Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8008,2,Mod(1,8008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("8008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8008.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: | \(63.9442019386\) |
Analytic rank: | \(1\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 3 x^{13} - 27 x^{12} + 78 x^{11} + 273 x^{10} - 750 x^{9} - 1306 x^{8} + 3378 x^{7} + 2996 x^{6} - 7275 x^{5} - 2804 x^{4} + 6417 x^{3} + 538 x^{2} - 1032 x - 128 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.22236\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8008.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.22236 | −1.86043 | −0.930215 | − | 0.367016i | \(-0.880379\pi\) | ||||
−0.930215 | + | 0.367016i | \(0.880379\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.94503 | 0.869842 | 0.434921 | − | 0.900469i | \(-0.356776\pi\) | ||||
0.434921 | + | 0.900469i | \(0.356776\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.38359 | 2.46120 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −6.26757 | −1.61828 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.63936 | 1.12521 | 0.562605 | − | 0.826726i | \(-0.309799\pi\) | ||||
0.562605 | + | 0.826726i | \(0.309799\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.17867 | −0.958652 | −0.479326 | − | 0.877637i | \(-0.659119\pi\) | ||||
−0.479326 | + | 0.877637i | \(0.659119\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.22236 | −0.703176 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.50523 | 1.35643 | 0.678217 | − | 0.734862i | \(-0.262753\pi\) | ||||
0.678217 | + | 0.734862i | \(0.262753\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.21688 | −0.243375 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −14.1255 | −2.71845 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.35077 | 0.622222 | 0.311111 | − | 0.950374i | \(-0.399299\pi\) | ||||
0.311111 | + | 0.950374i | \(0.399299\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.82311 | −1.40507 | −0.702536 | − | 0.711648i | \(-0.747949\pi\) | ||||
−0.702536 | + | 0.711648i | \(0.747949\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.22236 | 0.560940 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.94503 | 0.328769 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.35205 | 0.551074 | 0.275537 | − | 0.961290i | \(-0.411144\pi\) | ||||
0.275537 | + | 0.961290i | \(0.411144\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.22236 | 0.515990 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.66737 | −0.885094 | −0.442547 | − | 0.896745i | \(-0.645925\pi\) | ||||
−0.442547 | + | 0.896745i | \(0.645925\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.16924 | −0.178307 | −0.0891534 | − | 0.996018i | \(-0.528416\pi\) | ||||
−0.0891534 | + | 0.996018i | \(0.528416\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 14.3613 | 2.14085 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.7539 | 1.56861 | 0.784305 | − | 0.620375i | \(-0.213020\pi\) | ||||
0.784305 | + | 0.620375i | \(0.213020\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −14.9497 | −2.09337 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −11.5881 | −1.59174 | −0.795872 | − | 0.605465i | \(-0.792987\pi\) | ||||
−0.795872 | + | 0.605465i | \(0.792987\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.94503 | −0.262267 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 13.4652 | 1.78350 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.3841 | −1.35190 | −0.675948 | − | 0.736949i | \(-0.736266\pi\) | ||||
−0.675948 | + | 0.736949i | \(0.736266\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.96940 | −0.636266 | −0.318133 | − | 0.948046i | \(-0.603056\pi\) | ||||
−0.318133 | + | 0.948046i | \(0.603056\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.38359 | 0.930245 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.94503 | −0.241251 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.1690 | −1.24234 | −0.621170 | − | 0.783676i | \(-0.713342\pi\) | ||||
−0.621170 | + | 0.783676i | \(0.713342\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −20.9622 | −2.52355 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.157313 | −0.0186696 | −0.00933479 | − | 0.999956i | \(-0.502971\pi\) | ||||
−0.00933479 | + | 0.999956i | \(0.502971\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.45524 | 0.170323 | 0.0851617 | − | 0.996367i | \(-0.472859\pi\) | ||||
0.0851617 | + | 0.996367i | \(0.472859\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.92121 | 0.452782 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.4350 | −1.73657 | −0.868284 | − | 0.496067i | \(-0.834777\pi\) | ||||
−0.868284 | + | 0.496067i | \(0.834777\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 23.3666 | 2.59629 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.26464 | −0.468105 | −0.234052 | − | 0.972224i | \(-0.575199\pi\) | ||||
−0.234052 | + | 0.972224i | \(0.575199\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.02367 | 0.978755 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −10.7974 | −1.15760 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.4609 | 1.53286 | 0.766429 | − | 0.642329i | \(-0.222032\pi\) | ||||
0.766429 | + | 0.642329i | \(0.222032\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | −0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 25.2089 | 2.61404 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.12762 | −0.833876 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.52587 | −0.662602 | −0.331301 | − | 0.943525i | \(-0.607488\pi\) | ||||
−0.331301 | + | 0.943525i | \(0.607488\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −7.38359 | −0.742079 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.6419 | −1.15841 | −0.579205 | − | 0.815182i | \(-0.696637\pi\) | ||||
−0.579205 | + | 0.815182i | \(0.696637\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −17.3242 | −1.70701 | −0.853503 | − | 0.521088i | \(-0.825526\pi\) | ||||
−0.853503 | + | 0.521088i | \(0.825526\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.26757 | −0.611652 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.0034 | 1.54710 | 0.773552 | − | 0.633733i | \(-0.218478\pi\) | ||||
0.773552 | + | 0.633733i | \(0.218478\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.34207 | 0.703243 | 0.351622 | − | 0.936142i | \(-0.385630\pi\) | ||||
0.351622 | + | 0.936142i | \(0.385630\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.8015 | −1.02523 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.90102 | −0.272905 | −0.136453 | − | 0.990647i | \(-0.543570\pi\) | ||||
−0.136453 | + | 0.990647i | \(0.543570\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.6528 | 1.17988 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7.38359 | −0.682613 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.63936 | 0.425289 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 18.2623 | 1.64665 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.0920 | −1.08154 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.84033 | −0.695716 | −0.347858 | − | 0.937547i | \(-0.613091\pi\) | ||||
−0.347858 | + | 0.937547i | \(0.613091\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.76770 | 0.331727 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.68015 | 0.758389 | 0.379194 | − | 0.925317i | \(-0.376201\pi\) | ||||
0.379194 | + | 0.925317i | \(0.376201\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.17867 | −0.362336 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −27.4744 | −2.36462 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14.3959 | 1.22992 | 0.614960 | − | 0.788558i | \(-0.289172\pi\) | ||||
0.614960 | + | 0.788558i | \(0.289172\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.55146 | −0.810144 | −0.405072 | − | 0.914285i | \(-0.632754\pi\) | ||||
−0.405072 | + | 0.914285i | \(0.632754\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −34.6528 | −2.91829 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.00000 | 0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.51733 | 0.541235 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.22236 | −0.265776 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.1897 | 0.834773 | 0.417387 | − | 0.908729i | \(-0.362946\pi\) | ||||
0.417387 | + | 0.908729i | \(0.362946\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.0177 | 1.14074 | 0.570372 | − | 0.821386i | \(-0.306799\pi\) | ||||
0.570372 | + | 0.821386i | \(0.306799\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 34.2551 | 2.76936 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −15.2162 | −1.22219 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.0025 | 1.11752 | 0.558760 | − | 0.829330i | \(-0.311277\pi\) | ||||
0.558760 | + | 0.829330i | \(0.311277\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 37.3409 | 2.96133 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.50523 | 0.512684 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.73365 | −0.684073 | −0.342036 | − | 0.939687i | \(-0.611117\pi\) | ||||
−0.342036 | + | 0.939687i | \(0.611117\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6.26757 | 0.487929 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 16.1896 | 1.25279 | 0.626396 | − | 0.779505i | \(-0.284529\pi\) | ||||
0.626396 | + | 0.779505i | \(0.284529\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −30.8536 | −2.35943 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.08100 | −0.310273 | −0.155136 | − | 0.987893i | \(-0.549582\pi\) | ||||
−0.155136 | + | 0.987893i | \(0.549582\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.21688 | −0.0919872 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 33.4613 | 2.51511 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.02007 | 0.300474 | 0.150237 | − | 0.988650i | \(-0.451996\pi\) | ||||
0.150237 | + | 0.988650i | \(0.451996\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.4718 | 1.29867 | 0.649333 | − | 0.760504i | \(-0.275048\pi\) | ||||
0.649333 | + | 0.760504i | \(0.275048\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 16.0132 | 1.18373 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.51983 | 0.479347 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.63936 | −0.339264 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −14.1255 | −1.02748 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 24.8214 | 1.79602 | 0.898008 | − | 0.439979i | \(-0.145014\pi\) | ||||
0.898008 | + | 0.439979i | \(0.145014\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −22.8332 | −1.64357 | −0.821785 | − | 0.569798i | \(-0.807021\pi\) | ||||
−0.821785 | + | 0.569798i | \(0.807021\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.26757 | 0.448830 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.4540 | −0.816062 | −0.408031 | − | 0.912968i | \(-0.633784\pi\) | ||||
−0.408031 | + | 0.912968i | \(0.633784\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.24629 | −0.442788 | −0.221394 | − | 0.975184i | \(-0.571061\pi\) | ||||
−0.221394 | + | 0.975184i | \(0.571061\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 32.7681 | 2.31128 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.35077 | 0.235178 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.0232 | −0.769892 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 48.0319 | 3.33845 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.17867 | 0.289045 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.237993 | −0.0163841 | −0.00819205 | − | 0.999966i | \(-0.502608\pi\) | ||||
−0.00819205 | + | 0.999966i | \(0.502608\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.506918 | 0.0347334 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.27419 | −0.155099 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.82311 | −0.531067 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.68932 | −0.316875 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.63936 | −0.312077 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.4008 | −0.830420 | −0.415210 | − | 0.909726i | \(-0.636292\pi\) | ||||
−0.415210 | + | 0.909726i | \(0.636292\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −8.98491 | −0.598994 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.58726 | −0.171723 | −0.0858613 | − | 0.996307i | \(-0.527364\pi\) | ||||
−0.0858613 | + | 0.996307i | \(0.527364\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.3218 | −0.748164 | −0.374082 | − | 0.927396i | \(-0.622042\pi\) | ||||
−0.374082 | + | 0.927396i | \(0.622042\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.22236 | 0.212016 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.54283 | 0.428635 | 0.214317 | − | 0.976764i | \(-0.431247\pi\) | ||||
0.214317 | + | 0.976764i | \(0.431247\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 20.9165 | 1.36444 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 49.7369 | 3.23076 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.9464 | 0.966802 | 0.483401 | − | 0.875399i | \(-0.339401\pi\) | ||||
0.483401 | + | 0.875399i | \(0.339401\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −25.2096 | −1.62389 | −0.811946 | − | 0.583733i | \(-0.801592\pi\) | ||||
−0.811946 | + | 0.583733i | \(0.801592\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −32.9191 | −2.11176 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.94503 | 0.124263 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.17867 | 0.265882 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 13.7422 | 0.870876 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −21.9195 | −1.38355 | −0.691773 | − | 0.722115i | \(-0.743170\pi\) | ||||
−0.691773 | + | 0.722115i | \(0.743170\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.50523 | −0.408980 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −29.0775 | −1.82090 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.7181 | −0.668576 | −0.334288 | − | 0.942471i | \(-0.608496\pi\) | ||||
−0.334288 | + | 0.942471i | \(0.608496\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.35205 | 0.208286 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 24.7407 | 1.53141 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.0053 | −0.740281 | −0.370141 | − | 0.928976i | \(-0.620691\pi\) | ||||
−0.370141 | + | 0.928976i | \(0.620691\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −22.5391 | −1.38457 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −46.5984 | −2.85177 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 23.5986 | 1.43884 | 0.719418 | − | 0.694578i | \(-0.244409\pi\) | ||||
0.719418 | + | 0.694578i | \(0.244409\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.73470 | 0.348358 | 0.174179 | − | 0.984714i | \(-0.444273\pi\) | ||||
0.174179 | + | 0.984714i | \(0.444273\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.22236 | 0.195026 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.21688 | 0.0733804 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.88845 | −0.473971 | −0.236986 | − | 0.971513i | \(-0.576159\pi\) | ||||
−0.236986 | + | 0.971513i | \(0.576159\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −57.7626 | −3.45816 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.68971 | −0.458730 | −0.229365 | − | 0.973341i | \(-0.573665\pi\) | ||||
−0.229365 | + | 0.973341i | \(0.573665\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.38009 | −0.319813 | −0.159907 | − | 0.987132i | \(-0.551119\pi\) | ||||
−0.159907 | + | 0.987132i | \(0.551119\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 26.1901 | 1.55137 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.66737 | −0.334534 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.52365 | 0.266097 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 21.0287 | 1.23272 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −20.4984 | −1.19753 | −0.598764 | − | 0.800925i | \(-0.704341\pi\) | ||||
−0.598764 | + | 0.800925i | \(0.704341\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −20.1974 | −1.17594 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 14.1255 | 0.819644 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.50523 | −0.376207 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.16924 | −0.0673937 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 37.5143 | 2.15514 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9.66561 | −0.553451 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.9361 | 1.25196 | 0.625980 | − | 0.779839i | \(-0.284699\pi\) | ||||
0.625980 | + | 0.779839i | \(0.284699\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 55.8248 | 3.17576 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −32.9098 | −1.86614 | −0.933072 | − | 0.359691i | \(-0.882882\pi\) | ||||
−0.933072 | + | 0.359691i | \(0.882882\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.0173 | 0.679260 | 0.339630 | − | 0.940559i | \(-0.389698\pi\) | ||||
0.339630 | + | 0.940559i | \(0.389698\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 14.3613 | 0.809166 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.89263 | 0.106301 | 0.0531503 | − | 0.998587i | \(-0.483074\pi\) | ||||
0.0531503 | + | 0.998587i | \(0.483074\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.35077 | −0.187607 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −51.5685 | −2.87828 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −19.3863 | −1.07869 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.21688 | 0.0675001 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −23.6588 | −1.30833 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 10.7539 | 0.592879 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.84884 | −0.486376 | −0.243188 | − | 0.969979i | \(-0.578193\pi\) | ||||
−0.243188 | + | 0.969979i | \(0.578193\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 24.7502 | 1.35630 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −19.7789 | −1.08064 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.977482 | −0.0532469 | −0.0266234 | − | 0.999646i | \(-0.508476\pi\) | ||||
−0.0266234 | + | 0.999646i | \(0.508476\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9.34814 | 0.507721 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.82311 | 0.423645 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −40.7720 | −2.19509 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.22496 | 0.226808 | 0.113404 | − | 0.993549i | \(-0.463825\pi\) | ||||
0.113404 | + | 0.993549i | \(0.463825\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.94318 | 0.211074 | 0.105537 | − | 0.994415i | \(-0.466344\pi\) | ||||
0.105537 | + | 0.994415i | \(0.466344\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 14.1255 | 0.753963 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.6355 | −0.672522 | −0.336261 | − | 0.941769i | \(-0.609162\pi\) | ||||
−0.336261 | + | 0.941769i | \(0.609162\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.305977 | −0.0162396 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −14.9497 | −0.791221 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 25.3450 | 1.33766 | 0.668829 | − | 0.743416i | \(-0.266796\pi\) | ||||
0.668829 | + | 0.743416i | \(0.266796\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.53873 | −0.0809858 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.22236 | −0.169130 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.83049 | 0.148154 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.08499 | 0.317634 | 0.158817 | − | 0.987308i | \(-0.449232\pi\) | ||||
0.158817 | + | 0.987308i | \(0.449232\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −41.8455 | −2.17839 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.5881 | −0.601623 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −22.8749 | −1.18442 | −0.592209 | − | 0.805785i | \(-0.701744\pi\) | ||||
−0.592209 | + | 0.805785i | \(0.701744\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 38.9647 | 2.01213 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.35077 | −0.172573 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.64036 | 0.341093 | 0.170546 | − | 0.985350i | \(-0.445447\pi\) | ||||
0.170546 | + | 0.985350i | \(0.445447\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 25.2643 | 1.29433 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.43826 | 0.431175 | 0.215587 | − | 0.976485i | \(-0.430833\pi\) | ||||
0.215587 | + | 0.976485i | \(0.430833\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.94503 | −0.0991277 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.63316 | −0.438848 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.62741 | −0.0825132 | −0.0412566 | − | 0.999149i | \(-0.513136\pi\) | ||||
−0.0412566 | + | 0.999149i | \(0.513136\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 30.1801 | 1.52627 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −27.9706 | −1.41093 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −30.0214 | −1.51054 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −33.9426 | −1.70353 | −0.851764 | − | 0.523925i | \(-0.824467\pi\) | ||||
−0.851764 | + | 0.523925i | \(0.824467\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 13.4652 | 0.674101 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −30.2735 | −1.51179 | −0.755894 | − | 0.654694i | \(-0.772797\pi\) | ||||
−0.755894 | + | 0.654694i | \(0.772797\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.82311 | 0.389697 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 45.4487 | 2.25836 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.35205 | −0.166155 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.0225 | 0.643920 | 0.321960 | − | 0.946753i | \(-0.395658\pi\) | ||||
0.321960 | + | 0.946753i | \(0.395658\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −46.3886 | −2.28818 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −10.3841 | −0.510969 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.29483 | −0.407177 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 30.7782 | 1.50722 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 30.3550 | 1.48294 | 0.741469 | − | 0.670988i | \(-0.234130\pi\) | ||||
0.741469 | + | 0.670988i | \(0.234130\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.6664 | −0.861005 | −0.430503 | − | 0.902589i | \(-0.641664\pi\) | ||||
−0.430503 | + | 0.902589i | \(0.641664\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 79.4020 | 3.86066 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.64552 | −0.273848 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.96940 | −0.240486 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.22236 | −0.155577 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.88937 | 0.235513 | 0.117756 | − | 0.993043i | \(-0.462430\pi\) | ||||
0.117756 | + | 0.993043i | \(0.462430\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.53941 | −0.458435 | −0.229217 | − | 0.973375i | \(-0.573617\pi\) | ||||
−0.229217 | + | 0.973375i | \(0.573617\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −21.0012 | −1.00693 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −27.1832 | −1.30035 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −40.0531 | −1.91163 | −0.955815 | − | 0.293968i | \(-0.905024\pi\) | ||||
−0.955815 | + | 0.293968i | \(0.905024\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.38359 | 0.351599 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.19609 | 0.389408 | 0.194704 | − | 0.980862i | \(-0.437625\pi\) | ||||
0.194704 | + | 0.980862i | \(0.437625\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 28.1269 | 1.33334 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −32.8349 | −1.55304 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 39.4518 | 1.86185 | 0.930924 | − | 0.365214i | \(-0.119004\pi\) | ||||
0.930924 | + | 0.365214i | \(0.119004\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.66737 | 0.266866 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −45.1701 | −2.12227 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.94503 | −0.0911842 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.3862 | 0.485848 | 0.242924 | − | 0.970045i | \(-0.421893\pi\) | ||||
0.242924 | + | 0.970045i | \(0.421893\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −65.5332 | −3.05883 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −36.5107 | −1.70047 | −0.850236 | − | 0.526402i | \(-0.823541\pi\) | ||||
−0.850236 | + | 0.526402i | \(0.823541\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.84715 | −0.225266 | −0.112633 | − | 0.993637i | \(-0.535928\pi\) | ||||
−0.112633 | + | 0.993637i | \(0.535928\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 49.0319 | 2.27380 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.94525 | −0.182564 | −0.0912822 | − | 0.995825i | \(-0.529097\pi\) | ||||
−0.0912822 | + | 0.995825i | \(0.529097\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.1690 | −0.469560 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −45.1210 | −2.07907 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.16924 | 0.0537616 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.08492 | 0.233312 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −85.5616 | −3.91760 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 25.7591 | 1.17696 | 0.588482 | − | 0.808511i | \(-0.299726\pi\) | ||||
0.588482 | + | 0.808511i | \(0.299726\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.35205 | −0.152840 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −20.9622 | −0.953812 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −12.6930 | −0.576359 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −28.5178 | −1.29226 | −0.646132 | − | 0.763225i | \(-0.723615\pi\) | ||||
−0.646132 | + | 0.763225i | \(0.723615\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 28.1430 | 1.27267 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.7401 | 0.710343 | 0.355171 | − | 0.934801i | \(-0.384423\pi\) | ||||
0.355171 | + | 0.934801i | \(0.384423\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15.5454 | 0.700130 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −14.3613 | −0.645491 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.157313 | −0.00705644 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −30.3096 | −1.35684 | −0.678422 | − | 0.734672i | \(-0.737336\pi\) | ||||
−0.678422 | + | 0.734672i | \(0.737336\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −52.1688 | −2.33073 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −40.1739 | −1.79126 | −0.895632 | − | 0.444795i | \(-0.853276\pi\) | ||||
−0.895632 | + | 0.444795i | \(0.853276\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −22.6437 | −1.00763 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.22236 | −0.143110 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −11.0293 | −0.488866 | −0.244433 | − | 0.969666i | \(-0.578602\pi\) | ||||
−0.244433 | + | 0.969666i | \(0.578602\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.45524 | 0.0643762 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 59.0257 | 2.60605 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −33.6960 | −1.48482 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.7539 | −0.472954 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13.1504 | 0.577241 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 30.4186 | 1.33266 | 0.666331 | − | 0.745656i | \(-0.267864\pi\) | ||||
0.666331 | + | 0.745656i | \(0.267864\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.58986 | 0.288154 | 0.144077 | − | 0.989566i | \(-0.453979\pi\) | ||||
0.144077 | + | 0.989566i | \(0.453979\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.92121 | 0.171136 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −36.2942 | −1.58100 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.3180 | 0.839914 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −76.6720 | −3.32728 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.66737 | 0.245481 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 31.1269 | 1.34573 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −12.9541 | −0.559011 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.97756 | 0.0850219 | 0.0425109 | − | 0.999096i | \(-0.486464\pi\) | ||||
0.0425109 | + | 0.999096i | \(0.486464\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −56.3003 | −2.41608 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 14.2805 | 0.611710 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −24.0239 | −1.02719 | −0.513594 | − | 0.858033i | \(-0.671686\pi\) | ||||
−0.513594 | + | 0.858033i | \(0.671686\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −36.6920 | −1.56598 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −14.0017 | −0.596494 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15.4350 | −0.656361 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −21.0092 | −0.891792 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 17.3072 | 0.733331 | 0.366666 | − | 0.930353i | \(-0.380499\pi\) | ||||
0.366666 | + | 0.930353i | \(0.380499\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.16924 | 0.0494534 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 14.9497 | 0.631176 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15.0087 | 0.632541 | 0.316270 | − | 0.948669i | \(-0.397569\pi\) | ||||
0.316270 | + | 0.948669i | \(0.397569\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.64257 | −0.237385 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 23.3666 | 0.981306 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −23.4750 | −0.984124 | −0.492062 | − | 0.870560i | \(-0.663757\pi\) | ||||
−0.492062 | + | 0.870560i | \(0.663757\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.6163 | 0.695370 | 0.347685 | − | 0.937611i | \(-0.386968\pi\) | ||||
0.347685 | + | 0.937611i | \(0.386968\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −79.9836 | −3.34136 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.91606 | −0.330122 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.6288 | 0.442485 | 0.221242 | − | 0.975219i | \(-0.428989\pi\) | ||||
0.221242 | + | 0.975219i | \(0.428989\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 73.5767 | 3.05774 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.26464 | −0.176927 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11.5881 | 0.479929 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −14.3613 | −0.593765 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −20.4802 | −0.845309 | −0.422654 | − | 0.906291i | \(-0.638902\pi\) | ||||
−0.422654 | + | 0.906291i | \(0.638902\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 32.6902 | 1.34698 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 36.9088 | 1.51823 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.92003 | −0.284172 | −0.142086 | − | 0.989854i | \(-0.545381\pi\) | ||||
−0.142086 | + | 0.989854i | \(0.545381\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.02367 | 0.369934 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 20.1278 | 0.823776 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.64848 | −0.353367 | −0.176684 | − | 0.984268i | \(-0.556537\pi\) | ||||
−0.176684 | + | 0.984268i | \(0.556537\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 37.7783 | 1.54101 | 0.770505 | − | 0.637434i | \(-0.220004\pi\) | ||||
0.770505 | + | 0.637434i | \(0.220004\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −75.0836 | −3.05764 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.94503 | 0.0790765 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.8501 | −0.643335 | −0.321668 | − | 0.946853i | \(-0.604243\pi\) | ||||
−0.321668 | + | 0.946853i | \(0.604243\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −10.7974 | −0.437532 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −10.7539 | −0.435054 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15.8053 | −0.638368 | −0.319184 | − | 0.947693i | \(-0.603409\pi\) | ||||
−0.319184 | + | 0.947693i | \(0.603409\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 35.5206 | 1.43233 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18.0325 | −0.725963 | −0.362981 | − | 0.931796i | \(-0.618241\pi\) | ||||
−0.362981 | + | 0.931796i | \(0.618241\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −39.9213 | −1.60457 | −0.802287 | − | 0.596938i | \(-0.796384\pi\) | ||||
−0.802287 | + | 0.596938i | \(0.796384\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −91.8896 | −3.68740 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 14.4609 | 0.579366 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17.4348 | −0.697393 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −13.4652 | −0.537747 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 15.5514 | 0.620074 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.1986 | 0.565238 | 0.282619 | − | 0.959232i | \(-0.408797\pi\) | ||||
0.282619 | + | 0.959232i | \(0.408797\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.766898 | 0.0304815 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −15.2496 | −0.605163 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00000 | −0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.16153 | −0.0459495 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.31133 | 0.367776 | 0.183888 | − | 0.982947i | \(-0.441132\pi\) | ||||
0.183888 | + | 0.982947i | \(0.441132\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.9067 | 0.942787 | 0.471394 | − | 0.881923i | \(-0.343751\pi\) | ||||
0.471394 | + | 0.881923i | \(0.343751\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.32827 | 0.288550 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −42.3172 | −1.66366 | −0.831830 | − | 0.555031i | \(-0.812707\pi\) | ||||
−0.831830 | + | 0.555031i | \(0.812707\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.3841 | 0.407612 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 25.2089 | 0.988013 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −31.5512 | −1.23469 | −0.617346 | − | 0.786692i | \(-0.711792\pi\) | ||||
−0.617346 | + | 0.786692i | \(0.711792\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 16.8831 | 0.659678 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10.7449 | 0.419199 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −33.6398 | −1.31042 | −0.655211 | − | 0.755446i | \(-0.727420\pi\) | ||||
−0.655211 | + | 0.755446i | \(0.727420\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.6140 | 0.568420 | 0.284210 | − | 0.958762i | \(-0.408269\pi\) | ||||
0.284210 | + | 0.958762i | \(0.408269\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 14.9497 | 0.580597 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.12762 | −0.315175 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 21.7975 | 0.844003 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 39.9599 | 1.54494 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.96940 | 0.191842 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.91195 | −0.227889 | −0.113945 | − | 0.993487i | \(-0.536349\pi\) | ||||
−0.113945 | + | 0.993487i | \(0.536349\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 17.1890 | 0.661604 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 33.4033 | 1.28379 | 0.641897 | − | 0.766791i | \(-0.278148\pi\) | ||||
0.641897 | + | 0.766791i | \(0.278148\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.52587 | −0.250440 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8.33709 | 0.319478 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −28.0098 | −1.07177 | −0.535883 | − | 0.844292i | \(-0.680021\pi\) | ||||
−0.535883 | + | 0.844292i | \(0.680021\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 28.0003 | 1.06984 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 36.4828 | 1.39191 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 11.5881 | 0.441471 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −24.2259 | −0.921596 | −0.460798 | − | 0.887505i | \(-0.652437\pi\) | ||||
−0.460798 | + | 0.887505i | \(0.652437\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −7.38359 | −0.280479 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −18.5778 | −0.704697 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −26.2930 | −0.995917 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −21.0833 | −0.797445 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −27.2779 | −1.03027 | −0.515137 | − | 0.857108i | \(-0.672259\pi\) | ||||
−0.515137 | + | 0.857108i | \(0.672259\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14.0071 | −0.528288 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −67.4005 | −2.53845 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −11.6419 | −0.437837 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −35.9001 | −1.34826 | −0.674129 | − | 0.738614i | \(-0.735481\pi\) | ||||
−0.674129 | + | 0.738614i | \(0.735481\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −113.965 | −4.27403 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −50.8911 | −1.90589 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.94503 | 0.0727398 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −48.1626 | −1.79867 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −48.5196 | −1.80948 | −0.904738 | − | 0.425968i | \(-0.859933\pi\) | ||||
−0.904738 | + | 0.425968i | \(0.859933\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17.3242 | −0.645187 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 81.2343 | 3.02113 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.07747 | −0.151433 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 38.9907 | 1.44609 | 0.723043 | − | 0.690803i | \(-0.242743\pi\) | ||||
0.723043 | + | 0.690803i | \(0.242743\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 35.9774 | 1.33250 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.42451 | −0.200633 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −39.9311 | −1.47489 | −0.737444 | − | 0.675409i | \(-0.763967\pi\) | ||||
−0.737444 | + | 0.675409i | \(0.763967\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.26757 | −0.231183 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10.1690 | 0.374579 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13.2190 | 0.486270 | 0.243135 | − | 0.969992i | \(-0.421824\pi\) | ||||
0.243135 | + | 0.969992i | \(0.421824\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −13.4652 | −0.494655 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13.1167 | 0.481204 | 0.240602 | − | 0.970624i | \(-0.422655\pi\) | ||||
0.240602 | + | 0.970624i | \(0.422655\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 19.8192 | 0.726121 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −31.4883 | −1.15210 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 16.0034 | 0.584750 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 35.1996 | 1.28445 | 0.642225 | − | 0.766516i | \(-0.278011\pi\) | ||||
0.642225 | + | 0.766516i | \(0.278011\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 70.6324 | 2.57399 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 27.2648 | 0.992267 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18.9669 | 0.689365 | 0.344683 | − | 0.938719i | \(-0.387987\pi\) | ||||
0.344683 | + | 0.938719i | \(0.387987\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 20.9622 | 0.760879 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −29.0247 | −1.05214 | −0.526072 | − | 0.850440i | \(-0.676336\pi\) | ||||
−0.526072 | + | 0.850440i | \(0.676336\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.34207 | 0.265801 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 66.6271 | 2.40891 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 10.3841 | 0.374949 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.90811 | −0.249113 | −0.124556 | − | 0.992213i | \(-0.539751\pi\) | ||||
−0.124556 | + | 0.992213i | \(0.539751\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 34.5375 | 1.24384 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −26.4291 | −0.950589 | −0.475294 | − | 0.879827i | \(-0.657658\pi\) | ||||
−0.475294 | + | 0.879827i | \(0.657658\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.51976 | 0.341960 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −10.8015 | −0.387502 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 23.6820 | 0.848497 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.157313 | 0.00562909 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −47.3312 | −1.69148 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 27.2352 | 0.972065 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 27.1502 | 0.967802 | 0.483901 | − | 0.875123i | \(-0.339220\pi\) | ||||
0.483901 | + | 0.875123i | \(0.339220\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 38.6855 | 1.37724 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.90102 | −0.103149 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.96940 | 0.176469 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 72.6290 | 2.57589 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −28.9697 | −1.02616 | −0.513080 | − | 0.858341i | \(-0.671496\pi\) | ||||
−0.513080 | + | 0.858341i | \(0.671496\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 49.8910 | 1.76502 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 106.774 | 3.77266 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.45524 | −0.0513545 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 12.6528 | 0.445954 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −76.0433 | −2.67685 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 45.6503 | 1.60498 | 0.802489 | − | 0.596667i | \(-0.203509\pi\) | ||||
0.802489 | + | 0.596667i | \(0.203509\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −33.2250 | −1.16669 | −0.583344 | − | 0.812225i | \(-0.698256\pi\) | ||||
−0.583344 | + | 0.812225i | \(0.698256\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −18.4792 | −0.648095 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −16.9872 | −0.595035 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.88585 | 0.170934 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −7.38359 | −0.258003 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.17463 | −0.215496 | −0.107748 | − | 0.994178i | \(-0.534364\pi\) | ||||
−0.107748 | + | 0.994178i | \(0.534364\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17.2372 | −0.600849 | −0.300425 | − | 0.953806i | \(-0.597128\pi\) | ||||
−0.300425 | + | 0.953806i | \(0.597128\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.92121 | −0.136519 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 53.2678 | 1.85230 | 0.926151 | − | 0.377152i | \(-0.123096\pi\) | ||||
0.926151 | + | 0.377152i | \(0.123096\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37.7052 | 1.30955 | 0.654777 | − | 0.755822i | \(-0.272762\pi\) | ||||
0.654777 | + | 0.755822i | \(0.272762\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 25.4194 | 0.881789 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.63936 | 0.160744 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 31.4893 | 1.08973 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 110.505 | 3.81962 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −38.2253 | −1.31968 | −0.659842 | − | 0.751405i | \(-0.729377\pi\) | ||||
−0.659842 | + | 0.751405i | \(0.729377\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.7724 | −0.612840 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 24.7790 | 0.853434 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.94503 | 0.0669109 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.00000 | 0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 17.3366 | 0.594990 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 21.8059 | 0.747496 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21.8945 | −0.749655 | −0.374827 | − | 0.927095i | \(-0.622298\pi\) | ||||
−0.374827 | + | 0.927095i | \(0.622298\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −60.0110 | −2.05233 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 15.3307 | 0.523688 | 0.261844 | − | 0.965110i | \(-0.415669\pi\) | ||||
0.261844 | + | 0.965110i | \(0.415669\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 38.1887 | 1.30298 | 0.651491 | − | 0.758656i | \(-0.274144\pi\) | ||||
0.651491 | + | 0.758656i | \(0.274144\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 18.2623 | 0.622377 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −56.8779 | −1.93615 | −0.968073 | − | 0.250668i | \(-0.919350\pi\) | ||||
−0.968073 | + | 0.250668i | \(0.919350\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.93765 | −0.269888 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −14.5768 | −0.495055 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 15.4350 | 0.523595 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.1690 | 0.344563 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −48.1844 | −1.63079 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −12.0920 | −0.408784 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 49.6981 | 1.67818 | 0.839092 | − | 0.543990i | \(-0.183087\pi\) | ||||
0.839092 | + | 0.543990i | \(0.183087\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 66.0532 | 2.22792 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 47.7356 | 1.60825 | 0.804127 | − | 0.594457i | \(-0.202633\pi\) | ||||
0.804127 | + | 0.594457i | \(0.202633\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −39.9529 | −1.34452 | −0.672261 | − | 0.740314i | \(-0.734677\pi\) | ||||
−0.672261 | + | 0.740314i | \(0.734677\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 65.0831 | 2.18775 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −52.1489 | −1.75099 | −0.875495 | − | 0.483227i | \(-0.839465\pi\) | ||||
−0.875495 | + | 0.483227i | \(0.839465\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.84033 | −0.262956 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −23.3666 | −0.782811 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −44.9368 | −1.50375 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.81914 | 0.261365 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 20.9622 | 0.699907 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −26.2134 | −0.874267 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −53.7612 | −1.79105 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.76770 | 0.125381 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 33.9830 | 1.12963 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.574022 | −0.0190601 | −0.00953004 | − | 0.999955i | \(-0.503034\pi\) | ||||
−0.00953004 | + | 0.999955i | \(0.503034\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −85.9588 | −2.85107 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.5841 | 0.814509 | 0.407254 | − | 0.913315i | \(-0.366486\pi\) | ||||
0.407254 | + | 0.913315i | \(0.366486\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.26464 | 0.141139 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 31.1460 | 1.02966 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.68015 | 0.286644 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18.1925 | 0.600115 | 0.300057 | − | 0.953921i | \(-0.402994\pi\) | ||||
0.300057 | + | 0.953921i | \(0.402994\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −70.6860 | −2.32918 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.157313 | 0.00517801 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.07903 | −0.134118 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −127.915 | −4.20128 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −31.3954 | −1.03005 | −0.515026 | − | 0.857175i | \(-0.672218\pi\) | ||||
−0.515026 | + | 0.857175i | \(0.672218\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.17867 | −0.136950 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 106.047 | 3.47183 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −9.02367 | −0.295106 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −27.5483 | −0.899964 | −0.449982 | − | 0.893038i | \(-0.648570\pi\) | ||||
−0.449982 | + | 0.893038i | \(0.648570\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −38.7242 | −1.26371 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.9189 | 0.518943 | 0.259471 | − | 0.965751i | \(-0.416452\pi\) | ||||
0.259471 | + | 0.965751i | \(0.416452\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −36.8675 | −1.20057 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −27.4744 | −0.893744 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 19.4282 | 0.631330 | 0.315665 | − | 0.948871i | \(-0.397772\pi\) | ||||
0.315665 | + | 0.948871i | \(0.397772\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.45524 | −0.0472392 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.09873 | −0.197765 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −10.8945 | −0.352907 | −0.176454 | − | 0.984309i | \(-0.556463\pi\) | ||||
−0.176454 | + | 0.984309i | \(0.556463\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 48.2783 | 1.56225 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 10.7974 | 0.349029 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 14.3959 | 0.464866 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.2011 | 0.974228 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 118.162 | 3.80772 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −44.4112 | −1.42965 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 33.8901 | 1.08983 | 0.544916 | − | 0.838491i | \(-0.316562\pi\) | ||||
0.544916 | + | 0.838491i | \(0.316562\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 62.4697 | 2.00682 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 31.6814 | 1.01670 | 0.508352 | − | 0.861149i | \(-0.330255\pi\) | ||||
0.508352 | + | 0.861149i | \(0.330255\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.55146 | −0.306206 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.92121 | −0.125579 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −50.8388 | −1.62648 | −0.813239 | − | 0.581929i | \(-0.802298\pi\) | ||||
−0.813239 | + | 0.581929i | \(0.802298\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14.4609 | −0.462174 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 54.2108 | 1.73082 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.74912 | −0.119578 | −0.0597891 | − | 0.998211i | \(-0.519043\pi\) | ||||
−0.0597891 | + | 0.998211i | \(0.519043\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −22.2783 | −0.709845 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −34.6528 | −1.10301 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.60615 | −0.241862 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −14.5433 | −0.461982 | −0.230991 | − | 0.972956i | \(-0.574197\pi\) | ||||
−0.230991 | + | 0.972956i | \(0.574197\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 28.5141 | 0.904868 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −12.1492 | −0.385156 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −20.5492 | −0.650800 | −0.325400 | − | 0.945576i | \(-0.605499\pi\) | ||||
−0.325400 | + | 0.945576i | \(0.605499\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −47.3494 | −1.49807 |
(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 | 8008.2.a.y.1.2 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8008.2.a.y.1.2 | ✓ | 14 | 1.1 | even | 1 | trivial |