Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4334,2,Mod(1,4334)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4334, 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("4334.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4334 = 2 \cdot 11 \cdot 197 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4334.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: | \(34.6071642360\) |
Analytic rank: | \(1\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{15} - x^{14} - 23 x^{13} + 19 x^{12} + 194 x^{11} - 124 x^{10} - 761 x^{9} + 353 x^{8} + 1417 x^{7} - 465 x^{6} - 1128 x^{5} + 288 x^{4} + 316 x^{3} - 79 x^{2} - 20 x + 4 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Root | \(-1.70683\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4334.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.70683 | 0.985440 | 0.492720 | − | 0.870188i | \(-0.336003\pi\) | ||||
0.492720 | + | 0.870188i | \(0.336003\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.14577 | 0.512405 | 0.256203 | − | 0.966623i | \(-0.417529\pi\) | ||||
0.256203 | + | 0.966623i | \(0.417529\pi\) | |||||||
\(6\) | −1.70683 | −0.696811 | ||||||||
\(7\) | −1.19968 | −0.453435 | −0.226718 | − | 0.973961i | \(-0.572799\pi\) | ||||
−0.226718 | + | 0.973961i | \(0.572799\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.0867259 | −0.0289086 | ||||||||
\(10\) | −1.14577 | −0.362325 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 1.70683 | 0.492720 | ||||||||
\(13\) | 1.87419 | 0.519807 | 0.259903 | − | 0.965635i | \(-0.416309\pi\) | ||||
0.259903 | + | 0.965635i | \(0.416309\pi\) | |||||||
\(14\) | 1.19968 | 0.320627 | ||||||||
\(15\) | 1.95564 | 0.504944 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.53362 | −1.34210 | −0.671049 | − | 0.741413i | \(-0.734156\pi\) | ||||
−0.671049 | + | 0.741413i | \(0.734156\pi\) | |||||||
\(18\) | 0.0867259 | 0.0204415 | ||||||||
\(19\) | 1.61590 | 0.370712 | 0.185356 | − | 0.982671i | \(-0.440656\pi\) | ||||
0.185356 | + | 0.982671i | \(0.440656\pi\) | |||||||
\(20\) | 1.14577 | 0.256203 | ||||||||
\(21\) | −2.04765 | −0.446833 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | −5.50920 | −1.14875 | −0.574374 | − | 0.818593i | \(-0.694755\pi\) | ||||
−0.574374 | + | 0.818593i | \(0.694755\pi\) | |||||||
\(24\) | −1.70683 | −0.348406 | ||||||||
\(25\) | −3.68720 | −0.737441 | ||||||||
\(26\) | −1.87419 | −0.367559 | ||||||||
\(27\) | −5.26852 | −1.01393 | ||||||||
\(28\) | −1.19968 | −0.226718 | ||||||||
\(29\) | 8.88499 | 1.64990 | 0.824951 | − | 0.565205i | \(-0.191203\pi\) | ||||
0.824951 | + | 0.565205i | \(0.191203\pi\) | |||||||
\(30\) | −1.95564 | −0.357050 | ||||||||
\(31\) | −7.44726 | −1.33757 | −0.668783 | − | 0.743457i | \(-0.733185\pi\) | ||||
−0.668783 | + | 0.743457i | \(0.733185\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 1.70683 | 0.297121 | ||||||||
\(34\) | 5.53362 | 0.949007 | ||||||||
\(35\) | −1.37456 | −0.232343 | ||||||||
\(36\) | −0.0867259 | −0.0144543 | ||||||||
\(37\) | 3.02478 | 0.497271 | 0.248635 | − | 0.968597i | \(-0.420018\pi\) | ||||
0.248635 | + | 0.968597i | \(0.420018\pi\) | |||||||
\(38\) | −1.61590 | −0.262133 | ||||||||
\(39\) | 3.19893 | 0.512238 | ||||||||
\(40\) | −1.14577 | −0.181163 | ||||||||
\(41\) | −5.93132 | −0.926317 | −0.463158 | − | 0.886276i | \(-0.653284\pi\) | ||||
−0.463158 | + | 0.886276i | \(0.653284\pi\) | |||||||
\(42\) | 2.04765 | 0.315959 | ||||||||
\(43\) | −4.16246 | −0.634769 | −0.317385 | − | 0.948297i | \(-0.602805\pi\) | ||||
−0.317385 | + | 0.948297i | \(0.602805\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | −0.0993682 | −0.0148129 | ||||||||
\(46\) | 5.50920 | 0.812288 | ||||||||
\(47\) | −6.81072 | −0.993446 | −0.496723 | − | 0.867909i | \(-0.665463\pi\) | ||||
−0.496723 | + | 0.867909i | \(0.665463\pi\) | |||||||
\(48\) | 1.70683 | 0.246360 | ||||||||
\(49\) | −5.56078 | −0.794396 | ||||||||
\(50\) | 3.68720 | 0.521449 | ||||||||
\(51\) | −9.44495 | −1.32256 | ||||||||
\(52\) | 1.87419 | 0.259903 | ||||||||
\(53\) | −6.71218 | −0.921989 | −0.460994 | − | 0.887403i | \(-0.652507\pi\) | ||||
−0.460994 | + | 0.887403i | \(0.652507\pi\) | |||||||
\(54\) | 5.26852 | 0.716955 | ||||||||
\(55\) | 1.14577 | 0.154496 | ||||||||
\(56\) | 1.19968 | 0.160314 | ||||||||
\(57\) | 2.75806 | 0.365314 | ||||||||
\(58\) | −8.88499 | −1.16666 | ||||||||
\(59\) | 8.03264 | 1.04576 | 0.522881 | − | 0.852406i | \(-0.324857\pi\) | ||||
0.522881 | + | 0.852406i | \(0.324857\pi\) | |||||||
\(60\) | 1.95564 | 0.252472 | ||||||||
\(61\) | −8.11062 | −1.03846 | −0.519229 | − | 0.854635i | \(-0.673781\pi\) | ||||
−0.519229 | + | 0.854635i | \(0.673781\pi\) | |||||||
\(62\) | 7.44726 | 0.945802 | ||||||||
\(63\) | 0.104043 | 0.0131082 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.14740 | 0.266352 | ||||||||
\(66\) | −1.70683 | −0.210096 | ||||||||
\(67\) | 8.40718 | 1.02710 | 0.513550 | − | 0.858059i | \(-0.328330\pi\) | ||||
0.513550 | + | 0.858059i | \(0.328330\pi\) | |||||||
\(68\) | −5.53362 | −0.671049 | ||||||||
\(69\) | −9.40328 | −1.13202 | ||||||||
\(70\) | 1.37456 | 0.164291 | ||||||||
\(71\) | 1.08059 | 0.128242 | 0.0641210 | − | 0.997942i | \(-0.479576\pi\) | ||||
0.0641210 | + | 0.997942i | \(0.479576\pi\) | |||||||
\(72\) | 0.0867259 | 0.0102207 | ||||||||
\(73\) | −6.81363 | −0.797475 | −0.398738 | − | 0.917065i | \(-0.630552\pi\) | ||||
−0.398738 | + | 0.917065i | \(0.630552\pi\) | |||||||
\(74\) | −3.02478 | −0.351623 | ||||||||
\(75\) | −6.29344 | −0.726703 | ||||||||
\(76\) | 1.61590 | 0.185356 | ||||||||
\(77\) | −1.19968 | −0.136716 | ||||||||
\(78\) | −3.19893 | −0.362207 | ||||||||
\(79\) | −5.42875 | −0.610782 | −0.305391 | − | 0.952227i | \(-0.598787\pi\) | ||||
−0.305391 | + | 0.952227i | \(0.598787\pi\) | |||||||
\(80\) | 1.14577 | 0.128101 | ||||||||
\(81\) | −8.73230 | −0.970256 | ||||||||
\(82\) | 5.93132 | 0.655005 | ||||||||
\(83\) | 17.4686 | 1.91743 | 0.958715 | − | 0.284369i | \(-0.0917840\pi\) | ||||
0.958715 | + | 0.284369i | \(0.0917840\pi\) | |||||||
\(84\) | −2.04765 | −0.223417 | ||||||||
\(85\) | −6.34027 | −0.687699 | ||||||||
\(86\) | 4.16246 | 0.448850 | ||||||||
\(87\) | 15.1652 | 1.62588 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | −1.98437 | −0.210343 | −0.105171 | − | 0.994454i | \(-0.533539\pi\) | ||||
−0.105171 | + | 0.994454i | \(0.533539\pi\) | |||||||
\(90\) | 0.0993682 | 0.0104743 | ||||||||
\(91\) | −2.24842 | −0.235699 | ||||||||
\(92\) | −5.50920 | −0.574374 | ||||||||
\(93\) | −12.7112 | −1.31809 | ||||||||
\(94\) | 6.81072 | 0.702472 | ||||||||
\(95\) | 1.85145 | 0.189955 | ||||||||
\(96\) | −1.70683 | −0.174203 | ||||||||
\(97\) | 16.3133 | 1.65636 | 0.828181 | − | 0.560461i | \(-0.189376\pi\) | ||||
0.828181 | + | 0.560461i | \(0.189376\pi\) | |||||||
\(98\) | 5.56078 | 0.561723 | ||||||||
\(99\) | −0.0867259 | −0.00871628 | ||||||||
\(100\) | −3.68720 | −0.368720 | ||||||||
\(101\) | 10.2901 | 1.02391 | 0.511954 | − | 0.859013i | \(-0.328922\pi\) | ||||
0.511954 | + | 0.859013i | \(0.328922\pi\) | |||||||
\(102\) | 9.44495 | 0.935189 | ||||||||
\(103\) | −8.16069 | −0.804097 | −0.402048 | − | 0.915618i | \(-0.631702\pi\) | ||||
−0.402048 | + | 0.915618i | \(0.631702\pi\) | |||||||
\(104\) | −1.87419 | −0.183779 | ||||||||
\(105\) | −2.34614 | −0.228960 | ||||||||
\(106\) | 6.71218 | 0.651945 | ||||||||
\(107\) | 6.49869 | 0.628252 | 0.314126 | − | 0.949381i | \(-0.398288\pi\) | ||||
0.314126 | + | 0.949381i | \(0.398288\pi\) | |||||||
\(108\) | −5.26852 | −0.506964 | ||||||||
\(109\) | −10.7274 | −1.02750 | −0.513748 | − | 0.857941i | \(-0.671743\pi\) | ||||
−0.513748 | + | 0.857941i | \(0.671743\pi\) | |||||||
\(110\) | −1.14577 | −0.109245 | ||||||||
\(111\) | 5.16279 | 0.490030 | ||||||||
\(112\) | −1.19968 | −0.113359 | ||||||||
\(113\) | −13.9026 | −1.30785 | −0.653924 | − | 0.756561i | \(-0.726878\pi\) | ||||
−0.653924 | + | 0.756561i | \(0.726878\pi\) | |||||||
\(114\) | −2.75806 | −0.258316 | ||||||||
\(115\) | −6.31230 | −0.588625 | ||||||||
\(116\) | 8.88499 | 0.824951 | ||||||||
\(117\) | −0.162541 | −0.0150269 | ||||||||
\(118\) | −8.03264 | −0.739465 | ||||||||
\(119\) | 6.63855 | 0.608555 | ||||||||
\(120\) | −1.95564 | −0.178525 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 8.11062 | 0.734301 | ||||||||
\(123\) | −10.1238 | −0.912829 | ||||||||
\(124\) | −7.44726 | −0.668783 | ||||||||
\(125\) | −9.95356 | −0.890274 | ||||||||
\(126\) | −0.104043 | −0.00926889 | ||||||||
\(127\) | 13.7068 | 1.21628 | 0.608141 | − | 0.793829i | \(-0.291915\pi\) | ||||
0.608141 | + | 0.793829i | \(0.291915\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −7.10462 | −0.625527 | ||||||||
\(130\) | −2.14740 | −0.188339 | ||||||||
\(131\) | −18.6812 | −1.63218 | −0.816091 | − | 0.577923i | \(-0.803863\pi\) | ||||
−0.816091 | + | 0.577923i | \(0.803863\pi\) | |||||||
\(132\) | 1.70683 | 0.148561 | ||||||||
\(133\) | −1.93855 | −0.168094 | ||||||||
\(134\) | −8.40718 | −0.726270 | ||||||||
\(135\) | −6.03653 | −0.519542 | ||||||||
\(136\) | 5.53362 | 0.474504 | ||||||||
\(137\) | 7.98434 | 0.682148 | 0.341074 | − | 0.940036i | \(-0.389209\pi\) | ||||
0.341074 | + | 0.940036i | \(0.389209\pi\) | |||||||
\(138\) | 9.40328 | 0.800461 | ||||||||
\(139\) | −18.3920 | −1.55999 | −0.779993 | − | 0.625789i | \(-0.784777\pi\) | ||||
−0.779993 | + | 0.625789i | \(0.784777\pi\) | |||||||
\(140\) | −1.37456 | −0.116171 | ||||||||
\(141\) | −11.6248 | −0.978981 | ||||||||
\(142\) | −1.08059 | −0.0906808 | ||||||||
\(143\) | 1.87419 | 0.156728 | ||||||||
\(144\) | −0.0867259 | −0.00722716 | ||||||||
\(145\) | 10.1802 | 0.845418 | ||||||||
\(146\) | 6.81363 | 0.563900 | ||||||||
\(147\) | −9.49131 | −0.782830 | ||||||||
\(148\) | 3.02478 | 0.248635 | ||||||||
\(149\) | −8.92237 | −0.730949 | −0.365474 | − | 0.930821i | \(-0.619093\pi\) | ||||
−0.365474 | + | 0.930821i | \(0.619093\pi\) | |||||||
\(150\) | 6.29344 | 0.513857 | ||||||||
\(151\) | 1.46432 | 0.119165 | 0.0595825 | − | 0.998223i | \(-0.481023\pi\) | ||||
0.0595825 | + | 0.998223i | \(0.481023\pi\) | |||||||
\(152\) | −1.61590 | −0.131066 | ||||||||
\(153\) | 0.479908 | 0.0387982 | ||||||||
\(154\) | 1.19968 | 0.0966727 | ||||||||
\(155\) | −8.53286 | −0.685376 | ||||||||
\(156\) | 3.19893 | 0.256119 | ||||||||
\(157\) | −13.7949 | −1.10095 | −0.550477 | − | 0.834850i | \(-0.685554\pi\) | ||||
−0.550477 | + | 0.834850i | \(0.685554\pi\) | |||||||
\(158\) | 5.42875 | 0.431888 | ||||||||
\(159\) | −11.4566 | −0.908564 | ||||||||
\(160\) | −1.14577 | −0.0905813 | ||||||||
\(161\) | 6.60926 | 0.520883 | ||||||||
\(162\) | 8.73230 | 0.686074 | ||||||||
\(163\) | 2.63145 | 0.206111 | 0.103056 | − | 0.994676i | \(-0.467138\pi\) | ||||
0.103056 | + | 0.994676i | \(0.467138\pi\) | |||||||
\(164\) | −5.93132 | −0.463158 | ||||||||
\(165\) | 1.95564 | 0.152246 | ||||||||
\(166\) | −17.4686 | −1.35583 | ||||||||
\(167\) | −1.78283 | −0.137959 | −0.0689797 | − | 0.997618i | \(-0.521974\pi\) | ||||
−0.0689797 | + | 0.997618i | \(0.521974\pi\) | |||||||
\(168\) | 2.04765 | 0.157979 | ||||||||
\(169\) | −9.48741 | −0.729801 | ||||||||
\(170\) | 6.34027 | 0.486276 | ||||||||
\(171\) | −0.140140 | −0.0107168 | ||||||||
\(172\) | −4.16246 | −0.317385 | ||||||||
\(173\) | 12.1139 | 0.921003 | 0.460502 | − | 0.887659i | \(-0.347670\pi\) | ||||
0.460502 | + | 0.887659i | \(0.347670\pi\) | |||||||
\(174\) | −15.1652 | −1.14967 | ||||||||
\(175\) | 4.42345 | 0.334382 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 13.7104 | 1.03053 | ||||||||
\(178\) | 1.98437 | 0.148735 | ||||||||
\(179\) | −11.9199 | −0.890933 | −0.445467 | − | 0.895299i | \(-0.646962\pi\) | ||||
−0.445467 | + | 0.895299i | \(0.646962\pi\) | |||||||
\(180\) | −0.0993682 | −0.00740647 | ||||||||
\(181\) | 1.58015 | 0.117452 | 0.0587258 | − | 0.998274i | \(-0.481296\pi\) | ||||
0.0587258 | + | 0.998274i | \(0.481296\pi\) | |||||||
\(182\) | 2.24842 | 0.166664 | ||||||||
\(183\) | −13.8435 | −1.02334 | ||||||||
\(184\) | 5.50920 | 0.406144 | ||||||||
\(185\) | 3.46571 | 0.254804 | ||||||||
\(186\) | 12.7112 | 0.932031 | ||||||||
\(187\) | −5.53362 | −0.404658 | ||||||||
\(188\) | −6.81072 | −0.496723 | ||||||||
\(189\) | 6.32052 | 0.459750 | ||||||||
\(190\) | −1.85145 | −0.134318 | ||||||||
\(191\) | −18.8839 | −1.36639 | −0.683196 | − | 0.730235i | \(-0.739411\pi\) | ||||
−0.683196 | + | 0.730235i | \(0.739411\pi\) | |||||||
\(192\) | 1.70683 | 0.123180 | ||||||||
\(193\) | 10.5416 | 0.758800 | 0.379400 | − | 0.925233i | \(-0.376130\pi\) | ||||
0.379400 | + | 0.925233i | \(0.376130\pi\) | |||||||
\(194\) | −16.3133 | −1.17122 | ||||||||
\(195\) | 3.66524 | 0.262473 | ||||||||
\(196\) | −5.56078 | −0.397198 | ||||||||
\(197\) | 1.00000 | 0.0712470 | ||||||||
\(198\) | 0.0867259 | 0.00616334 | ||||||||
\(199\) | −6.29150 | −0.445992 | −0.222996 | − | 0.974819i | \(-0.571584\pi\) | ||||
−0.222996 | + | 0.974819i | \(0.571584\pi\) | |||||||
\(200\) | 3.68720 | 0.260725 | ||||||||
\(201\) | 14.3496 | 1.01215 | ||||||||
\(202\) | −10.2901 | −0.724012 | ||||||||
\(203\) | −10.6591 | −0.748124 | ||||||||
\(204\) | −9.44495 | −0.661279 | ||||||||
\(205\) | −6.79595 | −0.474650 | ||||||||
\(206\) | 8.16069 | 0.568582 | ||||||||
\(207\) | 0.477791 | 0.0332087 | ||||||||
\(208\) | 1.87419 | 0.129952 | ||||||||
\(209\) | 1.61590 | 0.111774 | ||||||||
\(210\) | 2.34614 | 0.161899 | ||||||||
\(211\) | 1.80977 | 0.124589 | 0.0622947 | − | 0.998058i | \(-0.480158\pi\) | ||||
0.0622947 | + | 0.998058i | \(0.480158\pi\) | |||||||
\(212\) | −6.71218 | −0.460994 | ||||||||
\(213\) | 1.84438 | 0.126375 | ||||||||
\(214\) | −6.49869 | −0.444242 | ||||||||
\(215\) | −4.76924 | −0.325259 | ||||||||
\(216\) | 5.26852 | 0.358477 | ||||||||
\(217\) | 8.93430 | 0.606500 | ||||||||
\(218\) | 10.7274 | 0.726549 | ||||||||
\(219\) | −11.6297 | −0.785864 | ||||||||
\(220\) | 1.14577 | 0.0772480 | ||||||||
\(221\) | −10.3710 | −0.697632 | ||||||||
\(222\) | −5.16279 | −0.346504 | ||||||||
\(223\) | −7.58628 | −0.508015 | −0.254007 | − | 0.967202i | \(-0.581749\pi\) | ||||
−0.254007 | + | 0.967202i | \(0.581749\pi\) | |||||||
\(224\) | 1.19968 | 0.0801568 | ||||||||
\(225\) | 0.319776 | 0.0213184 | ||||||||
\(226\) | 13.9026 | 0.924788 | ||||||||
\(227\) | 12.3775 | 0.821521 | 0.410761 | − | 0.911743i | \(-0.365263\pi\) | ||||
0.410761 | + | 0.911743i | \(0.365263\pi\) | |||||||
\(228\) | 2.75806 | 0.182657 | ||||||||
\(229\) | −4.25397 | −0.281110 | −0.140555 | − | 0.990073i | \(-0.544889\pi\) | ||||
−0.140555 | + | 0.990073i | \(0.544889\pi\) | |||||||
\(230\) | 6.31230 | 0.416221 | ||||||||
\(231\) | −2.04765 | −0.134725 | ||||||||
\(232\) | −8.88499 | −0.583328 | ||||||||
\(233\) | −7.59700 | −0.497696 | −0.248848 | − | 0.968543i | \(-0.580052\pi\) | ||||
−0.248848 | + | 0.968543i | \(0.580052\pi\) | |||||||
\(234\) | 0.162541 | 0.0106256 | ||||||||
\(235\) | −7.80354 | −0.509047 | ||||||||
\(236\) | 8.03264 | 0.522881 | ||||||||
\(237\) | −9.26595 | −0.601888 | ||||||||
\(238\) | −6.63855 | −0.430313 | ||||||||
\(239\) | 8.61541 | 0.557285 | 0.278642 | − | 0.960395i | \(-0.410116\pi\) | ||||
0.278642 | + | 0.960395i | \(0.410116\pi\) | |||||||
\(240\) | 1.95564 | 0.126236 | ||||||||
\(241\) | 21.9775 | 1.41569 | 0.707847 | − | 0.706366i | \(-0.249667\pi\) | ||||
0.707847 | + | 0.706366i | \(0.249667\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | 0.900997 | 0.0577990 | ||||||||
\(244\) | −8.11062 | −0.519229 | ||||||||
\(245\) | −6.37139 | −0.407053 | ||||||||
\(246\) | 10.1238 | 0.645468 | ||||||||
\(247\) | 3.02849 | 0.192698 | ||||||||
\(248\) | 7.44726 | 0.472901 | ||||||||
\(249\) | 29.8160 | 1.88951 | ||||||||
\(250\) | 9.95356 | 0.629519 | ||||||||
\(251\) | 8.67911 | 0.547821 | 0.273910 | − | 0.961755i | \(-0.411683\pi\) | ||||
0.273910 | + | 0.961755i | \(0.411683\pi\) | |||||||
\(252\) | 0.104043 | 0.00655410 | ||||||||
\(253\) | −5.50920 | −0.346361 | ||||||||
\(254\) | −13.7068 | −0.860042 | ||||||||
\(255\) | −10.8218 | −0.677685 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 15.4743 | 0.965259 | 0.482629 | − | 0.875825i | \(-0.339682\pi\) | ||||
0.482629 | + | 0.875825i | \(0.339682\pi\) | |||||||
\(258\) | 7.10462 | 0.442314 | ||||||||
\(259\) | −3.62876 | −0.225480 | ||||||||
\(260\) | 2.14740 | 0.133176 | ||||||||
\(261\) | −0.770559 | −0.0476964 | ||||||||
\(262\) | 18.6812 | 1.15413 | ||||||||
\(263\) | 30.1966 | 1.86200 | 0.931001 | − | 0.365016i | \(-0.118936\pi\) | ||||
0.931001 | + | 0.365016i | \(0.118936\pi\) | |||||||
\(264\) | −1.70683 | −0.105048 | ||||||||
\(265\) | −7.69063 | −0.472432 | ||||||||
\(266\) | 1.93855 | 0.118860 | ||||||||
\(267\) | −3.38698 | −0.207280 | ||||||||
\(268\) | 8.40718 | 0.513550 | ||||||||
\(269\) | −22.5400 | −1.37429 | −0.687145 | − | 0.726520i | \(-0.741136\pi\) | ||||
−0.687145 | + | 0.726520i | \(0.741136\pi\) | |||||||
\(270\) | 6.03653 | 0.367371 | ||||||||
\(271\) | 23.0806 | 1.40205 | 0.701024 | − | 0.713138i | \(-0.252727\pi\) | ||||
0.701024 | + | 0.713138i | \(0.252727\pi\) | |||||||
\(272\) | −5.53362 | −0.335525 | ||||||||
\(273\) | −3.83768 | −0.232267 | ||||||||
\(274\) | −7.98434 | −0.482352 | ||||||||
\(275\) | −3.68720 | −0.222347 | ||||||||
\(276\) | −9.40328 | −0.566011 | ||||||||
\(277\) | 26.9413 | 1.61875 | 0.809373 | − | 0.587294i | \(-0.199807\pi\) | ||||
0.809373 | + | 0.587294i | \(0.199807\pi\) | |||||||
\(278\) | 18.3920 | 1.10308 | ||||||||
\(279\) | 0.645870 | 0.0386672 | ||||||||
\(280\) | 1.37456 | 0.0821455 | ||||||||
\(281\) | 5.19557 | 0.309942 | 0.154971 | − | 0.987919i | \(-0.450472\pi\) | ||||
0.154971 | + | 0.987919i | \(0.450472\pi\) | |||||||
\(282\) | 11.6248 | 0.692244 | ||||||||
\(283\) | −7.02171 | −0.417397 | −0.208699 | − | 0.977980i | \(-0.566923\pi\) | ||||
−0.208699 | + | 0.977980i | \(0.566923\pi\) | |||||||
\(284\) | 1.08059 | 0.0641210 | ||||||||
\(285\) | 3.16011 | 0.187189 | ||||||||
\(286\) | −1.87419 | −0.110823 | ||||||||
\(287\) | 7.11567 | 0.420025 | ||||||||
\(288\) | 0.0867259 | 0.00511037 | ||||||||
\(289\) | 13.6209 | 0.801230 | ||||||||
\(290\) | −10.1802 | −0.597801 | ||||||||
\(291\) | 27.8440 | 1.63224 | ||||||||
\(292\) | −6.81363 | −0.398738 | ||||||||
\(293\) | 20.7718 | 1.21350 | 0.606752 | − | 0.794891i | \(-0.292472\pi\) | ||||
0.606752 | + | 0.794891i | \(0.292472\pi\) | |||||||
\(294\) | 9.49131 | 0.553544 | ||||||||
\(295\) | 9.20359 | 0.535854 | ||||||||
\(296\) | −3.02478 | −0.175812 | ||||||||
\(297\) | −5.26852 | −0.305711 | ||||||||
\(298\) | 8.92237 | 0.516859 | ||||||||
\(299\) | −10.3253 | −0.597127 | ||||||||
\(300\) | −6.29344 | −0.363352 | ||||||||
\(301\) | 4.99361 | 0.287827 | ||||||||
\(302\) | −1.46432 | −0.0842623 | ||||||||
\(303\) | 17.5636 | 1.00900 | ||||||||
\(304\) | 1.61590 | 0.0926779 | ||||||||
\(305\) | −9.29292 | −0.532111 | ||||||||
\(306\) | −0.479908 | −0.0274345 | ||||||||
\(307\) | −27.0682 | −1.54487 | −0.772433 | − | 0.635097i | \(-0.780960\pi\) | ||||
−0.772433 | + | 0.635097i | \(0.780960\pi\) | |||||||
\(308\) | −1.19968 | −0.0683579 | ||||||||
\(309\) | −13.9289 | −0.792389 | ||||||||
\(310\) | 8.53286 | 0.484634 | ||||||||
\(311\) | −9.87629 | −0.560033 | −0.280016 | − | 0.959995i | \(-0.590340\pi\) | ||||
−0.280016 | + | 0.959995i | \(0.590340\pi\) | |||||||
\(312\) | −3.19893 | −0.181103 | ||||||||
\(313\) | 2.58209 | 0.145949 | 0.0729743 | − | 0.997334i | \(-0.476751\pi\) | ||||
0.0729743 | + | 0.997334i | \(0.476751\pi\) | |||||||
\(314\) | 13.7949 | 0.778492 | ||||||||
\(315\) | 0.119210 | 0.00671671 | ||||||||
\(316\) | −5.42875 | −0.305391 | ||||||||
\(317\) | −2.07068 | −0.116301 | −0.0581505 | − | 0.998308i | \(-0.518520\pi\) | ||||
−0.0581505 | + | 0.998308i | \(0.518520\pi\) | |||||||
\(318\) | 11.4566 | 0.642452 | ||||||||
\(319\) | 8.88499 | 0.497464 | ||||||||
\(320\) | 1.14577 | 0.0640507 | ||||||||
\(321\) | 11.0922 | 0.619105 | ||||||||
\(322\) | −6.60926 | −0.368320 | ||||||||
\(323\) | −8.94174 | −0.497532 | ||||||||
\(324\) | −8.73230 | −0.485128 | ||||||||
\(325\) | −6.91052 | −0.383327 | ||||||||
\(326\) | −2.63145 | −0.145743 | ||||||||
\(327\) | −18.3098 | −1.01253 | ||||||||
\(328\) | 5.93132 | 0.327502 | ||||||||
\(329\) | 8.17066 | 0.450463 | ||||||||
\(330\) | −1.95564 | −0.107655 | ||||||||
\(331\) | 7.21290 | 0.396457 | 0.198228 | − | 0.980156i | \(-0.436481\pi\) | ||||
0.198228 | + | 0.980156i | \(0.436481\pi\) | |||||||
\(332\) | 17.4686 | 0.958715 | ||||||||
\(333\) | −0.262327 | −0.0143754 | ||||||||
\(334\) | 1.78283 | 0.0975520 | ||||||||
\(335\) | 9.63272 | 0.526292 | ||||||||
\(336\) | −2.04765 | −0.111708 | ||||||||
\(337\) | −24.1101 | −1.31336 | −0.656682 | − | 0.754168i | \(-0.728040\pi\) | ||||
−0.656682 | + | 0.754168i | \(0.728040\pi\) | |||||||
\(338\) | 9.48741 | 0.516047 | ||||||||
\(339\) | −23.7294 | −1.28880 | ||||||||
\(340\) | −6.34027 | −0.343849 | ||||||||
\(341\) | −7.44726 | −0.403291 | ||||||||
\(342\) | 0.140140 | 0.00757790 | ||||||||
\(343\) | 15.0689 | 0.813643 | ||||||||
\(344\) | 4.16246 | 0.224425 | ||||||||
\(345\) | −10.7740 | −0.580054 | ||||||||
\(346\) | −12.1139 | −0.651247 | ||||||||
\(347\) | 33.6719 | 1.80760 | 0.903802 | − | 0.427951i | \(-0.140764\pi\) | ||||
0.903802 | + | 0.427951i | \(0.140764\pi\) | |||||||
\(348\) | 15.1652 | 0.812939 | ||||||||
\(349\) | −10.9087 | −0.583932 | −0.291966 | − | 0.956429i | \(-0.594309\pi\) | ||||
−0.291966 | + | 0.956429i | \(0.594309\pi\) | |||||||
\(350\) | −4.42345 | −0.236444 | ||||||||
\(351\) | −9.87421 | −0.527046 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | −34.0928 | −1.81458 | −0.907288 | − | 0.420510i | \(-0.861851\pi\) | ||||
−0.907288 | + | 0.420510i | \(0.861851\pi\) | |||||||
\(354\) | −13.7104 | −0.728698 | ||||||||
\(355\) | 1.23811 | 0.0657119 | ||||||||
\(356\) | −1.98437 | −0.105171 | ||||||||
\(357\) | 11.3309 | 0.599694 | ||||||||
\(358\) | 11.9199 | 0.629985 | ||||||||
\(359\) | −12.5651 | −0.663162 | −0.331581 | − | 0.943427i | \(-0.607582\pi\) | ||||
−0.331581 | + | 0.943427i | \(0.607582\pi\) | |||||||
\(360\) | 0.0993682 | 0.00523716 | ||||||||
\(361\) | −16.3889 | −0.862573 | ||||||||
\(362\) | −1.58015 | −0.0830509 | ||||||||
\(363\) | 1.70683 | 0.0895854 | ||||||||
\(364\) | −2.24842 | −0.117849 | ||||||||
\(365\) | −7.80688 | −0.408631 | ||||||||
\(366\) | 13.8435 | 0.723609 | ||||||||
\(367\) | −2.14332 | −0.111880 | −0.0559401 | − | 0.998434i | \(-0.517816\pi\) | ||||
−0.0559401 | + | 0.998434i | \(0.517816\pi\) | |||||||
\(368\) | −5.50920 | −0.287187 | ||||||||
\(369\) | 0.514399 | 0.0267785 | ||||||||
\(370\) | −3.46571 | −0.180174 | ||||||||
\(371\) | 8.05245 | 0.418062 | ||||||||
\(372\) | −12.7112 | −0.659046 | ||||||||
\(373\) | −2.85050 | −0.147593 | −0.0737965 | − | 0.997273i | \(-0.523512\pi\) | ||||
−0.0737965 | + | 0.997273i | \(0.523512\pi\) | |||||||
\(374\) | 5.53362 | 0.286136 | ||||||||
\(375\) | −16.9891 | −0.877311 | ||||||||
\(376\) | 6.81072 | 0.351236 | ||||||||
\(377\) | 16.6522 | 0.857630 | ||||||||
\(378\) | −6.32052 | −0.325093 | ||||||||
\(379\) | −29.9256 | −1.53717 | −0.768586 | − | 0.639746i | \(-0.779039\pi\) | ||||
−0.768586 | + | 0.639746i | \(0.779039\pi\) | |||||||
\(380\) | 1.85145 | 0.0949773 | ||||||||
\(381\) | 23.3952 | 1.19857 | ||||||||
\(382\) | 18.8839 | 0.966185 | ||||||||
\(383\) | −13.3893 | −0.684161 | −0.342080 | − | 0.939671i | \(-0.611131\pi\) | ||||
−0.342080 | + | 0.939671i | \(0.611131\pi\) | |||||||
\(384\) | −1.70683 | −0.0871014 | ||||||||
\(385\) | −1.37456 | −0.0700539 | ||||||||
\(386\) | −10.5416 | −0.536553 | ||||||||
\(387\) | 0.360993 | 0.0183503 | ||||||||
\(388\) | 16.3133 | 0.828181 | ||||||||
\(389\) | 14.9613 | 0.758570 | 0.379285 | − | 0.925280i | \(-0.376170\pi\) | ||||
0.379285 | + | 0.925280i | \(0.376170\pi\) | |||||||
\(390\) | −3.66524 | −0.185597 | ||||||||
\(391\) | 30.4858 | 1.54173 | ||||||||
\(392\) | 5.56078 | 0.280862 | ||||||||
\(393\) | −31.8856 | −1.60842 | ||||||||
\(394\) | −1.00000 | −0.0503793 | ||||||||
\(395\) | −6.22011 | −0.312968 | ||||||||
\(396\) | −0.0867259 | −0.00435814 | ||||||||
\(397\) | −28.0241 | −1.40649 | −0.703244 | − | 0.710949i | \(-0.748266\pi\) | ||||
−0.703244 | + | 0.710949i | \(0.748266\pi\) | |||||||
\(398\) | 6.29150 | 0.315364 | ||||||||
\(399\) | −3.30878 | −0.165646 | ||||||||
\(400\) | −3.68720 | −0.184360 | ||||||||
\(401\) | −0.888495 | −0.0443693 | −0.0221847 | − | 0.999754i | \(-0.507062\pi\) | ||||
−0.0221847 | + | 0.999754i | \(0.507062\pi\) | |||||||
\(402\) | −14.3496 | −0.715695 | ||||||||
\(403\) | −13.9576 | −0.695276 | ||||||||
\(404\) | 10.2901 | 0.511954 | ||||||||
\(405\) | −10.0052 | −0.497164 | ||||||||
\(406\) | 10.6591 | 0.529003 | ||||||||
\(407\) | 3.02478 | 0.149933 | ||||||||
\(408\) | 9.44495 | 0.467595 | ||||||||
\(409\) | −8.93554 | −0.441834 | −0.220917 | − | 0.975293i | \(-0.570905\pi\) | ||||
−0.220917 | + | 0.975293i | \(0.570905\pi\) | |||||||
\(410\) | 6.79595 | 0.335628 | ||||||||
\(411\) | 13.6279 | 0.672216 | ||||||||
\(412\) | −8.16069 | −0.402048 | ||||||||
\(413\) | −9.63658 | −0.474185 | ||||||||
\(414\) | −0.477791 | −0.0234821 | ||||||||
\(415\) | 20.0151 | 0.982501 | ||||||||
\(416\) | −1.87419 | −0.0918897 | ||||||||
\(417\) | −31.3920 | −1.53727 | ||||||||
\(418\) | −1.61590 | −0.0790360 | ||||||||
\(419\) | 8.77232 | 0.428556 | 0.214278 | − | 0.976773i | \(-0.431260\pi\) | ||||
0.214278 | + | 0.976773i | \(0.431260\pi\) | |||||||
\(420\) | −2.34614 | −0.114480 | ||||||||
\(421\) | −34.4629 | −1.67962 | −0.839809 | − | 0.542882i | \(-0.817333\pi\) | ||||
−0.839809 | + | 0.542882i | \(0.817333\pi\) | |||||||
\(422\) | −1.80977 | −0.0880981 | ||||||||
\(423\) | 0.590666 | 0.0287192 | ||||||||
\(424\) | 6.71218 | 0.325972 | ||||||||
\(425\) | 20.4036 | 0.989719 | ||||||||
\(426\) | −1.84438 | −0.0893604 | ||||||||
\(427\) | 9.73012 | 0.470873 | ||||||||
\(428\) | 6.49869 | 0.314126 | ||||||||
\(429\) | 3.19893 | 0.154446 | ||||||||
\(430\) | 4.76924 | 0.229993 | ||||||||
\(431\) | −22.8149 | −1.09896 | −0.549479 | − | 0.835508i | \(-0.685174\pi\) | ||||
−0.549479 | + | 0.835508i | \(0.685174\pi\) | |||||||
\(432\) | −5.26852 | −0.253482 | ||||||||
\(433\) | 32.0875 | 1.54203 | 0.771014 | − | 0.636818i | \(-0.219750\pi\) | ||||
0.771014 | + | 0.636818i | \(0.219750\pi\) | |||||||
\(434\) | −8.93430 | −0.428860 | ||||||||
\(435\) | 17.3759 | 0.833109 | ||||||||
\(436\) | −10.7274 | −0.513748 | ||||||||
\(437\) | −8.90230 | −0.425855 | ||||||||
\(438\) | 11.6297 | 0.555690 | ||||||||
\(439\) | −32.1294 | −1.53345 | −0.766725 | − | 0.641975i | \(-0.778115\pi\) | ||||
−0.766725 | + | 0.641975i | \(0.778115\pi\) | |||||||
\(440\) | −1.14577 | −0.0546226 | ||||||||
\(441\) | 0.482263 | 0.0229649 | ||||||||
\(442\) | 10.3710 | 0.493300 | ||||||||
\(443\) | 10.6860 | 0.507705 | 0.253853 | − | 0.967243i | \(-0.418302\pi\) | ||||
0.253853 | + | 0.967243i | \(0.418302\pi\) | |||||||
\(444\) | 5.16279 | 0.245015 | ||||||||
\(445\) | −2.27364 | −0.107781 | ||||||||
\(446\) | 7.58628 | 0.359221 | ||||||||
\(447\) | −15.2290 | −0.720306 | ||||||||
\(448\) | −1.19968 | −0.0566794 | ||||||||
\(449\) | 18.0967 | 0.854037 | 0.427018 | − | 0.904243i | \(-0.359564\pi\) | ||||
0.427018 | + | 0.904243i | \(0.359564\pi\) | |||||||
\(450\) | −0.319776 | −0.0150744 | ||||||||
\(451\) | −5.93132 | −0.279295 | ||||||||
\(452\) | −13.9026 | −0.653924 | ||||||||
\(453\) | 2.49935 | 0.117430 | ||||||||
\(454\) | −12.3775 | −0.580903 | ||||||||
\(455\) | −2.57618 | −0.120773 | ||||||||
\(456\) | −2.75806 | −0.129158 | ||||||||
\(457\) | −10.3791 | −0.485512 | −0.242756 | − | 0.970087i | \(-0.578051\pi\) | ||||
−0.242756 | + | 0.970087i | \(0.578051\pi\) | |||||||
\(458\) | 4.25397 | 0.198775 | ||||||||
\(459\) | 29.1540 | 1.36079 | ||||||||
\(460\) | −6.31230 | −0.294312 | ||||||||
\(461\) | −13.4670 | −0.627222 | −0.313611 | − | 0.949552i | \(-0.601539\pi\) | ||||
−0.313611 | + | 0.949552i | \(0.601539\pi\) | |||||||
\(462\) | 2.04765 | 0.0952651 | ||||||||
\(463\) | 24.1611 | 1.12286 | 0.561430 | − | 0.827524i | \(-0.310251\pi\) | ||||
0.561430 | + | 0.827524i | \(0.310251\pi\) | |||||||
\(464\) | 8.88499 | 0.412475 | ||||||||
\(465\) | −14.5642 | −0.675397 | ||||||||
\(466\) | 7.59700 | 0.351924 | ||||||||
\(467\) | −30.2544 | −1.40000 | −0.700002 | − | 0.714141i | \(-0.746818\pi\) | ||||
−0.700002 | + | 0.714141i | \(0.746818\pi\) | |||||||
\(468\) | −0.162541 | −0.00751345 | ||||||||
\(469\) | −10.0859 | −0.465724 | ||||||||
\(470\) | 7.80354 | 0.359950 | ||||||||
\(471\) | −23.5456 | −1.08492 | ||||||||
\(472\) | −8.03264 | −0.369732 | ||||||||
\(473\) | −4.16246 | −0.191390 | ||||||||
\(474\) | 9.26595 | 0.425599 | ||||||||
\(475\) | −5.95814 | −0.273378 | ||||||||
\(476\) | 6.63855 | 0.304277 | ||||||||
\(477\) | 0.582120 | 0.0266534 | ||||||||
\(478\) | −8.61541 | −0.394060 | ||||||||
\(479\) | 15.8719 | 0.725204 | 0.362602 | − | 0.931944i | \(-0.381888\pi\) | ||||
0.362602 | + | 0.931944i | \(0.381888\pi\) | |||||||
\(480\) | −1.95564 | −0.0892624 | ||||||||
\(481\) | 5.66901 | 0.258485 | ||||||||
\(482\) | −21.9775 | −1.00105 | ||||||||
\(483\) | 11.2809 | 0.513299 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 18.6913 | 0.848728 | ||||||||
\(486\) | −0.900997 | −0.0408700 | ||||||||
\(487\) | 5.36705 | 0.243204 | 0.121602 | − | 0.992579i | \(-0.461197\pi\) | ||||
0.121602 | + | 0.992579i | \(0.461197\pi\) | |||||||
\(488\) | 8.11062 | 0.367150 | ||||||||
\(489\) | 4.49144 | 0.203110 | ||||||||
\(490\) | 6.37139 | 0.287830 | ||||||||
\(491\) | 38.8560 | 1.75355 | 0.876774 | − | 0.480902i | \(-0.159691\pi\) | ||||
0.876774 | + | 0.480902i | \(0.159691\pi\) | |||||||
\(492\) | −10.1238 | −0.456415 | ||||||||
\(493\) | −49.1661 | −2.21433 | ||||||||
\(494\) | −3.02849 | −0.136258 | ||||||||
\(495\) | −0.0993682 | −0.00446627 | ||||||||
\(496\) | −7.44726 | −0.334392 | ||||||||
\(497\) | −1.29635 | −0.0581494 | ||||||||
\(498\) | −29.8160 | −1.33609 | ||||||||
\(499\) | 3.60886 | 0.161555 | 0.0807773 | − | 0.996732i | \(-0.474260\pi\) | ||||
0.0807773 | + | 0.996732i | \(0.474260\pi\) | |||||||
\(500\) | −9.95356 | −0.445137 | ||||||||
\(501\) | −3.04299 | −0.135951 | ||||||||
\(502\) | −8.67911 | −0.387368 | ||||||||
\(503\) | 5.81700 | 0.259367 | 0.129684 | − | 0.991555i | \(-0.458604\pi\) | ||||
0.129684 | + | 0.991555i | \(0.458604\pi\) | |||||||
\(504\) | −0.104043 | −0.00463445 | ||||||||
\(505\) | 11.7902 | 0.524656 | ||||||||
\(506\) | 5.50920 | 0.244914 | ||||||||
\(507\) | −16.1934 | −0.719175 | ||||||||
\(508\) | 13.7068 | 0.608141 | ||||||||
\(509\) | −27.6151 | −1.22402 | −0.612009 | − | 0.790851i | \(-0.709638\pi\) | ||||
−0.612009 | + | 0.790851i | \(0.709638\pi\) | |||||||
\(510\) | 10.8218 | 0.479196 | ||||||||
\(511\) | 8.17416 | 0.361603 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −8.51338 | −0.375875 | ||||||||
\(514\) | −15.4743 | −0.682541 | ||||||||
\(515\) | −9.35030 | −0.412023 | ||||||||
\(516\) | −7.10462 | −0.312763 | ||||||||
\(517\) | −6.81072 | −0.299535 | ||||||||
\(518\) | 3.62876 | 0.159438 | ||||||||
\(519\) | 20.6764 | 0.907593 | ||||||||
\(520\) | −2.14740 | −0.0941695 | ||||||||
\(521\) | −36.4205 | −1.59561 | −0.797806 | − | 0.602914i | \(-0.794006\pi\) | ||||
−0.797806 | + | 0.602914i | \(0.794006\pi\) | |||||||
\(522\) | 0.770559 | 0.0337264 | ||||||||
\(523\) | −15.1819 | −0.663857 | −0.331928 | − | 0.943305i | \(-0.607699\pi\) | ||||
−0.331928 | + | 0.943305i | \(0.607699\pi\) | |||||||
\(524\) | −18.6812 | −0.816091 | ||||||||
\(525\) | 7.55009 | 0.329513 | ||||||||
\(526\) | −30.1966 | −1.31663 | ||||||||
\(527\) | 41.2102 | 1.79515 | ||||||||
\(528\) | 1.70683 | 0.0742803 | ||||||||
\(529\) | 7.35133 | 0.319623 | ||||||||
\(530\) | 7.69063 | 0.334060 | ||||||||
\(531\) | −0.696638 | −0.0302315 | ||||||||
\(532\) | −1.93855 | −0.0840469 | ||||||||
\(533\) | −11.1164 | −0.481506 | ||||||||
\(534\) | 3.38698 | 0.146569 | ||||||||
\(535\) | 7.44603 | 0.321920 | ||||||||
\(536\) | −8.40718 | −0.363135 | ||||||||
\(537\) | −20.3452 | −0.877961 | ||||||||
\(538\) | 22.5400 | 0.971770 | ||||||||
\(539\) | −5.56078 | −0.239520 | ||||||||
\(540\) | −6.03653 | −0.259771 | ||||||||
\(541\) | 22.5318 | 0.968719 | 0.484359 | − | 0.874869i | \(-0.339053\pi\) | ||||
0.484359 | + | 0.874869i | \(0.339053\pi\) | |||||||
\(542\) | −23.0806 | −0.991397 | ||||||||
\(543\) | 2.69705 | 0.115742 | ||||||||
\(544\) | 5.53362 | 0.237252 | ||||||||
\(545\) | −12.2911 | −0.526494 | ||||||||
\(546\) | 3.83768 | 0.164237 | ||||||||
\(547\) | −26.8040 | −1.14605 | −0.573027 | − | 0.819536i | \(-0.694231\pi\) | ||||
−0.573027 | + | 0.819536i | \(0.694231\pi\) | |||||||
\(548\) | 7.98434 | 0.341074 | ||||||||
\(549\) | 0.703400 | 0.0300204 | ||||||||
\(550\) | 3.68720 | 0.157223 | ||||||||
\(551\) | 14.3572 | 0.611638 | ||||||||
\(552\) | 9.40328 | 0.400230 | ||||||||
\(553\) | 6.51274 | 0.276950 | ||||||||
\(554\) | −26.9413 | −1.14463 | ||||||||
\(555\) | 5.91538 | 0.251094 | ||||||||
\(556\) | −18.3920 | −0.779993 | ||||||||
\(557\) | 39.3675 | 1.66806 | 0.834028 | − | 0.551722i | \(-0.186029\pi\) | ||||
0.834028 | + | 0.551722i | \(0.186029\pi\) | |||||||
\(558\) | −0.645870 | −0.0273418 | ||||||||
\(559\) | −7.80124 | −0.329957 | ||||||||
\(560\) | −1.37456 | −0.0580856 | ||||||||
\(561\) | −9.44495 | −0.398766 | ||||||||
\(562\) | −5.19557 | −0.219162 | ||||||||
\(563\) | −39.1964 | −1.65193 | −0.825966 | − | 0.563720i | \(-0.809370\pi\) | ||||
−0.825966 | + | 0.563720i | \(0.809370\pi\) | |||||||
\(564\) | −11.6248 | −0.489490 | ||||||||
\(565\) | −15.9292 | −0.670148 | ||||||||
\(566\) | 7.02171 | 0.295144 | ||||||||
\(567\) | 10.4759 | 0.439948 | ||||||||
\(568\) | −1.08059 | −0.0453404 | ||||||||
\(569\) | 27.6319 | 1.15839 | 0.579195 | − | 0.815189i | \(-0.303367\pi\) | ||||
0.579195 | + | 0.815189i | \(0.303367\pi\) | |||||||
\(570\) | −3.16011 | −0.132363 | ||||||||
\(571\) | 19.1761 | 0.802493 | 0.401246 | − | 0.915970i | \(-0.368577\pi\) | ||||
0.401246 | + | 0.915970i | \(0.368577\pi\) | |||||||
\(572\) | 1.87419 | 0.0783638 | ||||||||
\(573\) | −32.2317 | −1.34650 | ||||||||
\(574\) | −7.11567 | −0.297002 | ||||||||
\(575\) | 20.3136 | 0.847134 | ||||||||
\(576\) | −0.0867259 | −0.00361358 | ||||||||
\(577\) | 6.82894 | 0.284292 | 0.142146 | − | 0.989846i | \(-0.454600\pi\) | ||||
0.142146 | + | 0.989846i | \(0.454600\pi\) | |||||||
\(578\) | −13.6209 | −0.566555 | ||||||||
\(579\) | 17.9927 | 0.747752 | ||||||||
\(580\) | 10.1802 | 0.422709 | ||||||||
\(581\) | −20.9567 | −0.869430 | ||||||||
\(582\) | −27.8440 | −1.15417 | ||||||||
\(583\) | −6.71218 | −0.277990 | ||||||||
\(584\) | 6.81363 | 0.281950 | ||||||||
\(585\) | −0.186235 | −0.00769986 | ||||||||
\(586\) | −20.7718 | −0.858077 | ||||||||
\(587\) | 27.1012 | 1.11859 | 0.559293 | − | 0.828970i | \(-0.311073\pi\) | ||||
0.559293 | + | 0.828970i | \(0.311073\pi\) | |||||||
\(588\) | −9.49131 | −0.391415 | ||||||||
\(589\) | −12.0340 | −0.495852 | ||||||||
\(590\) | −9.20359 | −0.378906 | ||||||||
\(591\) | 1.70683 | 0.0702097 | ||||||||
\(592\) | 3.02478 | 0.124318 | ||||||||
\(593\) | 24.8088 | 1.01878 | 0.509388 | − | 0.860537i | \(-0.329872\pi\) | ||||
0.509388 | + | 0.860537i | \(0.329872\pi\) | |||||||
\(594\) | 5.26852 | 0.216170 | ||||||||
\(595\) | 7.60627 | 0.311827 | ||||||||
\(596\) | −8.92237 | −0.365474 | ||||||||
\(597\) | −10.7385 | −0.439499 | ||||||||
\(598\) | 10.3253 | 0.422233 | ||||||||
\(599\) | 21.2393 | 0.867816 | 0.433908 | − | 0.900957i | \(-0.357134\pi\) | ||||
0.433908 | + | 0.900957i | \(0.357134\pi\) | |||||||
\(600\) | 6.29344 | 0.256928 | ||||||||
\(601\) | −14.7481 | −0.601586 | −0.300793 | − | 0.953690i | \(-0.597251\pi\) | ||||
−0.300793 | + | 0.953690i | \(0.597251\pi\) | |||||||
\(602\) | −4.99361 | −0.203524 | ||||||||
\(603\) | −0.729120 | −0.0296921 | ||||||||
\(604\) | 1.46432 | 0.0595825 | ||||||||
\(605\) | 1.14577 | 0.0465823 | ||||||||
\(606\) | −17.5636 | −0.713470 | ||||||||
\(607\) | −16.6528 | −0.675915 | −0.337958 | − | 0.941161i | \(-0.609736\pi\) | ||||
−0.337958 | + | 0.941161i | \(0.609736\pi\) | |||||||
\(608\) | −1.61590 | −0.0655332 | ||||||||
\(609\) | −18.1933 | −0.737231 | ||||||||
\(610\) | 9.29292 | 0.376259 | ||||||||
\(611\) | −12.7646 | −0.516400 | ||||||||
\(612\) | 0.479908 | 0.0193991 | ||||||||
\(613\) | 13.8192 | 0.558150 | 0.279075 | − | 0.960269i | \(-0.409972\pi\) | ||||
0.279075 | + | 0.960269i | \(0.409972\pi\) | |||||||
\(614\) | 27.0682 | 1.09238 | ||||||||
\(615\) | −11.5995 | −0.467739 | ||||||||
\(616\) | 1.19968 | 0.0483364 | ||||||||
\(617\) | −6.89996 | −0.277782 | −0.138891 | − | 0.990308i | \(-0.544354\pi\) | ||||
−0.138891 | + | 0.990308i | \(0.544354\pi\) | |||||||
\(618\) | 13.9289 | 0.560303 | ||||||||
\(619\) | 15.9224 | 0.639974 | 0.319987 | − | 0.947422i | \(-0.396321\pi\) | ||||
0.319987 | + | 0.947422i | \(0.396321\pi\) | |||||||
\(620\) | −8.53286 | −0.342688 | ||||||||
\(621\) | 29.0254 | 1.16475 | ||||||||
\(622\) | 9.87629 | 0.396003 | ||||||||
\(623\) | 2.38060 | 0.0953767 | ||||||||
\(624\) | 3.19893 | 0.128060 | ||||||||
\(625\) | 7.03150 | 0.281260 | ||||||||
\(626\) | −2.58209 | −0.103201 | ||||||||
\(627\) | 2.75806 | 0.110146 | ||||||||
\(628\) | −13.7949 | −0.550477 | ||||||||
\(629\) | −16.7380 | −0.667386 | ||||||||
\(630\) | −0.119210 | −0.00474943 | ||||||||
\(631\) | 6.07520 | 0.241850 | 0.120925 | − | 0.992662i | \(-0.461414\pi\) | ||||
0.120925 | + | 0.992662i | \(0.461414\pi\) | |||||||
\(632\) | 5.42875 | 0.215944 | ||||||||
\(633\) | 3.08897 | 0.122775 | ||||||||
\(634\) | 2.07068 | 0.0822372 | ||||||||
\(635\) | 15.7049 | 0.623230 | ||||||||
\(636\) | −11.4566 | −0.454282 | ||||||||
\(637\) | −10.4219 | −0.412933 | ||||||||
\(638\) | −8.88499 | −0.351760 | ||||||||
\(639\) | −0.0937148 | −0.00370730 | ||||||||
\(640\) | −1.14577 | −0.0452907 | ||||||||
\(641\) | −34.2875 | −1.35427 | −0.677137 | − | 0.735857i | \(-0.736779\pi\) | ||||
−0.677137 | + | 0.735857i | \(0.736779\pi\) | |||||||
\(642\) | −11.0922 | −0.437773 | ||||||||
\(643\) | 29.4437 | 1.16115 | 0.580574 | − | 0.814208i | \(-0.302828\pi\) | ||||
0.580574 | + | 0.814208i | \(0.302828\pi\) | |||||||
\(644\) | 6.60926 | 0.260442 | ||||||||
\(645\) | −8.14028 | −0.320523 | ||||||||
\(646\) | 8.94174 | 0.351808 | ||||||||
\(647\) | −1.67685 | −0.0659237 | −0.0329619 | − | 0.999457i | \(-0.510494\pi\) | ||||
−0.0329619 | + | 0.999457i | \(0.510494\pi\) | |||||||
\(648\) | 8.73230 | 0.343037 | ||||||||
\(649\) | 8.03264 | 0.315309 | ||||||||
\(650\) | 6.91052 | 0.271053 | ||||||||
\(651\) | 15.2493 | 0.597669 | ||||||||
\(652\) | 2.63145 | 0.103056 | ||||||||
\(653\) | 36.8803 | 1.44324 | 0.721619 | − | 0.692291i | \(-0.243398\pi\) | ||||
0.721619 | + | 0.692291i | \(0.243398\pi\) | |||||||
\(654\) | 18.3098 | 0.715970 | ||||||||
\(655\) | −21.4044 | −0.836339 | ||||||||
\(656\) | −5.93132 | −0.231579 | ||||||||
\(657\) | 0.590918 | 0.0230539 | ||||||||
\(658\) | −8.17066 | −0.318526 | ||||||||
\(659\) | −17.0850 | −0.665537 | −0.332769 | − | 0.943009i | \(-0.607983\pi\) | ||||
−0.332769 | + | 0.943009i | \(0.607983\pi\) | |||||||
\(660\) | 1.95564 | 0.0761232 | ||||||||
\(661\) | 2.09579 | 0.0815169 | 0.0407584 | − | 0.999169i | \(-0.487023\pi\) | ||||
0.0407584 | + | 0.999169i | \(0.487023\pi\) | |||||||
\(662\) | −7.21290 | −0.280337 | ||||||||
\(663\) | −17.7016 | −0.687474 | ||||||||
\(664\) | −17.4686 | −0.677914 | ||||||||
\(665\) | −2.22114 | −0.0861321 | ||||||||
\(666\) | 0.262327 | 0.0101650 | ||||||||
\(667\) | −48.9492 | −1.89532 | ||||||||
\(668\) | −1.78283 | −0.0689797 | ||||||||
\(669\) | −12.9485 | −0.500618 | ||||||||
\(670\) | −9.63272 | −0.372145 | ||||||||
\(671\) | −8.11062 | −0.313107 | ||||||||
\(672\) | 2.04765 | 0.0789897 | ||||||||
\(673\) | −17.6802 | −0.681521 | −0.340761 | − | 0.940150i | \(-0.610685\pi\) | ||||
−0.340761 | + | 0.940150i | \(0.610685\pi\) | |||||||
\(674\) | 24.1101 | 0.928688 | ||||||||
\(675\) | 19.4261 | 0.747711 | ||||||||
\(676\) | −9.48741 | −0.364901 | ||||||||
\(677\) | 10.3928 | 0.399427 | 0.199713 | − | 0.979854i | \(-0.435999\pi\) | ||||
0.199713 | + | 0.979854i | \(0.435999\pi\) | |||||||
\(678\) | 23.7294 | 0.911323 | ||||||||
\(679\) | −19.5706 | −0.751053 | ||||||||
\(680\) | 6.34027 | 0.243138 | ||||||||
\(681\) | 21.1262 | 0.809559 | ||||||||
\(682\) | 7.44726 | 0.285170 | ||||||||
\(683\) | −6.20800 | −0.237542 | −0.118771 | − | 0.992922i | \(-0.537896\pi\) | ||||
−0.118771 | + | 0.992922i | \(0.537896\pi\) | |||||||
\(684\) | −0.140140 | −0.00535838 | ||||||||
\(685\) | 9.14824 | 0.349536 | ||||||||
\(686\) | −15.0689 | −0.575332 | ||||||||
\(687\) | −7.26081 | −0.277017 | ||||||||
\(688\) | −4.16246 | −0.158692 | ||||||||
\(689\) | −12.5799 | −0.479256 | ||||||||
\(690\) | 10.7740 | 0.410160 | ||||||||
\(691\) | −21.1760 | −0.805572 | −0.402786 | − | 0.915294i | \(-0.631958\pi\) | ||||
−0.402786 | + | 0.915294i | \(0.631958\pi\) | |||||||
\(692\) | 12.1139 | 0.460502 | ||||||||
\(693\) | 0.104043 | 0.00395227 | ||||||||
\(694\) | −33.6719 | −1.27817 | ||||||||
\(695\) | −21.0730 | −0.799345 | ||||||||
\(696\) | −15.1652 | −0.574835 | ||||||||
\(697\) | 32.8217 | 1.24321 | ||||||||
\(698\) | 10.9087 | 0.412902 | ||||||||
\(699\) | −12.9668 | −0.490449 | ||||||||
\(700\) | 4.42345 | 0.167191 | ||||||||
\(701\) | −12.9472 | −0.489007 | −0.244504 | − | 0.969648i | \(-0.578625\pi\) | ||||
−0.244504 | + | 0.969648i | \(0.578625\pi\) | |||||||
\(702\) | 9.87421 | 0.372678 | ||||||||
\(703\) | 4.88773 | 0.184344 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | −13.3193 | −0.501635 | ||||||||
\(706\) | 34.0928 | 1.28310 | ||||||||
\(707\) | −12.3449 | −0.464276 | ||||||||
\(708\) | 13.7104 | 0.515267 | ||||||||
\(709\) | −0.413937 | −0.0155457 | −0.00777287 | − | 0.999970i | \(-0.502474\pi\) | ||||
−0.00777287 | + | 0.999970i | \(0.502474\pi\) | |||||||
\(710\) | −1.23811 | −0.0464653 | ||||||||
\(711\) | 0.470813 | 0.0176569 | ||||||||
\(712\) | 1.98437 | 0.0743673 | ||||||||
\(713\) | 41.0284 | 1.53653 | ||||||||
\(714\) | −11.3309 | −0.424048 | ||||||||
\(715\) | 2.14740 | 0.0803080 | ||||||||
\(716\) | −11.9199 | −0.445467 | ||||||||
\(717\) | 14.7051 | 0.549171 | ||||||||
\(718\) | 12.5651 | 0.468927 | ||||||||
\(719\) | 28.6745 | 1.06938 | 0.534690 | − | 0.845049i | \(-0.320429\pi\) | ||||
0.534690 | + | 0.845049i | \(0.320429\pi\) | |||||||
\(720\) | −0.0993682 | −0.00370323 | ||||||||
\(721\) | 9.79019 | 0.364606 | ||||||||
\(722\) | 16.3889 | 0.609931 | ||||||||
\(723\) | 37.5119 | 1.39508 | ||||||||
\(724\) | 1.58015 | 0.0587258 | ||||||||
\(725\) | −32.7608 | −1.21670 | ||||||||
\(726\) | −1.70683 | −0.0633465 | ||||||||
\(727\) | −22.1091 | −0.819980 | −0.409990 | − | 0.912090i | \(-0.634468\pi\) | ||||
−0.409990 | + | 0.912090i | \(0.634468\pi\) | |||||||
\(728\) | 2.24842 | 0.0833321 | ||||||||
\(729\) | 27.7348 | 1.02721 | ||||||||
\(730\) | 7.80688 | 0.288945 | ||||||||
\(731\) | 23.0335 | 0.851923 | ||||||||
\(732\) | −13.8435 | −0.511669 | ||||||||
\(733\) | −35.2251 | −1.30107 | −0.650535 | − | 0.759476i | \(-0.725455\pi\) | ||||
−0.650535 | + | 0.759476i | \(0.725455\pi\) | |||||||
\(734\) | 2.14332 | 0.0791113 | ||||||||
\(735\) | −10.8749 | −0.401126 | ||||||||
\(736\) | 5.50920 | 0.203072 | ||||||||
\(737\) | 8.40718 | 0.309683 | ||||||||
\(738\) | −0.514399 | −0.0189353 | ||||||||
\(739\) | 28.4707 | 1.04731 | 0.523655 | − | 0.851930i | \(-0.324568\pi\) | ||||
0.523655 | + | 0.851930i | \(0.324568\pi\) | |||||||
\(740\) | 3.46571 | 0.127402 | ||||||||
\(741\) | 5.16913 | 0.189893 | ||||||||
\(742\) | −8.05245 | −0.295615 | ||||||||
\(743\) | −12.5455 | −0.460249 | −0.230125 | − | 0.973161i | \(-0.573913\pi\) | ||||
−0.230125 | + | 0.973161i | \(0.573913\pi\) | |||||||
\(744\) | 12.7112 | 0.466016 | ||||||||
\(745\) | −10.2230 | −0.374542 | ||||||||
\(746\) | 2.85050 | 0.104364 | ||||||||
\(747\) | −1.51498 | −0.0554303 | ||||||||
\(748\) | −5.53362 | −0.202329 | ||||||||
\(749\) | −7.79633 | −0.284872 | ||||||||
\(750\) | 16.9891 | 0.620353 | ||||||||
\(751\) | −8.96471 | −0.327127 | −0.163563 | − | 0.986533i | \(-0.552299\pi\) | ||||
−0.163563 | + | 0.986533i | \(0.552299\pi\) | |||||||
\(752\) | −6.81072 | −0.248361 | ||||||||
\(753\) | 14.8138 | 0.539844 | ||||||||
\(754\) | −16.6522 | −0.606436 | ||||||||
\(755\) | 1.67778 | 0.0610607 | ||||||||
\(756\) | 6.32052 | 0.229875 | ||||||||
\(757\) | 19.2191 | 0.698530 | 0.349265 | − | 0.937024i | \(-0.386431\pi\) | ||||
0.349265 | + | 0.937024i | \(0.386431\pi\) | |||||||
\(758\) | 29.9256 | 1.08694 | ||||||||
\(759\) | −9.40328 | −0.341318 | ||||||||
\(760\) | −1.85145 | −0.0671591 | ||||||||
\(761\) | −35.4948 | −1.28669 | −0.643343 | − | 0.765578i | \(-0.722453\pi\) | ||||
−0.643343 | + | 0.765578i | \(0.722453\pi\) | |||||||
\(762\) | −23.3952 | −0.847519 | ||||||||
\(763\) | 12.8694 | 0.465903 | ||||||||
\(764\) | −18.8839 | −0.683196 | ||||||||
\(765\) | 0.549865 | 0.0198804 | ||||||||
\(766\) | 13.3893 | 0.483775 | ||||||||
\(767\) | 15.0547 | 0.543594 | ||||||||
\(768\) | 1.70683 | 0.0615900 | ||||||||
\(769\) | −47.2942 | −1.70547 | −0.852736 | − | 0.522343i | \(-0.825058\pi\) | ||||
−0.852736 | + | 0.522343i | \(0.825058\pi\) | |||||||
\(770\) | 1.37456 | 0.0495356 | ||||||||
\(771\) | 26.4120 | 0.951204 | ||||||||
\(772\) | 10.5416 | 0.379400 | ||||||||
\(773\) | −0.0165424 | −0.000594989 0 | −0.000297495 | − | 1.00000i | \(-0.500095\pi\) | ||||
−0.000297495 | 1.00000i | \(0.500095\pi\) | ||||||||
\(774\) | −0.360993 | −0.0129756 | ||||||||
\(775\) | 27.4596 | 0.986376 | ||||||||
\(776\) | −16.3133 | −0.585612 | ||||||||
\(777\) | −6.19368 | −0.222197 | ||||||||
\(778\) | −14.9613 | −0.536390 | ||||||||
\(779\) | −9.58439 | −0.343397 | ||||||||
\(780\) | 3.66524 | 0.131237 | ||||||||
\(781\) | 1.08059 | 0.0386664 | ||||||||
\(782\) | −30.4858 | −1.09017 | ||||||||
\(783\) | −46.8108 | −1.67288 | ||||||||
\(784\) | −5.56078 | −0.198599 | ||||||||
\(785\) | −15.8058 | −0.564134 | ||||||||
\(786\) | 31.8856 | 1.13732 | ||||||||
\(787\) | −6.27120 | −0.223544 | −0.111772 | − | 0.993734i | \(-0.535653\pi\) | ||||
−0.111772 | + | 0.993734i | \(0.535653\pi\) | |||||||
\(788\) | 1.00000 | 0.0356235 | ||||||||
\(789\) | 51.5405 | 1.83489 | ||||||||
\(790\) | 6.22011 | 0.221302 | ||||||||
\(791\) | 16.6786 | 0.593024 | ||||||||
\(792\) | 0.0867259 | 0.00308167 | ||||||||
\(793\) | −15.2008 | −0.539797 | ||||||||
\(794\) | 28.0241 | 0.994537 | ||||||||
\(795\) | −13.1266 | −0.465553 | ||||||||
\(796\) | −6.29150 | −0.222996 | ||||||||
\(797\) | 35.5928 | 1.26076 | 0.630381 | − | 0.776286i | \(-0.282899\pi\) | ||||
0.630381 | + | 0.776286i | \(0.282899\pi\) | |||||||
\(798\) | 3.30878 | 0.117130 | ||||||||
\(799\) | 37.6879 | 1.33330 | ||||||||
\(800\) | 3.68720 | 0.130362 | ||||||||
\(801\) | 0.172096 | 0.00608072 | ||||||||
\(802\) | 0.888495 | 0.0313738 | ||||||||
\(803\) | −6.81363 | −0.240448 | ||||||||
\(804\) | 14.3496 | 0.506073 | ||||||||
\(805\) | 7.57272 | 0.266903 | ||||||||
\(806\) | 13.9576 | 0.491634 | ||||||||
\(807\) | −38.4720 | −1.35428 | ||||||||
\(808\) | −10.2901 | −0.362006 | ||||||||
\(809\) | 13.4244 | 0.471978 | 0.235989 | − | 0.971756i | \(-0.424167\pi\) | ||||
0.235989 | + | 0.971756i | \(0.424167\pi\) | |||||||
\(810\) | 10.0052 | 0.351548 | ||||||||
\(811\) | 22.7799 | 0.799911 | 0.399955 | − | 0.916535i | \(-0.369026\pi\) | ||||
0.399955 | + | 0.916535i | \(0.369026\pi\) | |||||||
\(812\) | −10.6591 | −0.374062 | ||||||||
\(813\) | 39.3947 | 1.38163 | ||||||||
\(814\) | −3.02478 | −0.106018 | ||||||||
\(815\) | 3.01504 | 0.105612 | ||||||||
\(816\) | −9.44495 | −0.330639 | ||||||||
\(817\) | −6.72610 | −0.235316 | ||||||||
\(818\) | 8.93554 | 0.312424 | ||||||||
\(819\) | 0.194996 | 0.00681372 | ||||||||
\(820\) | −6.79595 | −0.237325 | ||||||||
\(821\) | 21.6675 | 0.756200 | 0.378100 | − | 0.925765i | \(-0.376578\pi\) | ||||
0.378100 | + | 0.925765i | \(0.376578\pi\) | |||||||
\(822\) | −13.6279 | −0.475329 | ||||||||
\(823\) | −14.4015 | −0.502003 | −0.251002 | − | 0.967987i | \(-0.580760\pi\) | ||||
−0.251002 | + | 0.967987i | \(0.580760\pi\) | |||||||
\(824\) | 8.16069 | 0.284291 | ||||||||
\(825\) | −6.29344 | −0.219109 | ||||||||
\(826\) | 9.63658 | 0.335299 | ||||||||
\(827\) | −36.1731 | −1.25786 | −0.628931 | − | 0.777461i | \(-0.716507\pi\) | ||||
−0.628931 | + | 0.777461i | \(0.716507\pi\) | |||||||
\(828\) | 0.477791 | 0.0166044 | ||||||||
\(829\) | 8.16328 | 0.283523 | 0.141761 | − | 0.989901i | \(-0.454723\pi\) | ||||
0.141761 | + | 0.989901i | \(0.454723\pi\) | |||||||
\(830\) | −20.0151 | −0.694733 | ||||||||
\(831\) | 45.9843 | 1.59518 | ||||||||
\(832\) | 1.87419 | 0.0649758 | ||||||||
\(833\) | 30.7712 | 1.06616 | ||||||||
\(834\) | 31.3920 | 1.08702 | ||||||||
\(835\) | −2.04272 | −0.0706911 | ||||||||
\(836\) | 1.61590 | 0.0558869 | ||||||||
\(837\) | 39.2360 | 1.35620 | ||||||||
\(838\) | −8.77232 | −0.303035 | ||||||||
\(839\) | 20.6387 | 0.712527 | 0.356264 | − | 0.934386i | \(-0.384051\pi\) | ||||
0.356264 | + | 0.934386i | \(0.384051\pi\) | |||||||
\(840\) | 2.34614 | 0.0809494 | ||||||||
\(841\) | 49.9431 | 1.72218 | ||||||||
\(842\) | 34.4629 | 1.18767 | ||||||||
\(843\) | 8.86797 | 0.305429 | ||||||||
\(844\) | 1.80977 | 0.0622947 | ||||||||
\(845\) | −10.8704 | −0.373954 | ||||||||
\(846\) | −0.590666 | −0.0203075 | ||||||||
\(847\) | −1.19968 | −0.0412214 | ||||||||
\(848\) | −6.71218 | −0.230497 | ||||||||
\(849\) | −11.9849 | −0.411320 | ||||||||
\(850\) | −20.4036 | −0.699837 | ||||||||
\(851\) | −16.6641 | −0.571239 | ||||||||
\(852\) | 1.84438 | 0.0631874 | ||||||||
\(853\) | 3.24788 | 0.111205 | 0.0556026 | − | 0.998453i | \(-0.482292\pi\) | ||||
0.0556026 | + | 0.998453i | \(0.482292\pi\) | |||||||
\(854\) | −9.73012 | −0.332958 | ||||||||
\(855\) | −0.160569 | −0.00549133 | ||||||||
\(856\) | −6.49869 | −0.222121 | ||||||||
\(857\) | −3.52734 | −0.120492 | −0.0602458 | − | 0.998184i | \(-0.519188\pi\) | ||||
−0.0602458 | + | 0.998184i | \(0.519188\pi\) | |||||||
\(858\) | −3.19893 | −0.109210 | ||||||||
\(859\) | 5.52256 | 0.188427 | 0.0942136 | − | 0.995552i | \(-0.469966\pi\) | ||||
0.0942136 | + | 0.995552i | \(0.469966\pi\) | |||||||
\(860\) | −4.76924 | −0.162630 | ||||||||
\(861\) | 12.1452 | 0.413909 | ||||||||
\(862\) | 22.8149 | 0.777080 | ||||||||
\(863\) | 44.6795 | 1.52091 | 0.760454 | − | 0.649392i | \(-0.224977\pi\) | ||||
0.760454 | + | 0.649392i | \(0.224977\pi\) | |||||||
\(864\) | 5.26852 | 0.179239 | ||||||||
\(865\) | 13.8798 | 0.471927 | ||||||||
\(866\) | −32.0875 | −1.09038 | ||||||||
\(867\) | 23.2486 | 0.789564 | ||||||||
\(868\) | 8.93430 | 0.303250 | ||||||||
\(869\) | −5.42875 | −0.184158 | ||||||||
\(870\) | −17.3759 | −0.589097 | ||||||||
\(871\) | 15.7567 | 0.533894 | ||||||||
\(872\) | 10.7274 | 0.363275 | ||||||||
\(873\) | −1.41478 | −0.0478831 | ||||||||
\(874\) | 8.90230 | 0.301125 | ||||||||
\(875\) | 11.9411 | 0.403682 | ||||||||
\(876\) | −11.6297 | −0.392932 | ||||||||
\(877\) | −11.8032 | −0.398566 | −0.199283 | − | 0.979942i | \(-0.563861\pi\) | ||||
−0.199283 | + | 0.979942i | \(0.563861\pi\) | |||||||
\(878\) | 32.1294 | 1.08431 | ||||||||
\(879\) | 35.4540 | 1.19584 | ||||||||
\(880\) | 1.14577 | 0.0386240 | ||||||||
\(881\) | −2.57876 | −0.0868807 | −0.0434403 | − | 0.999056i | \(-0.513832\pi\) | ||||
−0.0434403 | + | 0.999056i | \(0.513832\pi\) | |||||||
\(882\) | −0.482263 | −0.0162386 | ||||||||
\(883\) | −19.5155 | −0.656748 | −0.328374 | − | 0.944548i | \(-0.606501\pi\) | ||||
−0.328374 | + | 0.944548i | \(0.606501\pi\) | |||||||
\(884\) | −10.3710 | −0.348816 | ||||||||
\(885\) | 15.7090 | 0.528051 | ||||||||
\(886\) | −10.6860 | −0.359002 | ||||||||
\(887\) | 54.2383 | 1.82114 | 0.910572 | − | 0.413350i | \(-0.135642\pi\) | ||||
0.910572 | + | 0.413350i | \(0.135642\pi\) | |||||||
\(888\) | −5.16279 | −0.173252 | ||||||||
\(889\) | −16.4437 | −0.551505 | ||||||||
\(890\) | 2.27364 | 0.0762124 | ||||||||
\(891\) | −8.73230 | −0.292543 | ||||||||
\(892\) | −7.58628 | −0.254007 | ||||||||
\(893\) | −11.0054 | −0.368282 | ||||||||
\(894\) | 15.2290 | 0.509333 | ||||||||
\(895\) | −13.6575 | −0.456519 | ||||||||
\(896\) | 1.19968 | 0.0400784 | ||||||||
\(897\) | −17.6235 | −0.588433 | ||||||||
\(898\) | −18.0967 | −0.603895 | ||||||||
\(899\) | −66.1688 | −2.20685 | ||||||||
\(900\) | 0.319776 | 0.0106592 | ||||||||
\(901\) | 37.1426 | 1.23740 | ||||||||
\(902\) | 5.93132 | 0.197491 | ||||||||
\(903\) | 8.52325 | 0.283636 | ||||||||
\(904\) | 13.9026 | 0.462394 | ||||||||
\(905\) | 1.81049 | 0.0601829 | ||||||||
\(906\) | −2.49935 | −0.0830355 | ||||||||
\(907\) | 11.8694 | 0.394118 | 0.197059 | − | 0.980392i | \(-0.436861\pi\) | ||||
0.197059 | + | 0.980392i | \(0.436861\pi\) | |||||||
\(908\) | 12.3775 | 0.410761 | ||||||||
\(909\) | −0.892422 | −0.0295998 | ||||||||
\(910\) | 2.57618 | 0.0853996 | ||||||||
\(911\) | 43.6223 | 1.44527 | 0.722636 | − | 0.691229i | \(-0.242930\pi\) | ||||
0.722636 | + | 0.691229i | \(0.242930\pi\) | |||||||
\(912\) | 2.75806 | 0.0913285 | ||||||||
\(913\) | 17.4686 | 0.578127 | ||||||||
\(914\) | 10.3791 | 0.343309 | ||||||||
\(915\) | −15.8615 | −0.524364 | ||||||||
\(916\) | −4.25397 | −0.140555 | ||||||||
\(917\) | 22.4114 | 0.740089 | ||||||||
\(918\) | −29.1540 | −0.962224 | ||||||||
\(919\) | −13.0653 | −0.430985 | −0.215492 | − | 0.976506i | \(-0.569136\pi\) | ||||
−0.215492 | + | 0.976506i | \(0.569136\pi\) | |||||||
\(920\) | 6.31230 | 0.208110 | ||||||||
\(921\) | −46.2009 | −1.52237 | ||||||||
\(922\) | 13.4670 | 0.443513 | ||||||||
\(923\) | 2.02522 | 0.0666610 | ||||||||
\(924\) | −2.04765 | −0.0673626 | ||||||||
\(925\) | −11.1530 | −0.366708 | ||||||||
\(926\) | −24.1611 | −0.793982 | ||||||||
\(927\) | 0.707743 | 0.0232453 | ||||||||
\(928\) | −8.88499 | −0.291664 | ||||||||
\(929\) | 14.3779 | 0.471724 | 0.235862 | − | 0.971787i | \(-0.424209\pi\) | ||||
0.235862 | + | 0.971787i | \(0.424209\pi\) | |||||||
\(930\) | 14.5642 | 0.477578 | ||||||||
\(931\) | −8.98563 | −0.294492 | ||||||||
\(932\) | −7.59700 | −0.248848 | ||||||||
\(933\) | −16.8572 | −0.551879 | ||||||||
\(934\) | 30.2544 | 0.989953 | ||||||||
\(935\) | −6.34027 | −0.207349 | ||||||||
\(936\) | 0.162541 | 0.00531281 | ||||||||
\(937\) | −56.7189 | −1.85292 | −0.926462 | − | 0.376388i | \(-0.877166\pi\) | ||||
−0.926462 | + | 0.376388i | \(0.877166\pi\) | |||||||
\(938\) | 10.0859 | 0.329316 | ||||||||
\(939\) | 4.40720 | 0.143824 | ||||||||
\(940\) | −7.80354 | −0.254523 | ||||||||
\(941\) | 36.4087 | 1.18689 | 0.593444 | − | 0.804875i | \(-0.297768\pi\) | ||||
0.593444 | + | 0.804875i | \(0.297768\pi\) | |||||||
\(942\) | 23.5456 | 0.767157 | ||||||||
\(943\) | 32.6769 | 1.06410 | ||||||||
\(944\) | 8.03264 | 0.261440 | ||||||||
\(945\) | 7.24188 | 0.235579 | ||||||||
\(946\) | 4.16246 | 0.135333 | ||||||||
\(947\) | −10.8371 | −0.352159 | −0.176079 | − | 0.984376i | \(-0.556342\pi\) | ||||
−0.176079 | + | 0.984376i | \(0.556342\pi\) | |||||||
\(948\) | −9.26595 | −0.300944 | ||||||||
\(949\) | −12.7700 | −0.414533 | ||||||||
\(950\) | 5.95814 | 0.193307 | ||||||||
\(951\) | −3.53430 | −0.114608 | ||||||||
\(952\) | −6.63855 | −0.215157 | ||||||||
\(953\) | −25.8897 | −0.838651 | −0.419325 | − | 0.907836i | \(-0.637733\pi\) | ||||
−0.419325 | + | 0.907836i | \(0.637733\pi\) | |||||||
\(954\) | −0.582120 | −0.0188468 | ||||||||
\(955\) | −21.6367 | −0.700146 | ||||||||
\(956\) | 8.61541 | 0.278642 | ||||||||
\(957\) | 15.1652 | 0.490221 | ||||||||
\(958\) | −15.8719 | −0.512797 | ||||||||
\(959\) | −9.57863 | −0.309310 | ||||||||
\(960\) | 1.95564 | 0.0631181 | ||||||||
\(961\) | 24.4616 | 0.789084 | ||||||||
\(962\) | −5.66901 | −0.182776 | ||||||||
\(963\) | −0.563605 | −0.0181619 | ||||||||
\(964\) | 21.9775 | 0.707847 | ||||||||
\(965\) | 12.0783 | 0.388813 | ||||||||
\(966\) | −11.2809 | −0.362957 | ||||||||
\(967\) | −3.72928 | −0.119926 | −0.0599628 | − | 0.998201i | \(-0.519098\pi\) | ||||
−0.0599628 | + | 0.998201i | \(0.519098\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | −15.2620 | −0.490288 | ||||||||
\(970\) | −18.6913 | −0.600141 | ||||||||
\(971\) | 2.01530 | 0.0646740 | 0.0323370 | − | 0.999477i | \(-0.489705\pi\) | ||||
0.0323370 | + | 0.999477i | \(0.489705\pi\) | |||||||
\(972\) | 0.900997 | 0.0288995 | ||||||||
\(973\) | 22.0644 | 0.707352 | ||||||||
\(974\) | −5.36705 | −0.171971 | ||||||||
\(975\) | −11.7951 | −0.377745 | ||||||||
\(976\) | −8.11062 | −0.259614 | ||||||||
\(977\) | −28.2612 | −0.904156 | −0.452078 | − | 0.891978i | \(-0.649317\pi\) | ||||
−0.452078 | + | 0.891978i | \(0.649317\pi\) | |||||||
\(978\) | −4.49144 | −0.143620 | ||||||||
\(979\) | −1.98437 | −0.0634207 | ||||||||
\(980\) | −6.37139 | −0.203526 | ||||||||
\(981\) | 0.930341 | 0.0297035 | ||||||||
\(982\) | −38.8560 | −1.23995 | ||||||||
\(983\) | 40.5240 | 1.29252 | 0.646258 | − | 0.763119i | \(-0.276333\pi\) | ||||
0.646258 | + | 0.763119i | \(0.276333\pi\) | |||||||
\(984\) | 10.1238 | 0.322734 | ||||||||
\(985\) | 1.14577 | 0.0365074 | ||||||||
\(986\) | 49.1661 | 1.56577 | ||||||||
\(987\) | 13.9459 | 0.443904 | ||||||||
\(988\) | 3.02849 | 0.0963492 | ||||||||
\(989\) | 22.9318 | 0.729190 | ||||||||
\(990\) | 0.0993682 | 0.00315813 | ||||||||
\(991\) | 30.4052 | 0.965852 | 0.482926 | − | 0.875661i | \(-0.339574\pi\) | ||||
0.482926 | + | 0.875661i | \(0.339574\pi\) | |||||||
\(992\) | 7.44726 | 0.236451 | ||||||||
\(993\) | 12.3112 | 0.390684 | ||||||||
\(994\) | 1.29635 | 0.0411179 | ||||||||
\(995\) | −7.20863 | −0.228529 | ||||||||
\(996\) | 29.8160 | 0.944756 | ||||||||
\(997\) | −20.2150 | −0.640216 | −0.320108 | − | 0.947381i | \(-0.603719\pi\) | ||||
−0.320108 | + | 0.947381i | \(0.603719\pi\) | |||||||
\(998\) | −3.60886 | −0.114236 | ||||||||
\(999\) | −15.9361 | −0.504196 |
(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 | 4334.2.a.a.1.12 | ✓ | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4334.2.a.a.1.12 | ✓ | 15 | 1.1 | even | 1 | trivial |