Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [619,2,Mod(1,619)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(619, 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("619.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 619 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 619.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: | \(4.94273988512\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 619.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.431096 | 0.304831 | 0.152415 | − | 0.988317i | \(-0.451295\pi\) | ||||
0.152415 | + | 0.988317i | \(0.451295\pi\) | |||||||
\(3\) | −1.56278 | −0.902271 | −0.451136 | − | 0.892455i | \(-0.648981\pi\) | ||||
−0.451136 | + | 0.892455i | \(0.648981\pi\) | |||||||
\(4\) | −1.81416 | −0.907078 | ||||||||
\(5\) | 1.50079 | 0.671175 | 0.335587 | − | 0.942009i | \(-0.391065\pi\) | ||||
0.335587 | + | 0.942009i | \(0.391065\pi\) | |||||||
\(6\) | −0.673708 | −0.275040 | ||||||||
\(7\) | −4.83036 | −1.82571 | −0.912853 | − | 0.408288i | \(-0.866126\pi\) | ||||
−0.912853 | + | 0.408288i | \(0.866126\pi\) | |||||||
\(8\) | −1.64427 | −0.581336 | ||||||||
\(9\) | −0.557720 | −0.185907 | ||||||||
\(10\) | 0.646986 | 0.204595 | ||||||||
\(11\) | 2.60102 | 0.784237 | 0.392118 | − | 0.919915i | \(-0.371742\pi\) | ||||
0.392118 | + | 0.919915i | \(0.371742\pi\) | |||||||
\(12\) | 2.83513 | 0.818430 | ||||||||
\(13\) | 5.36233 | 1.48724 | 0.743621 | − | 0.668601i | \(-0.233107\pi\) | ||||
0.743621 | + | 0.668601i | \(0.233107\pi\) | |||||||
\(14\) | −2.08235 | −0.556532 | ||||||||
\(15\) | −2.34541 | −0.605582 | ||||||||
\(16\) | 2.91948 | 0.729869 | ||||||||
\(17\) | 6.13234 | 1.48731 | 0.743656 | − | 0.668563i | \(-0.233090\pi\) | ||||
0.743656 | + | 0.668563i | \(0.233090\pi\) | |||||||
\(18\) | −0.240431 | −0.0566701 | ||||||||
\(19\) | 1.28647 | 0.295136 | 0.147568 | − | 0.989052i | \(-0.452855\pi\) | ||||
0.147568 | + | 0.989052i | \(0.452855\pi\) | |||||||
\(20\) | −2.72267 | −0.608808 | ||||||||
\(21\) | 7.54879 | 1.64728 | ||||||||
\(22\) | 1.12129 | 0.239060 | ||||||||
\(23\) | −3.55264 | −0.740776 | −0.370388 | − | 0.928877i | \(-0.620775\pi\) | ||||
−0.370388 | + | 0.928877i | \(0.620775\pi\) | |||||||
\(24\) | 2.56963 | 0.524523 | ||||||||
\(25\) | −2.74762 | −0.549524 | ||||||||
\(26\) | 2.31168 | 0.453357 | ||||||||
\(27\) | 5.55993 | 1.07001 | ||||||||
\(28\) | 8.76304 | 1.65606 | ||||||||
\(29\) | −1.96205 | −0.364343 | −0.182171 | − | 0.983267i | \(-0.558313\pi\) | ||||
−0.182171 | + | 0.983267i | \(0.558313\pi\) | |||||||
\(30\) | −1.01110 | −0.184600 | ||||||||
\(31\) | 7.06516 | 1.26894 | 0.634470 | − | 0.772947i | \(-0.281218\pi\) | ||||
0.634470 | + | 0.772947i | \(0.281218\pi\) | |||||||
\(32\) | 4.54711 | 0.803823 | ||||||||
\(33\) | −4.06482 | −0.707594 | ||||||||
\(34\) | 2.64363 | 0.453379 | ||||||||
\(35\) | −7.24937 | −1.22537 | ||||||||
\(36\) | 1.01179 | 0.168632 | ||||||||
\(37\) | 3.47725 | 0.571656 | 0.285828 | − | 0.958281i | \(-0.407731\pi\) | ||||
0.285828 | + | 0.958281i | \(0.407731\pi\) | |||||||
\(38\) | 0.554591 | 0.0899666 | ||||||||
\(39\) | −8.38014 | −1.34190 | ||||||||
\(40\) | −2.46770 | −0.390178 | ||||||||
\(41\) | 5.18803 | 0.810234 | 0.405117 | − | 0.914265i | \(-0.367231\pi\) | ||||
0.405117 | + | 0.914265i | \(0.367231\pi\) | |||||||
\(42\) | 3.25425 | 0.502142 | ||||||||
\(43\) | −8.24591 | −1.25749 | −0.628745 | − | 0.777612i | \(-0.716431\pi\) | ||||
−0.628745 | + | 0.777612i | \(0.716431\pi\) | |||||||
\(44\) | −4.71865 | −0.711364 | ||||||||
\(45\) | −0.837022 | −0.124776 | ||||||||
\(46\) | −1.53153 | −0.225811 | ||||||||
\(47\) | 4.95150 | 0.722250 | 0.361125 | − | 0.932517i | \(-0.382393\pi\) | ||||
0.361125 | + | 0.932517i | \(0.382393\pi\) | |||||||
\(48\) | −4.56250 | −0.658540 | ||||||||
\(49\) | 16.3324 | 2.33320 | ||||||||
\(50\) | −1.18449 | −0.167512 | ||||||||
\(51\) | −9.58350 | −1.34196 | ||||||||
\(52\) | −9.72810 | −1.34904 | ||||||||
\(53\) | −5.85664 | −0.804472 | −0.402236 | − | 0.915536i | \(-0.631767\pi\) | ||||
−0.402236 | + | 0.915536i | \(0.631767\pi\) | |||||||
\(54\) | 2.39686 | 0.326172 | ||||||||
\(55\) | 3.90359 | 0.526360 | ||||||||
\(56\) | 7.94241 | 1.06135 | ||||||||
\(57\) | −2.01047 | −0.266293 | ||||||||
\(58\) | −0.845830 | −0.111063 | ||||||||
\(59\) | −9.60280 | −1.25018 | −0.625089 | − | 0.780554i | \(-0.714937\pi\) | ||||
−0.625089 | + | 0.780554i | \(0.714937\pi\) | |||||||
\(60\) | 4.25494 | 0.549310 | ||||||||
\(61\) | 6.86922 | 0.879514 | 0.439757 | − | 0.898117i | \(-0.355065\pi\) | ||||
0.439757 | + | 0.898117i | \(0.355065\pi\) | |||||||
\(62\) | 3.04576 | 0.386812 | ||||||||
\(63\) | 2.69399 | 0.339411 | ||||||||
\(64\) | −3.87871 | −0.484839 | ||||||||
\(65\) | 8.04774 | 0.998200 | ||||||||
\(66\) | −1.75233 | −0.215697 | ||||||||
\(67\) | 14.9558 | 1.82714 | 0.913569 | − | 0.406683i | \(-0.133315\pi\) | ||||
0.913569 | + | 0.406683i | \(0.133315\pi\) | |||||||
\(68\) | −11.1250 | −1.34911 | ||||||||
\(69\) | 5.55199 | 0.668381 | ||||||||
\(70\) | −3.12518 | −0.373530 | ||||||||
\(71\) | −5.87145 | −0.696813 | −0.348407 | − | 0.937344i | \(-0.613277\pi\) | ||||
−0.348407 | + | 0.937344i | \(0.613277\pi\) | |||||||
\(72\) | 0.917041 | 0.108074 | ||||||||
\(73\) | 4.41927 | 0.517236 | 0.258618 | − | 0.965980i | \(-0.416733\pi\) | ||||
0.258618 | + | 0.965980i | \(0.416733\pi\) | |||||||
\(74\) | 1.49903 | 0.174258 | ||||||||
\(75\) | 4.29393 | 0.495820 | ||||||||
\(76\) | −2.33385 | −0.267711 | ||||||||
\(77\) | −12.5639 | −1.43179 | ||||||||
\(78\) | −3.61264 | −0.409051 | ||||||||
\(79\) | 8.82851 | 0.993285 | 0.496642 | − | 0.867955i | \(-0.334566\pi\) | ||||
0.496642 | + | 0.867955i | \(0.334566\pi\) | |||||||
\(80\) | 4.38153 | 0.489870 | ||||||||
\(81\) | −7.01579 | −0.779532 | ||||||||
\(82\) | 2.23654 | 0.246984 | ||||||||
\(83\) | 1.16250 | 0.127601 | 0.0638003 | − | 0.997963i | \(-0.479678\pi\) | ||||
0.0638003 | + | 0.997963i | \(0.479678\pi\) | |||||||
\(84\) | −13.6947 | −1.49421 | ||||||||
\(85\) | 9.20337 | 0.998246 | ||||||||
\(86\) | −3.55478 | −0.383322 | ||||||||
\(87\) | 3.06625 | 0.328736 | ||||||||
\(88\) | −4.27677 | −0.455905 | ||||||||
\(89\) | 14.0013 | 1.48414 | 0.742068 | − | 0.670325i | \(-0.233845\pi\) | ||||
0.742068 | + | 0.670325i | \(0.233845\pi\) | |||||||
\(90\) | −0.360837 | −0.0380356 | ||||||||
\(91\) | −25.9020 | −2.71527 | ||||||||
\(92\) | 6.44504 | 0.671942 | ||||||||
\(93\) | −11.0413 | −1.14493 | ||||||||
\(94\) | 2.13457 | 0.220164 | ||||||||
\(95\) | 1.93072 | 0.198088 | ||||||||
\(96\) | −7.10613 | −0.725266 | ||||||||
\(97\) | −5.05039 | −0.512790 | −0.256395 | − | 0.966572i | \(-0.582535\pi\) | ||||
−0.256395 | + | 0.966572i | \(0.582535\pi\) | |||||||
\(98\) | 7.04084 | 0.711232 | ||||||||
\(99\) | −1.45064 | −0.145795 | ||||||||
\(100\) | 4.98462 | 0.498462 | ||||||||
\(101\) | 8.50227 | 0.846007 | 0.423004 | − | 0.906128i | \(-0.360976\pi\) | ||||
0.423004 | + | 0.906128i | \(0.360976\pi\) | |||||||
\(102\) | −4.13141 | −0.409070 | ||||||||
\(103\) | 7.04198 | 0.693867 | 0.346934 | − | 0.937890i | \(-0.387223\pi\) | ||||
0.346934 | + | 0.937890i | \(0.387223\pi\) | |||||||
\(104\) | −8.81710 | −0.864588 | ||||||||
\(105\) | 11.3292 | 1.10561 | ||||||||
\(106\) | −2.52477 | −0.245228 | ||||||||
\(107\) | −14.6155 | −1.41293 | −0.706465 | − | 0.707748i | \(-0.749711\pi\) | ||||
−0.706465 | + | 0.707748i | \(0.749711\pi\) | |||||||
\(108\) | −10.0866 | −0.970582 | ||||||||
\(109\) | −3.64511 | −0.349138 | −0.174569 | − | 0.984645i | \(-0.555853\pi\) | ||||
−0.174569 | + | 0.984645i | \(0.555853\pi\) | |||||||
\(110\) | 1.68282 | 0.160451 | ||||||||
\(111\) | −5.43417 | −0.515789 | ||||||||
\(112\) | −14.1021 | −1.33253 | ||||||||
\(113\) | 9.10477 | 0.856505 | 0.428252 | − | 0.903659i | \(-0.359129\pi\) | ||||
0.428252 | + | 0.903659i | \(0.359129\pi\) | |||||||
\(114\) | −0.866704 | −0.0811742 | ||||||||
\(115\) | −5.33177 | −0.497190 | ||||||||
\(116\) | 3.55946 | 0.330487 | ||||||||
\(117\) | −2.99068 | −0.276488 | ||||||||
\(118\) | −4.13973 | −0.381093 | ||||||||
\(119\) | −29.6215 | −2.71539 | ||||||||
\(120\) | 3.85648 | 0.352047 | ||||||||
\(121\) | −4.23470 | −0.384973 | ||||||||
\(122\) | 2.96129 | 0.268103 | ||||||||
\(123\) | −8.10774 | −0.731051 | ||||||||
\(124\) | −12.8173 | −1.15103 | ||||||||
\(125\) | −11.6276 | −1.04000 | ||||||||
\(126\) | 1.16137 | 0.103463 | ||||||||
\(127\) | −13.4174 | −1.19060 | −0.595300 | − | 0.803504i | \(-0.702967\pi\) | ||||
−0.595300 | + | 0.803504i | \(0.702967\pi\) | |||||||
\(128\) | −10.7663 | −0.951617 | ||||||||
\(129\) | 12.8865 | 1.13460 | ||||||||
\(130\) | 3.46935 | 0.304282 | ||||||||
\(131\) | 16.5240 | 1.44371 | 0.721855 | − | 0.692044i | \(-0.243290\pi\) | ||||
0.721855 | + | 0.692044i | \(0.243290\pi\) | |||||||
\(132\) | 7.37422 | 0.641843 | ||||||||
\(133\) | −6.21411 | −0.538832 | ||||||||
\(134\) | 6.44737 | 0.556968 | ||||||||
\(135\) | 8.34430 | 0.718163 | ||||||||
\(136\) | −10.0832 | −0.864628 | ||||||||
\(137\) | −19.3142 | −1.65013 | −0.825063 | − | 0.565041i | \(-0.808860\pi\) | ||||
−0.825063 | + | 0.565041i | \(0.808860\pi\) | |||||||
\(138\) | 2.39344 | 0.203743 | ||||||||
\(139\) | −5.09316 | −0.431997 | −0.215998 | − | 0.976394i | \(-0.569301\pi\) | ||||
−0.215998 | + | 0.976394i | \(0.569301\pi\) | |||||||
\(140\) | 13.1515 | 1.11150 | ||||||||
\(141\) | −7.73810 | −0.651666 | ||||||||
\(142\) | −2.53116 | −0.212410 | ||||||||
\(143\) | 13.9475 | 1.16635 | ||||||||
\(144\) | −1.62825 | −0.135688 | ||||||||
\(145\) | −2.94462 | −0.244538 | ||||||||
\(146\) | 1.90513 | 0.157670 | ||||||||
\(147\) | −25.5240 | −2.10518 | ||||||||
\(148\) | −6.30827 | −0.518537 | ||||||||
\(149\) | 15.6367 | 1.28101 | 0.640504 | − | 0.767955i | \(-0.278726\pi\) | ||||
0.640504 | + | 0.767955i | \(0.278726\pi\) | |||||||
\(150\) | 1.85109 | 0.151141 | ||||||||
\(151\) | 14.9031 | 1.21279 | 0.606397 | − | 0.795162i | \(-0.292614\pi\) | ||||
0.606397 | + | 0.795162i | \(0.292614\pi\) | |||||||
\(152\) | −2.11530 | −0.171573 | ||||||||
\(153\) | −3.42013 | −0.276501 | ||||||||
\(154\) | −5.41623 | −0.436452 | ||||||||
\(155\) | 10.6033 | 0.851681 | ||||||||
\(156\) | 15.2029 | 1.21720 | ||||||||
\(157\) | 16.9495 | 1.35272 | 0.676359 | − | 0.736572i | \(-0.263557\pi\) | ||||
0.676359 | + | 0.736572i | \(0.263557\pi\) | |||||||
\(158\) | 3.80593 | 0.302784 | ||||||||
\(159\) | 9.15264 | 0.725851 | ||||||||
\(160\) | 6.82427 | 0.539506 | ||||||||
\(161\) | 17.1605 | 1.35244 | ||||||||
\(162\) | −3.02448 | −0.237625 | ||||||||
\(163\) | −15.9532 | −1.24955 | −0.624775 | − | 0.780805i | \(-0.714809\pi\) | ||||
−0.624775 | + | 0.780805i | \(0.714809\pi\) | |||||||
\(164\) | −9.41189 | −0.734945 | ||||||||
\(165\) | −6.10045 | −0.474919 | ||||||||
\(166\) | 0.501147 | 0.0388966 | ||||||||
\(167\) | 9.93294 | 0.768634 | 0.384317 | − | 0.923201i | \(-0.374437\pi\) | ||||
0.384317 | + | 0.923201i | \(0.374437\pi\) | |||||||
\(168\) | −12.4122 | −0.957625 | ||||||||
\(169\) | 15.7546 | 1.21189 | ||||||||
\(170\) | 3.96754 | 0.304296 | ||||||||
\(171\) | −0.717489 | −0.0548678 | ||||||||
\(172\) | 14.9594 | 1.14064 | ||||||||
\(173\) | −13.5963 | −1.03371 | −0.516855 | − | 0.856073i | \(-0.672897\pi\) | ||||
−0.516855 | + | 0.856073i | \(0.672897\pi\) | |||||||
\(174\) | 1.32185 | 0.100209 | ||||||||
\(175\) | 13.2720 | 1.00327 | ||||||||
\(176\) | 7.59361 | 0.572390 | ||||||||
\(177\) | 15.0071 | 1.12800 | ||||||||
\(178\) | 6.03591 | 0.452410 | ||||||||
\(179\) | 14.4590 | 1.08072 | 0.540358 | − | 0.841435i | \(-0.318289\pi\) | ||||
0.540358 | + | 0.841435i | \(0.318289\pi\) | |||||||
\(180\) | 1.51849 | 0.113181 | ||||||||
\(181\) | 5.91625 | 0.439752 | 0.219876 | − | 0.975528i | \(-0.429435\pi\) | ||||
0.219876 | + | 0.975528i | \(0.429435\pi\) | |||||||
\(182\) | −11.1662 | −0.827697 | ||||||||
\(183\) | −10.7351 | −0.793560 | ||||||||
\(184\) | 5.84149 | 0.430640 | ||||||||
\(185\) | 5.21863 | 0.383681 | ||||||||
\(186\) | −4.75986 | −0.349010 | ||||||||
\(187\) | 15.9503 | 1.16640 | ||||||||
\(188\) | −8.98279 | −0.655138 | ||||||||
\(189\) | −26.8565 | −1.95352 | ||||||||
\(190\) | 0.832326 | 0.0603833 | ||||||||
\(191\) | 22.2794 | 1.61208 | 0.806039 | − | 0.591862i | \(-0.201607\pi\) | ||||
0.806039 | + | 0.591862i | \(0.201607\pi\) | |||||||
\(192\) | 6.06157 | 0.437456 | ||||||||
\(193\) | −12.8221 | −0.922955 | −0.461478 | − | 0.887152i | \(-0.652681\pi\) | ||||
−0.461478 | + | 0.887152i | \(0.652681\pi\) | |||||||
\(194\) | −2.17720 | −0.156314 | ||||||||
\(195\) | −12.5768 | −0.900647 | ||||||||
\(196\) | −29.6296 | −2.11640 | ||||||||
\(197\) | 1.62495 | 0.115773 | 0.0578866 | − | 0.998323i | \(-0.481564\pi\) | ||||
0.0578866 | + | 0.998323i | \(0.481564\pi\) | |||||||
\(198\) | −0.625365 | −0.0444428 | ||||||||
\(199\) | 12.0603 | 0.854933 | 0.427466 | − | 0.904031i | \(-0.359406\pi\) | ||||
0.427466 | + | 0.904031i | \(0.359406\pi\) | |||||||
\(200\) | 4.51783 | 0.319459 | ||||||||
\(201\) | −23.3726 | −1.64857 | ||||||||
\(202\) | 3.66529 | 0.257889 | ||||||||
\(203\) | 9.47740 | 0.665183 | ||||||||
\(204\) | 17.3860 | 1.21726 | ||||||||
\(205\) | 7.78615 | 0.543809 | ||||||||
\(206\) | 3.03577 | 0.211512 | ||||||||
\(207\) | 1.98138 | 0.137715 | ||||||||
\(208\) | 15.6552 | 1.08549 | ||||||||
\(209\) | 3.34613 | 0.231456 | ||||||||
\(210\) | 4.88396 | 0.337025 | ||||||||
\(211\) | −21.0651 | −1.45018 | −0.725090 | − | 0.688654i | \(-0.758202\pi\) | ||||
−0.725090 | + | 0.688654i | \(0.758202\pi\) | |||||||
\(212\) | 10.6249 | 0.729719 | ||||||||
\(213\) | 9.17578 | 0.628714 | ||||||||
\(214\) | −6.30067 | −0.430705 | ||||||||
\(215\) | −12.3754 | −0.843995 | ||||||||
\(216\) | −9.14202 | −0.622035 | ||||||||
\(217\) | −34.1273 | −2.31671 | ||||||||
\(218\) | −1.57139 | −0.106428 | ||||||||
\(219\) | −6.90634 | −0.466687 | ||||||||
\(220\) | −7.08172 | −0.477450 | ||||||||
\(221\) | 32.8836 | 2.21199 | ||||||||
\(222\) | −2.34265 | −0.157228 | ||||||||
\(223\) | −2.07074 | −0.138667 | −0.0693336 | − | 0.997594i | \(-0.522087\pi\) | ||||
−0.0693336 | + | 0.997594i | \(0.522087\pi\) | |||||||
\(224\) | −21.9642 | −1.46754 | ||||||||
\(225\) | 1.53240 | 0.102160 | ||||||||
\(226\) | 3.92503 | 0.261089 | ||||||||
\(227\) | 1.64406 | 0.109120 | 0.0545599 | − | 0.998510i | \(-0.482624\pi\) | ||||
0.0545599 | + | 0.998510i | \(0.482624\pi\) | |||||||
\(228\) | 3.64730 | 0.241548 | ||||||||
\(229\) | −12.7092 | −0.839848 | −0.419924 | − | 0.907559i | \(-0.637943\pi\) | ||||
−0.419924 | + | 0.907559i | \(0.637943\pi\) | |||||||
\(230\) | −2.29851 | −0.151559 | ||||||||
\(231\) | 19.6346 | 1.29186 | ||||||||
\(232\) | 3.22613 | 0.211806 | ||||||||
\(233\) | 25.1543 | 1.64792 | 0.823958 | − | 0.566651i | \(-0.191761\pi\) | ||||
0.823958 | + | 0.566651i | \(0.191761\pi\) | |||||||
\(234\) | −1.28927 | −0.0842822 | ||||||||
\(235\) | 7.43117 | 0.484756 | ||||||||
\(236\) | 17.4210 | 1.13401 | ||||||||
\(237\) | −13.7970 | −0.896212 | ||||||||
\(238\) | −12.7697 | −0.827736 | ||||||||
\(239\) | 3.76267 | 0.243387 | 0.121693 | − | 0.992568i | \(-0.461168\pi\) | ||||
0.121693 | + | 0.992568i | \(0.461168\pi\) | |||||||
\(240\) | −6.84736 | −0.441995 | ||||||||
\(241\) | −5.67080 | −0.365289 | −0.182644 | − | 0.983179i | \(-0.558466\pi\) | ||||
−0.182644 | + | 0.983179i | \(0.558466\pi\) | |||||||
\(242\) | −1.82556 | −0.117352 | ||||||||
\(243\) | −5.71567 | −0.366660 | ||||||||
\(244\) | −12.4618 | −0.797788 | ||||||||
\(245\) | 24.5116 | 1.56599 | ||||||||
\(246\) | −3.49522 | −0.222847 | ||||||||
\(247\) | 6.89846 | 0.438939 | ||||||||
\(248\) | −11.6170 | −0.737682 | ||||||||
\(249\) | −1.81673 | −0.115130 | ||||||||
\(250\) | −5.01260 | −0.317025 | ||||||||
\(251\) | 10.1988 | 0.643741 | 0.321871 | − | 0.946784i | \(-0.395688\pi\) | ||||
0.321871 | + | 0.946784i | \(0.395688\pi\) | |||||||
\(252\) | −4.88732 | −0.307872 | ||||||||
\(253\) | −9.24048 | −0.580944 | ||||||||
\(254\) | −5.78418 | −0.362932 | ||||||||
\(255\) | −14.3828 | −0.900689 | ||||||||
\(256\) | 3.11611 | 0.194757 | ||||||||
\(257\) | 0.739967 | 0.0461579 | 0.0230789 | − | 0.999734i | \(-0.492653\pi\) | ||||
0.0230789 | + | 0.999734i | \(0.492653\pi\) | |||||||
\(258\) | 5.55533 | 0.345860 | ||||||||
\(259\) | −16.7964 | −1.04368 | ||||||||
\(260\) | −14.5999 | −0.905445 | ||||||||
\(261\) | 1.09427 | 0.0677338 | ||||||||
\(262\) | 7.12344 | 0.440087 | ||||||||
\(263\) | 11.6292 | 0.717090 | 0.358545 | − | 0.933513i | \(-0.383273\pi\) | ||||
0.358545 | + | 0.933513i | \(0.383273\pi\) | |||||||
\(264\) | 6.68365 | 0.411350 | ||||||||
\(265\) | −8.78960 | −0.539941 | ||||||||
\(266\) | −2.67888 | −0.164252 | ||||||||
\(267\) | −21.8810 | −1.33909 | ||||||||
\(268\) | −27.1321 | −1.65736 | ||||||||
\(269\) | 20.9998 | 1.28038 | 0.640190 | − | 0.768217i | \(-0.278856\pi\) | ||||
0.640190 | + | 0.768217i | \(0.278856\pi\) | |||||||
\(270\) | 3.59720 | 0.218918 | ||||||||
\(271\) | −20.4684 | −1.24337 | −0.621684 | − | 0.783268i | \(-0.713551\pi\) | ||||
−0.621684 | + | 0.783268i | \(0.713551\pi\) | |||||||
\(272\) | 17.9032 | 1.08554 | ||||||||
\(273\) | 40.4791 | 2.44991 | ||||||||
\(274\) | −8.32628 | −0.503009 | ||||||||
\(275\) | −7.14662 | −0.430957 | ||||||||
\(276\) | −10.0722 | −0.606274 | ||||||||
\(277\) | 8.22513 | 0.494200 | 0.247100 | − | 0.968990i | \(-0.420522\pi\) | ||||
0.247100 | + | 0.968990i | \(0.420522\pi\) | |||||||
\(278\) | −2.19564 | −0.131686 | ||||||||
\(279\) | −3.94038 | −0.235905 | ||||||||
\(280\) | 11.9199 | 0.712351 | ||||||||
\(281\) | 13.8741 | 0.827658 | 0.413829 | − | 0.910355i | \(-0.364191\pi\) | ||||
0.413829 | + | 0.910355i | \(0.364191\pi\) | |||||||
\(282\) | −3.33586 | −0.198648 | ||||||||
\(283\) | 30.4615 | 1.81075 | 0.905373 | − | 0.424616i | \(-0.139591\pi\) | ||||
0.905373 | + | 0.424616i | \(0.139591\pi\) | |||||||
\(284\) | 10.6517 | 0.632064 | ||||||||
\(285\) | −3.01729 | −0.178729 | ||||||||
\(286\) | 6.01272 | 0.355540 | ||||||||
\(287\) | −25.0601 | −1.47925 | ||||||||
\(288\) | −2.53601 | −0.149436 | ||||||||
\(289\) | 20.6056 | 1.21210 | ||||||||
\(290\) | −1.26942 | −0.0745427 | ||||||||
\(291\) | 7.89265 | 0.462675 | ||||||||
\(292\) | −8.01724 | −0.469174 | ||||||||
\(293\) | −27.5968 | −1.61222 | −0.806111 | − | 0.591765i | \(-0.798431\pi\) | ||||
−0.806111 | + | 0.591765i | \(0.798431\pi\) | |||||||
\(294\) | −11.0033 | −0.641724 | ||||||||
\(295\) | −14.4118 | −0.839088 | ||||||||
\(296\) | −5.71752 | −0.332324 | ||||||||
\(297\) | 14.4615 | 0.839141 | ||||||||
\(298\) | 6.74092 | 0.390491 | ||||||||
\(299\) | −19.0504 | −1.10171 | ||||||||
\(300\) | −7.78986 | −0.449748 | ||||||||
\(301\) | 39.8307 | 2.29581 | ||||||||
\(302\) | 6.42465 | 0.369697 | ||||||||
\(303\) | −13.2872 | −0.763328 | ||||||||
\(304\) | 3.75581 | 0.215411 | ||||||||
\(305\) | 10.3093 | 0.590307 | ||||||||
\(306\) | −1.47441 | −0.0842861 | ||||||||
\(307\) | −13.6959 | −0.781667 | −0.390834 | − | 0.920461i | \(-0.627813\pi\) | ||||
−0.390834 | + | 0.920461i | \(0.627813\pi\) | |||||||
\(308\) | 22.7928 | 1.29874 | ||||||||
\(309\) | −11.0051 | −0.626056 | ||||||||
\(310\) | 4.57106 | 0.259619 | ||||||||
\(311\) | −0.171615 | −0.00973139 | −0.00486569 | − | 0.999988i | \(-0.501549\pi\) | ||||
−0.00486569 | + | 0.999988i | \(0.501549\pi\) | |||||||
\(312\) | 13.7792 | 0.780093 | ||||||||
\(313\) | −17.5584 | −0.992461 | −0.496230 | − | 0.868191i | \(-0.665283\pi\) | ||||
−0.496230 | + | 0.868191i | \(0.665283\pi\) | |||||||
\(314\) | 7.30686 | 0.412350 | ||||||||
\(315\) | 4.04312 | 0.227804 | ||||||||
\(316\) | −16.0163 | −0.900987 | ||||||||
\(317\) | −1.72271 | −0.0967569 | −0.0483784 | − | 0.998829i | \(-0.515405\pi\) | ||||
−0.0483784 | + | 0.998829i | \(0.515405\pi\) | |||||||
\(318\) | 3.94567 | 0.221262 | ||||||||
\(319\) | −5.10332 | −0.285731 | ||||||||
\(320\) | −5.82114 | −0.325412 | ||||||||
\(321\) | 22.8408 | 1.27485 | ||||||||
\(322\) | 7.39784 | 0.412265 | ||||||||
\(323\) | 7.88906 | 0.438959 | ||||||||
\(324\) | 12.7277 | 0.707096 | ||||||||
\(325\) | −14.7337 | −0.817276 | ||||||||
\(326\) | −6.87736 | −0.380902 | ||||||||
\(327\) | 5.69650 | 0.315017 | ||||||||
\(328\) | −8.53051 | −0.471018 | ||||||||
\(329\) | −23.9175 | −1.31862 | ||||||||
\(330\) | −2.62988 | −0.144770 | ||||||||
\(331\) | 23.5273 | 1.29318 | 0.646590 | − | 0.762838i | \(-0.276195\pi\) | ||||
0.646590 | + | 0.762838i | \(0.276195\pi\) | |||||||
\(332\) | −2.10895 | −0.115744 | ||||||||
\(333\) | −1.93933 | −0.106275 | ||||||||
\(334\) | 4.28205 | 0.234303 | ||||||||
\(335\) | 22.4455 | 1.22633 | ||||||||
\(336\) | 22.0385 | 1.20230 | ||||||||
\(337\) | −8.02169 | −0.436969 | −0.218485 | − | 0.975840i | \(-0.570111\pi\) | ||||
−0.218485 | + | 0.975840i | \(0.570111\pi\) | |||||||
\(338\) | 6.79173 | 0.369421 | ||||||||
\(339\) | −14.2287 | −0.772799 | ||||||||
\(340\) | −16.6964 | −0.905487 | ||||||||
\(341\) | 18.3766 | 0.995150 | ||||||||
\(342\) | −0.309307 | −0.0167254 | ||||||||
\(343\) | −45.0790 | −2.43404 | ||||||||
\(344\) | 13.5585 | 0.731024 | ||||||||
\(345\) | 8.33238 | 0.448600 | ||||||||
\(346\) | −5.86133 | −0.315107 | ||||||||
\(347\) | −11.7465 | −0.630584 | −0.315292 | − | 0.948995i | \(-0.602102\pi\) | ||||
−0.315292 | + | 0.948995i | \(0.602102\pi\) | |||||||
\(348\) | −5.56265 | −0.298189 | ||||||||
\(349\) | 11.8697 | 0.635373 | 0.317686 | − | 0.948196i | \(-0.397094\pi\) | ||||
0.317686 | + | 0.948196i | \(0.397094\pi\) | |||||||
\(350\) | 5.72151 | 0.305828 | ||||||||
\(351\) | 29.8142 | 1.59136 | ||||||||
\(352\) | 11.8271 | 0.630387 | ||||||||
\(353\) | 22.4752 | 1.19624 | 0.598118 | − | 0.801408i | \(-0.295915\pi\) | ||||
0.598118 | + | 0.801408i | \(0.295915\pi\) | |||||||
\(354\) | 6.46948 | 0.343849 | ||||||||
\(355\) | −8.81183 | −0.467683 | ||||||||
\(356\) | −25.4006 | −1.34623 | ||||||||
\(357\) | 46.2918 | 2.45002 | ||||||||
\(358\) | 6.23322 | 0.329436 | ||||||||
\(359\) | −24.8782 | −1.31302 | −0.656510 | − | 0.754317i | \(-0.727968\pi\) | ||||
−0.656510 | + | 0.754317i | \(0.727968\pi\) | |||||||
\(360\) | 1.37629 | 0.0725368 | ||||||||
\(361\) | −17.3450 | −0.912895 | ||||||||
\(362\) | 2.55047 | 0.134050 | ||||||||
\(363\) | 6.61791 | 0.347350 | ||||||||
\(364\) | 46.9903 | 2.46296 | ||||||||
\(365\) | 6.63240 | 0.347156 | ||||||||
\(366\) | −4.62785 | −0.241902 | ||||||||
\(367\) | 32.9944 | 1.72230 | 0.861148 | − | 0.508355i | \(-0.169746\pi\) | ||||
0.861148 | + | 0.508355i | \(0.169746\pi\) | |||||||
\(368\) | −10.3718 | −0.540669 | ||||||||
\(369\) | −2.89347 | −0.150628 | ||||||||
\(370\) | 2.24973 | 0.116958 | ||||||||
\(371\) | 28.2897 | 1.46873 | ||||||||
\(372\) | 20.0306 | 1.03854 | ||||||||
\(373\) | −9.20405 | −0.476567 | −0.238284 | − | 0.971196i | \(-0.576585\pi\) | ||||
−0.238284 | + | 0.971196i | \(0.576585\pi\) | |||||||
\(374\) | 6.87613 | 0.355556 | ||||||||
\(375\) | 18.1713 | 0.938364 | ||||||||
\(376\) | −8.14159 | −0.419870 | ||||||||
\(377\) | −10.5211 | −0.541866 | ||||||||
\(378\) | −11.5777 | −0.595494 | ||||||||
\(379\) | 5.20872 | 0.267554 | 0.133777 | − | 0.991011i | \(-0.457289\pi\) | ||||
0.133777 | + | 0.991011i | \(0.457289\pi\) | |||||||
\(380\) | −3.50263 | −0.179681 | ||||||||
\(381\) | 20.9684 | 1.07424 | ||||||||
\(382\) | 9.60455 | 0.491411 | ||||||||
\(383\) | −12.3327 | −0.630174 | −0.315087 | − | 0.949063i | \(-0.602034\pi\) | ||||
−0.315087 | + | 0.949063i | \(0.602034\pi\) | |||||||
\(384\) | 16.8254 | 0.858616 | ||||||||
\(385\) | −18.8558 | −0.960978 | ||||||||
\(386\) | −5.52756 | −0.281345 | ||||||||
\(387\) | 4.59891 | 0.233776 | ||||||||
\(388\) | 9.16220 | 0.465140 | ||||||||
\(389\) | −16.7375 | −0.848626 | −0.424313 | − | 0.905516i | \(-0.639484\pi\) | ||||
−0.424313 | + | 0.905516i | \(0.639484\pi\) | |||||||
\(390\) | −5.42183 | −0.274545 | ||||||||
\(391\) | −21.7860 | −1.10176 | ||||||||
\(392\) | −26.8549 | −1.35638 | ||||||||
\(393\) | −25.8234 | −1.30262 | ||||||||
\(394\) | 0.700511 | 0.0352912 | ||||||||
\(395\) | 13.2498 | 0.666668 | ||||||||
\(396\) | 2.63169 | 0.132247 | ||||||||
\(397\) | 23.7860 | 1.19378 | 0.596892 | − | 0.802322i | \(-0.296402\pi\) | ||||
0.596892 | + | 0.802322i | \(0.296402\pi\) | |||||||
\(398\) | 5.19915 | 0.260610 | ||||||||
\(399\) | 9.71128 | 0.486172 | ||||||||
\(400\) | −8.02161 | −0.401081 | ||||||||
\(401\) | −2.86075 | −0.142859 | −0.0714295 | − | 0.997446i | \(-0.522756\pi\) | ||||
−0.0714295 | + | 0.997446i | \(0.522756\pi\) | |||||||
\(402\) | −10.0758 | −0.502536 | ||||||||
\(403\) | 37.8857 | 1.88722 | ||||||||
\(404\) | −15.4244 | −0.767395 | ||||||||
\(405\) | −10.5292 | −0.523202 | ||||||||
\(406\) | 4.08567 | 0.202768 | ||||||||
\(407\) | 9.04439 | 0.448314 | ||||||||
\(408\) | 15.7578 | 0.780129 | ||||||||
\(409\) | −6.71964 | −0.332265 | −0.166132 | − | 0.986103i | \(-0.553128\pi\) | ||||
−0.166132 | + | 0.986103i | \(0.553128\pi\) | |||||||
\(410\) | 3.35658 | 0.165770 | ||||||||
\(411\) | 30.1839 | 1.48886 | ||||||||
\(412\) | −12.7753 | −0.629392 | ||||||||
\(413\) | 46.3850 | 2.28246 | ||||||||
\(414\) | 0.854164 | 0.0419799 | ||||||||
\(415\) | 1.74467 | 0.0856423 | ||||||||
\(416\) | 24.3831 | 1.19548 | ||||||||
\(417\) | 7.95949 | 0.389778 | ||||||||
\(418\) | 1.44250 | 0.0705551 | ||||||||
\(419\) | −39.3202 | −1.92092 | −0.960459 | − | 0.278420i | \(-0.910189\pi\) | ||||
−0.960459 | + | 0.278420i | \(0.910189\pi\) | |||||||
\(420\) | −20.5529 | −1.00288 | ||||||||
\(421\) | 5.48595 | 0.267369 | 0.133685 | − | 0.991024i | \(-0.457319\pi\) | ||||
0.133685 | + | 0.991024i | \(0.457319\pi\) | |||||||
\(422\) | −9.08108 | −0.442060 | ||||||||
\(423\) | −2.76155 | −0.134271 | ||||||||
\(424\) | 9.62988 | 0.467669 | ||||||||
\(425\) | −16.8494 | −0.817314 | ||||||||
\(426\) | 3.95564 | 0.191652 | ||||||||
\(427\) | −33.1808 | −1.60573 | ||||||||
\(428\) | 26.5147 | 1.28164 | ||||||||
\(429\) | −21.7969 | −1.05236 | ||||||||
\(430\) | −5.33498 | −0.257276 | ||||||||
\(431\) | −5.47777 | −0.263855 | −0.131927 | − | 0.991259i | \(-0.542117\pi\) | ||||
−0.131927 | + | 0.991259i | \(0.542117\pi\) | |||||||
\(432\) | 16.2321 | 0.780967 | ||||||||
\(433\) | −25.3491 | −1.21820 | −0.609099 | − | 0.793094i | \(-0.708469\pi\) | ||||
−0.609099 | + | 0.793094i | \(0.708469\pi\) | |||||||
\(434\) | −14.7121 | −0.706206 | ||||||||
\(435\) | 4.60180 | 0.220639 | ||||||||
\(436\) | 6.61280 | 0.316696 | ||||||||
\(437\) | −4.57035 | −0.218630 | ||||||||
\(438\) | −2.97730 | −0.142261 | ||||||||
\(439\) | −8.92124 | −0.425788 | −0.212894 | − | 0.977075i | \(-0.568289\pi\) | ||||
−0.212894 | + | 0.977075i | \(0.568289\pi\) | |||||||
\(440\) | −6.41854 | −0.305992 | ||||||||
\(441\) | −9.10892 | −0.433758 | ||||||||
\(442\) | 14.1760 | 0.674284 | ||||||||
\(443\) | −39.4683 | −1.87520 | −0.937598 | − | 0.347720i | \(-0.886956\pi\) | ||||
−0.937598 | + | 0.347720i | \(0.886956\pi\) | |||||||
\(444\) | 9.85843 | 0.467861 | ||||||||
\(445\) | 21.0131 | 0.996114 | ||||||||
\(446\) | −0.892689 | −0.0422700 | ||||||||
\(447\) | −24.4367 | −1.15582 | ||||||||
\(448\) | 18.7356 | 0.885173 | ||||||||
\(449\) | −7.56629 | −0.357075 | −0.178538 | − | 0.983933i | \(-0.557137\pi\) | ||||
−0.178538 | + | 0.983933i | \(0.557137\pi\) | |||||||
\(450\) | 0.660613 | 0.0311416 | ||||||||
\(451\) | 13.4942 | 0.635415 | ||||||||
\(452\) | −16.5175 | −0.776917 | ||||||||
\(453\) | −23.2902 | −1.09427 | ||||||||
\(454\) | 0.708746 | 0.0332631 | ||||||||
\(455\) | −38.8735 | −1.82242 | ||||||||
\(456\) | 3.30574 | 0.154806 | ||||||||
\(457\) | −40.5680 | −1.89769 | −0.948846 | − | 0.315740i | \(-0.897747\pi\) | ||||
−0.948846 | + | 0.315740i | \(0.897747\pi\) | |||||||
\(458\) | −5.47888 | −0.256011 | ||||||||
\(459\) | 34.0954 | 1.59144 | ||||||||
\(460\) | 9.67267 | 0.450990 | ||||||||
\(461\) | −16.6102 | −0.773613 | −0.386807 | − | 0.922161i | \(-0.626422\pi\) | ||||
−0.386807 | + | 0.922161i | \(0.626422\pi\) | |||||||
\(462\) | 8.46438 | 0.393799 | ||||||||
\(463\) | −10.7052 | −0.497514 | −0.248757 | − | 0.968566i | \(-0.580022\pi\) | ||||
−0.248757 | + | 0.968566i | \(0.580022\pi\) | |||||||
\(464\) | −5.72815 | −0.265922 | ||||||||
\(465\) | −16.5707 | −0.768447 | ||||||||
\(466\) | 10.8439 | 0.502336 | ||||||||
\(467\) | −21.0194 | −0.972664 | −0.486332 | − | 0.873774i | \(-0.661665\pi\) | ||||
−0.486332 | + | 0.873774i | \(0.661665\pi\) | |||||||
\(468\) | 5.42556 | 0.250797 | ||||||||
\(469\) | −72.2418 | −3.33582 | ||||||||
\(470\) | 3.20355 | 0.147769 | ||||||||
\(471\) | −26.4883 | −1.22052 | ||||||||
\(472\) | 15.7896 | 0.726774 | ||||||||
\(473\) | −21.4478 | −0.986169 | ||||||||
\(474\) | −5.94784 | −0.273193 | ||||||||
\(475\) | −3.53473 | −0.162184 | ||||||||
\(476\) | 53.7379 | 2.46307 | ||||||||
\(477\) | 3.26637 | 0.149557 | ||||||||
\(478\) | 1.62207 | 0.0741918 | ||||||||
\(479\) | 11.8653 | 0.542139 | 0.271070 | − | 0.962560i | \(-0.412623\pi\) | ||||
0.271070 | + | 0.962560i | \(0.412623\pi\) | |||||||
\(480\) | −10.6648 | −0.486780 | ||||||||
\(481\) | 18.6461 | 0.850191 | ||||||||
\(482\) | −2.44466 | −0.111351 | ||||||||
\(483\) | −26.8181 | −1.22027 | ||||||||
\(484\) | 7.68241 | 0.349200 | ||||||||
\(485\) | −7.57959 | −0.344171 | ||||||||
\(486\) | −2.46400 | −0.111769 | ||||||||
\(487\) | 0.526452 | 0.0238558 | 0.0119279 | − | 0.999929i | \(-0.496203\pi\) | ||||
0.0119279 | + | 0.999929i | \(0.496203\pi\) | |||||||
\(488\) | −11.2948 | −0.511293 | ||||||||
\(489\) | 24.9313 | 1.12743 | ||||||||
\(490\) | 10.5668 | 0.477361 | ||||||||
\(491\) | 26.2774 | 1.18588 | 0.592940 | − | 0.805246i | \(-0.297967\pi\) | ||||
0.592940 | + | 0.805246i | \(0.297967\pi\) | |||||||
\(492\) | 14.7087 | 0.663120 | ||||||||
\(493\) | −12.0319 | −0.541891 | ||||||||
\(494\) | 2.97390 | 0.133802 | ||||||||
\(495\) | −2.17711 | −0.0978538 | ||||||||
\(496\) | 20.6266 | 0.926160 | ||||||||
\(497\) | 28.3612 | 1.27218 | ||||||||
\(498\) | −0.783183 | −0.0350953 | ||||||||
\(499\) | 19.1651 | 0.857950 | 0.428975 | − | 0.903316i | \(-0.358875\pi\) | ||||
0.428975 | + | 0.903316i | \(0.358875\pi\) | |||||||
\(500\) | 21.0942 | 0.943363 | ||||||||
\(501\) | −15.5230 | −0.693516 | ||||||||
\(502\) | 4.39665 | 0.196232 | ||||||||
\(503\) | 22.4963 | 1.00306 | 0.501531 | − | 0.865140i | \(-0.332770\pi\) | ||||
0.501531 | + | 0.865140i | \(0.332770\pi\) | |||||||
\(504\) | −4.42964 | −0.197312 | ||||||||
\(505\) | 12.7601 | 0.567819 | ||||||||
\(506\) | −3.98353 | −0.177090 | ||||||||
\(507\) | −24.6209 | −1.09345 | ||||||||
\(508\) | 24.3412 | 1.07997 | ||||||||
\(509\) | 11.4434 | 0.507222 | 0.253611 | − | 0.967306i | \(-0.418382\pi\) | ||||
0.253611 | + | 0.967306i | \(0.418382\pi\) | |||||||
\(510\) | −6.20039 | −0.274558 | ||||||||
\(511\) | −21.3467 | −0.944321 | ||||||||
\(512\) | 22.8760 | 1.01098 | ||||||||
\(513\) | 7.15267 | 0.315798 | ||||||||
\(514\) | 0.318997 | 0.0140703 | ||||||||
\(515\) | 10.5686 | 0.465706 | ||||||||
\(516\) | −23.3782 | −1.02917 | ||||||||
\(517\) | 12.8789 | 0.566415 | ||||||||
\(518\) | −7.24085 | −0.318145 | ||||||||
\(519\) | 21.2481 | 0.932687 | ||||||||
\(520\) | −13.2326 | −0.580290 | ||||||||
\(521\) | −6.38668 | −0.279805 | −0.139903 | − | 0.990165i | \(-0.544679\pi\) | ||||
−0.139903 | + | 0.990165i | \(0.544679\pi\) | |||||||
\(522\) | 0.471737 | 0.0206474 | ||||||||
\(523\) | 34.8404 | 1.52347 | 0.761733 | − | 0.647891i | \(-0.224349\pi\) | ||||
0.761733 | + | 0.647891i | \(0.224349\pi\) | |||||||
\(524\) | −29.9772 | −1.30956 | ||||||||
\(525\) | −20.7412 | −0.905222 | ||||||||
\(526\) | 5.01332 | 0.218591 | ||||||||
\(527\) | 43.3260 | 1.88731 | ||||||||
\(528\) | −11.8671 | −0.516451 | ||||||||
\(529\) | −10.3788 | −0.451251 | ||||||||
\(530\) | −3.78916 | −0.164591 | ||||||||
\(531\) | 5.35567 | 0.232416 | ||||||||
\(532\) | 11.2734 | 0.488762 | ||||||||
\(533\) | 27.8199 | 1.20501 | ||||||||
\(534\) | −9.43279 | −0.408197 | ||||||||
\(535\) | −21.9348 | −0.948324 | ||||||||
\(536\) | −24.5913 | −1.06218 | ||||||||
\(537\) | −22.5962 | −0.975099 | ||||||||
\(538\) | 9.05293 | 0.390299 | ||||||||
\(539\) | 42.4809 | 1.82978 | ||||||||
\(540\) | −15.1379 | −0.651430 | ||||||||
\(541\) | −34.2589 | −1.47291 | −0.736453 | − | 0.676489i | \(-0.763501\pi\) | ||||
−0.736453 | + | 0.676489i | \(0.763501\pi\) | |||||||
\(542\) | −8.82386 | −0.379017 | ||||||||
\(543\) | −9.24580 | −0.396775 | ||||||||
\(544\) | 27.8844 | 1.19554 | ||||||||
\(545\) | −5.47055 | −0.234333 | ||||||||
\(546\) | 17.4504 | 0.746807 | ||||||||
\(547\) | −21.6616 | −0.926184 | −0.463092 | − | 0.886310i | \(-0.653260\pi\) | ||||
−0.463092 | + | 0.886310i | \(0.653260\pi\) | |||||||
\(548\) | 35.0390 | 1.49679 | ||||||||
\(549\) | −3.83110 | −0.163508 | ||||||||
\(550\) | −3.08088 | −0.131369 | ||||||||
\(551\) | −2.52411 | −0.107531 | ||||||||
\(552\) | −9.12895 | −0.388554 | ||||||||
\(553\) | −42.6449 | −1.81345 | ||||||||
\(554\) | 3.54582 | 0.150647 | ||||||||
\(555\) | −8.15556 | −0.346184 | ||||||||
\(556\) | 9.23980 | 0.391855 | ||||||||
\(557\) | −25.7714 | −1.09197 | −0.545985 | − | 0.837795i | \(-0.683844\pi\) | ||||
−0.545985 | + | 0.837795i | \(0.683844\pi\) | |||||||
\(558\) | −1.69868 | −0.0719110 | ||||||||
\(559\) | −44.2173 | −1.87019 | ||||||||
\(560\) | −21.1644 | −0.894358 | ||||||||
\(561\) | −24.9269 | −1.05241 | ||||||||
\(562\) | 5.98106 | 0.252296 | ||||||||
\(563\) | 20.5069 | 0.864262 | 0.432131 | − | 0.901811i | \(-0.357762\pi\) | ||||
0.432131 | + | 0.901811i | \(0.357762\pi\) | |||||||
\(564\) | 14.0381 | 0.591112 | ||||||||
\(565\) | 13.6644 | 0.574864 | ||||||||
\(566\) | 13.1318 | 0.551972 | ||||||||
\(567\) | 33.8888 | 1.42320 | ||||||||
\(568\) | 9.65424 | 0.405083 | ||||||||
\(569\) | −44.5631 | −1.86818 | −0.934092 | − | 0.357032i | \(-0.883789\pi\) | ||||
−0.934092 | + | 0.357032i | \(0.883789\pi\) | |||||||
\(570\) | −1.30074 | −0.0544821 | ||||||||
\(571\) | 28.8727 | 1.20829 | 0.604143 | − | 0.796876i | \(-0.293515\pi\) | ||||
0.604143 | + | 0.796876i | \(0.293515\pi\) | |||||||
\(572\) | −25.3030 | −1.05797 | ||||||||
\(573\) | −34.8177 | −1.45453 | ||||||||
\(574\) | −10.8033 | −0.450921 | ||||||||
\(575\) | 9.76130 | 0.407075 | ||||||||
\(576\) | 2.16323 | 0.0901348 | ||||||||
\(577\) | −12.2296 | −0.509124 | −0.254562 | − | 0.967056i | \(-0.581931\pi\) | ||||
−0.254562 | + | 0.967056i | \(0.581931\pi\) | |||||||
\(578\) | 8.88301 | 0.369484 | ||||||||
\(579\) | 20.0381 | 0.832756 | ||||||||
\(580\) | 5.34201 | 0.221815 | ||||||||
\(581\) | −5.61528 | −0.232961 | ||||||||
\(582\) | 3.40249 | 0.141038 | ||||||||
\(583\) | −15.2332 | −0.630896 | ||||||||
\(584\) | −7.26646 | −0.300688 | ||||||||
\(585\) | −4.48839 | −0.185572 | ||||||||
\(586\) | −11.8969 | −0.491455 | ||||||||
\(587\) | −17.2501 | −0.711988 | −0.355994 | − | 0.934488i | \(-0.615858\pi\) | ||||
−0.355994 | + | 0.934488i | \(0.615858\pi\) | |||||||
\(588\) | 46.3045 | 1.90956 | ||||||||
\(589\) | 9.08911 | 0.374510 | ||||||||
\(590\) | −6.21287 | −0.255780 | ||||||||
\(591\) | −2.53944 | −0.104459 | ||||||||
\(592\) | 10.1517 | 0.417234 | ||||||||
\(593\) | 35.4901 | 1.45740 | 0.728702 | − | 0.684831i | \(-0.240124\pi\) | ||||
0.728702 | + | 0.684831i | \(0.240124\pi\) | |||||||
\(594\) | 6.23429 | 0.255796 | ||||||||
\(595\) | −44.4557 | −1.82250 | ||||||||
\(596\) | −28.3674 | −1.16197 | ||||||||
\(597\) | −18.8476 | −0.771381 | ||||||||
\(598\) | −8.21255 | −0.335836 | ||||||||
\(599\) | −27.9759 | −1.14306 | −0.571532 | − | 0.820580i | \(-0.693651\pi\) | ||||
−0.571532 | + | 0.820580i | \(0.693651\pi\) | |||||||
\(600\) | −7.06037 | −0.288238 | ||||||||
\(601\) | 3.04309 | 0.124130 | 0.0620652 | − | 0.998072i | \(-0.480231\pi\) | ||||
0.0620652 | + | 0.998072i | \(0.480231\pi\) | |||||||
\(602\) | 17.1709 | 0.699832 | ||||||||
\(603\) | −8.34114 | −0.339677 | ||||||||
\(604\) | −27.0365 | −1.10010 | ||||||||
\(605\) | −6.35541 | −0.258384 | ||||||||
\(606\) | −5.72805 | −0.232686 | ||||||||
\(607\) | −18.9064 | −0.767387 | −0.383694 | − | 0.923460i | \(-0.625348\pi\) | ||||
−0.383694 | + | 0.923460i | \(0.625348\pi\) | |||||||
\(608\) | 5.84971 | 0.237237 | ||||||||
\(609\) | −14.8111 | −0.600175 | ||||||||
\(610\) | 4.44429 | 0.179944 | ||||||||
\(611\) | 26.5516 | 1.07416 | ||||||||
\(612\) | 6.20465 | 0.250808 | ||||||||
\(613\) | 44.2346 | 1.78662 | 0.893309 | − | 0.449442i | \(-0.148377\pi\) | ||||
0.893309 | + | 0.449442i | \(0.148377\pi\) | |||||||
\(614\) | −5.90426 | −0.238276 | ||||||||
\(615\) | −12.1680 | −0.490663 | ||||||||
\(616\) | 20.6584 | 0.832349 | ||||||||
\(617\) | −1.91143 | −0.0769511 | −0.0384756 | − | 0.999260i | \(-0.512250\pi\) | ||||
−0.0384756 | + | 0.999260i | \(0.512250\pi\) | |||||||
\(618\) | −4.74424 | −0.190841 | ||||||||
\(619\) | 1.00000 | 0.0401934 | ||||||||
\(620\) | −19.2361 | −0.772541 | ||||||||
\(621\) | −19.7524 | −0.792637 | ||||||||
\(622\) | −0.0739825 | −0.00296643 | ||||||||
\(623\) | −67.6314 | −2.70960 | ||||||||
\(624\) | −24.4656 | −0.979408 | ||||||||
\(625\) | −3.71246 | −0.148499 | ||||||||
\(626\) | −7.56937 | −0.302533 | ||||||||
\(627\) | −5.22926 | −0.208836 | ||||||||
\(628\) | −30.7491 | −1.22702 | ||||||||
\(629\) | 21.3237 | 0.850231 | ||||||||
\(630\) | 1.74297 | 0.0694417 | ||||||||
\(631\) | −11.2642 | −0.448419 | −0.224210 | − | 0.974541i | \(-0.571980\pi\) | ||||
−0.224210 | + | 0.974541i | \(0.571980\pi\) | |||||||
\(632\) | −14.5164 | −0.577432 | ||||||||
\(633\) | 32.9201 | 1.30846 | ||||||||
\(634\) | −0.742652 | −0.0294945 | ||||||||
\(635\) | −20.1367 | −0.799100 | ||||||||
\(636\) | −16.6043 | −0.658404 | ||||||||
\(637\) | 87.5798 | 3.47004 | ||||||||
\(638\) | −2.20002 | −0.0870996 | ||||||||
\(639\) | 3.27463 | 0.129542 | ||||||||
\(640\) | −16.1580 | −0.638701 | ||||||||
\(641\) | 48.5425 | 1.91731 | 0.958657 | − | 0.284565i | \(-0.0918490\pi\) | ||||
0.958657 | + | 0.284565i | \(0.0918490\pi\) | |||||||
\(642\) | 9.84656 | 0.388613 | ||||||||
\(643\) | −6.33981 | −0.250018 | −0.125009 | − | 0.992156i | \(-0.539896\pi\) | ||||
−0.125009 | + | 0.992156i | \(0.539896\pi\) | |||||||
\(644\) | −31.1319 | −1.22677 | ||||||||
\(645\) | 19.3400 | 0.761512 | ||||||||
\(646\) | 3.40094 | 0.133808 | ||||||||
\(647\) | 5.36992 | 0.211113 | 0.105557 | − | 0.994413i | \(-0.466338\pi\) | ||||
0.105557 | + | 0.994413i | \(0.466338\pi\) | |||||||
\(648\) | 11.5358 | 0.453170 | ||||||||
\(649\) | −24.9771 | −0.980435 | ||||||||
\(650\) | −6.35162 | −0.249131 | ||||||||
\(651\) | 53.3335 | 2.09030 | ||||||||
\(652\) | 28.9416 | 1.13344 | ||||||||
\(653\) | 11.7733 | 0.460724 | 0.230362 | − | 0.973105i | \(-0.426009\pi\) | ||||
0.230362 | + | 0.973105i | \(0.426009\pi\) | |||||||
\(654\) | 2.45574 | 0.0960270 | ||||||||
\(655\) | 24.7991 | 0.968982 | ||||||||
\(656\) | 15.1463 | 0.591364 | ||||||||
\(657\) | −2.46471 | −0.0961577 | ||||||||
\(658\) | −10.3108 | −0.401955 | ||||||||
\(659\) | 0.123206 | 0.00479943 | 0.00239972 | − | 0.999997i | \(-0.499236\pi\) | ||||
0.00239972 | + | 0.999997i | \(0.499236\pi\) | |||||||
\(660\) | 11.0672 | 0.430789 | ||||||||
\(661\) | 9.04712 | 0.351892 | 0.175946 | − | 0.984400i | \(-0.443702\pi\) | ||||
0.175946 | + | 0.984400i | \(0.443702\pi\) | |||||||
\(662\) | 10.1425 | 0.394201 | ||||||||
\(663\) | −51.3899 | −1.99582 | ||||||||
\(664\) | −1.91145 | −0.0741788 | ||||||||
\(665\) | −9.32609 | −0.361650 | ||||||||
\(666\) | −0.836038 | −0.0323958 | ||||||||
\(667\) | 6.97044 | 0.269896 | ||||||||
\(668\) | −18.0199 | −0.697211 | ||||||||
\(669\) | 3.23611 | 0.125115 | ||||||||
\(670\) | 9.67617 | 0.373823 | ||||||||
\(671\) | 17.8670 | 0.689747 | ||||||||
\(672\) | 34.3252 | 1.32412 | ||||||||
\(673\) | −6.36878 | −0.245498 | −0.122749 | − | 0.992438i | \(-0.539171\pi\) | ||||
−0.122749 | + | 0.992438i | \(0.539171\pi\) | |||||||
\(674\) | −3.45812 | −0.133202 | ||||||||
\(675\) | −15.2766 | −0.587996 | ||||||||
\(676\) | −28.5812 | −1.09928 | ||||||||
\(677\) | 13.5905 | 0.522326 | 0.261163 | − | 0.965295i | \(-0.415894\pi\) | ||||
0.261163 | + | 0.965295i | \(0.415894\pi\) | |||||||
\(678\) | −6.13396 | −0.235573 | ||||||||
\(679\) | 24.3952 | 0.936203 | ||||||||
\(680\) | −15.1328 | −0.580317 | ||||||||
\(681\) | −2.56930 | −0.0984556 | ||||||||
\(682\) | 7.92209 | 0.303352 | ||||||||
\(683\) | −33.0393 | −1.26422 | −0.632108 | − | 0.774881i | \(-0.717810\pi\) | ||||
−0.632108 | + | 0.774881i | \(0.717810\pi\) | |||||||
\(684\) | 1.30164 | 0.0497693 | ||||||||
\(685\) | −28.9866 | −1.10752 | ||||||||
\(686\) | −19.4334 | −0.741969 | ||||||||
\(687\) | 19.8617 | 0.757770 | ||||||||
\(688\) | −24.0737 | −0.917802 | ||||||||
\(689\) | −31.4052 | −1.19644 | ||||||||
\(690\) | 3.59206 | 0.136747 | ||||||||
\(691\) | 47.4035 | 1.80331 | 0.901657 | − | 0.432453i | \(-0.142352\pi\) | ||||
0.901657 | + | 0.432453i | \(0.142352\pi\) | |||||||
\(692\) | 24.6659 | 0.937656 | ||||||||
\(693\) | 7.00712 | 0.266179 | ||||||||
\(694\) | −5.06386 | −0.192221 | ||||||||
\(695\) | −7.64378 | −0.289945 | ||||||||
\(696\) | −5.04173 | −0.191106 | ||||||||
\(697\) | 31.8148 | 1.20507 | ||||||||
\(698\) | 5.11700 | 0.193681 | ||||||||
\(699\) | −39.3107 | −1.48687 | ||||||||
\(700\) | −24.0775 | −0.910044 | ||||||||
\(701\) | −2.90566 | −0.109745 | −0.0548726 | − | 0.998493i | \(-0.517475\pi\) | ||||
−0.0548726 | + | 0.998493i | \(0.517475\pi\) | |||||||
\(702\) | 12.8528 | 0.485097 | ||||||||
\(703\) | 4.47337 | 0.168716 | ||||||||
\(704\) | −10.0886 | −0.380228 | ||||||||
\(705\) | −11.6133 | −0.437382 | ||||||||
\(706\) | 9.68898 | 0.364650 | ||||||||
\(707\) | −41.0691 | −1.54456 | ||||||||
\(708\) | −27.2251 | −1.02318 | ||||||||
\(709\) | −27.9104 | −1.04820 | −0.524099 | − | 0.851657i | \(-0.675598\pi\) | ||||
−0.524099 | + | 0.851657i | \(0.675598\pi\) | |||||||
\(710\) | −3.79874 | −0.142564 | ||||||||
\(711\) | −4.92384 | −0.184658 | ||||||||
\(712\) | −23.0219 | −0.862782 | ||||||||
\(713\) | −25.1000 | −0.940001 | ||||||||
\(714\) | 19.9562 | 0.746842 | ||||||||
\(715\) | 20.9323 | 0.782825 | ||||||||
\(716\) | −26.2309 | −0.980294 | ||||||||
\(717\) | −5.88022 | −0.219601 | ||||||||
\(718\) | −10.7249 | −0.400249 | ||||||||
\(719\) | 25.7321 | 0.959646 | 0.479823 | − | 0.877365i | \(-0.340701\pi\) | ||||
0.479823 | + | 0.877365i | \(0.340701\pi\) | |||||||
\(720\) | −2.44367 | −0.0910700 | ||||||||
\(721\) | −34.0153 | −1.26680 | ||||||||
\(722\) | −7.47736 | −0.278279 | ||||||||
\(723\) | 8.86221 | 0.329589 | ||||||||
\(724\) | −10.7330 | −0.398889 | ||||||||
\(725\) | 5.39096 | 0.200215 | ||||||||
\(726\) | 2.85295 | 0.105883 | ||||||||
\(727\) | −46.8285 | −1.73677 | −0.868386 | − | 0.495889i | \(-0.834842\pi\) | ||||
−0.868386 | + | 0.495889i | \(0.834842\pi\) | |||||||
\(728\) | 42.5898 | 1.57848 | ||||||||
\(729\) | 29.9797 | 1.11036 | ||||||||
\(730\) | 2.85920 | 0.105824 | ||||||||
\(731\) | −50.5667 | −1.87028 | ||||||||
\(732\) | 19.4751 | 0.719821 | ||||||||
\(733\) | −53.3687 | −1.97122 | −0.985609 | − | 0.169042i | \(-0.945933\pi\) | ||||
−0.985609 | + | 0.169042i | \(0.945933\pi\) | |||||||
\(734\) | 14.2238 | 0.525009 | ||||||||
\(735\) | −38.3062 | −1.41294 | ||||||||
\(736\) | −16.1542 | −0.595453 | ||||||||
\(737\) | 38.9002 | 1.43291 | ||||||||
\(738\) | −1.24736 | −0.0459160 | ||||||||
\(739\) | 4.94427 | 0.181878 | 0.0909390 | − | 0.995856i | \(-0.471013\pi\) | ||||
0.0909390 | + | 0.995856i | \(0.471013\pi\) | |||||||
\(740\) | −9.46740 | −0.348029 | ||||||||
\(741\) | −10.7808 | −0.396042 | ||||||||
\(742\) | 12.1956 | 0.447714 | ||||||||
\(743\) | 6.46500 | 0.237178 | 0.118589 | − | 0.992943i | \(-0.462163\pi\) | ||||
0.118589 | + | 0.992943i | \(0.462163\pi\) | |||||||
\(744\) | 18.1548 | 0.665589 | ||||||||
\(745\) | 23.4674 | 0.859780 | ||||||||
\(746\) | −3.96783 | −0.145272 | ||||||||
\(747\) | −0.648348 | −0.0237218 | ||||||||
\(748\) | −28.9364 | −1.05802 | ||||||||
\(749\) | 70.5980 | 2.57960 | ||||||||
\(750\) | 7.83359 | 0.286042 | ||||||||
\(751\) | 17.5196 | 0.639299 | 0.319649 | − | 0.947536i | \(-0.396435\pi\) | ||||
0.319649 | + | 0.947536i | \(0.396435\pi\) | |||||||
\(752\) | 14.4558 | 0.527148 | ||||||||
\(753\) | −15.9384 | −0.580829 | ||||||||
\(754\) | −4.53562 | −0.165178 | ||||||||
\(755\) | 22.3664 | 0.813997 | ||||||||
\(756\) | 48.7219 | 1.77200 | ||||||||
\(757\) | 22.6591 | 0.823560 | 0.411780 | − | 0.911283i | \(-0.364907\pi\) | ||||
0.411780 | + | 0.911283i | \(0.364907\pi\) | |||||||
\(758\) | 2.24546 | 0.0815587 | ||||||||
\(759\) | 14.4408 | 0.524169 | ||||||||
\(760\) | −3.17462 | −0.115156 | ||||||||
\(761\) | 34.8860 | 1.26462 | 0.632308 | − | 0.774717i | \(-0.282108\pi\) | ||||
0.632308 | + | 0.774717i | \(0.282108\pi\) | |||||||
\(762\) | 9.03939 | 0.327463 | ||||||||
\(763\) | 17.6072 | 0.637424 | ||||||||
\(764\) | −40.4183 | −1.46228 | ||||||||
\(765\) | −5.13291 | −0.185581 | ||||||||
\(766\) | −5.31660 | −0.192096 | ||||||||
\(767\) | −51.4934 | −1.85932 | ||||||||
\(768\) | −4.86979 | −0.175723 | ||||||||
\(769\) | −9.05317 | −0.326466 | −0.163233 | − | 0.986588i | \(-0.552192\pi\) | ||||
−0.163233 | + | 0.986588i | \(0.552192\pi\) | |||||||
\(770\) | −8.12864 | −0.292936 | ||||||||
\(771\) | −1.15640 | −0.0416469 | ||||||||
\(772\) | 23.2613 | 0.837192 | ||||||||
\(773\) | 25.6348 | 0.922020 | 0.461010 | − | 0.887395i | \(-0.347487\pi\) | ||||
0.461010 | + | 0.887395i | \(0.347487\pi\) | |||||||
\(774\) | 1.98257 | 0.0712621 | ||||||||
\(775\) | −19.4124 | −0.697314 | ||||||||
\(776\) | 8.30420 | 0.298103 | ||||||||
\(777\) | 26.2490 | 0.941678 | ||||||||
\(778\) | −7.21548 | −0.258688 | ||||||||
\(779\) | 6.67423 | 0.239129 | ||||||||
\(780\) | 22.8164 | 0.816957 | ||||||||
\(781\) | −15.2718 | −0.546466 | ||||||||
\(782\) | −9.39185 | −0.335852 | ||||||||
\(783\) | −10.9088 | −0.389850 | ||||||||
\(784\) | 47.6821 | 1.70293 | ||||||||
\(785\) | 25.4377 | 0.907910 | ||||||||
\(786\) | −11.1324 | −0.397078 | ||||||||
\(787\) | 0.199605 | 0.00711515 | 0.00355758 | − | 0.999994i | \(-0.498868\pi\) | ||||
0.00355758 | + | 0.999994i | \(0.498868\pi\) | |||||||
\(788\) | −2.94792 | −0.105015 | ||||||||
\(789\) | −18.1739 | −0.647009 | ||||||||
\(790\) | 5.71192 | 0.203221 | ||||||||
\(791\) | −43.9794 | −1.56373 | ||||||||
\(792\) | 2.38524 | 0.0847559 | ||||||||
\(793\) | 36.8350 | 1.30805 | ||||||||
\(794\) | 10.2540 | 0.363902 | ||||||||
\(795\) | 13.7362 | 0.487173 | ||||||||
\(796\) | −21.8793 | −0.775491 | ||||||||
\(797\) | −22.5822 | −0.799904 | −0.399952 | − | 0.916536i | \(-0.630973\pi\) | ||||
−0.399952 | + | 0.916536i | \(0.630973\pi\) | |||||||
\(798\) | 4.18649 | 0.148200 | ||||||||
\(799\) | 30.3643 | 1.07421 | ||||||||
\(800\) | −12.4937 | −0.441720 | ||||||||
\(801\) | −7.80881 | −0.275911 | ||||||||
\(802\) | −1.23326 | −0.0435478 | ||||||||
\(803\) | 11.4946 | 0.405636 | ||||||||
\(804\) | 42.4015 | 1.49539 | ||||||||
\(805\) | 25.7544 | 0.907723 | ||||||||
\(806\) | 16.3324 | 0.575284 | ||||||||
\(807\) | −32.8180 | −1.15525 | ||||||||
\(808\) | −13.9800 | −0.491815 | ||||||||
\(809\) | −2.59131 | −0.0911055 | −0.0455527 | − | 0.998962i | \(-0.514505\pi\) | ||||
−0.0455527 | + | 0.998962i | \(0.514505\pi\) | |||||||
\(810\) | −4.53911 | −0.159488 | ||||||||
\(811\) | −36.4445 | −1.27974 | −0.639870 | − | 0.768483i | \(-0.721012\pi\) | ||||
−0.639870 | + | 0.768483i | \(0.721012\pi\) | |||||||
\(812\) | −17.1935 | −0.603373 | ||||||||
\(813\) | 31.9876 | 1.12186 | ||||||||
\(814\) | 3.89900 | 0.136660 | ||||||||
\(815\) | −23.9424 | −0.838667 | ||||||||
\(816\) | −27.9788 | −0.979454 | ||||||||
\(817\) | −10.6081 | −0.371130 | ||||||||
\(818\) | −2.89681 | −0.101285 | ||||||||
\(819\) | 14.4461 | 0.504786 | ||||||||
\(820\) | −14.1253 | −0.493277 | ||||||||
\(821\) | 1.22959 | 0.0429129 | 0.0214565 | − | 0.999770i | \(-0.493170\pi\) | ||||
0.0214565 | + | 0.999770i | \(0.493170\pi\) | |||||||
\(822\) | 13.0121 | 0.453851 | ||||||||
\(823\) | 19.0447 | 0.663858 | 0.331929 | − | 0.943304i | \(-0.392301\pi\) | ||||
0.331929 | + | 0.943304i | \(0.392301\pi\) | |||||||
\(824\) | −11.5789 | −0.403370 | ||||||||
\(825\) | 11.1686 | 0.388840 | ||||||||
\(826\) | 19.9964 | 0.695763 | ||||||||
\(827\) | −1.35730 | −0.0471980 | −0.0235990 | − | 0.999722i | \(-0.507512\pi\) | ||||
−0.0235990 | + | 0.999722i | \(0.507512\pi\) | |||||||
\(828\) | −3.59453 | −0.124919 | ||||||||
\(829\) | 9.29337 | 0.322772 | 0.161386 | − | 0.986891i | \(-0.448404\pi\) | ||||
0.161386 | + | 0.986891i | \(0.448404\pi\) | |||||||
\(830\) | 0.752118 | 0.0261064 | ||||||||
\(831\) | −12.8541 | −0.445902 | ||||||||
\(832\) | −20.7989 | −0.721073 | ||||||||
\(833\) | 100.156 | 3.47020 | ||||||||
\(834\) | 3.43131 | 0.118816 | ||||||||
\(835\) | 14.9073 | 0.515888 | ||||||||
\(836\) | −6.07040 | −0.209949 | ||||||||
\(837\) | 39.2818 | 1.35778 | ||||||||
\(838\) | −16.9508 | −0.585555 | ||||||||
\(839\) | 41.4301 | 1.43033 | 0.715164 | − | 0.698957i | \(-0.246352\pi\) | ||||
0.715164 | + | 0.698957i | \(0.246352\pi\) | |||||||
\(840\) | −18.6282 | −0.642734 | ||||||||
\(841\) | −25.1504 | −0.867254 | ||||||||
\(842\) | 2.36497 | 0.0815023 | ||||||||
\(843\) | −21.6821 | −0.746772 | ||||||||
\(844\) | 38.2154 | 1.31543 | ||||||||
\(845\) | 23.6443 | 0.813390 | ||||||||
\(846\) | −1.19049 | −0.0409300 | ||||||||
\(847\) | 20.4552 | 0.702847 | ||||||||
\(848\) | −17.0983 | −0.587159 | ||||||||
\(849\) | −47.6046 | −1.63378 | ||||||||
\(850\) | −7.26369 | −0.249143 | ||||||||
\(851\) | −12.3534 | −0.423469 | ||||||||
\(852\) | −16.6463 | −0.570293 | ||||||||
\(853\) | −36.7516 | −1.25835 | −0.629176 | − | 0.777263i | \(-0.716607\pi\) | ||||
−0.629176 | + | 0.777263i | \(0.716607\pi\) | |||||||
\(854\) | −14.3041 | −0.489477 | ||||||||
\(855\) | −1.07680 | −0.0368259 | ||||||||
\(856\) | 24.0317 | 0.821388 | ||||||||
\(857\) | 28.9515 | 0.988963 | 0.494481 | − | 0.869188i | \(-0.335358\pi\) | ||||
0.494481 | + | 0.869188i | \(0.335358\pi\) | |||||||
\(858\) | −9.39655 | −0.320793 | ||||||||
\(859\) | 41.6194 | 1.42004 | 0.710018 | − | 0.704184i | \(-0.248687\pi\) | ||||
0.710018 | + | 0.704184i | \(0.248687\pi\) | |||||||
\(860\) | 22.4509 | 0.765569 | ||||||||
\(861\) | 39.1634 | 1.33468 | ||||||||
\(862\) | −2.36144 | −0.0804311 | ||||||||
\(863\) | −28.4643 | −0.968937 | −0.484469 | − | 0.874809i | \(-0.660987\pi\) | ||||
−0.484469 | + | 0.874809i | \(0.660987\pi\) | |||||||
\(864\) | 25.2816 | 0.860098 | ||||||||
\(865\) | −20.4053 | −0.693800 | ||||||||
\(866\) | −10.9279 | −0.371345 | ||||||||
\(867\) | −32.2021 | −1.09364 | ||||||||
\(868\) | 61.9123 | 2.10144 | ||||||||
\(869\) | 22.9631 | 0.778970 | ||||||||
\(870\) | 1.98382 | 0.0672577 | ||||||||
\(871\) | 80.1978 | 2.71740 | ||||||||
\(872\) | 5.99353 | 0.202967 | ||||||||
\(873\) | 2.81671 | 0.0953310 | ||||||||
\(874\) | −1.97026 | −0.0666451 | ||||||||
\(875\) | 56.1654 | 1.89874 | ||||||||
\(876\) | 12.5292 | 0.423322 | ||||||||
\(877\) | 4.10040 | 0.138461 | 0.0692303 | − | 0.997601i | \(-0.477946\pi\) | ||||
0.0692303 | + | 0.997601i | \(0.477946\pi\) | |||||||
\(878\) | −3.84591 | −0.129793 | ||||||||
\(879\) | 43.1277 | 1.45466 | ||||||||
\(880\) | 11.3964 | 0.384174 | ||||||||
\(881\) | 23.8628 | 0.803958 | 0.401979 | − | 0.915649i | \(-0.368322\pi\) | ||||
0.401979 | + | 0.915649i | \(0.368322\pi\) | |||||||
\(882\) | −3.92682 | −0.132223 | ||||||||
\(883\) | −13.3019 | −0.447645 | −0.223822 | − | 0.974630i | \(-0.571854\pi\) | ||||
−0.223822 | + | 0.974630i | \(0.571854\pi\) | |||||||
\(884\) | −59.6561 | −2.00645 | ||||||||
\(885\) | 22.5225 | 0.757085 | ||||||||
\(886\) | −17.0146 | −0.571618 | ||||||||
\(887\) | −21.2442 | −0.713310 | −0.356655 | − | 0.934236i | \(-0.616083\pi\) | ||||
−0.356655 | + | 0.934236i | \(0.616083\pi\) | |||||||
\(888\) | 8.93523 | 0.299847 | ||||||||
\(889\) | 64.8108 | 2.17369 | ||||||||
\(890\) | 9.05864 | 0.303646 | ||||||||
\(891\) | −18.2482 | −0.611338 | ||||||||
\(892\) | 3.75665 | 0.125782 | ||||||||
\(893\) | 6.36995 | 0.213162 | ||||||||
\(894\) | −10.5346 | −0.352329 | ||||||||
\(895\) | 21.7000 | 0.725350 | ||||||||
\(896\) | 52.0052 | 1.73737 | ||||||||
\(897\) | 29.7716 | 0.994044 | ||||||||
\(898\) | −3.26180 | −0.108848 | ||||||||
\(899\) | −13.8622 | −0.462330 | ||||||||
\(900\) | −2.78002 | −0.0926674 | ||||||||
\(901\) | −35.9149 | −1.19650 | ||||||||
\(902\) | 5.81728 | 0.193694 | ||||||||
\(903\) | −62.2467 | −2.07144 | ||||||||
\(904\) | −14.9707 | −0.497917 | ||||||||
\(905\) | 8.87907 | 0.295150 | ||||||||
\(906\) | −10.0403 | −0.333567 | ||||||||
\(907\) | −29.8311 | −0.990525 | −0.495262 | − | 0.868743i | \(-0.664928\pi\) | ||||
−0.495262 | + | 0.868743i | \(0.664928\pi\) | |||||||
\(908\) | −2.98257 | −0.0989802 | ||||||||
\(909\) | −4.74189 | −0.157278 | ||||||||
\(910\) | −16.7582 | −0.555530 | ||||||||
\(911\) | 26.4575 | 0.876578 | 0.438289 | − | 0.898834i | \(-0.355585\pi\) | ||||
0.438289 | + | 0.898834i | \(0.355585\pi\) | |||||||
\(912\) | −5.86950 | −0.194359 | ||||||||
\(913\) | 3.02367 | 0.100069 | ||||||||
\(914\) | −17.4887 | −0.578475 | ||||||||
\(915\) | −16.1111 | −0.532617 | ||||||||
\(916\) | 23.0565 | 0.761807 | ||||||||
\(917\) | −79.8170 | −2.63579 | ||||||||
\(918\) | 14.6984 | 0.485119 | ||||||||
\(919\) | 48.0450 | 1.58486 | 0.792429 | − | 0.609964i | \(-0.208816\pi\) | ||||
0.792429 | + | 0.609964i | \(0.208816\pi\) | |||||||
\(920\) | 8.76686 | 0.289035 | ||||||||
\(921\) | 21.4037 | 0.705276 | ||||||||
\(922\) | −7.16058 | −0.235821 | ||||||||
\(923\) | −31.4847 | −1.03633 | ||||||||
\(924\) | −35.6202 | −1.17182 | ||||||||
\(925\) | −9.55416 | −0.314139 | ||||||||
\(926\) | −4.61498 | −0.151658 | ||||||||
\(927\) | −3.92746 | −0.128995 | ||||||||
\(928\) | −8.92164 | −0.292867 | ||||||||
\(929\) | −17.1784 | −0.563605 | −0.281803 | − | 0.959472i | \(-0.590932\pi\) | ||||
−0.281803 | + | 0.959472i | \(0.590932\pi\) | |||||||
\(930\) | −7.14356 | −0.234247 | ||||||||
\(931\) | 21.0111 | 0.688612 | ||||||||
\(932\) | −45.6339 | −1.49479 | ||||||||
\(933\) | 0.268196 | 0.00878035 | ||||||||
\(934\) | −9.06140 | −0.296498 | ||||||||
\(935\) | 23.9381 | 0.782861 | ||||||||
\(936\) | 4.91748 | 0.160733 | ||||||||
\(937\) | −51.5569 | −1.68429 | −0.842145 | − | 0.539252i | \(-0.818707\pi\) | ||||
−0.842145 | + | 0.539252i | \(0.818707\pi\) | |||||||
\(938\) | −31.1432 | −1.01686 | ||||||||
\(939\) | 27.4399 | 0.895469 | ||||||||
\(940\) | −13.4813 | −0.439712 | ||||||||
\(941\) | 39.2864 | 1.28070 | 0.640349 | − | 0.768084i | \(-0.278790\pi\) | ||||
0.640349 | + | 0.768084i | \(0.278790\pi\) | |||||||
\(942\) | −11.4190 | −0.372052 | ||||||||
\(943\) | −18.4312 | −0.600202 | ||||||||
\(944\) | −28.0351 | −0.912466 | ||||||||
\(945\) | −40.3060 | −1.31116 | ||||||||
\(946\) | −9.24604 | −0.300615 | ||||||||
\(947\) | 15.5225 | 0.504413 | 0.252206 | − | 0.967673i | \(-0.418844\pi\) | ||||
0.252206 | + | 0.967673i | \(0.418844\pi\) | |||||||
\(948\) | 25.0299 | 0.812934 | ||||||||
\(949\) | 23.6976 | 0.769255 | ||||||||
\(950\) | −1.52381 | −0.0494388 | ||||||||
\(951\) | 2.69221 | 0.0873009 | ||||||||
\(952\) | 48.7056 | 1.57856 | ||||||||
\(953\) | 22.1294 | 0.716842 | 0.358421 | − | 0.933560i | \(-0.383315\pi\) | ||||
0.358421 | + | 0.933560i | \(0.383315\pi\) | |||||||
\(954\) | 1.40812 | 0.0455895 | ||||||||
\(955\) | 33.4367 | 1.08199 | ||||||||
\(956\) | −6.82607 | −0.220771 | ||||||||
\(957\) | 7.97536 | 0.257807 | ||||||||
\(958\) | 5.11508 | 0.165261 | ||||||||
\(959\) | 93.2947 | 3.01264 | ||||||||
\(960\) | 9.09716 | 0.293609 | ||||||||
\(961\) | 18.9165 | 0.610211 | ||||||||
\(962\) | 8.03828 | 0.259164 | ||||||||
\(963\) | 8.15134 | 0.262673 | ||||||||
\(964\) | 10.2877 | 0.331345 | ||||||||
\(965\) | −19.2433 | −0.619464 | ||||||||
\(966\) | −11.5612 | −0.371975 | ||||||||
\(967\) | −9.97343 | −0.320724 | −0.160362 | − | 0.987058i | \(-0.551266\pi\) | ||||
−0.160362 | + | 0.987058i | \(0.551266\pi\) | |||||||
\(968\) | 6.96298 | 0.223799 | ||||||||
\(969\) | −12.3289 | −0.396060 | ||||||||
\(970\) | −3.26753 | −0.104914 | ||||||||
\(971\) | −55.8372 | −1.79190 | −0.895951 | − | 0.444154i | \(-0.853504\pi\) | ||||
−0.895951 | + | 0.444154i | \(0.853504\pi\) | |||||||
\(972\) | 10.3691 | 0.332589 | ||||||||
\(973\) | 24.6018 | 0.788699 | ||||||||
\(974\) | 0.226952 | 0.00727200 | ||||||||
\(975\) | 23.0254 | 0.737405 | ||||||||
\(976\) | 20.0545 | 0.641930 | ||||||||
\(977\) | −26.9677 | −0.862772 | −0.431386 | − | 0.902167i | \(-0.641975\pi\) | ||||
−0.431386 | + | 0.902167i | \(0.641975\pi\) | |||||||
\(978\) | 10.7478 | 0.343677 | ||||||||
\(979\) | 36.4177 | 1.16391 | ||||||||
\(980\) | −44.4678 | −1.42047 | ||||||||
\(981\) | 2.03295 | 0.0649071 | ||||||||
\(982\) | 11.3281 | 0.361493 | ||||||||
\(983\) | 25.7677 | 0.821862 | 0.410931 | − | 0.911666i | \(-0.365204\pi\) | ||||
0.410931 | + | 0.911666i | \(0.365204\pi\) | |||||||
\(984\) | 13.3313 | 0.424986 | ||||||||
\(985\) | 2.43872 | 0.0777040 | ||||||||
\(986\) | −5.18692 | −0.165185 | ||||||||
\(987\) | 37.3779 | 1.18975 | ||||||||
\(988\) | −12.5149 | −0.398152 | ||||||||
\(989\) | 29.2947 | 0.931518 | ||||||||
\(990\) | −0.938544 | −0.0298289 | ||||||||
\(991\) | −45.7646 | −1.45376 | −0.726881 | − | 0.686763i | \(-0.759031\pi\) | ||||
−0.726881 | + | 0.686763i | \(0.759031\pi\) | |||||||
\(992\) | 32.1261 | 1.02000 | ||||||||
\(993\) | −36.7680 | −1.16680 | ||||||||
\(994\) | 12.2264 | 0.387799 | ||||||||
\(995\) | 18.1000 | 0.573809 | ||||||||
\(996\) | 3.29582 | 0.104432 | ||||||||
\(997\) | −19.9914 | −0.633133 | −0.316567 | − | 0.948570i | \(-0.602530\pi\) | ||||
−0.316567 | + | 0.948570i | \(0.602530\pi\) | |||||||
\(998\) | 8.26202 | 0.261530 | ||||||||
\(999\) | 19.3333 | 0.611677 |
(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 | 619.2.a.b.1.17 | ✓ | 30 | |
3.2 | odd | 2 | 5571.2.a.g.1.14 | 30 | |||
4.3 | odd | 2 | 9904.2.a.n.1.22 | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
619.2.a.b.1.17 | ✓ | 30 | 1.1 | even | 1 | trivial | |
5571.2.a.g.1.14 | 30 | 3.2 | odd | 2 | |||
9904.2.a.n.1.22 | 30 | 4.3 | odd | 2 |