Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [538,2,Mod(1,538)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(538, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("538.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 538 = 2 \cdot 269 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 538.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: | \(4.29595162874\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.4913.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 6x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.487928\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 538.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0.512072 | 0.295645 | 0.147822 | − | 0.989014i | \(-0.452774\pi\) | ||||
0.147822 | + | 0.989014i | \(0.452774\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.04948 | −0.469342 | −0.234671 | − | 0.972075i | \(-0.575401\pi\) | ||||
−0.234671 | + | 0.972075i | \(0.575401\pi\) | |||||||
\(6\) | −0.512072 | −0.209052 | ||||||||
\(7\) | −2.90570 | −1.09825 | −0.549126 | − | 0.835739i | \(-0.685039\pi\) | ||||
−0.549126 | + | 0.835739i | \(0.685039\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.73778 | −0.912594 | ||||||||
\(10\) | 1.04948 | 0.331875 | ||||||||
\(11\) | 2.34415 | 0.706788 | 0.353394 | − | 0.935475i | \(-0.385028\pi\) | ||||
0.353394 | + | 0.935475i | \(0.385028\pi\) | |||||||
\(12\) | 0.512072 | 0.147822 | ||||||||
\(13\) | 4.24985 | 1.17870 | 0.589349 | − | 0.807879i | \(-0.299384\pi\) | ||||
0.589349 | + | 0.807879i | \(0.299384\pi\) | |||||||
\(14\) | 2.90570 | 0.776582 | ||||||||
\(15\) | −0.537410 | −0.138759 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 7.66052 | 1.85795 | 0.928974 | − | 0.370145i | \(-0.120692\pi\) | ||||
0.928974 | + | 0.370145i | \(0.120692\pi\) | |||||||
\(18\) | 2.73778 | 0.645302 | ||||||||
\(19\) | 5.81141 | 1.33323 | 0.666614 | − | 0.745403i | \(-0.267743\pi\) | ||||
0.666614 | + | 0.745403i | \(0.267743\pi\) | |||||||
\(20\) | −1.04948 | −0.234671 | ||||||||
\(21\) | −1.48793 | −0.324693 | ||||||||
\(22\) | −2.34415 | −0.499775 | ||||||||
\(23\) | 6.53741 | 1.36314 | 0.681572 | − | 0.731751i | \(-0.261297\pi\) | ||||
0.681572 | + | 0.731751i | \(0.261297\pi\) | |||||||
\(24\) | −0.512072 | −0.104526 | ||||||||
\(25\) | −3.89859 | −0.779718 | ||||||||
\(26\) | −4.24985 | −0.833465 | ||||||||
\(27\) | −2.93816 | −0.565448 | ||||||||
\(28\) | −2.90570 | −0.549126 | ||||||||
\(29\) | 0.119634 | 0.0222155 | 0.0111078 | − | 0.999938i | \(-0.496464\pi\) | ||||
0.0111078 | + | 0.999938i | \(0.496464\pi\) | |||||||
\(30\) | 0.537410 | 0.0981171 | ||||||||
\(31\) | 3.75481 | 0.674384 | 0.337192 | − | 0.941436i | \(-0.390523\pi\) | ||||
0.337192 | + | 0.941436i | \(0.390523\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 1.20037 | 0.208958 | ||||||||
\(34\) | −7.66052 | −1.31377 | ||||||||
\(35\) | 3.04948 | 0.515456 | ||||||||
\(36\) | −2.73778 | −0.456297 | ||||||||
\(37\) | −3.27400 | −0.538242 | −0.269121 | − | 0.963106i | \(-0.586733\pi\) | ||||
−0.269121 | + | 0.963106i | \(0.586733\pi\) | |||||||
\(38\) | −5.81141 | −0.942735 | ||||||||
\(39\) | 2.17623 | 0.348476 | ||||||||
\(40\) | 1.04948 | 0.165938 | ||||||||
\(41\) | 4.46726 | 0.697668 | 0.348834 | − | 0.937184i | \(-0.386578\pi\) | ||||
0.348834 | + | 0.937184i | \(0.386578\pi\) | |||||||
\(42\) | 1.48793 | 0.229592 | ||||||||
\(43\) | −3.34051 | −0.509423 | −0.254711 | − | 0.967017i | \(-0.581980\pi\) | ||||
−0.254711 | + | 0.967017i | \(0.581980\pi\) | |||||||
\(44\) | 2.34415 | 0.353394 | ||||||||
\(45\) | 2.87325 | 0.428319 | ||||||||
\(46\) | −6.53741 | −0.963888 | ||||||||
\(47\) | 2.61468 | 0.381390 | 0.190695 | − | 0.981649i | \(-0.438926\pi\) | ||||
0.190695 | + | 0.981649i | \(0.438926\pi\) | |||||||
\(48\) | 0.512072 | 0.0739112 | ||||||||
\(49\) | 1.44311 | 0.206159 | ||||||||
\(50\) | 3.89859 | 0.551344 | ||||||||
\(51\) | 3.92273 | 0.549292 | ||||||||
\(52\) | 4.24985 | 0.589349 | ||||||||
\(53\) | 2.87689 | 0.395172 | 0.197586 | − | 0.980286i | \(-0.436690\pi\) | ||||
0.197586 | + | 0.980286i | \(0.436690\pi\) | |||||||
\(54\) | 2.93816 | 0.399832 | ||||||||
\(55\) | −2.46014 | −0.331725 | ||||||||
\(56\) | 2.90570 | 0.388291 | ||||||||
\(57\) | 2.97586 | 0.394162 | ||||||||
\(58\) | −0.119634 | −0.0157088 | ||||||||
\(59\) | 0.549773 | 0.0715743 | 0.0357871 | − | 0.999359i | \(-0.488606\pi\) | ||||
0.0357871 | + | 0.999359i | \(0.488606\pi\) | |||||||
\(60\) | −0.537410 | −0.0693793 | ||||||||
\(61\) | −8.24985 | −1.05629 | −0.528143 | − | 0.849156i | \(-0.677111\pi\) | ||||
−0.528143 | + | 0.849156i | \(0.677111\pi\) | |||||||
\(62\) | −3.75481 | −0.476862 | ||||||||
\(63\) | 7.95518 | 1.00226 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −4.46014 | −0.553213 | ||||||||
\(66\) | −1.20037 | −0.147756 | ||||||||
\(67\) | 1.09430 | 0.133690 | 0.0668448 | − | 0.997763i | \(-0.478707\pi\) | ||||
0.0668448 | + | 0.997763i | \(0.478707\pi\) | |||||||
\(68\) | 7.66052 | 0.928974 | ||||||||
\(69\) | 3.34762 | 0.403006 | ||||||||
\(70\) | −3.04948 | −0.364483 | ||||||||
\(71\) | −8.10363 | −0.961724 | −0.480862 | − | 0.876796i | \(-0.659676\pi\) | ||||
−0.480862 | + | 0.876796i | \(0.659676\pi\) | |||||||
\(72\) | 2.73778 | 0.322651 | ||||||||
\(73\) | 9.15191 | 1.07115 | 0.535575 | − | 0.844487i | \(-0.320095\pi\) | ||||
0.535575 | + | 0.844487i | \(0.320095\pi\) | |||||||
\(74\) | 3.27400 | 0.380594 | ||||||||
\(75\) | −1.99636 | −0.230519 | ||||||||
\(76\) | 5.81141 | 0.666614 | ||||||||
\(77\) | −6.81141 | −0.776232 | ||||||||
\(78\) | −2.17623 | −0.246410 | ||||||||
\(79\) | 0.426084 | 0.0479382 | 0.0239691 | − | 0.999713i | \(-0.492370\pi\) | ||||
0.0239691 | + | 0.999713i | \(0.492370\pi\) | |||||||
\(80\) | −1.04948 | −0.117336 | ||||||||
\(81\) | 6.70880 | 0.745422 | ||||||||
\(82\) | −4.46726 | −0.493326 | ||||||||
\(83\) | 7.84547 | 0.861152 | 0.430576 | − | 0.902554i | \(-0.358311\pi\) | ||||
0.430576 | + | 0.902554i | \(0.358311\pi\) | |||||||
\(84\) | −1.48793 | −0.162346 | ||||||||
\(85\) | −8.03957 | −0.872013 | ||||||||
\(86\) | 3.34051 | 0.360216 | ||||||||
\(87\) | 0.0612614 | 0.00656791 | ||||||||
\(88\) | −2.34415 | −0.249887 | ||||||||
\(89\) | 15.7424 | 1.66870 | 0.834348 | − | 0.551238i | \(-0.185844\pi\) | ||||
0.834348 | + | 0.551238i | \(0.185844\pi\) | |||||||
\(90\) | −2.87325 | −0.302867 | ||||||||
\(91\) | −12.3488 | −1.29451 | ||||||||
\(92\) | 6.53741 | 0.681572 | ||||||||
\(93\) | 1.92273 | 0.199378 | ||||||||
\(94\) | −2.61468 | −0.269683 | ||||||||
\(95\) | −6.09896 | −0.625740 | ||||||||
\(96\) | −0.512072 | −0.0522631 | ||||||||
\(97\) | −14.9051 | −1.51339 | −0.756693 | − | 0.653771i | \(-0.773186\pi\) | ||||
−0.756693 | + | 0.653771i | \(0.773186\pi\) | |||||||
\(98\) | −1.44311 | −0.145776 | ||||||||
\(99\) | −6.41778 | −0.645011 | ||||||||
\(100\) | −3.89859 | −0.389859 | ||||||||
\(101\) | −13.0300 | −1.29653 | −0.648267 | − | 0.761413i | \(-0.724506\pi\) | ||||
−0.648267 | + | 0.761413i | \(0.724506\pi\) | |||||||
\(102\) | −3.92273 | −0.388408 | ||||||||
\(103\) | 8.52505 | 0.839998 | 0.419999 | − | 0.907525i | \(-0.362030\pi\) | ||||
0.419999 | + | 0.907525i | \(0.362030\pi\) | |||||||
\(104\) | −4.24985 | −0.416732 | ||||||||
\(105\) | 1.56155 | 0.152392 | ||||||||
\(106\) | −2.87689 | −0.279429 | ||||||||
\(107\) | 11.0371 | 1.06700 | 0.533499 | − | 0.845801i | \(-0.320877\pi\) | ||||
0.533499 | + | 0.845801i | \(0.320877\pi\) | |||||||
\(108\) | −2.93816 | −0.282724 | ||||||||
\(109\) | −4.51919 | −0.432860 | −0.216430 | − | 0.976298i | \(-0.569441\pi\) | ||||
−0.216430 | + | 0.976298i | \(0.569441\pi\) | |||||||
\(110\) | 2.46014 | 0.234565 | ||||||||
\(111\) | −1.67652 | −0.159128 | ||||||||
\(112\) | −2.90570 | −0.274563 | ||||||||
\(113\) | −5.82616 | −0.548079 | −0.274039 | − | 0.961718i | \(-0.588360\pi\) | ||||
−0.274039 | + | 0.961718i | \(0.588360\pi\) | |||||||
\(114\) | −2.97586 | −0.278715 | ||||||||
\(115\) | −6.86089 | −0.639781 | ||||||||
\(116\) | 0.119634 | 0.0111078 | ||||||||
\(117\) | −11.6352 | −1.07567 | ||||||||
\(118\) | −0.549773 | −0.0506107 | ||||||||
\(119\) | −22.2592 | −2.04050 | ||||||||
\(120\) | 0.537410 | 0.0490586 | ||||||||
\(121\) | −5.50496 | −0.500451 | ||||||||
\(122\) | 8.24985 | 0.746907 | ||||||||
\(123\) | 2.28756 | 0.206262 | ||||||||
\(124\) | 3.75481 | 0.337192 | ||||||||
\(125\) | 9.33890 | 0.835297 | ||||||||
\(126\) | −7.95518 | −0.708704 | ||||||||
\(127\) | −5.97102 | −0.529842 | −0.264921 | − | 0.964270i | \(-0.585346\pi\) | ||||
−0.264921 | + | 0.964270i | \(0.585346\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −1.71058 | −0.150608 | ||||||||
\(130\) | 4.46014 | 0.391180 | ||||||||
\(131\) | 11.3535 | 0.991958 | 0.495979 | − | 0.868334i | \(-0.334809\pi\) | ||||
0.495979 | + | 0.868334i | \(0.334809\pi\) | |||||||
\(132\) | 1.20037 | 0.104479 | ||||||||
\(133\) | −16.8862 | −1.46422 | ||||||||
\(134\) | −1.09430 | −0.0945328 | ||||||||
\(135\) | 3.08354 | 0.265389 | ||||||||
\(136\) | −7.66052 | −0.656884 | ||||||||
\(137\) | 10.6240 | 0.907670 | 0.453835 | − | 0.891086i | \(-0.350055\pi\) | ||||
0.453835 | + | 0.891086i | \(0.350055\pi\) | |||||||
\(138\) | −3.34762 | −0.284969 | ||||||||
\(139\) | 8.41186 | 0.713484 | 0.356742 | − | 0.934203i | \(-0.383887\pi\) | ||||
0.356742 | + | 0.934203i | \(0.383887\pi\) | |||||||
\(140\) | 3.04948 | 0.257728 | ||||||||
\(141\) | 1.33890 | 0.112756 | ||||||||
\(142\) | 8.10363 | 0.680041 | ||||||||
\(143\) | 9.96230 | 0.833089 | ||||||||
\(144\) | −2.73778 | −0.228149 | ||||||||
\(145\) | −0.125554 | −0.0104267 | ||||||||
\(146\) | −9.15191 | −0.757418 | ||||||||
\(147\) | 0.738977 | 0.0609498 | ||||||||
\(148\) | −3.27400 | −0.269121 | ||||||||
\(149\) | −17.9321 | −1.46905 | −0.734526 | − | 0.678581i | \(-0.762595\pi\) | ||||
−0.734526 | + | 0.678581i | \(0.762595\pi\) | |||||||
\(150\) | 1.99636 | 0.163002 | ||||||||
\(151\) | −0.938156 | −0.0763460 | −0.0381730 | − | 0.999271i | \(-0.512154\pi\) | ||||
−0.0381730 | + | 0.999271i | \(0.512154\pi\) | |||||||
\(152\) | −5.81141 | −0.471367 | ||||||||
\(153\) | −20.9728 | −1.69555 | ||||||||
\(154\) | 6.81141 | 0.548879 | ||||||||
\(155\) | −3.94060 | −0.316517 | ||||||||
\(156\) | 2.17623 | 0.174238 | ||||||||
\(157\) | −1.01948 | −0.0813632 | −0.0406816 | − | 0.999172i | \(-0.512953\pi\) | ||||
−0.0406816 | + | 0.999172i | \(0.512953\pi\) | |||||||
\(158\) | −0.426084 | −0.0338974 | ||||||||
\(159\) | 1.47318 | 0.116830 | ||||||||
\(160\) | 1.04948 | 0.0829688 | ||||||||
\(161\) | −18.9958 | −1.49708 | ||||||||
\(162\) | −6.70880 | −0.527093 | ||||||||
\(163\) | 13.3440 | 1.04518 | 0.522591 | − | 0.852584i | \(-0.324966\pi\) | ||||
0.522591 | + | 0.852584i | \(0.324966\pi\) | |||||||
\(164\) | 4.46726 | 0.348834 | ||||||||
\(165\) | −1.25977 | −0.0980729 | ||||||||
\(166\) | −7.84547 | −0.608926 | ||||||||
\(167\) | 19.8414 | 1.53537 | 0.767687 | − | 0.640825i | \(-0.221407\pi\) | ||||
0.767687 | + | 0.640825i | \(0.221407\pi\) | |||||||
\(168\) | 1.48793 | 0.114796 | ||||||||
\(169\) | 5.06126 | 0.389328 | ||||||||
\(170\) | 8.03957 | 0.616607 | ||||||||
\(171\) | −15.9104 | −1.21670 | ||||||||
\(172\) | −3.34051 | −0.254711 | ||||||||
\(173\) | 14.7860 | 1.12416 | 0.562080 | − | 0.827083i | \(-0.310001\pi\) | ||||
0.562080 | + | 0.827083i | \(0.310001\pi\) | |||||||
\(174\) | −0.0612614 | −0.00464421 | ||||||||
\(175\) | 11.3281 | 0.856327 | ||||||||
\(176\) | 2.34415 | 0.176697 | ||||||||
\(177\) | 0.281523 | 0.0211606 | ||||||||
\(178\) | −15.7424 | −1.17995 | ||||||||
\(179\) | −13.1868 | −0.985624 | −0.492812 | − | 0.870136i | \(-0.664031\pi\) | ||||
−0.492812 | + | 0.870136i | \(0.664031\pi\) | |||||||
\(180\) | 2.87325 | 0.214160 | ||||||||
\(181\) | −21.7542 | −1.61698 | −0.808490 | − | 0.588511i | \(-0.799715\pi\) | ||||
−0.808490 | + | 0.588511i | \(0.799715\pi\) | |||||||
\(182\) | 12.3488 | 0.915355 | ||||||||
\(183\) | −4.22452 | −0.312285 | ||||||||
\(184\) | −6.53741 | −0.481944 | ||||||||
\(185\) | 3.43600 | 0.252620 | ||||||||
\(186\) | −1.92273 | −0.140982 | ||||||||
\(187\) | 17.9574 | 1.31318 | ||||||||
\(188\) | 2.61468 | 0.190695 | ||||||||
\(189\) | 8.53741 | 0.621005 | ||||||||
\(190\) | 6.09896 | 0.442465 | ||||||||
\(191\) | −1.23630 | −0.0894553 | −0.0447276 | − | 0.998999i | \(-0.514242\pi\) | ||||
−0.0447276 | + | 0.998999i | \(0.514242\pi\) | |||||||
\(192\) | 0.512072 | 0.0369556 | ||||||||
\(193\) | 1.52749 | 0.109951 | 0.0549757 | − | 0.998488i | \(-0.482492\pi\) | ||||
0.0549757 | + | 0.998488i | \(0.482492\pi\) | |||||||
\(194\) | 14.9051 | 1.07013 | ||||||||
\(195\) | −2.28391 | −0.163554 | ||||||||
\(196\) | 1.44311 | 0.103080 | ||||||||
\(197\) | −22.3689 | −1.59372 | −0.796859 | − | 0.604165i | \(-0.793507\pi\) | ||||
−0.796859 | + | 0.604165i | \(0.793507\pi\) | |||||||
\(198\) | 6.41778 | 0.456091 | ||||||||
\(199\) | −16.7266 | −1.18572 | −0.592859 | − | 0.805306i | \(-0.702001\pi\) | ||||
−0.592859 | + | 0.805306i | \(0.702001\pi\) | |||||||
\(200\) | 3.89859 | 0.275672 | ||||||||
\(201\) | 0.560358 | 0.0395246 | ||||||||
\(202\) | 13.0300 | 0.916788 | ||||||||
\(203\) | −0.347622 | −0.0243983 | ||||||||
\(204\) | 3.92273 | 0.274646 | ||||||||
\(205\) | −4.68830 | −0.327445 | ||||||||
\(206\) | −8.52505 | −0.593968 | ||||||||
\(207\) | −17.8980 | −1.24400 | ||||||||
\(208\) | 4.24985 | 0.294674 | ||||||||
\(209\) | 13.6228 | 0.942310 | ||||||||
\(210\) | −1.56155 | −0.107757 | ||||||||
\(211\) | −2.00644 | −0.138129 | −0.0690646 | − | 0.997612i | \(-0.522001\pi\) | ||||
−0.0690646 | + | 0.997612i | \(0.522001\pi\) | |||||||
\(212\) | 2.87689 | 0.197586 | ||||||||
\(213\) | −4.14964 | −0.284329 | ||||||||
\(214\) | −11.0371 | −0.754482 | ||||||||
\(215\) | 3.50580 | 0.239094 | ||||||||
\(216\) | 2.93816 | 0.199916 | ||||||||
\(217\) | −10.9104 | −0.740644 | ||||||||
\(218\) | 4.51919 | 0.306078 | ||||||||
\(219\) | 4.68644 | 0.316680 | ||||||||
\(220\) | −2.46014 | −0.165863 | ||||||||
\(221\) | 32.5561 | 2.18996 | ||||||||
\(222\) | 1.67652 | 0.112521 | ||||||||
\(223\) | 17.0201 | 1.13975 | 0.569875 | − | 0.821732i | \(-0.306992\pi\) | ||||
0.569875 | + | 0.821732i | \(0.306992\pi\) | |||||||
\(224\) | 2.90570 | 0.194145 | ||||||||
\(225\) | 10.6735 | 0.711566 | ||||||||
\(226\) | 5.82616 | 0.387550 | ||||||||
\(227\) | 17.9605 | 1.19208 | 0.596041 | − | 0.802954i | \(-0.296740\pi\) | ||||
0.596041 | + | 0.802954i | \(0.296740\pi\) | |||||||
\(228\) | 2.97586 | 0.197081 | ||||||||
\(229\) | 3.85377 | 0.254665 | 0.127332 | − | 0.991860i | \(-0.459359\pi\) | ||||
0.127332 | + | 0.991860i | \(0.459359\pi\) | |||||||
\(230\) | 6.86089 | 0.452394 | ||||||||
\(231\) | −3.48793 | −0.229489 | ||||||||
\(232\) | −0.119634 | −0.00785438 | ||||||||
\(233\) | 19.8538 | 1.30066 | 0.650332 | − | 0.759650i | \(-0.274630\pi\) | ||||
0.650332 | + | 0.759650i | \(0.274630\pi\) | |||||||
\(234\) | 11.6352 | 0.760615 | ||||||||
\(235\) | −2.74405 | −0.179002 | ||||||||
\(236\) | 0.549773 | 0.0357871 | ||||||||
\(237\) | 0.218186 | 0.0141727 | ||||||||
\(238\) | 22.2592 | 1.44285 | ||||||||
\(239\) | −11.1250 | −0.719615 | −0.359807 | − | 0.933027i | \(-0.617158\pi\) | ||||
−0.359807 | + | 0.933027i | \(0.617158\pi\) | |||||||
\(240\) | −0.537410 | −0.0346896 | ||||||||
\(241\) | −17.2740 | −1.11272 | −0.556358 | − | 0.830943i | \(-0.687802\pi\) | ||||
−0.556358 | + | 0.830943i | \(0.687802\pi\) | |||||||
\(242\) | 5.50496 | 0.353872 | ||||||||
\(243\) | 12.2499 | 0.785829 | ||||||||
\(244\) | −8.24985 | −0.528143 | ||||||||
\(245\) | −1.51452 | −0.0967591 | ||||||||
\(246\) | −2.28756 | −0.145849 | ||||||||
\(247\) | 24.6976 | 1.57147 | ||||||||
\(248\) | −3.75481 | −0.238431 | ||||||||
\(249\) | 4.01744 | 0.254595 | ||||||||
\(250\) | −9.33890 | −0.590644 | ||||||||
\(251\) | 2.07362 | 0.130886 | 0.0654430 | − | 0.997856i | \(-0.479154\pi\) | ||||
0.0654430 | + | 0.997856i | \(0.479154\pi\) | |||||||
\(252\) | 7.95518 | 0.501130 | ||||||||
\(253\) | 15.3247 | 0.963454 | ||||||||
\(254\) | 5.97102 | 0.374655 | ||||||||
\(255\) | −4.11683 | −0.257806 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −26.0799 | −1.62682 | −0.813411 | − | 0.581690i | \(-0.802392\pi\) | ||||
−0.813411 | + | 0.581690i | \(0.802392\pi\) | |||||||
\(258\) | 1.71058 | 0.106496 | ||||||||
\(259\) | 9.51327 | 0.591126 | ||||||||
\(260\) | −4.46014 | −0.276606 | ||||||||
\(261\) | −0.327533 | −0.0202738 | ||||||||
\(262\) | −11.3535 | −0.701420 | ||||||||
\(263\) | −9.93935 | −0.612887 | −0.306443 | − | 0.951889i | \(-0.599139\pi\) | ||||
−0.306443 | + | 0.951889i | \(0.599139\pi\) | |||||||
\(264\) | −1.20037 | −0.0738779 | ||||||||
\(265\) | −3.01925 | −0.185471 | ||||||||
\(266\) | 16.8862 | 1.03536 | ||||||||
\(267\) | 8.06126 | 0.493341 | ||||||||
\(268\) | 1.09430 | 0.0668448 | ||||||||
\(269\) | 1.00000 | 0.0609711 | ||||||||
\(270\) | −3.08354 | −0.187658 | ||||||||
\(271\) | 9.40702 | 0.571436 | 0.285718 | − | 0.958314i | \(-0.407768\pi\) | ||||
0.285718 | + | 0.958314i | \(0.407768\pi\) | |||||||
\(272\) | 7.66052 | 0.464487 | ||||||||
\(273\) | −6.32348 | −0.382714 | ||||||||
\(274\) | −10.6240 | −0.641820 | ||||||||
\(275\) | −9.13888 | −0.551095 | ||||||||
\(276\) | 3.34762 | 0.201503 | ||||||||
\(277\) | 1.10380 | 0.0663209 | 0.0331605 | − | 0.999450i | \(-0.489443\pi\) | ||||
0.0331605 | + | 0.999450i | \(0.489443\pi\) | |||||||
\(278\) | −8.41186 | −0.504510 | ||||||||
\(279\) | −10.2799 | −0.615439 | ||||||||
\(280\) | −3.04948 | −0.182241 | ||||||||
\(281\) | −16.2356 | −0.968536 | −0.484268 | − | 0.874920i | \(-0.660914\pi\) | ||||
−0.484268 | + | 0.874920i | \(0.660914\pi\) | |||||||
\(282\) | −1.33890 | −0.0797304 | ||||||||
\(283\) | 22.0635 | 1.31154 | 0.655771 | − | 0.754960i | \(-0.272344\pi\) | ||||
0.655771 | + | 0.754960i | \(0.272344\pi\) | |||||||
\(284\) | −8.10363 | −0.480862 | ||||||||
\(285\) | −3.12311 | −0.184997 | ||||||||
\(286\) | −9.96230 | −0.589083 | ||||||||
\(287\) | −12.9805 | −0.766216 | ||||||||
\(288\) | 2.73778 | 0.161325 | ||||||||
\(289\) | 41.6835 | 2.45197 | ||||||||
\(290\) | 0.125554 | 0.00737279 | ||||||||
\(291\) | −7.63249 | −0.447424 | ||||||||
\(292\) | 9.15191 | 0.535575 | ||||||||
\(293\) | 12.1496 | 0.709789 | 0.354895 | − | 0.934906i | \(-0.384517\pi\) | ||||
0.354895 | + | 0.934906i | \(0.384517\pi\) | |||||||
\(294\) | −0.738977 | −0.0430980 | ||||||||
\(295\) | −0.576976 | −0.0335928 | ||||||||
\(296\) | 3.27400 | 0.190297 | ||||||||
\(297\) | −6.88748 | −0.399652 | ||||||||
\(298\) | 17.9321 | 1.03878 | ||||||||
\(299\) | 27.7830 | 1.60673 | ||||||||
\(300\) | −1.99636 | −0.115260 | ||||||||
\(301\) | 9.70653 | 0.559475 | ||||||||
\(302\) | 0.938156 | 0.0539848 | ||||||||
\(303\) | −6.67230 | −0.383313 | ||||||||
\(304\) | 5.81141 | 0.333307 | ||||||||
\(305\) | 8.65807 | 0.495759 | ||||||||
\(306\) | 20.9728 | 1.19894 | ||||||||
\(307\) | −22.7400 | −1.29784 | −0.648920 | − | 0.760856i | \(-0.724779\pi\) | ||||
−0.648920 | + | 0.760856i | \(0.724779\pi\) | |||||||
\(308\) | −6.81141 | −0.388116 | ||||||||
\(309\) | 4.36543 | 0.248341 | ||||||||
\(310\) | 3.94060 | 0.223811 | ||||||||
\(311\) | −10.9941 | −0.623417 | −0.311709 | − | 0.950178i | \(-0.600901\pi\) | ||||
−0.311709 | + | 0.950178i | \(0.600901\pi\) | |||||||
\(312\) | −2.17623 | −0.123205 | ||||||||
\(313\) | −25.0357 | −1.41510 | −0.707551 | − | 0.706663i | \(-0.750200\pi\) | ||||
−0.707551 | + | 0.706663i | \(0.750200\pi\) | |||||||
\(314\) | 1.01948 | 0.0575324 | ||||||||
\(315\) | −8.34882 | −0.470403 | ||||||||
\(316\) | 0.426084 | 0.0239691 | ||||||||
\(317\) | 29.2168 | 1.64098 | 0.820490 | − | 0.571661i | \(-0.193701\pi\) | ||||
0.820490 | + | 0.571661i | \(0.193701\pi\) | |||||||
\(318\) | −1.47318 | −0.0826116 | ||||||||
\(319\) | 0.280441 | 0.0157017 | ||||||||
\(320\) | −1.04948 | −0.0586678 | ||||||||
\(321\) | 5.65180 | 0.315452 | ||||||||
\(322\) | 18.9958 | 1.05859 | ||||||||
\(323\) | 44.5184 | 2.47707 | ||||||||
\(324\) | 6.70880 | 0.372711 | ||||||||
\(325\) | −16.5684 | −0.919051 | ||||||||
\(326\) | −13.3440 | −0.739055 | ||||||||
\(327\) | −2.31415 | −0.127973 | ||||||||
\(328\) | −4.46726 | −0.246663 | ||||||||
\(329\) | −7.59748 | −0.418862 | ||||||||
\(330\) | 1.25977 | 0.0693480 | ||||||||
\(331\) | 15.9156 | 0.874801 | 0.437401 | − | 0.899267i | \(-0.355899\pi\) | ||||
0.437401 | + | 0.899267i | \(0.355899\pi\) | |||||||
\(332\) | 7.84547 | 0.430576 | ||||||||
\(333\) | 8.96349 | 0.491196 | ||||||||
\(334\) | −19.8414 | −1.08567 | ||||||||
\(335\) | −1.14844 | −0.0627462 | ||||||||
\(336\) | −1.48793 | −0.0811731 | ||||||||
\(337\) | −35.1956 | −1.91722 | −0.958612 | − | 0.284715i | \(-0.908101\pi\) | ||||
−0.958612 | + | 0.284715i | \(0.908101\pi\) | |||||||
\(338\) | −5.06126 | −0.275296 | ||||||||
\(339\) | −2.98341 | −0.162037 | ||||||||
\(340\) | −8.03957 | −0.436007 | ||||||||
\(341\) | 8.80184 | 0.476647 | ||||||||
\(342\) | 15.9104 | 0.860334 | ||||||||
\(343\) | 16.1467 | 0.871838 | ||||||||
\(344\) | 3.34051 | 0.180108 | ||||||||
\(345\) | −3.51327 | −0.189148 | ||||||||
\(346\) | −14.7860 | −0.794901 | ||||||||
\(347\) | −24.8903 | −1.33618 | −0.668091 | − | 0.744080i | \(-0.732888\pi\) | ||||
−0.668091 | + | 0.744080i | \(0.732888\pi\) | |||||||
\(348\) | 0.0612614 | 0.00328395 | ||||||||
\(349\) | 1.73175 | 0.0926985 | 0.0463492 | − | 0.998925i | \(-0.485241\pi\) | ||||
0.0463492 | + | 0.998925i | \(0.485241\pi\) | |||||||
\(350\) | −11.3281 | −0.605515 | ||||||||
\(351\) | −12.4867 | −0.666493 | ||||||||
\(352\) | −2.34415 | −0.124944 | ||||||||
\(353\) | −21.3682 | −1.13732 | −0.568658 | − | 0.822574i | \(-0.692537\pi\) | ||||
−0.568658 | + | 0.822574i | \(0.692537\pi\) | |||||||
\(354\) | −0.281523 | −0.0149628 | ||||||||
\(355\) | 8.50461 | 0.451378 | ||||||||
\(356\) | 15.7424 | 0.834348 | ||||||||
\(357\) | −11.3983 | −0.603262 | ||||||||
\(358\) | 13.1868 | 0.696942 | ||||||||
\(359\) | −19.8025 | −1.04514 | −0.522568 | − | 0.852597i | \(-0.675026\pi\) | ||||
−0.522568 | + | 0.852597i | \(0.675026\pi\) | |||||||
\(360\) | −2.87325 | −0.151434 | ||||||||
\(361\) | 14.7725 | 0.777497 | ||||||||
\(362\) | 21.7542 | 1.14338 | ||||||||
\(363\) | −2.81893 | −0.147956 | ||||||||
\(364\) | −12.3488 | −0.647254 | ||||||||
\(365\) | −9.60476 | −0.502736 | ||||||||
\(366\) | 4.22452 | 0.220819 | ||||||||
\(367\) | −1.72720 | −0.0901590 | −0.0450795 | − | 0.998983i | \(-0.514354\pi\) | ||||
−0.0450795 | + | 0.998983i | \(0.514354\pi\) | |||||||
\(368\) | 6.53741 | 0.340786 | ||||||||
\(369\) | −12.2304 | −0.636688 | ||||||||
\(370\) | −3.43600 | −0.178629 | ||||||||
\(371\) | −8.35940 | −0.433999 | ||||||||
\(372\) | 1.92273 | 0.0996890 | ||||||||
\(373\) | −31.3423 | −1.62284 | −0.811422 | − | 0.584461i | \(-0.801306\pi\) | ||||
−0.811422 | + | 0.584461i | \(0.801306\pi\) | |||||||
\(374\) | −17.9574 | −0.928555 | ||||||||
\(375\) | 4.78219 | 0.246951 | ||||||||
\(376\) | −2.61468 | −0.134842 | ||||||||
\(377\) | 0.508429 | 0.0261854 | ||||||||
\(378\) | −8.53741 | −0.439117 | ||||||||
\(379\) | 21.2263 | 1.09032 | 0.545161 | − | 0.838331i | \(-0.316468\pi\) | ||||
0.545161 | + | 0.838331i | \(0.316468\pi\) | |||||||
\(380\) | −6.09896 | −0.312870 | ||||||||
\(381\) | −3.05759 | −0.156645 | ||||||||
\(382\) | 1.23630 | 0.0632544 | ||||||||
\(383\) | −34.5798 | −1.76695 | −0.883473 | − | 0.468483i | \(-0.844801\pi\) | ||||
−0.883473 | + | 0.468483i | \(0.844801\pi\) | |||||||
\(384\) | −0.512072 | −0.0261315 | ||||||||
\(385\) | 7.14844 | 0.364318 | ||||||||
\(386\) | −1.52749 | −0.0777474 | ||||||||
\(387\) | 9.14558 | 0.464896 | ||||||||
\(388\) | −14.9051 | −0.756693 | ||||||||
\(389\) | 2.21454 | 0.112282 | 0.0561409 | − | 0.998423i | \(-0.482120\pi\) | ||||
0.0561409 | + | 0.998423i | \(0.482120\pi\) | |||||||
\(390\) | 2.28391 | 0.115650 | ||||||||
\(391\) | 50.0799 | 2.53265 | ||||||||
\(392\) | −1.44311 | −0.0728882 | ||||||||
\(393\) | 5.81380 | 0.293267 | ||||||||
\(394\) | 22.3689 | 1.12693 | ||||||||
\(395\) | −0.447167 | −0.0224994 | ||||||||
\(396\) | −6.41778 | −0.322505 | ||||||||
\(397\) | −28.7782 | −1.44434 | −0.722168 | − | 0.691717i | \(-0.756854\pi\) | ||||
−0.722168 | + | 0.691717i | \(0.756854\pi\) | |||||||
\(398\) | 16.7266 | 0.838429 | ||||||||
\(399\) | −8.64696 | −0.432889 | ||||||||
\(400\) | −3.89859 | −0.194929 | ||||||||
\(401\) | −9.00119 | −0.449498 | −0.224749 | − | 0.974417i | \(-0.572156\pi\) | ||||
−0.224749 | + | 0.974417i | \(0.572156\pi\) | |||||||
\(402\) | −0.560358 | −0.0279481 | ||||||||
\(403\) | 15.9574 | 0.794895 | ||||||||
\(404\) | −13.0300 | −0.648267 | ||||||||
\(405\) | −7.04076 | −0.349858 | ||||||||
\(406\) | 0.347622 | 0.0172522 | ||||||||
\(407\) | −7.67474 | −0.380423 | ||||||||
\(408\) | −3.92273 | −0.194204 | ||||||||
\(409\) | 36.6526 | 1.81236 | 0.906178 | − | 0.422896i | \(-0.138986\pi\) | ||||
0.906178 | + | 0.422896i | \(0.138986\pi\) | |||||||
\(410\) | 4.68830 | 0.231539 | ||||||||
\(411\) | 5.44025 | 0.268348 | ||||||||
\(412\) | 8.52505 | 0.419999 | ||||||||
\(413\) | −1.59748 | −0.0786067 | ||||||||
\(414\) | 17.8980 | 0.879639 | ||||||||
\(415\) | −8.23367 | −0.404175 | ||||||||
\(416\) | −4.24985 | −0.208366 | ||||||||
\(417\) | 4.30747 | 0.210938 | ||||||||
\(418\) | −13.6228 | −0.666314 | ||||||||
\(419\) | −1.67822 | −0.0819862 | −0.0409931 | − | 0.999159i | \(-0.513052\pi\) | ||||
−0.0409931 | + | 0.999159i | \(0.513052\pi\) | |||||||
\(420\) | 1.56155 | 0.0761960 | ||||||||
\(421\) | −8.60926 | −0.419589 | −0.209795 | − | 0.977745i | \(-0.567280\pi\) | ||||
−0.209795 | + | 0.977745i | \(0.567280\pi\) | |||||||
\(422\) | 2.00644 | 0.0976721 | ||||||||
\(423\) | −7.15842 | −0.348054 | ||||||||
\(424\) | −2.87689 | −0.139714 | ||||||||
\(425\) | −29.8652 | −1.44868 | ||||||||
\(426\) | 4.14964 | 0.201051 | ||||||||
\(427\) | 23.9716 | 1.16007 | ||||||||
\(428\) | 11.0371 | 0.533499 | ||||||||
\(429\) | 5.10141 | 0.246298 | ||||||||
\(430\) | −3.50580 | −0.169065 | ||||||||
\(431\) | 20.5339 | 0.989081 | 0.494540 | − | 0.869155i | \(-0.335336\pi\) | ||||
0.494540 | + | 0.869155i | \(0.335336\pi\) | |||||||
\(432\) | −2.93816 | −0.141362 | ||||||||
\(433\) | 0.678127 | 0.0325887 | 0.0162944 | − | 0.999867i | \(-0.494813\pi\) | ||||
0.0162944 | + | 0.999867i | \(0.494813\pi\) | |||||||
\(434\) | 10.9104 | 0.523714 | ||||||||
\(435\) | −0.0642926 | −0.00308260 | ||||||||
\(436\) | −4.51919 | −0.216430 | ||||||||
\(437\) | 37.9915 | 1.81738 | ||||||||
\(438\) | −4.68644 | −0.223927 | ||||||||
\(439\) | −33.4206 | −1.59508 | −0.797539 | − | 0.603267i | \(-0.793865\pi\) | ||||
−0.797539 | + | 0.603267i | \(0.793865\pi\) | |||||||
\(440\) | 2.46014 | 0.117283 | ||||||||
\(441\) | −3.95093 | −0.188140 | ||||||||
\(442\) | −32.5561 | −1.54853 | ||||||||
\(443\) | 21.7843 | 1.03500 | 0.517501 | − | 0.855682i | \(-0.326862\pi\) | ||||
0.517501 | + | 0.855682i | \(0.326862\pi\) | |||||||
\(444\) | −1.67652 | −0.0795642 | ||||||||
\(445\) | −16.5214 | −0.783190 | ||||||||
\(446\) | −17.0201 | −0.805925 | ||||||||
\(447\) | −9.18250 | −0.434317 | ||||||||
\(448\) | −2.90570 | −0.137282 | ||||||||
\(449\) | −15.6603 | −0.739057 | −0.369529 | − | 0.929219i | \(-0.620481\pi\) | ||||
−0.369529 | + | 0.929219i | \(0.620481\pi\) | |||||||
\(450\) | −10.6735 | −0.503153 | ||||||||
\(451\) | 10.4719 | 0.493104 | ||||||||
\(452\) | −5.82616 | −0.274039 | ||||||||
\(453\) | −0.480403 | −0.0225713 | ||||||||
\(454\) | −17.9605 | −0.842929 | ||||||||
\(455\) | 12.9599 | 0.607567 | ||||||||
\(456\) | −2.97586 | −0.139357 | ||||||||
\(457\) | −4.59453 | −0.214923 | −0.107461 | − | 0.994209i | \(-0.534272\pi\) | ||||
−0.107461 | + | 0.994209i | \(0.534272\pi\) | |||||||
\(458\) | −3.85377 | −0.180075 | ||||||||
\(459\) | −22.5078 | −1.05057 | ||||||||
\(460\) | −6.86089 | −0.319891 | ||||||||
\(461\) | −32.2651 | −1.50274 | −0.751368 | − | 0.659884i | \(-0.770606\pi\) | ||||
−0.751368 | + | 0.659884i | \(0.770606\pi\) | |||||||
\(462\) | 3.48793 | 0.162273 | ||||||||
\(463\) | 20.4853 | 0.952033 | 0.476017 | − | 0.879436i | \(-0.342080\pi\) | ||||
0.476017 | + | 0.879436i | \(0.342080\pi\) | |||||||
\(464\) | 0.119634 | 0.00555389 | ||||||||
\(465\) | −2.01787 | −0.0935766 | ||||||||
\(466\) | −19.8538 | −0.919708 | ||||||||
\(467\) | 36.5500 | 1.69133 | 0.845667 | − | 0.533711i | \(-0.179203\pi\) | ||||
0.845667 | + | 0.533711i | \(0.179203\pi\) | |||||||
\(468\) | −11.6352 | −0.537836 | ||||||||
\(469\) | −3.17970 | −0.146825 | ||||||||
\(470\) | 2.74405 | 0.126574 | ||||||||
\(471\) | −0.522045 | −0.0240546 | ||||||||
\(472\) | −0.549773 | −0.0253053 | ||||||||
\(473\) | −7.83065 | −0.360054 | ||||||||
\(474\) | −0.218186 | −0.0100216 | ||||||||
\(475\) | −22.6563 | −1.03954 | ||||||||
\(476\) | −22.2592 | −1.02025 | ||||||||
\(477\) | −7.87631 | −0.360632 | ||||||||
\(478\) | 11.1250 | 0.508844 | ||||||||
\(479\) | −36.6751 | −1.67573 | −0.837864 | − | 0.545879i | \(-0.816196\pi\) | ||||
−0.837864 | + | 0.545879i | \(0.816196\pi\) | |||||||
\(480\) | 0.537410 | 0.0245293 | ||||||||
\(481\) | −13.9140 | −0.634424 | ||||||||
\(482\) | 17.2740 | 0.786809 | ||||||||
\(483\) | −9.72720 | −0.442603 | ||||||||
\(484\) | −5.50496 | −0.250225 | ||||||||
\(485\) | 15.6426 | 0.710296 | ||||||||
\(486\) | −12.2499 | −0.555665 | ||||||||
\(487\) | 34.8684 | 1.58004 | 0.790020 | − | 0.613081i | \(-0.210070\pi\) | ||||
0.790020 | + | 0.613081i | \(0.210070\pi\) | |||||||
\(488\) | 8.24985 | 0.373453 | ||||||||
\(489\) | 6.83307 | 0.309002 | ||||||||
\(490\) | 1.51452 | 0.0684190 | ||||||||
\(491\) | −2.32389 | −0.104876 | −0.0524378 | − | 0.998624i | \(-0.516699\pi\) | ||||
−0.0524378 | + | 0.998624i | \(0.516699\pi\) | |||||||
\(492\) | 2.28756 | 0.103131 | ||||||||
\(493\) | 0.916461 | 0.0412753 | ||||||||
\(494\) | −24.6976 | −1.11120 | ||||||||
\(495\) | 6.73533 | 0.302731 | ||||||||
\(496\) | 3.75481 | 0.168596 | ||||||||
\(497\) | 23.5467 | 1.05622 | ||||||||
\(498\) | −4.01744 | −0.180026 | ||||||||
\(499\) | 25.6747 | 1.14936 | 0.574680 | − | 0.818378i | \(-0.305127\pi\) | ||||
0.574680 | + | 0.818378i | \(0.305127\pi\) | |||||||
\(500\) | 9.33890 | 0.417648 | ||||||||
\(501\) | 10.1602 | 0.453925 | ||||||||
\(502\) | −2.07362 | −0.0925504 | ||||||||
\(503\) | −35.8649 | −1.59914 | −0.799569 | − | 0.600575i | \(-0.794939\pi\) | ||||
−0.799569 | + | 0.600575i | \(0.794939\pi\) | |||||||
\(504\) | −7.95518 | −0.354352 | ||||||||
\(505\) | 13.6747 | 0.608518 | ||||||||
\(506\) | −15.3247 | −0.681265 | ||||||||
\(507\) | 2.59173 | 0.115103 | ||||||||
\(508\) | −5.97102 | −0.264921 | ||||||||
\(509\) | 26.1779 | 1.16032 | 0.580158 | − | 0.814504i | \(-0.302991\pi\) | ||||
0.580158 | + | 0.814504i | \(0.302991\pi\) | |||||||
\(510\) | 4.11683 | 0.182296 | ||||||||
\(511\) | −26.5928 | −1.17639 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −17.0748 | −0.753872 | ||||||||
\(514\) | 26.0799 | 1.15034 | ||||||||
\(515\) | −8.94688 | −0.394246 | ||||||||
\(516\) | −1.71058 | −0.0753041 | ||||||||
\(517\) | 6.12920 | 0.269562 | ||||||||
\(518\) | −9.51327 | −0.417989 | ||||||||
\(519\) | 7.57150 | 0.332352 | ||||||||
\(520\) | 4.46014 | 0.195590 | ||||||||
\(521\) | −30.9190 | −1.35459 | −0.677294 | − | 0.735713i | \(-0.736847\pi\) | ||||
−0.677294 | + | 0.735713i | \(0.736847\pi\) | |||||||
\(522\) | 0.327533 | 0.0143357 | ||||||||
\(523\) | −17.6068 | −0.769892 | −0.384946 | − | 0.922939i | \(-0.625780\pi\) | ||||
−0.384946 | + | 0.922939i | \(0.625780\pi\) | |||||||
\(524\) | 11.3535 | 0.495979 | ||||||||
\(525\) | 5.80082 | 0.253169 | ||||||||
\(526\) | 9.93935 | 0.433376 | ||||||||
\(527\) | 28.7638 | 1.25297 | ||||||||
\(528\) | 1.20037 | 0.0522395 | ||||||||
\(529\) | 19.7377 | 0.858162 | ||||||||
\(530\) | 3.01925 | 0.131148 | ||||||||
\(531\) | −1.50516 | −0.0653183 | ||||||||
\(532\) | −16.8862 | −0.732111 | ||||||||
\(533\) | 18.9852 | 0.822340 | ||||||||
\(534\) | −8.06126 | −0.348845 | ||||||||
\(535\) | −11.5832 | −0.500787 | ||||||||
\(536\) | −1.09430 | −0.0472664 | ||||||||
\(537\) | −6.75256 | −0.291395 | ||||||||
\(538\) | −1.00000 | −0.0431131 | ||||||||
\(539\) | 3.38287 | 0.145711 | ||||||||
\(540\) | 3.08354 | 0.132694 | ||||||||
\(541\) | 4.03939 | 0.173667 | 0.0868336 | − | 0.996223i | \(-0.472325\pi\) | ||||
0.0868336 | + | 0.996223i | \(0.472325\pi\) | |||||||
\(542\) | −9.40702 | −0.404066 | ||||||||
\(543\) | −11.1397 | −0.478051 | ||||||||
\(544\) | −7.66052 | −0.328442 | ||||||||
\(545\) | 4.74280 | 0.203159 | ||||||||
\(546\) | 6.32348 | 0.270620 | ||||||||
\(547\) | −40.7182 | −1.74098 | −0.870491 | − | 0.492184i | \(-0.836199\pi\) | ||||
−0.870491 | + | 0.492184i | \(0.836199\pi\) | |||||||
\(548\) | 10.6240 | 0.453835 | ||||||||
\(549\) | 22.5863 | 0.963960 | ||||||||
\(550\) | 9.13888 | 0.389683 | ||||||||
\(551\) | 0.695244 | 0.0296184 | ||||||||
\(552\) | −3.34762 | −0.142484 | ||||||||
\(553\) | −1.23807 | −0.0526483 | ||||||||
\(554\) | −1.10380 | −0.0468960 | ||||||||
\(555\) | 1.75948 | 0.0746857 | ||||||||
\(556\) | 8.41186 | 0.356742 | ||||||||
\(557\) | 19.3259 | 0.818866 | 0.409433 | − | 0.912340i | \(-0.365727\pi\) | ||||
0.409433 | + | 0.912340i | \(0.365727\pi\) | |||||||
\(558\) | 10.2799 | 0.435181 | ||||||||
\(559\) | −14.1967 | −0.600455 | ||||||||
\(560\) | 3.04948 | 0.128864 | ||||||||
\(561\) | 9.19548 | 0.388233 | ||||||||
\(562\) | 16.2356 | 0.684859 | ||||||||
\(563\) | −3.59240 | −0.151402 | −0.0757008 | − | 0.997131i | \(-0.524119\pi\) | ||||
−0.0757008 | + | 0.997131i | \(0.524119\pi\) | |||||||
\(564\) | 1.33890 | 0.0563779 | ||||||||
\(565\) | 6.11444 | 0.257237 | ||||||||
\(566\) | −22.0635 | −0.927400 | ||||||||
\(567\) | −19.4938 | −0.818662 | ||||||||
\(568\) | 8.10363 | 0.340021 | ||||||||
\(569\) | 15.0425 | 0.630616 | 0.315308 | − | 0.948989i | \(-0.397892\pi\) | ||||
0.315308 | + | 0.948989i | \(0.397892\pi\) | |||||||
\(570\) | 3.12311 | 0.130812 | ||||||||
\(571\) | −27.0643 | −1.13261 | −0.566303 | − | 0.824197i | \(-0.691627\pi\) | ||||
−0.566303 | + | 0.824197i | \(0.691627\pi\) | |||||||
\(572\) | 9.96230 | 0.416545 | ||||||||
\(573\) | −0.633072 | −0.0264470 | ||||||||
\(574\) | 12.9805 | 0.541797 | ||||||||
\(575\) | −25.4867 | −1.06287 | ||||||||
\(576\) | −2.73778 | −0.114074 | ||||||||
\(577\) | 16.5926 | 0.690761 | 0.345380 | − | 0.938463i | \(-0.387750\pi\) | ||||
0.345380 | + | 0.938463i | \(0.387750\pi\) | |||||||
\(578\) | −41.6835 | −1.73380 | ||||||||
\(579\) | 0.782187 | 0.0325066 | ||||||||
\(580\) | −0.125554 | −0.00521335 | ||||||||
\(581\) | −22.7966 | −0.945762 | ||||||||
\(582\) | 7.63249 | 0.316377 | ||||||||
\(583\) | 6.74387 | 0.279303 | ||||||||
\(584\) | −9.15191 | −0.378709 | ||||||||
\(585\) | 12.2109 | 0.504859 | ||||||||
\(586\) | −12.1496 | −0.501897 | ||||||||
\(587\) | −4.01362 | −0.165660 | −0.0828298 | − | 0.996564i | \(-0.526396\pi\) | ||||
−0.0828298 | + | 0.996564i | \(0.526396\pi\) | |||||||
\(588\) | 0.738977 | 0.0304749 | ||||||||
\(589\) | 21.8207 | 0.899108 | ||||||||
\(590\) | 0.576976 | 0.0237537 | ||||||||
\(591\) | −11.4545 | −0.471174 | ||||||||
\(592\) | −3.27400 | −0.134560 | ||||||||
\(593\) | 13.1761 | 0.541076 | 0.270538 | − | 0.962709i | \(-0.412798\pi\) | ||||
0.270538 | + | 0.962709i | \(0.412798\pi\) | |||||||
\(594\) | 6.88748 | 0.282597 | ||||||||
\(595\) | 23.3606 | 0.957691 | ||||||||
\(596\) | −17.9321 | −0.734526 | ||||||||
\(597\) | −8.56522 | −0.350551 | ||||||||
\(598\) | −27.7830 | −1.13613 | ||||||||
\(599\) | −6.44903 | −0.263500 | −0.131750 | − | 0.991283i | \(-0.542060\pi\) | ||||
−0.131750 | + | 0.991283i | \(0.542060\pi\) | |||||||
\(600\) | 1.99636 | 0.0815009 | ||||||||
\(601\) | 25.6859 | 1.04775 | 0.523876 | − | 0.851795i | \(-0.324486\pi\) | ||||
0.523876 | + | 0.851795i | \(0.324486\pi\) | |||||||
\(602\) | −9.70653 | −0.395608 | ||||||||
\(603\) | −2.99595 | −0.122004 | ||||||||
\(604\) | −0.938156 | −0.0381730 | ||||||||
\(605\) | 5.77735 | 0.234883 | ||||||||
\(606\) | 6.67230 | 0.271043 | ||||||||
\(607\) | −31.9037 | −1.29493 | −0.647466 | − | 0.762095i | \(-0.724171\pi\) | ||||
−0.647466 | + | 0.762095i | \(0.724171\pi\) | |||||||
\(608\) | −5.81141 | −0.235684 | ||||||||
\(609\) | −0.178007 | −0.00721322 | ||||||||
\(610\) | −8.65807 | −0.350555 | ||||||||
\(611\) | 11.1120 | 0.449543 | ||||||||
\(612\) | −20.9728 | −0.847776 | ||||||||
\(613\) | 20.5761 | 0.831062 | 0.415531 | − | 0.909579i | \(-0.363596\pi\) | ||||
0.415531 | + | 0.909579i | \(0.363596\pi\) | |||||||
\(614\) | 22.7400 | 0.917712 | ||||||||
\(615\) | −2.40075 | −0.0968074 | ||||||||
\(616\) | 6.81141 | 0.274439 | ||||||||
\(617\) | 35.3614 | 1.42360 | 0.711798 | − | 0.702384i | \(-0.247881\pi\) | ||||
0.711798 | + | 0.702384i | \(0.247881\pi\) | |||||||
\(618\) | −4.36543 | −0.175604 | ||||||||
\(619\) | 44.9921 | 1.80839 | 0.904193 | − | 0.427124i | \(-0.140473\pi\) | ||||
0.904193 | + | 0.427124i | \(0.140473\pi\) | |||||||
\(620\) | −3.94060 | −0.158258 | ||||||||
\(621\) | −19.2079 | −0.770788 | ||||||||
\(622\) | 10.9941 | 0.440822 | ||||||||
\(623\) | −45.7429 | −1.83265 | ||||||||
\(624\) | 2.17623 | 0.0871189 | ||||||||
\(625\) | 9.69194 | 0.387678 | ||||||||
\(626\) | 25.0357 | 1.00063 | ||||||||
\(627\) | 6.97586 | 0.278589 | ||||||||
\(628\) | −1.01948 | −0.0406816 | ||||||||
\(629\) | −25.0805 | −1.00003 | ||||||||
\(630\) | 8.34882 | 0.332625 | ||||||||
\(631\) | −39.3156 | −1.56513 | −0.782565 | − | 0.622569i | \(-0.786089\pi\) | ||||
−0.782565 | + | 0.622569i | \(0.786089\pi\) | |||||||
\(632\) | −0.426084 | −0.0169487 | ||||||||
\(633\) | −1.02744 | −0.0408372 | ||||||||
\(634\) | −29.2168 | −1.16035 | ||||||||
\(635\) | 6.26647 | 0.248677 | ||||||||
\(636\) | 1.47318 | 0.0584152 | ||||||||
\(637\) | 6.13302 | 0.242999 | ||||||||
\(638\) | −0.280441 | −0.0111028 | ||||||||
\(639\) | 22.1860 | 0.877664 | ||||||||
\(640\) | 1.04948 | 0.0414844 | ||||||||
\(641\) | 28.3628 | 1.12026 | 0.560132 | − | 0.828403i | \(-0.310750\pi\) | ||||
0.560132 | + | 0.828403i | \(0.310750\pi\) | |||||||
\(642\) | −5.65180 | −0.223059 | ||||||||
\(643\) | 46.4066 | 1.83010 | 0.915049 | − | 0.403343i | \(-0.132152\pi\) | ||||
0.915049 | + | 0.403343i | \(0.132152\pi\) | |||||||
\(644\) | −18.9958 | −0.748538 | ||||||||
\(645\) | 1.79522 | 0.0706867 | ||||||||
\(646\) | −44.5184 | −1.75155 | ||||||||
\(647\) | 9.47203 | 0.372384 | 0.186192 | − | 0.982513i | \(-0.440385\pi\) | ||||
0.186192 | + | 0.982513i | \(0.440385\pi\) | |||||||
\(648\) | −6.70880 | −0.263547 | ||||||||
\(649\) | 1.28875 | 0.0505879 | ||||||||
\(650\) | 16.5684 | 0.649868 | ||||||||
\(651\) | −5.58689 | −0.218968 | ||||||||
\(652\) | 13.3440 | 0.522591 | ||||||||
\(653\) | 25.5129 | 0.998398 | 0.499199 | − | 0.866487i | \(-0.333628\pi\) | ||||
0.499199 | + | 0.866487i | \(0.333628\pi\) | |||||||
\(654\) | 2.31415 | 0.0904903 | ||||||||
\(655\) | −11.9153 | −0.465568 | ||||||||
\(656\) | 4.46726 | 0.174417 | ||||||||
\(657\) | −25.0560 | −0.977526 | ||||||||
\(658\) | 7.59748 | 0.296180 | ||||||||
\(659\) | 11.7305 | 0.456955 | 0.228478 | − | 0.973549i | \(-0.426625\pi\) | ||||
0.228478 | + | 0.973549i | \(0.426625\pi\) | |||||||
\(660\) | −1.25977 | −0.0490364 | ||||||||
\(661\) | −20.7855 | −0.808462 | −0.404231 | − | 0.914657i | \(-0.632461\pi\) | ||||
−0.404231 | + | 0.914657i | \(0.632461\pi\) | |||||||
\(662\) | −15.9156 | −0.618578 | ||||||||
\(663\) | 16.6710 | 0.647450 | ||||||||
\(664\) | −7.84547 | −0.304463 | ||||||||
\(665\) | 17.7218 | 0.687221 | ||||||||
\(666\) | −8.96349 | −0.347328 | ||||||||
\(667\) | 0.782099 | 0.0302830 | ||||||||
\(668\) | 19.8414 | 0.767687 | ||||||||
\(669\) | 8.71550 | 0.336961 | ||||||||
\(670\) | 1.14844 | 0.0443682 | ||||||||
\(671\) | −19.3389 | −0.746570 | ||||||||
\(672\) | 1.48793 | 0.0573981 | ||||||||
\(673\) | −5.05829 | −0.194983 | −0.0974914 | − | 0.995236i | \(-0.531082\pi\) | ||||
−0.0974914 | + | 0.995236i | \(0.531082\pi\) | |||||||
\(674\) | 35.1956 | 1.35568 | ||||||||
\(675\) | 11.4547 | 0.440890 | ||||||||
\(676\) | 5.06126 | 0.194664 | ||||||||
\(677\) | 14.5131 | 0.557784 | 0.278892 | − | 0.960323i | \(-0.410033\pi\) | ||||
0.278892 | + | 0.960323i | \(0.410033\pi\) | |||||||
\(678\) | 2.98341 | 0.114577 | ||||||||
\(679\) | 43.3099 | 1.66208 | ||||||||
\(680\) | 8.03957 | 0.308303 | ||||||||
\(681\) | 9.19707 | 0.352433 | ||||||||
\(682\) | −8.80184 | −0.337040 | ||||||||
\(683\) | −48.9508 | −1.87305 | −0.936525 | − | 0.350601i | \(-0.885977\pi\) | ||||
−0.936525 | + | 0.350601i | \(0.885977\pi\) | |||||||
\(684\) | −15.9104 | −0.608348 | ||||||||
\(685\) | −11.1497 | −0.426008 | ||||||||
\(686\) | −16.1467 | −0.616483 | ||||||||
\(687\) | 1.97341 | 0.0752902 | ||||||||
\(688\) | −3.34051 | −0.127356 | ||||||||
\(689\) | 12.2264 | 0.465788 | ||||||||
\(690\) | 3.51327 | 0.133748 | ||||||||
\(691\) | −35.2573 | −1.34125 | −0.670626 | − | 0.741795i | \(-0.733975\pi\) | ||||
−0.670626 | + | 0.741795i | \(0.733975\pi\) | |||||||
\(692\) | 14.7860 | 0.562080 | ||||||||
\(693\) | 18.6482 | 0.708385 | ||||||||
\(694\) | 24.8903 | 0.944823 | ||||||||
\(695\) | −8.82808 | −0.334868 | ||||||||
\(696\) | −0.0612614 | −0.00232211 | ||||||||
\(697\) | 34.2215 | 1.29623 | ||||||||
\(698\) | −1.73175 | −0.0655477 | ||||||||
\(699\) | 10.1666 | 0.384534 | ||||||||
\(700\) | 11.3281 | 0.428164 | ||||||||
\(701\) | 21.9096 | 0.827515 | 0.413757 | − | 0.910387i | \(-0.364216\pi\) | ||||
0.413757 | + | 0.910387i | \(0.364216\pi\) | |||||||
\(702\) | 12.4867 | 0.471281 | ||||||||
\(703\) | −19.0265 | −0.717599 | ||||||||
\(704\) | 2.34415 | 0.0883485 | ||||||||
\(705\) | −1.40515 | −0.0529211 | ||||||||
\(706\) | 21.3682 | 0.804204 | ||||||||
\(707\) | 37.8613 | 1.42392 | ||||||||
\(708\) | 0.281523 | 0.0105803 | ||||||||
\(709\) | 7.16159 | 0.268959 | 0.134480 | − | 0.990916i | \(-0.457064\pi\) | ||||
0.134480 | + | 0.990916i | \(0.457064\pi\) | |||||||
\(710\) | −8.50461 | −0.319172 | ||||||||
\(711\) | −1.16653 | −0.0437481 | ||||||||
\(712\) | −15.7424 | −0.589973 | ||||||||
\(713\) | 24.5467 | 0.919283 | ||||||||
\(714\) | 11.3983 | 0.426571 | ||||||||
\(715\) | −10.4552 | −0.391004 | ||||||||
\(716\) | −13.1868 | −0.492812 | ||||||||
\(717\) | −5.69678 | −0.212750 | ||||||||
\(718\) | 19.8025 | 0.739023 | ||||||||
\(719\) | 13.0574 | 0.486958 | 0.243479 | − | 0.969906i | \(-0.421711\pi\) | ||||
0.243479 | + | 0.969906i | \(0.421711\pi\) | |||||||
\(720\) | 2.87325 | 0.107080 | ||||||||
\(721\) | −24.7713 | −0.922530 | ||||||||
\(722\) | −14.7725 | −0.549774 | ||||||||
\(723\) | −8.84552 | −0.328969 | ||||||||
\(724\) | −21.7542 | −0.808490 | ||||||||
\(725\) | −0.466405 | −0.0173219 | ||||||||
\(726\) | 2.81893 | 0.104620 | ||||||||
\(727\) | 39.8163 | 1.47670 | 0.738352 | − | 0.674416i | \(-0.235604\pi\) | ||||
0.738352 | + | 0.674416i | \(0.235604\pi\) | |||||||
\(728\) | 12.3488 | 0.457678 | ||||||||
\(729\) | −13.8536 | −0.513096 | ||||||||
\(730\) | 9.60476 | 0.355488 | ||||||||
\(731\) | −25.5900 | −0.946481 | ||||||||
\(732\) | −4.22452 | −0.156143 | ||||||||
\(733\) | −10.9054 | −0.402799 | −0.201399 | − | 0.979509i | \(-0.564549\pi\) | ||||
−0.201399 | + | 0.979509i | \(0.564549\pi\) | |||||||
\(734\) | 1.72720 | 0.0637520 | ||||||||
\(735\) | −0.775543 | −0.0286063 | ||||||||
\(736\) | −6.53741 | −0.240972 | ||||||||
\(737\) | 2.56520 | 0.0944902 | ||||||||
\(738\) | 12.2304 | 0.450206 | ||||||||
\(739\) | −51.0337 | −1.87731 | −0.938653 | − | 0.344862i | \(-0.887926\pi\) | ||||
−0.938653 | + | 0.344862i | \(0.887926\pi\) | |||||||
\(740\) | 3.43600 | 0.126310 | ||||||||
\(741\) | 12.6470 | 0.464598 | ||||||||
\(742\) | 8.35940 | 0.306883 | ||||||||
\(743\) | −20.1783 | −0.740269 | −0.370135 | − | 0.928978i | \(-0.620688\pi\) | ||||
−0.370135 | + | 0.928978i | \(0.620688\pi\) | |||||||
\(744\) | −1.92273 | −0.0704908 | ||||||||
\(745\) | 18.8194 | 0.689488 | ||||||||
\(746\) | 31.3423 | 1.14752 | ||||||||
\(747\) | −21.4792 | −0.785882 | ||||||||
\(748\) | 17.9574 | 0.656588 | ||||||||
\(749\) | −32.0706 | −1.17183 | ||||||||
\(750\) | −4.78219 | −0.174621 | ||||||||
\(751\) | 5.83301 | 0.212850 | 0.106425 | − | 0.994321i | \(-0.466060\pi\) | ||||
0.106425 | + | 0.994321i | \(0.466060\pi\) | |||||||
\(752\) | 2.61468 | 0.0953475 | ||||||||
\(753\) | 1.06184 | 0.0386958 | ||||||||
\(754\) | −0.508429 | −0.0185159 | ||||||||
\(755\) | 0.984577 | 0.0358324 | ||||||||
\(756\) | 8.53741 | 0.310503 | ||||||||
\(757\) | 37.8086 | 1.37418 | 0.687089 | − | 0.726573i | \(-0.258888\pi\) | ||||
0.687089 | + | 0.726573i | \(0.258888\pi\) | |||||||
\(758\) | −21.2263 | −0.770975 | ||||||||
\(759\) | 7.84733 | 0.284840 | ||||||||
\(760\) | 6.09896 | 0.221233 | ||||||||
\(761\) | −22.2483 | −0.806499 | −0.403249 | − | 0.915090i | \(-0.632119\pi\) | ||||
−0.403249 | + | 0.915090i | \(0.632119\pi\) | |||||||
\(762\) | 3.05759 | 0.110765 | ||||||||
\(763\) | 13.1314 | 0.475389 | ||||||||
\(764\) | −1.23630 | −0.0447276 | ||||||||
\(765\) | 22.0106 | 0.795794 | ||||||||
\(766\) | 34.5798 | 1.24942 | ||||||||
\(767\) | 2.33645 | 0.0843644 | ||||||||
\(768\) | 0.512072 | 0.0184778 | ||||||||
\(769\) | 7.40743 | 0.267119 | 0.133559 | − | 0.991041i | \(-0.457359\pi\) | ||||
0.133559 | + | 0.991041i | \(0.457359\pi\) | |||||||
\(770\) | −7.14844 | −0.257612 | ||||||||
\(771\) | −13.3548 | −0.480961 | ||||||||
\(772\) | 1.52749 | 0.0549757 | ||||||||
\(773\) | −28.3513 | −1.01973 | −0.509863 | − | 0.860256i | \(-0.670304\pi\) | ||||
−0.509863 | + | 0.860256i | \(0.670304\pi\) | |||||||
\(774\) | −9.14558 | −0.328731 | ||||||||
\(775\) | −14.6385 | −0.525829 | ||||||||
\(776\) | 14.9051 | 0.535063 | ||||||||
\(777\) | 4.87147 | 0.174763 | ||||||||
\(778\) | −2.21454 | −0.0793952 | ||||||||
\(779\) | 25.9610 | 0.930151 | ||||||||
\(780\) | −2.28391 | −0.0817772 | ||||||||
\(781\) | −18.9961 | −0.679735 | ||||||||
\(782\) | −50.0799 | −1.79085 | ||||||||
\(783\) | −0.351504 | −0.0125617 | ||||||||
\(784\) | 1.44311 | 0.0515398 | ||||||||
\(785\) | 1.06992 | 0.0381872 | ||||||||
\(786\) | −5.81380 | −0.207371 | ||||||||
\(787\) | −4.71084 | −0.167923 | −0.0839616 | − | 0.996469i | \(-0.526757\pi\) | ||||
−0.0839616 | + | 0.996469i | \(0.526757\pi\) | |||||||
\(788\) | −22.3689 | −0.796859 | ||||||||
\(789\) | −5.08966 | −0.181197 | ||||||||
\(790\) | 0.447167 | 0.0159095 | ||||||||
\(791\) | 16.9291 | 0.601929 | ||||||||
\(792\) | 6.41778 | 0.228046 | ||||||||
\(793\) | −35.0607 | −1.24504 | ||||||||
\(794\) | 28.7782 | 1.02130 | ||||||||
\(795\) | −1.54607 | −0.0548335 | ||||||||
\(796\) | −16.7266 | −0.592859 | ||||||||
\(797\) | −17.8537 | −0.632411 | −0.316206 | − | 0.948691i | \(-0.602409\pi\) | ||||
−0.316206 | + | 0.948691i | \(0.602409\pi\) | |||||||
\(798\) | 8.64696 | 0.306099 | ||||||||
\(799\) | 20.0298 | 0.708602 | ||||||||
\(800\) | 3.89859 | 0.137836 | ||||||||
\(801\) | −43.0994 | −1.52284 | ||||||||
\(802\) | 9.00119 | 0.317843 | ||||||||
\(803\) | 21.4535 | 0.757076 | ||||||||
\(804\) | 0.560358 | 0.0197623 | ||||||||
\(805\) | 19.9357 | 0.702641 | ||||||||
\(806\) | −15.9574 | −0.562076 | ||||||||
\(807\) | 0.512072 | 0.0180258 | ||||||||
\(808\) | 13.0300 | 0.458394 | ||||||||
\(809\) | −34.3781 | −1.20867 | −0.604334 | − | 0.796731i | \(-0.706561\pi\) | ||||
−0.604334 | + | 0.796731i | \(0.706561\pi\) | |||||||
\(810\) | 7.04076 | 0.247387 | ||||||||
\(811\) | −29.4277 | −1.03335 | −0.516673 | − | 0.856183i | \(-0.672830\pi\) | ||||
−0.516673 | + | 0.856183i | \(0.672830\pi\) | |||||||
\(812\) | −0.347622 | −0.0121991 | ||||||||
\(813\) | 4.81707 | 0.168942 | ||||||||
\(814\) | 7.67474 | 0.269000 | ||||||||
\(815\) | −14.0043 | −0.490548 | ||||||||
\(816\) | 3.92273 | 0.137323 | ||||||||
\(817\) | −19.4131 | −0.679177 | ||||||||
\(818\) | −36.6526 | −1.28153 | ||||||||
\(819\) | 33.8084 | 1.18136 | ||||||||
\(820\) | −4.68830 | −0.163723 | ||||||||
\(821\) | −29.8950 | −1.04334 | −0.521671 | − | 0.853147i | \(-0.674691\pi\) | ||||
−0.521671 | + | 0.853147i | \(0.674691\pi\) | |||||||
\(822\) | −5.44025 | −0.189751 | ||||||||
\(823\) | 25.6212 | 0.893099 | 0.446550 | − | 0.894759i | \(-0.352653\pi\) | ||||
0.446550 | + | 0.894759i | \(0.352653\pi\) | |||||||
\(824\) | −8.52505 | −0.296984 | ||||||||
\(825\) | −4.67976 | −0.162928 | ||||||||
\(826\) | 1.59748 | 0.0555833 | ||||||||
\(827\) | 33.6271 | 1.16933 | 0.584664 | − | 0.811276i | \(-0.301226\pi\) | ||||
0.584664 | + | 0.811276i | \(0.301226\pi\) | |||||||
\(828\) | −17.8980 | −0.621999 | ||||||||
\(829\) | −9.56047 | −0.332049 | −0.166024 | − | 0.986122i | \(-0.553093\pi\) | ||||
−0.166024 | + | 0.986122i | \(0.553093\pi\) | |||||||
\(830\) | 8.23367 | 0.285795 | ||||||||
\(831\) | 0.565225 | 0.0196074 | ||||||||
\(832\) | 4.24985 | 0.147337 | ||||||||
\(833\) | 11.0550 | 0.383033 | ||||||||
\(834\) | −4.30747 | −0.149156 | ||||||||
\(835\) | −20.8232 | −0.720616 | ||||||||
\(836\) | 13.6228 | 0.471155 | ||||||||
\(837\) | −11.0322 | −0.381329 | ||||||||
\(838\) | 1.67822 | 0.0579730 | ||||||||
\(839\) | −3.75123 | −0.129507 | −0.0647534 | − | 0.997901i | \(-0.520626\pi\) | ||||
−0.0647534 | + | 0.997901i | \(0.520626\pi\) | |||||||
\(840\) | −1.56155 | −0.0538787 | ||||||||
\(841\) | −28.9857 | −0.999506 | ||||||||
\(842\) | 8.60926 | 0.296695 | ||||||||
\(843\) | −8.31380 | −0.286343 | ||||||||
\(844\) | −2.00644 | −0.0690646 | ||||||||
\(845\) | −5.31170 | −0.182728 | ||||||||
\(846\) | 7.15842 | 0.246111 | ||||||||
\(847\) | 15.9958 | 0.549621 | ||||||||
\(848\) | 2.87689 | 0.0987930 | ||||||||
\(849\) | 11.2981 | 0.387750 | ||||||||
\(850\) | 29.8652 | 1.02437 | ||||||||
\(851\) | −21.4035 | −0.733701 | ||||||||
\(852\) | −4.14964 | −0.142164 | ||||||||
\(853\) | 23.1483 | 0.792583 | 0.396291 | − | 0.918125i | \(-0.370297\pi\) | ||||
0.396291 | + | 0.918125i | \(0.370297\pi\) | |||||||
\(854\) | −23.9716 | −0.820292 | ||||||||
\(855\) | 16.6976 | 0.571047 | ||||||||
\(856\) | −11.0371 | −0.377241 | ||||||||
\(857\) | −47.4439 | −1.62065 | −0.810326 | − | 0.585979i | \(-0.800710\pi\) | ||||
−0.810326 | + | 0.585979i | \(0.800710\pi\) | |||||||
\(858\) | −5.10141 | −0.174159 | ||||||||
\(859\) | −10.3635 | −0.353597 | −0.176798 | − | 0.984247i | \(-0.556574\pi\) | ||||
−0.176798 | + | 0.984247i | \(0.556574\pi\) | |||||||
\(860\) | 3.50580 | 0.119547 | ||||||||
\(861\) | −6.64696 | −0.226528 | ||||||||
\(862\) | −20.5339 | −0.699386 | ||||||||
\(863\) | 19.6044 | 0.667342 | 0.333671 | − | 0.942690i | \(-0.391713\pi\) | ||||
0.333671 | + | 0.942690i | \(0.391713\pi\) | |||||||
\(864\) | 2.93816 | 0.0999581 | ||||||||
\(865\) | −15.5176 | −0.527616 | ||||||||
\(866\) | −0.678127 | −0.0230437 | ||||||||
\(867\) | 21.3449 | 0.724912 | ||||||||
\(868\) | −10.9104 | −0.370322 | ||||||||
\(869\) | 0.998805 | 0.0338822 | ||||||||
\(870\) | 0.0642926 | 0.00217972 | ||||||||
\(871\) | 4.65060 | 0.157580 | ||||||||
\(872\) | 4.51919 | 0.153039 | ||||||||
\(873\) | 40.8070 | 1.38111 | ||||||||
\(874\) | −37.9915 | −1.28508 | ||||||||
\(875\) | −27.1361 | −0.917367 | ||||||||
\(876\) | 4.68644 | 0.158340 | ||||||||
\(877\) | 47.4632 | 1.60272 | 0.801359 | − | 0.598183i | \(-0.204111\pi\) | ||||
0.801359 | + | 0.598183i | \(0.204111\pi\) | |||||||
\(878\) | 33.4206 | 1.12789 | ||||||||
\(879\) | 6.22149 | 0.209845 | ||||||||
\(880\) | −2.46014 | −0.0829314 | ||||||||
\(881\) | 56.7144 | 1.91076 | 0.955379 | − | 0.295383i | \(-0.0954473\pi\) | ||||
0.955379 | + | 0.295383i | \(0.0954473\pi\) | |||||||
\(882\) | 3.95093 | 0.133035 | ||||||||
\(883\) | −45.3481 | −1.52609 | −0.763043 | − | 0.646348i | \(-0.776295\pi\) | ||||
−0.763043 | + | 0.646348i | \(0.776295\pi\) | |||||||
\(884\) | 32.5561 | 1.09498 | ||||||||
\(885\) | −0.295453 | −0.00993155 | ||||||||
\(886\) | −21.7843 | −0.731858 | ||||||||
\(887\) | −4.41133 | −0.148118 | −0.0740590 | − | 0.997254i | \(-0.523595\pi\) | ||||
−0.0740590 | + | 0.997254i | \(0.523595\pi\) | |||||||
\(888\) | 1.67652 | 0.0562604 | ||||||||
\(889\) | 17.3500 | 0.581901 | ||||||||
\(890\) | 16.5214 | 0.553799 | ||||||||
\(891\) | 15.7264 | 0.526856 | ||||||||
\(892\) | 17.0201 | 0.569875 | ||||||||
\(893\) | 15.1950 | 0.508480 | ||||||||
\(894\) | 9.18250 | 0.307109 | ||||||||
\(895\) | 13.8393 | 0.462595 | ||||||||
\(896\) | 2.90570 | 0.0970727 | ||||||||
\(897\) | 14.2269 | 0.475023 | ||||||||
\(898\) | 15.6603 | 0.522592 | ||||||||
\(899\) | 0.449204 | 0.0149818 | ||||||||
\(900\) | 10.6735 | 0.355783 | ||||||||
\(901\) | 22.0385 | 0.734209 | ||||||||
\(902\) | −10.4719 | −0.348677 | ||||||||
\(903\) | 4.97044 | 0.165406 | ||||||||
\(904\) | 5.82616 | 0.193775 | ||||||||
\(905\) | 22.8307 | 0.758917 | ||||||||
\(906\) | 0.480403 | 0.0159603 | ||||||||
\(907\) | 48.2246 | 1.60127 | 0.800635 | − | 0.599152i | \(-0.204496\pi\) | ||||
0.800635 | + | 0.599152i | \(0.204496\pi\) | |||||||
\(908\) | 17.9605 | 0.596041 | ||||||||
\(909\) | 35.6733 | 1.18321 | ||||||||
\(910\) | −12.9599 | −0.429615 | ||||||||
\(911\) | −9.66308 | −0.320152 | −0.160076 | − | 0.987105i | \(-0.551174\pi\) | ||||
−0.160076 | + | 0.987105i | \(0.551174\pi\) | |||||||
\(912\) | 2.97586 | 0.0985405 | ||||||||
\(913\) | 18.3910 | 0.608652 | ||||||||
\(914\) | 4.59453 | 0.151974 | ||||||||
\(915\) | 4.43355 | 0.146569 | ||||||||
\(916\) | 3.85377 | 0.127332 | ||||||||
\(917\) | −32.9899 | −1.08942 | ||||||||
\(918\) | 22.5078 | 0.742868 | ||||||||
\(919\) | −2.61634 | −0.0863052 | −0.0431526 | − | 0.999068i | \(-0.513740\pi\) | ||||
−0.0431526 | + | 0.999068i | \(0.513740\pi\) | |||||||
\(920\) | 6.86089 | 0.226197 | ||||||||
\(921\) | −11.6445 | −0.383700 | ||||||||
\(922\) | 32.2651 | 1.06259 | ||||||||
\(923\) | −34.4392 | −1.13358 | ||||||||
\(924\) | −3.48793 | −0.114744 | ||||||||
\(925\) | 12.7640 | 0.419677 | ||||||||
\(926\) | −20.4853 | −0.673189 | ||||||||
\(927\) | −23.3397 | −0.766577 | ||||||||
\(928\) | −0.119634 | −0.00392719 | ||||||||
\(929\) | 34.1534 | 1.12054 | 0.560268 | − | 0.828311i | \(-0.310698\pi\) | ||||
0.560268 | + | 0.828311i | \(0.310698\pi\) | |||||||
\(930\) | 2.01787 | 0.0661686 | ||||||||
\(931\) | 8.38652 | 0.274857 | ||||||||
\(932\) | 19.8538 | 0.650332 | ||||||||
\(933\) | −5.62976 | −0.184310 | ||||||||
\(934\) | −36.5500 | −1.19595 | ||||||||
\(935\) | −18.8460 | −0.616329 | ||||||||
\(936\) | 11.6352 | 0.380308 | ||||||||
\(937\) | −0.840971 | −0.0274733 | −0.0137367 | − | 0.999906i | \(-0.504373\pi\) | ||||
−0.0137367 | + | 0.999906i | \(0.504373\pi\) | |||||||
\(938\) | 3.17970 | 0.103821 | ||||||||
\(939\) | −12.8201 | −0.418367 | ||||||||
\(940\) | −2.74405 | −0.0895012 | ||||||||
\(941\) | −16.3930 | −0.534398 | −0.267199 | − | 0.963641i | \(-0.586098\pi\) | ||||
−0.267199 | + | 0.963641i | \(0.586098\pi\) | |||||||
\(942\) | 0.522045 | 0.0170092 | ||||||||
\(943\) | 29.2043 | 0.951022 | ||||||||
\(944\) | 0.549773 | 0.0178936 | ||||||||
\(945\) | −8.95985 | −0.291464 | ||||||||
\(946\) | 7.83065 | 0.254597 | ||||||||
\(947\) | −46.3550 | −1.50634 | −0.753168 | − | 0.657828i | \(-0.771475\pi\) | ||||
−0.753168 | + | 0.657828i | \(0.771475\pi\) | |||||||
\(948\) | 0.218186 | 0.00708634 | ||||||||
\(949\) | 38.8943 | 1.26256 | ||||||||
\(950\) | 22.6563 | 0.735067 | ||||||||
\(951\) | 14.9611 | 0.485147 | ||||||||
\(952\) | 22.2592 | 0.721424 | ||||||||
\(953\) | −56.3635 | −1.82579 | −0.912896 | − | 0.408191i | \(-0.866160\pi\) | ||||
−0.912896 | + | 0.408191i | \(0.866160\pi\) | |||||||
\(954\) | 7.87631 | 0.255005 | ||||||||
\(955\) | 1.29747 | 0.0419851 | ||||||||
\(956\) | −11.1250 | −0.359807 | ||||||||
\(957\) | 0.143606 | 0.00464212 | ||||||||
\(958\) | 36.6751 | 1.18492 | ||||||||
\(959\) | −30.8702 | −0.996851 | ||||||||
\(960\) | −0.537410 | −0.0173448 | ||||||||
\(961\) | −16.9014 | −0.545206 | ||||||||
\(962\) | 13.9140 | 0.448606 | ||||||||
\(963\) | −30.2172 | −0.973737 | ||||||||
\(964\) | −17.2740 | −0.556358 | ||||||||
\(965\) | −1.60308 | −0.0516049 | ||||||||
\(966\) | 9.72720 | 0.312967 | ||||||||
\(967\) | −50.1806 | −1.61370 | −0.806849 | − | 0.590758i | \(-0.798829\pi\) | ||||
−0.806849 | + | 0.590758i | \(0.798829\pi\) | |||||||
\(968\) | 5.50496 | 0.176936 | ||||||||
\(969\) | 22.7966 | 0.732332 | ||||||||
\(970\) | −15.6426 | −0.502255 | ||||||||
\(971\) | 20.7585 | 0.666173 | 0.333087 | − | 0.942896i | \(-0.391910\pi\) | ||||
0.333087 | + | 0.942896i | \(0.391910\pi\) | |||||||
\(972\) | 12.2499 | 0.392914 | ||||||||
\(973\) | −24.4424 | −0.783586 | ||||||||
\(974\) | −34.8684 | −1.11726 | ||||||||
\(975\) | −8.48423 | −0.271713 | ||||||||
\(976\) | −8.24985 | −0.264071 | ||||||||
\(977\) | 5.01009 | 0.160287 | 0.0801434 | − | 0.996783i | \(-0.474462\pi\) | ||||
0.0801434 | + | 0.996783i | \(0.474462\pi\) | |||||||
\(978\) | −6.83307 | −0.218498 | ||||||||
\(979\) | 36.9027 | 1.17941 | ||||||||
\(980\) | −1.51452 | −0.0483796 | ||||||||
\(981\) | 12.3725 | 0.395025 | ||||||||
\(982\) | 2.32389 | 0.0741583 | ||||||||
\(983\) | −20.6726 | −0.659355 | −0.329677 | − | 0.944094i | \(-0.606940\pi\) | ||||
−0.329677 | + | 0.944094i | \(0.606940\pi\) | |||||||
\(984\) | −2.28756 | −0.0729246 | ||||||||
\(985\) | 23.4757 | 0.747999 | ||||||||
\(986\) | −0.916461 | −0.0291861 | ||||||||
\(987\) | −3.89045 | −0.123834 | ||||||||
\(988\) | 24.6976 | 0.785736 | ||||||||
\(989\) | −21.8383 | −0.694416 | ||||||||
\(990\) | −6.73533 | −0.214063 | ||||||||
\(991\) | 43.4299 | 1.37960 | 0.689799 | − | 0.724001i | \(-0.257699\pi\) | ||||
0.689799 | + | 0.724001i | \(0.257699\pi\) | |||||||
\(992\) | −3.75481 | −0.119215 | ||||||||
\(993\) | 8.14994 | 0.258630 | ||||||||
\(994\) | −23.5467 | −0.746857 | ||||||||
\(995\) | 17.5543 | 0.556508 | ||||||||
\(996\) | 4.01744 | 0.127297 | ||||||||
\(997\) | −4.39494 | −0.139189 | −0.0695946 | − | 0.997575i | \(-0.522171\pi\) | ||||
−0.0695946 | + | 0.997575i | \(0.522171\pi\) | |||||||
\(998\) | −25.6747 | −0.812720 | ||||||||
\(999\) | 9.61951 | 0.304348 |
(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 | 538.2.a.c.1.2 | ✓ | 4 | |
3.2 | odd | 2 | 4842.2.a.j.1.4 | 4 | |||
4.3 | odd | 2 | 4304.2.a.e.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
538.2.a.c.1.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
4304.2.a.e.1.3 | 4 | 4.3 | odd | 2 | |||
4842.2.a.j.1.4 | 4 | 3.2 | odd | 2 |