Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4032,2,Mod(1,4032)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4032, 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("4032.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4032.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: | \(32.1956820950\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 2016) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4032.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.23607 | 0.552786 | 0.276393 | − | 0.961045i | \(-0.410861\pi\) | ||||
0.276393 | + | 0.961045i | \(0.410861\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.23607 | −0.372689 | −0.186344 | − | 0.982485i | \(-0.559664\pi\) | ||||
−0.186344 | + | 0.982485i | \(0.559664\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.47214 | 1.24035 | 0.620174 | − | 0.784465i | \(-0.287062\pi\) | ||||
0.620174 | + | 0.784465i | \(0.287062\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.23607 | 1.26993 | 0.634967 | − | 0.772540i | \(-0.281014\pi\) | ||||
0.634967 | + | 0.772540i | \(0.281014\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.47214 | −1.48481 | −0.742405 | − | 0.669951i | \(-0.766315\pi\) | ||||
−0.742405 | + | 0.669951i | \(0.766315\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.70820 | −1.60727 | −0.803636 | − | 0.595121i | \(-0.797104\pi\) | ||||
−0.803636 | + | 0.595121i | \(0.797104\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.47214 | −0.694427 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −10.4721 | −1.94463 | −0.972313 | − | 0.233681i | \(-0.924923\pi\) | ||||
−0.972313 | + | 0.233681i | \(0.924923\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.47214 | −1.16243 | −0.581215 | − | 0.813750i | \(-0.697422\pi\) | ||||
−0.581215 | + | 0.813750i | \(0.697422\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.23607 | −0.208934 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.47214 | −0.735215 | −0.367607 | − | 0.929981i | \(-0.619823\pi\) | ||||
−0.367607 | + | 0.929981i | \(0.619823\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.76393 | 0.431654 | 0.215827 | − | 0.976432i | \(-0.430755\pi\) | ||||
0.215827 | + | 0.976432i | \(0.430755\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.94427 | 0.753994 | 0.376997 | − | 0.926214i | \(-0.376957\pi\) | ||||
0.376997 | + | 0.926214i | \(0.376957\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.4721 | 1.52752 | 0.763759 | − | 0.645501i | \(-0.223352\pi\) | ||||
0.763759 | + | 0.645501i | \(0.223352\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.00000 | −1.09888 | −0.549442 | − | 0.835532i | \(-0.685160\pi\) | ||||
−0.549442 | + | 0.835532i | \(0.685160\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.52786 | −0.206017 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.47214 | −0.321845 | −0.160922 | − | 0.986967i | \(-0.551447\pi\) | ||||
−0.160922 | + | 0.986967i | \(0.551447\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.47214 | −0.572598 | −0.286299 | − | 0.958140i | \(-0.592425\pi\) | ||||
−0.286299 | + | 0.958140i | \(0.592425\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.52786 | 0.685647 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.00000 | −0.977356 | −0.488678 | − | 0.872464i | \(-0.662521\pi\) | ||||
−0.488678 | + | 0.872464i | \(0.662521\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.76393 | 0.328018 | 0.164009 | − | 0.986459i | \(-0.447557\pi\) | ||||
0.164009 | + | 0.986459i | \(0.447557\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.94427 | 0.344601 | 0.172300 | − | 0.985044i | \(-0.444880\pi\) | ||||
0.172300 | + | 0.985044i | \(0.444880\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.23607 | 0.140863 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.94427 | 0.556274 | 0.278137 | − | 0.960541i | \(-0.410283\pi\) | ||||
0.278137 | + | 0.960541i | \(0.410283\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.94427 | 0.542704 | 0.271352 | − | 0.962480i | \(-0.412529\pi\) | ||||
0.271352 | + | 0.962480i | \(0.412529\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.47214 | 0.702002 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.7082 | 1.66507 | 0.832533 | − | 0.553975i | \(-0.186890\pi\) | ||||
0.832533 | + | 0.553975i | \(0.186890\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.47214 | −0.468807 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.00000 | −0.820783 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.9443 | 1.11122 | 0.555611 | − | 0.831442i | \(-0.312484\pi\) | ||||
0.555611 | + | 0.831442i | \(0.312484\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.29180 | −0.427050 | −0.213525 | − | 0.976938i | \(-0.568494\pi\) | ||||
−0.213525 | + | 0.976938i | \(0.568494\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.52786 | −0.938808 | −0.469404 | − | 0.882983i | \(-0.655531\pi\) | ||||
−0.469404 | + | 0.882983i | \(0.655531\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.76393 | 0.653894 | 0.326947 | − | 0.945043i | \(-0.393980\pi\) | ||||
0.326947 | + | 0.945043i | \(0.393980\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.94427 | −0.665141 | −0.332570 | − | 0.943078i | \(-0.607916\pi\) | ||||
−0.332570 | + | 0.943078i | \(0.607916\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.94427 | −0.465118 | −0.232559 | − | 0.972582i | \(-0.574710\pi\) | ||||
−0.232559 | + | 0.972582i | \(0.574710\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.52786 | −0.888478 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.23607 | −0.479990 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.47214 | −0.861103 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.4721 | −0.936656 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.8885 | −1.58735 | −0.793676 | − | 0.608341i | \(-0.791835\pi\) | ||||
−0.793676 | + | 0.608341i | \(0.791835\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.0000 | −1.39793 | −0.698963 | − | 0.715158i | \(-0.746355\pi\) | ||||
−0.698963 | + | 0.715158i | \(0.746355\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.47214 | 0.561205 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.4721 | 0.894695 | 0.447347 | − | 0.894360i | \(-0.352369\pi\) | ||||
0.447347 | + | 0.894360i | \(0.352369\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.9443 | −1.09792 | −0.548959 | − | 0.835849i | \(-0.684976\pi\) | ||||
−0.548959 | + | 0.835849i | \(0.684976\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.52786 | −0.462263 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −12.9443 | −1.07496 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −17.8885 | −1.46549 | −0.732743 | − | 0.680505i | \(-0.761760\pi\) | ||||
−0.732743 | + | 0.680505i | \(0.761760\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −20.9443 | −1.70442 | −0.852210 | − | 0.523199i | \(-0.824738\pi\) | ||||
−0.852210 | + | 0.523199i | \(0.824738\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.00000 | −0.642575 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.52786 | −0.600789 | −0.300394 | − | 0.953815i | \(-0.597118\pi\) | ||||
−0.300394 | + | 0.953815i | \(0.597118\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.70820 | 0.607492 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.00000 | −0.626608 | −0.313304 | − | 0.949653i | \(-0.601436\pi\) | ||||
−0.313304 | + | 0.949653i | \(0.601436\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 15.4164 | 1.19296 | 0.596479 | − | 0.802629i | \(-0.296566\pi\) | ||||
0.596479 | + | 0.802629i | \(0.296566\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.00000 | 0.538462 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.29180 | −0.326299 | −0.163150 | − | 0.986601i | \(-0.552165\pi\) | ||||
−0.163150 | + | 0.986601i | \(0.552165\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.47214 | 0.262469 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 22.1803 | 1.65784 | 0.828918 | − | 0.559370i | \(-0.188957\pi\) | ||||
0.828918 | + | 0.559370i | \(0.188957\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.472136 | −0.0350936 | −0.0175468 | − | 0.999846i | \(-0.505586\pi\) | ||||
−0.0175468 | + | 0.999846i | \(0.505586\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.52786 | −0.406417 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.47214 | −0.473289 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.65248 | 0.336641 | 0.168321 | − | 0.985732i | \(-0.446166\pi\) | ||||
0.168321 | + | 0.985732i | \(0.446166\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.52786 | 0.253941 | 0.126971 | − | 0.991906i | \(-0.459475\pi\) | ||||
0.126971 | + | 0.991906i | \(0.459475\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.9443 | 0.922241 | 0.461121 | − | 0.887337i | \(-0.347448\pi\) | ||||
0.461121 | + | 0.887337i | \(0.347448\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.00000 | −0.567105 | −0.283552 | − | 0.958957i | \(-0.591513\pi\) | ||||
−0.283552 | + | 0.958957i | \(0.591513\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 10.4721 | 0.735000 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.41641 | 0.238612 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.00000 | 0.553372 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −24.0000 | −1.65223 | −0.826114 | − | 0.563503i | \(-0.809453\pi\) | ||||
−0.826114 | + | 0.563503i | \(0.809453\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.11146 | 0.416798 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.47214 | 0.439357 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 23.4164 | 1.57516 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.94427 | 0.331093 | 0.165546 | − | 0.986202i | \(-0.447061\pi\) | ||||
0.165546 | + | 0.986202i | \(0.447061\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 28.3607 | 1.88236 | 0.941182 | − | 0.337899i | \(-0.109716\pi\) | ||||
0.941182 | + | 0.337899i | \(0.109716\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.52786 | −0.233128 | −0.116564 | − | 0.993183i | \(-0.537188\pi\) | ||||
−0.116564 | + | 0.993183i | \(0.537188\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −20.3607 | −1.33387 | −0.666936 | − | 0.745115i | \(-0.732395\pi\) | ||||
−0.666936 | + | 0.745115i | \(0.732395\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.9443 | 0.844391 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.2361 | 0.856170 | 0.428085 | − | 0.903738i | \(-0.359188\pi\) | ||||
0.428085 | + | 0.903738i | \(0.359188\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −27.8885 | −1.79646 | −0.898230 | − | 0.439527i | \(-0.855146\pi\) | ||||
−0.898230 | + | 0.439527i | \(0.855146\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.23607 | 0.0789695 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −28.9443 | −1.84168 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −23.4164 | −1.47803 | −0.739015 | − | 0.673689i | \(-0.764709\pi\) | ||||
−0.739015 | + | 0.673689i | \(0.764709\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.52786 | 0.599012 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −16.2918 | −1.01625 | −0.508127 | − | 0.861282i | \(-0.669662\pi\) | ||||
−0.508127 | + | 0.861282i | \(0.669662\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.47214 | 0.277885 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.81966 | −0.358856 | −0.179428 | − | 0.983771i | \(-0.557425\pi\) | ||||
−0.179428 | + | 0.983771i | \(0.557425\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.88854 | −0.607448 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.23607 | 0.0753644 | 0.0376822 | − | 0.999290i | \(-0.488003\pi\) | ||||
0.0376822 | + | 0.999290i | \(0.488003\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.4164 | 1.17946 | 0.589731 | − | 0.807599i | \(-0.299234\pi\) | ||||
0.589731 | + | 0.807599i | \(0.299234\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.29180 | 0.258805 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.4721 | 1.23005 | 0.615026 | − | 0.788507i | \(-0.289146\pi\) | ||||
0.615026 | + | 0.788507i | \(0.289146\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.4164 | 0.919666 | 0.459833 | − | 0.888005i | \(-0.347909\pi\) | ||||
0.459833 | + | 0.888005i | \(0.347909\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.47214 | 0.384729 | 0.192364 | − | 0.981324i | \(-0.438384\pi\) | ||||
0.192364 | + | 0.981324i | \(0.438384\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.76393 | −0.163150 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.4164 | 0.612730 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.81966 | 0.573671 | 0.286835 | − | 0.957980i | \(-0.407397\pi\) | ||||
0.286835 | + | 0.957980i | \(0.407397\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.05573 | −0.177911 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −34.4721 | −1.99358 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.94427 | −0.284983 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.52786 | −0.316525 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.52786 | −0.543784 | −0.271892 | − | 0.962328i | \(-0.587649\pi\) | ||||
−0.271892 | + | 0.962328i | \(0.587649\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.4164 | −0.874184 | −0.437092 | − | 0.899417i | \(-0.643992\pi\) | ||||
−0.437092 | + | 0.899417i | \(0.643992\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.8885 | 1.12417 | 0.562083 | − | 0.827081i | \(-0.310000\pi\) | ||||
0.562083 | + | 0.827081i | \(0.310000\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.05573 | 0.171627 | 0.0858134 | − | 0.996311i | \(-0.472651\pi\) | ||||
0.0858134 | + | 0.996311i | \(0.472651\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.9443 | 0.724740 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −33.8885 | −1.88561 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −15.5279 | −0.861331 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −10.4721 | −0.577348 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.8885 | −0.983243 | −0.491622 | − | 0.870809i | \(-0.663596\pi\) | ||||
−0.491622 | + | 0.870809i | \(0.663596\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −9.88854 | −0.540269 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.8885 | 1.30129 | 0.650646 | − | 0.759381i | \(-0.274498\pi\) | ||||
0.650646 | + | 0.759381i | \(0.274498\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.00000 | 0.433224 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 25.2361 | 1.35474 | 0.677372 | − | 0.735641i | \(-0.263119\pi\) | ||||
0.677372 | + | 0.735641i | \(0.263119\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.5279 | 0.617072 | 0.308536 | − | 0.951213i | \(-0.400161\pi\) | ||||
0.308536 | + | 0.951213i | \(0.400161\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.1803 | 0.541845 | 0.270922 | − | 0.962601i | \(-0.412671\pi\) | ||||
0.270922 | + | 0.962601i | \(0.412671\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.41641 | 0.181324 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −21.2361 | −1.12080 | −0.560398 | − | 0.828223i | \(-0.689352\pi\) | ||||
−0.560398 | + | 0.828223i | \(0.689352\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 22.8885 | 1.20466 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.63932 | 0.190491 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.00000 | 0.417597 | 0.208798 | − | 0.977959i | \(-0.433045\pi\) | ||||
0.208798 | + | 0.977959i | \(0.433045\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.00000 | 0.415339 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −23.8885 | −1.23690 | −0.618451 | − | 0.785823i | \(-0.712239\pi\) | ||||
−0.618451 | + | 0.785823i | \(0.712239\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −46.8328 | −2.41201 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.0000 | 1.23280 | 0.616399 | − | 0.787434i | \(-0.288591\pi\) | ||||
0.616399 | + | 0.787434i | \(0.288591\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 32.0000 | 1.63512 | 0.817562 | − | 0.575841i | \(-0.195325\pi\) | ||||
0.817562 | + | 0.575841i | \(0.195325\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.52786 | 0.0778672 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.4721 | −0.530958 | −0.265479 | − | 0.964117i | \(-0.585530\pi\) | ||||
−0.265479 | + | 0.964117i | \(0.585530\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −40.3607 | −2.04113 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.11146 | 0.307501 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.47214 | 0.425204 | 0.212602 | − | 0.977139i | \(-0.431806\pi\) | ||||
0.212602 | + | 0.977139i | \(0.431806\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −26.4721 | −1.32196 | −0.660978 | − | 0.750406i | \(-0.729858\pi\) | ||||
−0.660978 | + | 0.750406i | \(0.729858\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −28.9443 | −1.44182 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.52786 | 0.274006 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −26.0000 | −1.28562 | −0.642809 | − | 0.766027i | \(-0.722231\pi\) | ||||
−0.642809 | + | 0.766027i | \(0.722231\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.47214 | 0.121646 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.11146 | 0.300000 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.47214 | −0.120772 | −0.0603859 | − | 0.998175i | \(-0.519233\pi\) | ||||
−0.0603859 | + | 0.998175i | \(0.519233\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.41641 | −0.263980 | −0.131990 | − | 0.991251i | \(-0.542137\pi\) | ||||
−0.131990 | + | 0.991251i | \(0.542137\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −18.1803 | −0.881876 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.47214 | 0.216422 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −31.1246 | −1.49922 | −0.749610 | − | 0.661880i | \(-0.769759\pi\) | ||||
−0.749610 | + | 0.661880i | \(0.769759\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.00000 | 0.0961139 | 0.0480569 | − | 0.998845i | \(-0.484697\pi\) | ||||
0.0480569 | + | 0.998845i | \(0.484697\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 49.8885 | 2.38649 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −30.8328 | −1.47157 | −0.735785 | − | 0.677215i | \(-0.763187\pi\) | ||||
−0.735785 | + | 0.677215i | \(0.763187\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 30.1803 | 1.43391 | 0.716956 | − | 0.697119i | \(-0.245535\pi\) | ||||
0.716956 | + | 0.697119i | \(0.245535\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 19.4164 | 0.920426 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.94427 | −0.233335 | −0.116667 | − | 0.993171i | \(-0.537221\pi\) | ||||
−0.116667 | + | 0.993171i | \(0.537221\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.41641 | −0.160872 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.52786 | −0.259150 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −35.8885 | −1.67880 | −0.839398 | − | 0.543518i | \(-0.817092\pi\) | ||||
−0.839398 | + | 0.543518i | \(0.817092\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.70820 | 0.172708 | 0.0863541 | − | 0.996265i | \(-0.472478\pi\) | ||||
0.0863541 | + | 0.996265i | \(0.472478\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.8885 | 0.831351 | 0.415676 | − | 0.909513i | \(-0.363545\pi\) | ||||
0.415676 | + | 0.909513i | \(0.363545\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −34.4721 | −1.59518 | −0.797590 | − | 0.603200i | \(-0.793892\pi\) | ||||
−0.797590 | + | 0.603200i | \(0.793892\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.00000 | 0.369406 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.11146 | −0.281005 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 22.4721 | 1.03109 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.583592 | −0.0266650 | −0.0133325 | − | 0.999911i | \(-0.504244\pi\) | ||||
−0.0133325 | + | 0.999911i | \(0.504244\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20.0000 | −0.911922 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 13.5279 | 0.614269 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 30.8328 | 1.39717 | 0.698584 | − | 0.715528i | \(-0.253814\pi\) | ||||
0.698584 | + | 0.715528i | \(0.253814\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.0689 | 0.725179 | 0.362589 | − | 0.931949i | \(-0.381893\pi\) | ||||
0.362589 | + | 0.931949i | \(0.381893\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −54.8328 | −2.46955 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.76393 | −0.123979 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11.0557 | −0.494922 | −0.247461 | − | 0.968898i | \(-0.579596\pi\) | ||||
−0.247461 | + | 0.968898i | \(0.579596\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 11.0557 | 0.492951 | 0.246475 | − | 0.969149i | \(-0.420728\pi\) | ||||
0.246475 | + | 0.969149i | \(0.420728\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.30495 | −0.236067 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 35.1246 | 1.55687 | 0.778436 | − | 0.627725i | \(-0.216014\pi\) | ||||
0.778436 | + | 0.627725i | \(0.216014\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.94427 | −0.130247 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11.7771 | −0.518960 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12.9443 | −0.569288 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.1246 | 0.662621 | 0.331311 | − | 0.943522i | \(-0.392509\pi\) | ||||
0.331311 | + | 0.943522i | \(0.392509\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.0000 | 0.699631 | 0.349816 | − | 0.936819i | \(-0.386244\pi\) | ||||
0.349816 | + | 0.936819i | \(0.386244\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −33.8885 | −1.47621 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 36.4164 | 1.58332 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.3607 | 0.535400 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.36068 | 0.361464 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.23607 | −0.0532412 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.36068 | 0.273467 | 0.136733 | − | 0.990608i | \(-0.456340\pi\) | ||||
0.136733 | + | 0.990608i | \(0.456340\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.58359 | −0.367681 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.8328 | −0.634205 | −0.317103 | − | 0.948391i | \(-0.602710\pi\) | ||||
−0.317103 | + | 0.948391i | \(0.602710\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 67.7771 | 2.88740 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.94427 | −0.210252 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.05573 | 0.129475 | 0.0647377 | − | 0.997902i | \(-0.479379\pi\) | ||||
0.0647377 | + | 0.997902i | \(0.479379\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 22.1115 | 0.935215 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −33.3050 | −1.40364 | −0.701818 | − | 0.712356i | \(-0.747628\pi\) | ||||
−0.701818 | + | 0.712356i | \(0.747628\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.11146 | −0.257111 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 26.4721 | 1.10977 | 0.554885 | − | 0.831927i | \(-0.312762\pi\) | ||||
0.554885 | + | 0.831927i | \(0.312762\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.0557 | 0.462668 | 0.231334 | − | 0.972874i | \(-0.425691\pi\) | ||||
0.231334 | + | 0.972874i | \(0.425691\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 26.7639 | 1.11613 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −30.0000 | −1.24892 | −0.624458 | − | 0.781058i | \(-0.714680\pi\) | ||||
−0.624458 | + | 0.781058i | \(0.714680\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.94427 | −0.205123 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.88854 | 0.409542 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.41641 | 0.306108 | 0.153054 | − | 0.988218i | \(-0.451089\pi\) | ||||
0.153054 | + | 0.988218i | \(0.451089\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 41.8885 | 1.72599 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 23.1246 | 0.949614 | 0.474807 | − | 0.880090i | \(-0.342518\pi\) | ||||
0.474807 | + | 0.880090i | \(0.342518\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.47214 | −0.265332 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −29.2361 | −1.19455 | −0.597277 | − | 0.802035i | \(-0.703751\pi\) | ||||
−0.597277 | + | 0.802035i | \(0.703751\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 35.8885 | 1.46392 | 0.731962 | − | 0.681345i | \(-0.238605\pi\) | ||||
0.731962 | + | 0.681345i | \(0.238605\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −11.7082 | −0.476006 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.0557 | 0.448738 | 0.224369 | − | 0.974504i | \(-0.427968\pi\) | ||||
0.224369 | + | 0.974504i | \(0.427968\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 46.8328 | 1.89465 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 40.8328 | 1.64922 | 0.824611 | − | 0.565700i | \(-0.191394\pi\) | ||||
0.824611 | + | 0.565700i | \(0.191394\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −37.5279 | −1.51081 | −0.755407 | − | 0.655255i | \(-0.772561\pi\) | ||||
−0.755407 | + | 0.655255i | \(0.772561\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 28.9443 | 1.16337 | 0.581684 | − | 0.813415i | \(-0.302394\pi\) | ||||
0.581684 | + | 0.813415i | \(0.302394\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −15.7082 | −0.629336 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.41641 | 0.176656 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −23.4164 | −0.933673 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.8885 | 0.712132 | 0.356066 | − | 0.934461i | \(-0.384118\pi\) | ||||
0.356066 | + | 0.934461i | \(0.384118\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −22.1115 | −0.877466 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.47214 | 0.177192 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −30.2492 | −1.19477 | −0.597386 | − | 0.801954i | \(-0.703794\pi\) | ||||
−0.597386 | + | 0.801954i | \(0.703794\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.41641 | 0.134730 | 0.0673650 | − | 0.997728i | \(-0.478541\pi\) | ||||
0.0673650 | + | 0.997728i | \(0.478541\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −21.5279 | −0.846348 | −0.423174 | − | 0.906049i | \(-0.639084\pi\) | ||||
−0.423174 | + | 0.906049i | \(0.639084\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.05573 | 0.119948 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15.4164 | 0.603291 | 0.301645 | − | 0.953420i | \(-0.402464\pi\) | ||||
0.301645 | + | 0.953420i | \(0.402464\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −19.7771 | −0.772755 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.652476 | 0.0254169 | 0.0127084 | − | 0.999919i | \(-0.495955\pi\) | ||||
0.0127084 | + | 0.999919i | \(0.495955\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.5279 | −0.603964 | −0.301982 | − | 0.953314i | \(-0.597648\pi\) | ||||
−0.301982 | + | 0.953314i | \(0.597648\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.00000 | 0.310227 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 80.7214 | 3.12554 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.52786 | 0.213401 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19.3050 | −0.744151 | −0.372076 | − | 0.928202i | \(-0.621354\pi\) | ||||
−0.372076 | + | 0.928202i | \(0.621354\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −45.0132 | −1.73000 | −0.864998 | − | 0.501775i | \(-0.832680\pi\) | ||||
−0.864998 | + | 0.501775i | \(0.832680\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.9443 | −0.420003 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 14.1803 | 0.542596 | 0.271298 | − | 0.962495i | \(-0.412547\pi\) | ||||
0.271298 | + | 0.962495i | \(0.412547\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.9443 | 0.494575 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −35.7771 | −1.36300 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.11146 | −0.232491 | −0.116245 | − | 0.993221i | \(-0.537086\pi\) | ||||
−0.116245 | + | 0.993221i | \(0.537086\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −16.0000 | −0.606915 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.4721 | 0.548171 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −15.4164 | −0.582270 | −0.291135 | − | 0.956682i | \(-0.594033\pi\) | ||||
−0.291135 | + | 0.956682i | \(0.594033\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 28.9443 | 1.09165 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.29180 | 0.161410 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14.9443 | −0.561244 | −0.280622 | − | 0.959818i | \(-0.590541\pi\) | ||||
−0.280622 | + | 0.959818i | \(0.590541\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 49.8885 | 1.86834 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.83282 | −0.255533 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 36.9443 | 1.37779 | 0.688894 | − | 0.724862i | \(-0.258096\pi\) | ||||
0.688894 | + | 0.724862i | \(0.258096\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.52786 | 0.354836 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 36.3607 | 1.35040 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.3607 | 1.20019 | 0.600096 | − | 0.799928i | \(-0.295129\pi\) | ||||
0.600096 | + | 0.799928i | \(0.295129\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 25.8885 | 0.957522 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15.3050 | −0.565301 | −0.282651 | − | 0.959223i | \(-0.591214\pi\) | ||||
−0.282651 | + | 0.959223i | \(0.591214\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9.88854 | 0.364249 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 40.0000 | 1.47142 | 0.735712 | − | 0.677295i | \(-0.236848\pi\) | ||||
0.735712 | + | 0.677295i | \(0.236848\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 35.4853 | 1.30183 | 0.650915 | − | 0.759151i | \(-0.274386\pi\) | ||||
0.650915 | + | 0.759151i | \(0.274386\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −22.1115 | −0.810101 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.76393 | −0.247149 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.0000 | 0.875772 | 0.437886 | − | 0.899030i | \(-0.355727\pi\) | ||||
0.437886 | + | 0.899030i | \(0.355727\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −25.8885 | −0.942181 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.05573 | 0.0383711 | 0.0191855 | − | 0.999816i | \(-0.493893\pi\) | ||||
0.0191855 | + | 0.999816i | \(0.493893\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10.1803 | −0.369037 | −0.184519 | − | 0.982829i | \(-0.559073\pi\) | ||||
−0.184519 | + | 0.982829i | \(0.559073\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.94427 | 0.251400 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −11.0557 | −0.399199 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.88854 | −0.284468 | −0.142234 | − | 0.989833i | \(-0.545429\pi\) | ||||
−0.142234 | + | 0.989833i | \(0.545429\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −25.2361 | −0.907678 | −0.453839 | − | 0.891084i | \(-0.649946\pi\) | ||||
−0.453839 | + | 0.891084i | \(0.649946\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 22.4721 | 0.807223 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −17.8885 | −0.640924 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.41641 | −0.122249 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9.30495 | −0.332108 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −54.8328 | −1.95458 | −0.977289 | − | 0.211909i | \(-0.932032\pi\) | ||||
−0.977289 | + | 0.211909i | \(0.932032\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.94427 | 0.175798 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −20.0000 | −0.710221 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 32.6525 | 1.15661 | 0.578305 | − | 0.815821i | \(-0.303714\pi\) | ||||
0.578305 | + | 0.815821i | \(0.303714\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 54.8328 | 1.93985 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.63932 | −0.128429 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.52786 | 0.335813 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 32.0000 | 1.12506 | 0.562530 | − | 0.826777i | \(-0.309828\pi\) | ||||
0.562530 | + | 0.826777i | \(0.309828\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 41.8885 | 1.47091 | 0.735453 | − | 0.677576i | \(-0.236969\pi\) | ||||
0.735453 | + | 0.677576i | \(0.236969\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.88854 | −0.346381 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −32.0000 | −1.11954 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −19.0557 | −0.665049 | −0.332525 | − | 0.943095i | \(-0.607900\pi\) | ||||
−0.332525 | + | 0.943095i | \(0.607900\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −36.9443 | −1.28780 | −0.643898 | − | 0.765111i | \(-0.722684\pi\) | ||||
−0.643898 | + | 0.765111i | \(0.722684\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −38.1803 | −1.32766 | −0.663830 | − | 0.747883i | \(-0.731070\pi\) | ||||
−0.663830 | + | 0.747883i | \(0.731070\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −40.4721 | −1.40566 | −0.702828 | − | 0.711360i | \(-0.748080\pi\) | ||||
−0.702828 | + | 0.711360i | \(0.748080\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.23607 | 0.181419 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 19.0557 | 0.659451 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −5.52786 | −0.190843 | −0.0954215 | − | 0.995437i | \(-0.530420\pi\) | ||||
−0.0954215 | + | 0.995437i | \(0.530420\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 80.6656 | 2.78157 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8.65248 | 0.297654 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.47214 | 0.325466 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 34.4721 | 1.18169 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 45.4164 | 1.55503 | 0.777514 | − | 0.628866i | \(-0.216480\pi\) | ||||
0.777514 | + | 0.628866i | \(0.216480\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −10.1803 | −0.347754 | −0.173877 | − | 0.984767i | \(-0.555629\pi\) | ||||
−0.173877 | + | 0.984767i | \(0.555629\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.5279 | 0.870999 | 0.435500 | − | 0.900189i | \(-0.356572\pi\) | ||||
0.435500 | + | 0.900189i | \(0.356572\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −21.8197 | −0.742750 | −0.371375 | − | 0.928483i | \(-0.621114\pi\) | ||||
−0.371375 | + | 0.928483i | \(0.621114\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.30495 | −0.180374 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.11146 | −0.207317 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −35.7771 | −1.21226 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10.4721 | 0.354023 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −44.8328 | −1.51390 | −0.756948 | − | 0.653475i | \(-0.773311\pi\) | ||||
−0.756948 | + | 0.653475i | \(0.773311\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 39.1246 | 1.31814 | 0.659071 | − | 0.752081i | \(-0.270950\pi\) | ||||
0.659071 | + | 0.752081i | \(0.270950\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.94427 | 0.166388 | 0.0831940 | − | 0.996533i | \(-0.473488\pi\) | ||||
0.0831940 | + | 0.996533i | \(0.473488\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 21.5279 | 0.722835 | 0.361417 | − | 0.932404i | \(-0.382293\pi\) | ||||
0.361417 | + | 0.932404i | \(0.382293\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 17.8885 | 0.599963 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −67.7771 | −2.26807 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 27.4164 | 0.916429 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 67.7771 | 2.26049 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −41.8885 | −1.39551 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.583592 | −0.0193993 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.94427 | −0.164172 | −0.0820859 | − | 0.996625i | \(-0.526158\pi\) | ||||
−0.0820859 | + | 0.996625i | \(0.526158\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15.1246 | −0.501101 | −0.250550 | − | 0.968104i | \(-0.580612\pi\) | ||||
−0.250550 | + | 0.968104i | \(0.580612\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.11146 | −0.202260 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 16.0000 | 0.528367 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 27.0557 | 0.892486 | 0.446243 | − | 0.894912i | \(-0.352762\pi\) | ||||
0.446243 | + | 0.894912i | \(0.352762\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 12.3607 | 0.406857 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15.5279 | 0.510553 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 50.7639 | 1.66551 | 0.832755 | − | 0.553641i | \(-0.186762\pi\) | ||||
0.832755 | + | 0.553641i | \(0.186762\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.47214 | −0.212116 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.00000 | −0.261628 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.94427 | −0.0961852 | −0.0480926 | − | 0.998843i | \(-0.515314\pi\) | ||||
−0.0480926 | + | 0.998843i | \(0.515314\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −52.4296 | −1.70915 | −0.854577 | − | 0.519324i | \(-0.826184\pi\) | ||||
−0.854577 | + | 0.519324i | \(0.826184\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −21.3050 | −0.693785 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −11.1246 | −0.361501 | −0.180751 | − | 0.983529i | \(-0.557853\pi\) | ||||
−0.180751 | + | 0.983529i | \(0.557853\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 13.1672 | 0.427425 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 51.7771 | 1.67722 | 0.838612 | − | 0.544729i | \(-0.183367\pi\) | ||||
0.838612 | + | 0.544729i | \(0.183367\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.75078 | 0.186091 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −10.4721 | −0.338163 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.8885 | 0.351243 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.36068 | 0.140375 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −59.7771 | −1.92230 | −0.961151 | − | 0.276024i | \(-0.910983\pi\) | ||||
−0.961151 | + | 0.276024i | \(0.910983\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −25.8885 | −0.830803 | −0.415401 | − | 0.909638i | \(-0.636359\pi\) | ||||
−0.415401 | + | 0.909638i | \(0.636359\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.9443 | 0.414974 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 30.2492 | 0.967758 | 0.483879 | − | 0.875135i | \(-0.339227\pi\) | ||||
0.483879 | + | 0.875135i | \(0.339227\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −19.4164 | −0.620551 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.94427 | −0.157698 | −0.0788489 | − | 0.996887i | \(-0.525124\pi\) | ||||
−0.0788489 | + | 0.996887i | \(0.525124\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 16.0000 | 0.509802 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −38.1115 | −1.21187 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 62.8328 | 1.99595 | 0.997975 | − | 0.0636060i | \(-0.0202601\pi\) | ||||
0.997975 | + | 0.0636060i | \(0.0202601\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.88854 | −0.313488 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.63932 | −0.178599 | −0.0892995 | − | 0.996005i | \(-0.528463\pi\) | ||||
−0.0892995 | + | 0.996005i | \(0.528463\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4032.2.a.bo.1.2 | 2 | ||
3.2 | odd | 2 | 4032.2.a.bu.1.1 | 2 | |||
4.3 | odd | 2 | 4032.2.a.bp.1.2 | 2 | |||
8.3 | odd | 2 | 2016.2.a.v.1.1 | yes | 2 | ||
8.5 | even | 2 | 2016.2.a.u.1.1 | yes | 2 | ||
12.11 | even | 2 | 4032.2.a.bx.1.1 | 2 | |||
24.5 | odd | 2 | 2016.2.a.p.1.2 | ✓ | 2 | ||
24.11 | even | 2 | 2016.2.a.q.1.2 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2016.2.a.p.1.2 | ✓ | 2 | 24.5 | odd | 2 | ||
2016.2.a.q.1.2 | yes | 2 | 24.11 | even | 2 | ||
2016.2.a.u.1.1 | yes | 2 | 8.5 | even | 2 | ||
2016.2.a.v.1.1 | yes | 2 | 8.3 | odd | 2 | ||
4032.2.a.bo.1.2 | 2 | 1.1 | even | 1 | trivial | ||
4032.2.a.bp.1.2 | 2 | 4.3 | odd | 2 | |||
4032.2.a.bu.1.1 | 2 | 3.2 | odd | 2 | |||
4032.2.a.bx.1.1 | 2 | 12.11 | even | 2 |