i | \(-0.379480\pi\) | ||||
0.369644 | + | 0.929173i | \(0.379480\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.71511 | 0.159935 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.0865597 | −0.00800245 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.824394 | −0.0755720 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.60726 | −0.691569 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −17.1294 | −1.54451 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.59326 | −0.410834 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.84052 | −0.873205 | −0.436602 | − | 0.899655i | \(-0.643818\pi\) | ||||
−0.436602 | + | 0.899655i | \(0.643818\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.51721 | 0.661854 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.02091 | −0.700791 | −0.350395 | − | 0.936602i | \(-0.613953\pi\) | ||||
−0.350395 | + | 0.936602i | \(0.613953\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.79861 | 0.329381 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.38779 | −0.205508 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 16.8434 | 1.43903 | 0.719516 | − | 0.694476i | \(-0.244364\pi\) | ||||
0.719516 | + | 0.694476i | \(0.244364\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.2506 | −0.954260 | −0.477130 | − | 0.878833i | \(-0.658323\pi\) | ||||
−0.477130 | + | 0.878833i | \(0.658323\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.20932 | 0.775565 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.29108 | −0.107965 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.59666 | 0.215641 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −10.4660 | −0.863224 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −18.8662 | −1.54558 | −0.772788 | − | 0.634664i | \(-0.781138\pi\) | ||||
−0.772788 | + | 0.634664i | \(0.781138\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.40292 | 0.521062 | 0.260531 | − | 0.965465i | \(-0.416102\pi\) | ||||
0.260531 | + | 0.965465i | \(0.416102\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.0980495 | 0.00792684 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.88203 | −0.231490 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.9254 | −1.19118 | −0.595589 | − | 0.803290i | \(-0.703081\pi\) | ||||
−0.595589 | + | 0.803290i | \(0.703081\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −12.3909 | −0.982665 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.79148 | −0.298811 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 20.3834 | 1.59655 | 0.798274 | − | 0.602294i | \(-0.205747\pi\) | ||||
0.798274 | + | 0.602294i | \(0.205747\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.52899 | 0.119032 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −15.8853 | −1.22924 | −0.614622 | − | 0.788822i | \(-0.710691\pi\) | ||||
−0.614622 | + | 0.788822i | \(0.710691\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.5087 | −0.962207 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.451789 | −0.0345492 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 16.4110 | 1.24771 | 0.623854 | − | 0.781541i | \(-0.285566\pi\) | ||||
0.623854 | + | 0.781541i | \(0.285566\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.96250 | 0.375130 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −12.3483 | −0.928151 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 20.4269 | 1.52678 | 0.763390 | − | 0.645938i | \(-0.223534\pi\) | ||||
0.763390 | + | 0.645938i | \(0.223534\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.3683 | −0.770666 | −0.385333 | − | 0.922778i | \(-0.625913\pi\) | ||||
−0.385333 | + | 0.922778i | \(0.625913\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.85173 | −0.506495 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.28279 | −0.0943122 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.46246 | 0.106945 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.27853 | 0.383957 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.95483 | 0.575591 | 0.287796 | − | 0.957692i | \(-0.407078\pi\) | ||||
0.287796 | + | 0.957692i | \(0.407078\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 23.9566 | 1.72443 | 0.862217 | − | 0.506539i | \(-0.169075\pi\) | ||||
0.862217 | + | 0.506539i | \(0.169075\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.581845 | −0.0416668 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.15127 | 0.367013 | 0.183506 | − | 0.983019i | \(-0.441255\pi\) | ||||
0.183506 | + | 0.983019i | \(0.441255\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.54311 | −0.109388 | −0.0546940 | − | 0.998503i | \(-0.517418\pi\) | ||||
−0.0546940 | + | 0.998503i | \(0.517418\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.02674 | 0.636697 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.74028 | −0.402889 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.55231 | −0.317947 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.450942 | 0.0313426 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.73864 | −0.466122 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.81178 | −0.606628 | −0.303314 | − | 0.952891i | \(-0.598093\pi\) | ||||
−0.303314 | + | 0.952891i | \(0.598093\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.35396 | −0.161291 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.99777 | 0.136247 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.37113 | 0.432501 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −13.8449 | −0.935555 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.556524 | −0.0374359 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −24.2050 | −1.62089 | −0.810445 | − | 0.585815i | \(-0.800774\pi\) | ||||
−0.810445 | + | 0.585815i | \(0.800774\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.590216 | −0.0393478 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.55162 | 0.235729 | 0.117865 | − | 0.993030i | \(-0.462395\pi\) | ||||
0.117865 | + | 0.993030i | \(0.462395\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.8164 | −1.24342 | −0.621711 | − | 0.783247i | \(-0.713562\pi\) | ||||
−0.621711 | + | 0.783247i | \(0.713562\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.38005 | −0.222391 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.1897 | 0.798575 | 0.399288 | − | 0.916826i | \(-0.369258\pi\) | ||||
0.399288 | + | 0.916826i | \(0.369258\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.44747 | 0.159655 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.70855 | −0.500724 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −30.6423 | −1.98208 | −0.991042 | − | 0.133553i | \(-0.957361\pi\) | ||||
−0.991042 | + | 0.133553i | \(0.957361\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.26294 | −0.467847 | −0.233924 | − | 0.972255i | \(-0.575157\pi\) | ||||
−0.233924 | + | 0.972255i | \(0.575157\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.28256 | −0.0822763 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.78145 | −0.177700 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.56433 | 0.163164 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 23.5671 | 1.49350 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 25.2813 | 1.59574 | 0.797871 | − | 0.602828i | \(-0.205959\pi\) | ||||
0.797871 | + | 0.602828i | \(0.205959\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.72601 | 0.422860 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.659078 | 0.0412731 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −26.5017 | −1.65313 | −0.826564 | − | 0.562842i | \(-0.809708\pi\) | ||||
−0.826564 | + | 0.562842i | \(0.809708\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.83578 | 0.176207 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.682723 | 0.0422595 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.5983 | −0.776845 | −0.388422 | − | 0.921481i | \(-0.626980\pi\) | ||||
−0.388422 | + | 0.921481i | \(0.626980\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.29301 | −0.202288 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.369129 | −0.0225903 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.45914 | 0.0889652 | 0.0444826 | − | 0.999010i | \(-0.485836\pi\) | ||||
0.0444826 | + | 0.999010i | \(0.485836\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.16205 | −0.313572 | −0.156786 | − | 0.987633i | \(-0.550113\pi\) | ||||
−0.156786 | + | 0.987633i | \(0.550113\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.28625 | 0.0778473 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −8.80336 | −0.530862 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.0110 | 0.841837 | 0.420918 | − | 0.907098i | \(-0.361708\pi\) | ||||
0.420918 | + | 0.907098i | \(0.361708\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.757753 | −0.0453655 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.3617 | 0.976059 | 0.488030 | − | 0.872827i | \(-0.337716\pi\) | ||||
0.488030 | + | 0.872827i | \(0.337716\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −18.5182 | −1.10079 | −0.550397 | − | 0.834903i | \(-0.685524\pi\) | ||||
−0.550397 | + | 0.834903i | \(0.685524\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.03687 | −0.179889 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.0635 | 0.594031 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.3696 | −0.962918 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.45771 | 0.319937 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 30.5239 | 1.78323 | 0.891613 | − | 0.452798i | \(-0.149574\pi\) | ||||
0.891613 | + | 0.452798i | \(0.149574\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.28167 | −0.191066 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −9.36400 | −0.543354 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.55952 | −0.148021 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.41636 | −0.254555 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −14.1433 | −0.812514 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.82092 | −0.104265 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.36035 | −0.191785 | −0.0958926 | − | 0.995392i | \(-0.530571\pi\) | ||||
−0.0958926 | + | 0.995392i | \(0.530571\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.76984 | 0.328235 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −26.0631 | −1.47791 | −0.738953 | − | 0.673757i | \(-0.764679\pi\) | ||||
−0.738953 | + | 0.673757i | \(0.764679\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −28.4960 | −1.61069 | −0.805345 | − | 0.592807i | \(-0.798020\pi\) | ||||
−0.805345 | + | 0.592807i | \(0.798020\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.0602249 | −0.00339329 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.26530 | −0.464225 | −0.232113 | − | 0.972689i | \(-0.574564\pi\) | ||||
−0.232113 | + | 0.972689i | \(0.574564\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.1831 | 0.570146 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 32.6754 | 1.82376 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.90472 | −0.161623 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.35004 | 0.185827 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −33.0085 | −1.82537 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.41047 | −0.298289 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.5162 | −0.687951 | −0.343976 | − | 0.938979i | \(-0.611774\pi\) | ||||
−0.343976 | + | 0.938979i | \(0.611774\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.337274 | −0.0184825 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.39895 | 0.131068 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.0461 | −1.09198 | −0.545990 | − | 0.837792i | \(-0.683846\pi\) | ||||
−0.545990 | + | 0.837792i | \(0.683846\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 13.8891 | 0.754351 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.3022 | −0.612051 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.4170 | 0.724448 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.03118 | 0.163193 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.748255 | −0.0401684 | −0.0200842 | − | 0.999798i | \(-0.506393\pi\) | ||||
−0.0200842 | + | 0.999798i | \(0.506393\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.16941 | 0.223183 | 0.111592 | − | 0.993754i | \(-0.464405\pi\) | ||||
0.111592 | + | 0.993754i | \(0.464405\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.56339 | 0.190200 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 28.9002 | 1.53820 | 0.769100 | − | 0.639128i | \(-0.220705\pi\) | ||||
0.769100 | + | 0.639128i | \(0.220705\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.625588 | −0.0332028 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.45698 | −0.0771118 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −22.5238 | −1.18876 | −0.594380 | − | 0.804185i | \(-0.702602\pi\) | ||||
−0.594380 | + | 0.804185i | \(0.702602\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.61576 | −0.295566 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −13.4446 | −0.705659 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.67943 | −0.192590 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.07935 | 0.160741 | 0.0803705 | − | 0.996765i | \(-0.474390\pi\) | ||||
0.0803705 | + | 0.996765i | \(0.474390\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.19691 | −0.0623085 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.27967 | 0.377942 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −23.8756 | −1.23623 | −0.618115 | − | 0.786088i | \(-0.712103\pi\) | ||||
−0.618115 | + | 0.786088i | \(0.712103\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −8.11786 | −0.419205 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.87510 | −0.199578 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.60479 | −0.185166 | −0.0925828 | − | 0.995705i | \(-0.529512\pi\) | ||||
−0.0925828 | + | 0.995705i | \(0.529512\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −17.3915 | −0.890996 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.63594 | 0.185788 | 0.0928939 | − | 0.995676i | \(-0.470388\pi\) | ||||
0.0928939 | + | 0.995676i | \(0.470388\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.898282 | −0.0457807 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.525261 | 0.0267005 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 21.6735 | 1.09889 | 0.549445 | − | 0.835530i | \(-0.314839\pi\) | ||||
0.549445 | + | 0.835530i | \(0.314839\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.89927 | 0.146622 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −14.1757 | −0.715069 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.04862 | −0.103077 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.59119 | 0.330802 | 0.165401 | − | 0.986226i | \(-0.447108\pi\) | ||||
0.165401 | + | 0.986226i | \(0.447108\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6.71343 | 0.336092 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.35340 | −0.217398 | −0.108699 | − | 0.994075i | \(-0.534668\pi\) | ||||
−0.108699 | + | 0.994075i | \(0.534668\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.30097 | 0.214246 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.39404 | −0.218342 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.03060 | −0.249358 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 31.8412 | 1.57445 | 0.787223 | − | 0.616668i | \(-0.211518\pi\) | ||||
0.787223 | + | 0.616668i | \(0.211518\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 29.7681 | 1.46835 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.25459 | 0.356975 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.26319 | 0.307448 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −19.8836 | −0.973703 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 29.8225 | 1.45692 | 0.728462 | − | 0.685087i | \(-0.240236\pi\) | ||||
0.728462 | + | 0.685087i | \(0.240236\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.93092 | −0.386530 | −0.193265 | − | 0.981147i | \(-0.561908\pi\) | ||||
−0.193265 | + | 0.981147i | \(0.561908\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.643496 | 0.0312879 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.79472 | −0.184071 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.02539 | 0.194802 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.28178 | −0.110165 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 24.9537 | 1.20198 | 0.600988 | − | 0.799258i | \(-0.294774\pi\) | ||||
0.600988 | + | 0.799258i | \(0.294774\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 23.1505 | 1.11254 | 0.556272 | − | 0.831000i | \(-0.312231\pi\) | ||||
0.556272 | + | 0.831000i | \(0.312231\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.58918 | 0.220035 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −13.3591 | −0.639054 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.9654 | −0.905167 | −0.452584 | − | 0.891722i | \(-0.649498\pi\) | ||||
−0.452584 | + | 0.891722i | \(0.649498\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.731308 | −0.0348242 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −21.6203 | −1.02721 | −0.513606 | − | 0.858026i | \(-0.671691\pi\) | ||||
−0.513606 | + | 0.858026i | \(0.671691\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.0980997 | −0.00465037 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −33.3429 | −1.57707 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.1299 | 0.714023 | 0.357011 | − | 0.934100i | \(-0.383796\pi\) | ||||
0.357011 | + | 0.934100i | \(0.383796\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −17.8524 | −0.840639 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11.3161 | 0.531678 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.341833 | 0.0160254 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.87882 | −0.368556 | −0.184278 | − | 0.982874i | \(-0.558995\pi\) | ||||
−0.184278 | + | 0.982874i | \(0.558995\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.03639 | −0.188402 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −33.2729 | −1.54967 | −0.774836 | − | 0.632162i | \(-0.782168\pi\) | ||||
−0.774836 | + | 0.632162i | \(0.782168\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −31.9493 | −1.48481 | −0.742405 | − | 0.669951i | \(-0.766315\pi\) | ||||
−0.742405 | + | 0.669951i | \(0.766315\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.09353 | −0.236207 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.03218 | −0.279136 | −0.139568 | − | 0.990213i | \(-0.544571\pi\) | ||||
−0.139568 | + | 0.990213i | \(0.544571\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.30320 | −0.244879 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −26.3783 | −1.21545 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.83451 | 0.360231 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 17.4852 | 0.802274 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.865810 | −0.0396427 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −18.1368 | −0.828693 | −0.414347 | − | 0.910119i | \(-0.635990\pi\) | ||||
−0.414347 | + | 0.910119i | \(0.635990\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.91435 | 0.0872869 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6.70084 | −0.304899 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.45044 | 0.0658612 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 23.3591 | 1.05850 | 0.529251 | − | 0.848465i | \(-0.322473\pi\) | ||||
0.529251 | + | 0.848465i | \(0.322473\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 36.0243 | 1.62908 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.28889 | 0.193555 | 0.0967775 | − | 0.995306i | \(-0.469146\pi\) | ||||
0.0967775 | + | 0.995306i | \(0.469146\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.38948 | 0.197692 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.106838 | 0.00480199 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.38295 | 0.0620338 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.0079 | 0.537549 | 0.268775 | − | 0.963203i | \(-0.413381\pi\) | ||||
0.268775 | + | 0.963203i | \(0.413381\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −28.0748 | −1.25429 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 22.0435 | 0.982872 | 0.491436 | − | 0.870914i | \(-0.336472\pi\) | ||||
0.491436 | + | 0.870914i | \(0.336472\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.75873 | −0.167261 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −22.1071 | −0.981811 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −11.9642 | −0.530302 | −0.265151 | − | 0.964207i | \(-0.585422\pi\) | ||||
−0.265151 | + | 0.964207i | \(0.585422\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.13390 | 0.359822 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 18.5987 | 0.821153 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.53339 | 0.0675693 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.59805 | 0.422122 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 29.0039 | 1.27313 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.47217 | −0.239740 | −0.119870 | − | 0.992790i | \(-0.538248\pi\) | ||||
−0.119870 | + | 0.992790i | \(0.538248\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 31.1363 | 1.36149 | 0.680747 | − | 0.732519i | \(-0.261655\pi\) | ||||
0.680747 | + | 0.732519i | \(0.261655\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 8.77042 | 0.382773 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.87187 | −0.212222 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.66591 | −0.420257 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.862827 | −0.0374435 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.79359 | 0.294263 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.68380 | 0.375434 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 36.1013 | 1.55789 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −10.9078 | −0.469832 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.0578 | −0.647387 | −0.323694 | − | 0.946162i | \(-0.604925\pi\) | ||||
−0.323694 | + | 0.946162i | \(0.604925\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −18.3242 | −0.786368 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.77234 | −0.375766 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.00000 | 0.0427569 | ||||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.478761 | −0.0204330 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −20.2257 | −0.861642 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.52877 | 0.192583 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.26712 | −0.0962338 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 23.5488 | 0.997796 | 0.498898 | − | 0.866661i | \(-0.333738\pi\) | ||||
0.498898 | + | 0.866661i | \(0.333738\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.98136 | −0.126098 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.58466 | 0.109124 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 29.0653 | 1.22496 | 0.612478 | − | 0.790488i | \(-0.290173\pi\) | ||||
0.612478 | + | 0.790488i | \(0.290173\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.69116 | 0.155288 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 9.71364 | 0.407934 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −0.227367 | −0.00953174 | −0.00476587 | − | 0.999989i | \(-0.501517\pi\) | ||||
−0.00476587 | + | 0.999989i | \(0.501517\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.874566 | −0.0365994 | −0.0182997 | − | 0.999833i | \(-0.505825\pi\) | ||||
−0.0182997 | + | 0.999833i | \(0.505825\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 14.0589 | 0.587319 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −17.4524 | −0.727814 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −29.2997 | −1.21976 | −0.609882 | − | 0.792492i | \(-0.708783\pi\) | ||||
−0.609882 | + | 0.792492i | \(0.708783\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 42.3395 | 1.75957 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −13.8457 | −0.574415 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.9140 | −0.534842 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.0406561 | −0.00168092 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 10.9789 | 0.453149 | 0.226574 | − | 0.973994i | \(-0.427247\pi\) | ||||
0.226574 | + | 0.973994i | \(0.427247\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 22.4484 | 0.924971 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.10404 | 0.374490 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −42.7926 | −1.75728 | −0.878641 | − | 0.477483i | \(-0.841549\pi\) | ||||
−0.878641 | + | 0.477483i | \(0.841549\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.387208 | −0.0158740 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.72720 | −0.111617 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.841737 | −0.0343925 | −0.0171962 | − | 0.999852i | \(-0.505474\pi\) | ||||
−0.0171962 | + | 0.999852i | \(0.505474\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.7479 | −0.805536 | −0.402768 | − | 0.915302i | \(-0.631952\pi\) | ||||
−0.402768 | + | 0.915302i | \(0.631952\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.630738 | 0.0256857 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.57304 | −0.145265 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.928802 | 0.0376989 | 0.0188495 | − | 0.999822i | \(-0.494000\pi\) | ||||
0.0188495 | + | 0.999822i | \(0.494000\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −10.1450 | −0.411098 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.65245 | −0.147762 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20.1162 | 0.812485 | 0.406242 | − | 0.913765i | \(-0.366839\pi\) | ||||
0.406242 | + | 0.913765i | \(0.366839\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8.04548 | −0.324425 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.2513 | −0.533479 | −0.266739 | − | 0.963769i | \(-0.585946\pi\) | ||||
−0.266739 | + | 0.963769i | \(0.585946\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 29.2870 | 1.17714 | 0.588572 | − | 0.808445i | \(-0.299690\pi\) | ||||
0.588572 | + | 0.808445i | \(0.299690\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −18.5638 | −0.744941 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.216863 | 0.00868844 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.7396 | 0.869583 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −11.9095 | −0.475619 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.16846 | −0.0864621 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 46.5766 | 1.85418 | 0.927092 | − | 0.374834i | \(-0.122300\pi\) | ||||
0.927092 | + | 0.374834i | \(0.122300\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −15.5734 | −0.618987 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.62197 | −0.183417 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.15087 | 0.164463 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.164482 | −0.00650679 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.11165 | −0.201898 | −0.100949 | − | 0.994892i | \(-0.532188\pi\) | ||||
−0.100949 | + | 0.994892i | \(0.532188\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.32994 | 0.170756 | 0.0853781 | − | 0.996349i | \(-0.472790\pi\) | ||||
0.0853781 | + | 0.996349i | \(0.472790\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.53074 | 0.139023 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.0401 | 0.473343 | 0.236672 | − | 0.971590i | \(-0.423943\pi\) | ||||
0.236672 | + | 0.971590i | \(0.423943\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12.8695 | −0.505171 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11.2600 | 0.441313 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 39.4366 | 1.54327 | 0.771636 | − | 0.636064i | \(-0.219439\pi\) | ||||
0.771636 | + | 0.636064i | \(0.219439\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.76733 | −0.147202 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.967408 | −0.0377422 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −43.8625 | −1.70864 | −0.854320 | − | 0.519748i | \(-0.826026\pi\) | ||||
−0.854320 | + | 0.519748i | \(0.826026\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.18941 | −0.201845 | −0.100922 | − | 0.994894i | \(-0.532179\pi\) | ||||
−0.100922 | + | 0.994894i | \(0.532179\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.983568 | −0.0381986 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.78416 | 0.0691868 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 20.1877 | 0.781672 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −42.7785 | −1.65391 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.14094 | −0.275673 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 37.7606 | 1.45557 | 0.727783 | − | 0.685808i | \(-0.240551\pi\) | ||||
0.727783 | + | 0.685808i | \(0.240551\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 24.2973 | 0.935205 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −36.6368 | −1.40806 | −0.704032 | − | 0.710168i | \(-0.748619\pi\) | ||||
−0.704032 | + | 0.710168i | \(0.748619\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.20640 | −0.123050 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.27692 | 0.240532 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −31.5096 | −1.20568 | −0.602841 | − | 0.797861i | \(-0.705965\pi\) | ||||
−0.602841 | + | 0.797861i | \(0.705965\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.91116 | 0.302270 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −33.2549 | −1.26876 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.91430 | 0.187220 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.9407 | −0.720540 | −0.360270 | − | 0.932848i | \(-0.617315\pi\) | ||||
−0.360270 | + | 0.932848i | \(0.617315\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.236179 | −0.00897171 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.28426 | −0.200443 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.69537 | −0.291483 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 21.5434 | 0.814846 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 42.8730 | 1.61929 | 0.809646 | − | 0.586919i | \(-0.199659\pi\) | ||||
0.809646 | + | 0.586919i | \(0.199659\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.99174 | 0.376846 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.32551 | 0.162908 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.30921 | 0.312500 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 35.4811 | 1.33252 | 0.666260 | − | 0.745719i | \(-0.267894\pi\) | ||||
0.666260 | + | 0.745719i | \(0.267894\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.538630 | −0.0202002 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −22.4063 | −0.839124 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.606404 | −0.0226782 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −54.1553 | −2.02247 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 24.4790 | 0.912913 | 0.456456 | − | 0.889746i | \(-0.349118\pi\) | ||||
0.456456 | + | 0.889746i | \(0.349118\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.38978 | −0.126242 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −12.8361 | −0.477379 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −26.4228 | −0.981317 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.7796 | 1.06737 | 0.533687 | − | 0.845682i | \(-0.320806\pi\) | ||||
0.533687 | + | 0.845682i | \(0.320806\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 25.7990 | 0.955517 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.37710 | 0.124906 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23.0494 | 0.851350 | 0.425675 | − | 0.904876i | \(-0.360037\pi\) | ||||
0.425675 | + | 0.904876i | \(0.360037\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4.91577 | −0.181321 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9.40776 | 0.346539 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.02906 | 0.332139 | 0.166070 | − | 0.986114i | \(-0.446892\pi\) | ||||
0.166070 | + | 0.986114i | \(0.446892\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.53205 | 0.166489 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 47.5028 | 1.74271 | 0.871355 | − | 0.490653i | \(-0.163242\pi\) | ||||
0.871355 | + | 0.490653i | \(0.163242\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.86121 | −0.324650 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.64674 | 0.0602510 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −19.1968 | −0.701434 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.5388 | 0.749473 | 0.374737 | − | 0.927131i | \(-0.377733\pi\) | ||||
0.374737 | + | 0.927131i | \(0.377733\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 44.6807 | 1.62825 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.00737 | 0.109450 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 36.3077 | 1.31962 | 0.659812 | − | 0.751430i | \(-0.270636\pi\) | ||||
0.659812 | + | 0.751430i | \(0.270636\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 11.8871 | 0.431476 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 23.0597 | 0.835915 | 0.417957 | − | 0.908467i | \(-0.362746\pi\) | ||||
0.417957 | + | 0.908467i | \(0.362746\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 19.3925 | 0.702055 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.0460527 | 0.00166504 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.89737 | 0.176834 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.40403 | 0.158813 | 0.0794066 | − | 0.996842i | \(-0.474697\pi\) | ||||
0.0794066 | + | 0.996842i | \(0.474697\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −46.8375 | −1.68681 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −25.6259 | −0.921699 | −0.460849 | − | 0.887478i | \(-0.652455\pi\) | ||||
−0.460849 | + | 0.887478i | \(0.652455\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 29.3266 | 1.05344 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.01178 | 0.179797 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 35.4584 | 1.27043 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.45332 | −0.0877867 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −28.1055 | −1.00441 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.01029 | −0.250208 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −46.4038 | −1.65412 | −0.827059 | − | 0.562115i | \(-0.809988\pi\) | ||||
−0.827059 | + | 0.562115i | \(0.809988\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −22.2655 | −0.792673 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.15982 | −0.290130 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.71742 | 0.0964985 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.81988 | −0.206410 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −33.6692 | −1.19262 | −0.596312 | − | 0.802753i | \(-0.703368\pi\) | ||||
−0.596312 | + | 0.802753i | \(0.703368\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.13727 | 0.146366 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.0257927 | −0.000911340 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −14.4293 | −0.509200 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.78082 | −0.0627655 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.57879 | 0.0907778 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 32.2939 | 1.13539 | 0.567696 | − | 0.823238i | \(-0.307835\pi\) | ||||
0.567696 | + | 0.823238i | \(0.307835\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −27.4278 | −0.963119 | −0.481559 | − | 0.876413i | \(-0.659929\pi\) | ||||
−0.481559 | + | 0.876413i | \(0.659929\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −9.12310 | −0.319961 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9.57382 | 0.335356 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −15.5609 | −0.544405 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.0898759 | 0.00314052 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −17.5646 | −0.613008 | −0.306504 | − | 0.951869i | \(-0.599159\pi\) | ||||
−0.306504 | + | 0.951869i | \(0.599159\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.94705 | 0.277017 | 0.138508 | − | 0.990361i | \(-0.455769\pi\) | ||||
0.138508 | + | 0.990361i | \(0.455769\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −15.5585 | −0.541678 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.16367 | 0.179558 | 0.0897792 | − | 0.995962i | \(-0.471384\pi\) | ||||
0.0897792 | + | 0.995962i | \(0.471384\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.0606 | −0.696734 | −0.348367 | − | 0.937358i | \(-0.613264\pi\) | ||||
−0.348367 | + | 0.937358i | \(0.613264\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 24.7621 | 0.858989 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.70185 | −0.162909 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.46115 | −0.258204 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 31.1943 | 1.07823 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −39.3019 | −1.35685 | −0.678426 | − | 0.734669i | \(-0.737338\pi\) | ||||
−0.678426 | + | 0.734669i | \(0.737338\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.56409 | 0.0539343 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 28.9168 | 0.995946 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5.87518 | −0.202112 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.89870 | 0.271403 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −32.7280 | −1.12322 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.97300 | −0.341870 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 41.2623 | 1.41280 | 0.706398 | − | 0.707815i | \(-0.250319\pi\) | ||||
0.706398 | + | 0.707815i | \(0.250319\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.212200 | −0.00725708 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.93880 | 0.168706 | 0.0843532 | − | 0.996436i | \(-0.473118\pi\) | ||||
0.0843532 | + | 0.996436i | \(0.473118\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 38.1044 | 1.30011 | 0.650053 | − | 0.759889i | \(-0.274747\pi\) | ||||
0.650053 | + | 0.759889i | \(0.274747\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 17.7857 | 0.606134 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.71273 | 0.0583019 | 0.0291510 | − | 0.999575i | \(-0.490720\pi\) | ||||
0.0291510 | + | 0.999575i | \(0.490720\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.70808 | 0.262082 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −28.9307 | −0.982537 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.03393 | −0.272532 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.58004 | −0.121305 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.381355 | 0.0129069 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.76924 | 0.161230 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19.2114 | 0.648724 | 0.324362 | − | 0.945933i | \(-0.394850\pi\) | ||||
0.324362 | + | 0.945933i | \(0.394850\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 53.9462 | 1.81956 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.0458679 | 0.00154533 | 0.000772664 | − | 1.00000i | \(-0.499754\pi\) | ||||
0.000772664 | 1.00000i | \(0.499754\pi\) | ||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −42.1763 | −1.41935 | −0.709674 | − | 0.704531i | \(-0.751158\pi\) | ||||
−0.709674 | + | 0.704531i | \(0.751158\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5.79983 | −0.194959 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −36.1371 | −1.21337 | −0.606683 | − | 0.794944i | \(-0.707500\pi\) | ||||
−0.606683 | + | 0.794944i | \(0.707500\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.2175 | 0.342685 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −17.2318 | −0.577286 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −19.0636 | −0.637938 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.59428 | 0.320701 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.52355 | −0.151037 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −33.9230 | −1.13140 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.56661 | −0.185451 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7.80520 | −0.259741 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.86985 | −0.161879 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21.2700 | 0.706259 | 0.353129 | − | 0.935574i | \(-0.385118\pi\) | ||||
0.353129 | + | 0.935574i | \(0.385118\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.988258 | −0.0327785 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10.2529 | 0.339694 | 0.169847 | − | 0.985470i | \(-0.445673\pi\) | ||||
0.169847 | + | 0.985470i | \(0.445673\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 24.5619 | 0.812880 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.21818 | −0.106390 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.32821 | 0.275022 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 39.3681 | 1.29864 | 0.649318 | − | 0.760517i | \(-0.275055\pi\) | ||||
0.649318 | + | 0.760517i | \(0.275055\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.93888 | −0.195693 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.933589 | 0.0307295 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 13.0532 | 0.429187 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.403164 | 0.0132416 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 48.6956 | 1.59765 | 0.798826 | − | 0.601562i | \(-0.205455\pi\) | ||||
0.798826 | + | 0.601562i | \(0.205455\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 21.6650 | 0.710042 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −46.0625 | −1.50802 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.686898 | 0.0224640 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12.4806 | −0.407723 | −0.203862 | − | 0.979000i | \(-0.565349\pi\) | ||||
−0.203862 | + | 0.979000i | \(0.565349\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −50.3621 | −1.64351 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −44.4531 | −1.44913 | −0.724565 | − | 0.689207i | \(-0.757959\pi\) | ||||
−0.724565 | + | 0.689207i | \(0.757959\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −35.3919 | −1.15252 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.47927 | 0.0806505 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.49160 | 0.243444 | 0.121722 | − | 0.992564i | \(-0.461158\pi\) | ||||
0.121722 | + | 0.992564i | \(0.461158\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.49096 | 0.178244 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −14.6076 | −0.473684 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −14.6341 | −0.474045 | −0.237023 | − | 0.971504i | \(-0.576172\pi\) | ||||
−0.237023 | + | 0.971504i | \(0.576172\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.73629 | 0.120903 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 17.9971 | 0.581762 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −17.4887 | −0.564741 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.65114 | 0.214553 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.28317 | 0.0735743 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 11.2521 | 0.362219 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.24602 | −0.0400692 | −0.0200346 | − | 0.999799i | \(-0.506378\pi\) | ||||
−0.0200346 | + | 0.999799i | \(0.506378\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.13362 | −0.164916 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15.4693 | −0.496434 | −0.248217 | − | 0.968704i | \(-0.579845\pi\) | ||||
−0.248217 | + | 0.968704i | \(0.579845\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.6816 | 0.374494 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.92066 | 0.189613 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 29.2177 | 0.934757 | 0.467379 | − | 0.884057i | \(-0.345199\pi\) | ||||
0.467379 | + | 0.884057i | \(0.345199\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.384710 | −0.0122954 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.30645 | −0.0736393 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.39930 | 0.0765259 | 0.0382629 | − | 0.999268i | \(-0.487818\pi\) | ||||
0.0382629 | + | 0.999268i | \(0.487818\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.41949 | 0.0770913 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −9.56214 | −0.304366 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 15.5317 | 0.493878 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −51.4773 | −1.63523 | −0.817614 | − | 0.575766i | \(-0.804704\pi\) | ||||
−0.817614 | + | 0.575766i | \(0.804704\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −22.1203 | −0.701968 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.724779 | −0.0229771 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −41.2171 | −1.30536 | −0.652680 | − | 0.757634i | \(-0.726355\pi\) | ||||
−0.652680 | + | 0.757634i | \(0.726355\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 13.8845 | 0.439286 |
(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 | 8752.2.a.s.1.13 | 18 | ||
4.3 | odd | 2 | 547.2.a.b.1.1 | ✓ | 18 | ||
12.11 | even | 2 | 4923.2.a.l.1.18 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
547.2.a.b.1.1 | ✓ | 18 | 4.3 | odd | 2 | ||
4923.2.a.l.1.18 | 18 | 12.11 | even | 2 | |||
8752.2.a.s.1.13 | 18 | 1.1 | even | 1 | trivial |