Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4025,2,Mod(1,4025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4025, 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("4025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4025 = 5^{2} \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4025.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: | \(32.1397868136\) |
Analytic rank: | \(0\) |
Dimension: | \(21\) |
Twist minimal: | no (minimal twist has level 805) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 4025.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.50084 | 1.06126 | 0.530628 | − | 0.847605i | \(-0.321956\pi\) | ||||
0.530628 | + | 0.847605i | \(0.321956\pi\) | |||||||
\(3\) | −0.816695 | −0.471519 | −0.235760 | − | 0.971811i | \(-0.575758\pi\) | ||||
−0.235760 | + | 0.971811i | \(0.575758\pi\) | |||||||
\(4\) | 0.252529 | 0.126265 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.22573 | −0.500403 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −2.62268 | −0.927257 | ||||||||
\(9\) | −2.33301 | −0.777670 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.57614 | −1.68127 | −0.840635 | − | 0.541601i | \(-0.817818\pi\) | ||||
−0.840635 | + | 0.541601i | \(0.817818\pi\) | |||||||
\(12\) | −0.206239 | −0.0595362 | ||||||||
\(13\) | 4.04443 | 1.12172 | 0.560862 | − | 0.827909i | \(-0.310470\pi\) | ||||
0.560862 | + | 0.827909i | \(0.310470\pi\) | |||||||
\(14\) | 1.50084 | 0.401117 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.44129 | −1.11032 | ||||||||
\(17\) | 6.57649 | 1.59503 | 0.797516 | − | 0.603297i | \(-0.206147\pi\) | ||||
0.797516 | + | 0.603297i | \(0.206147\pi\) | |||||||
\(18\) | −3.50148 | −0.825307 | ||||||||
\(19\) | 0.0315796 | 0.00724487 | 0.00362243 | − | 0.999993i | \(-0.498847\pi\) | ||||
0.00362243 | + | 0.999993i | \(0.498847\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.816695 | −0.178218 | ||||||||
\(22\) | −8.36892 | −1.78426 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 2.14193 | 0.437220 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 6.07006 | 1.19044 | ||||||||
\(27\) | 4.35544 | 0.838205 | ||||||||
\(28\) | 0.252529 | 0.0477235 | ||||||||
\(29\) | −6.35790 | −1.18063 | −0.590317 | − | 0.807172i | \(-0.700997\pi\) | ||||
−0.590317 | + | 0.807172i | \(0.700997\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.36927 | 0.245929 | 0.122964 | − | 0.992411i | \(-0.460760\pi\) | ||||
0.122964 | + | 0.992411i | \(0.460760\pi\) | |||||||
\(32\) | −1.42032 | −0.251079 | ||||||||
\(33\) | 4.55401 | 0.792752 | ||||||||
\(34\) | 9.87028 | 1.69274 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.589153 | −0.0981921 | ||||||||
\(37\) | −2.86325 | −0.470715 | −0.235357 | − | 0.971909i | \(-0.575626\pi\) | ||||
−0.235357 | + | 0.971909i | \(0.575626\pi\) | |||||||
\(38\) | 0.0473961 | 0.00768866 | ||||||||
\(39\) | −3.30307 | −0.528914 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.54127 | −0.709227 | −0.354613 | − | 0.935013i | \(-0.615388\pi\) | ||||
−0.354613 | + | 0.935013i | \(0.615388\pi\) | |||||||
\(42\) | −1.22573 | −0.189134 | ||||||||
\(43\) | 1.93731 | 0.295437 | 0.147718 | − | 0.989029i | \(-0.452807\pi\) | ||||
0.147718 | + | 0.989029i | \(0.452807\pi\) | |||||||
\(44\) | −1.40814 | −0.212285 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.50084 | 0.221287 | ||||||||
\(47\) | 1.87483 | 0.273472 | 0.136736 | − | 0.990608i | \(-0.456339\pi\) | ||||
0.136736 | + | 0.990608i | \(0.456339\pi\) | |||||||
\(48\) | 3.62718 | 0.523538 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.37099 | −0.752089 | ||||||||
\(52\) | 1.02134 | 0.141634 | ||||||||
\(53\) | 1.12976 | 0.155184 | 0.0775919 | − | 0.996985i | \(-0.475277\pi\) | ||||
0.0775919 | + | 0.996985i | \(0.475277\pi\) | |||||||
\(54\) | 6.53684 | 0.889551 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.62268 | −0.350470 | ||||||||
\(57\) | −0.0257909 | −0.00341609 | ||||||||
\(58\) | −9.54221 | −1.25295 | ||||||||
\(59\) | 5.50239 | 0.716350 | 0.358175 | − | 0.933654i | \(-0.383399\pi\) | ||||
0.358175 | + | 0.933654i | \(0.383399\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.8429 | 1.64437 | 0.822185 | − | 0.569221i | \(-0.192755\pi\) | ||||
0.822185 | + | 0.569221i | \(0.192755\pi\) | |||||||
\(62\) | 2.05506 | 0.260993 | ||||||||
\(63\) | −2.33301 | −0.293931 | ||||||||
\(64\) | 6.75090 | 0.843863 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 6.83485 | 0.841312 | ||||||||
\(67\) | −1.66458 | −0.203361 | −0.101680 | − | 0.994817i | \(-0.532422\pi\) | ||||
−0.101680 | + | 0.994817i | \(0.532422\pi\) | |||||||
\(68\) | 1.66075 | 0.201396 | ||||||||
\(69\) | −0.816695 | −0.0983186 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.4018 | 1.23446 | 0.617231 | − | 0.786782i | \(-0.288254\pi\) | ||||
0.617231 | + | 0.786782i | \(0.288254\pi\) | |||||||
\(72\) | 6.11873 | 0.721100 | ||||||||
\(73\) | 7.21105 | 0.843990 | 0.421995 | − | 0.906598i | \(-0.361330\pi\) | ||||
0.421995 | + | 0.906598i | \(0.361330\pi\) | |||||||
\(74\) | −4.29728 | −0.499549 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.00797478 | 0.000914770 0 | ||||||||
\(77\) | −5.57614 | −0.635461 | ||||||||
\(78\) | −4.95739 | −0.561313 | ||||||||
\(79\) | 5.58626 | 0.628504 | 0.314252 | − | 0.949340i | \(-0.398246\pi\) | ||||
0.314252 | + | 0.949340i | \(0.398246\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.44196 | 0.382440 | ||||||||
\(82\) | −6.81573 | −0.752671 | ||||||||
\(83\) | 11.1128 | 1.21979 | 0.609894 | − | 0.792483i | \(-0.291212\pi\) | ||||
0.609894 | + | 0.792483i | \(0.291212\pi\) | |||||||
\(84\) | −0.206239 | −0.0225026 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.90759 | 0.313534 | ||||||||
\(87\) | 5.19247 | 0.556691 | ||||||||
\(88\) | 14.6244 | 1.55897 | ||||||||
\(89\) | 16.6306 | 1.76284 | 0.881418 | − | 0.472337i | \(-0.156590\pi\) | ||||
0.881418 | + | 0.472337i | \(0.156590\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.04443 | 0.423972 | ||||||||
\(92\) | 0.252529 | 0.0263280 | ||||||||
\(93\) | −1.11828 | −0.115960 | ||||||||
\(94\) | 2.81383 | 0.290224 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.15997 | 0.118388 | ||||||||
\(97\) | −13.8986 | −1.41119 | −0.705597 | − | 0.708614i | \(-0.749321\pi\) | ||||
−0.705597 | + | 0.708614i | \(0.749321\pi\) | |||||||
\(98\) | 1.50084 | 0.151608 | ||||||||
\(99\) | 13.0092 | 1.30747 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.56886 | 0.852634 | 0.426317 | − | 0.904574i | \(-0.359811\pi\) | ||||
0.426317 | + | 0.904574i | \(0.359811\pi\) | |||||||
\(102\) | −8.06101 | −0.798159 | ||||||||
\(103\) | 7.41286 | 0.730411 | 0.365205 | − | 0.930927i | \(-0.380999\pi\) | ||||
0.365205 | + | 0.930927i | \(0.380999\pi\) | |||||||
\(104\) | −10.6072 | −1.04013 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.69559 | 0.164690 | ||||||||
\(107\) | −3.54317 | −0.342532 | −0.171266 | − | 0.985225i | \(-0.554786\pi\) | ||||
−0.171266 | + | 0.985225i | \(0.554786\pi\) | |||||||
\(108\) | 1.09988 | 0.105836 | ||||||||
\(109\) | −12.4712 | −1.19452 | −0.597261 | − | 0.802047i | \(-0.703744\pi\) | ||||
−0.597261 | + | 0.802047i | \(0.703744\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.33840 | 0.221951 | ||||||||
\(112\) | −4.44129 | −0.419662 | ||||||||
\(113\) | −9.56214 | −0.899530 | −0.449765 | − | 0.893147i | \(-0.648492\pi\) | ||||
−0.449765 | + | 0.893147i | \(0.648492\pi\) | |||||||
\(114\) | −0.0387082 | −0.00362535 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.60556 | −0.149072 | ||||||||
\(117\) | −9.43569 | −0.872330 | ||||||||
\(118\) | 8.25822 | 0.760231 | ||||||||
\(119\) | 6.57649 | 0.602866 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 20.0934 | 1.82667 | ||||||||
\(122\) | 19.2752 | 1.74510 | ||||||||
\(123\) | 3.70883 | 0.334414 | ||||||||
\(124\) | 0.345781 | 0.0310521 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −3.50148 | −0.311937 | ||||||||
\(127\) | 16.6954 | 1.48148 | 0.740739 | − | 0.671793i | \(-0.234476\pi\) | ||||
0.740739 | + | 0.671793i | \(0.234476\pi\) | |||||||
\(128\) | 12.9727 | 1.14663 | ||||||||
\(129\) | −1.58219 | −0.139304 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.51048 | −0.131972 | −0.0659858 | − | 0.997821i | \(-0.521019\pi\) | ||||
−0.0659858 | + | 0.997821i | \(0.521019\pi\) | |||||||
\(132\) | 1.15002 | 0.100096 | ||||||||
\(133\) | 0.0315796 | 0.00273830 | ||||||||
\(134\) | −2.49827 | −0.215818 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −17.2480 | −1.47901 | ||||||||
\(137\) | 5.80267 | 0.495756 | 0.247878 | − | 0.968791i | \(-0.420267\pi\) | ||||
0.247878 | + | 0.968791i | \(0.420267\pi\) | |||||||
\(138\) | −1.22573 | −0.104341 | ||||||||
\(139\) | −7.01912 | −0.595354 | −0.297677 | − | 0.954667i | \(-0.596212\pi\) | ||||
−0.297677 | + | 0.954667i | \(0.596212\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.53117 | −0.128947 | ||||||||
\(142\) | 15.6114 | 1.31008 | ||||||||
\(143\) | −22.5523 | −1.88592 | ||||||||
\(144\) | 10.3616 | 0.863464 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 10.8227 | 0.895689 | ||||||||
\(147\) | −0.816695 | −0.0673599 | ||||||||
\(148\) | −0.723053 | −0.0594346 | ||||||||
\(149\) | −21.2940 | −1.74447 | −0.872235 | − | 0.489087i | \(-0.837330\pi\) | ||||
−0.872235 | + | 0.489087i | \(0.837330\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.55312 | 0.207770 | 0.103885 | − | 0.994589i | \(-0.466873\pi\) | ||||
0.103885 | + | 0.994589i | \(0.466873\pi\) | |||||||
\(152\) | −0.0828233 | −0.00671785 | ||||||||
\(153\) | −15.3430 | −1.24041 | ||||||||
\(154\) | −8.36892 | −0.674386 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.834121 | −0.0667831 | ||||||||
\(157\) | 7.81119 | 0.623401 | 0.311700 | − | 0.950180i | \(-0.399101\pi\) | ||||
0.311700 | + | 0.950180i | \(0.399101\pi\) | |||||||
\(158\) | 8.38410 | 0.667003 | ||||||||
\(159\) | −0.922666 | −0.0731722 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.00000 | 0.0788110 | ||||||||
\(162\) | 5.16584 | 0.405866 | ||||||||
\(163\) | 23.2397 | 1.82027 | 0.910137 | − | 0.414307i | \(-0.135976\pi\) | ||||
0.910137 | + | 0.414307i | \(0.135976\pi\) | |||||||
\(164\) | −1.14680 | −0.0895502 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 16.6786 | 1.29451 | ||||||||
\(167\) | 10.4503 | 0.808672 | 0.404336 | − | 0.914611i | \(-0.367503\pi\) | ||||
0.404336 | + | 0.914611i | \(0.367503\pi\) | |||||||
\(168\) | 2.14193 | 0.165253 | ||||||||
\(169\) | 3.35743 | 0.258264 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.0736756 | −0.00563411 | ||||||||
\(172\) | 0.489226 | 0.0373032 | ||||||||
\(173\) | 11.1955 | 0.851177 | 0.425588 | − | 0.904917i | \(-0.360067\pi\) | ||||
0.425588 | + | 0.904917i | \(0.360067\pi\) | |||||||
\(174\) | 7.79308 | 0.590792 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 24.7653 | 1.86675 | ||||||||
\(177\) | −4.49377 | −0.337773 | ||||||||
\(178\) | 24.9599 | 1.87082 | ||||||||
\(179\) | −6.43423 | −0.480917 | −0.240458 | − | 0.970659i | \(-0.577298\pi\) | ||||
−0.240458 | + | 0.970659i | \(0.577298\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.3430 | −1.21476 | −0.607382 | − | 0.794410i | \(-0.707780\pi\) | ||||
−0.607382 | + | 0.794410i | \(0.707780\pi\) | |||||||
\(182\) | 6.07006 | 0.449942 | ||||||||
\(183\) | −10.4888 | −0.775352 | ||||||||
\(184\) | −2.62268 | −0.193346 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1.67836 | −0.123063 | ||||||||
\(187\) | −36.6714 | −2.68168 | ||||||||
\(188\) | 0.473449 | 0.0345298 | ||||||||
\(189\) | 4.35544 | 0.316812 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.4727 | 1.11957 | 0.559783 | − | 0.828639i | \(-0.310884\pi\) | ||||
0.559783 | + | 0.828639i | \(0.310884\pi\) | |||||||
\(192\) | −5.51343 | −0.397898 | ||||||||
\(193\) | −17.7528 | −1.27787 | −0.638936 | − | 0.769260i | \(-0.720625\pi\) | ||||
−0.638936 | + | 0.769260i | \(0.720625\pi\) | |||||||
\(194\) | −20.8597 | −1.49764 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.252529 | 0.0180378 | ||||||||
\(197\) | −12.4152 | −0.884546 | −0.442273 | − | 0.896880i | \(-0.645828\pi\) | ||||
−0.442273 | + | 0.896880i | \(0.645828\pi\) | |||||||
\(198\) | 19.5248 | 1.38756 | ||||||||
\(199\) | 13.7043 | 0.971473 | 0.485736 | − | 0.874105i | \(-0.338552\pi\) | ||||
0.485736 | + | 0.874105i | \(0.338552\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.35945 | 0.0958885 | ||||||||
\(202\) | 12.8605 | 0.904863 | ||||||||
\(203\) | −6.35790 | −0.446237 | ||||||||
\(204\) | −1.35633 | −0.0949621 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 11.1255 | 0.775153 | ||||||||
\(207\) | −2.33301 | −0.162155 | ||||||||
\(208\) | −17.9625 | −1.24547 | ||||||||
\(209\) | −0.176093 | −0.0121806 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.4605 | 1.13319 | 0.566595 | − | 0.823996i | \(-0.308260\pi\) | ||||
0.566595 | + | 0.823996i | \(0.308260\pi\) | |||||||
\(212\) | 0.285296 | 0.0195942 | ||||||||
\(213\) | −8.49508 | −0.582073 | ||||||||
\(214\) | −5.31775 | −0.363514 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −11.4229 | −0.777232 | ||||||||
\(217\) | 1.36927 | 0.0929523 | ||||||||
\(218\) | −18.7173 | −1.26769 | ||||||||
\(219\) | −5.88923 | −0.397957 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 26.5982 | 1.78919 | ||||||||
\(222\) | 3.50957 | 0.235547 | ||||||||
\(223\) | 14.8249 | 0.992749 | 0.496374 | − | 0.868108i | \(-0.334664\pi\) | ||||
0.496374 | + | 0.868108i | \(0.334664\pi\) | |||||||
\(224\) | −1.42032 | −0.0948988 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −14.3513 | −0.954632 | ||||||||
\(227\) | 18.2901 | 1.21396 | 0.606979 | − | 0.794718i | \(-0.292381\pi\) | ||||
0.606979 | + | 0.794718i | \(0.292381\pi\) | |||||||
\(228\) | −0.00651296 | −0.000431332 0 | ||||||||
\(229\) | 26.0017 | 1.71824 | 0.859120 | − | 0.511774i | \(-0.171011\pi\) | ||||
0.859120 | + | 0.511774i | \(0.171011\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.55401 | 0.299632 | ||||||||
\(232\) | 16.6747 | 1.09475 | ||||||||
\(233\) | −9.49697 | −0.622167 | −0.311084 | − | 0.950383i | \(-0.600692\pi\) | ||||
−0.311084 | + | 0.950383i | \(0.600692\pi\) | |||||||
\(234\) | −14.1615 | −0.925766 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.38951 | 0.0904496 | ||||||||
\(237\) | −4.56228 | −0.296352 | ||||||||
\(238\) | 9.87028 | 0.639795 | ||||||||
\(239\) | −26.3213 | −1.70258 | −0.851291 | − | 0.524694i | \(-0.824180\pi\) | ||||
−0.851291 | + | 0.524694i | \(0.824180\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.2193 | −0.722701 | −0.361351 | − | 0.932430i | \(-0.617684\pi\) | ||||
−0.361351 | + | 0.932430i | \(0.617684\pi\) | |||||||
\(242\) | 30.1570 | 1.93857 | ||||||||
\(243\) | −15.8774 | −1.01853 | ||||||||
\(244\) | 3.24322 | 0.207626 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 5.56637 | 0.354899 | ||||||||
\(247\) | 0.127722 | 0.00812674 | ||||||||
\(248\) | −3.59116 | −0.228039 | ||||||||
\(249\) | −9.07578 | −0.575154 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.14342 | −0.387769 | −0.193885 | − | 0.981024i | \(-0.562109\pi\) | ||||
−0.193885 | + | 0.981024i | \(0.562109\pi\) | |||||||
\(252\) | −0.589153 | −0.0371131 | ||||||||
\(253\) | −5.57614 | −0.350569 | ||||||||
\(254\) | 25.0572 | 1.57223 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5.96814 | 0.373009 | ||||||||
\(257\) | −22.3978 | −1.39714 | −0.698568 | − | 0.715544i | \(-0.746179\pi\) | ||||
−0.698568 | + | 0.715544i | \(0.746179\pi\) | |||||||
\(258\) | −2.37462 | −0.147837 | ||||||||
\(259\) | −2.86325 | −0.177913 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 14.8330 | 0.918142 | ||||||||
\(262\) | −2.26700 | −0.140056 | ||||||||
\(263\) | 20.5242 | 1.26558 | 0.632789 | − | 0.774324i | \(-0.281910\pi\) | ||||
0.632789 | + | 0.774324i | \(0.281910\pi\) | |||||||
\(264\) | −11.9437 | −0.735085 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.0473961 | 0.00290604 | ||||||||
\(267\) | −13.5821 | −0.831211 | ||||||||
\(268\) | −0.420355 | −0.0256772 | ||||||||
\(269\) | −18.4098 | −1.12246 | −0.561232 | − | 0.827658i | \(-0.689673\pi\) | ||||
−0.561232 | + | 0.827658i | \(0.689673\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.23951 | 0.257532 | 0.128766 | − | 0.991675i | \(-0.458898\pi\) | ||||
0.128766 | + | 0.991675i | \(0.458898\pi\) | |||||||
\(272\) | −29.2081 | −1.77100 | ||||||||
\(273\) | −3.30307 | −0.199911 | ||||||||
\(274\) | 8.70890 | 0.526124 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.206239 | −0.0124141 | ||||||||
\(277\) | −3.50266 | −0.210454 | −0.105227 | − | 0.994448i | \(-0.533557\pi\) | ||||
−0.105227 | + | 0.994448i | \(0.533557\pi\) | |||||||
\(278\) | −10.5346 | −0.631823 | ||||||||
\(279\) | −3.19452 | −0.191251 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −17.7739 | −1.06030 | −0.530151 | − | 0.847903i | \(-0.677865\pi\) | ||||
−0.530151 | + | 0.847903i | \(0.677865\pi\) | |||||||
\(282\) | −2.29804 | −0.136846 | ||||||||
\(283\) | −24.4579 | −1.45387 | −0.726934 | − | 0.686707i | \(-0.759056\pi\) | ||||
−0.726934 | + | 0.686707i | \(0.759056\pi\) | |||||||
\(284\) | 2.62675 | 0.155869 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −33.8475 | −2.00145 | ||||||||
\(287\) | −4.54127 | −0.268063 | ||||||||
\(288\) | 3.31361 | 0.195256 | ||||||||
\(289\) | 26.2502 | 1.54413 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.3510 | 0.665405 | ||||||||
\(292\) | 1.82100 | 0.106566 | ||||||||
\(293\) | −1.58615 | −0.0926639 | −0.0463320 | − | 0.998926i | \(-0.514753\pi\) | ||||
−0.0463320 | + | 0.998926i | \(0.514753\pi\) | |||||||
\(294\) | −1.22573 | −0.0714861 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 7.50938 | 0.436474 | ||||||||
\(297\) | −24.2866 | −1.40925 | ||||||||
\(298\) | −31.9589 | −1.85133 | ||||||||
\(299\) | 4.04443 | 0.233896 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.93731 | 0.111665 | ||||||||
\(302\) | 3.83183 | 0.220497 | ||||||||
\(303\) | −6.99815 | −0.402033 | ||||||||
\(304\) | −0.140254 | −0.00804413 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −23.0274 | −1.31639 | ||||||||
\(307\) | −9.24426 | −0.527598 | −0.263799 | − | 0.964578i | \(-0.584976\pi\) | ||||
−0.263799 | + | 0.964578i | \(0.584976\pi\) | |||||||
\(308\) | −1.40814 | −0.0802361 | ||||||||
\(309\) | −6.05405 | −0.344403 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −19.4611 | −1.10354 | −0.551768 | − | 0.833998i | \(-0.686047\pi\) | ||||
−0.551768 | + | 0.833998i | \(0.686047\pi\) | |||||||
\(312\) | 8.66289 | 0.490439 | ||||||||
\(313\) | 25.4236 | 1.43702 | 0.718512 | − | 0.695514i | \(-0.244823\pi\) | ||||
0.718512 | + | 0.695514i | \(0.244823\pi\) | |||||||
\(314\) | 11.7234 | 0.661588 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.41069 | 0.0793577 | ||||||||
\(317\) | −6.44839 | −0.362178 | −0.181089 | − | 0.983467i | \(-0.557962\pi\) | ||||
−0.181089 | + | 0.983467i | \(0.557962\pi\) | |||||||
\(318\) | −1.38478 | −0.0776544 | ||||||||
\(319\) | 35.4526 | 1.98496 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.89369 | 0.161510 | ||||||||
\(322\) | 1.50084 | 0.0836387 | ||||||||
\(323\) | 0.207683 | 0.0115558 | ||||||||
\(324\) | 0.869194 | 0.0482886 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 34.8791 | 1.93178 | ||||||||
\(327\) | 10.1851 | 0.563240 | ||||||||
\(328\) | 11.9103 | 0.657636 | ||||||||
\(329\) | 1.87483 | 0.103363 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23.7887 | 1.30755 | 0.653774 | − | 0.756690i | \(-0.273185\pi\) | ||||
0.653774 | + | 0.756690i | \(0.273185\pi\) | |||||||
\(332\) | 2.80631 | 0.154016 | ||||||||
\(333\) | 6.67998 | 0.366061 | ||||||||
\(334\) | 15.6843 | 0.858208 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 3.62718 | 0.197879 | ||||||||
\(337\) | 18.0792 | 0.984838 | 0.492419 | − | 0.870358i | \(-0.336113\pi\) | ||||
0.492419 | + | 0.870358i | \(0.336113\pi\) | |||||||
\(338\) | 5.03897 | 0.274084 | ||||||||
\(339\) | 7.80935 | 0.424146 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.63526 | −0.413473 | ||||||||
\(342\) | −0.110575 | −0.00597924 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −5.08094 | −0.273946 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 16.8027 | 0.903316 | ||||||||
\(347\) | −3.93025 | −0.210987 | −0.105494 | − | 0.994420i | \(-0.533642\pi\) | ||||
−0.105494 | + | 0.994420i | \(0.533642\pi\) | |||||||
\(348\) | 1.31125 | 0.0702904 | ||||||||
\(349\) | −9.77290 | −0.523131 | −0.261566 | − | 0.965186i | \(-0.584239\pi\) | ||||
−0.261566 | + | 0.965186i | \(0.584239\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 17.6153 | 0.940235 | ||||||||
\(352\) | 7.91989 | 0.422131 | ||||||||
\(353\) | 23.1310 | 1.23114 | 0.615570 | − | 0.788082i | \(-0.288926\pi\) | ||||
0.615570 | + | 0.788082i | \(0.288926\pi\) | |||||||
\(354\) | −6.74445 | −0.358463 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 4.19970 | 0.222584 | ||||||||
\(357\) | −5.37099 | −0.284263 | ||||||||
\(358\) | −9.65677 | −0.510376 | ||||||||
\(359\) | 6.64008 | 0.350450 | 0.175225 | − | 0.984528i | \(-0.443935\pi\) | ||||
0.175225 | + | 0.984528i | \(0.443935\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9990 | −0.999948 | ||||||||
\(362\) | −24.5282 | −1.28918 | ||||||||
\(363\) | −16.4102 | −0.861311 | ||||||||
\(364\) | 1.02134 | 0.0535326 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −15.7420 | −0.822847 | ||||||||
\(367\) | −12.6692 | −0.661325 | −0.330662 | − | 0.943749i | \(-0.607272\pi\) | ||||
−0.330662 | + | 0.943749i | \(0.607272\pi\) | |||||||
\(368\) | −4.44129 | −0.231518 | ||||||||
\(369\) | 10.5948 | 0.551544 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.12976 | 0.0586540 | ||||||||
\(372\) | −0.282398 | −0.0146416 | ||||||||
\(373\) | −6.00241 | −0.310793 | −0.155396 | − | 0.987852i | \(-0.549665\pi\) | ||||
−0.155396 | + | 0.987852i | \(0.549665\pi\) | |||||||
\(374\) | −55.0381 | −2.84595 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.91708 | −0.253579 | ||||||||
\(377\) | −25.7141 | −1.32434 | ||||||||
\(378\) | 6.53684 | 0.336219 | ||||||||
\(379\) | 31.3566 | 1.61068 | 0.805340 | − | 0.592814i | \(-0.201983\pi\) | ||||
0.805340 | + | 0.592814i | \(0.201983\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −13.6351 | −0.698545 | ||||||||
\(382\) | 23.2221 | 1.18815 | ||||||||
\(383\) | 5.53739 | 0.282948 | 0.141474 | − | 0.989942i | \(-0.454816\pi\) | ||||
0.141474 | + | 0.989942i | \(0.454816\pi\) | |||||||
\(384\) | −10.5947 | −0.540660 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −26.6441 | −1.35615 | ||||||||
\(387\) | −4.51976 | −0.229752 | ||||||||
\(388\) | −3.50981 | −0.178184 | ||||||||
\(389\) | 8.20381 | 0.415950 | 0.207975 | − | 0.978134i | \(-0.433313\pi\) | ||||
0.207975 | + | 0.978134i | \(0.433313\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.57649 | 0.332587 | ||||||||
\(392\) | −2.62268 | −0.132465 | ||||||||
\(393\) | 1.23361 | 0.0622272 | ||||||||
\(394\) | −18.6333 | −0.938730 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 3.28520 | 0.165087 | ||||||||
\(397\) | 9.62114 | 0.482871 | 0.241436 | − | 0.970417i | \(-0.422382\pi\) | ||||
0.241436 | + | 0.970417i | \(0.422382\pi\) | |||||||
\(398\) | 20.5680 | 1.03098 | ||||||||
\(399\) | −0.0257909 | −0.00129116 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 26.8333 | 1.33999 | 0.669996 | − | 0.742365i | \(-0.266296\pi\) | ||||
0.669996 | + | 0.742365i | \(0.266296\pi\) | |||||||
\(402\) | 2.04033 | 0.101762 | ||||||||
\(403\) | 5.53793 | 0.275864 | ||||||||
\(404\) | 2.16389 | 0.107657 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −9.54221 | −0.473572 | ||||||||
\(407\) | 15.9659 | 0.791399 | ||||||||
\(408\) | 14.0864 | 0.697380 | ||||||||
\(409\) | 36.4908 | 1.80436 | 0.902178 | − | 0.431365i | \(-0.141968\pi\) | ||||
0.902178 | + | 0.431365i | \(0.141968\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.73902 | −0.233758 | ||||||||
\(412\) | 1.87196 | 0.0922250 | ||||||||
\(413\) | 5.50239 | 0.270755 | ||||||||
\(414\) | −3.50148 | −0.172088 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −5.74437 | −0.281641 | ||||||||
\(417\) | 5.73248 | 0.280721 | ||||||||
\(418\) | −0.264287 | −0.0129267 | ||||||||
\(419\) | −11.8204 | −0.577465 | −0.288733 | − | 0.957410i | \(-0.593234\pi\) | ||||
−0.288733 | + | 0.957410i | \(0.593234\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.0249 | −0.488583 | −0.244291 | − | 0.969702i | \(-0.578555\pi\) | ||||
−0.244291 | + | 0.969702i | \(0.578555\pi\) | |||||||
\(422\) | 24.7047 | 1.20261 | ||||||||
\(423\) | −4.37400 | −0.212671 | ||||||||
\(424\) | −2.96299 | −0.143895 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −12.7498 | −0.617728 | ||||||||
\(427\) | 12.8429 | 0.621513 | ||||||||
\(428\) | −0.894754 | −0.0432496 | ||||||||
\(429\) | 18.4184 | 0.889248 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −27.9864 | −1.34806 | −0.674029 | − | 0.738705i | \(-0.735438\pi\) | ||||
−0.674029 | + | 0.738705i | \(0.735438\pi\) | |||||||
\(432\) | −19.3438 | −0.930678 | ||||||||
\(433\) | −17.0989 | −0.821719 | −0.410859 | − | 0.911699i | \(-0.634771\pi\) | ||||
−0.410859 | + | 0.911699i | \(0.634771\pi\) | |||||||
\(434\) | 2.05506 | 0.0986462 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.14933 | −0.150826 | ||||||||
\(437\) | 0.0315796 | 0.00151066 | ||||||||
\(438\) | −8.83881 | −0.422335 | ||||||||
\(439\) | 24.6894 | 1.17836 | 0.589180 | − | 0.808002i | \(-0.299451\pi\) | ||||
0.589180 | + | 0.808002i | \(0.299451\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.33301 | −0.111096 | ||||||||
\(442\) | 39.9197 | 1.89878 | ||||||||
\(443\) | −22.3512 | −1.06194 | −0.530968 | − | 0.847392i | \(-0.678172\pi\) | ||||
−0.530968 | + | 0.847392i | \(0.678172\pi\) | |||||||
\(444\) | 0.590514 | 0.0280246 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 22.2499 | 1.05356 | ||||||||
\(447\) | 17.3907 | 0.822551 | ||||||||
\(448\) | 6.75090 | 0.318950 | ||||||||
\(449\) | −14.0885 | −0.664878 | −0.332439 | − | 0.943125i | \(-0.607871\pi\) | ||||
−0.332439 | + | 0.943125i | \(0.607871\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 25.3228 | 1.19240 | ||||||||
\(452\) | −2.41472 | −0.113579 | ||||||||
\(453\) | −2.08512 | −0.0979675 | ||||||||
\(454\) | 27.4506 | 1.28832 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.0676414 | 0.00316760 | ||||||||
\(457\) | 29.8888 | 1.39814 | 0.699070 | − | 0.715054i | \(-0.253598\pi\) | ||||
0.699070 | + | 0.715054i | \(0.253598\pi\) | |||||||
\(458\) | 39.0245 | 1.82349 | ||||||||
\(459\) | 28.6435 | 1.33697 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −29.6760 | −1.38215 | −0.691074 | − | 0.722784i | \(-0.742862\pi\) | ||||
−0.691074 | + | 0.722784i | \(0.742862\pi\) | |||||||
\(462\) | 6.83485 | 0.317986 | ||||||||
\(463\) | 13.0213 | 0.605153 | 0.302576 | − | 0.953125i | \(-0.402153\pi\) | ||||
0.302576 | + | 0.953125i | \(0.402153\pi\) | |||||||
\(464\) | 28.2373 | 1.31088 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −14.2535 | −0.660279 | ||||||||
\(467\) | 9.14341 | 0.423107 | 0.211553 | − | 0.977366i | \(-0.432148\pi\) | ||||
0.211553 | + | 0.977366i | \(0.432148\pi\) | |||||||
\(468\) | −2.38279 | −0.110144 | ||||||||
\(469\) | −1.66458 | −0.0768631 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.37936 | −0.293945 | ||||||||
\(472\) | −14.4310 | −0.664241 | ||||||||
\(473\) | −10.8027 | −0.496709 | ||||||||
\(474\) | −6.84726 | −0.314505 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.66075 | 0.0761206 | ||||||||
\(477\) | −2.63573 | −0.120682 | ||||||||
\(478\) | −39.5041 | −1.80688 | ||||||||
\(479\) | −9.02717 | −0.412462 | −0.206231 | − | 0.978503i | \(-0.566120\pi\) | ||||
−0.206231 | + | 0.978503i | \(0.566120\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.5802 | −0.528012 | ||||||||
\(482\) | −16.8385 | −0.766971 | ||||||||
\(483\) | −0.816695 | −0.0371609 | ||||||||
\(484\) | 5.07416 | 0.230644 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −23.8294 | −1.08092 | ||||||||
\(487\) | −32.3124 | −1.46421 | −0.732107 | − | 0.681189i | \(-0.761463\pi\) | ||||
−0.732107 | + | 0.681189i | \(0.761463\pi\) | |||||||
\(488\) | −33.6829 | −1.52475 | ||||||||
\(489\) | −18.9798 | −0.858294 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.5131 | 0.925742 | 0.462871 | − | 0.886426i | \(-0.346819\pi\) | ||||
0.462871 | + | 0.886426i | \(0.346819\pi\) | |||||||
\(492\) | 0.936588 | 0.0422246 | ||||||||
\(493\) | −41.8127 | −1.88315 | ||||||||
\(494\) | 0.191690 | 0.00862455 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.08133 | −0.273060 | ||||||||
\(497\) | 10.4018 | 0.466583 | ||||||||
\(498\) | −13.6213 | −0.610386 | ||||||||
\(499\) | 24.9439 | 1.11664 | 0.558322 | − | 0.829624i | \(-0.311445\pi\) | ||||
0.558322 | + | 0.829624i | \(0.311445\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.53474 | −0.381304 | ||||||||
\(502\) | −9.22031 | −0.411523 | ||||||||
\(503\) | −18.3089 | −0.816353 | −0.408177 | − | 0.912903i | \(-0.633835\pi\) | ||||
−0.408177 | + | 0.912903i | \(0.633835\pi\) | |||||||
\(504\) | 6.11873 | 0.272550 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −8.36892 | −0.372044 | ||||||||
\(507\) | −2.74200 | −0.121776 | ||||||||
\(508\) | 4.21607 | 0.187058 | ||||||||
\(509\) | 15.6600 | 0.694118 | 0.347059 | − | 0.937843i | \(-0.387180\pi\) | ||||
0.347059 | + | 0.937843i | \(0.387180\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.21105 | 0.318998 | ||||||||
\(512\) | −16.9881 | −0.750776 | ||||||||
\(513\) | 0.137543 | 0.00607269 | ||||||||
\(514\) | −33.6156 | −1.48272 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.399549 | −0.0175892 | ||||||||
\(517\) | −10.4543 | −0.459781 | ||||||||
\(518\) | −4.29728 | −0.188812 | ||||||||
\(519\) | −9.14330 | −0.401346 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21.8013 | −0.955131 | −0.477566 | − | 0.878596i | \(-0.658481\pi\) | ||||
−0.477566 | + | 0.878596i | \(0.658481\pi\) | |||||||
\(522\) | 22.2621 | 0.974384 | ||||||||
\(523\) | 24.7544 | 1.08244 | 0.541218 | − | 0.840883i | \(-0.317964\pi\) | ||||
0.541218 | + | 0.840883i | \(0.317964\pi\) | |||||||
\(524\) | −0.381441 | −0.0166633 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 30.8036 | 1.34310 | ||||||||
\(527\) | 9.00501 | 0.392264 | ||||||||
\(528\) | −20.2257 | −0.880209 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −12.8371 | −0.557084 | ||||||||
\(532\) | 0.00797478 | 0.000345751 0 | ||||||||
\(533\) | −18.3668 | −0.795557 | ||||||||
\(534\) | −20.3846 | −0.882128 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4.36566 | 0.188568 | ||||||||
\(537\) | 5.25481 | 0.226762 | ||||||||
\(538\) | −27.6302 | −1.19122 | ||||||||
\(539\) | −5.57614 | −0.240182 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 25.9715 | 1.11660 | 0.558302 | − | 0.829638i | \(-0.311453\pi\) | ||||
0.558302 | + | 0.829638i | \(0.311453\pi\) | |||||||
\(542\) | 6.36283 | 0.273307 | ||||||||
\(543\) | 13.3472 | 0.572785 | ||||||||
\(544\) | −9.34069 | −0.400479 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −4.95739 | −0.212157 | ||||||||
\(547\) | −18.5380 | −0.792626 | −0.396313 | − | 0.918115i | \(-0.629711\pi\) | ||||
−0.396313 | + | 0.918115i | \(0.629711\pi\) | |||||||
\(548\) | 1.46534 | 0.0625964 | ||||||||
\(549\) | −29.9627 | −1.27878 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.200780 | −0.00855353 | ||||||||
\(552\) | 2.14193 | 0.0911666 | ||||||||
\(553\) | 5.58626 | 0.237552 | ||||||||
\(554\) | −5.25694 | −0.223346 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.77253 | −0.0751721 | ||||||||
\(557\) | −0.901162 | −0.0381834 | −0.0190917 | − | 0.999818i | \(-0.506077\pi\) | ||||
−0.0190917 | + | 0.999818i | \(0.506077\pi\) | |||||||
\(558\) | −4.79448 | −0.202967 | ||||||||
\(559\) | 7.83531 | 0.331398 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 29.9494 | 1.26446 | ||||||||
\(562\) | −26.6758 | −1.12525 | ||||||||
\(563\) | −38.6739 | −1.62991 | −0.814955 | − | 0.579525i | \(-0.803238\pi\) | ||||
−0.814955 | + | 0.579525i | \(0.803238\pi\) | |||||||
\(564\) | −0.386664 | −0.0162815 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −36.7074 | −1.54293 | ||||||||
\(567\) | 3.44196 | 0.144549 | ||||||||
\(568\) | −27.2805 | −1.14466 | ||||||||
\(569\) | 12.1566 | 0.509631 | 0.254816 | − | 0.966990i | \(-0.417985\pi\) | ||||
0.254816 | + | 0.966990i | \(0.417985\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −43.6516 | −1.82676 | −0.913382 | − | 0.407104i | \(-0.866539\pi\) | ||||
−0.913382 | + | 0.407104i | \(0.866539\pi\) | |||||||
\(572\) | −5.69512 | −0.238125 | ||||||||
\(573\) | −12.6365 | −0.527897 | ||||||||
\(574\) | −6.81573 | −0.284483 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −15.7499 | −0.656247 | ||||||||
\(577\) | −9.86386 | −0.410638 | −0.205319 | − | 0.978695i | \(-0.565823\pi\) | ||||
−0.205319 | + | 0.978695i | \(0.565823\pi\) | |||||||
\(578\) | 39.3974 | 1.63872 | ||||||||
\(579\) | 14.4986 | 0.602541 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11.1128 | 0.461037 | ||||||||
\(582\) | 17.0360 | 0.706165 | ||||||||
\(583\) | −6.29968 | −0.260906 | ||||||||
\(584\) | −18.9123 | −0.782595 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.38056 | −0.0983401 | ||||||||
\(587\) | 42.5969 | 1.75816 | 0.879080 | − | 0.476674i | \(-0.158158\pi\) | ||||
0.879080 | + | 0.476674i | \(0.158158\pi\) | |||||||
\(588\) | −0.206239 | −0.00850517 | ||||||||
\(589\) | 0.0432411 | 0.00178172 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 10.1394 | 0.417080 | ||||||||
\(592\) | 12.7165 | 0.522645 | ||||||||
\(593\) | −9.47386 | −0.389045 | −0.194522 | − | 0.980898i | \(-0.562316\pi\) | ||||
−0.194522 | + | 0.980898i | \(0.562316\pi\) | |||||||
\(594\) | −36.4503 | −1.49558 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −5.37735 | −0.220265 | ||||||||
\(597\) | −11.1922 | −0.458068 | ||||||||
\(598\) | 6.07006 | 0.248223 | ||||||||
\(599\) | 38.5320 | 1.57438 | 0.787188 | − | 0.616713i | \(-0.211536\pi\) | ||||
0.787188 | + | 0.616713i | \(0.211536\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 36.3755 | 1.48379 | 0.741895 | − | 0.670517i | \(-0.233927\pi\) | ||||
0.741895 | + | 0.670517i | \(0.233927\pi\) | |||||||
\(602\) | 2.90759 | 0.118505 | ||||||||
\(603\) | 3.88348 | 0.158147 | ||||||||
\(604\) | 0.644737 | 0.0262340 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −10.5031 | −0.426660 | ||||||||
\(607\) | −15.4526 | −0.627202 | −0.313601 | − | 0.949555i | \(-0.601535\pi\) | ||||
−0.313601 | + | 0.949555i | \(0.601535\pi\) | |||||||
\(608\) | −0.0448531 | −0.00181903 | ||||||||
\(609\) | 5.19247 | 0.210410 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.58263 | 0.306760 | ||||||||
\(612\) | −3.87456 | −0.156620 | ||||||||
\(613\) | −33.8611 | −1.36764 | −0.683818 | − | 0.729653i | \(-0.739682\pi\) | ||||
−0.683818 | + | 0.729653i | \(0.739682\pi\) | |||||||
\(614\) | −13.8742 | −0.559916 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 14.6244 | 0.589235 | ||||||||
\(617\) | −45.4881 | −1.83128 | −0.915640 | − | 0.401998i | \(-0.868316\pi\) | ||||
−0.915640 | + | 0.401998i | \(0.868316\pi\) | |||||||
\(618\) | −9.08617 | −0.365500 | ||||||||
\(619\) | 1.72666 | 0.0694001 | 0.0347001 | − | 0.999398i | \(-0.488952\pi\) | ||||
0.0347001 | + | 0.999398i | \(0.488952\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.35544 | 0.174778 | ||||||||
\(622\) | −29.2080 | −1.17113 | ||||||||
\(623\) | 16.6306 | 0.666289 | ||||||||
\(624\) | 14.6699 | 0.587265 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 38.1568 | 1.52505 | ||||||||
\(627\) | 0.143814 | 0.00574338 | ||||||||
\(628\) | 1.97255 | 0.0787134 | ||||||||
\(629\) | −18.8301 | −0.750806 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −37.8555 | −1.50700 | −0.753502 | − | 0.657446i | \(-0.771637\pi\) | ||||
−0.753502 | + | 0.657446i | \(0.771637\pi\) | |||||||
\(632\) | −14.6510 | −0.582785 | ||||||||
\(633\) | −13.4432 | −0.534321 | ||||||||
\(634\) | −9.67803 | −0.384363 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.233000 | −0.00923905 | ||||||||
\(637\) | 4.04443 | 0.160246 | ||||||||
\(638\) | 53.2088 | 2.10656 | ||||||||
\(639\) | −24.2674 | −0.960004 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −37.6517 | −1.48715 | −0.743577 | − | 0.668650i | \(-0.766872\pi\) | ||||
−0.743577 | + | 0.668650i | \(0.766872\pi\) | |||||||
\(642\) | 4.34298 | 0.171404 | ||||||||
\(643\) | 34.8532 | 1.37448 | 0.687238 | − | 0.726433i | \(-0.258823\pi\) | ||||
0.687238 | + | 0.726433i | \(0.258823\pi\) | |||||||
\(644\) | 0.252529 | 0.00995104 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.311700 | 0.0122637 | ||||||||
\(647\) | −5.50383 | −0.216378 | −0.108189 | − | 0.994130i | \(-0.534505\pi\) | ||||
−0.108189 | + | 0.994130i | \(0.534505\pi\) | |||||||
\(648\) | −9.02715 | −0.354620 | ||||||||
\(649\) | −30.6821 | −1.20438 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.11828 | −0.0438288 | ||||||||
\(652\) | 5.86870 | 0.229836 | ||||||||
\(653\) | 31.9836 | 1.25162 | 0.625808 | − | 0.779977i | \(-0.284770\pi\) | ||||
0.625808 | + | 0.779977i | \(0.284770\pi\) | |||||||
\(654\) | 15.2863 | 0.597742 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 20.1691 | 0.787470 | ||||||||
\(657\) | −16.8234 | −0.656345 | ||||||||
\(658\) | 2.81383 | 0.109694 | ||||||||
\(659\) | −12.6793 | −0.493915 | −0.246958 | − | 0.969026i | \(-0.579431\pi\) | ||||
−0.246958 | + | 0.969026i | \(0.579431\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.9284 | 0.580647 | 0.290323 | − | 0.956929i | \(-0.406237\pi\) | ||||
0.290323 | + | 0.956929i | \(0.406237\pi\) | |||||||
\(662\) | 35.7032 | 1.38764 | ||||||||
\(663\) | −21.7226 | −0.843636 | ||||||||
\(664\) | −29.1453 | −1.13106 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 10.0256 | 0.388484 | ||||||||
\(667\) | −6.35790 | −0.246179 | ||||||||
\(668\) | 2.63901 | 0.102107 | ||||||||
\(669\) | −12.1074 | −0.468100 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −71.6141 | −2.76463 | ||||||||
\(672\) | 1.15997 | 0.0447466 | ||||||||
\(673\) | 35.8357 | 1.38136 | 0.690682 | − | 0.723158i | \(-0.257310\pi\) | ||||
0.690682 | + | 0.723158i | \(0.257310\pi\) | |||||||
\(674\) | 27.1341 | 1.04517 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.847848 | 0.0326095 | ||||||||
\(677\) | −3.09993 | −0.119140 | −0.0595700 | − | 0.998224i | \(-0.518973\pi\) | ||||
−0.0595700 | + | 0.998224i | \(0.518973\pi\) | |||||||
\(678\) | 11.7206 | 0.450127 | ||||||||
\(679\) | −13.8986 | −0.533381 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14.9374 | −0.572404 | ||||||||
\(682\) | −11.4593 | −0.438800 | ||||||||
\(683\) | −21.9949 | −0.841610 | −0.420805 | − | 0.907151i | \(-0.638252\pi\) | ||||
−0.420805 | + | 0.907151i | \(0.638252\pi\) | |||||||
\(684\) | −0.0186052 | −0.000711389 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.50084 | 0.0573024 | ||||||||
\(687\) | −21.2355 | −0.810183 | ||||||||
\(688\) | −8.60414 | −0.328030 | ||||||||
\(689\) | 4.56922 | 0.174073 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 26.7812 | 1.01881 | 0.509403 | − | 0.860528i | \(-0.329866\pi\) | ||||
0.509403 | + | 0.860528i | \(0.329866\pi\) | |||||||
\(692\) | 2.82718 | 0.107473 | ||||||||
\(693\) | 13.0092 | 0.494178 | ||||||||
\(694\) | −5.89869 | −0.223911 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −13.6182 | −0.516196 | ||||||||
\(697\) | −29.8656 | −1.13124 | ||||||||
\(698\) | −14.6676 | −0.555176 | ||||||||
\(699\) | 7.75613 | 0.293364 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16.1107 | −0.608493 | −0.304246 | − | 0.952593i | \(-0.598405\pi\) | ||||
−0.304246 | + | 0.952593i | \(0.598405\pi\) | |||||||
\(702\) | 26.4378 | 0.997830 | ||||||||
\(703\) | −0.0904203 | −0.00341027 | ||||||||
\(704\) | −37.6440 | −1.41876 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 34.7161 | 1.30656 | ||||||||
\(707\) | 8.56886 | 0.322265 | ||||||||
\(708\) | −1.13481 | −0.0426487 | ||||||||
\(709\) | −51.1562 | −1.92121 | −0.960606 | − | 0.277913i | \(-0.910357\pi\) | ||||
−0.960606 | + | 0.277913i | \(0.910357\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13.0328 | −0.488768 | ||||||||
\(712\) | −43.6166 | −1.63460 | ||||||||
\(713\) | 1.36927 | 0.0512797 | ||||||||
\(714\) | −8.06101 | −0.301676 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.62483 | −0.0607227 | ||||||||
\(717\) | 21.4965 | 0.802800 | ||||||||
\(718\) | 9.96572 | 0.371917 | ||||||||
\(719\) | 23.1532 | 0.863467 | 0.431734 | − | 0.902001i | \(-0.357902\pi\) | ||||
0.431734 | + | 0.902001i | \(0.357902\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.41286 | 0.276069 | ||||||||
\(722\) | −28.5145 | −1.06120 | ||||||||
\(723\) | 9.16278 | 0.340767 | ||||||||
\(724\) | −4.12708 | −0.153382 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −24.6291 | −0.914071 | ||||||||
\(727\) | −15.4927 | −0.574593 | −0.287297 | − | 0.957842i | \(-0.592757\pi\) | ||||
−0.287297 | + | 0.957842i | \(0.592757\pi\) | |||||||
\(728\) | −10.6072 | −0.393131 | ||||||||
\(729\) | 2.64110 | 0.0978184 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.7407 | 0.471231 | ||||||||
\(732\) | −2.64872 | −0.0978995 | ||||||||
\(733\) | −3.41564 | −0.126159 | −0.0630797 | − | 0.998008i | \(-0.520092\pi\) | ||||
−0.0630797 | + | 0.998008i | \(0.520092\pi\) | |||||||
\(734\) | −19.0144 | −0.701835 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.42032 | −0.0523535 | ||||||||
\(737\) | 9.28193 | 0.341904 | ||||||||
\(738\) | 15.9012 | 0.585330 | ||||||||
\(739\) | 17.9699 | 0.661033 | 0.330516 | − | 0.943800i | \(-0.392777\pi\) | ||||
0.330516 | + | 0.943800i | \(0.392777\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.104310 | −0.00383191 | ||||||||
\(742\) | 1.69559 | 0.0622469 | ||||||||
\(743\) | 1.24775 | 0.0457755 | 0.0228877 | − | 0.999738i | \(-0.492714\pi\) | ||||
0.0228877 | + | 0.999738i | \(0.492714\pi\) | |||||||
\(744\) | 2.93289 | 0.107525 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −9.00867 | −0.329831 | ||||||||
\(747\) | −25.9263 | −0.948593 | ||||||||
\(748\) | −9.26061 | −0.338601 | ||||||||
\(749\) | −3.54317 | −0.129465 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 47.7360 | 1.74191 | 0.870956 | − | 0.491361i | \(-0.163501\pi\) | ||||
0.870956 | + | 0.491361i | \(0.163501\pi\) | |||||||
\(752\) | −8.32666 | −0.303642 | ||||||||
\(753\) | 5.01731 | 0.182841 | ||||||||
\(754\) | −38.5928 | −1.40547 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.09988 | 0.0400021 | ||||||||
\(757\) | 2.61944 | 0.0952052 | 0.0476026 | − | 0.998866i | \(-0.484842\pi\) | ||||
0.0476026 | + | 0.998866i | \(0.484842\pi\) | |||||||
\(758\) | 47.0613 | 1.70934 | ||||||||
\(759\) | 4.55401 | 0.165300 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 27.4578 | 0.995346 | 0.497673 | − | 0.867365i | \(-0.334188\pi\) | ||||
0.497673 | + | 0.867365i | \(0.334188\pi\) | |||||||
\(762\) | −20.4641 | −0.741335 | ||||||||
\(763\) | −12.4712 | −0.451487 | ||||||||
\(764\) | 3.90731 | 0.141362 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8.31076 | 0.300280 | ||||||||
\(767\) | 22.2540 | 0.803547 | ||||||||
\(768\) | −4.87415 | −0.175881 | ||||||||
\(769\) | −15.8642 | −0.572077 | −0.286038 | − | 0.958218i | \(-0.592338\pi\) | ||||
−0.286038 | + | 0.958218i | \(0.592338\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.2922 | 0.658777 | ||||||||
\(772\) | −4.48309 | −0.161350 | ||||||||
\(773\) | 44.2624 | 1.59201 | 0.796004 | − | 0.605292i | \(-0.206944\pi\) | ||||
0.796004 | + | 0.605292i | \(0.206944\pi\) | |||||||
\(774\) | −6.78344 | −0.243826 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 36.4517 | 1.30854 | ||||||||
\(777\) | 2.33840 | 0.0838896 | ||||||||
\(778\) | 12.3126 | 0.441429 | ||||||||
\(779\) | −0.143412 | −0.00513826 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −58.0018 | −2.07547 | ||||||||
\(782\) | 9.87028 | 0.352960 | ||||||||
\(783\) | −27.6915 | −0.989613 | ||||||||
\(784\) | −4.44129 | −0.158617 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.85145 | 0.0660390 | ||||||||
\(787\) | 13.2515 | 0.472367 | 0.236183 | − | 0.971709i | \(-0.424103\pi\) | ||||
0.236183 | + | 0.971709i | \(0.424103\pi\) | |||||||
\(788\) | −3.13520 | −0.111687 | ||||||||
\(789\) | −16.7620 | −0.596744 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.56214 | −0.339990 | ||||||||
\(792\) | −34.1189 | −1.21236 | ||||||||
\(793\) | 51.9424 | 1.84453 | ||||||||
\(794\) | 14.4398 | 0.512450 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.46074 | 0.122663 | ||||||||
\(797\) | 22.6458 | 0.802156 | 0.401078 | − | 0.916044i | \(-0.368636\pi\) | ||||
0.401078 | + | 0.916044i | \(0.368636\pi\) | |||||||
\(798\) | −0.0387082 | −0.00137025 | ||||||||
\(799\) | 12.3298 | 0.436197 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −38.7992 | −1.37090 | ||||||||
\(802\) | 40.2726 | 1.42207 | ||||||||
\(803\) | −40.2099 | −1.41898 | ||||||||
\(804\) | 0.343302 | 0.0121073 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 8.31156 | 0.292762 | ||||||||
\(807\) | 15.0352 | 0.529264 | ||||||||
\(808\) | −22.4734 | −0.790610 | ||||||||
\(809\) | −1.76330 | −0.0619942 | −0.0309971 | − | 0.999519i | \(-0.509868\pi\) | ||||
−0.0309971 | + | 0.999519i | \(0.509868\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18.9434 | −0.665194 | −0.332597 | − | 0.943069i | \(-0.607925\pi\) | ||||
−0.332597 | + | 0.943069i | \(0.607925\pi\) | |||||||
\(812\) | −1.60556 | −0.0563440 | ||||||||
\(813\) | −3.46239 | −0.121431 | ||||||||
\(814\) | 23.9623 | 0.839877 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 23.8541 | 0.835060 | ||||||||
\(817\) | 0.0611795 | 0.00214040 | ||||||||
\(818\) | 54.7670 | 1.91488 | ||||||||
\(819\) | −9.43569 | −0.329710 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −52.4982 | −1.83220 | −0.916099 | − | 0.400952i | \(-0.868679\pi\) | ||||
−0.916099 | + | 0.400952i | \(0.868679\pi\) | |||||||
\(822\) | −7.11252 | −0.248078 | ||||||||
\(823\) | −31.5761 | −1.10067 | −0.550336 | − | 0.834943i | \(-0.685500\pi\) | ||||
−0.550336 | + | 0.834943i | \(0.685500\pi\) | |||||||
\(824\) | −19.4416 | −0.677279 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.25822 | 0.287340 | ||||||||
\(827\) | 0.407237 | 0.0141610 | 0.00708050 | − | 0.999975i | \(-0.497746\pi\) | ||||
0.00708050 | + | 0.999975i | \(0.497746\pi\) | |||||||
\(828\) | −0.589153 | −0.0204745 | ||||||||
\(829\) | 46.9030 | 1.62901 | 0.814504 | − | 0.580158i | \(-0.197009\pi\) | ||||
0.814504 | + | 0.580158i | \(0.197009\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.86060 | 0.0992333 | ||||||||
\(832\) | 27.3036 | 0.946581 | ||||||||
\(833\) | 6.57649 | 0.227862 | ||||||||
\(834\) | 8.60355 | 0.297917 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.0444685 | −0.00153798 | ||||||||
\(837\) | 5.96379 | 0.206139 | ||||||||
\(838\) | −17.7406 | −0.612838 | ||||||||
\(839\) | 42.3064 | 1.46058 | 0.730289 | − | 0.683138i | \(-0.239385\pi\) | ||||
0.730289 | + | 0.683138i | \(0.239385\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.4229 | 0.393895 | ||||||||
\(842\) | −15.0458 | −0.518511 | ||||||||
\(843\) | 14.5159 | 0.499953 | ||||||||
\(844\) | 4.15676 | 0.143082 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −6.56468 | −0.225698 | ||||||||
\(847\) | 20.0934 | 0.690417 | ||||||||
\(848\) | −5.01757 | −0.172304 | ||||||||
\(849\) | 19.9746 | 0.685527 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.86325 | −0.0981508 | ||||||||
\(852\) | −2.14525 | −0.0734952 | ||||||||
\(853\) | −0.228036 | −0.00780779 | −0.00390390 | − | 0.999992i | \(-0.501243\pi\) | ||||
−0.00390390 | + | 0.999992i | \(0.501243\pi\) | |||||||
\(854\) | 19.2752 | 0.659585 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.29261 | 0.317615 | ||||||||
\(857\) | 25.4818 | 0.870440 | 0.435220 | − | 0.900324i | \(-0.356671\pi\) | ||||
0.435220 | + | 0.900324i | \(0.356671\pi\) | |||||||
\(858\) | 27.6431 | 0.943720 | ||||||||
\(859\) | −47.1913 | −1.61015 | −0.805073 | − | 0.593175i | \(-0.797874\pi\) | ||||
−0.805073 | + | 0.593175i | \(0.797874\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.70883 | 0.126397 | ||||||||
\(862\) | −42.0032 | −1.43063 | ||||||||
\(863\) | 1.79277 | 0.0610267 | 0.0305133 | − | 0.999534i | \(-0.490286\pi\) | ||||
0.0305133 | + | 0.999534i | \(0.490286\pi\) | |||||||
\(864\) | −6.18610 | −0.210456 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −25.6627 | −0.872054 | ||||||||
\(867\) | −21.4384 | −0.728087 | ||||||||
\(868\) | 0.345781 | 0.0117366 | ||||||||
\(869\) | −31.1498 | −1.05668 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.73227 | −0.228114 | ||||||||
\(872\) | 32.7079 | 1.10763 | ||||||||
\(873\) | 32.4257 | 1.09744 | ||||||||
\(874\) | 0.0473961 | 0.00160320 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.48720 | −0.0502479 | ||||||||
\(877\) | −32.3361 | −1.09191 | −0.545957 | − | 0.837813i | \(-0.683834\pi\) | ||||
−0.545957 | + | 0.837813i | \(0.683834\pi\) | |||||||
\(878\) | 37.0549 | 1.25054 | ||||||||
\(879\) | 1.29540 | 0.0436928 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 47.1294 | 1.58783 | 0.793914 | − | 0.608030i | \(-0.208040\pi\) | ||||
0.793914 | + | 0.608030i | \(0.208040\pi\) | |||||||
\(882\) | −3.50148 | −0.117901 | ||||||||
\(883\) | −53.7694 | −1.80948 | −0.904742 | − | 0.425960i | \(-0.859936\pi\) | ||||
−0.904742 | + | 0.425960i | \(0.859936\pi\) | |||||||
\(884\) | 6.71681 | 0.225911 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −33.5456 | −1.12699 | ||||||||
\(887\) | 13.4916 | 0.453005 | 0.226502 | − | 0.974011i | \(-0.427271\pi\) | ||||
0.226502 | + | 0.974011i | \(0.427271\pi\) | |||||||
\(888\) | −6.13287 | −0.205806 | ||||||||
\(889\) | 16.6954 | 0.559946 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −19.1928 | −0.642984 | ||||||||
\(892\) | 3.74372 | 0.125349 | ||||||||
\(893\) | 0.0592065 | 0.00198127 | ||||||||
\(894\) | 26.1007 | 0.872938 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 12.9727 | 0.433387 | ||||||||
\(897\) | −3.30307 | −0.110286 | ||||||||
\(898\) | −21.1446 | −0.705605 | ||||||||
\(899\) | −8.70570 | −0.290351 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.42983 | 0.247523 | ||||||||
\(902\) | 38.0055 | 1.26544 | ||||||||
\(903\) | −1.58219 | −0.0526520 | ||||||||
\(904\) | 25.0784 | 0.834096 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −3.12944 | −0.103969 | ||||||||
\(907\) | 32.7055 | 1.08597 | 0.542985 | − | 0.839742i | \(-0.317294\pi\) | ||||
0.542985 | + | 0.839742i | \(0.317294\pi\) | |||||||
\(908\) | 4.61878 | 0.153280 | ||||||||
\(909\) | −19.9912 | −0.663067 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.0799151 | 0.00264771 | 0.00132385 | − | 0.999999i | \(-0.499579\pi\) | ||||
0.00132385 | + | 0.999999i | \(0.499579\pi\) | |||||||
\(912\) | 0.114545 | 0.00379296 | ||||||||
\(913\) | −61.9666 | −2.05080 | ||||||||
\(914\) | 44.8584 | 1.48378 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 6.56618 | 0.216953 | ||||||||
\(917\) | −1.51048 | −0.0498806 | ||||||||
\(918\) | 42.9894 | 1.41886 | ||||||||
\(919\) | 42.9841 | 1.41792 | 0.708958 | − | 0.705251i | \(-0.249166\pi\) | ||||
0.708958 | + | 0.705251i | \(0.249166\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.54974 | 0.248773 | ||||||||
\(922\) | −44.5389 | −1.46681 | ||||||||
\(923\) | 42.0692 | 1.38473 | ||||||||
\(924\) | 1.15002 | 0.0378329 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 19.5430 | 0.642222 | ||||||||
\(927\) | −17.2943 | −0.568018 | ||||||||
\(928\) | 9.03023 | 0.296432 | ||||||||
\(929\) | 23.3398 | 0.765754 | 0.382877 | − | 0.923799i | \(-0.374933\pi\) | ||||
0.382877 | + | 0.923799i | \(0.374933\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.0315796 | 0.00103498 | ||||||||
\(932\) | −2.39826 | −0.0785577 | ||||||||
\(933\) | 15.8938 | 0.520339 | ||||||||
\(934\) | 13.7228 | 0.449024 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 24.7468 | 0.808874 | ||||||||
\(937\) | 11.7697 | 0.384500 | 0.192250 | − | 0.981346i | \(-0.438422\pi\) | ||||
0.192250 | + | 0.981346i | \(0.438422\pi\) | |||||||
\(938\) | −2.49827 | −0.0815714 | ||||||||
\(939\) | −20.7633 | −0.677585 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.51567 | −0.147207 | −0.0736034 | − | 0.997288i | \(-0.523450\pi\) | ||||
−0.0736034 | + | 0.997288i | \(0.523450\pi\) | |||||||
\(942\) | −9.57442 | −0.311951 | ||||||||
\(943\) | −4.54127 | −0.147884 | ||||||||
\(944\) | −24.4377 | −0.795379 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −16.2132 | −0.527135 | ||||||||
\(947\) | −19.0220 | −0.618133 | −0.309066 | − | 0.951040i | \(-0.600017\pi\) | ||||
−0.309066 | + | 0.951040i | \(0.600017\pi\) | |||||||
\(948\) | −1.15211 | −0.0374187 | ||||||||
\(949\) | 29.1646 | 0.946723 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.26637 | 0.170774 | ||||||||
\(952\) | −17.2480 | −0.559012 | ||||||||
\(953\) | 43.3856 | 1.40540 | 0.702699 | − | 0.711488i | \(-0.251978\pi\) | ||||
0.702699 | + | 0.711488i | \(0.251978\pi\) | |||||||
\(954\) | −3.95582 | −0.128074 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −6.64689 | −0.214976 | ||||||||
\(957\) | −28.9540 | −0.935949 | ||||||||
\(958\) | −13.5484 | −0.437728 | ||||||||
\(959\) | 5.80267 | 0.187378 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.1251 | −0.939519 | ||||||||
\(962\) | −17.3801 | −0.560356 | ||||||||
\(963\) | 8.26625 | 0.266376 | ||||||||
\(964\) | −2.83321 | −0.0912515 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.22573 | −0.0394373 | ||||||||
\(967\) | −41.0523 | −1.32015 | −0.660076 | − | 0.751199i | \(-0.729476\pi\) | ||||
−0.660076 | + | 0.751199i | \(0.729476\pi\) | |||||||
\(968\) | −52.6985 | −1.69379 | ||||||||
\(969\) | −0.169614 | −0.00544878 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −38.5361 | −1.23668 | −0.618341 | − | 0.785910i | \(-0.712195\pi\) | ||||
−0.618341 | + | 0.785910i | \(0.712195\pi\) | |||||||
\(972\) | −4.00949 | −0.128605 | ||||||||
\(973\) | −7.01912 | −0.225023 | ||||||||
\(974\) | −48.4958 | −1.55391 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −57.0392 | −1.82578 | ||||||||
\(977\) | 37.5284 | 1.20064 | 0.600320 | − | 0.799760i | \(-0.295040\pi\) | ||||
0.600320 | + | 0.799760i | \(0.295040\pi\) | |||||||
\(978\) | −28.4856 | −0.910870 | ||||||||
\(979\) | −92.7344 | −2.96380 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 29.0953 | 0.928943 | ||||||||
\(982\) | 30.7869 | 0.982449 | ||||||||
\(983\) | 48.9074 | 1.55990 | 0.779952 | − | 0.625839i | \(-0.215243\pi\) | ||||
0.779952 | + | 0.625839i | \(0.215243\pi\) | |||||||
\(984\) | −9.72708 | −0.310088 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −62.7543 | −1.99850 | ||||||||
\(987\) | −1.53117 | −0.0487375 | ||||||||
\(988\) | 0.0322534 | 0.00102612 | ||||||||
\(989\) | 1.93731 | 0.0616028 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.69537 | −0.276217 | −0.138109 | − | 0.990417i | \(-0.544102\pi\) | ||||
−0.138109 | + | 0.990417i | \(0.544102\pi\) | |||||||
\(992\) | −1.94480 | −0.0617474 | ||||||||
\(993\) | −19.4282 | −0.616534 | ||||||||
\(994\) | 15.6114 | 0.495164 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −2.29190 | −0.0726215 | ||||||||
\(997\) | 13.9339 | 0.441290 | 0.220645 | − | 0.975354i | \(-0.429184\pi\) | ||||
0.220645 | + | 0.975354i | \(0.429184\pi\) | |||||||
\(998\) | 37.4369 | 1.18505 | ||||||||
\(999\) | −12.4707 | −0.394556 |
(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 | 4025.2.a.be.1.15 | 21 | ||
5.2 | odd | 4 | 805.2.c.c.484.30 | yes | 42 | ||
5.3 | odd | 4 | 805.2.c.c.484.13 | ✓ | 42 | ||
5.4 | even | 2 | 4025.2.a.bd.1.7 | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
805.2.c.c.484.13 | ✓ | 42 | 5.3 | odd | 4 | ||
805.2.c.c.484.30 | yes | 42 | 5.2 | odd | 4 | ||
4025.2.a.bd.1.7 | 21 | 5.4 | even | 2 | |||
4025.2.a.be.1.15 | 21 | 1.1 | even | 1 | trivial |