Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2646,2,Mod(1,2646)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2646, 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("2646.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2646.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: | \(21.1284163748\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2646.1 |
$q$-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 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.58579 | 0.709185 | 0.354593 | − | 0.935021i | \(-0.384620\pi\) | ||||
0.354593 | + | 0.935021i | \(0.384620\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.58579 | 0.501470 | ||||||||
\(11\) | 1.00000 | 0.301511 | 0.150756 | − | 0.988571i | \(-0.451829\pi\) | ||||
0.150756 | + | 0.988571i | \(0.451829\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.24264 | 1.17670 | 0.588348 | − | 0.808608i | \(-0.299778\pi\) | ||||
0.588348 | + | 0.808608i | \(0.299778\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.82843 | 0.685994 | 0.342997 | − | 0.939336i | \(-0.388558\pi\) | ||||
0.342997 | + | 0.939336i | \(0.388558\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.171573 | 0.0393615 | 0.0196808 | − | 0.999806i | \(-0.493735\pi\) | ||||
0.0196808 | + | 0.999806i | \(0.493735\pi\) | |||||||
\(20\) | 1.58579 | 0.354593 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | 3.24264 | 0.676137 | 0.338069 | − | 0.941121i | \(-0.390226\pi\) | ||||
0.338069 | + | 0.941121i | \(0.390226\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.48528 | −0.497056 | ||||||||
\(26\) | 4.24264 | 0.832050 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.24264 | −1.53062 | −0.765310 | − | 0.643662i | \(-0.777414\pi\) | ||||
−0.765310 | + | 0.643662i | \(0.777414\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.24264 | −0.223185 | −0.111592 | − | 0.993754i | \(-0.535595\pi\) | ||||
−0.111592 | + | 0.993754i | \(0.535595\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.82843 | 0.485071 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.24264 | −0.533087 | −0.266543 | − | 0.963823i | \(-0.585882\pi\) | ||||
−0.266543 | + | 0.963823i | \(0.585882\pi\) | |||||||
\(38\) | 0.171573 | 0.0278328 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.58579 | 0.250735 | ||||||||
\(41\) | 11.8284 | 1.84729 | 0.923645 | − | 0.383249i | \(-0.125195\pi\) | ||||
0.923645 | + | 0.383249i | \(0.125195\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.4853 | 1.59899 | 0.799495 | − | 0.600672i | \(-0.205100\pi\) | ||||
0.799495 | + | 0.600672i | \(0.205100\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.24264 | 0.478101 | ||||||||
\(47\) | 0.343146 | 0.0500530 | 0.0250265 | − | 0.999687i | \(-0.492033\pi\) | ||||
0.0250265 | + | 0.999687i | \(0.492033\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2.48528 | −0.351472 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.24264 | 0.588348 | ||||||||
\(53\) | −8.00000 | −1.09888 | −0.549442 | − | 0.835532i | \(-0.685160\pi\) | ||||
−0.549442 | + | 0.835532i | \(0.685160\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.58579 | 0.213827 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −8.24264 | −1.08231 | ||||||||
\(59\) | 0.343146 | 0.0446738 | 0.0223369 | − | 0.999751i | \(-0.492889\pi\) | ||||
0.0223369 | + | 0.999751i | \(0.492889\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.17157 | −1.17430 | −0.587150 | − | 0.809478i | \(-0.699750\pi\) | ||||
−0.587150 | + | 0.809478i | \(0.699750\pi\) | |||||||
\(62\) | −1.24264 | −0.157816 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 6.72792 | 0.834496 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.2426 | −1.25134 | −0.625669 | − | 0.780089i | \(-0.715174\pi\) | ||||
−0.625669 | + | 0.780089i | \(0.715174\pi\) | |||||||
\(68\) | 2.82843 | 0.342997 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.24264 | −0.859543 | −0.429772 | − | 0.902938i | \(-0.641406\pi\) | ||||
−0.429772 | + | 0.902938i | \(0.641406\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.82843 | 1.03329 | 0.516645 | − | 0.856200i | \(-0.327181\pi\) | ||||
0.516645 | + | 0.856200i | \(0.327181\pi\) | |||||||
\(74\) | −3.24264 | −0.376949 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.171573 | 0.0196808 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.4853 | 1.17969 | 0.589843 | − | 0.807518i | \(-0.299190\pi\) | ||||
0.589843 | + | 0.807518i | \(0.299190\pi\) | |||||||
\(80\) | 1.58579 | 0.177296 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 11.8284 | 1.30623 | ||||||||
\(83\) | 15.8995 | 1.74520 | 0.872598 | − | 0.488439i | \(-0.162433\pi\) | ||||
0.872598 | + | 0.488439i | \(0.162433\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.48528 | 0.486497 | ||||||||
\(86\) | 10.4853 | 1.13066 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | 14.6569 | 1.55362 | 0.776812 | − | 0.629733i | \(-0.216836\pi\) | ||||
0.776812 | + | 0.629733i | \(0.216836\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 3.24264 | 0.338069 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.343146 | 0.0353928 | ||||||||
\(95\) | 0.272078 | 0.0279146 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.3137 | −1.14873 | −0.574367 | − | 0.818598i | \(-0.694752\pi\) | ||||
−0.574367 | + | 0.818598i | \(0.694752\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.48528 | −0.248528 | ||||||||
\(101\) | 2.48528 | 0.247295 | 0.123647 | − | 0.992326i | \(-0.460541\pi\) | ||||
0.123647 | + | 0.992326i | \(0.460541\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.07107 | 0.401134 | 0.200567 | − | 0.979680i | \(-0.435722\pi\) | ||||
0.200567 | + | 0.979680i | \(0.435722\pi\) | |||||||
\(104\) | 4.24264 | 0.416025 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.00000 | −0.777029 | ||||||||
\(107\) | 18.9706 | 1.83395 | 0.916977 | − | 0.398941i | \(-0.130622\pi\) | ||||
0.916977 | + | 0.398941i | \(0.130622\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.75736 | −0.647238 | −0.323619 | − | 0.946188i | \(-0.604900\pi\) | ||||
−0.323619 | + | 0.946188i | \(0.604900\pi\) | |||||||
\(110\) | 1.58579 | 0.151199 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.24264 | 0.399114 | 0.199557 | − | 0.979886i | \(-0.436050\pi\) | ||||
0.199557 | + | 0.979886i | \(0.436050\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.14214 | 0.479507 | ||||||||
\(116\) | −8.24264 | −0.765310 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.343146 | 0.0315891 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.0000 | −0.909091 | ||||||||
\(122\) | −9.17157 | −0.830355 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.24264 | −0.111592 | ||||||||
\(125\) | −11.8701 | −1.06169 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.75736 | −0.333412 | −0.166706 | − | 0.986007i | \(-0.553313\pi\) | ||||
−0.166706 | + | 0.986007i | \(0.553313\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 6.72792 | 0.590078 | ||||||||
\(131\) | −2.48528 | −0.217140 | −0.108570 | − | 0.994089i | \(-0.534627\pi\) | ||||
−0.108570 | + | 0.994089i | \(0.534627\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −10.2426 | −0.884829 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.82843 | 0.242536 | ||||||||
\(137\) | −10.2426 | −0.875088 | −0.437544 | − | 0.899197i | \(-0.644152\pi\) | ||||
−0.437544 | + | 0.899197i | \(0.644152\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.17157 | 0.269009 | 0.134505 | − | 0.990913i | \(-0.457056\pi\) | ||||
0.134505 | + | 0.990913i | \(0.457056\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −7.24264 | −0.607789 | ||||||||
\(143\) | 4.24264 | 0.354787 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −13.0711 | −1.08549 | ||||||||
\(146\) | 8.82843 | 0.730646 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.24264 | −0.266543 | ||||||||
\(149\) | 14.2426 | 1.16680 | 0.583401 | − | 0.812184i | \(-0.301722\pi\) | ||||
0.583401 | + | 0.812184i | \(0.301722\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.7279 | −0.873026 | −0.436513 | − | 0.899698i | \(-0.643787\pi\) | ||||
−0.436513 | + | 0.899698i | \(0.643787\pi\) | |||||||
\(152\) | 0.171573 | 0.0139164 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.97056 | −0.158279 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −19.0711 | −1.52204 | −0.761018 | − | 0.648730i | \(-0.775300\pi\) | ||||
−0.761018 | + | 0.648730i | \(0.775300\pi\) | |||||||
\(158\) | 10.4853 | 0.834164 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.58579 | 0.125367 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.7279 | 0.840276 | 0.420138 | − | 0.907460i | \(-0.361982\pi\) | ||||
0.420138 | + | 0.907460i | \(0.361982\pi\) | |||||||
\(164\) | 11.8284 | 0.923645 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 15.8995 | 1.23404 | ||||||||
\(167\) | 24.3848 | 1.88695 | 0.943475 | − | 0.331443i | \(-0.107535\pi\) | ||||
0.943475 | + | 0.331443i | \(0.107535\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.00000 | 0.384615 | ||||||||
\(170\) | 4.48528 | 0.344005 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 10.4853 | 0.799495 | ||||||||
\(173\) | −4.75736 | −0.361695 | −0.180848 | − | 0.983511i | \(-0.557884\pi\) | ||||
−0.180848 | + | 0.983511i | \(0.557884\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 14.6569 | 1.09858 | ||||||||
\(179\) | −22.9706 | −1.71690 | −0.858450 | − | 0.512897i | \(-0.828572\pi\) | ||||
−0.858450 | + | 0.512897i | \(0.828572\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.75736 | −0.130623 | −0.0653117 | − | 0.997865i | \(-0.520804\pi\) | ||||
−0.0653117 | + | 0.997865i | \(0.520804\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.24264 | 0.239051 | ||||||||
\(185\) | −5.14214 | −0.378057 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.82843 | 0.206835 | ||||||||
\(188\) | 0.343146 | 0.0250265 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.272078 | 0.0197386 | ||||||||
\(191\) | 9.24264 | 0.668774 | 0.334387 | − | 0.942436i | \(-0.391471\pi\) | ||||
0.334387 | + | 0.942436i | \(0.391471\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.4853 | −0.898710 | −0.449355 | − | 0.893353i | \(-0.648346\pi\) | ||||
−0.449355 | + | 0.893353i | \(0.648346\pi\) | |||||||
\(194\) | −11.3137 | −0.812277 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −22.7279 | −1.61930 | −0.809649 | − | 0.586915i | \(-0.800342\pi\) | ||||
−0.809649 | + | 0.586915i | \(0.800342\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.2426 | −0.938746 | −0.469373 | − | 0.883000i | \(-0.655520\pi\) | ||||
−0.469373 | + | 0.883000i | \(0.655520\pi\) | |||||||
\(200\) | −2.48528 | −0.175736 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.48528 | 0.174864 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 18.7574 | 1.31007 | ||||||||
\(206\) | 4.07107 | 0.283645 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.24264 | 0.294174 | ||||||||
\(209\) | 0.171573 | 0.0118679 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.7279 | −0.876226 | −0.438113 | − | 0.898920i | \(-0.644353\pi\) | ||||
−0.438113 | + | 0.898920i | \(0.644353\pi\) | |||||||
\(212\) | −8.00000 | −0.549442 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 18.9706 | 1.29680 | ||||||||
\(215\) | 16.6274 | 1.13398 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −6.75736 | −0.457666 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.58579 | 0.106914 | ||||||||
\(221\) | 12.0000 | 0.807207 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.24264 | 0.0832134 | 0.0416067 | − | 0.999134i | \(-0.486752\pi\) | ||||
0.0416067 | + | 0.999134i | \(0.486752\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.24264 | 0.282216 | ||||||||
\(227\) | −12.7279 | −0.844782 | −0.422391 | − | 0.906414i | \(-0.638809\pi\) | ||||
−0.422391 | + | 0.906414i | \(0.638809\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.0000 | −0.792982 | −0.396491 | − | 0.918039i | \(-0.629772\pi\) | ||||
−0.396491 | + | 0.918039i | \(0.629772\pi\) | |||||||
\(230\) | 5.14214 | 0.339062 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.24264 | −0.541156 | ||||||||
\(233\) | −7.75736 | −0.508202 | −0.254101 | − | 0.967178i | \(-0.581779\pi\) | ||||
−0.254101 | + | 0.967178i | \(0.581779\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.544156 | 0.0354968 | ||||||||
\(236\) | 0.343146 | 0.0223369 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.0000 | 1.16432 | 0.582162 | − | 0.813073i | \(-0.302207\pi\) | ||||
0.582162 | + | 0.813073i | \(0.302207\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.4853 | −0.933079 | −0.466539 | − | 0.884500i | \(-0.654499\pi\) | ||||
−0.466539 | + | 0.884500i | \(0.654499\pi\) | |||||||
\(242\) | −10.0000 | −0.642824 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −9.17157 | −0.587150 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.727922 | 0.0463166 | ||||||||
\(248\) | −1.24264 | −0.0789078 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −11.8701 | −0.750728 | ||||||||
\(251\) | −11.3137 | −0.714115 | −0.357057 | − | 0.934082i | \(-0.616220\pi\) | ||||
−0.357057 | + | 0.934082i | \(0.616220\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.24264 | 0.203863 | ||||||||
\(254\) | −3.75736 | −0.235758 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 5.48528 | 0.342162 | 0.171081 | − | 0.985257i | \(-0.445274\pi\) | ||||
0.171081 | + | 0.985257i | \(0.445274\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 6.72792 | 0.417248 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.48528 | −0.153541 | ||||||||
\(263\) | 21.7279 | 1.33980 | 0.669901 | − | 0.742451i | \(-0.266337\pi\) | ||||
0.669901 | + | 0.742451i | \(0.266337\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.6863 | −0.779313 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −10.2426 | −0.625669 | ||||||||
\(269\) | 21.3848 | 1.30385 | 0.651926 | − | 0.758282i | \(-0.273961\pi\) | ||||
0.651926 | + | 0.758282i | \(0.273961\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −29.3137 | −1.78068 | −0.890340 | − | 0.455295i | \(-0.849534\pi\) | ||||
−0.890340 | + | 0.455295i | \(0.849534\pi\) | |||||||
\(272\) | 2.82843 | 0.171499 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10.2426 | −0.618781 | ||||||||
\(275\) | −2.48528 | −0.149868 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 28.2132 | 1.69517 | 0.847584 | − | 0.530662i | \(-0.178057\pi\) | ||||
0.847584 | + | 0.530662i | \(0.178057\pi\) | |||||||
\(278\) | 3.17157 | 0.190218 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.48528 | 0.386879 | 0.193440 | − | 0.981112i | \(-0.438036\pi\) | ||||
0.193440 | + | 0.981112i | \(0.438036\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −20.1421 | −1.19733 | −0.598663 | − | 0.801001i | \(-0.704301\pi\) | ||||
−0.598663 | + | 0.801001i | \(0.704301\pi\) | |||||||
\(284\) | −7.24264 | −0.429772 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.24264 | 0.250873 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.00000 | −0.529412 | ||||||||
\(290\) | −13.0711 | −0.767560 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 8.82843 | 0.516645 | ||||||||
\(293\) | 11.6569 | 0.681001 | 0.340500 | − | 0.940244i | \(-0.389404\pi\) | ||||
0.340500 | + | 0.940244i | \(0.389404\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.544156 | 0.0316820 | ||||||||
\(296\) | −3.24264 | −0.188475 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 14.2426 | 0.825054 | ||||||||
\(299\) | 13.7574 | 0.795609 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −10.7279 | −0.617323 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.171573 | 0.00984038 | ||||||||
\(305\) | −14.5442 | −0.832796 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.7990 | 0.958769 | 0.479384 | − | 0.877605i | \(-0.340860\pi\) | ||||
0.479384 | + | 0.877605i | \(0.340860\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.97056 | −0.111920 | ||||||||
\(311\) | −15.5563 | −0.882120 | −0.441060 | − | 0.897478i | \(-0.645397\pi\) | ||||
−0.441060 | + | 0.897478i | \(0.645397\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.2426 | 0.578948 | 0.289474 | − | 0.957186i | \(-0.406520\pi\) | ||||
0.289474 | + | 0.957186i | \(0.406520\pi\) | |||||||
\(314\) | −19.0711 | −1.07624 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.4853 | 0.589843 | ||||||||
\(317\) | 10.0000 | 0.561656 | 0.280828 | − | 0.959758i | \(-0.409391\pi\) | ||||
0.280828 | + | 0.959758i | \(0.409391\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.24264 | −0.461499 | ||||||||
\(320\) | 1.58579 | 0.0886482 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.485281 | 0.0270018 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −10.5442 | −0.584885 | ||||||||
\(326\) | 10.7279 | 0.594165 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 11.8284 | 0.653116 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.4853 | 1.34583 | 0.672916 | − | 0.739719i | \(-0.265041\pi\) | ||||
0.672916 | + | 0.739719i | \(0.265041\pi\) | |||||||
\(332\) | 15.8995 | 0.872598 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 24.3848 | 1.33428 | ||||||||
\(335\) | −16.2426 | −0.887430 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.4853 | 0.734590 | 0.367295 | − | 0.930104i | \(-0.380284\pi\) | ||||
0.367295 | + | 0.930104i | \(0.380284\pi\) | |||||||
\(338\) | 5.00000 | 0.271964 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.48528 | 0.243249 | ||||||||
\(341\) | −1.24264 | −0.0672928 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 10.4853 | 0.565328 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.75736 | −0.255757 | ||||||||
\(347\) | 35.4853 | 1.90495 | 0.952475 | − | 0.304617i | \(-0.0985285\pi\) | ||||
0.952475 | + | 0.304617i | \(0.0985285\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.2426 | −1.19062 | −0.595311 | − | 0.803496i | \(-0.702971\pi\) | ||||
−0.595311 | + | 0.803496i | \(0.702971\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | −8.65685 | −0.460758 | −0.230379 | − | 0.973101i | \(-0.573997\pi\) | ||||
−0.230379 | + | 0.973101i | \(0.573997\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −11.4853 | −0.609575 | ||||||||
\(356\) | 14.6569 | 0.776812 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −22.9706 | −1.21403 | ||||||||
\(359\) | −33.4558 | −1.76573 | −0.882866 | − | 0.469625i | \(-0.844389\pi\) | ||||
−0.882866 | + | 0.469625i | \(0.844389\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9706 | −0.998451 | ||||||||
\(362\) | −1.75736 | −0.0923648 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.0000 | 0.732793 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.1005 | 0.579442 | 0.289721 | − | 0.957111i | \(-0.406438\pi\) | ||||
0.289721 | + | 0.957111i | \(0.406438\pi\) | |||||||
\(368\) | 3.24264 | 0.169034 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −5.14214 | −0.267327 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.75736 | −0.349883 | −0.174941 | − | 0.984579i | \(-0.555974\pi\) | ||||
−0.174941 | + | 0.984579i | \(0.555974\pi\) | |||||||
\(374\) | 2.82843 | 0.146254 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.343146 | 0.0176964 | ||||||||
\(377\) | −34.9706 | −1.80108 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −30.9706 | −1.59085 | −0.795425 | − | 0.606051i | \(-0.792753\pi\) | ||||
−0.795425 | + | 0.606051i | \(0.792753\pi\) | |||||||
\(380\) | 0.272078 | 0.0139573 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 9.24264 | 0.472895 | ||||||||
\(383\) | −30.0416 | −1.53506 | −0.767528 | − | 0.641016i | \(-0.778513\pi\) | ||||
−0.767528 | + | 0.641016i | \(0.778513\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −12.4853 | −0.635484 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −11.3137 | −0.574367 | ||||||||
\(389\) | 3.02944 | 0.153599 | 0.0767993 | − | 0.997047i | \(-0.475530\pi\) | ||||
0.0767993 | + | 0.997047i | \(0.475530\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.17157 | 0.463826 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −22.7279 | −1.14502 | ||||||||
\(395\) | 16.6274 | 0.836616 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.5858 | −0.832417 | −0.416208 | − | 0.909269i | \(-0.636641\pi\) | ||||
−0.416208 | + | 0.909269i | \(0.636641\pi\) | |||||||
\(398\) | −13.2426 | −0.663794 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.48528 | −0.124264 | ||||||||
\(401\) | −10.2426 | −0.511493 | −0.255747 | − | 0.966744i | \(-0.582321\pi\) | ||||
−0.255747 | + | 0.966744i | \(0.582321\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.27208 | −0.262621 | ||||||||
\(404\) | 2.48528 | 0.123647 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.24264 | −0.160732 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.00000 | 0.296681 | 0.148340 | − | 0.988936i | \(-0.452607\pi\) | ||||
0.148340 | + | 0.988936i | \(0.452607\pi\) | |||||||
\(410\) | 18.7574 | 0.926360 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 4.07107 | 0.200567 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 25.2132 | 1.23767 | ||||||||
\(416\) | 4.24264 | 0.208013 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.171573 | 0.00839190 | ||||||||
\(419\) | 12.0416 | 0.588272 | 0.294136 | − | 0.955764i | \(-0.404968\pi\) | ||||
0.294136 | + | 0.955764i | \(0.404968\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.2132 | 0.887657 | 0.443829 | − | 0.896112i | \(-0.353620\pi\) | ||||
0.443829 | + | 0.896112i | \(0.353620\pi\) | |||||||
\(422\) | −12.7279 | −0.619586 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −8.00000 | −0.388514 | ||||||||
\(425\) | −7.02944 | −0.340978 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 18.9706 | 0.916977 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 16.6274 | 0.801845 | ||||||||
\(431\) | −19.2426 | −0.926885 | −0.463443 | − | 0.886127i | \(-0.653386\pi\) | ||||
−0.463443 | + | 0.886127i | \(0.653386\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −30.7279 | −1.47669 | −0.738345 | − | 0.674423i | \(-0.764392\pi\) | ||||
−0.738345 | + | 0.674423i | \(0.764392\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6.75736 | −0.323619 | ||||||||
\(437\) | 0.556349 | 0.0266138 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 28.9706 | 1.38269 | 0.691345 | − | 0.722525i | \(-0.257019\pi\) | ||||
0.691345 | + | 0.722525i | \(0.257019\pi\) | |||||||
\(440\) | 1.58579 | 0.0755994 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 12.0000 | 0.570782 | ||||||||
\(443\) | −28.9411 | −1.37503 | −0.687517 | − | 0.726168i | \(-0.741299\pi\) | ||||
−0.687517 | + | 0.726168i | \(0.741299\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 23.2426 | 1.10181 | ||||||||
\(446\) | 1.24264 | 0.0588407 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11.2721 | −0.531962 | −0.265981 | − | 0.963978i | \(-0.585696\pi\) | ||||
−0.265981 | + | 0.963978i | \(0.585696\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.8284 | 0.556979 | ||||||||
\(452\) | 4.24264 | 0.199557 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −12.7279 | −0.597351 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.9706 | −0.653515 | −0.326758 | − | 0.945108i | \(-0.605956\pi\) | ||||
−0.326758 | + | 0.945108i | \(0.605956\pi\) | |||||||
\(458\) | −12.0000 | −0.560723 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 5.14214 | 0.239753 | ||||||||
\(461\) | 6.89949 | 0.321342 | 0.160671 | − | 0.987008i | \(-0.448634\pi\) | ||||
0.160671 | + | 0.987008i | \(0.448634\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.2721 | −0.616806 | −0.308403 | − | 0.951256i | \(-0.599794\pi\) | ||||
−0.308403 | + | 0.951256i | \(0.599794\pi\) | |||||||
\(464\) | −8.24264 | −0.382655 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −7.75736 | −0.359353 | ||||||||
\(467\) | −23.6569 | −1.09471 | −0.547354 | − | 0.836901i | \(-0.684365\pi\) | ||||
−0.547354 | + | 0.836901i | \(0.684365\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0.544156 | 0.0251000 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0.343146 | 0.0157946 | ||||||||
\(473\) | 10.4853 | 0.482114 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.426407 | −0.0195649 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 18.0000 | 0.823301 | ||||||||
\(479\) | 18.3431 | 0.838120 | 0.419060 | − | 0.907959i | \(-0.362360\pi\) | ||||
0.419060 | + | 0.907959i | \(0.362360\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.7574 | −0.627282 | ||||||||
\(482\) | −14.4853 | −0.659786 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.0000 | −0.454545 | ||||||||
\(485\) | −17.9411 | −0.814665 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −21.5147 | −0.974925 | −0.487462 | − | 0.873144i | \(-0.662077\pi\) | ||||
−0.487462 | + | 0.873144i | \(0.662077\pi\) | |||||||
\(488\) | −9.17157 | −0.415178 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.514719 | −0.0232289 | −0.0116145 | − | 0.999933i | \(-0.503697\pi\) | ||||
−0.0116145 | + | 0.999933i | \(0.503697\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −23.3137 | −1.05000 | ||||||||
\(494\) | 0.727922 | 0.0327508 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.24264 | −0.0557962 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.9706 | 0.849239 | 0.424620 | − | 0.905372i | \(-0.360408\pi\) | ||||
0.424620 | + | 0.905372i | \(0.360408\pi\) | |||||||
\(500\) | −11.8701 | −0.530845 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −11.3137 | −0.504956 | ||||||||
\(503\) | −39.5563 | −1.76373 | −0.881865 | − | 0.471502i | \(-0.843712\pi\) | ||||
−0.881865 | + | 0.471502i | \(0.843712\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.94113 | 0.175378 | ||||||||
\(506\) | 3.24264 | 0.144153 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.75736 | −0.166706 | ||||||||
\(509\) | −22.2843 | −0.987733 | −0.493866 | − | 0.869538i | \(-0.664417\pi\) | ||||
−0.493866 | + | 0.869538i | \(0.664417\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 5.48528 | 0.241945 | ||||||||
\(515\) | 6.45584 | 0.284478 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.343146 | 0.0150915 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 6.72792 | 0.295039 | ||||||||
\(521\) | −5.14214 | −0.225281 | −0.112641 | − | 0.993636i | \(-0.535931\pi\) | ||||
−0.112641 | + | 0.993636i | \(0.535931\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.514719 | 0.0225071 | 0.0112535 | − | 0.999937i | \(-0.496418\pi\) | ||||
0.0112535 | + | 0.999937i | \(0.496418\pi\) | |||||||
\(524\) | −2.48528 | −0.108570 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 21.7279 | 0.947382 | ||||||||
\(527\) | −3.51472 | −0.153104 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12.4853 | −0.542838 | ||||||||
\(530\) | −12.6863 | −0.551057 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 50.1838 | 2.17370 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 30.0833 | 1.30061 | ||||||||
\(536\) | −10.2426 | −0.442415 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 21.3848 | 0.921963 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −33.2426 | −1.42921 | −0.714606 | − | 0.699527i | \(-0.753394\pi\) | ||||
−0.714606 | + | 0.699527i | \(0.753394\pi\) | |||||||
\(542\) | −29.3137 | −1.25913 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.82843 | 0.121268 | ||||||||
\(545\) | −10.7157 | −0.459011 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.51472 | 0.321306 | 0.160653 | − | 0.987011i | \(-0.448640\pi\) | ||||
0.160653 | + | 0.987011i | \(0.448640\pi\) | |||||||
\(548\) | −10.2426 | −0.437544 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.48528 | −0.105973 | ||||||||
\(551\) | −1.41421 | −0.0602475 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 28.2132 | 1.19866 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.17157 | 0.134505 | ||||||||
\(557\) | 6.72792 | 0.285071 | 0.142536 | − | 0.989790i | \(-0.454474\pi\) | ||||
0.142536 | + | 0.989790i | \(0.454474\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 44.4853 | 1.88153 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6.48528 | 0.273565 | ||||||||
\(563\) | −19.4142 | −0.818212 | −0.409106 | − | 0.912487i | \(-0.634159\pi\) | ||||
−0.409106 | + | 0.912487i | \(0.634159\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.72792 | 0.283046 | ||||||||
\(566\) | −20.1421 | −0.846637 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −7.24264 | −0.303894 | ||||||||
\(569\) | −36.2426 | −1.51937 | −0.759685 | − | 0.650291i | \(-0.774647\pi\) | ||||
−0.759685 | + | 0.650291i | \(0.774647\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −41.2132 | −1.72472 | −0.862359 | − | 0.506297i | \(-0.831014\pi\) | ||||
−0.862359 | + | 0.506297i | \(0.831014\pi\) | |||||||
\(572\) | 4.24264 | 0.177394 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.05887 | −0.336078 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 28.2426 | 1.17576 | 0.587878 | − | 0.808949i | \(-0.299963\pi\) | ||||
0.587878 | + | 0.808949i | \(0.299963\pi\) | |||||||
\(578\) | −9.00000 | −0.374351 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −13.0711 | −0.542747 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.00000 | −0.331326 | ||||||||
\(584\) | 8.82843 | 0.365323 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 11.6569 | 0.481540 | ||||||||
\(587\) | −16.2426 | −0.670406 | −0.335203 | − | 0.942146i | \(-0.608805\pi\) | ||||
−0.335203 | + | 0.942146i | \(0.608805\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.213203 | −0.00878489 | ||||||||
\(590\) | 0.544156 | 0.0224025 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.24264 | −0.133272 | ||||||||
\(593\) | 8.65685 | 0.355494 | 0.177747 | − | 0.984076i | \(-0.443119\pi\) | ||||
0.177747 | + | 0.984076i | \(0.443119\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 14.2426 | 0.583401 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 13.7574 | 0.562580 | ||||||||
\(599\) | 5.72792 | 0.234037 | 0.117018 | − | 0.993130i | \(-0.462666\pi\) | ||||
0.117018 | + | 0.993130i | \(0.462666\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.27208 | −0.215053 | −0.107526 | − | 0.994202i | \(-0.534293\pi\) | ||||
−0.107526 | + | 0.994202i | \(0.534293\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −10.7279 | −0.436513 | ||||||||
\(605\) | −15.8579 | −0.644714 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 30.0000 | 1.21766 | 0.608831 | − | 0.793300i | \(-0.291639\pi\) | ||||
0.608831 | + | 0.793300i | \(0.291639\pi\) | |||||||
\(608\) | 0.171573 | 0.00695820 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −14.5442 | −0.588876 | ||||||||
\(611\) | 1.45584 | 0.0588971 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.72792 | 0.150569 | 0.0752847 | − | 0.997162i | \(-0.476013\pi\) | ||||
0.0752847 | + | 0.997162i | \(0.476013\pi\) | |||||||
\(614\) | 16.7990 | 0.677952 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.97056 | −0.280624 | −0.140312 | − | 0.990107i | \(-0.544811\pi\) | ||||
−0.140312 | + | 0.990107i | \(0.544811\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22.7990 | −0.916369 | −0.458184 | − | 0.888857i | \(-0.651500\pi\) | ||||
−0.458184 | + | 0.888857i | \(0.651500\pi\) | |||||||
\(620\) | −1.97056 | −0.0791397 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −15.5563 | −0.623753 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.39697 | −0.255879 | ||||||||
\(626\) | 10.2426 | 0.409378 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −19.0711 | −0.761018 | ||||||||
\(629\) | −9.17157 | −0.365695 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.0000 | 0.557331 | 0.278666 | − | 0.960388i | \(-0.410108\pi\) | ||||
0.278666 | + | 0.960388i | \(0.410108\pi\) | |||||||
\(632\) | 10.4853 | 0.417082 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 10.0000 | 0.397151 | ||||||||
\(635\) | −5.95837 | −0.236451 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −8.24264 | −0.326329 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.58579 | 0.0626837 | ||||||||
\(641\) | −1.21320 | −0.0479187 | −0.0239593 | − | 0.999713i | \(-0.507627\pi\) | ||||
−0.0239593 | + | 0.999713i | \(0.507627\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.171573 | 0.00676617 | 0.00338309 | − | 0.999994i | \(-0.498923\pi\) | ||||
0.00338309 | + | 0.999994i | \(0.498923\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.485281 | 0.0190931 | ||||||||
\(647\) | −21.5147 | −0.845831 | −0.422915 | − | 0.906169i | \(-0.638993\pi\) | ||||
−0.422915 | + | 0.906169i | \(0.638993\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.343146 | 0.0134696 | ||||||||
\(650\) | −10.5442 | −0.413576 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 10.7279 | 0.420138 | ||||||||
\(653\) | −27.9411 | −1.09342 | −0.546710 | − | 0.837322i | \(-0.684120\pi\) | ||||
−0.546710 | + | 0.837322i | \(0.684120\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.94113 | −0.153993 | ||||||||
\(656\) | 11.8284 | 0.461822 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.9411 | 0.971568 | 0.485784 | − | 0.874079i | \(-0.338534\pi\) | ||||
0.485784 | + | 0.874079i | \(0.338534\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.727922 | −0.0283129 | −0.0141564 | − | 0.999900i | \(-0.504506\pi\) | ||||
−0.0141564 | + | 0.999900i | \(0.504506\pi\) | |||||||
\(662\) | 24.4853 | 0.951647 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 15.8995 | 0.617020 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −26.7279 | −1.03491 | ||||||||
\(668\) | 24.3848 | 0.943475 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −16.2426 | −0.627508 | ||||||||
\(671\) | −9.17157 | −0.354065 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 49.4558 | 1.90638 | 0.953191 | − | 0.302368i | \(-0.0977771\pi\) | ||||
0.953191 | + | 0.302368i | \(0.0977771\pi\) | |||||||
\(674\) | 13.4853 | 0.519434 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.00000 | 0.192308 | ||||||||
\(677\) | −38.6985 | −1.48730 | −0.743652 | − | 0.668567i | \(-0.766908\pi\) | ||||
−0.743652 | + | 0.668567i | \(0.766908\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 4.48528 | 0.172003 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.24264 | −0.0475832 | ||||||||
\(683\) | −13.9706 | −0.534569 | −0.267284 | − | 0.963618i | \(-0.586126\pi\) | ||||
−0.267284 | + | 0.963618i | \(0.586126\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −16.2426 | −0.620599 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 10.4853 | 0.399748 | ||||||||
\(689\) | −33.9411 | −1.29305 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21.9411 | 0.834680 | 0.417340 | − | 0.908750i | \(-0.362962\pi\) | ||||
0.417340 | + | 0.908750i | \(0.362962\pi\) | |||||||
\(692\) | −4.75736 | −0.180848 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 35.4853 | 1.34700 | ||||||||
\(695\) | 5.02944 | 0.190777 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 33.4558 | 1.26723 | ||||||||
\(698\) | −22.2426 | −0.841896 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19.7574 | 0.746225 | 0.373113 | − | 0.927786i | \(-0.378291\pi\) | ||||
0.373113 | + | 0.927786i | \(0.378291\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.556349 | −0.0209831 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8.65685 | −0.325805 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −27.2426 | −1.02312 | −0.511559 | − | 0.859248i | \(-0.670932\pi\) | ||||
−0.511559 | + | 0.859248i | \(0.670932\pi\) | |||||||
\(710\) | −11.4853 | −0.431035 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 14.6569 | 0.549289 | ||||||||
\(713\) | −4.02944 | −0.150904 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.72792 | 0.251610 | ||||||||
\(716\) | −22.9706 | −0.858450 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −33.4558 | −1.24856 | ||||||||
\(719\) | −23.6569 | −0.882252 | −0.441126 | − | 0.897445i | \(-0.645421\pi\) | ||||
−0.441126 | + | 0.897445i | \(0.645421\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −18.9706 | −0.706011 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.75736 | −0.0653117 | ||||||||
\(725\) | 20.4853 | 0.760804 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.1421 | 0.524503 | 0.262251 | − | 0.965000i | \(-0.415535\pi\) | ||||
0.262251 | + | 0.965000i | \(0.415535\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 14.0000 | 0.518163 | ||||||||
\(731\) | 29.6569 | 1.09690 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −27.9411 | −1.03203 | −0.516015 | − | 0.856580i | \(-0.672585\pi\) | ||||
−0.516015 | + | 0.856580i | \(0.672585\pi\) | |||||||
\(734\) | 11.1005 | 0.409727 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.24264 | 0.119525 | ||||||||
\(737\) | −10.2426 | −0.377293 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 48.7279 | 1.79249 | 0.896243 | − | 0.443564i | \(-0.146286\pi\) | ||||
0.896243 | + | 0.443564i | \(0.146286\pi\) | |||||||
\(740\) | −5.14214 | −0.189029 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14.7574 | 0.541395 | 0.270698 | − | 0.962664i | \(-0.412746\pi\) | ||||
0.270698 | + | 0.962664i | \(0.412746\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 22.5858 | 0.827479 | ||||||||
\(746\) | −6.75736 | −0.247405 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.82843 | 0.103418 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 39.4558 | 1.43976 | 0.719882 | − | 0.694096i | \(-0.244196\pi\) | ||||
0.719882 | + | 0.694096i | \(0.244196\pi\) | |||||||
\(752\) | 0.343146 | 0.0125132 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −34.9706 | −1.27355 | ||||||||
\(755\) | −17.0122 | −0.619137 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −47.4558 | −1.72481 | −0.862406 | − | 0.506217i | \(-0.831043\pi\) | ||||
−0.862406 | + | 0.506217i | \(0.831043\pi\) | |||||||
\(758\) | −30.9706 | −1.12490 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.272078 | 0.00986930 | ||||||||
\(761\) | −29.3137 | −1.06262 | −0.531311 | − | 0.847177i | \(-0.678300\pi\) | ||||
−0.531311 | + | 0.847177i | \(0.678300\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 9.24264 | 0.334387 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −30.0416 | −1.08545 | ||||||||
\(767\) | 1.45584 | 0.0525675 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 44.1838 | 1.59331 | 0.796654 | − | 0.604436i | \(-0.206601\pi\) | ||||
0.796654 | + | 0.604436i | \(0.206601\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −12.4853 | −0.449355 | ||||||||
\(773\) | 39.3848 | 1.41657 | 0.708286 | − | 0.705926i | \(-0.249469\pi\) | ||||
0.708286 | + | 0.705926i | \(0.249469\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.08831 | 0.110935 | ||||||||
\(776\) | −11.3137 | −0.406138 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.02944 | 0.108611 | ||||||||
\(779\) | 2.02944 | 0.0727121 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.24264 | −0.259162 | ||||||||
\(782\) | 9.17157 | 0.327975 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −30.2426 | −1.07941 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 53.3137 | 1.90043 | 0.950214 | − | 0.311597i | \(-0.100864\pi\) | ||||
0.950214 | + | 0.311597i | \(0.100864\pi\) | |||||||
\(788\) | −22.7279 | −0.809649 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 16.6274 | 0.591577 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −38.9117 | −1.38179 | ||||||||
\(794\) | −16.5858 | −0.588608 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −13.2426 | −0.469373 | ||||||||
\(797\) | −25.2426 | −0.894140 | −0.447070 | − | 0.894499i | \(-0.647533\pi\) | ||||
−0.447070 | + | 0.894499i | \(0.647533\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.970563 | 0.0343360 | ||||||||
\(800\) | −2.48528 | −0.0878680 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −10.2426 | −0.361680 | ||||||||
\(803\) | 8.82843 | 0.311548 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −5.27208 | −0.185701 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2.48528 | 0.0874319 | ||||||||
\(809\) | 18.2426 | 0.641377 | 0.320689 | − | 0.947185i | \(-0.396086\pi\) | ||||
0.320689 | + | 0.947185i | \(0.396086\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 45.4264 | 1.59514 | 0.797568 | − | 0.603228i | \(-0.206119\pi\) | ||||
0.797568 | + | 0.603228i | \(0.206119\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −3.24264 | −0.113654 | ||||||||
\(815\) | 17.0122 | 0.595911 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.79899 | 0.0629387 | ||||||||
\(818\) | 6.00000 | 0.209785 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 18.7574 | 0.655035 | ||||||||
\(821\) | 13.0294 | 0.454730 | 0.227365 | − | 0.973810i | \(-0.426989\pi\) | ||||
0.227365 | + | 0.973810i | \(0.426989\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 29.7574 | 1.03728 | 0.518638 | − | 0.854994i | \(-0.326439\pi\) | ||||
0.518638 | + | 0.854994i | \(0.326439\pi\) | |||||||
\(824\) | 4.07107 | 0.141822 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12.9411 | −0.450007 | −0.225004 | − | 0.974358i | \(-0.572239\pi\) | ||||
−0.225004 | + | 0.974358i | \(0.572239\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15.8579 | 0.550766 | 0.275383 | − | 0.961335i | \(-0.411195\pi\) | ||||
0.275383 | + | 0.961335i | \(0.411195\pi\) | |||||||
\(830\) | 25.2132 | 0.875163 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4.24264 | 0.147087 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 38.6690 | 1.33820 | ||||||||
\(836\) | 0.171573 | 0.00593397 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 12.0416 | 0.415971 | ||||||||
\(839\) | 17.6152 | 0.608145 | 0.304073 | − | 0.952649i | \(-0.401653\pi\) | ||||
0.304073 | + | 0.952649i | \(0.401653\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 38.9411 | 1.34280 | ||||||||
\(842\) | 18.2132 | 0.627668 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −12.7279 | −0.438113 | ||||||||
\(845\) | 7.92893 | 0.272764 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −8.00000 | −0.274721 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −7.02944 | −0.241108 | ||||||||
\(851\) | −10.5147 | −0.360440 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −24.0000 | −0.821744 | −0.410872 | − | 0.911693i | \(-0.634776\pi\) | ||||
−0.410872 | + | 0.911693i | \(0.634776\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 18.9706 | 0.648400 | ||||||||
\(857\) | −33.7696 | −1.15355 | −0.576773 | − | 0.816904i | \(-0.695688\pi\) | ||||
−0.576773 | + | 0.816904i | \(0.695688\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 29.8284 | 1.01773 | 0.508866 | − | 0.860846i | \(-0.330065\pi\) | ||||
0.508866 | + | 0.860846i | \(0.330065\pi\) | |||||||
\(860\) | 16.6274 | 0.566990 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −19.2426 | −0.655407 | ||||||||
\(863\) | −2.97056 | −0.101119 | −0.0505596 | − | 0.998721i | \(-0.516100\pi\) | ||||
−0.0505596 | + | 0.998721i | \(0.516100\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.54416 | −0.256509 | ||||||||
\(866\) | −30.7279 | −1.04418 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 10.4853 | 0.355689 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −43.4558 | −1.47245 | ||||||||
\(872\) | −6.75736 | −0.228833 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.556349 | 0.0188188 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14.9706 | −0.505520 | −0.252760 | − | 0.967529i | \(-0.581338\pi\) | ||||
−0.252760 | + | 0.967529i | \(0.581338\pi\) | |||||||
\(878\) | 28.9706 | 0.977709 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.58579 | 0.0534568 | ||||||||
\(881\) | 54.9411 | 1.85101 | 0.925507 | − | 0.378731i | \(-0.123639\pi\) | ||||
0.925507 | + | 0.378731i | \(0.123639\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.5147 | 0.387501 | 0.193751 | − | 0.981051i | \(-0.437935\pi\) | ||||
0.193751 | + | 0.981051i | \(0.437935\pi\) | |||||||
\(884\) | 12.0000 | 0.403604 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −28.9411 | −0.972296 | ||||||||
\(887\) | 47.3553 | 1.59004 | 0.795018 | − | 0.606585i | \(-0.207461\pi\) | ||||
0.795018 | + | 0.606585i | \(0.207461\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 23.2426 | 0.779095 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.24264 | 0.0416067 | ||||||||
\(893\) | 0.0588745 | 0.00197016 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −36.4264 | −1.21760 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −11.2721 | −0.376154 | ||||||||
\(899\) | 10.2426 | 0.341611 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −22.6274 | −0.753829 | ||||||||
\(902\) | 11.8284 | 0.393844 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4.24264 | 0.141108 | ||||||||
\(905\) | −2.78680 | −0.0926363 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.72792 | −0.289806 | −0.144903 | − | 0.989446i | \(-0.546287\pi\) | ||||
−0.144903 | + | 0.989446i | \(0.546287\pi\) | |||||||
\(908\) | −12.7279 | −0.422391 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12.4853 | −0.413656 | −0.206828 | − | 0.978377i | \(-0.566314\pi\) | ||||
−0.206828 | + | 0.978377i | \(0.566314\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15.8995 | 0.526196 | ||||||||
\(914\) | −13.9706 | −0.462105 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −12.0000 | −0.396491 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.4853 | 0.411851 | 0.205926 | − | 0.978568i | \(-0.433979\pi\) | ||||
0.205926 | + | 0.978568i | \(0.433979\pi\) | |||||||
\(920\) | 5.14214 | 0.169531 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 6.89949 | 0.227223 | ||||||||
\(923\) | −30.7279 | −1.01142 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.05887 | 0.264974 | ||||||||
\(926\) | −13.2721 | −0.436148 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −8.24264 | −0.270578 | ||||||||
\(929\) | 16.2843 | 0.534270 | 0.267135 | − | 0.963659i | \(-0.413923\pi\) | ||||
0.267135 | + | 0.963659i | \(0.413923\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −7.75736 | −0.254101 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −23.6569 | −0.774076 | ||||||||
\(935\) | 4.48528 | 0.146684 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.686292 | 0.0224202 | 0.0112101 | − | 0.999937i | \(-0.496432\pi\) | ||||
0.0112101 | + | 0.999937i | \(0.496432\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.544156 | 0.0177484 | ||||||||
\(941\) | 10.0711 | 0.328307 | 0.164154 | − | 0.986435i | \(-0.447511\pi\) | ||||
0.164154 | + | 0.986435i | \(0.447511\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 38.3553 | 1.24902 | ||||||||
\(944\) | 0.343146 | 0.0111684 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 10.4853 | 0.340906 | ||||||||
\(947\) | −16.0294 | −0.520887 | −0.260443 | − | 0.965489i | \(-0.583869\pi\) | ||||
−0.260443 | + | 0.965489i | \(0.583869\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 37.4558 | 1.21587 | ||||||||
\(950\) | −0.426407 | −0.0138345 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 17.7574 | 0.575217 | 0.287609 | − | 0.957748i | \(-0.407140\pi\) | ||||
0.287609 | + | 0.957748i | \(0.407140\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 14.6569 | 0.474285 | ||||||||
\(956\) | 18.0000 | 0.582162 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 18.3431 | 0.592640 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.4558 | −0.950189 | ||||||||
\(962\) | −13.7574 | −0.443555 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −14.4853 | −0.466539 | ||||||||
\(965\) | −19.7990 | −0.637352 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −52.6690 | −1.69372 | −0.846861 | − | 0.531814i | \(-0.821511\pi\) | ||||
−0.846861 | + | 0.531814i | \(0.821511\pi\) | |||||||
\(968\) | −10.0000 | −0.321412 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −17.9411 | −0.576055 | ||||||||
\(971\) | 55.4975 | 1.78100 | 0.890499 | − | 0.454984i | \(-0.150355\pi\) | ||||
0.890499 | + | 0.454984i | \(0.150355\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −21.5147 | −0.689376 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.17157 | −0.293575 | ||||||||
\(977\) | 16.9706 | 0.542936 | 0.271468 | − | 0.962447i | \(-0.412491\pi\) | ||||
0.271468 | + | 0.962447i | \(0.412491\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14.6569 | 0.468435 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −0.514719 | −0.0164253 | ||||||||
\(983\) | −1.79899 | −0.0573789 | −0.0286894 | − | 0.999588i | \(-0.509133\pi\) | ||||
−0.0286894 | + | 0.999588i | \(0.509133\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −36.0416 | −1.14838 | ||||||||
\(986\) | −23.3137 | −0.742460 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.727922 | 0.0231583 | ||||||||
\(989\) | 34.0000 | 1.08114 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.242641 | 0.00770774 | 0.00385387 | − | 0.999993i | \(-0.498773\pi\) | ||||
0.00385387 | + | 0.999993i | \(0.498773\pi\) | |||||||
\(992\) | −1.24264 | −0.0394539 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −21.0000 | −0.665745 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −39.8995 | −1.26363 | −0.631815 | − | 0.775119i | \(-0.717690\pi\) | ||||
−0.631815 | + | 0.775119i | \(0.717690\pi\) | |||||||
\(998\) | 18.9706 | 0.600503 | ||||||||
\(999\) | 0 | 0 |
(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 | 2646.2.a.bp.1.1 | yes | 2 | |
3.2 | odd | 2 | 2646.2.a.be.1.2 | ✓ | 2 | ||
7.6 | odd | 2 | 2646.2.a.bk.1.2 | yes | 2 | ||
21.20 | even | 2 | 2646.2.a.bj.1.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2646.2.a.be.1.2 | ✓ | 2 | 3.2 | odd | 2 | ||
2646.2.a.bj.1.1 | yes | 2 | 21.20 | even | 2 | ||
2646.2.a.bk.1.2 | yes | 2 | 7.6 | odd | 2 | ||
2646.2.a.bp.1.1 | yes | 2 | 1.1 | even | 1 | trivial |