Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7098,2,Mod(1,7098)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7098, 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("7098.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7098.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: | \(56.6778153547\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{14})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.80194\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7098.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.80194 | −1.25306 | −0.626532 | − | 0.779395i | \(-0.715526\pi\) | ||||
−0.626532 | + | 0.779395i | \(0.715526\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.80194 | −0.886051 | ||||||||
\(11\) | 1.33513 | 0.402556 | 0.201278 | − | 0.979534i | \(-0.435491\pi\) | ||||
0.201278 | + | 0.979534i | \(0.435491\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 2.80194 | 0.723457 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.356896 | 0.0865600 | 0.0432800 | − | 0.999063i | \(-0.486219\pi\) | ||||
0.0432800 | + | 0.999063i | \(0.486219\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −2.44504 | −0.560931 | −0.280466 | − | 0.959864i | \(-0.590489\pi\) | ||||
−0.280466 | + | 0.959864i | \(0.590489\pi\) | |||||||
\(20\) | −2.80194 | −0.626532 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 1.33513 | 0.284650 | ||||||||
\(23\) | 2.51573 | 0.524566 | 0.262283 | − | 0.964991i | \(-0.415525\pi\) | ||||
0.262283 | + | 0.964991i | \(0.415525\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 2.85086 | 0.570171 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | −5.63102 | −1.04565 | −0.522827 | − | 0.852439i | \(-0.675123\pi\) | ||||
−0.522827 | + | 0.852439i | \(0.675123\pi\) | |||||||
\(30\) | 2.80194 | 0.511562 | ||||||||
\(31\) | −9.54288 | −1.71395 | −0.856976 | − | 0.515357i | \(-0.827659\pi\) | ||||
−0.856976 | + | 0.515357i | \(0.827659\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −1.33513 | −0.232416 | ||||||||
\(34\) | 0.356896 | 0.0612071 | ||||||||
\(35\) | −2.80194 | −0.473614 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 1.69202 | 0.278167 | 0.139083 | − | 0.990281i | \(-0.455584\pi\) | ||||
0.139083 | + | 0.990281i | \(0.455584\pi\) | |||||||
\(38\) | −2.44504 | −0.396638 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.80194 | −0.443025 | ||||||||
\(41\) | 2.80194 | 0.437589 | 0.218795 | − | 0.975771i | \(-0.429788\pi\) | ||||
0.218795 | + | 0.975771i | \(0.429788\pi\) | |||||||
\(42\) | −1.00000 | −0.154303 | ||||||||
\(43\) | 6.51573 | 0.993639 | 0.496820 | − | 0.867854i | \(-0.334501\pi\) | ||||
0.496820 | + | 0.867854i | \(0.334501\pi\) | |||||||
\(44\) | 1.33513 | 0.201278 | ||||||||
\(45\) | −2.80194 | −0.417688 | ||||||||
\(46\) | 2.51573 | 0.370924 | ||||||||
\(47\) | 5.09783 | 0.743596 | 0.371798 | − | 0.928314i | \(-0.378741\pi\) | ||||
0.371798 | + | 0.928314i | \(0.378741\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 2.85086 | 0.403172 | ||||||||
\(51\) | −0.356896 | −0.0499754 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.25667 | 1.13414 | 0.567070 | − | 0.823669i | \(-0.308077\pi\) | ||||
0.567070 | + | 0.823669i | \(0.308077\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −3.74094 | −0.504428 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 2.44504 | 0.323854 | ||||||||
\(58\) | −5.63102 | −0.739389 | ||||||||
\(59\) | −4.18598 | −0.544968 | −0.272484 | − | 0.962160i | \(-0.587845\pi\) | ||||
−0.272484 | + | 0.962160i | \(0.587845\pi\) | |||||||
\(60\) | 2.80194 | 0.361729 | ||||||||
\(61\) | −7.00000 | −0.896258 | −0.448129 | − | 0.893969i | \(-0.647910\pi\) | ||||
−0.448129 | + | 0.893969i | \(0.647910\pi\) | |||||||
\(62\) | −9.54288 | −1.21195 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.33513 | −0.164343 | ||||||||
\(67\) | 8.83877 | 1.07983 | 0.539914 | − | 0.841720i | \(-0.318457\pi\) | ||||
0.539914 | + | 0.841720i | \(0.318457\pi\) | |||||||
\(68\) | 0.356896 | 0.0432800 | ||||||||
\(69\) | −2.51573 | −0.302858 | ||||||||
\(70\) | −2.80194 | −0.334896 | ||||||||
\(71\) | −5.20775 | −0.618046 | −0.309023 | − | 0.951055i | \(-0.600002\pi\) | ||||
−0.309023 | + | 0.951055i | \(0.600002\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 0.850855 | 0.0995851 | 0.0497925 | − | 0.998760i | \(-0.484144\pi\) | ||||
0.0497925 | + | 0.998760i | \(0.484144\pi\) | |||||||
\(74\) | 1.69202 | 0.196694 | ||||||||
\(75\) | −2.85086 | −0.329188 | ||||||||
\(76\) | −2.44504 | −0.280466 | ||||||||
\(77\) | 1.33513 | 0.152152 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.80194 | −0.990295 | −0.495148 | − | 0.868809i | \(-0.664886\pi\) | ||||
−0.495148 | + | 0.868809i | \(0.664886\pi\) | |||||||
\(80\) | −2.80194 | −0.313266 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 2.80194 | 0.309422 | ||||||||
\(83\) | −10.4450 | −1.14649 | −0.573246 | − | 0.819383i | \(-0.694316\pi\) | ||||
−0.573246 | + | 0.819383i | \(0.694316\pi\) | |||||||
\(84\) | −1.00000 | −0.109109 | ||||||||
\(85\) | −1.00000 | −0.108465 | ||||||||
\(86\) | 6.51573 | 0.702609 | ||||||||
\(87\) | 5.63102 | 0.603709 | ||||||||
\(88\) | 1.33513 | 0.142325 | ||||||||
\(89\) | −3.40044 | −0.360446 | −0.180223 | − | 0.983626i | \(-0.557682\pi\) | ||||
−0.180223 | + | 0.983626i | \(0.557682\pi\) | |||||||
\(90\) | −2.80194 | −0.295350 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2.51573 | 0.262283 | ||||||||
\(93\) | 9.54288 | 0.989550 | ||||||||
\(94\) | 5.09783 | 0.525801 | ||||||||
\(95\) | 6.85086 | 0.702883 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −8.08815 | −0.821227 | −0.410613 | − | 0.911810i | \(-0.634685\pi\) | ||||
−0.410613 | + | 0.911810i | \(0.634685\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 1.33513 | 0.134185 | ||||||||
\(100\) | 2.85086 | 0.285086 | ||||||||
\(101\) | −6.53319 | −0.650076 | −0.325038 | − | 0.945701i | \(-0.605377\pi\) | ||||
−0.325038 | + | 0.945701i | \(0.605377\pi\) | |||||||
\(102\) | −0.356896 | −0.0353380 | ||||||||
\(103\) | 0.225209 | 0.0221905 | 0.0110953 | − | 0.999938i | \(-0.496468\pi\) | ||||
0.0110953 | + | 0.999938i | \(0.496468\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.80194 | 0.273441 | ||||||||
\(106\) | 8.25667 | 0.801959 | ||||||||
\(107\) | 4.50604 | 0.435615 | 0.217808 | − | 0.975992i | \(-0.430109\pi\) | ||||
0.217808 | + | 0.975992i | \(0.430109\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −7.10752 | −0.680777 | −0.340389 | − | 0.940285i | \(-0.610559\pi\) | ||||
−0.340389 | + | 0.940285i | \(0.610559\pi\) | |||||||
\(110\) | −3.74094 | −0.356685 | ||||||||
\(111\) | −1.69202 | −0.160600 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | 2.86831 | 0.269828 | 0.134914 | − | 0.990857i | \(-0.456924\pi\) | ||||
0.134914 | + | 0.990857i | \(0.456924\pi\) | |||||||
\(114\) | 2.44504 | 0.228999 | ||||||||
\(115\) | −7.04892 | −0.657315 | ||||||||
\(116\) | −5.63102 | −0.522827 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.18598 | −0.385351 | ||||||||
\(119\) | 0.356896 | 0.0327166 | ||||||||
\(120\) | 2.80194 | 0.255781 | ||||||||
\(121\) | −9.21744 | −0.837949 | ||||||||
\(122\) | −7.00000 | −0.633750 | ||||||||
\(123\) | −2.80194 | −0.252642 | ||||||||
\(124\) | −9.54288 | −0.856976 | ||||||||
\(125\) | 6.02177 | 0.538604 | ||||||||
\(126\) | 1.00000 | 0.0890871 | ||||||||
\(127\) | 2.57673 | 0.228648 | 0.114324 | − | 0.993444i | \(-0.463530\pi\) | ||||
0.114324 | + | 0.993444i | \(0.463530\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −6.51573 | −0.573678 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.7724 | 1.11593 | 0.557965 | − | 0.829865i | \(-0.311582\pi\) | ||||
0.557965 | + | 0.829865i | \(0.311582\pi\) | |||||||
\(132\) | −1.33513 | −0.116208 | ||||||||
\(133\) | −2.44504 | −0.212012 | ||||||||
\(134\) | 8.83877 | 0.763554 | ||||||||
\(135\) | 2.80194 | 0.241152 | ||||||||
\(136\) | 0.356896 | 0.0306036 | ||||||||
\(137\) | −7.30798 | −0.624363 | −0.312181 | − | 0.950023i | \(-0.601060\pi\) | ||||
−0.312181 | + | 0.950023i | \(0.601060\pi\) | |||||||
\(138\) | −2.51573 | −0.214153 | ||||||||
\(139\) | 22.9812 | 1.94924 | 0.974621 | − | 0.223863i | \(-0.0718669\pi\) | ||||
0.974621 | + | 0.223863i | \(0.0718669\pi\) | |||||||
\(140\) | −2.80194 | −0.236807 | ||||||||
\(141\) | −5.09783 | −0.429315 | ||||||||
\(142\) | −5.20775 | −0.437025 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 15.7778 | 1.31027 | ||||||||
\(146\) | 0.850855 | 0.0704173 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 1.69202 | 0.139083 | ||||||||
\(149\) | 3.95108 | 0.323685 | 0.161843 | − | 0.986817i | \(-0.448256\pi\) | ||||
0.161843 | + | 0.986817i | \(0.448256\pi\) | |||||||
\(150\) | −2.85086 | −0.232771 | ||||||||
\(151\) | −5.26875 | −0.428765 | −0.214382 | − | 0.976750i | \(-0.568774\pi\) | ||||
−0.214382 | + | 0.976750i | \(0.568774\pi\) | |||||||
\(152\) | −2.44504 | −0.198319 | ||||||||
\(153\) | 0.356896 | 0.0288533 | ||||||||
\(154\) | 1.33513 | 0.107587 | ||||||||
\(155\) | 26.7385 | 2.14769 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.1521 | −1.28908 | −0.644540 | − | 0.764570i | \(-0.722951\pi\) | ||||
−0.644540 | + | 0.764570i | \(0.722951\pi\) | |||||||
\(158\) | −8.80194 | −0.700245 | ||||||||
\(159\) | −8.25667 | −0.654796 | ||||||||
\(160\) | −2.80194 | −0.221513 | ||||||||
\(161\) | 2.51573 | 0.198267 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −11.9825 | −0.938545 | −0.469273 | − | 0.883053i | \(-0.655484\pi\) | ||||
−0.469273 | + | 0.883053i | \(0.655484\pi\) | |||||||
\(164\) | 2.80194 | 0.218795 | ||||||||
\(165\) | 3.74094 | 0.291232 | ||||||||
\(166\) | −10.4450 | −0.810692 | ||||||||
\(167\) | −18.6069 | −1.43984 | −0.719921 | − | 0.694056i | \(-0.755822\pi\) | ||||
−0.719921 | + | 0.694056i | \(0.755822\pi\) | |||||||
\(168\) | −1.00000 | −0.0771517 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −1.00000 | −0.0766965 | ||||||||
\(171\) | −2.44504 | −0.186977 | ||||||||
\(172\) | 6.51573 | 0.496820 | ||||||||
\(173\) | 15.0422 | 1.14364 | 0.571819 | − | 0.820380i | \(-0.306238\pi\) | ||||
0.571819 | + | 0.820380i | \(0.306238\pi\) | |||||||
\(174\) | 5.63102 | 0.426887 | ||||||||
\(175\) | 2.85086 | 0.215504 | ||||||||
\(176\) | 1.33513 | 0.100639 | ||||||||
\(177\) | 4.18598 | 0.314638 | ||||||||
\(178\) | −3.40044 | −0.254873 | ||||||||
\(179\) | −23.6112 | −1.76478 | −0.882391 | − | 0.470517i | \(-0.844067\pi\) | ||||
−0.882391 | + | 0.470517i | \(0.844067\pi\) | |||||||
\(180\) | −2.80194 | −0.208844 | ||||||||
\(181\) | 15.6679 | 1.16458 | 0.582291 | − | 0.812980i | \(-0.302156\pi\) | ||||
0.582291 | + | 0.812980i | \(0.302156\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.00000 | 0.517455 | ||||||||
\(184\) | 2.51573 | 0.185462 | ||||||||
\(185\) | −4.74094 | −0.348561 | ||||||||
\(186\) | 9.54288 | 0.699718 | ||||||||
\(187\) | 0.476501 | 0.0348452 | ||||||||
\(188\) | 5.09783 | 0.371798 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 6.85086 | 0.497013 | ||||||||
\(191\) | −22.5526 | −1.63185 | −0.815923 | − | 0.578160i | \(-0.803771\pi\) | ||||
−0.815923 | + | 0.578160i | \(0.803771\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −24.2610 | −1.74634 | −0.873172 | − | 0.487413i | \(-0.837941\pi\) | ||||
−0.873172 | + | 0.487413i | \(0.837941\pi\) | |||||||
\(194\) | −8.08815 | −0.580695 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −0.411190 | −0.0292961 | −0.0146480 | − | 0.999893i | \(-0.504663\pi\) | ||||
−0.0146480 | + | 0.999893i | \(0.504663\pi\) | |||||||
\(198\) | 1.33513 | 0.0948832 | ||||||||
\(199\) | −5.73125 | −0.406278 | −0.203139 | − | 0.979150i | \(-0.565114\pi\) | ||||
−0.203139 | + | 0.979150i | \(0.565114\pi\) | |||||||
\(200\) | 2.85086 | 0.201586 | ||||||||
\(201\) | −8.83877 | −0.623439 | ||||||||
\(202\) | −6.53319 | −0.459673 | ||||||||
\(203\) | −5.63102 | −0.395220 | ||||||||
\(204\) | −0.356896 | −0.0249877 | ||||||||
\(205\) | −7.85086 | −0.548328 | ||||||||
\(206\) | 0.225209 | 0.0156911 | ||||||||
\(207\) | 2.51573 | 0.174855 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.26444 | −0.225806 | ||||||||
\(210\) | 2.80194 | 0.193352 | ||||||||
\(211\) | −24.5284 | −1.68860 | −0.844302 | − | 0.535867i | \(-0.819985\pi\) | ||||
−0.844302 | + | 0.535867i | \(0.819985\pi\) | |||||||
\(212\) | 8.25667 | 0.567070 | ||||||||
\(213\) | 5.20775 | 0.356829 | ||||||||
\(214\) | 4.50604 | 0.308027 | ||||||||
\(215\) | −18.2567 | −1.24509 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −9.54288 | −0.647813 | ||||||||
\(218\) | −7.10752 | −0.481382 | ||||||||
\(219\) | −0.850855 | −0.0574955 | ||||||||
\(220\) | −3.74094 | −0.252214 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −1.69202 | −0.113561 | ||||||||
\(223\) | −21.0532 | −1.40983 | −0.704914 | − | 0.709293i | \(-0.749015\pi\) | ||||
−0.704914 | + | 0.709293i | \(0.749015\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 2.85086 | 0.190057 | ||||||||
\(226\) | 2.86831 | 0.190797 | ||||||||
\(227\) | 3.49827 | 0.232188 | 0.116094 | − | 0.993238i | \(-0.462963\pi\) | ||||
0.116094 | + | 0.993238i | \(0.462963\pi\) | |||||||
\(228\) | 2.44504 | 0.161927 | ||||||||
\(229\) | −22.0097 | −1.45444 | −0.727221 | − | 0.686404i | \(-0.759188\pi\) | ||||
−0.727221 | + | 0.686404i | \(0.759188\pi\) | |||||||
\(230\) | −7.04892 | −0.464792 | ||||||||
\(231\) | −1.33513 | −0.0878448 | ||||||||
\(232\) | −5.63102 | −0.369695 | ||||||||
\(233\) | 21.2204 | 1.39020 | 0.695098 | − | 0.718915i | \(-0.255361\pi\) | ||||
0.695098 | + | 0.718915i | \(0.255361\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −14.2838 | −0.931773 | ||||||||
\(236\) | −4.18598 | −0.272484 | ||||||||
\(237\) | 8.80194 | 0.571747 | ||||||||
\(238\) | 0.356896 | 0.0231341 | ||||||||
\(239\) | −2.09783 | −0.135698 | −0.0678488 | − | 0.997696i | \(-0.521614\pi\) | ||||
−0.0678488 | + | 0.997696i | \(0.521614\pi\) | |||||||
\(240\) | 2.80194 | 0.180864 | ||||||||
\(241\) | −5.22952 | −0.336863 | −0.168432 | − | 0.985713i | \(-0.553870\pi\) | ||||
−0.168432 | + | 0.985713i | \(0.553870\pi\) | |||||||
\(242\) | −9.21744 | −0.592519 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −7.00000 | −0.448129 | ||||||||
\(245\) | −2.80194 | −0.179009 | ||||||||
\(246\) | −2.80194 | −0.178645 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −9.54288 | −0.605973 | ||||||||
\(249\) | 10.4450 | 0.661928 | ||||||||
\(250\) | 6.02177 | 0.380850 | ||||||||
\(251\) | −11.4426 | −0.722254 | −0.361127 | − | 0.932517i | \(-0.617608\pi\) | ||||
−0.361127 | + | 0.932517i | \(0.617608\pi\) | |||||||
\(252\) | 1.00000 | 0.0629941 | ||||||||
\(253\) | 3.35881 | 0.211167 | ||||||||
\(254\) | 2.57673 | 0.161678 | ||||||||
\(255\) | 1.00000 | 0.0626224 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −21.5623 | −1.34502 | −0.672508 | − | 0.740090i | \(-0.734783\pi\) | ||||
−0.672508 | + | 0.740090i | \(0.734783\pi\) | |||||||
\(258\) | −6.51573 | −0.405652 | ||||||||
\(259\) | 1.69202 | 0.105137 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.63102 | −0.348552 | ||||||||
\(262\) | 12.7724 | 0.789081 | ||||||||
\(263\) | −11.5284 | −0.710872 | −0.355436 | − | 0.934701i | \(-0.615668\pi\) | ||||
−0.355436 | + | 0.934701i | \(0.615668\pi\) | |||||||
\(264\) | −1.33513 | −0.0821713 | ||||||||
\(265\) | −23.1347 | −1.42115 | ||||||||
\(266\) | −2.44504 | −0.149915 | ||||||||
\(267\) | 3.40044 | 0.208103 | ||||||||
\(268\) | 8.83877 | 0.539914 | ||||||||
\(269\) | −30.5211 | −1.86090 | −0.930452 | − | 0.366413i | \(-0.880586\pi\) | ||||
−0.930452 | + | 0.366413i | \(0.880586\pi\) | |||||||
\(270\) | 2.80194 | 0.170521 | ||||||||
\(271\) | −12.6160 | −0.766365 | −0.383182 | − | 0.923673i | \(-0.625172\pi\) | ||||
−0.383182 | + | 0.923673i | \(0.625172\pi\) | |||||||
\(272\) | 0.356896 | 0.0216400 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −7.30798 | −0.441491 | ||||||||
\(275\) | 3.80625 | 0.229525 | ||||||||
\(276\) | −2.51573 | −0.151429 | ||||||||
\(277\) | 14.7899 | 0.888636 | 0.444318 | − | 0.895869i | \(-0.353446\pi\) | ||||
0.444318 | + | 0.895869i | \(0.353446\pi\) | |||||||
\(278\) | 22.9812 | 1.37832 | ||||||||
\(279\) | −9.54288 | −0.571317 | ||||||||
\(280\) | −2.80194 | −0.167448 | ||||||||
\(281\) | 15.5623 | 0.928366 | 0.464183 | − | 0.885739i | \(-0.346348\pi\) | ||||
0.464183 | + | 0.885739i | \(0.346348\pi\) | |||||||
\(282\) | −5.09783 | −0.303572 | ||||||||
\(283\) | 17.5894 | 1.04558 | 0.522791 | − | 0.852461i | \(-0.324891\pi\) | ||||
0.522791 | + | 0.852461i | \(0.324891\pi\) | |||||||
\(284\) | −5.20775 | −0.309023 | ||||||||
\(285\) | −6.85086 | −0.405810 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.80194 | 0.165393 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −16.8726 | −0.992507 | ||||||||
\(290\) | 15.7778 | 0.926503 | ||||||||
\(291\) | 8.08815 | 0.474136 | ||||||||
\(292\) | 0.850855 | 0.0497925 | ||||||||
\(293\) | 11.4263 | 0.667529 | 0.333764 | − | 0.942656i | \(-0.391681\pi\) | ||||
0.333764 | + | 0.942656i | \(0.391681\pi\) | |||||||
\(294\) | −1.00000 | −0.0583212 | ||||||||
\(295\) | 11.7289 | 0.682880 | ||||||||
\(296\) | 1.69202 | 0.0983468 | ||||||||
\(297\) | −1.33513 | −0.0774718 | ||||||||
\(298\) | 3.95108 | 0.228880 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −2.85086 | −0.164594 | ||||||||
\(301\) | 6.51573 | 0.375560 | ||||||||
\(302\) | −5.26875 | −0.303182 | ||||||||
\(303\) | 6.53319 | 0.375322 | ||||||||
\(304\) | −2.44504 | −0.140233 | ||||||||
\(305\) | 19.6136 | 1.12307 | ||||||||
\(306\) | 0.356896 | 0.0204024 | ||||||||
\(307\) | −10.5670 | −0.603093 | −0.301546 | − | 0.953452i | \(-0.597503\pi\) | ||||
−0.301546 | + | 0.953452i | \(0.597503\pi\) | |||||||
\(308\) | 1.33513 | 0.0760758 | ||||||||
\(309\) | −0.225209 | −0.0128117 | ||||||||
\(310\) | 26.7385 | 1.51865 | ||||||||
\(311\) | −7.40821 | −0.420081 | −0.210040 | − | 0.977693i | \(-0.567360\pi\) | ||||
−0.210040 | + | 0.977693i | \(0.567360\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.12737 | −0.120246 | −0.0601232 | − | 0.998191i | \(-0.519149\pi\) | ||||
−0.0601232 | + | 0.998191i | \(0.519149\pi\) | |||||||
\(314\) | −16.1521 | −0.911517 | ||||||||
\(315\) | −2.80194 | −0.157871 | ||||||||
\(316\) | −8.80194 | −0.495148 | ||||||||
\(317\) | 32.6383 | 1.83315 | 0.916575 | − | 0.399862i | \(-0.130942\pi\) | ||||
0.916575 | + | 0.399862i | \(0.130942\pi\) | |||||||
\(318\) | −8.25667 | −0.463011 | ||||||||
\(319\) | −7.51812 | −0.420934 | ||||||||
\(320\) | −2.80194 | −0.156633 | ||||||||
\(321\) | −4.50604 | −0.251503 | ||||||||
\(322\) | 2.51573 | 0.140196 | ||||||||
\(323\) | −0.872625 | −0.0485542 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −11.9825 | −0.663652 | ||||||||
\(327\) | 7.10752 | 0.393047 | ||||||||
\(328\) | 2.80194 | 0.154711 | ||||||||
\(329\) | 5.09783 | 0.281053 | ||||||||
\(330\) | 3.74094 | 0.205932 | ||||||||
\(331\) | −30.0006 | −1.64898 | −0.824491 | − | 0.565875i | \(-0.808538\pi\) | ||||
−0.824491 | + | 0.565875i | \(0.808538\pi\) | |||||||
\(332\) | −10.4450 | −0.573246 | ||||||||
\(333\) | 1.69202 | 0.0927222 | ||||||||
\(334\) | −18.6069 | −1.01812 | ||||||||
\(335\) | −24.7657 | −1.35309 | ||||||||
\(336\) | −1.00000 | −0.0545545 | ||||||||
\(337\) | 12.5472 | 0.683489 | 0.341744 | − | 0.939793i | \(-0.388982\pi\) | ||||
0.341744 | + | 0.939793i | \(0.388982\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.86831 | −0.155785 | ||||||||
\(340\) | −1.00000 | −0.0542326 | ||||||||
\(341\) | −12.7409 | −0.689961 | ||||||||
\(342\) | −2.44504 | −0.132213 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 6.51573 | 0.351305 | ||||||||
\(345\) | 7.04892 | 0.379501 | ||||||||
\(346\) | 15.0422 | 0.808674 | ||||||||
\(347\) | 25.5719 | 1.37277 | 0.686387 | − | 0.727237i | \(-0.259196\pi\) | ||||
0.686387 | + | 0.727237i | \(0.259196\pi\) | |||||||
\(348\) | 5.63102 | 0.301854 | ||||||||
\(349\) | −22.9855 | −1.23039 | −0.615193 | − | 0.788376i | \(-0.710922\pi\) | ||||
−0.615193 | + | 0.788376i | \(0.710922\pi\) | |||||||
\(350\) | 2.85086 | 0.152385 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.33513 | 0.0711624 | ||||||||
\(353\) | 22.4397 | 1.19434 | 0.597171 | − | 0.802114i | \(-0.296291\pi\) | ||||
0.597171 | + | 0.802114i | \(0.296291\pi\) | |||||||
\(354\) | 4.18598 | 0.222482 | ||||||||
\(355\) | 14.5918 | 0.774452 | ||||||||
\(356\) | −3.40044 | −0.180223 | ||||||||
\(357\) | −0.356896 | −0.0188889 | ||||||||
\(358\) | −23.6112 | −1.24789 | ||||||||
\(359\) | 6.80492 | 0.359150 | 0.179575 | − | 0.983744i | \(-0.442528\pi\) | ||||
0.179575 | + | 0.983744i | \(0.442528\pi\) | |||||||
\(360\) | −2.80194 | −0.147675 | ||||||||
\(361\) | −13.0218 | −0.685356 | ||||||||
\(362\) | 15.6679 | 0.823484 | ||||||||
\(363\) | 9.21744 | 0.483790 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.38404 | −0.124787 | ||||||||
\(366\) | 7.00000 | 0.365896 | ||||||||
\(367\) | −21.9409 | −1.14531 | −0.572653 | − | 0.819798i | \(-0.694086\pi\) | ||||
−0.572653 | + | 0.819798i | \(0.694086\pi\) | |||||||
\(368\) | 2.51573 | 0.131141 | ||||||||
\(369\) | 2.80194 | 0.145863 | ||||||||
\(370\) | −4.74094 | −0.246470 | ||||||||
\(371\) | 8.25667 | 0.428665 | ||||||||
\(372\) | 9.54288 | 0.494775 | ||||||||
\(373\) | −18.3207 | −0.948607 | −0.474304 | − | 0.880361i | \(-0.657300\pi\) | ||||
−0.474304 | + | 0.880361i | \(0.657300\pi\) | |||||||
\(374\) | 0.476501 | 0.0246393 | ||||||||
\(375\) | −6.02177 | −0.310963 | ||||||||
\(376\) | 5.09783 | 0.262901 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −1.00000 | −0.0514344 | ||||||||
\(379\) | −25.8950 | −1.33014 | −0.665068 | − | 0.746783i | \(-0.731597\pi\) | ||||
−0.665068 | + | 0.746783i | \(0.731597\pi\) | |||||||
\(380\) | 6.85086 | 0.351441 | ||||||||
\(381\) | −2.57673 | −0.132010 | ||||||||
\(382\) | −22.5526 | −1.15389 | ||||||||
\(383\) | −20.0218 | −1.02306 | −0.511532 | − | 0.859264i | \(-0.670922\pi\) | ||||
−0.511532 | + | 0.859264i | \(0.670922\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −3.74094 | −0.190656 | ||||||||
\(386\) | −24.2610 | −1.23485 | ||||||||
\(387\) | 6.51573 | 0.331213 | ||||||||
\(388\) | −8.08815 | −0.410613 | ||||||||
\(389\) | 13.7952 | 0.699446 | 0.349723 | − | 0.936853i | \(-0.386276\pi\) | ||||
0.349723 | + | 0.936853i | \(0.386276\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.897853 | 0.0454064 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | −12.7724 | −0.644282 | ||||||||
\(394\) | −0.411190 | −0.0207155 | ||||||||
\(395\) | 24.6625 | 1.24090 | ||||||||
\(396\) | 1.33513 | 0.0670926 | ||||||||
\(397\) | −7.07846 | −0.355258 | −0.177629 | − | 0.984098i | \(-0.556843\pi\) | ||||
−0.177629 | + | 0.984098i | \(0.556843\pi\) | |||||||
\(398\) | −5.73125 | −0.287282 | ||||||||
\(399\) | 2.44504 | 0.122405 | ||||||||
\(400\) | 2.85086 | 0.142543 | ||||||||
\(401\) | −2.94869 | −0.147251 | −0.0736253 | − | 0.997286i | \(-0.523457\pi\) | ||||
−0.0736253 | + | 0.997286i | \(0.523457\pi\) | |||||||
\(402\) | −8.83877 | −0.440838 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −6.53319 | −0.325038 | ||||||||
\(405\) | −2.80194 | −0.139229 | ||||||||
\(406\) | −5.63102 | −0.279463 | ||||||||
\(407\) | 2.25906 | 0.111978 | ||||||||
\(408\) | −0.356896 | −0.0176690 | ||||||||
\(409\) | −8.41358 | −0.416025 | −0.208012 | − | 0.978126i | \(-0.566699\pi\) | ||||
−0.208012 | + | 0.978126i | \(0.566699\pi\) | |||||||
\(410\) | −7.85086 | −0.387726 | ||||||||
\(411\) | 7.30798 | 0.360476 | ||||||||
\(412\) | 0.225209 | 0.0110953 | ||||||||
\(413\) | −4.18598 | −0.205979 | ||||||||
\(414\) | 2.51573 | 0.123641 | ||||||||
\(415\) | 29.2664 | 1.43663 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −22.9812 | −1.12539 | ||||||||
\(418\) | −3.26444 | −0.159669 | ||||||||
\(419\) | 36.9168 | 1.80350 | 0.901751 | − | 0.432256i | \(-0.142282\pi\) | ||||
0.901751 | + | 0.432256i | \(0.142282\pi\) | |||||||
\(420\) | 2.80194 | 0.136721 | ||||||||
\(421\) | 5.42221 | 0.264262 | 0.132131 | − | 0.991232i | \(-0.457818\pi\) | ||||
0.132131 | + | 0.991232i | \(0.457818\pi\) | |||||||
\(422\) | −24.5284 | −1.19402 | ||||||||
\(423\) | 5.09783 | 0.247865 | ||||||||
\(424\) | 8.25667 | 0.400979 | ||||||||
\(425\) | 1.01746 | 0.0493540 | ||||||||
\(426\) | 5.20775 | 0.252316 | ||||||||
\(427\) | −7.00000 | −0.338754 | ||||||||
\(428\) | 4.50604 | 0.217808 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −18.2567 | −0.880415 | ||||||||
\(431\) | −29.8442 | −1.43754 | −0.718771 | − | 0.695247i | \(-0.755295\pi\) | ||||
−0.718771 | + | 0.695247i | \(0.755295\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −19.4873 | −0.936498 | −0.468249 | − | 0.883597i | \(-0.655115\pi\) | ||||
−0.468249 | + | 0.883597i | \(0.655115\pi\) | |||||||
\(434\) | −9.54288 | −0.458073 | ||||||||
\(435\) | −15.7778 | −0.756486 | ||||||||
\(436\) | −7.10752 | −0.340389 | ||||||||
\(437\) | −6.15106 | −0.294245 | ||||||||
\(438\) | −0.850855 | −0.0406554 | ||||||||
\(439\) | 36.6450 | 1.74897 | 0.874486 | − | 0.485051i | \(-0.161199\pi\) | ||||
0.874486 | + | 0.485051i | \(0.161199\pi\) | |||||||
\(440\) | −3.74094 | −0.178342 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 34.6679 | 1.64712 | 0.823560 | − | 0.567229i | \(-0.191985\pi\) | ||||
0.823560 | + | 0.567229i | \(0.191985\pi\) | |||||||
\(444\) | −1.69202 | −0.0802998 | ||||||||
\(445\) | 9.52781 | 0.451662 | ||||||||
\(446\) | −21.0532 | −0.996899 | ||||||||
\(447\) | −3.95108 | −0.186880 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | 8.72455 | 0.411737 | 0.205868 | − | 0.978580i | \(-0.433998\pi\) | ||||
0.205868 | + | 0.978580i | \(0.433998\pi\) | |||||||
\(450\) | 2.85086 | 0.134391 | ||||||||
\(451\) | 3.74094 | 0.176154 | ||||||||
\(452\) | 2.86831 | 0.134914 | ||||||||
\(453\) | 5.26875 | 0.247547 | ||||||||
\(454\) | 3.49827 | 0.164182 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.44504 | 0.114500 | ||||||||
\(457\) | −19.4300 | −0.908896 | −0.454448 | − | 0.890773i | \(-0.650163\pi\) | ||||
−0.454448 | + | 0.890773i | \(0.650163\pi\) | |||||||
\(458\) | −22.0097 | −1.02845 | ||||||||
\(459\) | −0.356896 | −0.0166585 | ||||||||
\(460\) | −7.04892 | −0.328657 | ||||||||
\(461\) | 35.0573 | 1.63278 | 0.816390 | − | 0.577501i | \(-0.195972\pi\) | ||||
0.816390 | + | 0.577501i | \(0.195972\pi\) | |||||||
\(462\) | −1.33513 | −0.0621157 | ||||||||
\(463\) | 2.20105 | 0.102291 | 0.0511456 | − | 0.998691i | \(-0.483713\pi\) | ||||
0.0511456 | + | 0.998691i | \(0.483713\pi\) | |||||||
\(464\) | −5.63102 | −0.261414 | ||||||||
\(465\) | −26.7385 | −1.23997 | ||||||||
\(466\) | 21.2204 | 0.983017 | ||||||||
\(467\) | −8.25667 | −0.382073 | −0.191037 | − | 0.981583i | \(-0.561185\pi\) | ||||
−0.191037 | + | 0.981583i | \(0.561185\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.83877 | 0.408137 | ||||||||
\(470\) | −14.2838 | −0.658863 | ||||||||
\(471\) | 16.1521 | 0.744251 | ||||||||
\(472\) | −4.18598 | −0.192675 | ||||||||
\(473\) | 8.69932 | 0.399995 | ||||||||
\(474\) | 8.80194 | 0.404286 | ||||||||
\(475\) | −6.97046 | −0.319827 | ||||||||
\(476\) | 0.356896 | 0.0163583 | ||||||||
\(477\) | 8.25667 | 0.378047 | ||||||||
\(478\) | −2.09783 | −0.0959527 | ||||||||
\(479\) | −28.9439 | −1.32248 | −0.661240 | − | 0.750174i | \(-0.729970\pi\) | ||||
−0.661240 | + | 0.750174i | \(0.729970\pi\) | |||||||
\(480\) | 2.80194 | 0.127890 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −5.22952 | −0.238198 | ||||||||
\(483\) | −2.51573 | −0.114470 | ||||||||
\(484\) | −9.21744 | −0.418975 | ||||||||
\(485\) | 22.6625 | 1.02905 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 3.39804 | 0.153980 | 0.0769900 | − | 0.997032i | \(-0.475469\pi\) | ||||
0.0769900 | + | 0.997032i | \(0.475469\pi\) | |||||||
\(488\) | −7.00000 | −0.316875 | ||||||||
\(489\) | 11.9825 | 0.541869 | ||||||||
\(490\) | −2.80194 | −0.126579 | ||||||||
\(491\) | 28.3327 | 1.27864 | 0.639319 | − | 0.768941i | \(-0.279216\pi\) | ||||
0.639319 | + | 0.768941i | \(0.279216\pi\) | |||||||
\(492\) | −2.80194 | −0.126321 | ||||||||
\(493\) | −2.00969 | −0.0905118 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.74094 | −0.168143 | ||||||||
\(496\) | −9.54288 | −0.428488 | ||||||||
\(497\) | −5.20775 | −0.233600 | ||||||||
\(498\) | 10.4450 | 0.468054 | ||||||||
\(499\) | 11.2664 | 0.504351 | 0.252176 | − | 0.967681i | \(-0.418854\pi\) | ||||
0.252176 | + | 0.967681i | \(0.418854\pi\) | |||||||
\(500\) | 6.02177 | 0.269302 | ||||||||
\(501\) | 18.6069 | 0.831293 | ||||||||
\(502\) | −11.4426 | −0.510710 | ||||||||
\(503\) | −3.75063 | −0.167232 | −0.0836161 | − | 0.996498i | \(-0.526647\pi\) | ||||
−0.0836161 | + | 0.996498i | \(0.526647\pi\) | |||||||
\(504\) | 1.00000 | 0.0445435 | ||||||||
\(505\) | 18.3056 | 0.814588 | ||||||||
\(506\) | 3.35881 | 0.149318 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.57673 | 0.114324 | ||||||||
\(509\) | −0.450419 | −0.0199645 | −0.00998223 | − | 0.999950i | \(-0.503177\pi\) | ||||
−0.00998223 | + | 0.999950i | \(0.503177\pi\) | |||||||
\(510\) | 1.00000 | 0.0442807 | ||||||||
\(511\) | 0.850855 | 0.0376396 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 2.44504 | 0.107951 | ||||||||
\(514\) | −21.5623 | −0.951070 | ||||||||
\(515\) | −0.631023 | −0.0278062 | ||||||||
\(516\) | −6.51573 | −0.286839 | ||||||||
\(517\) | 6.80625 | 0.299339 | ||||||||
\(518\) | 1.69202 | 0.0743432 | ||||||||
\(519\) | −15.0422 | −0.660280 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −22.8485 | −1.00101 | −0.500505 | − | 0.865734i | \(-0.666852\pi\) | ||||
−0.500505 | + | 0.865734i | \(0.666852\pi\) | |||||||
\(522\) | −5.63102 | −0.246463 | ||||||||
\(523\) | −14.3478 | −0.627385 | −0.313693 | − | 0.949525i | \(-0.601566\pi\) | ||||
−0.313693 | + | 0.949525i | \(0.601566\pi\) | |||||||
\(524\) | 12.7724 | 0.557965 | ||||||||
\(525\) | −2.85086 | −0.124422 | ||||||||
\(526\) | −11.5284 | −0.502662 | ||||||||
\(527\) | −3.40581 | −0.148360 | ||||||||
\(528\) | −1.33513 | −0.0581039 | ||||||||
\(529\) | −16.6711 | −0.724831 | ||||||||
\(530\) | −23.1347 | −1.00491 | ||||||||
\(531\) | −4.18598 | −0.181656 | ||||||||
\(532\) | −2.44504 | −0.106006 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 3.40044 | 0.147151 | ||||||||
\(535\) | −12.6256 | −0.545854 | ||||||||
\(536\) | 8.83877 | 0.381777 | ||||||||
\(537\) | 23.6112 | 1.01890 | ||||||||
\(538\) | −30.5211 | −1.31586 | ||||||||
\(539\) | 1.33513 | 0.0575079 | ||||||||
\(540\) | 2.80194 | 0.120576 | ||||||||
\(541\) | −43.7342 | −1.88028 | −0.940141 | − | 0.340786i | \(-0.889307\pi\) | ||||
−0.940141 | + | 0.340786i | \(0.889307\pi\) | |||||||
\(542\) | −12.6160 | −0.541902 | ||||||||
\(543\) | −15.6679 | −0.672372 | ||||||||
\(544\) | 0.356896 | 0.0153018 | ||||||||
\(545\) | 19.9148 | 0.853058 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.8224 | 0.591002 | 0.295501 | − | 0.955342i | \(-0.404513\pi\) | ||||
0.295501 | + | 0.955342i | \(0.404513\pi\) | |||||||
\(548\) | −7.30798 | −0.312181 | ||||||||
\(549\) | −7.00000 | −0.298753 | ||||||||
\(550\) | 3.80625 | 0.162299 | ||||||||
\(551\) | 13.7681 | 0.586540 | ||||||||
\(552\) | −2.51573 | −0.107077 | ||||||||
\(553\) | −8.80194 | −0.374296 | ||||||||
\(554\) | 14.7899 | 0.628361 | ||||||||
\(555\) | 4.74094 | 0.201242 | ||||||||
\(556\) | 22.9812 | 0.974621 | ||||||||
\(557\) | −42.5846 | −1.80437 | −0.902184 | − | 0.431351i | \(-0.858037\pi\) | ||||
−0.902184 | + | 0.431351i | \(0.858037\pi\) | |||||||
\(558\) | −9.54288 | −0.403982 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −2.80194 | −0.118403 | ||||||||
\(561\) | −0.476501 | −0.0201179 | ||||||||
\(562\) | 15.5623 | 0.656454 | ||||||||
\(563\) | −11.3491 | −0.478309 | −0.239154 | − | 0.970982i | \(-0.576870\pi\) | ||||
−0.239154 | + | 0.970982i | \(0.576870\pi\) | |||||||
\(564\) | −5.09783 | −0.214658 | ||||||||
\(565\) | −8.03684 | −0.338112 | ||||||||
\(566\) | 17.5894 | 0.739338 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | −5.20775 | −0.218512 | ||||||||
\(569\) | 3.52052 | 0.147588 | 0.0737938 | − | 0.997274i | \(-0.476489\pi\) | ||||
0.0737938 | + | 0.997274i | \(0.476489\pi\) | |||||||
\(570\) | −6.85086 | −0.286951 | ||||||||
\(571\) | 19.8847 | 0.832149 | 0.416075 | − | 0.909331i | \(-0.363406\pi\) | ||||
0.416075 | + | 0.909331i | \(0.363406\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 22.5526 | 0.942147 | ||||||||
\(574\) | 2.80194 | 0.116951 | ||||||||
\(575\) | 7.17198 | 0.299092 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −5.61356 | −0.233696 | −0.116848 | − | 0.993150i | \(-0.537279\pi\) | ||||
−0.116848 | + | 0.993150i | \(0.537279\pi\) | |||||||
\(578\) | −16.8726 | −0.701809 | ||||||||
\(579\) | 24.2610 | 1.00825 | ||||||||
\(580\) | 15.7778 | 0.655136 | ||||||||
\(581\) | −10.4450 | −0.433333 | ||||||||
\(582\) | 8.08815 | 0.335264 | ||||||||
\(583\) | 11.0237 | 0.456555 | ||||||||
\(584\) | 0.850855 | 0.0352086 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 11.4263 | 0.472014 | ||||||||
\(587\) | 4.46011 | 0.184088 | 0.0920442 | − | 0.995755i | \(-0.470660\pi\) | ||||
0.0920442 | + | 0.995755i | \(0.470660\pi\) | |||||||
\(588\) | −1.00000 | −0.0412393 | ||||||||
\(589\) | 23.3327 | 0.961409 | ||||||||
\(590\) | 11.7289 | 0.482869 | ||||||||
\(591\) | 0.411190 | 0.0169141 | ||||||||
\(592\) | 1.69202 | 0.0695417 | ||||||||
\(593\) | −1.06100 | −0.0435700 | −0.0217850 | − | 0.999763i | \(-0.506935\pi\) | ||||
−0.0217850 | + | 0.999763i | \(0.506935\pi\) | |||||||
\(594\) | −1.33513 | −0.0547809 | ||||||||
\(595\) | −1.00000 | −0.0409960 | ||||||||
\(596\) | 3.95108 | 0.161843 | ||||||||
\(597\) | 5.73125 | 0.234564 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.22282 | −0.131681 | −0.0658404 | − | 0.997830i | \(-0.520973\pi\) | ||||
−0.0658404 | + | 0.997830i | \(0.520973\pi\) | |||||||
\(600\) | −2.85086 | −0.116386 | ||||||||
\(601\) | 22.8616 | 0.932544 | 0.466272 | − | 0.884641i | \(-0.345597\pi\) | ||||
0.466272 | + | 0.884641i | \(0.345597\pi\) | |||||||
\(602\) | 6.51573 | 0.265561 | ||||||||
\(603\) | 8.83877 | 0.359943 | ||||||||
\(604\) | −5.26875 | −0.214382 | ||||||||
\(605\) | 25.8267 | 1.05000 | ||||||||
\(606\) | 6.53319 | 0.265393 | ||||||||
\(607\) | 43.4892 | 1.76517 | 0.882586 | − | 0.470152i | \(-0.155801\pi\) | ||||
0.882586 | + | 0.470152i | \(0.155801\pi\) | |||||||
\(608\) | −2.44504 | −0.0991595 | ||||||||
\(609\) | 5.63102 | 0.228181 | ||||||||
\(610\) | 19.6136 | 0.794130 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0.356896 | 0.0144267 | ||||||||
\(613\) | 1.81833 | 0.0734417 | 0.0367209 | − | 0.999326i | \(-0.488309\pi\) | ||||
0.0367209 | + | 0.999326i | \(0.488309\pi\) | |||||||
\(614\) | −10.5670 | −0.426451 | ||||||||
\(615\) | 7.85086 | 0.316577 | ||||||||
\(616\) | 1.33513 | 0.0537937 | ||||||||
\(617\) | 9.77777 | 0.393638 | 0.196819 | − | 0.980440i | \(-0.436939\pi\) | ||||
0.196819 | + | 0.980440i | \(0.436939\pi\) | |||||||
\(618\) | −0.225209 | −0.00905925 | ||||||||
\(619\) | 31.8079 | 1.27847 | 0.639234 | − | 0.769012i | \(-0.279252\pi\) | ||||
0.639234 | + | 0.769012i | \(0.279252\pi\) | |||||||
\(620\) | 26.7385 | 1.07385 | ||||||||
\(621\) | −2.51573 | −0.100953 | ||||||||
\(622\) | −7.40821 | −0.297042 | ||||||||
\(623\) | −3.40044 | −0.136236 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.1269 | −1.24508 | ||||||||
\(626\) | −2.12737 | −0.0850270 | ||||||||
\(627\) | 3.26444 | 0.130369 | ||||||||
\(628\) | −16.1521 | −0.644540 | ||||||||
\(629\) | 0.603875 | 0.0240781 | ||||||||
\(630\) | −2.80194 | −0.111632 | ||||||||
\(631\) | 18.0030 | 0.716687 | 0.358344 | − | 0.933590i | \(-0.383342\pi\) | ||||
0.358344 | + | 0.933590i | \(0.383342\pi\) | |||||||
\(632\) | −8.80194 | −0.350122 | ||||||||
\(633\) | 24.5284 | 0.974916 | ||||||||
\(634\) | 32.6383 | 1.29623 | ||||||||
\(635\) | −7.21983 | −0.286510 | ||||||||
\(636\) | −8.25667 | −0.327398 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −7.51812 | −0.297645 | ||||||||
\(639\) | −5.20775 | −0.206015 | ||||||||
\(640\) | −2.80194 | −0.110756 | ||||||||
\(641\) | 20.0006 | 0.789976 | 0.394988 | − | 0.918686i | \(-0.370749\pi\) | ||||
0.394988 | + | 0.918686i | \(0.370749\pi\) | |||||||
\(642\) | −4.50604 | −0.177839 | ||||||||
\(643\) | −40.5719 | −1.60000 | −0.800001 | − | 0.599999i | \(-0.795168\pi\) | ||||
−0.800001 | + | 0.599999i | \(0.795168\pi\) | |||||||
\(644\) | 2.51573 | 0.0991336 | ||||||||
\(645\) | 18.2567 | 0.718856 | ||||||||
\(646\) | −0.872625 | −0.0343330 | ||||||||
\(647\) | 12.9226 | 0.508040 | 0.254020 | − | 0.967199i | \(-0.418247\pi\) | ||||
0.254020 | + | 0.967199i | \(0.418247\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −5.58881 | −0.219380 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.54288 | 0.374015 | ||||||||
\(652\) | −11.9825 | −0.469273 | ||||||||
\(653\) | 30.5187 | 1.19429 | 0.597145 | − | 0.802133i | \(-0.296302\pi\) | ||||
0.597145 | + | 0.802133i | \(0.296302\pi\) | |||||||
\(654\) | 7.10752 | 0.277926 | ||||||||
\(655\) | −35.7875 | −1.39833 | ||||||||
\(656\) | 2.80194 | 0.109397 | ||||||||
\(657\) | 0.850855 | 0.0331950 | ||||||||
\(658\) | 5.09783 | 0.198734 | ||||||||
\(659\) | 4.65950 | 0.181508 | 0.0907541 | − | 0.995873i | \(-0.471072\pi\) | ||||
0.0907541 | + | 0.995873i | \(0.471072\pi\) | |||||||
\(660\) | 3.74094 | 0.145616 | ||||||||
\(661\) | −27.0097 | −1.05056 | −0.525278 | − | 0.850931i | \(-0.676039\pi\) | ||||
−0.525278 | + | 0.850931i | \(0.676039\pi\) | |||||||
\(662\) | −30.0006 | −1.16601 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −10.4450 | −0.405346 | ||||||||
\(665\) | 6.85086 | 0.265665 | ||||||||
\(666\) | 1.69202 | 0.0655645 | ||||||||
\(667\) | −14.1661 | −0.548515 | ||||||||
\(668\) | −18.6069 | −0.719921 | ||||||||
\(669\) | 21.0532 | 0.813965 | ||||||||
\(670\) | −24.7657 | −0.956782 | ||||||||
\(671\) | −9.34588 | −0.360794 | ||||||||
\(672\) | −1.00000 | −0.0385758 | ||||||||
\(673\) | 21.1491 | 0.815240 | 0.407620 | − | 0.913152i | \(-0.366359\pi\) | ||||
0.407620 | + | 0.913152i | \(0.366359\pi\) | |||||||
\(674\) | 12.5472 | 0.483300 | ||||||||
\(675\) | −2.85086 | −0.109729 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 22.0968 | 0.849248 | 0.424624 | − | 0.905370i | \(-0.360406\pi\) | ||||
0.424624 | + | 0.905370i | \(0.360406\pi\) | |||||||
\(678\) | −2.86831 | −0.110157 | ||||||||
\(679\) | −8.08815 | −0.310395 | ||||||||
\(680\) | −1.00000 | −0.0383482 | ||||||||
\(681\) | −3.49827 | −0.134054 | ||||||||
\(682\) | −12.7409 | −0.487876 | ||||||||
\(683\) | −28.0170 | −1.07204 | −0.536020 | − | 0.844205i | \(-0.680073\pi\) | ||||
−0.536020 | + | 0.844205i | \(0.680073\pi\) | |||||||
\(684\) | −2.44504 | −0.0934885 | ||||||||
\(685\) | 20.4765 | 0.782367 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 22.0097 | 0.839722 | ||||||||
\(688\) | 6.51573 | 0.248410 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 7.04892 | 0.268348 | ||||||||
\(691\) | 16.2422 | 0.617882 | 0.308941 | − | 0.951081i | \(-0.400025\pi\) | ||||
0.308941 | + | 0.951081i | \(0.400025\pi\) | |||||||
\(692\) | 15.0422 | 0.571819 | ||||||||
\(693\) | 1.33513 | 0.0507172 | ||||||||
\(694\) | 25.5719 | 0.970698 | ||||||||
\(695\) | −64.3919 | −2.44253 | ||||||||
\(696\) | 5.63102 | 0.213443 | ||||||||
\(697\) | 1.00000 | 0.0378777 | ||||||||
\(698\) | −22.9855 | −0.870015 | ||||||||
\(699\) | −21.2204 | −0.802630 | ||||||||
\(700\) | 2.85086 | 0.107752 | ||||||||
\(701\) | 0.0502453 | 0.00189774 | 0.000948869 | − | 1.00000i | \(-0.499698\pi\) | ||||
0.000948869 | 1.00000i | \(0.499698\pi\) | ||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.13706 | −0.156032 | ||||||||
\(704\) | 1.33513 | 0.0503194 | ||||||||
\(705\) | 14.2838 | 0.537960 | ||||||||
\(706\) | 22.4397 | 0.844528 | ||||||||
\(707\) | −6.53319 | −0.245706 | ||||||||
\(708\) | 4.18598 | 0.157319 | ||||||||
\(709\) | 39.6544 | 1.48925 | 0.744627 | − | 0.667481i | \(-0.232627\pi\) | ||||
0.744627 | + | 0.667481i | \(0.232627\pi\) | |||||||
\(710\) | 14.5918 | 0.547620 | ||||||||
\(711\) | −8.80194 | −0.330098 | ||||||||
\(712\) | −3.40044 | −0.127437 | ||||||||
\(713\) | −24.0073 | −0.899080 | ||||||||
\(714\) | −0.356896 | −0.0133565 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −23.6112 | −0.882391 | ||||||||
\(717\) | 2.09783 | 0.0783451 | ||||||||
\(718\) | 6.80492 | 0.253957 | ||||||||
\(719\) | 17.0694 | 0.636580 | 0.318290 | − | 0.947993i | \(-0.396891\pi\) | ||||
0.318290 | + | 0.947993i | \(0.396891\pi\) | |||||||
\(720\) | −2.80194 | −0.104422 | ||||||||
\(721\) | 0.225209 | 0.00838723 | ||||||||
\(722\) | −13.0218 | −0.484620 | ||||||||
\(723\) | 5.22952 | 0.194488 | ||||||||
\(724\) | 15.6679 | 0.582291 | ||||||||
\(725\) | −16.0532 | −0.596202 | ||||||||
\(726\) | 9.21744 | 0.342091 | ||||||||
\(727\) | −0.154048 | −0.00571332 | −0.00285666 | − | 0.999996i | \(-0.500909\pi\) | ||||
−0.00285666 | + | 0.999996i | \(0.500909\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −2.38404 | −0.0882374 | ||||||||
\(731\) | 2.32544 | 0.0860094 | ||||||||
\(732\) | 7.00000 | 0.258727 | ||||||||
\(733\) | −31.5415 | −1.16501 | −0.582507 | − | 0.812826i | \(-0.697928\pi\) | ||||
−0.582507 | + | 0.812826i | \(0.697928\pi\) | |||||||
\(734\) | −21.9409 | −0.809854 | ||||||||
\(735\) | 2.80194 | 0.103351 | ||||||||
\(736\) | 2.51573 | 0.0927310 | ||||||||
\(737\) | 11.8009 | 0.434691 | ||||||||
\(738\) | 2.80194 | 0.103141 | ||||||||
\(739\) | 15.6679 | 0.576351 | 0.288176 | − | 0.957578i | \(-0.406951\pi\) | ||||
0.288176 | + | 0.957578i | \(0.406951\pi\) | |||||||
\(740\) | −4.74094 | −0.174280 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 8.25667 | 0.303112 | ||||||||
\(743\) | 7.94677 | 0.291539 | 0.145769 | − | 0.989319i | \(-0.453434\pi\) | ||||
0.145769 | + | 0.989319i | \(0.453434\pi\) | |||||||
\(744\) | 9.54288 | 0.349859 | ||||||||
\(745\) | −11.0707 | −0.405599 | ||||||||
\(746\) | −18.3207 | −0.670767 | ||||||||
\(747\) | −10.4450 | −0.382164 | ||||||||
\(748\) | 0.476501 | 0.0174226 | ||||||||
\(749\) | 4.50604 | 0.164647 | ||||||||
\(750\) | −6.02177 | −0.219884 | ||||||||
\(751\) | 34.5026 | 1.25902 | 0.629509 | − | 0.776994i | \(-0.283256\pi\) | ||||
0.629509 | + | 0.776994i | \(0.283256\pi\) | |||||||
\(752\) | 5.09783 | 0.185899 | ||||||||
\(753\) | 11.4426 | 0.416993 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 14.7627 | 0.537270 | ||||||||
\(756\) | −1.00000 | −0.0363696 | ||||||||
\(757\) | −20.6732 | −0.751382 | −0.375691 | − | 0.926745i | \(-0.622595\pi\) | ||||
−0.375691 | + | 0.926745i | \(0.622595\pi\) | |||||||
\(758\) | −25.8950 | −0.940548 | ||||||||
\(759\) | −3.35881 | −0.121917 | ||||||||
\(760\) | 6.85086 | 0.248507 | ||||||||
\(761\) | −7.67994 | −0.278398 | −0.139199 | − | 0.990264i | \(-0.544453\pi\) | ||||
−0.139199 | + | 0.990264i | \(0.544453\pi\) | |||||||
\(762\) | −2.57673 | −0.0933450 | ||||||||
\(763\) | −7.10752 | −0.257310 | ||||||||
\(764\) | −22.5526 | −0.815923 | ||||||||
\(765\) | −1.00000 | −0.0361551 | ||||||||
\(766\) | −20.0218 | −0.723416 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 12.3086 | 0.443858 | 0.221929 | − | 0.975063i | \(-0.428765\pi\) | ||||
0.221929 | + | 0.975063i | \(0.428765\pi\) | |||||||
\(770\) | −3.74094 | −0.134814 | ||||||||
\(771\) | 21.5623 | 0.776546 | ||||||||
\(772\) | −24.2610 | −0.873172 | ||||||||
\(773\) | 25.8291 | 0.929008 | 0.464504 | − | 0.885571i | \(-0.346233\pi\) | ||||
0.464504 | + | 0.885571i | \(0.346233\pi\) | |||||||
\(774\) | 6.51573 | 0.234203 | ||||||||
\(775\) | −27.2054 | −0.977245 | ||||||||
\(776\) | −8.08815 | −0.290348 | ||||||||
\(777\) | −1.69202 | −0.0607009 | ||||||||
\(778\) | 13.7952 | 0.494583 | ||||||||
\(779\) | −6.85086 | −0.245457 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.95300 | −0.248798 | ||||||||
\(782\) | 0.897853 | 0.0321072 | ||||||||
\(783\) | 5.63102 | 0.201236 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 45.2573 | 1.61530 | ||||||||
\(786\) | −12.7724 | −0.455576 | ||||||||
\(787\) | −17.0248 | −0.606867 | −0.303433 | − | 0.952853i | \(-0.598133\pi\) | ||||
−0.303433 | + | 0.952853i | \(0.598133\pi\) | |||||||
\(788\) | −0.411190 | −0.0146480 | ||||||||
\(789\) | 11.5284 | 0.410422 | ||||||||
\(790\) | 24.6625 | 0.877452 | ||||||||
\(791\) | 2.86831 | 0.101985 | ||||||||
\(792\) | 1.33513 | 0.0474416 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −7.07846 | −0.251205 | ||||||||
\(795\) | 23.1347 | 0.820502 | ||||||||
\(796\) | −5.73125 | −0.203139 | ||||||||
\(797\) | −48.3919 | −1.71413 | −0.857065 | − | 0.515208i | \(-0.827715\pi\) | ||||
−0.857065 | + | 0.515208i | \(0.827715\pi\) | |||||||
\(798\) | 2.44504 | 0.0865535 | ||||||||
\(799\) | 1.81940 | 0.0643656 | ||||||||
\(800\) | 2.85086 | 0.100793 | ||||||||
\(801\) | −3.40044 | −0.120149 | ||||||||
\(802\) | −2.94869 | −0.104122 | ||||||||
\(803\) | 1.13600 | 0.0400885 | ||||||||
\(804\) | −8.83877 | −0.311720 | ||||||||
\(805\) | −7.04892 | −0.248442 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 30.5211 | 1.07439 | ||||||||
\(808\) | −6.53319 | −0.229837 | ||||||||
\(809\) | −1.51440 | −0.0532435 | −0.0266218 | − | 0.999646i | \(-0.508475\pi\) | ||||
−0.0266218 | + | 0.999646i | \(0.508475\pi\) | |||||||
\(810\) | −2.80194 | −0.0984501 | ||||||||
\(811\) | −23.0170 | −0.808236 | −0.404118 | − | 0.914707i | \(-0.632421\pi\) | ||||
−0.404118 | + | 0.914707i | \(0.632421\pi\) | |||||||
\(812\) | −5.63102 | −0.197610 | ||||||||
\(813\) | 12.6160 | 0.442461 | ||||||||
\(814\) | 2.25906 | 0.0791801 | ||||||||
\(815\) | 33.5743 | 1.17606 | ||||||||
\(816\) | −0.356896 | −0.0124939 | ||||||||
\(817\) | −15.9312 | −0.557363 | ||||||||
\(818\) | −8.41358 | −0.294174 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −7.85086 | −0.274164 | ||||||||
\(821\) | −5.90754 | −0.206175 | −0.103087 | − | 0.994672i | \(-0.532872\pi\) | ||||
−0.103087 | + | 0.994672i | \(0.532872\pi\) | |||||||
\(822\) | 7.30798 | 0.254895 | ||||||||
\(823\) | 45.2567 | 1.57755 | 0.788774 | − | 0.614683i | \(-0.210716\pi\) | ||||
0.788774 | + | 0.614683i | \(0.210716\pi\) | |||||||
\(824\) | 0.225209 | 0.00784554 | ||||||||
\(825\) | −3.80625 | −0.132517 | ||||||||
\(826\) | −4.18598 | −0.145649 | ||||||||
\(827\) | 28.6534 | 0.996376 | 0.498188 | − | 0.867069i | \(-0.333999\pi\) | ||||
0.498188 | + | 0.867069i | \(0.333999\pi\) | |||||||
\(828\) | 2.51573 | 0.0874276 | ||||||||
\(829\) | −20.4257 | −0.709413 | −0.354706 | − | 0.934978i | \(-0.615419\pi\) | ||||
−0.354706 | + | 0.934978i | \(0.615419\pi\) | |||||||
\(830\) | 29.2664 | 1.01585 | ||||||||
\(831\) | −14.7899 | −0.513054 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.356896 | 0.0123657 | ||||||||
\(834\) | −22.9812 | −0.795774 | ||||||||
\(835\) | 52.1353 | 1.80422 | ||||||||
\(836\) | −3.26444 | −0.112903 | ||||||||
\(837\) | 9.54288 | 0.329850 | ||||||||
\(838\) | 36.9168 | 1.27527 | ||||||||
\(839\) | 43.5623 | 1.50394 | 0.751968 | − | 0.659200i | \(-0.229105\pi\) | ||||
0.751968 | + | 0.659200i | \(0.229105\pi\) | |||||||
\(840\) | 2.80194 | 0.0966760 | ||||||||
\(841\) | 2.70841 | 0.0933936 | ||||||||
\(842\) | 5.42221 | 0.186862 | ||||||||
\(843\) | −15.5623 | −0.535992 | ||||||||
\(844\) | −24.5284 | −0.844302 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 5.09783 | 0.175267 | ||||||||
\(847\) | −9.21744 | −0.316715 | ||||||||
\(848\) | 8.25667 | 0.283535 | ||||||||
\(849\) | −17.5894 | −0.603667 | ||||||||
\(850\) | 1.01746 | 0.0348985 | ||||||||
\(851\) | 4.25667 | 0.145917 | ||||||||
\(852\) | 5.20775 | 0.178415 | ||||||||
\(853\) | 2.45473 | 0.0840484 | 0.0420242 | − | 0.999117i | \(-0.486619\pi\) | ||||
0.0420242 | + | 0.999117i | \(0.486619\pi\) | |||||||
\(854\) | −7.00000 | −0.239535 | ||||||||
\(855\) | 6.85086 | 0.234294 | ||||||||
\(856\) | 4.50604 | 0.154013 | ||||||||
\(857\) | −1.14616 | −0.0391521 | −0.0195761 | − | 0.999808i | \(-0.506232\pi\) | ||||
−0.0195761 | + | 0.999808i | \(0.506232\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33.7162 | 1.15038 | 0.575191 | − | 0.818019i | \(-0.304928\pi\) | ||||
0.575191 | + | 0.818019i | \(0.304928\pi\) | |||||||
\(860\) | −18.2567 | −0.622547 | ||||||||
\(861\) | −2.80194 | −0.0954898 | ||||||||
\(862\) | −29.8442 | −1.01650 | ||||||||
\(863\) | 40.5924 | 1.38178 | 0.690890 | − | 0.722959i | \(-0.257219\pi\) | ||||
0.690890 | + | 0.722959i | \(0.257219\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −42.1473 | −1.43305 | ||||||||
\(866\) | −19.4873 | −0.662204 | ||||||||
\(867\) | 16.8726 | 0.573024 | ||||||||
\(868\) | −9.54288 | −0.323906 | ||||||||
\(869\) | −11.7517 | −0.398649 | ||||||||
\(870\) | −15.7778 | −0.534917 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −7.10752 | −0.240691 | ||||||||
\(873\) | −8.08815 | −0.273742 | ||||||||
\(874\) | −6.15106 | −0.208063 | ||||||||
\(875\) | 6.02177 | 0.203573 | ||||||||
\(876\) | −0.850855 | −0.0287477 | ||||||||
\(877\) | −28.4969 | −0.962273 | −0.481137 | − | 0.876646i | \(-0.659776\pi\) | ||||
−0.481137 | + | 0.876646i | \(0.659776\pi\) | |||||||
\(878\) | 36.6450 | 1.23671 | ||||||||
\(879\) | −11.4263 | −0.385398 | ||||||||
\(880\) | −3.74094 | −0.126107 | ||||||||
\(881\) | 30.6883 | 1.03392 | 0.516958 | − | 0.856011i | \(-0.327064\pi\) | ||||
0.516958 | + | 0.856011i | \(0.327064\pi\) | |||||||
\(882\) | 1.00000 | 0.0336718 | ||||||||
\(883\) | 44.5230 | 1.49832 | 0.749160 | − | 0.662390i | \(-0.230458\pi\) | ||||
0.749160 | + | 0.662390i | \(0.230458\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −11.7289 | −0.394261 | ||||||||
\(886\) | 34.6679 | 1.16469 | ||||||||
\(887\) | −2.76749 | −0.0929234 | −0.0464617 | − | 0.998920i | \(-0.514795\pi\) | ||||
−0.0464617 | + | 0.998920i | \(0.514795\pi\) | |||||||
\(888\) | −1.69202 | −0.0567805 | ||||||||
\(889\) | 2.57673 | 0.0864207 | ||||||||
\(890\) | 9.52781 | 0.319373 | ||||||||
\(891\) | 1.33513 | 0.0447284 | ||||||||
\(892\) | −21.0532 | −0.704914 | ||||||||
\(893\) | −12.4644 | −0.417106 | ||||||||
\(894\) | −3.95108 | −0.132144 | ||||||||
\(895\) | 66.1570 | 2.21139 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 8.72455 | 0.291142 | ||||||||
\(899\) | 53.7362 | 1.79220 | ||||||||
\(900\) | 2.85086 | 0.0950285 | ||||||||
\(901\) | 2.94677 | 0.0981712 | ||||||||
\(902\) | 3.74094 | 0.124560 | ||||||||
\(903\) | −6.51573 | −0.216830 | ||||||||
\(904\) | 2.86831 | 0.0953987 | ||||||||
\(905\) | −43.9004 | −1.45930 | ||||||||
\(906\) | 5.26875 | 0.175042 | ||||||||
\(907\) | 16.7496 | 0.556160 | 0.278080 | − | 0.960558i | \(-0.410302\pi\) | ||||
0.278080 | + | 0.960558i | \(0.410302\pi\) | |||||||
\(908\) | 3.49827 | 0.116094 | ||||||||
\(909\) | −6.53319 | −0.216692 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −34.1866 | −1.13265 | −0.566326 | − | 0.824181i | \(-0.691636\pi\) | ||||
−0.566326 | + | 0.824181i | \(0.691636\pi\) | |||||||
\(912\) | 2.44504 | 0.0809634 | ||||||||
\(913\) | −13.9454 | −0.461527 | ||||||||
\(914\) | −19.4300 | −0.642686 | ||||||||
\(915\) | −19.6136 | −0.648404 | ||||||||
\(916\) | −22.0097 | −0.727221 | ||||||||
\(917\) | 12.7724 | 0.421782 | ||||||||
\(918\) | −0.356896 | −0.0117793 | ||||||||
\(919\) | −28.4118 | −0.937218 | −0.468609 | − | 0.883406i | \(-0.655245\pi\) | ||||
−0.468609 | + | 0.883406i | \(0.655245\pi\) | |||||||
\(920\) | −7.04892 | −0.232396 | ||||||||
\(921\) | 10.5670 | 0.348196 | ||||||||
\(922\) | 35.0573 | 1.15455 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −1.33513 | −0.0439224 | ||||||||
\(925\) | 4.82371 | 0.158603 | ||||||||
\(926\) | 2.20105 | 0.0723309 | ||||||||
\(927\) | 0.225209 | 0.00739685 | ||||||||
\(928\) | −5.63102 | −0.184847 | ||||||||
\(929\) | −23.9366 | −0.785335 | −0.392667 | − | 0.919681i | \(-0.628448\pi\) | ||||
−0.392667 | + | 0.919681i | \(0.628448\pi\) | |||||||
\(930\) | −26.7385 | −0.876791 | ||||||||
\(931\) | −2.44504 | −0.0801330 | ||||||||
\(932\) | 21.2204 | 0.695098 | ||||||||
\(933\) | 7.40821 | 0.242534 | ||||||||
\(934\) | −8.25667 | −0.270166 | ||||||||
\(935\) | −1.33513 | −0.0436633 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18.6219 | 0.608352 | 0.304176 | − | 0.952616i | \(-0.401619\pi\) | ||||
0.304176 | + | 0.952616i | \(0.401619\pi\) | |||||||
\(938\) | 8.83877 | 0.288596 | ||||||||
\(939\) | 2.12737 | 0.0694242 | ||||||||
\(940\) | −14.2838 | −0.465887 | ||||||||
\(941\) | 37.4677 | 1.22141 | 0.610706 | − | 0.791858i | \(-0.290886\pi\) | ||||
0.610706 | + | 0.791858i | \(0.290886\pi\) | |||||||
\(942\) | 16.1521 | 0.526265 | ||||||||
\(943\) | 7.04892 | 0.229544 | ||||||||
\(944\) | −4.18598 | −0.136242 | ||||||||
\(945\) | 2.80194 | 0.0911470 | ||||||||
\(946\) | 8.69932 | 0.282839 | ||||||||
\(947\) | −15.4588 | −0.502343 | −0.251171 | − | 0.967943i | \(-0.580816\pi\) | ||||
−0.251171 | + | 0.967943i | \(0.580816\pi\) | |||||||
\(948\) | 8.80194 | 0.285874 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −6.97046 | −0.226152 | ||||||||
\(951\) | −32.6383 | −1.05837 | ||||||||
\(952\) | 0.356896 | 0.0115671 | ||||||||
\(953\) | 0.151064 | 0.00489344 | 0.00244672 | − | 0.999997i | \(-0.499221\pi\) | ||||
0.00244672 | + | 0.999997i | \(0.499221\pi\) | |||||||
\(954\) | 8.25667 | 0.267320 | ||||||||
\(955\) | 63.1909 | 2.04481 | ||||||||
\(956\) | −2.09783 | −0.0678488 | ||||||||
\(957\) | 7.51812 | 0.243026 | ||||||||
\(958\) | −28.9439 | −0.935135 | ||||||||
\(959\) | −7.30798 | −0.235987 | ||||||||
\(960\) | 2.80194 | 0.0904322 | ||||||||
\(961\) | 60.0665 | 1.93763 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.50604 | 0.145205 | ||||||||
\(964\) | −5.22952 | −0.168432 | ||||||||
\(965\) | 67.9778 | 2.18828 | ||||||||
\(966\) | −2.51573 | −0.0809423 | ||||||||
\(967\) | −17.5532 | −0.564471 | −0.282236 | − | 0.959345i | \(-0.591076\pi\) | ||||
−0.282236 | + | 0.959345i | \(0.591076\pi\) | |||||||
\(968\) | −9.21744 | −0.296260 | ||||||||
\(969\) | 0.872625 | 0.0280328 | ||||||||
\(970\) | 22.6625 | 0.727648 | ||||||||
\(971\) | 30.2228 | 0.969896 | 0.484948 | − | 0.874543i | \(-0.338838\pi\) | ||||
0.484948 | + | 0.874543i | \(0.338838\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 22.9812 | 0.736744 | ||||||||
\(974\) | 3.39804 | 0.108880 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.00000 | −0.224065 | ||||||||
\(977\) | −47.7230 | −1.52679 | −0.763397 | − | 0.645929i | \(-0.776470\pi\) | ||||
−0.763397 | + | 0.645929i | \(0.776470\pi\) | |||||||
\(978\) | 11.9825 | 0.383159 | ||||||||
\(979\) | −4.54001 | −0.145099 | ||||||||
\(980\) | −2.80194 | −0.0895046 | ||||||||
\(981\) | −7.10752 | −0.226926 | ||||||||
\(982\) | 28.3327 | 0.904134 | ||||||||
\(983\) | −23.3317 | −0.744165 | −0.372082 | − | 0.928200i | \(-0.621356\pi\) | ||||
−0.372082 | + | 0.928200i | \(0.621356\pi\) | |||||||
\(984\) | −2.80194 | −0.0893225 | ||||||||
\(985\) | 1.15213 | 0.0367099 | ||||||||
\(986\) | −2.00969 | −0.0640015 | ||||||||
\(987\) | −5.09783 | −0.162266 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16.3918 | 0.521229 | ||||||||
\(990\) | −3.74094 | −0.118895 | ||||||||
\(991\) | −7.16229 | −0.227518 | −0.113759 | − | 0.993508i | \(-0.536289\pi\) | ||||
−0.113759 | + | 0.993508i | \(0.536289\pi\) | |||||||
\(992\) | −9.54288 | −0.302987 | ||||||||
\(993\) | 30.0006 | 0.952040 | ||||||||
\(994\) | −5.20775 | −0.165180 | ||||||||
\(995\) | 16.0586 | 0.509092 | ||||||||
\(996\) | 10.4450 | 0.330964 | ||||||||
\(997\) | 24.4537 | 0.774455 | 0.387228 | − | 0.921984i | \(-0.373433\pi\) | ||||
0.387228 | + | 0.921984i | \(0.373433\pi\) | |||||||
\(998\) | 11.2664 | 0.356630 | ||||||||
\(999\) | −1.69202 | −0.0535332 |
(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 | 7098.2.a.ch.1.1 | yes | 3 | |
13.12 | even | 2 | 7098.2.a.ce.1.3 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7098.2.a.ce.1.3 | ✓ | 3 | 13.12 | even | 2 | ||
7098.2.a.ch.1.1 | yes | 3 | 1.1 | even | 1 | trivial |