Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6034,2,Mod(1,6034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6034, 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("6034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6034 = 2 \cdot 7 \cdot 431 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6034.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: | \(48.1817325796\) |
Analytic rank: | \(1\) |
Dimension: | \(25\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Character | \(\chi\) | \(=\) | 6034.1 |
$q$-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 | ||||||||
\(3\) | −2.93664 | −1.69547 | −0.847735 | − | 0.530419i | \(-0.822034\pi\) | ||||
−0.847735 | + | 0.530419i | \(0.822034\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.14962 | 0.514126 | 0.257063 | − | 0.966395i | \(-0.417245\pi\) | ||||
0.257063 | + | 0.966395i | \(0.417245\pi\) | |||||||
\(6\) | 2.93664 | 1.19888 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 5.62386 | 1.87462 | ||||||||
\(10\) | −1.14962 | −0.363542 | ||||||||
\(11\) | 1.78532 | 0.538293 | 0.269146 | − | 0.963099i | \(-0.413258\pi\) | ||||
0.269146 | + | 0.963099i | \(0.413258\pi\) | |||||||
\(12\) | −2.93664 | −0.847735 | ||||||||
\(13\) | −1.58629 | −0.439957 | −0.219979 | − | 0.975505i | \(-0.570599\pi\) | ||||
−0.219979 | + | 0.975505i | \(0.570599\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | −3.37602 | −0.871685 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.75836 | 1.15407 | 0.577036 | − | 0.816718i | \(-0.304209\pi\) | ||||
0.577036 | + | 0.816718i | \(0.304209\pi\) | |||||||
\(18\) | −5.62386 | −1.32556 | ||||||||
\(19\) | −8.25798 | −1.89451 | −0.947255 | − | 0.320481i | \(-0.896155\pi\) | ||||
−0.947255 | + | 0.320481i | \(0.896155\pi\) | |||||||
\(20\) | 1.14962 | 0.257063 | ||||||||
\(21\) | 2.93664 | 0.640828 | ||||||||
\(22\) | −1.78532 | −0.380631 | ||||||||
\(23\) | 5.21027 | 1.08642 | 0.543208 | − | 0.839598i | \(-0.317209\pi\) | ||||
0.543208 | + | 0.839598i | \(0.317209\pi\) | |||||||
\(24\) | 2.93664 | 0.599439 | ||||||||
\(25\) | −3.67837 | −0.735675 | ||||||||
\(26\) | 1.58629 | 0.311097 | ||||||||
\(27\) | −7.70535 | −1.48289 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | 5.51319 | 1.02377 | 0.511887 | − | 0.859053i | \(-0.328947\pi\) | ||||
0.511887 | + | 0.859053i | \(0.328947\pi\) | |||||||
\(30\) | 3.37602 | 0.616374 | ||||||||
\(31\) | −4.05434 | −0.728181 | −0.364090 | − | 0.931364i | \(-0.618620\pi\) | ||||
−0.364090 | + | 0.931364i | \(0.618620\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −5.24283 | −0.912660 | ||||||||
\(34\) | −4.75836 | −0.816053 | ||||||||
\(35\) | −1.14962 | −0.194321 | ||||||||
\(36\) | 5.62386 | 0.937311 | ||||||||
\(37\) | 9.55503 | 1.57084 | 0.785419 | − | 0.618965i | \(-0.212448\pi\) | ||||
0.785419 | + | 0.618965i | \(0.212448\pi\) | |||||||
\(38\) | 8.25798 | 1.33962 | ||||||||
\(39\) | 4.65836 | 0.745935 | ||||||||
\(40\) | −1.14962 | −0.181771 | ||||||||
\(41\) | 3.24985 | 0.507542 | 0.253771 | − | 0.967264i | \(-0.418329\pi\) | ||||
0.253771 | + | 0.967264i | \(0.418329\pi\) | |||||||
\(42\) | −2.93664 | −0.453134 | ||||||||
\(43\) | −9.79019 | −1.49299 | −0.746495 | − | 0.665391i | \(-0.768265\pi\) | ||||
−0.746495 | + | 0.665391i | \(0.768265\pi\) | |||||||
\(44\) | 1.78532 | 0.269146 | ||||||||
\(45\) | 6.46531 | 0.963791 | ||||||||
\(46\) | −5.21027 | −0.768212 | ||||||||
\(47\) | −2.57995 | −0.376324 | −0.188162 | − | 0.982138i | \(-0.560253\pi\) | ||||
−0.188162 | + | 0.982138i | \(0.560253\pi\) | |||||||
\(48\) | −2.93664 | −0.423868 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 3.67837 | 0.520201 | ||||||||
\(51\) | −13.9736 | −1.95670 | ||||||||
\(52\) | −1.58629 | −0.219979 | ||||||||
\(53\) | −2.33214 | −0.320344 | −0.160172 | − | 0.987089i | \(-0.551205\pi\) | ||||
−0.160172 | + | 0.987089i | \(0.551205\pi\) | |||||||
\(54\) | 7.70535 | 1.04856 | ||||||||
\(55\) | 2.05243 | 0.276750 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 24.2507 | 3.21209 | ||||||||
\(58\) | −5.51319 | −0.723917 | ||||||||
\(59\) | −5.81789 | −0.757425 | −0.378712 | − | 0.925514i | \(-0.623633\pi\) | ||||
−0.378712 | + | 0.925514i | \(0.623633\pi\) | |||||||
\(60\) | −3.37602 | −0.435843 | ||||||||
\(61\) | −11.6438 | −1.49083 | −0.745415 | − | 0.666601i | \(-0.767749\pi\) | ||||
−0.745415 | + | 0.666601i | \(0.767749\pi\) | |||||||
\(62\) | 4.05434 | 0.514902 | ||||||||
\(63\) | −5.62386 | −0.708540 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.82363 | −0.226193 | ||||||||
\(66\) | 5.24283 | 0.645348 | ||||||||
\(67\) | 8.12281 | 0.992360 | 0.496180 | − | 0.868220i | \(-0.334736\pi\) | ||||
0.496180 | + | 0.868220i | \(0.334736\pi\) | |||||||
\(68\) | 4.75836 | 0.577036 | ||||||||
\(69\) | −15.3007 | −1.84199 | ||||||||
\(70\) | 1.14962 | 0.137406 | ||||||||
\(71\) | −3.84447 | −0.456255 | −0.228128 | − | 0.973631i | \(-0.573260\pi\) | ||||
−0.228128 | + | 0.973631i | \(0.573260\pi\) | |||||||
\(72\) | −5.62386 | −0.662779 | ||||||||
\(73\) | −8.13616 | −0.952265 | −0.476133 | − | 0.879373i | \(-0.657962\pi\) | ||||
−0.476133 | + | 0.879373i | \(0.657962\pi\) | |||||||
\(74\) | −9.55503 | −1.11075 | ||||||||
\(75\) | 10.8021 | 1.24732 | ||||||||
\(76\) | −8.25798 | −0.947255 | ||||||||
\(77\) | −1.78532 | −0.203456 | ||||||||
\(78\) | −4.65836 | −0.527456 | ||||||||
\(79\) | −2.39952 | −0.269967 | −0.134984 | − | 0.990848i | \(-0.543098\pi\) | ||||
−0.134984 | + | 0.990848i | \(0.543098\pi\) | |||||||
\(80\) | 1.14962 | 0.128531 | ||||||||
\(81\) | 5.75625 | 0.639584 | ||||||||
\(82\) | −3.24985 | −0.358886 | ||||||||
\(83\) | −1.26492 | −0.138843 | −0.0694214 | − | 0.997587i | \(-0.522115\pi\) | ||||
−0.0694214 | + | 0.997587i | \(0.522115\pi\) | |||||||
\(84\) | 2.93664 | 0.320414 | ||||||||
\(85\) | 5.47031 | 0.593339 | ||||||||
\(86\) | 9.79019 | 1.05570 | ||||||||
\(87\) | −16.1903 | −1.73578 | ||||||||
\(88\) | −1.78532 | −0.190315 | ||||||||
\(89\) | −0.725700 | −0.0769240 | −0.0384620 | − | 0.999260i | \(-0.512246\pi\) | ||||
−0.0384620 | + | 0.999260i | \(0.512246\pi\) | |||||||
\(90\) | −6.46531 | −0.681503 | ||||||||
\(91\) | 1.58629 | 0.166288 | ||||||||
\(92\) | 5.21027 | 0.543208 | ||||||||
\(93\) | 11.9061 | 1.23461 | ||||||||
\(94\) | 2.57995 | 0.266101 | ||||||||
\(95\) | −9.49353 | −0.974016 | ||||||||
\(96\) | 2.93664 | 0.299720 | ||||||||
\(97\) | −8.02371 | −0.814685 | −0.407342 | − | 0.913276i | \(-0.633544\pi\) | ||||
−0.407342 | + | 0.913276i | \(0.633544\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 10.0404 | 1.00910 | ||||||||
\(100\) | −3.67837 | −0.367837 | ||||||||
\(101\) | 9.51584 | 0.946862 | 0.473431 | − | 0.880831i | \(-0.343015\pi\) | ||||
0.473431 | + | 0.880831i | \(0.343015\pi\) | |||||||
\(102\) | 13.9736 | 1.38359 | ||||||||
\(103\) | 9.23894 | 0.910339 | 0.455170 | − | 0.890405i | \(-0.349579\pi\) | ||||
0.455170 | + | 0.890405i | \(0.349579\pi\) | |||||||
\(104\) | 1.58629 | 0.155548 | ||||||||
\(105\) | 3.37602 | 0.329466 | ||||||||
\(106\) | 2.33214 | 0.226517 | ||||||||
\(107\) | 18.3654 | 1.77545 | 0.887724 | − | 0.460376i | \(-0.152285\pi\) | ||||
0.887724 | + | 0.460376i | \(0.152285\pi\) | |||||||
\(108\) | −7.70535 | −0.741447 | ||||||||
\(109\) | −1.35820 | −0.130092 | −0.0650458 | − | 0.997882i | \(-0.520719\pi\) | ||||
−0.0650458 | + | 0.997882i | \(0.520719\pi\) | |||||||
\(110\) | −2.05243 | −0.195692 | ||||||||
\(111\) | −28.0597 | −2.66331 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | 15.4891 | 1.45709 | 0.728546 | − | 0.684997i | \(-0.240196\pi\) | ||||
0.728546 | + | 0.684997i | \(0.240196\pi\) | |||||||
\(114\) | −24.2507 | −2.27129 | ||||||||
\(115\) | 5.98983 | 0.558555 | ||||||||
\(116\) | 5.51319 | 0.511887 | ||||||||
\(117\) | −8.92107 | −0.824753 | ||||||||
\(118\) | 5.81789 | 0.535580 | ||||||||
\(119\) | −4.75836 | −0.436199 | ||||||||
\(120\) | 3.37602 | 0.308187 | ||||||||
\(121\) | −7.81265 | −0.710241 | ||||||||
\(122\) | 11.6438 | 1.05418 | ||||||||
\(123\) | −9.54365 | −0.860522 | ||||||||
\(124\) | −4.05434 | −0.364090 | ||||||||
\(125\) | −9.97683 | −0.892355 | ||||||||
\(126\) | 5.62386 | 0.501014 | ||||||||
\(127\) | −14.3508 | −1.27343 | −0.636714 | − | 0.771100i | \(-0.719707\pi\) | ||||
−0.636714 | + | 0.771100i | \(0.719707\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 28.7503 | 2.53132 | ||||||||
\(130\) | 1.82363 | 0.159943 | ||||||||
\(131\) | 22.3860 | 1.95588 | 0.977939 | − | 0.208890i | \(-0.0669852\pi\) | ||||
0.977939 | + | 0.208890i | \(0.0669852\pi\) | |||||||
\(132\) | −5.24283 | −0.456330 | ||||||||
\(133\) | 8.25798 | 0.716057 | ||||||||
\(134\) | −8.12281 | −0.701704 | ||||||||
\(135\) | −8.85822 | −0.762394 | ||||||||
\(136\) | −4.75836 | −0.408026 | ||||||||
\(137\) | −1.74164 | −0.148798 | −0.0743990 | − | 0.997229i | \(-0.523704\pi\) | ||||
−0.0743990 | + | 0.997229i | \(0.523704\pi\) | |||||||
\(138\) | 15.3007 | 1.30248 | ||||||||
\(139\) | 12.4073 | 1.05237 | 0.526185 | − | 0.850370i | \(-0.323622\pi\) | ||||
0.526185 | + | 0.850370i | \(0.323622\pi\) | |||||||
\(140\) | −1.14962 | −0.0971606 | ||||||||
\(141\) | 7.57638 | 0.638046 | ||||||||
\(142\) | 3.84447 | 0.322621 | ||||||||
\(143\) | −2.83203 | −0.236826 | ||||||||
\(144\) | 5.62386 | 0.468655 | ||||||||
\(145\) | 6.33807 | 0.526348 | ||||||||
\(146\) | 8.13616 | 0.673353 | ||||||||
\(147\) | −2.93664 | −0.242210 | ||||||||
\(148\) | 9.55503 | 0.785419 | ||||||||
\(149\) | 16.8812 | 1.38296 | 0.691480 | − | 0.722395i | \(-0.256959\pi\) | ||||
0.691480 | + | 0.722395i | \(0.256959\pi\) | |||||||
\(150\) | −10.8021 | −0.881985 | ||||||||
\(151\) | −12.5442 | −1.02083 | −0.510416 | − | 0.859928i | \(-0.670508\pi\) | ||||
−0.510416 | + | 0.859928i | \(0.670508\pi\) | |||||||
\(152\) | 8.25798 | 0.669810 | ||||||||
\(153\) | 26.7604 | 2.16345 | ||||||||
\(154\) | 1.78532 | 0.143865 | ||||||||
\(155\) | −4.66095 | −0.374376 | ||||||||
\(156\) | 4.65836 | 0.372967 | ||||||||
\(157\) | 24.5152 | 1.95652 | 0.978262 | − | 0.207371i | \(-0.0664908\pi\) | ||||
0.978262 | + | 0.207371i | \(0.0664908\pi\) | |||||||
\(158\) | 2.39952 | 0.190896 | ||||||||
\(159\) | 6.84866 | 0.543134 | ||||||||
\(160\) | −1.14962 | −0.0908854 | ||||||||
\(161\) | −5.21027 | −0.410627 | ||||||||
\(162\) | −5.75625 | −0.452254 | ||||||||
\(163\) | −11.8060 | −0.924720 | −0.462360 | − | 0.886692i | \(-0.652997\pi\) | ||||
−0.462360 | + | 0.886692i | \(0.652997\pi\) | |||||||
\(164\) | 3.24985 | 0.253771 | ||||||||
\(165\) | −6.02726 | −0.469222 | ||||||||
\(166\) | 1.26492 | 0.0981767 | ||||||||
\(167\) | −20.8750 | −1.61536 | −0.807679 | − | 0.589622i | \(-0.799277\pi\) | ||||
−0.807679 | + | 0.589622i | \(0.799277\pi\) | |||||||
\(168\) | −2.93664 | −0.226567 | ||||||||
\(169\) | −10.4837 | −0.806438 | ||||||||
\(170\) | −5.47031 | −0.419554 | ||||||||
\(171\) | −46.4417 | −3.55149 | ||||||||
\(172\) | −9.79019 | −0.746495 | ||||||||
\(173\) | −6.10704 | −0.464310 | −0.232155 | − | 0.972679i | \(-0.574578\pi\) | ||||
−0.232155 | + | 0.972679i | \(0.574578\pi\) | |||||||
\(174\) | 16.1903 | 1.22738 | ||||||||
\(175\) | 3.67837 | 0.278059 | ||||||||
\(176\) | 1.78532 | 0.134573 | ||||||||
\(177\) | 17.0851 | 1.28419 | ||||||||
\(178\) | 0.725700 | 0.0543935 | ||||||||
\(179\) | 16.6851 | 1.24711 | 0.623553 | − | 0.781781i | \(-0.285689\pi\) | ||||
0.623553 | + | 0.781781i | \(0.285689\pi\) | |||||||
\(180\) | 6.46531 | 0.481895 | ||||||||
\(181\) | −11.4665 | −0.852301 | −0.426151 | − | 0.904652i | \(-0.640131\pi\) | ||||
−0.426151 | + | 0.904652i | \(0.640131\pi\) | |||||||
\(182\) | −1.58629 | −0.117584 | ||||||||
\(183\) | 34.1935 | 2.52766 | ||||||||
\(184\) | −5.21027 | −0.384106 | ||||||||
\(185\) | 10.9847 | 0.807608 | ||||||||
\(186\) | −11.9061 | −0.873001 | ||||||||
\(187\) | 8.49518 | 0.621229 | ||||||||
\(188\) | −2.57995 | −0.188162 | ||||||||
\(189\) | 7.70535 | 0.560482 | ||||||||
\(190\) | 9.49353 | 0.688733 | ||||||||
\(191\) | −16.0121 | −1.15860 | −0.579298 | − | 0.815116i | \(-0.696673\pi\) | ||||
−0.579298 | + | 0.815116i | \(0.696673\pi\) | |||||||
\(192\) | −2.93664 | −0.211934 | ||||||||
\(193\) | 20.0663 | 1.44441 | 0.722203 | − | 0.691681i | \(-0.243129\pi\) | ||||
0.722203 | + | 0.691681i | \(0.243129\pi\) | |||||||
\(194\) | 8.02371 | 0.576069 | ||||||||
\(195\) | 5.35535 | 0.383504 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 22.1819 | 1.58040 | 0.790198 | − | 0.612851i | \(-0.209977\pi\) | ||||
0.790198 | + | 0.612851i | \(0.209977\pi\) | |||||||
\(198\) | −10.0404 | −0.713538 | ||||||||
\(199\) | −7.23178 | −0.512647 | −0.256324 | − | 0.966591i | \(-0.582511\pi\) | ||||
−0.256324 | + | 0.966591i | \(0.582511\pi\) | |||||||
\(200\) | 3.67837 | 0.260100 | ||||||||
\(201\) | −23.8538 | −1.68252 | ||||||||
\(202\) | −9.51584 | −0.669532 | ||||||||
\(203\) | −5.51319 | −0.386950 | ||||||||
\(204\) | −13.9736 | −0.978348 | ||||||||
\(205\) | 3.73610 | 0.260940 | ||||||||
\(206\) | −9.23894 | −0.643707 | ||||||||
\(207\) | 29.3018 | 2.03662 | ||||||||
\(208\) | −1.58629 | −0.109989 | ||||||||
\(209\) | −14.7431 | −1.01980 | ||||||||
\(210\) | −3.37602 | −0.232968 | ||||||||
\(211\) | −26.3059 | −1.81097 | −0.905485 | − | 0.424378i | \(-0.860493\pi\) | ||||
−0.905485 | + | 0.424378i | \(0.860493\pi\) | |||||||
\(212\) | −2.33214 | −0.160172 | ||||||||
\(213\) | 11.2898 | 0.773567 | ||||||||
\(214\) | −18.3654 | −1.25543 | ||||||||
\(215\) | −11.2550 | −0.767585 | ||||||||
\(216\) | 7.70535 | 0.524282 | ||||||||
\(217\) | 4.05434 | 0.275226 | ||||||||
\(218\) | 1.35820 | 0.0919886 | ||||||||
\(219\) | 23.8930 | 1.61454 | ||||||||
\(220\) | 2.05243 | 0.138375 | ||||||||
\(221\) | −7.54814 | −0.507743 | ||||||||
\(222\) | 28.0597 | 1.88324 | ||||||||
\(223\) | 9.15737 | 0.613223 | 0.306611 | − | 0.951835i | \(-0.400805\pi\) | ||||
0.306611 | + | 0.951835i | \(0.400805\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | −20.6867 | −1.37911 | ||||||||
\(226\) | −15.4891 | −1.03032 | ||||||||
\(227\) | −10.2369 | −0.679444 | −0.339722 | − | 0.940526i | \(-0.610333\pi\) | ||||
−0.339722 | + | 0.940526i | \(0.610333\pi\) | |||||||
\(228\) | 24.2507 | 1.60604 | ||||||||
\(229\) | 0.0238752 | 0.00157772 | 0.000788859 | − | 1.00000i | \(-0.499749\pi\) | ||||
0.000788859 | 1.00000i | \(0.499749\pi\) | ||||||||
\(230\) | −5.98983 | −0.394958 | ||||||||
\(231\) | 5.24283 | 0.344953 | ||||||||
\(232\) | −5.51319 | −0.361959 | ||||||||
\(233\) | 0.281238 | 0.0184245 | 0.00921226 | − | 0.999958i | \(-0.497068\pi\) | ||||
0.00921226 | + | 0.999958i | \(0.497068\pi\) | |||||||
\(234\) | 8.92107 | 0.583189 | ||||||||
\(235\) | −2.96596 | −0.193478 | ||||||||
\(236\) | −5.81789 | −0.378712 | ||||||||
\(237\) | 7.04654 | 0.457722 | ||||||||
\(238\) | 4.75836 | 0.308439 | ||||||||
\(239\) | 5.22424 | 0.337928 | 0.168964 | − | 0.985622i | \(-0.445958\pi\) | ||||
0.168964 | + | 0.985622i | \(0.445958\pi\) | |||||||
\(240\) | −3.37602 | −0.217921 | ||||||||
\(241\) | −23.8541 | −1.53658 | −0.768290 | − | 0.640102i | \(-0.778892\pi\) | ||||
−0.768290 | + | 0.640102i | \(0.778892\pi\) | |||||||
\(242\) | 7.81265 | 0.502216 | ||||||||
\(243\) | 6.21199 | 0.398500 | ||||||||
\(244\) | −11.6438 | −0.745415 | ||||||||
\(245\) | 1.14962 | 0.0734465 | ||||||||
\(246\) | 9.54365 | 0.608481 | ||||||||
\(247\) | 13.0995 | 0.833503 | ||||||||
\(248\) | 4.05434 | 0.257451 | ||||||||
\(249\) | 3.71461 | 0.235404 | ||||||||
\(250\) | 9.97683 | 0.630990 | ||||||||
\(251\) | 11.1379 | 0.703017 | 0.351508 | − | 0.936185i | \(-0.385669\pi\) | ||||
0.351508 | + | 0.936185i | \(0.385669\pi\) | |||||||
\(252\) | −5.62386 | −0.354270 | ||||||||
\(253\) | 9.30198 | 0.584810 | ||||||||
\(254\) | 14.3508 | 0.900450 | ||||||||
\(255\) | −16.0643 | −1.00599 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −9.90011 | −0.617552 | −0.308776 | − | 0.951135i | \(-0.599919\pi\) | ||||
−0.308776 | + | 0.951135i | \(0.599919\pi\) | |||||||
\(258\) | −28.7503 | −1.78991 | ||||||||
\(259\) | −9.55503 | −0.593721 | ||||||||
\(260\) | −1.82363 | −0.113097 | ||||||||
\(261\) | 31.0054 | 1.91919 | ||||||||
\(262\) | −22.3860 | −1.38301 | ||||||||
\(263\) | 7.22031 | 0.445223 | 0.222612 | − | 0.974907i | \(-0.428542\pi\) | ||||
0.222612 | + | 0.974907i | \(0.428542\pi\) | |||||||
\(264\) | 5.24283 | 0.322674 | ||||||||
\(265\) | −2.68107 | −0.164697 | ||||||||
\(266\) | −8.25798 | −0.506329 | ||||||||
\(267\) | 2.13112 | 0.130422 | ||||||||
\(268\) | 8.12281 | 0.496180 | ||||||||
\(269\) | −1.70941 | −0.104225 | −0.0521123 | − | 0.998641i | \(-0.516595\pi\) | ||||
−0.0521123 | + | 0.998641i | \(0.516595\pi\) | |||||||
\(270\) | 8.85822 | 0.539094 | ||||||||
\(271\) | 16.5082 | 1.00280 | 0.501402 | − | 0.865214i | \(-0.332818\pi\) | ||||
0.501402 | + | 0.865214i | \(0.332818\pi\) | |||||||
\(272\) | 4.75836 | 0.288518 | ||||||||
\(273\) | −4.65836 | −0.281937 | ||||||||
\(274\) | 1.74164 | 0.105216 | ||||||||
\(275\) | −6.56706 | −0.396008 | ||||||||
\(276\) | −15.3007 | −0.920994 | ||||||||
\(277\) | 18.1539 | 1.09076 | 0.545381 | − | 0.838188i | \(-0.316385\pi\) | ||||
0.545381 | + | 0.838188i | \(0.316385\pi\) | |||||||
\(278\) | −12.4073 | −0.744138 | ||||||||
\(279\) | −22.8010 | −1.36506 | ||||||||
\(280\) | 1.14962 | 0.0687029 | ||||||||
\(281\) | −22.0851 | −1.31748 | −0.658742 | − | 0.752369i | \(-0.728911\pi\) | ||||
−0.658742 | + | 0.752369i | \(0.728911\pi\) | |||||||
\(282\) | −7.57638 | −0.451167 | ||||||||
\(283\) | 29.3599 | 1.74526 | 0.872631 | − | 0.488380i | \(-0.162412\pi\) | ||||
0.872631 | + | 0.488380i | \(0.162412\pi\) | |||||||
\(284\) | −3.84447 | −0.228128 | ||||||||
\(285\) | 27.8791 | 1.65142 | ||||||||
\(286\) | 2.83203 | 0.167461 | ||||||||
\(287\) | −3.24985 | −0.191833 | ||||||||
\(288\) | −5.62386 | −0.331389 | ||||||||
\(289\) | 5.64203 | 0.331884 | ||||||||
\(290\) | −6.33807 | −0.372184 | ||||||||
\(291\) | 23.5628 | 1.38127 | ||||||||
\(292\) | −8.13616 | −0.476133 | ||||||||
\(293\) | 3.54694 | 0.207214 | 0.103607 | − | 0.994618i | \(-0.466962\pi\) | ||||
0.103607 | + | 0.994618i | \(0.466962\pi\) | |||||||
\(294\) | 2.93664 | 0.171268 | ||||||||
\(295\) | −6.68836 | −0.389412 | ||||||||
\(296\) | −9.55503 | −0.555375 | ||||||||
\(297\) | −13.7565 | −0.798232 | ||||||||
\(298\) | −16.8812 | −0.977901 | ||||||||
\(299\) | −8.26499 | −0.477977 | ||||||||
\(300\) | 10.8021 | 0.623658 | ||||||||
\(301\) | 9.79019 | 0.564297 | ||||||||
\(302\) | 12.5442 | 0.721837 | ||||||||
\(303\) | −27.9446 | −1.60538 | ||||||||
\(304\) | −8.25798 | −0.473627 | ||||||||
\(305\) | −13.3859 | −0.766474 | ||||||||
\(306\) | −26.7604 | −1.52979 | ||||||||
\(307\) | 12.7006 | 0.724864 | 0.362432 | − | 0.932010i | \(-0.381947\pi\) | ||||
0.362432 | + | 0.932010i | \(0.381947\pi\) | |||||||
\(308\) | −1.78532 | −0.101728 | ||||||||
\(309\) | −27.1314 | −1.54345 | ||||||||
\(310\) | 4.66095 | 0.264724 | ||||||||
\(311\) | −10.0942 | −0.572390 | −0.286195 | − | 0.958171i | \(-0.592391\pi\) | ||||
−0.286195 | + | 0.958171i | \(0.592391\pi\) | |||||||
\(312\) | −4.65836 | −0.263728 | ||||||||
\(313\) | −15.8054 | −0.893376 | −0.446688 | − | 0.894690i | \(-0.647397\pi\) | ||||
−0.446688 | + | 0.894690i | \(0.647397\pi\) | |||||||
\(314\) | −24.5152 | −1.38347 | ||||||||
\(315\) | −6.46531 | −0.364279 | ||||||||
\(316\) | −2.39952 | −0.134984 | ||||||||
\(317\) | −34.7649 | −1.95259 | −0.976295 | − | 0.216443i | \(-0.930554\pi\) | ||||
−0.976295 | + | 0.216443i | \(0.930554\pi\) | |||||||
\(318\) | −6.84866 | −0.384054 | ||||||||
\(319\) | 9.84278 | 0.551090 | ||||||||
\(320\) | 1.14962 | 0.0642657 | ||||||||
\(321\) | −53.9325 | −3.01022 | ||||||||
\(322\) | 5.21027 | 0.290357 | ||||||||
\(323\) | −39.2945 | −2.18640 | ||||||||
\(324\) | 5.75625 | 0.319792 | ||||||||
\(325\) | 5.83496 | 0.323666 | ||||||||
\(326\) | 11.8060 | 0.653876 | ||||||||
\(327\) | 3.98853 | 0.220566 | ||||||||
\(328\) | −3.24985 | −0.179443 | ||||||||
\(329\) | 2.57995 | 0.142237 | ||||||||
\(330\) | 6.02726 | 0.331790 | ||||||||
\(331\) | −20.4265 | −1.12274 | −0.561372 | − | 0.827564i | \(-0.689726\pi\) | ||||
−0.561372 | + | 0.827564i | \(0.689726\pi\) | |||||||
\(332\) | −1.26492 | −0.0694214 | ||||||||
\(333\) | 53.7362 | 2.94473 | ||||||||
\(334\) | 20.8750 | 1.14223 | ||||||||
\(335\) | 9.33815 | 0.510198 | ||||||||
\(336\) | 2.93664 | 0.160207 | ||||||||
\(337\) | −24.2917 | −1.32325 | −0.661626 | − | 0.749834i | \(-0.730133\pi\) | ||||
−0.661626 | + | 0.749834i | \(0.730133\pi\) | |||||||
\(338\) | 10.4837 | 0.570237 | ||||||||
\(339\) | −45.4859 | −2.47046 | ||||||||
\(340\) | 5.47031 | 0.296669 | ||||||||
\(341\) | −7.23827 | −0.391975 | ||||||||
\(342\) | 46.4417 | 2.51128 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 9.79019 | 0.527852 | ||||||||
\(345\) | −17.5900 | −0.947013 | ||||||||
\(346\) | 6.10704 | 0.328317 | ||||||||
\(347\) | −4.05420 | −0.217641 | −0.108820 | − | 0.994061i | \(-0.534707\pi\) | ||||
−0.108820 | + | 0.994061i | \(0.534707\pi\) | |||||||
\(348\) | −16.1903 | −0.867889 | ||||||||
\(349\) | 1.93402 | 0.103526 | 0.0517630 | − | 0.998659i | \(-0.483516\pi\) | ||||
0.0517630 | + | 0.998659i | \(0.483516\pi\) | |||||||
\(350\) | −3.67837 | −0.196617 | ||||||||
\(351\) | 12.2229 | 0.652410 | ||||||||
\(352\) | −1.78532 | −0.0951576 | ||||||||
\(353\) | −4.31153 | −0.229480 | −0.114740 | − | 0.993396i | \(-0.536603\pi\) | ||||
−0.114740 | + | 0.993396i | \(0.536603\pi\) | |||||||
\(354\) | −17.0851 | −0.908061 | ||||||||
\(355\) | −4.41968 | −0.234572 | ||||||||
\(356\) | −0.725700 | −0.0384620 | ||||||||
\(357\) | 13.9736 | 0.739562 | ||||||||
\(358\) | −16.6851 | −0.881837 | ||||||||
\(359\) | 24.5126 | 1.29373 | 0.646863 | − | 0.762606i | \(-0.276081\pi\) | ||||
0.646863 | + | 0.762606i | \(0.276081\pi\) | |||||||
\(360\) | −6.46531 | −0.340752 | ||||||||
\(361\) | 49.1942 | 2.58917 | ||||||||
\(362\) | 11.4665 | 0.602668 | ||||||||
\(363\) | 22.9429 | 1.20419 | ||||||||
\(364\) | 1.58629 | 0.0831441 | ||||||||
\(365\) | −9.35349 | −0.489584 | ||||||||
\(366\) | −34.1935 | −1.78732 | ||||||||
\(367\) | 29.9890 | 1.56541 | 0.782707 | − | 0.622390i | \(-0.213838\pi\) | ||||
0.782707 | + | 0.622390i | \(0.213838\pi\) | |||||||
\(368\) | 5.21027 | 0.271604 | ||||||||
\(369\) | 18.2767 | 0.951448 | ||||||||
\(370\) | −10.9847 | −0.571065 | ||||||||
\(371\) | 2.33214 | 0.121079 | ||||||||
\(372\) | 11.9061 | 0.617305 | ||||||||
\(373\) | −34.3875 | −1.78052 | −0.890259 | − | 0.455456i | \(-0.849476\pi\) | ||||
−0.890259 | + | 0.455456i | \(0.849476\pi\) | |||||||
\(374\) | −8.49518 | −0.439275 | ||||||||
\(375\) | 29.2984 | 1.51296 | ||||||||
\(376\) | 2.57995 | 0.133051 | ||||||||
\(377\) | −8.74551 | −0.450417 | ||||||||
\(378\) | −7.70535 | −0.396320 | ||||||||
\(379\) | −31.3604 | −1.61088 | −0.805438 | − | 0.592680i | \(-0.798070\pi\) | ||||
−0.805438 | + | 0.592680i | \(0.798070\pi\) | |||||||
\(380\) | −9.49353 | −0.487008 | ||||||||
\(381\) | 42.1432 | 2.15906 | ||||||||
\(382\) | 16.0121 | 0.819252 | ||||||||
\(383\) | −8.61714 | −0.440315 | −0.220158 | − | 0.975464i | \(-0.570657\pi\) | ||||
−0.220158 | + | 0.975464i | \(0.570657\pi\) | |||||||
\(384\) | 2.93664 | 0.149860 | ||||||||
\(385\) | −2.05243 | −0.104602 | ||||||||
\(386\) | −20.0663 | −1.02135 | ||||||||
\(387\) | −55.0587 | −2.79879 | ||||||||
\(388\) | −8.02371 | −0.407342 | ||||||||
\(389\) | 26.2878 | 1.33284 | 0.666421 | − | 0.745575i | \(-0.267825\pi\) | ||||
0.666421 | + | 0.745575i | \(0.267825\pi\) | |||||||
\(390\) | −5.35535 | −0.271178 | ||||||||
\(391\) | 24.7924 | 1.25380 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | −65.7398 | −3.31613 | ||||||||
\(394\) | −22.1819 | −1.11751 | ||||||||
\(395\) | −2.75854 | −0.138797 | ||||||||
\(396\) | 10.0404 | 0.504548 | ||||||||
\(397\) | 2.36140 | 0.118515 | 0.0592576 | − | 0.998243i | \(-0.481127\pi\) | ||||
0.0592576 | + | 0.998243i | \(0.481127\pi\) | |||||||
\(398\) | 7.23178 | 0.362496 | ||||||||
\(399\) | −24.2507 | −1.21405 | ||||||||
\(400\) | −3.67837 | −0.183919 | ||||||||
\(401\) | 16.1640 | 0.807194 | 0.403597 | − | 0.914937i | \(-0.367760\pi\) | ||||
0.403597 | + | 0.914937i | \(0.367760\pi\) | |||||||
\(402\) | 23.8538 | 1.18972 | ||||||||
\(403\) | 6.43135 | 0.320368 | ||||||||
\(404\) | 9.51584 | 0.473431 | ||||||||
\(405\) | 6.61750 | 0.328826 | ||||||||
\(406\) | 5.51319 | 0.273615 | ||||||||
\(407\) | 17.0587 | 0.845571 | ||||||||
\(408\) | 13.9736 | 0.691797 | ||||||||
\(409\) | −25.5539 | −1.26356 | −0.631780 | − | 0.775148i | \(-0.717676\pi\) | ||||
−0.631780 | + | 0.775148i | \(0.717676\pi\) | |||||||
\(410\) | −3.73610 | −0.184513 | ||||||||
\(411\) | 5.11456 | 0.252283 | ||||||||
\(412\) | 9.23894 | 0.455170 | ||||||||
\(413\) | 5.81789 | 0.286280 | ||||||||
\(414\) | −29.3018 | −1.44011 | ||||||||
\(415\) | −1.45418 | −0.0713827 | ||||||||
\(416\) | 1.58629 | 0.0777742 | ||||||||
\(417\) | −36.4357 | −1.78426 | ||||||||
\(418\) | 14.7431 | 0.721108 | ||||||||
\(419\) | −35.7791 | −1.74792 | −0.873961 | − | 0.485996i | \(-0.838457\pi\) | ||||
−0.873961 | + | 0.485996i | \(0.838457\pi\) | |||||||
\(420\) | 3.37602 | 0.164733 | ||||||||
\(421\) | 29.7343 | 1.44916 | 0.724581 | − | 0.689190i | \(-0.242033\pi\) | ||||
0.724581 | + | 0.689190i | \(0.242033\pi\) | |||||||
\(422\) | 26.3059 | 1.28055 | ||||||||
\(423\) | −14.5093 | −0.705465 | ||||||||
\(424\) | 2.33214 | 0.113259 | ||||||||
\(425\) | −17.5030 | −0.849022 | ||||||||
\(426\) | −11.2898 | −0.546995 | ||||||||
\(427\) | 11.6438 | 0.563481 | ||||||||
\(428\) | 18.3654 | 0.887724 | ||||||||
\(429\) | 8.31664 | 0.401531 | ||||||||
\(430\) | 11.2550 | 0.542764 | ||||||||
\(431\) | −1.00000 | −0.0481683 | ||||||||
\(432\) | −7.70535 | −0.370724 | ||||||||
\(433\) | −3.86209 | −0.185600 | −0.0928001 | − | 0.995685i | \(-0.529582\pi\) | ||||
−0.0928001 | + | 0.995685i | \(0.529582\pi\) | |||||||
\(434\) | −4.05434 | −0.194615 | ||||||||
\(435\) | −18.6126 | −0.892408 | ||||||||
\(436\) | −1.35820 | −0.0650458 | ||||||||
\(437\) | −43.0263 | −2.05823 | ||||||||
\(438\) | −23.8930 | −1.14165 | ||||||||
\(439\) | −32.6481 | −1.55821 | −0.779105 | − | 0.626893i | \(-0.784326\pi\) | ||||
−0.779105 | + | 0.626893i | \(0.784326\pi\) | |||||||
\(440\) | −2.05243 | −0.0978460 | ||||||||
\(441\) | 5.62386 | 0.267803 | ||||||||
\(442\) | 7.54814 | 0.359028 | ||||||||
\(443\) | −18.9858 | −0.902043 | −0.451022 | − | 0.892513i | \(-0.648940\pi\) | ||||
−0.451022 | + | 0.892513i | \(0.648940\pi\) | |||||||
\(444\) | −28.0597 | −1.33165 | ||||||||
\(445\) | −0.834279 | −0.0395486 | ||||||||
\(446\) | −9.15737 | −0.433614 | ||||||||
\(447\) | −49.5740 | −2.34477 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | −32.1436 | −1.51695 | −0.758474 | − | 0.651703i | \(-0.774055\pi\) | ||||
−0.758474 | + | 0.651703i | \(0.774055\pi\) | |||||||
\(450\) | 20.6867 | 0.975179 | ||||||||
\(451\) | 5.80201 | 0.273206 | ||||||||
\(452\) | 15.4891 | 0.728546 | ||||||||
\(453\) | 36.8378 | 1.73079 | ||||||||
\(454\) | 10.2369 | 0.480440 | ||||||||
\(455\) | 1.82363 | 0.0854931 | ||||||||
\(456\) | −24.2507 | −1.13564 | ||||||||
\(457\) | 27.0189 | 1.26389 | 0.631945 | − | 0.775013i | \(-0.282257\pi\) | ||||
0.631945 | + | 0.775013i | \(0.282257\pi\) | |||||||
\(458\) | −0.0238752 | −0.00111561 | ||||||||
\(459\) | −36.6649 | −1.71137 | ||||||||
\(460\) | 5.98983 | 0.279277 | ||||||||
\(461\) | −35.2448 | −1.64151 | −0.820756 | − | 0.571278i | \(-0.806448\pi\) | ||||
−0.820756 | + | 0.571278i | \(0.806448\pi\) | |||||||
\(462\) | −5.24283 | −0.243919 | ||||||||
\(463\) | −41.8483 | −1.94485 | −0.972427 | − | 0.233208i | \(-0.925078\pi\) | ||||
−0.972427 | + | 0.233208i | \(0.925078\pi\) | |||||||
\(464\) | 5.51319 | 0.255943 | ||||||||
\(465\) | 13.6875 | 0.634744 | ||||||||
\(466\) | −0.281238 | −0.0130281 | ||||||||
\(467\) | −34.5464 | −1.59862 | −0.799308 | − | 0.600921i | \(-0.794800\pi\) | ||||
−0.799308 | + | 0.600921i | \(0.794800\pi\) | |||||||
\(468\) | −8.92107 | −0.412377 | ||||||||
\(469\) | −8.12281 | −0.375077 | ||||||||
\(470\) | 2.96596 | 0.136809 | ||||||||
\(471\) | −71.9923 | −3.31723 | ||||||||
\(472\) | 5.81789 | 0.267790 | ||||||||
\(473\) | −17.4786 | −0.803666 | ||||||||
\(474\) | −7.04654 | −0.323658 | ||||||||
\(475\) | 30.3759 | 1.39374 | ||||||||
\(476\) | −4.75836 | −0.218099 | ||||||||
\(477\) | −13.1156 | −0.600524 | ||||||||
\(478\) | −5.22424 | −0.238951 | ||||||||
\(479\) | −30.6571 | −1.40076 | −0.700379 | − | 0.713771i | \(-0.746986\pi\) | ||||
−0.700379 | + | 0.713771i | \(0.746986\pi\) | |||||||
\(480\) | 3.37602 | 0.154094 | ||||||||
\(481\) | −15.1570 | −0.691101 | ||||||||
\(482\) | 23.8541 | 1.08653 | ||||||||
\(483\) | 15.3007 | 0.696206 | ||||||||
\(484\) | −7.81265 | −0.355120 | ||||||||
\(485\) | −9.22422 | −0.418850 | ||||||||
\(486\) | −6.21199 | −0.281782 | ||||||||
\(487\) | −3.75623 | −0.170211 | −0.0851056 | − | 0.996372i | \(-0.527123\pi\) | ||||
−0.0851056 | + | 0.996372i | \(0.527123\pi\) | |||||||
\(488\) | 11.6438 | 0.527088 | ||||||||
\(489\) | 34.6701 | 1.56784 | ||||||||
\(490\) | −1.14962 | −0.0519345 | ||||||||
\(491\) | −9.39835 | −0.424141 | −0.212071 | − | 0.977254i | \(-0.568021\pi\) | ||||
−0.212071 | + | 0.977254i | \(0.568021\pi\) | |||||||
\(492\) | −9.54365 | −0.430261 | ||||||||
\(493\) | 26.2338 | 1.18151 | ||||||||
\(494\) | −13.0995 | −0.589376 | ||||||||
\(495\) | 11.5426 | 0.518802 | ||||||||
\(496\) | −4.05434 | −0.182045 | ||||||||
\(497\) | 3.84447 | 0.172448 | ||||||||
\(498\) | −3.71461 | −0.166456 | ||||||||
\(499\) | −7.39766 | −0.331165 | −0.165582 | − | 0.986196i | \(-0.552950\pi\) | ||||
−0.165582 | + | 0.986196i | \(0.552950\pi\) | |||||||
\(500\) | −9.97683 | −0.446178 | ||||||||
\(501\) | 61.3025 | 2.73879 | ||||||||
\(502\) | −11.1379 | −0.497108 | ||||||||
\(503\) | −37.2938 | −1.66285 | −0.831424 | − | 0.555639i | \(-0.812474\pi\) | ||||
−0.831424 | + | 0.555639i | \(0.812474\pi\) | |||||||
\(504\) | 5.62386 | 0.250507 | ||||||||
\(505\) | 10.9396 | 0.486806 | ||||||||
\(506\) | −9.30198 | −0.413523 | ||||||||
\(507\) | 30.7868 | 1.36729 | ||||||||
\(508\) | −14.3508 | −0.636714 | ||||||||
\(509\) | −17.4490 | −0.773415 | −0.386707 | − | 0.922203i | \(-0.626388\pi\) | ||||
−0.386707 | + | 0.922203i | \(0.626388\pi\) | |||||||
\(510\) | 16.0643 | 0.711341 | ||||||||
\(511\) | 8.13616 | 0.359922 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 63.6306 | 2.80936 | ||||||||
\(514\) | 9.90011 | 0.436675 | ||||||||
\(515\) | 10.6213 | 0.468029 | ||||||||
\(516\) | 28.7503 | 1.26566 | ||||||||
\(517\) | −4.60602 | −0.202572 | ||||||||
\(518\) | 9.55503 | 0.419824 | ||||||||
\(519\) | 17.9342 | 0.787224 | ||||||||
\(520\) | 1.82363 | 0.0799714 | ||||||||
\(521\) | 16.4279 | 0.719721 | 0.359861 | − | 0.933006i | \(-0.382824\pi\) | ||||
0.359861 | + | 0.933006i | \(0.382824\pi\) | |||||||
\(522\) | −31.0054 | −1.35707 | ||||||||
\(523\) | 27.1811 | 1.18855 | 0.594273 | − | 0.804263i | \(-0.297440\pi\) | ||||
0.594273 | + | 0.804263i | \(0.297440\pi\) | |||||||
\(524\) | 22.3860 | 0.977939 | ||||||||
\(525\) | −10.8021 | −0.471441 | ||||||||
\(526\) | −7.22031 | −0.314821 | ||||||||
\(527\) | −19.2920 | −0.840374 | ||||||||
\(528\) | −5.24283 | −0.228165 | ||||||||
\(529\) | 4.14691 | 0.180301 | ||||||||
\(530\) | 2.68107 | 0.116458 | ||||||||
\(531\) | −32.7190 | −1.41988 | ||||||||
\(532\) | 8.25798 | 0.358029 | ||||||||
\(533\) | −5.15521 | −0.223297 | ||||||||
\(534\) | −2.13112 | −0.0922226 | ||||||||
\(535\) | 21.1132 | 0.912804 | ||||||||
\(536\) | −8.12281 | −0.350852 | ||||||||
\(537\) | −48.9983 | −2.11443 | ||||||||
\(538\) | 1.70941 | 0.0736979 | ||||||||
\(539\) | 1.78532 | 0.0768990 | ||||||||
\(540\) | −8.85822 | −0.381197 | ||||||||
\(541\) | −29.4861 | −1.26771 | −0.633854 | − | 0.773453i | \(-0.718528\pi\) | ||||
−0.633854 | + | 0.773453i | \(0.718528\pi\) | |||||||
\(542\) | −16.5082 | −0.709090 | ||||||||
\(543\) | 33.6731 | 1.44505 | ||||||||
\(544\) | −4.75836 | −0.204013 | ||||||||
\(545\) | −1.56141 | −0.0668834 | ||||||||
\(546\) | 4.65836 | 0.199359 | ||||||||
\(547\) | 32.1106 | 1.37295 | 0.686476 | − | 0.727152i | \(-0.259157\pi\) | ||||
0.686476 | + | 0.727152i | \(0.259157\pi\) | |||||||
\(548\) | −1.74164 | −0.0743990 | ||||||||
\(549\) | −65.4829 | −2.79474 | ||||||||
\(550\) | 6.56706 | 0.280020 | ||||||||
\(551\) | −45.5278 | −1.93955 | ||||||||
\(552\) | 15.3007 | 0.651241 | ||||||||
\(553\) | 2.39952 | 0.102038 | ||||||||
\(554\) | −18.1539 | −0.771285 | ||||||||
\(555\) | −32.2580 | −1.36928 | ||||||||
\(556\) | 12.4073 | 0.526185 | ||||||||
\(557\) | 39.0697 | 1.65544 | 0.827719 | − | 0.561143i | \(-0.189638\pi\) | ||||
0.827719 | + | 0.561143i | \(0.189638\pi\) | |||||||
\(558\) | 22.8010 | 0.965245 | ||||||||
\(559\) | 15.5301 | 0.656852 | ||||||||
\(560\) | −1.14962 | −0.0485803 | ||||||||
\(561\) | −24.9473 | −1.05328 | ||||||||
\(562\) | 22.0851 | 0.931602 | ||||||||
\(563\) | 1.88705 | 0.0795298 | 0.0397649 | − | 0.999209i | \(-0.487339\pi\) | ||||
0.0397649 | + | 0.999209i | \(0.487339\pi\) | |||||||
\(564\) | 7.57638 | 0.319023 | ||||||||
\(565\) | 17.8066 | 0.749128 | ||||||||
\(566\) | −29.3599 | −1.23409 | ||||||||
\(567\) | −5.75625 | −0.241740 | ||||||||
\(568\) | 3.84447 | 0.161311 | ||||||||
\(569\) | 4.96763 | 0.208254 | 0.104127 | − | 0.994564i | \(-0.466795\pi\) | ||||
0.104127 | + | 0.994564i | \(0.466795\pi\) | |||||||
\(570\) | −27.8791 | −1.16773 | ||||||||
\(571\) | −0.671131 | −0.0280860 | −0.0140430 | − | 0.999901i | \(-0.504470\pi\) | ||||
−0.0140430 | + | 0.999901i | \(0.504470\pi\) | |||||||
\(572\) | −2.83203 | −0.118413 | ||||||||
\(573\) | 47.0219 | 1.96437 | ||||||||
\(574\) | 3.24985 | 0.135646 | ||||||||
\(575\) | −19.1653 | −0.799249 | ||||||||
\(576\) | 5.62386 | 0.234328 | ||||||||
\(577\) | −43.8914 | −1.82722 | −0.913612 | − | 0.406586i | \(-0.866719\pi\) | ||||
−0.913612 | + | 0.406586i | \(0.866719\pi\) | |||||||
\(578\) | −5.64203 | −0.234678 | ||||||||
\(579\) | −58.9276 | −2.44895 | ||||||||
\(580\) | 6.33807 | 0.263174 | ||||||||
\(581\) | 1.26492 | 0.0524776 | ||||||||
\(582\) | −23.5628 | −0.976708 | ||||||||
\(583\) | −4.16361 | −0.172439 | ||||||||
\(584\) | 8.13616 | 0.336677 | ||||||||
\(585\) | −10.2558 | −0.424027 | ||||||||
\(586\) | −3.54694 | −0.146523 | ||||||||
\(587\) | −8.59868 | −0.354905 | −0.177453 | − | 0.984129i | \(-0.556786\pi\) | ||||
−0.177453 | + | 0.984129i | \(0.556786\pi\) | |||||||
\(588\) | −2.93664 | −0.121105 | ||||||||
\(589\) | 33.4806 | 1.37955 | ||||||||
\(590\) | 6.68836 | 0.275356 | ||||||||
\(591\) | −65.1404 | −2.67952 | ||||||||
\(592\) | 9.55503 | 0.392709 | ||||||||
\(593\) | 27.7616 | 1.14003 | 0.570015 | − | 0.821634i | \(-0.306937\pi\) | ||||
0.570015 | + | 0.821634i | \(0.306937\pi\) | |||||||
\(594\) | 13.7565 | 0.564435 | ||||||||
\(595\) | −5.47031 | −0.224261 | ||||||||
\(596\) | 16.8812 | 0.691480 | ||||||||
\(597\) | 21.2371 | 0.869178 | ||||||||
\(598\) | 8.26499 | 0.337981 | ||||||||
\(599\) | −12.7583 | −0.521292 | −0.260646 | − | 0.965434i | \(-0.583936\pi\) | ||||
−0.260646 | + | 0.965434i | \(0.583936\pi\) | |||||||
\(600\) | −10.8021 | −0.440992 | ||||||||
\(601\) | −17.0307 | −0.694698 | −0.347349 | − | 0.937736i | \(-0.612918\pi\) | ||||
−0.347349 | + | 0.937736i | \(0.612918\pi\) | |||||||
\(602\) | −9.79019 | −0.399018 | ||||||||
\(603\) | 45.6816 | 1.86030 | ||||||||
\(604\) | −12.5442 | −0.510416 | ||||||||
\(605\) | −8.98158 | −0.365153 | ||||||||
\(606\) | 27.9446 | 1.13517 | ||||||||
\(607\) | 9.80151 | 0.397831 | 0.198916 | − | 0.980017i | \(-0.436258\pi\) | ||||
0.198916 | + | 0.980017i | \(0.436258\pi\) | |||||||
\(608\) | 8.25798 | 0.334905 | ||||||||
\(609\) | 16.1903 | 0.656062 | ||||||||
\(610\) | 13.3859 | 0.541979 | ||||||||
\(611\) | 4.09254 | 0.165566 | ||||||||
\(612\) | 26.7604 | 1.08172 | ||||||||
\(613\) | −2.61015 | −0.105423 | −0.0527116 | − | 0.998610i | \(-0.516786\pi\) | ||||
−0.0527116 | + | 0.998610i | \(0.516786\pi\) | |||||||
\(614\) | −12.7006 | −0.512556 | ||||||||
\(615\) | −10.9716 | −0.442417 | ||||||||
\(616\) | 1.78532 | 0.0719324 | ||||||||
\(617\) | −34.3615 | −1.38334 | −0.691670 | − | 0.722213i | \(-0.743125\pi\) | ||||
−0.691670 | + | 0.722213i | \(0.743125\pi\) | |||||||
\(618\) | 27.1314 | 1.09139 | ||||||||
\(619\) | −43.8047 | −1.76066 | −0.880329 | − | 0.474364i | \(-0.842678\pi\) | ||||
−0.880329 | + | 0.474364i | \(0.842678\pi\) | |||||||
\(620\) | −4.66095 | −0.187188 | ||||||||
\(621\) | −40.1469 | −1.61104 | ||||||||
\(622\) | 10.0942 | 0.404741 | ||||||||
\(623\) | 0.725700 | 0.0290745 | ||||||||
\(624\) | 4.65836 | 0.186484 | ||||||||
\(625\) | 6.92230 | 0.276892 | ||||||||
\(626\) | 15.8054 | 0.631712 | ||||||||
\(627\) | 43.2952 | 1.72904 | ||||||||
\(628\) | 24.5152 | 0.978262 | ||||||||
\(629\) | 45.4663 | 1.81286 | ||||||||
\(630\) | 6.46531 | 0.257584 | ||||||||
\(631\) | −10.9189 | −0.434676 | −0.217338 | − | 0.976096i | \(-0.569737\pi\) | ||||
−0.217338 | + | 0.976096i | \(0.569737\pi\) | |||||||
\(632\) | 2.39952 | 0.0954479 | ||||||||
\(633\) | 77.2509 | 3.07045 | ||||||||
\(634\) | 34.7649 | 1.38069 | ||||||||
\(635\) | −16.4980 | −0.654702 | ||||||||
\(636\) | 6.84866 | 0.271567 | ||||||||
\(637\) | −1.58629 | −0.0628511 | ||||||||
\(638\) | −9.84278 | −0.389679 | ||||||||
\(639\) | −21.6208 | −0.855306 | ||||||||
\(640\) | −1.14962 | −0.0454427 | ||||||||
\(641\) | −32.6922 | −1.29126 | −0.645631 | − | 0.763649i | \(-0.723406\pi\) | ||||
−0.645631 | + | 0.763649i | \(0.723406\pi\) | |||||||
\(642\) | 53.9325 | 2.12855 | ||||||||
\(643\) | −49.7617 | −1.96241 | −0.981204 | − | 0.192972i | \(-0.938187\pi\) | ||||
−0.981204 | + | 0.192972i | \(0.938187\pi\) | |||||||
\(644\) | −5.21027 | −0.205313 | ||||||||
\(645\) | 33.0519 | 1.30142 | ||||||||
\(646\) | 39.2945 | 1.54602 | ||||||||
\(647\) | 47.5690 | 1.87013 | 0.935065 | − | 0.354475i | \(-0.115341\pi\) | ||||
0.935065 | + | 0.354475i | \(0.115341\pi\) | |||||||
\(648\) | −5.75625 | −0.226127 | ||||||||
\(649\) | −10.3868 | −0.407716 | ||||||||
\(650\) | −5.83496 | −0.228866 | ||||||||
\(651\) | −11.9061 | −0.466638 | ||||||||
\(652\) | −11.8060 | −0.462360 | ||||||||
\(653\) | −26.9639 | −1.05518 | −0.527589 | − | 0.849500i | \(-0.676904\pi\) | ||||
−0.527589 | + | 0.849500i | \(0.676904\pi\) | |||||||
\(654\) | −3.98853 | −0.155964 | ||||||||
\(655\) | 25.7354 | 1.00557 | ||||||||
\(656\) | 3.24985 | 0.126885 | ||||||||
\(657\) | −45.7566 | −1.78514 | ||||||||
\(658\) | −2.57995 | −0.100577 | ||||||||
\(659\) | 29.0508 | 1.13166 | 0.565830 | − | 0.824522i | \(-0.308556\pi\) | ||||
0.565830 | + | 0.824522i | \(0.308556\pi\) | |||||||
\(660\) | −6.02726 | −0.234611 | ||||||||
\(661\) | −9.87168 | −0.383964 | −0.191982 | − | 0.981398i | \(-0.561492\pi\) | ||||
−0.191982 | + | 0.981398i | \(0.561492\pi\) | |||||||
\(662\) | 20.4265 | 0.793899 | ||||||||
\(663\) | 22.1662 | 0.860863 | ||||||||
\(664\) | 1.26492 | 0.0490883 | ||||||||
\(665\) | 9.49353 | 0.368143 | ||||||||
\(666\) | −53.7362 | −2.08224 | ||||||||
\(667\) | 28.7252 | 1.11224 | ||||||||
\(668\) | −20.8750 | −0.807679 | ||||||||
\(669\) | −26.8919 | −1.03970 | ||||||||
\(670\) | −9.33815 | −0.360764 | ||||||||
\(671\) | −20.7878 | −0.802503 | ||||||||
\(672\) | −2.93664 | −0.113283 | ||||||||
\(673\) | 11.4677 | 0.442046 | 0.221023 | − | 0.975269i | \(-0.429060\pi\) | ||||
0.221023 | + | 0.975269i | \(0.429060\pi\) | |||||||
\(674\) | 24.2917 | 0.935681 | ||||||||
\(675\) | 28.3431 | 1.09093 | ||||||||
\(676\) | −10.4837 | −0.403219 | ||||||||
\(677\) | −42.0191 | −1.61493 | −0.807463 | − | 0.589918i | \(-0.799160\pi\) | ||||
−0.807463 | + | 0.589918i | \(0.799160\pi\) | |||||||
\(678\) | 45.4859 | 1.74688 | ||||||||
\(679\) | 8.02371 | 0.307922 | ||||||||
\(680\) | −5.47031 | −0.209777 | ||||||||
\(681\) | 30.0620 | 1.15198 | ||||||||
\(682\) | 7.23827 | 0.277168 | ||||||||
\(683\) | 36.7505 | 1.40622 | 0.703109 | − | 0.711082i | \(-0.251795\pi\) | ||||
0.703109 | + | 0.711082i | \(0.251795\pi\) | |||||||
\(684\) | −46.4417 | −1.77574 | ||||||||
\(685\) | −2.00222 | −0.0765009 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | −0.0701129 | −0.00267497 | ||||||||
\(688\) | −9.79019 | −0.373248 | ||||||||
\(689\) | 3.69945 | 0.140938 | ||||||||
\(690\) | 17.5900 | 0.669639 | ||||||||
\(691\) | −48.3547 | −1.83950 | −0.919750 | − | 0.392505i | \(-0.871609\pi\) | ||||
−0.919750 | + | 0.392505i | \(0.871609\pi\) | |||||||
\(692\) | −6.10704 | −0.232155 | ||||||||
\(693\) | −10.0404 | −0.381402 | ||||||||
\(694\) | 4.05420 | 0.153895 | ||||||||
\(695\) | 14.2636 | 0.541050 | ||||||||
\(696\) | 16.1903 | 0.613690 | ||||||||
\(697\) | 15.4640 | 0.585740 | ||||||||
\(698\) | −1.93402 | −0.0732039 | ||||||||
\(699\) | −0.825896 | −0.0312382 | ||||||||
\(700\) | 3.67837 | 0.139029 | ||||||||
\(701\) | 0.866545 | 0.0327290 | 0.0163645 | − | 0.999866i | \(-0.494791\pi\) | ||||
0.0163645 | + | 0.999866i | \(0.494791\pi\) | |||||||
\(702\) | −12.2229 | −0.461324 | ||||||||
\(703\) | −78.9052 | −2.97597 | ||||||||
\(704\) | 1.78532 | 0.0672866 | ||||||||
\(705\) | 8.70996 | 0.328036 | ||||||||
\(706\) | 4.31153 | 0.162267 | ||||||||
\(707\) | −9.51584 | −0.357880 | ||||||||
\(708\) | 17.0851 | 0.642096 | ||||||||
\(709\) | −8.02004 | −0.301199 | −0.150599 | − | 0.988595i | \(-0.548120\pi\) | ||||
−0.150599 | + | 0.988595i | \(0.548120\pi\) | |||||||
\(710\) | 4.41968 | 0.165868 | ||||||||
\(711\) | −13.4946 | −0.506087 | ||||||||
\(712\) | 0.725700 | 0.0271967 | ||||||||
\(713\) | −21.1242 | −0.791108 | ||||||||
\(714\) | −13.9736 | −0.522949 | ||||||||
\(715\) | −3.25575 | −0.121758 | ||||||||
\(716\) | 16.6851 | 0.623553 | ||||||||
\(717\) | −15.3417 | −0.572947 | ||||||||
\(718\) | −24.5126 | −0.914802 | ||||||||
\(719\) | 23.6970 | 0.883747 | 0.441874 | − | 0.897077i | \(-0.354314\pi\) | ||||
0.441874 | + | 0.897077i | \(0.354314\pi\) | |||||||
\(720\) | 6.46531 | 0.240948 | ||||||||
\(721\) | −9.23894 | −0.344076 | ||||||||
\(722\) | −49.1942 | −1.83082 | ||||||||
\(723\) | 70.0511 | 2.60523 | ||||||||
\(724\) | −11.4665 | −0.426151 | ||||||||
\(725\) | −20.2796 | −0.753164 | ||||||||
\(726\) | −22.9429 | −0.851493 | ||||||||
\(727\) | 9.88893 | 0.366760 | 0.183380 | − | 0.983042i | \(-0.441296\pi\) | ||||
0.183380 | + | 0.983042i | \(0.441296\pi\) | |||||||
\(728\) | −1.58629 | −0.0587918 | ||||||||
\(729\) | −35.5112 | −1.31523 | ||||||||
\(730\) | 9.35349 | 0.346188 | ||||||||
\(731\) | −46.5853 | −1.72302 | ||||||||
\(732\) | 34.1935 | 1.26383 | ||||||||
\(733\) | 49.0859 | 1.81303 | 0.906515 | − | 0.422173i | \(-0.138733\pi\) | ||||
0.906515 | + | 0.422173i | \(0.138733\pi\) | |||||||
\(734\) | −29.9890 | −1.10692 | ||||||||
\(735\) | −3.37602 | −0.124526 | ||||||||
\(736\) | −5.21027 | −0.192053 | ||||||||
\(737\) | 14.5018 | 0.534180 | ||||||||
\(738\) | −18.2767 | −0.672776 | ||||||||
\(739\) | −22.2093 | −0.816983 | −0.408491 | − | 0.912762i | \(-0.633945\pi\) | ||||
−0.408491 | + | 0.912762i | \(0.633945\pi\) | |||||||
\(740\) | 10.9847 | 0.403804 | ||||||||
\(741\) | −38.4686 | −1.41318 | ||||||||
\(742\) | −2.33214 | −0.0856156 | ||||||||
\(743\) | 21.2031 | 0.777865 | 0.388933 | − | 0.921266i | \(-0.372844\pi\) | ||||
0.388933 | + | 0.921266i | \(0.372844\pi\) | |||||||
\(744\) | −11.9061 | −0.436500 | ||||||||
\(745\) | 19.4069 | 0.711016 | ||||||||
\(746\) | 34.3875 | 1.25902 | ||||||||
\(747\) | −7.11373 | −0.260278 | ||||||||
\(748\) | 8.49518 | 0.310615 | ||||||||
\(749\) | −18.3654 | −0.671056 | ||||||||
\(750\) | −29.2984 | −1.06983 | ||||||||
\(751\) | −27.0852 | −0.988355 | −0.494177 | − | 0.869361i | \(-0.664531\pi\) | ||||
−0.494177 | + | 0.869361i | \(0.664531\pi\) | |||||||
\(752\) | −2.57995 | −0.0940810 | ||||||||
\(753\) | −32.7080 | −1.19194 | ||||||||
\(754\) | 8.74551 | 0.318493 | ||||||||
\(755\) | −14.4211 | −0.524836 | ||||||||
\(756\) | 7.70535 | 0.280241 | ||||||||
\(757\) | −13.1285 | −0.477164 | −0.238582 | − | 0.971122i | \(-0.576683\pi\) | ||||
−0.238582 | + | 0.971122i | \(0.576683\pi\) | |||||||
\(758\) | 31.3604 | 1.13906 | ||||||||
\(759\) | −27.3166 | −0.991529 | ||||||||
\(760\) | 9.49353 | 0.344367 | ||||||||
\(761\) | 36.9079 | 1.33791 | 0.668955 | − | 0.743303i | \(-0.266742\pi\) | ||||
0.668955 | + | 0.743303i | \(0.266742\pi\) | |||||||
\(762\) | −42.1432 | −1.52669 | ||||||||
\(763\) | 1.35820 | 0.0491700 | ||||||||
\(764\) | −16.0121 | −0.579298 | ||||||||
\(765\) | 30.7643 | 1.11229 | ||||||||
\(766\) | 8.61714 | 0.311350 | ||||||||
\(767\) | 9.22885 | 0.333235 | ||||||||
\(768\) | −2.93664 | −0.105967 | ||||||||
\(769\) | −22.0176 | −0.793977 | −0.396988 | − | 0.917824i | \(-0.629945\pi\) | ||||
−0.396988 | + | 0.917824i | \(0.629945\pi\) | |||||||
\(770\) | 2.05243 | 0.0739646 | ||||||||
\(771\) | 29.0731 | 1.04704 | ||||||||
\(772\) | 20.0663 | 0.722203 | ||||||||
\(773\) | 11.3044 | 0.406592 | 0.203296 | − | 0.979117i | \(-0.434835\pi\) | ||||
0.203296 | + | 0.979117i | \(0.434835\pi\) | |||||||
\(774\) | 55.0587 | 1.97904 | ||||||||
\(775\) | 14.9134 | 0.535704 | ||||||||
\(776\) | 8.02371 | 0.288035 | ||||||||
\(777\) | 28.0597 | 1.00664 | ||||||||
\(778\) | −26.2878 | −0.942462 | ||||||||
\(779\) | −26.8372 | −0.961543 | ||||||||
\(780\) | 5.35535 | 0.191752 | ||||||||
\(781\) | −6.86360 | −0.245599 | ||||||||
\(782\) | −24.7924 | −0.886573 | ||||||||
\(783\) | −42.4810 | −1.51815 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 28.1831 | 1.00590 | ||||||||
\(786\) | 65.7398 | 2.34486 | ||||||||
\(787\) | −40.7721 | −1.45337 | −0.726684 | − | 0.686972i | \(-0.758940\pi\) | ||||
−0.726684 | + | 0.686972i | \(0.758940\pi\) | |||||||
\(788\) | 22.1819 | 0.790198 | ||||||||
\(789\) | −21.2035 | −0.754863 | ||||||||
\(790\) | 2.75854 | 0.0981444 | ||||||||
\(791\) | −15.4891 | −0.550729 | ||||||||
\(792\) | −10.0404 | −0.356769 | ||||||||
\(793\) | 18.4704 | 0.655901 | ||||||||
\(794\) | −2.36140 | −0.0838029 | ||||||||
\(795\) | 7.87336 | 0.279239 | ||||||||
\(796\) | −7.23178 | −0.256324 | ||||||||
\(797\) | −37.4043 | −1.32493 | −0.662464 | − | 0.749094i | \(-0.730489\pi\) | ||||
−0.662464 | + | 0.749094i | \(0.730489\pi\) | |||||||
\(798\) | 24.2507 | 0.858466 | ||||||||
\(799\) | −12.2763 | −0.434305 | ||||||||
\(800\) | 3.67837 | 0.130050 | ||||||||
\(801\) | −4.08124 | −0.144203 | ||||||||
\(802\) | −16.1640 | −0.570772 | ||||||||
\(803\) | −14.5256 | −0.512598 | ||||||||
\(804\) | −23.8538 | −0.841258 | ||||||||
\(805\) | −5.98983 | −0.211114 | ||||||||
\(806\) | −6.43135 | −0.226535 | ||||||||
\(807\) | 5.01992 | 0.176710 | ||||||||
\(808\) | −9.51584 | −0.334766 | ||||||||
\(809\) | 5.38580 | 0.189355 | 0.0946774 | − | 0.995508i | \(-0.469818\pi\) | ||||
0.0946774 | + | 0.995508i | \(0.469818\pi\) | |||||||
\(810\) | −6.61750 | −0.232515 | ||||||||
\(811\) | 5.87662 | 0.206356 | 0.103178 | − | 0.994663i | \(-0.467099\pi\) | ||||
0.103178 | + | 0.994663i | \(0.467099\pi\) | |||||||
\(812\) | −5.51319 | −0.193475 | ||||||||
\(813\) | −48.4788 | −1.70023 | ||||||||
\(814\) | −17.0587 | −0.597909 | ||||||||
\(815\) | −13.5724 | −0.475422 | ||||||||
\(816\) | −13.9736 | −0.489174 | ||||||||
\(817\) | 80.8472 | 2.82848 | ||||||||
\(818\) | 25.5539 | 0.893472 | ||||||||
\(819\) | 8.92107 | 0.311727 | ||||||||
\(820\) | 3.73610 | 0.130470 | ||||||||
\(821\) | −22.1183 | −0.771932 | −0.385966 | − | 0.922513i | \(-0.626132\pi\) | ||||
−0.385966 | + | 0.922513i | \(0.626132\pi\) | |||||||
\(822\) | −5.11456 | −0.178391 | ||||||||
\(823\) | −10.5988 | −0.369451 | −0.184726 | − | 0.982790i | \(-0.559140\pi\) | ||||
−0.184726 | + | 0.982790i | \(0.559140\pi\) | |||||||
\(824\) | −9.23894 | −0.321854 | ||||||||
\(825\) | 19.2851 | 0.671421 | ||||||||
\(826\) | −5.81789 | −0.202430 | ||||||||
\(827\) | −23.2879 | −0.809799 | −0.404900 | − | 0.914361i | \(-0.632694\pi\) | ||||
−0.404900 | + | 0.914361i | \(0.632694\pi\) | |||||||
\(828\) | 29.3018 | 1.01831 | ||||||||
\(829\) | 40.1267 | 1.39366 | 0.696828 | − | 0.717238i | \(-0.254594\pi\) | ||||
0.696828 | + | 0.717238i | \(0.254594\pi\) | |||||||
\(830\) | 1.45418 | 0.0504752 | ||||||||
\(831\) | −53.3115 | −1.84935 | ||||||||
\(832\) | −1.58629 | −0.0549947 | ||||||||
\(833\) | 4.75836 | 0.164868 | ||||||||
\(834\) | 36.4357 | 1.26166 | ||||||||
\(835\) | −23.9983 | −0.830497 | ||||||||
\(836\) | −14.7431 | −0.509901 | ||||||||
\(837\) | 31.2401 | 1.07982 | ||||||||
\(838\) | 35.7791 | 1.23597 | ||||||||
\(839\) | 37.6068 | 1.29833 | 0.649166 | − | 0.760647i | \(-0.275118\pi\) | ||||
0.649166 | + | 0.760647i | \(0.275118\pi\) | |||||||
\(840\) | −3.37602 | −0.116484 | ||||||||
\(841\) | 1.39525 | 0.0481121 | ||||||||
\(842\) | −29.7343 | −1.02471 | ||||||||
\(843\) | 64.8559 | 2.23376 | ||||||||
\(844\) | −26.3059 | −0.905485 | ||||||||
\(845\) | −12.0523 | −0.414610 | ||||||||
\(846\) | 14.5093 | 0.498839 | ||||||||
\(847\) | 7.81265 | 0.268446 | ||||||||
\(848\) | −2.33214 | −0.0800860 | ||||||||
\(849\) | −86.2194 | −2.95904 | ||||||||
\(850\) | 17.5030 | 0.600349 | ||||||||
\(851\) | 49.7843 | 1.70658 | ||||||||
\(852\) | 11.2898 | 0.386784 | ||||||||
\(853\) | 33.2606 | 1.13882 | 0.569410 | − | 0.822054i | \(-0.307172\pi\) | ||||
0.569410 | + | 0.822054i | \(0.307172\pi\) | |||||||
\(854\) | −11.6438 | −0.398441 | ||||||||
\(855\) | −53.3903 | −1.82591 | ||||||||
\(856\) | −18.3654 | −0.627716 | ||||||||
\(857\) | −8.69842 | −0.297132 | −0.148566 | − | 0.988902i | \(-0.547466\pi\) | ||||
−0.148566 | + | 0.988902i | \(0.547466\pi\) | |||||||
\(858\) | −8.31664 | −0.283926 | ||||||||
\(859\) | 37.6302 | 1.28393 | 0.641963 | − | 0.766736i | \(-0.278120\pi\) | ||||
0.641963 | + | 0.766736i | \(0.278120\pi\) | |||||||
\(860\) | −11.2550 | −0.383792 | ||||||||
\(861\) | 9.54365 | 0.325247 | ||||||||
\(862\) | 1.00000 | 0.0340601 | ||||||||
\(863\) | −43.5982 | −1.48410 | −0.742050 | − | 0.670345i | \(-0.766146\pi\) | ||||
−0.742050 | + | 0.670345i | \(0.766146\pi\) | |||||||
\(864\) | 7.70535 | 0.262141 | ||||||||
\(865\) | −7.02078 | −0.238714 | ||||||||
\(866\) | 3.86209 | 0.131239 | ||||||||
\(867\) | −16.5686 | −0.562700 | ||||||||
\(868\) | 4.05434 | 0.137613 | ||||||||
\(869\) | −4.28391 | −0.145322 | ||||||||
\(870\) | 18.6126 | 0.631028 | ||||||||
\(871\) | −12.8851 | −0.436596 | ||||||||
\(872\) | 1.35820 | 0.0459943 | ||||||||
\(873\) | −45.1243 | −1.52723 | ||||||||
\(874\) | 43.0263 | 1.45539 | ||||||||
\(875\) | 9.97683 | 0.337278 | ||||||||
\(876\) | 23.8930 | 0.807269 | ||||||||
\(877\) | 6.13303 | 0.207098 | 0.103549 | − | 0.994624i | \(-0.466980\pi\) | ||||
0.103549 | + | 0.994624i | \(0.466980\pi\) | |||||||
\(878\) | 32.6481 | 1.10182 | ||||||||
\(879\) | −10.4161 | −0.351326 | ||||||||
\(880\) | 2.05243 | 0.0691875 | ||||||||
\(881\) | 3.47957 | 0.117230 | 0.0586148 | − | 0.998281i | \(-0.481332\pi\) | ||||
0.0586148 | + | 0.998281i | \(0.481332\pi\) | |||||||
\(882\) | −5.62386 | −0.189365 | ||||||||
\(883\) | −35.4174 | −1.19189 | −0.595946 | − | 0.803025i | \(-0.703223\pi\) | ||||
−0.595946 | + | 0.803025i | \(0.703223\pi\) | |||||||
\(884\) | −7.54814 | −0.253871 | ||||||||
\(885\) | 19.6413 | 0.660236 | ||||||||
\(886\) | 18.9858 | 0.637841 | ||||||||
\(887\) | −17.2559 | −0.579396 | −0.289698 | − | 0.957118i | \(-0.593555\pi\) | ||||
−0.289698 | + | 0.957118i | \(0.593555\pi\) | |||||||
\(888\) | 28.0597 | 0.941622 | ||||||||
\(889\) | 14.3508 | 0.481311 | ||||||||
\(890\) | 0.834279 | 0.0279651 | ||||||||
\(891\) | 10.2767 | 0.344283 | ||||||||
\(892\) | 9.15737 | 0.306611 | ||||||||
\(893\) | 21.3051 | 0.712949 | ||||||||
\(894\) | 49.5740 | 1.65800 | ||||||||
\(895\) | 19.1816 | 0.641169 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 24.2713 | 0.810396 | ||||||||
\(898\) | 32.1436 | 1.07264 | ||||||||
\(899\) | −22.3523 | −0.745492 | ||||||||
\(900\) | −20.6867 | −0.689556 | ||||||||
\(901\) | −11.0972 | −0.369700 | ||||||||
\(902\) | −5.80201 | −0.193186 | ||||||||
\(903\) | −28.7503 | −0.956750 | ||||||||
\(904\) | −15.4891 | −0.515160 | ||||||||
\(905\) | −13.1822 | −0.438190 | ||||||||
\(906\) | −36.8378 | −1.22385 | ||||||||
\(907\) | −30.6143 | −1.01653 | −0.508265 | − | 0.861201i | \(-0.669713\pi\) | ||||
−0.508265 | + | 0.861201i | \(0.669713\pi\) | |||||||
\(908\) | −10.2369 | −0.339722 | ||||||||
\(909\) | 53.5158 | 1.77501 | ||||||||
\(910\) | −1.82363 | −0.0604527 | ||||||||
\(911\) | −34.7533 | −1.15143 | −0.575715 | − | 0.817651i | \(-0.695276\pi\) | ||||
−0.575715 | + | 0.817651i | \(0.695276\pi\) | |||||||
\(912\) | 24.2507 | 0.803021 | ||||||||
\(913\) | −2.25828 | −0.0747381 | ||||||||
\(914\) | −27.0189 | −0.893705 | ||||||||
\(915\) | 39.3096 | 1.29953 | ||||||||
\(916\) | 0.0238752 | 0.000788859 0 | ||||||||
\(917\) | −22.3860 | −0.739252 | ||||||||
\(918\) | 36.6649 | 1.21012 | ||||||||
\(919\) | 19.4075 | 0.640195 | 0.320097 | − | 0.947385i | \(-0.396284\pi\) | ||||
0.320097 | + | 0.947385i | \(0.396284\pi\) | |||||||
\(920\) | −5.98983 | −0.197479 | ||||||||
\(921\) | −37.2972 | −1.22899 | ||||||||
\(922\) | 35.2448 | 1.16072 | ||||||||
\(923\) | 6.09845 | 0.200733 | ||||||||
\(924\) | 5.24283 | 0.172476 | ||||||||
\(925\) | −35.1470 | −1.15563 | ||||||||
\(926\) | 41.8483 | 1.37522 | ||||||||
\(927\) | 51.9585 | 1.70654 | ||||||||
\(928\) | −5.51319 | −0.180979 | ||||||||
\(929\) | 10.9966 | 0.360785 | 0.180393 | − | 0.983595i | \(-0.442263\pi\) | ||||
0.180393 | + | 0.983595i | \(0.442263\pi\) | |||||||
\(930\) | −13.6875 | −0.448832 | ||||||||
\(931\) | −8.25798 | −0.270644 | ||||||||
\(932\) | 0.281238 | 0.00921226 | ||||||||
\(933\) | 29.6431 | 0.970471 | ||||||||
\(934\) | 34.5464 | 1.13039 | ||||||||
\(935\) | 9.76623 | 0.319390 | ||||||||
\(936\) | 8.92107 | 0.291594 | ||||||||
\(937\) | −34.4259 | −1.12464 | −0.562322 | − | 0.826918i | \(-0.690092\pi\) | ||||
−0.562322 | + | 0.826918i | \(0.690092\pi\) | |||||||
\(938\) | 8.12281 | 0.265219 | ||||||||
\(939\) | 46.4149 | 1.51469 | ||||||||
\(940\) | −2.96596 | −0.0967389 | ||||||||
\(941\) | −32.9705 | −1.07481 | −0.537403 | − | 0.843325i | \(-0.680595\pi\) | ||||
−0.537403 | + | 0.843325i | \(0.680595\pi\) | |||||||
\(942\) | 71.9923 | 2.34564 | ||||||||
\(943\) | 16.9326 | 0.551402 | ||||||||
\(944\) | −5.81789 | −0.189356 | ||||||||
\(945\) | 8.85822 | 0.288158 | ||||||||
\(946\) | 17.4786 | 0.568278 | ||||||||
\(947\) | 20.1854 | 0.655936 | 0.327968 | − | 0.944689i | \(-0.393636\pi\) | ||||
0.327968 | + | 0.944689i | \(0.393636\pi\) | |||||||
\(948\) | 7.04654 | 0.228861 | ||||||||
\(949\) | 12.9063 | 0.418956 | ||||||||
\(950\) | −30.3759 | −0.985525 | ||||||||
\(951\) | 102.092 | 3.31056 | ||||||||
\(952\) | 4.75836 | 0.154219 | ||||||||
\(953\) | −2.27054 | −0.0735501 | −0.0367750 | − | 0.999324i | \(-0.511708\pi\) | ||||
−0.0367750 | + | 0.999324i | \(0.511708\pi\) | |||||||
\(954\) | 13.1156 | 0.424634 | ||||||||
\(955\) | −18.4079 | −0.595664 | ||||||||
\(956\) | 5.22424 | 0.168964 | ||||||||
\(957\) | −28.9047 | −0.934357 | ||||||||
\(958\) | 30.6571 | 0.990486 | ||||||||
\(959\) | 1.74164 | 0.0562404 | ||||||||
\(960\) | −3.37602 | −0.108961 | ||||||||
\(961\) | −14.5623 | −0.469753 | ||||||||
\(962\) | 15.1570 | 0.488683 | ||||||||
\(963\) | 103.284 | 3.32829 | ||||||||
\(964\) | −23.8541 | −0.768290 | ||||||||
\(965\) | 23.0687 | 0.742607 | ||||||||
\(966\) | −15.3007 | −0.492292 | ||||||||
\(967\) | 49.9533 | 1.60639 | 0.803195 | − | 0.595716i | \(-0.203132\pi\) | ||||
0.803195 | + | 0.595716i | \(0.203132\pi\) | |||||||
\(968\) | 7.81265 | 0.251108 | ||||||||
\(969\) | 115.394 | 3.70698 | ||||||||
\(970\) | 9.22422 | 0.296172 | ||||||||
\(971\) | −33.9991 | −1.09108 | −0.545542 | − | 0.838084i | \(-0.683676\pi\) | ||||
−0.545542 | + | 0.838084i | \(0.683676\pi\) | |||||||
\(972\) | 6.21199 | 0.199250 | ||||||||
\(973\) | −12.4073 | −0.397758 | ||||||||
\(974\) | 3.75623 | 0.120357 | ||||||||
\(975\) | −17.1352 | −0.548765 | ||||||||
\(976\) | −11.6438 | −0.372707 | ||||||||
\(977\) | 27.3932 | 0.876386 | 0.438193 | − | 0.898881i | \(-0.355619\pi\) | ||||
0.438193 | + | 0.898881i | \(0.355619\pi\) | |||||||
\(978\) | −34.6701 | −1.10863 | ||||||||
\(979\) | −1.29560 | −0.0414076 | ||||||||
\(980\) | 1.14962 | 0.0367233 | ||||||||
\(981\) | −7.63831 | −0.243872 | ||||||||
\(982\) | 9.39835 | 0.299913 | ||||||||
\(983\) | 35.4177 | 1.12965 | 0.564825 | − | 0.825210i | \(-0.308944\pi\) | ||||
0.564825 | + | 0.825210i | \(0.308944\pi\) | |||||||
\(984\) | 9.54365 | 0.304241 | ||||||||
\(985\) | 25.5008 | 0.812523 | ||||||||
\(986\) | −26.2338 | −0.835453 | ||||||||
\(987\) | −7.57638 | −0.241159 | ||||||||
\(988\) | 13.0995 | 0.416752 | ||||||||
\(989\) | −51.0095 | −1.62201 | ||||||||
\(990\) | −11.5426 | −0.366848 | ||||||||
\(991\) | 5.05835 | 0.160684 | 0.0803419 | − | 0.996767i | \(-0.474399\pi\) | ||||
0.0803419 | + | 0.996767i | \(0.474399\pi\) | |||||||
\(992\) | 4.05434 | 0.128725 | ||||||||
\(993\) | 59.9854 | 1.90358 | ||||||||
\(994\) | −3.84447 | −0.121939 | ||||||||
\(995\) | −8.31380 | −0.263565 | ||||||||
\(996\) | 3.71461 | 0.117702 | ||||||||
\(997\) | 37.8114 | 1.19750 | 0.598750 | − | 0.800936i | \(-0.295664\pi\) | ||||
0.598750 | + | 0.800936i | \(0.295664\pi\) | |||||||
\(998\) | 7.39766 | 0.234169 | ||||||||
\(999\) | −73.6248 | −2.32939 |
(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 | 6034.2.a.o.1.3 | ✓ | 25 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6034.2.a.o.1.3 | ✓ | 25 | 1.1 | even | 1 | trivial |