Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [799,2,Mod(1,799)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(799, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("799.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 799 = 17 \cdot 47 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 799.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: | \(6.38004712150\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 4 x^{19} - 24 x^{18} + 108 x^{17} + 221 x^{16} - 1200 x^{15} - 931 x^{14} + 7128 x^{13} + 1280 x^{12} - 24559 x^{11} + 3411 x^{10} + 49829 x^{9} - 15132 x^{8} - 58070 x^{7} + \cdots + 63 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(-0.0537041\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 799.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.0537041 | −0.0379745 | −0.0189873 | − | 0.999820i | \(-0.506044\pi\) | ||||
−0.0189873 | + | 0.999820i | \(0.506044\pi\) | |||||||
\(3\) | −1.20296 | −0.694527 | −0.347264 | − | 0.937768i | \(-0.612889\pi\) | ||||
−0.347264 | + | 0.937768i | \(0.612889\pi\) | |||||||
\(4\) | −1.99712 | −0.998558 | ||||||||
\(5\) | 1.78333 | 0.797530 | 0.398765 | − | 0.917053i | \(-0.369439\pi\) | ||||
0.398765 | + | 0.917053i | \(0.369439\pi\) | |||||||
\(6\) | 0.0646037 | 0.0263743 | ||||||||
\(7\) | 2.05218 | 0.775652 | 0.387826 | − | 0.921733i | \(-0.373226\pi\) | ||||
0.387826 | + | 0.921733i | \(0.373226\pi\) | |||||||
\(8\) | 0.214661 | 0.0758943 | ||||||||
\(9\) | −1.55290 | −0.517632 | ||||||||
\(10\) | −0.0957722 | −0.0302858 | ||||||||
\(11\) | 1.15863 | 0.349341 | 0.174670 | − | 0.984627i | \(-0.444114\pi\) | ||||
0.174670 | + | 0.984627i | \(0.444114\pi\) | |||||||
\(12\) | 2.40244 | 0.693526 | ||||||||
\(13\) | −1.26010 | −0.349490 | −0.174745 | − | 0.984614i | \(-0.555910\pi\) | ||||
−0.174745 | + | 0.984614i | \(0.555910\pi\) | |||||||
\(14\) | −0.110210 | −0.0294550 | ||||||||
\(15\) | −2.14527 | −0.553906 | ||||||||
\(16\) | 3.98270 | 0.995676 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 0.0833969 | 0.0196568 | ||||||||
\(19\) | −0.107776 | −0.0247254 | −0.0123627 | − | 0.999924i | \(-0.503935\pi\) | ||||
−0.0123627 | + | 0.999924i | \(0.503935\pi\) | |||||||
\(20\) | −3.56152 | −0.796380 | ||||||||
\(21\) | −2.46868 | −0.538711 | ||||||||
\(22\) | −0.0622233 | −0.0132660 | ||||||||
\(23\) | −1.11863 | −0.233250 | −0.116625 | − | 0.993176i | \(-0.537208\pi\) | ||||
−0.116625 | + | 0.993176i | \(0.537208\pi\) | |||||||
\(24\) | −0.258228 | −0.0527106 | ||||||||
\(25\) | −1.81973 | −0.363946 | ||||||||
\(26\) | 0.0676728 | 0.0132717 | ||||||||
\(27\) | 5.47694 | 1.05404 | ||||||||
\(28\) | −4.09844 | −0.774533 | ||||||||
\(29\) | 7.49117 | 1.39108 | 0.695538 | − | 0.718489i | \(-0.255166\pi\) | ||||
0.695538 | + | 0.718489i | \(0.255166\pi\) | |||||||
\(30\) | 0.115210 | 0.0210343 | ||||||||
\(31\) | 7.10636 | 1.27634 | 0.638170 | − | 0.769895i | \(-0.279692\pi\) | ||||
0.638170 | + | 0.769895i | \(0.279692\pi\) | |||||||
\(32\) | −0.643210 | −0.113705 | ||||||||
\(33\) | −1.39378 | −0.242627 | ||||||||
\(34\) | 0.0537041 | 0.00921017 | ||||||||
\(35\) | 3.65972 | 0.618605 | ||||||||
\(36\) | 3.10131 | 0.516886 | ||||||||
\(37\) | 1.62483 | 0.267120 | 0.133560 | − | 0.991041i | \(-0.457359\pi\) | ||||
0.133560 | + | 0.991041i | \(0.457359\pi\) | |||||||
\(38\) | 0.00578799 | 0.000938935 0 | ||||||||
\(39\) | 1.51585 | 0.242730 | ||||||||
\(40\) | 0.382812 | 0.0605280 | ||||||||
\(41\) | 4.79805 | 0.749330 | 0.374665 | − | 0.927160i | \(-0.377758\pi\) | ||||
0.374665 | + | 0.927160i | \(0.377758\pi\) | |||||||
\(42\) | 0.132578 | 0.0204573 | ||||||||
\(43\) | 9.71471 | 1.48148 | 0.740740 | − | 0.671792i | \(-0.234475\pi\) | ||||
0.740740 | + | 0.671792i | \(0.234475\pi\) | |||||||
\(44\) | −2.31392 | −0.348837 | ||||||||
\(45\) | −2.76933 | −0.412827 | ||||||||
\(46\) | 0.0600748 | 0.00885754 | ||||||||
\(47\) | 1.00000 | 0.145865 | ||||||||
\(48\) | −4.79102 | −0.691524 | ||||||||
\(49\) | −2.78855 | −0.398365 | ||||||||
\(50\) | 0.0977269 | 0.0138207 | ||||||||
\(51\) | 1.20296 | 0.168448 | ||||||||
\(52\) | 2.51658 | 0.348986 | ||||||||
\(53\) | 8.88526 | 1.22048 | 0.610242 | − | 0.792215i | \(-0.291072\pi\) | ||||
0.610242 | + | 0.792215i | \(0.291072\pi\) | |||||||
\(54\) | −0.294134 | −0.0400265 | ||||||||
\(55\) | 2.06622 | 0.278610 | ||||||||
\(56\) | 0.440524 | 0.0588675 | ||||||||
\(57\) | 0.129649 | 0.0171725 | ||||||||
\(58\) | −0.402307 | −0.0528255 | ||||||||
\(59\) | −7.34515 | −0.956257 | −0.478129 | − | 0.878290i | \(-0.658685\pi\) | ||||
−0.478129 | + | 0.878290i | \(0.658685\pi\) | |||||||
\(60\) | 4.28435 | 0.553108 | ||||||||
\(61\) | 14.3783 | 1.84095 | 0.920477 | − | 0.390797i | \(-0.127801\pi\) | ||||
0.920477 | + | 0.390797i | \(0.127801\pi\) | |||||||
\(62\) | −0.381641 | −0.0484684 | ||||||||
\(63\) | −3.18682 | −0.401502 | ||||||||
\(64\) | −7.93086 | −0.991358 | ||||||||
\(65\) | −2.24718 | −0.278729 | ||||||||
\(66\) | 0.0748519 | 0.00921363 | ||||||||
\(67\) | −4.99602 | −0.610362 | −0.305181 | − | 0.952294i | \(-0.598717\pi\) | ||||
−0.305181 | + | 0.952294i | \(0.598717\pi\) | |||||||
\(68\) | 1.99712 | 0.242186 | ||||||||
\(69\) | 1.34566 | 0.161998 | ||||||||
\(70\) | −0.196542 | −0.0234912 | ||||||||
\(71\) | 7.36114 | 0.873607 | 0.436803 | − | 0.899557i | \(-0.356111\pi\) | ||||
0.436803 | + | 0.899557i | \(0.356111\pi\) | |||||||
\(72\) | −0.333347 | −0.0392853 | ||||||||
\(73\) | 16.7209 | 1.95704 | 0.978518 | − | 0.206163i | \(-0.0660978\pi\) | ||||
0.978518 | + | 0.206163i | \(0.0660978\pi\) | |||||||
\(74\) | −0.0872599 | −0.0101438 | ||||||||
\(75\) | 2.18905 | 0.252770 | ||||||||
\(76\) | 0.215240 | 0.0246898 | ||||||||
\(77\) | 2.37772 | 0.270967 | ||||||||
\(78\) | −0.0814074 | −0.00921757 | ||||||||
\(79\) | −3.88664 | −0.437281 | −0.218641 | − | 0.975805i | \(-0.570162\pi\) | ||||
−0.218641 | + | 0.975805i | \(0.570162\pi\) | |||||||
\(80\) | 7.10248 | 0.794081 | ||||||||
\(81\) | −1.92983 | −0.214425 | ||||||||
\(82\) | −0.257675 | −0.0284554 | ||||||||
\(83\) | 0.850462 | 0.0933503 | 0.0466752 | − | 0.998910i | \(-0.485137\pi\) | ||||
0.0466752 | + | 0.998910i | \(0.485137\pi\) | |||||||
\(84\) | 4.93025 | 0.537934 | ||||||||
\(85\) | −1.78333 | −0.193429 | ||||||||
\(86\) | −0.521720 | −0.0562585 | ||||||||
\(87\) | −9.01156 | −0.966140 | ||||||||
\(88\) | 0.248714 | 0.0265130 | ||||||||
\(89\) | −8.65991 | −0.917949 | −0.458974 | − | 0.888450i | \(-0.651783\pi\) | ||||
−0.458974 | + | 0.888450i | \(0.651783\pi\) | |||||||
\(90\) | 0.148724 | 0.0156769 | ||||||||
\(91\) | −2.58596 | −0.271083 | ||||||||
\(92\) | 2.23403 | 0.232913 | ||||||||
\(93\) | −8.54864 | −0.886453 | ||||||||
\(94\) | −0.0537041 | −0.00553915 | ||||||||
\(95\) | −0.192200 | −0.0197193 | ||||||||
\(96\) | 0.773754 | 0.0789709 | ||||||||
\(97\) | 6.75261 | 0.685623 | 0.342812 | − | 0.939404i | \(-0.388621\pi\) | ||||
0.342812 | + | 0.939404i | \(0.388621\pi\) | |||||||
\(98\) | 0.149757 | 0.0151277 | ||||||||
\(99\) | −1.79924 | −0.180830 | ||||||||
\(100\) | 3.63421 | 0.363421 | ||||||||
\(101\) | 1.70454 | 0.169608 | 0.0848040 | − | 0.996398i | \(-0.472974\pi\) | ||||
0.0848040 | + | 0.996398i | \(0.472974\pi\) | |||||||
\(102\) | −0.0646037 | −0.00639672 | ||||||||
\(103\) | −18.8444 | −1.85680 | −0.928399 | − | 0.371584i | \(-0.878815\pi\) | ||||
−0.928399 | + | 0.371584i | \(0.878815\pi\) | |||||||
\(104\) | −0.270496 | −0.0265243 | ||||||||
\(105\) | −4.40248 | −0.429638 | ||||||||
\(106\) | −0.477175 | −0.0463473 | ||||||||
\(107\) | −13.7971 | −1.33382 | −0.666909 | − | 0.745140i | \(-0.732383\pi\) | ||||
−0.666909 | + | 0.745140i | \(0.732383\pi\) | |||||||
\(108\) | −10.9381 | −1.05252 | ||||||||
\(109\) | 9.87378 | 0.945736 | 0.472868 | − | 0.881133i | \(-0.343219\pi\) | ||||
0.472868 | + | 0.881133i | \(0.343219\pi\) | |||||||
\(110\) | −0.110965 | −0.0105801 | ||||||||
\(111\) | −1.95460 | −0.185522 | ||||||||
\(112\) | 8.17323 | 0.772298 | ||||||||
\(113\) | 7.67911 | 0.722390 | 0.361195 | − | 0.932490i | \(-0.382369\pi\) | ||||
0.361195 | + | 0.932490i | \(0.382369\pi\) | |||||||
\(114\) | −0.00696270 | −0.000652116 0 | ||||||||
\(115\) | −1.99488 | −0.186024 | ||||||||
\(116\) | −14.9607 | −1.38907 | ||||||||
\(117\) | 1.95681 | 0.180907 | ||||||||
\(118\) | 0.394465 | 0.0363134 | ||||||||
\(119\) | −2.05218 | −0.188123 | ||||||||
\(120\) | −0.460507 | −0.0420383 | ||||||||
\(121\) | −9.65757 | −0.877961 | ||||||||
\(122\) | −0.772174 | −0.0699093 | ||||||||
\(123\) | −5.77185 | −0.520430 | ||||||||
\(124\) | −14.1922 | −1.27450 | ||||||||
\(125\) | −12.1618 | −1.08779 | ||||||||
\(126\) | 0.171145 | 0.0152468 | ||||||||
\(127\) | −1.80978 | −0.160592 | −0.0802961 | − | 0.996771i | \(-0.525587\pi\) | ||||
−0.0802961 | + | 0.996771i | \(0.525587\pi\) | |||||||
\(128\) | 1.71234 | 0.151351 | ||||||||
\(129\) | −11.6864 | −1.02893 | ||||||||
\(130\) | 0.120683 | 0.0105846 | ||||||||
\(131\) | −0.145721 | −0.0127317 | −0.00636587 | − | 0.999980i | \(-0.502026\pi\) | ||||
−0.00636587 | + | 0.999980i | \(0.502026\pi\) | |||||||
\(132\) | 2.78355 | 0.242277 | ||||||||
\(133\) | −0.221175 | −0.0191783 | ||||||||
\(134\) | 0.268307 | 0.0231782 | ||||||||
\(135\) | 9.76719 | 0.840626 | ||||||||
\(136\) | −0.214661 | −0.0184071 | ||||||||
\(137\) | 3.85798 | 0.329609 | 0.164805 | − | 0.986326i | \(-0.447301\pi\) | ||||
0.164805 | + | 0.986326i | \(0.447301\pi\) | |||||||
\(138\) | −0.0722673 | −0.00615181 | ||||||||
\(139\) | −8.55663 | −0.725764 | −0.362882 | − | 0.931835i | \(-0.618207\pi\) | ||||
−0.362882 | + | 0.931835i | \(0.618207\pi\) | |||||||
\(140\) | −7.30888 | −0.617713 | ||||||||
\(141\) | −1.20296 | −0.101307 | ||||||||
\(142\) | −0.395323 | −0.0331748 | ||||||||
\(143\) | −1.46000 | −0.122091 | ||||||||
\(144\) | −6.18472 | −0.515394 | ||||||||
\(145\) | 13.3592 | 1.10943 | ||||||||
\(146\) | −0.897981 | −0.0743175 | ||||||||
\(147\) | 3.35451 | 0.276675 | ||||||||
\(148\) | −3.24497 | −0.266735 | ||||||||
\(149\) | −0.389262 | −0.0318896 | −0.0159448 | − | 0.999873i | \(-0.505076\pi\) | ||||
−0.0159448 | + | 0.999873i | \(0.505076\pi\) | |||||||
\(150\) | −0.117561 | −0.00959883 | ||||||||
\(151\) | 3.62728 | 0.295184 | 0.147592 | − | 0.989048i | \(-0.452848\pi\) | ||||
0.147592 | + | 0.989048i | \(0.452848\pi\) | |||||||
\(152\) | −0.0231353 | −0.00187652 | ||||||||
\(153\) | 1.55290 | 0.125544 | ||||||||
\(154\) | −0.127693 | −0.0102898 | ||||||||
\(155\) | 12.6730 | 1.01792 | ||||||||
\(156\) | −3.02733 | −0.242380 | ||||||||
\(157\) | 10.9728 | 0.875724 | 0.437862 | − | 0.899042i | \(-0.355736\pi\) | ||||
0.437862 | + | 0.899042i | \(0.355736\pi\) | |||||||
\(158\) | 0.208729 | 0.0166055 | ||||||||
\(159\) | −10.6886 | −0.847660 | ||||||||
\(160\) | −1.14706 | −0.0906828 | ||||||||
\(161\) | −2.29562 | −0.180920 | ||||||||
\(162\) | 0.103640 | 0.00814269 | ||||||||
\(163\) | −21.3056 | −1.66879 | −0.834393 | − | 0.551170i | \(-0.814182\pi\) | ||||
−0.834393 | + | 0.551170i | \(0.814182\pi\) | |||||||
\(164\) | −9.58227 | −0.748249 | ||||||||
\(165\) | −2.48558 | −0.193502 | ||||||||
\(166\) | −0.0456733 | −0.00354493 | ||||||||
\(167\) | 11.4622 | 0.886971 | 0.443486 | − | 0.896282i | \(-0.353742\pi\) | ||||
0.443486 | + | 0.896282i | \(0.353742\pi\) | |||||||
\(168\) | −0.529931 | −0.0408851 | ||||||||
\(169\) | −11.4121 | −0.877857 | ||||||||
\(170\) | 0.0957722 | 0.00734539 | ||||||||
\(171\) | 0.167364 | 0.0127987 | ||||||||
\(172\) | −19.4014 | −1.47934 | ||||||||
\(173\) | −19.1260 | −1.45412 | −0.727061 | − | 0.686573i | \(-0.759114\pi\) | ||||
−0.727061 | + | 0.686573i | \(0.759114\pi\) | |||||||
\(174\) | 0.483957 | 0.0366887 | ||||||||
\(175\) | −3.73441 | −0.282295 | ||||||||
\(176\) | 4.61449 | 0.347830 | ||||||||
\(177\) | 8.83590 | 0.664147 | ||||||||
\(178\) | 0.465073 | 0.0348587 | ||||||||
\(179\) | 16.0162 | 1.19710 | 0.598552 | − | 0.801084i | \(-0.295743\pi\) | ||||
0.598552 | + | 0.801084i | \(0.295743\pi\) | |||||||
\(180\) | 5.53067 | 0.412232 | ||||||||
\(181\) | 3.82937 | 0.284635 | 0.142317 | − | 0.989821i | \(-0.454545\pi\) | ||||
0.142317 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(182\) | 0.138877 | 0.0102942 | ||||||||
\(183\) | −17.2965 | −1.27859 | ||||||||
\(184\) | −0.240126 | −0.0177023 | ||||||||
\(185\) | 2.89761 | 0.213036 | ||||||||
\(186\) | 0.459097 | 0.0336626 | ||||||||
\(187\) | −1.15863 | −0.0847276 | ||||||||
\(188\) | −1.99712 | −0.145655 | ||||||||
\(189\) | 11.2397 | 0.817565 | ||||||||
\(190\) | 0.0103219 | 0.000748829 0 | ||||||||
\(191\) | −3.92689 | −0.284140 | −0.142070 | − | 0.989857i | \(-0.545376\pi\) | ||||
−0.142070 | + | 0.989857i | \(0.545376\pi\) | |||||||
\(192\) | 9.54048 | 0.688525 | ||||||||
\(193\) | −4.46618 | −0.321482 | −0.160741 | − | 0.986997i | \(-0.551388\pi\) | ||||
−0.160741 | + | 0.986997i | \(0.551388\pi\) | |||||||
\(194\) | −0.362643 | −0.0260362 | ||||||||
\(195\) | 2.70326 | 0.193585 | ||||||||
\(196\) | 5.56906 | 0.397790 | ||||||||
\(197\) | 24.7118 | 1.76064 | 0.880322 | − | 0.474377i | \(-0.157327\pi\) | ||||
0.880322 | + | 0.474377i | \(0.157327\pi\) | |||||||
\(198\) | 0.0966263 | 0.00686693 | ||||||||
\(199\) | −1.93889 | −0.137444 | −0.0687221 | − | 0.997636i | \(-0.521892\pi\) | ||||
−0.0687221 | + | 0.997636i | \(0.521892\pi\) | |||||||
\(200\) | −0.390626 | −0.0276214 | ||||||||
\(201\) | 6.01000 | 0.423913 | ||||||||
\(202\) | −0.0915407 | −0.00644078 | ||||||||
\(203\) | 15.3732 | 1.07899 | ||||||||
\(204\) | −2.40244 | −0.168205 | ||||||||
\(205\) | 8.55652 | 0.597613 | ||||||||
\(206\) | 1.01202 | 0.0705110 | ||||||||
\(207\) | 1.73711 | 0.120737 | ||||||||
\(208\) | −5.01862 | −0.347979 | ||||||||
\(209\) | −0.124872 | −0.00863759 | ||||||||
\(210\) | 0.236431 | 0.0163153 | ||||||||
\(211\) | −10.5427 | −0.725791 | −0.362895 | − | 0.931830i | \(-0.618212\pi\) | ||||
−0.362895 | + | 0.931830i | \(0.618212\pi\) | |||||||
\(212\) | −17.7449 | −1.21872 | ||||||||
\(213\) | −8.85513 | −0.606744 | ||||||||
\(214\) | 0.740961 | 0.0506511 | ||||||||
\(215\) | 17.3246 | 1.18152 | ||||||||
\(216\) | 1.17569 | 0.0799954 | ||||||||
\(217\) | 14.5835 | 0.989995 | ||||||||
\(218\) | −0.530262 | −0.0359139 | ||||||||
\(219\) | −20.1145 | −1.35921 | ||||||||
\(220\) | −4.12649 | −0.278208 | ||||||||
\(221\) | 1.26010 | 0.0847638 | ||||||||
\(222\) | 0.104970 | 0.00704512 | ||||||||
\(223\) | 2.83758 | 0.190018 | 0.0950091 | − | 0.995476i | \(-0.469712\pi\) | ||||
0.0950091 | + | 0.995476i | \(0.469712\pi\) | |||||||
\(224\) | −1.31998 | −0.0881951 | ||||||||
\(225\) | 2.82585 | 0.188390 | ||||||||
\(226\) | −0.412400 | −0.0274324 | ||||||||
\(227\) | 7.87506 | 0.522686 | 0.261343 | − | 0.965246i | \(-0.415835\pi\) | ||||
0.261343 | + | 0.965246i | \(0.415835\pi\) | |||||||
\(228\) | −0.258925 | −0.0171477 | ||||||||
\(229\) | −5.68520 | −0.375689 | −0.187844 | − | 0.982199i | \(-0.560150\pi\) | ||||
−0.187844 | + | 0.982199i | \(0.560150\pi\) | |||||||
\(230\) | 0.107133 | 0.00706416 | ||||||||
\(231\) | −2.86030 | −0.188194 | ||||||||
\(232\) | 1.60807 | 0.105575 | ||||||||
\(233\) | 28.6251 | 1.87529 | 0.937647 | − | 0.347589i | \(-0.113000\pi\) | ||||
0.937647 | + | 0.347589i | \(0.113000\pi\) | |||||||
\(234\) | −0.105089 | −0.00686987 | ||||||||
\(235\) | 1.78333 | 0.116332 | ||||||||
\(236\) | 14.6691 | 0.954878 | ||||||||
\(237\) | 4.67546 | 0.303704 | ||||||||
\(238\) | 0.110210 | 0.00714389 | ||||||||
\(239\) | 12.9200 | 0.835727 | 0.417863 | − | 0.908510i | \(-0.362779\pi\) | ||||
0.417863 | + | 0.908510i | \(0.362779\pi\) | |||||||
\(240\) | −8.54397 | −0.551511 | ||||||||
\(241\) | −14.8446 | −0.956222 | −0.478111 | − | 0.878299i | \(-0.658678\pi\) | ||||
−0.478111 | + | 0.878299i | \(0.658678\pi\) | |||||||
\(242\) | 0.518651 | 0.0333402 | ||||||||
\(243\) | −14.1093 | −0.905113 | ||||||||
\(244\) | −28.7151 | −1.83830 | ||||||||
\(245\) | −4.97291 | −0.317708 | ||||||||
\(246\) | 0.309972 | 0.0197631 | ||||||||
\(247\) | 0.135808 | 0.00864129 | ||||||||
\(248\) | 1.52546 | 0.0968669 | ||||||||
\(249\) | −1.02307 | −0.0648343 | ||||||||
\(250\) | 0.653140 | 0.0413082 | ||||||||
\(251\) | −13.2109 | −0.833862 | −0.416931 | − | 0.908938i | \(-0.636894\pi\) | ||||
−0.416931 | + | 0.908938i | \(0.636894\pi\) | |||||||
\(252\) | 6.36446 | 0.400923 | ||||||||
\(253\) | −1.29608 | −0.0814836 | ||||||||
\(254\) | 0.0971927 | 0.00609841 | ||||||||
\(255\) | 2.14527 | 0.134342 | ||||||||
\(256\) | 15.7698 | 0.985611 | ||||||||
\(257\) | −25.3870 | −1.58360 | −0.791798 | − | 0.610783i | \(-0.790855\pi\) | ||||
−0.791798 | + | 0.610783i | \(0.790855\pi\) | |||||||
\(258\) | 0.627606 | 0.0390731 | ||||||||
\(259\) | 3.33444 | 0.207192 | ||||||||
\(260\) | 4.48789 | 0.278327 | ||||||||
\(261\) | −11.6330 | −0.720066 | ||||||||
\(262\) | 0.00782583 | 0.000483482 0 | ||||||||
\(263\) | −5.69051 | −0.350892 | −0.175446 | − | 0.984489i | \(-0.556137\pi\) | ||||
−0.175446 | + | 0.984489i | \(0.556137\pi\) | |||||||
\(264\) | −0.299192 | −0.0184140 | ||||||||
\(265\) | 15.8454 | 0.973373 | ||||||||
\(266\) | 0.0118780 | 0.000728287 0 | ||||||||
\(267\) | 10.4175 | 0.637540 | ||||||||
\(268\) | 9.97764 | 0.609481 | ||||||||
\(269\) | 22.7426 | 1.38664 | 0.693322 | − | 0.720628i | \(-0.256146\pi\) | ||||
0.693322 | + | 0.720628i | \(0.256146\pi\) | |||||||
\(270\) | −0.524538 | −0.0319224 | ||||||||
\(271\) | −2.26702 | −0.137712 | −0.0688559 | − | 0.997627i | \(-0.521935\pi\) | ||||
−0.0688559 | + | 0.997627i | \(0.521935\pi\) | |||||||
\(272\) | −3.98270 | −0.241487 | ||||||||
\(273\) | 3.11080 | 0.188274 | ||||||||
\(274\) | −0.207189 | −0.0125168 | ||||||||
\(275\) | −2.10840 | −0.127141 | ||||||||
\(276\) | −2.68744 | −0.161765 | ||||||||
\(277\) | −15.2541 | −0.916533 | −0.458266 | − | 0.888815i | \(-0.651529\pi\) | ||||
−0.458266 | + | 0.888815i | \(0.651529\pi\) | |||||||
\(278\) | 0.459526 | 0.0275605 | ||||||||
\(279\) | −11.0354 | −0.660674 | ||||||||
\(280\) | 0.785601 | 0.0469486 | ||||||||
\(281\) | 17.3868 | 1.03721 | 0.518606 | − | 0.855014i | \(-0.326451\pi\) | ||||
0.518606 | + | 0.855014i | \(0.326451\pi\) | |||||||
\(282\) | 0.0646037 | 0.00384709 | ||||||||
\(283\) | −15.6798 | −0.932069 | −0.466034 | − | 0.884767i | \(-0.654318\pi\) | ||||
−0.466034 | + | 0.884767i | \(0.654318\pi\) | |||||||
\(284\) | −14.7011 | −0.872347 | ||||||||
\(285\) | 0.231208 | 0.0136956 | ||||||||
\(286\) | 0.0784078 | 0.00463635 | ||||||||
\(287\) | 9.84647 | 0.581219 | ||||||||
\(288\) | 0.998839 | 0.0588571 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −0.717446 | −0.0421299 | ||||||||
\(291\) | −8.12309 | −0.476184 | ||||||||
\(292\) | −33.3936 | −1.95421 | ||||||||
\(293\) | −8.35007 | −0.487817 | −0.243908 | − | 0.969798i | \(-0.578430\pi\) | ||||
−0.243908 | + | 0.969798i | \(0.578430\pi\) | |||||||
\(294\) | −0.180151 | −0.0105066 | ||||||||
\(295\) | −13.0988 | −0.762644 | ||||||||
\(296\) | 0.348788 | 0.0202729 | ||||||||
\(297\) | 6.34575 | 0.368218 | ||||||||
\(298\) | 0.0209050 | 0.00121099 | ||||||||
\(299\) | 1.40959 | 0.0815185 | ||||||||
\(300\) | −4.37180 | −0.252406 | ||||||||
\(301\) | 19.9364 | 1.14911 | ||||||||
\(302\) | −0.194800 | −0.0112095 | ||||||||
\(303\) | −2.05049 | −0.117797 | ||||||||
\(304\) | −0.429238 | −0.0246185 | ||||||||
\(305\) | 25.6413 | 1.46822 | ||||||||
\(306\) | −0.0833969 | −0.00476748 | ||||||||
\(307\) | −34.3115 | −1.95826 | −0.979130 | − | 0.203234i | \(-0.934855\pi\) | ||||
−0.979130 | + | 0.203234i | \(0.934855\pi\) | |||||||
\(308\) | −4.74859 | −0.270576 | ||||||||
\(309\) | 22.6690 | 1.28960 | ||||||||
\(310\) | −0.680592 | −0.0386550 | ||||||||
\(311\) | 23.3976 | 1.32676 | 0.663379 | − | 0.748284i | \(-0.269122\pi\) | ||||
0.663379 | + | 0.748284i | \(0.269122\pi\) | |||||||
\(312\) | 0.325395 | 0.0184219 | ||||||||
\(313\) | 4.09805 | 0.231636 | 0.115818 | − | 0.993270i | \(-0.463051\pi\) | ||||
0.115818 | + | 0.993270i | \(0.463051\pi\) | |||||||
\(314\) | −0.589283 | −0.0332552 | ||||||||
\(315\) | −5.68316 | −0.320210 | ||||||||
\(316\) | 7.76207 | 0.436651 | ||||||||
\(317\) | −11.7024 | −0.657270 | −0.328635 | − | 0.944457i | \(-0.606589\pi\) | ||||
−0.328635 | + | 0.944457i | \(0.606589\pi\) | |||||||
\(318\) | 0.574021 | 0.0321895 | ||||||||
\(319\) | 8.67952 | 0.485960 | ||||||||
\(320\) | −14.1434 | −0.790638 | ||||||||
\(321\) | 16.5973 | 0.926372 | ||||||||
\(322\) | 0.123284 | 0.00687037 | ||||||||
\(323\) | 0.107776 | 0.00599679 | ||||||||
\(324\) | 3.85409 | 0.214116 | ||||||||
\(325\) | 2.29305 | 0.127195 | ||||||||
\(326\) | 1.14420 | 0.0633714 | ||||||||
\(327\) | −11.8777 | −0.656840 | ||||||||
\(328\) | 1.02996 | 0.0568699 | ||||||||
\(329\) | 2.05218 | 0.113140 | ||||||||
\(330\) | 0.133486 | 0.00734815 | ||||||||
\(331\) | 17.6210 | 0.968540 | 0.484270 | − | 0.874919i | \(-0.339085\pi\) | ||||
0.484270 | + | 0.874919i | \(0.339085\pi\) | |||||||
\(332\) | −1.69847 | −0.0932157 | ||||||||
\(333\) | −2.52319 | −0.138270 | ||||||||
\(334\) | −0.615566 | −0.0336823 | ||||||||
\(335\) | −8.90957 | −0.486782 | ||||||||
\(336\) | −9.83204 | −0.536382 | ||||||||
\(337\) | 14.9955 | 0.816855 | 0.408427 | − | 0.912791i | \(-0.366077\pi\) | ||||
0.408427 | + | 0.912791i | \(0.366077\pi\) | |||||||
\(338\) | 0.612878 | 0.0333362 | ||||||||
\(339\) | −9.23764 | −0.501720 | ||||||||
\(340\) | 3.56152 | 0.193151 | ||||||||
\(341\) | 8.23366 | 0.445878 | ||||||||
\(342\) | −0.00898814 | −0.000486023 0 | ||||||||
\(343\) | −20.0879 | −1.08464 | ||||||||
\(344\) | 2.08537 | 0.112436 | ||||||||
\(345\) | 2.39975 | 0.129198 | ||||||||
\(346\) | 1.02714 | 0.0552196 | ||||||||
\(347\) | −8.87025 | −0.476180 | −0.238090 | − | 0.971243i | \(-0.576521\pi\) | ||||
−0.238090 | + | 0.971243i | \(0.576521\pi\) | |||||||
\(348\) | 17.9971 | 0.964747 | ||||||||
\(349\) | 27.6937 | 1.48241 | 0.741205 | − | 0.671278i | \(-0.234254\pi\) | ||||
0.741205 | + | 0.671278i | \(0.234254\pi\) | |||||||
\(350\) | 0.200553 | 0.0107200 | ||||||||
\(351\) | −6.90151 | −0.368375 | ||||||||
\(352\) | −0.745244 | −0.0397216 | ||||||||
\(353\) | 3.56917 | 0.189968 | 0.0949839 | − | 0.995479i | \(-0.469720\pi\) | ||||
0.0949839 | + | 0.995479i | \(0.469720\pi\) | |||||||
\(354\) | −0.474524 | −0.0252206 | ||||||||
\(355\) | 13.1274 | 0.696728 | ||||||||
\(356\) | 17.2948 | 0.916625 | ||||||||
\(357\) | 2.46868 | 0.130657 | ||||||||
\(358\) | −0.860133 | −0.0454594 | ||||||||
\(359\) | 11.6002 | 0.612235 | 0.306117 | − | 0.951994i | \(-0.400970\pi\) | ||||
0.306117 | + | 0.951994i | \(0.400970\pi\) | |||||||
\(360\) | −0.594468 | −0.0313312 | ||||||||
\(361\) | −18.9884 | −0.999389 | ||||||||
\(362\) | −0.205653 | −0.0108089 | ||||||||
\(363\) | 11.6176 | 0.609768 | ||||||||
\(364\) | 5.16447 | 0.270692 | ||||||||
\(365\) | 29.8189 | 1.56079 | ||||||||
\(366\) | 0.928891 | 0.0485539 | ||||||||
\(367\) | 4.06335 | 0.212105 | 0.106053 | − | 0.994361i | \(-0.466179\pi\) | ||||
0.106053 | + | 0.994361i | \(0.466179\pi\) | |||||||
\(368\) | −4.45516 | −0.232241 | ||||||||
\(369\) | −7.45088 | −0.387877 | ||||||||
\(370\) | −0.155613 | −0.00808996 | ||||||||
\(371\) | 18.2342 | 0.946671 | ||||||||
\(372\) | 17.0726 | 0.885175 | ||||||||
\(373\) | −23.2574 | −1.20423 | −0.602113 | − | 0.798411i | \(-0.705674\pi\) | ||||
−0.602113 | + | 0.798411i | \(0.705674\pi\) | |||||||
\(374\) | 0.0622233 | 0.00321749 | ||||||||
\(375\) | 14.6302 | 0.755498 | ||||||||
\(376\) | 0.214661 | 0.0110703 | ||||||||
\(377\) | −9.43967 | −0.486167 | ||||||||
\(378\) | −0.603616 | −0.0310466 | ||||||||
\(379\) | −25.5834 | −1.31413 | −0.657065 | − | 0.753834i | \(-0.728202\pi\) | ||||
−0.657065 | + | 0.753834i | \(0.728202\pi\) | |||||||
\(380\) | 0.383845 | 0.0196908 | ||||||||
\(381\) | 2.17709 | 0.111536 | ||||||||
\(382\) | 0.210890 | 0.0107901 | ||||||||
\(383\) | 13.1760 | 0.673263 | 0.336632 | − | 0.941636i | \(-0.390712\pi\) | ||||
0.336632 | + | 0.941636i | \(0.390712\pi\) | |||||||
\(384\) | −2.05987 | −0.105117 | ||||||||
\(385\) | 4.24027 | 0.216104 | ||||||||
\(386\) | 0.239852 | 0.0122081 | ||||||||
\(387\) | −15.0859 | −0.766861 | ||||||||
\(388\) | −13.4857 | −0.684635 | ||||||||
\(389\) | 11.8538 | 0.601010 | 0.300505 | − | 0.953780i | \(-0.402845\pi\) | ||||
0.300505 | + | 0.953780i | \(0.402845\pi\) | |||||||
\(390\) | −0.145176 | −0.00735129 | ||||||||
\(391\) | 1.11863 | 0.0565714 | ||||||||
\(392\) | −0.598595 | −0.0302336 | ||||||||
\(393\) | 0.175296 | 0.00884254 | ||||||||
\(394\) | −1.32713 | −0.0668596 | ||||||||
\(395\) | −6.93117 | −0.348745 | ||||||||
\(396\) | 3.59328 | 0.180569 | ||||||||
\(397\) | −13.2441 | −0.664705 | −0.332352 | − | 0.943155i | \(-0.607842\pi\) | ||||
−0.332352 | + | 0.943155i | \(0.607842\pi\) | |||||||
\(398\) | 0.104126 | 0.00521938 | ||||||||
\(399\) | 0.266064 | 0.0133199 | ||||||||
\(400\) | −7.24744 | −0.362372 | ||||||||
\(401\) | −11.3475 | −0.566667 | −0.283333 | − | 0.959021i | \(-0.591440\pi\) | ||||
−0.283333 | + | 0.959021i | \(0.591440\pi\) | |||||||
\(402\) | −0.322762 | −0.0160979 | ||||||||
\(403\) | −8.95476 | −0.446068 | ||||||||
\(404\) | −3.40416 | −0.169363 | ||||||||
\(405\) | −3.44152 | −0.171010 | ||||||||
\(406\) | −0.825606 | −0.0409741 | ||||||||
\(407\) | 1.88258 | 0.0933160 | ||||||||
\(408\) | 0.258228 | 0.0127842 | ||||||||
\(409\) | 14.6735 | 0.725557 | 0.362778 | − | 0.931875i | \(-0.381828\pi\) | ||||
0.362778 | + | 0.931875i | \(0.381828\pi\) | |||||||
\(410\) | −0.459520 | −0.0226941 | ||||||||
\(411\) | −4.64098 | −0.228923 | ||||||||
\(412\) | 37.6345 | 1.85412 | ||||||||
\(413\) | −15.0736 | −0.741722 | ||||||||
\(414\) | −0.0932899 | −0.00458495 | ||||||||
\(415\) | 1.51666 | 0.0744497 | ||||||||
\(416\) | 0.810512 | 0.0397386 | ||||||||
\(417\) | 10.2933 | 0.504063 | ||||||||
\(418\) | 0.00670615 | 0.000328008 0 | ||||||||
\(419\) | −27.1956 | −1.32859 | −0.664296 | − | 0.747470i | \(-0.731268\pi\) | ||||
−0.664296 | + | 0.747470i | \(0.731268\pi\) | |||||||
\(420\) | 8.79227 | 0.429019 | ||||||||
\(421\) | 31.1619 | 1.51874 | 0.759368 | − | 0.650661i | \(-0.225508\pi\) | ||||
0.759368 | + | 0.650661i | \(0.225508\pi\) | |||||||
\(422\) | 0.566187 | 0.0275616 | ||||||||
\(423\) | −1.55290 | −0.0755044 | ||||||||
\(424\) | 1.90732 | 0.0926278 | ||||||||
\(425\) | 1.81973 | 0.0882698 | ||||||||
\(426\) | 0.475557 | 0.0230408 | ||||||||
\(427\) | 29.5069 | 1.42794 | ||||||||
\(428\) | 27.5544 | 1.33189 | ||||||||
\(429\) | 1.75631 | 0.0847956 | ||||||||
\(430\) | −0.930399 | −0.0448678 | ||||||||
\(431\) | −25.8000 | −1.24274 | −0.621371 | − | 0.783517i | \(-0.713424\pi\) | ||||
−0.621371 | + | 0.783517i | \(0.713424\pi\) | |||||||
\(432\) | 21.8130 | 1.04948 | ||||||||
\(433\) | −17.6242 | −0.846966 | −0.423483 | − | 0.905904i | \(-0.639193\pi\) | ||||
−0.423483 | + | 0.905904i | \(0.639193\pi\) | |||||||
\(434\) | −0.783196 | −0.0375946 | ||||||||
\(435\) | −16.0706 | −0.770526 | ||||||||
\(436\) | −19.7191 | −0.944373 | ||||||||
\(437\) | 0.120561 | 0.00576719 | ||||||||
\(438\) | 1.08023 | 0.0516155 | ||||||||
\(439\) | 22.6146 | 1.07934 | 0.539668 | − | 0.841878i | \(-0.318550\pi\) | ||||
0.539668 | + | 0.841878i | \(0.318550\pi\) | |||||||
\(440\) | 0.443539 | 0.0211449 | ||||||||
\(441\) | 4.33033 | 0.206206 | ||||||||
\(442\) | −0.0676728 | −0.00321887 | ||||||||
\(443\) | −1.75864 | −0.0835554 | −0.0417777 | − | 0.999127i | \(-0.513302\pi\) | ||||
−0.0417777 | + | 0.999127i | \(0.513302\pi\) | |||||||
\(444\) | 3.90356 | 0.185255 | ||||||||
\(445\) | −15.4435 | −0.732092 | ||||||||
\(446\) | −0.152389 | −0.00721585 | ||||||||
\(447\) | 0.468265 | 0.0221482 | ||||||||
\(448\) | −16.2756 | −0.768948 | ||||||||
\(449\) | 3.14730 | 0.148530 | 0.0742650 | − | 0.997239i | \(-0.476339\pi\) | ||||
0.0742650 | + | 0.997239i | \(0.476339\pi\) | |||||||
\(450\) | −0.151760 | −0.00715402 | ||||||||
\(451\) | 5.55918 | 0.261771 | ||||||||
\(452\) | −15.3361 | −0.721348 | ||||||||
\(453\) | −4.36346 | −0.205013 | ||||||||
\(454\) | −0.422923 | −0.0198487 | ||||||||
\(455\) | −4.61163 | −0.216197 | ||||||||
\(456\) | 0.0278307 | 0.00130329 | ||||||||
\(457\) | −22.5430 | −1.05452 | −0.527258 | − | 0.849706i | \(-0.676780\pi\) | ||||
−0.527258 | + | 0.849706i | \(0.676780\pi\) | |||||||
\(458\) | 0.305319 | 0.0142666 | ||||||||
\(459\) | −5.47694 | −0.255641 | ||||||||
\(460\) | 3.98401 | 0.185755 | ||||||||
\(461\) | 4.94533 | 0.230327 | 0.115163 | − | 0.993347i | \(-0.463261\pi\) | ||||
0.115163 | + | 0.993347i | \(0.463261\pi\) | |||||||
\(462\) | 0.153610 | 0.00714657 | ||||||||
\(463\) | 8.12748 | 0.377716 | 0.188858 | − | 0.982004i | \(-0.439521\pi\) | ||||
0.188858 | + | 0.982004i | \(0.439521\pi\) | |||||||
\(464\) | 29.8351 | 1.38506 | ||||||||
\(465\) | −15.2451 | −0.706973 | ||||||||
\(466\) | −1.53729 | −0.0712134 | ||||||||
\(467\) | 38.0876 | 1.76248 | 0.881242 | − | 0.472665i | \(-0.156708\pi\) | ||||
0.881242 | + | 0.472665i | \(0.156708\pi\) | |||||||
\(468\) | −3.90798 | −0.180646 | ||||||||
\(469\) | −10.2527 | −0.473428 | ||||||||
\(470\) | −0.0957722 | −0.00441764 | ||||||||
\(471\) | −13.1998 | −0.608214 | ||||||||
\(472\) | −1.57672 | −0.0725744 | ||||||||
\(473\) | 11.2558 | 0.517541 | ||||||||
\(474\) | −0.251091 | −0.0115330 | ||||||||
\(475\) | 0.196122 | 0.00899871 | ||||||||
\(476\) | 4.09844 | 0.187852 | ||||||||
\(477\) | −13.7979 | −0.631762 | ||||||||
\(478\) | −0.693858 | −0.0317363 | ||||||||
\(479\) | 11.8897 | 0.543256 | 0.271628 | − | 0.962402i | \(-0.412438\pi\) | ||||
0.271628 | + | 0.962402i | \(0.412438\pi\) | |||||||
\(480\) | 1.37986 | 0.0629817 | ||||||||
\(481\) | −2.04745 | −0.0933559 | ||||||||
\(482\) | 0.797213 | 0.0363121 | ||||||||
\(483\) | 2.76153 | 0.125654 | ||||||||
\(484\) | 19.2873 | 0.876695 | ||||||||
\(485\) | 12.0421 | 0.546805 | ||||||||
\(486\) | 0.757727 | 0.0343712 | ||||||||
\(487\) | −4.00978 | −0.181700 | −0.0908502 | − | 0.995865i | \(-0.528958\pi\) | ||||
−0.0908502 | + | 0.995865i | \(0.528958\pi\) | |||||||
\(488\) | 3.08647 | 0.139718 | ||||||||
\(489\) | 25.6298 | 1.15902 | ||||||||
\(490\) | 0.267066 | 0.0120648 | ||||||||
\(491\) | 30.9954 | 1.39880 | 0.699402 | − | 0.714729i | \(-0.253450\pi\) | ||||
0.699402 | + | 0.714729i | \(0.253450\pi\) | |||||||
\(492\) | 11.5271 | 0.519680 | ||||||||
\(493\) | −7.49117 | −0.337386 | ||||||||
\(494\) | −0.00729347 | −0.000328149 0 | ||||||||
\(495\) | −3.20863 | −0.144217 | ||||||||
\(496\) | 28.3025 | 1.27082 | ||||||||
\(497\) | 15.1064 | 0.677614 | ||||||||
\(498\) | 0.0549430 | 0.00246205 | ||||||||
\(499\) | −36.6978 | −1.64282 | −0.821410 | − | 0.570338i | \(-0.806812\pi\) | ||||
−0.821410 | + | 0.570338i | \(0.806812\pi\) | |||||||
\(500\) | 24.2886 | 1.08622 | ||||||||
\(501\) | −13.7885 | −0.616025 | ||||||||
\(502\) | 0.709477 | 0.0316655 | ||||||||
\(503\) | 35.8560 | 1.59874 | 0.799369 | − | 0.600840i | \(-0.205167\pi\) | ||||
0.799369 | + | 0.600840i | \(0.205167\pi\) | |||||||
\(504\) | −0.684088 | −0.0304717 | ||||||||
\(505\) | 3.03976 | 0.135267 | ||||||||
\(506\) | 0.0696046 | 0.00309430 | ||||||||
\(507\) | 13.7283 | 0.609695 | ||||||||
\(508\) | 3.61435 | 0.160361 | ||||||||
\(509\) | 30.6393 | 1.35806 | 0.679031 | − | 0.734109i | \(-0.262400\pi\) | ||||
0.679031 | + | 0.734109i | \(0.262400\pi\) | |||||||
\(510\) | −0.115210 | −0.00510157 | ||||||||
\(511\) | 34.3143 | 1.51798 | ||||||||
\(512\) | −4.27158 | −0.188779 | ||||||||
\(513\) | −0.590280 | −0.0260615 | ||||||||
\(514\) | 1.36338 | 0.0601363 | ||||||||
\(515\) | −33.6059 | −1.48085 | ||||||||
\(516\) | 23.3390 | 1.02744 | ||||||||
\(517\) | 1.15863 | 0.0509566 | ||||||||
\(518\) | −0.179073 | −0.00786803 | ||||||||
\(519\) | 23.0077 | 1.00993 | ||||||||
\(520\) | −0.482384 | −0.0211539 | ||||||||
\(521\) | −17.4727 | −0.765491 | −0.382745 | − | 0.923854i | \(-0.625021\pi\) | ||||
−0.382745 | + | 0.923854i | \(0.625021\pi\) | |||||||
\(522\) | 0.624740 | 0.0273441 | ||||||||
\(523\) | −27.0469 | −1.18268 | −0.591339 | − | 0.806423i | \(-0.701401\pi\) | ||||
−0.591339 | + | 0.806423i | \(0.701401\pi\) | |||||||
\(524\) | 0.291022 | 0.0127134 | ||||||||
\(525\) | 4.49234 | 0.196062 | ||||||||
\(526\) | 0.305604 | 0.0133250 | ||||||||
\(527\) | −7.10636 | −0.309558 | ||||||||
\(528\) | −5.55103 | −0.241577 | ||||||||
\(529\) | −21.7487 | −0.945595 | ||||||||
\(530\) | −0.850961 | −0.0369634 | ||||||||
\(531\) | 11.4063 | 0.494989 | ||||||||
\(532\) | 0.441712 | 0.0191506 | ||||||||
\(533\) | −6.04605 | −0.261883 | ||||||||
\(534\) | −0.559462 | −0.0242103 | ||||||||
\(535\) | −24.6048 | −1.06376 | ||||||||
\(536\) | −1.07245 | −0.0463230 | ||||||||
\(537\) | −19.2667 | −0.831421 | ||||||||
\(538\) | −1.22137 | −0.0526571 | ||||||||
\(539\) | −3.23091 | −0.139165 | ||||||||
\(540\) | −19.5062 | −0.839414 | ||||||||
\(541\) | 22.4061 | 0.963314 | 0.481657 | − | 0.876360i | \(-0.340035\pi\) | ||||
0.481657 | + | 0.876360i | \(0.340035\pi\) | |||||||
\(542\) | 0.121748 | 0.00522954 | ||||||||
\(543\) | −4.60657 | −0.197687 | ||||||||
\(544\) | 0.643210 | 0.0275774 | ||||||||
\(545\) | 17.6082 | 0.754253 | ||||||||
\(546\) | −0.167063 | −0.00714962 | ||||||||
\(547\) | 9.91293 | 0.423846 | 0.211923 | − | 0.977286i | \(-0.432027\pi\) | ||||
0.211923 | + | 0.977286i | \(0.432027\pi\) | |||||||
\(548\) | −7.70483 | −0.329134 | ||||||||
\(549\) | −22.3280 | −0.952937 | ||||||||
\(550\) | 0.113229 | 0.00482812 | ||||||||
\(551\) | −0.807365 | −0.0343949 | ||||||||
\(552\) | 0.288861 | 0.0122947 | ||||||||
\(553\) | −7.97609 | −0.339178 | ||||||||
\(554\) | 0.819210 | 0.0348049 | ||||||||
\(555\) | −3.48570 | −0.147960 | ||||||||
\(556\) | 17.0886 | 0.724717 | ||||||||
\(557\) | −14.2121 | −0.602184 | −0.301092 | − | 0.953595i | \(-0.597351\pi\) | ||||
−0.301092 | + | 0.953595i | \(0.597351\pi\) | |||||||
\(558\) | 0.592648 | 0.0250888 | ||||||||
\(559\) | −12.2416 | −0.517763 | ||||||||
\(560\) | 14.5756 | 0.615930 | ||||||||
\(561\) | 1.39378 | 0.0588456 | ||||||||
\(562\) | −0.933744 | −0.0393876 | ||||||||
\(563\) | −25.1266 | −1.05896 | −0.529480 | − | 0.848322i | \(-0.677613\pi\) | ||||
−0.529480 | + | 0.848322i | \(0.677613\pi\) | |||||||
\(564\) | 2.40244 | 0.101161 | ||||||||
\(565\) | 13.6944 | 0.576128 | ||||||||
\(566\) | 0.842070 | 0.0353949 | ||||||||
\(567\) | −3.96035 | −0.166319 | ||||||||
\(568\) | 1.58015 | 0.0663018 | ||||||||
\(569\) | 36.4735 | 1.52905 | 0.764524 | − | 0.644596i | \(-0.222974\pi\) | ||||
0.764524 | + | 0.644596i | \(0.222974\pi\) | |||||||
\(570\) | −0.0124168 | −0.000520082 0 | ||||||||
\(571\) | −34.6876 | −1.45163 | −0.725815 | − | 0.687889i | \(-0.758537\pi\) | ||||
−0.725815 | + | 0.687889i | \(0.758537\pi\) | |||||||
\(572\) | 2.91578 | 0.121915 | ||||||||
\(573\) | 4.72388 | 0.197343 | ||||||||
\(574\) | −0.528796 | −0.0220715 | ||||||||
\(575\) | 2.03560 | 0.0848902 | ||||||||
\(576\) | 12.3158 | 0.513159 | ||||||||
\(577\) | −37.2637 | −1.55131 | −0.775655 | − | 0.631157i | \(-0.782580\pi\) | ||||
−0.775655 | + | 0.631157i | \(0.782580\pi\) | |||||||
\(578\) | −0.0537041 | −0.00223380 | ||||||||
\(579\) | 5.37262 | 0.223278 | ||||||||
\(580\) | −26.6800 | −1.10783 | ||||||||
\(581\) | 1.74530 | 0.0724073 | ||||||||
\(582\) | 0.436243 | 0.0180829 | ||||||||
\(583\) | 10.2948 | 0.426365 | ||||||||
\(584\) | 3.58934 | 0.148528 | ||||||||
\(585\) | 3.48964 | 0.144279 | ||||||||
\(586\) | 0.448433 | 0.0185246 | ||||||||
\(587\) | −23.6599 | −0.976548 | −0.488274 | − | 0.872690i | \(-0.662373\pi\) | ||||
−0.488274 | + | 0.872690i | \(0.662373\pi\) | |||||||
\(588\) | −6.69934 | −0.276276 | ||||||||
\(589\) | −0.765892 | −0.0315580 | ||||||||
\(590\) | 0.703461 | 0.0289610 | ||||||||
\(591\) | −29.7272 | −1.22282 | ||||||||
\(592\) | 6.47121 | 0.265965 | ||||||||
\(593\) | 21.5070 | 0.883187 | 0.441593 | − | 0.897215i | \(-0.354413\pi\) | ||||
0.441593 | + | 0.897215i | \(0.354413\pi\) | |||||||
\(594\) | −0.340793 | −0.0139829 | ||||||||
\(595\) | −3.65972 | −0.150034 | ||||||||
\(596\) | 0.777401 | 0.0318436 | ||||||||
\(597\) | 2.33240 | 0.0954588 | ||||||||
\(598\) | −0.0757005 | −0.00309562 | ||||||||
\(599\) | 37.8168 | 1.54515 | 0.772576 | − | 0.634923i | \(-0.218968\pi\) | ||||
0.772576 | + | 0.634923i | \(0.218968\pi\) | |||||||
\(600\) | 0.469906 | 0.0191838 | ||||||||
\(601\) | 28.8899 | 1.17844 | 0.589222 | − | 0.807971i | \(-0.299434\pi\) | ||||
0.589222 | + | 0.807971i | \(0.299434\pi\) | |||||||
\(602\) | −1.07066 | −0.0436370 | ||||||||
\(603\) | 7.75831 | 0.315943 | ||||||||
\(604\) | −7.24410 | −0.294758 | ||||||||
\(605\) | −17.2227 | −0.700200 | ||||||||
\(606\) | 0.110119 | 0.00447330 | ||||||||
\(607\) | 17.6846 | 0.717794 | 0.358897 | − | 0.933377i | \(-0.383153\pi\) | ||||
0.358897 | + | 0.933377i | \(0.383153\pi\) | |||||||
\(608\) | 0.0693223 | 0.00281139 | ||||||||
\(609\) | −18.4933 | −0.749388 | ||||||||
\(610\) | −1.37704 | −0.0557548 | ||||||||
\(611\) | −1.26010 | −0.0509784 | ||||||||
\(612\) | −3.10131 | −0.125363 | ||||||||
\(613\) | −12.9620 | −0.523529 | −0.261764 | − | 0.965132i | \(-0.584304\pi\) | ||||
−0.261764 | + | 0.965132i | \(0.584304\pi\) | |||||||
\(614\) | 1.84267 | 0.0743640 | ||||||||
\(615\) | −10.2931 | −0.415059 | ||||||||
\(616\) | 0.510405 | 0.0205648 | ||||||||
\(617\) | 14.5493 | 0.585732 | 0.292866 | − | 0.956153i | \(-0.405391\pi\) | ||||
0.292866 | + | 0.956153i | \(0.405391\pi\) | |||||||
\(618\) | −1.21742 | −0.0489718 | ||||||||
\(619\) | −32.4564 | −1.30453 | −0.652267 | − | 0.757989i | \(-0.726182\pi\) | ||||
−0.652267 | + | 0.757989i | \(0.726182\pi\) | |||||||
\(620\) | −25.3094 | −1.01645 | ||||||||
\(621\) | −6.12664 | −0.245854 | ||||||||
\(622\) | −1.25655 | −0.0503830 | ||||||||
\(623\) | −17.7717 | −0.712008 | ||||||||
\(624\) | 6.03719 | 0.241681 | ||||||||
\(625\) | −12.5899 | −0.503598 | ||||||||
\(626\) | −0.220082 | −0.00879626 | ||||||||
\(627\) | 0.150216 | 0.00599904 | ||||||||
\(628\) | −21.9139 | −0.874461 | ||||||||
\(629\) | −1.62483 | −0.0647862 | ||||||||
\(630\) | 0.305209 | 0.0121598 | ||||||||
\(631\) | −33.3426 | −1.32735 | −0.663674 | − | 0.748022i | \(-0.731004\pi\) | ||||
−0.663674 | + | 0.748022i | \(0.731004\pi\) | |||||||
\(632\) | −0.834312 | −0.0331872 | ||||||||
\(633\) | 12.6824 | 0.504081 | ||||||||
\(634\) | 0.628464 | 0.0249595 | ||||||||
\(635\) | −3.22744 | −0.128077 | ||||||||
\(636\) | 21.3463 | 0.846438 | ||||||||
\(637\) | 3.51387 | 0.139225 | ||||||||
\(638\) | −0.466125 | −0.0184541 | ||||||||
\(639\) | −11.4311 | −0.452207 | ||||||||
\(640\) | 3.05367 | 0.120707 | ||||||||
\(641\) | −4.01316 | −0.158510 | −0.0792551 | − | 0.996854i | \(-0.525254\pi\) | ||||
−0.0792551 | + | 0.996854i | \(0.525254\pi\) | |||||||
\(642\) | −0.891344 | −0.0351785 | ||||||||
\(643\) | 10.8029 | 0.426024 | 0.213012 | − | 0.977050i | \(-0.431673\pi\) | ||||
0.213012 | + | 0.977050i | \(0.431673\pi\) | |||||||
\(644\) | 4.58463 | 0.180660 | ||||||||
\(645\) | −20.8407 | −0.820601 | ||||||||
\(646\) | −0.00578799 | −0.000227725 0 | ||||||||
\(647\) | −38.7589 | −1.52377 | −0.761885 | − | 0.647712i | \(-0.775726\pi\) | ||||
−0.761885 | + | 0.647712i | \(0.775726\pi\) | |||||||
\(648\) | −0.414259 | −0.0162736 | ||||||||
\(649\) | −8.51033 | −0.334060 | ||||||||
\(650\) | −0.123146 | −0.00483019 | ||||||||
\(651\) | −17.5434 | −0.687579 | ||||||||
\(652\) | 42.5498 | 1.66638 | ||||||||
\(653\) | −30.5560 | −1.19575 | −0.597874 | − | 0.801590i | \(-0.703988\pi\) | ||||
−0.597874 | + | 0.801590i | \(0.703988\pi\) | |||||||
\(654\) | 0.637882 | 0.0249432 | ||||||||
\(655\) | −0.259869 | −0.0101539 | ||||||||
\(656\) | 19.1092 | 0.746090 | ||||||||
\(657\) | −25.9658 | −1.01302 | ||||||||
\(658\) | −0.110210 | −0.00429645 | ||||||||
\(659\) | −0.720343 | −0.0280606 | −0.0140303 | − | 0.999902i | \(-0.504466\pi\) | ||||
−0.0140303 | + | 0.999902i | \(0.504466\pi\) | |||||||
\(660\) | 4.96399 | 0.193223 | ||||||||
\(661\) | −21.2213 | −0.825412 | −0.412706 | − | 0.910864i | \(-0.635416\pi\) | ||||
−0.412706 | + | 0.910864i | \(0.635416\pi\) | |||||||
\(662\) | −0.946322 | −0.0367798 | ||||||||
\(663\) | −1.51585 | −0.0588708 | ||||||||
\(664\) | 0.182561 | 0.00708476 | ||||||||
\(665\) | −0.394428 | −0.0152953 | ||||||||
\(666\) | 0.135506 | 0.00525074 | ||||||||
\(667\) | −8.37982 | −0.324468 | ||||||||
\(668\) | −22.8913 | −0.885692 | ||||||||
\(669\) | −3.41348 | −0.131973 | ||||||||
\(670\) | 0.478480 | 0.0184853 | ||||||||
\(671\) | 16.6592 | 0.643120 | ||||||||
\(672\) | 1.58788 | 0.0612539 | ||||||||
\(673\) | −44.1209 | −1.70074 | −0.850368 | − | 0.526188i | \(-0.823621\pi\) | ||||
−0.850368 | + | 0.526188i | \(0.823621\pi\) | |||||||
\(674\) | −0.805318 | −0.0310197 | ||||||||
\(675\) | −9.96654 | −0.383612 | ||||||||
\(676\) | 22.7914 | 0.876591 | ||||||||
\(677\) | 49.1546 | 1.88916 | 0.944582 | − | 0.328276i | \(-0.106468\pi\) | ||||
0.944582 | + | 0.328276i | \(0.106468\pi\) | |||||||
\(678\) | 0.496099 | 0.0190526 | ||||||||
\(679\) | 13.8576 | 0.531805 | ||||||||
\(680\) | −0.382812 | −0.0146802 | ||||||||
\(681\) | −9.47335 | −0.363020 | ||||||||
\(682\) | −0.442181 | −0.0169320 | ||||||||
\(683\) | −46.7356 | −1.78829 | −0.894144 | − | 0.447779i | \(-0.852215\pi\) | ||||
−0.894144 | + | 0.447779i | \(0.852215\pi\) | |||||||
\(684\) | −0.334246 | −0.0127802 | ||||||||
\(685\) | 6.88006 | 0.262873 | ||||||||
\(686\) | 1.07880 | 0.0411888 | ||||||||
\(687\) | 6.83905 | 0.260926 | ||||||||
\(688\) | 38.6908 | 1.47507 | ||||||||
\(689\) | −11.1964 | −0.426547 | ||||||||
\(690\) | −0.128877 | −0.00490625 | ||||||||
\(691\) | 29.7904 | 1.13328 | 0.566640 | − | 0.823965i | \(-0.308243\pi\) | ||||
0.566640 | + | 0.823965i | \(0.308243\pi\) | |||||||
\(692\) | 38.1968 | 1.45203 | ||||||||
\(693\) | −3.69236 | −0.140261 | ||||||||
\(694\) | 0.476368 | 0.0180827 | ||||||||
\(695\) | −15.2593 | −0.578818 | ||||||||
\(696\) | −1.93443 | −0.0733245 | ||||||||
\(697\) | −4.79805 | −0.181739 | ||||||||
\(698\) | −1.48727 | −0.0562938 | ||||||||
\(699\) | −34.4348 | −1.30244 | ||||||||
\(700\) | 7.45806 | 0.281888 | ||||||||
\(701\) | −9.77679 | −0.369264 | −0.184632 | − | 0.982808i | \(-0.559109\pi\) | ||||
−0.184632 | + | 0.982808i | \(0.559109\pi\) | |||||||
\(702\) | 0.370639 | 0.0139889 | ||||||||
\(703\) | −0.175117 | −0.00660466 | ||||||||
\(704\) | −9.18895 | −0.346322 | ||||||||
\(705\) | −2.14527 | −0.0807955 | ||||||||
\(706\) | −0.191679 | −0.00721394 | ||||||||
\(707\) | 3.49802 | 0.131557 | ||||||||
\(708\) | −17.6463 | −0.663189 | ||||||||
\(709\) | 14.3071 | 0.537313 | 0.268656 | − | 0.963236i | \(-0.413420\pi\) | ||||
0.268656 | + | 0.963236i | \(0.413420\pi\) | |||||||
\(710\) | −0.704993 | −0.0264579 | ||||||||
\(711\) | 6.03555 | 0.226351 | ||||||||
\(712\) | −1.85895 | −0.0696671 | ||||||||
\(713\) | −7.94936 | −0.297706 | ||||||||
\(714\) | −0.132578 | −0.00496162 | ||||||||
\(715\) | −2.60366 | −0.0973714 | ||||||||
\(716\) | −31.9861 | −1.19538 | ||||||||
\(717\) | −15.5422 | −0.580435 | ||||||||
\(718\) | −0.622978 | −0.0232493 | ||||||||
\(719\) | 33.7718 | 1.25947 | 0.629737 | − | 0.776808i | \(-0.283162\pi\) | ||||
0.629737 | + | 0.776808i | \(0.283162\pi\) | |||||||
\(720\) | −11.0294 | −0.411042 | ||||||||
\(721\) | −38.6722 | −1.44023 | ||||||||
\(722\) | 1.01975 | 0.0379513 | ||||||||
\(723\) | 17.8574 | 0.664122 | ||||||||
\(724\) | −7.64770 | −0.284224 | ||||||||
\(725\) | −13.6319 | −0.506276 | ||||||||
\(726\) | −0.623915 | −0.0231556 | ||||||||
\(727\) | −10.1616 | −0.376871 | −0.188436 | − | 0.982086i | \(-0.560342\pi\) | ||||
−0.188436 | + | 0.982086i | \(0.560342\pi\) | |||||||
\(728\) | −0.555107 | −0.0205736 | ||||||||
\(729\) | 22.7624 | 0.843050 | ||||||||
\(730\) | −1.60140 | −0.0592704 | ||||||||
\(731\) | −9.71471 | −0.359312 | ||||||||
\(732\) | 34.5431 | 1.27675 | ||||||||
\(733\) | −2.70369 | −0.0998630 | −0.0499315 | − | 0.998753i | \(-0.515900\pi\) | ||||
−0.0499315 | + | 0.998753i | \(0.515900\pi\) | |||||||
\(734\) | −0.218219 | −0.00805460 | ||||||||
\(735\) | 5.98220 | 0.220657 | ||||||||
\(736\) | 0.719512 | 0.0265216 | ||||||||
\(737\) | −5.78855 | −0.213224 | ||||||||
\(738\) | 0.400143 | 0.0147294 | ||||||||
\(739\) | 52.3725 | 1.92655 | 0.963277 | − | 0.268510i | \(-0.0865312\pi\) | ||||
0.963277 | + | 0.268510i | \(0.0865312\pi\) | |||||||
\(740\) | −5.78686 | −0.212729 | ||||||||
\(741\) | −0.163372 | −0.00600161 | ||||||||
\(742\) | −0.979249 | −0.0359494 | ||||||||
\(743\) | −7.72560 | −0.283425 | −0.141712 | − | 0.989908i | \(-0.545261\pi\) | ||||
−0.141712 | + | 0.989908i | \(0.545261\pi\) | |||||||
\(744\) | −1.83506 | −0.0672767 | ||||||||
\(745\) | −0.694183 | −0.0254329 | ||||||||
\(746\) | 1.24902 | 0.0457299 | ||||||||
\(747\) | −1.32068 | −0.0483211 | ||||||||
\(748\) | 2.31392 | 0.0846054 | ||||||||
\(749\) | −28.3142 | −1.03458 | ||||||||
\(750\) | −0.785699 | −0.0286897 | ||||||||
\(751\) | 8.62146 | 0.314601 | 0.157301 | − | 0.987551i | \(-0.449721\pi\) | ||||
0.157301 | + | 0.987551i | \(0.449721\pi\) | |||||||
\(752\) | 3.98270 | 0.145234 | ||||||||
\(753\) | 15.8921 | 0.579140 | ||||||||
\(754\) | 0.506949 | 0.0184620 | ||||||||
\(755\) | 6.46864 | 0.235418 | ||||||||
\(756\) | −22.4469 | −0.816386 | ||||||||
\(757\) | −10.8630 | −0.394823 | −0.197411 | − | 0.980321i | \(-0.563254\pi\) | ||||
−0.197411 | + | 0.980321i | \(0.563254\pi\) | |||||||
\(758\) | 1.37393 | 0.0499035 | ||||||||
\(759\) | 1.55912 | 0.0565926 | ||||||||
\(760\) | −0.0412578 | −0.00149658 | ||||||||
\(761\) | −42.8962 | −1.55499 | −0.777493 | − | 0.628892i | \(-0.783509\pi\) | ||||
−0.777493 | + | 0.628892i | \(0.783509\pi\) | |||||||
\(762\) | −0.116919 | −0.00423551 | ||||||||
\(763\) | 20.2628 | 0.733562 | ||||||||
\(764\) | 7.84245 | 0.283730 | ||||||||
\(765\) | 2.76933 | 0.100125 | ||||||||
\(766\) | −0.707606 | −0.0255669 | ||||||||
\(767\) | 9.25566 | 0.334202 | ||||||||
\(768\) | −18.9703 | −0.684533 | ||||||||
\(769\) | 33.4014 | 1.20448 | 0.602242 | − | 0.798314i | \(-0.294274\pi\) | ||||
0.602242 | + | 0.798314i | \(0.294274\pi\) | |||||||
\(770\) | −0.227720 | −0.00820645 | ||||||||
\(771\) | 30.5394 | 1.09985 | ||||||||
\(772\) | 8.91947 | 0.321019 | ||||||||
\(773\) | −26.4878 | −0.952701 | −0.476350 | − | 0.879256i | \(-0.658041\pi\) | ||||
−0.476350 | + | 0.879256i | \(0.658041\pi\) | |||||||
\(774\) | 0.810177 | 0.0291212 | ||||||||
\(775\) | −12.9317 | −0.464519 | ||||||||
\(776\) | 1.44952 | 0.0520349 | ||||||||
\(777\) | −4.01119 | −0.143901 | ||||||||
\(778\) | −0.636596 | −0.0228231 | ||||||||
\(779\) | −0.517113 | −0.0185275 | ||||||||
\(780\) | −5.39873 | −0.193306 | ||||||||
\(781\) | 8.52885 | 0.305186 | ||||||||
\(782\) | −0.0600748 | −0.00214827 | ||||||||
\(783\) | 41.0287 | 1.46625 | ||||||||
\(784\) | −11.1060 | −0.396642 | ||||||||
\(785\) | 19.5681 | 0.698416 | ||||||||
\(786\) | −0.00941413 | −0.000335791 0 | ||||||||
\(787\) | 6.28921 | 0.224186 | 0.112093 | − | 0.993698i | \(-0.464245\pi\) | ||||
0.112093 | + | 0.993698i | \(0.464245\pi\) | |||||||
\(788\) | −49.3524 | −1.75810 | ||||||||
\(789\) | 6.84544 | 0.243704 | ||||||||
\(790\) | 0.372232 | 0.0132434 | ||||||||
\(791\) | 15.7589 | 0.560323 | ||||||||
\(792\) | −0.386226 | −0.0137240 | ||||||||
\(793\) | −18.1182 | −0.643395 | ||||||||
\(794\) | 0.711265 | 0.0252418 | ||||||||
\(795\) | −19.0613 | −0.676034 | ||||||||
\(796\) | 3.87219 | 0.137246 | ||||||||
\(797\) | −25.5794 | −0.906067 | −0.453034 | − | 0.891493i | \(-0.649658\pi\) | ||||
−0.453034 | + | 0.891493i | \(0.649658\pi\) | |||||||
\(798\) | −0.0142887 | −0.000505815 0 | ||||||||
\(799\) | −1.00000 | −0.0353775 | ||||||||
\(800\) | 1.17047 | 0.0413823 | ||||||||
\(801\) | 13.4479 | 0.475160 | ||||||||
\(802\) | 0.609407 | 0.0215189 | ||||||||
\(803\) | 19.3734 | 0.683672 | ||||||||
\(804\) | −12.0027 | −0.423301 | ||||||||
\(805\) | −4.09386 | −0.144290 | ||||||||
\(806\) | 0.480907 | 0.0169392 | ||||||||
\(807\) | −27.3584 | −0.963062 | ||||||||
\(808\) | 0.365899 | 0.0128723 | ||||||||
\(809\) | 1.79712 | 0.0631834 | 0.0315917 | − | 0.999501i | \(-0.489942\pi\) | ||||
0.0315917 | + | 0.999501i | \(0.489942\pi\) | |||||||
\(810\) | 0.184824 | 0.00649404 | ||||||||
\(811\) | 20.1649 | 0.708085 | 0.354042 | − | 0.935229i | \(-0.384807\pi\) | ||||
0.354042 | + | 0.935229i | \(0.384807\pi\) | |||||||
\(812\) | −30.7022 | −1.07743 | ||||||||
\(813\) | 2.72713 | 0.0956446 | ||||||||
\(814\) | −0.101102 | −0.00354363 | ||||||||
\(815\) | −37.9950 | −1.33091 | ||||||||
\(816\) | 4.79102 | 0.167719 | ||||||||
\(817\) | −1.04701 | −0.0366302 | ||||||||
\(818\) | −0.788026 | −0.0275527 | ||||||||
\(819\) | 4.01573 | 0.140321 | ||||||||
\(820\) | −17.0884 | −0.596751 | ||||||||
\(821\) | −17.1159 | −0.597347 | −0.298674 | − | 0.954355i | \(-0.596544\pi\) | ||||
−0.298674 | + | 0.954355i | \(0.596544\pi\) | |||||||
\(822\) | 0.249240 | 0.00869323 | ||||||||
\(823\) | −0.855836 | −0.0298326 | −0.0149163 | − | 0.999889i | \(-0.504748\pi\) | ||||
−0.0149163 | + | 0.999889i | \(0.504748\pi\) | |||||||
\(824\) | −4.04518 | −0.140920 | ||||||||
\(825\) | 2.53631 | 0.0883029 | ||||||||
\(826\) | 0.809513 | 0.0281665 | ||||||||
\(827\) | 14.6203 | 0.508398 | 0.254199 | − | 0.967152i | \(-0.418188\pi\) | ||||
0.254199 | + | 0.967152i | \(0.418188\pi\) | |||||||
\(828\) | −3.46921 | −0.120563 | ||||||||
\(829\) | 39.2278 | 1.36244 | 0.681219 | − | 0.732080i | \(-0.261450\pi\) | ||||
0.681219 | + | 0.732080i | \(0.261450\pi\) | |||||||
\(830\) | −0.0814506 | −0.00282719 | ||||||||
\(831\) | 18.3501 | 0.636557 | ||||||||
\(832\) | 9.99372 | 0.346470 | ||||||||
\(833\) | 2.78855 | 0.0966176 | ||||||||
\(834\) | −0.552790 | −0.0191415 | ||||||||
\(835\) | 20.4409 | 0.707386 | ||||||||
\(836\) | 0.249384 | 0.00862513 | ||||||||
\(837\) | 38.9211 | 1.34531 | ||||||||
\(838\) | 1.46051 | 0.0504526 | ||||||||
\(839\) | −24.1087 | −0.832324 | −0.416162 | − | 0.909290i | \(-0.636625\pi\) | ||||
−0.416162 | + | 0.909290i | \(0.636625\pi\) | |||||||
\(840\) | −0.945043 | −0.0326071 | ||||||||
\(841\) | 27.1177 | 0.935093 | ||||||||
\(842\) | −1.67352 | −0.0576733 | ||||||||
\(843\) | −20.9156 | −0.720372 | ||||||||
\(844\) | 21.0550 | 0.724744 | ||||||||
\(845\) | −20.3516 | −0.700117 | ||||||||
\(846\) | 0.0833969 | 0.00286724 | ||||||||
\(847\) | −19.8191 | −0.680992 | ||||||||
\(848\) | 35.3874 | 1.21521 | ||||||||
\(849\) | 18.8621 | 0.647347 | ||||||||
\(850\) | −0.0977269 | −0.00335200 | ||||||||
\(851\) | −1.81758 | −0.0623057 | ||||||||
\(852\) | 17.6847 | 0.605869 | ||||||||
\(853\) | −19.2066 | −0.657622 | −0.328811 | − | 0.944396i | \(-0.606648\pi\) | ||||
−0.328811 | + | 0.944396i | \(0.606648\pi\) | |||||||
\(854\) | −1.58464 | −0.0542253 | ||||||||
\(855\) | 0.298466 | 0.0102073 | ||||||||
\(856\) | −2.96171 | −0.101229 | ||||||||
\(857\) | 2.55045 | 0.0871218 | 0.0435609 | − | 0.999051i | \(-0.486130\pi\) | ||||
0.0435609 | + | 0.999051i | \(0.486130\pi\) | |||||||
\(858\) | −0.0943212 | −0.00322007 | ||||||||
\(859\) | −14.5411 | −0.496136 | −0.248068 | − | 0.968743i | \(-0.579796\pi\) | ||||
−0.248068 | + | 0.968743i | \(0.579796\pi\) | |||||||
\(860\) | −34.5991 | −1.17982 | ||||||||
\(861\) | −11.8449 | −0.403672 | ||||||||
\(862\) | 1.38556 | 0.0471925 | ||||||||
\(863\) | −29.2219 | −0.994726 | −0.497363 | − | 0.867543i | \(-0.665698\pi\) | ||||
−0.497363 | + | 0.867543i | \(0.665698\pi\) | |||||||
\(864\) | −3.52282 | −0.119849 | ||||||||
\(865\) | −34.1080 | −1.15971 | ||||||||
\(866\) | 0.946493 | 0.0321631 | ||||||||
\(867\) | −1.20296 | −0.0408545 | ||||||||
\(868\) | −29.1250 | −0.988568 | ||||||||
\(869\) | −4.50319 | −0.152760 | ||||||||
\(870\) | 0.863056 | 0.0292604 | ||||||||
\(871\) | 6.29551 | 0.213315 | ||||||||
\(872\) | 2.11952 | 0.0717760 | ||||||||
\(873\) | −10.4861 | −0.354901 | ||||||||
\(874\) | −0.00647459 | −0.000219006 0 | ||||||||
\(875\) | −24.9583 | −0.843744 | ||||||||
\(876\) | 40.1711 | 1.35725 | ||||||||
\(877\) | −20.9049 | −0.705909 | −0.352955 | − | 0.935640i | \(-0.614823\pi\) | ||||
−0.352955 | + | 0.935640i | \(0.614823\pi\) | |||||||
\(878\) | −1.21450 | −0.0409873 | ||||||||
\(879\) | 10.0448 | 0.338802 | ||||||||
\(880\) | 8.22916 | 0.277405 | ||||||||
\(881\) | 37.6761 | 1.26934 | 0.634670 | − | 0.772783i | \(-0.281136\pi\) | ||||
0.634670 | + | 0.772783i | \(0.281136\pi\) | |||||||
\(882\) | −0.232557 | −0.00783059 | ||||||||
\(883\) | 28.2157 | 0.949532 | 0.474766 | − | 0.880112i | \(-0.342533\pi\) | ||||
0.474766 | + | 0.880112i | \(0.342533\pi\) | |||||||
\(884\) | −2.51658 | −0.0846416 | ||||||||
\(885\) | 15.7573 | 0.529677 | ||||||||
\(886\) | 0.0944460 | 0.00317298 | ||||||||
\(887\) | 22.1836 | 0.744851 | 0.372426 | − | 0.928062i | \(-0.378526\pi\) | ||||
0.372426 | + | 0.928062i | \(0.378526\pi\) | |||||||
\(888\) | −0.419577 | −0.0140801 | ||||||||
\(889\) | −3.71400 | −0.124564 | ||||||||
\(890\) | 0.829379 | 0.0278008 | ||||||||
\(891\) | −2.23596 | −0.0749074 | ||||||||
\(892\) | −5.66697 | −0.189744 | ||||||||
\(893\) | −0.107776 | −0.00360657 | ||||||||
\(894\) | −0.0251477 | −0.000841066 0 | ||||||||
\(895\) | 28.5621 | 0.954726 | ||||||||
\(896\) | 3.51403 | 0.117396 | ||||||||
\(897\) | −1.69567 | −0.0566168 | ||||||||
\(898\) | −0.169023 | −0.00564036 | ||||||||
\(899\) | 53.2350 | 1.77549 | ||||||||
\(900\) | −5.64355 | −0.188118 | ||||||||
\(901\) | −8.88526 | −0.296011 | ||||||||
\(902\) | −0.298551 | −0.00994065 | ||||||||
\(903\) | −23.9826 | −0.798090 | ||||||||
\(904\) | 1.64841 | 0.0548253 | ||||||||
\(905\) | 6.82904 | 0.227005 | ||||||||
\(906\) | 0.234336 | 0.00778528 | ||||||||
\(907\) | −8.38001 | −0.278254 | −0.139127 | − | 0.990275i | \(-0.544430\pi\) | ||||
−0.139127 | + | 0.990275i | \(0.544430\pi\) | |||||||
\(908\) | −15.7274 | −0.521932 | ||||||||
\(909\) | −2.64697 | −0.0877945 | ||||||||
\(910\) | 0.247663 | 0.00820996 | ||||||||
\(911\) | −33.6818 | −1.11593 | −0.557964 | − | 0.829865i | \(-0.688417\pi\) | ||||
−0.557964 | + | 0.829865i | \(0.688417\pi\) | |||||||
\(912\) | 0.516355 | 0.0170982 | ||||||||
\(913\) | 0.985373 | 0.0326111 | ||||||||
\(914\) | 1.21065 | 0.0400447 | ||||||||
\(915\) | −30.8453 | −1.01972 | ||||||||
\(916\) | 11.3540 | 0.375147 | ||||||||
\(917\) | −0.299047 | −0.00987539 | ||||||||
\(918\) | 0.294134 | 0.00970786 | ||||||||
\(919\) | −38.7034 | −1.27671 | −0.638353 | − | 0.769744i | \(-0.720384\pi\) | ||||
−0.638353 | + | 0.769744i | \(0.720384\pi\) | |||||||
\(920\) | −0.428224 | −0.0141181 | ||||||||
\(921\) | 41.2752 | 1.36007 | ||||||||
\(922\) | −0.265584 | −0.00874655 | ||||||||
\(923\) | −9.27581 | −0.305317 | ||||||||
\(924\) | 5.71234 | 0.187922 | ||||||||
\(925\) | −2.95675 | −0.0972173 | ||||||||
\(926\) | −0.436479 | −0.0143436 | ||||||||
\(927\) | 29.2635 | 0.961138 | ||||||||
\(928\) | −4.81840 | −0.158172 | ||||||||
\(929\) | −3.15067 | −0.103370 | −0.0516851 | − | 0.998663i | \(-0.516459\pi\) | ||||
−0.0516851 | + | 0.998663i | \(0.516459\pi\) | |||||||
\(930\) | 0.818722 | 0.0268470 | ||||||||
\(931\) | 0.300538 | 0.00984973 | ||||||||
\(932\) | −57.1677 | −1.87259 | ||||||||
\(933\) | −28.1463 | −0.921469 | ||||||||
\(934\) | −2.04546 | −0.0669295 | ||||||||
\(935\) | −2.06622 | −0.0675728 | ||||||||
\(936\) | 0.420052 | 0.0137298 | ||||||||
\(937\) | −9.19856 | −0.300504 | −0.150252 | − | 0.988648i | \(-0.548008\pi\) | ||||
−0.150252 | + | 0.988648i | \(0.548008\pi\) | |||||||
\(938\) | 0.550614 | 0.0179782 | ||||||||
\(939\) | −4.92978 | −0.160877 | ||||||||
\(940\) | −3.56152 | −0.116164 | ||||||||
\(941\) | 16.6310 | 0.542154 | 0.271077 | − | 0.962558i | \(-0.412620\pi\) | ||||
0.271077 | + | 0.962558i | \(0.412620\pi\) | |||||||
\(942\) | 0.708882 | 0.0230966 | ||||||||
\(943\) | −5.36723 | −0.174781 | ||||||||
\(944\) | −29.2536 | −0.952122 | ||||||||
\(945\) | 20.0440 | 0.652033 | ||||||||
\(946\) | −0.604481 | −0.0196534 | ||||||||
\(947\) | −48.6626 | −1.58132 | −0.790660 | − | 0.612255i | \(-0.790263\pi\) | ||||
−0.790660 | + | 0.612255i | \(0.790263\pi\) | |||||||
\(948\) | −9.33744 | −0.303266 | ||||||||
\(949\) | −21.0701 | −0.683965 | ||||||||
\(950\) | −0.0105326 | −0.000341722 0 | ||||||||
\(951\) | 14.0774 | 0.456492 | ||||||||
\(952\) | −0.440524 | −0.0142775 | ||||||||
\(953\) | −17.4665 | −0.565796 | −0.282898 | − | 0.959150i | \(-0.591296\pi\) | ||||
−0.282898 | + | 0.959150i | \(0.591296\pi\) | |||||||
\(954\) | 0.741003 | 0.0239909 | ||||||||
\(955\) | −7.00295 | −0.226610 | ||||||||
\(956\) | −25.8028 | −0.834521 | ||||||||
\(957\) | −10.4411 | −0.337512 | ||||||||
\(958\) | −0.638527 | −0.0206299 | ||||||||
\(959\) | 7.91727 | 0.255662 | ||||||||
\(960\) | 17.0138 | 0.549119 | ||||||||
\(961\) | 19.5004 | 0.629044 | ||||||||
\(962\) | 0.109957 | 0.00354515 | ||||||||
\(963\) | 21.4255 | 0.690426 | ||||||||
\(964\) | 29.6463 | 0.954843 | ||||||||
\(965\) | −7.96467 | −0.256392 | ||||||||
\(966\) | −0.148306 | −0.00477166 | ||||||||
\(967\) | 25.9162 | 0.833407 | 0.416704 | − | 0.909042i | \(-0.363185\pi\) | ||||
0.416704 | + | 0.909042i | \(0.363185\pi\) | |||||||
\(968\) | −2.07311 | −0.0666322 | ||||||||
\(969\) | −0.129649 | −0.00416493 | ||||||||
\(970\) | −0.646712 | −0.0207647 | ||||||||
\(971\) | −29.2187 | −0.937674 | −0.468837 | − | 0.883285i | \(-0.655327\pi\) | ||||
−0.468837 | + | 0.883285i | \(0.655327\pi\) | |||||||
\(972\) | 28.1779 | 0.903807 | ||||||||
\(973\) | −17.5598 | −0.562940 | ||||||||
\(974\) | 0.215341 | 0.00689998 | ||||||||
\(975\) | −2.75844 | −0.0883407 | ||||||||
\(976\) | 57.2645 | 1.83299 | ||||||||
\(977\) | −11.7352 | −0.375443 | −0.187721 | − | 0.982222i | \(-0.560110\pi\) | ||||
−0.187721 | + | 0.982222i | \(0.560110\pi\) | |||||||
\(978\) | −1.37642 | −0.0440131 | ||||||||
\(979\) | −10.0337 | −0.320677 | ||||||||
\(980\) | 9.93149 | 0.317250 | ||||||||
\(981\) | −15.3329 | −0.489543 | ||||||||
\(982\) | −1.66458 | −0.0531189 | ||||||||
\(983\) | −24.2313 | −0.772860 | −0.386430 | − | 0.922319i | \(-0.626292\pi\) | ||||
−0.386430 | + | 0.922319i | \(0.626292\pi\) | |||||||
\(984\) | −1.23899 | −0.0394977 | ||||||||
\(985\) | 44.0694 | 1.40417 | ||||||||
\(986\) | 0.402307 | 0.0128121 | ||||||||
\(987\) | −2.46868 | −0.0785791 | ||||||||
\(988\) | −0.271225 | −0.00862883 | ||||||||
\(989\) | −10.8671 | −0.345555 | ||||||||
\(990\) | 0.172317 | 0.00547658 | ||||||||
\(991\) | 28.2402 | 0.897080 | 0.448540 | − | 0.893763i | \(-0.351944\pi\) | ||||
0.448540 | + | 0.893763i | \(0.351944\pi\) | |||||||
\(992\) | −4.57088 | −0.145126 | ||||||||
\(993\) | −21.1973 | −0.672677 | ||||||||
\(994\) | −0.811275 | −0.0257321 | ||||||||
\(995\) | −3.45768 | −0.109616 | ||||||||
\(996\) | 2.04319 | 0.0647408 | ||||||||
\(997\) | 6.34163 | 0.200842 | 0.100421 | − | 0.994945i | \(-0.467981\pi\) | ||||
0.100421 | + | 0.994945i | \(0.467981\pi\) | |||||||
\(998\) | 1.97082 | 0.0623853 | ||||||||
\(999\) | 8.89908 | 0.281555 |
(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 | 799.2.a.g.1.10 | ✓ | 20 | |
3.2 | odd | 2 | 7191.2.a.bb.1.11 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
799.2.a.g.1.10 | ✓ | 20 | 1.1 | even | 1 | trivial | |
7191.2.a.bb.1.11 | 20 | 3.2 | odd | 2 |