Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5054,2,Mod(1,5054)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5054, 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("5054.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5054 = 2 \cdot 7 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5054.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: | \(40.3563931816\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5054.1 |
$q$-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 | ||||||||
\(3\) | −0.618034 | −0.356822 | −0.178411 | − | 0.983956i | \(-0.557096\pi\) | ||||
−0.178411 | + | 0.983956i | \(0.557096\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | 0.223607 | − | 0.974679i | \(-0.428217\pi\) | ||||
0.223607 | + | 0.974679i | \(0.428217\pi\) | |||||||
\(6\) | −0.618034 | −0.252311 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.61803 | −0.872678 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −5.00000 | −1.50756 | −0.753778 | − | 0.657129i | \(-0.771771\pi\) | ||||
−0.753778 | + | 0.657129i | \(0.771771\pi\) | |||||||
\(12\) | −0.618034 | −0.178411 | ||||||||
\(13\) | 4.85410 | 1.34629 | 0.673143 | − | 0.739512i | \(-0.264944\pi\) | ||||
0.673143 | + | 0.739512i | \(0.264944\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | −0.618034 | −0.159576 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.85410 | 1.66236 | 0.831182 | − | 0.556001i | \(-0.187665\pi\) | ||||
0.831182 | + | 0.556001i | \(0.187665\pi\) | |||||||
\(18\) | −2.61803 | −0.617077 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 0.618034 | 0.134866 | ||||||||
\(22\) | −5.00000 | −1.06600 | ||||||||
\(23\) | −3.76393 | −0.784834 | −0.392417 | − | 0.919787i | \(-0.628361\pi\) | ||||
−0.392417 | + | 0.919787i | \(0.628361\pi\) | |||||||
\(24\) | −0.618034 | −0.126156 | ||||||||
\(25\) | −4.00000 | −0.800000 | ||||||||
\(26\) | 4.85410 | 0.951968 | ||||||||
\(27\) | 3.47214 | 0.668213 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | −8.23607 | −1.52940 | −0.764700 | − | 0.644387i | \(-0.777113\pi\) | ||||
−0.764700 | + | 0.644387i | \(0.777113\pi\) | |||||||
\(30\) | −0.618034 | −0.112837 | ||||||||
\(31\) | −6.70820 | −1.20483 | −0.602414 | − | 0.798183i | \(-0.705795\pi\) | ||||
−0.602414 | + | 0.798183i | \(0.705795\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 3.09017 | 0.537930 | ||||||||
\(34\) | 6.85410 | 1.17547 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | −2.61803 | −0.436339 | ||||||||
\(37\) | 5.94427 | 0.977232 | 0.488616 | − | 0.872499i | \(-0.337502\pi\) | ||||
0.488616 | + | 0.872499i | \(0.337502\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.00000 | −0.480384 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −1.09017 | −0.170256 | −0.0851280 | − | 0.996370i | \(-0.527130\pi\) | ||||
−0.0851280 | + | 0.996370i | \(0.527130\pi\) | |||||||
\(42\) | 0.618034 | 0.0953647 | ||||||||
\(43\) | −6.85410 | −1.04524 | −0.522620 | − | 0.852566i | \(-0.675045\pi\) | ||||
−0.522620 | + | 0.852566i | \(0.675045\pi\) | |||||||
\(44\) | −5.00000 | −0.753778 | ||||||||
\(45\) | −2.61803 | −0.390273 | ||||||||
\(46\) | −3.76393 | −0.554962 | ||||||||
\(47\) | 7.94427 | 1.15879 | 0.579396 | − | 0.815046i | \(-0.303289\pi\) | ||||
0.579396 | + | 0.815046i | \(0.303289\pi\) | |||||||
\(48\) | −0.618034 | −0.0892055 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −4.00000 | −0.565685 | ||||||||
\(51\) | −4.23607 | −0.593168 | ||||||||
\(52\) | 4.85410 | 0.673143 | ||||||||
\(53\) | −12.7082 | −1.74561 | −0.872803 | − | 0.488073i | \(-0.837700\pi\) | ||||
−0.872803 | + | 0.488073i | \(0.837700\pi\) | |||||||
\(54\) | 3.47214 | 0.472498 | ||||||||
\(55\) | −5.00000 | −0.674200 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −8.23607 | −1.08145 | ||||||||
\(59\) | 11.0000 | 1.43208 | 0.716039 | − | 0.698060i | \(-0.245953\pi\) | ||||
0.716039 | + | 0.698060i | \(0.245953\pi\) | |||||||
\(60\) | −0.618034 | −0.0797878 | ||||||||
\(61\) | 7.47214 | 0.956709 | 0.478354 | − | 0.878167i | \(-0.341233\pi\) | ||||
0.478354 | + | 0.878167i | \(0.341233\pi\) | |||||||
\(62\) | −6.70820 | −0.851943 | ||||||||
\(63\) | 2.61803 | 0.329841 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 4.85410 | 0.602077 | ||||||||
\(66\) | 3.09017 | 0.380374 | ||||||||
\(67\) | 7.85410 | 0.959531 | 0.479766 | − | 0.877397i | \(-0.340722\pi\) | ||||
0.479766 | + | 0.877397i | \(0.340722\pi\) | |||||||
\(68\) | 6.85410 | 0.831182 | ||||||||
\(69\) | 2.32624 | 0.280046 | ||||||||
\(70\) | −1.00000 | −0.119523 | ||||||||
\(71\) | −10.0000 | −1.18678 | −0.593391 | − | 0.804914i | \(-0.702211\pi\) | ||||
−0.593391 | + | 0.804914i | \(0.702211\pi\) | |||||||
\(72\) | −2.61803 | −0.308538 | ||||||||
\(73\) | −14.5623 | −1.70439 | −0.852194 | − | 0.523225i | \(-0.824729\pi\) | ||||
−0.852194 | + | 0.523225i | \(0.824729\pi\) | |||||||
\(74\) | 5.94427 | 0.691008 | ||||||||
\(75\) | 2.47214 | 0.285458 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.00000 | 0.569803 | ||||||||
\(78\) | −3.00000 | −0.339683 | ||||||||
\(79\) | −8.85410 | −0.996164 | −0.498082 | − | 0.867130i | \(-0.665962\pi\) | ||||
−0.498082 | + | 0.867130i | \(0.665962\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 5.70820 | 0.634245 | ||||||||
\(82\) | −1.09017 | −0.120389 | ||||||||
\(83\) | −15.4164 | −1.69217 | −0.846085 | − | 0.533048i | \(-0.821047\pi\) | ||||
−0.846085 | + | 0.533048i | \(0.821047\pi\) | |||||||
\(84\) | 0.618034 | 0.0674330 | ||||||||
\(85\) | 6.85410 | 0.743432 | ||||||||
\(86\) | −6.85410 | −0.739097 | ||||||||
\(87\) | 5.09017 | 0.545724 | ||||||||
\(88\) | −5.00000 | −0.533002 | ||||||||
\(89\) | 4.85410 | 0.514534 | 0.257267 | − | 0.966340i | \(-0.417178\pi\) | ||||
0.257267 | + | 0.966340i | \(0.417178\pi\) | |||||||
\(90\) | −2.61803 | −0.275965 | ||||||||
\(91\) | −4.85410 | −0.508848 | ||||||||
\(92\) | −3.76393 | −0.392417 | ||||||||
\(93\) | 4.14590 | 0.429910 | ||||||||
\(94\) | 7.94427 | 0.819389 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.618034 | −0.0630778 | ||||||||
\(97\) | −9.47214 | −0.961750 | −0.480875 | − | 0.876789i | \(-0.659681\pi\) | ||||
−0.480875 | + | 0.876789i | \(0.659681\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 13.0902 | 1.31561 | ||||||||
\(100\) | −4.00000 | −0.400000 | ||||||||
\(101\) | 4.14590 | 0.412532 | 0.206266 | − | 0.978496i | \(-0.433869\pi\) | ||||
0.206266 | + | 0.978496i | \(0.433869\pi\) | |||||||
\(102\) | −4.23607 | −0.419433 | ||||||||
\(103\) | −15.0902 | −1.48688 | −0.743439 | − | 0.668803i | \(-0.766807\pi\) | ||||
−0.743439 | + | 0.668803i | \(0.766807\pi\) | |||||||
\(104\) | 4.85410 | 0.475984 | ||||||||
\(105\) | 0.618034 | 0.0603139 | ||||||||
\(106\) | −12.7082 | −1.23433 | ||||||||
\(107\) | −13.9443 | −1.34804 | −0.674022 | − | 0.738711i | \(-0.735435\pi\) | ||||
−0.674022 | + | 0.738711i | \(0.735435\pi\) | |||||||
\(108\) | 3.47214 | 0.334106 | ||||||||
\(109\) | −13.5623 | −1.29903 | −0.649517 | − | 0.760347i | \(-0.725029\pi\) | ||||
−0.649517 | + | 0.760347i | \(0.725029\pi\) | |||||||
\(110\) | −5.00000 | −0.476731 | ||||||||
\(111\) | −3.67376 | −0.348698 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | 3.85410 | 0.362563 | 0.181282 | − | 0.983431i | \(-0.441975\pi\) | ||||
0.181282 | + | 0.983431i | \(0.441975\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.76393 | −0.350988 | ||||||||
\(116\) | −8.23607 | −0.764700 | ||||||||
\(117\) | −12.7082 | −1.17487 | ||||||||
\(118\) | 11.0000 | 1.01263 | ||||||||
\(119\) | −6.85410 | −0.628314 | ||||||||
\(120\) | −0.618034 | −0.0564185 | ||||||||
\(121\) | 14.0000 | 1.27273 | ||||||||
\(122\) | 7.47214 | 0.676495 | ||||||||
\(123\) | 0.673762 | 0.0607511 | ||||||||
\(124\) | −6.70820 | −0.602414 | ||||||||
\(125\) | −9.00000 | −0.804984 | ||||||||
\(126\) | 2.61803 | 0.233233 | ||||||||
\(127\) | −7.32624 | −0.650098 | −0.325049 | − | 0.945697i | \(-0.605381\pi\) | ||||
−0.325049 | + | 0.945697i | \(0.605381\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 4.23607 | 0.372965 | ||||||||
\(130\) | 4.85410 | 0.425733 | ||||||||
\(131\) | −4.38197 | −0.382854 | −0.191427 | − | 0.981507i | \(-0.561312\pi\) | ||||
−0.191427 | + | 0.981507i | \(0.561312\pi\) | |||||||
\(132\) | 3.09017 | 0.268965 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 7.85410 | 0.678491 | ||||||||
\(135\) | 3.47214 | 0.298834 | ||||||||
\(136\) | 6.85410 | 0.587734 | ||||||||
\(137\) | 21.1246 | 1.80480 | 0.902399 | − | 0.430902i | \(-0.141805\pi\) | ||||
0.902399 | + | 0.430902i | \(0.141805\pi\) | |||||||
\(138\) | 2.32624 | 0.198023 | ||||||||
\(139\) | −0.236068 | −0.0200230 | −0.0100115 | − | 0.999950i | \(-0.503187\pi\) | ||||
−0.0100115 | + | 0.999950i | \(0.503187\pi\) | |||||||
\(140\) | −1.00000 | −0.0845154 | ||||||||
\(141\) | −4.90983 | −0.413482 | ||||||||
\(142\) | −10.0000 | −0.839181 | ||||||||
\(143\) | −24.2705 | −2.02960 | ||||||||
\(144\) | −2.61803 | −0.218169 | ||||||||
\(145\) | −8.23607 | −0.683968 | ||||||||
\(146\) | −14.5623 | −1.20519 | ||||||||
\(147\) | −0.618034 | −0.0509746 | ||||||||
\(148\) | 5.94427 | 0.488616 | ||||||||
\(149\) | 1.38197 | 0.113215 | 0.0566075 | − | 0.998397i | \(-0.481972\pi\) | ||||
0.0566075 | + | 0.998397i | \(0.481972\pi\) | |||||||
\(150\) | 2.47214 | 0.201849 | ||||||||
\(151\) | −14.2361 | −1.15851 | −0.579257 | − | 0.815145i | \(-0.696657\pi\) | ||||
−0.579257 | + | 0.815145i | \(0.696657\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −17.9443 | −1.45071 | ||||||||
\(154\) | 5.00000 | 0.402911 | ||||||||
\(155\) | −6.70820 | −0.538816 | ||||||||
\(156\) | −3.00000 | −0.240192 | ||||||||
\(157\) | 22.3262 | 1.78183 | 0.890914 | − | 0.454172i | \(-0.150065\pi\) | ||||
0.890914 | + | 0.454172i | \(0.150065\pi\) | |||||||
\(158\) | −8.85410 | −0.704395 | ||||||||
\(159\) | 7.85410 | 0.622871 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 3.76393 | 0.296639 | ||||||||
\(162\) | 5.70820 | 0.448479 | ||||||||
\(163\) | 0.472136 | 0.0369805 | 0.0184903 | − | 0.999829i | \(-0.494114\pi\) | ||||
0.0184903 | + | 0.999829i | \(0.494114\pi\) | |||||||
\(164\) | −1.09017 | −0.0851280 | ||||||||
\(165\) | 3.09017 | 0.240569 | ||||||||
\(166\) | −15.4164 | −1.19655 | ||||||||
\(167\) | 1.81966 | 0.140810 | 0.0704048 | − | 0.997519i | \(-0.477571\pi\) | ||||
0.0704048 | + | 0.997519i | \(0.477571\pi\) | |||||||
\(168\) | 0.618034 | 0.0476824 | ||||||||
\(169\) | 10.5623 | 0.812485 | ||||||||
\(170\) | 6.85410 | 0.525686 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6.85410 | −0.522620 | ||||||||
\(173\) | 1.76393 | 0.134109 | 0.0670546 | − | 0.997749i | \(-0.478640\pi\) | ||||
0.0670546 | + | 0.997749i | \(0.478640\pi\) | |||||||
\(174\) | 5.09017 | 0.385885 | ||||||||
\(175\) | 4.00000 | 0.302372 | ||||||||
\(176\) | −5.00000 | −0.376889 | ||||||||
\(177\) | −6.79837 | −0.510997 | ||||||||
\(178\) | 4.85410 | 0.363830 | ||||||||
\(179\) | 9.03444 | 0.675266 | 0.337633 | − | 0.941278i | \(-0.390374\pi\) | ||||
0.337633 | + | 0.941278i | \(0.390374\pi\) | |||||||
\(180\) | −2.61803 | −0.195137 | ||||||||
\(181\) | −15.7639 | −1.17172 | −0.585862 | − | 0.810411i | \(-0.699244\pi\) | ||||
−0.585862 | + | 0.810411i | \(0.699244\pi\) | |||||||
\(182\) | −4.85410 | −0.359810 | ||||||||
\(183\) | −4.61803 | −0.341375 | ||||||||
\(184\) | −3.76393 | −0.277481 | ||||||||
\(185\) | 5.94427 | 0.437032 | ||||||||
\(186\) | 4.14590 | 0.303992 | ||||||||
\(187\) | −34.2705 | −2.50611 | ||||||||
\(188\) | 7.94427 | 0.579396 | ||||||||
\(189\) | −3.47214 | −0.252561 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.81966 | 0.204023 | 0.102012 | − | 0.994783i | \(-0.467472\pi\) | ||||
0.102012 | + | 0.994783i | \(0.467472\pi\) | |||||||
\(192\) | −0.618034 | −0.0446028 | ||||||||
\(193\) | −10.1803 | −0.732797 | −0.366398 | − | 0.930458i | \(-0.619409\pi\) | ||||
−0.366398 | + | 0.930458i | \(0.619409\pi\) | |||||||
\(194\) | −9.47214 | −0.680060 | ||||||||
\(195\) | −3.00000 | −0.214834 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −7.56231 | −0.538792 | −0.269396 | − | 0.963029i | \(-0.586824\pi\) | ||||
−0.269396 | + | 0.963029i | \(0.586824\pi\) | |||||||
\(198\) | 13.0902 | 0.930278 | ||||||||
\(199\) | −4.90983 | −0.348049 | −0.174024 | − | 0.984741i | \(-0.555677\pi\) | ||||
−0.174024 | + | 0.984741i | \(0.555677\pi\) | |||||||
\(200\) | −4.00000 | −0.282843 | ||||||||
\(201\) | −4.85410 | −0.342382 | ||||||||
\(202\) | 4.14590 | 0.291704 | ||||||||
\(203\) | 8.23607 | 0.578059 | ||||||||
\(204\) | −4.23607 | −0.296584 | ||||||||
\(205\) | −1.09017 | −0.0761408 | ||||||||
\(206\) | −15.0902 | −1.05138 | ||||||||
\(207\) | 9.85410 | 0.684907 | ||||||||
\(208\) | 4.85410 | 0.336571 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0.618034 | 0.0426484 | ||||||||
\(211\) | −4.05573 | −0.279208 | −0.139604 | − | 0.990207i | \(-0.544583\pi\) | ||||
−0.139604 | + | 0.990207i | \(0.544583\pi\) | |||||||
\(212\) | −12.7082 | −0.872803 | ||||||||
\(213\) | 6.18034 | 0.423470 | ||||||||
\(214\) | −13.9443 | −0.953211 | ||||||||
\(215\) | −6.85410 | −0.467446 | ||||||||
\(216\) | 3.47214 | 0.236249 | ||||||||
\(217\) | 6.70820 | 0.455383 | ||||||||
\(218\) | −13.5623 | −0.918555 | ||||||||
\(219\) | 9.00000 | 0.608164 | ||||||||
\(220\) | −5.00000 | −0.337100 | ||||||||
\(221\) | 33.2705 | 2.23802 | ||||||||
\(222\) | −3.67376 | −0.246567 | ||||||||
\(223\) | 5.65248 | 0.378518 | 0.189259 | − | 0.981927i | \(-0.439391\pi\) | ||||
0.189259 | + | 0.981927i | \(0.439391\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 10.4721 | 0.698142 | ||||||||
\(226\) | 3.85410 | 0.256371 | ||||||||
\(227\) | −14.2361 | −0.944881 | −0.472441 | − | 0.881363i | \(-0.656627\pi\) | ||||
−0.472441 | + | 0.881363i | \(0.656627\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.0902 | −0.666777 | −0.333389 | − | 0.942790i | \(-0.608192\pi\) | ||||
−0.333389 | + | 0.942790i | \(0.608192\pi\) | |||||||
\(230\) | −3.76393 | −0.248186 | ||||||||
\(231\) | −3.09017 | −0.203318 | ||||||||
\(232\) | −8.23607 | −0.540724 | ||||||||
\(233\) | −11.0344 | −0.722890 | −0.361445 | − | 0.932393i | \(-0.617717\pi\) | ||||
−0.361445 | + | 0.932393i | \(0.617717\pi\) | |||||||
\(234\) | −12.7082 | −0.830761 | ||||||||
\(235\) | 7.94427 | 0.518227 | ||||||||
\(236\) | 11.0000 | 0.716039 | ||||||||
\(237\) | 5.47214 | 0.355453 | ||||||||
\(238\) | −6.85410 | −0.444285 | ||||||||
\(239\) | −11.1459 | −0.720968 | −0.360484 | − | 0.932765i | \(-0.617388\pi\) | ||||
−0.360484 | + | 0.932765i | \(0.617388\pi\) | |||||||
\(240\) | −0.618034 | −0.0398939 | ||||||||
\(241\) | 7.90983 | 0.509517 | 0.254758 | − | 0.967005i | \(-0.418004\pi\) | ||||
0.254758 | + | 0.967005i | \(0.418004\pi\) | |||||||
\(242\) | 14.0000 | 0.899954 | ||||||||
\(243\) | −13.9443 | −0.894525 | ||||||||
\(244\) | 7.47214 | 0.478354 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 0.673762 | 0.0429575 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −6.70820 | −0.425971 | ||||||||
\(249\) | 9.52786 | 0.603804 | ||||||||
\(250\) | −9.00000 | −0.569210 | ||||||||
\(251\) | 6.47214 | 0.408518 | 0.204259 | − | 0.978917i | \(-0.434522\pi\) | ||||
0.204259 | + | 0.978917i | \(0.434522\pi\) | |||||||
\(252\) | 2.61803 | 0.164921 | ||||||||
\(253\) | 18.8197 | 1.18318 | ||||||||
\(254\) | −7.32624 | −0.459689 | ||||||||
\(255\) | −4.23607 | −0.265273 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 8.05573 | 0.502503 | 0.251251 | − | 0.967922i | \(-0.419158\pi\) | ||||
0.251251 | + | 0.967922i | \(0.419158\pi\) | |||||||
\(258\) | 4.23607 | 0.263726 | ||||||||
\(259\) | −5.94427 | −0.369359 | ||||||||
\(260\) | 4.85410 | 0.301039 | ||||||||
\(261\) | 21.5623 | 1.33467 | ||||||||
\(262\) | −4.38197 | −0.270719 | ||||||||
\(263\) | −25.1803 | −1.55269 | −0.776343 | − | 0.630311i | \(-0.782928\pi\) | ||||
−0.776343 | + | 0.630311i | \(0.782928\pi\) | |||||||
\(264\) | 3.09017 | 0.190187 | ||||||||
\(265\) | −12.7082 | −0.780659 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.00000 | −0.183597 | ||||||||
\(268\) | 7.85410 | 0.479766 | ||||||||
\(269\) | 9.18034 | 0.559735 | 0.279868 | − | 0.960039i | \(-0.409709\pi\) | ||||
0.279868 | + | 0.960039i | \(0.409709\pi\) | |||||||
\(270\) | 3.47214 | 0.211307 | ||||||||
\(271\) | 1.65248 | 0.100381 | 0.0501904 | − | 0.998740i | \(-0.484017\pi\) | ||||
0.0501904 | + | 0.998740i | \(0.484017\pi\) | |||||||
\(272\) | 6.85410 | 0.415591 | ||||||||
\(273\) | 3.00000 | 0.181568 | ||||||||
\(274\) | 21.1246 | 1.27618 | ||||||||
\(275\) | 20.0000 | 1.20605 | ||||||||
\(276\) | 2.32624 | 0.140023 | ||||||||
\(277\) | −8.00000 | −0.480673 | −0.240337 | − | 0.970690i | \(-0.577258\pi\) | ||||
−0.240337 | + | 0.970690i | \(0.577258\pi\) | |||||||
\(278\) | −0.236068 | −0.0141584 | ||||||||
\(279\) | 17.5623 | 1.05143 | ||||||||
\(280\) | −1.00000 | −0.0597614 | ||||||||
\(281\) | −12.2361 | −0.729943 | −0.364971 | − | 0.931019i | \(-0.618921\pi\) | ||||
−0.364971 | + | 0.931019i | \(0.618921\pi\) | |||||||
\(282\) | −4.90983 | −0.292376 | ||||||||
\(283\) | 6.43769 | 0.382681 | 0.191341 | − | 0.981524i | \(-0.438716\pi\) | ||||
0.191341 | + | 0.981524i | \(0.438716\pi\) | |||||||
\(284\) | −10.0000 | −0.593391 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −24.2705 | −1.43515 | ||||||||
\(287\) | 1.09017 | 0.0643507 | ||||||||
\(288\) | −2.61803 | −0.154269 | ||||||||
\(289\) | 29.9787 | 1.76345 | ||||||||
\(290\) | −8.23607 | −0.483639 | ||||||||
\(291\) | 5.85410 | 0.343174 | ||||||||
\(292\) | −14.5623 | −0.852194 | ||||||||
\(293\) | 16.2361 | 0.948521 | 0.474261 | − | 0.880385i | \(-0.342715\pi\) | ||||
0.474261 | + | 0.880385i | \(0.342715\pi\) | |||||||
\(294\) | −0.618034 | −0.0360445 | ||||||||
\(295\) | 11.0000 | 0.640445 | ||||||||
\(296\) | 5.94427 | 0.345504 | ||||||||
\(297\) | −17.3607 | −1.00737 | ||||||||
\(298\) | 1.38197 | 0.0800551 | ||||||||
\(299\) | −18.2705 | −1.05661 | ||||||||
\(300\) | 2.47214 | 0.142729 | ||||||||
\(301\) | 6.85410 | 0.395064 | ||||||||
\(302\) | −14.2361 | −0.819194 | ||||||||
\(303\) | −2.56231 | −0.147201 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.47214 | 0.427853 | ||||||||
\(306\) | −17.9443 | −1.02581 | ||||||||
\(307\) | 4.94427 | 0.282185 | 0.141092 | − | 0.989996i | \(-0.454939\pi\) | ||||
0.141092 | + | 0.989996i | \(0.454939\pi\) | |||||||
\(308\) | 5.00000 | 0.284901 | ||||||||
\(309\) | 9.32624 | 0.530551 | ||||||||
\(310\) | −6.70820 | −0.381000 | ||||||||
\(311\) | 19.7639 | 1.12071 | 0.560355 | − | 0.828253i | \(-0.310665\pi\) | ||||
0.560355 | + | 0.828253i | \(0.310665\pi\) | |||||||
\(312\) | −3.00000 | −0.169842 | ||||||||
\(313\) | 18.9098 | 1.06885 | 0.534423 | − | 0.845217i | \(-0.320529\pi\) | ||||
0.534423 | + | 0.845217i | \(0.320529\pi\) | |||||||
\(314\) | 22.3262 | 1.25994 | ||||||||
\(315\) | 2.61803 | 0.147510 | ||||||||
\(316\) | −8.85410 | −0.498082 | ||||||||
\(317\) | 8.41641 | 0.472713 | 0.236356 | − | 0.971666i | \(-0.424047\pi\) | ||||
0.236356 | + | 0.971666i | \(0.424047\pi\) | |||||||
\(318\) | 7.85410 | 0.440436 | ||||||||
\(319\) | 41.1803 | 2.30566 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 8.61803 | 0.481012 | ||||||||
\(322\) | 3.76393 | 0.209756 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 5.70820 | 0.317122 | ||||||||
\(325\) | −19.4164 | −1.07703 | ||||||||
\(326\) | 0.472136 | 0.0261492 | ||||||||
\(327\) | 8.38197 | 0.463524 | ||||||||
\(328\) | −1.09017 | −0.0601946 | ||||||||
\(329\) | −7.94427 | −0.437982 | ||||||||
\(330\) | 3.09017 | 0.170108 | ||||||||
\(331\) | 12.4721 | 0.685531 | 0.342765 | − | 0.939421i | \(-0.388636\pi\) | ||||
0.342765 | + | 0.939421i | \(0.388636\pi\) | |||||||
\(332\) | −15.4164 | −0.846085 | ||||||||
\(333\) | −15.5623 | −0.852809 | ||||||||
\(334\) | 1.81966 | 0.0995674 | ||||||||
\(335\) | 7.85410 | 0.429115 | ||||||||
\(336\) | 0.618034 | 0.0337165 | ||||||||
\(337\) | −33.4508 | −1.82218 | −0.911092 | − | 0.412203i | \(-0.864759\pi\) | ||||
−0.911092 | + | 0.412203i | \(0.864759\pi\) | |||||||
\(338\) | 10.5623 | 0.574514 | ||||||||
\(339\) | −2.38197 | −0.129371 | ||||||||
\(340\) | 6.85410 | 0.371716 | ||||||||
\(341\) | 33.5410 | 1.81635 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −6.85410 | −0.369548 | ||||||||
\(345\) | 2.32624 | 0.125240 | ||||||||
\(346\) | 1.76393 | 0.0948296 | ||||||||
\(347\) | −5.05573 | −0.271406 | −0.135703 | − | 0.990750i | \(-0.543329\pi\) | ||||
−0.135703 | + | 0.990750i | \(0.543329\pi\) | |||||||
\(348\) | 5.09017 | 0.272862 | ||||||||
\(349\) | −6.70820 | −0.359082 | −0.179541 | − | 0.983750i | \(-0.557461\pi\) | ||||
−0.179541 | + | 0.983750i | \(0.557461\pi\) | |||||||
\(350\) | 4.00000 | 0.213809 | ||||||||
\(351\) | 16.8541 | 0.899605 | ||||||||
\(352\) | −5.00000 | −0.266501 | ||||||||
\(353\) | 13.0902 | 0.696719 | 0.348360 | − | 0.937361i | \(-0.386739\pi\) | ||||
0.348360 | + | 0.937361i | \(0.386739\pi\) | |||||||
\(354\) | −6.79837 | −0.361329 | ||||||||
\(355\) | −10.0000 | −0.530745 | ||||||||
\(356\) | 4.85410 | 0.257267 | ||||||||
\(357\) | 4.23607 | 0.224196 | ||||||||
\(358\) | 9.03444 | 0.477485 | ||||||||
\(359\) | 27.9443 | 1.47484 | 0.737421 | − | 0.675433i | \(-0.236043\pi\) | ||||
0.737421 | + | 0.675433i | \(0.236043\pi\) | |||||||
\(360\) | −2.61803 | −0.137983 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | −15.7639 | −0.828534 | ||||||||
\(363\) | −8.65248 | −0.454137 | ||||||||
\(364\) | −4.85410 | −0.254424 | ||||||||
\(365\) | −14.5623 | −0.762226 | ||||||||
\(366\) | −4.61803 | −0.241389 | ||||||||
\(367\) | 9.67376 | 0.504966 | 0.252483 | − | 0.967601i | \(-0.418753\pi\) | ||||
0.252483 | + | 0.967601i | \(0.418753\pi\) | |||||||
\(368\) | −3.76393 | −0.196209 | ||||||||
\(369\) | 2.85410 | 0.148579 | ||||||||
\(370\) | 5.94427 | 0.309028 | ||||||||
\(371\) | 12.7082 | 0.659777 | ||||||||
\(372\) | 4.14590 | 0.214955 | ||||||||
\(373\) | −6.85410 | −0.354892 | −0.177446 | − | 0.984131i | \(-0.556784\pi\) | ||||
−0.177446 | + | 0.984131i | \(0.556784\pi\) | |||||||
\(374\) | −34.2705 | −1.77209 | ||||||||
\(375\) | 5.56231 | 0.287236 | ||||||||
\(376\) | 7.94427 | 0.409695 | ||||||||
\(377\) | −39.9787 | −2.05901 | ||||||||
\(378\) | −3.47214 | −0.178587 | ||||||||
\(379\) | 12.0344 | 0.618168 | 0.309084 | − | 0.951035i | \(-0.399978\pi\) | ||||
0.309084 | + | 0.951035i | \(0.399978\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.52786 | 0.231970 | ||||||||
\(382\) | 2.81966 | 0.144266 | ||||||||
\(383\) | 5.94427 | 0.303738 | 0.151869 | − | 0.988401i | \(-0.451471\pi\) | ||||
0.151869 | + | 0.988401i | \(0.451471\pi\) | |||||||
\(384\) | −0.618034 | −0.0315389 | ||||||||
\(385\) | 5.00000 | 0.254824 | ||||||||
\(386\) | −10.1803 | −0.518166 | ||||||||
\(387\) | 17.9443 | 0.912159 | ||||||||
\(388\) | −9.47214 | −0.480875 | ||||||||
\(389\) | 11.3820 | 0.577089 | 0.288544 | − | 0.957467i | \(-0.406829\pi\) | ||||
0.288544 | + | 0.957467i | \(0.406829\pi\) | |||||||
\(390\) | −3.00000 | −0.151911 | ||||||||
\(391\) | −25.7984 | −1.30468 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | 2.70820 | 0.136611 | ||||||||
\(394\) | −7.56231 | −0.380983 | ||||||||
\(395\) | −8.85410 | −0.445498 | ||||||||
\(396\) | 13.0902 | 0.657806 | ||||||||
\(397\) | −32.2705 | −1.61961 | −0.809805 | − | 0.586699i | \(-0.800427\pi\) | ||||
−0.809805 | + | 0.586699i | \(0.800427\pi\) | |||||||
\(398\) | −4.90983 | −0.246108 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.00000 | −0.200000 | ||||||||
\(401\) | −6.58359 | −0.328769 | −0.164384 | − | 0.986396i | \(-0.552564\pi\) | ||||
−0.164384 | + | 0.986396i | \(0.552564\pi\) | |||||||
\(402\) | −4.85410 | −0.242101 | ||||||||
\(403\) | −32.5623 | −1.62204 | ||||||||
\(404\) | 4.14590 | 0.206266 | ||||||||
\(405\) | 5.70820 | 0.283643 | ||||||||
\(406\) | 8.23607 | 0.408749 | ||||||||
\(407\) | −29.7214 | −1.47323 | ||||||||
\(408\) | −4.23607 | −0.209717 | ||||||||
\(409\) | 17.2148 | 0.851216 | 0.425608 | − | 0.904908i | \(-0.360060\pi\) | ||||
0.425608 | + | 0.904908i | \(0.360060\pi\) | |||||||
\(410\) | −1.09017 | −0.0538397 | ||||||||
\(411\) | −13.0557 | −0.643992 | ||||||||
\(412\) | −15.0902 | −0.743439 | ||||||||
\(413\) | −11.0000 | −0.541275 | ||||||||
\(414\) | 9.85410 | 0.484303 | ||||||||
\(415\) | −15.4164 | −0.756762 | ||||||||
\(416\) | 4.85410 | 0.237992 | ||||||||
\(417\) | 0.145898 | 0.00714466 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −25.7426 | −1.25761 | −0.628805 | − | 0.777563i | \(-0.716456\pi\) | ||||
−0.628805 | + | 0.777563i | \(0.716456\pi\) | |||||||
\(420\) | 0.618034 | 0.0301570 | ||||||||
\(421\) | −8.05573 | −0.392612 | −0.196306 | − | 0.980543i | \(-0.562895\pi\) | ||||
−0.196306 | + | 0.980543i | \(0.562895\pi\) | |||||||
\(422\) | −4.05573 | −0.197430 | ||||||||
\(423\) | −20.7984 | −1.01125 | ||||||||
\(424\) | −12.7082 | −0.617165 | ||||||||
\(425\) | −27.4164 | −1.32989 | ||||||||
\(426\) | 6.18034 | 0.299438 | ||||||||
\(427\) | −7.47214 | −0.361602 | ||||||||
\(428\) | −13.9443 | −0.674022 | ||||||||
\(429\) | 15.0000 | 0.724207 | ||||||||
\(430\) | −6.85410 | −0.330534 | ||||||||
\(431\) | 2.94427 | 0.141821 | 0.0709103 | − | 0.997483i | \(-0.477410\pi\) | ||||
0.0709103 | + | 0.997483i | \(0.477410\pi\) | |||||||
\(432\) | 3.47214 | 0.167053 | ||||||||
\(433\) | −27.6180 | −1.32724 | −0.663619 | − | 0.748071i | \(-0.730980\pi\) | ||||
−0.663619 | + | 0.748071i | \(0.730980\pi\) | |||||||
\(434\) | 6.70820 | 0.322004 | ||||||||
\(435\) | 5.09017 | 0.244055 | ||||||||
\(436\) | −13.5623 | −0.649517 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 9.00000 | 0.430037 | ||||||||
\(439\) | −22.0557 | −1.05266 | −0.526331 | − | 0.850280i | \(-0.676433\pi\) | ||||
−0.526331 | + | 0.850280i | \(0.676433\pi\) | |||||||
\(440\) | −5.00000 | −0.238366 | ||||||||
\(441\) | −2.61803 | −0.124668 | ||||||||
\(442\) | 33.2705 | 1.58252 | ||||||||
\(443\) | 17.2148 | 0.817899 | 0.408949 | − | 0.912557i | \(-0.365895\pi\) | ||||
0.408949 | + | 0.912557i | \(0.365895\pi\) | |||||||
\(444\) | −3.67376 | −0.174349 | ||||||||
\(445\) | 4.85410 | 0.230107 | ||||||||
\(446\) | 5.65248 | 0.267652 | ||||||||
\(447\) | −0.854102 | −0.0403976 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | −22.1803 | −1.04675 | −0.523377 | − | 0.852101i | \(-0.675328\pi\) | ||||
−0.523377 | + | 0.852101i | \(0.675328\pi\) | |||||||
\(450\) | 10.4721 | 0.493661 | ||||||||
\(451\) | 5.45085 | 0.256670 | ||||||||
\(452\) | 3.85410 | 0.181282 | ||||||||
\(453\) | 8.79837 | 0.413384 | ||||||||
\(454\) | −14.2361 | −0.668132 | ||||||||
\(455\) | −4.85410 | −0.227564 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 29.8885 | 1.39813 | 0.699064 | − | 0.715060i | \(-0.253600\pi\) | ||||
0.699064 | + | 0.715060i | \(0.253600\pi\) | |||||||
\(458\) | −10.0902 | −0.471483 | ||||||||
\(459\) | 23.7984 | 1.11081 | ||||||||
\(460\) | −3.76393 | −0.175494 | ||||||||
\(461\) | 42.5410 | 1.98133 | 0.990666 | − | 0.136309i | \(-0.0435239\pi\) | ||||
0.990666 | + | 0.136309i | \(0.0435239\pi\) | |||||||
\(462\) | −3.09017 | −0.143768 | ||||||||
\(463\) | −13.5623 | −0.630294 | −0.315147 | − | 0.949043i | \(-0.602054\pi\) | ||||
−0.315147 | + | 0.949043i | \(0.602054\pi\) | |||||||
\(464\) | −8.23607 | −0.382350 | ||||||||
\(465\) | 4.14590 | 0.192261 | ||||||||
\(466\) | −11.0344 | −0.511161 | ||||||||
\(467\) | 33.4721 | 1.54891 | 0.774453 | − | 0.632632i | \(-0.218025\pi\) | ||||
0.774453 | + | 0.632632i | \(0.218025\pi\) | |||||||
\(468\) | −12.7082 | −0.587437 | ||||||||
\(469\) | −7.85410 | −0.362669 | ||||||||
\(470\) | 7.94427 | 0.366442 | ||||||||
\(471\) | −13.7984 | −0.635796 | ||||||||
\(472\) | 11.0000 | 0.506316 | ||||||||
\(473\) | 34.2705 | 1.57576 | ||||||||
\(474\) | 5.47214 | 0.251344 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −6.85410 | −0.314157 | ||||||||
\(477\) | 33.2705 | 1.52335 | ||||||||
\(478\) | −11.1459 | −0.509802 | ||||||||
\(479\) | −0.180340 | −0.00823994 | −0.00411997 | − | 0.999992i | \(-0.501311\pi\) | ||||
−0.00411997 | + | 0.999992i | \(0.501311\pi\) | |||||||
\(480\) | −0.618034 | −0.0282093 | ||||||||
\(481\) | 28.8541 | 1.31563 | ||||||||
\(482\) | 7.90983 | 0.360283 | ||||||||
\(483\) | −2.32624 | −0.105847 | ||||||||
\(484\) | 14.0000 | 0.636364 | ||||||||
\(485\) | −9.47214 | −0.430108 | ||||||||
\(486\) | −13.9443 | −0.632525 | ||||||||
\(487\) | 11.1803 | 0.506630 | 0.253315 | − | 0.967384i | \(-0.418479\pi\) | ||||
0.253315 | + | 0.967384i | \(0.418479\pi\) | |||||||
\(488\) | 7.47214 | 0.338248 | ||||||||
\(489\) | −0.291796 | −0.0131955 | ||||||||
\(490\) | 1.00000 | 0.0451754 | ||||||||
\(491\) | −19.5967 | −0.884389 | −0.442194 | − | 0.896919i | \(-0.645800\pi\) | ||||
−0.442194 | + | 0.896919i | \(0.645800\pi\) | |||||||
\(492\) | 0.673762 | 0.0303755 | ||||||||
\(493\) | −56.4508 | −2.54242 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 13.0902 | 0.588359 | ||||||||
\(496\) | −6.70820 | −0.301207 | ||||||||
\(497\) | 10.0000 | 0.448561 | ||||||||
\(498\) | 9.52786 | 0.426954 | ||||||||
\(499\) | 16.4164 | 0.734899 | 0.367450 | − | 0.930043i | \(-0.380231\pi\) | ||||
0.367450 | + | 0.930043i | \(0.380231\pi\) | |||||||
\(500\) | −9.00000 | −0.402492 | ||||||||
\(501\) | −1.12461 | −0.0502439 | ||||||||
\(502\) | 6.47214 | 0.288866 | ||||||||
\(503\) | 31.7771 | 1.41687 | 0.708435 | − | 0.705776i | \(-0.249401\pi\) | ||||
0.708435 | + | 0.705776i | \(0.249401\pi\) | |||||||
\(504\) | 2.61803 | 0.116617 | ||||||||
\(505\) | 4.14590 | 0.184490 | ||||||||
\(506\) | 18.8197 | 0.836636 | ||||||||
\(507\) | −6.52786 | −0.289913 | ||||||||
\(508\) | −7.32624 | −0.325049 | ||||||||
\(509\) | 1.41641 | 0.0627812 | 0.0313906 | − | 0.999507i | \(-0.490006\pi\) | ||||
0.0313906 | + | 0.999507i | \(0.490006\pi\) | |||||||
\(510\) | −4.23607 | −0.187576 | ||||||||
\(511\) | 14.5623 | 0.644198 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 8.05573 | 0.355323 | ||||||||
\(515\) | −15.0902 | −0.664952 | ||||||||
\(516\) | 4.23607 | 0.186482 | ||||||||
\(517\) | −39.7214 | −1.74694 | ||||||||
\(518\) | −5.94427 | −0.261176 | ||||||||
\(519\) | −1.09017 | −0.0478531 | ||||||||
\(520\) | 4.85410 | 0.212866 | ||||||||
\(521\) | 25.6525 | 1.12386 | 0.561928 | − | 0.827186i | \(-0.310060\pi\) | ||||
0.561928 | + | 0.827186i | \(0.310060\pi\) | |||||||
\(522\) | 21.5623 | 0.943756 | ||||||||
\(523\) | −35.1591 | −1.53740 | −0.768699 | − | 0.639611i | \(-0.779096\pi\) | ||||
−0.768699 | + | 0.639611i | \(0.779096\pi\) | |||||||
\(524\) | −4.38197 | −0.191427 | ||||||||
\(525\) | −2.47214 | −0.107893 | ||||||||
\(526\) | −25.1803 | −1.09791 | ||||||||
\(527\) | −45.9787 | −2.00286 | ||||||||
\(528\) | 3.09017 | 0.134482 | ||||||||
\(529\) | −8.83282 | −0.384035 | ||||||||
\(530\) | −12.7082 | −0.552009 | ||||||||
\(531\) | −28.7984 | −1.24974 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.29180 | −0.229213 | ||||||||
\(534\) | −3.00000 | −0.129823 | ||||||||
\(535\) | −13.9443 | −0.602863 | ||||||||
\(536\) | 7.85410 | 0.339246 | ||||||||
\(537\) | −5.58359 | −0.240950 | ||||||||
\(538\) | 9.18034 | 0.395793 | ||||||||
\(539\) | −5.00000 | −0.215365 | ||||||||
\(540\) | 3.47214 | 0.149417 | ||||||||
\(541\) | −30.3050 | −1.30291 | −0.651456 | − | 0.758687i | \(-0.725841\pi\) | ||||
−0.651456 | + | 0.758687i | \(0.725841\pi\) | |||||||
\(542\) | 1.65248 | 0.0709799 | ||||||||
\(543\) | 9.74265 | 0.418097 | ||||||||
\(544\) | 6.85410 | 0.293867 | ||||||||
\(545\) | −13.5623 | −0.580945 | ||||||||
\(546\) | 3.00000 | 0.128388 | ||||||||
\(547\) | 9.18034 | 0.392523 | 0.196261 | − | 0.980552i | \(-0.437120\pi\) | ||||
0.196261 | + | 0.980552i | \(0.437120\pi\) | |||||||
\(548\) | 21.1246 | 0.902399 | ||||||||
\(549\) | −19.5623 | −0.834899 | ||||||||
\(550\) | 20.0000 | 0.852803 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 2.32624 | 0.0990113 | ||||||||
\(553\) | 8.85410 | 0.376515 | ||||||||
\(554\) | −8.00000 | −0.339887 | ||||||||
\(555\) | −3.67376 | −0.155943 | ||||||||
\(556\) | −0.236068 | −0.0100115 | ||||||||
\(557\) | −27.7639 | −1.17640 | −0.588198 | − | 0.808717i | \(-0.700162\pi\) | ||||
−0.588198 | + | 0.808717i | \(0.700162\pi\) | |||||||
\(558\) | 17.5623 | 0.743472 | ||||||||
\(559\) | −33.2705 | −1.40719 | ||||||||
\(560\) | −1.00000 | −0.0422577 | ||||||||
\(561\) | 21.1803 | 0.894235 | ||||||||
\(562\) | −12.2361 | −0.516147 | ||||||||
\(563\) | 36.0689 | 1.52012 | 0.760061 | − | 0.649852i | \(-0.225169\pi\) | ||||
0.760061 | + | 0.649852i | \(0.225169\pi\) | |||||||
\(564\) | −4.90983 | −0.206741 | ||||||||
\(565\) | 3.85410 | 0.162143 | ||||||||
\(566\) | 6.43769 | 0.270596 | ||||||||
\(567\) | −5.70820 | −0.239722 | ||||||||
\(568\) | −10.0000 | −0.419591 | ||||||||
\(569\) | −30.2705 | −1.26901 | −0.634503 | − | 0.772920i | \(-0.718795\pi\) | ||||
−0.634503 | + | 0.772920i | \(0.718795\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 31.0132 | 1.29786 | 0.648930 | − | 0.760848i | \(-0.275217\pi\) | ||||
0.648930 | + | 0.760848i | \(0.275217\pi\) | |||||||
\(572\) | −24.2705 | −1.01480 | ||||||||
\(573\) | −1.74265 | −0.0728001 | ||||||||
\(574\) | 1.09017 | 0.0455028 | ||||||||
\(575\) | 15.0557 | 0.627867 | ||||||||
\(576\) | −2.61803 | −0.109085 | ||||||||
\(577\) | −3.29180 | −0.137039 | −0.0685196 | − | 0.997650i | \(-0.521828\pi\) | ||||
−0.0685196 | + | 0.997650i | \(0.521828\pi\) | |||||||
\(578\) | 29.9787 | 1.24695 | ||||||||
\(579\) | 6.29180 | 0.261478 | ||||||||
\(580\) | −8.23607 | −0.341984 | ||||||||
\(581\) | 15.4164 | 0.639580 | ||||||||
\(582\) | 5.85410 | 0.242660 | ||||||||
\(583\) | 63.5410 | 2.63160 | ||||||||
\(584\) | −14.5623 | −0.602593 | ||||||||
\(585\) | −12.7082 | −0.525420 | ||||||||
\(586\) | 16.2361 | 0.670706 | ||||||||
\(587\) | −41.9443 | −1.73123 | −0.865613 | − | 0.500714i | \(-0.833071\pi\) | ||||
−0.865613 | + | 0.500714i | \(0.833071\pi\) | |||||||
\(588\) | −0.618034 | −0.0254873 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 11.0000 | 0.452863 | ||||||||
\(591\) | 4.67376 | 0.192253 | ||||||||
\(592\) | 5.94427 | 0.244308 | ||||||||
\(593\) | 5.43769 | 0.223299 | 0.111650 | − | 0.993748i | \(-0.464387\pi\) | ||||
0.111650 | + | 0.993748i | \(0.464387\pi\) | |||||||
\(594\) | −17.3607 | −0.712317 | ||||||||
\(595\) | −6.85410 | −0.280991 | ||||||||
\(596\) | 1.38197 | 0.0566075 | ||||||||
\(597\) | 3.03444 | 0.124191 | ||||||||
\(598\) | −18.2705 | −0.747137 | ||||||||
\(599\) | 17.0000 | 0.694601 | 0.347301 | − | 0.937754i | \(-0.387098\pi\) | ||||
0.347301 | + | 0.937754i | \(0.387098\pi\) | |||||||
\(600\) | 2.47214 | 0.100925 | ||||||||
\(601\) | 14.1246 | 0.576155 | 0.288077 | − | 0.957607i | \(-0.406984\pi\) | ||||
0.288077 | + | 0.957607i | \(0.406984\pi\) | |||||||
\(602\) | 6.85410 | 0.279352 | ||||||||
\(603\) | −20.5623 | −0.837362 | ||||||||
\(604\) | −14.2361 | −0.579257 | ||||||||
\(605\) | 14.0000 | 0.569181 | ||||||||
\(606\) | −2.56231 | −0.104087 | ||||||||
\(607\) | 16.9443 | 0.687747 | 0.343873 | − | 0.939016i | \(-0.388261\pi\) | ||||
0.343873 | + | 0.939016i | \(0.388261\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.09017 | −0.206264 | ||||||||
\(610\) | 7.47214 | 0.302538 | ||||||||
\(611\) | 38.5623 | 1.56006 | ||||||||
\(612\) | −17.9443 | −0.725354 | ||||||||
\(613\) | −10.6525 | −0.430249 | −0.215125 | − | 0.976587i | \(-0.569016\pi\) | ||||
−0.215125 | + | 0.976587i | \(0.569016\pi\) | |||||||
\(614\) | 4.94427 | 0.199535 | ||||||||
\(615\) | 0.673762 | 0.0271687 | ||||||||
\(616\) | 5.00000 | 0.201456 | ||||||||
\(617\) | −24.3262 | −0.979337 | −0.489669 | − | 0.871909i | \(-0.662882\pi\) | ||||
−0.489669 | + | 0.871909i | \(0.662882\pi\) | |||||||
\(618\) | 9.32624 | 0.375156 | ||||||||
\(619\) | −34.7984 | −1.39866 | −0.699332 | − | 0.714797i | \(-0.746519\pi\) | ||||
−0.699332 | + | 0.714797i | \(0.746519\pi\) | |||||||
\(620\) | −6.70820 | −0.269408 | ||||||||
\(621\) | −13.0689 | −0.524436 | ||||||||
\(622\) | 19.7639 | 0.792461 | ||||||||
\(623\) | −4.85410 | −0.194475 | ||||||||
\(624\) | −3.00000 | −0.120096 | ||||||||
\(625\) | 11.0000 | 0.440000 | ||||||||
\(626\) | 18.9098 | 0.755789 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 22.3262 | 0.890914 | ||||||||
\(629\) | 40.7426 | 1.62452 | ||||||||
\(630\) | 2.61803 | 0.104305 | ||||||||
\(631\) | 12.9443 | 0.515303 | 0.257652 | − | 0.966238i | \(-0.417051\pi\) | ||||
0.257652 | + | 0.966238i | \(0.417051\pi\) | |||||||
\(632\) | −8.85410 | −0.352197 | ||||||||
\(633\) | 2.50658 | 0.0996275 | ||||||||
\(634\) | 8.41641 | 0.334258 | ||||||||
\(635\) | −7.32624 | −0.290733 | ||||||||
\(636\) | 7.85410 | 0.311435 | ||||||||
\(637\) | 4.85410 | 0.192327 | ||||||||
\(638\) | 41.1803 | 1.63035 | ||||||||
\(639\) | 26.1803 | 1.03568 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 18.9098 | 0.746893 | 0.373447 | − | 0.927652i | \(-0.378176\pi\) | ||||
0.373447 | + | 0.927652i | \(0.378176\pi\) | |||||||
\(642\) | 8.61803 | 0.340127 | ||||||||
\(643\) | 22.6525 | 0.893326 | 0.446663 | − | 0.894702i | \(-0.352612\pi\) | ||||
0.446663 | + | 0.894702i | \(0.352612\pi\) | |||||||
\(644\) | 3.76393 | 0.148320 | ||||||||
\(645\) | 4.23607 | 0.166795 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −41.1033 | −1.61594 | −0.807969 | − | 0.589225i | \(-0.799433\pi\) | ||||
−0.807969 | + | 0.589225i | \(0.799433\pi\) | |||||||
\(648\) | 5.70820 | 0.224239 | ||||||||
\(649\) | −55.0000 | −2.15894 | ||||||||
\(650\) | −19.4164 | −0.761574 | ||||||||
\(651\) | −4.14590 | −0.162491 | ||||||||
\(652\) | 0.472136 | 0.0184903 | ||||||||
\(653\) | 23.6869 | 0.926941 | 0.463470 | − | 0.886112i | \(-0.346604\pi\) | ||||
0.463470 | + | 0.886112i | \(0.346604\pi\) | |||||||
\(654\) | 8.38197 | 0.327761 | ||||||||
\(655\) | −4.38197 | −0.171218 | ||||||||
\(656\) | −1.09017 | −0.0425640 | ||||||||
\(657\) | 38.1246 | 1.48738 | ||||||||
\(658\) | −7.94427 | −0.309700 | ||||||||
\(659\) | 33.5410 | 1.30657 | 0.653286 | − | 0.757111i | \(-0.273390\pi\) | ||||
0.653286 | + | 0.757111i | \(0.273390\pi\) | |||||||
\(660\) | 3.09017 | 0.120285 | ||||||||
\(661\) | −11.8328 | −0.460243 | −0.230122 | − | 0.973162i | \(-0.573912\pi\) | ||||
−0.230122 | + | 0.973162i | \(0.573912\pi\) | |||||||
\(662\) | 12.4721 | 0.484743 | ||||||||
\(663\) | −20.5623 | −0.798574 | ||||||||
\(664\) | −15.4164 | −0.598273 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −15.5623 | −0.603027 | ||||||||
\(667\) | 31.0000 | 1.20032 | ||||||||
\(668\) | 1.81966 | 0.0704048 | ||||||||
\(669\) | −3.49342 | −0.135064 | ||||||||
\(670\) | 7.85410 | 0.303430 | ||||||||
\(671\) | −37.3607 | −1.44229 | ||||||||
\(672\) | 0.618034 | 0.0238412 | ||||||||
\(673\) | 20.9098 | 0.806015 | 0.403007 | − | 0.915197i | \(-0.367965\pi\) | ||||
0.403007 | + | 0.915197i | \(0.367965\pi\) | |||||||
\(674\) | −33.4508 | −1.28848 | ||||||||
\(675\) | −13.8885 | −0.534570 | ||||||||
\(676\) | 10.5623 | 0.406243 | ||||||||
\(677\) | 3.70820 | 0.142518 | 0.0712589 | − | 0.997458i | \(-0.477298\pi\) | ||||
0.0712589 | + | 0.997458i | \(0.477298\pi\) | |||||||
\(678\) | −2.38197 | −0.0914789 | ||||||||
\(679\) | 9.47214 | 0.363507 | ||||||||
\(680\) | 6.85410 | 0.262843 | ||||||||
\(681\) | 8.79837 | 0.337154 | ||||||||
\(682\) | 33.5410 | 1.28435 | ||||||||
\(683\) | −20.2705 | −0.775630 | −0.387815 | − | 0.921737i | \(-0.626770\pi\) | ||||
−0.387815 | + | 0.921737i | \(0.626770\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 21.1246 | 0.807130 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 6.23607 | 0.237921 | ||||||||
\(688\) | −6.85410 | −0.261310 | ||||||||
\(689\) | −61.6869 | −2.35008 | ||||||||
\(690\) | 2.32624 | 0.0885584 | ||||||||
\(691\) | 9.47214 | 0.360337 | 0.180169 | − | 0.983636i | \(-0.442336\pi\) | ||||
0.180169 | + | 0.983636i | \(0.442336\pi\) | |||||||
\(692\) | 1.76393 | 0.0670546 | ||||||||
\(693\) | −13.0902 | −0.497254 | ||||||||
\(694\) | −5.05573 | −0.191913 | ||||||||
\(695\) | −0.236068 | −0.00895457 | ||||||||
\(696\) | 5.09017 | 0.192942 | ||||||||
\(697\) | −7.47214 | −0.283027 | ||||||||
\(698\) | −6.70820 | −0.253909 | ||||||||
\(699\) | 6.81966 | 0.257943 | ||||||||
\(700\) | 4.00000 | 0.151186 | ||||||||
\(701\) | 1.72949 | 0.0653219 | 0.0326610 | − | 0.999466i | \(-0.489602\pi\) | ||||
0.0326610 | + | 0.999466i | \(0.489602\pi\) | |||||||
\(702\) | 16.8541 | 0.636117 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −5.00000 | −0.188445 | ||||||||
\(705\) | −4.90983 | −0.184915 | ||||||||
\(706\) | 13.0902 | 0.492655 | ||||||||
\(707\) | −4.14590 | −0.155923 | ||||||||
\(708\) | −6.79837 | −0.255499 | ||||||||
\(709\) | 39.6525 | 1.48918 | 0.744590 | − | 0.667522i | \(-0.232645\pi\) | ||||
0.744590 | + | 0.667522i | \(0.232645\pi\) | |||||||
\(710\) | −10.0000 | −0.375293 | ||||||||
\(711\) | 23.1803 | 0.869331 | ||||||||
\(712\) | 4.85410 | 0.181915 | ||||||||
\(713\) | 25.2492 | 0.945591 | ||||||||
\(714\) | 4.23607 | 0.158531 | ||||||||
\(715\) | −24.2705 | −0.907666 | ||||||||
\(716\) | 9.03444 | 0.337633 | ||||||||
\(717\) | 6.88854 | 0.257257 | ||||||||
\(718\) | 27.9443 | 1.04287 | ||||||||
\(719\) | 39.8328 | 1.48551 | 0.742757 | − | 0.669561i | \(-0.233518\pi\) | ||||
0.742757 | + | 0.669561i | \(0.233518\pi\) | |||||||
\(720\) | −2.61803 | −0.0975684 | ||||||||
\(721\) | 15.0902 | 0.561987 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4.88854 | −0.181807 | ||||||||
\(724\) | −15.7639 | −0.585862 | ||||||||
\(725\) | 32.9443 | 1.22352 | ||||||||
\(726\) | −8.65248 | −0.321123 | ||||||||
\(727\) | 7.87539 | 0.292082 | 0.146041 | − | 0.989279i | \(-0.453347\pi\) | ||||
0.146041 | + | 0.989279i | \(0.453347\pi\) | |||||||
\(728\) | −4.85410 | −0.179905 | ||||||||
\(729\) | −8.50658 | −0.315058 | ||||||||
\(730\) | −14.5623 | −0.538975 | ||||||||
\(731\) | −46.9787 | −1.73757 | ||||||||
\(732\) | −4.61803 | −0.170687 | ||||||||
\(733\) | 12.3475 | 0.456066 | 0.228033 | − | 0.973653i | \(-0.426771\pi\) | ||||
0.228033 | + | 0.973653i | \(0.426771\pi\) | |||||||
\(734\) | 9.67376 | 0.357065 | ||||||||
\(735\) | −0.618034 | −0.0227965 | ||||||||
\(736\) | −3.76393 | −0.138740 | ||||||||
\(737\) | −39.2705 | −1.44655 | ||||||||
\(738\) | 2.85410 | 0.105061 | ||||||||
\(739\) | 11.4164 | 0.419959 | 0.209980 | − | 0.977706i | \(-0.432660\pi\) | ||||
0.209980 | + | 0.977706i | \(0.432660\pi\) | |||||||
\(740\) | 5.94427 | 0.218516 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 12.7082 | 0.466533 | ||||||||
\(743\) | −50.5066 | −1.85291 | −0.926453 | − | 0.376410i | \(-0.877159\pi\) | ||||
−0.926453 | + | 0.376410i | \(0.877159\pi\) | |||||||
\(744\) | 4.14590 | 0.151996 | ||||||||
\(745\) | 1.38197 | 0.0506313 | ||||||||
\(746\) | −6.85410 | −0.250947 | ||||||||
\(747\) | 40.3607 | 1.47672 | ||||||||
\(748\) | −34.2705 | −1.25305 | ||||||||
\(749\) | 13.9443 | 0.509513 | ||||||||
\(750\) | 5.56231 | 0.203107 | ||||||||
\(751\) | 12.1803 | 0.444467 | 0.222233 | − | 0.974993i | \(-0.428665\pi\) | ||||
0.222233 | + | 0.974993i | \(0.428665\pi\) | |||||||
\(752\) | 7.94427 | 0.289698 | ||||||||
\(753\) | −4.00000 | −0.145768 | ||||||||
\(754\) | −39.9787 | −1.45594 | ||||||||
\(755\) | −14.2361 | −0.518104 | ||||||||
\(756\) | −3.47214 | −0.126280 | ||||||||
\(757\) | −5.88854 | −0.214023 | −0.107011 | − | 0.994258i | \(-0.534128\pi\) | ||||
−0.107011 | + | 0.994258i | \(0.534128\pi\) | |||||||
\(758\) | 12.0344 | 0.437111 | ||||||||
\(759\) | −11.6312 | −0.422185 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13.8328 | 0.501439 | 0.250720 | − | 0.968060i | \(-0.419333\pi\) | ||||
0.250720 | + | 0.968060i | \(0.419333\pi\) | |||||||
\(762\) | 4.52786 | 0.164027 | ||||||||
\(763\) | 13.5623 | 0.490988 | ||||||||
\(764\) | 2.81966 | 0.102012 | ||||||||
\(765\) | −17.9443 | −0.648777 | ||||||||
\(766\) | 5.94427 | 0.214775 | ||||||||
\(767\) | 53.3951 | 1.92799 | ||||||||
\(768\) | −0.618034 | −0.0223014 | ||||||||
\(769\) | 39.4164 | 1.42139 | 0.710696 | − | 0.703499i | \(-0.248380\pi\) | ||||
0.710696 | + | 0.703499i | \(0.248380\pi\) | |||||||
\(770\) | 5.00000 | 0.180187 | ||||||||
\(771\) | −4.97871 | −0.179304 | ||||||||
\(772\) | −10.1803 | −0.366398 | ||||||||
\(773\) | 0.437694 | 0.0157428 | 0.00787138 | − | 0.999969i | \(-0.497494\pi\) | ||||
0.00787138 | + | 0.999969i | \(0.497494\pi\) | |||||||
\(774\) | 17.9443 | 0.644994 | ||||||||
\(775\) | 26.8328 | 0.963863 | ||||||||
\(776\) | −9.47214 | −0.340030 | ||||||||
\(777\) | 3.67376 | 0.131795 | ||||||||
\(778\) | 11.3820 | 0.408063 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −3.00000 | −0.107417 | ||||||||
\(781\) | 50.0000 | 1.78914 | ||||||||
\(782\) | −25.7984 | −0.922548 | ||||||||
\(783\) | −28.5967 | −1.02196 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 22.3262 | 0.796858 | ||||||||
\(786\) | 2.70820 | 0.0965984 | ||||||||
\(787\) | −18.6738 | −0.665648 | −0.332824 | − | 0.942989i | \(-0.608001\pi\) | ||||
−0.332824 | + | 0.942989i | \(0.608001\pi\) | |||||||
\(788\) | −7.56231 | −0.269396 | ||||||||
\(789\) | 15.5623 | 0.554033 | ||||||||
\(790\) | −8.85410 | −0.315015 | ||||||||
\(791\) | −3.85410 | −0.137036 | ||||||||
\(792\) | 13.0902 | 0.465139 | ||||||||
\(793\) | 36.2705 | 1.28800 | ||||||||
\(794\) | −32.2705 | −1.14524 | ||||||||
\(795\) | 7.85410 | 0.278556 | ||||||||
\(796\) | −4.90983 | −0.174024 | ||||||||
\(797\) | 12.7984 | 0.453342 | 0.226671 | − | 0.973971i | \(-0.427216\pi\) | ||||
0.226671 | + | 0.973971i | \(0.427216\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 54.4508 | 1.92633 | ||||||||
\(800\) | −4.00000 | −0.141421 | ||||||||
\(801\) | −12.7082 | −0.449022 | ||||||||
\(802\) | −6.58359 | −0.232475 | ||||||||
\(803\) | 72.8115 | 2.56946 | ||||||||
\(804\) | −4.85410 | −0.171191 | ||||||||
\(805\) | 3.76393 | 0.132661 | ||||||||
\(806\) | −32.5623 | −1.14696 | ||||||||
\(807\) | −5.67376 | −0.199726 | ||||||||
\(808\) | 4.14590 | 0.145852 | ||||||||
\(809\) | −26.1459 | −0.919241 | −0.459620 | − | 0.888115i | \(-0.652015\pi\) | ||||
−0.459620 | + | 0.888115i | \(0.652015\pi\) | |||||||
\(810\) | 5.70820 | 0.200566 | ||||||||
\(811\) | −40.5410 | −1.42359 | −0.711794 | − | 0.702388i | \(-0.752117\pi\) | ||||
−0.711794 | + | 0.702388i | \(0.752117\pi\) | |||||||
\(812\) | 8.23607 | 0.289029 | ||||||||
\(813\) | −1.02129 | −0.0358181 | ||||||||
\(814\) | −29.7214 | −1.04173 | ||||||||
\(815\) | 0.472136 | 0.0165382 | ||||||||
\(816\) | −4.23607 | −0.148292 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 17.2148 | 0.601901 | ||||||||
\(819\) | 12.7082 | 0.444061 | ||||||||
\(820\) | −1.09017 | −0.0380704 | ||||||||
\(821\) | 9.76393 | 0.340764 | 0.170382 | − | 0.985378i | \(-0.445500\pi\) | ||||
0.170382 | + | 0.985378i | \(0.445500\pi\) | |||||||
\(822\) | −13.0557 | −0.455371 | ||||||||
\(823\) | −33.7639 | −1.17694 | −0.588468 | − | 0.808520i | \(-0.700269\pi\) | ||||
−0.588468 | + | 0.808520i | \(0.700269\pi\) | |||||||
\(824\) | −15.0902 | −0.525691 | ||||||||
\(825\) | −12.3607 | −0.430344 | ||||||||
\(826\) | −11.0000 | −0.382739 | ||||||||
\(827\) | 13.3820 | 0.465337 | 0.232668 | − | 0.972556i | \(-0.425254\pi\) | ||||
0.232668 | + | 0.972556i | \(0.425254\pi\) | |||||||
\(828\) | 9.85410 | 0.342454 | ||||||||
\(829\) | 6.88854 | 0.239249 | 0.119625 | − | 0.992819i | \(-0.461831\pi\) | ||||
0.119625 | + | 0.992819i | \(0.461831\pi\) | |||||||
\(830\) | −15.4164 | −0.535111 | ||||||||
\(831\) | 4.94427 | 0.171515 | ||||||||
\(832\) | 4.85410 | 0.168286 | ||||||||
\(833\) | 6.85410 | 0.237481 | ||||||||
\(834\) | 0.145898 | 0.00505204 | ||||||||
\(835\) | 1.81966 | 0.0629719 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −23.2918 | −0.805082 | ||||||||
\(838\) | −25.7426 | −0.889265 | ||||||||
\(839\) | 41.1803 | 1.42170 | 0.710852 | − | 0.703342i | \(-0.248310\pi\) | ||||
0.710852 | + | 0.703342i | \(0.248310\pi\) | |||||||
\(840\) | 0.618034 | 0.0213242 | ||||||||
\(841\) | 38.8328 | 1.33906 | ||||||||
\(842\) | −8.05573 | −0.277619 | ||||||||
\(843\) | 7.56231 | 0.260460 | ||||||||
\(844\) | −4.05573 | −0.139604 | ||||||||
\(845\) | 10.5623 | 0.363354 | ||||||||
\(846\) | −20.7984 | −0.715063 | ||||||||
\(847\) | −14.0000 | −0.481046 | ||||||||
\(848\) | −12.7082 | −0.436402 | ||||||||
\(849\) | −3.97871 | −0.136549 | ||||||||
\(850\) | −27.4164 | −0.940375 | ||||||||
\(851\) | −22.3738 | −0.766965 | ||||||||
\(852\) | 6.18034 | 0.211735 | ||||||||
\(853\) | 38.9574 | 1.33388 | 0.666938 | − | 0.745113i | \(-0.267604\pi\) | ||||
0.666938 | + | 0.745113i | \(0.267604\pi\) | |||||||
\(854\) | −7.47214 | −0.255691 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −13.9443 | −0.476605 | ||||||||
\(857\) | 17.7426 | 0.606077 | 0.303039 | − | 0.952978i | \(-0.401999\pi\) | ||||
0.303039 | + | 0.952978i | \(0.401999\pi\) | |||||||
\(858\) | 15.0000 | 0.512092 | ||||||||
\(859\) | −5.06888 | −0.172948 | −0.0864740 | − | 0.996254i | \(-0.527560\pi\) | ||||
−0.0864740 | + | 0.996254i | \(0.527560\pi\) | |||||||
\(860\) | −6.85410 | −0.233723 | ||||||||
\(861\) | −0.673762 | −0.0229618 | ||||||||
\(862\) | 2.94427 | 0.100282 | ||||||||
\(863\) | −7.29180 | −0.248216 | −0.124108 | − | 0.992269i | \(-0.539607\pi\) | ||||
−0.124108 | + | 0.992269i | \(0.539607\pi\) | |||||||
\(864\) | 3.47214 | 0.118124 | ||||||||
\(865\) | 1.76393 | 0.0599755 | ||||||||
\(866\) | −27.6180 | −0.938499 | ||||||||
\(867\) | −18.5279 | −0.629239 | ||||||||
\(868\) | 6.70820 | 0.227691 | ||||||||
\(869\) | 44.2705 | 1.50177 | ||||||||
\(870\) | 5.09017 | 0.172573 | ||||||||
\(871\) | 38.1246 | 1.29180 | ||||||||
\(872\) | −13.5623 | −0.459278 | ||||||||
\(873\) | 24.7984 | 0.839298 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9.00000 | 0.304256 | ||||||||
\(876\) | 9.00000 | 0.304082 | ||||||||
\(877\) | 5.32624 | 0.179854 | 0.0899271 | − | 0.995948i | \(-0.471337\pi\) | ||||
0.0899271 | + | 0.995948i | \(0.471337\pi\) | |||||||
\(878\) | −22.0557 | −0.744345 | ||||||||
\(879\) | −10.0344 | −0.338453 | ||||||||
\(880\) | −5.00000 | −0.168550 | ||||||||
\(881\) | 14.1459 | 0.476587 | 0.238294 | − | 0.971193i | \(-0.423412\pi\) | ||||
0.238294 | + | 0.971193i | \(0.423412\pi\) | |||||||
\(882\) | −2.61803 | −0.0881538 | ||||||||
\(883\) | −11.0213 | −0.370896 | −0.185448 | − | 0.982654i | \(-0.559374\pi\) | ||||
−0.185448 | + | 0.982654i | \(0.559374\pi\) | |||||||
\(884\) | 33.2705 | 1.11901 | ||||||||
\(885\) | −6.79837 | −0.228525 | ||||||||
\(886\) | 17.2148 | 0.578342 | ||||||||
\(887\) | 20.8328 | 0.699497 | 0.349749 | − | 0.936844i | \(-0.386267\pi\) | ||||
0.349749 | + | 0.936844i | \(0.386267\pi\) | |||||||
\(888\) | −3.67376 | −0.123283 | ||||||||
\(889\) | 7.32624 | 0.245714 | ||||||||
\(890\) | 4.85410 | 0.162710 | ||||||||
\(891\) | −28.5410 | −0.956160 | ||||||||
\(892\) | 5.65248 | 0.189259 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −0.854102 | −0.0285654 | ||||||||
\(895\) | 9.03444 | 0.301988 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 11.2918 | 0.377022 | ||||||||
\(898\) | −22.1803 | −0.740168 | ||||||||
\(899\) | 55.2492 | 1.84266 | ||||||||
\(900\) | 10.4721 | 0.349071 | ||||||||
\(901\) | −87.1033 | −2.90183 | ||||||||
\(902\) | 5.45085 | 0.181493 | ||||||||
\(903\) | −4.23607 | −0.140968 | ||||||||
\(904\) | 3.85410 | 0.128186 | ||||||||
\(905\) | −15.7639 | −0.524011 | ||||||||
\(906\) | 8.79837 | 0.292306 | ||||||||
\(907\) | 16.6738 | 0.553643 | 0.276822 | − | 0.960921i | \(-0.410719\pi\) | ||||
0.276822 | + | 0.960921i | \(0.410719\pi\) | |||||||
\(908\) | −14.2361 | −0.472441 | ||||||||
\(909\) | −10.8541 | −0.360008 | ||||||||
\(910\) | −4.85410 | −0.160912 | ||||||||
\(911\) | 46.1591 | 1.52932 | 0.764659 | − | 0.644435i | \(-0.222907\pi\) | ||||
0.764659 | + | 0.644435i | \(0.222907\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 77.0820 | 2.55104 | ||||||||
\(914\) | 29.8885 | 0.988625 | ||||||||
\(915\) | −4.61803 | −0.152667 | ||||||||
\(916\) | −10.0902 | −0.333389 | ||||||||
\(917\) | 4.38197 | 0.144705 | ||||||||
\(918\) | 23.7984 | 0.785463 | ||||||||
\(919\) | 10.0344 | 0.331006 | 0.165503 | − | 0.986209i | \(-0.447075\pi\) | ||||
0.165503 | + | 0.986209i | \(0.447075\pi\) | |||||||
\(920\) | −3.76393 | −0.124093 | ||||||||
\(921\) | −3.05573 | −0.100690 | ||||||||
\(922\) | 42.5410 | 1.40101 | ||||||||
\(923\) | −48.5410 | −1.59775 | ||||||||
\(924\) | −3.09017 | −0.101659 | ||||||||
\(925\) | −23.7771 | −0.781786 | ||||||||
\(926\) | −13.5623 | −0.445685 | ||||||||
\(927\) | 39.5066 | 1.29757 | ||||||||
\(928\) | −8.23607 | −0.270362 | ||||||||
\(929\) | −26.8885 | −0.882185 | −0.441092 | − | 0.897462i | \(-0.645409\pi\) | ||||
−0.441092 | + | 0.897462i | \(0.645409\pi\) | |||||||
\(930\) | 4.14590 | 0.135949 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −11.0344 | −0.361445 | ||||||||
\(933\) | −12.2148 | −0.399894 | ||||||||
\(934\) | 33.4721 | 1.09524 | ||||||||
\(935\) | −34.2705 | −1.12077 | ||||||||
\(936\) | −12.7082 | −0.415381 | ||||||||
\(937\) | 40.3951 | 1.31965 | 0.659826 | − | 0.751419i | \(-0.270630\pi\) | ||||
0.659826 | + | 0.751419i | \(0.270630\pi\) | |||||||
\(938\) | −7.85410 | −0.256446 | ||||||||
\(939\) | −11.6869 | −0.381388 | ||||||||
\(940\) | 7.94427 | 0.259114 | ||||||||
\(941\) | 27.2148 | 0.887177 | 0.443588 | − | 0.896231i | \(-0.353705\pi\) | ||||
0.443588 | + | 0.896231i | \(0.353705\pi\) | |||||||
\(942\) | −13.7984 | −0.449575 | ||||||||
\(943\) | 4.10333 | 0.133623 | ||||||||
\(944\) | 11.0000 | 0.358020 | ||||||||
\(945\) | −3.47214 | −0.112949 | ||||||||
\(946\) | 34.2705 | 1.11423 | ||||||||
\(947\) | 49.8885 | 1.62116 | 0.810580 | − | 0.585628i | \(-0.199152\pi\) | ||||
0.810580 | + | 0.585628i | \(0.199152\pi\) | |||||||
\(948\) | 5.47214 | 0.177727 | ||||||||
\(949\) | −70.6869 | −2.29459 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.20163 | −0.168674 | ||||||||
\(952\) | −6.85410 | −0.222143 | ||||||||
\(953\) | −30.7771 | −0.996968 | −0.498484 | − | 0.866899i | \(-0.666110\pi\) | ||||
−0.498484 | + | 0.866899i | \(0.666110\pi\) | |||||||
\(954\) | 33.2705 | 1.07717 | ||||||||
\(955\) | 2.81966 | 0.0912421 | ||||||||
\(956\) | −11.1459 | −0.360484 | ||||||||
\(957\) | −25.4508 | −0.822709 | ||||||||
\(958\) | −0.180340 | −0.00582652 | ||||||||
\(959\) | −21.1246 | −0.682149 | ||||||||
\(960\) | −0.618034 | −0.0199470 | ||||||||
\(961\) | 14.0000 | 0.451613 | ||||||||
\(962\) | 28.8541 | 0.930294 | ||||||||
\(963\) | 36.5066 | 1.17641 | ||||||||
\(964\) | 7.90983 | 0.254758 | ||||||||
\(965\) | −10.1803 | −0.327717 | ||||||||
\(966\) | −2.32624 | −0.0748455 | ||||||||
\(967\) | −55.2705 | −1.77738 | −0.888690 | − | 0.458509i | \(-0.848384\pi\) | ||||
−0.888690 | + | 0.458509i | \(0.848384\pi\) | |||||||
\(968\) | 14.0000 | 0.449977 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −9.47214 | −0.304132 | ||||||||
\(971\) | −34.4164 | −1.10448 | −0.552238 | − | 0.833687i | \(-0.686226\pi\) | ||||
−0.552238 | + | 0.833687i | \(0.686226\pi\) | |||||||
\(972\) | −13.9443 | −0.447263 | ||||||||
\(973\) | 0.236068 | 0.00756799 | ||||||||
\(974\) | 11.1803 | 0.358241 | ||||||||
\(975\) | 12.0000 | 0.384308 | ||||||||
\(976\) | 7.47214 | 0.239177 | ||||||||
\(977\) | −48.7771 | −1.56052 | −0.780259 | − | 0.625457i | \(-0.784913\pi\) | ||||
−0.780259 | + | 0.625457i | \(0.784913\pi\) | |||||||
\(978\) | −0.291796 | −0.00933061 | ||||||||
\(979\) | −24.2705 | −0.775689 | ||||||||
\(980\) | 1.00000 | 0.0319438 | ||||||||
\(981\) | 35.5066 | 1.13364 | ||||||||
\(982\) | −19.5967 | −0.625357 | ||||||||
\(983\) | 9.49342 | 0.302793 | 0.151397 | − | 0.988473i | \(-0.451623\pi\) | ||||
0.151397 | + | 0.988473i | \(0.451623\pi\) | |||||||
\(984\) | 0.673762 | 0.0214788 | ||||||||
\(985\) | −7.56231 | −0.240955 | ||||||||
\(986\) | −56.4508 | −1.79776 | ||||||||
\(987\) | 4.90983 | 0.156282 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 25.7984 | 0.820341 | ||||||||
\(990\) | 13.0902 | 0.416033 | ||||||||
\(991\) | −25.4164 | −0.807379 | −0.403689 | − | 0.914896i | \(-0.632272\pi\) | ||||
−0.403689 | + | 0.914896i | \(0.632272\pi\) | |||||||
\(992\) | −6.70820 | −0.212986 | ||||||||
\(993\) | −7.70820 | −0.244612 | ||||||||
\(994\) | 10.0000 | 0.317181 | ||||||||
\(995\) | −4.90983 | −0.155652 | ||||||||
\(996\) | 9.52786 | 0.301902 | ||||||||
\(997\) | 31.0344 | 0.982871 | 0.491435 | − | 0.870914i | \(-0.336472\pi\) | ||||
0.491435 | + | 0.870914i | \(0.336472\pi\) | |||||||
\(998\) | 16.4164 | 0.519652 | ||||||||
\(999\) | 20.6393 | 0.652999 |
(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 | 5054.2.a.p.1.1 | yes | 2 | |
19.18 | odd | 2 | 5054.2.a.f.1.2 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5054.2.a.f.1.2 | ✓ | 2 | 19.18 | odd | 2 | ||
5054.2.a.p.1.1 | yes | 2 | 1.1 | even | 1 | trivial |