Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8036,2,Mod(1,8036)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8036, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8036.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8036 = 2^{2} \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8036.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: | \(64.1677830643\) |
Analytic rank: | \(0\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - x^{14} - 37 x^{13} + 39 x^{12} + 537 x^{11} - 616 x^{10} - 3853 x^{9} + 4929 x^{8} + \cdots + 3381 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 1148) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(0.515082\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8036.1 |
$q$-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 | ||||||||
\(3\) | −0.515082 | −0.297383 | −0.148691 | − | 0.988884i | \(-0.547506\pi\) | ||||
−0.148691 | + | 0.988884i | \(0.547506\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.19964 | 0.983707 | 0.491853 | − | 0.870678i | \(-0.336320\pi\) | ||||
0.491853 | + | 0.870678i | \(0.336320\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.73469 | −0.911564 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.22160 | 1.27286 | 0.636430 | − | 0.771335i | \(-0.280410\pi\) | ||||
0.636430 | + | 0.771335i | \(0.280410\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.63941 | 1.00939 | 0.504696 | − | 0.863297i | \(-0.331605\pi\) | ||||
0.504696 | + | 0.863297i | \(0.331605\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.13299 | −0.292537 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.98698 | −1.93713 | −0.968563 | − | 0.248768i | \(-0.919974\pi\) | ||||
−0.968563 | + | 0.248768i | \(0.919974\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.14014 | 0.261566 | 0.130783 | − | 0.991411i | \(-0.458251\pi\) | ||||
0.130783 | + | 0.991411i | \(0.458251\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.43446 | −1.55019 | −0.775096 | − | 0.631844i | \(-0.782298\pi\) | ||||
−0.775096 | + | 0.631844i | \(0.782298\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.161604 | −0.0323208 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.95383 | 0.568466 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.08068 | 1.12915 | 0.564577 | − | 0.825380i | \(-0.309039\pi\) | ||||
0.564577 | + | 0.825380i | \(0.309039\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.33243 | −0.239311 | −0.119655 | − | 0.992815i | \(-0.538179\pi\) | ||||
−0.119655 | + | 0.992815i | \(0.538179\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.17447 | −0.378526 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.87776 | −0.473101 | −0.236551 | − | 0.971619i | \(-0.576017\pi\) | ||||
−0.236551 | + | 0.971619i | \(0.576017\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.87460 | −0.300176 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.14701 | 0.784912 | 0.392456 | − | 0.919771i | \(-0.371626\pi\) | ||||
0.392456 | + | 0.919771i | \(0.371626\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.01532 | −0.896711 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.12473 | 1.18511 | 0.592557 | − | 0.805529i | \(-0.298119\pi\) | ||||
0.592557 | + | 0.805529i | \(0.298119\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.11395 | 0.576068 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.63075 | −0.224001 | −0.112001 | − | 0.993708i | \(-0.535726\pi\) | ||||
−0.112001 | + | 0.993708i | \(0.535726\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.28598 | 1.25212 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.587265 | −0.0777852 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.97978 | −0.387935 | −0.193967 | − | 0.981008i | \(-0.562136\pi\) | ||||
−0.193967 | + | 0.981008i | \(0.562136\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.2708 | 1.31505 | 0.657524 | − | 0.753434i | \(-0.271604\pi\) | ||||
0.657524 | + | 0.753434i | \(0.271604\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.00538 | 0.992946 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.46808 | 0.301525 | 0.150762 | − | 0.988570i | \(-0.451827\pi\) | ||||
0.150762 | + | 0.988570i | \(0.451827\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.82935 | 0.461000 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.0326 | 1.54668 | 0.773342 | − | 0.633989i | \(-0.218584\pi\) | ||||
0.773342 | + | 0.633989i | \(0.218584\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.5199 | 1.34831 | 0.674154 | − | 0.738591i | \(-0.264509\pi\) | ||||
0.674154 | + | 0.738591i | \(0.264509\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.0832393 | 0.00961165 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.06941 | 1.02039 | 0.510194 | − | 0.860059i | \(-0.329573\pi\) | ||||
0.510194 | + | 0.860059i | \(0.329573\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.68261 | 0.742512 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.51957 | 0.825380 | 0.412690 | − | 0.910872i | \(-0.364589\pi\) | ||||
0.412690 | + | 0.910872i | \(0.364589\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −17.5684 | −1.90556 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.13205 | −0.335791 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −17.9819 | −1.90608 | −0.953041 | − | 0.302840i | \(-0.902065\pi\) | ||||
−0.953041 | + | 0.302840i | \(0.902065\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.686309 | 0.0711669 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.50789 | 0.257304 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.2426 | 1.34459 | 0.672293 | − | 0.740285i | \(-0.265309\pi\) | ||||
0.672293 | + | 0.740285i | \(0.265309\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −11.5448 | −1.16029 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.90610 | 0.587678 | 0.293839 | − | 0.955855i | \(-0.405067\pi\) | ||||
0.293839 | + | 0.955855i | \(0.405067\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.32873 | −0.426522 | −0.213261 | − | 0.976995i | \(-0.568409\pi\) | ||||
−0.213261 | + | 0.976995i | \(0.568409\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.6786 | −1.12901 | −0.564504 | − | 0.825430i | \(-0.690933\pi\) | ||||
−0.564504 | + | 0.825430i | \(0.690933\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.2466 | 1.46036 | 0.730178 | − | 0.683257i | \(-0.239437\pi\) | ||||
0.730178 | + | 0.683257i | \(0.239437\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.48228 | 0.140692 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.2122 | 1.61919 | 0.809594 | − | 0.586990i | \(-0.199687\pi\) | ||||
0.809594 | + | 0.586990i | \(0.199687\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −16.3531 | −1.52493 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −9.95267 | −0.920125 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.82189 | 0.620172 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.515082 | 0.0464434 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.3536 | −1.01550 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.42630 | −0.747713 | −0.373857 | − | 0.927487i | \(-0.621965\pi\) | ||||
−0.373857 | + | 0.927487i | \(0.621965\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.65113 | −0.233419 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.8466 | −1.03504 | −0.517522 | − | 0.855670i | \(-0.673145\pi\) | ||||
−0.517522 | + | 0.855670i | \(0.673145\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 6.49736 | 0.559204 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −17.6176 | −1.50518 | −0.752589 | − | 0.658491i | \(-0.771195\pi\) | ||||
−0.752589 | + | 0.658491i | \(0.771195\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.43664 | −0.291492 | −0.145746 | − | 0.989322i | \(-0.546558\pi\) | ||||
−0.145746 | + | 0.989322i | \(0.546558\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.18490 | −0.352432 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 15.3641 | 1.28481 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 13.3753 | 1.11076 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 20.2855 | 1.66185 | 0.830926 | − | 0.556383i | \(-0.187811\pi\) | ||||
0.830926 | + | 0.556383i | \(0.187811\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.792622 | 0.0645027 | 0.0322513 | − | 0.999480i | \(-0.489732\pi\) | ||||
0.0322513 | + | 0.999480i | \(0.489732\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 21.8419 | 1.76581 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.93085 | −0.235412 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.29832 | 0.422852 | 0.211426 | − | 0.977394i | \(-0.432189\pi\) | ||||
0.211426 | + | 0.977394i | \(0.432189\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.839972 | 0.0666141 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.33217 | 0.730952 | 0.365476 | − | 0.930821i | \(-0.380906\pi\) | ||||
0.365476 | + | 0.930821i | \(0.380906\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.78304 | −0.372359 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.22005 | 0.403939 | 0.201970 | − | 0.979392i | \(-0.435266\pi\) | ||||
0.201970 | + | 0.979392i | \(0.435266\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.245336 | 0.0188720 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.11793 | −0.238434 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.187866 | −0.0142832 | −0.00714158 | − | 0.999974i | \(-0.502273\pi\) | ||||
−0.00714158 | + | 0.999974i | \(0.502273\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.53483 | 0.115365 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.3865 | 1.00055 | 0.500277 | − | 0.865865i | \(-0.333231\pi\) | ||||
0.500277 | + | 0.865865i | \(0.333231\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.303123 | −0.0225309 | −0.0112655 | − | 0.999937i | \(-0.503586\pi\) | ||||
−0.0112655 | + | 0.999937i | \(0.503586\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.29033 | −0.391072 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.33003 | −0.465393 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −33.7178 | −2.46569 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.01783 | −0.0736479 | −0.0368239 | − | 0.999322i | \(-0.511724\pi\) | ||||
−0.0368239 | + | 0.999322i | \(0.511724\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.1199 | 1.23231 | 0.616157 | − | 0.787623i | \(-0.288689\pi\) | ||||
0.616157 | + | 0.787623i | \(0.288689\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.12343 | −0.295285 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.81082 | −0.342757 | −0.171379 | − | 0.985205i | \(-0.554822\pi\) | ||||
−0.171379 | + | 0.985205i | \(0.554822\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.5535 | −0.889892 | −0.444946 | − | 0.895557i | \(-0.646777\pi\) | ||||
−0.444946 | + | 0.895557i | \(0.646777\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.27127 | −0.0896681 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.19964 | −0.153629 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 20.3309 | 1.41310 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.81321 | 0.332937 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.7515 | 1.42859 | 0.714297 | − | 0.699843i | \(-0.246747\pi\) | ||||
0.714297 | + | 0.699843i | \(0.246747\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.71285 | −0.459957 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 11.3215 | 0.772123 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.93371 | −0.400963 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −29.0679 | −1.95532 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.6034 | −0.777022 | −0.388511 | − | 0.921444i | \(-0.627010\pi\) | ||||
−0.388511 | + | 0.921444i | \(0.627010\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.441937 | 0.0294625 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.694596 | −0.0461020 | −0.0230510 | − | 0.999734i | \(-0.507338\pi\) | ||||
−0.0230510 | + | 0.999734i | \(0.507338\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 25.1712 | 1.66336 | 0.831681 | − | 0.555254i | \(-0.187379\pi\) | ||||
0.831681 | + | 0.555254i | \(0.187379\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.94397 | 0.192866 | 0.0964330 | − | 0.995339i | \(-0.469257\pi\) | ||||
0.0964330 | + | 0.995339i | \(0.469257\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 17.8714 | 1.16580 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.67149 | −0.303446 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.56259 | 0.489183 | 0.244592 | − | 0.969626i | \(-0.421346\pi\) | ||||
0.244592 | + | 0.969626i | \(0.421346\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.59060 | −0.488953 | −0.244477 | − | 0.969655i | \(-0.578616\pi\) | ||||
−0.244477 | + | 0.969655i | \(0.578616\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −12.3036 | −0.789276 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.14944 | 0.264023 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.87319 | −0.245454 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −23.7549 | −1.49940 | −0.749698 | − | 0.661780i | \(-0.769801\pi\) | ||||
−0.749698 | + | 0.661780i | \(0.769801\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −31.3853 | −1.97318 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 9.04918 | 0.566682 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.53771 | −0.0959198 | −0.0479599 | − | 0.998849i | \(-0.515272\pi\) | ||||
−0.0479599 | + | 0.998849i | \(0.515272\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −16.6288 | −1.02930 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 16.3727 | 1.00958 | 0.504791 | − | 0.863242i | \(-0.331570\pi\) | ||||
0.504791 | + | 0.863242i | \(0.331570\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.58707 | −0.220352 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.26217 | 0.566836 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 18.6581 | 1.13760 | 0.568801 | − | 0.822475i | \(-0.307407\pi\) | ||||
0.568801 | + | 0.822475i | \(0.307407\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.3271 | 0.991800 | 0.495900 | − | 0.868380i | \(-0.334838\pi\) | ||||
0.495900 | + | 0.868380i | \(0.334838\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.682228 | −0.0411399 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −19.2494 | −1.15659 | −0.578293 | − | 0.815829i | \(-0.696281\pi\) | ||||
−0.578293 | + | 0.815829i | \(0.696281\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.64378 | 0.218147 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 25.4587 | 1.51874 | 0.759369 | − | 0.650660i | \(-0.225508\pi\) | ||||
0.759369 | + | 0.650660i | \(0.225508\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.72536 | −0.399781 | −0.199891 | − | 0.979818i | \(-0.564059\pi\) | ||||
−0.199891 | + | 0.979818i | \(0.564059\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.29177 | −0.0765178 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 46.7918 | 2.75246 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.82104 | −0.399857 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −14.0817 | −0.822660 | −0.411330 | − | 0.911487i | \(-0.634936\pi\) | ||||
−0.411330 | + | 0.911487i | \(0.634936\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.55444 | −0.381614 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 12.4699 | 0.723577 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −27.0571 | −1.56475 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.04212 | −0.174765 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 22.5921 | 1.29362 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −22.4646 | −1.28212 | −0.641062 | − | 0.767489i | \(-0.721506\pi\) | ||||
−0.641062 | + | 0.767489i | \(0.721506\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.22965 | 0.126840 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.1252 | −0.857671 | −0.428835 | − | 0.903383i | \(-0.641076\pi\) | ||||
−0.428835 | + | 0.903383i | \(0.641076\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.4123 | −1.09725 | −0.548625 | − | 0.836068i | \(-0.684849\pi\) | ||||
−0.548625 | + | 0.836068i | \(0.684849\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.76362 | 0.0990546 | 0.0495273 | − | 0.998773i | \(-0.484229\pi\) | ||||
0.0495273 | + | 0.998773i | \(0.484229\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 25.6702 | 1.43725 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.01541 | 0.335747 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.10627 | −0.506686 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.588144 | −0.0326244 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7.85322 | −0.434284 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.1176 | 0.666045 | 0.333023 | − | 0.942919i | \(-0.391931\pi\) | ||||
0.333023 | + | 0.942919i | \(0.391931\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.86979 | 0.431262 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.42889 | 0.296612 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.78905 | 0.315349 | 0.157675 | − | 0.987491i | \(-0.449600\pi\) | ||||
0.157675 | + | 0.987491i | \(0.449600\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8.86569 | −0.481518 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.62497 | −0.304609 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8.42318 | 0.453489 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11.9344 | 0.640672 | 0.320336 | − | 0.947304i | \(-0.396204\pi\) | ||||
0.320336 | + | 0.947304i | \(0.396204\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.41253 | −0.182669 | −0.0913344 | − | 0.995820i | \(-0.529113\pi\) | ||||
−0.0913344 | + | 0.995820i | \(0.529113\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 10.7502 | 0.573805 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.72027 | −0.198010 | −0.0990049 | − | 0.995087i | \(-0.531566\pi\) | ||||
−0.0990049 | + | 0.995087i | \(0.531566\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 28.6669 | 1.52148 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 25.3819 | 1.33961 | 0.669803 | − | 0.742539i | \(-0.266379\pi\) | ||||
0.669803 | + | 0.742539i | \(0.266379\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.7001 | −0.931583 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.51383 | −0.184428 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 25.3397 | 1.32634 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.66006 | −0.399852 | −0.199926 | − | 0.979811i | \(-0.564070\pi\) | ||||
−0.199926 | + | 0.979811i | \(0.564070\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.73469 | 0.142362 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 32.1886 | 1.66666 | 0.833331 | − | 0.552774i | \(-0.186431\pi\) | ||||
0.833331 | + | 0.552774i | \(0.186431\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.84806 | 0.301992 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 22.1301 | 1.13976 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.38797 | −0.225395 | −0.112697 | − | 0.993629i | \(-0.535949\pi\) | ||||
−0.112697 | + | 0.993629i | \(0.535949\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.34023 | 0.222357 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.35384 | 0.273568 | 0.136784 | − | 0.990601i | \(-0.456323\pi\) | ||||
0.136784 | + | 0.990601i | \(0.456323\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −14.0755 | −0.715497 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.67620 | 0.0849866 | 0.0424933 | − | 0.999097i | \(-0.486470\pi\) | ||||
0.0424933 | + | 0.999097i | \(0.486470\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 59.3788 | 3.00292 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.10198 | 0.307804 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 19.9494 | 1.00376 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.85249 | 0.394105 | 0.197053 | − | 0.980393i | \(-0.436863\pi\) | ||||
0.197053 | + | 0.980393i | \(0.436863\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.10274 | 0.254819 | 0.127409 | − | 0.991850i | \(-0.459334\pi\) | ||||
0.127409 | + | 0.991850i | \(0.459334\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.84925 | −0.241559 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 14.6993 | 0.730414 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −12.1488 | −0.602192 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 21.6135 | 1.06872 | 0.534360 | − | 0.845257i | \(-0.320553\pi\) | ||||
0.534360 | + | 0.845257i | \(0.320553\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.07453 | 0.447614 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 16.5403 | 0.811932 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.77015 | 0.0866848 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −29.2736 | −1.43011 | −0.715054 | − | 0.699069i | \(-0.753598\pi\) | ||||
−0.715054 | + | 0.699069i | \(0.753598\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.32720 | −0.0646837 | −0.0323419 | − | 0.999477i | \(-0.510297\pi\) | ||||
−0.0323419 | + | 0.999477i | \(0.510297\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −22.2186 | −1.08031 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.29073 | 0.0626095 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7.91379 | −0.382081 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.2691 | −0.639151 | −0.319575 | − | 0.947561i | \(-0.603540\pi\) | ||||
−0.319575 | + | 0.947561i | \(0.603540\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −20.4388 | −0.982225 | −0.491113 | − | 0.871096i | \(-0.663410\pi\) | ||||
−0.491113 | + | 0.871096i | \(0.663410\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.88936 | −0.330320 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8.47632 | −0.405477 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.64250 | 0.0783922 | 0.0391961 | − | 0.999232i | \(-0.487520\pi\) | ||||
0.0391961 | + | 0.999232i | \(0.487520\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −16.3859 | −0.778518 | −0.389259 | − | 0.921128i | \(-0.627269\pi\) | ||||
−0.389259 | + | 0.921128i | \(0.627269\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −39.5537 | −1.87503 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −10.4487 | −0.494206 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 39.6265 | 1.87009 | 0.935045 | − | 0.354528i | \(-0.115358\pi\) | ||||
0.935045 | + | 0.354528i | \(0.115358\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.22160 | −0.198787 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.408265 | −0.0191820 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.21966 | 0.337721 | 0.168861 | − | 0.985640i | \(-0.445991\pi\) | ||||
0.168861 | + | 0.985640i | \(0.445991\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −23.5922 | −1.10119 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19.4564 | 0.906176 | 0.453088 | − | 0.891466i | \(-0.350322\pi\) | ||||
0.453088 | + | 0.891466i | \(0.350322\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.9014 | −0.831950 | −0.415975 | − | 0.909376i | \(-0.636560\pi\) | ||||
−0.415975 | + | 0.909376i | \(0.636560\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.50963 | 0.0700074 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.60602 | −0.0743176 | −0.0371588 | − | 0.999309i | \(-0.511831\pi\) | ||||
−0.0371588 | + | 0.999309i | \(0.511831\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.72907 | −0.125749 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 21.7286 | 0.999082 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.184251 | −0.00845403 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.45961 | 0.204191 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.93345 | 0.0883415 | 0.0441708 | − | 0.999024i | \(-0.485935\pi\) | ||||
0.0441708 | + | 0.999024i | \(0.485935\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.4734 | −0.477545 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 29.1290 | 1.32268 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 31.5340 | 1.42894 | 0.714471 | − | 0.699665i | \(-0.246667\pi\) | ||||
0.714471 | + | 0.699665i | \(0.246667\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.80683 | −0.217372 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −41.6704 | −1.88056 | −0.940279 | − | 0.340404i | \(-0.889436\pi\) | ||||
−0.940279 | + | 0.340404i | \(0.889436\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −48.5663 | −2.18731 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −25.3943 | −1.14139 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.75198 | 0.257494 | 0.128747 | − | 0.991677i | \(-0.458904\pi\) | ||||
0.128747 | + | 0.991677i | \(0.458904\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.68875 | −0.120125 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 40.6067 | 1.81057 | 0.905283 | − | 0.424810i | \(-0.139659\pi\) | ||||
0.905283 | + | 0.424810i | \(0.139659\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.9913 | 0.578103 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.126368 | −0.00561220 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13.1720 | −0.583837 | −0.291919 | − | 0.956443i | \(-0.594294\pi\) | ||||
−0.291919 | + | 0.956443i | \(0.594294\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.36778 | 0.148691 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −9.52163 | −0.419573 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 34.2993 | 1.50848 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.0967662 | 0.00424757 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 34.1957 | 1.49814 | 0.749070 | − | 0.662491i | \(-0.230501\pi\) | ||||
0.749070 | + | 0.662491i | \(0.230501\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 35.1253 | 1.53592 | 0.767961 | − | 0.640497i | \(-0.221271\pi\) | ||||
0.767961 | + | 0.640497i | \(0.221271\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10.6421 | 0.463576 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 32.2711 | 1.40309 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.14879 | 0.353627 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.63941 | −0.157641 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −25.6886 | −1.11061 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.89515 | −0.297548 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 24.0445 | 1.03376 | 0.516878 | − | 0.856059i | \(-0.327094\pi\) | ||||
0.516878 | + | 0.856059i | \(0.327094\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.156133 | 0.00670031 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 33.5369 | 1.43656 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −34.5404 | −1.47684 | −0.738421 | − | 0.674340i | \(-0.764428\pi\) | ||||
−0.738421 | + | 0.674340i | \(0.764428\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −28.0876 | −1.19875 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.93283 | 0.295348 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.26048 | 0.138400 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 26.6174 | 1.12782 | 0.563908 | − | 0.825837i | \(-0.309297\pi\) | ||||
0.563908 | + | 0.825837i | \(0.309297\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 18.7321 | 0.792283 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 17.3674 | 0.733253 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −38.4714 | −1.62137 | −0.810687 | − | 0.585479i | \(-0.800906\pi\) | ||||
−0.810687 | + | 0.585479i | \(0.800906\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 37.8606 | 1.59281 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −22.1979 | −0.930583 | −0.465291 | − | 0.885158i | \(-0.654050\pi\) | ||||
−0.465291 | + | 0.885158i | \(0.654050\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −32.3436 | −1.35354 | −0.676769 | − | 0.736196i | \(-0.736620\pi\) | ||||
−0.676769 | + | 0.736196i | \(0.736620\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.524268 | 0.0219016 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.20144 | 0.0501035 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23.4107 | 0.974599 | 0.487299 | − | 0.873235i | \(-0.337982\pi\) | ||||
0.487299 | + | 0.873235i | \(0.337982\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −8.81813 | −0.366469 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.88439 | −0.285122 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −21.8923 | −0.905133 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.45509 | −0.266430 | −0.133215 | − | 0.991087i | \(-0.542530\pi\) | ||||
−0.133215 | + | 0.991087i | \(0.542530\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.51915 | −0.0625956 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.47797 | 0.101930 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −38.1095 | −1.56497 | −0.782484 | − | 0.622671i | \(-0.786048\pi\) | ||||
−0.782484 | + | 0.622671i | \(0.786048\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.46606 | 0.264638 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −16.4950 | −0.673967 | −0.336983 | − | 0.941511i | \(-0.609407\pi\) | ||||
−0.336983 | + | 0.941511i | \(0.609407\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.14054 | 0.168896 | 0.0844482 | − | 0.996428i | \(-0.473087\pi\) | ||||
0.0844482 | + | 0.996428i | \(0.473087\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.74945 | −0.274859 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 15.0057 | 0.610067 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −40.8860 | −1.65951 | −0.829756 | − | 0.558127i | \(-0.811520\pi\) | ||||
−0.829756 | + | 0.558127i | \(0.811520\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 29.5693 | 1.19624 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 38.5223 | 1.55590 | 0.777951 | − | 0.628325i | \(-0.216259\pi\) | ||||
0.777951 | + | 0.628325i | \(0.216259\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.13299 | 0.0456867 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −26.2855 | −1.05822 | −0.529108 | − | 0.848555i | \(-0.677473\pi\) | ||||
−0.529108 | + | 0.848555i | \(0.677473\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −47.3181 | −1.90188 | −0.950938 | − | 0.309383i | \(-0.899878\pi\) | ||||
−0.950938 | + | 0.309383i | \(0.899878\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −21.9602 | −0.881231 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.1659 | −0.966635 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.47920 | −0.0990096 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 22.9846 | 0.916457 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.48510 | 0.178549 | 0.0892746 | − | 0.996007i | \(-0.471545\pi\) | ||||
0.0892746 | + | 0.996007i | \(0.471545\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −10.6887 | −0.424839 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −18.5348 | −0.735531 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −35.6401 | −1.40990 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −35.7692 | −1.41280 | −0.706399 | − | 0.707814i | \(-0.749682\pi\) | ||||
−0.706399 | + | 0.707814i | \(0.749682\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 30.7547 | 1.21285 | 0.606424 | − | 0.795142i | \(-0.292603\pi\) | ||||
0.606424 | + | 0.795142i | \(0.292603\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.83152 | −0.229616 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 44.6457 | 1.75520 | 0.877602 | − | 0.479391i | \(-0.159142\pi\) | ||||
0.877602 | + | 0.479391i | \(0.159142\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12.5795 | −0.493787 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −29.4217 | −1.15136 | −0.575680 | − | 0.817675i | \(-0.695263\pi\) | ||||
−0.575680 | + | 0.817675i | \(0.695263\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −26.0583 | −1.01818 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −31.5035 | −1.22907 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 39.7367 | 1.54792 | 0.773961 | − | 0.633234i | \(-0.218273\pi\) | ||||
0.773961 | + | 0.633234i | \(0.218273\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.58987 | −0.373003 | −0.186501 | − | 0.982455i | \(-0.559715\pi\) | ||||
−0.186501 | + | 0.982455i | \(0.559715\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 14.9724 | 0.581478 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −45.2066 | −1.75040 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.97670 | 0.231073 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 43.3594 | 1.67387 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28.1956 | 1.08686 | 0.543431 | − | 0.839454i | \(-0.317125\pi\) | ||||
0.543431 | + | 0.839454i | \(0.317125\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.477352 | −0.0183733 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.29576 | −0.357265 | −0.178633 | − | 0.983916i | \(-0.557167\pi\) | ||||
−0.178633 | + | 0.983916i | \(0.557167\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.357774 | 0.0137099 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 13.2127 | 0.505570 | 0.252785 | − | 0.967522i | \(-0.418653\pi\) | ||||
0.252785 | + | 0.967522i | \(0.418653\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −38.7524 | −1.48065 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −12.9652 | −0.494655 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.93499 | −0.226105 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.77498 | −0.257732 | −0.128866 | − | 0.991662i | \(-0.541134\pi\) | ||||
−0.128866 | + | 0.991662i | \(0.541134\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.55937 | −0.286743 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.98698 | 0.302528 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.51639 | −0.0573550 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 29.8871 | 1.12882 | 0.564410 | − | 0.825494i | \(-0.309104\pi\) | ||||
0.564410 | + | 0.825494i | \(0.309104\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.28105 | −0.123747 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −9.20525 | −0.346690 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.95367 | 0.186039 | 0.0930194 | − | 0.995664i | \(-0.470348\pi\) | ||||
0.0930194 | + | 0.995664i | \(0.470348\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −24.8020 | −0.930149 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.90587 | 0.370978 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 33.7955 | 1.26388 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.89535 | −0.145475 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −18.8348 | −0.702418 | −0.351209 | − | 0.936297i | \(-0.614229\pi\) | ||||
−0.351209 | + | 0.936297i | \(0.614229\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.90978 | 0.145406 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.982663 | −0.0364952 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −42.1079 | −1.56169 | −0.780847 | − | 0.624722i | \(-0.785212\pi\) | ||||
−0.780847 | + | 0.624722i | \(0.785212\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −13.7105 | −0.507795 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −41.1090 | −1.52047 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15.6455 | 0.577881 | 0.288940 | − | 0.957347i | \(-0.406697\pi\) | ||||
0.288940 | + | 0.957347i | \(0.406697\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10.4193 | 0.383798 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 32.1517 | 1.18272 | 0.591360 | − | 0.806407i | \(-0.298591\pi\) | ||||
0.591360 | + | 0.806407i | \(0.298591\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.13730 | −0.0785157 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.81171 | −0.139838 | −0.0699190 | − | 0.997553i | \(-0.522274\pi\) | ||||
−0.0699190 | + | 0.997553i | \(0.522274\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 44.6207 | 1.63478 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −20.5637 | −0.752386 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19.1017 | −0.697030 | −0.348515 | − | 0.937303i | \(-0.613314\pi\) | ||||
−0.348515 | + | 0.937303i | \(0.613314\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 12.2357 | 0.445894 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.74348 | 0.0634517 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 30.1926 | 1.09737 | 0.548684 | − | 0.836030i | \(-0.315129\pi\) | ||||
0.548684 | + | 0.836030i | \(0.315129\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 16.1660 | 0.586788 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 51.0772 | 1.85155 | 0.925774 | − | 0.378076i | \(-0.123414\pi\) | ||||
0.925774 | + | 0.378076i | \(0.123414\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 48.0442 | 1.73704 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −10.8447 | −0.391578 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −30.8036 | −1.11081 | −0.555404 | − | 0.831581i | \(-0.687436\pi\) | ||||
−0.555404 | + | 0.831581i | \(0.687436\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.792047 | 0.0285249 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 31.1901 | 1.12183 | 0.560916 | − | 0.827873i | \(-0.310449\pi\) | ||||
0.560916 | + | 0.827873i | \(0.310449\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.215326 | 0.00773473 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.14014 | −0.0408498 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 55.0184 | 1.96871 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 17.9613 | 0.641885 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11.6544 | 0.415963 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.4267 | 0.442963 | 0.221481 | − | 0.975165i | \(-0.428911\pi\) | ||||
0.221481 | + | 0.975165i | \(0.428911\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −8.43326 | −0.300232 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 37.3799 | 1.32740 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.84763 | 0.0655287 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 17.3519 | 0.614636 | 0.307318 | − | 0.951607i | \(-0.400568\pi\) | ||||
0.307318 | + | 0.951607i | \(0.400568\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −64.8920 | −2.29571 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 49.1751 | 1.73752 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 48.6326 | 1.71621 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −9.61043 | −0.338303 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 26.0371 | 0.915416 | 0.457708 | − | 0.889103i | \(-0.348670\pi\) | ||||
0.457708 | + | 0.889103i | \(0.348670\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16.2483 | 0.570557 | 0.285278 | − | 0.958445i | \(-0.407914\pi\) | ||||
0.285278 | + | 0.958445i | \(0.407914\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.40978 | −0.294944 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 20.5274 | 0.719042 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.86831 | 0.205306 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 30.5449 | 1.06603 | 0.533013 | − | 0.846107i | \(-0.321060\pi\) | ||||
0.533013 | + | 0.846107i | \(0.321060\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −47.3618 | −1.65093 | −0.825464 | − | 0.564455i | \(-0.809086\pi\) | ||||
−0.825464 | + | 0.564455i | \(0.809086\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.351403 | 0.0122343 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −49.3914 | −1.71751 | −0.858754 | − | 0.512388i | \(-0.828761\pi\) | ||||
−0.858754 | + | 0.512388i | \(0.828761\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.74976 | −0.0607717 | −0.0303859 | − | 0.999538i | \(-0.509674\pi\) | ||||
−0.0303859 | + | 0.999538i | \(0.509674\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9.91502 | 0.343948 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 11.4822 | 0.397358 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.93577 | −0.136040 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 48.9756 | 1.69083 | 0.845413 | − | 0.534113i | \(-0.179354\pi\) | ||||
0.845413 | + | 0.534113i | \(0.179354\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.97468 | 0.274989 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −13.1133 | −0.451646 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.539649 | 0.0185645 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.46411 | 0.118888 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 21.3946 | 0.733397 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −26.3270 | −0.901420 | −0.450710 | − | 0.892670i | \(-0.648829\pi\) | ||||
−0.450710 | + | 0.892670i | \(0.648829\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.85831 | −0.234549 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −41.2096 | −1.40769 | −0.703847 | − | 0.710352i | \(-0.748536\pi\) | ||||
−0.703847 | + | 0.710352i | \(0.748536\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13.1281 | −0.447925 | −0.223962 | − | 0.974598i | \(-0.571899\pi\) | ||||
−0.223962 | + | 0.974598i | \(0.571899\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −33.7054 | −1.14735 | −0.573673 | − | 0.819084i | \(-0.694482\pi\) | ||||
−0.573673 | + | 0.819084i | \(0.694482\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.413236 | −0.0140505 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −24.1016 | −0.818533 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 38.2874 | 1.29881 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.98238 | 0.304356 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −36.2145 | −1.22568 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 12.0469 | 0.406795 | 0.203398 | − | 0.979096i | \(-0.434802\pi\) | ||||
0.203398 | + | 0.979096i | \(0.434802\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 7.25321 | 0.244645 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −25.8023 | −0.869302 | −0.434651 | − | 0.900599i | \(-0.643128\pi\) | ||||
−0.434651 | + | 0.900599i | \(0.643128\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 55.2747 | 1.86014 | 0.930070 | − | 0.367381i | \(-0.119746\pi\) | ||||
0.930070 | + | 0.367381i | \(0.119746\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.37607 | 0.113485 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 52.5771 | 1.76536 | 0.882682 | − | 0.469970i | \(-0.155735\pi\) | ||||
0.882682 | + | 0.469970i | \(0.155735\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 28.2113 | 0.945113 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9.26333 | 0.309985 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 29.4454 | 0.984252 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 13.9366 | 0.465330 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −8.10206 | −0.270219 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.0248 | 0.433919 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.666759 | −0.0221638 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −35.7961 | −1.18859 | −0.594294 | − | 0.804248i | \(-0.702569\pi\) | ||||
−0.594294 | + | 0.804248i | \(0.702569\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −16.1513 | −0.535706 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.12715 | 0.169870 | 0.0849350 | − | 0.996386i | \(-0.472932\pi\) | ||||
0.0849350 | + | 0.996386i | \(0.472932\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 31.7446 | 1.05059 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −11.6368 | −0.384700 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.73713 | 0.0902897 | 0.0451449 | − | 0.998980i | \(-0.485625\pi\) | ||||
0.0451449 | + | 0.998980i | \(0.485625\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 11.5711 | 0.381281 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 47.4310 | 1.56121 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.465058 | 0.0152910 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 11.8377 | 0.388802 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 13.6670 | 0.448399 | 0.224199 | − | 0.974543i | \(-0.428023\pi\) | ||||
0.224199 | + | 0.974543i | \(0.428023\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 7.79071 | 0.255056 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −74.1669 | −2.42552 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.96389 | 0.227500 | 0.113750 | − | 0.993509i | \(-0.463714\pi\) | ||||
0.113750 | + | 0.993509i | \(0.463714\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.99895 | 0.326303 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −22.5498 | −0.735102 | −0.367551 | − | 0.930003i | \(-0.619804\pi\) | ||||
−0.367551 | + | 0.930003i | \(0.619804\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.43446 | 0.242099 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −43.9769 | −1.42906 | −0.714528 | − | 0.699607i | \(-0.753358\pi\) | ||||
−0.714528 | + | 0.699607i | \(0.753358\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 41.9258 | 1.36097 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.908407 | −0.0294571 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.89729 | 0.223425 | 0.111713 | − | 0.993741i | \(-0.464366\pi\) | ||||
0.111713 | + | 0.993741i | \(0.464366\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.23886 | −0.0724479 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −13.2222 | −0.427415 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.2246 | −0.942730 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 31.9372 | 1.02916 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 37.6574 | 1.21224 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24.7226 | 0.795025 | 0.397512 | − | 0.917597i | \(-0.369874\pi\) | ||||
0.397512 | + | 0.917597i | \(0.369874\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.69047 | 0.150680 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 51.8477 | 1.66387 | 0.831937 | − | 0.554871i | \(-0.187232\pi\) | ||||
0.831937 | + | 0.554871i | \(0.187232\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.302942 | 0.00970192 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 9.99891 | 0.319893 | 0.159947 | − | 0.987126i | \(-0.448868\pi\) | ||||
0.159947 | + | 0.987126i | \(0.448868\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −75.9126 | −2.42618 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −41.6946 | −1.33121 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.22767 | 0.0391566 | 0.0195783 | − | 0.999808i | \(-0.493768\pi\) | ||||
0.0195783 | + | 0.999808i | \(0.493768\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10.5821 | −0.337172 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −38.2652 | −1.21676 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 43.7198 | 1.38881 | 0.694403 | − | 0.719586i | \(-0.255669\pi\) | ||||
0.694403 | + | 0.719586i | \(0.255669\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6.24157 | −0.198070 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −27.6131 | −0.875393 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.79205 | 0.183436 | 0.0917180 | − | 0.995785i | \(-0.470764\pi\) | ||||
0.0917180 | + | 0.995785i | \(0.470764\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.50044 | −0.268942 |
(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 | 8036.2.a.q.1.8 | 15 | ||
7.2 | even | 3 | 1148.2.i.e.165.8 | ✓ | 30 | ||
7.4 | even | 3 | 1148.2.i.e.821.8 | yes | 30 | ||
7.6 | odd | 2 | 8036.2.a.r.1.8 | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1148.2.i.e.165.8 | ✓ | 30 | 7.2 | even | 3 | ||
1148.2.i.e.821.8 | yes | 30 | 7.4 | even | 3 | ||
8036.2.a.q.1.8 | 15 | 1.1 | even | 1 | trivial | ||
8036.2.a.r.1.8 | 15 | 7.6 | odd | 2 |