Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [671,2,Mod(1,671)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(671, 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("671.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 671 = 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 671.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: | \(5.35796197563\) |
Analytic rank: | \(0\) |
Dimension: | \(19\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{19} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{19} - 5 x^{18} - 18 x^{17} + 122 x^{16} + 78 x^{15} - 1177 x^{14} + 387 x^{13} + 5755 x^{12} + \cdots - 43 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Root | \(1.31423\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 671.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.31423 | 0.929298 | 0.464649 | − | 0.885495i | \(-0.346181\pi\) | ||||
0.464649 | + | 0.885495i | \(0.346181\pi\) | |||||||
\(3\) | −1.97692 | −1.14137 | −0.570687 | − | 0.821168i | \(-0.693323\pi\) | ||||
−0.570687 | + | 0.821168i | \(0.693323\pi\) | |||||||
\(4\) | −0.272811 | −0.136406 | ||||||||
\(5\) | −1.38757 | −0.620541 | −0.310271 | − | 0.950648i | \(-0.600420\pi\) | ||||
−0.310271 | + | 0.950648i | \(0.600420\pi\) | |||||||
\(6\) | −2.59812 | −1.06068 | ||||||||
\(7\) | 2.03012 | 0.767315 | 0.383657 | − | 0.923476i | \(-0.374664\pi\) | ||||
0.383657 | + | 0.923476i | \(0.374664\pi\) | |||||||
\(8\) | −2.98699 | −1.05606 | ||||||||
\(9\) | 0.908205 | 0.302735 | ||||||||
\(10\) | −1.82358 | −0.576668 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0.539326 | 0.155690 | ||||||||
\(13\) | 5.73746 | 1.59129 | 0.795643 | − | 0.605766i | \(-0.207133\pi\) | ||||
0.795643 | + | 0.605766i | \(0.207133\pi\) | |||||||
\(14\) | 2.66804 | 0.713064 | ||||||||
\(15\) | 2.74312 | 0.708270 | ||||||||
\(16\) | −3.37995 | −0.844988 | ||||||||
\(17\) | 6.94204 | 1.68369 | 0.841846 | − | 0.539718i | \(-0.181469\pi\) | ||||
0.841846 | + | 0.539718i | \(0.181469\pi\) | |||||||
\(18\) | 1.19359 | 0.281331 | ||||||||
\(19\) | −3.55211 | −0.814911 | −0.407455 | − | 0.913225i | \(-0.633584\pi\) | ||||
−0.407455 | + | 0.913225i | \(0.633584\pi\) | |||||||
\(20\) | 0.378545 | 0.0846453 | ||||||||
\(21\) | −4.01339 | −0.875793 | ||||||||
\(22\) | 1.31423 | 0.280194 | ||||||||
\(23\) | 0.806289 | 0.168123 | 0.0840615 | − | 0.996461i | \(-0.473211\pi\) | ||||
0.0840615 | + | 0.996461i | \(0.473211\pi\) | |||||||
\(24\) | 5.90503 | 1.20536 | ||||||||
\(25\) | −3.07464 | −0.614929 | ||||||||
\(26\) | 7.54032 | 1.47878 | ||||||||
\(27\) | 4.13531 | 0.795840 | ||||||||
\(28\) | −0.553841 | −0.104666 | ||||||||
\(29\) | 8.32766 | 1.54641 | 0.773204 | − | 0.634158i | \(-0.218653\pi\) | ||||
0.773204 | + | 0.634158i | \(0.218653\pi\) | |||||||
\(30\) | 3.60507 | 0.658193 | ||||||||
\(31\) | 4.54221 | 0.815804 | 0.407902 | − | 0.913026i | \(-0.366260\pi\) | ||||
0.407902 | + | 0.913026i | \(0.366260\pi\) | |||||||
\(32\) | 1.53195 | 0.270814 | ||||||||
\(33\) | −1.97692 | −0.344137 | ||||||||
\(34\) | 9.12341 | 1.56465 | ||||||||
\(35\) | −2.81694 | −0.476150 | ||||||||
\(36\) | −0.247769 | −0.0412948 | ||||||||
\(37\) | 8.85665 | 1.45602 | 0.728012 | − | 0.685565i | \(-0.240445\pi\) | ||||
0.728012 | + | 0.685565i | \(0.240445\pi\) | |||||||
\(38\) | −4.66828 | −0.757295 | ||||||||
\(39\) | −11.3425 | −1.81625 | ||||||||
\(40\) | 4.14466 | 0.655328 | ||||||||
\(41\) | −4.04638 | −0.631939 | −0.315969 | − | 0.948769i | \(-0.602330\pi\) | ||||
−0.315969 | + | 0.948769i | \(0.602330\pi\) | |||||||
\(42\) | −5.27450 | −0.813873 | ||||||||
\(43\) | 0.832544 | 0.126962 | 0.0634809 | − | 0.997983i | \(-0.479780\pi\) | ||||
0.0634809 | + | 0.997983i | \(0.479780\pi\) | |||||||
\(44\) | −0.272811 | −0.0411279 | ||||||||
\(45\) | −1.26020 | −0.187860 | ||||||||
\(46\) | 1.05965 | 0.156236 | ||||||||
\(47\) | 4.66753 | 0.680829 | 0.340414 | − | 0.940276i | \(-0.389433\pi\) | ||||
0.340414 | + | 0.940276i | \(0.389433\pi\) | |||||||
\(48\) | 6.68189 | 0.964447 | ||||||||
\(49\) | −2.87860 | −0.411228 | ||||||||
\(50\) | −4.04077 | −0.571452 | ||||||||
\(51\) | −13.7238 | −1.92172 | ||||||||
\(52\) | −1.56524 | −0.217060 | ||||||||
\(53\) | −9.49286 | −1.30394 | −0.651972 | − | 0.758243i | \(-0.726058\pi\) | ||||
−0.651972 | + | 0.758243i | \(0.726058\pi\) | |||||||
\(54\) | 5.43473 | 0.739573 | ||||||||
\(55\) | −1.38757 | −0.187100 | ||||||||
\(56\) | −6.06395 | −0.810330 | ||||||||
\(57\) | 7.02224 | 0.930118 | ||||||||
\(58\) | 10.9444 | 1.43707 | ||||||||
\(59\) | −12.6362 | −1.64510 | −0.822549 | − | 0.568694i | \(-0.807449\pi\) | ||||
−0.822549 | + | 0.568694i | \(0.807449\pi\) | |||||||
\(60\) | −0.748353 | −0.0966120 | ||||||||
\(61\) | −1.00000 | −0.128037 | ||||||||
\(62\) | 5.96948 | 0.758125 | ||||||||
\(63\) | 1.84377 | 0.232293 | ||||||||
\(64\) | 8.77324 | 1.09665 | ||||||||
\(65\) | −7.96114 | −0.987458 | ||||||||
\(66\) | −2.59812 | −0.319806 | ||||||||
\(67\) | 6.13660 | 0.749705 | 0.374852 | − | 0.927085i | \(-0.377693\pi\) | ||||
0.374852 | + | 0.927085i | \(0.377693\pi\) | |||||||
\(68\) | −1.89387 | −0.229665 | ||||||||
\(69\) | −1.59397 | −0.191891 | ||||||||
\(70\) | −3.70210 | −0.442486 | ||||||||
\(71\) | 12.3352 | 1.46392 | 0.731958 | − | 0.681350i | \(-0.238607\pi\) | ||||
0.731958 | + | 0.681350i | \(0.238607\pi\) | |||||||
\(72\) | −2.71280 | −0.319706 | ||||||||
\(73\) | 8.32305 | 0.974139 | 0.487070 | − | 0.873363i | \(-0.338066\pi\) | ||||
0.487070 | + | 0.873363i | \(0.338066\pi\) | |||||||
\(74\) | 11.6396 | 1.35308 | ||||||||
\(75\) | 6.07832 | 0.701864 | ||||||||
\(76\) | 0.969057 | 0.111158 | ||||||||
\(77\) | 2.03012 | 0.231354 | ||||||||
\(78\) | −14.9066 | −1.68784 | ||||||||
\(79\) | 3.78450 | 0.425789 | 0.212895 | − | 0.977075i | \(-0.431711\pi\) | ||||
0.212895 | + | 0.977075i | \(0.431711\pi\) | |||||||
\(80\) | 4.68993 | 0.524350 | ||||||||
\(81\) | −10.8998 | −1.21109 | ||||||||
\(82\) | −5.31786 | −0.587259 | ||||||||
\(83\) | −12.6260 | −1.38588 | −0.692939 | − | 0.720996i | \(-0.743685\pi\) | ||||
−0.692939 | + | 0.720996i | \(0.743685\pi\) | |||||||
\(84\) | 1.09490 | 0.119463 | ||||||||
\(85\) | −9.63258 | −1.04480 | ||||||||
\(86\) | 1.09415 | 0.117985 | ||||||||
\(87\) | −16.4631 | −1.76503 | ||||||||
\(88\) | −2.98699 | −0.318414 | ||||||||
\(89\) | −14.8592 | −1.57507 | −0.787534 | − | 0.616271i | \(-0.788643\pi\) | ||||
−0.787534 | + | 0.616271i | \(0.788643\pi\) | |||||||
\(90\) | −1.65619 | −0.174577 | ||||||||
\(91\) | 11.6478 | 1.22102 | ||||||||
\(92\) | −0.219965 | −0.0229329 | ||||||||
\(93\) | −8.97957 | −0.931138 | ||||||||
\(94\) | 6.13418 | 0.632693 | ||||||||
\(95\) | 4.92881 | 0.505686 | ||||||||
\(96\) | −3.02855 | −0.309100 | ||||||||
\(97\) | 7.09938 | 0.720833 | 0.360417 | − | 0.932791i | \(-0.382635\pi\) | ||||
0.360417 | + | 0.932791i | \(0.382635\pi\) | |||||||
\(98\) | −3.78312 | −0.382153 | ||||||||
\(99\) | 0.908205 | 0.0912780 | ||||||||
\(100\) | 0.838797 | 0.0838797 | ||||||||
\(101\) | 14.2585 | 1.41877 | 0.709387 | − | 0.704819i | \(-0.248972\pi\) | ||||
0.709387 | + | 0.704819i | \(0.248972\pi\) | |||||||
\(102\) | −18.0362 | −1.78585 | ||||||||
\(103\) | 1.69876 | 0.167384 | 0.0836920 | − | 0.996492i | \(-0.473329\pi\) | ||||
0.0836920 | + | 0.996492i | \(0.473329\pi\) | |||||||
\(104\) | −17.1377 | −1.68049 | ||||||||
\(105\) | 5.56887 | 0.543466 | ||||||||
\(106\) | −12.4758 | −1.21175 | ||||||||
\(107\) | −14.6034 | −1.41176 | −0.705881 | − | 0.708331i | \(-0.749449\pi\) | ||||
−0.705881 | + | 0.708331i | \(0.749449\pi\) | |||||||
\(108\) | −1.12816 | −0.108557 | ||||||||
\(109\) | 7.22627 | 0.692151 | 0.346076 | − | 0.938207i | \(-0.387514\pi\) | ||||
0.346076 | + | 0.938207i | \(0.387514\pi\) | |||||||
\(110\) | −1.82358 | −0.173872 | ||||||||
\(111\) | −17.5089 | −1.66187 | ||||||||
\(112\) | −6.86172 | −0.648372 | ||||||||
\(113\) | 17.4970 | 1.64598 | 0.822990 | − | 0.568056i | \(-0.192304\pi\) | ||||
0.822990 | + | 0.568056i | \(0.192304\pi\) | |||||||
\(114\) | 9.22880 | 0.864357 | ||||||||
\(115\) | −1.11878 | −0.104327 | ||||||||
\(116\) | −2.27188 | −0.210939 | ||||||||
\(117\) | 5.21079 | 0.481738 | ||||||||
\(118\) | −16.6069 | −1.52879 | ||||||||
\(119\) | 14.0932 | 1.29192 | ||||||||
\(120\) | −8.19365 | −0.747975 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −1.31423 | −0.118984 | ||||||||
\(123\) | 7.99936 | 0.721278 | ||||||||
\(124\) | −1.23917 | −0.111280 | ||||||||
\(125\) | 11.2042 | 1.00213 | ||||||||
\(126\) | 2.42313 | 0.215869 | ||||||||
\(127\) | 2.20928 | 0.196042 | 0.0980209 | − | 0.995184i | \(-0.468749\pi\) | ||||
0.0980209 | + | 0.995184i | \(0.468749\pi\) | |||||||
\(128\) | 8.46610 | 0.748305 | ||||||||
\(129\) | −1.64587 | −0.144911 | ||||||||
\(130\) | −10.4627 | −0.917643 | ||||||||
\(131\) | −2.07784 | −0.181541 | −0.0907707 | − | 0.995872i | \(-0.528933\pi\) | ||||
−0.0907707 | + | 0.995872i | \(0.528933\pi\) | |||||||
\(132\) | 0.539326 | 0.0469423 | ||||||||
\(133\) | −7.21123 | −0.625293 | ||||||||
\(134\) | 8.06487 | 0.696699 | ||||||||
\(135\) | −5.73804 | −0.493852 | ||||||||
\(136\) | −20.7358 | −1.77808 | ||||||||
\(137\) | 10.7795 | 0.920951 | 0.460476 | − | 0.887672i | \(-0.347679\pi\) | ||||
0.460476 | + | 0.887672i | \(0.347679\pi\) | |||||||
\(138\) | −2.09483 | −0.178324 | ||||||||
\(139\) | −11.4790 | −0.973636 | −0.486818 | − | 0.873504i | \(-0.661842\pi\) | ||||
−0.486818 | + | 0.873504i | \(0.661842\pi\) | |||||||
\(140\) | 0.768494 | 0.0649496 | ||||||||
\(141\) | −9.22732 | −0.777080 | ||||||||
\(142\) | 16.2112 | 1.36041 | ||||||||
\(143\) | 5.73746 | 0.479791 | ||||||||
\(144\) | −3.06969 | −0.255807 | ||||||||
\(145\) | −11.5552 | −0.959609 | ||||||||
\(146\) | 10.9384 | 0.905266 | ||||||||
\(147\) | 5.69075 | 0.469365 | ||||||||
\(148\) | −2.41619 | −0.198610 | ||||||||
\(149\) | −11.4894 | −0.941246 | −0.470623 | − | 0.882334i | \(-0.655971\pi\) | ||||
−0.470623 | + | 0.882334i | \(0.655971\pi\) | |||||||
\(150\) | 7.98828 | 0.652240 | ||||||||
\(151\) | −2.05463 | −0.167204 | −0.0836018 | − | 0.996499i | \(-0.526642\pi\) | ||||
−0.0836018 | + | 0.996499i | \(0.526642\pi\) | |||||||
\(152\) | 10.6101 | 0.860594 | ||||||||
\(153\) | 6.30479 | 0.509712 | ||||||||
\(154\) | 2.66804 | 0.214997 | ||||||||
\(155\) | −6.30264 | −0.506240 | ||||||||
\(156\) | 3.09436 | 0.247747 | ||||||||
\(157\) | 24.4022 | 1.94751 | 0.973755 | − | 0.227600i | \(-0.0730879\pi\) | ||||
0.973755 | + | 0.227600i | \(0.0730879\pi\) | |||||||
\(158\) | 4.97368 | 0.395685 | ||||||||
\(159\) | 18.7666 | 1.48829 | ||||||||
\(160\) | −2.12570 | −0.168051 | ||||||||
\(161\) | 1.63687 | 0.129003 | ||||||||
\(162\) | −14.3248 | −1.12546 | ||||||||
\(163\) | −9.62670 | −0.754021 | −0.377011 | − | 0.926209i | \(-0.623048\pi\) | ||||
−0.377011 | + | 0.926209i | \(0.623048\pi\) | |||||||
\(164\) | 1.10390 | 0.0862000 | ||||||||
\(165\) | 2.74312 | 0.213551 | ||||||||
\(166\) | −16.5933 | −1.28789 | ||||||||
\(167\) | −16.8772 | −1.30600 | −0.652999 | − | 0.757359i | \(-0.726489\pi\) | ||||
−0.652999 | + | 0.757359i | \(0.726489\pi\) | |||||||
\(168\) | 11.9879 | 0.924890 | ||||||||
\(169\) | 19.9185 | 1.53219 | ||||||||
\(170\) | −12.6594 | −0.970930 | ||||||||
\(171\) | −3.22605 | −0.246702 | ||||||||
\(172\) | −0.227127 | −0.0173183 | ||||||||
\(173\) | −5.79912 | −0.440899 | −0.220450 | − | 0.975398i | \(-0.570752\pi\) | ||||
−0.220450 | + | 0.975398i | \(0.570752\pi\) | |||||||
\(174\) | −21.6362 | −1.64024 | ||||||||
\(175\) | −6.24191 | −0.471844 | ||||||||
\(176\) | −3.37995 | −0.254773 | ||||||||
\(177\) | 24.9808 | 1.87767 | ||||||||
\(178\) | −19.5283 | −1.46371 | ||||||||
\(179\) | 4.27998 | 0.319900 | 0.159950 | − | 0.987125i | \(-0.448867\pi\) | ||||
0.159950 | + | 0.987125i | \(0.448867\pi\) | |||||||
\(180\) | 0.343797 | 0.0256251 | ||||||||
\(181\) | −20.1052 | −1.49441 | −0.747205 | − | 0.664594i | \(-0.768605\pi\) | ||||
−0.747205 | + | 0.664594i | \(0.768605\pi\) | |||||||
\(182\) | 15.3078 | 1.13469 | ||||||||
\(183\) | 1.97692 | 0.146138 | ||||||||
\(184\) | −2.40837 | −0.177548 | ||||||||
\(185\) | −12.2892 | −0.903523 | ||||||||
\(186\) | −11.8012 | −0.865304 | ||||||||
\(187\) | 6.94204 | 0.507652 | ||||||||
\(188\) | −1.27335 | −0.0928689 | ||||||||
\(189\) | 8.39519 | 0.610660 | ||||||||
\(190\) | 6.47757 | 0.469933 | ||||||||
\(191\) | 9.14553 | 0.661748 | 0.330874 | − | 0.943675i | \(-0.392657\pi\) | ||||
0.330874 | + | 0.943675i | \(0.392657\pi\) | |||||||
\(192\) | −17.3440 | −1.25169 | ||||||||
\(193\) | 19.5388 | 1.40644 | 0.703218 | − | 0.710974i | \(-0.251746\pi\) | ||||
0.703218 | + | 0.710974i | \(0.251746\pi\) | |||||||
\(194\) | 9.33019 | 0.669869 | ||||||||
\(195\) | 15.7385 | 1.12706 | ||||||||
\(196\) | 0.785314 | 0.0560938 | ||||||||
\(197\) | −21.7664 | −1.55079 | −0.775395 | − | 0.631476i | \(-0.782449\pi\) | ||||
−0.775395 | + | 0.631476i | \(0.782449\pi\) | |||||||
\(198\) | 1.19359 | 0.0848245 | ||||||||
\(199\) | 21.7232 | 1.53992 | 0.769958 | − | 0.638094i | \(-0.220277\pi\) | ||||
0.769958 | + | 0.638094i | \(0.220277\pi\) | |||||||
\(200\) | 9.18392 | 0.649401 | ||||||||
\(201\) | −12.1316 | −0.855694 | ||||||||
\(202\) | 18.7389 | 1.31846 | ||||||||
\(203\) | 16.9062 | 1.18658 | ||||||||
\(204\) | 3.74402 | 0.262134 | ||||||||
\(205\) | 5.61465 | 0.392144 | ||||||||
\(206\) | 2.23256 | 0.155550 | ||||||||
\(207\) | 0.732276 | 0.0508967 | ||||||||
\(208\) | −19.3923 | −1.34462 | ||||||||
\(209\) | −3.55211 | −0.245705 | ||||||||
\(210\) | 7.31875 | 0.505042 | ||||||||
\(211\) | 3.03388 | 0.208861 | 0.104430 | − | 0.994532i | \(-0.466698\pi\) | ||||
0.104430 | + | 0.994532i | \(0.466698\pi\) | |||||||
\(212\) | 2.58976 | 0.177865 | ||||||||
\(213\) | −24.3856 | −1.67087 | ||||||||
\(214\) | −19.1921 | −1.31195 | ||||||||
\(215\) | −1.15522 | −0.0787850 | ||||||||
\(216\) | −12.3521 | −0.840454 | ||||||||
\(217\) | 9.22124 | 0.625979 | ||||||||
\(218\) | 9.49695 | 0.643215 | ||||||||
\(219\) | −16.4540 | −1.11186 | ||||||||
\(220\) | 0.378545 | 0.0255215 | ||||||||
\(221\) | 39.8297 | 2.67924 | ||||||||
\(222\) | −23.0106 | −1.54437 | ||||||||
\(223\) | 4.76902 | 0.319357 | 0.159678 | − | 0.987169i | \(-0.448954\pi\) | ||||
0.159678 | + | 0.987169i | \(0.448954\pi\) | |||||||
\(224\) | 3.11006 | 0.207800 | ||||||||
\(225\) | −2.79241 | −0.186160 | ||||||||
\(226\) | 22.9950 | 1.52961 | ||||||||
\(227\) | −26.6405 | −1.76819 | −0.884095 | − | 0.467307i | \(-0.845224\pi\) | ||||
−0.884095 | + | 0.467307i | \(0.845224\pi\) | |||||||
\(228\) | −1.91575 | −0.126873 | ||||||||
\(229\) | 11.6882 | 0.772377 | 0.386188 | − | 0.922420i | \(-0.373792\pi\) | ||||
0.386188 | + | 0.922420i | \(0.373792\pi\) | |||||||
\(230\) | −1.47034 | −0.0969510 | ||||||||
\(231\) | −4.01339 | −0.264062 | ||||||||
\(232\) | −24.8746 | −1.63310 | ||||||||
\(233\) | −3.48827 | −0.228524 | −0.114262 | − | 0.993451i | \(-0.536450\pi\) | ||||
−0.114262 | + | 0.993451i | \(0.536450\pi\) | |||||||
\(234\) | 6.84816 | 0.447678 | ||||||||
\(235\) | −6.47653 | −0.422482 | ||||||||
\(236\) | 3.44731 | 0.224401 | ||||||||
\(237\) | −7.48164 | −0.485985 | ||||||||
\(238\) | 18.5216 | 1.20058 | ||||||||
\(239\) | 18.1468 | 1.17382 | 0.586911 | − | 0.809652i | \(-0.300344\pi\) | ||||
0.586911 | + | 0.809652i | \(0.300344\pi\) | |||||||
\(240\) | −9.27160 | −0.598479 | ||||||||
\(241\) | −4.01737 | −0.258782 | −0.129391 | − | 0.991594i | \(-0.541302\pi\) | ||||
−0.129391 | + | 0.991594i | \(0.541302\pi\) | |||||||
\(242\) | 1.31423 | 0.0844816 | ||||||||
\(243\) | 9.14205 | 0.586463 | ||||||||
\(244\) | 0.272811 | 0.0174650 | ||||||||
\(245\) | 3.99426 | 0.255184 | ||||||||
\(246\) | 10.5130 | 0.670282 | ||||||||
\(247\) | −20.3801 | −1.29676 | ||||||||
\(248\) | −13.5675 | −0.861538 | ||||||||
\(249\) | 24.9605 | 1.58181 | ||||||||
\(250\) | 14.7248 | 0.931277 | ||||||||
\(251\) | −7.05879 | −0.445547 | −0.222774 | − | 0.974870i | \(-0.571511\pi\) | ||||
−0.222774 | + | 0.974870i | \(0.571511\pi\) | |||||||
\(252\) | −0.503001 | −0.0316861 | ||||||||
\(253\) | 0.806289 | 0.0506910 | ||||||||
\(254\) | 2.90349 | 0.182181 | ||||||||
\(255\) | 19.0428 | 1.19251 | ||||||||
\(256\) | −6.42011 | −0.401257 | ||||||||
\(257\) | −6.03995 | −0.376762 | −0.188381 | − | 0.982096i | \(-0.560324\pi\) | ||||
−0.188381 | + | 0.982096i | \(0.560324\pi\) | |||||||
\(258\) | −2.16305 | −0.134665 | ||||||||
\(259\) | 17.9801 | 1.11723 | ||||||||
\(260\) | 2.17189 | 0.134695 | ||||||||
\(261\) | 7.56322 | 0.468152 | ||||||||
\(262\) | −2.73075 | −0.168706 | ||||||||
\(263\) | 11.0908 | 0.683890 | 0.341945 | − | 0.939720i | \(-0.388914\pi\) | ||||
0.341945 | + | 0.939720i | \(0.388914\pi\) | |||||||
\(264\) | 5.90503 | 0.363429 | ||||||||
\(265\) | 13.1720 | 0.809151 | ||||||||
\(266\) | −9.47718 | −0.581083 | ||||||||
\(267\) | 29.3754 | 1.79774 | ||||||||
\(268\) | −1.67413 | −0.102264 | ||||||||
\(269\) | 5.22740 | 0.318720 | 0.159360 | − | 0.987221i | \(-0.449057\pi\) | ||||
0.159360 | + | 0.987221i | \(0.449057\pi\) | |||||||
\(270\) | −7.54108 | −0.458935 | ||||||||
\(271\) | −13.4323 | −0.815956 | −0.407978 | − | 0.912992i | \(-0.633766\pi\) | ||||
−0.407978 | + | 0.912992i | \(0.633766\pi\) | |||||||
\(272\) | −23.4638 | −1.42270 | ||||||||
\(273\) | −23.0267 | −1.39364 | ||||||||
\(274\) | 14.1666 | 0.855838 | ||||||||
\(275\) | −3.07464 | −0.185408 | ||||||||
\(276\) | 0.434852 | 0.0261750 | ||||||||
\(277\) | 31.7919 | 1.91019 | 0.955096 | − | 0.296297i | \(-0.0957518\pi\) | ||||
0.955096 | + | 0.296297i | \(0.0957518\pi\) | |||||||
\(278\) | −15.0860 | −0.904797 | ||||||||
\(279\) | 4.12525 | 0.246972 | ||||||||
\(280\) | 8.41417 | 0.502843 | ||||||||
\(281\) | 22.8024 | 1.36028 | 0.680140 | − | 0.733083i | \(-0.261919\pi\) | ||||
0.680140 | + | 0.733083i | \(0.261919\pi\) | |||||||
\(282\) | −12.1268 | −0.722139 | ||||||||
\(283\) | −19.0479 | −1.13228 | −0.566140 | − | 0.824309i | \(-0.691564\pi\) | ||||
−0.566140 | + | 0.824309i | \(0.691564\pi\) | |||||||
\(284\) | −3.36517 | −0.199686 | ||||||||
\(285\) | −9.74386 | −0.577177 | ||||||||
\(286\) | 7.54032 | 0.445868 | ||||||||
\(287\) | −8.21466 | −0.484896 | ||||||||
\(288\) | 1.39133 | 0.0819848 | ||||||||
\(289\) | 31.1919 | 1.83482 | ||||||||
\(290\) | −15.1862 | −0.891763 | ||||||||
\(291\) | −14.0349 | −0.822740 | ||||||||
\(292\) | −2.27062 | −0.132878 | ||||||||
\(293\) | −4.36266 | −0.254869 | −0.127435 | − | 0.991847i | \(-0.540674\pi\) | ||||
−0.127435 | + | 0.991847i | \(0.540674\pi\) | |||||||
\(294\) | 7.47893 | 0.436180 | ||||||||
\(295\) | 17.5337 | 1.02085 | ||||||||
\(296\) | −26.4547 | −1.53765 | ||||||||
\(297\) | 4.13531 | 0.239955 | ||||||||
\(298\) | −15.0996 | −0.874698 | ||||||||
\(299\) | 4.62605 | 0.267532 | ||||||||
\(300\) | −1.65823 | −0.0957382 | ||||||||
\(301\) | 1.69017 | 0.0974197 | ||||||||
\(302\) | −2.70025 | −0.155382 | ||||||||
\(303\) | −28.1879 | −1.61935 | ||||||||
\(304\) | 12.0060 | 0.688590 | ||||||||
\(305\) | 1.38757 | 0.0794522 | ||||||||
\(306\) | 8.28592 | 0.473675 | ||||||||
\(307\) | −11.4166 | −0.651580 | −0.325790 | − | 0.945442i | \(-0.605630\pi\) | ||||
−0.325790 | + | 0.945442i | \(0.605630\pi\) | |||||||
\(308\) | −0.553841 | −0.0315580 | ||||||||
\(309\) | −3.35831 | −0.191048 | ||||||||
\(310\) | −8.28309 | −0.470448 | ||||||||
\(311\) | −30.5731 | −1.73364 | −0.866820 | − | 0.498621i | \(-0.833840\pi\) | ||||
−0.866820 | + | 0.498621i | \(0.833840\pi\) | |||||||
\(312\) | 33.8799 | 1.91807 | ||||||||
\(313\) | 9.04130 | 0.511044 | 0.255522 | − | 0.966803i | \(-0.417753\pi\) | ||||
0.255522 | + | 0.966803i | \(0.417753\pi\) | |||||||
\(314\) | 32.0700 | 1.80982 | ||||||||
\(315\) | −2.55836 | −0.144147 | ||||||||
\(316\) | −1.03245 | −0.0580801 | ||||||||
\(317\) | −21.5081 | −1.20802 | −0.604009 | − | 0.796978i | \(-0.706431\pi\) | ||||
−0.604009 | + | 0.796978i | \(0.706431\pi\) | |||||||
\(318\) | 24.6636 | 1.38306 | ||||||||
\(319\) | 8.32766 | 0.466259 | ||||||||
\(320\) | −12.1735 | −0.680519 | ||||||||
\(321\) | 28.8697 | 1.61135 | ||||||||
\(322\) | 2.15121 | 0.119882 | ||||||||
\(323\) | −24.6589 | −1.37206 | ||||||||
\(324\) | 2.97358 | 0.165199 | ||||||||
\(325\) | −17.6406 | −0.978527 | ||||||||
\(326\) | −12.6517 | −0.700710 | ||||||||
\(327\) | −14.2858 | −0.790004 | ||||||||
\(328\) | 12.0865 | 0.667365 | ||||||||
\(329\) | 9.47566 | 0.522410 | ||||||||
\(330\) | 3.60507 | 0.198453 | ||||||||
\(331\) | −23.2813 | −1.27966 | −0.639829 | − | 0.768518i | \(-0.720995\pi\) | ||||
−0.639829 | + | 0.768518i | \(0.720995\pi\) | |||||||
\(332\) | 3.44450 | 0.189042 | ||||||||
\(333\) | 8.04365 | 0.440789 | ||||||||
\(334\) | −22.1804 | −1.21366 | ||||||||
\(335\) | −8.51497 | −0.465223 | ||||||||
\(336\) | 13.5651 | 0.740035 | ||||||||
\(337\) | −13.9809 | −0.761586 | −0.380793 | − | 0.924660i | \(-0.624349\pi\) | ||||
−0.380793 | + | 0.924660i | \(0.624349\pi\) | |||||||
\(338\) | 26.1774 | 1.42386 | ||||||||
\(339\) | −34.5902 | −1.87868 | ||||||||
\(340\) | 2.62788 | 0.142517 | ||||||||
\(341\) | 4.54221 | 0.245974 | ||||||||
\(342\) | −4.23975 | −0.229260 | ||||||||
\(343\) | −20.0548 | −1.08286 | ||||||||
\(344\) | −2.48680 | −0.134079 | ||||||||
\(345\) | 2.21175 | 0.119076 | ||||||||
\(346\) | −7.62135 | −0.409726 | ||||||||
\(347\) | −21.9732 | −1.17959 | −0.589793 | − | 0.807555i | \(-0.700791\pi\) | ||||
−0.589793 | + | 0.807555i | \(0.700791\pi\) | |||||||
\(348\) | 4.49132 | 0.240760 | ||||||||
\(349\) | 12.0629 | 0.645710 | 0.322855 | − | 0.946448i | \(-0.395357\pi\) | ||||
0.322855 | + | 0.946448i | \(0.395357\pi\) | |||||||
\(350\) | −8.20327 | −0.438483 | ||||||||
\(351\) | 23.7262 | 1.26641 | ||||||||
\(352\) | 1.53195 | 0.0816535 | ||||||||
\(353\) | −1.86971 | −0.0995146 | −0.0497573 | − | 0.998761i | \(-0.515845\pi\) | ||||
−0.0497573 | + | 0.998761i | \(0.515845\pi\) | |||||||
\(354\) | 32.8304 | 1.74492 | ||||||||
\(355\) | −17.1159 | −0.908420 | ||||||||
\(356\) | 4.05375 | 0.214848 | ||||||||
\(357\) | −27.8611 | −1.47457 | ||||||||
\(358\) | 5.62485 | 0.297283 | ||||||||
\(359\) | 32.2819 | 1.70377 | 0.851886 | − | 0.523727i | \(-0.175459\pi\) | ||||
0.851886 | + | 0.523727i | \(0.175459\pi\) | |||||||
\(360\) | 3.76420 | 0.198391 | ||||||||
\(361\) | −6.38249 | −0.335921 | ||||||||
\(362\) | −26.4228 | −1.38875 | ||||||||
\(363\) | −1.97692 | −0.103761 | ||||||||
\(364\) | −3.17764 | −0.166554 | ||||||||
\(365\) | −11.5488 | −0.604494 | ||||||||
\(366\) | 2.59812 | 0.135806 | ||||||||
\(367\) | 15.1555 | 0.791112 | 0.395556 | − | 0.918442i | \(-0.370552\pi\) | ||||
0.395556 | + | 0.918442i | \(0.370552\pi\) | |||||||
\(368\) | −2.72522 | −0.142062 | ||||||||
\(369\) | −3.67494 | −0.191310 | ||||||||
\(370\) | −16.1508 | −0.839642 | ||||||||
\(371\) | −19.2717 | −1.00054 | ||||||||
\(372\) | 2.44973 | 0.127012 | ||||||||
\(373\) | −4.47779 | −0.231851 | −0.115926 | − | 0.993258i | \(-0.536983\pi\) | ||||
−0.115926 | + | 0.993258i | \(0.536983\pi\) | |||||||
\(374\) | 9.12341 | 0.471760 | ||||||||
\(375\) | −22.1497 | −1.14380 | ||||||||
\(376\) | −13.9418 | −0.718996 | ||||||||
\(377\) | 47.7796 | 2.46078 | ||||||||
\(378\) | 11.0332 | 0.567485 | ||||||||
\(379\) | 12.5805 | 0.646215 | 0.323107 | − | 0.946362i | \(-0.395273\pi\) | ||||
0.323107 | + | 0.946362i | \(0.395273\pi\) | |||||||
\(380\) | −1.34464 | −0.0689784 | ||||||||
\(381\) | −4.36756 | −0.223757 | ||||||||
\(382\) | 12.0193 | 0.614961 | ||||||||
\(383\) | −4.18886 | −0.214041 | −0.107020 | − | 0.994257i | \(-0.534131\pi\) | ||||
−0.107020 | + | 0.994257i | \(0.534131\pi\) | |||||||
\(384\) | −16.7368 | −0.854096 | ||||||||
\(385\) | −2.81694 | −0.143565 | ||||||||
\(386\) | 25.6784 | 1.30700 | ||||||||
\(387\) | 0.756121 | 0.0384358 | ||||||||
\(388\) | −1.93679 | −0.0983257 | ||||||||
\(389\) | −21.2015 | −1.07496 | −0.537480 | − | 0.843277i | \(-0.680623\pi\) | ||||
−0.537480 | + | 0.843277i | \(0.680623\pi\) | |||||||
\(390\) | 20.6840 | 1.04737 | ||||||||
\(391\) | 5.59729 | 0.283067 | ||||||||
\(392\) | 8.59833 | 0.434281 | ||||||||
\(393\) | 4.10771 | 0.207207 | ||||||||
\(394\) | −28.6059 | −1.44115 | ||||||||
\(395\) | −5.25127 | −0.264220 | ||||||||
\(396\) | −0.247769 | −0.0124508 | ||||||||
\(397\) | 6.72041 | 0.337288 | 0.168644 | − | 0.985677i | \(-0.446061\pi\) | ||||
0.168644 | + | 0.985677i | \(0.446061\pi\) | |||||||
\(398\) | 28.5492 | 1.43104 | ||||||||
\(399\) | 14.2560 | 0.713693 | ||||||||
\(400\) | 10.3921 | 0.519607 | ||||||||
\(401\) | 2.60439 | 0.130057 | 0.0650286 | − | 0.997883i | \(-0.479286\pi\) | ||||
0.0650286 | + | 0.997883i | \(0.479286\pi\) | |||||||
\(402\) | −15.9436 | −0.795194 | ||||||||
\(403\) | 26.0607 | 1.29818 | ||||||||
\(404\) | −3.88988 | −0.193529 | ||||||||
\(405\) | 15.1242 | 0.751529 | ||||||||
\(406\) | 22.2185 | 1.10269 | ||||||||
\(407\) | 8.85665 | 0.439008 | ||||||||
\(408\) | 40.9929 | 2.02945 | ||||||||
\(409\) | 2.08400 | 0.103047 | 0.0515237 | − | 0.998672i | \(-0.483592\pi\) | ||||
0.0515237 | + | 0.998672i | \(0.483592\pi\) | |||||||
\(410\) | 7.37891 | 0.364418 | ||||||||
\(411\) | −21.3101 | −1.05115 | ||||||||
\(412\) | −0.463441 | −0.0228321 | ||||||||
\(413\) | −25.6531 | −1.26231 | ||||||||
\(414\) | 0.962375 | 0.0472982 | ||||||||
\(415\) | 17.5194 | 0.859995 | ||||||||
\(416\) | 8.78953 | 0.430942 | ||||||||
\(417\) | 22.6930 | 1.11128 | ||||||||
\(418\) | −4.66828 | −0.228333 | ||||||||
\(419\) | −24.0304 | −1.17396 | −0.586982 | − | 0.809600i | \(-0.699684\pi\) | ||||
−0.586982 | + | 0.809600i | \(0.699684\pi\) | |||||||
\(420\) | −1.51925 | −0.0741318 | ||||||||
\(421\) | 1.01272 | 0.0493568 | 0.0246784 | − | 0.999695i | \(-0.492144\pi\) | ||||
0.0246784 | + | 0.999695i | \(0.492144\pi\) | |||||||
\(422\) | 3.98720 | 0.194094 | ||||||||
\(423\) | 4.23907 | 0.206111 | ||||||||
\(424\) | 28.3550 | 1.37704 | ||||||||
\(425\) | −21.3443 | −1.03535 | ||||||||
\(426\) | −32.0482 | −1.55274 | ||||||||
\(427\) | −2.03012 | −0.0982446 | ||||||||
\(428\) | 3.98397 | 0.192572 | ||||||||
\(429\) | −11.3425 | −0.547621 | ||||||||
\(430\) | −1.51821 | −0.0732147 | ||||||||
\(431\) | −16.4442 | −0.792088 | −0.396044 | − | 0.918232i | \(-0.629617\pi\) | ||||
−0.396044 | + | 0.918232i | \(0.629617\pi\) | |||||||
\(432\) | −13.9771 | −0.672475 | ||||||||
\(433\) | −22.5857 | −1.08540 | −0.542700 | − | 0.839926i | \(-0.682598\pi\) | ||||
−0.542700 | + | 0.839926i | \(0.682598\pi\) | |||||||
\(434\) | 12.1188 | 0.581721 | ||||||||
\(435\) | 22.8437 | 1.09527 | ||||||||
\(436\) | −1.97141 | −0.0944134 | ||||||||
\(437\) | −2.86403 | −0.137005 | ||||||||
\(438\) | −21.6243 | −1.03325 | ||||||||
\(439\) | −34.8689 | −1.66420 | −0.832101 | − | 0.554625i | \(-0.812862\pi\) | ||||
−0.832101 | + | 0.554625i | \(0.812862\pi\) | |||||||
\(440\) | 4.14466 | 0.197589 | ||||||||
\(441\) | −2.61436 | −0.124493 | ||||||||
\(442\) | 52.3452 | 2.48981 | ||||||||
\(443\) | −31.1718 | −1.48102 | −0.740508 | − | 0.672048i | \(-0.765415\pi\) | ||||
−0.740508 | + | 0.672048i | \(0.765415\pi\) | |||||||
\(444\) | 4.77662 | 0.226688 | ||||||||
\(445\) | 20.6182 | 0.977395 | ||||||||
\(446\) | 6.26756 | 0.296778 | ||||||||
\(447\) | 22.7135 | 1.07431 | ||||||||
\(448\) | 17.8108 | 0.841479 | ||||||||
\(449\) | 25.8963 | 1.22212 | 0.611060 | − | 0.791584i | \(-0.290743\pi\) | ||||
0.611060 | + | 0.791584i | \(0.290743\pi\) | |||||||
\(450\) | −3.66985 | −0.172998 | ||||||||
\(451\) | −4.04638 | −0.190537 | ||||||||
\(452\) | −4.77338 | −0.224521 | ||||||||
\(453\) | 4.06184 | 0.190842 | ||||||||
\(454\) | −35.0116 | −1.64317 | ||||||||
\(455\) | −16.1621 | −0.757691 | ||||||||
\(456\) | −20.9753 | −0.982260 | ||||||||
\(457\) | 6.73065 | 0.314847 | 0.157423 | − | 0.987531i | \(-0.449681\pi\) | ||||
0.157423 | + | 0.987531i | \(0.449681\pi\) | |||||||
\(458\) | 15.3609 | 0.717768 | ||||||||
\(459\) | 28.7075 | 1.33995 | ||||||||
\(460\) | 0.305217 | 0.0142308 | ||||||||
\(461\) | 38.5957 | 1.79758 | 0.898791 | − | 0.438378i | \(-0.144447\pi\) | ||||
0.898791 | + | 0.438378i | \(0.144447\pi\) | |||||||
\(462\) | −5.27450 | −0.245392 | ||||||||
\(463\) | 28.2081 | 1.31094 | 0.655472 | − | 0.755220i | \(-0.272470\pi\) | ||||
0.655472 | + | 0.755220i | \(0.272470\pi\) | |||||||
\(464\) | −28.1471 | −1.30670 | ||||||||
\(465\) | 12.4598 | 0.577809 | ||||||||
\(466\) | −4.58437 | −0.212367 | ||||||||
\(467\) | −16.3664 | −0.757346 | −0.378673 | − | 0.925531i | \(-0.623619\pi\) | ||||
−0.378673 | + | 0.925531i | \(0.623619\pi\) | |||||||
\(468\) | −1.42156 | −0.0657118 | ||||||||
\(469\) | 12.4581 | 0.575260 | ||||||||
\(470\) | −8.51162 | −0.392612 | ||||||||
\(471\) | −48.2412 | −2.22284 | ||||||||
\(472\) | 37.7443 | 1.73732 | ||||||||
\(473\) | 0.832544 | 0.0382804 | ||||||||
\(474\) | −9.83257 | −0.451625 | ||||||||
\(475\) | 10.9215 | 0.501112 | ||||||||
\(476\) | −3.84478 | −0.176225 | ||||||||
\(477\) | −8.62146 | −0.394750 | ||||||||
\(478\) | 23.8490 | 1.09083 | ||||||||
\(479\) | −16.7773 | −0.766572 | −0.383286 | − | 0.923630i | \(-0.625208\pi\) | ||||
−0.383286 | + | 0.923630i | \(0.625208\pi\) | |||||||
\(480\) | 4.20233 | 0.191809 | ||||||||
\(481\) | 50.8147 | 2.31695 | ||||||||
\(482\) | −5.27974 | −0.240485 | ||||||||
\(483\) | −3.23595 | −0.147241 | ||||||||
\(484\) | −0.272811 | −0.0124005 | ||||||||
\(485\) | −9.85091 | −0.447307 | ||||||||
\(486\) | 12.0147 | 0.544998 | ||||||||
\(487\) | −28.7178 | −1.30133 | −0.650665 | − | 0.759365i | \(-0.725510\pi\) | ||||
−0.650665 | + | 0.759365i | \(0.725510\pi\) | |||||||
\(488\) | 2.98699 | 0.135215 | ||||||||
\(489\) | 19.0312 | 0.860621 | ||||||||
\(490\) | 5.24936 | 0.237142 | ||||||||
\(491\) | 32.6549 | 1.47369 | 0.736847 | − | 0.676060i | \(-0.236314\pi\) | ||||
0.736847 | + | 0.676060i | \(0.236314\pi\) | |||||||
\(492\) | −2.18232 | −0.0983864 | ||||||||
\(493\) | 57.8109 | 2.60367 | ||||||||
\(494\) | −26.7841 | −1.20507 | ||||||||
\(495\) | −1.26020 | −0.0566418 | ||||||||
\(496\) | −15.3524 | −0.689345 | ||||||||
\(497\) | 25.0419 | 1.12328 | ||||||||
\(498\) | 32.8037 | 1.46997 | ||||||||
\(499\) | −7.11998 | −0.318734 | −0.159367 | − | 0.987219i | \(-0.550945\pi\) | ||||
−0.159367 | + | 0.987219i | \(0.550945\pi\) | |||||||
\(500\) | −3.05662 | −0.136696 | ||||||||
\(501\) | 33.3648 | 1.49063 | ||||||||
\(502\) | −9.27685 | −0.414046 | ||||||||
\(503\) | −12.3496 | −0.550641 | −0.275321 | − | 0.961352i | \(-0.588784\pi\) | ||||
−0.275321 | + | 0.961352i | \(0.588784\pi\) | |||||||
\(504\) | −5.50731 | −0.245315 | ||||||||
\(505\) | −19.7847 | −0.880408 | ||||||||
\(506\) | 1.05965 | 0.0471070 | ||||||||
\(507\) | −39.3772 | −1.74880 | ||||||||
\(508\) | −0.602716 | −0.0267412 | ||||||||
\(509\) | −11.4262 | −0.506459 | −0.253229 | − | 0.967406i | \(-0.581493\pi\) | ||||
−0.253229 | + | 0.967406i | \(0.581493\pi\) | |||||||
\(510\) | 25.0266 | 1.10819 | ||||||||
\(511\) | 16.8968 | 0.747472 | ||||||||
\(512\) | −25.3697 | −1.12119 | ||||||||
\(513\) | −14.6891 | −0.648539 | ||||||||
\(514\) | −7.93786 | −0.350124 | ||||||||
\(515\) | −2.35715 | −0.103869 | ||||||||
\(516\) | 0.449012 | 0.0197667 | ||||||||
\(517\) | 4.66753 | 0.205278 | ||||||||
\(518\) | 23.6299 | 1.03824 | ||||||||
\(519\) | 11.4644 | 0.503231 | ||||||||
\(520\) | 23.7798 | 1.04281 | ||||||||
\(521\) | −30.2067 | −1.32338 | −0.661690 | − | 0.749777i | \(-0.730161\pi\) | ||||
−0.661690 | + | 0.749777i | \(0.730161\pi\) | |||||||
\(522\) | 9.93978 | 0.435052 | ||||||||
\(523\) | −2.64676 | −0.115735 | −0.0578674 | − | 0.998324i | \(-0.518430\pi\) | ||||
−0.0578674 | + | 0.998324i | \(0.518430\pi\) | |||||||
\(524\) | 0.566857 | 0.0247633 | ||||||||
\(525\) | 12.3397 | 0.538550 | ||||||||
\(526\) | 14.5758 | 0.635537 | ||||||||
\(527\) | 31.5322 | 1.37356 | ||||||||
\(528\) | 6.68189 | 0.290792 | ||||||||
\(529\) | −22.3499 | −0.971735 | ||||||||
\(530\) | 17.3110 | 0.751943 | ||||||||
\(531\) | −11.4763 | −0.498029 | ||||||||
\(532\) | 1.96731 | 0.0852935 | ||||||||
\(533\) | −23.2160 | −1.00559 | ||||||||
\(534\) | 38.6058 | 1.67064 | ||||||||
\(535\) | 20.2632 | 0.876056 | ||||||||
\(536\) | −18.3299 | −0.791733 | ||||||||
\(537\) | −8.46116 | −0.365126 | ||||||||
\(538\) | 6.86998 | 0.296186 | ||||||||
\(539\) | −2.87860 | −0.123990 | ||||||||
\(540\) | 1.56540 | 0.0673642 | ||||||||
\(541\) | 16.9705 | 0.729617 | 0.364809 | − | 0.931082i | \(-0.381134\pi\) | ||||
0.364809 | + | 0.931082i | \(0.381134\pi\) | |||||||
\(542\) | −17.6531 | −0.758266 | ||||||||
\(543\) | 39.7464 | 1.70568 | ||||||||
\(544\) | 10.6349 | 0.455967 | ||||||||
\(545\) | −10.0270 | −0.429509 | ||||||||
\(546\) | −30.2622 | −1.29510 | ||||||||
\(547\) | −12.3888 | −0.529707 | −0.264853 | − | 0.964289i | \(-0.585324\pi\) | ||||
−0.264853 | + | 0.964289i | \(0.585324\pi\) | |||||||
\(548\) | −2.94076 | −0.125623 | ||||||||
\(549\) | −0.908205 | −0.0387612 | ||||||||
\(550\) | −4.04077 | −0.172299 | ||||||||
\(551\) | −29.5808 | −1.26018 | ||||||||
\(552\) | 4.76116 | 0.202648 | ||||||||
\(553\) | 7.68300 | 0.326714 | ||||||||
\(554\) | 41.7818 | 1.77514 | ||||||||
\(555\) | 24.2948 | 1.03126 | ||||||||
\(556\) | 3.13160 | 0.132809 | ||||||||
\(557\) | −28.0597 | −1.18893 | −0.594463 | − | 0.804123i | \(-0.702635\pi\) | ||||
−0.594463 | + | 0.804123i | \(0.702635\pi\) | |||||||
\(558\) | 5.42151 | 0.229511 | ||||||||
\(559\) | 4.77669 | 0.202033 | ||||||||
\(560\) | 9.52113 | 0.402341 | ||||||||
\(561\) | −13.7238 | −0.579421 | ||||||||
\(562\) | 29.9675 | 1.26410 | ||||||||
\(563\) | 34.0521 | 1.43513 | 0.717563 | − | 0.696493i | \(-0.245257\pi\) | ||||
0.717563 | + | 0.696493i | \(0.245257\pi\) | |||||||
\(564\) | 2.51732 | 0.105998 | ||||||||
\(565\) | −24.2784 | −1.02140 | ||||||||
\(566\) | −25.0332 | −1.05223 | ||||||||
\(567\) | −22.1279 | −0.929285 | ||||||||
\(568\) | −36.8450 | −1.54598 | ||||||||
\(569\) | −4.18354 | −0.175383 | −0.0876916 | − | 0.996148i | \(-0.527949\pi\) | ||||
−0.0876916 | + | 0.996148i | \(0.527949\pi\) | |||||||
\(570\) | −12.8056 | −0.536369 | ||||||||
\(571\) | −19.9054 | −0.833013 | −0.416507 | − | 0.909133i | \(-0.636746\pi\) | ||||
−0.416507 | + | 0.909133i | \(0.636746\pi\) | |||||||
\(572\) | −1.56524 | −0.0654462 | ||||||||
\(573\) | −18.0800 | −0.755302 | ||||||||
\(574\) | −10.7959 | −0.450613 | ||||||||
\(575\) | −2.47905 | −0.103384 | ||||||||
\(576\) | 7.96790 | 0.331996 | ||||||||
\(577\) | −26.0834 | −1.08587 | −0.542933 | − | 0.839776i | \(-0.682686\pi\) | ||||
−0.542933 | + | 0.839776i | \(0.682686\pi\) | |||||||
\(578\) | 40.9932 | 1.70509 | ||||||||
\(579\) | −38.6267 | −1.60527 | ||||||||
\(580\) | 3.15240 | 0.130896 | ||||||||
\(581\) | −25.6322 | −1.06340 | ||||||||
\(582\) | −18.4450 | −0.764571 | ||||||||
\(583\) | −9.49286 | −0.393154 | ||||||||
\(584\) | −24.8608 | −1.02875 | ||||||||
\(585\) | −7.23035 | −0.298938 | ||||||||
\(586\) | −5.73352 | −0.236849 | ||||||||
\(587\) | −16.9706 | −0.700451 | −0.350225 | − | 0.936665i | \(-0.613895\pi\) | ||||
−0.350225 | + | 0.936665i | \(0.613895\pi\) | |||||||
\(588\) | −1.55250 | −0.0640240 | ||||||||
\(589\) | −16.1344 | −0.664808 | ||||||||
\(590\) | 23.0432 | 0.948675 | ||||||||
\(591\) | 43.0304 | 1.77003 | ||||||||
\(592\) | −29.9350 | −1.23032 | ||||||||
\(593\) | −28.1953 | −1.15784 | −0.578921 | − | 0.815383i | \(-0.696526\pi\) | ||||
−0.578921 | + | 0.815383i | \(0.696526\pi\) | |||||||
\(594\) | 5.43473 | 0.222990 | ||||||||
\(595\) | −19.5553 | −0.801691 | ||||||||
\(596\) | 3.13443 | 0.128391 | ||||||||
\(597\) | −42.9450 | −1.75762 | ||||||||
\(598\) | 6.07968 | 0.248617 | ||||||||
\(599\) | 16.6875 | 0.681834 | 0.340917 | − | 0.940093i | \(-0.389263\pi\) | ||||
0.340917 | + | 0.940093i | \(0.389263\pi\) | |||||||
\(600\) | −18.1559 | −0.741210 | ||||||||
\(601\) | −34.9576 | −1.42595 | −0.712975 | − | 0.701189i | \(-0.752653\pi\) | ||||
−0.712975 | + | 0.701189i | \(0.752653\pi\) | |||||||
\(602\) | 2.22126 | 0.0905319 | ||||||||
\(603\) | 5.57329 | 0.226962 | ||||||||
\(604\) | 0.560527 | 0.0228075 | ||||||||
\(605\) | −1.38757 | −0.0564128 | ||||||||
\(606\) | −37.0452 | −1.50486 | ||||||||
\(607\) | 16.5940 | 0.673528 | 0.336764 | − | 0.941589i | \(-0.390668\pi\) | ||||
0.336764 | + | 0.941589i | \(0.390668\pi\) | |||||||
\(608\) | −5.44168 | −0.220689 | ||||||||
\(609\) | −33.4221 | −1.35433 | ||||||||
\(610\) | 1.82358 | 0.0738347 | ||||||||
\(611\) | 26.7798 | 1.08339 | ||||||||
\(612\) | −1.72002 | −0.0695277 | ||||||||
\(613\) | 8.29426 | 0.335002 | 0.167501 | − | 0.985872i | \(-0.446430\pi\) | ||||
0.167501 | + | 0.985872i | \(0.446430\pi\) | |||||||
\(614\) | −15.0040 | −0.605512 | ||||||||
\(615\) | −11.0997 | −0.447583 | ||||||||
\(616\) | −6.06395 | −0.244324 | ||||||||
\(617\) | 39.9235 | 1.60726 | 0.803630 | − | 0.595129i | \(-0.202899\pi\) | ||||
0.803630 | + | 0.595129i | \(0.202899\pi\) | |||||||
\(618\) | −4.41358 | −0.177540 | ||||||||
\(619\) | 6.86944 | 0.276106 | 0.138053 | − | 0.990425i | \(-0.455916\pi\) | ||||
0.138053 | + | 0.990425i | \(0.455916\pi\) | |||||||
\(620\) | 1.71943 | 0.0690540 | ||||||||
\(621\) | 3.33425 | 0.133799 | ||||||||
\(622\) | −40.1799 | −1.61107 | ||||||||
\(623\) | −30.1660 | −1.20857 | ||||||||
\(624\) | 38.3371 | 1.53471 | ||||||||
\(625\) | −0.173355 | −0.00693420 | ||||||||
\(626\) | 11.8823 | 0.474912 | ||||||||
\(627\) | 7.02224 | 0.280441 | ||||||||
\(628\) | −6.65720 | −0.265651 | ||||||||
\(629\) | 61.4832 | 2.45150 | ||||||||
\(630\) | −3.36226 | −0.133956 | ||||||||
\(631\) | −37.2753 | −1.48390 | −0.741952 | − | 0.670453i | \(-0.766100\pi\) | ||||
−0.741952 | + | 0.670453i | \(0.766100\pi\) | |||||||
\(632\) | −11.3042 | −0.449659 | ||||||||
\(633\) | −5.99772 | −0.238388 | ||||||||
\(634\) | −28.2666 | −1.12261 | ||||||||
\(635\) | −3.06553 | −0.121652 | ||||||||
\(636\) | −5.11974 | −0.203011 | ||||||||
\(637\) | −16.5158 | −0.654381 | ||||||||
\(638\) | 10.9444 | 0.433294 | ||||||||
\(639\) | 11.2029 | 0.443178 | ||||||||
\(640\) | −11.7473 | −0.464354 | ||||||||
\(641\) | −28.5638 | −1.12820 | −0.564101 | − | 0.825706i | \(-0.690777\pi\) | ||||
−0.564101 | + | 0.825706i | \(0.690777\pi\) | |||||||
\(642\) | 37.9413 | 1.49742 | ||||||||
\(643\) | 13.8862 | 0.547618 | 0.273809 | − | 0.961784i | \(-0.411716\pi\) | ||||
0.273809 | + | 0.961784i | \(0.411716\pi\) | |||||||
\(644\) | −0.446556 | −0.0175968 | ||||||||
\(645\) | 2.28377 | 0.0899232 | ||||||||
\(646\) | −32.4074 | −1.27505 | ||||||||
\(647\) | −2.36581 | −0.0930097 | −0.0465048 | − | 0.998918i | \(-0.514808\pi\) | ||||
−0.0465048 | + | 0.998918i | \(0.514808\pi\) | |||||||
\(648\) | 32.5575 | 1.27898 | ||||||||
\(649\) | −12.6362 | −0.496016 | ||||||||
\(650\) | −23.1838 | −0.909343 | ||||||||
\(651\) | −18.2296 | −0.714476 | ||||||||
\(652\) | 2.62627 | 0.102853 | ||||||||
\(653\) | −44.6721 | −1.74815 | −0.874077 | − | 0.485788i | \(-0.838533\pi\) | ||||
−0.874077 | + | 0.485788i | \(0.838533\pi\) | |||||||
\(654\) | −18.7747 | −0.734149 | ||||||||
\(655\) | 2.88315 | 0.112654 | ||||||||
\(656\) | 13.6766 | 0.533980 | ||||||||
\(657\) | 7.55904 | 0.294906 | ||||||||
\(658\) | 12.4532 | 0.485474 | ||||||||
\(659\) | −3.04987 | −0.118806 | −0.0594031 | − | 0.998234i | \(-0.518920\pi\) | ||||
−0.0594031 | + | 0.998234i | \(0.518920\pi\) | |||||||
\(660\) | −0.748353 | −0.0291296 | ||||||||
\(661\) | 15.0839 | 0.586694 | 0.293347 | − | 0.956006i | \(-0.405231\pi\) | ||||
0.293347 | + | 0.956006i | \(0.405231\pi\) | |||||||
\(662\) | −30.5969 | −1.18918 | ||||||||
\(663\) | −78.7400 | −3.05801 | ||||||||
\(664\) | 37.7135 | 1.46357 | ||||||||
\(665\) | 10.0061 | 0.388020 | ||||||||
\(666\) | 10.5712 | 0.409625 | ||||||||
\(667\) | 6.71450 | 0.259986 | ||||||||
\(668\) | 4.60429 | 0.178145 | ||||||||
\(669\) | −9.42795 | −0.364506 | ||||||||
\(670\) | −11.1906 | −0.432330 | ||||||||
\(671\) | −1.00000 | −0.0386046 | ||||||||
\(672\) | −6.14833 | −0.237177 | ||||||||
\(673\) | 0.744519 | 0.0286991 | 0.0143495 | − | 0.999897i | \(-0.495432\pi\) | ||||
0.0143495 | + | 0.999897i | \(0.495432\pi\) | |||||||
\(674\) | −18.3740 | −0.707740 | ||||||||
\(675\) | −12.7146 | −0.489385 | ||||||||
\(676\) | −5.43399 | −0.208999 | ||||||||
\(677\) | −21.5042 | −0.826475 | −0.413237 | − | 0.910623i | \(-0.635602\pi\) | ||||
−0.413237 | + | 0.910623i | \(0.635602\pi\) | |||||||
\(678\) | −45.4593 | −1.74585 | ||||||||
\(679\) | 14.4126 | 0.553106 | ||||||||
\(680\) | 28.7724 | 1.10337 | ||||||||
\(681\) | 52.6660 | 2.01817 | ||||||||
\(682\) | 5.96948 | 0.228583 | ||||||||
\(683\) | 32.8678 | 1.25765 | 0.628825 | − | 0.777547i | \(-0.283536\pi\) | ||||
0.628825 | + | 0.777547i | \(0.283536\pi\) | |||||||
\(684\) | 0.880102 | 0.0336515 | ||||||||
\(685\) | −14.9573 | −0.571488 | ||||||||
\(686\) | −26.3565 | −1.00630 | ||||||||
\(687\) | −23.1066 | −0.881571 | ||||||||
\(688\) | −2.81396 | −0.107281 | ||||||||
\(689\) | −54.4649 | −2.07495 | ||||||||
\(690\) | 2.90673 | 0.110657 | ||||||||
\(691\) | 40.7898 | 1.55172 | 0.775859 | − | 0.630906i | \(-0.217317\pi\) | ||||
0.775859 | + | 0.630906i | \(0.217317\pi\) | |||||||
\(692\) | 1.58207 | 0.0601411 | ||||||||
\(693\) | 1.84377 | 0.0700390 | ||||||||
\(694\) | −28.8778 | −1.09619 | ||||||||
\(695\) | 15.9279 | 0.604181 | ||||||||
\(696\) | 49.1750 | 1.86398 | ||||||||
\(697\) | −28.0901 | −1.06399 | ||||||||
\(698\) | 15.8533 | 0.600057 | ||||||||
\(699\) | 6.89602 | 0.260831 | ||||||||
\(700\) | 1.70286 | 0.0643622 | ||||||||
\(701\) | 16.5302 | 0.624339 | 0.312169 | − | 0.950026i | \(-0.398944\pi\) | ||||
0.312169 | + | 0.950026i | \(0.398944\pi\) | |||||||
\(702\) | 31.1815 | 1.17687 | ||||||||
\(703\) | −31.4598 | −1.18653 | ||||||||
\(704\) | 8.77324 | 0.330654 | ||||||||
\(705\) | 12.8036 | 0.482210 | ||||||||
\(706\) | −2.45722 | −0.0924787 | ||||||||
\(707\) | 28.9465 | 1.08865 | ||||||||
\(708\) | −6.81505 | −0.256125 | ||||||||
\(709\) | 9.67562 | 0.363375 | 0.181688 | − | 0.983356i | \(-0.441844\pi\) | ||||
0.181688 | + | 0.983356i | \(0.441844\pi\) | |||||||
\(710\) | −22.4942 | −0.844192 | ||||||||
\(711\) | 3.43710 | 0.128901 | ||||||||
\(712\) | 44.3841 | 1.66337 | ||||||||
\(713\) | 3.66233 | 0.137155 | ||||||||
\(714\) | −36.6158 | −1.37031 | ||||||||
\(715\) | −7.96114 | −0.297730 | ||||||||
\(716\) | −1.16763 | −0.0436362 | ||||||||
\(717\) | −35.8748 | −1.33977 | ||||||||
\(718\) | 42.4257 | 1.58331 | ||||||||
\(719\) | 0.412582 | 0.0153867 | 0.00769336 | − | 0.999970i | \(-0.497551\pi\) | ||||
0.00769336 | + | 0.999970i | \(0.497551\pi\) | |||||||
\(720\) | 4.25941 | 0.158739 | ||||||||
\(721\) | 3.44870 | 0.128436 | ||||||||
\(722\) | −8.38803 | −0.312170 | ||||||||
\(723\) | 7.94202 | 0.295367 | ||||||||
\(724\) | 5.48493 | 0.203846 | ||||||||
\(725\) | −25.6046 | −0.950930 | ||||||||
\(726\) | −2.59812 | −0.0964251 | ||||||||
\(727\) | −3.71500 | −0.137782 | −0.0688908 | − | 0.997624i | \(-0.521946\pi\) | ||||
−0.0688908 | + | 0.997624i | \(0.521946\pi\) | |||||||
\(728\) | −34.7917 | −1.28947 | ||||||||
\(729\) | 14.6263 | 0.541713 | ||||||||
\(730\) | −15.1778 | −0.561755 | ||||||||
\(731\) | 5.77955 | 0.213765 | ||||||||
\(732\) | −0.539326 | −0.0199340 | ||||||||
\(733\) | −20.3180 | −0.750464 | −0.375232 | − | 0.926931i | \(-0.622437\pi\) | ||||
−0.375232 | + | 0.926931i | \(0.622437\pi\) | |||||||
\(734\) | 19.9178 | 0.735179 | ||||||||
\(735\) | −7.89633 | −0.291260 | ||||||||
\(736\) | 1.23520 | 0.0455300 | ||||||||
\(737\) | 6.13660 | 0.226044 | ||||||||
\(738\) | −4.82970 | −0.177784 | ||||||||
\(739\) | −13.1912 | −0.485248 | −0.242624 | − | 0.970120i | \(-0.578008\pi\) | ||||
−0.242624 | + | 0.970120i | \(0.578008\pi\) | |||||||
\(740\) | 3.35264 | 0.123246 | ||||||||
\(741\) | 40.2898 | 1.48008 | ||||||||
\(742\) | −25.3273 | −0.929796 | ||||||||
\(743\) | 36.2465 | 1.32975 | 0.664877 | − | 0.746953i | \(-0.268484\pi\) | ||||
0.664877 | + | 0.746953i | \(0.268484\pi\) | |||||||
\(744\) | 26.8219 | 0.983337 | ||||||||
\(745\) | 15.9423 | 0.584082 | ||||||||
\(746\) | −5.88483 | −0.215459 | ||||||||
\(747\) | −11.4670 | −0.419554 | ||||||||
\(748\) | −1.89387 | −0.0692466 | ||||||||
\(749\) | −29.6467 | −1.08327 | ||||||||
\(750\) | −29.1097 | −1.06294 | ||||||||
\(751\) | 25.4285 | 0.927901 | 0.463950 | − | 0.885861i | \(-0.346432\pi\) | ||||
0.463950 | + | 0.885861i | \(0.346432\pi\) | |||||||
\(752\) | −15.7760 | −0.575292 | ||||||||
\(753\) | 13.9547 | 0.508536 | ||||||||
\(754\) | 62.7932 | 2.28679 | ||||||||
\(755\) | 2.85095 | 0.103757 | ||||||||
\(756\) | −2.29030 | −0.0832975 | ||||||||
\(757\) | −1.51402 | −0.0550280 | −0.0275140 | − | 0.999621i | \(-0.508759\pi\) | ||||
−0.0275140 | + | 0.999621i | \(0.508759\pi\) | |||||||
\(758\) | 16.5336 | 0.600526 | ||||||||
\(759\) | −1.59397 | −0.0578574 | ||||||||
\(760\) | −14.7223 | −0.534034 | ||||||||
\(761\) | −22.5979 | −0.819172 | −0.409586 | − | 0.912272i | \(-0.634327\pi\) | ||||
−0.409586 | + | 0.912272i | \(0.634327\pi\) | |||||||
\(762\) | −5.73996 | −0.207937 | ||||||||
\(763\) | 14.6702 | 0.531098 | ||||||||
\(764\) | −2.49501 | −0.0902661 | ||||||||
\(765\) | −8.74836 | −0.316298 | ||||||||
\(766\) | −5.50510 | −0.198907 | ||||||||
\(767\) | −72.4999 | −2.61782 | ||||||||
\(768\) | 12.6920 | 0.457984 | ||||||||
\(769\) | −11.8829 | −0.428509 | −0.214254 | − | 0.976778i | \(-0.568732\pi\) | ||||
−0.214254 | + | 0.976778i | \(0.568732\pi\) | |||||||
\(770\) | −3.70210 | −0.133414 | ||||||||
\(771\) | 11.9405 | 0.430026 | ||||||||
\(772\) | −5.33042 | −0.191846 | ||||||||
\(773\) | −14.3931 | −0.517683 | −0.258841 | − | 0.965920i | \(-0.583341\pi\) | ||||
−0.258841 | + | 0.965920i | \(0.583341\pi\) | |||||||
\(774\) | 0.993713 | 0.0357183 | ||||||||
\(775\) | −13.9657 | −0.501661 | ||||||||
\(776\) | −21.2058 | −0.761243 | ||||||||
\(777\) | −35.5452 | −1.27518 | ||||||||
\(778\) | −27.8636 | −0.998957 | ||||||||
\(779\) | 14.3732 | 0.514973 | ||||||||
\(780\) | −4.29365 | −0.153737 | ||||||||
\(781\) | 12.3352 | 0.441387 | ||||||||
\(782\) | 7.35610 | 0.263054 | ||||||||
\(783\) | 34.4374 | 1.23069 | ||||||||
\(784\) | 9.72952 | 0.347483 | ||||||||
\(785\) | −33.8598 | −1.20851 | ||||||||
\(786\) | 5.39846 | 0.192557 | ||||||||
\(787\) | −4.50354 | −0.160534 | −0.0802668 | − | 0.996773i | \(-0.525577\pi\) | ||||
−0.0802668 | + | 0.996773i | \(0.525577\pi\) | |||||||
\(788\) | 5.93812 | 0.211537 | ||||||||
\(789\) | −21.9257 | −0.780574 | ||||||||
\(790\) | −6.90135 | −0.245539 | ||||||||
\(791\) | 35.5211 | 1.26298 | ||||||||
\(792\) | −2.71280 | −0.0963950 | ||||||||
\(793\) | −5.73746 | −0.203743 | ||||||||
\(794\) | 8.83213 | 0.313441 | ||||||||
\(795\) | −26.0400 | −0.923544 | ||||||||
\(796\) | −5.92633 | −0.210053 | ||||||||
\(797\) | 0.483472 | 0.0171255 | 0.00856273 | − | 0.999963i | \(-0.497274\pi\) | ||||
0.00856273 | + | 0.999963i | \(0.497274\pi\) | |||||||
\(798\) | 18.7356 | 0.663234 | ||||||||
\(799\) | 32.4022 | 1.14631 | ||||||||
\(800\) | −4.71021 | −0.166531 | ||||||||
\(801\) | −13.4952 | −0.476828 | ||||||||
\(802\) | 3.42276 | 0.120862 | ||||||||
\(803\) | 8.32305 | 0.293714 | ||||||||
\(804\) | 3.30962 | 0.116721 | ||||||||
\(805\) | −2.27127 | −0.0800518 | ||||||||
\(806\) | 34.2497 | 1.20639 | ||||||||
\(807\) | −10.3341 | −0.363779 | ||||||||
\(808\) | −42.5899 | −1.49831 | ||||||||
\(809\) | −13.2547 | −0.466010 | −0.233005 | − | 0.972476i | \(-0.574856\pi\) | ||||
−0.233005 | + | 0.972476i | \(0.574856\pi\) | |||||||
\(810\) | 19.8767 | 0.698394 | ||||||||
\(811\) | −25.8912 | −0.909162 | −0.454581 | − | 0.890705i | \(-0.650211\pi\) | ||||
−0.454581 | + | 0.890705i | \(0.650211\pi\) | |||||||
\(812\) | −4.61220 | −0.161856 | ||||||||
\(813\) | 26.5546 | 0.931311 | ||||||||
\(814\) | 11.6396 | 0.407969 | ||||||||
\(815\) | 13.3577 | 0.467901 | ||||||||
\(816\) | 46.3859 | 1.62383 | ||||||||
\(817\) | −2.95729 | −0.103463 | ||||||||
\(818\) | 2.73885 | 0.0957617 | ||||||||
\(819\) | 10.5786 | 0.369645 | ||||||||
\(820\) | −1.53174 | −0.0534906 | ||||||||
\(821\) | −29.0101 | −1.01246 | −0.506230 | − | 0.862399i | \(-0.668961\pi\) | ||||
−0.506230 | + | 0.862399i | \(0.668961\pi\) | |||||||
\(822\) | −28.0063 | −0.976831 | ||||||||
\(823\) | 51.9525 | 1.81095 | 0.905476 | − | 0.424398i | \(-0.139514\pi\) | ||||
0.905476 | + | 0.424398i | \(0.139514\pi\) | |||||||
\(824\) | −5.07418 | −0.176767 | ||||||||
\(825\) | 6.07832 | 0.211620 | ||||||||
\(826\) | −33.7140 | −1.17306 | ||||||||
\(827\) | −7.79500 | −0.271059 | −0.135529 | − | 0.990773i | \(-0.543273\pi\) | ||||
−0.135529 | + | 0.990773i | \(0.543273\pi\) | |||||||
\(828\) | −0.199773 | −0.00694260 | ||||||||
\(829\) | 21.1894 | 0.735940 | 0.367970 | − | 0.929838i | \(-0.380053\pi\) | ||||
0.367970 | + | 0.929838i | \(0.380053\pi\) | |||||||
\(830\) | 23.0245 | 0.799191 | ||||||||
\(831\) | −62.8500 | −2.18024 | ||||||||
\(832\) | 50.3361 | 1.74509 | ||||||||
\(833\) | −19.9833 | −0.692381 | ||||||||
\(834\) | 29.8238 | 1.03271 | ||||||||
\(835\) | 23.4183 | 0.810425 | ||||||||
\(836\) | 0.969057 | 0.0335155 | ||||||||
\(837\) | 18.7834 | 0.649250 | ||||||||
\(838\) | −31.5814 | −1.09096 | ||||||||
\(839\) | −16.8696 | −0.582402 | −0.291201 | − | 0.956662i | \(-0.594055\pi\) | ||||
−0.291201 | + | 0.956662i | \(0.594055\pi\) | |||||||
\(840\) | −16.6341 | −0.573932 | ||||||||
\(841\) | 40.3499 | 1.39138 | ||||||||
\(842\) | 1.33094 | 0.0458672 | ||||||||
\(843\) | −45.0785 | −1.55259 | ||||||||
\(844\) | −0.827675 | −0.0284898 | ||||||||
\(845\) | −27.6383 | −0.950787 | ||||||||
\(846\) | 5.57110 | 0.191538 | ||||||||
\(847\) | 2.03012 | 0.0697559 | ||||||||
\(848\) | 32.0854 | 1.10182 | ||||||||
\(849\) | 37.6561 | 1.29236 | ||||||||
\(850\) | −28.0512 | −0.962149 | ||||||||
\(851\) | 7.14102 | 0.244791 | ||||||||
\(852\) | 6.65267 | 0.227917 | ||||||||
\(853\) | 40.2710 | 1.37885 | 0.689426 | − | 0.724356i | \(-0.257863\pi\) | ||||
0.689426 | + | 0.724356i | \(0.257863\pi\) | |||||||
\(854\) | −2.66804 | −0.0912985 | ||||||||
\(855\) | 4.47637 | 0.153089 | ||||||||
\(856\) | 43.6201 | 1.49090 | ||||||||
\(857\) | 54.7718 | 1.87097 | 0.935485 | − | 0.353366i | \(-0.114963\pi\) | ||||
0.935485 | + | 0.353366i | \(0.114963\pi\) | |||||||
\(858\) | −14.9066 | −0.508903 | ||||||||
\(859\) | 25.8871 | 0.883257 | 0.441629 | − | 0.897198i | \(-0.354401\pi\) | ||||
0.441629 | + | 0.897198i | \(0.354401\pi\) | |||||||
\(860\) | 0.315156 | 0.0107467 | ||||||||
\(861\) | 16.2397 | 0.553447 | ||||||||
\(862\) | −21.6114 | −0.736086 | ||||||||
\(863\) | −13.5251 | −0.460399 | −0.230199 | − | 0.973143i | \(-0.573938\pi\) | ||||
−0.230199 | + | 0.973143i | \(0.573938\pi\) | |||||||
\(864\) | 6.33510 | 0.215525 | ||||||||
\(865\) | 8.04670 | 0.273596 | ||||||||
\(866\) | −29.6827 | −1.00866 | ||||||||
\(867\) | −61.6639 | −2.09421 | ||||||||
\(868\) | −2.51566 | −0.0853870 | ||||||||
\(869\) | 3.78450 | 0.128380 | ||||||||
\(870\) | 30.0218 | 1.01784 | ||||||||
\(871\) | 35.2085 | 1.19299 | ||||||||
\(872\) | −21.5848 | −0.730953 | ||||||||
\(873\) | 6.44769 | 0.218221 | ||||||||
\(874\) | −3.76398 | −0.127319 | ||||||||
\(875\) | 22.7458 | 0.768949 | ||||||||
\(876\) | 4.48883 | 0.151664 | ||||||||
\(877\) | 50.5645 | 1.70744 | 0.853721 | − | 0.520730i | \(-0.174340\pi\) | ||||
0.853721 | + | 0.520730i | \(0.174340\pi\) | |||||||
\(878\) | −45.8256 | −1.54654 | ||||||||
\(879\) | 8.62462 | 0.290901 | ||||||||
\(880\) | 4.68993 | 0.158097 | ||||||||
\(881\) | 24.1533 | 0.813744 | 0.406872 | − | 0.913485i | \(-0.366619\pi\) | ||||
0.406872 | + | 0.913485i | \(0.366619\pi\) | |||||||
\(882\) | −3.43585 | −0.115691 | ||||||||
\(883\) | −52.5172 | −1.76735 | −0.883673 | − | 0.468105i | \(-0.844937\pi\) | ||||
−0.883673 | + | 0.468105i | \(0.844937\pi\) | |||||||
\(884\) | −10.8660 | −0.365463 | ||||||||
\(885\) | −34.6627 | −1.16517 | ||||||||
\(886\) | −40.9667 | −1.37630 | ||||||||
\(887\) | 24.0349 | 0.807013 | 0.403507 | − | 0.914977i | \(-0.367791\pi\) | ||||
0.403507 | + | 0.914977i | \(0.367791\pi\) | |||||||
\(888\) | 52.2987 | 1.75503 | ||||||||
\(889\) | 4.48511 | 0.150426 | ||||||||
\(890\) | 27.0969 | 0.908291 | ||||||||
\(891\) | −10.8998 | −0.365156 | ||||||||
\(892\) | −1.30104 | −0.0435621 | ||||||||
\(893\) | −16.5796 | −0.554815 | ||||||||
\(894\) | 29.8507 | 0.998358 | ||||||||
\(895\) | −5.93878 | −0.198511 | ||||||||
\(896\) | 17.1872 | 0.574185 | ||||||||
\(897\) | −9.14533 | −0.305354 | ||||||||
\(898\) | 34.0335 | 1.13571 | ||||||||
\(899\) | 37.8259 | 1.26157 | ||||||||
\(900\) | 0.761800 | 0.0253933 | ||||||||
\(901\) | −65.8998 | −2.19544 | ||||||||
\(902\) | −5.31786 | −0.177065 | ||||||||
\(903\) | −3.34132 | −0.111192 | ||||||||
\(904\) | −52.2633 | −1.73825 | ||||||||
\(905\) | 27.8975 | 0.927343 | ||||||||
\(906\) | 5.33817 | 0.177349 | ||||||||
\(907\) | −27.3556 | −0.908328 | −0.454164 | − | 0.890918i | \(-0.650062\pi\) | ||||
−0.454164 | + | 0.890918i | \(0.650062\pi\) | |||||||
\(908\) | 7.26782 | 0.241191 | ||||||||
\(909\) | 12.9496 | 0.429512 | ||||||||
\(910\) | −21.2407 | −0.704121 | ||||||||
\(911\) | 3.27520 | 0.108512 | 0.0542562 | − | 0.998527i | \(-0.482721\pi\) | ||||
0.0542562 | + | 0.998527i | \(0.482721\pi\) | |||||||
\(912\) | −23.7348 | −0.785938 | ||||||||
\(913\) | −12.6260 | −0.417858 | ||||||||
\(914\) | 8.84559 | 0.292586 | ||||||||
\(915\) | −2.74312 | −0.0906846 | ||||||||
\(916\) | −3.18867 | −0.105357 | ||||||||
\(917\) | −4.21827 | −0.139299 | ||||||||
\(918\) | 37.7281 | 1.24521 | ||||||||
\(919\) | −9.33515 | −0.307938 | −0.153969 | − | 0.988076i | \(-0.549206\pi\) | ||||
−0.153969 | + | 0.988076i | \(0.549206\pi\) | |||||||
\(920\) | 3.34179 | 0.110176 | ||||||||
\(921\) | 22.5697 | 0.743696 | ||||||||
\(922\) | 50.7235 | 1.67049 | ||||||||
\(923\) | 70.7726 | 2.32951 | ||||||||
\(924\) | 1.09490 | 0.0360195 | ||||||||
\(925\) | −27.2310 | −0.895351 | ||||||||
\(926\) | 37.0718 | 1.21826 | ||||||||
\(927\) | 1.54282 | 0.0506730 | ||||||||
\(928\) | 12.7576 | 0.418789 | ||||||||
\(929\) | −41.7443 | −1.36958 | −0.684792 | − | 0.728738i | \(-0.740107\pi\) | ||||
−0.684792 | + | 0.728738i | \(0.740107\pi\) | |||||||
\(930\) | 16.3750 | 0.536957 | ||||||||
\(931\) | 10.2251 | 0.335114 | ||||||||
\(932\) | 0.951639 | 0.0311720 | ||||||||
\(933\) | 60.4405 | 1.97873 | ||||||||
\(934\) | −21.5091 | −0.703800 | ||||||||
\(935\) | −9.63258 | −0.315019 | ||||||||
\(936\) | −15.5646 | −0.508744 | ||||||||
\(937\) | 17.4250 | 0.569250 | 0.284625 | − | 0.958639i | \(-0.408131\pi\) | ||||
0.284625 | + | 0.958639i | \(0.408131\pi\) | |||||||
\(938\) | 16.3727 | 0.534587 | ||||||||
\(939\) | −17.8739 | −0.583293 | ||||||||
\(940\) | 1.76687 | 0.0576290 | ||||||||
\(941\) | 29.2922 | 0.954899 | 0.477450 | − | 0.878659i | \(-0.341561\pi\) | ||||
0.477450 | + | 0.878659i | \(0.341561\pi\) | |||||||
\(942\) | −63.3998 | −2.06568 | ||||||||
\(943\) | −3.26255 | −0.106243 | ||||||||
\(944\) | 42.7099 | 1.39009 | ||||||||
\(945\) | −11.6489 | −0.378940 | ||||||||
\(946\) | 1.09415 | 0.0355739 | ||||||||
\(947\) | 8.76532 | 0.284835 | 0.142417 | − | 0.989807i | \(-0.454513\pi\) | ||||
0.142417 | + | 0.989807i | \(0.454513\pi\) | |||||||
\(948\) | 2.04108 | 0.0662911 | ||||||||
\(949\) | 47.7532 | 1.55013 | ||||||||
\(950\) | 14.3533 | 0.465682 | ||||||||
\(951\) | 42.5198 | 1.37880 | ||||||||
\(952\) | −42.0962 | −1.36435 | ||||||||
\(953\) | −32.0962 | −1.03970 | −0.519849 | − | 0.854258i | \(-0.674012\pi\) | ||||
−0.519849 | + | 0.854258i | \(0.674012\pi\) | |||||||
\(954\) | −11.3305 | −0.366840 | ||||||||
\(955\) | −12.6901 | −0.410642 | ||||||||
\(956\) | −4.95066 | −0.160116 | ||||||||
\(957\) | −16.4631 | −0.532176 | ||||||||
\(958\) | −22.0491 | −0.712374 | ||||||||
\(959\) | 21.8836 | 0.706659 | ||||||||
\(960\) | 24.0660 | 0.776727 | ||||||||
\(961\) | −10.3684 | −0.334463 | ||||||||
\(962\) | 66.7819 | 2.15314 | ||||||||
\(963\) | −13.2629 | −0.427390 | ||||||||
\(964\) | 1.09599 | 0.0352993 | ||||||||
\(965\) | −27.1116 | −0.872752 | ||||||||
\(966\) | −4.25277 | −0.136831 | ||||||||
\(967\) | 6.77178 | 0.217766 | 0.108883 | − | 0.994055i | \(-0.465273\pi\) | ||||
0.108883 | + | 0.994055i | \(0.465273\pi\) | |||||||
\(968\) | −2.98699 | −0.0960054 | ||||||||
\(969\) | 48.7486 | 1.56603 | ||||||||
\(970\) | −12.9463 | −0.415681 | ||||||||
\(971\) | 24.4938 | 0.786045 | 0.393022 | − | 0.919529i | \(-0.371429\pi\) | ||||
0.393022 | + | 0.919529i | \(0.371429\pi\) | |||||||
\(972\) | −2.49405 | −0.0799968 | ||||||||
\(973\) | −23.3038 | −0.747085 | ||||||||
\(974\) | −37.7417 | −1.20932 | ||||||||
\(975\) | 34.8741 | 1.11687 | ||||||||
\(976\) | 3.37995 | 0.108190 | ||||||||
\(977\) | −34.4114 | −1.10092 | −0.550459 | − | 0.834862i | \(-0.685547\pi\) | ||||
−0.550459 | + | 0.834862i | \(0.685547\pi\) | |||||||
\(978\) | 25.0113 | 0.799773 | ||||||||
\(979\) | −14.8592 | −0.474901 | ||||||||
\(980\) | −1.08968 | −0.0348085 | ||||||||
\(981\) | 6.56294 | 0.209538 | ||||||||
\(982\) | 42.9158 | 1.36950 | ||||||||
\(983\) | −24.8714 | −0.793275 | −0.396638 | − | 0.917975i | \(-0.629823\pi\) | ||||
−0.396638 | + | 0.917975i | \(0.629823\pi\) | |||||||
\(984\) | −23.8940 | −0.761713 | ||||||||
\(985\) | 30.2024 | 0.962329 | ||||||||
\(986\) | 75.9766 | 2.41959 | ||||||||
\(987\) | −18.7326 | −0.596265 | ||||||||
\(988\) | 5.55993 | 0.176885 | ||||||||
\(989\) | 0.671271 | 0.0213452 | ||||||||
\(990\) | −1.65619 | −0.0526371 | ||||||||
\(991\) | 30.8026 | 0.978475 | 0.489238 | − | 0.872151i | \(-0.337275\pi\) | ||||
0.489238 | + | 0.872151i | \(0.337275\pi\) | |||||||
\(992\) | 6.95845 | 0.220931 | ||||||||
\(993\) | 46.0253 | 1.46057 | ||||||||
\(994\) | 32.9107 | 1.04387 | ||||||||
\(995\) | −30.1425 | −0.955582 | ||||||||
\(996\) | −6.80950 | −0.215767 | ||||||||
\(997\) | 23.9102 | 0.757244 | 0.378622 | − | 0.925551i | \(-0.376398\pi\) | ||||
0.378622 | + | 0.925551i | \(0.376398\pi\) | |||||||
\(998\) | −9.35726 | −0.296199 | ||||||||
\(999\) | 36.6250 | 1.15876 |
(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 | 671.2.a.c.1.13 | ✓ | 19 | |
3.2 | odd | 2 | 6039.2.a.k.1.7 | 19 | |||
11.10 | odd | 2 | 7381.2.a.i.1.7 | 19 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
671.2.a.c.1.13 | ✓ | 19 | 1.1 | even | 1 | trivial | |
6039.2.a.k.1.7 | 19 | 3.2 | odd | 2 | |||
7381.2.a.i.1.7 | 19 | 11.10 | odd | 2 |