Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2001,2,Mod(1,2001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("2001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2001 = 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2001.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: | \(15.9780654445\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{6}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 6 \) |
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 | 1.2 | ||
Root | \(-2.44949\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2001.1 |
$q$-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 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −2.00000 | −1.00000 | ||||||||
\(5\) | 2.44949 | 1.09545 | 0.547723 | − | 0.836660i | \(-0.315495\pi\) | ||||
0.547723 | + | 0.836660i | \(0.315495\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.44949 | −1.68175 | −0.840875 | − | 0.541230i | \(-0.817959\pi\) | ||||
−0.840875 | + | 0.541230i | \(0.817959\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | −2.00000 | −0.577350 | ||||||||
\(13\) | 1.00000 | 0.277350 | 0.138675 | − | 0.990338i | \(-0.455716\pi\) | ||||
0.138675 | + | 0.990338i | \(0.455716\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.44949 | 0.632456 | ||||||||
\(16\) | 4.00000 | 1.00000 | ||||||||
\(17\) | −1.44949 | −0.351553 | −0.175776 | − | 0.984430i | \(-0.556244\pi\) | ||||
−0.175776 | + | 0.984430i | \(0.556244\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | −0.114708 | − | 0.993399i | \(-0.536593\pi\) | ||||
−0.114708 | + | 0.993399i | \(0.536593\pi\) | |||||||
\(20\) | −4.89898 | −1.09545 | ||||||||
\(21\) | −4.44949 | −0.970958 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 8.89898 | 1.68175 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.4495 | −1.87678 | −0.938392 | − | 0.345573i | \(-0.887685\pi\) | ||||
−0.938392 | + | 0.345573i | \(0.887685\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −10.8990 | −1.84226 | ||||||||
\(36\) | −2.00000 | −0.333333 | ||||||||
\(37\) | 9.89898 | 1.62738 | 0.813691 | − | 0.581298i | \(-0.197455\pi\) | ||||
0.813691 | + | 0.581298i | \(0.197455\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.34847 | −1.45999 | −0.729993 | − | 0.683455i | \(-0.760477\pi\) | ||||
−0.729993 | + | 0.683455i | \(0.760477\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.101021 | −0.0154055 | −0.00770274 | − | 0.999970i | \(-0.502452\pi\) | ||||
−0.00770274 | + | 0.999970i | \(0.502452\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.44949 | 0.365148 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −12.4495 | −1.81594 | −0.907972 | − | 0.419030i | \(-0.862370\pi\) | ||||
−0.907972 | + | 0.419030i | \(0.862370\pi\) | |||||||
\(48\) | 4.00000 | 0.577350 | ||||||||
\(49\) | 12.7980 | 1.82828 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.44949 | −0.202969 | ||||||||
\(52\) | −2.00000 | −0.277350 | ||||||||
\(53\) | −2.00000 | −0.274721 | −0.137361 | − | 0.990521i | \(-0.543862\pi\) | ||||
−0.137361 | + | 0.990521i | \(0.543862\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.00000 | −0.132453 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.550510 | −0.0716703 | −0.0358352 | − | 0.999358i | \(-0.511409\pi\) | ||||
−0.0358352 | + | 0.999358i | \(0.511409\pi\) | |||||||
\(60\) | −4.89898 | −0.632456 | ||||||||
\(61\) | −3.10102 | −0.397045 | −0.198522 | − | 0.980096i | \(-0.563614\pi\) | ||||
−0.198522 | + | 0.980096i | \(0.563614\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.44949 | −0.560583 | ||||||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | 2.44949 | 0.303822 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.89898 | −1.08718 | −0.543592 | − | 0.839350i | \(-0.682936\pi\) | ||||
−0.543592 | + | 0.839350i | \(0.682936\pi\) | |||||||
\(68\) | 2.89898 | 0.351553 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.3485 | −1.46549 | −0.732747 | − | 0.680501i | \(-0.761762\pi\) | ||||
−0.732747 | + | 0.680501i | \(0.761762\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14.2474 | −1.66754 | −0.833769 | − | 0.552114i | \(-0.813821\pi\) | ||||
−0.833769 | + | 0.552114i | \(0.813821\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 2.00000 | 0.229416 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.89898 | 0.663687 | 0.331844 | − | 0.943334i | \(-0.392329\pi\) | ||||
0.331844 | + | 0.943334i | \(0.392329\pi\) | |||||||
\(80\) | 9.79796 | 1.09545 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.55051 | −0.828776 | −0.414388 | − | 0.910100i | \(-0.636004\pi\) | ||||
−0.414388 | + | 0.910100i | \(0.636004\pi\) | |||||||
\(84\) | 8.89898 | 0.970958 | ||||||||
\(85\) | −3.55051 | −0.385107 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.00000 | 0.107211 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.44949 | 0.577645 | 0.288822 | − | 0.957383i | \(-0.406736\pi\) | ||||
0.288822 | + | 0.957383i | \(0.406736\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.44949 | −0.466433 | ||||||||
\(92\) | 2.00000 | 0.208514 | ||||||||
\(93\) | −10.4495 | −1.08356 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.44949 | −0.251312 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.8990 | 1.71583 | 0.857916 | − | 0.513790i | \(-0.171759\pi\) | ||||
0.857916 | + | 0.513790i | \(0.171759\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.00000 | −0.200000 | ||||||||
\(101\) | 10.4495 | 1.03976 | 0.519882 | − | 0.854238i | \(-0.325976\pi\) | ||||
0.519882 | + | 0.854238i | \(0.325976\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.79796 | 0.177158 | 0.0885791 | − | 0.996069i | \(-0.471767\pi\) | ||||
0.0885791 | + | 0.996069i | \(0.471767\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −10.8990 | −1.06363 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −14.2474 | −1.37735 | −0.688676 | − | 0.725069i | \(-0.741808\pi\) | ||||
−0.688676 | + | 0.725069i | \(0.741808\pi\) | |||||||
\(108\) | −2.00000 | −0.192450 | ||||||||
\(109\) | −6.44949 | −0.617749 | −0.308875 | − | 0.951103i | \(-0.599952\pi\) | ||||
−0.308875 | + | 0.951103i | \(0.599952\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.89898 | 0.939570 | ||||||||
\(112\) | −17.7980 | −1.68175 | ||||||||
\(113\) | −16.8990 | −1.58972 | −0.794861 | − | 0.606791i | \(-0.792456\pi\) | ||||
−0.794861 | + | 0.606791i | \(0.792456\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.44949 | −0.228416 | ||||||||
\(116\) | −2.00000 | −0.185695 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.44949 | 0.591224 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −9.34847 | −0.842923 | ||||||||
\(124\) | 20.8990 | 1.87678 | ||||||||
\(125\) | −9.79796 | −0.876356 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.2474 | 0.909314 | 0.454657 | − | 0.890667i | \(-0.349762\pi\) | ||||
0.454657 | + | 0.890667i | \(0.349762\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.101021 | −0.00889436 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 18.6969 | 1.63356 | 0.816780 | − | 0.576950i | \(-0.195757\pi\) | ||||
0.816780 | + | 0.576950i | \(0.195757\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.44949 | 0.385820 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.44949 | 0.210819 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 20.1464 | 1.72123 | 0.860613 | − | 0.509260i | \(-0.170081\pi\) | ||||
0.860613 | + | 0.509260i | \(0.170081\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.00000 | 0.508913 | 0.254457 | − | 0.967084i | \(-0.418103\pi\) | ||||
0.254457 | + | 0.967084i | \(0.418103\pi\) | |||||||
\(140\) | 21.7980 | 1.84226 | ||||||||
\(141\) | −12.4495 | −1.04844 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 4.00000 | 0.333333 | ||||||||
\(145\) | 2.44949 | 0.203419 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 12.7980 | 1.05556 | ||||||||
\(148\) | −19.7980 | −1.62738 | ||||||||
\(149\) | −0.898979 | −0.0736473 | −0.0368236 | − | 0.999322i | \(-0.511724\pi\) | ||||
−0.0368236 | + | 0.999322i | \(0.511724\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.5959 | 1.51331 | 0.756657 | − | 0.653812i | \(-0.226831\pi\) | ||||
0.756657 | + | 0.653812i | \(0.226831\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.44949 | −0.117184 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −25.5959 | −2.05591 | ||||||||
\(156\) | −2.00000 | −0.160128 | ||||||||
\(157\) | −20.5959 | −1.64373 | −0.821867 | − | 0.569680i | \(-0.807067\pi\) | ||||
−0.821867 | + | 0.569680i | \(0.807067\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.00000 | −0.158610 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.44949 | 0.350669 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.8990 | 1.01033 | 0.505163 | − | 0.863024i | \(-0.331432\pi\) | ||||
0.505163 | + | 0.863024i | \(0.331432\pi\) | |||||||
\(164\) | 18.6969 | 1.45999 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.34847 | 0.491259 | 0.245630 | − | 0.969364i | \(-0.421005\pi\) | ||||
0.245630 | + | 0.969364i | \(0.421005\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.0000 | −0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.00000 | −0.0764719 | ||||||||
\(172\) | 0.202041 | 0.0154055 | ||||||||
\(173\) | 23.2474 | 1.76747 | 0.883735 | − | 0.467987i | \(-0.155021\pi\) | ||||
0.883735 | + | 0.467987i | \(0.155021\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.44949 | −0.336350 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.550510 | −0.0413789 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.65153 | 0.123441 | 0.0617206 | − | 0.998093i | \(-0.480341\pi\) | ||||
0.0617206 | + | 0.998093i | \(0.480341\pi\) | |||||||
\(180\) | −4.89898 | −0.365148 | ||||||||
\(181\) | −15.7980 | −1.17425 | −0.587127 | − | 0.809495i | \(-0.699741\pi\) | ||||
−0.587127 | + | 0.809495i | \(0.699741\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.10102 | −0.229234 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 24.2474 | 1.78271 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 24.8990 | 1.81594 | ||||||||
\(189\) | −4.44949 | −0.323653 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −22.1464 | −1.60246 | −0.801230 | − | 0.598357i | \(-0.795820\pi\) | ||||
−0.801230 | + | 0.598357i | \(0.795820\pi\) | |||||||
\(192\) | −8.00000 | −0.577350 | ||||||||
\(193\) | −15.7980 | −1.13716 | −0.568581 | − | 0.822627i | \(-0.692507\pi\) | ||||
−0.568581 | + | 0.822627i | \(0.692507\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.44949 | 0.175412 | ||||||||
\(196\) | −25.5959 | −1.82828 | ||||||||
\(197\) | 24.1464 | 1.72036 | 0.860181 | − | 0.509989i | \(-0.170351\pi\) | ||||
0.860181 | + | 0.509989i | \(0.170351\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.2474 | −1.43530 | −0.717652 | − | 0.696402i | \(-0.754783\pi\) | ||||
−0.717652 | + | 0.696402i | \(0.754783\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.89898 | −0.627686 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.44949 | −0.312293 | ||||||||
\(204\) | 2.89898 | 0.202969 | ||||||||
\(205\) | −22.8990 | −1.59933 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | 4.00000 | 0.277350 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.0454 | −1.24230 | −0.621149 | − | 0.783693i | \(-0.713334\pi\) | ||||
−0.621149 | + | 0.783693i | \(0.713334\pi\) | |||||||
\(212\) | 4.00000 | 0.274721 | ||||||||
\(213\) | −12.3485 | −0.846103 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.247449 | −0.0168759 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 46.4949 | 3.15628 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −14.2474 | −0.962753 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.44949 | −0.0975032 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −21.8990 | −1.46646 | −0.733232 | − | 0.679978i | \(-0.761989\pi\) | ||||
−0.733232 | + | 0.679978i | \(0.761989\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 14.0000 | 0.929213 | 0.464606 | − | 0.885517i | \(-0.346196\pi\) | ||||
0.464606 | + | 0.885517i | \(0.346196\pi\) | |||||||
\(228\) | 2.00000 | 0.132453 | ||||||||
\(229\) | −7.20204 | −0.475924 | −0.237962 | − | 0.971274i | \(-0.576479\pi\) | ||||
−0.237962 | + | 0.971274i | \(0.576479\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.1464 | −0.795739 | −0.397869 | − | 0.917442i | \(-0.630250\pi\) | ||||
−0.397869 | + | 0.917442i | \(0.630250\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −30.4949 | −1.98927 | ||||||||
\(236\) | 1.10102 | 0.0716703 | ||||||||
\(237\) | 5.89898 | 0.383180 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.55051 | 0.553087 | 0.276543 | − | 0.961001i | \(-0.410811\pi\) | ||||
0.276543 | + | 0.961001i | \(0.410811\pi\) | |||||||
\(240\) | 9.79796 | 0.632456 | ||||||||
\(241\) | 20.6969 | 1.33321 | 0.666604 | − | 0.745412i | \(-0.267747\pi\) | ||||
0.666604 | + | 0.745412i | \(0.267747\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 6.20204 | 0.397045 | ||||||||
\(245\) | 31.3485 | 2.00278 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.00000 | −0.0636285 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.55051 | −0.478494 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.55051 | −0.539703 | −0.269852 | − | 0.962902i | \(-0.586975\pi\) | ||||
−0.269852 | + | 0.962902i | \(0.586975\pi\) | |||||||
\(252\) | 8.89898 | 0.560583 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.55051 | −0.222342 | ||||||||
\(256\) | 16.0000 | 1.00000 | ||||||||
\(257\) | 15.4495 | 0.963713 | 0.481856 | − | 0.876250i | \(-0.339963\pi\) | ||||
0.481856 | + | 0.876250i | \(0.339963\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −44.0454 | −2.73685 | ||||||||
\(260\) | −4.89898 | −0.303822 | ||||||||
\(261\) | 1.00000 | 0.0618984 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −16.8990 | −1.04204 | −0.521018 | − | 0.853546i | \(-0.674448\pi\) | ||||
−0.521018 | + | 0.853546i | \(0.674448\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.89898 | −0.300942 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.44949 | 0.333503 | ||||||||
\(268\) | 17.7980 | 1.08718 | ||||||||
\(269\) | −23.5959 | −1.43867 | −0.719334 | − | 0.694664i | \(-0.755553\pi\) | ||||
−0.719334 | + | 0.694664i | \(0.755553\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.10102 | 0.431356 | 0.215678 | − | 0.976465i | \(-0.430804\pi\) | ||||
0.215678 | + | 0.976465i | \(0.430804\pi\) | |||||||
\(272\) | −5.79796 | −0.351553 | ||||||||
\(273\) | −4.44949 | −0.269295 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.00000 | 0.120386 | ||||||||
\(277\) | −7.00000 | −0.420589 | −0.210295 | − | 0.977638i | \(-0.567442\pi\) | ||||
−0.210295 | + | 0.977638i | \(0.567442\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −10.4495 | −0.625595 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.4949 | 1.46124 | 0.730622 | − | 0.682783i | \(-0.239230\pi\) | ||||
0.730622 | + | 0.682783i | \(0.239230\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 22.0454 | 1.31046 | 0.655232 | − | 0.755428i | \(-0.272571\pi\) | ||||
0.655232 | + | 0.755428i | \(0.272571\pi\) | |||||||
\(284\) | 24.6969 | 1.46549 | ||||||||
\(285\) | −2.44949 | −0.145095 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 41.5959 | 2.45533 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.8990 | −0.876411 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 16.8990 | 0.990636 | ||||||||
\(292\) | 28.4949 | 1.66754 | ||||||||
\(293\) | −2.75255 | −0.160806 | −0.0804029 | − | 0.996762i | \(-0.525621\pi\) | ||||
−0.0804029 | + | 0.996762i | \(0.525621\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.34847 | −0.0785109 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.00000 | −0.0578315 | ||||||||
\(300\) | −2.00000 | −0.115470 | ||||||||
\(301\) | 0.449490 | 0.0259082 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 10.4495 | 0.600308 | ||||||||
\(304\) | −4.00000 | −0.229416 | ||||||||
\(305\) | −7.59592 | −0.434941 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 27.3485 | 1.56086 | 0.780430 | − | 0.625243i | \(-0.215000\pi\) | ||||
0.780430 | + | 0.625243i | \(0.215000\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.79796 | 0.102282 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.79796 | 0.555591 | 0.277796 | − | 0.960640i | \(-0.410396\pi\) | ||||
0.277796 | + | 0.960640i | \(0.410396\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.3485 | 0.867547 | 0.433773 | − | 0.901022i | \(-0.357182\pi\) | ||||
0.433773 | + | 0.901022i | \(0.357182\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −10.8990 | −0.614088 | ||||||||
\(316\) | −11.7980 | −0.663687 | ||||||||
\(317\) | −6.24745 | −0.350892 | −0.175446 | − | 0.984489i | \(-0.556137\pi\) | ||||
−0.175446 | + | 0.984489i | \(0.556137\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −19.5959 | −1.09545 | ||||||||
\(321\) | −14.2474 | −0.795215 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.44949 | 0.0806518 | ||||||||
\(324\) | −2.00000 | −0.111111 | ||||||||
\(325\) | 1.00000 | 0.0554700 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.44949 | −0.356658 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 55.3939 | 3.05396 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 33.5959 | 1.84660 | 0.923299 | − | 0.384081i | \(-0.125482\pi\) | ||||
0.923299 | + | 0.384081i | \(0.125482\pi\) | |||||||
\(332\) | 15.1010 | 0.828776 | ||||||||
\(333\) | 9.89898 | 0.542461 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −21.7980 | −1.19095 | ||||||||
\(336\) | −17.7980 | −0.970958 | ||||||||
\(337\) | 6.79796 | 0.370308 | 0.185154 | − | 0.982709i | \(-0.440722\pi\) | ||||
0.185154 | + | 0.982709i | \(0.440722\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −16.8990 | −0.917827 | ||||||||
\(340\) | 7.10102 | 0.385107 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −25.7980 | −1.39296 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.44949 | −0.131876 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.1464 | −0.652054 | −0.326027 | − | 0.945360i | \(-0.605710\pi\) | ||||
−0.326027 | + | 0.945360i | \(0.605710\pi\) | |||||||
\(348\) | −2.00000 | −0.107211 | ||||||||
\(349\) | 17.6969 | 0.947295 | 0.473648 | − | 0.880714i | \(-0.342937\pi\) | ||||
0.473648 | + | 0.880714i | \(0.342937\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.89898 | 0.473645 | 0.236822 | − | 0.971553i | \(-0.423894\pi\) | ||||
0.236822 | + | 0.971553i | \(0.423894\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −30.2474 | −1.60537 | ||||||||
\(356\) | −10.8990 | −0.577645 | ||||||||
\(357\) | 6.44949 | 0.341343 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 15.0454 | 0.794066 | 0.397033 | − | 0.917804i | \(-0.370040\pi\) | ||||
0.397033 | + | 0.917804i | \(0.370040\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.0000 | −0.947368 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −11.0000 | −0.577350 | ||||||||
\(364\) | 8.89898 | 0.466433 | ||||||||
\(365\) | −34.8990 | −1.82670 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.0000 | −0.730794 | −0.365397 | − | 0.930852i | \(-0.619067\pi\) | ||||
−0.365397 | + | 0.930852i | \(0.619067\pi\) | |||||||
\(368\) | −4.00000 | −0.208514 | ||||||||
\(369\) | −9.34847 | −0.486662 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.89898 | 0.462012 | ||||||||
\(372\) | 20.8990 | 1.08356 | ||||||||
\(373\) | −4.65153 | −0.240847 | −0.120424 | − | 0.992723i | \(-0.538425\pi\) | ||||
−0.120424 | + | 0.992723i | \(0.538425\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −9.79796 | −0.505964 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.00000 | 0.0515026 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.00000 | −0.256833 | −0.128416 | − | 0.991720i | \(-0.540989\pi\) | ||||
−0.128416 | + | 0.991720i | \(0.540989\pi\) | |||||||
\(380\) | 4.89898 | 0.251312 | ||||||||
\(381\) | 10.2474 | 0.524993 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 15.7980 | 0.807238 | 0.403619 | − | 0.914927i | \(-0.367752\pi\) | ||||
0.403619 | + | 0.914927i | \(0.367752\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.101021 | −0.00513516 | ||||||||
\(388\) | −33.7980 | −1.71583 | ||||||||
\(389\) | 30.3485 | 1.53873 | 0.769364 | − | 0.638810i | \(-0.220573\pi\) | ||||
0.769364 | + | 0.638810i | \(0.220573\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.44949 | 0.0733038 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 18.6969 | 0.943136 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 14.4495 | 0.727033 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.69694 | 0.336110 | 0.168055 | − | 0.985778i | \(-0.446251\pi\) | ||||
0.168055 | + | 0.985778i | \(0.446251\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.44949 | 0.222753 | ||||||||
\(400\) | 4.00000 | 0.200000 | ||||||||
\(401\) | −12.6969 | −0.634055 | −0.317027 | − | 0.948416i | \(-0.602685\pi\) | ||||
−0.317027 | + | 0.948416i | \(0.602685\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.4495 | −0.520526 | ||||||||
\(404\) | −20.8990 | −1.03976 | ||||||||
\(405\) | 2.44949 | 0.121716 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 23.1464 | 1.14452 | 0.572259 | − | 0.820073i | \(-0.306067\pi\) | ||||
0.572259 | + | 0.820073i | \(0.306067\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 20.1464 | 0.993750 | ||||||||
\(412\) | −3.59592 | −0.177158 | ||||||||
\(413\) | 2.44949 | 0.120532 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −18.4949 | −0.907879 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.00000 | 0.293821 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.59592 | −0.371085 | −0.185542 | − | 0.982636i | \(-0.559404\pi\) | ||||
−0.185542 | + | 0.982636i | \(0.559404\pi\) | |||||||
\(420\) | 21.7980 | 1.06363 | ||||||||
\(421\) | −9.69694 | −0.472600 | −0.236300 | − | 0.971680i | \(-0.575935\pi\) | ||||
−0.236300 | + | 0.971680i | \(0.575935\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −12.4495 | −0.605315 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.44949 | −0.0703106 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13.7980 | 0.667730 | ||||||||
\(428\) | 28.4949 | 1.37735 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −34.4949 | −1.66156 | −0.830780 | − | 0.556600i | \(-0.812105\pi\) | ||||
−0.830780 | + | 0.556600i | \(0.812105\pi\) | |||||||
\(432\) | 4.00000 | 0.192450 | ||||||||
\(433\) | −6.00000 | −0.288342 | −0.144171 | − | 0.989553i | \(-0.546051\pi\) | ||||
−0.144171 | + | 0.989553i | \(0.546051\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.44949 | 0.117444 | ||||||||
\(436\) | 12.8990 | 0.617749 | ||||||||
\(437\) | 1.00000 | 0.0478365 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.30306 | 0.396284 | 0.198142 | − | 0.980173i | \(-0.436509\pi\) | ||||
0.198142 | + | 0.980173i | \(0.436509\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 12.7980 | 0.609427 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11.1464 | 0.529583 | 0.264791 | − | 0.964306i | \(-0.414697\pi\) | ||||
0.264791 | + | 0.964306i | \(0.414697\pi\) | |||||||
\(444\) | −19.7980 | −0.939570 | ||||||||
\(445\) | 13.3485 | 0.632778 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.898979 | −0.0425203 | ||||||||
\(448\) | 35.5959 | 1.68175 | ||||||||
\(449\) | 14.2020 | 0.670236 | 0.335118 | − | 0.942176i | \(-0.391224\pi\) | ||||
0.335118 | + | 0.942176i | \(0.391224\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 33.7980 | 1.58972 | ||||||||
\(453\) | 18.5959 | 0.873712 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −10.8990 | −0.510952 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.4495 | 0.769475 | 0.384737 | − | 0.923026i | \(-0.374292\pi\) | ||||
0.384737 | + | 0.923026i | \(0.374292\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.44949 | −0.0676564 | ||||||||
\(460\) | 4.89898 | 0.228416 | ||||||||
\(461\) | 4.00000 | 0.186299 | 0.0931493 | − | 0.995652i | \(-0.470307\pi\) | ||||
0.0931493 | + | 0.995652i | \(0.470307\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.10102 | 0.190591 | 0.0952953 | − | 0.995449i | \(-0.469620\pi\) | ||||
0.0952953 | + | 0.995449i | \(0.469620\pi\) | |||||||
\(464\) | 4.00000 | 0.185695 | ||||||||
\(465\) | −25.5959 | −1.18698 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −30.1464 | −1.39501 | −0.697505 | − | 0.716580i | \(-0.745707\pi\) | ||||
−0.697505 | + | 0.716580i | \(0.745707\pi\) | |||||||
\(468\) | −2.00000 | −0.0924500 | ||||||||
\(469\) | 39.5959 | 1.82837 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −20.5959 | −0.949010 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.00000 | −0.0458831 | ||||||||
\(476\) | −12.8990 | −0.591224 | ||||||||
\(477\) | −2.00000 | −0.0915737 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16.8990 | 0.772134 | 0.386067 | − | 0.922471i | \(-0.373833\pi\) | ||||
0.386067 | + | 0.922471i | \(0.373833\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.89898 | 0.451355 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.44949 | 0.202459 | ||||||||
\(484\) | 22.0000 | 1.00000 | ||||||||
\(485\) | 41.3939 | 1.87960 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 24.6969 | 1.11913 | 0.559563 | − | 0.828788i | \(-0.310969\pi\) | ||||
0.559563 | + | 0.828788i | \(0.310969\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 12.8990 | 0.583312 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.5505 | −0.701785 | −0.350892 | − | 0.936416i | \(-0.614122\pi\) | ||||
−0.350892 | + | 0.936416i | \(0.614122\pi\) | |||||||
\(492\) | 18.6969 | 0.842923 | ||||||||
\(493\) | −1.44949 | −0.0652817 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −41.7980 | −1.87678 | ||||||||
\(497\) | 54.9444 | 2.46459 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −28.1010 | −1.25797 | −0.628987 | − | 0.777416i | \(-0.716530\pi\) | ||||
−0.628987 | + | 0.777416i | \(0.716530\pi\) | |||||||
\(500\) | 19.5959 | 0.876356 | ||||||||
\(501\) | 6.34847 | 0.283629 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −0.752551 | −0.0335546 | −0.0167773 | − | 0.999859i | \(-0.505341\pi\) | ||||
−0.0167773 | + | 0.999859i | \(0.505341\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 25.5959 | 1.13900 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.0000 | −0.532939 | ||||||||
\(508\) | −20.4949 | −0.909314 | ||||||||
\(509\) | 1.85357 | 0.0821581 | 0.0410791 | − | 0.999156i | \(-0.486920\pi\) | ||||
0.0410791 | + | 0.999156i | \(0.486920\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 63.3939 | 2.80438 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.00000 | −0.0441511 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.40408 | 0.194067 | ||||||||
\(516\) | 0.202041 | 0.00889436 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 23.2474 | 1.02045 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −26.0454 | −1.14107 | −0.570535 | − | 0.821273i | \(-0.693264\pi\) | ||||
−0.570535 | + | 0.821273i | \(0.693264\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.34847 | −0.0589644 | −0.0294822 | − | 0.999565i | \(-0.509386\pi\) | ||||
−0.0294822 | + | 0.999565i | \(0.509386\pi\) | |||||||
\(524\) | −37.3939 | −1.63356 | ||||||||
\(525\) | −4.44949 | −0.194192 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 15.1464 | 0.659789 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.550510 | −0.0238901 | ||||||||
\(532\) | −8.89898 | −0.385820 | ||||||||
\(533\) | −9.34847 | −0.404927 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −34.8990 | −1.50881 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.65153 | 0.0712688 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −4.89898 | −0.210819 | ||||||||
\(541\) | −16.8990 | −0.726544 | −0.363272 | − | 0.931683i | \(-0.618340\pi\) | ||||
−0.363272 | + | 0.931683i | \(0.618340\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −15.7980 | −0.677955 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −15.7980 | −0.676710 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.6969 | −0.585639 | −0.292819 | − | 0.956168i | \(-0.594593\pi\) | ||||
−0.292819 | + | 0.956168i | \(0.594593\pi\) | |||||||
\(548\) | −40.2929 | −1.72123 | ||||||||
\(549\) | −3.10102 | −0.132348 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.00000 | −0.0426014 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −26.2474 | −1.11616 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 24.2474 | 1.02925 | ||||||||
\(556\) | −12.0000 | −0.508913 | ||||||||
\(557\) | −35.1464 | −1.48920 | −0.744601 | − | 0.667510i | \(-0.767360\pi\) | ||||
−0.744601 | + | 0.667510i | \(0.767360\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.101021 | −0.00427271 | ||||||||
\(560\) | −43.5959 | −1.84226 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9.24745 | −0.389733 | −0.194867 | − | 0.980830i | \(-0.562427\pi\) | ||||
−0.194867 | + | 0.980830i | \(0.562427\pi\) | |||||||
\(564\) | 24.8990 | 1.04844 | ||||||||
\(565\) | −41.3939 | −1.74145 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.44949 | −0.186861 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −16.2020 | −0.679225 | −0.339612 | − | 0.940565i | \(-0.610296\pi\) | ||||
−0.339612 | + | 0.940565i | \(0.610296\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 34.0454 | 1.42476 | 0.712378 | − | 0.701796i | \(-0.247618\pi\) | ||||
0.712378 | + | 0.701796i | \(0.247618\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −22.1464 | −0.925180 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.00000 | −0.0417029 | ||||||||
\(576\) | −8.00000 | −0.333333 | ||||||||
\(577\) | 28.2474 | 1.17596 | 0.587978 | − | 0.808877i | \(-0.299924\pi\) | ||||
0.587978 | + | 0.808877i | \(0.299924\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −15.7980 | −0.656541 | ||||||||
\(580\) | −4.89898 | −0.203419 | ||||||||
\(581\) | 33.5959 | 1.39379 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.44949 | 0.101274 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −21.0454 | −0.868637 | −0.434318 | − | 0.900759i | \(-0.643011\pi\) | ||||
−0.434318 | + | 0.900759i | \(0.643011\pi\) | |||||||
\(588\) | −25.5959 | −1.05556 | ||||||||
\(589\) | 10.4495 | 0.430564 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 24.1464 | 0.993251 | ||||||||
\(592\) | 39.5959 | 1.62738 | ||||||||
\(593\) | 39.2474 | 1.61170 | 0.805850 | − | 0.592120i | \(-0.201709\pi\) | ||||
0.805850 | + | 0.592120i | \(0.201709\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 15.7980 | 0.647653 | ||||||||
\(596\) | 1.79796 | 0.0736473 | ||||||||
\(597\) | −20.2474 | −0.828673 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 13.3485 | 0.545404 | 0.272702 | − | 0.962099i | \(-0.412083\pi\) | ||||
0.272702 | + | 0.962099i | \(0.412083\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.30306 | 0.0531530 | 0.0265765 | − | 0.999647i | \(-0.491539\pi\) | ||||
0.0265765 | + | 0.999647i | \(0.491539\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.89898 | −0.362394 | ||||||||
\(604\) | −37.1918 | −1.51331 | ||||||||
\(605\) | −26.9444 | −1.09545 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.34847 | 0.217088 | 0.108544 | − | 0.994092i | \(-0.465381\pi\) | ||||
0.108544 | + | 0.994092i | \(0.465381\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.44949 | −0.180302 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.4495 | −0.503652 | ||||||||
\(612\) | 2.89898 | 0.117184 | ||||||||
\(613\) | 10.0000 | 0.403896 | 0.201948 | − | 0.979396i | \(-0.435273\pi\) | ||||
0.201948 | + | 0.979396i | \(0.435273\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −22.8990 | −0.923376 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.20204 | 0.330202 | 0.165101 | − | 0.986277i | \(-0.447205\pi\) | ||||
0.165101 | + | 0.986277i | \(0.447205\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.7980 | 0.434007 | 0.217003 | − | 0.976171i | \(-0.430372\pi\) | ||||
0.217003 | + | 0.976171i | \(0.430372\pi\) | |||||||
\(620\) | 51.1918 | 2.05591 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −24.2474 | −0.971454 | ||||||||
\(624\) | 4.00000 | 0.160128 | ||||||||
\(625\) | −29.0000 | −1.16000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 41.1918 | 1.64373 | ||||||||
\(629\) | −14.3485 | −0.572111 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −32.6969 | −1.30164 | −0.650822 | − | 0.759230i | \(-0.725576\pi\) | ||||
−0.650822 | + | 0.759230i | \(0.725576\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −18.0454 | −0.717241 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 25.1010 | 0.996104 | ||||||||
\(636\) | 4.00000 | 0.158610 | ||||||||
\(637\) | 12.7980 | 0.507074 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −12.3485 | −0.488498 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −33.0454 | −1.30522 | −0.652608 | − | 0.757696i | \(-0.726325\pi\) | ||||
−0.652608 | + | 0.757696i | \(0.726325\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.10102 | −0.122292 | −0.0611462 | − | 0.998129i | \(-0.519476\pi\) | ||||
−0.0611462 | + | 0.998129i | \(0.519476\pi\) | |||||||
\(644\) | −8.89898 | −0.350669 | ||||||||
\(645\) | −0.247449 | −0.00974328 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.24745 | −0.0490423 | −0.0245211 | − | 0.999699i | \(-0.507806\pi\) | ||||
−0.0245211 | + | 0.999699i | \(0.507806\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 46.4949 | 1.82228 | ||||||||
\(652\) | −25.7980 | −1.01033 | ||||||||
\(653\) | 42.7423 | 1.67264 | 0.836319 | − | 0.548244i | \(-0.184703\pi\) | ||||
0.836319 | + | 0.548244i | \(0.184703\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 45.7980 | 1.78947 | ||||||||
\(656\) | −37.3939 | −1.45999 | ||||||||
\(657\) | −14.2474 | −0.555846 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.44949 | −0.368100 | −0.184050 | − | 0.982917i | \(-0.558921\pi\) | ||||
−0.184050 | + | 0.982917i | \(0.558921\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.34847 | −0.285822 | −0.142911 | − | 0.989736i | \(-0.545646\pi\) | ||||
−0.142911 | + | 0.989736i | \(0.545646\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.44949 | −0.0562935 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 10.8990 | 0.422644 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | −12.6969 | −0.491259 | ||||||||
\(669\) | −21.8990 | −0.846663 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.89898 | 0.0732003 | 0.0366001 | − | 0.999330i | \(-0.488347\pi\) | ||||
0.0366001 | + | 0.999330i | \(0.488347\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 24.0000 | 0.923077 | ||||||||
\(677\) | 23.7980 | 0.914630 | 0.457315 | − | 0.889305i | \(-0.348811\pi\) | ||||
0.457315 | + | 0.889305i | \(0.348811\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −75.1918 | −2.88560 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 14.0000 | 0.536481 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 26.6969 | 1.02153 | 0.510765 | − | 0.859720i | \(-0.329362\pi\) | ||||
0.510765 | + | 0.859720i | \(0.329362\pi\) | |||||||
\(684\) | 2.00000 | 0.0764719 | ||||||||
\(685\) | 49.3485 | 1.88551 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.20204 | −0.274775 | ||||||||
\(688\) | −0.404082 | −0.0154055 | ||||||||
\(689\) | −2.00000 | −0.0761939 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29.1010 | 1.10705 | 0.553527 | − | 0.832831i | \(-0.313281\pi\) | ||||
0.553527 | + | 0.832831i | \(0.313281\pi\) | |||||||
\(692\) | −46.4949 | −1.76747 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 14.6969 | 0.557487 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13.5505 | 0.513262 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −12.1464 | −0.459420 | ||||||||
\(700\) | 8.89898 | 0.336350 | ||||||||
\(701\) | −17.7526 | −0.670505 | −0.335252 | − | 0.942128i | \(-0.608822\pi\) | ||||
−0.335252 | + | 0.942128i | \(0.608822\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.89898 | −0.373347 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −30.4949 | −1.14850 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −46.4949 | −1.74862 | ||||||||
\(708\) | 1.10102 | 0.0413789 | ||||||||
\(709\) | 15.3485 | 0.576424 | 0.288212 | − | 0.957567i | \(-0.406939\pi\) | ||||
0.288212 | + | 0.957567i | \(0.406939\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.89898 | 0.221229 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10.4495 | 0.391336 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −3.30306 | −0.123441 | ||||||||
\(717\) | 8.55051 | 0.319325 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 21.7423 | 0.810853 | 0.405426 | − | 0.914128i | \(-0.367123\pi\) | ||||
0.405426 | + | 0.914128i | \(0.367123\pi\) | |||||||
\(720\) | 9.79796 | 0.365148 | ||||||||
\(721\) | −8.00000 | −0.297936 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 20.6969 | 0.769727 | ||||||||
\(724\) | 31.5959 | 1.17425 | ||||||||
\(725\) | 1.00000 | 0.0371391 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −35.5959 | −1.32018 | −0.660090 | − | 0.751187i | \(-0.729482\pi\) | ||||
−0.660090 | + | 0.751187i | \(0.729482\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.146428 | 0.00541584 | ||||||||
\(732\) | 6.20204 | 0.229234 | ||||||||
\(733\) | −40.8990 | −1.51064 | −0.755319 | − | 0.655357i | \(-0.772518\pi\) | ||||
−0.755319 | + | 0.655357i | \(0.772518\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 31.3485 | 1.15631 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 35.7980 | 1.31685 | 0.658425 | − | 0.752647i | \(-0.271223\pi\) | ||||
0.658425 | + | 0.752647i | \(0.271223\pi\) | |||||||
\(740\) | −48.4949 | −1.78271 | ||||||||
\(741\) | −1.00000 | −0.0367359 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.7526 | 0.614591 | 0.307296 | − | 0.951614i | \(-0.400576\pi\) | ||||
0.307296 | + | 0.951614i | \(0.400576\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.20204 | −0.0806765 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7.55051 | −0.276259 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 63.3939 | 2.31636 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.4949 | −0.419455 | −0.209727 | − | 0.977760i | \(-0.567258\pi\) | ||||
−0.209727 | + | 0.977760i | \(0.567258\pi\) | |||||||
\(752\) | −49.7980 | −1.81594 | ||||||||
\(753\) | −8.55051 | −0.311598 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 45.5505 | 1.65775 | ||||||||
\(756\) | 8.89898 | 0.323653 | ||||||||
\(757\) | 12.1010 | 0.439819 | 0.219910 | − | 0.975520i | \(-0.429424\pi\) | ||||
0.219910 | + | 0.975520i | \(0.429424\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.24745 | −0.117720 | −0.0588600 | − | 0.998266i | \(-0.518747\pi\) | ||||
−0.0588600 | + | 0.998266i | \(0.518747\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 28.6969 | 1.03890 | ||||||||
\(764\) | 44.2929 | 1.60246 | ||||||||
\(765\) | −3.55051 | −0.128369 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.550510 | −0.0198778 | ||||||||
\(768\) | 16.0000 | 0.577350 | ||||||||
\(769\) | −42.1010 | −1.51820 | −0.759101 | − | 0.650973i | \(-0.774361\pi\) | ||||
−0.759101 | + | 0.650973i | \(0.774361\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15.4495 | 0.556400 | ||||||||
\(772\) | 31.5959 | 1.13716 | ||||||||
\(773\) | −36.6969 | −1.31990 | −0.659949 | − | 0.751311i | \(-0.729422\pi\) | ||||
−0.659949 | + | 0.751311i | \(0.729422\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −10.4495 | −0.375357 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −44.0454 | −1.58012 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.34847 | 0.334944 | ||||||||
\(780\) | −4.89898 | −0.175412 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.00000 | 0.0357371 | ||||||||
\(784\) | 51.1918 | 1.82828 | ||||||||
\(785\) | −50.4495 | −1.80062 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −40.2929 | −1.43629 | −0.718143 | − | 0.695896i | \(-0.755007\pi\) | ||||
−0.718143 | + | 0.695896i | \(0.755007\pi\) | |||||||
\(788\) | −48.2929 | −1.72036 | ||||||||
\(789\) | −16.8990 | −0.601620 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 75.1918 | 2.67351 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.10102 | −0.110120 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.89898 | −0.173749 | ||||||||
\(796\) | 40.4949 | 1.43530 | ||||||||
\(797\) | 32.6969 | 1.15818 | 0.579092 | − | 0.815262i | \(-0.303407\pi\) | ||||
0.579092 | + | 0.815262i | \(0.303407\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18.0454 | 0.638401 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.44949 | 0.192548 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 17.7980 | 0.627686 | ||||||||
\(805\) | 10.8990 | 0.384139 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −23.5959 | −0.830616 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 21.1010 | 0.741872 | 0.370936 | − | 0.928658i | \(-0.379037\pi\) | ||||
0.370936 | + | 0.928658i | \(0.379037\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.3031 | 0.677822 | 0.338911 | − | 0.940818i | \(-0.389941\pi\) | ||||
0.338911 | + | 0.940818i | \(0.389941\pi\) | |||||||
\(812\) | 8.89898 | 0.312293 | ||||||||
\(813\) | 7.10102 | 0.249044 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 31.5959 | 1.10676 | ||||||||
\(816\) | −5.79796 | −0.202969 | ||||||||
\(817\) | 0.101021 | 0.00353426 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.44949 | −0.155478 | ||||||||
\(820\) | 45.7980 | 1.59933 | ||||||||
\(821\) | −24.3485 | −0.849767 | −0.424884 | − | 0.905248i | \(-0.639685\pi\) | ||||
−0.424884 | + | 0.905248i | \(0.639685\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.8536 | −0.587479 | −0.293739 | − | 0.955886i | \(-0.594900\pi\) | ||||
−0.293739 | + | 0.955886i | \(0.594900\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −22.3485 | −0.777132 | −0.388566 | − | 0.921421i | \(-0.627030\pi\) | ||||
−0.388566 | + | 0.921421i | \(0.627030\pi\) | |||||||
\(828\) | 2.00000 | 0.0695048 | ||||||||
\(829\) | −50.2929 | −1.74674 | −0.873372 | − | 0.487055i | \(-0.838071\pi\) | ||||
−0.873372 | + | 0.487055i | \(0.838071\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.00000 | −0.242827 | ||||||||
\(832\) | −8.00000 | −0.277350 | ||||||||
\(833\) | −18.5505 | −0.642737 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 15.5505 | 0.538148 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −10.4495 | −0.361187 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 51.3939 | 1.77431 | 0.887157 | − | 0.461468i | \(-0.152677\pi\) | ||||
0.887157 | + | 0.461468i | \(0.152677\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 24.4949 | 0.843649 | ||||||||
\(844\) | 36.0908 | 1.24230 | ||||||||
\(845\) | −29.3939 | −1.01118 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 48.9444 | 1.68175 | ||||||||
\(848\) | −8.00000 | −0.274721 | ||||||||
\(849\) | 22.0454 | 0.756596 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.89898 | −0.339333 | ||||||||
\(852\) | 24.6969 | 0.846103 | ||||||||
\(853\) | −23.3939 | −0.800991 | −0.400496 | − | 0.916299i | \(-0.631162\pi\) | ||||
−0.400496 | + | 0.916299i | \(0.631162\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.44949 | −0.0837708 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 40.2929 | 1.37638 | 0.688189 | − | 0.725532i | \(-0.258406\pi\) | ||||
0.688189 | + | 0.725532i | \(0.258406\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.6515 | −0.431665 | −0.215832 | − | 0.976430i | \(-0.569246\pi\) | ||||
−0.215832 | + | 0.976430i | \(0.569246\pi\) | |||||||
\(860\) | 0.494897 | 0.0168759 | ||||||||
\(861\) | 41.5959 | 1.41759 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 30.2929 | 1.03118 | 0.515590 | − | 0.856835i | \(-0.327573\pi\) | ||||
0.515590 | + | 0.856835i | \(0.327573\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 56.9444 | 1.93617 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −14.8990 | −0.505996 | ||||||||
\(868\) | −92.9898 | −3.15628 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.89898 | −0.301530 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 16.8990 | 0.571944 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 43.5959 | 1.47381 | ||||||||
\(876\) | 28.4949 | 0.962753 | ||||||||
\(877\) | −46.5959 | −1.57343 | −0.786716 | − | 0.617315i | \(-0.788220\pi\) | ||||
−0.786716 | + | 0.617315i | \(0.788220\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.75255 | −0.0928413 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.348469 | 0.0117402 | 0.00587011 | − | 0.999983i | \(-0.498131\pi\) | ||||
0.00587011 | + | 0.999983i | \(0.498131\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35.0908 | −1.18090 | −0.590450 | − | 0.807074i | \(-0.701050\pi\) | ||||
−0.590450 | + | 0.807074i | \(0.701050\pi\) | |||||||
\(884\) | 2.89898 | 0.0975032 | ||||||||
\(885\) | −1.34847 | −0.0453283 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 42.5403 | 1.42836 | 0.714182 | − | 0.699960i | \(-0.246799\pi\) | ||||
0.714182 | + | 0.699960i | \(0.246799\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −45.5959 | −1.52924 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 43.7980 | 1.46646 | ||||||||
\(893\) | 12.4495 | 0.416606 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.04541 | 0.135223 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.00000 | −0.0333890 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −10.4495 | −0.348510 | ||||||||
\(900\) | −2.00000 | −0.0666667 | ||||||||
\(901\) | 2.89898 | 0.0965790 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.449490 | 0.0149581 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −38.6969 | −1.28633 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −26.5959 | −0.883103 | −0.441551 | − | 0.897236i | \(-0.645572\pi\) | ||||
−0.441551 | + | 0.897236i | \(0.645572\pi\) | |||||||
\(908\) | −28.0000 | −0.929213 | ||||||||
\(909\) | 10.4495 | 0.346588 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −47.4495 | −1.57207 | −0.786036 | − | 0.618181i | \(-0.787870\pi\) | ||||
−0.786036 | + | 0.618181i | \(0.787870\pi\) | |||||||
\(912\) | −4.00000 | −0.132453 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −7.59592 | −0.251113 | ||||||||
\(916\) | 14.4041 | 0.475924 | ||||||||
\(917\) | −83.1918 | −2.74724 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −28.6969 | −0.946625 | −0.473312 | − | 0.880895i | \(-0.656942\pi\) | ||||
−0.473312 | + | 0.880895i | \(0.656942\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 27.3485 | 0.901163 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −12.3485 | −0.406455 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.89898 | 0.325476 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.79796 | 0.0590527 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4.84337 | −0.158906 | −0.0794529 | − | 0.996839i | \(-0.525317\pi\) | ||||
−0.0794529 | + | 0.996839i | \(0.525317\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −12.7980 | −0.419436 | ||||||||
\(932\) | 24.2929 | 0.795739 | ||||||||
\(933\) | 9.79796 | 0.320771 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 29.1918 | 0.953656 | 0.476828 | − | 0.878997i | \(-0.341787\pi\) | ||||
0.476828 | + | 0.878997i | \(0.341787\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 15.3485 | 0.500878 | ||||||||
\(940\) | 60.9898 | 1.98927 | ||||||||
\(941\) | −32.4949 | −1.05930 | −0.529652 | − | 0.848215i | \(-0.677677\pi\) | ||||
−0.529652 | + | 0.848215i | \(0.677677\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.34847 | 0.304428 | ||||||||
\(944\) | −2.20204 | −0.0716703 | ||||||||
\(945\) | −10.8990 | −0.354544 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −6.69694 | −0.217621 | −0.108811 | − | 0.994062i | \(-0.534704\pi\) | ||||
−0.108811 | + | 0.994062i | \(0.534704\pi\) | |||||||
\(948\) | −11.7980 | −0.383180 | ||||||||
\(949\) | −14.2474 | −0.462492 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.24745 | −0.202587 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −26.6515 | −0.863328 | −0.431664 | − | 0.902035i | \(-0.642073\pi\) | ||||
−0.431664 | + | 0.902035i | \(0.642073\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −54.2474 | −1.75541 | ||||||||
\(956\) | −17.1010 | −0.553087 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −89.6413 | −2.89467 | ||||||||
\(960\) | −19.5959 | −0.632456 | ||||||||
\(961\) | 78.1918 | 2.52232 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −14.2474 | −0.459118 | ||||||||
\(964\) | −41.3939 | −1.33321 | ||||||||
\(965\) | −38.6969 | −1.24570 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −21.5505 | −0.693018 | −0.346509 | − | 0.938047i | \(-0.612633\pi\) | ||||
−0.346509 | + | 0.938047i | \(0.612633\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.44949 | 0.0465643 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22.2929 | 0.715412 | 0.357706 | − | 0.933834i | \(-0.383559\pi\) | ||||
0.357706 | + | 0.933834i | \(0.383559\pi\) | |||||||
\(972\) | −2.00000 | −0.0641500 | ||||||||
\(973\) | −26.6969 | −0.855865 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.00000 | 0.0320256 | ||||||||
\(976\) | −12.4041 | −0.397045 | ||||||||
\(977\) | 26.4495 | 0.846194 | 0.423097 | − | 0.906084i | \(-0.360943\pi\) | ||||
0.423097 | + | 0.906084i | \(0.360943\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −62.6969 | −2.00278 | ||||||||
\(981\) | −6.44949 | −0.205916 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 11.7423 | 0.374523 | 0.187261 | − | 0.982310i | \(-0.440039\pi\) | ||||
0.187261 | + | 0.982310i | \(0.440039\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 59.1464 | 1.88456 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 55.3939 | 1.76321 | ||||||||
\(988\) | 2.00000 | 0.0636285 | ||||||||
\(989\) | 0.101021 | 0.00321227 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −51.5959 | −1.63900 | −0.819499 | − | 0.573080i | \(-0.805748\pi\) | ||||
−0.819499 | + | 0.573080i | \(0.805748\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 33.5959 | 1.06613 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −49.5959 | −1.57230 | ||||||||
\(996\) | 15.1010 | 0.478494 | ||||||||
\(997\) | −60.9898 | −1.93157 | −0.965783 | − | 0.259351i | \(-0.916491\pi\) | ||||
−0.965783 | + | 0.259351i | \(0.916491\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9.89898 | 0.313190 |
(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 | 2001.2.a.e.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 6003.2.a.e.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2001.2.a.e.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
6003.2.a.e.1.1 | 2 | 3.2 | odd | 2 |