Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4923,2,Mod(1,4923)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4923, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4923.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4923 = 3^{2} \cdot 547 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4923.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: | \(39.3103529151\) |
Analytic rank: | \(0\) |
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 | 1.18 | ||
Root | \(2.72204\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4923.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.72204 | 1.92478 | 0.962388 | − | 0.271679i | \(-0.0875790\pi\) | ||||
0.962388 | + | 0.271679i | \(0.0875790\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 5.40952 | 2.70476 | ||||||||
\(5\) | −0.469688 | −0.210051 | −0.105025 | − | 0.994470i | \(-0.533492\pi\) | ||||
−0.105025 | + | 0.994470i | \(0.533492\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.03831 | 0.392445 | 0.196222 | − | 0.980559i | \(-0.437133\pi\) | ||||
0.196222 | + | 0.980559i | \(0.437133\pi\) | |||||||
\(8\) | 9.28087 | 3.28128 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.27851 | −0.404301 | ||||||||
\(11\) | 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 | \(0.530989\pi\) | |||||||
\(14\) | 2.82633 | 0.755368 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 14.4439 | 3.61097 | ||||||||
\(17\) | −0.793975 | −0.192567 | −0.0962837 | − | 0.995354i | \(-0.530696\pi\) | ||||
−0.0962837 | + | 0.995354i | \(0.530696\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.65845 | 0.839306 | 0.419653 | − | 0.907685i | \(-0.362152\pi\) | ||||
0.419653 | + | 0.907685i | \(0.362152\pi\) | |||||||
\(20\) | −2.54079 | −0.568138 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.01384 | 1.06895 | ||||||||
\(23\) | 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 | ||||||||
\(26\) | −1.90797 | −0.374184 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 5.61677 | 1.06147 | ||||||||
\(29\) | −5.52848 | −1.02661 | −0.513307 | − | 0.858205i | \(-0.671580\pi\) | ||||
−0.513307 | + | 0.858205i | \(0.671580\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.13605 | 1.10207 | 0.551034 | − | 0.834483i | \(-0.314234\pi\) | ||||
0.551034 | + | 0.834483i | \(0.314234\pi\) | |||||||
\(32\) | 20.7552 | 3.66903 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.16124 | −0.370649 | ||||||||
\(35\) | −0.487683 | −0.0824334 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.73114 | −0.448997 | −0.224498 | − | 0.974474i | \(-0.572074\pi\) | ||||
−0.224498 | + | 0.974474i | \(0.572074\pi\) | |||||||
\(38\) | 9.95846 | 1.61547 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.35911 | −0.689237 | ||||||||
\(41\) | 9.69220 | 1.51367 | 0.756833 | − | 0.653608i | \(-0.226745\pi\) | ||||
0.756833 | + | 0.653608i | \(0.226745\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.25340 | −0.648638 | −0.324319 | − | 0.945948i | \(-0.605135\pi\) | ||||
−0.324319 | + | 0.945948i | \(0.605135\pi\) | |||||||
\(44\) | 9.96402 | 1.50213 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 9.93978 | 1.46554 | ||||||||
\(47\) | 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 | ||||||||
\(50\) | −13.0097 | −1.83985 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.79172 | −0.525817 | ||||||||
\(53\) | 7.01107 | 0.963044 | 0.481522 | − | 0.876434i | \(-0.340084\pi\) | ||||
0.481522 | + | 0.876434i | \(0.340084\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.865138 | −0.116655 | ||||||||
\(56\) | 9.63643 | 1.28772 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −15.0488 | −1.97600 | ||||||||
\(59\) | −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 | \(0.579836\pi\) | |||||||
\(62\) | 16.7026 | 2.12123 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 27.6087 | 3.45109 | ||||||||
\(65\) | 0.329220 | 0.0408348 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.10753 | −0.623984 | −0.311992 | − | 0.950085i | \(-0.600996\pi\) | ||||
−0.311992 | + | 0.950085i | \(0.600996\pi\) | |||||||
\(68\) | −4.29503 | −0.520849 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.32749 | −0.158666 | ||||||||
\(71\) | −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 | \(0.651591\pi\) | |||||||
\(74\) | −7.43429 | −0.864218 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 19.7905 | 2.27012 | ||||||||
\(77\) | 1.91251 | 0.217950 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.36166 | 0.490726 | 0.245363 | − | 0.969431i | \(-0.421093\pi\) | ||||
0.245363 | + | 0.969431i | \(0.421093\pi\) | |||||||
\(80\) | −6.78412 | −0.758488 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 26.3826 | 2.91347 | ||||||||
\(83\) | 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 | ||||||||
\(86\) | −11.5779 | −1.24848 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 17.0948 | 1.82231 | ||||||||
\(89\) | 0.208861 | 0.0221393 | 0.0110696 | − | 0.999939i | \(-0.496476\pi\) | ||||
0.0110696 | + | 0.999939i | \(0.496476\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.727788 | −0.0762929 | ||||||||
\(92\) | 19.7533 | 2.05943 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 14.1841 | 1.46298 | ||||||||
\(95\) | −1.71833 | −0.176297 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.08809 | 0.313549 | 0.156774 | − | 0.987634i | \(-0.449890\pi\) | ||||
0.156774 | + | 0.987634i | \(0.449890\pi\) | |||||||
\(98\) | −16.1197 | −1.62834 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −25.8542 | −2.58542 | ||||||||
\(101\) | 8.00261 | 0.796290 | 0.398145 | − | 0.917323i | \(-0.369654\pi\) | ||||
0.398145 | + | 0.917323i | \(0.369654\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.26470 | −0.321681 | −0.160840 | − | 0.986980i | \(-0.551420\pi\) | ||||
−0.160840 | + | 0.986980i | \(0.551420\pi\) | |||||||
\(104\) | −6.50528 | −0.637895 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 19.0844 | 1.85364 | ||||||||
\(107\) | 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 | \(0.852442\pi\) | |||||||
\(110\) | −2.35494 | −0.224535 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 14.9973 | 1.41711 | ||||||||
\(113\) | −7.85874 | −0.739288 | −0.369644 | − | 0.929173i | \(-0.620520\pi\) | ||||
−0.369644 | + | 0.929173i | \(0.620520\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.71511 | −0.159935 | ||||||||
\(116\) | −29.9064 | −2.77674 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −19.0187 | −1.75081 | ||||||||
\(119\) | −0.824394 | −0.0755720 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.60726 | −0.691569 | ||||||||
\(122\) | −10.5530 | −0.955422 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 33.1931 | 2.98083 | ||||||||
\(125\) | 4.59326 | 0.410834 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.84052 | 0.873205 | 0.436602 | − | 0.899655i | \(-0.356182\pi\) | ||||
0.436602 | + | 0.899655i | \(0.356182\pi\) | |||||||
\(128\) | 33.6417 | 2.97354 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.896152 | 0.0785978 | ||||||||
\(131\) | −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 | ||||||||
\(134\) | −13.9029 | −1.20103 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7.36878 | −0.631868 | ||||||||
\(137\) | −16.8434 | −1.43903 | −0.719516 | − | 0.694476i | \(-0.755636\pi\) | ||||
−0.719516 | + | 0.694476i | \(0.755636\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.2506 | 0.954260 | 0.477130 | − | 0.878833i | \(-0.341677\pi\) | ||||
0.477130 | + | 0.878833i | \(0.341677\pi\) | |||||||
\(140\) | −2.63813 | −0.222963 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.62555 | −0.304249 | ||||||||
\(143\) | −1.29108 | −0.107965 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.59666 | 0.215641 | ||||||||
\(146\) | −21.3239 | −1.76478 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −14.7742 | −1.21443 | ||||||||
\(149\) | 18.8662 | 1.54558 | 0.772788 | − | 0.634664i | \(-0.218862\pi\) | ||||
0.772788 | + | 0.634664i | \(0.218862\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.40292 | −0.521062 | −0.260531 | − | 0.965465i | \(-0.583898\pi\) | ||||
−0.260531 | + | 0.965465i | \(0.583898\pi\) | |||||||
\(152\) | 33.9536 | 2.75400 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 5.20593 | 0.419506 | ||||||||
\(155\) | −2.88203 | −0.231490 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.9254 | −1.19118 | −0.595589 | − | 0.803290i | \(-0.703081\pi\) | ||||
−0.595589 | + | 0.803290i | \(0.703081\pi\) | |||||||
\(158\) | 11.8726 | 0.944537 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −9.74845 | −0.770683 | ||||||||
\(161\) | 3.79148 | 0.298811 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −20.3834 | −1.59655 | −0.798274 | − | 0.602294i | \(-0.794253\pi\) | ||||
−0.798274 | + | 0.602294i | \(0.794253\pi\) | |||||||
\(164\) | 52.4302 | 4.09411 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 36.2979 | 2.81726 | ||||||||
\(167\) | −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 | ||||||||
\(170\) | 1.01511 | 0.0778551 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −23.0089 | −1.75441 | ||||||||
\(173\) | −16.4110 | −1.24771 | −0.623854 | − | 0.781541i | \(-0.714434\pi\) | ||||
−0.623854 | + | 0.781541i | \(0.714434\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.96250 | −0.375130 | ||||||||
\(176\) | 26.6048 | 2.00541 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.568530 | 0.0426131 | ||||||||
\(179\) | 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 | \(0.625913\pi\) | |||||||
\(182\) | −1.98107 | −0.146847 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 33.8899 | 2.49840 | ||||||||
\(185\) | 1.28279 | 0.0943122 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.46246 | −0.106945 | ||||||||
\(188\) | 28.1881 | 2.05583 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.67737 | −0.339332 | ||||||||
\(191\) | 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 | \(0.169075\pi\) | |||||||
\(194\) | 8.40593 | 0.603511 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −32.0347 | −2.28819 | ||||||||
\(197\) | −5.15127 | −0.367013 | −0.183506 | − | 0.983019i | \(-0.558745\pi\) | ||||
−0.183506 | + | 0.983019i | \(0.558745\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.54311 | 0.109388 | 0.0546940 | − | 0.998503i | \(-0.482582\pi\) | ||||
0.0546940 | + | 0.998503i | \(0.482582\pi\) | |||||||
\(200\) | −44.3569 | −3.13651 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 21.7835 | 1.53268 | ||||||||
\(203\) | −5.74028 | −0.402889 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.55231 | −0.317947 | ||||||||
\(206\) | −8.88666 | −0.619163 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −10.1242 | −0.701988 | ||||||||
\(209\) | 6.73864 | 0.466122 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.81178 | 0.606628 | 0.303314 | − | 0.952891i | \(-0.401907\pi\) | ||||
0.303314 | + | 0.952891i | \(0.401907\pi\) | |||||||
\(212\) | 37.9265 | 2.60480 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 50.3264 | 3.44024 | ||||||||
\(215\) | 1.99777 | 0.136247 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.37113 | 0.432501 | ||||||||
\(218\) | −50.8395 | −3.44328 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −4.67998 | −0.315524 | ||||||||
\(221\) | 0.556524 | 0.0374359 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 24.2050 | 1.62089 | 0.810445 | − | 0.585815i | \(-0.199226\pi\) | ||||
0.810445 | + | 0.585815i | \(0.199226\pi\) | |||||||
\(224\) | 21.5503 | 1.43989 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −21.3918 | −1.42296 | ||||||||
\(227\) | 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 | \(0.713562\pi\) | |||||||
\(230\) | −4.66860 | −0.307838 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −51.3091 | −3.36861 | ||||||||
\(233\) | −12.1897 | −0.798575 | −0.399288 | − | 0.916826i | \(-0.630742\pi\) | ||||
−0.399288 | + | 0.916826i | \(0.630742\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.44747 | −0.159655 | ||||||||
\(236\) | −37.7959 | −2.46030 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.24404 | −0.145459 | ||||||||
\(239\) | −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 | \(0.575157\pi\) | |||||||
\(242\) | −20.7073 | −1.33111 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −20.9720 | −1.34259 | ||||||||
\(245\) | 2.78145 | 0.177700 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.56433 | −0.163164 | ||||||||
\(248\) | 56.9479 | 3.61620 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 12.5031 | 0.790764 | ||||||||
\(251\) | 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 | ||||||||
\(254\) | 26.7863 | 1.68072 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 36.3569 | 2.27230 | ||||||||
\(257\) | 26.5017 | 1.65313 | 0.826564 | − | 0.562842i | \(-0.190292\pi\) | ||||
0.826564 | + | 0.562842i | \(0.190292\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.83578 | −0.176207 | ||||||||
\(260\) | 1.78093 | 0.110448 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −21.8333 | −1.34886 | ||||||||
\(263\) | −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 | ||||||||
\(266\) | 10.3400 | 0.633985 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −27.6293 | −1.68773 | ||||||||
\(269\) | −1.45914 | −0.0889652 | −0.0444826 | − | 0.999010i | \(-0.514164\pi\) | ||||
−0.0444826 | + | 0.999010i | \(0.514164\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.16205 | 0.313572 | 0.156786 | − | 0.987633i | \(-0.449887\pi\) | ||||
0.156786 | + | 0.987633i | \(0.449887\pi\) | |||||||
\(272\) | −11.4681 | −0.695355 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −45.8486 | −2.76981 | ||||||||
\(275\) | −8.80336 | −0.530862 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.0110 | 0.841837 | 0.420918 | − | 0.907098i | \(-0.361708\pi\) | ||||
0.420918 | + | 0.907098i | \(0.361708\pi\) | |||||||
\(278\) | 30.6245 | 1.83674 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −4.52612 | −0.270487 | ||||||||
\(281\) | −16.3617 | −0.976059 | −0.488030 | − | 0.872827i | \(-0.662284\pi\) | ||||
−0.488030 | + | 0.872827i | \(0.662284\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 18.5182 | 1.10079 | 0.550397 | − | 0.834903i | \(-0.314476\pi\) | ||||
0.550397 | + | 0.834903i | \(0.314476\pi\) | |||||||
\(284\) | −7.20506 | −0.427542 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.51437 | −0.207809 | ||||||||
\(287\) | 10.0635 | 0.594031 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.3696 | −0.962918 | ||||||||
\(290\) | 7.06823 | 0.415061 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −42.3770 | −2.47993 | ||||||||
\(293\) | −30.5239 | −1.78323 | −0.891613 | − | 0.452798i | \(-0.850426\pi\) | ||||
−0.891613 | + | 0.452798i | \(0.850426\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.28167 | 0.191066 | ||||||||
\(296\) | −25.3474 | −1.47329 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 51.3545 | 2.97489 | ||||||||
\(299\) | −2.55952 | −0.148021 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.41636 | −0.254555 | ||||||||
\(302\) | −17.4290 | −1.00293 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 52.8422 | 3.03071 | ||||||||
\(305\) | 1.82092 | 0.104265 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.36035 | 0.191785 | 0.0958926 | − | 0.995392i | \(-0.469429\pi\) | ||||
0.0958926 | + | 0.995392i | \(0.469429\pi\) | |||||||
\(308\) | 10.3458 | 0.589504 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −7.84501 | −0.445567 | ||||||||
\(311\) | −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 | \(0.798020\pi\) | |||||||
\(314\) | −40.6276 | −2.29275 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 23.5945 | 1.32730 | ||||||||
\(317\) | 8.26530 | 0.464225 | 0.232113 | − | 0.972689i | \(-0.425436\pi\) | ||||
0.232113 | + | 0.972689i | \(0.425436\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10.1831 | −0.570146 | ||||||||
\(320\) | −12.9675 | −0.724904 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 10.3206 | 0.575144 | ||||||||
\(323\) | −2.90472 | −0.161623 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.35004 | 0.185827 | ||||||||
\(326\) | −55.4844 | −3.07300 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 89.9520 | 4.96677 | ||||||||
\(329\) | 5.41047 | 0.298289 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.5162 | 0.687951 | 0.343976 | − | 0.938979i | \(-0.388226\pi\) | ||||
0.343976 | + | 0.938979i | \(0.388226\pi\) | |||||||
\(332\) | 72.1348 | 3.95891 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −43.2406 | −2.36602 | ||||||||
\(335\) | 2.39895 | 0.131068 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.0461 | −1.09198 | −0.545990 | − | 0.837792i | \(-0.683846\pi\) | ||||
−0.545990 | + | 0.837792i | \(0.683846\pi\) | |||||||
\(338\) | −34.0492 | −1.85203 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.01732 | 0.109405 | ||||||||
\(341\) | 11.3022 | 0.612051 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.4170 | −0.724448 | ||||||||
\(344\) | −39.4753 | −2.12836 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −44.6716 | −2.40156 | ||||||||
\(347\) | −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 | \(0.464405\pi\) | |||||||
\(350\) | −13.5081 | −0.722040 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 38.2298 | 2.03765 | ||||||||
\(353\) | −28.9002 | −1.53820 | −0.769100 | − | 0.639128i | \(-0.779295\pi\) | ||||
−0.769100 | + | 0.639128i | \(0.779295\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.625588 | 0.0332028 | ||||||||
\(356\) | 1.12984 | 0.0598814 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 55.6030 | 2.93871 | ||||||||
\(359\) | −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 | ||||||||
\(362\) | −28.2228 | −1.48336 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.93698 | −0.206354 | ||||||||
\(365\) | 3.67943 | 0.192590 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.07935 | −0.160741 | −0.0803705 | − | 0.996765i | \(-0.525610\pi\) | ||||
−0.0803705 | + | 0.996765i | \(0.525610\pi\) | |||||||
\(368\) | 52.7431 | 2.74943 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3.49180 | 0.181530 | ||||||||
\(371\) | 7.27967 | 0.377942 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −23.8756 | −1.23623 | −0.618115 | − | 0.786088i | \(-0.712103\pi\) | ||||
−0.618115 | + | 0.786088i | \(0.712103\pi\) | |||||||
\(374\) | −3.98087 | −0.205846 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 48.3611 | 2.49403 | ||||||||
\(377\) | 3.87510 | 0.199578 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.60479 | 0.185166 | 0.0925828 | − | 0.995705i | \(-0.470488\pi\) | ||||
0.0925828 | + | 0.995705i | \(0.470488\pi\) | |||||||
\(380\) | −9.29534 | −0.476841 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 21.6534 | 1.10788 | ||||||||
\(383\) | 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 | ||||||||
\(386\) | 65.2109 | 3.31915 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 16.7051 | 0.848074 | ||||||||
\(389\) | −21.6735 | −1.09889 | −0.549445 | − | 0.835530i | \(-0.685161\pi\) | ||||
−0.549445 | + | 0.835530i | \(0.685161\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.89927 | −0.146622 | ||||||||
\(392\) | −54.9605 | −2.77592 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −14.0220 | −0.706417 | ||||||||
\(395\) | −2.04862 | −0.103077 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.59119 | 0.330802 | 0.165401 | − | 0.986226i | \(-0.447108\pi\) | ||||
0.165401 | + | 0.986226i | \(0.447108\pi\) | |||||||
\(398\) | 4.20041 | 0.210547 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −69.0330 | −3.45165 | ||||||||
\(401\) | 4.35340 | 0.217398 | 0.108699 | − | 0.994075i | \(-0.465332\pi\) | ||||
0.108699 | + | 0.994075i | \(0.465332\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.30097 | −0.214246 | ||||||||
\(404\) | 43.2903 | 2.15377 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −15.6253 | −0.775471 | ||||||||
\(407\) | −5.03060 | −0.249358 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 31.8412 | 1.57445 | 0.787223 | − | 0.616668i | \(-0.211518\pi\) | ||||
0.787223 | + | 0.616668i | \(0.211518\pi\) | |||||||
\(410\) | −12.3916 | −0.611977 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −17.6605 | −0.870069 | ||||||||
\(413\) | −7.25459 | −0.356975 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.26319 | −0.307448 | ||||||||
\(416\) | −14.5480 | −0.713274 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 18.3429 | 0.897180 | ||||||||
\(419\) | 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 | \(0.561908\pi\) | |||||||
\(422\) | 23.9860 | 1.16762 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 65.0688 | 3.16002 | ||||||||
\(425\) | 3.79472 | 0.184071 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.02539 | −0.194802 | ||||||||
\(428\) | 100.014 | 4.83434 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5.43803 | 0.262245 | ||||||||
\(431\) | 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 | \(0.312231\pi\) | |||||||
\(434\) | 17.3425 | 0.832467 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −101.033 | −4.83862 | ||||||||
\(437\) | 13.3591 | 0.639054 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.9654 | 0.905167 | 0.452584 | − | 0.891722i | \(-0.350502\pi\) | ||||
0.452584 | + | 0.891722i | \(0.350502\pi\) | |||||||
\(440\) | −8.02923 | −0.382778 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.51488 | 0.0720557 | ||||||||
\(443\) | −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 | ||||||||
\(446\) | 65.8872 | 3.11985 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 28.6664 | 1.35436 | ||||||||
\(449\) | −15.1299 | −0.714023 | −0.357011 | − | 0.934100i | \(-0.616204\pi\) | ||||
−0.357011 | + | 0.934100i | \(0.616204\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 17.8524 | 0.840639 | ||||||||
\(452\) | −42.5121 | −1.99960 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 9.66767 | 0.453726 | ||||||||
\(455\) | 0.341833 | 0.0160254 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.87882 | −0.368556 | −0.184278 | − | 0.982874i | \(-0.558995\pi\) | ||||
−0.184278 | + | 0.982874i | \(0.558995\pi\) | |||||||
\(458\) | −51.2190 | −2.39331 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −9.27791 | −0.432585 | ||||||||
\(461\) | 33.2729 | 1.54967 | 0.774836 | − | 0.632162i | \(-0.217832\pi\) | ||||
0.774836 | + | 0.632162i | \(0.217832\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 31.9493 | 1.48481 | 0.742405 | − | 0.669951i | \(-0.233685\pi\) | ||||
0.742405 | + | 0.669951i | \(0.233685\pi\) | |||||||
\(464\) | −79.8528 | −3.70707 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −33.1810 | −1.53708 | ||||||||
\(467\) | −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 | ||||||||
\(470\) | −6.66211 | −0.307300 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −64.8446 | −2.98472 | ||||||||
\(473\) | −7.83451 | −0.360231 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −17.4852 | −0.802274 | ||||||||
\(476\) | −4.45958 | −0.204404 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −83.4096 | −3.81507 | ||||||||
\(479\) | −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 | ||||||||
\(482\) | −19.7700 | −0.900501 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −41.1516 | −1.87053 | ||||||||
\(485\) | −1.45044 | −0.0658612 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −23.3591 | −1.05850 | −0.529251 | − | 0.848465i | \(-0.677527\pi\) | ||||
−0.529251 | + | 0.848465i | \(0.677527\pi\) | |||||||
\(488\) | −35.9806 | −1.62877 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 7.57123 | 0.342033 | ||||||||
\(491\) | 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 | ||||||||
\(494\) | −6.98022 | −0.314055 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 88.6285 | 3.97954 | ||||||||
\(497\) | −1.38295 | −0.0620338 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.0079 | −0.537549 | −0.268775 | − | 0.963203i | \(-0.586619\pi\) | ||||
−0.268775 | + | 0.963203i | \(0.586619\pi\) | |||||||
\(500\) | 24.8474 | 1.11121 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 68.8169 | 3.07145 | ||||||||
\(503\) | 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 | ||||||||
\(506\) | 18.3085 | 0.813911 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 53.2325 | 2.36181 | ||||||||
\(509\) | 11.9642 | 0.530302 | 0.265151 | − | 0.964207i | \(-0.414578\pi\) | ||||
0.265151 | + | 0.964207i | \(0.414578\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.13390 | −0.359822 | ||||||||
\(512\) | 31.6816 | 1.40014 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 72.1387 | 3.18190 | ||||||||
\(515\) | 1.53339 | 0.0675693 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.59805 | 0.422122 | ||||||||
\(518\) | −7.71911 | −0.339158 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 3.05545 | 0.133990 | ||||||||
\(521\) | 5.47217 | 0.239740 | 0.119870 | − | 0.992790i | \(-0.461752\pi\) | ||||
0.119870 | + | 0.992790i | \(0.461752\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −31.1363 | −1.36149 | −0.680747 | − | 0.732519i | \(-0.738345\pi\) | ||||
−0.680747 | + | 0.732519i | \(0.738345\pi\) | |||||||
\(524\) | −43.3893 | −1.89547 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −34.2931 | −1.49525 | ||||||||
\(527\) | −4.87187 | −0.212222 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.66591 | −0.420257 | ||||||||
\(530\) | −8.96373 | −0.389360 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 20.5487 | 0.890897 | ||||||||
\(533\) | −6.79359 | −0.294263 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.68380 | −0.375434 | ||||||||
\(536\) | −47.4023 | −2.04747 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −3.97183 | −0.171238 | ||||||||
\(539\) | −10.9078 | −0.469832 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.0578 | −0.647387 | −0.323694 | − | 0.946162i | \(-0.604925\pi\) | ||||
−0.323694 | + | 0.946162i | \(0.604925\pi\) | |||||||
\(542\) | 14.0513 | 0.603556 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −16.4791 | −0.706535 | ||||||||
\(545\) | 8.77234 | 0.375766 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.00000 | −0.0427569 | ||||||||
\(548\) | −91.1150 | −3.89224 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −23.9631 | −1.02179 | ||||||||
\(551\) | −20.2257 | −0.861642 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.52877 | 0.192583 | ||||||||
\(554\) | 38.1384 | 1.62035 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 60.8602 | 2.58105 | ||||||||
\(557\) | −23.5488 | −0.997796 | −0.498898 | − | 0.866661i | \(-0.666262\pi\) | ||||
−0.498898 | + | 0.866661i | \(0.666262\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.98136 | 0.126098 | ||||||||
\(560\) | −7.04403 | −0.297665 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −44.5374 | −1.87869 | ||||||||
\(563\) | 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 | ||||||||
\(566\) | 50.4074 | 2.11878 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −12.3614 | −0.518673 | ||||||||
\(569\) | 0.227367 | 0.00953174 | 0.00476587 | − | 0.999989i | \(-0.498483\pi\) | ||||
0.00476587 | + | 0.999989i | \(0.498483\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.874566 | 0.0365994 | 0.0182997 | − | 0.999833i | \(-0.494175\pi\) | ||||
0.0182997 | + | 0.999833i | \(0.494175\pi\) | |||||||
\(572\) | −6.98412 | −0.292021 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 27.3933 | 1.14338 | ||||||||
\(575\) | −17.4524 | −0.727814 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −29.2997 | −1.21976 | −0.609882 | − | 0.792492i | \(-0.708783\pi\) | ||||
−0.609882 | + | 0.792492i | \(0.708783\pi\) | |||||||
\(578\) | −44.5588 | −1.85340 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 14.0467 | 0.583257 | ||||||||
\(581\) | 13.8457 | 0.574415 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.9140 | 0.534842 | ||||||||
\(584\) | −72.7042 | −3.00852 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −83.0875 | −3.43231 | ||||||||
\(587\) | 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 | ||||||||
\(590\) | 8.93285 | 0.367760 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −39.4483 | −1.62132 | ||||||||
\(593\) | 42.7926 | 1.75728 | 0.878641 | − | 0.477483i | \(-0.158451\pi\) | ||||
0.878641 | + | 0.477483i | \(0.158451\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.387208 | 0.0158740 | ||||||||
\(596\) | 102.057 | 4.18042 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −6.96713 | −0.284907 | ||||||||
\(599\) | −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 | \(0.631952\pi\) | |||||||
\(602\) | −12.0215 | −0.489960 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −34.6367 | −1.40935 | ||||||||
\(605\) | 3.57304 | 0.145265 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.928802 | −0.0376989 | −0.0188495 | − | 0.999822i | \(-0.506000\pi\) | ||||
−0.0188495 | + | 0.999822i | \(0.506000\pi\) | |||||||
\(608\) | 75.9317 | 3.07944 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.95661 | 0.200687 | ||||||||
\(611\) | −3.65245 | −0.147762 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20.1162 | 0.812485 | 0.406242 | − | 0.913765i | \(-0.366839\pi\) | ||||
0.406242 | + | 0.913765i | \(0.366839\pi\) | |||||||
\(614\) | 9.14702 | 0.369144 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 17.7497 | 0.715157 | ||||||||
\(617\) | 13.2513 | 0.533479 | 0.266739 | − | 0.963769i | \(-0.414054\pi\) | ||||
0.266739 | + | 0.963769i | \(0.414054\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −29.2870 | −1.17714 | −0.588572 | − | 0.808445i | \(-0.700310\pi\) | ||||
−0.588572 | + | 0.808445i | \(0.700310\pi\) | |||||||
\(620\) | −15.5904 | −0.626126 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −70.9450 | −2.84464 | ||||||||
\(623\) | 0.216863 | 0.00868844 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.7396 | 0.869583 | ||||||||
\(626\) | −77.5674 | −3.10022 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −80.7393 | −3.22185 | ||||||||
\(629\) | 2.16846 | 0.0864621 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −46.5766 | −1.85418 | −0.927092 | − | 0.374834i | \(-0.877700\pi\) | ||||
−0.927092 | + | 0.374834i | \(0.877700\pi\) | |||||||
\(632\) | 40.4800 | 1.61021 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 22.4985 | 0.893530 | ||||||||
\(635\) | −4.62197 | −0.183417 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.15087 | 0.164463 | ||||||||
\(638\) | −27.7189 | −1.09740 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −15.8011 | −0.624594 | ||||||||
\(641\) | 5.11165 | 0.201898 | 0.100949 | − | 0.994892i | \(-0.467812\pi\) | ||||
0.100949 | + | 0.994892i | \(0.467812\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.32994 | −0.170756 | −0.0853781 | − | 0.996349i | \(-0.527210\pi\) | ||||
−0.0853781 | + | 0.996349i | \(0.527210\pi\) | |||||||
\(644\) | 20.5101 | 0.808212 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7.90677 | −0.311088 | ||||||||
\(647\) | 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 | ||||||||
\(650\) | 9.11895 | 0.357675 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −110.264 | −4.31828 | ||||||||
\(653\) | −39.4366 | −1.54327 | −0.771636 | − | 0.636064i | \(-0.780561\pi\) | ||||
−0.771636 | + | 0.636064i | \(0.780561\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.76733 | 0.147202 | ||||||||
\(656\) | 139.993 | 5.46581 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 14.7275 | 0.574139 | ||||||||
\(659\) | −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 | \(0.532179\pi\) | |||||||
\(662\) | 34.0696 | 1.32415 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 123.758 | 4.80276 | ||||||||
\(665\) | −1.78416 | −0.0691868 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −20.1877 | −0.781672 | ||||||||
\(668\) | −85.9321 | −3.32481 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 6.53003 | 0.252277 | ||||||||
\(671\) | −7.14094 | −0.275673 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 37.7606 | 1.45557 | 0.727783 | − | 0.685808i | \(-0.240551\pi\) | ||||
0.727783 | + | 0.685808i | \(0.240551\pi\) | |||||||
\(674\) | −54.5663 | −2.10182 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −67.6661 | −2.60254 | ||||||||
\(677\) | 36.6368 | 1.40806 | 0.704032 | − | 0.710168i | \(-0.251381\pi\) | ||||
0.704032 | + | 0.710168i | \(0.251381\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.20640 | 0.123050 | ||||||||
\(680\) | 3.46103 | 0.132724 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 30.7652 | 1.17806 | ||||||||
\(683\) | −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 | ||||||||
\(686\) | −36.5216 | −1.39440 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −61.4357 | −2.34221 | ||||||||
\(689\) | −4.91430 | −0.187220 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.9407 | 0.720540 | 0.360270 | − | 0.932848i | \(-0.382685\pi\) | ||||
0.360270 | + | 0.932848i | \(0.382685\pi\) | |||||||
\(692\) | −88.7759 | −3.37475 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.03678 | −0.0773153 | ||||||||
\(695\) | −5.28426 | −0.200443 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.69537 | −0.291483 | ||||||||
\(698\) | 11.3493 | 0.429578 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −26.8447 | −1.01464 | ||||||||
\(701\) | −42.8730 | −1.61929 | −0.809646 | − | 0.586919i | \(-0.800341\pi\) | ||||
−0.809646 | + | 0.586919i | \(0.800341\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.99174 | −0.376846 | ||||||||
\(704\) | 50.8535 | 1.91662 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −78.6675 | −2.96069 | ||||||||
\(707\) | 8.30921 | 0.312500 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 35.4811 | 1.33252 | 0.666260 | − | 0.745719i | \(-0.267894\pi\) | ||||
0.666260 | + | 0.745719i | \(0.267894\pi\) | |||||||
\(710\) | 1.70288 | 0.0639079 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.93842 | 0.0726452 | ||||||||
\(713\) | 22.4063 | 0.839124 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.606404 | 0.0226782 | ||||||||
\(716\) | 110.500 | 4.12957 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −61.3107 | −2.28810 | ||||||||
\(719\) | 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 | ||||||||
\(722\) | −15.2863 | −0.568899 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −56.0873 | −2.08447 | ||||||||
\(725\) | 26.4228 | 0.981317 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −28.7796 | −1.06737 | −0.533687 | − | 0.845682i | \(-0.679194\pi\) | ||||
−0.533687 | + | 0.845682i | \(0.679194\pi\) | |||||||
\(728\) | −6.75450 | −0.250339 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 10.0156 | 0.370693 | ||||||||
\(731\) | 3.37710 | 0.124906 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23.0494 | 0.851350 | 0.425675 | − | 0.904876i | \(-0.360037\pi\) | ||||
0.425675 | + | 0.904876i | \(0.360037\pi\) | |||||||
\(734\) | −8.38213 | −0.309390 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 75.7893 | 2.79363 | ||||||||
\(737\) | −9.40776 | −0.346539 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.02906 | −0.332139 | −0.166070 | − | 0.986114i | \(-0.553108\pi\) | ||||
−0.166070 | + | 0.986114i | \(0.553108\pi\) | |||||||
\(740\) | 6.93925 | 0.255092 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 19.8156 | 0.727453 | ||||||||
\(743\) | 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 | ||||||||
\(746\) | −64.9903 | −2.37947 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −7.91118 | −0.289262 | ||||||||
\(749\) | 19.1968 | 0.701434 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.5388 | −0.749473 | −0.374737 | − | 0.927131i | \(-0.622267\pi\) | ||||
−0.374737 | + | 0.927131i | \(0.622267\pi\) | |||||||
\(752\) | 75.2647 | 2.74462 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 10.5482 | 0.384143 | ||||||||
\(755\) | 3.00737 | 0.109450 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 36.3077 | 1.31962 | 0.659812 | − | 0.751430i | \(-0.270636\pi\) | ||||
0.659812 | + | 0.751430i | \(0.270636\pi\) | |||||||
\(758\) | 9.81240 | 0.356402 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −15.9476 | −0.578480 | ||||||||
\(761\) | −23.0597 | −0.835915 | −0.417957 | − | 0.908467i | \(-0.637254\pi\) | ||||
−0.417957 | + | 0.908467i | \(0.637254\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −19.3925 | −0.702055 | ||||||||
\(764\) | 43.0318 | 1.55684 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9.89719 | 0.357600 | ||||||||
\(767\) | 4.89737 | 0.176834 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.40403 | 0.158813 | 0.0794066 | − | 0.996842i | \(-0.474697\pi\) | ||||
0.0794066 | + | 0.996842i | \(0.474697\pi\) | |||||||
\(770\) | −2.44516 | −0.0881176 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 129.594 | 4.66418 | ||||||||
\(773\) | 25.6259 | 0.921699 | 0.460849 | − | 0.887478i | \(-0.347545\pi\) | ||||
0.460849 | + | 0.887478i | \(0.347545\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −29.3266 | −1.05344 | ||||||||
\(776\) | 28.6602 | 1.02884 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −58.9962 | −2.11512 | ||||||||
\(779\) | 35.4584 | 1.27043 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.45332 | −0.0877867 | ||||||||
\(782\) | −7.89194 | −0.282215 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −85.5354 | −3.05484 | ||||||||
\(785\) | 7.01029 | 0.250208 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 46.4038 | 1.65412 | 0.827059 | − | 0.562115i | \(-0.190012\pi\) | ||||
0.827059 | + | 0.562115i | \(0.190012\pi\) | |||||||
\(788\) | −27.8659 | −0.992681 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −5.57644 | −0.198401 | ||||||||
\(791\) | −8.15982 | −0.290130 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.71742 | 0.0964985 | ||||||||
\(794\) | 17.9415 | 0.636720 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.34748 | 0.295868 | ||||||||
\(797\) | 33.6692 | 1.19262 | 0.596312 | − | 0.802753i | \(-0.296632\pi\) | ||||
0.596312 | + | 0.802753i | \(0.296632\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.13727 | −0.146366 | ||||||||
\(800\) | −99.1971 | −3.50715 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 11.8501 | 0.418443 | ||||||||
\(803\) | −14.4293 | −0.509200 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.78082 | −0.0627655 | ||||||||
\(806\) | −11.7074 | −0.412376 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 74.2712 | 2.61285 | ||||||||
\(809\) | −32.2939 | −1.13539 | −0.567696 | − | 0.823238i | \(-0.692165\pi\) | ||||
−0.567696 | + | 0.823238i | \(0.692165\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27.4278 | 0.963119 | 0.481559 | − | 0.876413i | \(-0.340071\pi\) | ||||
0.481559 | + | 0.876413i | \(0.340071\pi\) | |||||||
\(812\) | −31.0522 | −1.08972 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −13.6935 | −0.479957 | ||||||||
\(815\) | 9.57382 | 0.335356 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −15.5609 | −0.544405 | ||||||||
\(818\) | 86.6732 | 3.03046 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −24.6258 | −0.859971 | ||||||||
\(821\) | 17.5646 | 0.613008 | 0.306504 | − | 0.951869i | \(-0.400841\pi\) | ||||
0.306504 | + | 0.951869i | \(0.400841\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.94705 | −0.277017 | −0.138508 | − | 0.990361i | \(-0.544231\pi\) | ||||
−0.138508 | + | 0.990361i | \(0.544231\pi\) | |||||||
\(824\) | −30.2993 | −1.05552 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −19.7473 | −0.687097 | ||||||||
\(827\) | 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 | \(0.613264\pi\) | |||||||
\(830\) | −17.0487 | −0.591768 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −19.3519 | −0.670905 | ||||||||
\(833\) | 4.70185 | 0.162909 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.46115 | 0.258204 | ||||||||
\(836\) | 36.4528 | 1.26075 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 81.1781 | 2.80425 | ||||||||
\(839\) | −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 | ||||||||
\(842\) | −21.5883 | −0.743983 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 47.6675 | 1.64078 | ||||||||
\(845\) | 5.87518 | 0.202112 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.89870 | −0.271403 | ||||||||
\(848\) | 101.267 | 3.47753 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 10.3294 | 0.354295 | ||||||||
\(851\) | −9.97300 | −0.341870 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 41.2623 | 1.41280 | 0.706398 | − | 0.707815i | \(-0.250319\pi\) | ||||
0.706398 | + | 0.707815i | \(0.250319\pi\) | |||||||
\(854\) | −10.9573 | −0.374950 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 171.589 | 5.86479 | ||||||||
\(857\) | −4.93880 | −0.168706 | −0.0843532 | − | 0.996436i | \(-0.526882\pi\) | ||||
−0.0843532 | + | 0.996436i | \(0.526882\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −38.1044 | −1.30011 | −0.650053 | − | 0.759889i | \(-0.725253\pi\) | ||||
−0.650053 | + | 0.759889i | \(0.725253\pi\) | |||||||
\(860\) | 10.8070 | 0.368516 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 67.9250 | 2.31353 | ||||||||
\(863\) | 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 | ||||||||
\(866\) | 63.0168 | 2.14140 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 34.4648 | 1.16981 | ||||||||
\(869\) | 8.03393 | 0.272532 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.58004 | 0.121305 | ||||||||
\(872\) | −173.338 | −5.86997 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 36.3642 | 1.23004 | ||||||||
\(875\) | 4.76924 | 0.161230 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19.2114 | 0.648724 | 0.324362 | − | 0.945933i | \(-0.394850\pi\) | ||||
0.324362 | + | 0.945933i | \(0.394850\pi\) | |||||||
\(878\) | 51.6245 | 1.74224 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −12.4960 | −0.421238 | ||||||||
\(881\) | −0.0458679 | −0.00154533 | −0.000772664 | − | 1.00000i | \(-0.500246\pi\) | ||||
−0.000772664 | 1.00000i | \(0.500246\pi\) | ||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 42.1763 | 1.41935 | 0.709674 | − | 0.704531i | \(-0.248842\pi\) | ||||
0.709674 | + | 0.704531i | \(0.248842\pi\) | |||||||
\(884\) | 3.01053 | 0.101255 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −58.8515 | −1.97715 | ||||||||
\(887\) | −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 | ||||||||
\(890\) | −0.267032 | −0.00895093 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 130.938 | 4.38412 | ||||||||
\(893\) | 19.0636 | 0.637938 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.59428 | −0.320701 | ||||||||
\(896\) | 34.9306 | 1.16695 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −41.1842 | −1.37433 | ||||||||
\(899\) | −33.9230 | −1.13140 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.56661 | −0.185451 | ||||||||
\(902\) | 48.5951 | 1.61804 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −72.9360 | −2.42581 | ||||||||
\(905\) | 4.86985 | 0.161879 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −21.2700 | −0.706259 | −0.353129 | − | 0.935574i | \(-0.614882\pi\) | ||||
−0.353129 | + | 0.935574i | \(0.614882\pi\) | |||||||
\(908\) | 19.2126 | 0.637592 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0.930485 | 0.0308453 | ||||||||
\(911\) | 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 | ||||||||
\(914\) | −21.4465 | −0.709387 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −101.788 | −3.36316 | ||||||||
\(917\) | −8.32821 | −0.275022 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −39.3681 | −1.29864 | −0.649318 | − | 0.760517i | \(-0.724945\pi\) | ||||
−0.649318 | + | 0.760517i | \(0.724945\pi\) | |||||||
\(920\) | −15.9177 | −0.524791 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 90.5703 | 2.98277 | ||||||||
\(923\) | 0.933589 | 0.0307295 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 13.0532 | 0.429187 | ||||||||
\(926\) | 86.9674 | 2.85793 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −114.745 | −3.76667 | ||||||||
\(929\) | −48.6956 | −1.59765 | −0.798826 | − | 0.601562i | \(-0.794545\pi\) | ||||
−0.798826 | + | 0.601562i | \(0.794545\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −21.6650 | −0.710042 | ||||||||
\(932\) | −65.9406 | −2.15996 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −16.4198 | −0.537274 | ||||||||
\(935\) | 0.686898 | 0.0224640 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12.4806 | −0.407723 | −0.203862 | − | 0.979000i | \(-0.565349\pi\) | ||||
−0.203862 | + | 0.979000i | \(0.565349\pi\) | |||||||
\(938\) | −14.4356 | −0.471338 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −13.2396 | −0.431829 | ||||||||
\(941\) | 44.4531 | 1.44913 | 0.724565 | − | 0.689207i | \(-0.242041\pi\) | ||||
0.724565 | + | 0.689207i | \(0.242041\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 35.3919 | 1.15252 | ||||||||
\(944\) | −100.918 | −3.28461 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −21.3259 | −0.693365 | ||||||||
\(947\) | 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 | ||||||||
\(950\) | −47.5954 | −1.54420 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −7.65109 | −0.247973 | ||||||||
\(953\) | 14.6341 | 0.474045 | 0.237023 | − | 0.971504i | \(-0.423828\pi\) | ||||
0.237023 | + | 0.971504i | \(0.423828\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.73629 | −0.120903 | ||||||||
\(956\) | −165.760 | −5.36106 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −49.3693 | −1.59505 | ||||||||
\(959\) | −17.4887 | −0.564741 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.65114 | 0.214553 | ||||||||
\(962\) | 5.21095 | 0.168008 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −39.2891 | −1.26542 | ||||||||
\(965\) | −11.2521 | −0.362219 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.24602 | 0.0400692 | 0.0200346 | − | 0.999799i | \(-0.493622\pi\) | ||||
0.0200346 | + | 0.999799i | \(0.493622\pi\) | |||||||
\(968\) | −70.6020 | −2.26923 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −3.94817 | −0.126768 | ||||||||
\(971\) | −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 | ||||||||
\(974\) | −63.5846 | −2.03738 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −55.9969 | −1.79242 | ||||||||
\(977\) | −29.2177 | −0.934757 | −0.467379 | − | 0.884057i | \(-0.654801\pi\) | ||||
−0.467379 | + | 0.884057i | \(0.654801\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.384710 | 0.0122954 | ||||||||
\(980\) | 15.0463 | 0.480637 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 11.6745 | 0.372550 | ||||||||
\(983\) | 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 | ||||||||
\(986\) | 11.9483 | 0.380513 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −13.8718 | −0.441321 | ||||||||
\(989\) | −15.5317 | −0.493878 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 51.4773 | 1.63523 | 0.817614 | − | 0.575766i | \(-0.195296\pi\) | ||||
0.817614 | + | 0.575766i | \(0.195296\pi\) | |||||||
\(992\) | 127.355 | 4.04352 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −3.76445 | −0.119401 | ||||||||
\(995\) | −0.724779 | −0.0229771 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −41.2171 | −1.30536 | −0.652680 | − | 0.757634i | \(-0.726355\pi\) | ||||
−0.652680 | + | 0.757634i | \(0.726355\pi\) | |||||||
\(998\) | −32.6862 | −1.03466 | ||||||||
\(999\) | 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 | 4923.2.a.l.1.18 | 18 | ||
3.2 | odd | 2 | 547.2.a.b.1.1 | ✓ | 18 | ||
12.11 | even | 2 | 8752.2.a.s.1.13 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
547.2.a.b.1.1 | ✓ | 18 | 3.2 | odd | 2 | ||
4923.2.a.l.1.18 | 18 | 1.1 | even | 1 | trivial | ||
8752.2.a.s.1.13 | 18 | 12.11 | even | 2 |