Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4536,2,Mod(1,4536)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4536, 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("4536.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4536 = 2^{3} \cdot 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4536.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: | \(36.2201423569\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.22545.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 6x^{2} + 5x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 504) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.519120\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4536.1 |
$q$-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 | ||||||||
\(5\) | 0.936586 | 0.418854 | 0.209427 | − | 0.977824i | \(-0.432840\pi\) | ||||
0.209427 | + | 0.977824i | \(0.432840\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.97483 | 1.49997 | 0.749983 | − | 0.661457i | \(-0.230061\pi\) | ||||
0.749983 | + | 0.661457i | \(0.230061\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.24431 | 0.345110 | 0.172555 | − | 0.985000i | \(-0.444798\pi\) | ||||
0.172555 | + | 0.985000i | \(0.444798\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.22446 | 1.26712 | 0.633559 | − | 0.773694i | \(-0.281593\pi\) | ||||
0.633559 | + | 0.773694i | \(0.281593\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.18622 | 1.18980 | 0.594900 | − | 0.803800i | \(-0.297192\pi\) | ||||
0.594900 | + | 0.803800i | \(0.297192\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.00532 | −0.418138 | −0.209069 | − | 0.977901i | \(-0.567043\pi\) | ||||
−0.209069 | + | 0.977901i | \(0.567043\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.12281 | −0.824561 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.87849 | 1.27730 | 0.638652 | − | 0.769496i | \(-0.279492\pi\) | ||||
0.638652 | + | 0.769496i | \(0.279492\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.73051 | −1.02923 | −0.514615 | − | 0.857421i | \(-0.672065\pi\) | ||||
−0.514615 | + | 0.857421i | \(0.672065\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.936586 | 0.158312 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.73051 | 1.59969 | 0.799843 | − | 0.600209i | \(-0.204916\pi\) | ||||
0.799843 | + | 0.600209i | \(0.204916\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.4741 | −1.79195 | −0.895976 | − | 0.444102i | \(-0.853523\pi\) | ||||
−0.895976 | + | 0.444102i | \(0.853523\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.60369 | 1.46455 | 0.732274 | − | 0.681010i | \(-0.238459\pi\) | ||||
0.732274 | + | 0.681010i | \(0.238459\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.96951 | −0.287282 | −0.143641 | − | 0.989630i | \(-0.545881\pi\) | ||||
−0.143641 | + | 0.989630i | \(0.545881\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.63418 | −1.04864 | −0.524318 | − | 0.851523i | \(-0.675680\pi\) | ||||
−0.524318 | + | 0.851523i | \(0.675680\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.65935 | 0.628267 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.87849 | 0.635126 | 0.317563 | − | 0.948237i | \(-0.397136\pi\) | ||||
0.317563 | + | 0.948237i | \(0.397136\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.04356 | −0.389688 | −0.194844 | − | 0.980834i | \(-0.562420\pi\) | ||||
−0.194844 | + | 0.980834i | \(0.562420\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.16541 | 0.144551 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.14798 | −0.140248 | −0.0701240 | − | 0.997538i | \(-0.522340\pi\) | ||||
−0.0701240 | + | 0.997538i | \(0.522340\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.83749 | −1.04882 | −0.524409 | − | 0.851467i | \(-0.675714\pi\) | ||||
−0.524409 | + | 0.851467i | \(0.675714\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.10698 | 0.714768 | 0.357384 | − | 0.933958i | \(-0.383669\pi\) | ||||
0.357384 | + | 0.933958i | \(0.383669\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.97483 | 0.566934 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.1083 | −1.36229 | −0.681144 | − | 0.732150i | \(-0.738517\pi\) | ||||
−0.681144 | + | 0.732150i | \(0.738517\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.862663 | −0.0946896 | −0.0473448 | − | 0.998879i | \(-0.515076\pi\) | ||||
−0.0473448 | + | 0.998879i | \(0.515076\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.89316 | 0.530737 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.8480 | −1.14989 | −0.574943 | − | 0.818194i | \(-0.694976\pi\) | ||||
−0.574943 | + | 0.818194i | \(0.694976\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.24431 | 0.130439 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.85734 | 0.498353 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.57043 | 0.768661 | 0.384330 | − | 0.923196i | \(-0.374432\pi\) | ||||
0.384330 | + | 0.923196i | \(0.374432\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.05939 | 0.503428 | 0.251714 | − | 0.967802i | \(-0.419006\pi\) | ||||
0.251714 | + | 0.967802i | \(0.419006\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.238992 | 0.0235485 | 0.0117743 | − | 0.999931i | \(-0.496252\pi\) | ||||
0.0117743 | + | 0.999931i | \(0.496252\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.25496 | 0.894710 | 0.447355 | − | 0.894356i | \(-0.352366\pi\) | ||||
0.447355 | + | 0.894356i | \(0.352366\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.5453 | −1.01005 | −0.505026 | − | 0.863104i | \(-0.668517\pi\) | ||||
−0.505026 | + | 0.863104i | \(0.668517\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.1281 | −0.952774 | −0.476387 | − | 0.879236i | \(-0.658054\pi\) | ||||
−0.476387 | + | 0.879236i | \(0.658054\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.87816 | −0.175139 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.22446 | 0.478926 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 13.7489 | 1.24990 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.54429 | −0.764225 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.52720 | 0.579196 | 0.289598 | − | 0.957148i | \(-0.406478\pi\) | ||||
0.289598 | + | 0.957148i | \(0.406478\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.53495 | −0.308850 | −0.154425 | − | 0.988005i | \(-0.549353\pi\) | ||||
−0.154425 | + | 0.988005i | \(0.549353\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.18622 | 0.449702 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.97206 | 0.424792 | 0.212396 | − | 0.977184i | \(-0.431873\pi\) | ||||
0.212396 | + | 0.977184i | \(0.431873\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.75133 | 0.827097 | 0.413548 | − | 0.910482i | \(-0.364289\pi\) | ||||
0.413548 | + | 0.910482i | \(0.364289\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.19024 | 0.517654 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.44230 | 0.535004 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.7822 | −1.04716 | −0.523578 | − | 0.851978i | \(-0.675403\pi\) | ||||
−0.523578 | + | 0.851978i | \(0.675403\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 22.9563 | 1.86816 | 0.934078 | − | 0.357070i | \(-0.116224\pi\) | ||||
0.934078 | + | 0.357070i | \(0.116224\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.36712 | −0.431097 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.5098 | 1.31762 | 0.658812 | − | 0.752308i | \(-0.271059\pi\) | ||||
0.658812 | + | 0.752308i | \(0.271059\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.00532 | −0.158041 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.2245 | 1.34912 | 0.674562 | − | 0.738218i | \(-0.264333\pi\) | ||||
0.674562 | + | 0.738218i | \(0.264333\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13.1281 | 1.01589 | 0.507943 | − | 0.861391i | \(-0.330406\pi\) | ||||
0.507943 | + | 0.861391i | \(0.330406\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.4517 | −0.880899 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −18.9882 | −1.44365 | −0.721824 | − | 0.692076i | \(-0.756696\pi\) | ||||
−0.721824 | + | 0.692076i | \(0.756696\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.12281 | −0.311655 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.61835 | 0.569422 | 0.284711 | − | 0.958613i | \(-0.408102\pi\) | ||||
0.284711 | + | 0.958613i | \(0.408102\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.27737 | −0.689581 | −0.344791 | − | 0.938680i | \(-0.612050\pi\) | ||||
−0.344791 | + | 0.938680i | \(0.612050\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9.11346 | 0.670035 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 25.9908 | 1.90063 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.60239 | 0.694804 | 0.347402 | − | 0.937716i | \(-0.387064\pi\) | ||||
0.347402 | + | 0.937716i | \(0.387064\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15.0831 | −1.08571 | −0.542853 | − | 0.839828i | \(-0.682656\pi\) | ||||
−0.542853 | + | 0.839828i | \(0.682656\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.0712 | −0.788788 | −0.394394 | − | 0.918942i | \(-0.629045\pi\) | ||||
−0.394394 | + | 0.918942i | \(0.629045\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.3368 | 1.29986 | 0.649929 | − | 0.759995i | \(-0.274799\pi\) | ||||
0.649929 | + | 0.759995i | \(0.274799\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.87849 | 0.482776 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10.7465 | −0.750567 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 25.8005 | 1.78466 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.61822 | 0.180245 | 0.0901227 | − | 0.995931i | \(-0.471274\pi\) | ||||
0.0901227 | + | 0.995931i | \(0.471274\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.99468 | 0.613432 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.73051 | −0.389013 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.50087 | 0.437296 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −25.0884 | −1.68005 | −0.840023 | − | 0.542551i | \(-0.817458\pi\) | ||||
−0.840023 | + | 0.542551i | \(0.817458\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −25.5562 | −1.69623 | −0.848113 | − | 0.529815i | \(-0.822262\pi\) | ||||
−0.848113 | + | 0.529815i | \(0.822262\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.47313 | 0.361675 | 0.180837 | − | 0.983513i | \(-0.442119\pi\) | ||||
0.180837 | + | 0.983513i | \(0.442119\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.6774 | 0.699500 | 0.349750 | − | 0.936843i | \(-0.386267\pi\) | ||||
0.349750 | + | 0.936843i | \(0.386267\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.84461 | −0.120329 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.00000 | 0.323423 | 0.161712 | − | 0.986838i | \(-0.448299\pi\) | ||||
0.161712 | + | 0.986838i | \(0.448299\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.3368 | 1.31001 | 0.655003 | − | 0.755626i | \(-0.272667\pi\) | ||||
0.655003 | + | 0.755626i | \(0.272667\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.936586 | 0.0598363 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.45328 | 0.410612 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 19.8151 | 1.25072 | 0.625358 | − | 0.780338i | \(-0.284953\pi\) | ||||
0.625358 | + | 0.780338i | \(0.284953\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.97613 | −0.627194 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.93901 | −0.120952 | −0.0604761 | − | 0.998170i | \(-0.519262\pi\) | ||||
−0.0604761 | + | 0.998170i | \(0.519262\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.73051 | 0.604625 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −13.3554 | −0.823526 | −0.411763 | − | 0.911291i | \(-0.635087\pi\) | ||||
−0.411763 | + | 0.911291i | \(0.635087\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.15007 | −0.439225 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.15040 | 0.253055 | 0.126527 | − | 0.991963i | \(-0.459617\pi\) | ||||
0.126527 | + | 0.991963i | \(0.459617\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.6050 | −1.00868 | −0.504341 | − | 0.863505i | \(-0.668264\pi\) | ||||
−0.504341 | + | 0.863505i | \(0.668264\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −20.5102 | −1.23681 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.1083 | 1.02794 | 0.513968 | − | 0.857809i | \(-0.328175\pi\) | ||||
0.513968 | + | 0.857809i | \(0.328175\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.9801 | −0.893641 | −0.446820 | − | 0.894624i | \(-0.647444\pi\) | ||||
−0.446820 | + | 0.894624i | \(0.647444\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −18.0116 | −1.07068 | −0.535339 | − | 0.844637i | \(-0.679816\pi\) | ||||
−0.535339 | + | 0.844637i | \(0.679816\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −11.4741 | −0.677294 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.2950 | 0.605588 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −27.6724 | −1.61664 | −0.808320 | − | 0.588743i | \(-0.799623\pi\) | ||||
−0.808320 | + | 0.588743i | \(0.799623\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.56913 | 0.266025 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.49525 | −0.144304 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.60369 | 0.553547 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.85056 | −0.163222 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.10040 | −0.348168 | −0.174084 | − | 0.984731i | \(-0.555696\pi\) | ||||
−0.174084 | + | 0.984731i | \(0.555696\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 26.6553 | 1.51149 | 0.755743 | − | 0.654869i | \(-0.227276\pi\) | ||||
0.755743 | + | 0.654869i | \(0.227276\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.1362 | 1.36426 | 0.682130 | − | 0.731231i | \(-0.261054\pi\) | ||||
0.682130 | + | 0.731231i | \(0.261054\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −17.6009 | −0.988566 | −0.494283 | − | 0.869301i | \(-0.664569\pi\) | ||||
−0.494283 | + | 0.869301i | \(0.664569\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 34.2193 | 1.91591 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 27.0952 | 1.50762 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.13006 | −0.284565 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.96951 | −0.108582 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.2995 | 1.33562 | 0.667810 | − | 0.744332i | \(-0.267232\pi\) | ||||
0.667810 | + | 0.744332i | \(0.267232\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.07518 | −0.0587435 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.9443 | 1.24986 | 0.624929 | − | 0.780682i | \(-0.285128\pi\) | ||||
0.624929 | + | 0.780682i | \(0.285128\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −28.5083 | −1.54381 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.7386 | −0.683844 | −0.341922 | − | 0.939728i | \(-0.611078\pi\) | ||||
−0.341922 | + | 0.939728i | \(0.611078\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.98936 | −0.427660 | −0.213830 | − | 0.976871i | \(-0.568594\pi\) | ||||
−0.213830 | + | 0.976871i | \(0.568594\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −21.9563 | −1.16861 | −0.584307 | − | 0.811532i | \(-0.698634\pi\) | ||||
−0.584307 | + | 0.811532i | \(0.698634\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.27707 | −0.439301 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 20.4673 | 1.08022 | 0.540112 | − | 0.841593i | \(-0.318382\pi\) | ||||
0.540112 | + | 0.841593i | \(0.318382\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.89688 | 0.415625 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.71971 | 0.299383 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19.8835 | −1.03791 | −0.518955 | − | 0.854802i | \(-0.673679\pi\) | ||||
−0.518955 | + | 0.854802i | \(0.673679\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.63418 | −0.396347 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 34.2876 | 1.77534 | 0.887672 | − | 0.460477i | \(-0.152322\pi\) | ||||
0.887672 | + | 0.460477i | \(0.152322\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.55900 | 0.440811 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.6248 | 0.956694 | 0.478347 | − | 0.878171i | \(-0.341236\pi\) | ||||
0.478347 | + | 0.878171i | \(0.341236\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 32.8720 | 1.67968 | 0.839842 | − | 0.542832i | \(-0.182648\pi\) | ||||
0.839842 | + | 0.542832i | \(0.182648\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.65935 | 0.237463 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −21.6500 | −1.09770 | −0.548850 | − | 0.835921i | \(-0.684934\pi\) | ||||
−0.548850 | + | 0.835921i | \(0.684934\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.4767 | −0.529831 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −11.3404 | −0.570600 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.2721 | 0.816673 | 0.408336 | − | 0.912832i | \(-0.366109\pi\) | ||||
0.408336 | + | 0.912832i | \(0.366109\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.14266 | −0.456563 | −0.228281 | − | 0.973595i | \(-0.573311\pi\) | ||||
−0.228281 | + | 0.973595i | \(0.573311\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.13055 | −0.355198 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 48.4076 | 2.39948 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −22.1953 | −1.09749 | −0.548743 | − | 0.835991i | \(-0.684893\pi\) | ||||
−0.548743 | + | 0.835991i | \(0.684893\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.87849 | 0.240055 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.807958 | −0.0396611 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 27.9201 | 1.36399 | 0.681994 | − | 0.731358i | \(-0.261113\pi\) | ||||
0.681994 | + | 0.731358i | \(0.261113\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.0883 | 1.17399 | 0.586996 | − | 0.809590i | \(-0.300311\pi\) | ||||
0.586996 | + | 0.809590i | \(0.300311\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −21.5394 | −1.04482 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.04356 | −0.147288 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −26.1623 | −1.26020 | −0.630098 | − | 0.776516i | \(-0.716985\pi\) | ||||
−0.630098 | + | 0.776516i | \(0.716985\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.5630 | −0.892082 | −0.446041 | − | 0.895013i | \(-0.647166\pi\) | ||||
−0.446041 | + | 0.895013i | \(0.647166\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −10.4000 | −0.497501 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.70790 | 0.367878 | 0.183939 | − | 0.982938i | \(-0.441115\pi\) | ||||
0.183939 | + | 0.982938i | \(0.441115\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 33.0408 | 1.56982 | 0.784909 | − | 0.619611i | \(-0.212710\pi\) | ||||
0.784909 | + | 0.619611i | \(0.212710\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.1601 | −0.481634 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 19.9283 | 0.940477 | 0.470238 | − | 0.882540i | \(-0.344168\pi\) | ||||
0.470238 | + | 0.882540i | \(0.344168\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −57.0816 | −2.68787 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.16541 | 0.0546351 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −33.8653 | −1.58415 | −0.792075 | − | 0.610424i | \(-0.790999\pi\) | ||||
−0.792075 | + | 0.610424i | \(0.790999\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14.5070 | −0.675659 | −0.337830 | − | 0.941207i | \(-0.609693\pi\) | ||||
−0.337830 | + | 0.941207i | \(0.609693\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 25.0697 | 1.16509 | 0.582544 | − | 0.812799i | \(-0.302057\pi\) | ||||
0.582544 | + | 0.812799i | \(0.302057\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −0.102955 | −0.00476419 | −0.00238209 | − | 0.999997i | \(-0.500758\pi\) | ||||
−0.00238209 | + | 0.999997i | \(0.500758\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.14798 | −0.0530088 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 47.7767 | 2.19677 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −21.3818 | −0.981064 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.25336 | 0.240032 | 0.120016 | − | 0.992772i | \(-0.461705\pi\) | ||||
0.120016 | + | 0.992772i | \(0.461705\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.1078 | 0.552068 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.09036 | 0.321957 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −30.7319 | −1.39260 | −0.696299 | − | 0.717752i | \(-0.745171\pi\) | ||||
−0.696299 | + | 0.717752i | \(0.745171\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.71841 | −0.212939 | −0.106469 | − | 0.994316i | \(-0.533955\pi\) | ||||
−0.106469 | + | 0.994316i | \(0.533955\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 35.9364 | 1.61850 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8.83749 | −0.396416 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.7132 | 1.10632 | 0.553158 | − | 0.833076i | \(-0.313423\pi\) | ||||
0.553158 | + | 0.833076i | \(0.313423\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −19.4083 | −0.865371 | −0.432686 | − | 0.901545i | \(-0.642434\pi\) | ||||
−0.432686 | + | 0.901545i | \(0.642434\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.73856 | 0.210863 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.45701 | 0.241878 | 0.120939 | − | 0.992660i | \(-0.461410\pi\) | ||||
0.120939 | + | 0.992660i | \(0.461410\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.10698 | 0.270157 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.223836 | 0.00986340 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.79795 | −0.430913 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −24.7683 | −1.08512 | −0.542558 | − | 0.840018i | \(-0.682544\pi\) | ||||
−0.542558 | + | 0.840018i | \(0.682544\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −32.7530 | −1.43219 | −0.716094 | − | 0.698004i | \(-0.754072\pi\) | ||||
−0.716094 | + | 0.698004i | \(0.754072\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −29.9388 | −1.30416 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.9787 | −0.825160 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −14.2774 | −0.618421 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.66806 | 0.374753 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.97483 | 0.214281 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 37.8575 | 1.62762 | 0.813811 | − | 0.581130i | \(-0.197389\pi\) | ||||
0.813811 | + | 0.581130i | \(0.197389\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9.87654 | −0.423064 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.49671 | 0.149509 | 0.0747543 | − | 0.997202i | \(-0.476183\pi\) | ||||
0.0747543 | + | 0.997202i | \(0.476183\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 35.6734 | 1.51974 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.1083 | −0.514896 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −34.1226 | −1.44582 | −0.722911 | − | 0.690941i | \(-0.757197\pi\) | ||||
−0.722911 | + | 0.690941i | \(0.757197\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11.9500 | 0.505431 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15.3014 | 0.644878 | 0.322439 | − | 0.946590i | \(-0.395497\pi\) | ||||
0.322439 | + | 0.946590i | \(0.395497\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.48586 | −0.399073 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 32.9907 | 1.38304 | 0.691520 | − | 0.722357i | \(-0.256941\pi\) | ||||
0.691520 | + | 0.722357i | \(0.256941\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.4300 | −0.896819 | −0.448410 | − | 0.893828i | \(-0.648009\pi\) | ||||
−0.448410 | + | 0.893828i | \(0.648009\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.26755 | 0.344781 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −38.4188 | −1.59939 | −0.799697 | − | 0.600404i | \(-0.795007\pi\) | ||||
−0.799697 | + | 0.600404i | \(0.795007\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.862663 | −0.0357893 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −37.9787 | −1.57292 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −16.8754 | −0.696524 | −0.348262 | − | 0.937397i | \(-0.613228\pi\) | ||||
−0.348262 | + | 0.937397i | \(0.613228\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −29.7197 | −1.22458 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 21.7817 | 0.894467 | 0.447233 | − | 0.894417i | \(-0.352409\pi\) | ||||
0.447233 | + | 0.894417i | \(0.352409\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.89316 | 0.200600 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −26.7555 | −1.09320 | −0.546601 | − | 0.837393i | \(-0.684078\pi\) | ||||
−0.546601 | + | 0.837393i | \(0.684078\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25.1229 | −1.02479 | −0.512393 | − | 0.858751i | \(-0.671241\pi\) | ||||
−0.512393 | + | 0.858751i | \(0.671241\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 12.8770 | 0.523526 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.63950 | 0.350667 | 0.175333 | − | 0.984509i | \(-0.443900\pi\) | ||||
0.175333 | + | 0.984509i | \(0.443900\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.45068 | −0.0991440 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 46.1789 | 1.86515 | 0.932575 | − | 0.360977i | \(-0.117557\pi\) | ||||
0.932575 | + | 0.360977i | \(0.117557\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −11.5244 | −0.463957 | −0.231978 | − | 0.972721i | \(-0.574520\pi\) | ||||
−0.231978 | + | 0.972721i | \(0.574520\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 39.2650 | 1.57819 | 0.789096 | − | 0.614270i | \(-0.210549\pi\) | ||||
0.789096 | + | 0.614270i | \(0.210549\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −10.8480 | −0.434616 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.6116 | 0.504463 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 50.8367 | 2.02699 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.8387 | 0.909193 | 0.454596 | − | 0.890698i | \(-0.349784\pi\) | ||||
0.454596 | + | 0.890698i | \(0.349784\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.11329 | 0.242598 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.24431 | 0.0493015 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18.0980 | −0.714827 | −0.357413 | − | 0.933946i | \(-0.616341\pi\) | ||||
−0.357413 | + | 0.933946i | \(0.616341\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −30.0833 | −1.18637 | −0.593184 | − | 0.805067i | \(-0.702129\pi\) | ||||
−0.593184 | + | 0.805067i | \(0.702129\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −25.1323 | −0.988054 | −0.494027 | − | 0.869447i | \(-0.664476\pi\) | ||||
−0.494027 | + | 0.869447i | \(0.664476\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 24.2697 | 0.952668 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10.4977 | 0.410806 | 0.205403 | − | 0.978678i | \(-0.434150\pi\) | ||||
0.205403 | + | 0.978678i | \(0.434150\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.31079 | −0.129363 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.08277 | −0.314860 | −0.157430 | − | 0.987530i | \(-0.550321\pi\) | ||||
−0.157430 | + | 0.987530i | \(0.550321\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26.9059 | −1.04652 | −0.523260 | − | 0.852173i | \(-0.675284\pi\) | ||||
−0.523260 | + | 0.852173i | \(0.675284\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.85734 | 0.188360 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −13.7936 | −0.534090 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −15.1412 | −0.584519 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.2232 | −0.471170 | −0.235585 | − | 0.971854i | \(-0.575701\pi\) | ||||
−0.235585 | + | 0.971854i | \(0.575701\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.68030 | 0.256745 | 0.128372 | − | 0.991726i | \(-0.459025\pi\) | ||||
0.128372 | + | 0.991726i | \(0.459025\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.57043 | 0.290526 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 19.2125 | 0.735146 | 0.367573 | − | 0.929995i | \(-0.380189\pi\) | ||||
0.367573 | + | 0.929995i | \(0.380189\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.65677 | 0.177926 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −9.49931 | −0.361895 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.4541 | −0.435735 | −0.217867 | − | 0.975978i | \(-0.569910\pi\) | ||||
−0.217867 | + | 0.975978i | \(0.569910\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9.13296 | 0.346433 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −59.9460 | −2.27062 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.29596 | −0.162256 | −0.0811281 | − | 0.996704i | \(-0.525852\pi\) | ||||
−0.0811281 | + | 0.996704i | \(0.525852\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 50.4646 | 1.90331 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.05939 | 0.190278 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.8901 | 0.484099 | 0.242049 | − | 0.970264i | \(-0.422180\pi\) | ||||
0.242049 | + | 0.970264i | \(0.422180\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 11.4915 | 0.430361 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.79769 | 0.216821 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.46489 | 0.203806 | 0.101903 | − | 0.994794i | \(-0.467507\pi\) | ||||
0.101903 | + | 0.994794i | \(0.467507\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.238992 | 0.00890051 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −28.3587 | −1.05322 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −49.8599 | −1.84920 | −0.924601 | − | 0.380936i | \(-0.875602\pi\) | ||||
−0.924601 | + | 0.380936i | \(0.875602\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 50.1741 | 1.85576 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −35.2246 | −1.30105 | −0.650525 | − | 0.759485i | \(-0.725451\pi\) | ||||
−0.650525 | + | 0.759485i | \(0.725451\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.71100 | −0.210367 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −35.7209 | −1.31401 | −0.657007 | − | 0.753885i | \(-0.728178\pi\) | ||||
−0.657007 | + | 0.753885i | \(0.728178\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13.0609 | 0.479156 | 0.239578 | − | 0.970877i | \(-0.422991\pi\) | ||||
0.239578 | + | 0.970877i | \(0.422991\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11.9716 | −0.438605 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.25496 | 0.338169 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.22446 | −0.0811717 | −0.0405859 | − | 0.999176i | \(-0.512922\pi\) | ||||
−0.0405859 | + | 0.999176i | \(0.512922\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 21.5005 | 0.782484 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.27335 | 0.155317 | 0.0776587 | − | 0.996980i | \(-0.475256\pi\) | ||||
0.0776587 | + | 0.996980i | \(0.475256\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 50.4411 | 1.82849 | 0.914245 | − | 0.405162i | \(-0.132785\pi\) | ||||
0.914245 | + | 0.405162i | \(0.132785\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.5453 | −0.381764 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.07037 | 0.219188 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.06986 | −0.0746411 | −0.0373205 | − | 0.999303i | \(-0.511882\pi\) | ||||
−0.0373205 | + | 0.999303i | \(0.511882\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −28.3739 | −1.02054 | −0.510269 | − | 0.860015i | \(-0.670454\pi\) | ||||
−0.510269 | + | 0.860015i | \(0.670454\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 23.6258 | 0.848664 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −59.5072 | −2.13207 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −43.9650 | −1.57319 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 15.4628 | 0.551892 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.45072 | −0.123005 | −0.0615025 | − | 0.998107i | \(-0.519589\pi\) | ||||
−0.0615025 | + | 0.998107i | \(0.519589\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.1281 | −0.360115 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.78714 | −0.134485 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −22.4460 | −0.795079 | −0.397540 | − | 0.917585i | \(-0.630136\pi\) | ||||
−0.397540 | + | 0.917585i | \(0.630136\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.2896 | −0.364020 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 30.3812 | 1.07213 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.87816 | −0.0661963 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 18.2366 | 0.641164 | 0.320582 | − | 0.947221i | \(-0.396122\pi\) | ||||
0.320582 | + | 0.947221i | \(0.396122\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16.8280 | 0.590910 | 0.295455 | − | 0.955357i | \(-0.404529\pi\) | ||||
0.295455 | + | 0.955357i | \(0.404529\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 16.1322 | 0.565086 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 49.8068 | 1.74252 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −37.2298 | −1.29933 | −0.649665 | − | 0.760221i | \(-0.725091\pi\) | ||||
−0.649665 | + | 0.760221i | \(0.725091\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.2749 | −0.427878 | −0.213939 | − | 0.976847i | \(-0.568629\pi\) | ||||
−0.213939 | + | 0.976847i | \(0.568629\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.60355 | −0.299175 | −0.149587 | − | 0.988749i | \(-0.547795\pi\) | ||||
−0.149587 | + | 0.988749i | \(0.547795\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −44.2887 | −1.53821 | −0.769105 | − | 0.639123i | \(-0.779298\pi\) | ||||
−0.769105 | + | 0.639123i | \(0.779298\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.22446 | 0.181017 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.2956 | 0.425508 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 47.2307 | 1.63059 | 0.815293 | − | 0.579048i | \(-0.196576\pi\) | ||||
0.815293 | + | 0.579048i | \(0.196576\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 18.3137 | 0.631506 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −10.7255 | −0.368968 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 13.7489 | 0.472418 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −19.5128 | −0.668890 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −23.9650 | −0.820546 | −0.410273 | − | 0.911963i | \(-0.634567\pi\) | ||||
−0.410273 | + | 0.911963i | \(0.634567\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 13.0181 | 0.444688 | 0.222344 | − | 0.974968i | \(-0.428629\pi\) | ||||
0.222344 | + | 0.974968i | \(0.428629\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.0947371 | −0.00323239 | −0.00161619 | − | 0.999999i | \(-0.500514\pi\) | ||||
−0.00161619 | + | 0.999999i | \(0.500514\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −25.8729 | −0.880723 | −0.440361 | − | 0.897821i | \(-0.645150\pi\) | ||||
−0.440361 | + | 0.897821i | \(0.645150\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −17.7841 | −0.604678 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −60.2366 | −2.04339 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.42845 | −0.0484010 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −8.54429 | −0.288850 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −53.8083 | −1.81698 | −0.908489 | − | 0.417908i | \(-0.862763\pi\) | ||||
−0.908489 | + | 0.417908i | \(0.862763\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −42.8689 | −1.44429 | −0.722144 | − | 0.691743i | \(-0.756843\pi\) | ||||
−0.722144 | + | 0.691743i | \(0.756843\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 34.5967 | 1.16427 | 0.582136 | − | 0.813092i | \(-0.302217\pi\) | ||||
0.582136 | + | 0.813092i | \(0.302217\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −20.4555 | −0.686830 | −0.343415 | − | 0.939184i | \(-0.611584\pi\) | ||||
−0.343415 | + | 0.939184i | \(0.611584\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.52720 | 0.218915 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −10.2143 | −0.341808 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.13524 | 0.238505 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −39.4173 | −1.31464 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −39.8845 | −1.32874 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −8.68905 | −0.288834 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.84912 | −0.260626 | −0.130313 | − | 0.991473i | \(-0.541598\pi\) | ||||
−0.130313 | + | 0.991473i | \(0.541598\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.74379 | −0.256563 | −0.128282 | − | 0.991738i | \(-0.540946\pi\) | ||||
−0.128282 | + | 0.991738i | \(0.540946\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.29160 | −0.142031 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.53495 | −0.116734 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 19.3702 | 0.638963 | 0.319482 | − | 0.947592i | \(-0.396491\pi\) | ||||
0.319482 | + | 0.947592i | \(0.396491\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10.9966 | −0.361958 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −40.1170 | −1.31904 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.55979 | −0.116793 | −0.0583964 | − | 0.998293i | \(-0.518599\pi\) | ||||
−0.0583964 | + | 0.998293i | \(0.518599\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.18622 | 0.169972 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 24.3426 | 0.796089 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −34.2230 | −1.11802 | −0.559008 | − | 0.829162i | \(-0.688818\pi\) | ||||
−0.559008 | + | 0.829162i | \(0.688818\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12.0407 | −0.392514 | −0.196257 | − | 0.980552i | \(-0.562879\pi\) | ||||
−0.196257 | + | 0.980552i | \(0.562879\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 23.0093 | 0.749284 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −22.7247 | −0.738453 | −0.369227 | − | 0.929339i | \(-0.620377\pi\) | ||||
−0.369227 | + | 0.929339i | \(0.620377\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.59899 | 0.246674 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6.74488 | −0.218488 | −0.109244 | − | 0.994015i | \(-0.534843\pi\) | ||||
−0.109244 | + | 0.994015i | \(0.534843\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.99346 | 0.291022 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.97206 | 0.160556 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.83879 | 0.0593158 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −14.1266 | −0.454752 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −25.6534 | −0.824958 | −0.412479 | − | 0.910967i | \(-0.635337\pi\) | ||||
−0.412479 | + | 0.910967i | \(0.635337\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 40.9298 | 1.31350 | 0.656750 | − | 0.754108i | \(-0.271931\pi\) | ||||
0.656750 | + | 0.754108i | \(0.271931\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.75133 | 0.312613 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 44.4730 | 1.42282 | 0.711408 | − | 0.702779i | \(-0.248058\pi\) | ||||
0.711408 | + | 0.702779i | \(0.248058\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −53.9669 | −1.72479 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −56.9100 | −1.81515 | −0.907573 | − | 0.419893i | \(-0.862067\pi\) | ||||
−0.907573 | + | 0.419893i | \(0.862067\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10.3691 | −0.330387 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −19.2585 | −0.612384 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −44.7331 | −1.42099 | −0.710496 | − | 0.703701i | \(-0.751530\pi\) | ||||
−0.710496 | + | 0.703701i | \(0.751530\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 17.1740 | 0.544451 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −18.7336 | −0.593300 | −0.296650 | − | 0.954986i | \(-0.595869\pi\) | ||||
−0.296650 | + | 0.954986i | \(0.595869\pi\) | |||||||
\(998\) | 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 | 4536.2.a.x.1.3 | 4 | ||
3.2 | odd | 2 | 4536.2.a.ba.1.2 | 4 | |||
4.3 | odd | 2 | 9072.2.a.ce.1.3 | 4 | |||
9.2 | odd | 6 | 1512.2.r.d.1009.3 | 8 | |||
9.4 | even | 3 | 504.2.r.d.169.2 | ✓ | 8 | ||
9.5 | odd | 6 | 1512.2.r.d.505.3 | 8 | |||
9.7 | even | 3 | 504.2.r.d.337.2 | yes | 8 | ||
12.11 | even | 2 | 9072.2.a.cl.1.2 | 4 | |||
36.7 | odd | 6 | 1008.2.r.m.337.3 | 8 | |||
36.11 | even | 6 | 3024.2.r.l.1009.3 | 8 | |||
36.23 | even | 6 | 3024.2.r.l.2017.3 | 8 | |||
36.31 | odd | 6 | 1008.2.r.m.673.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.r.d.169.2 | ✓ | 8 | 9.4 | even | 3 | ||
504.2.r.d.337.2 | yes | 8 | 9.7 | even | 3 | ||
1008.2.r.m.337.3 | 8 | 36.7 | odd | 6 | |||
1008.2.r.m.673.3 | 8 | 36.31 | odd | 6 | |||
1512.2.r.d.505.3 | 8 | 9.5 | odd | 6 | |||
1512.2.r.d.1009.3 | 8 | 9.2 | odd | 6 | |||
3024.2.r.l.1009.3 | 8 | 36.11 | even | 6 | |||
3024.2.r.l.2017.3 | 8 | 36.23 | even | 6 | |||
4536.2.a.x.1.3 | 4 | 1.1 | even | 1 | trivial | ||
4536.2.a.ba.1.2 | 4 | 3.2 | odd | 2 | |||
9072.2.a.ce.1.3 | 4 | 4.3 | odd | 2 | |||
9072.2.a.cl.1.2 | 4 | 12.11 | even | 2 |