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: | \(0\) |
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 | ||||||||
\(3\) | 0.381966 | 0.220528 | 0.110264 | − | 0.993902i | \(-0.464830\pi\) | ||||
0.110264 | + | 0.993902i | \(0.464830\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −4.23607 | −1.89443 | −0.947214 | − | 0.320603i | \(-0.896114\pi\) | ||||
−0.947214 | + | 0.320603i | \(0.896114\pi\) | |||||||
\(6\) | −0.381966 | −0.155937 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.85410 | −0.951367 | ||||||||
\(10\) | 4.23607 | 1.33956 | ||||||||
\(11\) | 3.00000 | 0.904534 | 0.452267 | − | 0.891883i | \(-0.350615\pi\) | ||||
0.452267 | + | 0.891883i | \(0.350615\pi\) | |||||||
\(12\) | 0.381966 | 0.110264 | ||||||||
\(13\) | −3.85410 | −1.06894 | −0.534468 | − | 0.845189i | \(-0.679488\pi\) | ||||
−0.534468 | + | 0.845189i | \(0.679488\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | −1.61803 | −0.417775 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.85410 | 0.449686 | 0.224843 | − | 0.974395i | \(-0.427813\pi\) | ||||
0.224843 | + | 0.974395i | \(0.427813\pi\) | |||||||
\(18\) | 2.85410 | 0.672718 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | −4.23607 | −0.947214 | ||||||||
\(21\) | −0.381966 | −0.0833518 | ||||||||
\(22\) | −3.00000 | −0.639602 | ||||||||
\(23\) | −6.70820 | −1.39876 | −0.699379 | − | 0.714751i | \(-0.746540\pi\) | ||||
−0.699379 | + | 0.714751i | \(0.746540\pi\) | |||||||
\(24\) | −0.381966 | −0.0779685 | ||||||||
\(25\) | 12.9443 | 2.58885 | ||||||||
\(26\) | 3.85410 | 0.755852 | ||||||||
\(27\) | −2.23607 | −0.430331 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | −8.23607 | −1.52940 | −0.764700 | − | 0.644387i | \(-0.777113\pi\) | ||||
−0.764700 | + | 0.644387i | \(0.777113\pi\) | |||||||
\(30\) | 1.61803 | 0.295411 | ||||||||
\(31\) | 5.00000 | 0.898027 | 0.449013 | − | 0.893525i | \(-0.351776\pi\) | ||||
0.449013 | + | 0.893525i | \(0.351776\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 1.14590 | 0.199475 | ||||||||
\(34\) | −1.85410 | −0.317976 | ||||||||
\(35\) | 4.23607 | 0.716026 | ||||||||
\(36\) | −2.85410 | −0.475684 | ||||||||
\(37\) | −5.00000 | −0.821995 | −0.410997 | − | 0.911636i | \(-0.634819\pi\) | ||||
−0.410997 | + | 0.911636i | \(0.634819\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.47214 | −0.235730 | ||||||||
\(40\) | 4.23607 | 0.669781 | ||||||||
\(41\) | −4.09017 | −0.638777 | −0.319389 | − | 0.947624i | \(-0.603478\pi\) | ||||
−0.319389 | + | 0.947624i | \(0.603478\pi\) | |||||||
\(42\) | 0.381966 | 0.0589386 | ||||||||
\(43\) | −11.5623 | −1.76324 | −0.881618 | − | 0.471964i | \(-0.843545\pi\) | ||||
−0.881618 | + | 0.471964i | \(0.843545\pi\) | |||||||
\(44\) | 3.00000 | 0.452267 | ||||||||
\(45\) | 12.0902 | 1.80230 | ||||||||
\(46\) | 6.70820 | 0.989071 | ||||||||
\(47\) | −6.23607 | −0.909624 | −0.454812 | − | 0.890587i | \(-0.650294\pi\) | ||||
−0.454812 | + | 0.890587i | \(0.650294\pi\) | |||||||
\(48\) | 0.381966 | 0.0551320 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −12.9443 | −1.83060 | ||||||||
\(51\) | 0.708204 | 0.0991684 | ||||||||
\(52\) | −3.85410 | −0.534468 | ||||||||
\(53\) | −12.7082 | −1.74561 | −0.872803 | − | 0.488073i | \(-0.837700\pi\) | ||||
−0.872803 | + | 0.488073i | \(0.837700\pi\) | |||||||
\(54\) | 2.23607 | 0.304290 | ||||||||
\(55\) | −12.7082 | −1.71357 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 8.23607 | 1.08145 | ||||||||
\(59\) | 10.2361 | 1.33262 | 0.666311 | − | 0.745674i | \(-0.267872\pi\) | ||||
0.666311 | + | 0.745674i | \(0.267872\pi\) | |||||||
\(60\) | −1.61803 | −0.208887 | ||||||||
\(61\) | −6.70820 | −0.858898 | −0.429449 | − | 0.903091i | \(-0.641292\pi\) | ||||
−0.429449 | + | 0.903091i | \(0.641292\pi\) | |||||||
\(62\) | −5.00000 | −0.635001 | ||||||||
\(63\) | 2.85410 | 0.359583 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 16.3262 | 2.02502 | ||||||||
\(66\) | −1.14590 | −0.141050 | ||||||||
\(67\) | −4.56231 | −0.557374 | −0.278687 | − | 0.960382i | \(-0.589899\pi\) | ||||
−0.278687 | + | 0.960382i | \(0.589899\pi\) | |||||||
\(68\) | 1.85410 | 0.224843 | ||||||||
\(69\) | −2.56231 | −0.308465 | ||||||||
\(70\) | −4.23607 | −0.506307 | ||||||||
\(71\) | 3.52786 | 0.418680 | 0.209340 | − | 0.977843i | \(-0.432868\pi\) | ||||
0.209340 | + | 0.977843i | \(0.432868\pi\) | |||||||
\(72\) | 2.85410 | 0.336359 | ||||||||
\(73\) | −9.09017 | −1.06392 | −0.531962 | − | 0.846768i | \(-0.678545\pi\) | ||||
−0.531962 | + | 0.846768i | \(0.678545\pi\) | |||||||
\(74\) | 5.00000 | 0.581238 | ||||||||
\(75\) | 4.94427 | 0.570915 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.00000 | −0.341882 | ||||||||
\(78\) | 1.47214 | 0.166687 | ||||||||
\(79\) | 10.1459 | 1.14150 | 0.570751 | − | 0.821123i | \(-0.306652\pi\) | ||||
0.570751 | + | 0.821123i | \(0.306652\pi\) | |||||||
\(80\) | −4.23607 | −0.473607 | ||||||||
\(81\) | 7.70820 | 0.856467 | ||||||||
\(82\) | 4.09017 | 0.451684 | ||||||||
\(83\) | −6.47214 | −0.710409 | −0.355205 | − | 0.934789i | \(-0.615589\pi\) | ||||
−0.355205 | + | 0.934789i | \(0.615589\pi\) | |||||||
\(84\) | −0.381966 | −0.0416759 | ||||||||
\(85\) | −7.85410 | −0.851897 | ||||||||
\(86\) | 11.5623 | 1.24680 | ||||||||
\(87\) | −3.14590 | −0.337276 | ||||||||
\(88\) | −3.00000 | −0.319801 | ||||||||
\(89\) | −1.38197 | −0.146488 | −0.0732441 | − | 0.997314i | \(-0.523335\pi\) | ||||
−0.0732441 | + | 0.997314i | \(0.523335\pi\) | |||||||
\(90\) | −12.0902 | −1.27442 | ||||||||
\(91\) | 3.85410 | 0.404020 | ||||||||
\(92\) | −6.70820 | −0.699379 | ||||||||
\(93\) | 1.90983 | 0.198040 | ||||||||
\(94\) | 6.23607 | 0.643201 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.381966 | −0.0389842 | ||||||||
\(97\) | −5.29180 | −0.537300 | −0.268650 | − | 0.963238i | \(-0.586578\pi\) | ||||
−0.268650 | + | 0.963238i | \(0.586578\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | −8.56231 | −0.860544 | ||||||||
\(100\) | 12.9443 | 1.29443 | ||||||||
\(101\) | −8.09017 | −0.805002 | −0.402501 | − | 0.915420i | \(-0.631859\pi\) | ||||
−0.402501 | + | 0.915420i | \(0.631859\pi\) | |||||||
\(102\) | −0.708204 | −0.0701226 | ||||||||
\(103\) | 6.85410 | 0.675355 | 0.337677 | − | 0.941262i | \(-0.390359\pi\) | ||||
0.337677 | + | 0.941262i | \(0.390359\pi\) | |||||||
\(104\) | 3.85410 | 0.377926 | ||||||||
\(105\) | 1.61803 | 0.157904 | ||||||||
\(106\) | 12.7082 | 1.23433 | ||||||||
\(107\) | −13.4721 | −1.30240 | −0.651200 | − | 0.758906i | \(-0.725734\pi\) | ||||
−0.651200 | + | 0.758906i | \(0.725734\pi\) | |||||||
\(108\) | −2.23607 | −0.215166 | ||||||||
\(109\) | 4.85410 | 0.464939 | 0.232469 | − | 0.972604i | \(-0.425319\pi\) | ||||
0.232469 | + | 0.972604i | \(0.425319\pi\) | |||||||
\(110\) | 12.7082 | 1.21168 | ||||||||
\(111\) | −1.90983 | −0.181273 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | 11.7984 | 1.10990 | 0.554949 | − | 0.831884i | \(-0.312738\pi\) | ||||
0.554949 | + | 0.831884i | \(0.312738\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 28.4164 | 2.64984 | ||||||||
\(116\) | −8.23607 | −0.764700 | ||||||||
\(117\) | 11.0000 | 1.01695 | ||||||||
\(118\) | −10.2361 | −0.942306 | ||||||||
\(119\) | −1.85410 | −0.169965 | ||||||||
\(120\) | 1.61803 | 0.147706 | ||||||||
\(121\) | −2.00000 | −0.181818 | ||||||||
\(122\) | 6.70820 | 0.607332 | ||||||||
\(123\) | −1.56231 | −0.140868 | ||||||||
\(124\) | 5.00000 | 0.449013 | ||||||||
\(125\) | −33.6525 | −3.00997 | ||||||||
\(126\) | −2.85410 | −0.254264 | ||||||||
\(127\) | 20.0344 | 1.77777 | 0.888885 | − | 0.458131i | \(-0.151481\pi\) | ||||
0.888885 | + | 0.458131i | \(0.151481\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −4.41641 | −0.388843 | ||||||||
\(130\) | −16.3262 | −1.43191 | ||||||||
\(131\) | −3.38197 | −0.295484 | −0.147742 | − | 0.989026i | \(-0.547200\pi\) | ||||
−0.147742 | + | 0.989026i | \(0.547200\pi\) | |||||||
\(132\) | 1.14590 | 0.0997376 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 4.56231 | 0.394123 | ||||||||
\(135\) | 9.47214 | 0.815232 | ||||||||
\(136\) | −1.85410 | −0.158988 | ||||||||
\(137\) | 9.23607 | 0.789091 | 0.394545 | − | 0.918877i | \(-0.370902\pi\) | ||||
0.394545 | + | 0.918877i | \(0.370902\pi\) | |||||||
\(138\) | 2.56231 | 0.218118 | ||||||||
\(139\) | 19.0000 | 1.61156 | 0.805779 | − | 0.592216i | \(-0.201747\pi\) | ||||
0.805779 | + | 0.592216i | \(0.201747\pi\) | |||||||
\(140\) | 4.23607 | 0.358013 | ||||||||
\(141\) | −2.38197 | −0.200598 | ||||||||
\(142\) | −3.52786 | −0.296052 | ||||||||
\(143\) | −11.5623 | −0.966889 | ||||||||
\(144\) | −2.85410 | −0.237842 | ||||||||
\(145\) | 34.8885 | 2.89734 | ||||||||
\(146\) | 9.09017 | 0.752308 | ||||||||
\(147\) | 0.381966 | 0.0315040 | ||||||||
\(148\) | −5.00000 | −0.410997 | ||||||||
\(149\) | −1.90983 | −0.156459 | −0.0782297 | − | 0.996935i | \(-0.524927\pi\) | ||||
−0.0782297 | + | 0.996935i | \(0.524927\pi\) | |||||||
\(150\) | −4.94427 | −0.403698 | ||||||||
\(151\) | 0.236068 | 0.0192109 | 0.00960547 | − | 0.999954i | \(-0.496942\pi\) | ||||
0.00960547 | + | 0.999954i | \(0.496942\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.29180 | −0.427816 | ||||||||
\(154\) | 3.00000 | 0.241747 | ||||||||
\(155\) | −21.1803 | −1.70125 | ||||||||
\(156\) | −1.47214 | −0.117865 | ||||||||
\(157\) | −10.3820 | −0.828571 | −0.414286 | − | 0.910147i | \(-0.635969\pi\) | ||||
−0.414286 | + | 0.910147i | \(0.635969\pi\) | |||||||
\(158\) | −10.1459 | −0.807164 | ||||||||
\(159\) | −4.85410 | −0.384955 | ||||||||
\(160\) | 4.23607 | 0.334891 | ||||||||
\(161\) | 6.70820 | 0.528681 | ||||||||
\(162\) | −7.70820 | −0.605614 | ||||||||
\(163\) | −3.52786 | −0.276324 | −0.138162 | − | 0.990410i | \(-0.544119\pi\) | ||||
−0.138162 | + | 0.990410i | \(0.544119\pi\) | |||||||
\(164\) | −4.09017 | −0.319389 | ||||||||
\(165\) | −4.85410 | −0.377891 | ||||||||
\(166\) | 6.47214 | 0.502335 | ||||||||
\(167\) | 12.7639 | 0.987703 | 0.493851 | − | 0.869546i | \(-0.335589\pi\) | ||||
0.493851 | + | 0.869546i | \(0.335589\pi\) | |||||||
\(168\) | 0.381966 | 0.0294693 | ||||||||
\(169\) | 1.85410 | 0.142623 | ||||||||
\(170\) | 7.85410 | 0.602382 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −11.5623 | −0.881618 | ||||||||
\(173\) | −4.41641 | −0.335773 | −0.167887 | − | 0.985806i | \(-0.553694\pi\) | ||||
−0.167887 | + | 0.985806i | \(0.553694\pi\) | |||||||
\(174\) | 3.14590 | 0.238490 | ||||||||
\(175\) | −12.9443 | −0.978495 | ||||||||
\(176\) | 3.00000 | 0.226134 | ||||||||
\(177\) | 3.90983 | 0.293881 | ||||||||
\(178\) | 1.38197 | 0.103583 | ||||||||
\(179\) | 3.67376 | 0.274590 | 0.137295 | − | 0.990530i | \(-0.456159\pi\) | ||||
0.137295 | + | 0.990530i | \(0.456159\pi\) | |||||||
\(180\) | 12.0902 | 0.901148 | ||||||||
\(181\) | 15.9443 | 1.18513 | 0.592564 | − | 0.805523i | \(-0.298116\pi\) | ||||
0.592564 | + | 0.805523i | \(0.298116\pi\) | |||||||
\(182\) | −3.85410 | −0.285685 | ||||||||
\(183\) | −2.56231 | −0.189411 | ||||||||
\(184\) | 6.70820 | 0.494535 | ||||||||
\(185\) | 21.1803 | 1.55721 | ||||||||
\(186\) | −1.90983 | −0.140036 | ||||||||
\(187\) | 5.56231 | 0.406756 | ||||||||
\(188\) | −6.23607 | −0.454812 | ||||||||
\(189\) | 2.23607 | 0.162650 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.76393 | −0.561778 | −0.280889 | − | 0.959740i | \(-0.590629\pi\) | ||||
−0.280889 | + | 0.959740i | \(0.590629\pi\) | |||||||
\(192\) | 0.381966 | 0.0275660 | ||||||||
\(193\) | −4.18034 | −0.300907 | −0.150454 | − | 0.988617i | \(-0.548073\pi\) | ||||
−0.150454 | + | 0.988617i | \(0.548073\pi\) | |||||||
\(194\) | 5.29180 | 0.379929 | ||||||||
\(195\) | 6.23607 | 0.446574 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 19.0344 | 1.35615 | 0.678074 | − | 0.734994i | \(-0.262815\pi\) | ||||
0.678074 | + | 0.734994i | \(0.262815\pi\) | |||||||
\(198\) | 8.56231 | 0.608497 | ||||||||
\(199\) | 15.7984 | 1.11992 | 0.559959 | − | 0.828521i | \(-0.310817\pi\) | ||||
0.559959 | + | 0.828521i | \(0.310817\pi\) | |||||||
\(200\) | −12.9443 | −0.915298 | ||||||||
\(201\) | −1.74265 | −0.122917 | ||||||||
\(202\) | 8.09017 | 0.569222 | ||||||||
\(203\) | 8.23607 | 0.578059 | ||||||||
\(204\) | 0.708204 | 0.0495842 | ||||||||
\(205\) | 17.3262 | 1.21012 | ||||||||
\(206\) | −6.85410 | −0.477548 | ||||||||
\(207\) | 19.1459 | 1.33073 | ||||||||
\(208\) | −3.85410 | −0.267234 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −1.61803 | −0.111655 | ||||||||
\(211\) | 21.0000 | 1.44570 | 0.722850 | − | 0.691005i | \(-0.242832\pi\) | ||||
0.722850 | + | 0.691005i | \(0.242832\pi\) | |||||||
\(212\) | −12.7082 | −0.872803 | ||||||||
\(213\) | 1.34752 | 0.0923308 | ||||||||
\(214\) | 13.4721 | 0.920936 | ||||||||
\(215\) | 48.9787 | 3.34032 | ||||||||
\(216\) | 2.23607 | 0.152145 | ||||||||
\(217\) | −5.00000 | −0.339422 | ||||||||
\(218\) | −4.85410 | −0.328761 | ||||||||
\(219\) | −3.47214 | −0.234625 | ||||||||
\(220\) | −12.7082 | −0.856787 | ||||||||
\(221\) | −7.14590 | −0.480685 | ||||||||
\(222\) | 1.90983 | 0.128179 | ||||||||
\(223\) | 9.00000 | 0.602685 | 0.301342 | − | 0.953516i | \(-0.402565\pi\) | ||||
0.301342 | + | 0.953516i | \(0.402565\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | −36.9443 | −2.46295 | ||||||||
\(226\) | −11.7984 | −0.784816 | ||||||||
\(227\) | 27.0000 | 1.79205 | 0.896026 | − | 0.444001i | \(-0.146441\pi\) | ||||
0.896026 | + | 0.444001i | \(0.146441\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.5623 | −1.16055 | −0.580275 | − | 0.814421i | \(-0.697055\pi\) | ||||
−0.580275 | + | 0.814421i | \(0.697055\pi\) | |||||||
\(230\) | −28.4164 | −1.87372 | ||||||||
\(231\) | −1.14590 | −0.0753946 | ||||||||
\(232\) | 8.23607 | 0.540724 | ||||||||
\(233\) | −16.7984 | −1.10050 | −0.550249 | − | 0.835001i | \(-0.685467\pi\) | ||||
−0.550249 | + | 0.835001i | \(0.685467\pi\) | |||||||
\(234\) | −11.0000 | −0.719092 | ||||||||
\(235\) | 26.4164 | 1.72322 | ||||||||
\(236\) | 10.2361 | 0.666311 | ||||||||
\(237\) | 3.87539 | 0.251734 | ||||||||
\(238\) | 1.85410 | 0.120184 | ||||||||
\(239\) | 4.03444 | 0.260966 | 0.130483 | − | 0.991451i | \(-0.458347\pi\) | ||||
0.130483 | + | 0.991451i | \(0.458347\pi\) | |||||||
\(240\) | −1.61803 | −0.104444 | ||||||||
\(241\) | 20.1459 | 1.29771 | 0.648856 | − | 0.760911i | \(-0.275248\pi\) | ||||
0.648856 | + | 0.760911i | \(0.275248\pi\) | |||||||
\(242\) | 2.00000 | 0.128565 | ||||||||
\(243\) | 9.65248 | 0.619207 | ||||||||
\(244\) | −6.70820 | −0.429449 | ||||||||
\(245\) | −4.23607 | −0.270632 | ||||||||
\(246\) | 1.56231 | 0.0996090 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −5.00000 | −0.317500 | ||||||||
\(249\) | −2.47214 | −0.156665 | ||||||||
\(250\) | 33.6525 | 2.12837 | ||||||||
\(251\) | 16.3607 | 1.03268 | 0.516338 | − | 0.856385i | \(-0.327295\pi\) | ||||
0.516338 | + | 0.856385i | \(0.327295\pi\) | |||||||
\(252\) | 2.85410 | 0.179792 | ||||||||
\(253\) | −20.1246 | −1.26522 | ||||||||
\(254\) | −20.0344 | −1.25707 | ||||||||
\(255\) | −3.00000 | −0.187867 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −0.708204 | −0.0441765 | −0.0220883 | − | 0.999756i | \(-0.507031\pi\) | ||||
−0.0220883 | + | 0.999756i | \(0.507031\pi\) | |||||||
\(258\) | 4.41641 | 0.274954 | ||||||||
\(259\) | 5.00000 | 0.310685 | ||||||||
\(260\) | 16.3262 | 1.01251 | ||||||||
\(261\) | 23.5066 | 1.45502 | ||||||||
\(262\) | 3.38197 | 0.208939 | ||||||||
\(263\) | −5.29180 | −0.326306 | −0.163153 | − | 0.986601i | \(-0.552166\pi\) | ||||
−0.163153 | + | 0.986601i | \(0.552166\pi\) | |||||||
\(264\) | −1.14590 | −0.0705251 | ||||||||
\(265\) | 53.8328 | 3.30692 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.527864 | −0.0323048 | ||||||||
\(268\) | −4.56231 | −0.278687 | ||||||||
\(269\) | −31.4721 | −1.91889 | −0.959445 | − | 0.281896i | \(-0.909037\pi\) | ||||
−0.959445 | + | 0.281896i | \(0.909037\pi\) | |||||||
\(270\) | −9.47214 | −0.576456 | ||||||||
\(271\) | 3.58359 | 0.217688 | 0.108844 | − | 0.994059i | \(-0.465285\pi\) | ||||
0.108844 | + | 0.994059i | \(0.465285\pi\) | |||||||
\(272\) | 1.85410 | 0.112421 | ||||||||
\(273\) | 1.47214 | 0.0890977 | ||||||||
\(274\) | −9.23607 | −0.557971 | ||||||||
\(275\) | 38.8328 | 2.34171 | ||||||||
\(276\) | −2.56231 | −0.154233 | ||||||||
\(277\) | −18.4721 | −1.10988 | −0.554942 | − | 0.831889i | \(-0.687259\pi\) | ||||
−0.554942 | + | 0.831889i | \(0.687259\pi\) | |||||||
\(278\) | −19.0000 | −1.13954 | ||||||||
\(279\) | −14.2705 | −0.854353 | ||||||||
\(280\) | −4.23607 | −0.253153 | ||||||||
\(281\) | −15.6525 | −0.933748 | −0.466874 | − | 0.884324i | \(-0.654620\pi\) | ||||
−0.466874 | + | 0.884324i | \(0.654620\pi\) | |||||||
\(282\) | 2.38197 | 0.141844 | ||||||||
\(283\) | 15.0344 | 0.893705 | 0.446852 | − | 0.894608i | \(-0.352545\pi\) | ||||
0.446852 | + | 0.894608i | \(0.352545\pi\) | |||||||
\(284\) | 3.52786 | 0.209340 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 11.5623 | 0.683693 | ||||||||
\(287\) | 4.09017 | 0.241435 | ||||||||
\(288\) | 2.85410 | 0.168180 | ||||||||
\(289\) | −13.5623 | −0.797783 | ||||||||
\(290\) | −34.8885 | −2.04873 | ||||||||
\(291\) | −2.02129 | −0.118490 | ||||||||
\(292\) | −9.09017 | −0.531962 | ||||||||
\(293\) | −1.58359 | −0.0925144 | −0.0462572 | − | 0.998930i | \(-0.514729\pi\) | ||||
−0.0462572 | + | 0.998930i | \(0.514729\pi\) | |||||||
\(294\) | −0.381966 | −0.0222767 | ||||||||
\(295\) | −43.3607 | −2.52456 | ||||||||
\(296\) | 5.00000 | 0.290619 | ||||||||
\(297\) | −6.70820 | −0.389249 | ||||||||
\(298\) | 1.90983 | 0.110633 | ||||||||
\(299\) | 25.8541 | 1.49518 | ||||||||
\(300\) | 4.94427 | 0.285458 | ||||||||
\(301\) | 11.5623 | 0.666440 | ||||||||
\(302\) | −0.236068 | −0.0135842 | ||||||||
\(303\) | −3.09017 | −0.177526 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 28.4164 | 1.62712 | ||||||||
\(306\) | 5.29180 | 0.302512 | ||||||||
\(307\) | 26.8328 | 1.53143 | 0.765715 | − | 0.643180i | \(-0.222385\pi\) | ||||
0.765715 | + | 0.643180i | \(0.222385\pi\) | |||||||
\(308\) | −3.00000 | −0.170941 | ||||||||
\(309\) | 2.61803 | 0.148935 | ||||||||
\(310\) | 21.1803 | 1.20296 | ||||||||
\(311\) | −33.9443 | −1.92480 | −0.962402 | − | 0.271631i | \(-0.912437\pi\) | ||||
−0.962402 | + | 0.271631i | \(0.912437\pi\) | |||||||
\(312\) | 1.47214 | 0.0833433 | ||||||||
\(313\) | −4.27051 | −0.241383 | −0.120692 | − | 0.992690i | \(-0.538511\pi\) | ||||
−0.120692 | + | 0.992690i | \(0.538511\pi\) | |||||||
\(314\) | 10.3820 | 0.585888 | ||||||||
\(315\) | −12.0902 | −0.681204 | ||||||||
\(316\) | 10.1459 | 0.570751 | ||||||||
\(317\) | −18.5279 | −1.04063 | −0.520314 | − | 0.853975i | \(-0.674185\pi\) | ||||
−0.520314 | + | 0.853975i | \(0.674185\pi\) | |||||||
\(318\) | 4.85410 | 0.272205 | ||||||||
\(319\) | −24.7082 | −1.38339 | ||||||||
\(320\) | −4.23607 | −0.236803 | ||||||||
\(321\) | −5.14590 | −0.287216 | ||||||||
\(322\) | −6.70820 | −0.373834 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 7.70820 | 0.428234 | ||||||||
\(325\) | −49.8885 | −2.76732 | ||||||||
\(326\) | 3.52786 | 0.195390 | ||||||||
\(327\) | 1.85410 | 0.102532 | ||||||||
\(328\) | 4.09017 | 0.225842 | ||||||||
\(329\) | 6.23607 | 0.343806 | ||||||||
\(330\) | 4.85410 | 0.267210 | ||||||||
\(331\) | −0.472136 | −0.0259509 | −0.0129755 | − | 0.999916i | \(-0.504130\pi\) | ||||
−0.0129755 | + | 0.999916i | \(0.504130\pi\) | |||||||
\(332\) | −6.47214 | −0.355205 | ||||||||
\(333\) | 14.2705 | 0.782019 | ||||||||
\(334\) | −12.7639 | −0.698411 | ||||||||
\(335\) | 19.3262 | 1.05591 | ||||||||
\(336\) | −0.381966 | −0.0208380 | ||||||||
\(337\) | −8.56231 | −0.466419 | −0.233209 | − | 0.972427i | \(-0.574923\pi\) | ||||
−0.233209 | + | 0.972427i | \(0.574923\pi\) | |||||||
\(338\) | −1.85410 | −0.100850 | ||||||||
\(339\) | 4.50658 | 0.244764 | ||||||||
\(340\) | −7.85410 | −0.425948 | ||||||||
\(341\) | 15.0000 | 0.812296 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 11.5623 | 0.623398 | ||||||||
\(345\) | 10.8541 | 0.584365 | ||||||||
\(346\) | 4.41641 | 0.237428 | ||||||||
\(347\) | 4.47214 | 0.240077 | 0.120038 | − | 0.992769i | \(-0.461698\pi\) | ||||
0.120038 | + | 0.992769i | \(0.461698\pi\) | |||||||
\(348\) | −3.14590 | −0.168638 | ||||||||
\(349\) | 21.8328 | 1.16868 | 0.584342 | − | 0.811508i | \(-0.301353\pi\) | ||||
0.584342 | + | 0.811508i | \(0.301353\pi\) | |||||||
\(350\) | 12.9443 | 0.691900 | ||||||||
\(351\) | 8.61803 | 0.459997 | ||||||||
\(352\) | −3.00000 | −0.159901 | ||||||||
\(353\) | 25.7984 | 1.37311 | 0.686554 | − | 0.727078i | \(-0.259122\pi\) | ||||
0.686554 | + | 0.727078i | \(0.259122\pi\) | |||||||
\(354\) | −3.90983 | −0.207805 | ||||||||
\(355\) | −14.9443 | −0.793160 | ||||||||
\(356\) | −1.38197 | −0.0732441 | ||||||||
\(357\) | −0.708204 | −0.0374821 | ||||||||
\(358\) | −3.67376 | −0.194164 | ||||||||
\(359\) | −1.94427 | −0.102615 | −0.0513074 | − | 0.998683i | \(-0.516339\pi\) | ||||
−0.0513074 | + | 0.998683i | \(0.516339\pi\) | |||||||
\(360\) | −12.0902 | −0.637208 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | −15.9443 | −0.838012 | ||||||||
\(363\) | −0.763932 | −0.0400960 | ||||||||
\(364\) | 3.85410 | 0.202010 | ||||||||
\(365\) | 38.5066 | 2.01553 | ||||||||
\(366\) | 2.56231 | 0.133934 | ||||||||
\(367\) | 1.43769 | 0.0750470 | 0.0375235 | − | 0.999296i | \(-0.488053\pi\) | ||||
0.0375235 | + | 0.999296i | \(0.488053\pi\) | |||||||
\(368\) | −6.70820 | −0.349689 | ||||||||
\(369\) | 11.6738 | 0.607712 | ||||||||
\(370\) | −21.1803 | −1.10111 | ||||||||
\(371\) | 12.7082 | 0.659777 | ||||||||
\(372\) | 1.90983 | 0.0990201 | ||||||||
\(373\) | −11.8541 | −0.613782 | −0.306891 | − | 0.951745i | \(-0.599289\pi\) | ||||
−0.306891 | + | 0.951745i | \(0.599289\pi\) | |||||||
\(374\) | −5.56231 | −0.287620 | ||||||||
\(375\) | −12.8541 | −0.663783 | ||||||||
\(376\) | 6.23607 | 0.321601 | ||||||||
\(377\) | 31.7426 | 1.63483 | ||||||||
\(378\) | −2.23607 | −0.115011 | ||||||||
\(379\) | −12.2705 | −0.630294 | −0.315147 | − | 0.949043i | \(-0.602054\pi\) | ||||
−0.315147 | + | 0.949043i | \(0.602054\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.65248 | 0.392048 | ||||||||
\(382\) | 7.76393 | 0.397237 | ||||||||
\(383\) | −0.708204 | −0.0361875 | −0.0180938 | − | 0.999836i | \(-0.505760\pi\) | ||||
−0.0180938 | + | 0.999836i | \(0.505760\pi\) | |||||||
\(384\) | −0.381966 | −0.0194921 | ||||||||
\(385\) | 12.7082 | 0.647670 | ||||||||
\(386\) | 4.18034 | 0.212774 | ||||||||
\(387\) | 33.0000 | 1.67748 | ||||||||
\(388\) | −5.29180 | −0.268650 | ||||||||
\(389\) | 10.2016 | 0.517243 | 0.258621 | − | 0.965979i | \(-0.416732\pi\) | ||||
0.258621 | + | 0.965979i | \(0.416732\pi\) | |||||||
\(390\) | −6.23607 | −0.315776 | ||||||||
\(391\) | −12.4377 | −0.629001 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | −1.29180 | −0.0651625 | ||||||||
\(394\) | −19.0344 | −0.958941 | ||||||||
\(395\) | −42.9787 | −2.16249 | ||||||||
\(396\) | −8.56231 | −0.430272 | ||||||||
\(397\) | −14.3262 | −0.719013 | −0.359507 | − | 0.933143i | \(-0.617055\pi\) | ||||
−0.359507 | + | 0.933143i | \(0.617055\pi\) | |||||||
\(398\) | −15.7984 | −0.791901 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 12.9443 | 0.647214 | ||||||||
\(401\) | −24.4721 | −1.22208 | −0.611040 | − | 0.791600i | \(-0.709249\pi\) | ||||
−0.611040 | + | 0.791600i | \(0.709249\pi\) | |||||||
\(402\) | 1.74265 | 0.0869153 | ||||||||
\(403\) | −19.2705 | −0.959932 | ||||||||
\(404\) | −8.09017 | −0.402501 | ||||||||
\(405\) | −32.6525 | −1.62251 | ||||||||
\(406\) | −8.23607 | −0.408749 | ||||||||
\(407\) | −15.0000 | −0.743522 | ||||||||
\(408\) | −0.708204 | −0.0350613 | ||||||||
\(409\) | 16.1459 | 0.798363 | 0.399182 | − | 0.916872i | \(-0.369294\pi\) | ||||
0.399182 | + | 0.916872i | \(0.369294\pi\) | |||||||
\(410\) | −17.3262 | −0.855682 | ||||||||
\(411\) | 3.52786 | 0.174017 | ||||||||
\(412\) | 6.85410 | 0.337677 | ||||||||
\(413\) | −10.2361 | −0.503684 | ||||||||
\(414\) | −19.1459 | −0.940970 | ||||||||
\(415\) | 27.4164 | 1.34582 | ||||||||
\(416\) | 3.85410 | 0.188963 | ||||||||
\(417\) | 7.25735 | 0.355394 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −28.0902 | −1.37229 | −0.686147 | − | 0.727463i | \(-0.740699\pi\) | ||||
−0.686147 | + | 0.727463i | \(0.740699\pi\) | |||||||
\(420\) | 1.61803 | 0.0789520 | ||||||||
\(421\) | −16.8885 | −0.823097 | −0.411549 | − | 0.911388i | \(-0.635012\pi\) | ||||
−0.411549 | + | 0.911388i | \(0.635012\pi\) | |||||||
\(422\) | −21.0000 | −1.02226 | ||||||||
\(423\) | 17.7984 | 0.865387 | ||||||||
\(424\) | 12.7082 | 0.617165 | ||||||||
\(425\) | 24.0000 | 1.16417 | ||||||||
\(426\) | −1.34752 | −0.0652878 | ||||||||
\(427\) | 6.70820 | 0.324633 | ||||||||
\(428\) | −13.4721 | −0.651200 | ||||||||
\(429\) | −4.41641 | −0.213226 | ||||||||
\(430\) | −48.9787 | −2.36196 | ||||||||
\(431\) | 22.3607 | 1.07708 | 0.538538 | − | 0.842601i | \(-0.318977\pi\) | ||||
0.538538 | + | 0.842601i | \(0.318977\pi\) | |||||||
\(432\) | −2.23607 | −0.107583 | ||||||||
\(433\) | −25.8541 | −1.24247 | −0.621234 | − | 0.783625i | \(-0.713369\pi\) | ||||
−0.621234 | + | 0.783625i | \(0.713369\pi\) | |||||||
\(434\) | 5.00000 | 0.240008 | ||||||||
\(435\) | 13.3262 | 0.638944 | ||||||||
\(436\) | 4.85410 | 0.232469 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 3.47214 | 0.165905 | ||||||||
\(439\) | 13.7639 | 0.656917 | 0.328458 | − | 0.944518i | \(-0.393471\pi\) | ||||
0.328458 | + | 0.944518i | \(0.393471\pi\) | |||||||
\(440\) | 12.7082 | 0.605840 | ||||||||
\(441\) | −2.85410 | −0.135910 | ||||||||
\(442\) | 7.14590 | 0.339896 | ||||||||
\(443\) | 26.5066 | 1.25937 | 0.629683 | − | 0.776852i | \(-0.283185\pi\) | ||||
0.629683 | + | 0.776852i | \(0.283185\pi\) | |||||||
\(444\) | −1.90983 | −0.0906365 | ||||||||
\(445\) | 5.85410 | 0.277511 | ||||||||
\(446\) | −9.00000 | −0.426162 | ||||||||
\(447\) | −0.729490 | −0.0345037 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | −28.7639 | −1.35745 | −0.678727 | − | 0.734391i | \(-0.737468\pi\) | ||||
−0.678727 | + | 0.734391i | \(0.737468\pi\) | |||||||
\(450\) | 36.9443 | 1.74157 | ||||||||
\(451\) | −12.2705 | −0.577796 | ||||||||
\(452\) | 11.7984 | 0.554949 | ||||||||
\(453\) | 0.0901699 | 0.00423655 | ||||||||
\(454\) | −27.0000 | −1.26717 | ||||||||
\(455\) | −16.3262 | −0.765386 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −37.8885 | −1.77235 | −0.886176 | − | 0.463349i | \(-0.846647\pi\) | ||||
−0.886176 | + | 0.463349i | \(0.846647\pi\) | |||||||
\(458\) | 17.5623 | 0.820633 | ||||||||
\(459\) | −4.14590 | −0.193514 | ||||||||
\(460\) | 28.4164 | 1.32492 | ||||||||
\(461\) | −21.7082 | −1.01105 | −0.505526 | − | 0.862811i | \(-0.668702\pi\) | ||||
−0.505526 | + | 0.862811i | \(0.668702\pi\) | |||||||
\(462\) | 1.14590 | 0.0533120 | ||||||||
\(463\) | 33.9787 | 1.57912 | 0.789562 | − | 0.613670i | \(-0.210308\pi\) | ||||
0.789562 | + | 0.613670i | \(0.210308\pi\) | |||||||
\(464\) | −8.23607 | −0.382350 | ||||||||
\(465\) | −8.09017 | −0.375173 | ||||||||
\(466\) | 16.7984 | 0.778170 | ||||||||
\(467\) | 38.1246 | 1.76420 | 0.882098 | − | 0.471065i | \(-0.156130\pi\) | ||||
0.882098 | + | 0.471065i | \(0.156130\pi\) | |||||||
\(468\) | 11.0000 | 0.508475 | ||||||||
\(469\) | 4.56231 | 0.210668 | ||||||||
\(470\) | −26.4164 | −1.21850 | ||||||||
\(471\) | −3.96556 | −0.182723 | ||||||||
\(472\) | −10.2361 | −0.471153 | ||||||||
\(473\) | −34.6869 | −1.59491 | ||||||||
\(474\) | −3.87539 | −0.178002 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.85410 | −0.0849826 | ||||||||
\(477\) | 36.2705 | 1.66071 | ||||||||
\(478\) | −4.03444 | −0.184531 | ||||||||
\(479\) | −27.7082 | −1.26602 | −0.633010 | − | 0.774144i | \(-0.718181\pi\) | ||||
−0.633010 | + | 0.774144i | \(0.718181\pi\) | |||||||
\(480\) | 1.61803 | 0.0738528 | ||||||||
\(481\) | 19.2705 | 0.878660 | ||||||||
\(482\) | −20.1459 | −0.917621 | ||||||||
\(483\) | 2.56231 | 0.116589 | ||||||||
\(484\) | −2.00000 | −0.0909091 | ||||||||
\(485\) | 22.4164 | 1.01788 | ||||||||
\(486\) | −9.65248 | −0.437845 | ||||||||
\(487\) | −10.3475 | −0.468891 | −0.234446 | − | 0.972129i | \(-0.575327\pi\) | ||||
−0.234446 | + | 0.972129i | \(0.575327\pi\) | |||||||
\(488\) | 6.70820 | 0.303666 | ||||||||
\(489\) | −1.34752 | −0.0609371 | ||||||||
\(490\) | 4.23607 | 0.191366 | ||||||||
\(491\) | −24.0689 | −1.08621 | −0.543107 | − | 0.839664i | \(-0.682752\pi\) | ||||
−0.543107 | + | 0.839664i | \(0.682752\pi\) | |||||||
\(492\) | −1.56231 | −0.0704342 | ||||||||
\(493\) | −15.2705 | −0.687749 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 36.2705 | 1.63024 | ||||||||
\(496\) | 5.00000 | 0.224507 | ||||||||
\(497\) | −3.52786 | −0.158246 | ||||||||
\(498\) | 2.47214 | 0.110779 | ||||||||
\(499\) | −3.00000 | −0.134298 | −0.0671492 | − | 0.997743i | \(-0.521390\pi\) | ||||
−0.0671492 | + | 0.997743i | \(0.521390\pi\) | |||||||
\(500\) | −33.6525 | −1.50498 | ||||||||
\(501\) | 4.87539 | 0.217816 | ||||||||
\(502\) | −16.3607 | −0.730213 | ||||||||
\(503\) | −12.9443 | −0.577157 | −0.288578 | − | 0.957456i | \(-0.593183\pi\) | ||||
−0.288578 | + | 0.957456i | \(0.593183\pi\) | |||||||
\(504\) | −2.85410 | −0.127132 | ||||||||
\(505\) | 34.2705 | 1.52502 | ||||||||
\(506\) | 20.1246 | 0.894648 | ||||||||
\(507\) | 0.708204 | 0.0314524 | ||||||||
\(508\) | 20.0344 | 0.888885 | ||||||||
\(509\) | 30.0000 | 1.32973 | 0.664863 | − | 0.746965i | \(-0.268490\pi\) | ||||
0.664863 | + | 0.746965i | \(0.268490\pi\) | |||||||
\(510\) | 3.00000 | 0.132842 | ||||||||
\(511\) | 9.09017 | 0.402125 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0.708204 | 0.0312375 | ||||||||
\(515\) | −29.0344 | −1.27941 | ||||||||
\(516\) | −4.41641 | −0.194422 | ||||||||
\(517\) | −18.7082 | −0.822786 | ||||||||
\(518\) | −5.00000 | −0.219687 | ||||||||
\(519\) | −1.68692 | −0.0740475 | ||||||||
\(520\) | −16.3262 | −0.715953 | ||||||||
\(521\) | 10.8885 | 0.477036 | 0.238518 | − | 0.971138i | \(-0.423338\pi\) | ||||
0.238518 | + | 0.971138i | \(0.423338\pi\) | |||||||
\(522\) | −23.5066 | −1.02885 | ||||||||
\(523\) | 30.0902 | 1.31575 | 0.657876 | − | 0.753127i | \(-0.271455\pi\) | ||||
0.657876 | + | 0.753127i | \(0.271455\pi\) | |||||||
\(524\) | −3.38197 | −0.147742 | ||||||||
\(525\) | −4.94427 | −0.215786 | ||||||||
\(526\) | 5.29180 | 0.230733 | ||||||||
\(527\) | 9.27051 | 0.403830 | ||||||||
\(528\) | 1.14590 | 0.0498688 | ||||||||
\(529\) | 22.0000 | 0.956522 | ||||||||
\(530\) | −53.8328 | −2.33835 | ||||||||
\(531\) | −29.2148 | −1.26781 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 15.7639 | 0.682812 | ||||||||
\(534\) | 0.527864 | 0.0228429 | ||||||||
\(535\) | 57.0689 | 2.46730 | ||||||||
\(536\) | 4.56231 | 0.197062 | ||||||||
\(537\) | 1.40325 | 0.0605548 | ||||||||
\(538\) | 31.4721 | 1.35686 | ||||||||
\(539\) | 3.00000 | 0.129219 | ||||||||
\(540\) | 9.47214 | 0.407616 | ||||||||
\(541\) | −3.47214 | −0.149279 | −0.0746394 | − | 0.997211i | \(-0.523781\pi\) | ||||
−0.0746394 | + | 0.997211i | \(0.523781\pi\) | |||||||
\(542\) | −3.58359 | −0.153928 | ||||||||
\(543\) | 6.09017 | 0.261354 | ||||||||
\(544\) | −1.85410 | −0.0794940 | ||||||||
\(545\) | −20.5623 | −0.880792 | ||||||||
\(546\) | −1.47214 | −0.0630016 | ||||||||
\(547\) | 21.1803 | 0.905606 | 0.452803 | − | 0.891611i | \(-0.350424\pi\) | ||||
0.452803 | + | 0.891611i | \(0.350424\pi\) | |||||||
\(548\) | 9.23607 | 0.394545 | ||||||||
\(549\) | 19.1459 | 0.817127 | ||||||||
\(550\) | −38.8328 | −1.65584 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 2.56231 | 0.109059 | ||||||||
\(553\) | −10.1459 | −0.431447 | ||||||||
\(554\) | 18.4721 | 0.784806 | ||||||||
\(555\) | 8.09017 | 0.343409 | ||||||||
\(556\) | 19.0000 | 0.805779 | ||||||||
\(557\) | −37.7639 | −1.60011 | −0.800055 | − | 0.599927i | \(-0.795196\pi\) | ||||
−0.800055 | + | 0.599927i | \(0.795196\pi\) | |||||||
\(558\) | 14.2705 | 0.604119 | ||||||||
\(559\) | 44.5623 | 1.88478 | ||||||||
\(560\) | 4.23607 | 0.179007 | ||||||||
\(561\) | 2.12461 | 0.0897012 | ||||||||
\(562\) | 15.6525 | 0.660260 | ||||||||
\(563\) | −12.1803 | −0.513340 | −0.256670 | − | 0.966499i | \(-0.582625\pi\) | ||||
−0.256670 | + | 0.966499i | \(0.582625\pi\) | |||||||
\(564\) | −2.38197 | −0.100299 | ||||||||
\(565\) | −49.9787 | −2.10262 | ||||||||
\(566\) | −15.0344 | −0.631945 | ||||||||
\(567\) | −7.70820 | −0.323714 | ||||||||
\(568\) | −3.52786 | −0.148026 | ||||||||
\(569\) | −21.3820 | −0.896379 | −0.448189 | − | 0.893939i | \(-0.647931\pi\) | ||||
−0.448189 | + | 0.893939i | \(0.647931\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.34752 | 0.307484 | 0.153742 | − | 0.988111i | \(-0.450867\pi\) | ||||
0.153742 | + | 0.988111i | \(0.450867\pi\) | |||||||
\(572\) | −11.5623 | −0.483444 | ||||||||
\(573\) | −2.96556 | −0.123888 | ||||||||
\(574\) | −4.09017 | −0.170720 | ||||||||
\(575\) | −86.8328 | −3.62118 | ||||||||
\(576\) | −2.85410 | −0.118921 | ||||||||
\(577\) | 38.4164 | 1.59930 | 0.799648 | − | 0.600469i | \(-0.205019\pi\) | ||||
0.799648 | + | 0.600469i | \(0.205019\pi\) | |||||||
\(578\) | 13.5623 | 0.564118 | ||||||||
\(579\) | −1.59675 | −0.0663586 | ||||||||
\(580\) | 34.8885 | 1.44867 | ||||||||
\(581\) | 6.47214 | 0.268509 | ||||||||
\(582\) | 2.02129 | 0.0837850 | ||||||||
\(583\) | −38.1246 | −1.57896 | ||||||||
\(584\) | 9.09017 | 0.376154 | ||||||||
\(585\) | −46.5967 | −1.92654 | ||||||||
\(586\) | 1.58359 | 0.0654176 | ||||||||
\(587\) | −5.65248 | −0.233303 | −0.116651 | − | 0.993173i | \(-0.537216\pi\) | ||||
−0.116651 | + | 0.993173i | \(0.537216\pi\) | |||||||
\(588\) | 0.381966 | 0.0157520 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 43.3607 | 1.78513 | ||||||||
\(591\) | 7.27051 | 0.299069 | ||||||||
\(592\) | −5.00000 | −0.205499 | ||||||||
\(593\) | −5.67376 | −0.232993 | −0.116497 | − | 0.993191i | \(-0.537166\pi\) | ||||
−0.116497 | + | 0.993191i | \(0.537166\pi\) | |||||||
\(594\) | 6.70820 | 0.275241 | ||||||||
\(595\) | 7.85410 | 0.321987 | ||||||||
\(596\) | −1.90983 | −0.0782297 | ||||||||
\(597\) | 6.03444 | 0.246973 | ||||||||
\(598\) | −25.8541 | −1.05725 | ||||||||
\(599\) | 13.4721 | 0.550457 | 0.275228 | − | 0.961379i | \(-0.411247\pi\) | ||||
0.275228 | + | 0.961379i | \(0.411247\pi\) | |||||||
\(600\) | −4.94427 | −0.201849 | ||||||||
\(601\) | 37.8328 | 1.54323 | 0.771616 | − | 0.636088i | \(-0.219449\pi\) | ||||
0.771616 | + | 0.636088i | \(0.219449\pi\) | |||||||
\(602\) | −11.5623 | −0.471244 | ||||||||
\(603\) | 13.0213 | 0.530268 | ||||||||
\(604\) | 0.236068 | 0.00960547 | ||||||||
\(605\) | 8.47214 | 0.344441 | ||||||||
\(606\) | 3.09017 | 0.125530 | ||||||||
\(607\) | 30.8328 | 1.25147 | 0.625733 | − | 0.780038i | \(-0.284800\pi\) | ||||
0.625733 | + | 0.780038i | \(0.284800\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.14590 | 0.127478 | ||||||||
\(610\) | −28.4164 | −1.15055 | ||||||||
\(611\) | 24.0344 | 0.972329 | ||||||||
\(612\) | −5.29180 | −0.213908 | ||||||||
\(613\) | −18.1803 | −0.734297 | −0.367149 | − | 0.930162i | \(-0.619666\pi\) | ||||
−0.367149 | + | 0.930162i | \(0.619666\pi\) | |||||||
\(614\) | −26.8328 | −1.08288 | ||||||||
\(615\) | 6.61803 | 0.266865 | ||||||||
\(616\) | 3.00000 | 0.120873 | ||||||||
\(617\) | 13.7984 | 0.555502 | 0.277751 | − | 0.960653i | \(-0.410411\pi\) | ||||
0.277751 | + | 0.960653i | \(0.410411\pi\) | |||||||
\(618\) | −2.61803 | −0.105313 | ||||||||
\(619\) | 6.85410 | 0.275490 | 0.137745 | − | 0.990468i | \(-0.456015\pi\) | ||||
0.137745 | + | 0.990468i | \(0.456015\pi\) | |||||||
\(620\) | −21.1803 | −0.850623 | ||||||||
\(621\) | 15.0000 | 0.601929 | ||||||||
\(622\) | 33.9443 | 1.36104 | ||||||||
\(623\) | 1.38197 | 0.0553673 | ||||||||
\(624\) | −1.47214 | −0.0589326 | ||||||||
\(625\) | 77.8328 | 3.11331 | ||||||||
\(626\) | 4.27051 | 0.170684 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −10.3820 | −0.414286 | ||||||||
\(629\) | −9.27051 | −0.369639 | ||||||||
\(630\) | 12.0902 | 0.481684 | ||||||||
\(631\) | 14.8328 | 0.590485 | 0.295243 | − | 0.955422i | \(-0.404600\pi\) | ||||
0.295243 | + | 0.955422i | \(0.404600\pi\) | |||||||
\(632\) | −10.1459 | −0.403582 | ||||||||
\(633\) | 8.02129 | 0.318818 | ||||||||
\(634\) | 18.5279 | 0.735835 | ||||||||
\(635\) | −84.8673 | −3.36785 | ||||||||
\(636\) | −4.85410 | −0.192478 | ||||||||
\(637\) | −3.85410 | −0.152705 | ||||||||
\(638\) | 24.7082 | 0.978207 | ||||||||
\(639\) | −10.0689 | −0.398319 | ||||||||
\(640\) | 4.23607 | 0.167445 | ||||||||
\(641\) | 23.7984 | 0.939979 | 0.469990 | − | 0.882672i | \(-0.344258\pi\) | ||||
0.469990 | + | 0.882672i | \(0.344258\pi\) | |||||||
\(642\) | 5.14590 | 0.203092 | ||||||||
\(643\) | 5.59675 | 0.220714 | 0.110357 | − | 0.993892i | \(-0.464801\pi\) | ||||
0.110357 | + | 0.993892i | \(0.464801\pi\) | |||||||
\(644\) | 6.70820 | 0.264340 | ||||||||
\(645\) | 18.7082 | 0.736635 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6.79837 | −0.267272 | −0.133636 | − | 0.991031i | \(-0.542665\pi\) | ||||
−0.133636 | + | 0.991031i | \(0.542665\pi\) | |||||||
\(648\) | −7.70820 | −0.302807 | ||||||||
\(649\) | 30.7082 | 1.20540 | ||||||||
\(650\) | 49.8885 | 1.95679 | ||||||||
\(651\) | −1.90983 | −0.0748521 | ||||||||
\(652\) | −3.52786 | −0.138162 | ||||||||
\(653\) | 7.67376 | 0.300298 | 0.150149 | − | 0.988663i | \(-0.452025\pi\) | ||||
0.150149 | + | 0.988663i | \(0.452025\pi\) | |||||||
\(654\) | −1.85410 | −0.0725011 | ||||||||
\(655\) | 14.3262 | 0.559772 | ||||||||
\(656\) | −4.09017 | −0.159694 | ||||||||
\(657\) | 25.9443 | 1.01218 | ||||||||
\(658\) | −6.23607 | −0.243107 | ||||||||
\(659\) | 2.34752 | 0.0914466 | 0.0457233 | − | 0.998954i | \(-0.485441\pi\) | ||||
0.0457233 | + | 0.998954i | \(0.485441\pi\) | |||||||
\(660\) | −4.85410 | −0.188946 | ||||||||
\(661\) | −11.2918 | −0.439200 | −0.219600 | − | 0.975590i | \(-0.570475\pi\) | ||||
−0.219600 | + | 0.975590i | \(0.570475\pi\) | |||||||
\(662\) | 0.472136 | 0.0183501 | ||||||||
\(663\) | −2.72949 | −0.106005 | ||||||||
\(664\) | 6.47214 | 0.251168 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −14.2705 | −0.552971 | ||||||||
\(667\) | 55.2492 | 2.13926 | ||||||||
\(668\) | 12.7639 | 0.493851 | ||||||||
\(669\) | 3.43769 | 0.132909 | ||||||||
\(670\) | −19.3262 | −0.746638 | ||||||||
\(671\) | −20.1246 | −0.776902 | ||||||||
\(672\) | 0.381966 | 0.0147347 | ||||||||
\(673\) | −9.61803 | −0.370748 | −0.185374 | − | 0.982668i | \(-0.559350\pi\) | ||||
−0.185374 | + | 0.982668i | \(0.559350\pi\) | |||||||
\(674\) | 8.56231 | 0.329808 | ||||||||
\(675\) | −28.9443 | −1.11407 | ||||||||
\(676\) | 1.85410 | 0.0713116 | ||||||||
\(677\) | 34.0689 | 1.30937 | 0.654687 | − | 0.755900i | \(-0.272801\pi\) | ||||
0.654687 | + | 0.755900i | \(0.272801\pi\) | |||||||
\(678\) | −4.50658 | −0.173074 | ||||||||
\(679\) | 5.29180 | 0.203080 | ||||||||
\(680\) | 7.85410 | 0.301191 | ||||||||
\(681\) | 10.3131 | 0.395198 | ||||||||
\(682\) | −15.0000 | −0.574380 | ||||||||
\(683\) | −43.7426 | −1.67377 | −0.836883 | − | 0.547382i | \(-0.815625\pi\) | ||||
−0.836883 | + | 0.547382i | \(0.815625\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −39.1246 | −1.49487 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | −6.70820 | −0.255934 | ||||||||
\(688\) | −11.5623 | −0.440809 | ||||||||
\(689\) | 48.9787 | 1.86594 | ||||||||
\(690\) | −10.8541 | −0.413209 | ||||||||
\(691\) | −32.1246 | −1.22208 | −0.611039 | − | 0.791601i | \(-0.709248\pi\) | ||||
−0.611039 | + | 0.791601i | \(0.709248\pi\) | |||||||
\(692\) | −4.41641 | −0.167887 | ||||||||
\(693\) | 8.56231 | 0.325255 | ||||||||
\(694\) | −4.47214 | −0.169760 | ||||||||
\(695\) | −80.4853 | −3.05298 | ||||||||
\(696\) | 3.14590 | 0.119245 | ||||||||
\(697\) | −7.58359 | −0.287249 | ||||||||
\(698\) | −21.8328 | −0.826384 | ||||||||
\(699\) | −6.41641 | −0.242691 | ||||||||
\(700\) | −12.9443 | −0.489247 | ||||||||
\(701\) | 8.21478 | 0.310268 | 0.155134 | − | 0.987893i | \(-0.450419\pi\) | ||||
0.155134 | + | 0.987893i | \(0.450419\pi\) | |||||||
\(702\) | −8.61803 | −0.325267 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 3.00000 | 0.113067 | ||||||||
\(705\) | 10.0902 | 0.380018 | ||||||||
\(706\) | −25.7984 | −0.970935 | ||||||||
\(707\) | 8.09017 | 0.304262 | ||||||||
\(708\) | 3.90983 | 0.146940 | ||||||||
\(709\) | −36.2361 | −1.36087 | −0.680437 | − | 0.732807i | \(-0.738210\pi\) | ||||
−0.680437 | + | 0.732807i | \(0.738210\pi\) | |||||||
\(710\) | 14.9443 | 0.560849 | ||||||||
\(711\) | −28.9574 | −1.08599 | ||||||||
\(712\) | 1.38197 | 0.0517914 | ||||||||
\(713\) | −33.5410 | −1.25612 | ||||||||
\(714\) | 0.708204 | 0.0265039 | ||||||||
\(715\) | 48.9787 | 1.83170 | ||||||||
\(716\) | 3.67376 | 0.137295 | ||||||||
\(717\) | 1.54102 | 0.0575504 | ||||||||
\(718\) | 1.94427 | 0.0725596 | ||||||||
\(719\) | 41.0689 | 1.53161 | 0.765805 | − | 0.643072i | \(-0.222341\pi\) | ||||
0.765805 | + | 0.643072i | \(0.222341\pi\) | |||||||
\(720\) | 12.0902 | 0.450574 | ||||||||
\(721\) | −6.85410 | −0.255260 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.69505 | 0.286182 | ||||||||
\(724\) | 15.9443 | 0.592564 | ||||||||
\(725\) | −106.610 | −3.95939 | ||||||||
\(726\) | 0.763932 | 0.0283522 | ||||||||
\(727\) | 0.639320 | 0.0237111 | 0.0118555 | − | 0.999930i | \(-0.496226\pi\) | ||||
0.0118555 | + | 0.999930i | \(0.496226\pi\) | |||||||
\(728\) | −3.85410 | −0.142843 | ||||||||
\(729\) | −19.4377 | −0.719915 | ||||||||
\(730\) | −38.5066 | −1.42519 | ||||||||
\(731\) | −21.4377 | −0.792902 | ||||||||
\(732\) | −2.56231 | −0.0947056 | ||||||||
\(733\) | 31.0000 | 1.14501 | 0.572506 | − | 0.819901i | \(-0.305971\pi\) | ||||
0.572506 | + | 0.819901i | \(0.305971\pi\) | |||||||
\(734\) | −1.43769 | −0.0530663 | ||||||||
\(735\) | −1.61803 | −0.0596821 | ||||||||
\(736\) | 6.70820 | 0.247268 | ||||||||
\(737\) | −13.6869 | −0.504164 | ||||||||
\(738\) | −11.6738 | −0.429717 | ||||||||
\(739\) | −14.8328 | −0.545634 | −0.272817 | − | 0.962066i | \(-0.587955\pi\) | ||||
−0.272817 | + | 0.962066i | \(0.587955\pi\) | |||||||
\(740\) | 21.1803 | 0.778605 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −12.7082 | −0.466533 | ||||||||
\(743\) | −7.14590 | −0.262158 | −0.131079 | − | 0.991372i | \(-0.541844\pi\) | ||||
−0.131079 | + | 0.991372i | \(0.541844\pi\) | |||||||
\(744\) | −1.90983 | −0.0700178 | ||||||||
\(745\) | 8.09017 | 0.296401 | ||||||||
\(746\) | 11.8541 | 0.434010 | ||||||||
\(747\) | 18.4721 | 0.675860 | ||||||||
\(748\) | 5.56231 | 0.203378 | ||||||||
\(749\) | 13.4721 | 0.492261 | ||||||||
\(750\) | 12.8541 | 0.469365 | ||||||||
\(751\) | −15.1246 | −0.551905 | −0.275952 | − | 0.961171i | \(-0.588993\pi\) | ||||
−0.275952 | + | 0.961171i | \(0.588993\pi\) | |||||||
\(752\) | −6.23607 | −0.227406 | ||||||||
\(753\) | 6.24922 | 0.227734 | ||||||||
\(754\) | −31.7426 | −1.15600 | ||||||||
\(755\) | −1.00000 | −0.0363937 | ||||||||
\(756\) | 2.23607 | 0.0813250 | ||||||||
\(757\) | 27.4164 | 0.996466 | 0.498233 | − | 0.867043i | \(-0.333982\pi\) | ||||
0.498233 | + | 0.867043i | \(0.333982\pi\) | |||||||
\(758\) | 12.2705 | 0.445685 | ||||||||
\(759\) | −7.68692 | −0.279017 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −20.1246 | −0.729517 | −0.364758 | − | 0.931102i | \(-0.618848\pi\) | ||||
−0.364758 | + | 0.931102i | \(0.618848\pi\) | |||||||
\(762\) | −7.65248 | −0.277220 | ||||||||
\(763\) | −4.85410 | −0.175730 | ||||||||
\(764\) | −7.76393 | −0.280889 | ||||||||
\(765\) | 22.4164 | 0.810467 | ||||||||
\(766\) | 0.708204 | 0.0255884 | ||||||||
\(767\) | −39.4508 | −1.42449 | ||||||||
\(768\) | 0.381966 | 0.0137830 | ||||||||
\(769\) | 30.2492 | 1.09081 | 0.545407 | − | 0.838171i | \(-0.316375\pi\) | ||||
0.545407 | + | 0.838171i | \(0.316375\pi\) | |||||||
\(770\) | −12.7082 | −0.457972 | ||||||||
\(771\) | −0.270510 | −0.00974217 | ||||||||
\(772\) | −4.18034 | −0.150454 | ||||||||
\(773\) | 17.2148 | 0.619173 | 0.309586 | − | 0.950871i | \(-0.399809\pi\) | ||||
0.309586 | + | 0.950871i | \(0.399809\pi\) | |||||||
\(774\) | −33.0000 | −1.18616 | ||||||||
\(775\) | 64.7214 | 2.32486 | ||||||||
\(776\) | 5.29180 | 0.189964 | ||||||||
\(777\) | 1.90983 | 0.0685148 | ||||||||
\(778\) | −10.2016 | −0.365746 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 6.23607 | 0.223287 | ||||||||
\(781\) | 10.5836 | 0.378711 | ||||||||
\(782\) | 12.4377 | 0.444771 | ||||||||
\(783\) | 18.4164 | 0.658149 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 43.9787 | 1.56967 | ||||||||
\(786\) | 1.29180 | 0.0460768 | ||||||||
\(787\) | 39.0902 | 1.39341 | 0.696707 | − | 0.717356i | \(-0.254648\pi\) | ||||
0.696707 | + | 0.717356i | \(0.254648\pi\) | |||||||
\(788\) | 19.0344 | 0.678074 | ||||||||
\(789\) | −2.02129 | −0.0719597 | ||||||||
\(790\) | 42.9787 | 1.52911 | ||||||||
\(791\) | −11.7984 | −0.419502 | ||||||||
\(792\) | 8.56231 | 0.304248 | ||||||||
\(793\) | 25.8541 | 0.918106 | ||||||||
\(794\) | 14.3262 | 0.508419 | ||||||||
\(795\) | 20.5623 | 0.729270 | ||||||||
\(796\) | 15.7984 | 0.559959 | ||||||||
\(797\) | 13.7984 | 0.488763 | 0.244382 | − | 0.969679i | \(-0.421415\pi\) | ||||
0.244382 | + | 0.969679i | \(0.421415\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −11.5623 | −0.409045 | ||||||||
\(800\) | −12.9443 | −0.457649 | ||||||||
\(801\) | 3.94427 | 0.139364 | ||||||||
\(802\) | 24.4721 | 0.864141 | ||||||||
\(803\) | −27.2705 | −0.962355 | ||||||||
\(804\) | −1.74265 | −0.0614584 | ||||||||
\(805\) | −28.4164 | −1.00155 | ||||||||
\(806\) | 19.2705 | 0.678775 | ||||||||
\(807\) | −12.0213 | −0.423169 | ||||||||
\(808\) | 8.09017 | 0.284611 | ||||||||
\(809\) | 11.7295 | 0.412387 | 0.206193 | − | 0.978511i | \(-0.433892\pi\) | ||||
0.206193 | + | 0.978511i | \(0.433892\pi\) | |||||||
\(810\) | 32.6525 | 1.14729 | ||||||||
\(811\) | 1.23607 | 0.0434042 | 0.0217021 | − | 0.999764i | \(-0.493091\pi\) | ||||
0.0217021 | + | 0.999764i | \(0.493091\pi\) | |||||||
\(812\) | 8.23607 | 0.289029 | ||||||||
\(813\) | 1.36881 | 0.0480063 | ||||||||
\(814\) | 15.0000 | 0.525750 | ||||||||
\(815\) | 14.9443 | 0.523475 | ||||||||
\(816\) | 0.708204 | 0.0247921 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −16.1459 | −0.564528 | ||||||||
\(819\) | −11.0000 | −0.384371 | ||||||||
\(820\) | 17.3262 | 0.605058 | ||||||||
\(821\) | −13.1803 | −0.459997 | −0.229999 | − | 0.973191i | \(-0.573872\pi\) | ||||
−0.229999 | + | 0.973191i | \(0.573872\pi\) | |||||||
\(822\) | −3.52786 | −0.123048 | ||||||||
\(823\) | −33.0689 | −1.15271 | −0.576354 | − | 0.817200i | \(-0.695525\pi\) | ||||
−0.576354 | + | 0.817200i | \(0.695525\pi\) | |||||||
\(824\) | −6.85410 | −0.238774 | ||||||||
\(825\) | 14.8328 | 0.516412 | ||||||||
\(826\) | 10.2361 | 0.356158 | ||||||||
\(827\) | −7.61803 | −0.264905 | −0.132452 | − | 0.991189i | \(-0.542285\pi\) | ||||
−0.132452 | + | 0.991189i | \(0.542285\pi\) | |||||||
\(828\) | 19.1459 | 0.665366 | ||||||||
\(829\) | 54.1246 | 1.87983 | 0.939913 | − | 0.341415i | \(-0.110906\pi\) | ||||
0.939913 | + | 0.341415i | \(0.110906\pi\) | |||||||
\(830\) | −27.4164 | −0.951637 | ||||||||
\(831\) | −7.05573 | −0.244760 | ||||||||
\(832\) | −3.85410 | −0.133617 | ||||||||
\(833\) | 1.85410 | 0.0642408 | ||||||||
\(834\) | −7.25735 | −0.251302 | ||||||||
\(835\) | −54.0689 | −1.87113 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −11.1803 | −0.386449 | ||||||||
\(838\) | 28.0902 | 0.970359 | ||||||||
\(839\) | −51.4721 | −1.77702 | −0.888508 | − | 0.458862i | \(-0.848257\pi\) | ||||
−0.888508 | + | 0.458862i | \(0.848257\pi\) | |||||||
\(840\) | −1.61803 | −0.0558275 | ||||||||
\(841\) | 38.8328 | 1.33906 | ||||||||
\(842\) | 16.8885 | 0.582018 | ||||||||
\(843\) | −5.97871 | −0.205918 | ||||||||
\(844\) | 21.0000 | 0.722850 | ||||||||
\(845\) | −7.85410 | −0.270189 | ||||||||
\(846\) | −17.7984 | −0.611921 | ||||||||
\(847\) | 2.00000 | 0.0687208 | ||||||||
\(848\) | −12.7082 | −0.436402 | ||||||||
\(849\) | 5.74265 | 0.197087 | ||||||||
\(850\) | −24.0000 | −0.823193 | ||||||||
\(851\) | 33.5410 | 1.14977 | ||||||||
\(852\) | 1.34752 | 0.0461654 | ||||||||
\(853\) | −41.0000 | −1.40381 | −0.701907 | − | 0.712269i | \(-0.747668\pi\) | ||||
−0.701907 | + | 0.712269i | \(0.747668\pi\) | |||||||
\(854\) | −6.70820 | −0.229550 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 13.4721 | 0.460468 | ||||||||
\(857\) | −10.2016 | −0.348481 | −0.174240 | − | 0.984703i | \(-0.555747\pi\) | ||||
−0.174240 | + | 0.984703i | \(0.555747\pi\) | |||||||
\(858\) | 4.41641 | 0.150774 | ||||||||
\(859\) | 54.3050 | 1.85286 | 0.926431 | − | 0.376466i | \(-0.122861\pi\) | ||||
0.926431 | + | 0.376466i | \(0.122861\pi\) | |||||||
\(860\) | 48.9787 | 1.67016 | ||||||||
\(861\) | 1.56231 | 0.0532432 | ||||||||
\(862\) | −22.3607 | −0.761608 | ||||||||
\(863\) | −51.6525 | −1.75827 | −0.879135 | − | 0.476572i | \(-0.841879\pi\) | ||||
−0.879135 | + | 0.476572i | \(0.841879\pi\) | |||||||
\(864\) | 2.23607 | 0.0760726 | ||||||||
\(865\) | 18.7082 | 0.636098 | ||||||||
\(866\) | 25.8541 | 0.878558 | ||||||||
\(867\) | −5.18034 | −0.175934 | ||||||||
\(868\) | −5.00000 | −0.169711 | ||||||||
\(869\) | 30.4377 | 1.03253 | ||||||||
\(870\) | −13.3262 | −0.451802 | ||||||||
\(871\) | 17.5836 | 0.595797 | ||||||||
\(872\) | −4.85410 | −0.164381 | ||||||||
\(873\) | 15.1033 | 0.511170 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 33.6525 | 1.13766 | ||||||||
\(876\) | −3.47214 | −0.117313 | ||||||||
\(877\) | 2.32624 | 0.0785515 | 0.0392757 | − | 0.999228i | \(-0.487495\pi\) | ||||
0.0392757 | + | 0.999228i | \(0.487495\pi\) | |||||||
\(878\) | −13.7639 | −0.464510 | ||||||||
\(879\) | −0.604878 | −0.0204020 | ||||||||
\(880\) | −12.7082 | −0.428393 | ||||||||
\(881\) | 4.74265 | 0.159784 | 0.0798919 | − | 0.996804i | \(-0.474542\pi\) | ||||
0.0798919 | + | 0.996804i | \(0.474542\pi\) | |||||||
\(882\) | 2.85410 | 0.0961026 | ||||||||
\(883\) | 43.1033 | 1.45054 | 0.725271 | − | 0.688463i | \(-0.241714\pi\) | ||||
0.725271 | + | 0.688463i | \(0.241714\pi\) | |||||||
\(884\) | −7.14590 | −0.240343 | ||||||||
\(885\) | −16.5623 | −0.556736 | ||||||||
\(886\) | −26.5066 | −0.890506 | ||||||||
\(887\) | 41.7771 | 1.40274 | 0.701369 | − | 0.712799i | \(-0.252573\pi\) | ||||
0.701369 | + | 0.712799i | \(0.252573\pi\) | |||||||
\(888\) | 1.90983 | 0.0640897 | ||||||||
\(889\) | −20.0344 | −0.671934 | ||||||||
\(890\) | −5.85410 | −0.196230 | ||||||||
\(891\) | 23.1246 | 0.774704 | ||||||||
\(892\) | 9.00000 | 0.301342 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0.729490 | 0.0243978 | ||||||||
\(895\) | −15.5623 | −0.520191 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 9.87539 | 0.329730 | ||||||||
\(898\) | 28.7639 | 0.959865 | ||||||||
\(899\) | −41.1803 | −1.37344 | ||||||||
\(900\) | −36.9443 | −1.23148 | ||||||||
\(901\) | −23.5623 | −0.784974 | ||||||||
\(902\) | 12.2705 | 0.408563 | ||||||||
\(903\) | 4.41641 | 0.146969 | ||||||||
\(904\) | −11.7984 | −0.392408 | ||||||||
\(905\) | −67.5410 | −2.24514 | ||||||||
\(906\) | −0.0901699 | −0.00299570 | ||||||||
\(907\) | 22.1459 | 0.735342 | 0.367671 | − | 0.929956i | \(-0.380155\pi\) | ||||
0.367671 | + | 0.929956i | \(0.380155\pi\) | |||||||
\(908\) | 27.0000 | 0.896026 | ||||||||
\(909\) | 23.0902 | 0.765853 | ||||||||
\(910\) | 16.3262 | 0.541210 | ||||||||
\(911\) | 7.74265 | 0.256525 | 0.128263 | − | 0.991740i | \(-0.459060\pi\) | ||||
0.128263 | + | 0.991740i | \(0.459060\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −19.4164 | −0.642589 | ||||||||
\(914\) | 37.8885 | 1.25324 | ||||||||
\(915\) | 10.8541 | 0.358826 | ||||||||
\(916\) | −17.5623 | −0.580275 | ||||||||
\(917\) | 3.38197 | 0.111682 | ||||||||
\(918\) | 4.14590 | 0.136835 | ||||||||
\(919\) | −35.3951 | −1.16758 | −0.583789 | − | 0.811906i | \(-0.698430\pi\) | ||||
−0.583789 | + | 0.811906i | \(0.698430\pi\) | |||||||
\(920\) | −28.4164 | −0.936861 | ||||||||
\(921\) | 10.2492 | 0.337723 | ||||||||
\(922\) | 21.7082 | 0.714922 | ||||||||
\(923\) | −13.5967 | −0.447542 | ||||||||
\(924\) | −1.14590 | −0.0376973 | ||||||||
\(925\) | −64.7214 | −2.12803 | ||||||||
\(926\) | −33.9787 | −1.11661 | ||||||||
\(927\) | −19.5623 | −0.642510 | ||||||||
\(928\) | 8.23607 | 0.270362 | ||||||||
\(929\) | 31.0689 | 1.01934 | 0.509669 | − | 0.860371i | \(-0.329768\pi\) | ||||
0.509669 | + | 0.860371i | \(0.329768\pi\) | |||||||
\(930\) | 8.09017 | 0.265287 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −16.7984 | −0.550249 | ||||||||
\(933\) | −12.9656 | −0.424473 | ||||||||
\(934\) | −38.1246 | −1.24748 | ||||||||
\(935\) | −23.5623 | −0.770570 | ||||||||
\(936\) | −11.0000 | −0.359546 | ||||||||
\(937\) | −39.0344 | −1.27520 | −0.637600 | − | 0.770368i | \(-0.720073\pi\) | ||||
−0.637600 | + | 0.770368i | \(0.720073\pi\) | |||||||
\(938\) | −4.56231 | −0.148965 | ||||||||
\(939\) | −1.63119 | −0.0532319 | ||||||||
\(940\) | 26.4164 | 0.861608 | ||||||||
\(941\) | 8.61803 | 0.280940 | 0.140470 | − | 0.990085i | \(-0.455139\pi\) | ||||
0.140470 | + | 0.990085i | \(0.455139\pi\) | |||||||
\(942\) | 3.96556 | 0.129205 | ||||||||
\(943\) | 27.4377 | 0.893494 | ||||||||
\(944\) | 10.2361 | 0.333156 | ||||||||
\(945\) | −9.47214 | −0.308129 | ||||||||
\(946\) | 34.6869 | 1.12777 | ||||||||
\(947\) | −37.5279 | −1.21949 | −0.609746 | − | 0.792597i | \(-0.708728\pi\) | ||||
−0.609746 | + | 0.792597i | \(0.708728\pi\) | |||||||
\(948\) | 3.87539 | 0.125867 | ||||||||
\(949\) | 35.0344 | 1.13727 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7.07701 | −0.229488 | ||||||||
\(952\) | 1.85410 | 0.0600918 | ||||||||
\(953\) | 34.4164 | 1.11486 | 0.557428 | − | 0.830225i | \(-0.311788\pi\) | ||||
0.557428 | + | 0.830225i | \(0.311788\pi\) | |||||||
\(954\) | −36.2705 | −1.17430 | ||||||||
\(955\) | 32.8885 | 1.06425 | ||||||||
\(956\) | 4.03444 | 0.130483 | ||||||||
\(957\) | −9.43769 | −0.305077 | ||||||||
\(958\) | 27.7082 | 0.895211 | ||||||||
\(959\) | −9.23607 | −0.298248 | ||||||||
\(960\) | −1.61803 | −0.0522218 | ||||||||
\(961\) | −6.00000 | −0.193548 | ||||||||
\(962\) | −19.2705 | −0.621306 | ||||||||
\(963\) | 38.4508 | 1.23906 | ||||||||
\(964\) | 20.1459 | 0.648856 | ||||||||
\(965\) | 17.7082 | 0.570047 | ||||||||
\(966\) | −2.56231 | −0.0824408 | ||||||||
\(967\) | −8.56231 | −0.275345 | −0.137673 | − | 0.990478i | \(-0.543962\pi\) | ||||
−0.137673 | + | 0.990478i | \(0.543962\pi\) | |||||||
\(968\) | 2.00000 | 0.0642824 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −22.4164 | −0.719747 | ||||||||
\(971\) | 20.2361 | 0.649406 | 0.324703 | − | 0.945816i | \(-0.394736\pi\) | ||||
0.324703 | + | 0.945816i | \(0.394736\pi\) | |||||||
\(972\) | 9.65248 | 0.309603 | ||||||||
\(973\) | −19.0000 | −0.609112 | ||||||||
\(974\) | 10.3475 | 0.331556 | ||||||||
\(975\) | −19.0557 | −0.610272 | ||||||||
\(976\) | −6.70820 | −0.214724 | ||||||||
\(977\) | −32.5279 | −1.04066 | −0.520329 | − | 0.853966i | \(-0.674191\pi\) | ||||
−0.520329 | + | 0.853966i | \(0.674191\pi\) | |||||||
\(978\) | 1.34752 | 0.0430891 | ||||||||
\(979\) | −4.14590 | −0.132503 | ||||||||
\(980\) | −4.23607 | −0.135316 | ||||||||
\(981\) | −13.8541 | −0.442327 | ||||||||
\(982\) | 24.0689 | 0.768069 | ||||||||
\(983\) | 23.7984 | 0.759050 | 0.379525 | − | 0.925181i | \(-0.376087\pi\) | ||||
0.379525 | + | 0.925181i | \(0.376087\pi\) | |||||||
\(984\) | 1.56231 | 0.0498045 | ||||||||
\(985\) | −80.6312 | −2.56912 | ||||||||
\(986\) | 15.2705 | 0.486312 | ||||||||
\(987\) | 2.38197 | 0.0758188 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 77.5623 | 2.46634 | ||||||||
\(990\) | −36.2705 | −1.15275 | ||||||||
\(991\) | 13.4164 | 0.426186 | 0.213093 | − | 0.977032i | \(-0.431646\pi\) | ||||
0.213093 | + | 0.977032i | \(0.431646\pi\) | |||||||
\(992\) | −5.00000 | −0.158750 | ||||||||
\(993\) | −0.180340 | −0.00572291 | ||||||||
\(994\) | 3.52786 | 0.111897 | ||||||||
\(995\) | −66.9230 | −2.12160 | ||||||||
\(996\) | −2.47214 | −0.0783326 | ||||||||
\(997\) | −15.9656 | −0.505634 | −0.252817 | − | 0.967514i | \(-0.581357\pi\) | ||||
−0.252817 | + | 0.967514i | \(0.581357\pi\) | |||||||
\(998\) | 3.00000 | 0.0949633 | ||||||||
\(999\) | 11.1803 | 0.353730 |
(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.i.1.1 | ✓ | 2 | |
19.18 | odd | 2 | 5054.2.a.j.1.2 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5054.2.a.i.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
5054.2.a.j.1.2 | yes | 2 | 19.18 | odd | 2 |