Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2940,2,Mod(1,2940)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2940, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("2940.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2940 = 2^{2} \cdot 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2940.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: | \(23.4760181943\) |
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: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 420) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2940.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.24264 | 1.27920 | 0.639602 | − | 0.768706i | \(-0.279099\pi\) | ||||
0.639602 | + | 0.768706i | \(0.279099\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.24264 | 1.45405 | 0.727023 | − | 0.686613i | \(-0.240903\pi\) | ||||
0.727023 | + | 0.686613i | \(0.240903\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.24264 | 1.02899 | 0.514496 | − | 0.857493i | \(-0.327979\pi\) | ||||
0.514496 | + | 0.857493i | \(0.327979\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.00000 | 1.60591 | 0.802955 | − | 0.596040i | \(-0.203260\pi\) | ||||
0.802955 | + | 0.596040i | \(0.203260\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.24264 | 0.884652 | 0.442326 | − | 0.896854i | \(-0.354153\pi\) | ||||
0.442326 | + | 0.896854i | \(0.354153\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −10.2426 | −1.90201 | −0.951005 | − | 0.309175i | \(-0.899947\pi\) | ||||
−0.951005 | + | 0.309175i | \(0.899947\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.48528 | −1.34440 | −0.672198 | − | 0.740371i | \(-0.734650\pi\) | ||||
−0.672198 | + | 0.740371i | \(0.734650\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.24264 | −0.738549 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.24264 | −0.861885 | −0.430942 | − | 0.902379i | \(-0.641819\pi\) | ||||
−0.430942 | + | 0.902379i | \(0.641819\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.24264 | −0.839494 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.24264 | −0.662589 | −0.331295 | − | 0.943527i | \(-0.607485\pi\) | ||||
−0.331295 | + | 0.943527i | \(0.607485\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.24264 | −0.799495 | −0.399748 | − | 0.916625i | \(-0.630902\pi\) | ||||
−0.399748 | + | 0.916625i | \(0.630902\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.00000 | 0.875190 | 0.437595 | − | 0.899172i | \(-0.355830\pi\) | ||||
0.437595 | + | 0.899172i | \(0.355830\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.24264 | −0.594089 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.48528 | −1.16554 | −0.582772 | − | 0.812636i | \(-0.698032\pi\) | ||||
−0.582772 | + | 0.812636i | \(0.698032\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.24264 | 0.572078 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.00000 | −0.927173 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.75736 | 0.228789 | 0.114394 | − | 0.993435i | \(-0.463507\pi\) | ||||
0.114394 | + | 0.993435i | \(0.463507\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.4853 | 1.59858 | 0.799288 | − | 0.600948i | \(-0.205210\pi\) | ||||
0.799288 | + | 0.600948i | \(0.205210\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.24264 | 0.650270 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.24264 | 0.396152 | 0.198076 | − | 0.980187i | \(-0.436531\pi\) | ||||
0.198076 | + | 0.980187i | \(0.436531\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.24264 | −0.510754 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.7279 | 1.51053 | 0.755263 | − | 0.655422i | \(-0.227509\pi\) | ||||
0.755263 | + | 0.655422i | \(0.227509\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.757359 | −0.0886422 | −0.0443211 | − | 0.999017i | \(-0.514112\pi\) | ||||
−0.0443211 | + | 0.999017i | \(0.514112\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.0000 | 1.23760 | 0.618798 | − | 0.785550i | \(-0.287620\pi\) | ||||
0.618798 | + | 0.785550i | \(0.287620\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.75736 | 0.192895 | 0.0964476 | − | 0.995338i | \(-0.469252\pi\) | ||||
0.0964476 | + | 0.995338i | \(0.469252\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.24264 | 0.460179 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 10.2426 | 1.09813 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.75736 | 0.186280 | 0.0931399 | − | 0.995653i | \(-0.470310\pi\) | ||||
0.0931399 | + | 0.995653i | \(0.470310\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.48528 | 0.776188 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.00000 | 0.718185 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16.4853 | −1.67383 | −0.836913 | − | 0.547335i | \(-0.815642\pi\) | ||||
−0.836913 | + | 0.547335i | \(0.815642\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.24264 | 0.426401 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 16.2426 | 1.61620 | 0.808102 | − | 0.589043i | \(-0.200495\pi\) | ||||
0.808102 | + | 0.589043i | \(0.200495\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.75736 | 0.862888 | 0.431444 | − | 0.902140i | \(-0.358004\pi\) | ||||
0.431444 | + | 0.902140i | \(0.358004\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.7279 | −1.23045 | −0.615227 | − | 0.788350i | \(-0.710936\pi\) | ||||
−0.615227 | + | 0.788350i | \(0.710936\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.48528 | 0.716960 | 0.358480 | − | 0.933537i | \(-0.383295\pi\) | ||||
0.358480 | + | 0.933537i | \(0.383295\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.24264 | 0.497609 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −18.0000 | −1.69330 | −0.846649 | − | 0.532152i | \(-0.821383\pi\) | ||||
−0.846649 | + | 0.532152i | \(0.821383\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.24264 | 0.395628 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.24264 | 0.484682 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.00000 | 0.636364 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.24264 | 0.382546 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.2426 | −0.997623 | −0.498812 | − | 0.866710i | \(-0.666230\pi\) | ||||
−0.498812 | + | 0.866710i | \(0.666230\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.24264 | 0.461589 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.48528 | 0.217140 | 0.108570 | − | 0.994089i | \(-0.465373\pi\) | ||||
0.108570 | + | 0.994089i | \(0.465373\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.24264 | −0.362473 | −0.181237 | − | 0.983440i | \(-0.558010\pi\) | ||||
−0.181237 | + | 0.983440i | \(0.558010\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.48528 | −0.125980 | −0.0629900 | − | 0.998014i | \(-0.520064\pi\) | ||||
−0.0629900 | + | 0.998014i | \(0.520064\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.00000 | −0.505291 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 22.2426 | 1.86002 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.2426 | −0.850605 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.0000 | −0.983078 | −0.491539 | − | 0.870855i | \(-0.663566\pi\) | ||||
−0.491539 | + | 0.870855i | \(0.663566\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.51472 | 0.448781 | 0.224391 | − | 0.974499i | \(-0.427961\pi\) | ||||
0.224391 | + | 0.974499i | \(0.427961\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.24264 | 0.342997 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.48528 | −0.601232 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.4853 | −0.836817 | −0.418408 | − | 0.908259i | \(-0.637412\pi\) | ||||
−0.418408 | + | 0.908259i | \(0.637412\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.48528 | 0.672927 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.00000 | 0.626608 | 0.313304 | − | 0.949653i | \(-0.398564\pi\) | ||||
0.313304 | + | 0.949653i | \(0.398564\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.24264 | −0.330289 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.72792 | 0.520622 | 0.260311 | − | 0.965525i | \(-0.416175\pi\) | ||||
0.260311 | + | 0.965525i | \(0.416175\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 14.4853 | 1.11425 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.00000 | 0.535303 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.51472 | 0.267219 | 0.133610 | − | 0.991034i | \(-0.457343\pi\) | ||||
0.133610 | + | 0.991034i | \(0.457343\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.75736 | −0.132091 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.00000 | −0.448461 | −0.224231 | − | 0.974536i | \(-0.571987\pi\) | ||||
−0.224231 | + | 0.974536i | \(0.571987\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.0000 | 0.966282 | 0.483141 | − | 0.875542i | \(-0.339496\pi\) | ||||
0.483141 | + | 0.875542i | \(0.339496\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12.4853 | −0.922939 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.24264 | −0.385447 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 18.0000 | 1.31629 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.00000 | 0.434145 | 0.217072 | − | 0.976156i | \(-0.430349\pi\) | ||||
0.217072 | + | 0.976156i | \(0.430349\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.2426 | 1.09719 | 0.548595 | − | 0.836088i | \(-0.315163\pi\) | ||||
0.548595 | + | 0.836088i | \(0.315163\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.24264 | −0.375433 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.75736 | −0.552689 | −0.276344 | − | 0.961059i | \(-0.589123\pi\) | ||||
−0.276344 | + | 0.961059i | \(0.589123\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.48528 | 0.459729 | 0.229865 | − | 0.973223i | \(-0.426172\pi\) | ||||
0.229865 | + | 0.973223i | \(0.426172\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.24264 | −0.228718 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.24264 | −0.296319 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.24264 | 0.294884 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 29.6985 | 2.05429 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.51472 | 0.379649 | 0.189824 | − | 0.981818i | \(-0.439208\pi\) | ||||
0.189824 | + | 0.981818i | \(0.439208\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −12.7279 | −0.872103 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.24264 | −0.357545 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.757359 | 0.0511776 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 22.2426 | 1.49620 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 24.4853 | 1.63966 | 0.819828 | − | 0.572610i | \(-0.194069\pi\) | ||||
0.819828 | + | 0.572610i | \(0.194069\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −27.2132 | −1.80620 | −0.903102 | − | 0.429426i | \(-0.858716\pi\) | ||||
−0.903102 | + | 0.429426i | \(0.858716\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.00000 | 0.462573 | 0.231287 | − | 0.972886i | \(-0.425707\pi\) | ||||
0.231287 | + | 0.972886i | \(0.425707\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.48528 | −0.162816 | −0.0814081 | − | 0.996681i | \(-0.525942\pi\) | ||||
−0.0814081 | + | 0.996681i | \(0.525942\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.00000 | 0.391397 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −11.0000 | −0.714527 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −22.9706 | −1.48584 | −0.742921 | − | 0.669379i | \(-0.766560\pi\) | ||||
−0.742921 | + | 0.669379i | \(0.766560\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.00000 | 0.257663 | 0.128831 | − | 0.991667i | \(-0.458877\pi\) | ||||
0.128831 | + | 0.991667i | \(0.458877\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 36.6985 | 2.33507 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.75736 | −0.111368 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.72792 | −0.424663 | −0.212331 | − | 0.977198i | \(-0.568106\pi\) | ||||
−0.212331 | + | 0.977198i | \(0.568106\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 18.0000 | 1.13165 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.24264 | −0.265684 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.75736 | −0.109621 | −0.0548105 | − | 0.998497i | \(-0.517455\pi\) | ||||
−0.0548105 | + | 0.998497i | \(0.517455\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −10.2426 | −0.634004 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8.48528 | 0.523225 | 0.261612 | − | 0.965173i | \(-0.415746\pi\) | ||||
0.261612 | + | 0.965173i | \(0.415746\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.48528 | −0.521247 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.75736 | −0.107549 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.4853 | −0.883183 | −0.441592 | − | 0.897216i | \(-0.645586\pi\) | ||||
−0.441592 | + | 0.897216i | \(0.645586\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −27.4558 | −1.66782 | −0.833912 | − | 0.551898i | \(-0.813904\pi\) | ||||
−0.833912 | + | 0.551898i | \(0.813904\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.24264 | 0.255841 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.72792 | −0.464326 | −0.232163 | − | 0.972677i | \(-0.574580\pi\) | ||||
−0.232163 | + | 0.972677i | \(0.574580\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.48528 | −0.448132 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.97056 | −0.296519 | −0.148259 | − | 0.988948i | \(-0.547367\pi\) | ||||
−0.148259 | + | 0.988948i | \(0.547367\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.72792 | 0.102714 | 0.0513572 | − | 0.998680i | \(-0.483645\pi\) | ||||
0.0513572 | + | 0.998680i | \(0.483645\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −7.00000 | −0.414644 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 16.4853 | 0.966384 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −28.9706 | −1.69248 | −0.846239 | − | 0.532803i | \(-0.821139\pi\) | ||||
−0.846239 | + | 0.532803i | \(0.821139\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.75736 | 0.102317 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.24264 | −0.246183 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 22.2426 | 1.28633 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −16.2426 | −0.933115 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12.4853 | 0.714905 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.24264 | 0.299213 | 0.149607 | − | 0.988746i | \(-0.452199\pi\) | ||||
0.149607 | + | 0.988746i | \(0.452199\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.75736 | −0.498189 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 21.2132 | 1.20289 | 0.601445 | − | 0.798914i | \(-0.294592\pi\) | ||||
0.601445 | + | 0.798914i | \(0.294592\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.72792 | 0.0976679 | 0.0488340 | − | 0.998807i | \(-0.484449\pi\) | ||||
0.0488340 | + | 0.998807i | \(0.484449\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.727922 | 0.0408842 | 0.0204421 | − | 0.999791i | \(-0.493493\pi\) | ||||
0.0204421 | + | 0.999791i | \(0.493493\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −43.4558 | −2.43306 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.7279 | 0.710403 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 29.6985 | 1.65247 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.24264 | 0.290809 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7.48528 | −0.413937 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.0000 | 0.934405 | 0.467202 | − | 0.884150i | \(-0.345262\pi\) | ||||
0.467202 | + | 0.884150i | \(0.345262\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5.24264 | −0.287295 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.24264 | 0.177164 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.7279 | 0.638861 | 0.319430 | − | 0.947610i | \(-0.396508\pi\) | ||||
0.319430 | + | 0.947610i | \(0.396508\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 18.0000 | 0.977626 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −31.7574 | −1.71976 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.24264 | −0.228416 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −24.0000 | −1.28839 | −0.644194 | − | 0.764862i | \(-0.722807\pi\) | ||||
−0.644194 | + | 0.764862i | \(0.722807\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.0000 | 0.535288 | 0.267644 | − | 0.963518i | \(-0.413755\pi\) | ||||
0.267644 | + | 0.963518i | \(0.413755\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.24264 | −0.279831 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.75736 | 0.0935348 | 0.0467674 | − | 0.998906i | \(-0.485108\pi\) | ||||
0.0467674 | + | 0.998906i | \(0.485108\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 12.7279 | 0.675528 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10.2426 | 0.540586 | 0.270293 | − | 0.962778i | \(-0.412879\pi\) | ||||
0.270293 | + | 0.962778i | \(0.412879\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 30.0000 | 1.57895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −7.00000 | −0.367405 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.757359 | −0.0396420 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.2721 | −0.536198 | −0.268099 | − | 0.963391i | \(-0.586395\pi\) | ||||
−0.268099 | + | 0.963391i | \(0.586395\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.24264 | −0.220863 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.72792 | −0.400137 | −0.200068 | − | 0.979782i | \(-0.564116\pi\) | ||||
−0.200068 | + | 0.979782i | \(0.564116\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −53.6985 | −2.76561 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 30.4558 | 1.56441 | 0.782206 | − | 0.623020i | \(-0.214095\pi\) | ||||
0.782206 | + | 0.623020i | \(0.214095\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 11.2426 | 0.575978 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 25.4558 | 1.30073 | 0.650366 | − | 0.759621i | \(-0.274615\pi\) | ||||
0.650366 | + | 0.759621i | \(0.274615\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.24264 | −0.266498 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 21.2132 | 1.07555 | 0.537776 | − | 0.843088i | \(-0.319265\pi\) | ||||
0.537776 | + | 0.843088i | \(0.319265\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.0000 | 0.910299 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.48528 | −0.125366 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 11.0000 | 0.553470 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.2426 | 0.865383 | 0.432692 | − | 0.901542i | \(-0.357564\pi\) | ||||
0.432692 | + | 0.901542i | \(0.357564\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −20.4853 | −1.02299 | −0.511493 | − | 0.859287i | \(-0.670907\pi\) | ||||
−0.511493 | + | 0.859287i | \(0.670907\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −39.2426 | −1.95482 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −22.2426 | −1.10253 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.0000 | −0.840596 | −0.420298 | − | 0.907386i | \(-0.638074\pi\) | ||||
−0.420298 | + | 0.907386i | \(0.638074\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.24264 | 0.209274 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.75736 | 0.0862654 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.48528 | 0.0727345 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.48528 | −0.121414 | −0.0607070 | − | 0.998156i | \(-0.519336\pi\) | ||||
−0.0607070 | + | 0.998156i | \(0.519336\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.5147 | 0.707404 | 0.353702 | − | 0.935358i | \(-0.384923\pi\) | ||||
0.353702 | + | 0.935358i | \(0.384923\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.00000 | 0.291730 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.24264 | 0.205798 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −22.2426 | −1.07388 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −31.4558 | −1.51517 | −0.757587 | − | 0.652734i | \(-0.773622\pi\) | ||||
−0.757587 | + | 0.652734i | \(0.773622\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −24.7574 | −1.18976 | −0.594881 | − | 0.803814i | \(-0.702801\pi\) | ||||
−0.594881 | + | 0.803814i | \(0.702801\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 10.2426 | 0.491097 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 29.6985 | 1.42067 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.0000 | 0.477274 | 0.238637 | − | 0.971109i | \(-0.423299\pi\) | ||||
0.238637 | + | 0.971109i | \(0.423299\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.51472 | 0.166989 | 0.0834947 | − | 0.996508i | \(-0.473392\pi\) | ||||
0.0834947 | + | 0.996508i | \(0.473392\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.75736 | 0.0833068 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.0000 | 0.567581 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.00000 | −0.283158 | −0.141579 | − | 0.989927i | \(-0.545218\pi\) | ||||
−0.141579 | + | 0.989927i | \(0.545218\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −18.0000 | −0.847587 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.51472 | −0.259104 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.2132 | −0.477754 | −0.238877 | − | 0.971050i | \(-0.576779\pi\) | ||||
−0.238877 | + | 0.971050i | \(0.576779\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.24264 | −0.198030 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.72792 | 0.313351 | 0.156675 | − | 0.987650i | \(-0.449922\pi\) | ||||
0.156675 | + | 0.987650i | \(0.449922\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 35.7279 | 1.66042 | 0.830209 | − | 0.557453i | \(-0.188221\pi\) | ||||
0.830209 | + | 0.557453i | \(0.188221\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 7.48528 | 0.347122 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −22.9706 | −1.06295 | −0.531475 | − | 0.847074i | \(-0.678362\pi\) | ||||
−0.531475 | + | 0.847074i | \(0.678362\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10.4853 | 0.483136 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −22.2426 | −1.02272 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.00000 | 0.321182 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.48528 | −0.388514 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12.0000 | −0.548294 | −0.274147 | − | 0.961688i | \(-0.588395\pi\) | ||||
−0.274147 | + | 0.961688i | \(0.588395\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −27.4853 | −1.25322 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −16.4853 | −0.748558 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.2721 | −0.556101 | −0.278050 | − | 0.960566i | \(-0.589688\pi\) | ||||
−0.278050 | + | 0.960566i | \(0.589688\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8.00000 | −0.361773 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 32.4853 | 1.46604 | 0.733020 | − | 0.680207i | \(-0.238110\pi\) | ||||
0.733020 | + | 0.680207i | \(0.238110\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −43.4558 | −1.95715 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.24264 | 0.190693 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.51472 | 0.112574 | 0.0562871 | − | 0.998415i | \(-0.482074\pi\) | ||||
0.0562871 | + | 0.998415i | \(0.482074\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.72792 | −0.300581 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.51472 | 0.424240 | 0.212120 | − | 0.977244i | \(-0.431963\pi\) | ||||
0.212120 | + | 0.977244i | \(0.431963\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 16.2426 | 0.722788 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −14.4853 | −0.643314 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −31.4558 | −1.39426 | −0.697128 | − | 0.716947i | \(-0.745539\pi\) | ||||
−0.697128 | + | 0.716947i | \(0.745539\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7.00000 | −0.309058 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.75736 | 0.385895 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 25.4558 | 1.11955 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.51472 | −0.154279 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −37.4558 | −1.64097 | −0.820485 | − | 0.571668i | \(-0.806297\pi\) | ||||
−0.820485 | + | 0.571668i | \(0.806297\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.24264 | −0.141791 | −0.0708954 | − | 0.997484i | \(-0.522586\pi\) | ||||
−0.0708954 | + | 0.997484i | \(0.522586\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −31.7574 | −1.38337 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.00000 | −0.217391 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.75736 | 0.0762629 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −22.2426 | −0.963436 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.7279 | −0.550276 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.00000 | 0.258919 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 26.9411 | 1.15829 | 0.579145 | − | 0.815225i | \(-0.303387\pi\) | ||||
0.579145 | + | 0.815225i | \(0.303387\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −13.0000 | −0.557883 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.48528 | 0.320634 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.4558 | −0.746358 | −0.373179 | − | 0.927759i | \(-0.621732\pi\) | ||||
−0.373179 | + | 0.927759i | \(0.621732\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 12.4853 | 0.532859 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −71.6985 | −3.05446 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.24264 | 0.222538 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −30.0000 | −1.27114 | −0.635570 | − | 0.772043i | \(-0.719235\pi\) | ||||
−0.635570 | + | 0.772043i | \(0.719235\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −27.4853 | −1.16250 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −18.0000 | −0.759961 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.00000 | 0.252870 | 0.126435 | − | 0.991975i | \(-0.459647\pi\) | ||||
0.126435 | + | 0.991975i | \(0.459647\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −18.0000 | −0.757266 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 17.6985 | 0.741959 | 0.370980 | − | 0.928641i | \(-0.379022\pi\) | ||||
0.370980 | + | 0.928641i | \(0.379022\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 38.9411 | 1.62964 | 0.814818 | − | 0.579717i | \(-0.196837\pi\) | ||||
0.814818 | + | 0.579717i | \(0.196837\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.00000 | −0.250654 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.24264 | 0.176930 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −21.2426 | −0.884343 | −0.442171 | − | 0.896931i | \(-0.645792\pi\) | ||||
−0.442171 | + | 0.896931i | \(0.645792\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −15.2426 | −0.633463 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −36.0000 | −1.49097 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.24264 | 0.216757 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.78680 | −0.115023 | −0.0575117 | − | 0.998345i | \(-0.518317\pi\) | ||||
−0.0575117 | + | 0.998345i | \(0.518317\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −52.3970 | −2.15898 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.75736 | 0.319095 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 39.2132 | 1.61029 | 0.805147 | − | 0.593076i | \(-0.202087\pi\) | ||||
0.805147 | + | 0.593076i | \(0.202087\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6.48528 | −0.265425 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −15.5147 | −0.633914 | −0.316957 | − | 0.948440i | \(-0.602661\pi\) | ||||
−0.316957 | + | 0.948440i | \(0.602661\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.4853 | −0.550076 | −0.275038 | − | 0.961433i | \(-0.588690\pi\) | ||||
−0.275038 | + | 0.961433i | \(0.588690\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.24264 | 0.132051 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.00000 | 0.284590 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20.7574 | 0.842515 | 0.421258 | − | 0.906941i | \(-0.361589\pi\) | ||||
0.421258 | + | 0.906941i | \(0.361589\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 31.4558 | 1.27257 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 45.4558 | 1.83594 | 0.917972 | − | 0.396645i | \(-0.129826\pi\) | ||||
0.917972 | + | 0.396645i | \(0.129826\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.24264 | 0.171080 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9.51472 | −0.383048 | −0.191524 | − | 0.981488i | \(-0.561343\pi\) | ||||
−0.191524 | + | 0.981488i | \(0.561343\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −21.9706 | −0.883071 | −0.441536 | − | 0.897244i | \(-0.645566\pi\) | ||||
−0.441536 | + | 0.897244i | \(0.645566\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.24264 | −0.170251 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −29.6985 | −1.18604 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −22.2426 | −0.886872 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.00000 | 0.318475 | 0.159237 | − | 0.987240i | \(-0.449096\pi\) | ||||
0.159237 | + | 0.987240i | \(0.449096\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.51472 | −0.219190 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −11.2426 | −0.446151 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12.7279 | 0.503509 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 25.7574 | 1.01735 | 0.508677 | − | 0.860957i | \(-0.330135\pi\) | ||||
0.508677 | + | 0.860957i | \(0.330135\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.72792 | −0.225887 | −0.112944 | − | 0.993601i | \(-0.536028\pi\) | ||||
−0.112944 | + | 0.993601i | \(0.536028\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.24264 | 0.206429 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.75736 | −0.0690889 | −0.0345445 | − | 0.999403i | \(-0.510998\pi\) | ||||
−0.0345445 | + | 0.999403i | \(0.510998\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.45584 | 0.292667 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.75736 | 0.0687708 | 0.0343854 | − | 0.999409i | \(-0.489053\pi\) | ||||
0.0343854 | + | 0.999409i | \(0.489053\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.48528 | 0.0971080 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.757359 | −0.0295474 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.02944 | 0.273828 | 0.136914 | − | 0.990583i | \(-0.456282\pi\) | ||||
0.136914 | + | 0.990583i | \(0.456282\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 35.9706 | 1.39909 | 0.699546 | − | 0.714587i | \(-0.253385\pi\) | ||||
0.699546 | + | 0.714587i | \(0.253385\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −22.2426 | −0.863833 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −43.4558 | −1.68262 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −24.4853 | −0.946656 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 52.9706 | 2.04491 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.27208 | 0.164677 | 0.0823383 | − | 0.996604i | \(-0.473761\pi\) | ||||
0.0823383 | + | 0.996604i | \(0.473761\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12.7279 | 0.489174 | 0.244587 | − | 0.969627i | \(-0.421348\pi\) | ||||
0.244587 | + | 0.969627i | \(0.421348\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 27.2132 | 1.04281 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9.21320 | −0.352533 | −0.176267 | − | 0.984342i | \(-0.556402\pi\) | ||||
−0.176267 | + | 0.984342i | \(0.556402\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.24264 | −0.162103 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.00000 | −0.267067 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −44.4853 | −1.69475 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 40.9411 | 1.55747 | 0.778737 | − | 0.627351i | \(-0.215861\pi\) | ||||
0.778737 | + | 0.627351i | \(0.215861\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.48528 | −0.0563399 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18.0000 | −0.681799 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.48528 | 0.0940020 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 51.2132 | 1.93430 | 0.967148 | − | 0.254214i | \(-0.0818167\pi\) | ||||
0.967148 | + | 0.254214i | \(0.0818167\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −36.6985 | −1.38411 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.00000 | −0.225973 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −19.5147 | −0.732891 | −0.366445 | − | 0.930440i | \(-0.619425\pi\) | ||||
−0.366445 | + | 0.930440i | \(0.619425\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 11.0000 | 0.412532 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −31.7574 | −1.18932 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 22.2426 | 0.831828 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 22.9706 | 0.857851 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9.51472 | −0.354839 | −0.177420 | − | 0.984135i | \(-0.556775\pi\) | ||||
−0.177420 | + | 0.984135i | \(0.556775\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4.00000 | −0.148762 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −10.2426 | −0.380402 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.24264 | −0.342791 | −0.171395 | − | 0.985202i | \(-0.554828\pi\) | ||||
−0.171395 | + | 0.985202i | \(0.554828\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −22.2426 | −0.822674 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −44.2132 | −1.63305 | −0.816526 | − | 0.577309i | \(-0.804103\pi\) | ||||
−0.816526 | + | 0.577309i | \(0.804103\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13.7574 | 0.506759 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.48528 | 0.0546370 | 0.0273185 | − | 0.999627i | \(-0.491303\pi\) | ||||
0.0273185 | + | 0.999627i | \(0.491303\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −36.6985 | −1.34815 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −27.2132 | −0.998356 | −0.499178 | − | 0.866500i | \(-0.666365\pi\) | ||||
−0.499178 | + | 0.866500i | \(0.666365\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12.0000 | −0.439646 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.75736 | 0.0642984 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.9411 | −0.837134 | −0.418567 | − | 0.908186i | \(-0.637467\pi\) | ||||
−0.418567 | + | 0.908186i | \(0.637467\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.72792 | 0.245179 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.51472 | 0.200701 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 42.9706 | 1.56179 | 0.780896 | − | 0.624661i | \(-0.214763\pi\) | ||||
0.780896 | + | 0.624661i | \(0.214763\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −18.0000 | −0.653359 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −37.7574 | −1.36870 | −0.684352 | − | 0.729152i | \(-0.739915\pi\) | ||||
−0.684352 | + | 0.729152i | \(0.739915\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.24264 | 0.153393 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.21320 | 0.332669 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.00000 | −0.180305 | −0.0901523 | − | 0.995928i | \(-0.528735\pi\) | ||||
−0.0901523 | + | 0.995928i | \(0.528735\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.75736 | 0.0632897 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 47.6985 | 1.71560 | 0.857798 | − | 0.513988i | \(-0.171832\pi\) | ||||
0.857798 | + | 0.513988i | \(0.171832\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.48528 | −0.268879 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −29.6985 | −1.06406 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 54.0000 | 1.93227 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 10.2426 | 0.366042 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −10.4853 | −0.374236 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11.5147 | −0.410455 | −0.205228 | − | 0.978714i | \(-0.565793\pi\) | ||||
−0.205228 | + | 0.978714i | \(0.565793\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −8.48528 | −0.302084 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 65.4558 | 2.32441 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 8.48528 | 0.300942 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 40.2426 | 1.42547 | 0.712734 | − | 0.701435i | \(-0.247457\pi\) | ||||
0.712734 | + | 0.701435i | \(0.247457\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 25.4558 | 0.900563 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.75736 | 0.0620932 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.21320 | −0.113391 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 14.4853 | 0.509906 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −39.9411 | −1.40426 | −0.702128 | − | 0.712051i | \(-0.747766\pi\) | ||||
−0.702128 | + | 0.712051i | \(0.747766\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 55.9411 | 1.96436 | 0.982179 | − | 0.187946i | \(-0.0601831\pi\) | ||||
0.982179 | + | 0.187946i | \(0.0601831\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 27.4558 | 0.962918 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.00000 | 0.280228 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −36.6985 | −1.28392 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −53.6985 | −1.87409 | −0.937045 | − | 0.349209i | \(-0.886450\pi\) | ||||
−0.937045 | + | 0.349209i | \(0.886450\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.02944 | −0.175315 | −0.0876576 | − | 0.996151i | \(-0.527938\pi\) | ||||
−0.0876576 | + | 0.996151i | \(0.527938\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.24264 | −0.147710 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7.45584 | −0.259265 | −0.129633 | − | 0.991562i | \(-0.541380\pi\) | ||||
−0.129633 | + | 0.991562i | \(0.541380\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.0000 | −0.382046 | −0.191023 | − | 0.981586i | \(-0.561180\pi\) | ||||
−0.191023 | + | 0.981586i | \(0.561180\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.72792 | 0.268079 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.72792 | 0.232829 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.48528 | 0.258729 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −34.2426 | −1.18219 | −0.591094 | − | 0.806603i | \(-0.701304\pi\) | ||||
−0.591094 | + | 0.806603i | \(0.701304\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 75.9117 | 2.61764 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.97056 | 0.171195 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 14.4853 | 0.498309 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.72792 | −0.0593021 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −22.2426 | −0.762468 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.272078 | 0.00931577 | 0.00465789 | − | 0.999989i | \(-0.498517\pi\) | ||||
0.00465789 | + | 0.999989i | \(0.498517\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.00000 | 0.239395 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.24264 | 0.144926 | 0.0724629 | − | 0.997371i | \(-0.476914\pi\) | ||||
0.0724629 | + | 0.997371i | \(0.476914\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22.0000 | 0.750630 | 0.375315 | − | 0.926897i | \(-0.377534\pi\) | ||||
0.375315 | + | 0.926897i | \(0.377534\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −38.4853 | −1.31005 | −0.655027 | − | 0.755605i | \(-0.727343\pi\) | ||||
−0.655027 | + | 0.755605i | \(0.727343\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.51472 | 0.119504 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 46.6690 | 1.58314 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17.0000 | 0.576023 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −16.4853 | −0.557942 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −10.0000 | −0.337676 | −0.168838 | − | 0.985644i | \(-0.554001\pi\) | ||||
−0.168838 | + | 0.985644i | \(0.554001\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 28.9706 | 0.977153 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.02944 | −0.236828 | −0.118414 | − | 0.992964i | \(-0.537781\pi\) | ||||
−0.118414 | + | 0.992964i | \(0.537781\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19.7279 | −0.663897 | −0.331949 | − | 0.943297i | \(-0.607706\pi\) | ||||
−0.331949 | + | 0.943297i | \(0.607706\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.75736 | −0.0590730 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 27.2132 | 0.913730 | 0.456865 | − | 0.889536i | \(-0.348972\pi\) | ||||
0.456865 | + | 0.889536i | \(0.348972\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.24264 | 0.142134 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 42.0000 | 1.40548 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.00000 | −0.200558 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −22.2426 | −0.742660 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 76.6690 | 2.55706 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −36.0000 | −1.19933 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 13.0000 | 0.432135 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −55.7279 | −1.85042 | −0.925208 | − | 0.379461i | \(-0.876109\pi\) | ||||
−0.925208 | + | 0.379461i | \(0.876109\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 16.2426 | 0.538734 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.78680 | 0.291120 | 0.145560 | − | 0.989349i | \(-0.453502\pi\) | ||||
0.145560 | + | 0.989349i | \(0.453502\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.45584 | 0.246752 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −12.4853 | −0.412751 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.0294373 | 0.000971045 0 | 0.000485523 | − | 1.00000i | \(-0.499845\pi\) | ||||
0.000485523 | 1.00000i | \(0.499845\pi\) | ||||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.24264 | −0.172751 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 66.7279 | 2.19638 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.24264 | −0.172377 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8.75736 | 0.287629 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −11.2721 | −0.369825 | −0.184912 | − | 0.982755i | \(-0.559200\pi\) | ||||
−0.184912 | + | 0.982755i | \(0.559200\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −21.2132 | −0.694489 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 18.0000 | 0.588663 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −40.6985 | −1.32956 | −0.664781 | − | 0.747039i | \(-0.731475\pi\) | ||||
−0.664781 | + | 0.747039i | \(0.731475\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.72792 | −0.0563886 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11.6985 | −0.381360 | −0.190680 | − | 0.981652i | \(-0.561069\pi\) | ||||
−0.190680 | + | 0.981652i | \(0.561069\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −18.0000 | −0.586161 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 39.2132 | 1.27426 | 0.637129 | − | 0.770757i | \(-0.280122\pi\) | ||||
0.637129 | + | 0.770757i | \(0.280122\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.97056 | −0.128890 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.727922 | −0.0236045 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −44.4853 | −1.44102 | −0.720510 | − | 0.693445i | \(-0.756092\pi\) | ||||
−0.720510 | + | 0.693445i | \(0.756092\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.00000 | 0.194155 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 43.4558 | 1.40473 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 25.0294 | 0.807401 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12.7279 | −0.410152 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 15.2426 | 0.490678 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −26.7574 | −0.860459 | −0.430229 | − | 0.902720i | \(-0.641567\pi\) | ||||
−0.430229 | + | 0.902720i | \(0.641567\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −29.6985 | −0.954053 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19.0294 | −0.610684 | −0.305342 | − | 0.952243i | \(-0.598771\pi\) | ||||
−0.305342 | + | 0.952243i | \(0.598771\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −5.24264 | −0.167899 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −51.2132 | −1.63846 | −0.819228 | − | 0.573468i | \(-0.805598\pi\) | ||||
−0.819228 | + | 0.573468i | \(0.805598\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.45584 | 0.238290 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.48528 | 0.238987 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −17.6985 | −0.564494 | −0.282247 | − | 0.959342i | \(-0.591080\pi\) | ||||
−0.282247 | + | 0.959342i | \(0.591080\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.75736 | −0.247170 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −22.2426 | −0.707275 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −52.9411 | −1.68173 | −0.840865 | − | 0.541245i | \(-0.817953\pi\) | ||||
−0.840865 | + | 0.541245i | \(0.817953\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −17.0000 | −0.539479 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.48528 | 0.205597 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.272078 | 0.00861679 | 0.00430840 | − | 0.999991i | \(-0.498629\pi\) | ||||
0.00430840 | + | 0.999991i | \(0.498629\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.24264 | 0.165870 |
(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 | 2940.2.a.p.1.2 | 2 | ||
3.2 | odd | 2 | 8820.2.a.bf.1.1 | 2 | |||
7.2 | even | 3 | 2940.2.q.q.361.1 | 4 | |||
7.3 | odd | 6 | 420.2.q.d.121.1 | ✓ | 4 | ||
7.4 | even | 3 | 2940.2.q.q.961.1 | 4 | |||
7.5 | odd | 6 | 420.2.q.d.361.1 | yes | 4 | ||
7.6 | odd | 2 | 2940.2.a.r.1.2 | 2 | |||
21.5 | even | 6 | 1260.2.s.e.361.1 | 4 | |||
21.17 | even | 6 | 1260.2.s.e.541.1 | 4 | |||
21.20 | even | 2 | 8820.2.a.bk.1.1 | 2 | |||
28.3 | even | 6 | 1680.2.bg.t.961.2 | 4 | |||
28.19 | even | 6 | 1680.2.bg.t.1201.2 | 4 | |||
35.3 | even | 12 | 2100.2.bc.f.1549.3 | 8 | |||
35.12 | even | 12 | 2100.2.bc.f.949.3 | 8 | |||
35.17 | even | 12 | 2100.2.bc.f.1549.2 | 8 | |||
35.19 | odd | 6 | 2100.2.q.k.1201.2 | 4 | |||
35.24 | odd | 6 | 2100.2.q.k.1801.2 | 4 | |||
35.33 | even | 12 | 2100.2.bc.f.949.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
420.2.q.d.121.1 | ✓ | 4 | 7.3 | odd | 6 | ||
420.2.q.d.361.1 | yes | 4 | 7.5 | odd | 6 | ||
1260.2.s.e.361.1 | 4 | 21.5 | even | 6 | |||
1260.2.s.e.541.1 | 4 | 21.17 | even | 6 | |||
1680.2.bg.t.961.2 | 4 | 28.3 | even | 6 | |||
1680.2.bg.t.1201.2 | 4 | 28.19 | even | 6 | |||
2100.2.q.k.1201.2 | 4 | 35.19 | odd | 6 | |||
2100.2.q.k.1801.2 | 4 | 35.24 | odd | 6 | |||
2100.2.bc.f.949.2 | 8 | 35.33 | even | 12 | |||
2100.2.bc.f.949.3 | 8 | 35.12 | even | 12 | |||
2100.2.bc.f.1549.2 | 8 | 35.17 | even | 12 | |||
2100.2.bc.f.1549.3 | 8 | 35.3 | even | 12 | |||
2940.2.a.p.1.2 | 2 | 1.1 | even | 1 | trivial | ||
2940.2.a.r.1.2 | 2 | 7.6 | odd | 2 | |||
2940.2.q.q.361.1 | 4 | 7.2 | even | 3 | |||
2940.2.q.q.961.1 | 4 | 7.4 | even | 3 | |||
8820.2.a.bf.1.1 | 2 | 3.2 | odd | 2 | |||
8820.2.a.bk.1.1 | 2 | 21.20 | even | 2 |