Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6422,2,Mod(1,6422)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6422, 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("6422.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6422 = 2 \cdot 13^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6422.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: | \(51.2799281781\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 2x^{6} - 16x^{5} + 29x^{4} + 60x^{3} - 79x^{2} - 47x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 494) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.95679\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6422.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.95679 | −1.12975 | −0.564876 | − | 0.825176i | \(-0.691076\pi\) | ||||
−0.564876 | + | 0.825176i | \(0.691076\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.613661 | −0.274438 | −0.137219 | − | 0.990541i | \(-0.543816\pi\) | ||||
−0.137219 | + | 0.990541i | \(0.543816\pi\) | |||||||
\(6\) | 1.95679 | 0.798855 | ||||||||
\(7\) | −0.465830 | −0.176067 | −0.0880335 | − | 0.996118i | \(-0.528058\pi\) | ||||
−0.0880335 | + | 0.996118i | \(0.528058\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0.829012 | 0.276337 | ||||||||
\(10\) | 0.613661 | 0.194057 | ||||||||
\(11\) | −4.22291 | −1.27325 | −0.636627 | − | 0.771172i | \(-0.719671\pi\) | ||||
−0.636627 | + | 0.771172i | \(0.719671\pi\) | |||||||
\(12\) | −1.95679 | −0.564876 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0.465830 | 0.124498 | ||||||||
\(15\) | 1.20080 | 0.310046 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.33414 | 1.29372 | 0.646860 | − | 0.762609i | \(-0.276082\pi\) | ||||
0.646860 | + | 0.762609i | \(0.276082\pi\) | |||||||
\(18\) | −0.829012 | −0.195400 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | −0.613661 | −0.137219 | ||||||||
\(21\) | 0.911529 | 0.198912 | ||||||||
\(22\) | 4.22291 | 0.900327 | ||||||||
\(23\) | −6.57915 | −1.37185 | −0.685924 | − | 0.727673i | \(-0.740602\pi\) | ||||
−0.685924 | + | 0.727673i | \(0.740602\pi\) | |||||||
\(24\) | 1.95679 | 0.399427 | ||||||||
\(25\) | −4.62342 | −0.924684 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.24816 | 0.817559 | ||||||||
\(28\) | −0.465830 | −0.0880335 | ||||||||
\(29\) | 8.11549 | 1.50701 | 0.753504 | − | 0.657443i | \(-0.228362\pi\) | ||||
0.753504 | + | 0.657443i | \(0.228362\pi\) | |||||||
\(30\) | −1.20080 | −0.219236 | ||||||||
\(31\) | 4.04042 | 0.725680 | 0.362840 | − | 0.931851i | \(-0.381807\pi\) | ||||
0.362840 | + | 0.931851i | \(0.381807\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 8.26332 | 1.43846 | ||||||||
\(34\) | −5.33414 | −0.914798 | ||||||||
\(35\) | 0.285862 | 0.0483194 | ||||||||
\(36\) | 0.829012 | 0.138169 | ||||||||
\(37\) | −1.69618 | −0.278850 | −0.139425 | − | 0.990233i | \(-0.544525\pi\) | ||||
−0.139425 | + | 0.990233i | \(0.544525\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.613661 | 0.0970284 | ||||||||
\(41\) | −4.71828 | −0.736871 | −0.368436 | − | 0.929653i | \(-0.620107\pi\) | ||||
−0.368436 | + | 0.929653i | \(0.620107\pi\) | |||||||
\(42\) | −0.911529 | −0.140652 | ||||||||
\(43\) | 2.48682 | 0.379236 | 0.189618 | − | 0.981858i | \(-0.439275\pi\) | ||||
0.189618 | + | 0.981858i | \(0.439275\pi\) | |||||||
\(44\) | −4.22291 | −0.636627 | ||||||||
\(45\) | −0.508733 | −0.0758374 | ||||||||
\(46\) | 6.57915 | 0.970043 | ||||||||
\(47\) | −12.8042 | −1.86769 | −0.933844 | − | 0.357680i | \(-0.883568\pi\) | ||||
−0.933844 | + | 0.357680i | \(0.883568\pi\) | |||||||
\(48\) | −1.95679 | −0.282438 | ||||||||
\(49\) | −6.78300 | −0.969000 | ||||||||
\(50\) | 4.62342 | 0.653850 | ||||||||
\(51\) | −10.4378 | −1.46158 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.74778 | −0.514797 | −0.257399 | − | 0.966305i | \(-0.582865\pi\) | ||||
−0.257399 | + | 0.966305i | \(0.582865\pi\) | |||||||
\(54\) | −4.24816 | −0.578101 | ||||||||
\(55\) | 2.59143 | 0.349429 | ||||||||
\(56\) | 0.465830 | 0.0622491 | ||||||||
\(57\) | 1.95679 | 0.259183 | ||||||||
\(58\) | −8.11549 | −1.06562 | ||||||||
\(59\) | −12.6011 | −1.64052 | −0.820262 | − | 0.571988i | \(-0.806172\pi\) | ||||
−0.820262 | + | 0.571988i | \(0.806172\pi\) | |||||||
\(60\) | 1.20080 | 0.155023 | ||||||||
\(61\) | −4.02624 | −0.515508 | −0.257754 | − | 0.966211i | \(-0.582982\pi\) | ||||
−0.257754 | + | 0.966211i | \(0.582982\pi\) | |||||||
\(62\) | −4.04042 | −0.513134 | ||||||||
\(63\) | −0.386178 | −0.0486539 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −8.26332 | −1.01714 | ||||||||
\(67\) | −9.47090 | −1.15705 | −0.578527 | − | 0.815663i | \(-0.696372\pi\) | ||||
−0.578527 | + | 0.815663i | \(0.696372\pi\) | |||||||
\(68\) | 5.33414 | 0.646860 | ||||||||
\(69\) | 12.8740 | 1.54985 | ||||||||
\(70\) | −0.285862 | −0.0341670 | ||||||||
\(71\) | 16.6857 | 1.98022 | 0.990112 | − | 0.140279i | \(-0.0448001\pi\) | ||||
0.990112 | + | 0.140279i | \(0.0448001\pi\) | |||||||
\(72\) | −0.829012 | −0.0977000 | ||||||||
\(73\) | 14.0690 | 1.64665 | 0.823325 | − | 0.567571i | \(-0.192117\pi\) | ||||
0.823325 | + | 0.567571i | \(0.192117\pi\) | |||||||
\(74\) | 1.69618 | 0.197177 | ||||||||
\(75\) | 9.04704 | 1.04466 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 1.96715 | 0.224178 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.66829 | −0.750241 | −0.375121 | − | 0.926976i | \(-0.622399\pi\) | ||||
−0.375121 | + | 0.926976i | \(0.622399\pi\) | |||||||
\(80\) | −0.613661 | −0.0686094 | ||||||||
\(81\) | −10.7998 | −1.19998 | ||||||||
\(82\) | 4.71828 | 0.521047 | ||||||||
\(83\) | −6.70032 | −0.735456 | −0.367728 | − | 0.929933i | \(-0.619864\pi\) | ||||
−0.367728 | + | 0.929933i | \(0.619864\pi\) | |||||||
\(84\) | 0.911529 | 0.0994559 | ||||||||
\(85\) | −3.27336 | −0.355046 | ||||||||
\(86\) | −2.48682 | −0.268160 | ||||||||
\(87\) | −15.8803 | −1.70255 | ||||||||
\(88\) | 4.22291 | 0.450163 | ||||||||
\(89\) | −11.0322 | −1.16941 | −0.584706 | − | 0.811245i | \(-0.698790\pi\) | ||||
−0.584706 | + | 0.811245i | \(0.698790\pi\) | |||||||
\(90\) | 0.508733 | 0.0536251 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −6.57915 | −0.685924 | ||||||||
\(93\) | −7.90623 | −0.819838 | ||||||||
\(94\) | 12.8042 | 1.32066 | ||||||||
\(95\) | 0.613661 | 0.0629603 | ||||||||
\(96\) | 1.95679 | 0.199714 | ||||||||
\(97\) | 11.9535 | 1.21369 | 0.606846 | − | 0.794819i | \(-0.292434\pi\) | ||||
0.606846 | + | 0.794819i | \(0.292434\pi\) | |||||||
\(98\) | 6.78300 | 0.685187 | ||||||||
\(99\) | −3.50084 | −0.351848 | ||||||||
\(100\) | −4.62342 | −0.462342 | ||||||||
\(101\) | 12.2449 | 1.21841 | 0.609204 | − | 0.793013i | \(-0.291489\pi\) | ||||
0.609204 | + | 0.793013i | \(0.291489\pi\) | |||||||
\(102\) | 10.4378 | 1.03349 | ||||||||
\(103\) | −10.6048 | −1.04492 | −0.522461 | − | 0.852663i | \(-0.674986\pi\) | ||||
−0.522461 | + | 0.852663i | \(0.674986\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.559370 | −0.0545889 | ||||||||
\(106\) | 3.74778 | 0.364017 | ||||||||
\(107\) | 13.9570 | 1.34928 | 0.674638 | − | 0.738149i | \(-0.264300\pi\) | ||||
0.674638 | + | 0.738149i | \(0.264300\pi\) | |||||||
\(108\) | 4.24816 | 0.408779 | ||||||||
\(109\) | 2.18305 | 0.209099 | 0.104549 | − | 0.994520i | \(-0.466660\pi\) | ||||
0.104549 | + | 0.994520i | \(0.466660\pi\) | |||||||
\(110\) | −2.59143 | −0.247084 | ||||||||
\(111\) | 3.31906 | 0.315031 | ||||||||
\(112\) | −0.465830 | −0.0440168 | ||||||||
\(113\) | 2.84523 | 0.267657 | 0.133828 | − | 0.991005i | \(-0.457273\pi\) | ||||
0.133828 | + | 0.991005i | \(0.457273\pi\) | |||||||
\(114\) | −1.95679 | −0.183270 | ||||||||
\(115\) | 4.03737 | 0.376487 | ||||||||
\(116\) | 8.11549 | 0.753504 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 12.6011 | 1.16003 | ||||||||
\(119\) | −2.48480 | −0.227781 | ||||||||
\(120\) | −1.20080 | −0.109618 | ||||||||
\(121\) | 6.83293 | 0.621176 | ||||||||
\(122\) | 4.02624 | 0.364519 | ||||||||
\(123\) | 9.23266 | 0.832481 | ||||||||
\(124\) | 4.04042 | 0.362840 | ||||||||
\(125\) | 5.90552 | 0.528206 | ||||||||
\(126\) | 0.386178 | 0.0344035 | ||||||||
\(127\) | −4.34142 | −0.385239 | −0.192619 | − | 0.981274i | \(-0.561698\pi\) | ||||
−0.192619 | + | 0.981274i | \(0.561698\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −4.86617 | −0.428442 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −22.2320 | −1.94241 | −0.971207 | − | 0.238236i | \(-0.923431\pi\) | ||||
−0.971207 | + | 0.238236i | \(0.923431\pi\) | |||||||
\(132\) | 8.26332 | 0.719230 | ||||||||
\(133\) | 0.465830 | 0.0403925 | ||||||||
\(134\) | 9.47090 | 0.818161 | ||||||||
\(135\) | −2.60693 | −0.224369 | ||||||||
\(136\) | −5.33414 | −0.457399 | ||||||||
\(137\) | −10.4930 | −0.896481 | −0.448240 | − | 0.893913i | \(-0.647949\pi\) | ||||
−0.448240 | + | 0.893913i | \(0.647949\pi\) | |||||||
\(138\) | −12.8740 | −1.09591 | ||||||||
\(139\) | 14.1682 | 1.20173 | 0.600867 | − | 0.799349i | \(-0.294822\pi\) | ||||
0.600867 | + | 0.799349i | \(0.294822\pi\) | |||||||
\(140\) | 0.285862 | 0.0241597 | ||||||||
\(141\) | 25.0551 | 2.11002 | ||||||||
\(142\) | −16.6857 | −1.40023 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.829012 | 0.0690844 | ||||||||
\(145\) | −4.98016 | −0.413580 | ||||||||
\(146\) | −14.0690 | −1.16436 | ||||||||
\(147\) | 13.2729 | 1.09473 | ||||||||
\(148\) | −1.69618 | −0.139425 | ||||||||
\(149\) | −20.7814 | −1.70248 | −0.851241 | − | 0.524775i | \(-0.824150\pi\) | ||||
−0.851241 | + | 0.524775i | \(0.824150\pi\) | |||||||
\(150\) | −9.04704 | −0.738688 | ||||||||
\(151\) | −16.5451 | −1.34643 | −0.673213 | − | 0.739449i | \(-0.735086\pi\) | ||||
−0.673213 | + | 0.739449i | \(0.735086\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | 4.42207 | 0.357503 | ||||||||
\(154\) | −1.96715 | −0.158518 | ||||||||
\(155\) | −2.47945 | −0.199154 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.20936 | 0.575370 | 0.287685 | − | 0.957725i | \(-0.407114\pi\) | ||||
0.287685 | + | 0.957725i | \(0.407114\pi\) | |||||||
\(158\) | 6.66829 | 0.530501 | ||||||||
\(159\) | 7.33360 | 0.581593 | ||||||||
\(160\) | 0.613661 | 0.0485142 | ||||||||
\(161\) | 3.06476 | 0.241537 | ||||||||
\(162\) | 10.7998 | 0.848511 | ||||||||
\(163\) | 1.57738 | 0.123550 | 0.0617751 | − | 0.998090i | \(-0.480324\pi\) | ||||
0.0617751 | + | 0.998090i | \(0.480324\pi\) | |||||||
\(164\) | −4.71828 | −0.368436 | ||||||||
\(165\) | −5.07088 | −0.394768 | ||||||||
\(166\) | 6.70032 | 0.520046 | ||||||||
\(167\) | 5.83293 | 0.451366 | 0.225683 | − | 0.974201i | \(-0.427539\pi\) | ||||
0.225683 | + | 0.974201i | \(0.427539\pi\) | |||||||
\(168\) | −0.911529 | −0.0703260 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 3.27336 | 0.251055 | ||||||||
\(171\) | −0.829012 | −0.0633962 | ||||||||
\(172\) | 2.48682 | 0.189618 | ||||||||
\(173\) | −5.59479 | −0.425364 | −0.212682 | − | 0.977121i | \(-0.568220\pi\) | ||||
−0.212682 | + | 0.977121i | \(0.568220\pi\) | |||||||
\(174\) | 15.8803 | 1.20388 | ||||||||
\(175\) | 2.15373 | 0.162806 | ||||||||
\(176\) | −4.22291 | −0.318313 | ||||||||
\(177\) | 24.6577 | 1.85338 | ||||||||
\(178\) | 11.0322 | 0.826900 | ||||||||
\(179\) | −1.65521 | −0.123716 | −0.0618580 | − | 0.998085i | \(-0.519703\pi\) | ||||
−0.0618580 | + | 0.998085i | \(0.519703\pi\) | |||||||
\(180\) | −0.508733 | −0.0379187 | ||||||||
\(181\) | −10.8505 | −0.806509 | −0.403254 | − | 0.915088i | \(-0.632121\pi\) | ||||
−0.403254 | + | 0.915088i | \(0.632121\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.87850 | 0.582395 | ||||||||
\(184\) | 6.57915 | 0.485022 | ||||||||
\(185\) | 1.04088 | 0.0765269 | ||||||||
\(186\) | 7.90623 | 0.579713 | ||||||||
\(187\) | −22.5256 | −1.64723 | ||||||||
\(188\) | −12.8042 | −0.933844 | ||||||||
\(189\) | −1.97892 | −0.143945 | ||||||||
\(190\) | −0.613661 | −0.0445197 | ||||||||
\(191\) | −11.6513 | −0.843060 | −0.421530 | − | 0.906814i | \(-0.638507\pi\) | ||||
−0.421530 | + | 0.906814i | \(0.638507\pi\) | |||||||
\(192\) | −1.95679 | −0.141219 | ||||||||
\(193\) | −6.22352 | −0.447979 | −0.223989 | − | 0.974592i | \(-0.571908\pi\) | ||||
−0.223989 | + | 0.974592i | \(0.571908\pi\) | |||||||
\(194\) | −11.9535 | −0.858210 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.78300 | −0.484500 | ||||||||
\(197\) | −9.70754 | −0.691633 | −0.345817 | − | 0.938302i | \(-0.612398\pi\) | ||||
−0.345817 | + | 0.938302i | \(0.612398\pi\) | |||||||
\(198\) | 3.50084 | 0.248794 | ||||||||
\(199\) | 16.4151 | 1.16364 | 0.581819 | − | 0.813318i | \(-0.302341\pi\) | ||||
0.581819 | + | 0.813318i | \(0.302341\pi\) | |||||||
\(200\) | 4.62342 | 0.326925 | ||||||||
\(201\) | 18.5325 | 1.30718 | ||||||||
\(202\) | −12.2449 | −0.861545 | ||||||||
\(203\) | −3.78044 | −0.265335 | ||||||||
\(204\) | −10.4378 | −0.730791 | ||||||||
\(205\) | 2.89543 | 0.202225 | ||||||||
\(206\) | 10.6048 | 0.738871 | ||||||||
\(207\) | −5.45420 | −0.379093 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.22291 | 0.292104 | ||||||||
\(210\) | 0.559370 | 0.0386002 | ||||||||
\(211\) | 11.0380 | 0.759886 | 0.379943 | − | 0.925010i | \(-0.375944\pi\) | ||||
0.379943 | + | 0.925010i | \(0.375944\pi\) | |||||||
\(212\) | −3.74778 | −0.257399 | ||||||||
\(213\) | −32.6503 | −2.23716 | ||||||||
\(214\) | −13.9570 | −0.954082 | ||||||||
\(215\) | −1.52606 | −0.104077 | ||||||||
\(216\) | −4.24816 | −0.289051 | ||||||||
\(217\) | −1.88215 | −0.127768 | ||||||||
\(218\) | −2.18305 | −0.147855 | ||||||||
\(219\) | −27.5300 | −1.86030 | ||||||||
\(220\) | 2.59143 | 0.174714 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −3.31906 | −0.222761 | ||||||||
\(223\) | −22.0677 | −1.47776 | −0.738882 | − | 0.673834i | \(-0.764646\pi\) | ||||
−0.738882 | + | 0.673834i | \(0.764646\pi\) | |||||||
\(224\) | 0.465830 | 0.0311245 | ||||||||
\(225\) | −3.83287 | −0.255525 | ||||||||
\(226\) | −2.84523 | −0.189262 | ||||||||
\(227\) | −25.6025 | −1.69930 | −0.849650 | − | 0.527347i | \(-0.823187\pi\) | ||||
−0.849650 | + | 0.527347i | \(0.823187\pi\) | |||||||
\(228\) | 1.95679 | 0.129591 | ||||||||
\(229\) | 15.8683 | 1.04861 | 0.524303 | − | 0.851532i | \(-0.324326\pi\) | ||||
0.524303 | + | 0.851532i | \(0.324326\pi\) | |||||||
\(230\) | −4.03737 | −0.266216 | ||||||||
\(231\) | −3.84930 | −0.253265 | ||||||||
\(232\) | −8.11549 | −0.532808 | ||||||||
\(233\) | 2.90658 | 0.190417 | 0.0952084 | − | 0.995457i | \(-0.469648\pi\) | ||||
0.0952084 | + | 0.995457i | \(0.469648\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.85746 | 0.512564 | ||||||||
\(236\) | −12.6011 | −0.820262 | ||||||||
\(237\) | 13.0484 | 0.847586 | ||||||||
\(238\) | 2.48480 | 0.161066 | ||||||||
\(239\) | 4.13013 | 0.267156 | 0.133578 | − | 0.991038i | \(-0.457353\pi\) | ||||
0.133578 | + | 0.991038i | \(0.457353\pi\) | |||||||
\(240\) | 1.20080 | 0.0775116 | ||||||||
\(241\) | 23.5902 | 1.51958 | 0.759789 | − | 0.650170i | \(-0.225302\pi\) | ||||
0.759789 | + | 0.650170i | \(0.225302\pi\) | |||||||
\(242\) | −6.83293 | −0.439238 | ||||||||
\(243\) | 8.38838 | 0.538115 | ||||||||
\(244\) | −4.02624 | −0.257754 | ||||||||
\(245\) | 4.16247 | 0.265930 | ||||||||
\(246\) | −9.23266 | −0.588653 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −4.04042 | −0.256567 | ||||||||
\(249\) | 13.1111 | 0.830882 | ||||||||
\(250\) | −5.90552 | −0.373498 | ||||||||
\(251\) | 25.0428 | 1.58069 | 0.790343 | − | 0.612664i | \(-0.209902\pi\) | ||||
0.790343 | + | 0.612664i | \(0.209902\pi\) | |||||||
\(252\) | −0.386178 | −0.0243270 | ||||||||
\(253\) | 27.7831 | 1.74671 | ||||||||
\(254\) | 4.34142 | 0.272405 | ||||||||
\(255\) | 6.40526 | 0.401113 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 10.2457 | 0.639112 | 0.319556 | − | 0.947567i | \(-0.396466\pi\) | ||||
0.319556 | + | 0.947567i | \(0.396466\pi\) | |||||||
\(258\) | 4.86617 | 0.302954 | ||||||||
\(259\) | 0.790130 | 0.0490963 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.72784 | 0.416443 | ||||||||
\(262\) | 22.2320 | 1.37349 | ||||||||
\(263\) | 29.1596 | 1.79806 | 0.899029 | − | 0.437889i | \(-0.144274\pi\) | ||||
0.899029 | + | 0.437889i | \(0.144274\pi\) | |||||||
\(264\) | −8.26332 | −0.508572 | ||||||||
\(265\) | 2.29987 | 0.141280 | ||||||||
\(266\) | −0.465830 | −0.0285618 | ||||||||
\(267\) | 21.5877 | 1.32115 | ||||||||
\(268\) | −9.47090 | −0.578527 | ||||||||
\(269\) | 13.5732 | 0.827570 | 0.413785 | − | 0.910375i | \(-0.364207\pi\) | ||||
0.413785 | + | 0.910375i | \(0.364207\pi\) | |||||||
\(270\) | 2.60693 | 0.158653 | ||||||||
\(271\) | −3.79910 | −0.230779 | −0.115389 | − | 0.993320i | \(-0.536812\pi\) | ||||
−0.115389 | + | 0.993320i | \(0.536812\pi\) | |||||||
\(272\) | 5.33414 | 0.323430 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 10.4930 | 0.633908 | ||||||||
\(275\) | 19.5243 | 1.17736 | ||||||||
\(276\) | 12.8740 | 0.774923 | ||||||||
\(277\) | −9.78766 | −0.588084 | −0.294042 | − | 0.955793i | \(-0.595000\pi\) | ||||
−0.294042 | + | 0.955793i | \(0.595000\pi\) | |||||||
\(278\) | −14.1682 | −0.849754 | ||||||||
\(279\) | 3.34956 | 0.200533 | ||||||||
\(280\) | −0.285862 | −0.0170835 | ||||||||
\(281\) | −16.2314 | −0.968285 | −0.484142 | − | 0.874989i | \(-0.660868\pi\) | ||||
−0.484142 | + | 0.874989i | \(0.660868\pi\) | |||||||
\(282\) | −25.0551 | −1.49201 | ||||||||
\(283\) | 22.1491 | 1.31662 | 0.658312 | − | 0.752745i | \(-0.271271\pi\) | ||||
0.658312 | + | 0.752745i | \(0.271271\pi\) | |||||||
\(284\) | 16.6857 | 0.990112 | ||||||||
\(285\) | −1.20080 | −0.0711295 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.19791 | 0.129739 | ||||||||
\(288\) | −0.829012 | −0.0488500 | ||||||||
\(289\) | 11.4531 | 0.673712 | ||||||||
\(290\) | 4.98016 | 0.292445 | ||||||||
\(291\) | −23.3904 | −1.37117 | ||||||||
\(292\) | 14.0690 | 0.823325 | ||||||||
\(293\) | −4.79987 | −0.280411 | −0.140206 | − | 0.990122i | \(-0.544776\pi\) | ||||
−0.140206 | + | 0.990122i | \(0.544776\pi\) | |||||||
\(294\) | −13.2729 | −0.774090 | ||||||||
\(295\) | 7.73281 | 0.450222 | ||||||||
\(296\) | 1.69618 | 0.0985883 | ||||||||
\(297\) | −17.9396 | −1.04096 | ||||||||
\(298\) | 20.7814 | 1.20384 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 9.04704 | 0.522331 | ||||||||
\(301\) | −1.15843 | −0.0667709 | ||||||||
\(302\) | 16.5451 | 0.952066 | ||||||||
\(303\) | −23.9606 | −1.37650 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | 2.47075 | 0.141475 | ||||||||
\(306\) | −4.42207 | −0.252793 | ||||||||
\(307\) | 21.2921 | 1.21520 | 0.607601 | − | 0.794243i | \(-0.292132\pi\) | ||||
0.607601 | + | 0.794243i | \(0.292132\pi\) | |||||||
\(308\) | 1.96715 | 0.112089 | ||||||||
\(309\) | 20.7513 | 1.18050 | ||||||||
\(310\) | 2.47945 | 0.140823 | ||||||||
\(311\) | 3.78811 | 0.214804 | 0.107402 | − | 0.994216i | \(-0.465747\pi\) | ||||
0.107402 | + | 0.994216i | \(0.465747\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.1236 | 1.19398 | 0.596988 | − | 0.802250i | \(-0.296364\pi\) | ||||
0.596988 | + | 0.802250i | \(0.296364\pi\) | |||||||
\(314\) | −7.20936 | −0.406848 | ||||||||
\(315\) | 0.236983 | 0.0133525 | ||||||||
\(316\) | −6.66829 | −0.375121 | ||||||||
\(317\) | −1.72135 | −0.0966805 | −0.0483402 | − | 0.998831i | \(-0.515393\pi\) | ||||
−0.0483402 | + | 0.998831i | \(0.515393\pi\) | |||||||
\(318\) | −7.33360 | −0.411248 | ||||||||
\(319\) | −34.2710 | −1.91881 | ||||||||
\(320\) | −0.613661 | −0.0343047 | ||||||||
\(321\) | −27.3109 | −1.52435 | ||||||||
\(322\) | −3.06476 | −0.170793 | ||||||||
\(323\) | −5.33414 | −0.296800 | ||||||||
\(324\) | −10.7998 | −0.599988 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.57738 | −0.0873632 | ||||||||
\(327\) | −4.27177 | −0.236229 | ||||||||
\(328\) | 4.71828 | 0.260523 | ||||||||
\(329\) | 5.96459 | 0.328838 | ||||||||
\(330\) | 5.07088 | 0.279143 | ||||||||
\(331\) | −7.09167 | −0.389793 | −0.194897 | − | 0.980824i | \(-0.562437\pi\) | ||||
−0.194897 | + | 0.980824i | \(0.562437\pi\) | |||||||
\(332\) | −6.70032 | −0.367728 | ||||||||
\(333\) | −1.40615 | −0.0770567 | ||||||||
\(334\) | −5.83293 | −0.319164 | ||||||||
\(335\) | 5.81192 | 0.317539 | ||||||||
\(336\) | 0.911529 | 0.0497280 | ||||||||
\(337\) | 8.82879 | 0.480935 | 0.240467 | − | 0.970657i | \(-0.422699\pi\) | ||||
0.240467 | + | 0.970657i | \(0.422699\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.56751 | −0.302386 | ||||||||
\(340\) | −3.27336 | −0.177523 | ||||||||
\(341\) | −17.0623 | −0.923976 | ||||||||
\(342\) | 0.829012 | 0.0448279 | ||||||||
\(343\) | 6.42053 | 0.346676 | ||||||||
\(344\) | −2.48682 | −0.134080 | ||||||||
\(345\) | −7.90027 | −0.425336 | ||||||||
\(346\) | 5.59479 | 0.300778 | ||||||||
\(347\) | −26.7555 | −1.43631 | −0.718156 | − | 0.695882i | \(-0.755014\pi\) | ||||
−0.718156 | + | 0.695882i | \(0.755014\pi\) | |||||||
\(348\) | −15.8803 | −0.851273 | ||||||||
\(349\) | −4.80791 | −0.257361 | −0.128681 | − | 0.991686i | \(-0.541074\pi\) | ||||
−0.128681 | + | 0.991686i | \(0.541074\pi\) | |||||||
\(350\) | −2.15373 | −0.115121 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.22291 | 0.225082 | ||||||||
\(353\) | 31.8519 | 1.69531 | 0.847653 | − | 0.530551i | \(-0.178015\pi\) | ||||
0.847653 | + | 0.530551i | \(0.178015\pi\) | |||||||
\(354\) | −24.6577 | −1.31054 | ||||||||
\(355\) | −10.2393 | −0.543448 | ||||||||
\(356\) | −11.0322 | −0.584706 | ||||||||
\(357\) | 4.86223 | 0.257336 | ||||||||
\(358\) | 1.65521 | 0.0874804 | ||||||||
\(359\) | −2.93468 | −0.154887 | −0.0774434 | − | 0.996997i | \(-0.524676\pi\) | ||||
−0.0774434 | + | 0.996997i | \(0.524676\pi\) | |||||||
\(360\) | 0.508733 | 0.0268126 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 10.8505 | 0.570288 | ||||||||
\(363\) | −13.3706 | −0.701774 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.63359 | −0.451903 | ||||||||
\(366\) | −7.87850 | −0.411816 | ||||||||
\(367\) | 2.48889 | 0.129919 | 0.0649595 | − | 0.997888i | \(-0.479308\pi\) | ||||
0.0649595 | + | 0.997888i | \(0.479308\pi\) | |||||||
\(368\) | −6.57915 | −0.342962 | ||||||||
\(369\) | −3.91151 | −0.203625 | ||||||||
\(370\) | −1.04088 | −0.0541127 | ||||||||
\(371\) | 1.74583 | 0.0906388 | ||||||||
\(372\) | −7.90623 | −0.409919 | ||||||||
\(373\) | 10.6864 | 0.553318 | 0.276659 | − | 0.960968i | \(-0.410773\pi\) | ||||
0.276659 | + | 0.960968i | \(0.410773\pi\) | |||||||
\(374\) | 22.5256 | 1.16477 | ||||||||
\(375\) | −11.5558 | −0.596741 | ||||||||
\(376\) | 12.8042 | 0.660328 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 1.97892 | 0.101785 | ||||||||
\(379\) | −11.7057 | −0.601284 | −0.300642 | − | 0.953737i | \(-0.597201\pi\) | ||||
−0.300642 | + | 0.953737i | \(0.597201\pi\) | |||||||
\(380\) | 0.613661 | 0.0314802 | ||||||||
\(381\) | 8.49524 | 0.435224 | ||||||||
\(382\) | 11.6513 | 0.596134 | ||||||||
\(383\) | 7.81394 | 0.399274 | 0.199637 | − | 0.979870i | \(-0.436024\pi\) | ||||
0.199637 | + | 0.979870i | \(0.436024\pi\) | |||||||
\(384\) | 1.95679 | 0.0998568 | ||||||||
\(385\) | −1.20717 | −0.0615229 | ||||||||
\(386\) | 6.22352 | 0.316769 | ||||||||
\(387\) | 2.06160 | 0.104797 | ||||||||
\(388\) | 11.9535 | 0.606846 | ||||||||
\(389\) | 3.45288 | 0.175068 | 0.0875339 | − | 0.996162i | \(-0.472101\pi\) | ||||
0.0875339 | + | 0.996162i | \(0.472101\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −35.0941 | −1.77479 | ||||||||
\(392\) | 6.78300 | 0.342593 | ||||||||
\(393\) | 43.5032 | 2.19444 | ||||||||
\(394\) | 9.70754 | 0.489059 | ||||||||
\(395\) | 4.09207 | 0.205894 | ||||||||
\(396\) | −3.50084 | −0.175924 | ||||||||
\(397\) | 22.5431 | 1.13141 | 0.565703 | − | 0.824609i | \(-0.308605\pi\) | ||||
0.565703 | + | 0.824609i | \(0.308605\pi\) | |||||||
\(398\) | −16.4151 | −0.822816 | ||||||||
\(399\) | −0.911529 | −0.0456335 | ||||||||
\(400\) | −4.62342 | −0.231171 | ||||||||
\(401\) | −29.5703 | −1.47667 | −0.738336 | − | 0.674433i | \(-0.764388\pi\) | ||||
−0.738336 | + | 0.674433i | \(0.764388\pi\) | |||||||
\(402\) | −18.5325 | −0.924318 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 12.2449 | 0.609204 | ||||||||
\(405\) | 6.62740 | 0.329318 | ||||||||
\(406\) | 3.78044 | 0.187620 | ||||||||
\(407\) | 7.16280 | 0.355047 | ||||||||
\(408\) | 10.4378 | 0.516747 | ||||||||
\(409\) | 2.74046 | 0.135507 | 0.0677536 | − | 0.997702i | \(-0.478417\pi\) | ||||
0.0677536 | + | 0.997702i | \(0.478417\pi\) | |||||||
\(410\) | −2.89543 | −0.142995 | ||||||||
\(411\) | 20.5326 | 1.01280 | ||||||||
\(412\) | −10.6048 | −0.522461 | ||||||||
\(413\) | 5.86997 | 0.288842 | ||||||||
\(414\) | 5.45420 | 0.268059 | ||||||||
\(415\) | 4.11173 | 0.201837 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −27.7242 | −1.35766 | ||||||||
\(418\) | −4.22291 | −0.206549 | ||||||||
\(419\) | −32.2035 | −1.57324 | −0.786622 | − | 0.617435i | \(-0.788172\pi\) | ||||
−0.786622 | + | 0.617435i | \(0.788172\pi\) | |||||||
\(420\) | −0.559370 | −0.0272945 | ||||||||
\(421\) | 13.3021 | 0.648305 | 0.324153 | − | 0.946005i | \(-0.394921\pi\) | ||||
0.324153 | + | 0.946005i | \(0.394921\pi\) | |||||||
\(422\) | −11.0380 | −0.537320 | ||||||||
\(423\) | −10.6149 | −0.516112 | ||||||||
\(424\) | 3.74778 | 0.182008 | ||||||||
\(425\) | −24.6620 | −1.19628 | ||||||||
\(426\) | 32.6503 | 1.58191 | ||||||||
\(427\) | 1.87554 | 0.0907639 | ||||||||
\(428\) | 13.9570 | 0.674638 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.52606 | 0.0735933 | ||||||||
\(431\) | −25.9693 | −1.25090 | −0.625449 | − | 0.780265i | \(-0.715084\pi\) | ||||
−0.625449 | + | 0.780265i | \(0.715084\pi\) | |||||||
\(432\) | 4.24816 | 0.204390 | ||||||||
\(433\) | 8.35232 | 0.401387 | 0.200693 | − | 0.979654i | \(-0.435680\pi\) | ||||
0.200693 | + | 0.979654i | \(0.435680\pi\) | |||||||
\(434\) | 1.88215 | 0.0903459 | ||||||||
\(435\) | 9.74512 | 0.467243 | ||||||||
\(436\) | 2.18305 | 0.104549 | ||||||||
\(437\) | 6.57915 | 0.314724 | ||||||||
\(438\) | 27.5300 | 1.31543 | ||||||||
\(439\) | 1.50999 | 0.0720677 | 0.0360338 | − | 0.999351i | \(-0.488528\pi\) | ||||
0.0360338 | + | 0.999351i | \(0.488528\pi\) | |||||||
\(440\) | −2.59143 | −0.123542 | ||||||||
\(441\) | −5.62319 | −0.267771 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 35.9799 | 1.70946 | 0.854729 | − | 0.519074i | \(-0.173723\pi\) | ||||
0.854729 | + | 0.519074i | \(0.173723\pi\) | |||||||
\(444\) | 3.31906 | 0.157515 | ||||||||
\(445\) | 6.77004 | 0.320931 | ||||||||
\(446\) | 22.0677 | 1.04494 | ||||||||
\(447\) | 40.6649 | 1.92338 | ||||||||
\(448\) | −0.465830 | −0.0220084 | ||||||||
\(449\) | 8.07052 | 0.380871 | 0.190436 | − | 0.981700i | \(-0.439010\pi\) | ||||
0.190436 | + | 0.981700i | \(0.439010\pi\) | |||||||
\(450\) | 3.83287 | 0.180683 | ||||||||
\(451\) | 19.9248 | 0.938224 | ||||||||
\(452\) | 2.84523 | 0.133828 | ||||||||
\(453\) | 32.3753 | 1.52113 | ||||||||
\(454\) | 25.6025 | 1.20159 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.95679 | −0.0916349 | ||||||||
\(457\) | −18.3167 | −0.856818 | −0.428409 | − | 0.903585i | \(-0.640926\pi\) | ||||
−0.428409 | + | 0.903585i | \(0.640926\pi\) | |||||||
\(458\) | −15.8683 | −0.741476 | ||||||||
\(459\) | 22.6603 | 1.05769 | ||||||||
\(460\) | 4.03737 | 0.188243 | ||||||||
\(461\) | 4.10208 | 0.191053 | 0.0955264 | − | 0.995427i | \(-0.469547\pi\) | ||||
0.0955264 | + | 0.995427i | \(0.469547\pi\) | |||||||
\(462\) | 3.84930 | 0.179086 | ||||||||
\(463\) | 4.75527 | 0.220996 | 0.110498 | − | 0.993876i | \(-0.464755\pi\) | ||||
0.110498 | + | 0.993876i | \(0.464755\pi\) | |||||||
\(464\) | 8.11549 | 0.376752 | ||||||||
\(465\) | 4.85175 | 0.224995 | ||||||||
\(466\) | −2.90658 | −0.134645 | ||||||||
\(467\) | 5.92185 | 0.274031 | 0.137015 | − | 0.990569i | \(-0.456249\pi\) | ||||
0.137015 | + | 0.990569i | \(0.456249\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.41182 | 0.203719 | ||||||||
\(470\) | −7.85746 | −0.362438 | ||||||||
\(471\) | −14.1072 | −0.650025 | ||||||||
\(472\) | 12.6011 | 0.580013 | ||||||||
\(473\) | −10.5016 | −0.482864 | ||||||||
\(474\) | −13.0484 | −0.599334 | ||||||||
\(475\) | 4.62342 | 0.212137 | ||||||||
\(476\) | −2.48480 | −0.113891 | ||||||||
\(477\) | −3.10696 | −0.142258 | ||||||||
\(478\) | −4.13013 | −0.188908 | ||||||||
\(479\) | 1.18632 | 0.0542043 | 0.0271021 | − | 0.999633i | \(-0.491372\pi\) | ||||
0.0271021 | + | 0.999633i | \(0.491372\pi\) | |||||||
\(480\) | −1.20080 | −0.0548090 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −23.5902 | −1.07450 | ||||||||
\(483\) | −5.99709 | −0.272877 | ||||||||
\(484\) | 6.83293 | 0.310588 | ||||||||
\(485\) | −7.33539 | −0.333083 | ||||||||
\(486\) | −8.38838 | −0.380504 | ||||||||
\(487\) | −2.65959 | −0.120518 | −0.0602588 | − | 0.998183i | \(-0.519193\pi\) | ||||
−0.0602588 | + | 0.998183i | \(0.519193\pi\) | |||||||
\(488\) | 4.02624 | 0.182259 | ||||||||
\(489\) | −3.08660 | −0.139581 | ||||||||
\(490\) | −4.16247 | −0.188041 | ||||||||
\(491\) | 7.52332 | 0.339523 | 0.169761 | − | 0.985485i | \(-0.445700\pi\) | ||||
0.169761 | + | 0.985485i | \(0.445700\pi\) | |||||||
\(492\) | 9.23266 | 0.416241 | ||||||||
\(493\) | 43.2892 | 1.94965 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.14833 | 0.0965603 | ||||||||
\(496\) | 4.04042 | 0.181420 | ||||||||
\(497\) | −7.77267 | −0.348652 | ||||||||
\(498\) | −13.1111 | −0.587522 | ||||||||
\(499\) | 31.1291 | 1.39353 | 0.696766 | − | 0.717299i | \(-0.254622\pi\) | ||||
0.696766 | + | 0.717299i | \(0.254622\pi\) | |||||||
\(500\) | 5.90552 | 0.264103 | ||||||||
\(501\) | −11.4138 | −0.509931 | ||||||||
\(502\) | −25.0428 | −1.11771 | ||||||||
\(503\) | −4.32945 | −0.193041 | −0.0965203 | − | 0.995331i | \(-0.530771\pi\) | ||||
−0.0965203 | + | 0.995331i | \(0.530771\pi\) | |||||||
\(504\) | 0.386178 | 0.0172018 | ||||||||
\(505\) | −7.51420 | −0.334377 | ||||||||
\(506\) | −27.7831 | −1.23511 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.34142 | −0.192619 | ||||||||
\(509\) | 40.2171 | 1.78259 | 0.891296 | − | 0.453422i | \(-0.149797\pi\) | ||||
0.891296 | + | 0.453422i | \(0.149797\pi\) | |||||||
\(510\) | −6.40526 | −0.283630 | ||||||||
\(511\) | −6.55374 | −0.289921 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −4.24816 | −0.187561 | ||||||||
\(514\) | −10.2457 | −0.451920 | ||||||||
\(515\) | 6.50775 | 0.286766 | ||||||||
\(516\) | −4.86617 | −0.214221 | ||||||||
\(517\) | 54.0710 | 2.37804 | ||||||||
\(518\) | −0.790130 | −0.0347163 | ||||||||
\(519\) | 10.9478 | 0.480556 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.16600 | 0.270137 | 0.135069 | − | 0.990836i | \(-0.456874\pi\) | ||||
0.135069 | + | 0.990836i | \(0.456874\pi\) | |||||||
\(522\) | −6.72784 | −0.294470 | ||||||||
\(523\) | −5.11015 | −0.223451 | −0.111726 | − | 0.993739i | \(-0.535638\pi\) | ||||
−0.111726 | + | 0.993739i | \(0.535638\pi\) | |||||||
\(524\) | −22.2320 | −0.971207 | ||||||||
\(525\) | −4.21438 | −0.183931 | ||||||||
\(526\) | −29.1596 | −1.27142 | ||||||||
\(527\) | 21.5522 | 0.938827 | ||||||||
\(528\) | 8.26332 | 0.359615 | ||||||||
\(529\) | 20.2852 | 0.881967 | ||||||||
\(530\) | −2.29987 | −0.0998999 | ||||||||
\(531\) | −10.4465 | −0.453338 | ||||||||
\(532\) | 0.465830 | 0.0201963 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −21.5877 | −0.934191 | ||||||||
\(535\) | −8.56488 | −0.370292 | ||||||||
\(536\) | 9.47090 | 0.409081 | ||||||||
\(537\) | 3.23889 | 0.139768 | ||||||||
\(538\) | −13.5732 | −0.585180 | ||||||||
\(539\) | 28.6440 | 1.23378 | ||||||||
\(540\) | −2.60693 | −0.112184 | ||||||||
\(541\) | −1.78112 | −0.0765763 | −0.0382882 | − | 0.999267i | \(-0.512190\pi\) | ||||
−0.0382882 | + | 0.999267i | \(0.512190\pi\) | |||||||
\(542\) | 3.79910 | 0.163185 | ||||||||
\(543\) | 21.2320 | 0.911154 | ||||||||
\(544\) | −5.33414 | −0.228700 | ||||||||
\(545\) | −1.33966 | −0.0573846 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 30.0616 | 1.28534 | 0.642670 | − | 0.766143i | \(-0.277827\pi\) | ||||
0.642670 | + | 0.766143i | \(0.277827\pi\) | |||||||
\(548\) | −10.4930 | −0.448240 | ||||||||
\(549\) | −3.33780 | −0.142454 | ||||||||
\(550\) | −19.5243 | −0.832517 | ||||||||
\(551\) | −8.11549 | −0.345732 | ||||||||
\(552\) | −12.8740 | −0.547954 | ||||||||
\(553\) | 3.10629 | 0.132093 | ||||||||
\(554\) | 9.78766 | 0.415838 | ||||||||
\(555\) | −2.03678 | −0.0864564 | ||||||||
\(556\) | 14.1682 | 0.600867 | ||||||||
\(557\) | 11.7171 | 0.496470 | 0.248235 | − | 0.968700i | \(-0.420149\pi\) | ||||
0.248235 | + | 0.968700i | \(0.420149\pi\) | |||||||
\(558\) | −3.34956 | −0.141798 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0.285862 | 0.0120799 | ||||||||
\(561\) | 44.0778 | 1.86096 | ||||||||
\(562\) | 16.2314 | 0.684681 | ||||||||
\(563\) | 26.1397 | 1.10166 | 0.550828 | − | 0.834619i | \(-0.314312\pi\) | ||||
0.550828 | + | 0.834619i | \(0.314312\pi\) | |||||||
\(564\) | 25.0551 | 1.05501 | ||||||||
\(565\) | −1.74601 | −0.0734551 | ||||||||
\(566\) | −22.1491 | −0.930994 | ||||||||
\(567\) | 5.03085 | 0.211276 | ||||||||
\(568\) | −16.6857 | −0.700115 | ||||||||
\(569\) | −29.2732 | −1.22720 | −0.613598 | − | 0.789618i | \(-0.710279\pi\) | ||||
−0.613598 | + | 0.789618i | \(0.710279\pi\) | |||||||
\(570\) | 1.20080 | 0.0502961 | ||||||||
\(571\) | 9.21263 | 0.385537 | 0.192768 | − | 0.981244i | \(-0.438253\pi\) | ||||
0.192768 | + | 0.981244i | \(0.438253\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 22.7992 | 0.952448 | ||||||||
\(574\) | −2.19791 | −0.0917392 | ||||||||
\(575\) | 30.4182 | 1.26853 | ||||||||
\(576\) | 0.829012 | 0.0345422 | ||||||||
\(577\) | 26.1726 | 1.08958 | 0.544790 | − | 0.838572i | \(-0.316609\pi\) | ||||
0.544790 | + | 0.838572i | \(0.316609\pi\) | |||||||
\(578\) | −11.4531 | −0.476386 | ||||||||
\(579\) | 12.1781 | 0.506104 | ||||||||
\(580\) | −4.98016 | −0.206790 | ||||||||
\(581\) | 3.12121 | 0.129489 | ||||||||
\(582\) | 23.3904 | 0.969564 | ||||||||
\(583\) | 15.8265 | 0.655468 | ||||||||
\(584\) | −14.0690 | −0.582178 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.79987 | 0.198281 | ||||||||
\(587\) | −27.2063 | −1.12292 | −0.561462 | − | 0.827503i | \(-0.689761\pi\) | ||||
−0.561462 | + | 0.827503i | \(0.689761\pi\) | |||||||
\(588\) | 13.2729 | 0.547365 | ||||||||
\(589\) | −4.04042 | −0.166483 | ||||||||
\(590\) | −7.73281 | −0.318355 | ||||||||
\(591\) | 18.9956 | 0.781373 | ||||||||
\(592\) | −1.69618 | −0.0697125 | ||||||||
\(593\) | 40.3463 | 1.65682 | 0.828412 | − | 0.560120i | \(-0.189245\pi\) | ||||
0.828412 | + | 0.560120i | \(0.189245\pi\) | |||||||
\(594\) | 17.9396 | 0.736070 | ||||||||
\(595\) | 1.52483 | 0.0625118 | ||||||||
\(596\) | −20.7814 | −0.851241 | ||||||||
\(597\) | −32.1209 | −1.31462 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.71500 | 0.0700732 | 0.0350366 | − | 0.999386i | \(-0.488845\pi\) | ||||
0.0350366 | + | 0.999386i | \(0.488845\pi\) | |||||||
\(600\) | −9.04704 | −0.369344 | ||||||||
\(601\) | −20.6190 | −0.841067 | −0.420533 | − | 0.907277i | \(-0.638157\pi\) | ||||
−0.420533 | + | 0.907277i | \(0.638157\pi\) | |||||||
\(602\) | 1.15843 | 0.0472142 | ||||||||
\(603\) | −7.85149 | −0.319737 | ||||||||
\(604\) | −16.5451 | −0.673213 | ||||||||
\(605\) | −4.19311 | −0.170474 | ||||||||
\(606\) | 23.9606 | 0.973332 | ||||||||
\(607\) | −6.28705 | −0.255184 | −0.127592 | − | 0.991827i | \(-0.540725\pi\) | ||||
−0.127592 | + | 0.991827i | \(0.540725\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | 7.39750 | 0.299762 | ||||||||
\(610\) | −2.47075 | −0.100038 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 4.42207 | 0.178752 | ||||||||
\(613\) | 34.1026 | 1.37739 | 0.688695 | − | 0.725051i | \(-0.258184\pi\) | ||||
0.688695 | + | 0.725051i | \(0.258184\pi\) | |||||||
\(614\) | −21.2921 | −0.859277 | ||||||||
\(615\) | −5.66573 | −0.228464 | ||||||||
\(616\) | −1.96715 | −0.0792589 | ||||||||
\(617\) | −32.7088 | −1.31680 | −0.658402 | − | 0.752666i | \(-0.728768\pi\) | ||||
−0.658402 | + | 0.752666i | \(0.728768\pi\) | |||||||
\(618\) | −20.7513 | −0.834740 | ||||||||
\(619\) | 31.3560 | 1.26030 | 0.630152 | − | 0.776472i | \(-0.282992\pi\) | ||||
0.630152 | + | 0.776472i | \(0.282992\pi\) | |||||||
\(620\) | −2.47945 | −0.0995770 | ||||||||
\(621\) | −27.9493 | −1.12157 | ||||||||
\(622\) | −3.78811 | −0.151890 | ||||||||
\(623\) | 5.13913 | 0.205895 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.4931 | 0.779724 | ||||||||
\(626\) | −21.1236 | −0.844268 | ||||||||
\(627\) | −8.26332 | −0.330005 | ||||||||
\(628\) | 7.20936 | 0.287685 | ||||||||
\(629\) | −9.04766 | −0.360754 | ||||||||
\(630\) | −0.236983 | −0.00944162 | ||||||||
\(631\) | 34.2884 | 1.36500 | 0.682500 | − | 0.730886i | \(-0.260893\pi\) | ||||
0.682500 | + | 0.730886i | \(0.260893\pi\) | |||||||
\(632\) | 6.66829 | 0.265250 | ||||||||
\(633\) | −21.5990 | −0.858482 | ||||||||
\(634\) | 1.72135 | 0.0683634 | ||||||||
\(635\) | 2.66416 | 0.105724 | ||||||||
\(636\) | 7.33360 | 0.290796 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 34.2710 | 1.35680 | ||||||||
\(639\) | 13.8326 | 0.547210 | ||||||||
\(640\) | 0.613661 | 0.0242571 | ||||||||
\(641\) | 16.0556 | 0.634158 | 0.317079 | − | 0.948399i | \(-0.397298\pi\) | ||||
0.317079 | + | 0.948399i | \(0.397298\pi\) | |||||||
\(642\) | 27.3109 | 1.07788 | ||||||||
\(643\) | 23.7368 | 0.936089 | 0.468045 | − | 0.883705i | \(-0.344959\pi\) | ||||
0.468045 | + | 0.883705i | \(0.344959\pi\) | |||||||
\(644\) | 3.06476 | 0.120769 | ||||||||
\(645\) | 2.98618 | 0.117581 | ||||||||
\(646\) | 5.33414 | 0.209869 | ||||||||
\(647\) | −0.927777 | −0.0364747 | −0.0182373 | − | 0.999834i | \(-0.505805\pi\) | ||||
−0.0182373 | + | 0.999834i | \(0.505805\pi\) | |||||||
\(648\) | 10.7998 | 0.424255 | ||||||||
\(649\) | 53.2133 | 2.08880 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.68296 | 0.144346 | ||||||||
\(652\) | 1.57738 | 0.0617751 | ||||||||
\(653\) | 14.4520 | 0.565551 | 0.282775 | − | 0.959186i | \(-0.408745\pi\) | ||||
0.282775 | + | 0.959186i | \(0.408745\pi\) | |||||||
\(654\) | 4.27177 | 0.167039 | ||||||||
\(655\) | 13.6429 | 0.533072 | ||||||||
\(656\) | −4.71828 | −0.184218 | ||||||||
\(657\) | 11.6634 | 0.455031 | ||||||||
\(658\) | −5.96459 | −0.232524 | ||||||||
\(659\) | 13.3107 | 0.518510 | 0.259255 | − | 0.965809i | \(-0.416523\pi\) | ||||
0.259255 | + | 0.965809i | \(0.416523\pi\) | |||||||
\(660\) | −5.07088 | −0.197384 | ||||||||
\(661\) | 24.5314 | 0.954162 | 0.477081 | − | 0.878859i | \(-0.341695\pi\) | ||||
0.477081 | + | 0.878859i | \(0.341695\pi\) | |||||||
\(662\) | 7.09167 | 0.275626 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.70032 | 0.260023 | ||||||||
\(665\) | −0.285862 | −0.0110852 | ||||||||
\(666\) | 1.40615 | 0.0544873 | ||||||||
\(667\) | −53.3931 | −2.06739 | ||||||||
\(668\) | 5.83293 | 0.225683 | ||||||||
\(669\) | 43.1818 | 1.66951 | ||||||||
\(670\) | −5.81192 | −0.224534 | ||||||||
\(671\) | 17.0024 | 0.656372 | ||||||||
\(672\) | −0.911529 | −0.0351630 | ||||||||
\(673\) | 14.5625 | 0.561342 | 0.280671 | − | 0.959804i | \(-0.409443\pi\) | ||||
0.280671 | + | 0.959804i | \(0.409443\pi\) | |||||||
\(674\) | −8.82879 | −0.340072 | ||||||||
\(675\) | −19.6410 | −0.755983 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 36.1083 | 1.38776 | 0.693878 | − | 0.720093i | \(-0.255901\pi\) | ||||
0.693878 | + | 0.720093i | \(0.255901\pi\) | |||||||
\(678\) | 5.56751 | 0.213819 | ||||||||
\(679\) | −5.56829 | −0.213691 | ||||||||
\(680\) | 3.27336 | 0.125528 | ||||||||
\(681\) | 50.0987 | 1.91979 | ||||||||
\(682\) | 17.0623 | 0.653349 | ||||||||
\(683\) | 15.7902 | 0.604196 | 0.302098 | − | 0.953277i | \(-0.402313\pi\) | ||||
0.302098 | + | 0.953277i | \(0.402313\pi\) | |||||||
\(684\) | −0.829012 | −0.0316981 | ||||||||
\(685\) | 6.43917 | 0.246028 | ||||||||
\(686\) | −6.42053 | −0.245137 | ||||||||
\(687\) | −31.0508 | −1.18466 | ||||||||
\(688\) | 2.48682 | 0.0948090 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 7.90027 | 0.300758 | ||||||||
\(691\) | 4.36561 | 0.166075 | 0.0830377 | − | 0.996546i | \(-0.473538\pi\) | ||||
0.0830377 | + | 0.996546i | \(0.473538\pi\) | |||||||
\(692\) | −5.59479 | −0.212682 | ||||||||
\(693\) | 1.63080 | 0.0619488 | ||||||||
\(694\) | 26.7555 | 1.01563 | ||||||||
\(695\) | −8.69450 | −0.329801 | ||||||||
\(696\) | 15.8803 | 0.601941 | ||||||||
\(697\) | −25.1680 | −0.953305 | ||||||||
\(698\) | 4.80791 | 0.181982 | ||||||||
\(699\) | −5.68757 | −0.215123 | ||||||||
\(700\) | 2.15373 | 0.0814032 | ||||||||
\(701\) | −43.4925 | −1.64269 | −0.821344 | − | 0.570433i | \(-0.806776\pi\) | ||||
−0.821344 | + | 0.570433i | \(0.806776\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.69618 | 0.0639726 | ||||||||
\(704\) | −4.22291 | −0.159157 | ||||||||
\(705\) | −15.3754 | −0.579070 | ||||||||
\(706\) | −31.8519 | −1.19876 | ||||||||
\(707\) | −5.70402 | −0.214522 | ||||||||
\(708\) | 24.6577 | 0.926692 | ||||||||
\(709\) | 42.2279 | 1.58590 | 0.792952 | − | 0.609284i | \(-0.208543\pi\) | ||||
0.792952 | + | 0.609284i | \(0.208543\pi\) | |||||||
\(710\) | 10.2393 | 0.384276 | ||||||||
\(711\) | −5.52809 | −0.207320 | ||||||||
\(712\) | 11.0322 | 0.413450 | ||||||||
\(713\) | −26.5825 | −0.995523 | ||||||||
\(714\) | −4.86223 | −0.181964 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.65521 | −0.0618580 | ||||||||
\(717\) | −8.08178 | −0.301820 | ||||||||
\(718\) | 2.93468 | 0.109521 | ||||||||
\(719\) | −13.2090 | −0.492612 | −0.246306 | − | 0.969192i | \(-0.579217\pi\) | ||||
−0.246306 | + | 0.969192i | \(0.579217\pi\) | |||||||
\(720\) | −0.508733 | −0.0189594 | ||||||||
\(721\) | 4.94003 | 0.183976 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | −46.1610 | −1.71674 | ||||||||
\(724\) | −10.8505 | −0.403254 | ||||||||
\(725\) | −37.5213 | −1.39351 | ||||||||
\(726\) | 13.3706 | 0.496229 | ||||||||
\(727\) | −15.7688 | −0.584831 | −0.292415 | − | 0.956291i | \(-0.594459\pi\) | ||||
−0.292415 | + | 0.956291i | \(0.594459\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 15.9851 | 0.592040 | ||||||||
\(730\) | 8.63359 | 0.319543 | ||||||||
\(731\) | 13.2650 | 0.490625 | ||||||||
\(732\) | 7.87850 | 0.291198 | ||||||||
\(733\) | 10.4745 | 0.386884 | 0.193442 | − | 0.981112i | \(-0.438035\pi\) | ||||
0.193442 | + | 0.981112i | \(0.438035\pi\) | |||||||
\(734\) | −2.48889 | −0.0918666 | ||||||||
\(735\) | −8.14506 | −0.300435 | ||||||||
\(736\) | 6.57915 | 0.242511 | ||||||||
\(737\) | 39.9947 | 1.47322 | ||||||||
\(738\) | 3.91151 | 0.143985 | ||||||||
\(739\) | −31.4004 | −1.15508 | −0.577542 | − | 0.816361i | \(-0.695988\pi\) | ||||
−0.577542 | + | 0.816361i | \(0.695988\pi\) | |||||||
\(740\) | 1.04088 | 0.0382635 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.74583 | −0.0640913 | ||||||||
\(743\) | −7.82445 | −0.287051 | −0.143526 | − | 0.989647i | \(-0.545844\pi\) | ||||
−0.143526 | + | 0.989647i | \(0.545844\pi\) | |||||||
\(744\) | 7.90623 | 0.289857 | ||||||||
\(745\) | 12.7528 | 0.467225 | ||||||||
\(746\) | −10.6864 | −0.391255 | ||||||||
\(747\) | −5.55465 | −0.203234 | ||||||||
\(748\) | −22.5256 | −0.823617 | ||||||||
\(749\) | −6.50159 | −0.237563 | ||||||||
\(750\) | 11.5558 | 0.421960 | ||||||||
\(751\) | 49.9634 | 1.82319 | 0.911596 | − | 0.411088i | \(-0.134851\pi\) | ||||
0.911596 | + | 0.411088i | \(0.134851\pi\) | |||||||
\(752\) | −12.8042 | −0.466922 | ||||||||
\(753\) | −49.0034 | −1.78578 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10.1531 | 0.369510 | ||||||||
\(756\) | −1.97892 | −0.0719725 | ||||||||
\(757\) | −32.1991 | −1.17030 | −0.585149 | − | 0.810926i | \(-0.698964\pi\) | ||||
−0.585149 | + | 0.810926i | \(0.698964\pi\) | |||||||
\(758\) | 11.7057 | 0.425172 | ||||||||
\(759\) | −54.3657 | −1.97335 | ||||||||
\(760\) | −0.613661 | −0.0222598 | ||||||||
\(761\) | −44.5923 | −1.61647 | −0.808235 | − | 0.588860i | \(-0.799577\pi\) | ||||
−0.808235 | + | 0.588860i | \(0.799577\pi\) | |||||||
\(762\) | −8.49524 | −0.307750 | ||||||||
\(763\) | −1.01693 | −0.0368154 | ||||||||
\(764\) | −11.6513 | −0.421530 | ||||||||
\(765\) | −2.71365 | −0.0981124 | ||||||||
\(766\) | −7.81394 | −0.282329 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.95679 | −0.0706094 | ||||||||
\(769\) | 29.5367 | 1.06512 | 0.532561 | − | 0.846392i | \(-0.321230\pi\) | ||||
0.532561 | + | 0.846392i | \(0.321230\pi\) | |||||||
\(770\) | 1.20717 | 0.0435033 | ||||||||
\(771\) | −20.0487 | −0.722038 | ||||||||
\(772\) | −6.22352 | −0.223989 | ||||||||
\(773\) | −36.0063 | −1.29506 | −0.647528 | − | 0.762042i | \(-0.724197\pi\) | ||||
−0.647528 | + | 0.762042i | \(0.724197\pi\) | |||||||
\(774\) | −2.06160 | −0.0741027 | ||||||||
\(775\) | −18.6805 | −0.671025 | ||||||||
\(776\) | −11.9535 | −0.429105 | ||||||||
\(777\) | −1.54611 | −0.0554666 | ||||||||
\(778\) | −3.45288 | −0.123792 | ||||||||
\(779\) | 4.71828 | 0.169050 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −70.4620 | −2.52133 | ||||||||
\(782\) | 35.0941 | 1.25496 | ||||||||
\(783\) | 34.4759 | 1.23207 | ||||||||
\(784\) | −6.78300 | −0.242250 | ||||||||
\(785\) | −4.42411 | −0.157903 | ||||||||
\(786\) | −43.5032 | −1.55171 | ||||||||
\(787\) | −9.65981 | −0.344335 | −0.172168 | − | 0.985068i | \(-0.555077\pi\) | ||||
−0.172168 | + | 0.985068i | \(0.555077\pi\) | |||||||
\(788\) | −9.70754 | −0.345817 | ||||||||
\(789\) | −57.0591 | −2.03136 | ||||||||
\(790\) | −4.09207 | −0.145589 | ||||||||
\(791\) | −1.32539 | −0.0471255 | ||||||||
\(792\) | 3.50084 | 0.124397 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −22.5431 | −0.800025 | ||||||||
\(795\) | −4.50035 | −0.159611 | ||||||||
\(796\) | 16.4151 | 0.581819 | ||||||||
\(797\) | 54.4760 | 1.92964 | 0.964819 | − | 0.262913i | \(-0.0846833\pi\) | ||||
0.964819 | + | 0.262913i | \(0.0846833\pi\) | |||||||
\(798\) | 0.911529 | 0.0322678 | ||||||||
\(799\) | −68.2996 | −2.41627 | ||||||||
\(800\) | 4.62342 | 0.163463 | ||||||||
\(801\) | −9.14584 | −0.323152 | ||||||||
\(802\) | 29.5703 | 1.04416 | ||||||||
\(803\) | −59.4120 | −2.09660 | ||||||||
\(804\) | 18.5325 | 0.653592 | ||||||||
\(805\) | −1.88073 | −0.0662869 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −26.5598 | −0.934948 | ||||||||
\(808\) | −12.2449 | −0.430773 | ||||||||
\(809\) | −16.9543 | −0.596082 | −0.298041 | − | 0.954553i | \(-0.596333\pi\) | ||||
−0.298041 | + | 0.954553i | \(0.596333\pi\) | |||||||
\(810\) | −6.62740 | −0.232863 | ||||||||
\(811\) | −30.8121 | −1.08196 | −0.540980 | − | 0.841036i | \(-0.681947\pi\) | ||||
−0.540980 | + | 0.841036i | \(0.681947\pi\) | |||||||
\(812\) | −3.78044 | −0.132667 | ||||||||
\(813\) | 7.43402 | 0.260722 | ||||||||
\(814\) | −7.16280 | −0.251056 | ||||||||
\(815\) | −0.967980 | −0.0339068 | ||||||||
\(816\) | −10.4378 | −0.365395 | ||||||||
\(817\) | −2.48682 | −0.0870027 | ||||||||
\(818\) | −2.74046 | −0.0958180 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.89543 | 0.101113 | ||||||||
\(821\) | 21.2566 | 0.741862 | 0.370931 | − | 0.928661i | \(-0.379039\pi\) | ||||
0.370931 | + | 0.928661i | \(0.379039\pi\) | |||||||
\(822\) | −20.5326 | −0.716158 | ||||||||
\(823\) | 12.3494 | 0.430474 | 0.215237 | − | 0.976562i | \(-0.430948\pi\) | ||||
0.215237 | + | 0.976562i | \(0.430948\pi\) | |||||||
\(824\) | 10.6048 | 0.369435 | ||||||||
\(825\) | −38.2048 | −1.33012 | ||||||||
\(826\) | −5.86997 | −0.204242 | ||||||||
\(827\) | 9.26600 | 0.322210 | 0.161105 | − | 0.986937i | \(-0.448494\pi\) | ||||
0.161105 | + | 0.986937i | \(0.448494\pi\) | |||||||
\(828\) | −5.45420 | −0.189546 | ||||||||
\(829\) | −44.5534 | −1.54740 | −0.773701 | − | 0.633551i | \(-0.781597\pi\) | ||||
−0.773701 | + | 0.633551i | \(0.781597\pi\) | |||||||
\(830\) | −4.11173 | −0.142720 | ||||||||
\(831\) | 19.1524 | 0.664388 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −36.1815 | −1.25362 | ||||||||
\(834\) | 27.7242 | 0.960011 | ||||||||
\(835\) | −3.57944 | −0.123872 | ||||||||
\(836\) | 4.22291 | 0.146052 | ||||||||
\(837\) | 17.1643 | 0.593286 | ||||||||
\(838\) | 32.2035 | 1.11245 | ||||||||
\(839\) | 40.9342 | 1.41321 | 0.706603 | − | 0.707610i | \(-0.250227\pi\) | ||||
0.706603 | + | 0.707610i | \(0.250227\pi\) | |||||||
\(840\) | 0.559370 | 0.0193001 | ||||||||
\(841\) | 36.8612 | 1.27108 | ||||||||
\(842\) | −13.3021 | −0.458421 | ||||||||
\(843\) | 31.7614 | 1.09392 | ||||||||
\(844\) | 11.0380 | 0.379943 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 10.6149 | 0.364946 | ||||||||
\(847\) | −3.18298 | −0.109369 | ||||||||
\(848\) | −3.74778 | −0.128699 | ||||||||
\(849\) | −43.3410 | −1.48746 | ||||||||
\(850\) | 24.6620 | 0.845899 | ||||||||
\(851\) | 11.1594 | 0.382540 | ||||||||
\(852\) | −32.6503 | −1.11858 | ||||||||
\(853\) | 53.3185 | 1.82559 | 0.912795 | − | 0.408418i | \(-0.133919\pi\) | ||||
0.912795 | + | 0.408418i | \(0.133919\pi\) | |||||||
\(854\) | −1.87554 | −0.0641797 | ||||||||
\(855\) | 0.508733 | 0.0173983 | ||||||||
\(856\) | −13.9570 | −0.477041 | ||||||||
\(857\) | −5.51407 | −0.188357 | −0.0941786 | − | 0.995555i | \(-0.530022\pi\) | ||||
−0.0941786 | + | 0.995555i | \(0.530022\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21.7316 | 0.741472 | 0.370736 | − | 0.928738i | \(-0.379105\pi\) | ||||
0.370736 | + | 0.928738i | \(0.379105\pi\) | |||||||
\(860\) | −1.52606 | −0.0520383 | ||||||||
\(861\) | −4.30085 | −0.146572 | ||||||||
\(862\) | 25.9693 | 0.884519 | ||||||||
\(863\) | 11.5532 | 0.393277 | 0.196638 | − | 0.980476i | \(-0.436997\pi\) | ||||
0.196638 | + | 0.980476i | \(0.436997\pi\) | |||||||
\(864\) | −4.24816 | −0.144525 | ||||||||
\(865\) | 3.43331 | 0.116736 | ||||||||
\(866\) | −8.35232 | −0.283823 | ||||||||
\(867\) | −22.4113 | −0.761126 | ||||||||
\(868\) | −1.88215 | −0.0638842 | ||||||||
\(869\) | 28.1596 | 0.955248 | ||||||||
\(870\) | −9.74512 | −0.330390 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −2.18305 | −0.0739276 | ||||||||
\(873\) | 9.90959 | 0.335389 | ||||||||
\(874\) | −6.57915 | −0.222543 | ||||||||
\(875\) | −2.75097 | −0.0929996 | ||||||||
\(876\) | −27.5300 | −0.930152 | ||||||||
\(877\) | 26.4528 | 0.893247 | 0.446623 | − | 0.894722i | \(-0.352626\pi\) | ||||
0.446623 | + | 0.894722i | \(0.352626\pi\) | |||||||
\(878\) | −1.50999 | −0.0509595 | ||||||||
\(879\) | 9.39232 | 0.316795 | ||||||||
\(880\) | 2.59143 | 0.0873572 | ||||||||
\(881\) | −36.6167 | −1.23365 | −0.616823 | − | 0.787102i | \(-0.711581\pi\) | ||||
−0.616823 | + | 0.787102i | \(0.711581\pi\) | |||||||
\(882\) | 5.62319 | 0.189343 | ||||||||
\(883\) | 38.0108 | 1.27917 | 0.639583 | − | 0.768722i | \(-0.279107\pi\) | ||||
0.639583 | + | 0.768722i | \(0.279107\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −15.1315 | −0.508638 | ||||||||
\(886\) | −35.9799 | −1.20877 | ||||||||
\(887\) | −33.2559 | −1.11662 | −0.558312 | − | 0.829631i | \(-0.688551\pi\) | ||||
−0.558312 | + | 0.829631i | \(0.688551\pi\) | |||||||
\(888\) | −3.31906 | −0.111380 | ||||||||
\(889\) | 2.02236 | 0.0678279 | ||||||||
\(890\) | −6.77004 | −0.226932 | ||||||||
\(891\) | 45.6064 | 1.52787 | ||||||||
\(892\) | −22.0677 | −0.738882 | ||||||||
\(893\) | 12.8042 | 0.428477 | ||||||||
\(894\) | −40.6649 | −1.36004 | ||||||||
\(895\) | 1.01574 | 0.0339523 | ||||||||
\(896\) | 0.465830 | 0.0155623 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −8.07052 | −0.269317 | ||||||||
\(899\) | 32.7900 | 1.09361 | ||||||||
\(900\) | −3.83287 | −0.127762 | ||||||||
\(901\) | −19.9912 | −0.666003 | ||||||||
\(902\) | −19.9248 | −0.663425 | ||||||||
\(903\) | 2.26680 | 0.0754345 | ||||||||
\(904\) | −2.84523 | −0.0946310 | ||||||||
\(905\) | 6.65851 | 0.221336 | ||||||||
\(906\) | −32.3753 | −1.07560 | ||||||||
\(907\) | 6.68987 | 0.222134 | 0.111067 | − | 0.993813i | \(-0.464573\pi\) | ||||
0.111067 | + | 0.993813i | \(0.464573\pi\) | |||||||
\(908\) | −25.6025 | −0.849650 | ||||||||
\(909\) | 10.1511 | 0.336692 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.562558 | −0.0186384 | −0.00931919 | − | 0.999957i | \(-0.502966\pi\) | ||||
−0.00931919 | + | 0.999957i | \(0.502966\pi\) | |||||||
\(912\) | 1.95679 | 0.0647957 | ||||||||
\(913\) | 28.2948 | 0.936422 | ||||||||
\(914\) | 18.3167 | 0.605862 | ||||||||
\(915\) | −4.83473 | −0.159831 | ||||||||
\(916\) | 15.8683 | 0.524303 | ||||||||
\(917\) | 10.3563 | 0.341995 | ||||||||
\(918\) | −22.6603 | −0.747901 | ||||||||
\(919\) | 10.5952 | 0.349505 | 0.174752 | − | 0.984612i | \(-0.444088\pi\) | ||||
0.174752 | + | 0.984612i | \(0.444088\pi\) | |||||||
\(920\) | −4.03737 | −0.133108 | ||||||||
\(921\) | −41.6640 | −1.37288 | ||||||||
\(922\) | −4.10208 | −0.135095 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −3.84930 | −0.126633 | ||||||||
\(925\) | 7.84214 | 0.257848 | ||||||||
\(926\) | −4.75527 | −0.156268 | ||||||||
\(927\) | −8.79150 | −0.288751 | ||||||||
\(928\) | −8.11549 | −0.266404 | ||||||||
\(929\) | 7.72458 | 0.253435 | 0.126718 | − | 0.991939i | \(-0.459556\pi\) | ||||
0.126718 | + | 0.991939i | \(0.459556\pi\) | |||||||
\(930\) | −4.85175 | −0.159095 | ||||||||
\(931\) | 6.78300 | 0.222304 | ||||||||
\(932\) | 2.90658 | 0.0952084 | ||||||||
\(933\) | −7.41253 | −0.242675 | ||||||||
\(934\) | −5.92185 | −0.193769 | ||||||||
\(935\) | 13.8231 | 0.452063 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −35.1091 | −1.14696 | −0.573482 | − | 0.819218i | \(-0.694408\pi\) | ||||
−0.573482 | + | 0.819218i | \(0.694408\pi\) | |||||||
\(938\) | −4.41182 | −0.144051 | ||||||||
\(939\) | −41.3344 | −1.34890 | ||||||||
\(940\) | 7.85746 | 0.256282 | ||||||||
\(941\) | −30.6568 | −0.999383 | −0.499692 | − | 0.866203i | \(-0.666553\pi\) | ||||
−0.499692 | + | 0.866203i | \(0.666553\pi\) | |||||||
\(942\) | 14.1072 | 0.459637 | ||||||||
\(943\) | 31.0423 | 1.01088 | ||||||||
\(944\) | −12.6011 | −0.410131 | ||||||||
\(945\) | 1.21439 | 0.0395040 | ||||||||
\(946\) | 10.5016 | 0.341436 | ||||||||
\(947\) | 11.5703 | 0.375983 | 0.187991 | − | 0.982171i | \(-0.439802\pi\) | ||||
0.187991 | + | 0.982171i | \(0.439802\pi\) | |||||||
\(948\) | 13.0484 | 0.423793 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −4.62342 | −0.150004 | ||||||||
\(951\) | 3.36831 | 0.109225 | ||||||||
\(952\) | 2.48480 | 0.0805329 | ||||||||
\(953\) | −3.39587 | −0.110003 | −0.0550016 | − | 0.998486i | \(-0.517516\pi\) | ||||
−0.0550016 | + | 0.998486i | \(0.517516\pi\) | |||||||
\(954\) | 3.10696 | 0.100591 | ||||||||
\(955\) | 7.14997 | 0.231368 | ||||||||
\(956\) | 4.13013 | 0.133578 | ||||||||
\(957\) | 67.0609 | 2.16777 | ||||||||
\(958\) | −1.18632 | −0.0383282 | ||||||||
\(959\) | 4.88797 | 0.157841 | ||||||||
\(960\) | 1.20080 | 0.0387558 | ||||||||
\(961\) | −14.6750 | −0.473388 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 11.5705 | 0.372855 | ||||||||
\(964\) | 23.5902 | 0.759789 | ||||||||
\(965\) | 3.81913 | 0.122942 | ||||||||
\(966\) | 5.99709 | 0.192953 | ||||||||
\(967\) | −49.2494 | −1.58375 | −0.791877 | − | 0.610681i | \(-0.790896\pi\) | ||||
−0.791877 | + | 0.610681i | \(0.790896\pi\) | |||||||
\(968\) | −6.83293 | −0.219619 | ||||||||
\(969\) | 10.4378 | 0.335310 | ||||||||
\(970\) | 7.33539 | 0.235525 | ||||||||
\(971\) | 43.4284 | 1.39368 | 0.696841 | − | 0.717225i | \(-0.254588\pi\) | ||||
0.696841 | + | 0.717225i | \(0.254588\pi\) | |||||||
\(972\) | 8.38838 | 0.269057 | ||||||||
\(973\) | −6.59998 | −0.211586 | ||||||||
\(974\) | 2.65959 | 0.0852188 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.02624 | −0.128877 | ||||||||
\(977\) | −4.07927 | −0.130508 | −0.0652538 | − | 0.997869i | \(-0.520786\pi\) | ||||
−0.0652538 | + | 0.997869i | \(0.520786\pi\) | |||||||
\(978\) | 3.08660 | 0.0986987 | ||||||||
\(979\) | 46.5880 | 1.48896 | ||||||||
\(980\) | 4.16247 | 0.132965 | ||||||||
\(981\) | 1.80978 | 0.0577818 | ||||||||
\(982\) | −7.52332 | −0.240079 | ||||||||
\(983\) | −9.77783 | −0.311864 | −0.155932 | − | 0.987768i | \(-0.549838\pi\) | ||||
−0.155932 | + | 0.987768i | \(0.549838\pi\) | |||||||
\(984\) | −9.23266 | −0.294327 | ||||||||
\(985\) | 5.95714 | 0.189810 | ||||||||
\(986\) | −43.2892 | −1.37861 | ||||||||
\(987\) | −11.6714 | −0.371505 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −16.3611 | −0.520254 | ||||||||
\(990\) | −2.14833 | −0.0682784 | ||||||||
\(991\) | −38.9014 | −1.23574 | −0.617871 | − | 0.786279i | \(-0.712005\pi\) | ||||
−0.617871 | + | 0.786279i | \(0.712005\pi\) | |||||||
\(992\) | −4.04042 | −0.128283 | ||||||||
\(993\) | 13.8769 | 0.440370 | ||||||||
\(994\) | 7.77267 | 0.246534 | ||||||||
\(995\) | −10.0733 | −0.319346 | ||||||||
\(996\) | 13.1111 | 0.415441 | ||||||||
\(997\) | 35.3972 | 1.12104 | 0.560521 | − | 0.828140i | \(-0.310601\pi\) | ||||
0.560521 | + | 0.828140i | \(0.310601\pi\) | |||||||
\(998\) | −31.1291 | −0.985376 | ||||||||
\(999\) | −7.20563 | −0.227976 |
(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 | 6422.2.a.be.1.2 | 7 | ||
13.5 | odd | 4 | 494.2.d.c.77.9 | yes | 14 | ||
13.8 | odd | 4 | 494.2.d.c.77.2 | ✓ | 14 | ||
13.12 | even | 2 | 6422.2.a.bf.1.2 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
494.2.d.c.77.2 | ✓ | 14 | 13.8 | odd | 4 | ||
494.2.d.c.77.9 | yes | 14 | 13.5 | odd | 4 | ||
6422.2.a.be.1.2 | 7 | 1.1 | even | 1 | trivial | ||
6422.2.a.bf.1.2 | 7 | 13.12 | even | 2 |