Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8064,2,Mod(1,8064)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8064, 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("8064.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8064 = 2^{7} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8064.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: | \(64.3913641900\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.316.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 896) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.81361\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8064.1 |
$q$-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 | ||||||||
\(5\) | 2.52444 | 1.12896 | 0.564481 | − | 0.825446i | \(-0.309076\pi\) | ||||
0.564481 | + | 0.825446i | \(0.309076\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.62721 | −1.09365 | −0.546823 | − | 0.837248i | \(-0.684163\pi\) | ||||
−0.546823 | + | 0.837248i | \(0.684163\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.72999 | 1.31186 | 0.655931 | − | 0.754821i | \(-0.272276\pi\) | ||||
0.655931 | + | 0.754821i | \(0.272276\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.20555 | −1.02000 | −0.509998 | − | 0.860176i | \(-0.670354\pi\) | ||||
−0.509998 | + | 0.860176i | \(0.670354\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.10278 | −1.62949 | −0.814744 | − | 0.579821i | \(-0.803123\pi\) | ||||
−0.814744 | + | 0.579821i | \(0.803123\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.578337 | 0.120592 | 0.0602958 | − | 0.998181i | \(-0.480796\pi\) | ||||
0.0602958 | + | 0.998181i | \(0.480796\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.37279 | 0.274557 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.20555 | 1.52373 | 0.761866 | − | 0.647734i | \(-0.224283\pi\) | ||||
0.761866 | + | 0.647734i | \(0.224283\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.04888 | −0.906805 | −0.453402 | − | 0.891306i | \(-0.649790\pi\) | ||||
−0.453402 | + | 0.891306i | \(0.649790\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.52444 | −0.426708 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.04888 | 0.501232 | 0.250616 | − | 0.968087i | \(-0.419367\pi\) | ||||
0.250616 | + | 0.968087i | \(0.419367\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.205550 | 0.0321015 | 0.0160508 | − | 0.999871i | \(-0.494891\pi\) | ||||
0.0160508 | + | 0.999871i | \(0.494891\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.78389 | 0.729536 | 0.364768 | − | 0.931098i | \(-0.381148\pi\) | ||||
0.364768 | + | 0.931098i | \(0.381148\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.20555 | 0.905173 | 0.452586 | − | 0.891721i | \(-0.350501\pi\) | ||||
0.452586 | + | 0.891721i | \(0.350501\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.00000 | −0.274721 | −0.137361 | − | 0.990521i | \(-0.543862\pi\) | ||||
−0.137361 | + | 0.990521i | \(0.543862\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −9.15667 | −1.23469 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −12.5628 | −1.63553 | −0.817765 | − | 0.575552i | \(-0.804787\pi\) | ||||
−0.817765 | + | 0.575552i | \(0.804787\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.5244 | −1.34752 | −0.673758 | − | 0.738952i | \(-0.735321\pi\) | ||||
−0.673758 | + | 0.738952i | \(0.735321\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 11.9406 | 1.48104 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.57834 | 0.803672 | 0.401836 | − | 0.915712i | \(-0.368372\pi\) | ||||
0.401836 | + | 0.915712i | \(0.368372\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.25443 | −1.08315 | −0.541574 | − | 0.840653i | \(-0.682172\pi\) | ||||
−0.541574 | + | 0.840653i | \(0.682172\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.62721 | 0.413359 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.15667 | −0.580171 | −0.290086 | − | 0.957001i | \(-0.593684\pi\) | ||||
−0.290086 | + | 0.957001i | \(0.593684\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.94610 | −0.652669 | −0.326335 | − | 0.945254i | \(-0.605814\pi\) | ||||
−0.326335 | + | 0.945254i | \(0.605814\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.6167 | −1.15154 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.4111 | 1.10357 | 0.551787 | − | 0.833985i | \(-0.313946\pi\) | ||||
0.551787 | + | 0.833985i | \(0.313946\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.72999 | −0.495837 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −17.9305 | −1.83963 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.36222 | −0.950590 | −0.475295 | − | 0.879827i | \(-0.657659\pi\) | ||||
−0.475295 | + | 0.879827i | \(0.657659\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.31889 | 0.429745 | 0.214873 | − | 0.976642i | \(-0.431066\pi\) | ||||
0.214873 | + | 0.976642i | \(0.431066\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.04888 | −0.497481 | −0.248740 | − | 0.968570i | \(-0.580017\pi\) | ||||
−0.248740 | + | 0.968570i | \(0.580017\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.83276 | 0.950569 | 0.475285 | − | 0.879832i | \(-0.342345\pi\) | ||||
0.475285 | + | 0.879832i | \(0.342345\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −19.4600 | −1.86393 | −0.931964 | − | 0.362551i | \(-0.881906\pi\) | ||||
−0.931964 | + | 0.362551i | \(0.881906\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.78389 | −0.826319 | −0.413159 | − | 0.910659i | \(-0.635575\pi\) | ||||
−0.413159 | + | 0.910659i | \(0.635575\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.45998 | 0.136143 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.20555 | 0.385522 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.15667 | 0.196061 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.15667 | −0.818998 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.6761 | −1.30229 | −0.651146 | − | 0.758952i | \(-0.725712\pi\) | ||||
−0.651146 | + | 0.758952i | \(0.725712\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.15165 | 0.362731 | 0.181366 | − | 0.983416i | \(-0.441948\pi\) | ||||
0.181366 | + | 0.983416i | \(0.441948\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.10278 | 0.615889 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.25443 | −0.448916 | −0.224458 | − | 0.974484i | \(-0.572061\pi\) | ||||
−0.224458 | + | 0.974484i | \(0.572061\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.89722 | −0.754653 | −0.377326 | − | 0.926080i | \(-0.623157\pi\) | ||||
−0.377326 | + | 0.926080i | \(0.623157\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −17.1567 | −1.43471 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 20.7144 | 1.72024 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 21.6655 | 1.77491 | 0.887455 | − | 0.460895i | \(-0.152472\pi\) | ||||
0.887455 | + | 0.460895i | \(0.152472\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.98944 | 0.406035 | 0.203017 | − | 0.979175i | \(-0.434925\pi\) | ||||
0.203017 | + | 0.979175i | \(0.434925\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −12.7456 | −1.02375 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −20.0922 | −1.60353 | −0.801767 | − | 0.597637i | \(-0.796106\pi\) | ||||
−0.801767 | + | 0.597637i | \(0.796106\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.578337 | −0.0455793 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.0383 | −1.25622 | −0.628109 | − | 0.778126i | \(-0.716171\pi\) | ||||
−0.628109 | + | 0.778126i | \(0.716171\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.79445 | 0.138859 | 0.0694294 | − | 0.997587i | \(-0.477882\pi\) | ||||
0.0694294 | + | 0.997587i | \(0.477882\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.37279 | 0.720984 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −22.8277 | −1.73556 | −0.867780 | − | 0.496948i | \(-0.834454\pi\) | ||||
−0.867780 | + | 0.496948i | \(0.834454\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.37279 | −0.103773 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.51941 | 0.263053 | 0.131527 | − | 0.991313i | \(-0.458012\pi\) | ||||
0.131527 | + | 0.991313i | \(0.458012\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.9355 | 0.812832 | 0.406416 | − | 0.913688i | \(-0.366778\pi\) | ||||
0.406416 | + | 0.913688i | \(0.366778\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.69670 | 0.565872 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.2544 | 1.11551 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.745574 | −0.0539478 | −0.0269739 | − | 0.999636i | \(-0.508587\pi\) | ||||
−0.0269739 | + | 0.999636i | \(0.508587\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.1361 | −1.01754 | −0.508768 | − | 0.860904i | \(-0.669899\pi\) | ||||
−0.508768 | + | 0.860904i | \(0.669899\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.0000 | −0.712470 | −0.356235 | − | 0.934396i | \(-0.615940\pi\) | ||||
−0.356235 | + | 0.934396i | \(0.615940\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.637776 | 0.0452107 | 0.0226054 | − | 0.999744i | \(-0.492804\pi\) | ||||
0.0226054 | + | 0.999744i | \(0.492804\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.20555 | −0.575917 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.518898 | 0.0362414 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 25.7633 | 1.78208 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.676089 | 0.0465439 | 0.0232719 | − | 0.999729i | \(-0.492592\pi\) | ||||
0.0232719 | + | 0.999729i | \(0.492592\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 12.0766 | 0.823619 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.04888 | 0.342740 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −19.8922 | −1.33809 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 23.6655 | 1.58476 | 0.792380 | − | 0.610027i | \(-0.208842\pi\) | ||||
0.792380 | + | 0.610027i | \(0.208842\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.89722 | −0.590530 | −0.295265 | − | 0.955415i | \(-0.595408\pi\) | ||||
−0.295265 | + | 0.955415i | \(0.595408\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.68111 | −0.507582 | −0.253791 | − | 0.967259i | \(-0.581678\pi\) | ||||
−0.253791 | + | 0.967259i | \(0.581678\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.66553 | −0.371161 | −0.185580 | − | 0.982629i | \(-0.559417\pi\) | ||||
−0.185580 | + | 0.982629i | \(0.559417\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 15.6655 | 1.02191 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.4217 | 0.738806 | 0.369403 | − | 0.929269i | \(-0.379562\pi\) | ||||
0.369403 | + | 0.929269i | \(0.379562\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.5577 | 1.13099 | 0.565496 | − | 0.824751i | \(-0.308685\pi\) | ||||
0.565496 | + | 0.824751i | \(0.308685\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.52444 | 0.161280 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −33.5960 | −2.13766 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.1517 | −0.767005 | −0.383503 | − | 0.923540i | \(-0.625282\pi\) | ||||
−0.383503 | + | 0.923540i | \(0.625282\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.09775 | −0.131885 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.41110 | −0.399913 | −0.199957 | − | 0.979805i | \(-0.564080\pi\) | ||||
−0.199957 | + | 0.979805i | \(0.564080\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.04888 | −0.189448 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 10.3133 | 0.635948 | 0.317974 | − | 0.948099i | \(-0.396997\pi\) | ||||
0.317974 | + | 0.948099i | \(0.396997\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.04888 | −0.310150 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 15.6811 | 0.956094 | 0.478047 | − | 0.878334i | \(-0.341345\pi\) | ||||
0.478047 | + | 0.878334i | \(0.341345\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.7633 | 1.56501 | 0.782504 | − | 0.622646i | \(-0.213942\pi\) | ||||
0.782504 | + | 0.622646i | \(0.213942\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.97939 | −0.300269 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −17.2544 | −1.03672 | −0.518359 | − | 0.855163i | \(-0.673457\pi\) | ||||
−0.518359 | + | 0.855163i | \(0.673457\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 32.5089 | 1.93932 | 0.969658 | − | 0.244466i | \(-0.0786128\pi\) | ||||
0.969658 | + | 0.244466i | \(0.0786128\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −22.9950 | −1.36691 | −0.683455 | − | 0.729993i | \(-0.739523\pi\) | ||||
−0.683455 | + | 0.729993i | \(0.739523\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.205550 | −0.0121332 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.686652 | 0.0403913 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.72999 | 0.510011 | 0.255006 | − | 0.966940i | \(-0.417923\pi\) | ||||
0.255006 | + | 0.966940i | \(0.417923\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −31.7139 | −1.84645 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.73553 | 0.158200 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.78389 | −0.275739 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −26.5683 | −1.52130 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −26.6605 | −1.52160 | −0.760798 | − | 0.648989i | \(-0.775192\pi\) | ||||
−0.760798 | + | 0.648989i | \(0.775192\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.0978 | 0.572591 | 0.286295 | − | 0.958141i | \(-0.407576\pi\) | ||||
0.286295 | + | 0.958141i | \(0.407576\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.205550 | −0.0116184 | −0.00580919 | − | 0.999983i | \(-0.501849\pi\) | ||||
−0.00580919 | + | 0.999983i | \(0.501849\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −30.4111 | −1.70806 | −0.854029 | − | 0.520226i | \(-0.825848\pi\) | ||||
−0.854029 | + | 0.520226i | \(0.825848\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −29.7633 | −1.66642 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 29.8711 | 1.66207 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.49327 | 0.360182 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.20555 | −0.342123 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.47054 | 0.135793 | 0.0678965 | − | 0.997692i | \(-0.478371\pi\) | ||||
0.0678965 | + | 0.997692i | \(0.478371\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 16.6066 | 0.907316 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.2927 | −0.615155 | −0.307577 | − | 0.951523i | \(-0.599518\pi\) | ||||
−0.307577 | + | 0.951523i | \(0.599518\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 18.3133 | 0.991723 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.68614 | −0.144199 | −0.0720997 | − | 0.997397i | \(-0.522970\pi\) | ||||
−0.0720997 | + | 0.997397i | \(0.522970\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.4756 | −0.935445 | −0.467723 | − | 0.883875i | \(-0.654925\pi\) | ||||
−0.467723 | + | 0.883875i | \(0.654925\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.05892 | −0.0563608 | −0.0281804 | − | 0.999603i | \(-0.508971\pi\) | ||||
−0.0281804 | + | 0.999603i | \(0.508971\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −11.8328 | −0.624509 | −0.312255 | − | 0.949998i | \(-0.601084\pi\) | ||||
−0.312255 | + | 0.949998i | \(0.601084\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 31.4494 | 1.65523 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −23.3622 | −1.22283 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.2544 | 1.00507 | 0.502536 | − | 0.864556i | \(-0.332400\pi\) | ||||
0.502536 | + | 0.864556i | \(0.332400\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.00000 | 0.103835 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.66553 | 0.500462 | 0.250231 | − | 0.968186i | \(-0.419493\pi\) | ||||
0.250231 | + | 0.968186i | \(0.419493\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 38.8122 | 1.99893 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.0383 | −0.618367 | −0.309183 | − | 0.951002i | \(-0.600056\pi\) | ||||
−0.309183 | + | 0.951002i | \(0.600056\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −31.0278 | −1.58544 | −0.792722 | − | 0.609583i | \(-0.791337\pi\) | ||||
−0.792722 | + | 0.609583i | \(0.791337\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.15667 | 0.466667 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −13.1466 | −0.666560 | −0.333280 | − | 0.942828i | \(-0.608156\pi\) | ||||
−0.333280 | + | 0.942828i | \(0.608156\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.43223 | −0.123003 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −13.0177 | −0.654992 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.47556 | −0.0740563 | −0.0370282 | − | 0.999314i | \(-0.511789\pi\) | ||||
−0.0370282 | + | 0.999314i | \(0.511789\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.9794 | 0.648160 | 0.324080 | − | 0.946030i | \(-0.394945\pi\) | ||||
0.324080 | + | 0.946030i | \(0.394945\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −23.8811 | −1.18960 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11.0589 | −0.548170 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.36222 | −0.0673577 | −0.0336788 | − | 0.999433i | \(-0.510722\pi\) | ||||
−0.0336788 | + | 0.999433i | \(0.510722\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 12.5628 | 0.618173 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −15.0106 | −0.736840 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −25.3083 | −1.23639 | −0.618196 | − | 0.786024i | \(-0.712136\pi\) | ||||
−0.618196 | + | 0.786024i | \(0.712136\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.05892 | 0.0516087 | 0.0258044 | − | 0.999667i | \(-0.491785\pi\) | ||||
0.0258044 | + | 0.999667i | \(0.491785\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.77332 | −0.280047 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.5244 | 0.509313 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.2439 | −0.589766 | −0.294883 | − | 0.955533i | \(-0.595281\pi\) | ||||
−0.294883 | + | 0.955533i | \(0.595281\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 37.0278 | 1.77944 | 0.889720 | − | 0.456507i | \(-0.150899\pi\) | ||||
0.889720 | + | 0.456507i | \(0.150899\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.10780 | −0.196503 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.33447 | −0.397783 | −0.198891 | − | 0.980022i | \(-0.563734\pi\) | ||||
−0.198891 | + | 0.980022i | \(0.563734\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 27.5960 | 1.31113 | 0.655564 | − | 0.755140i | \(-0.272431\pi\) | ||||
0.655564 | + | 0.755140i | \(0.272431\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 26.2822 | 1.24589 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.66553 | 0.0786010 | 0.0393005 | − | 0.999227i | \(-0.487487\pi\) | ||||
0.0393005 | + | 0.999227i | \(0.487487\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.745574 | −0.0351077 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −11.9406 | −0.559782 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 25.7250 | 1.20336 | 0.601682 | − | 0.798736i | \(-0.294498\pi\) | ||||
0.601682 | + | 0.798736i | \(0.294498\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.4267 | −0.578768 | −0.289384 | − | 0.957213i | \(-0.593451\pi\) | ||||
−0.289384 | + | 0.957213i | \(0.593451\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.33447 | −0.201440 | −0.100720 | − | 0.994915i | \(-0.532115\pi\) | ||||
−0.100720 | + | 0.994915i | \(0.532115\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10.6917 | 0.494752 | 0.247376 | − | 0.968920i | \(-0.420432\pi\) | ||||
0.247376 | + | 0.968920i | \(0.420432\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.57834 | −0.303759 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −17.3522 | −0.797854 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9.75060 | −0.447388 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.95112 | 0.134840 | 0.0674202 | − | 0.997725i | \(-0.478523\pi\) | ||||
0.0674202 | + | 0.997725i | \(0.478523\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.4211 | 0.657548 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −23.6344 | −1.07318 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.93051 | 0.268737 | 0.134369 | − | 0.990931i | \(-0.457099\pi\) | ||||
0.134369 | + | 0.990931i | \(0.457099\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 21.3028 | 0.961381 | 0.480691 | − | 0.876890i | \(-0.340386\pi\) | ||||
0.480691 | + | 0.876890i | \(0.340386\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −34.5089 | −1.55420 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −36.6761 | −1.64185 | −0.820924 | − | 0.571038i | \(-0.806541\pi\) | ||||
−0.820924 | + | 0.571038i | \(0.806541\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 20.7456 | 0.924999 | 0.462500 | − | 0.886619i | \(-0.346953\pi\) | ||||
0.462500 | + | 0.886619i | \(0.346953\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.9028 | 0.485167 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −21.0333 | −0.932284 | −0.466142 | − | 0.884710i | \(-0.654356\pi\) | ||||
−0.466142 | + | 0.884710i | \(0.654356\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.25443 | 0.409392 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −12.7456 | −0.561637 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −22.5089 | −0.989938 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.7355 | 0.557954 | 0.278977 | − | 0.960298i | \(-0.410005\pi\) | ||||
0.278977 | + | 0.960298i | \(0.410005\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.151651 | 0.00663123 | 0.00331562 | − | 0.999995i | \(-0.498945\pi\) | ||||
0.00331562 | + | 0.999995i | \(0.498945\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 21.2333 | 0.924937 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.6655 | −0.985458 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.972250 | 0.0421128 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 24.8222 | 1.07316 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.62721 | −0.156235 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.5678 | −0.497337 | −0.248669 | − | 0.968589i | \(-0.579993\pi\) | ||||
−0.248669 | + | 0.968589i | \(0.579993\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −49.1255 | −2.10431 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.0594 | 0.430111 | 0.215055 | − | 0.976602i | \(-0.431007\pi\) | ||||
0.215055 | + | 0.976602i | \(0.431007\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −58.2822 | −2.48290 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.15667 | 0.219284 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.50885 | 0.191046 | 0.0955231 | − | 0.995427i | \(-0.469548\pi\) | ||||
0.0955231 | + | 0.995427i | \(0.469548\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 22.6277 | 0.957051 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 24.9739 | 1.05252 | 0.526261 | − | 0.850323i | \(-0.323593\pi\) | ||||
0.526261 | + | 0.850323i | \(0.323593\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −22.1744 | −0.932883 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 21.9406 | 0.919796 | 0.459898 | − | 0.887972i | \(-0.347886\pi\) | ||||
0.459898 | + | 0.887972i | \(0.347886\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.2161 | −0.804169 | −0.402085 | − | 0.915602i | \(-0.631714\pi\) | ||||
−0.402085 | + | 0.915602i | \(0.631714\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.793934 | 0.0331093 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −0.432226 | −0.0179938 | −0.00899689 | − | 0.999960i | \(-0.502864\pi\) | ||||
−0.00899689 | + | 0.999960i | \(0.502864\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.94610 | 0.246686 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.25443 | 0.300448 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13.3083 | 0.549293 | 0.274647 | − | 0.961545i | \(-0.411439\pi\) | ||||
0.274647 | + | 0.961545i | \(0.411439\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 35.8610 | 1.47763 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −7.68665 | −0.315653 | −0.157826 | − | 0.987467i | \(-0.550449\pi\) | ||||
−0.157826 | + | 0.987467i | \(0.550449\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.6167 | 0.435240 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −37.0177 | −1.51250 | −0.756251 | − | 0.654281i | \(-0.772971\pi\) | ||||
−0.756251 | + | 0.654281i | \(0.772971\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.78440 | 0.399114 | 0.199557 | − | 0.979886i | \(-0.436050\pi\) | ||||
0.199557 | + | 0.979886i | \(0.436050\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.44439 | 0.221346 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −40.6066 | −1.64817 | −0.824086 | − | 0.566465i | \(-0.808311\pi\) | ||||
−0.824086 | + | 0.566465i | \(0.808311\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 29.3522 | 1.18746 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −24.8122 | −1.00215 | −0.501077 | − | 0.865403i | \(-0.667063\pi\) | ||||
−0.501077 | + | 0.865403i | \(0.667063\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 40.4494 | 1.62843 | 0.814216 | − | 0.580562i | \(-0.197167\pi\) | ||||
0.814216 | + | 0.580562i | \(0.197167\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.20053 | 0.209027 | 0.104513 | − | 0.994523i | \(-0.466671\pi\) | ||||
0.104513 | + | 0.994523i | \(0.466671\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −10.4111 | −0.417112 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.9794 | −1.19918 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −12.8222 | −0.511255 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 43.7422 | 1.74135 | 0.870674 | − | 0.491861i | \(-0.163683\pi\) | ||||
0.870674 | + | 0.491861i | \(0.163683\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −37.0489 | −1.47024 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.72999 | 0.187409 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.21611 | −0.285019 | −0.142510 | − | 0.989793i | \(-0.545517\pi\) | ||||
−0.142510 | + | 0.989793i | \(0.545517\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20.3472 | −0.802413 | −0.401207 | − | 0.915988i | \(-0.631409\pi\) | ||||
−0.401207 | + | 0.915988i | \(0.631409\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 11.5577 | 0.454381 | 0.227191 | − | 0.973850i | \(-0.427046\pi\) | ||||
0.227191 | + | 0.973850i | \(0.427046\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 45.5678 | 1.78869 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14.3033 | −0.559731 | −0.279866 | − | 0.960039i | \(-0.590290\pi\) | ||||
−0.279866 | + | 0.960039i | \(0.590290\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10.4806 | 0.409510 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19.7038 | −0.767553 | −0.383776 | − | 0.923426i | \(-0.625377\pi\) | ||||
−0.383776 | + | 0.923426i | \(0.625377\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.7789 | 1.15826 | 0.579132 | − | 0.815234i | \(-0.303392\pi\) | ||||
0.579132 | + | 0.815234i | \(0.303392\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 17.9305 | 0.695316 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.74557 | 0.183749 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 38.1744 | 1.47371 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 32.9200 | 1.26897 | 0.634485 | − | 0.772935i | \(-0.281212\pi\) | ||||
0.634485 | + | 0.772935i | \(0.281212\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 22.7089 | 0.872772 | 0.436386 | − | 0.899759i | \(-0.356258\pi\) | ||||
0.436386 | + | 0.899759i | \(0.356258\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.36222 | 0.359289 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 23.5194 | 0.899945 | 0.449973 | − | 0.893042i | \(-0.351434\pi\) | ||||
0.449973 | + | 0.893042i | \(0.351434\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13.2645 | −0.506809 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −9.45998 | −0.360396 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 35.1794 | 1.33829 | 0.669144 | − | 0.743133i | \(-0.266661\pi\) | ||||
0.669144 | + | 0.743133i | \(0.266661\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −22.4605 | −0.851975 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.864451 | −0.0327434 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.48110 | 0.0559404 | 0.0279702 | − | 0.999609i | \(-0.491096\pi\) | ||||
0.0279702 | + | 0.999609i | \(0.491096\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −21.6555 | −0.816752 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.31889 | −0.162428 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 29.3622 | 1.10272 | 0.551361 | − | 0.834267i | \(-0.314109\pi\) | ||||
0.551361 | + | 0.834267i | \(0.314109\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.91995 | −0.109353 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −43.3110 | −1.61974 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 13.3833 | 0.499115 | 0.249557 | − | 0.968360i | \(-0.419715\pi\) | ||||
0.249557 | + | 0.968360i | \(0.419715\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.04888 | 0.188030 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 11.2645 | 0.418352 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −21.5366 | −0.798748 | −0.399374 | − | 0.916788i | \(-0.630773\pi\) | ||||
−0.399374 | + | 0.916788i | \(0.630773\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −20.1189 | −0.744124 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 30.2978 | 1.11907 | 0.559537 | − | 0.828806i | \(-0.310979\pi\) | ||||
0.559537 | + | 0.828806i | \(0.310979\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −23.8610 | −0.878932 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12.9794 | 0.477455 | 0.238727 | − | 0.971087i | \(-0.423270\pi\) | ||||
0.238727 | + | 0.971087i | \(0.423270\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 50.0071 | 1.83458 | 0.917292 | − | 0.398215i | \(-0.130370\pi\) | ||||
0.917292 | + | 0.398215i | \(0.130370\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 54.6933 | 2.00381 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.83276 | −0.359281 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.8917 | −0.835329 | −0.417665 | − | 0.908601i | \(-0.637151\pi\) | ||||
−0.417665 | + | 0.908601i | \(0.637151\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.5955 | 0.458398 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29.0278 | 1.05503 | 0.527516 | − | 0.849545i | \(-0.323124\pi\) | ||||
0.527516 | + | 0.849545i | \(0.323124\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −36.8122 | −1.33444 | −0.667220 | − | 0.744861i | \(-0.732516\pi\) | ||||
−0.667220 | + | 0.744861i | \(0.732516\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 19.4600 | 0.704498 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −59.4217 | −2.14559 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −47.8711 | −1.72628 | −0.863138 | − | 0.504969i | \(-0.831504\pi\) | ||||
−0.863138 | + | 0.504969i | \(0.831504\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 41.2489 | 1.48362 | 0.741810 | − | 0.670610i | \(-0.233968\pi\) | ||||
0.741810 | + | 0.670610i | \(0.233968\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.93103 | −0.248970 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.45998 | −0.0523091 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −50.7215 | −1.81033 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.79947 | 0.242375 | 0.121188 | − | 0.992630i | \(-0.461330\pi\) | ||||
0.121188 | + | 0.992630i | \(0.461330\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.78389 | 0.312319 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −49.7805 | −1.76776 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6.18996 | 0.219260 | 0.109630 | − | 0.993972i | \(-0.465033\pi\) | ||||
0.109630 | + | 0.993972i | \(0.465033\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −26.0978 | −0.923272 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 33.5678 | 1.18458 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.45998 | −0.0514574 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −30.3517 | −1.06711 | −0.533554 | − | 0.845766i | \(-0.679144\pi\) | ||||
−0.533554 | + | 0.845766i | \(0.679144\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −40.0328 | −1.40574 | −0.702870 | − | 0.711318i | \(-0.748099\pi\) | ||||
−0.702870 | + | 0.711318i | \(0.748099\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −40.4877 | −1.41822 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −33.9789 | −1.18877 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −51.9789 | −1.81408 | −0.907038 | − | 0.421050i | \(-0.861662\pi\) | ||||
−0.907038 | + | 0.421050i | \(0.861662\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −26.9200 | −0.938371 | −0.469185 | − | 0.883100i | \(-0.655452\pi\) | ||||
−0.469185 | + | 0.883100i | \(0.655452\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −47.5960 | −1.65508 | −0.827538 | − | 0.561409i | \(-0.810259\pi\) | ||||
−0.827538 | + | 0.561409i | \(0.810259\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.21109 | −0.285183 | −0.142591 | − | 0.989782i | \(-0.545544\pi\) | ||||
−0.142591 | + | 0.989782i | \(0.545544\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.20555 | −0.145714 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.52998 | 0.156766 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −5.04888 | −0.174307 | −0.0871533 | − | 0.996195i | \(-0.527777\pi\) | ||||
−0.0871533 | + | 0.996195i | \(0.527777\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 38.3311 | 1.32176 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 23.6610 | 0.813964 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.15667 | −0.0741042 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.76328 | 0.0604444 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.14109 | 0.0390701 | 0.0195351 | − | 0.999809i | \(-0.493781\pi\) | ||||
0.0195351 | + | 0.999809i | \(0.493781\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.45998 | 0.118191 | 0.0590953 | − | 0.998252i | \(-0.481178\pi\) | ||||
0.0590953 | + | 0.998252i | \(0.481178\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.15165 | 0.141653 | 0.0708263 | − | 0.997489i | \(-0.477436\pi\) | ||||
0.0708263 | + | 0.997489i | \(0.477436\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −13.7633 | −0.468507 | −0.234254 | − | 0.972175i | \(-0.575265\pi\) | ||||
−0.234254 | + | 0.972175i | \(0.575265\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −57.6272 | −1.95938 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 18.7044 | 0.634502 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 31.1155 | 1.05431 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9.15667 | 0.309552 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 53.9688 | 1.82240 | 0.911199 | − | 0.411967i | \(-0.135158\pi\) | ||||
0.911199 | + | 0.411967i | \(0.135158\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −56.1744 | −1.89256 | −0.946281 | − | 0.323344i | \(-0.895193\pi\) | ||||
−0.946281 | + | 0.323344i | \(0.895193\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 52.5371 | 1.76801 | 0.884007 | − | 0.467473i | \(-0.154835\pi\) | ||||
0.884007 | + | 0.467473i | \(0.154835\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −44.4988 | −1.49412 | −0.747062 | − | 0.664755i | \(-0.768536\pi\) | ||||
−0.747062 | + | 0.664755i | \(0.768536\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 14.6761 | 0.492220 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −44.0766 | −1.47497 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.88454 | 0.296978 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −41.4288 | −1.38173 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.41110 | 0.280214 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 27.6061 | 0.917657 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −44.4182 | −1.47488 | −0.737442 | − | 0.675411i | \(-0.763966\pi\) | ||||
−0.737442 | + | 0.675411i | \(0.763966\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −48.9894 | −1.62309 | −0.811546 | − | 0.584288i | \(-0.801374\pi\) | ||||
−0.811546 | + | 0.584288i | \(0.801374\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 21.5678 | 0.713789 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.15165 | −0.137100 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −34.9200 | −1.15190 | −0.575951 | − | 0.817484i | \(-0.695368\pi\) | ||||
−0.575951 | + | 0.817484i | \(0.695368\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.18546 | 0.137617 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.98995 | −0.130906 | −0.0654531 | − | 0.997856i | \(-0.520849\pi\) | ||||
−0.0654531 | + | 0.997856i | \(0.520849\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.10278 | −0.232784 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 38.5089 | 1.25937 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −47.9789 | −1.56740 | −0.783701 | − | 0.621139i | \(-0.786670\pi\) | ||||
−0.783701 | + | 0.621139i | \(0.786670\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −26.1900 | −0.853768 | −0.426884 | − | 0.904306i | \(-0.640389\pi\) | ||||
−0.426884 | + | 0.904306i | \(0.640389\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.118877 | 0.00387118 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −57.3905 | −1.86494 | −0.932470 | − | 0.361247i | \(-0.882351\pi\) | ||||
−0.932470 | + | 0.361247i | \(0.882351\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −43.7733 | −1.42094 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.68665 | 0.119422 | 0.0597112 | − | 0.998216i | \(-0.480982\pi\) | ||||
0.0597112 | + | 0.998216i | \(0.480982\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.88216 | −0.0609051 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.25443 | 0.169674 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.50885 | −0.177705 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −35.6856 | −1.14876 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 27.6172 | 0.888108 | 0.444054 | − | 0.896000i | \(-0.353540\pi\) | ||||
0.444054 | + | 0.896000i | \(0.353540\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.94610 | 0.319186 | 0.159593 | − | 0.987183i | \(-0.448982\pi\) | ||||
0.159593 | + | 0.987183i | \(0.448982\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.89722 | 0.285232 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 21.2544 | 0.679989 | 0.339995 | − | 0.940427i | \(-0.389575\pi\) | ||||
0.339995 | + | 0.940427i | \(0.389575\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −37.7633 | −1.20692 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −16.1844 | −0.516203 | −0.258101 | − | 0.966118i | \(-0.583097\pi\) | ||||
−0.258101 | + | 0.966118i | \(0.583097\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −25.2444 | −0.804353 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.76670 | 0.0879759 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.0766 | 0.510691 | 0.255345 | − | 0.966850i | \(-0.417811\pi\) | ||||
0.255345 | + | 0.966850i | \(0.417811\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.61003 | 0.0510412 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −29.4444 | −0.932513 | −0.466257 | − | 0.884650i | \(-0.654398\pi\) | ||||
−0.466257 | + | 0.884650i | \(0.654398\pi\) | |||||||
\(998\) | 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 | 8064.2.a.ce.1.2 | 3 | ||
3.2 | odd | 2 | 896.2.a.i.1.1 | ✓ | 3 | ||
4.3 | odd | 2 | 8064.2.a.ch.1.2 | 3 | |||
8.3 | odd | 2 | 8064.2.a.cb.1.2 | 3 | |||
8.5 | even | 2 | 8064.2.a.bu.1.2 | 3 | |||
12.11 | even | 2 | 896.2.a.k.1.3 | yes | 3 | ||
21.20 | even | 2 | 6272.2.a.x.1.3 | 3 | |||
24.5 | odd | 2 | 896.2.a.l.1.3 | yes | 3 | ||
24.11 | even | 2 | 896.2.a.j.1.1 | yes | 3 | ||
48.5 | odd | 4 | 1792.2.b.p.897.6 | 6 | |||
48.11 | even | 4 | 1792.2.b.o.897.1 | 6 | |||
48.29 | odd | 4 | 1792.2.b.p.897.1 | 6 | |||
48.35 | even | 4 | 1792.2.b.o.897.6 | 6 | |||
84.83 | odd | 2 | 6272.2.a.v.1.1 | 3 | |||
168.83 | odd | 2 | 6272.2.a.w.1.3 | 3 | |||
168.125 | even | 2 | 6272.2.a.u.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
896.2.a.i.1.1 | ✓ | 3 | 3.2 | odd | 2 | ||
896.2.a.j.1.1 | yes | 3 | 24.11 | even | 2 | ||
896.2.a.k.1.3 | yes | 3 | 12.11 | even | 2 | ||
896.2.a.l.1.3 | yes | 3 | 24.5 | odd | 2 | ||
1792.2.b.o.897.1 | 6 | 48.11 | even | 4 | |||
1792.2.b.o.897.6 | 6 | 48.35 | even | 4 | |||
1792.2.b.p.897.1 | 6 | 48.29 | odd | 4 | |||
1792.2.b.p.897.6 | 6 | 48.5 | odd | 4 | |||
6272.2.a.u.1.1 | 3 | 168.125 | even | 2 | |||
6272.2.a.v.1.1 | 3 | 84.83 | odd | 2 | |||
6272.2.a.w.1.3 | 3 | 168.83 | odd | 2 | |||
6272.2.a.x.1.3 | 3 | 21.20 | even | 2 | |||
8064.2.a.bu.1.2 | 3 | 8.5 | even | 2 | |||
8064.2.a.cb.1.2 | 3 | 8.3 | odd | 2 | |||
8064.2.a.ce.1.2 | 3 | 1.1 | even | 1 | trivial | ||
8064.2.a.ch.1.2 | 3 | 4.3 | odd | 2 |