Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, 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("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.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: | \(63.8883066572\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 6 x^{17} - 11 x^{16} + 123 x^{15} - 35 x^{14} - 982 x^{13} + 988 x^{12} + 3872 x^{11} - 5421 x^{10} - 7882 x^{9} + 13376 x^{8} + 7948 x^{7} - 15795 x^{6} - 3858 x^{5} + \cdots + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2\cdot 5 \) |
Twist minimal: | no (minimal twist has level 2667) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-1.33766\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.33766 | −0.945869 | −0.472935 | − | 0.881098i | \(-0.656805\pi\) | ||||
−0.472935 | + | 0.881098i | \(0.656805\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.210663 | −0.105332 | ||||||||
\(5\) | 0.660635 | 0.295445 | 0.147722 | − | 0.989029i | \(-0.452806\pi\) | ||||
0.147722 | + | 0.989029i | \(0.452806\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 2.95712 | 1.04550 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.883705 | −0.279452 | ||||||||
\(11\) | 2.50246 | 0.754519 | 0.377259 | − | 0.926108i | \(-0.376867\pi\) | ||||
0.377259 | + | 0.926108i | \(0.376867\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.59818 | 0.997955 | 0.498977 | − | 0.866615i | \(-0.333709\pi\) | ||||
0.498977 | + | 0.866615i | \(0.333709\pi\) | |||||||
\(14\) | −1.33766 | −0.357505 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.53429 | −0.883574 | ||||||||
\(17\) | −0.647641 | −0.157076 | −0.0785380 | − | 0.996911i | \(-0.525025\pi\) | ||||
−0.0785380 | + | 0.996911i | \(0.525025\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.90149 | 1.12448 | 0.562239 | − | 0.826975i | \(-0.309940\pi\) | ||||
0.562239 | + | 0.826975i | \(0.309940\pi\) | |||||||
\(20\) | −0.139171 | −0.0311197 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.34744 | −0.713676 | ||||||||
\(23\) | −4.27804 | −0.892033 | −0.446017 | − | 0.895025i | \(-0.647158\pi\) | ||||
−0.446017 | + | 0.895025i | \(0.647158\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.56356 | −0.912712 | ||||||||
\(26\) | −4.81314 | −0.943935 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.210663 | −0.0398116 | ||||||||
\(29\) | 7.60208 | 1.41167 | 0.705835 | − | 0.708376i | \(-0.250572\pi\) | ||||
0.705835 | + | 0.708376i | \(0.250572\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.73462 | −0.491152 | −0.245576 | − | 0.969377i | \(-0.578977\pi\) | ||||
−0.245576 | + | 0.969377i | \(0.578977\pi\) | |||||||
\(32\) | −1.18655 | −0.209754 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.866324 | 0.148573 | ||||||||
\(35\) | 0.660635 | 0.111668 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.693776 | 0.114056 | 0.0570280 | − | 0.998373i | \(-0.481838\pi\) | ||||
0.0570280 | + | 0.998373i | \(0.481838\pi\) | |||||||
\(38\) | −6.55653 | −1.06361 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.95357 | 0.308887 | ||||||||
\(41\) | 11.1859 | 1.74694 | 0.873470 | − | 0.486878i | \(-0.161864\pi\) | ||||
0.873470 | + | 0.486878i | \(0.161864\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.57216 | −0.239751 | −0.119876 | − | 0.992789i | \(-0.538250\pi\) | ||||
−0.119876 | + | 0.992789i | \(0.538250\pi\) | |||||||
\(44\) | −0.527175 | −0.0794746 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.72257 | 0.843747 | ||||||||
\(47\) | 6.59069 | 0.961350 | 0.480675 | − | 0.876899i | \(-0.340392\pi\) | ||||
0.480675 | + | 0.876899i | \(0.340392\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 6.10450 | 0.863306 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.758003 | −0.105116 | ||||||||
\(53\) | −7.27823 | −0.999742 | −0.499871 | − | 0.866100i | \(-0.666619\pi\) | ||||
−0.499871 | + | 0.866100i | \(0.666619\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.65321 | 0.222919 | ||||||||
\(56\) | 2.95712 | 0.395161 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −10.1690 | −1.33526 | ||||||||
\(59\) | 9.88118 | 1.28642 | 0.643210 | − | 0.765690i | \(-0.277602\pi\) | ||||
0.643210 | + | 0.765690i | \(0.277602\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.382234 | 0.0489401 | 0.0244700 | − | 0.999701i | \(-0.492210\pi\) | ||||
0.0244700 | + | 0.999701i | \(0.492210\pi\) | |||||||
\(62\) | 3.65799 | 0.464566 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.65579 | 1.08197 | ||||||||
\(65\) | 2.37708 | 0.294841 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.37009 | −0.533892 | −0.266946 | − | 0.963712i | \(-0.586015\pi\) | ||||
−0.266946 | + | 0.963712i | \(0.586015\pi\) | |||||||
\(68\) | 0.136434 | 0.0165451 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.883705 | −0.105623 | ||||||||
\(71\) | 13.1847 | 1.56474 | 0.782371 | − | 0.622813i | \(-0.214010\pi\) | ||||
0.782371 | + | 0.622813i | \(0.214010\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.43665 | 0.519271 | 0.259635 | − | 0.965707i | \(-0.416398\pi\) | ||||
0.259635 | + | 0.965707i | \(0.416398\pi\) | |||||||
\(74\) | −0.928037 | −0.107882 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.03256 | −0.118443 | ||||||||
\(77\) | 2.50246 | 0.285181 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.44755 | −0.725406 | −0.362703 | − | 0.931905i | \(-0.618146\pi\) | ||||
−0.362703 | + | 0.931905i | \(0.618146\pi\) | |||||||
\(80\) | −2.33488 | −0.261047 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −14.9629 | −1.65238 | ||||||||
\(83\) | 4.82194 | 0.529276 | 0.264638 | − | 0.964348i | \(-0.414747\pi\) | ||||
0.264638 | + | 0.964348i | \(0.414747\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.427854 | −0.0464073 | ||||||||
\(86\) | 2.10301 | 0.226774 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 7.40006 | 0.788849 | ||||||||
\(89\) | 9.63534 | 1.02134 | 0.510672 | − | 0.859775i | \(-0.329397\pi\) | ||||
0.510672 | + | 0.859775i | \(0.329397\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.59818 | 0.377191 | ||||||||
\(92\) | 0.901226 | 0.0939593 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −8.81610 | −0.909312 | ||||||||
\(95\) | 3.23809 | 0.332221 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.182292 | −0.0185089 | −0.00925446 | − | 0.999957i | \(-0.502946\pi\) | ||||
−0.00925446 | + | 0.999957i | \(0.502946\pi\) | |||||||
\(98\) | −1.33766 | −0.135124 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.961374 | 0.0961374 | ||||||||
\(101\) | 14.8172 | 1.47436 | 0.737181 | − | 0.675695i | \(-0.236156\pi\) | ||||
0.737181 | + | 0.675695i | \(0.236156\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.22841 | −0.416638 | −0.208319 | − | 0.978061i | \(-0.566799\pi\) | ||||
−0.208319 | + | 0.978061i | \(0.566799\pi\) | |||||||
\(104\) | 10.6402 | 1.04336 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 9.73581 | 0.945625 | ||||||||
\(107\) | −3.60740 | −0.348740 | −0.174370 | − | 0.984680i | \(-0.555789\pi\) | ||||
−0.174370 | + | 0.984680i | \(0.555789\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.1924 | −0.976259 | −0.488129 | − | 0.872771i | \(-0.662321\pi\) | ||||
−0.488129 | + | 0.872771i | \(0.662321\pi\) | |||||||
\(110\) | −2.21143 | −0.210852 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.53429 | −0.333959 | ||||||||
\(113\) | −5.90567 | −0.555559 | −0.277780 | − | 0.960645i | \(-0.589598\pi\) | ||||
−0.277780 | + | 0.960645i | \(0.589598\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.82622 | −0.263547 | ||||||||
\(116\) | −1.60148 | −0.148693 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −13.2177 | −1.21679 | ||||||||
\(119\) | −0.647641 | −0.0593692 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.73772 | −0.430702 | ||||||||
\(122\) | −0.511300 | −0.0462909 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.576083 | 0.0517338 | ||||||||
\(125\) | −6.31802 | −0.565101 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.00000 | 0.0887357 | ||||||||
\(128\) | −9.20541 | −0.813651 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.17973 | −0.278881 | ||||||||
\(131\) | −1.15626 | −0.101023 | −0.0505116 | − | 0.998723i | \(-0.516085\pi\) | ||||
−0.0505116 | + | 0.998723i | \(0.516085\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.90149 | 0.425013 | ||||||||
\(134\) | 5.84570 | 0.504992 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.91515 | −0.164223 | ||||||||
\(137\) | −12.7644 | −1.09054 | −0.545270 | − | 0.838260i | \(-0.683573\pi\) | ||||
−0.545270 | + | 0.838260i | \(0.683573\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.66110 | −0.140892 | −0.0704461 | − | 0.997516i | \(-0.522442\pi\) | ||||
−0.0704461 | + | 0.997516i | \(0.522442\pi\) | |||||||
\(140\) | −0.139171 | −0.0117621 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −17.6367 | −1.48004 | ||||||||
\(143\) | 9.00428 | 0.752976 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.02220 | 0.417071 | ||||||||
\(146\) | −5.93473 | −0.491162 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.146153 | −0.0120137 | ||||||||
\(149\) | 2.58333 | 0.211634 | 0.105817 | − | 0.994386i | \(-0.466254\pi\) | ||||
0.105817 | + | 0.994386i | \(0.466254\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.2335 | 1.15831 | 0.579153 | − | 0.815219i | \(-0.303384\pi\) | ||||
0.579153 | + | 0.815219i | \(0.303384\pi\) | |||||||
\(152\) | 14.4943 | 1.17564 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.34744 | −0.269744 | ||||||||
\(155\) | −1.80658 | −0.145108 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.1240 | −1.12722 | −0.563611 | − | 0.826040i | \(-0.690588\pi\) | ||||
−0.563611 | + | 0.826040i | \(0.690588\pi\) | |||||||
\(158\) | 8.62463 | 0.686139 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.783874 | −0.0619707 | ||||||||
\(161\) | −4.27804 | −0.337157 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.0883 | 0.790173 | 0.395087 | − | 0.918644i | \(-0.370715\pi\) | ||||
0.395087 | + | 0.918644i | \(0.370715\pi\) | |||||||
\(164\) | −2.35645 | −0.184008 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.45012 | −0.500626 | ||||||||
\(167\) | −6.93188 | −0.536405 | −0.268203 | − | 0.963363i | \(-0.586430\pi\) | ||||
−0.268203 | + | 0.963363i | \(0.586430\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.0531190 | −0.00408608 | ||||||||
\(170\) | 0.572324 | 0.0438952 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.331195 | 0.0252534 | ||||||||
\(173\) | 9.68261 | 0.736155 | 0.368078 | − | 0.929795i | \(-0.380016\pi\) | ||||
0.368078 | + | 0.929795i | \(0.380016\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.56356 | −0.344973 | ||||||||
\(176\) | −8.84441 | −0.666673 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −12.8888 | −0.966058 | ||||||||
\(179\) | −4.48504 | −0.335228 | −0.167614 | − | 0.985853i | \(-0.553606\pi\) | ||||
−0.167614 | + | 0.985853i | \(0.553606\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.293930 | 0.0218476 | 0.0109238 | − | 0.999940i | \(-0.496523\pi\) | ||||
0.0109238 | + | 0.999940i | \(0.496523\pi\) | |||||||
\(182\) | −4.81314 | −0.356774 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −12.6507 | −0.932620 | ||||||||
\(185\) | 0.458332 | 0.0336972 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.62069 | −0.118517 | ||||||||
\(188\) | −1.38841 | −0.101261 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.33147 | −0.314238 | ||||||||
\(191\) | −13.1650 | −0.952583 | −0.476291 | − | 0.879287i | \(-0.658019\pi\) | ||||
−0.476291 | + | 0.879287i | \(0.658019\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.75824 | −0.486469 | −0.243234 | − | 0.969968i | \(-0.578208\pi\) | ||||
−0.243234 | + | 0.969968i | \(0.578208\pi\) | |||||||
\(194\) | 0.243845 | 0.0175070 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.210663 | −0.0150474 | ||||||||
\(197\) | −16.8067 | −1.19743 | −0.598714 | − | 0.800963i | \(-0.704321\pi\) | ||||
−0.598714 | + | 0.800963i | \(0.704321\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.39126 | 0.311288 | 0.155644 | − | 0.987813i | \(-0.450255\pi\) | ||||
0.155644 | + | 0.987813i | \(0.450255\pi\) | |||||||
\(200\) | −13.4950 | −0.954240 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −19.8203 | −1.39455 | ||||||||
\(203\) | 7.60208 | 0.533561 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.38977 | 0.516124 | ||||||||
\(206\) | 5.65618 | 0.394085 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −12.7170 | −0.881767 | ||||||||
\(209\) | 12.2658 | 0.848440 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.300003 | 0.0206530 | 0.0103265 | − | 0.999947i | \(-0.496713\pi\) | ||||
0.0103265 | + | 0.999947i | \(0.496713\pi\) | |||||||
\(212\) | 1.53326 | 0.105304 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.82547 | 0.329863 | ||||||||
\(215\) | −1.03862 | −0.0708333 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.73462 | −0.185638 | ||||||||
\(218\) | 13.6340 | 0.923413 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.348270 | −0.0234804 | ||||||||
\(221\) | −2.33033 | −0.156755 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −25.5960 | −1.71404 | −0.857018 | − | 0.515286i | \(-0.827686\pi\) | ||||
−0.857018 | + | 0.515286i | \(0.827686\pi\) | |||||||
\(224\) | −1.18655 | −0.0792795 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7.89979 | 0.525486 | ||||||||
\(227\) | 8.55148 | 0.567582 | 0.283791 | − | 0.958886i | \(-0.408408\pi\) | ||||
0.283791 | + | 0.958886i | \(0.408408\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.2641 | 0.876518 | 0.438259 | − | 0.898849i | \(-0.355595\pi\) | ||||
0.438259 | + | 0.898849i | \(0.355595\pi\) | |||||||
\(230\) | 3.78053 | 0.249281 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 22.4802 | 1.47590 | ||||||||
\(233\) | −9.75984 | −0.639389 | −0.319694 | − | 0.947521i | \(-0.603580\pi\) | ||||
−0.319694 | + | 0.947521i | \(0.603580\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.35403 | 0.284026 | ||||||||
\(236\) | −2.08160 | −0.135501 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.866324 | 0.0561555 | ||||||||
\(239\) | 3.32098 | 0.214816 | 0.107408 | − | 0.994215i | \(-0.465745\pi\) | ||||
0.107408 | + | 0.994215i | \(0.465745\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.1150 | −0.844812 | −0.422406 | − | 0.906407i | \(-0.638814\pi\) | ||||
−0.422406 | + | 0.906407i | \(0.638814\pi\) | |||||||
\(242\) | 6.33746 | 0.407387 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −0.0805226 | −0.00515493 | ||||||||
\(245\) | 0.660635 | 0.0422064 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 17.6364 | 1.12218 | ||||||||
\(248\) | −8.08659 | −0.513499 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 8.45137 | 0.534511 | ||||||||
\(251\) | 27.6002 | 1.74211 | 0.871056 | − | 0.491184i | \(-0.163436\pi\) | ||||
0.871056 | + | 0.491184i | \(0.163436\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −10.7056 | −0.673056 | ||||||||
\(254\) | −1.33766 | −0.0839323 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4.99785 | −0.312366 | ||||||||
\(257\) | 7.72105 | 0.481626 | 0.240813 | − | 0.970572i | \(-0.422586\pi\) | ||||
0.240813 | + | 0.970572i | \(0.422586\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.693776 | 0.0431091 | ||||||||
\(260\) | −0.500763 | −0.0310560 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.54669 | 0.0955547 | ||||||||
\(263\) | −18.2383 | −1.12462 | −0.562310 | − | 0.826926i | \(-0.690087\pi\) | ||||
−0.562310 | + | 0.826926i | \(0.690087\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.80825 | −0.295369 | ||||||||
\(266\) | −6.55653 | −0.402007 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.920618 | 0.0562357 | ||||||||
\(269\) | 12.9944 | 0.792284 | 0.396142 | − | 0.918189i | \(-0.370349\pi\) | ||||
0.396142 | + | 0.918189i | \(0.370349\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.1311 | 1.16213 | 0.581065 | − | 0.813857i | \(-0.302636\pi\) | ||||
0.581065 | + | 0.813857i | \(0.302636\pi\) | |||||||
\(272\) | 2.28895 | 0.138788 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 17.0745 | 1.03151 | ||||||||
\(275\) | −11.4201 | −0.688659 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 21.3254 | 1.28132 | 0.640660 | − | 0.767825i | \(-0.278661\pi\) | ||||
0.640660 | + | 0.767825i | \(0.278661\pi\) | |||||||
\(278\) | 2.22198 | 0.133266 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.95357 | 0.116748 | ||||||||
\(281\) | 30.3475 | 1.81038 | 0.905189 | − | 0.425009i | \(-0.139729\pi\) | ||||
0.905189 | + | 0.425009i | \(0.139729\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.32015 | 0.197362 | 0.0986811 | − | 0.995119i | \(-0.468538\pi\) | ||||
0.0986811 | + | 0.995119i | \(0.468538\pi\) | |||||||
\(284\) | −2.77754 | −0.164817 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −12.0447 | −0.712216 | ||||||||
\(287\) | 11.1859 | 0.660281 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.5806 | −0.975327 | ||||||||
\(290\) | −6.71800 | −0.394494 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.934639 | −0.0546956 | ||||||||
\(293\) | 8.00402 | 0.467600 | 0.233800 | − | 0.972285i | \(-0.424884\pi\) | ||||
0.233800 | + | 0.972285i | \(0.424884\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.52785 | 0.380066 | ||||||||
\(296\) | 2.05158 | 0.119245 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.45562 | −0.200179 | ||||||||
\(299\) | −15.3932 | −0.890209 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.57216 | −0.0906175 | ||||||||
\(302\) | −19.0396 | −1.09561 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −17.3233 | −0.993560 | ||||||||
\(305\) | 0.252517 | 0.0144591 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.27243 | −0.186768 | −0.0933838 | − | 0.995630i | \(-0.529768\pi\) | ||||
−0.0933838 | + | 0.995630i | \(0.529768\pi\) | |||||||
\(308\) | −0.527175 | −0.0300386 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.41660 | 0.137253 | ||||||||
\(311\) | −23.9348 | −1.35722 | −0.678608 | − | 0.734500i | \(-0.737417\pi\) | ||||
−0.678608 | + | 0.734500i | \(0.737417\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.9219 | −0.673866 | −0.336933 | − | 0.941529i | \(-0.609390\pi\) | ||||
−0.336933 | + | 0.941529i | \(0.609390\pi\) | |||||||
\(314\) | 18.8932 | 1.06620 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.35826 | 0.0764081 | ||||||||
\(317\) | 13.8807 | 0.779620 | 0.389810 | − | 0.920895i | \(-0.372541\pi\) | ||||
0.389810 | + | 0.920895i | \(0.372541\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 19.0239 | 1.06513 | ||||||||
\(320\) | 5.71831 | 0.319663 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 5.72257 | 0.318906 | ||||||||
\(323\) | −3.17441 | −0.176629 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −16.4205 | −0.910846 | ||||||||
\(326\) | −13.4947 | −0.747400 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 33.0779 | 1.82642 | ||||||||
\(329\) | 6.59069 | 0.363356 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.63180 | 0.419482 | 0.209741 | − | 0.977757i | \(-0.432738\pi\) | ||||
0.209741 | + | 0.977757i | \(0.432738\pi\) | |||||||
\(332\) | −1.01580 | −0.0557495 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 9.27251 | 0.507369 | ||||||||
\(335\) | −2.88703 | −0.157736 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.476513 | −0.0259573 | −0.0129786 | − | 0.999916i | \(-0.504131\pi\) | ||||
−0.0129786 | + | 0.999916i | \(0.504131\pi\) | |||||||
\(338\) | 0.0710552 | 0.00386489 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.0901331 | 0.00488815 | ||||||||
\(341\) | −6.84326 | −0.370583 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −4.64905 | −0.250660 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −12.9520 | −0.696307 | ||||||||
\(347\) | −1.27343 | −0.0683613 | −0.0341806 | − | 0.999416i | \(-0.510882\pi\) | ||||
−0.0341806 | + | 0.999416i | \(0.510882\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.92179 | −0.531101 | −0.265551 | − | 0.964097i | \(-0.585554\pi\) | ||||
−0.265551 | + | 0.964097i | \(0.585554\pi\) | |||||||
\(350\) | 6.10450 | 0.326299 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.96928 | −0.158263 | ||||||||
\(353\) | −21.2141 | −1.12911 | −0.564556 | − | 0.825395i | \(-0.690952\pi\) | ||||
−0.564556 | + | 0.825395i | \(0.690952\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.71030 | 0.462295 | ||||||||
\(356\) | −2.02981 | −0.107580 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5.99947 | 0.317082 | ||||||||
\(359\) | 19.1882 | 1.01271 | 0.506356 | − | 0.862324i | \(-0.330992\pi\) | ||||
0.506356 | + | 0.862324i | \(0.330992\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.02459 | 0.264452 | ||||||||
\(362\) | −0.393179 | −0.0206650 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.758003 | −0.0397302 | ||||||||
\(365\) | 2.93100 | 0.153416 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 33.0463 | 1.72500 | 0.862501 | − | 0.506055i | \(-0.168897\pi\) | ||||
0.862501 | + | 0.506055i | \(0.168897\pi\) | |||||||
\(368\) | 15.1199 | 0.788177 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.613093 | −0.0318732 | ||||||||
\(371\) | −7.27823 | −0.377867 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.79344 | −0.455307 | −0.227654 | − | 0.973742i | \(-0.573105\pi\) | ||||
−0.227654 | + | 0.973742i | \(0.573105\pi\) | |||||||
\(374\) | 2.16794 | 0.112101 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 19.4894 | 1.00509 | ||||||||
\(377\) | 27.3536 | 1.40878 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.9657 | −0.768735 | −0.384368 | − | 0.923180i | \(-0.625580\pi\) | ||||
−0.384368 | + | 0.923180i | \(0.625580\pi\) | |||||||
\(380\) | −0.682147 | −0.0349934 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 17.6103 | 0.901019 | ||||||||
\(383\) | 1.59337 | 0.0814172 | 0.0407086 | − | 0.999171i | \(-0.487038\pi\) | ||||
0.0407086 | + | 0.999171i | \(0.487038\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.65321 | 0.0842553 | ||||||||
\(386\) | 9.04023 | 0.460136 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0.0384021 | 0.00194957 | ||||||||
\(389\) | 23.3352 | 1.18314 | 0.591570 | − | 0.806254i | \(-0.298509\pi\) | ||||
0.591570 | + | 0.806254i | \(0.298509\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.77064 | 0.140117 | ||||||||
\(392\) | 2.95712 | 0.149357 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 22.4817 | 1.13261 | ||||||||
\(395\) | −4.25947 | −0.214317 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.8324 | 0.945171 | 0.472586 | − | 0.881285i | \(-0.343321\pi\) | ||||
0.472586 | + | 0.881285i | \(0.343321\pi\) | |||||||
\(398\) | −5.87402 | −0.294438 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 16.1290 | 0.806449 | ||||||||
\(401\) | −25.1525 | −1.25606 | −0.628029 | − | 0.778190i | \(-0.716138\pi\) | ||||
−0.628029 | + | 0.778190i | \(0.716138\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.83964 | −0.490148 | ||||||||
\(404\) | −3.12143 | −0.155297 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −10.1690 | −0.504679 | ||||||||
\(407\) | 1.73614 | 0.0860574 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.86404 | −0.191064 | −0.0955322 | − | 0.995426i | \(-0.530455\pi\) | ||||
−0.0955322 | + | 0.995426i | \(0.530455\pi\) | |||||||
\(410\) | −9.88501 | −0.488186 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.890771 | 0.0438851 | ||||||||
\(413\) | 9.88118 | 0.486221 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.18554 | 0.156372 | ||||||||
\(416\) | −4.26941 | −0.209325 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −16.4074 | −0.802513 | ||||||||
\(419\) | 1.66627 | 0.0814028 | 0.0407014 | − | 0.999171i | \(-0.487041\pi\) | ||||
0.0407014 | + | 0.999171i | \(0.487041\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.9101 | 1.16531 | 0.582653 | − | 0.812721i | \(-0.302015\pi\) | ||||
0.582653 | + | 0.812721i | \(0.302015\pi\) | |||||||
\(422\) | −0.401302 | −0.0195351 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −21.5226 | −1.04523 | ||||||||
\(425\) | 2.95555 | 0.143365 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.382234 | 0.0184976 | ||||||||
\(428\) | 0.759945 | 0.0367333 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.38932 | 0.0669990 | ||||||||
\(431\) | −14.2316 | −0.685513 | −0.342757 | − | 0.939424i | \(-0.611361\pi\) | ||||
−0.342757 | + | 0.939424i | \(0.611361\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.4071 | 0.740420 | 0.370210 | − | 0.928948i | \(-0.379286\pi\) | ||||
0.370210 | + | 0.928948i | \(0.379286\pi\) | |||||||
\(434\) | 3.65799 | 0.175589 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.14717 | 0.102831 | ||||||||
\(437\) | −20.9688 | −1.00307 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.7032 | 0.606291 | 0.303145 | − | 0.952944i | \(-0.401963\pi\) | ||||
0.303145 | + | 0.952944i | \(0.401963\pi\) | |||||||
\(440\) | 4.88873 | 0.233061 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.11719 | 0.148270 | ||||||||
\(443\) | 13.1778 | 0.626098 | 0.313049 | − | 0.949737i | \(-0.398650\pi\) | ||||
0.313049 | + | 0.949737i | \(0.398650\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.36544 | 0.301751 | ||||||||
\(446\) | 34.2388 | 1.62125 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 8.65579 | 0.408948 | ||||||||
\(449\) | −13.5598 | −0.639928 | −0.319964 | − | 0.947430i | \(-0.603671\pi\) | ||||
−0.319964 | + | 0.947430i | \(0.603671\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 27.9921 | 1.31810 | ||||||||
\(452\) | 1.24411 | 0.0585179 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −11.4390 | −0.536858 | ||||||||
\(455\) | 2.37708 | 0.111439 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.3099 | −0.716168 | −0.358084 | − | 0.933689i | \(-0.616570\pi\) | ||||
−0.358084 | + | 0.933689i | \(0.616570\pi\) | |||||||
\(458\) | −17.7429 | −0.829071 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.595381 | 0.0277598 | ||||||||
\(461\) | −14.0827 | −0.655897 | −0.327948 | − | 0.944696i | \(-0.606357\pi\) | ||||
−0.327948 | + | 0.944696i | \(0.606357\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.6093 | −0.725424 | −0.362712 | − | 0.931901i | \(-0.618149\pi\) | ||||
−0.362712 | + | 0.931901i | \(0.618149\pi\) | |||||||
\(464\) | −26.8680 | −1.24732 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 13.0554 | 0.604778 | ||||||||
\(467\) | −37.3868 | −1.73005 | −0.865027 | − | 0.501725i | \(-0.832699\pi\) | ||||
−0.865027 | + | 0.501725i | \(0.832699\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.37009 | −0.201792 | ||||||||
\(470\) | −5.82422 | −0.268651 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 29.2198 | 1.34495 | ||||||||
\(473\) | −3.93425 | −0.180897 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −22.3682 | −1.02633 | ||||||||
\(476\) | 0.136434 | 0.00625345 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4.44234 | −0.203188 | ||||||||
\(479\) | −28.4334 | −1.29915 | −0.649577 | − | 0.760296i | \(-0.725054\pi\) | ||||
−0.649577 | + | 0.760296i | \(0.725054\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.49633 | 0.113823 | ||||||||
\(482\) | 17.5434 | 0.799082 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.998062 | 0.0453665 | ||||||||
\(485\) | −0.120428 | −0.00546836 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 37.0313 | 1.67805 | 0.839024 | − | 0.544095i | \(-0.183127\pi\) | ||||
0.839024 | + | 0.544095i | \(0.183127\pi\) | |||||||
\(488\) | 1.13031 | 0.0511668 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.883705 | −0.0399217 | ||||||||
\(491\) | −15.7040 | −0.708711 | −0.354356 | − | 0.935111i | \(-0.615300\pi\) | ||||
−0.354356 | + | 0.935111i | \(0.615300\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.92342 | −0.221740 | ||||||||
\(494\) | −23.5916 | −1.06143 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9.66495 | 0.433969 | ||||||||
\(497\) | 13.1847 | 0.591417 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 32.0326 | 1.43398 | 0.716989 | − | 0.697085i | \(-0.245520\pi\) | ||||
0.716989 | + | 0.697085i | \(0.245520\pi\) | |||||||
\(500\) | 1.33097 | 0.0595230 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −36.9198 | −1.64781 | ||||||||
\(503\) | 3.50362 | 0.156219 | 0.0781093 | − | 0.996945i | \(-0.475112\pi\) | ||||
0.0781093 | + | 0.996945i | \(0.475112\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.78873 | 0.435593 | ||||||||
\(506\) | 14.3205 | 0.636623 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.210663 | −0.00934667 | ||||||||
\(509\) | 33.3038 | 1.47616 | 0.738082 | − | 0.674711i | \(-0.235732\pi\) | ||||
0.738082 | + | 0.674711i | \(0.235732\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.43665 | 0.196266 | ||||||||
\(512\) | 25.0963 | 1.10911 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −10.3281 | −0.455555 | ||||||||
\(515\) | −2.79344 | −0.123093 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 16.4929 | 0.725357 | ||||||||
\(518\) | −0.928037 | −0.0407756 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 7.02931 | 0.308255 | ||||||||
\(521\) | 3.99571 | 0.175055 | 0.0875276 | − | 0.996162i | \(-0.472103\pi\) | ||||
0.0875276 | + | 0.996162i | \(0.472103\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.41299 | 0.149240 | 0.0746199 | − | 0.997212i | \(-0.476226\pi\) | ||||
0.0746199 | + | 0.997212i | \(0.476226\pi\) | |||||||
\(524\) | 0.243582 | 0.0106409 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 24.3966 | 1.06374 | ||||||||
\(527\) | 1.77105 | 0.0771482 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.69836 | −0.204276 | ||||||||
\(530\) | 6.43181 | 0.279380 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.03256 | −0.0447673 | ||||||||
\(533\) | 40.2488 | 1.74337 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.38317 | −0.103033 | ||||||||
\(536\) | −12.9229 | −0.558183 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −17.3821 | −0.749397 | ||||||||
\(539\) | 2.50246 | 0.107788 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −28.7529 | −1.23618 | −0.618092 | − | 0.786106i | \(-0.712094\pi\) | ||||
−0.618092 | + | 0.786106i | \(0.712094\pi\) | |||||||
\(542\) | −25.5909 | −1.09922 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.768457 | 0.0329473 | ||||||||
\(545\) | −6.73348 | −0.288431 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.81775 | 0.419777 | 0.209888 | − | 0.977725i | \(-0.432690\pi\) | ||||
0.209888 | + | 0.977725i | \(0.432690\pi\) | |||||||
\(548\) | 2.68900 | 0.114868 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 15.2762 | 0.651381 | ||||||||
\(551\) | 37.2615 | 1.58739 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.44755 | −0.274178 | ||||||||
\(554\) | −28.5262 | −1.21196 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.349932 | 0.0148404 | ||||||||
\(557\) | 11.4402 | 0.484735 | 0.242368 | − | 0.970184i | \(-0.422076\pi\) | ||||
0.242368 | + | 0.970184i | \(0.422076\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.65689 | −0.239261 | ||||||||
\(560\) | −2.33488 | −0.0986666 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −40.5946 | −1.71238 | ||||||||
\(563\) | 19.8032 | 0.834605 | 0.417303 | − | 0.908768i | \(-0.362975\pi\) | ||||
0.417303 | + | 0.908768i | \(0.362975\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.90149 | −0.164137 | ||||||||
\(566\) | −4.44123 | −0.186679 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 38.9888 | 1.63594 | ||||||||
\(569\) | 9.19690 | 0.385554 | 0.192777 | − | 0.981243i | \(-0.438251\pi\) | ||||
0.192777 | + | 0.981243i | \(0.438251\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 34.6547 | 1.45026 | 0.725128 | − | 0.688615i | \(-0.241781\pi\) | ||||
0.725128 | + | 0.688615i | \(0.241781\pi\) | |||||||
\(572\) | −1.89687 | −0.0793121 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −14.9629 | −0.624540 | ||||||||
\(575\) | 19.5231 | 0.814170 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.7858 | 0.490648 | 0.245324 | − | 0.969441i | \(-0.421106\pi\) | ||||
0.245324 | + | 0.969441i | \(0.421106\pi\) | |||||||
\(578\) | 22.1792 | 0.922532 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.05799 | −0.0439307 | ||||||||
\(581\) | 4.82194 | 0.200048 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −18.2135 | −0.754324 | ||||||||
\(584\) | 13.1197 | 0.542897 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −10.7067 | −0.442288 | ||||||||
\(587\) | 12.7673 | 0.526961 | 0.263480 | − | 0.964665i | \(-0.415130\pi\) | ||||
0.263480 | + | 0.964665i | \(0.415130\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13.4037 | −0.552290 | ||||||||
\(590\) | −8.73205 | −0.359493 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.45201 | −0.100777 | ||||||||
\(593\) | 31.8244 | 1.30687 | 0.653435 | − | 0.756983i | \(-0.273327\pi\) | ||||
0.653435 | + | 0.756983i | \(0.273327\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.427854 | −0.0175403 | ||||||||
\(596\) | −0.544212 | −0.0222918 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 20.5908 | 0.842021 | ||||||||
\(599\) | −19.8627 | −0.811570 | −0.405785 | − | 0.913969i | \(-0.633002\pi\) | ||||
−0.405785 | + | 0.913969i | \(0.633002\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 29.6711 | 1.21031 | 0.605154 | − | 0.796108i | \(-0.293111\pi\) | ||||
0.605154 | + | 0.796108i | \(0.293111\pi\) | |||||||
\(602\) | 2.10301 | 0.0857123 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2.99847 | −0.122006 | ||||||||
\(605\) | −3.12990 | −0.127249 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17.8654 | −0.725136 | −0.362568 | − | 0.931957i | \(-0.618100\pi\) | ||||
−0.362568 | + | 0.931957i | \(0.618100\pi\) | |||||||
\(608\) | −5.81585 | −0.235864 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.337782 | −0.0136764 | ||||||||
\(611\) | 23.7145 | 0.959384 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21.2972 | 0.860186 | 0.430093 | − | 0.902785i | \(-0.358481\pi\) | ||||
0.430093 | + | 0.902785i | \(0.358481\pi\) | |||||||
\(614\) | 4.37740 | 0.176658 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7.40006 | 0.298157 | ||||||||
\(617\) | −27.3251 | −1.10007 | −0.550034 | − | 0.835142i | \(-0.685385\pi\) | ||||
−0.550034 | + | 0.835142i | \(0.685385\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.2893 | −0.413562 | −0.206781 | − | 0.978387i | \(-0.566299\pi\) | ||||
−0.206781 | + | 0.978387i | \(0.566299\pi\) | |||||||
\(620\) | 0.380581 | 0.0152845 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 32.0166 | 1.28375 | ||||||||
\(623\) | 9.63534 | 0.386032 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 18.6439 | 0.745756 | ||||||||
\(626\) | 15.9475 | 0.637389 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.97542 | 0.118732 | ||||||||
\(629\) | −0.449318 | −0.0179155 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.6828 | 1.06223 | 0.531113 | − | 0.847301i | \(-0.321774\pi\) | ||||
0.531113 | + | 0.847301i | \(0.321774\pi\) | |||||||
\(632\) | −19.0662 | −0.758411 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −18.5677 | −0.737419 | ||||||||
\(635\) | 0.660635 | 0.0262165 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.59818 | 0.142565 | ||||||||
\(638\) | −25.4475 | −1.00748 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −6.08141 | −0.240389 | ||||||||
\(641\) | 24.1029 | 0.952005 | 0.476003 | − | 0.879444i | \(-0.342085\pi\) | ||||
0.476003 | + | 0.879444i | \(0.342085\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15.6694 | −0.617940 | −0.308970 | − | 0.951072i | \(-0.599984\pi\) | ||||
−0.308970 | + | 0.951072i | \(0.599984\pi\) | |||||||
\(644\) | 0.901226 | 0.0355133 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.24628 | 0.167068 | ||||||||
\(647\) | −5.20075 | −0.204463 | −0.102231 | − | 0.994761i | \(-0.532598\pi\) | ||||
−0.102231 | + | 0.994761i | \(0.532598\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 24.7272 | 0.970628 | ||||||||
\(650\) | 21.9651 | 0.861541 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.12522 | −0.0832302 | ||||||||
\(653\) | −14.1774 | −0.554804 | −0.277402 | − | 0.960754i | \(-0.589473\pi\) | ||||
−0.277402 | + | 0.960754i | \(0.589473\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.763867 | −0.0298468 | ||||||||
\(656\) | −39.5342 | −1.54355 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −8.81610 | −0.343687 | ||||||||
\(659\) | 5.06889 | 0.197456 | 0.0987280 | − | 0.995114i | \(-0.468523\pi\) | ||||
0.0987280 | + | 0.995114i | \(0.468523\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −44.1647 | −1.71781 | −0.858905 | − | 0.512136i | \(-0.828855\pi\) | ||||
−0.858905 | + | 0.512136i | \(0.828855\pi\) | |||||||
\(662\) | −10.2088 | −0.396775 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 14.2590 | 0.553358 | ||||||||
\(665\) | 3.23809 | 0.125568 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −32.5220 | −1.25926 | ||||||||
\(668\) | 1.46029 | 0.0565004 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 3.86187 | 0.149197 | ||||||||
\(671\) | 0.956524 | 0.0369262 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 34.6780 | 1.33674 | 0.668369 | − | 0.743830i | \(-0.266993\pi\) | ||||
0.668369 | + | 0.743830i | \(0.266993\pi\) | |||||||
\(674\) | 0.637412 | 0.0245522 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.0111902 | 0.000430393 0 | ||||||||
\(677\) | 31.0973 | 1.19517 | 0.597583 | − | 0.801807i | \(-0.296128\pi\) | ||||
0.597583 | + | 0.801807i | \(0.296128\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.182292 | −0.00699571 | ||||||||
\(680\) | −1.26522 | −0.0485188 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 9.15396 | 0.350523 | ||||||||
\(683\) | 49.0636 | 1.87736 | 0.938682 | − | 0.344783i | \(-0.112047\pi\) | ||||
0.938682 | + | 0.344783i | \(0.112047\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.43263 | −0.322194 | ||||||||
\(686\) | −1.33766 | −0.0510721 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.55646 | 0.211838 | ||||||||
\(689\) | −26.1884 | −0.997698 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.63843 | 0.328621 | 0.164311 | − | 0.986409i | \(-0.447460\pi\) | ||||
0.164311 | + | 0.986409i | \(0.447460\pi\) | |||||||
\(692\) | −2.03977 | −0.0775404 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.70342 | 0.0646608 | ||||||||
\(695\) | −1.09738 | −0.0416259 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.24443 | −0.274402 | ||||||||
\(698\) | 13.2720 | 0.502352 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.961374 | 0.0363365 | ||||||||
\(701\) | −3.58228 | −0.135301 | −0.0676505 | − | 0.997709i | \(-0.521550\pi\) | ||||
−0.0676505 | + | 0.997709i | \(0.521550\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.40053 | 0.128254 | ||||||||
\(704\) | 21.6607 | 0.816369 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 28.3772 | 1.06799 | ||||||||
\(707\) | 14.8172 | 0.557257 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −19.5844 | −0.735509 | −0.367755 | − | 0.929923i | \(-0.619873\pi\) | ||||
−0.367755 | + | 0.929923i | \(0.619873\pi\) | |||||||
\(710\) | −11.6514 | −0.437270 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 28.4928 | 1.06781 | ||||||||
\(713\) | 11.6988 | 0.438124 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.94854 | 0.222463 | ||||||||
\(716\) | 0.944833 | 0.0353101 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −25.6673 | −0.957894 | ||||||||
\(719\) | −35.2147 | −1.31329 | −0.656643 | − | 0.754201i | \(-0.728024\pi\) | ||||
−0.656643 | + | 0.754201i | \(0.728024\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.22841 | −0.157474 | ||||||||
\(722\) | −6.72120 | −0.250137 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −0.0619202 | −0.00230125 | ||||||||
\(725\) | −34.6926 | −1.28845 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.146995 | −0.00545173 | −0.00272587 | − | 0.999996i | \(-0.500868\pi\) | ||||
−0.00272587 | + | 0.999996i | \(0.500868\pi\) | |||||||
\(728\) | 10.6402 | 0.394353 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −3.92069 | −0.145111 | ||||||||
\(731\) | 1.01819 | 0.0376592 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12.9512 | −0.478364 | −0.239182 | − | 0.970975i | \(-0.576879\pi\) | ||||
−0.239182 | + | 0.970975i | \(0.576879\pi\) | |||||||
\(734\) | −44.2047 | −1.63163 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.07610 | 0.187108 | ||||||||
\(737\) | −10.9360 | −0.402831 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −33.8631 | −1.24567 | −0.622836 | − | 0.782352i | \(-0.714020\pi\) | ||||
−0.622836 | + | 0.782352i | \(0.714020\pi\) | |||||||
\(740\) | −0.0965537 | −0.00354938 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 9.73581 | 0.357413 | ||||||||
\(743\) | −18.3992 | −0.675001 | −0.337500 | − | 0.941325i | \(-0.609581\pi\) | ||||
−0.337500 | + | 0.941325i | \(0.609581\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.70664 | 0.0625263 | ||||||||
\(746\) | 11.7626 | 0.430661 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.341420 | 0.0124836 | ||||||||
\(749\) | −3.60740 | −0.131811 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19.8382 | −0.723904 | −0.361952 | − | 0.932197i | \(-0.617890\pi\) | ||||
−0.361952 | + | 0.932197i | \(0.617890\pi\) | |||||||
\(752\) | −23.2934 | −0.849424 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −36.5899 | −1.33252 | ||||||||
\(755\) | 9.40314 | 0.342215 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20.6741 | 0.751413 | 0.375706 | − | 0.926739i | \(-0.377400\pi\) | ||||
0.375706 | + | 0.926739i | \(0.377400\pi\) | |||||||
\(758\) | 20.0190 | 0.727123 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 9.57542 | 0.347337 | ||||||||
\(761\) | −1.94280 | −0.0704264 | −0.0352132 | − | 0.999380i | \(-0.511211\pi\) | ||||
−0.0352132 | + | 0.999380i | \(0.511211\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.1924 | −0.368991 | ||||||||
\(764\) | 2.77337 | 0.100337 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.13138 | −0.0770100 | ||||||||
\(767\) | 35.5542 | 1.28379 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −26.6560 | −0.961241 | −0.480621 | − | 0.876929i | \(-0.659589\pi\) | ||||
−0.480621 | + | 0.876929i | \(0.659589\pi\) | |||||||
\(770\) | −2.21143 | −0.0796945 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.42371 | 0.0512405 | ||||||||
\(773\) | 5.12985 | 0.184508 | 0.0922540 | − | 0.995736i | \(-0.470593\pi\) | ||||
0.0922540 | + | 0.995736i | \(0.470593\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 12.4796 | 0.448281 | ||||||||
\(776\) | −0.539058 | −0.0193511 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −31.2145 | −1.11909 | ||||||||
\(779\) | 54.8274 | 1.96440 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 32.9942 | 1.18063 | ||||||||
\(782\) | −3.70617 | −0.132532 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.53429 | −0.126225 | ||||||||
\(785\) | −9.33083 | −0.333032 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 35.0310 | 1.24872 | 0.624360 | − | 0.781137i | \(-0.285360\pi\) | ||||
0.624360 | + | 0.781137i | \(0.285360\pi\) | |||||||
\(788\) | 3.54055 | 0.126127 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 5.69773 | 0.202716 | ||||||||
\(791\) | −5.90567 | −0.209982 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.37535 | 0.0488400 | ||||||||
\(794\) | −25.1914 | −0.894008 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.925076 | −0.0327885 | ||||||||
\(797\) | 30.9196 | 1.09523 | 0.547614 | − | 0.836731i | \(-0.315536\pi\) | ||||
0.547614 | + | 0.836731i | \(0.315536\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.26840 | −0.151005 | ||||||||
\(800\) | 5.41488 | 0.191445 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 33.6456 | 1.18807 | ||||||||
\(803\) | 11.1025 | 0.391799 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.82622 | −0.0996112 | ||||||||
\(806\) | 13.1621 | 0.463615 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 43.8161 | 1.54144 | ||||||||
\(809\) | −29.9617 | −1.05340 | −0.526699 | − | 0.850052i | \(-0.676570\pi\) | ||||
−0.526699 | + | 0.850052i | \(0.676570\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −23.8090 | −0.836045 | −0.418023 | − | 0.908437i | \(-0.637277\pi\) | ||||
−0.418023 | + | 0.908437i | \(0.637277\pi\) | |||||||
\(812\) | −1.60148 | −0.0562009 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2.32237 | −0.0813990 | ||||||||
\(815\) | 6.66465 | 0.233452 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.70590 | −0.269595 | ||||||||
\(818\) | 5.16877 | 0.180722 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.55675 | −0.0543642 | ||||||||
\(821\) | 45.4733 | 1.58703 | 0.793514 | − | 0.608552i | \(-0.208249\pi\) | ||||
0.793514 | + | 0.608552i | \(0.208249\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.4083 | 0.571958 | 0.285979 | − | 0.958236i | \(-0.407681\pi\) | ||||
0.285979 | + | 0.958236i | \(0.407681\pi\) | |||||||
\(824\) | −12.5039 | −0.435594 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −13.2177 | −0.459902 | ||||||||
\(827\) | 14.0064 | 0.487049 | 0.243524 | − | 0.969895i | \(-0.421696\pi\) | ||||
0.243524 | + | 0.969895i | \(0.421696\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15.3602 | 0.533480 | 0.266740 | − | 0.963768i | \(-0.414053\pi\) | ||||
0.266740 | + | 0.963768i | \(0.414053\pi\) | |||||||
\(830\) | −4.26117 | −0.147907 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 31.1451 | 1.07976 | ||||||||
\(833\) | −0.647641 | −0.0224394 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.57944 | −0.158478 | ||||||||
\(836\) | −2.58394 | −0.0893675 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −2.22891 | −0.0769964 | ||||||||
\(839\) | 40.9499 | 1.41375 | 0.706874 | − | 0.707339i | \(-0.250105\pi\) | ||||
0.706874 | + | 0.707339i | \(0.250105\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.7916 | 0.992814 | ||||||||
\(842\) | −31.9836 | −1.10223 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −0.0631995 | −0.00217542 | ||||||||
\(845\) | −0.0350922 | −0.00120721 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.73772 | −0.162790 | ||||||||
\(848\) | 25.7234 | 0.883346 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −3.95352 | −0.135605 | ||||||||
\(851\) | −2.96800 | −0.101742 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −34.1821 | −1.17037 | −0.585186 | − | 0.810899i | \(-0.698979\pi\) | ||||
−0.585186 | + | 0.810899i | \(0.698979\pi\) | |||||||
\(854\) | −0.511300 | −0.0174963 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −10.6675 | −0.364607 | ||||||||
\(857\) | −8.93481 | −0.305207 | −0.152604 | − | 0.988287i | \(-0.548766\pi\) | ||||
−0.152604 | + | 0.988287i | \(0.548766\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.55658 | 0.121349 | 0.0606745 | − | 0.998158i | \(-0.480675\pi\) | ||||
0.0606745 | + | 0.998158i | \(0.480675\pi\) | |||||||
\(860\) | 0.218799 | 0.00746098 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 19.0371 | 0.648406 | ||||||||
\(863\) | 1.17289 | 0.0399258 | 0.0199629 | − | 0.999801i | \(-0.493645\pi\) | ||||
0.0199629 | + | 0.999801i | \(0.493645\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.39667 | 0.217493 | ||||||||
\(866\) | −20.6095 | −0.700340 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.576083 | 0.0195535 | ||||||||
\(869\) | −16.1347 | −0.547332 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −15.7244 | −0.532800 | ||||||||
\(872\) | −30.1402 | −1.02068 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 28.0491 | 0.948775 | ||||||||
\(875\) | −6.31802 | −0.213588 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 29.5713 | 0.998553 | 0.499276 | − | 0.866443i | \(-0.333599\pi\) | ||||
0.499276 | + | 0.866443i | \(0.333599\pi\) | |||||||
\(878\) | −16.9926 | −0.573472 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −5.84293 | −0.196965 | ||||||||
\(881\) | 17.2056 | 0.579673 | 0.289837 | − | 0.957076i | \(-0.406399\pi\) | ||||
0.289837 | + | 0.957076i | \(0.406399\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 39.9725 | 1.34518 | 0.672592 | − | 0.740014i | \(-0.265181\pi\) | ||||
0.672592 | + | 0.740014i | \(0.265181\pi\) | |||||||
\(884\) | 0.490914 | 0.0165112 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −17.6275 | −0.592207 | ||||||||
\(887\) | −45.9422 | −1.54259 | −0.771294 | − | 0.636479i | \(-0.780390\pi\) | ||||
−0.771294 | + | 0.636479i | \(0.780390\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00000 | 0.0335389 | ||||||||
\(890\) | −8.51480 | −0.285417 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 5.39214 | 0.180542 | ||||||||
\(893\) | 32.3042 | 1.08102 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.96297 | −0.0990413 | ||||||||
\(896\) | −9.20541 | −0.307531 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 18.1385 | 0.605288 | ||||||||
\(899\) | −20.7888 | −0.693345 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.71368 | 0.157036 | ||||||||
\(902\) | −37.4440 | −1.24675 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −17.4638 | −0.580836 | ||||||||
\(905\) | 0.194180 | 0.00645477 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −40.3826 | −1.34088 | −0.670441 | − | 0.741963i | \(-0.733895\pi\) | ||||
−0.670441 | + | 0.741963i | \(0.733895\pi\) | |||||||
\(908\) | −1.80148 | −0.0597843 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −3.17973 | −0.105407 | ||||||||
\(911\) | 24.9950 | 0.828122 | 0.414061 | − | 0.910249i | \(-0.364110\pi\) | ||||
0.414061 | + | 0.910249i | \(0.364110\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.0667 | 0.399349 | ||||||||
\(914\) | 20.4795 | 0.677401 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.79426 | −0.0923250 | ||||||||
\(917\) | −1.15626 | −0.0381832 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −32.3880 | −1.06838 | −0.534190 | − | 0.845364i | \(-0.679383\pi\) | ||||
−0.534190 | + | 0.845364i | \(0.679383\pi\) | |||||||
\(920\) | −8.35747 | −0.275538 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 18.8379 | 0.620393 | ||||||||
\(923\) | 47.4410 | 1.56154 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.16609 | −0.104100 | ||||||||
\(926\) | 20.8799 | 0.686156 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −9.02023 | −0.296103 | ||||||||
\(929\) | 24.9473 | 0.818495 | 0.409248 | − | 0.912423i | \(-0.365791\pi\) | ||||
0.409248 | + | 0.912423i | \(0.365791\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.90149 | 0.160640 | ||||||||
\(932\) | 2.05604 | 0.0673478 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 50.0108 | 1.63640 | ||||||||
\(935\) | −1.07069 | −0.0350152 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −47.5858 | −1.55456 | −0.777280 | − | 0.629155i | \(-0.783401\pi\) | ||||
−0.777280 | + | 0.629155i | \(0.783401\pi\) | |||||||
\(938\) | 5.84570 | 0.190869 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.917234 | −0.0299169 | ||||||||
\(941\) | 18.8073 | 0.613101 | 0.306550 | − | 0.951854i | \(-0.400825\pi\) | ||||
0.306550 | + | 0.951854i | \(0.400825\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −47.8536 | −1.55833 | ||||||||
\(944\) | −34.9230 | −1.13665 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.26269 | 0.171105 | ||||||||
\(947\) | 20.7650 | 0.674773 | 0.337387 | − | 0.941366i | \(-0.390457\pi\) | ||||
0.337387 | + | 0.941366i | \(0.390457\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 15.9639 | 0.518209 | ||||||||
\(950\) | 29.9211 | 0.970770 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.91515 | −0.0620704 | ||||||||
\(953\) | 57.6890 | 1.86873 | 0.934365 | − | 0.356316i | \(-0.115967\pi\) | ||||
0.934365 | + | 0.356316i | \(0.115967\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.69723 | −0.281436 | ||||||||
\(956\) | −0.699607 | −0.0226269 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 38.0342 | 1.22883 | ||||||||
\(959\) | −12.7644 | −0.412186 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.5219 | −0.758770 | ||||||||
\(962\) | −3.33924 | −0.107661 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.76285 | 0.0889854 | ||||||||
\(965\) | −4.46473 | −0.143725 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −11.8196 | −0.380093 | −0.190046 | − | 0.981775i | \(-0.560864\pi\) | ||||
−0.190046 | + | 0.981775i | \(0.560864\pi\) | |||||||
\(968\) | −14.0100 | −0.450298 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.161092 | 0.00517236 | ||||||||
\(971\) | 6.79796 | 0.218157 | 0.109078 | − | 0.994033i | \(-0.465210\pi\) | ||||
0.109078 | + | 0.994033i | \(0.465210\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.66110 | −0.0532523 | ||||||||
\(974\) | −49.5353 | −1.58721 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.35093 | −0.0432422 | ||||||||
\(977\) | −37.7861 | −1.20889 | −0.604443 | − | 0.796649i | \(-0.706604\pi\) | ||||
−0.604443 | + | 0.796649i | \(0.706604\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 24.1120 | 0.770623 | ||||||||
\(980\) | −0.139171 | −0.00444567 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 21.0066 | 0.670348 | ||||||||
\(983\) | 34.4511 | 1.09882 | 0.549409 | − | 0.835554i | \(-0.314853\pi\) | ||||
0.549409 | + | 0.835554i | \(0.314853\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.1031 | −0.353774 | ||||||||
\(986\) | 6.58587 | 0.209737 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.71534 | −0.118201 | ||||||||
\(989\) | 6.72575 | 0.213866 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 44.8723 | 1.42542 | 0.712708 | − | 0.701461i | \(-0.247468\pi\) | ||||
0.712708 | + | 0.701461i | \(0.247468\pi\) | |||||||
\(992\) | 3.24475 | 0.103021 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −17.6367 | −0.559403 | ||||||||
\(995\) | 2.90102 | 0.0919684 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −48.8594 | −1.54739 | −0.773696 | − | 0.633557i | \(-0.781594\pi\) | ||||
−0.773696 | + | 0.633557i | \(0.781594\pi\) | |||||||
\(998\) | −42.8488 | −1.35635 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8001.2.a.u.1.5 | 18 | ||
3.2 | odd | 2 | 2667.2.a.p.1.14 | ✓ | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2667.2.a.p.1.14 | ✓ | 18 | 3.2 | odd | 2 | ||
8001.2.a.u.1.5 | 18 | 1.1 | even | 1 | trivial |