Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4017,2,Mod(1,4017)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4017, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("4017.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4017 = 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4017.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: | \(32.0759064919\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 4017.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.0298243 | 0.0210890 | 0.0105445 | − | 0.999944i | \(-0.496644\pi\) | ||||
0.0105445 | + | 0.999944i | \(0.496644\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.99911 | −0.999555 | ||||||||
\(5\) | 3.06004 | 1.36849 | 0.684246 | − | 0.729252i | \(-0.260132\pi\) | ||||
0.684246 | + | 0.729252i | \(0.260132\pi\) | |||||||
\(6\) | −0.0298243 | −0.0121757 | ||||||||
\(7\) | −1.69214 | −0.639571 | −0.319785 | − | 0.947490i | \(-0.603611\pi\) | ||||
−0.319785 | + | 0.947490i | \(0.603611\pi\) | |||||||
\(8\) | −0.119271 | −0.0421686 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.0912635 | 0.0288601 | ||||||||
\(11\) | 4.60629 | 1.38885 | 0.694424 | − | 0.719566i | \(-0.255659\pi\) | ||||
0.694424 | + | 0.719566i | \(0.255659\pi\) | |||||||
\(12\) | 1.99911 | 0.577093 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | −0.0504670 | −0.0134879 | ||||||||
\(15\) | −3.06004 | −0.790099 | ||||||||
\(16\) | 3.99466 | 0.998666 | ||||||||
\(17\) | 3.22816 | 0.782943 | 0.391472 | − | 0.920190i | \(-0.371966\pi\) | ||||
0.391472 | + | 0.920190i | \(0.371966\pi\) | |||||||
\(18\) | 0.0298243 | 0.00702966 | ||||||||
\(19\) | 3.92996 | 0.901595 | 0.450797 | − | 0.892626i | \(-0.351140\pi\) | ||||
0.450797 | + | 0.892626i | \(0.351140\pi\) | |||||||
\(20\) | −6.11736 | −1.36788 | ||||||||
\(21\) | 1.69214 | 0.369256 | ||||||||
\(22\) | 0.137379 | 0.0292894 | ||||||||
\(23\) | 4.33457 | 0.903821 | 0.451910 | − | 0.892063i | \(-0.350743\pi\) | ||||
0.451910 | + | 0.892063i | \(0.350743\pi\) | |||||||
\(24\) | 0.119271 | 0.0243460 | ||||||||
\(25\) | 4.36384 | 0.872768 | ||||||||
\(26\) | −0.0298243 | −0.00584903 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 3.38278 | 0.639286 | ||||||||
\(29\) | −0.592940 | −0.110106 | −0.0550531 | − | 0.998483i | \(-0.517533\pi\) | ||||
−0.0550531 | + | 0.998483i | \(0.517533\pi\) | |||||||
\(30\) | −0.0912635 | −0.0166624 | ||||||||
\(31\) | −4.96202 | −0.891205 | −0.445602 | − | 0.895231i | \(-0.647010\pi\) | ||||
−0.445602 | + | 0.895231i | \(0.647010\pi\) | |||||||
\(32\) | 0.357679 | 0.0632294 | ||||||||
\(33\) | −4.60629 | −0.801852 | ||||||||
\(34\) | 0.0962775 | 0.0165115 | ||||||||
\(35\) | −5.17803 | −0.875247 | ||||||||
\(36\) | −1.99911 | −0.333185 | ||||||||
\(37\) | −2.80816 | −0.461658 | −0.230829 | − | 0.972994i | \(-0.574144\pi\) | ||||
−0.230829 | + | 0.972994i | \(0.574144\pi\) | |||||||
\(38\) | 0.117208 | 0.0190137 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | −0.364973 | −0.0577073 | ||||||||
\(41\) | −3.44430 | −0.537910 | −0.268955 | − | 0.963153i | \(-0.586678\pi\) | ||||
−0.268955 | + | 0.963153i | \(0.586678\pi\) | |||||||
\(42\) | 0.0504670 | 0.00778723 | ||||||||
\(43\) | 8.82134 | 1.34524 | 0.672621 | − | 0.739987i | \(-0.265169\pi\) | ||||
0.672621 | + | 0.739987i | \(0.265169\pi\) | |||||||
\(44\) | −9.20848 | −1.38823 | ||||||||
\(45\) | 3.06004 | 0.456164 | ||||||||
\(46\) | 0.129276 | 0.0190606 | ||||||||
\(47\) | −0.175510 | −0.0256008 | −0.0128004 | − | 0.999918i | \(-0.504075\pi\) | ||||
−0.0128004 | + | 0.999918i | \(0.504075\pi\) | |||||||
\(48\) | −3.99466 | −0.576580 | ||||||||
\(49\) | −4.13665 | −0.590949 | ||||||||
\(50\) | 0.130149 | 0.0184058 | ||||||||
\(51\) | −3.22816 | −0.452032 | ||||||||
\(52\) | 1.99911 | 0.277227 | ||||||||
\(53\) | −0.255619 | −0.0351119 | −0.0175560 | − | 0.999846i | \(-0.505589\pi\) | ||||
−0.0175560 | + | 0.999846i | \(0.505589\pi\) | |||||||
\(54\) | −0.0298243 | −0.00405857 | ||||||||
\(55\) | 14.0954 | 1.90063 | ||||||||
\(56\) | 0.201823 | 0.0269698 | ||||||||
\(57\) | −3.92996 | −0.520536 | ||||||||
\(58\) | −0.0176840 | −0.00232203 | ||||||||
\(59\) | −12.5860 | −1.63856 | −0.819278 | − | 0.573397i | \(-0.805625\pi\) | ||||
−0.819278 | + | 0.573397i | \(0.805625\pi\) | |||||||
\(60\) | 6.11736 | 0.789747 | ||||||||
\(61\) | 12.7051 | 1.62672 | 0.813362 | − | 0.581758i | \(-0.197635\pi\) | ||||
0.813362 | + | 0.581758i | \(0.197635\pi\) | |||||||
\(62\) | −0.147989 | −0.0187946 | ||||||||
\(63\) | −1.69214 | −0.213190 | ||||||||
\(64\) | −7.97866 | −0.997333 | ||||||||
\(65\) | −3.06004 | −0.379551 | ||||||||
\(66\) | −0.137379 | −0.0169102 | ||||||||
\(67\) | −5.34184 | −0.652609 | −0.326305 | − | 0.945265i | \(-0.605804\pi\) | ||||
−0.326305 | + | 0.945265i | \(0.605804\pi\) | |||||||
\(68\) | −6.45344 | −0.782595 | ||||||||
\(69\) | −4.33457 | −0.521821 | ||||||||
\(70\) | −0.154431 | −0.0184581 | ||||||||
\(71\) | 7.61726 | 0.904003 | 0.452001 | − | 0.892017i | \(-0.350710\pi\) | ||||
0.452001 | + | 0.892017i | \(0.350710\pi\) | |||||||
\(72\) | −0.119271 | −0.0140562 | ||||||||
\(73\) | 2.64161 | 0.309177 | 0.154589 | − | 0.987979i | \(-0.450595\pi\) | ||||
0.154589 | + | 0.987979i | \(0.450595\pi\) | |||||||
\(74\) | −0.0837513 | −0.00973589 | ||||||||
\(75\) | −4.36384 | −0.503893 | ||||||||
\(76\) | −7.85643 | −0.901194 | ||||||||
\(77\) | −7.79451 | −0.888266 | ||||||||
\(78\) | 0.0298243 | 0.00337694 | ||||||||
\(79\) | 14.2734 | 1.60588 | 0.802939 | − | 0.596061i | \(-0.203268\pi\) | ||||
0.802939 | + | 0.596061i | \(0.203268\pi\) | |||||||
\(80\) | 12.2238 | 1.36667 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.102724 | −0.0113440 | ||||||||
\(83\) | −4.88639 | −0.536351 | −0.268176 | − | 0.963370i | \(-0.586421\pi\) | ||||
−0.268176 | + | 0.963370i | \(0.586421\pi\) | |||||||
\(84\) | −3.38278 | −0.369092 | ||||||||
\(85\) | 9.87829 | 1.07145 | ||||||||
\(86\) | 0.263090 | 0.0283698 | ||||||||
\(87\) | 0.592940 | 0.0635698 | ||||||||
\(88\) | −0.549395 | −0.0585657 | ||||||||
\(89\) | −16.4565 | −1.74439 | −0.872194 | − | 0.489160i | \(-0.837303\pi\) | ||||
−0.872194 | + | 0.489160i | \(0.837303\pi\) | |||||||
\(90\) | 0.0912635 | 0.00962002 | ||||||||
\(91\) | 1.69214 | 0.177385 | ||||||||
\(92\) | −8.66529 | −0.903419 | ||||||||
\(93\) | 4.96202 | 0.514537 | ||||||||
\(94\) | −0.00523447 | −0.000539895 0 | ||||||||
\(95\) | 12.0258 | 1.23382 | ||||||||
\(96\) | −0.357679 | −0.0365055 | ||||||||
\(97\) | 8.65835 | 0.879122 | 0.439561 | − | 0.898213i | \(-0.355134\pi\) | ||||
0.439561 | + | 0.898213i | \(0.355134\pi\) | |||||||
\(98\) | −0.123373 | −0.0124625 | ||||||||
\(99\) | 4.60629 | 0.462949 | ||||||||
\(100\) | −8.72380 | −0.872380 | ||||||||
\(101\) | 12.2260 | 1.21654 | 0.608268 | − | 0.793731i | \(-0.291864\pi\) | ||||
0.608268 | + | 0.793731i | \(0.291864\pi\) | |||||||
\(102\) | −0.0962775 | −0.00953290 | ||||||||
\(103\) | 1.00000 | 0.0985329 | ||||||||
\(104\) | 0.119271 | 0.0116955 | ||||||||
\(105\) | 5.17803 | 0.505324 | ||||||||
\(106\) | −0.00762364 | −0.000740474 0 | ||||||||
\(107\) | 11.7861 | 1.13941 | 0.569703 | − | 0.821851i | \(-0.307058\pi\) | ||||
0.569703 | + | 0.821851i | \(0.307058\pi\) | |||||||
\(108\) | 1.99911 | 0.192364 | ||||||||
\(109\) | −9.11561 | −0.873117 | −0.436558 | − | 0.899676i | \(-0.643803\pi\) | ||||
−0.436558 | + | 0.899676i | \(0.643803\pi\) | |||||||
\(110\) | 0.420386 | 0.0400823 | ||||||||
\(111\) | 2.80816 | 0.266538 | ||||||||
\(112\) | −6.75955 | −0.638717 | ||||||||
\(113\) | 10.9023 | 1.02561 | 0.512803 | − | 0.858506i | \(-0.328607\pi\) | ||||
0.512803 | + | 0.858506i | \(0.328607\pi\) | |||||||
\(114\) | −0.117208 | −0.0109776 | ||||||||
\(115\) | 13.2640 | 1.23687 | ||||||||
\(116\) | 1.18535 | 0.110057 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | −0.375368 | −0.0345555 | ||||||||
\(119\) | −5.46251 | −0.500747 | ||||||||
\(120\) | 0.364973 | 0.0333173 | ||||||||
\(121\) | 10.2179 | 0.928899 | ||||||||
\(122\) | 0.378921 | 0.0343059 | ||||||||
\(123\) | 3.44430 | 0.310562 | ||||||||
\(124\) | 9.91962 | 0.890808 | ||||||||
\(125\) | −1.94667 | −0.174116 | ||||||||
\(126\) | −0.0504670 | −0.00449596 | ||||||||
\(127\) | −15.1737 | −1.34645 | −0.673223 | − | 0.739439i | \(-0.735091\pi\) | ||||
−0.673223 | + | 0.739439i | \(0.735091\pi\) | |||||||
\(128\) | −0.953317 | −0.0842621 | ||||||||
\(129\) | −8.82134 | −0.776676 | ||||||||
\(130\) | −0.0912635 | −0.00800434 | ||||||||
\(131\) | −5.65098 | −0.493729 | −0.246864 | − | 0.969050i | \(-0.579400\pi\) | ||||
−0.246864 | + | 0.969050i | \(0.579400\pi\) | |||||||
\(132\) | 9.20848 | 0.801495 | ||||||||
\(133\) | −6.65006 | −0.576634 | ||||||||
\(134\) | −0.159317 | −0.0137629 | ||||||||
\(135\) | −3.06004 | −0.263366 | ||||||||
\(136\) | −0.385025 | −0.0330156 | ||||||||
\(137\) | 4.42445 | 0.378006 | 0.189003 | − | 0.981977i | \(-0.439474\pi\) | ||||
0.189003 | + | 0.981977i | \(0.439474\pi\) | |||||||
\(138\) | −0.129276 | −0.0110047 | ||||||||
\(139\) | 13.9763 | 1.18545 | 0.592725 | − | 0.805405i | \(-0.298052\pi\) | ||||
0.592725 | + | 0.805405i | \(0.298052\pi\) | |||||||
\(140\) | 10.3515 | 0.874857 | ||||||||
\(141\) | 0.175510 | 0.0147806 | ||||||||
\(142\) | 0.227180 | 0.0190645 | ||||||||
\(143\) | −4.60629 | −0.385197 | ||||||||
\(144\) | 3.99466 | 0.332889 | ||||||||
\(145\) | −1.81442 | −0.150679 | ||||||||
\(146\) | 0.0787843 | 0.00652023 | ||||||||
\(147\) | 4.13665 | 0.341185 | ||||||||
\(148\) | 5.61381 | 0.461453 | ||||||||
\(149\) | 1.51911 | 0.124451 | 0.0622253 | − | 0.998062i | \(-0.480180\pi\) | ||||
0.0622253 | + | 0.998062i | \(0.480180\pi\) | |||||||
\(150\) | −0.130149 | −0.0106266 | ||||||||
\(151\) | 5.41580 | 0.440731 | 0.220366 | − | 0.975417i | \(-0.429275\pi\) | ||||
0.220366 | + | 0.975417i | \(0.429275\pi\) | |||||||
\(152\) | −0.468729 | −0.0380190 | ||||||||
\(153\) | 3.22816 | 0.260981 | ||||||||
\(154\) | −0.232466 | −0.0187326 | ||||||||
\(155\) | −15.1840 | −1.21961 | ||||||||
\(156\) | −1.99911 | −0.160057 | ||||||||
\(157\) | 17.5237 | 1.39855 | 0.699273 | − | 0.714855i | \(-0.253507\pi\) | ||||
0.699273 | + | 0.714855i | \(0.253507\pi\) | |||||||
\(158\) | 0.425693 | 0.0338663 | ||||||||
\(159\) | 0.255619 | 0.0202719 | ||||||||
\(160\) | 1.09451 | 0.0865289 | ||||||||
\(161\) | −7.33472 | −0.578057 | ||||||||
\(162\) | 0.0298243 | 0.00234322 | ||||||||
\(163\) | 1.82150 | 0.142671 | 0.0713355 | − | 0.997452i | \(-0.477274\pi\) | ||||
0.0713355 | + | 0.997452i | \(0.477274\pi\) | |||||||
\(164\) | 6.88555 | 0.537671 | ||||||||
\(165\) | −14.0954 | −1.09733 | ||||||||
\(166\) | −0.145733 | −0.0113111 | ||||||||
\(167\) | −19.8258 | −1.53416 | −0.767081 | − | 0.641550i | \(-0.778292\pi\) | ||||
−0.767081 | + | 0.641550i | \(0.778292\pi\) | |||||||
\(168\) | −0.201823 | −0.0155710 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0.294613 | 0.0225958 | ||||||||
\(171\) | 3.92996 | 0.300532 | ||||||||
\(172\) | −17.6348 | −1.34464 | ||||||||
\(173\) | −15.1355 | −1.15073 | −0.575365 | − | 0.817897i | \(-0.695140\pi\) | ||||
−0.575365 | + | 0.817897i | \(0.695140\pi\) | |||||||
\(174\) | 0.0176840 | 0.00134062 | ||||||||
\(175\) | −7.38425 | −0.558197 | ||||||||
\(176\) | 18.4006 | 1.38700 | ||||||||
\(177\) | 12.5860 | 0.946021 | ||||||||
\(178\) | −0.490804 | −0.0367873 | ||||||||
\(179\) | 21.8052 | 1.62979 | 0.814897 | − | 0.579605i | \(-0.196793\pi\) | ||||
0.814897 | + | 0.579605i | \(0.196793\pi\) | |||||||
\(180\) | −6.11736 | −0.455961 | ||||||||
\(181\) | −11.6142 | −0.863280 | −0.431640 | − | 0.902046i | \(-0.642065\pi\) | ||||
−0.431640 | + | 0.902046i | \(0.642065\pi\) | |||||||
\(182\) | 0.0504670 | 0.00374087 | ||||||||
\(183\) | −12.7051 | −0.939190 | ||||||||
\(184\) | −0.516987 | −0.0381128 | ||||||||
\(185\) | −8.59307 | −0.631775 | ||||||||
\(186\) | 0.147989 | 0.0108511 | ||||||||
\(187\) | 14.8698 | 1.08739 | ||||||||
\(188\) | 0.350865 | 0.0255894 | ||||||||
\(189\) | 1.69214 | 0.123085 | ||||||||
\(190\) | 0.358662 | 0.0260201 | ||||||||
\(191\) | 12.1789 | 0.881236 | 0.440618 | − | 0.897695i | \(-0.354759\pi\) | ||||
0.440618 | + | 0.897695i | \(0.354759\pi\) | |||||||
\(192\) | 7.97866 | 0.575810 | ||||||||
\(193\) | 19.1182 | 1.37616 | 0.688079 | − | 0.725635i | \(-0.258454\pi\) | ||||
0.688079 | + | 0.725635i | \(0.258454\pi\) | |||||||
\(194\) | 0.258229 | 0.0185398 | ||||||||
\(195\) | 3.06004 | 0.219134 | ||||||||
\(196\) | 8.26961 | 0.590687 | ||||||||
\(197\) | −14.8035 | −1.05471 | −0.527354 | − | 0.849646i | \(-0.676816\pi\) | ||||
−0.527354 | + | 0.849646i | \(0.676816\pi\) | |||||||
\(198\) | 0.137379 | 0.00976313 | ||||||||
\(199\) | 10.0910 | 0.715331 | 0.357665 | − | 0.933850i | \(-0.383573\pi\) | ||||
0.357665 | + | 0.933850i | \(0.383573\pi\) | |||||||
\(200\) | −0.520478 | −0.0368034 | ||||||||
\(201\) | 5.34184 | 0.376784 | ||||||||
\(202\) | 0.364633 | 0.0256555 | ||||||||
\(203\) | 1.00334 | 0.0704207 | ||||||||
\(204\) | 6.45344 | 0.451831 | ||||||||
\(205\) | −10.5397 | −0.736125 | ||||||||
\(206\) | 0.0298243 | 0.00207796 | ||||||||
\(207\) | 4.33457 | 0.301274 | ||||||||
\(208\) | −3.99466 | −0.276980 | ||||||||
\(209\) | 18.1025 | 1.25218 | ||||||||
\(210\) | 0.154431 | 0.0106568 | ||||||||
\(211\) | 6.26999 | 0.431644 | 0.215822 | − | 0.976433i | \(-0.430757\pi\) | ||||
0.215822 | + | 0.976433i | \(0.430757\pi\) | |||||||
\(212\) | 0.511010 | 0.0350963 | ||||||||
\(213\) | −7.61726 | −0.521926 | ||||||||
\(214\) | 0.351512 | 0.0240289 | ||||||||
\(215\) | 26.9936 | 1.84095 | ||||||||
\(216\) | 0.119271 | 0.00811534 | ||||||||
\(217\) | 8.39645 | 0.569988 | ||||||||
\(218\) | −0.271867 | −0.0184131 | ||||||||
\(219\) | −2.64161 | −0.178504 | ||||||||
\(220\) | −28.1783 | −1.89978 | ||||||||
\(221\) | −3.22816 | −0.217149 | ||||||||
\(222\) | 0.0837513 | 0.00562102 | ||||||||
\(223\) | 24.3195 | 1.62855 | 0.814277 | − | 0.580477i | \(-0.197134\pi\) | ||||
0.814277 | + | 0.580477i | \(0.197134\pi\) | |||||||
\(224\) | −0.605245 | −0.0404397 | ||||||||
\(225\) | 4.36384 | 0.290923 | ||||||||
\(226\) | 0.325155 | 0.0216290 | ||||||||
\(227\) | 0.112801 | 0.00748685 | 0.00374342 | − | 0.999993i | \(-0.498808\pi\) | ||||
0.00374342 | + | 0.999993i | \(0.498808\pi\) | |||||||
\(228\) | 7.85643 | 0.520305 | ||||||||
\(229\) | −2.07740 | −0.137278 | −0.0686392 | − | 0.997642i | \(-0.521866\pi\) | ||||
−0.0686392 | + | 0.997642i | \(0.521866\pi\) | |||||||
\(230\) | 0.395588 | 0.0260843 | ||||||||
\(231\) | 7.79451 | 0.512841 | ||||||||
\(232\) | 0.0707203 | 0.00464302 | ||||||||
\(233\) | 14.8944 | 0.975766 | 0.487883 | − | 0.872909i | \(-0.337769\pi\) | ||||
0.487883 | + | 0.872909i | \(0.337769\pi\) | |||||||
\(234\) | −0.0298243 | −0.00194968 | ||||||||
\(235\) | −0.537069 | −0.0350345 | ||||||||
\(236\) | 25.1608 | 1.63783 | ||||||||
\(237\) | −14.2734 | −0.927154 | ||||||||
\(238\) | −0.162916 | −0.0105602 | ||||||||
\(239\) | 9.00916 | 0.582754 | 0.291377 | − | 0.956608i | \(-0.405887\pi\) | ||||
0.291377 | + | 0.956608i | \(0.405887\pi\) | |||||||
\(240\) | −12.2238 | −0.789045 | ||||||||
\(241\) | −18.5937 | −1.19772 | −0.598861 | − | 0.800853i | \(-0.704380\pi\) | ||||
−0.598861 | + | 0.800853i | \(0.704380\pi\) | |||||||
\(242\) | 0.304742 | 0.0195895 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −25.3989 | −1.62600 | ||||||||
\(245\) | −12.6583 | −0.808709 | ||||||||
\(246\) | 0.102724 | 0.00654944 | ||||||||
\(247\) | −3.92996 | −0.250057 | ||||||||
\(248\) | 0.591823 | 0.0375808 | ||||||||
\(249\) | 4.88639 | 0.309662 | ||||||||
\(250\) | −0.0580581 | −0.00367192 | ||||||||
\(251\) | 1.63413 | 0.103145 | 0.0515726 | − | 0.998669i | \(-0.483577\pi\) | ||||
0.0515726 | + | 0.998669i | \(0.483577\pi\) | |||||||
\(252\) | 3.38278 | 0.213095 | ||||||||
\(253\) | 19.9663 | 1.25527 | ||||||||
\(254\) | −0.452545 | −0.0283952 | ||||||||
\(255\) | −9.87829 | −0.618602 | ||||||||
\(256\) | 15.9289 | 0.995556 | ||||||||
\(257\) | 10.9198 | 0.681157 | 0.340578 | − | 0.940216i | \(-0.389377\pi\) | ||||
0.340578 | + | 0.940216i | \(0.389377\pi\) | |||||||
\(258\) | −0.263090 | −0.0163793 | ||||||||
\(259\) | 4.75181 | 0.295263 | ||||||||
\(260\) | 6.11736 | 0.379382 | ||||||||
\(261\) | −0.592940 | −0.0367021 | ||||||||
\(262\) | −0.168537 | −0.0104122 | ||||||||
\(263\) | 11.6090 | 0.715839 | 0.357920 | − | 0.933752i | \(-0.383486\pi\) | ||||
0.357920 | + | 0.933752i | \(0.383486\pi\) | |||||||
\(264\) | 0.549395 | 0.0338129 | ||||||||
\(265\) | −0.782203 | −0.0480503 | ||||||||
\(266\) | −0.198333 | −0.0121606 | ||||||||
\(267\) | 16.4565 | 1.00712 | ||||||||
\(268\) | 10.6789 | 0.652319 | ||||||||
\(269\) | 1.35757 | 0.0827725 | 0.0413863 | − | 0.999143i | \(-0.486823\pi\) | ||||
0.0413863 | + | 0.999143i | \(0.486823\pi\) | |||||||
\(270\) | −0.0912635 | −0.00555412 | ||||||||
\(271\) | −20.6130 | −1.25215 | −0.626076 | − | 0.779762i | \(-0.715340\pi\) | ||||
−0.626076 | + | 0.779762i | \(0.715340\pi\) | |||||||
\(272\) | 12.8954 | 0.781899 | ||||||||
\(273\) | −1.69214 | −0.102413 | ||||||||
\(274\) | 0.131956 | 0.00797176 | ||||||||
\(275\) | 20.1011 | 1.21214 | ||||||||
\(276\) | 8.66529 | 0.521589 | ||||||||
\(277\) | 24.1056 | 1.44837 | 0.724184 | − | 0.689607i | \(-0.242217\pi\) | ||||
0.724184 | + | 0.689607i | \(0.242217\pi\) | |||||||
\(278\) | 0.416832 | 0.0249999 | ||||||||
\(279\) | −4.96202 | −0.297068 | ||||||||
\(280\) | 0.617587 | 0.0369079 | ||||||||
\(281\) | −18.7524 | −1.11867 | −0.559337 | − | 0.828940i | \(-0.688944\pi\) | ||||
−0.559337 | + | 0.828940i | \(0.688944\pi\) | |||||||
\(282\) | 0.00523447 | 0.000311708 0 | ||||||||
\(283\) | 27.8394 | 1.65488 | 0.827440 | − | 0.561555i | \(-0.189797\pi\) | ||||
0.827440 | + | 0.561555i | \(0.189797\pi\) | |||||||
\(284\) | −15.2277 | −0.903601 | ||||||||
\(285\) | −12.0258 | −0.712349 | ||||||||
\(286\) | −0.137379 | −0.00812341 | ||||||||
\(287\) | 5.82826 | 0.344031 | ||||||||
\(288\) | 0.357679 | 0.0210765 | ||||||||
\(289\) | −6.57900 | −0.387000 | ||||||||
\(290\) | −0.0541138 | −0.00317767 | ||||||||
\(291\) | −8.65835 | −0.507561 | ||||||||
\(292\) | −5.28088 | −0.309040 | ||||||||
\(293\) | 7.02330 | 0.410306 | 0.205153 | − | 0.978730i | \(-0.434231\pi\) | ||||
0.205153 | + | 0.978730i | \(0.434231\pi\) | |||||||
\(294\) | 0.123373 | 0.00719524 | ||||||||
\(295\) | −38.5136 | −2.24235 | ||||||||
\(296\) | 0.334931 | 0.0194674 | ||||||||
\(297\) | −4.60629 | −0.267284 | ||||||||
\(298\) | 0.0453065 | 0.00262454 | ||||||||
\(299\) | −4.33457 | −0.250675 | ||||||||
\(300\) | 8.72380 | 0.503669 | ||||||||
\(301\) | −14.9270 | −0.860377 | ||||||||
\(302\) | 0.161522 | 0.00929457 | ||||||||
\(303\) | −12.2260 | −0.702368 | ||||||||
\(304\) | 15.6989 | 0.900392 | ||||||||
\(305\) | 38.8782 | 2.22616 | ||||||||
\(306\) | 0.0962775 | 0.00550382 | ||||||||
\(307\) | 17.8124 | 1.01661 | 0.508304 | − | 0.861178i | \(-0.330273\pi\) | ||||
0.508304 | + | 0.861178i | \(0.330273\pi\) | |||||||
\(308\) | 15.5821 | 0.887871 | ||||||||
\(309\) | −1.00000 | −0.0568880 | ||||||||
\(310\) | −0.452851 | −0.0257202 | ||||||||
\(311\) | 5.03954 | 0.285766 | 0.142883 | − | 0.989740i | \(-0.454363\pi\) | ||||
0.142883 | + | 0.989740i | \(0.454363\pi\) | |||||||
\(312\) | −0.119271 | −0.00675237 | ||||||||
\(313\) | −19.7835 | −1.11823 | −0.559116 | − | 0.829089i | \(-0.688859\pi\) | ||||
−0.559116 | + | 0.829089i | \(0.688859\pi\) | |||||||
\(314\) | 0.522633 | 0.0294939 | ||||||||
\(315\) | −5.17803 | −0.291749 | ||||||||
\(316\) | −28.5340 | −1.60516 | ||||||||
\(317\) | 7.66086 | 0.430277 | 0.215138 | − | 0.976584i | \(-0.430980\pi\) | ||||
0.215138 | + | 0.976584i | \(0.430980\pi\) | |||||||
\(318\) | 0.00762364 | 0.000427513 0 | ||||||||
\(319\) | −2.73125 | −0.152921 | ||||||||
\(320\) | −24.4150 | −1.36484 | ||||||||
\(321\) | −11.7861 | −0.657836 | ||||||||
\(322\) | −0.218753 | −0.0121906 | ||||||||
\(323\) | 12.6865 | 0.705897 | ||||||||
\(324\) | −1.99911 | −0.111062 | ||||||||
\(325\) | −4.36384 | −0.242062 | ||||||||
\(326\) | 0.0543250 | 0.00300878 | ||||||||
\(327\) | 9.11561 | 0.504094 | ||||||||
\(328\) | 0.410805 | 0.0226829 | ||||||||
\(329\) | 0.296989 | 0.0163735 | ||||||||
\(330\) | −0.420386 | −0.0231415 | ||||||||
\(331\) | −8.34360 | −0.458606 | −0.229303 | − | 0.973355i | \(-0.573645\pi\) | ||||
−0.229303 | + | 0.973355i | \(0.573645\pi\) | |||||||
\(332\) | 9.76844 | 0.536113 | ||||||||
\(333\) | −2.80816 | −0.153886 | ||||||||
\(334\) | −0.591289 | −0.0323539 | ||||||||
\(335\) | −16.3462 | −0.893090 | ||||||||
\(336\) | 6.75955 | 0.368764 | ||||||||
\(337\) | −12.9548 | −0.705692 | −0.352846 | − | 0.935681i | \(-0.614786\pi\) | ||||
−0.352846 | + | 0.935681i | \(0.614786\pi\) | |||||||
\(338\) | 0.0298243 | 0.00162223 | ||||||||
\(339\) | −10.9023 | −0.592134 | ||||||||
\(340\) | −19.7478 | −1.07097 | ||||||||
\(341\) | −22.8565 | −1.23775 | ||||||||
\(342\) | 0.117208 | 0.00633790 | ||||||||
\(343\) | 18.8448 | 1.01752 | ||||||||
\(344\) | −1.05213 | −0.0567269 | ||||||||
\(345\) | −13.2640 | −0.714108 | ||||||||
\(346\) | −0.451406 | −0.0242677 | ||||||||
\(347\) | 29.1738 | 1.56613 | 0.783066 | − | 0.621939i | \(-0.213655\pi\) | ||||
0.783066 | + | 0.621939i | \(0.213655\pi\) | |||||||
\(348\) | −1.18535 | −0.0635416 | ||||||||
\(349\) | 12.3398 | 0.660532 | 0.330266 | − | 0.943888i | \(-0.392862\pi\) | ||||
0.330266 | + | 0.943888i | \(0.392862\pi\) | |||||||
\(350\) | −0.220230 | −0.0117718 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 1.64757 | 0.0878160 | ||||||||
\(353\) | −7.51777 | −0.400131 | −0.200065 | − | 0.979783i | \(-0.564115\pi\) | ||||
−0.200065 | + | 0.979783i | \(0.564115\pi\) | |||||||
\(354\) | 0.375368 | 0.0199506 | ||||||||
\(355\) | 23.3091 | 1.23712 | ||||||||
\(356\) | 32.8984 | 1.74361 | ||||||||
\(357\) | 5.46251 | 0.289107 | ||||||||
\(358\) | 0.650324 | 0.0343707 | ||||||||
\(359\) | 4.01242 | 0.211768 | 0.105884 | − | 0.994379i | \(-0.466233\pi\) | ||||
0.105884 | + | 0.994379i | \(0.466233\pi\) | |||||||
\(360\) | −0.364973 | −0.0192358 | ||||||||
\(361\) | −3.55541 | −0.187127 | ||||||||
\(362\) | −0.346387 | −0.0182057 | ||||||||
\(363\) | −10.2179 | −0.536300 | ||||||||
\(364\) | −3.38278 | −0.177306 | ||||||||
\(365\) | 8.08344 | 0.423107 | ||||||||
\(366\) | −0.378921 | −0.0198065 | ||||||||
\(367\) | −28.6589 | −1.49598 | −0.747990 | − | 0.663709i | \(-0.768981\pi\) | ||||
−0.747990 | + | 0.663709i | \(0.768981\pi\) | |||||||
\(368\) | 17.3152 | 0.902615 | ||||||||
\(369\) | −3.44430 | −0.179303 | ||||||||
\(370\) | −0.256282 | −0.0133235 | ||||||||
\(371\) | 0.432544 | 0.0224565 | ||||||||
\(372\) | −9.91962 | −0.514308 | ||||||||
\(373\) | −10.8170 | −0.560083 | −0.280041 | − | 0.959988i | \(-0.590348\pi\) | ||||
−0.280041 | + | 0.959988i | \(0.590348\pi\) | |||||||
\(374\) | 0.443482 | 0.0229319 | ||||||||
\(375\) | 1.94667 | 0.100526 | ||||||||
\(376\) | 0.0209332 | 0.00107955 | ||||||||
\(377\) | 0.592940 | 0.0305380 | ||||||||
\(378\) | 0.0504670 | 0.00259574 | ||||||||
\(379\) | −1.16673 | −0.0599311 | −0.0299655 | − | 0.999551i | \(-0.509540\pi\) | ||||
−0.0299655 | + | 0.999551i | \(0.509540\pi\) | |||||||
\(380\) | −24.0410 | −1.23328 | ||||||||
\(381\) | 15.1737 | 0.777371 | ||||||||
\(382\) | 0.363228 | 0.0185844 | ||||||||
\(383\) | 17.3293 | 0.885485 | 0.442743 | − | 0.896649i | \(-0.354006\pi\) | ||||
0.442743 | + | 0.896649i | \(0.354006\pi\) | |||||||
\(384\) | 0.953317 | 0.0486487 | ||||||||
\(385\) | −23.8515 | −1.21558 | ||||||||
\(386\) | 0.570187 | 0.0290218 | ||||||||
\(387\) | 8.82134 | 0.448414 | ||||||||
\(388\) | −17.3090 | −0.878731 | ||||||||
\(389\) | 29.6106 | 1.50132 | 0.750658 | − | 0.660691i | \(-0.229737\pi\) | ||||
0.750658 | + | 0.660691i | \(0.229737\pi\) | |||||||
\(390\) | 0.0912635 | 0.00462131 | ||||||||
\(391\) | 13.9927 | 0.707640 | ||||||||
\(392\) | 0.493381 | 0.0249195 | ||||||||
\(393\) | 5.65098 | 0.285054 | ||||||||
\(394\) | −0.441505 | −0.0222427 | ||||||||
\(395\) | 43.6770 | 2.19763 | ||||||||
\(396\) | −9.20848 | −0.462744 | ||||||||
\(397\) | 5.36573 | 0.269298 | 0.134649 | − | 0.990893i | \(-0.457009\pi\) | ||||
0.134649 | + | 0.990893i | \(0.457009\pi\) | |||||||
\(398\) | 0.300956 | 0.0150856 | ||||||||
\(399\) | 6.65006 | 0.332920 | ||||||||
\(400\) | 17.4321 | 0.871604 | ||||||||
\(401\) | −9.60580 | −0.479691 | −0.239845 | − | 0.970811i | \(-0.577097\pi\) | ||||
−0.239845 | + | 0.970811i | \(0.577097\pi\) | |||||||
\(402\) | 0.159317 | 0.00794599 | ||||||||
\(403\) | 4.96202 | 0.247176 | ||||||||
\(404\) | −24.4412 | −1.21600 | ||||||||
\(405\) | 3.06004 | 0.152055 | ||||||||
\(406\) | 0.0299239 | 0.00148510 | ||||||||
\(407\) | −12.9352 | −0.641173 | ||||||||
\(408\) | 0.385025 | 0.0190616 | ||||||||
\(409\) | −18.1156 | −0.895757 | −0.447879 | − | 0.894094i | \(-0.647820\pi\) | ||||
−0.447879 | + | 0.894094i | \(0.647820\pi\) | |||||||
\(410\) | −0.314339 | −0.0155241 | ||||||||
\(411\) | −4.42445 | −0.218242 | ||||||||
\(412\) | −1.99911 | −0.0984891 | ||||||||
\(413\) | 21.2973 | 1.04797 | ||||||||
\(414\) | 0.129276 | 0.00635355 | ||||||||
\(415\) | −14.9526 | −0.733992 | ||||||||
\(416\) | −0.357679 | −0.0175367 | ||||||||
\(417\) | −13.9763 | −0.684420 | ||||||||
\(418\) | 0.539895 | 0.0264071 | ||||||||
\(419\) | −7.10706 | −0.347203 | −0.173601 | − | 0.984816i | \(-0.555540\pi\) | ||||
−0.173601 | + | 0.984816i | \(0.555540\pi\) | |||||||
\(420\) | −10.3515 | −0.505099 | ||||||||
\(421\) | −19.0647 | −0.929157 | −0.464579 | − | 0.885532i | \(-0.653794\pi\) | ||||
−0.464579 | + | 0.885532i | \(0.653794\pi\) | |||||||
\(422\) | 0.186998 | 0.00910292 | ||||||||
\(423\) | −0.175510 | −0.00853361 | ||||||||
\(424\) | 0.0304878 | 0.00148062 | ||||||||
\(425\) | 14.0872 | 0.683328 | ||||||||
\(426\) | −0.227180 | −0.0110069 | ||||||||
\(427\) | −21.4989 | −1.04040 | ||||||||
\(428\) | −23.5617 | −1.13890 | ||||||||
\(429\) | 4.60629 | 0.222394 | ||||||||
\(430\) | 0.805067 | 0.0388238 | ||||||||
\(431\) | 36.5047 | 1.75837 | 0.879185 | − | 0.476480i | \(-0.158088\pi\) | ||||
0.879185 | + | 0.476480i | \(0.158088\pi\) | |||||||
\(432\) | −3.99466 | −0.192193 | ||||||||
\(433\) | 25.5072 | 1.22580 | 0.612898 | − | 0.790162i | \(-0.290004\pi\) | ||||
0.612898 | + | 0.790162i | \(0.290004\pi\) | |||||||
\(434\) | 0.250418 | 0.0120205 | ||||||||
\(435\) | 1.81442 | 0.0869948 | ||||||||
\(436\) | 18.2231 | 0.872729 | ||||||||
\(437\) | 17.0347 | 0.814880 | ||||||||
\(438\) | −0.0787843 | −0.00376446 | ||||||||
\(439\) | −4.65970 | −0.222395 | −0.111198 | − | 0.993798i | \(-0.535469\pi\) | ||||
−0.111198 | + | 0.993798i | \(0.535469\pi\) | |||||||
\(440\) | −1.68117 | −0.0801467 | ||||||||
\(441\) | −4.13665 | −0.196983 | ||||||||
\(442\) | −0.0962775 | −0.00457946 | ||||||||
\(443\) | −0.143465 | −0.00681622 | −0.00340811 | − | 0.999994i | \(-0.501085\pi\) | ||||
−0.00340811 | + | 0.999994i | \(0.501085\pi\) | |||||||
\(444\) | −5.61381 | −0.266420 | ||||||||
\(445\) | −50.3576 | −2.38718 | ||||||||
\(446\) | 0.725312 | 0.0343445 | ||||||||
\(447\) | −1.51911 | −0.0718516 | ||||||||
\(448\) | 13.5010 | 0.637865 | ||||||||
\(449\) | −1.84722 | −0.0871759 | −0.0435879 | − | 0.999050i | \(-0.513879\pi\) | ||||
−0.0435879 | + | 0.999050i | \(0.513879\pi\) | |||||||
\(450\) | 0.130149 | 0.00613526 | ||||||||
\(451\) | −15.8655 | −0.747075 | ||||||||
\(452\) | −21.7950 | −1.02515 | ||||||||
\(453\) | −5.41580 | −0.254456 | ||||||||
\(454\) | 0.00336420 | 0.000157890 0 | ||||||||
\(455\) | 5.17803 | 0.242750 | ||||||||
\(456\) | 0.468729 | 0.0219503 | ||||||||
\(457\) | −1.76511 | −0.0825685 | −0.0412842 | − | 0.999147i | \(-0.513145\pi\) | ||||
−0.0412842 | + | 0.999147i | \(0.513145\pi\) | |||||||
\(458\) | −0.0619570 | −0.00289506 | ||||||||
\(459\) | −3.22816 | −0.150677 | ||||||||
\(460\) | −26.5161 | −1.23632 | ||||||||
\(461\) | 6.44028 | 0.299954 | 0.149977 | − | 0.988690i | \(-0.452080\pi\) | ||||
0.149977 | + | 0.988690i | \(0.452080\pi\) | |||||||
\(462\) | 0.232466 | 0.0108153 | ||||||||
\(463\) | 16.4323 | 0.763675 | 0.381837 | − | 0.924229i | \(-0.375291\pi\) | ||||
0.381837 | + | 0.924229i | \(0.375291\pi\) | |||||||
\(464\) | −2.36860 | −0.109959 | ||||||||
\(465\) | 15.1840 | 0.704140 | ||||||||
\(466\) | 0.444216 | 0.0205779 | ||||||||
\(467\) | −9.44012 | −0.436836 | −0.218418 | − | 0.975855i | \(-0.570090\pi\) | ||||
−0.218418 | + | 0.975855i | \(0.570090\pi\) | |||||||
\(468\) | 1.99911 | 0.0924089 | ||||||||
\(469\) | 9.03916 | 0.417390 | ||||||||
\(470\) | −0.0160177 | −0.000738841 0 | ||||||||
\(471\) | −17.5237 | −0.807451 | ||||||||
\(472\) | 1.50114 | 0.0690955 | ||||||||
\(473\) | 40.6336 | 1.86834 | ||||||||
\(474\) | −0.425693 | −0.0195527 | ||||||||
\(475\) | 17.1497 | 0.786883 | ||||||||
\(476\) | 10.9202 | 0.500525 | ||||||||
\(477\) | −0.255619 | −0.0117040 | ||||||||
\(478\) | 0.268692 | 0.0122897 | ||||||||
\(479\) | −12.8252 | −0.585998 | −0.292999 | − | 0.956113i | \(-0.594653\pi\) | ||||
−0.292999 | + | 0.956113i | \(0.594653\pi\) | |||||||
\(480\) | −1.09451 | −0.0499575 | ||||||||
\(481\) | 2.80816 | 0.128041 | ||||||||
\(482\) | −0.554543 | −0.0252587 | ||||||||
\(483\) | 7.33472 | 0.333742 | ||||||||
\(484\) | −20.4267 | −0.928486 | ||||||||
\(485\) | 26.4949 | 1.20307 | ||||||||
\(486\) | −0.0298243 | −0.00135286 | ||||||||
\(487\) | 35.2979 | 1.59950 | 0.799751 | − | 0.600332i | \(-0.204965\pi\) | ||||
0.799751 | + | 0.600332i | \(0.204965\pi\) | |||||||
\(488\) | −1.51535 | −0.0685966 | ||||||||
\(489\) | −1.82150 | −0.0823711 | ||||||||
\(490\) | −0.377525 | −0.0170548 | ||||||||
\(491\) | 29.9174 | 1.35015 | 0.675077 | − | 0.737747i | \(-0.264110\pi\) | ||||
0.675077 | + | 0.737747i | \(0.264110\pi\) | |||||||
\(492\) | −6.88555 | −0.310424 | ||||||||
\(493\) | −1.91410 | −0.0862069 | ||||||||
\(494\) | −0.117208 | −0.00527345 | ||||||||
\(495\) | 14.0954 | 0.633542 | ||||||||
\(496\) | −19.8216 | −0.890016 | ||||||||
\(497\) | −12.8895 | −0.578174 | ||||||||
\(498\) | 0.145733 | 0.00653046 | ||||||||
\(499\) | −4.36023 | −0.195190 | −0.0975952 | − | 0.995226i | \(-0.531115\pi\) | ||||
−0.0975952 | + | 0.995226i | \(0.531115\pi\) | |||||||
\(500\) | 3.89161 | 0.174038 | ||||||||
\(501\) | 19.8258 | 0.885749 | ||||||||
\(502\) | 0.0487368 | 0.00217523 | ||||||||
\(503\) | −16.3239 | −0.727846 | −0.363923 | − | 0.931429i | \(-0.618563\pi\) | ||||
−0.363923 | + | 0.931429i | \(0.618563\pi\) | |||||||
\(504\) | 0.201823 | 0.00898992 | ||||||||
\(505\) | 37.4122 | 1.66482 | ||||||||
\(506\) | 0.595481 | 0.0264723 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 30.3339 | 1.34585 | ||||||||
\(509\) | −10.9778 | −0.486581 | −0.243291 | − | 0.969953i | \(-0.578227\pi\) | ||||
−0.243291 | + | 0.969953i | \(0.578227\pi\) | |||||||
\(510\) | −0.294613 | −0.0130457 | ||||||||
\(511\) | −4.46999 | −0.197741 | ||||||||
\(512\) | 2.38170 | 0.105257 | ||||||||
\(513\) | −3.92996 | −0.173512 | ||||||||
\(514\) | 0.325675 | 0.0143649 | ||||||||
\(515\) | 3.06004 | 0.134841 | ||||||||
\(516\) | 17.6348 | 0.776330 | ||||||||
\(517\) | −0.808451 | −0.0355556 | ||||||||
\(518\) | 0.141719 | 0.00622679 | ||||||||
\(519\) | 15.1355 | 0.664374 | ||||||||
\(520\) | 0.364973 | 0.0160051 | ||||||||
\(521\) | −34.3218 | −1.50367 | −0.751833 | − | 0.659354i | \(-0.770830\pi\) | ||||
−0.751833 | + | 0.659354i | \(0.770830\pi\) | |||||||
\(522\) | −0.0176840 | −0.000774009 0 | ||||||||
\(523\) | −22.0037 | −0.962152 | −0.481076 | − | 0.876679i | \(-0.659754\pi\) | ||||
−0.481076 | + | 0.876679i | \(0.659754\pi\) | |||||||
\(524\) | 11.2969 | 0.493509 | ||||||||
\(525\) | 7.38425 | 0.322275 | ||||||||
\(526\) | 0.346229 | 0.0150963 | ||||||||
\(527\) | −16.0182 | −0.697763 | ||||||||
\(528\) | −18.4006 | −0.800782 | ||||||||
\(529\) | −4.21148 | −0.183108 | ||||||||
\(530\) | −0.0233287 | −0.00101333 | ||||||||
\(531\) | −12.5860 | −0.546185 | ||||||||
\(532\) | 13.2942 | 0.576377 | ||||||||
\(533\) | 3.44430 | 0.149189 | ||||||||
\(534\) | 0.490804 | 0.0212392 | ||||||||
\(535\) | 36.0659 | 1.55927 | ||||||||
\(536\) | 0.637124 | 0.0275196 | ||||||||
\(537\) | −21.8052 | −0.940963 | ||||||||
\(538\) | 0.0404886 | 0.00174559 | ||||||||
\(539\) | −19.0546 | −0.820739 | ||||||||
\(540\) | 6.11736 | 0.263249 | ||||||||
\(541\) | −14.5633 | −0.626127 | −0.313063 | − | 0.949732i | \(-0.601355\pi\) | ||||
−0.313063 | + | 0.949732i | \(0.601355\pi\) | |||||||
\(542\) | −0.614769 | −0.0264066 | ||||||||
\(543\) | 11.6142 | 0.498415 | ||||||||
\(544\) | 1.15465 | 0.0495050 | ||||||||
\(545\) | −27.8941 | −1.19485 | ||||||||
\(546\) | −0.0504670 | −0.00215979 | ||||||||
\(547\) | −8.56516 | −0.366220 | −0.183110 | − | 0.983092i | \(-0.558616\pi\) | ||||
−0.183110 | + | 0.983092i | \(0.558616\pi\) | |||||||
\(548\) | −8.84496 | −0.377838 | ||||||||
\(549\) | 12.7051 | 0.542241 | ||||||||
\(550\) | 0.599502 | 0.0255628 | ||||||||
\(551\) | −2.33023 | −0.0992712 | ||||||||
\(552\) | 0.516987 | 0.0220044 | ||||||||
\(553\) | −24.1526 | −1.02707 | ||||||||
\(554\) | 0.718934 | 0.0305446 | ||||||||
\(555\) | 8.59307 | 0.364755 | ||||||||
\(556\) | −27.9401 | −1.18492 | ||||||||
\(557\) | 9.38728 | 0.397752 | 0.198876 | − | 0.980025i | \(-0.436271\pi\) | ||||
0.198876 | + | 0.980025i | \(0.436271\pi\) | |||||||
\(558\) | −0.147989 | −0.00626486 | ||||||||
\(559\) | −8.82134 | −0.373103 | ||||||||
\(560\) | −20.6845 | −0.874079 | ||||||||
\(561\) | −14.8698 | −0.627804 | ||||||||
\(562\) | −0.559277 | −0.0235917 | ||||||||
\(563\) | 11.8967 | 0.501385 | 0.250692 | − | 0.968067i | \(-0.419342\pi\) | ||||
0.250692 | + | 0.968067i | \(0.419342\pi\) | |||||||
\(564\) | −0.350865 | −0.0147741 | ||||||||
\(565\) | 33.3616 | 1.40353 | ||||||||
\(566\) | 0.830290 | 0.0348997 | ||||||||
\(567\) | −1.69214 | −0.0710634 | ||||||||
\(568\) | −0.908516 | −0.0381205 | ||||||||
\(569\) | −16.1566 | −0.677320 | −0.338660 | − | 0.940909i | \(-0.609974\pi\) | ||||
−0.338660 | + | 0.940909i | \(0.609974\pi\) | |||||||
\(570\) | −0.358662 | −0.0150227 | ||||||||
\(571\) | 27.7464 | 1.16115 | 0.580575 | − | 0.814207i | \(-0.302828\pi\) | ||||
0.580575 | + | 0.814207i | \(0.302828\pi\) | |||||||
\(572\) | 9.20848 | 0.385026 | ||||||||
\(573\) | −12.1789 | −0.508782 | ||||||||
\(574\) | 0.173824 | 0.00725527 | ||||||||
\(575\) | 18.9154 | 0.788826 | ||||||||
\(576\) | −7.97866 | −0.332444 | ||||||||
\(577\) | 4.64568 | 0.193402 | 0.0967011 | − | 0.995313i | \(-0.469171\pi\) | ||||
0.0967011 | + | 0.995313i | \(0.469171\pi\) | |||||||
\(578\) | −0.196214 | −0.00816143 | ||||||||
\(579\) | −19.1182 | −0.794526 | ||||||||
\(580\) | 3.62722 | 0.150612 | ||||||||
\(581\) | 8.26848 | 0.343034 | ||||||||
\(582\) | −0.258229 | −0.0107039 | ||||||||
\(583\) | −1.17745 | −0.0487651 | ||||||||
\(584\) | −0.315067 | −0.0130376 | ||||||||
\(585\) | −3.06004 | −0.126517 | ||||||||
\(586\) | 0.209465 | 0.00865292 | ||||||||
\(587\) | −15.3149 | −0.632112 | −0.316056 | − | 0.948741i | \(-0.602359\pi\) | ||||
−0.316056 | + | 0.948741i | \(0.602359\pi\) | |||||||
\(588\) | −8.26961 | −0.341033 | ||||||||
\(589\) | −19.5005 | −0.803506 | ||||||||
\(590\) | −1.14864 | −0.0472888 | ||||||||
\(591\) | 14.8035 | 0.608936 | ||||||||
\(592\) | −11.2176 | −0.461042 | ||||||||
\(593\) | −16.8272 | −0.691009 | −0.345505 | − | 0.938417i | \(-0.612292\pi\) | ||||
−0.345505 | + | 0.938417i | \(0.612292\pi\) | |||||||
\(594\) | −0.137379 | −0.00563674 | ||||||||
\(595\) | −16.7155 | −0.685268 | ||||||||
\(596\) | −3.03688 | −0.124395 | ||||||||
\(597\) | −10.0910 | −0.412996 | ||||||||
\(598\) | −0.129276 | −0.00528647 | ||||||||
\(599\) | 21.0065 | 0.858301 | 0.429151 | − | 0.903233i | \(-0.358813\pi\) | ||||
0.429151 | + | 0.903233i | \(0.358813\pi\) | |||||||
\(600\) | 0.520478 | 0.0212484 | ||||||||
\(601\) | 38.2296 | 1.55942 | 0.779710 | − | 0.626141i | \(-0.215367\pi\) | ||||
0.779710 | + | 0.626141i | \(0.215367\pi\) | |||||||
\(602\) | −0.445187 | −0.0181445 | ||||||||
\(603\) | −5.34184 | −0.217536 | ||||||||
\(604\) | −10.8268 | −0.440535 | ||||||||
\(605\) | 31.2672 | 1.27119 | ||||||||
\(606\) | −0.364633 | −0.0148122 | ||||||||
\(607\) | −43.2393 | −1.75503 | −0.877515 | − | 0.479548i | \(-0.840801\pi\) | ||||
−0.877515 | + | 0.479548i | \(0.840801\pi\) | |||||||
\(608\) | 1.40567 | 0.0570073 | ||||||||
\(609\) | −1.00334 | −0.0406574 | ||||||||
\(610\) | 1.15951 | 0.0469474 | ||||||||
\(611\) | 0.175510 | 0.00710039 | ||||||||
\(612\) | −6.45344 | −0.260865 | ||||||||
\(613\) | −27.6480 | −1.11669 | −0.558347 | − | 0.829608i | \(-0.688564\pi\) | ||||
−0.558347 | + | 0.829608i | \(0.688564\pi\) | |||||||
\(614\) | 0.531243 | 0.0214392 | ||||||||
\(615\) | 10.5397 | 0.425002 | ||||||||
\(616\) | 0.929656 | 0.0374569 | ||||||||
\(617\) | −38.8213 | −1.56289 | −0.781444 | − | 0.623976i | \(-0.785516\pi\) | ||||
−0.781444 | + | 0.623976i | \(0.785516\pi\) | |||||||
\(618\) | −0.0298243 | −0.00119971 | ||||||||
\(619\) | −32.6015 | −1.31037 | −0.655183 | − | 0.755470i | \(-0.727409\pi\) | ||||
−0.655183 | + | 0.755470i | \(0.727409\pi\) | |||||||
\(620\) | 30.3544 | 1.21906 | ||||||||
\(621\) | −4.33457 | −0.173940 | ||||||||
\(622\) | 0.150301 | 0.00602651 | ||||||||
\(623\) | 27.8468 | 1.11566 | ||||||||
\(624\) | 3.99466 | 0.159915 | ||||||||
\(625\) | −27.7761 | −1.11104 | ||||||||
\(626\) | −0.590030 | −0.0235824 | ||||||||
\(627\) | −18.1025 | −0.722946 | ||||||||
\(628\) | −35.0319 | −1.39792 | ||||||||
\(629\) | −9.06517 | −0.361452 | ||||||||
\(630\) | −0.154431 | −0.00615268 | ||||||||
\(631\) | 10.9258 | 0.434950 | 0.217475 | − | 0.976066i | \(-0.430218\pi\) | ||||
0.217475 | + | 0.976066i | \(0.430218\pi\) | |||||||
\(632\) | −1.70239 | −0.0677176 | ||||||||
\(633\) | −6.26999 | −0.249210 | ||||||||
\(634\) | 0.228480 | 0.00907410 | ||||||||
\(635\) | −46.4321 | −1.84260 | ||||||||
\(636\) | −0.511010 | −0.0202629 | ||||||||
\(637\) | 4.13665 | 0.163900 | ||||||||
\(638\) | −0.0814577 | −0.00322494 | ||||||||
\(639\) | 7.61726 | 0.301334 | ||||||||
\(640\) | −2.91719 | −0.115312 | ||||||||
\(641\) | −28.2294 | −1.11499 | −0.557497 | − | 0.830179i | \(-0.688238\pi\) | ||||
−0.557497 | + | 0.830179i | \(0.688238\pi\) | |||||||
\(642\) | −0.351512 | −0.0138731 | ||||||||
\(643\) | 20.6457 | 0.814187 | 0.407093 | − | 0.913387i | \(-0.366542\pi\) | ||||
0.407093 | + | 0.913387i | \(0.366542\pi\) | |||||||
\(644\) | 14.6629 | 0.577800 | ||||||||
\(645\) | −26.9936 | −1.06287 | ||||||||
\(646\) | 0.378367 | 0.0148866 | ||||||||
\(647\) | 20.4026 | 0.802109 | 0.401054 | − | 0.916054i | \(-0.368644\pi\) | ||||
0.401054 | + | 0.916054i | \(0.368644\pi\) | |||||||
\(648\) | −0.119271 | −0.00468540 | ||||||||
\(649\) | −57.9747 | −2.27571 | ||||||||
\(650\) | −0.130149 | −0.00510484 | ||||||||
\(651\) | −8.39645 | −0.329083 | ||||||||
\(652\) | −3.64138 | −0.142607 | ||||||||
\(653\) | −13.0210 | −0.509550 | −0.254775 | − | 0.967000i | \(-0.582001\pi\) | ||||
−0.254775 | + | 0.967000i | \(0.582001\pi\) | |||||||
\(654\) | 0.271867 | 0.0106308 | ||||||||
\(655\) | −17.2922 | −0.675663 | ||||||||
\(656\) | −13.7588 | −0.537192 | ||||||||
\(657\) | 2.64161 | 0.103059 | ||||||||
\(658\) | 0.00885749 | 0.000345301 0 | ||||||||
\(659\) | −46.8236 | −1.82399 | −0.911995 | − | 0.410201i | \(-0.865458\pi\) | ||||
−0.911995 | + | 0.410201i | \(0.865458\pi\) | |||||||
\(660\) | 28.1783 | 1.09684 | ||||||||
\(661\) | −38.7458 | −1.50704 | −0.753519 | − | 0.657426i | \(-0.771645\pi\) | ||||
−0.753519 | + | 0.657426i | \(0.771645\pi\) | |||||||
\(662\) | −0.248842 | −0.00967152 | ||||||||
\(663\) | 3.22816 | 0.125371 | ||||||||
\(664\) | 0.582803 | 0.0226172 | ||||||||
\(665\) | −20.3495 | −0.789118 | ||||||||
\(666\) | −0.0837513 | −0.00324530 | ||||||||
\(667\) | −2.57014 | −0.0995163 | ||||||||
\(668\) | 39.6339 | 1.53348 | ||||||||
\(669\) | −24.3195 | −0.940246 | ||||||||
\(670\) | −0.487515 | −0.0188343 | ||||||||
\(671\) | 58.5235 | 2.25927 | ||||||||
\(672\) | 0.605245 | 0.0233478 | ||||||||
\(673\) | 16.7438 | 0.645425 | 0.322713 | − | 0.946497i | \(-0.395405\pi\) | ||||
0.322713 | + | 0.946497i | \(0.395405\pi\) | |||||||
\(674\) | −0.386367 | −0.0148823 | ||||||||
\(675\) | −4.36384 | −0.167964 | ||||||||
\(676\) | −1.99911 | −0.0768889 | ||||||||
\(677\) | 31.3519 | 1.20495 | 0.602475 | − | 0.798138i | \(-0.294181\pi\) | ||||
0.602475 | + | 0.798138i | \(0.294181\pi\) | |||||||
\(678\) | −0.325155 | −0.0124875 | ||||||||
\(679\) | −14.6512 | −0.562261 | ||||||||
\(680\) | −1.17819 | −0.0451815 | ||||||||
\(681\) | −0.112801 | −0.00432253 | ||||||||
\(682\) | −0.681679 | −0.0261028 | ||||||||
\(683\) | 9.45935 | 0.361952 | 0.180976 | − | 0.983488i | \(-0.442074\pi\) | ||||
0.180976 | + | 0.983488i | \(0.442074\pi\) | |||||||
\(684\) | −7.85643 | −0.300398 | ||||||||
\(685\) | 13.5390 | 0.517298 | ||||||||
\(686\) | 0.562034 | 0.0214585 | ||||||||
\(687\) | 2.07740 | 0.0792578 | ||||||||
\(688\) | 35.2383 | 1.34345 | ||||||||
\(689\) | 0.255619 | 0.00973829 | ||||||||
\(690\) | −0.395588 | −0.0150598 | ||||||||
\(691\) | 52.0566 | 1.98033 | 0.990163 | − | 0.139916i | \(-0.0446833\pi\) | ||||
0.990163 | + | 0.139916i | \(0.0446833\pi\) | |||||||
\(692\) | 30.2575 | 1.15022 | ||||||||
\(693\) | −7.79451 | −0.296089 | ||||||||
\(694\) | 0.870088 | 0.0330281 | ||||||||
\(695\) | 42.7679 | 1.62228 | ||||||||
\(696\) | −0.0707203 | −0.00268065 | ||||||||
\(697\) | −11.1188 | −0.421153 | ||||||||
\(698\) | 0.368025 | 0.0139299 | ||||||||
\(699\) | −14.8944 | −0.563359 | ||||||||
\(700\) | 14.7619 | 0.557949 | ||||||||
\(701\) | 6.26342 | 0.236566 | 0.118283 | − | 0.992980i | \(-0.462261\pi\) | ||||
0.118283 | + | 0.992980i | \(0.462261\pi\) | |||||||
\(702\) | 0.0298243 | 0.00112565 | ||||||||
\(703\) | −11.0359 | −0.416228 | ||||||||
\(704\) | −36.7520 | −1.38514 | ||||||||
\(705\) | 0.537069 | 0.0202272 | ||||||||
\(706\) | −0.224212 | −0.00843834 | ||||||||
\(707\) | −20.6882 | −0.778061 | ||||||||
\(708\) | −25.1608 | −0.945600 | ||||||||
\(709\) | −17.8043 | −0.668656 | −0.334328 | − | 0.942457i | \(-0.608509\pi\) | ||||
−0.334328 | + | 0.942457i | \(0.608509\pi\) | |||||||
\(710\) | 0.695178 | 0.0260896 | ||||||||
\(711\) | 14.2734 | 0.535293 | ||||||||
\(712\) | 1.96278 | 0.0735583 | ||||||||
\(713\) | −21.5082 | −0.805489 | ||||||||
\(714\) | 0.162916 | 0.00609696 | ||||||||
\(715\) | −14.0954 | −0.527139 | ||||||||
\(716\) | −43.5909 | −1.62907 | ||||||||
\(717\) | −9.00916 | −0.336453 | ||||||||
\(718\) | 0.119668 | 0.00446596 | ||||||||
\(719\) | −43.8075 | −1.63375 | −0.816873 | − | 0.576818i | \(-0.804294\pi\) | ||||
−0.816873 | + | 0.576818i | \(0.804294\pi\) | |||||||
\(720\) | 12.2238 | 0.455555 | ||||||||
\(721\) | −1.69214 | −0.0630188 | ||||||||
\(722\) | −0.106038 | −0.00394631 | ||||||||
\(723\) | 18.5937 | 0.691506 | ||||||||
\(724\) | 23.2181 | 0.862896 | ||||||||
\(725\) | −2.58750 | −0.0960972 | ||||||||
\(726\) | −0.304742 | −0.0113100 | ||||||||
\(727\) | −15.0653 | −0.558740 | −0.279370 | − | 0.960184i | \(-0.590126\pi\) | ||||
−0.279370 | + | 0.960184i | \(0.590126\pi\) | |||||||
\(728\) | −0.201823 | −0.00748007 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0.241083 | 0.00892288 | ||||||||
\(731\) | 28.4767 | 1.05325 | ||||||||
\(732\) | 25.3989 | 0.938772 | ||||||||
\(733\) | 3.75227 | 0.138593 | 0.0692966 | − | 0.997596i | \(-0.477925\pi\) | ||||
0.0692966 | + | 0.997596i | \(0.477925\pi\) | |||||||
\(734\) | −0.854731 | −0.0315487 | ||||||||
\(735\) | 12.6583 | 0.466908 | ||||||||
\(736\) | 1.55039 | 0.0571480 | ||||||||
\(737\) | −24.6060 | −0.906375 | ||||||||
\(738\) | −0.102724 | −0.00378132 | ||||||||
\(739\) | −9.36283 | −0.344417 | −0.172209 | − | 0.985061i | \(-0.555090\pi\) | ||||
−0.172209 | + | 0.985061i | \(0.555090\pi\) | |||||||
\(740\) | 17.1785 | 0.631494 | ||||||||
\(741\) | 3.92996 | 0.144371 | ||||||||
\(742\) | 0.0129003 | 0.000473585 0 | ||||||||
\(743\) | 26.7907 | 0.982854 | 0.491427 | − | 0.870919i | \(-0.336475\pi\) | ||||
0.491427 | + | 0.870919i | \(0.336475\pi\) | |||||||
\(744\) | −0.591823 | −0.0216973 | ||||||||
\(745\) | 4.64855 | 0.170310 | ||||||||
\(746\) | −0.322609 | −0.0118116 | ||||||||
\(747\) | −4.88639 | −0.178784 | ||||||||
\(748\) | −29.7264 | −1.08691 | ||||||||
\(749\) | −19.9438 | −0.728730 | ||||||||
\(750\) | 0.0580581 | 0.00211998 | ||||||||
\(751\) | −18.4998 | −0.675067 | −0.337534 | − | 0.941313i | \(-0.609593\pi\) | ||||
−0.337534 | + | 0.941313i | \(0.609593\pi\) | |||||||
\(752\) | −0.701105 | −0.0255667 | ||||||||
\(753\) | −1.63413 | −0.0595510 | ||||||||
\(754\) | 0.0176840 | 0.000644014 0 | ||||||||
\(755\) | 16.5726 | 0.603137 | ||||||||
\(756\) | −3.38278 | −0.123031 | ||||||||
\(757\) | −17.3037 | −0.628912 | −0.314456 | − | 0.949272i | \(-0.601822\pi\) | ||||
−0.314456 | + | 0.949272i | \(0.601822\pi\) | |||||||
\(758\) | −0.0347970 | −0.00126388 | ||||||||
\(759\) | −19.9663 | −0.724730 | ||||||||
\(760\) | −1.43433 | −0.0520286 | ||||||||
\(761\) | 27.2794 | 0.988879 | 0.494439 | − | 0.869212i | \(-0.335373\pi\) | ||||
0.494439 | + | 0.869212i | \(0.335373\pi\) | |||||||
\(762\) | 0.452545 | 0.0163940 | ||||||||
\(763\) | 15.4249 | 0.558420 | ||||||||
\(764\) | −24.3470 | −0.880844 | ||||||||
\(765\) | 9.87829 | 0.357150 | ||||||||
\(766\) | 0.516834 | 0.0186740 | ||||||||
\(767\) | 12.5860 | 0.454454 | ||||||||
\(768\) | −15.9289 | −0.574784 | ||||||||
\(769\) | −34.8016 | −1.25498 | −0.627489 | − | 0.778626i | \(-0.715917\pi\) | ||||
−0.627489 | + | 0.778626i | \(0.715917\pi\) | |||||||
\(770\) | −0.711354 | −0.0256354 | ||||||||
\(771\) | −10.9198 | −0.393266 | ||||||||
\(772\) | −38.2194 | −1.37555 | ||||||||
\(773\) | 54.2257 | 1.95036 | 0.975181 | − | 0.221409i | \(-0.0710656\pi\) | ||||
0.975181 | + | 0.221409i | \(0.0710656\pi\) | |||||||
\(774\) | 0.263090 | 0.00945659 | ||||||||
\(775\) | −21.6535 | −0.777815 | ||||||||
\(776\) | −1.03269 | −0.0370713 | ||||||||
\(777\) | −4.75181 | −0.170470 | ||||||||
\(778\) | 0.883115 | 0.0316612 | ||||||||
\(779\) | −13.5360 | −0.484977 | ||||||||
\(780\) | −6.11736 | −0.219037 | ||||||||
\(781\) | 35.0873 | 1.25552 | ||||||||
\(782\) | 0.417322 | 0.0149234 | ||||||||
\(783\) | 0.592940 | 0.0211899 | ||||||||
\(784\) | −16.5245 | −0.590161 | ||||||||
\(785\) | 53.6233 | 1.91390 | ||||||||
\(786\) | 0.168537 | 0.00601150 | ||||||||
\(787\) | 47.3647 | 1.68837 | 0.844184 | − | 0.536054i | \(-0.180086\pi\) | ||||
0.844184 | + | 0.536054i | \(0.180086\pi\) | |||||||
\(788\) | 29.5939 | 1.05424 | ||||||||
\(789\) | −11.6090 | −0.413290 | ||||||||
\(790\) | 1.30264 | 0.0463458 | ||||||||
\(791\) | −18.4483 | −0.655947 | ||||||||
\(792\) | −0.549395 | −0.0195219 | ||||||||
\(793\) | −12.7051 | −0.451172 | ||||||||
\(794\) | 0.160029 | 0.00567923 | ||||||||
\(795\) | 0.782203 | 0.0277419 | ||||||||
\(796\) | −20.1730 | −0.715012 | ||||||||
\(797\) | −24.9570 | −0.884022 | −0.442011 | − | 0.897010i | \(-0.645735\pi\) | ||||
−0.442011 | + | 0.897010i | \(0.645735\pi\) | |||||||
\(798\) | 0.198333 | 0.00702093 | ||||||||
\(799\) | −0.566575 | −0.0200440 | ||||||||
\(800\) | 1.56086 | 0.0551846 | ||||||||
\(801\) | −16.4565 | −0.581463 | ||||||||
\(802\) | −0.286486 | −0.0101162 | ||||||||
\(803\) | 12.1680 | 0.429400 | ||||||||
\(804\) | −10.6789 | −0.376617 | ||||||||
\(805\) | −22.4445 | −0.791066 | ||||||||
\(806\) | 0.147989 | 0.00521268 | ||||||||
\(807\) | −1.35757 | −0.0477887 | ||||||||
\(808\) | −1.45821 | −0.0512996 | ||||||||
\(809\) | −44.9595 | −1.58069 | −0.790346 | − | 0.612660i | \(-0.790099\pi\) | ||||
−0.790346 | + | 0.612660i | \(0.790099\pi\) | |||||||
\(810\) | 0.0912635 | 0.00320667 | ||||||||
\(811\) | −38.0789 | −1.33713 | −0.668566 | − | 0.743652i | \(-0.733092\pi\) | ||||
−0.668566 | + | 0.743652i | \(0.733092\pi\) | |||||||
\(812\) | −2.00579 | −0.0703894 | ||||||||
\(813\) | 20.6130 | 0.722931 | ||||||||
\(814\) | −0.385783 | −0.0135217 | ||||||||
\(815\) | 5.57386 | 0.195244 | ||||||||
\(816\) | −12.8954 | −0.451429 | ||||||||
\(817\) | 34.6675 | 1.21286 | ||||||||
\(818\) | −0.540284 | −0.0188906 | ||||||||
\(819\) | 1.69214 | 0.0591283 | ||||||||
\(820\) | 21.0700 | 0.735798 | ||||||||
\(821\) | −52.7186 | −1.83989 | −0.919946 | − | 0.392044i | \(-0.871768\pi\) | ||||
−0.919946 | + | 0.392044i | \(0.871768\pi\) | |||||||
\(822\) | −0.131956 | −0.00460250 | ||||||||
\(823\) | −1.17106 | −0.0408206 | −0.0204103 | − | 0.999792i | \(-0.506497\pi\) | ||||
−0.0204103 | + | 0.999792i | \(0.506497\pi\) | |||||||
\(824\) | −0.119271 | −0.00415499 | ||||||||
\(825\) | −20.1011 | −0.699831 | ||||||||
\(826\) | 0.635177 | 0.0221007 | ||||||||
\(827\) | −52.3926 | −1.82187 | −0.910934 | − | 0.412552i | \(-0.864638\pi\) | ||||
−0.910934 | + | 0.412552i | \(0.864638\pi\) | |||||||
\(828\) | −8.66529 | −0.301140 | ||||||||
\(829\) | −12.5108 | −0.434516 | −0.217258 | − | 0.976114i | \(-0.569711\pi\) | ||||
−0.217258 | + | 0.976114i | \(0.569711\pi\) | |||||||
\(830\) | −0.445949 | −0.0154791 | ||||||||
\(831\) | −24.1056 | −0.836215 | ||||||||
\(832\) | 7.97866 | 0.276610 | ||||||||
\(833\) | −13.3537 | −0.462680 | ||||||||
\(834\) | −0.416832 | −0.0144337 | ||||||||
\(835\) | −60.6676 | −2.09949 | ||||||||
\(836\) | −36.1890 | −1.25162 | ||||||||
\(837\) | 4.96202 | 0.171512 | ||||||||
\(838\) | −0.211963 | −0.00732215 | ||||||||
\(839\) | 6.26052 | 0.216137 | 0.108069 | − | 0.994143i | \(-0.465533\pi\) | ||||
0.108069 | + | 0.994143i | \(0.465533\pi\) | |||||||
\(840\) | −0.617587 | −0.0213088 | ||||||||
\(841\) | −28.6484 | −0.987877 | ||||||||
\(842\) | −0.568592 | −0.0195950 | ||||||||
\(843\) | 18.7524 | 0.645867 | ||||||||
\(844\) | −12.5344 | −0.431452 | ||||||||
\(845\) | 3.06004 | 0.105269 | ||||||||
\(846\) | −0.00523447 | −0.000179965 0 | ||||||||
\(847\) | −17.2902 | −0.594097 | ||||||||
\(848\) | −1.02111 | −0.0350651 | ||||||||
\(849\) | −27.8394 | −0.955445 | ||||||||
\(850\) | 0.420140 | 0.0144107 | ||||||||
\(851\) | −12.1722 | −0.417256 | ||||||||
\(852\) | 15.2277 | 0.521694 | ||||||||
\(853\) | −32.1438 | −1.10058 | −0.550291 | − | 0.834973i | \(-0.685483\pi\) | ||||
−0.550291 | + | 0.834973i | \(0.685483\pi\) | |||||||
\(854\) | −0.641190 | −0.0219411 | ||||||||
\(855\) | 12.0258 | 0.411275 | ||||||||
\(856\) | −1.40574 | −0.0480471 | ||||||||
\(857\) | 18.3549 | 0.626991 | 0.313496 | − | 0.949590i | \(-0.398500\pi\) | ||||
0.313496 | + | 0.949590i | \(0.398500\pi\) | |||||||
\(858\) | 0.137379 | 0.00469005 | ||||||||
\(859\) | 25.4143 | 0.867126 | 0.433563 | − | 0.901123i | \(-0.357256\pi\) | ||||
0.433563 | + | 0.901123i | \(0.357256\pi\) | |||||||
\(860\) | −53.9633 | −1.84013 | ||||||||
\(861\) | −5.82826 | −0.198627 | ||||||||
\(862\) | 1.08873 | 0.0370822 | ||||||||
\(863\) | 12.3570 | 0.420637 | 0.210319 | − | 0.977633i | \(-0.432550\pi\) | ||||
0.210319 | + | 0.977633i | \(0.432550\pi\) | |||||||
\(864\) | −0.357679 | −0.0121685 | ||||||||
\(865\) | −46.3152 | −1.57476 | ||||||||
\(866\) | 0.760733 | 0.0258508 | ||||||||
\(867\) | 6.57900 | 0.223435 | ||||||||
\(868\) | −16.7854 | −0.569735 | ||||||||
\(869\) | 65.7472 | 2.23032 | ||||||||
\(870\) | 0.0541138 | 0.00183463 | ||||||||
\(871\) | 5.34184 | 0.181001 | ||||||||
\(872\) | 1.08722 | 0.0368181 | ||||||||
\(873\) | 8.65835 | 0.293041 | ||||||||
\(874\) | 0.508048 | 0.0171850 | ||||||||
\(875\) | 3.29405 | 0.111359 | ||||||||
\(876\) | 5.28088 | 0.178424 | ||||||||
\(877\) | 39.3862 | 1.32998 | 0.664990 | − | 0.746853i | \(-0.268436\pi\) | ||||
0.664990 | + | 0.746853i | \(0.268436\pi\) | |||||||
\(878\) | −0.138972 | −0.00469009 | ||||||||
\(879\) | −7.02330 | −0.236890 | ||||||||
\(880\) | 56.3065 | 1.89809 | ||||||||
\(881\) | −45.8855 | −1.54592 | −0.772961 | − | 0.634453i | \(-0.781225\pi\) | ||||
−0.772961 | + | 0.634453i | \(0.781225\pi\) | |||||||
\(882\) | −0.123373 | −0.00415417 | ||||||||
\(883\) | −21.3311 | −0.717850 | −0.358925 | − | 0.933366i | \(-0.616857\pi\) | ||||
−0.358925 | + | 0.933366i | \(0.616857\pi\) | |||||||
\(884\) | 6.45344 | 0.217053 | ||||||||
\(885\) | 38.5136 | 1.29462 | ||||||||
\(886\) | −0.00427874 | −0.000143747 0 | ||||||||
\(887\) | −29.2078 | −0.980701 | −0.490351 | − | 0.871525i | \(-0.663131\pi\) | ||||
−0.490351 | + | 0.871525i | \(0.663131\pi\) | |||||||
\(888\) | −0.334931 | −0.0112395 | ||||||||
\(889\) | 25.6761 | 0.861148 | ||||||||
\(890\) | −1.50188 | −0.0503432 | ||||||||
\(891\) | 4.60629 | 0.154316 | ||||||||
\(892\) | −48.6174 | −1.62783 | ||||||||
\(893\) | −0.689749 | −0.0230816 | ||||||||
\(894\) | −0.0453065 | −0.00151528 | ||||||||
\(895\) | 66.7247 | 2.23036 | ||||||||
\(896\) | 1.61315 | 0.0538916 | ||||||||
\(897\) | 4.33457 | 0.144727 | ||||||||
\(898\) | −0.0550922 | −0.00183845 | ||||||||
\(899\) | 2.94218 | 0.0981272 | ||||||||
\(900\) | −8.72380 | −0.290793 | ||||||||
\(901\) | −0.825177 | −0.0274906 | ||||||||
\(902\) | −0.473176 | −0.0157550 | ||||||||
\(903\) | 14.9270 | 0.496739 | ||||||||
\(904\) | −1.30033 | −0.0432483 | ||||||||
\(905\) | −35.5400 | −1.18139 | ||||||||
\(906\) | −0.161522 | −0.00536622 | ||||||||
\(907\) | −38.6611 | −1.28372 | −0.641860 | − | 0.766822i | \(-0.721837\pi\) | ||||
−0.641860 | + | 0.766822i | \(0.721837\pi\) | |||||||
\(908\) | −0.225501 | −0.00748352 | ||||||||
\(909\) | 12.2260 | 0.405512 | ||||||||
\(910\) | 0.154431 | 0.00511934 | ||||||||
\(911\) | −23.7854 | −0.788046 | −0.394023 | − | 0.919101i | \(-0.628917\pi\) | ||||
−0.394023 | + | 0.919101i | \(0.628917\pi\) | |||||||
\(912\) | −15.6989 | −0.519842 | ||||||||
\(913\) | −22.5081 | −0.744910 | ||||||||
\(914\) | −0.0526433 | −0.00174128 | ||||||||
\(915\) | −38.8782 | −1.28527 | ||||||||
\(916\) | 4.15295 | 0.137217 | ||||||||
\(917\) | 9.56228 | 0.315774 | ||||||||
\(918\) | −0.0962775 | −0.00317763 | ||||||||
\(919\) | 51.7768 | 1.70796 | 0.853979 | − | 0.520307i | \(-0.174182\pi\) | ||||
0.853979 | + | 0.520307i | \(0.174182\pi\) | |||||||
\(920\) | −1.58200 | −0.0521571 | ||||||||
\(921\) | −17.8124 | −0.586939 | ||||||||
\(922\) | 0.192077 | 0.00632571 | ||||||||
\(923\) | −7.61726 | −0.250725 | ||||||||
\(924\) | −15.5821 | −0.512613 | ||||||||
\(925\) | −12.2543 | −0.402920 | ||||||||
\(926\) | 0.490083 | 0.0161051 | ||||||||
\(927\) | 1.00000 | 0.0328443 | ||||||||
\(928\) | −0.212082 | −0.00696195 | ||||||||
\(929\) | 19.1854 | 0.629452 | 0.314726 | − | 0.949183i | \(-0.398087\pi\) | ||||
0.314726 | + | 0.949183i | \(0.398087\pi\) | |||||||
\(930\) | 0.452851 | 0.0148496 | ||||||||
\(931\) | −16.2569 | −0.532797 | ||||||||
\(932\) | −29.7756 | −0.975332 | ||||||||
\(933\) | −5.03954 | −0.164987 | ||||||||
\(934\) | −0.281545 | −0.00921243 | ||||||||
\(935\) | 45.5022 | 1.48808 | ||||||||
\(936\) | 0.119271 | 0.00389848 | ||||||||
\(937\) | −36.9394 | −1.20676 | −0.603379 | − | 0.797454i | \(-0.706179\pi\) | ||||
−0.603379 | + | 0.797454i | \(0.706179\pi\) | |||||||
\(938\) | 0.269587 | 0.00880232 | ||||||||
\(939\) | 19.7835 | 0.645612 | ||||||||
\(940\) | 1.07366 | 0.0350189 | ||||||||
\(941\) | 46.4950 | 1.51569 | 0.757846 | − | 0.652433i | \(-0.226252\pi\) | ||||
0.757846 | + | 0.652433i | \(0.226252\pi\) | |||||||
\(942\) | −0.522633 | −0.0170283 | ||||||||
\(943\) | −14.9296 | −0.486174 | ||||||||
\(944\) | −50.2768 | −1.63637 | ||||||||
\(945\) | 5.17803 | 0.168441 | ||||||||
\(946\) | 1.21187 | 0.0394013 | ||||||||
\(947\) | −29.6802 | −0.964477 | −0.482238 | − | 0.876040i | \(-0.660176\pi\) | ||||
−0.482238 | + | 0.876040i | \(0.660176\pi\) | |||||||
\(948\) | 28.5340 | 0.926742 | ||||||||
\(949\) | −2.64161 | −0.0857504 | ||||||||
\(950\) | 0.511479 | 0.0165946 | ||||||||
\(951\) | −7.66086 | −0.248421 | ||||||||
\(952\) | 0.651517 | 0.0211158 | ||||||||
\(953\) | 56.1856 | 1.82003 | 0.910015 | − | 0.414576i | \(-0.136070\pi\) | ||||
0.910015 | + | 0.414576i | \(0.136070\pi\) | |||||||
\(954\) | −0.00762364 | −0.000246825 0 | ||||||||
\(955\) | 37.2680 | 1.20596 | ||||||||
\(956\) | −18.0103 | −0.582495 | ||||||||
\(957\) | 2.73125 | 0.0882888 | ||||||||
\(958\) | −0.382502 | −0.0123581 | ||||||||
\(959\) | −7.48681 | −0.241762 | ||||||||
\(960\) | 24.4150 | 0.787991 | ||||||||
\(961\) | −6.37837 | −0.205754 | ||||||||
\(962\) | 0.0837513 | 0.00270025 | ||||||||
\(963\) | 11.7861 | 0.379802 | ||||||||
\(964\) | 37.1708 | 1.19719 | ||||||||
\(965\) | 58.5025 | 1.88326 | ||||||||
\(966\) | 0.218753 | 0.00703826 | ||||||||
\(967\) | 11.0987 | 0.356911 | 0.178455 | − | 0.983948i | \(-0.442890\pi\) | ||||
0.178455 | + | 0.983948i | \(0.442890\pi\) | |||||||
\(968\) | −1.21870 | −0.0391703 | ||||||||
\(969\) | −12.6865 | −0.407550 | ||||||||
\(970\) | 0.790191 | 0.0253715 | ||||||||
\(971\) | 24.0228 | 0.770930 | 0.385465 | − | 0.922722i | \(-0.374041\pi\) | ||||
0.385465 | + | 0.922722i | \(0.374041\pi\) | |||||||
\(972\) | 1.99911 | 0.0641215 | ||||||||
\(973\) | −23.6498 | −0.758179 | ||||||||
\(974\) | 1.05274 | 0.0337318 | ||||||||
\(975\) | 4.36384 | 0.139755 | ||||||||
\(976\) | 50.7527 | 1.62455 | ||||||||
\(977\) | −31.4465 | −1.00606 | −0.503031 | − | 0.864269i | \(-0.667782\pi\) | ||||
−0.503031 | + | 0.864269i | \(0.667782\pi\) | |||||||
\(978\) | −0.0543250 | −0.00173712 | ||||||||
\(979\) | −75.8035 | −2.42269 | ||||||||
\(980\) | 25.3053 | 0.808349 | ||||||||
\(981\) | −9.11561 | −0.291039 | ||||||||
\(982\) | 0.892267 | 0.0284734 | ||||||||
\(983\) | −36.8778 | −1.17622 | −0.588110 | − | 0.808781i | \(-0.700128\pi\) | ||||
−0.588110 | + | 0.808781i | \(0.700128\pi\) | |||||||
\(984\) | −0.410805 | −0.0130960 | ||||||||
\(985\) | −45.2994 | −1.44336 | ||||||||
\(986\) | −0.0570868 | −0.00181801 | ||||||||
\(987\) | −0.296989 | −0.00945326 | ||||||||
\(988\) | 7.85643 | 0.249946 | ||||||||
\(989\) | 38.2367 | 1.21586 | ||||||||
\(990\) | 0.420386 | 0.0133608 | ||||||||
\(991\) | 6.91455 | 0.219648 | 0.109824 | − | 0.993951i | \(-0.464971\pi\) | ||||
0.109824 | + | 0.993951i | \(0.464971\pi\) | |||||||
\(992\) | −1.77481 | −0.0563503 | ||||||||
\(993\) | 8.34360 | 0.264776 | ||||||||
\(994\) | −0.384421 | −0.0121931 | ||||||||
\(995\) | 30.8788 | 0.978924 | ||||||||
\(996\) | −9.76844 | −0.309525 | ||||||||
\(997\) | −18.8800 | −0.597935 | −0.298968 | − | 0.954263i | \(-0.596642\pi\) | ||||
−0.298968 | + | 0.954263i | \(0.596642\pi\) | |||||||
\(998\) | −0.130041 | −0.00411637 | ||||||||
\(999\) | 2.80816 | 0.0888461 |
(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 | 4017.2.a.g.1.12 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4017.2.a.g.1.12 | ✓ | 24 | 1.1 | even | 1 | trivial |