Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6012,2,Mod(1,6012)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6012, 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("6012.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6012 = 2^{2} \cdot 3^{2} \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6012.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: | \(48.0060616952\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.149169.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 6x^{3} - 3x^{2} + 4x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2004) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.25464\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6012.1 |
$q$-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 | ||||||||
\(5\) | 0.171230 | 0.0765766 | 0.0382883 | − | 0.999267i | \(-0.487809\pi\) | ||||
0.0382883 | + | 0.999267i | \(0.487809\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.92708 | 1.10633 | 0.553166 | − | 0.833071i | \(-0.313420\pi\) | ||||
0.553166 | + | 0.833071i | \(0.313420\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.171230 | −0.0516279 | −0.0258140 | − | 0.999667i | \(-0.508218\pi\) | ||||
−0.0258140 | + | 0.999667i | \(0.508218\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.29824 | −0.914769 | −0.457384 | − | 0.889269i | \(-0.651214\pi\) | ||||
−0.457384 | + | 0.889269i | \(0.651214\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.91520 | 0.949577 | 0.474788 | − | 0.880100i | \(-0.342525\pi\) | ||||
0.474788 | + | 0.880100i | \(0.342525\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.81055 | −1.33303 | −0.666516 | − | 0.745491i | \(-0.732215\pi\) | ||||
−0.666516 | + | 0.745491i | \(0.732215\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.35674 | 0.491415 | 0.245708 | − | 0.969344i | \(-0.420980\pi\) | ||||
0.245708 | + | 0.969344i | \(0.420980\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.97068 | −0.994136 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.91568 | −1.65560 | −0.827800 | − | 0.561024i | \(-0.810408\pi\) | ||||
−0.827800 | + | 0.561024i | \(0.810408\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.15936 | −0.208227 | −0.104113 | − | 0.994565i | \(-0.533200\pi\) | ||||
−0.104113 | + | 0.994565i | \(0.533200\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.501205 | 0.0847191 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.88598 | 1.13205 | 0.566024 | − | 0.824389i | \(-0.308481\pi\) | ||||
0.566024 | + | 0.824389i | \(0.308481\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.93593 | 1.08321 | 0.541605 | − | 0.840633i | \(-0.317817\pi\) | ||||
0.541605 | + | 0.840633i | \(0.317817\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.1872 | −1.70604 | −0.853020 | − | 0.521879i | \(-0.825231\pi\) | ||||
−0.853020 | + | 0.521879i | \(0.825231\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.22165 | −0.324061 | −0.162030 | − | 0.986786i | \(-0.551804\pi\) | ||||
−0.162030 | + | 0.986786i | \(0.551804\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.56778 | 0.223969 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.5783 | −1.45304 | −0.726519 | − | 0.687147i | \(-0.758863\pi\) | ||||
−0.726519 | + | 0.687147i | \(0.758863\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.0293199 | −0.00395349 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.88853 | −0.245866 | −0.122933 | − | 0.992415i | \(-0.539230\pi\) | ||||
−0.122933 | + | 0.992415i | \(0.539230\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.31996 | −1.19330 | −0.596649 | − | 0.802502i | \(-0.703502\pi\) | ||||
−0.596649 | + | 0.802502i | \(0.703502\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.564760 | −0.0700499 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.04904 | 0.861177 | 0.430588 | − | 0.902548i | \(-0.358306\pi\) | ||||
0.430588 | + | 0.902548i | \(0.358306\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.10327 | −0.368290 | −0.184145 | − | 0.982899i | \(-0.558952\pi\) | ||||
−0.184145 | + | 0.982899i | \(0.558952\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.0274 | −1.29066 | −0.645331 | − | 0.763903i | \(-0.723280\pi\) | ||||
−0.645331 | + | 0.763903i | \(0.723280\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.501205 | −0.0571176 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.12636 | −0.576761 | −0.288381 | − | 0.957516i | \(-0.593117\pi\) | ||||
−0.288381 | + | 0.957516i | \(0.593117\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.60127 | 0.614820 | 0.307410 | − | 0.951577i | \(-0.400538\pi\) | ||||
0.307410 | + | 0.951577i | \(0.400538\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.670402 | 0.0727153 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.0682 | 1.38523 | 0.692614 | − | 0.721308i | \(-0.256459\pi\) | ||||
0.692614 | + | 0.721308i | \(0.256459\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.65422 | −1.01204 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.994944 | −0.102079 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.2166 | −1.34194 | −0.670970 | − | 0.741485i | \(-0.734122\pi\) | ||||
−0.670970 | + | 0.741485i | \(0.734122\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.31616 | 0.926993 | 0.463497 | − | 0.886099i | \(-0.346595\pi\) | ||||
0.463497 | + | 0.886099i | \(0.346595\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.73046 | −0.367573 | −0.183787 | − | 0.982966i | \(-0.558836\pi\) | ||||
−0.183787 | + | 0.982966i | \(0.558836\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.04546 | −0.777784 | −0.388892 | − | 0.921283i | \(-0.627142\pi\) | ||||
−0.388892 | + | 0.921283i | \(0.627142\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.2314 | −1.17155 | −0.585776 | − | 0.810473i | \(-0.699210\pi\) | ||||
−0.585776 | + | 0.810473i | \(0.699210\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.18970 | 0.676350 | 0.338175 | − | 0.941083i | \(-0.390190\pi\) | ||||
0.338175 | + | 0.941083i | \(0.390190\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.403546 | 0.0376309 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 11.4601 | 1.05055 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9707 | −0.997335 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.70728 | −0.152704 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.3571 | 0.919044 | 0.459522 | − | 0.888166i | \(-0.348021\pi\) | ||||
0.459522 | + | 0.888166i | \(0.348021\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.29366 | −0.724621 | −0.362310 | − | 0.932058i | \(-0.618012\pi\) | ||||
−0.362310 | + | 0.932058i | \(0.618012\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −17.0079 | −1.47478 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 15.6198 | 1.33449 | 0.667247 | − | 0.744837i | \(-0.267473\pi\) | ||||
0.667247 | + | 0.744837i | \(0.267473\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.0894 | 1.02541 | 0.512705 | − | 0.858565i | \(-0.328643\pi\) | ||||
0.512705 | + | 0.858565i | \(0.328643\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.564760 | 0.0472276 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.52664 | −0.126780 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.07824 | −0.170256 | −0.0851278 | − | 0.996370i | \(-0.527130\pi\) | ||||
−0.0851278 | + | 0.996370i | \(0.527130\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.7897 | 1.12219 | 0.561094 | − | 0.827752i | \(-0.310380\pi\) | ||||
0.561094 | + | 0.827752i | \(0.310380\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.198517 | −0.0159453 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.05129 | 0.482945 | 0.241473 | − | 0.970408i | \(-0.422370\pi\) | ||||
0.241473 | + | 0.970408i | \(0.422370\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.89837 | 0.543668 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.43528 | −0.190746 | −0.0953728 | − | 0.995442i | \(-0.530404\pi\) | ||||
−0.0953728 | + | 0.995442i | \(0.530404\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.00000 | −0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.12158 | −0.163199 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.68421 | −0.356134 | −0.178067 | − | 0.984018i | \(-0.556984\pi\) | ||||
−0.178067 | + | 0.984018i | \(0.556984\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −14.5496 | −1.09984 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.53179 | −0.488209 | −0.244104 | − | 0.969749i | \(-0.578494\pi\) | ||||
−0.244104 | + | 0.969749i | \(0.578494\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.03552 | −0.671605 | −0.335803 | − | 0.941932i | \(-0.609007\pi\) | ||||
−0.335803 | + | 0.941932i | \(0.609007\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.17909 | 0.0866884 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.670402 | −0.0490247 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.4848 | 1.40987 | 0.704935 | − | 0.709272i | \(-0.250976\pi\) | ||||
0.704935 | + | 0.709272i | \(0.250976\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.5049 | 0.828139 | 0.414070 | − | 0.910245i | \(-0.364107\pi\) | ||||
0.414070 | + | 0.910245i | \(0.364107\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.0763 | 0.931644 | 0.465822 | − | 0.884878i | \(-0.345759\pi\) | ||||
0.465822 | + | 0.884878i | \(0.345759\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.9013 | −1.33987 | −0.669937 | − | 0.742418i | \(-0.733679\pi\) | ||||
−0.669937 | + | 0.742418i | \(0.733679\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −26.0969 | −1.83164 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.18764 | 0.0829485 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.994944 | 0.0688217 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.276376 | 0.0190265 | 0.00951324 | − | 0.999955i | \(-0.496972\pi\) | ||||
0.00951324 | + | 0.999955i | \(0.496972\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.91560 | −0.130643 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.39353 | −0.230368 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −12.9133 | −0.868643 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.1248 | 0.744974 | 0.372487 | − | 0.928037i | \(-0.378505\pi\) | ||||
0.372487 | + | 0.928037i | \(0.378505\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −13.5523 | −0.899496 | −0.449748 | − | 0.893155i | \(-0.648486\pi\) | ||||
−0.449748 | + | 0.893155i | \(0.648486\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.31695 | −0.351354 | −0.175677 | − | 0.984448i | \(-0.556211\pi\) | ||||
−0.175677 | + | 0.984448i | \(0.556211\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −23.9680 | −1.57020 | −0.785098 | − | 0.619371i | \(-0.787388\pi\) | ||||
−0.785098 | + | 0.619371i | \(0.787388\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.380414 | −0.0248155 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −25.2667 | −1.63437 | −0.817184 | − | 0.576376i | \(-0.804466\pi\) | ||||
−0.817184 | + | 0.576376i | \(0.804466\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.3538 | −0.795780 | −0.397890 | − | 0.917433i | \(-0.630257\pi\) | ||||
−0.397890 | + | 0.917433i | \(0.630257\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.268452 | 0.0171508 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 19.1646 | 1.21942 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.7102 | −0.739141 | −0.369570 | − | 0.929203i | \(-0.620495\pi\) | ||||
−0.369570 | + | 0.929203i | \(0.620495\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.403546 | −0.0253707 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 23.3845 | 1.45868 | 0.729342 | − | 0.684149i | \(-0.239826\pi\) | ||||
0.729342 | + | 0.684149i | \(0.239826\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 20.1558 | 1.25242 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 23.2296 | 1.43240 | 0.716201 | − | 0.697894i | \(-0.245880\pi\) | ||||
0.716201 | + | 0.697894i | \(0.245880\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.81132 | −0.111269 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −18.4648 | −1.12582 | −0.562910 | − | 0.826518i | \(-0.690318\pi\) | ||||
−0.562910 | + | 0.826518i | \(0.690318\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.12219 | −0.250406 | −0.125203 | − | 0.992131i | \(-0.539958\pi\) | ||||
−0.125203 | + | 0.992131i | \(0.539958\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.851132 | 0.0513252 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.6333 | 0.819143 | 0.409571 | − | 0.912278i | \(-0.365678\pi\) | ||||
0.409571 | + | 0.912278i | \(0.365678\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.52562 | 0.448941 | 0.224471 | − | 0.974481i | \(-0.427935\pi\) | ||||
0.224471 | + | 0.974481i | \(0.427935\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −25.7323 | −1.52963 | −0.764813 | − | 0.644252i | \(-0.777169\pi\) | ||||
−0.764813 | + | 0.644252i | \(0.777169\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 20.3020 | 1.19839 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.67117 | −0.0983042 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.13069 | −0.416579 | −0.208290 | − | 0.978067i | \(-0.566790\pi\) | ||||
−0.208290 | + | 0.978067i | \(0.566790\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.323374 | −0.0188276 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −7.77312 | −0.449531 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −32.7459 | −1.88744 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.59586 | −0.0913787 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 27.5691 | 1.57345 | 0.786725 | − | 0.617303i | \(-0.211775\pi\) | ||||
0.786725 | + | 0.617303i | \(0.211775\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −30.4457 | −1.72642 | −0.863208 | − | 0.504848i | \(-0.831548\pi\) | ||||
−0.863208 | + | 0.504848i | \(0.831548\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.8279 | 0.894643 | 0.447322 | − | 0.894373i | \(-0.352378\pi\) | ||||
0.447322 | + | 0.894373i | \(0.352378\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 17.2233 | 0.967359 | 0.483680 | − | 0.875245i | \(-0.339300\pi\) | ||||
0.483680 | + | 0.875245i | \(0.339300\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.52664 | 0.0854752 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −22.7495 | −1.26582 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 16.3945 | 0.909404 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.50294 | −0.358519 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −22.3052 | −1.22600 | −0.613002 | − | 0.790081i | \(-0.710038\pi\) | ||||
−0.613002 | + | 0.790081i | \(0.710038\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.20701 | 0.0659460 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.90740 | 0.212850 | 0.106425 | − | 0.994321i | \(-0.466060\pi\) | ||||
0.106425 | + | 0.994321i | \(0.466060\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.198517 | 0.0107503 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.9005 | −0.858547 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.363481 | −0.0195127 | −0.00975633 | − | 0.999952i | \(-0.503106\pi\) | ||||
−0.00975633 | + | 0.999952i | \(0.503106\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 29.9181 | 1.60148 | 0.800740 | − | 0.599012i | \(-0.204440\pi\) | ||||
0.800740 | + | 0.599012i | \(0.204440\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.51556 | 0.346788 | 0.173394 | − | 0.984853i | \(-0.444527\pi\) | ||||
0.173394 | + | 0.984853i | \(0.444527\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.531374 | −0.0282024 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 33.4888 | 1.76747 | 0.883736 | − | 0.467985i | \(-0.155020\pi\) | ||||
0.883736 | + | 0.467985i | \(0.155020\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.7625 | 0.776975 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.88823 | −0.0988345 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.4075 | −0.856465 | −0.428233 | − | 0.903669i | \(-0.640864\pi\) | ||||
−0.428233 | + | 0.903669i | \(0.640864\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −30.9634 | −1.60754 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.7315 | 0.607434 | 0.303717 | − | 0.952762i | \(-0.401772\pi\) | ||||
0.303717 | + | 0.952762i | \(0.401772\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 29.4061 | 1.51449 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −26.0199 | −1.33655 | −0.668275 | − | 0.743914i | \(-0.732967\pi\) | ||||
−0.668275 | + | 0.743914i | \(0.732967\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −37.3246 | −1.90720 | −0.953599 | − | 0.301081i | \(-0.902653\pi\) | ||||
−0.953599 | + | 0.301081i | \(0.902653\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.0858215 | −0.00437387 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −16.5360 | −0.838410 | −0.419205 | − | 0.907892i | \(-0.637691\pi\) | ||||
−0.419205 | + | 0.907892i | \(0.637691\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.22713 | 0.466636 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.877790 | −0.0441664 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.0055 | −0.702916 | −0.351458 | − | 0.936204i | \(-0.614314\pi\) | ||||
−0.351458 | + | 0.936204i | \(0.614314\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.97675 | 0.348402 | 0.174201 | − | 0.984710i | \(-0.444266\pi\) | ||||
0.174201 | + | 0.984710i | \(0.444266\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.82385 | 0.190479 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.17909 | −0.0584453 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.27762 | −0.260961 | −0.130481 | − | 0.991451i | \(-0.541652\pi\) | ||||
−0.130481 | + | 0.991451i | \(0.541652\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5.52788 | −0.272009 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.959109 | 0.0470808 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.33784 | −0.0653579 | −0.0326789 | − | 0.999466i | \(-0.510404\pi\) | ||||
−0.0326789 | + | 0.999466i | \(0.510404\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −27.6500 | −1.34758 | −0.673790 | − | 0.738923i | \(-0.735335\pi\) | ||||
−0.673790 | + | 0.738923i | \(0.735335\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −19.4612 | −0.944008 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −27.2802 | −1.32018 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.87617 | −0.234877 | −0.117438 | − | 0.993080i | \(-0.537468\pi\) | ||||
−0.117438 | + | 0.993080i | \(0.537468\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −28.0176 | −1.34644 | −0.673221 | − | 0.739441i | \(-0.735090\pi\) | ||||
−0.673221 | + | 0.739441i | \(0.735090\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −13.6940 | −0.655072 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.2469 | 0.679967 | 0.339984 | − | 0.940431i | \(-0.389578\pi\) | ||||
0.339984 | + | 0.940431i | \(0.389578\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 22.1345 | 1.05164 | 0.525821 | − | 0.850595i | \(-0.323758\pi\) | ||||
0.525821 | + | 0.850595i | \(0.323758\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.23768 | 0.106076 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −38.7231 | −1.82746 | −0.913728 | − | 0.406325i | \(-0.866810\pi\) | ||||
−0.913728 | + | 0.406325i | \(0.866810\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.18764 | −0.0559239 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.65310 | −0.0774984 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 34.0042 | 1.59065 | 0.795326 | − | 0.606183i | \(-0.207300\pi\) | ||||
0.795326 | + | 0.606183i | \(0.207300\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.72427 | −0.313181 | −0.156590 | − | 0.987664i | \(-0.550050\pi\) | ||||
−0.156590 | + | 0.987664i | \(0.550050\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.18126 | 0.426689 | 0.213345 | − | 0.976977i | \(-0.431564\pi\) | ||||
0.213345 | + | 0.976977i | \(0.431564\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −35.4583 | −1.64081 | −0.820406 | − | 0.571781i | \(-0.806253\pi\) | ||||
−0.820406 | + | 0.571781i | \(0.806253\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 20.6331 | 0.952747 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.91560 | 0.0880793 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 28.8824 | 1.32522 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14.5746 | −0.665930 | −0.332965 | − | 0.942939i | \(-0.608049\pi\) | ||||
−0.332965 | + | 0.942939i | \(0.608049\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −22.7117 | −1.03556 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.26308 | −0.102761 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.54755 | 0.0701262 | 0.0350631 | − | 0.999385i | \(-0.488837\pi\) | ||||
0.0350631 | + | 0.999385i | \(0.488837\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.2473 | −0.597843 | −0.298921 | − | 0.954278i | \(-0.596627\pi\) | ||||
−0.298921 | + | 0.954278i | \(0.596627\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −34.9067 | −1.57212 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.08351 | −0.407451 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.13932 | −0.0510030 | −0.0255015 | − | 0.999675i | \(-0.508118\pi\) | ||||
−0.0255015 | + | 0.999675i | \(0.508118\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −34.3692 | −1.53245 | −0.766224 | − | 0.642574i | \(-0.777867\pi\) | ||||
−0.766224 | + | 0.642574i | \(0.777867\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.59521 | 0.0709860 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 40.7043 | 1.80419 | 0.902093 | − | 0.431541i | \(-0.142030\pi\) | ||||
0.902093 | + | 0.431541i | \(0.142030\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −32.2781 | −1.42790 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.638769 | −0.0281475 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.380414 | 0.0167306 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.15675 | 0.401164 | 0.200582 | − | 0.979677i | \(-0.435717\pi\) | ||||
0.200582 | + | 0.979677i | \(0.435717\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.9466 | −0.609844 | −0.304922 | − | 0.952377i | \(-0.598630\pi\) | ||||
−0.304922 | + | 0.952377i | \(0.598630\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.53912 | −0.197727 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.4458 | −0.758511 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −22.8764 | −0.990886 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.37763 | −0.0595600 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.268452 | −0.0115631 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.88638 | −0.0811017 | −0.0405509 | − | 0.999177i | \(-0.512911\pi\) | ||||
−0.0405509 | + | 0.999177i | \(0.512911\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.09438 | −0.0897135 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.23617 | 0.0956119 | 0.0478059 | − | 0.998857i | \(-0.484777\pi\) | ||||
0.0478059 | + | 0.998857i | \(0.484777\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 51.8050 | 2.20697 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15.0053 | −0.638089 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −44.5503 | −1.88766 | −0.943828 | − | 0.330437i | \(-0.892804\pi\) | ||||
−0.943828 | + | 0.330437i | \(0.892804\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 36.8983 | 1.56063 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 44.6653 | 1.88242 | 0.941210 | − | 0.337823i | \(-0.109691\pi\) | ||||
0.941210 | + | 0.337823i | \(0.109691\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.23110 | 0.0517926 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −25.7100 | −1.07782 | −0.538910 | − | 0.842364i | \(-0.681164\pi\) | ||||
−0.538910 | + | 0.842364i | \(0.681164\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −33.9580 | −1.42110 | −0.710550 | − | 0.703647i | \(-0.751554\pi\) | ||||
−0.710550 | + | 0.703647i | \(0.751554\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −11.7146 | −0.488533 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 46.3514 | 1.92963 | 0.964817 | − | 0.262922i | \(-0.0846860\pi\) | ||||
0.964817 | + | 0.262922i | \(0.0846860\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 16.3954 | 0.680194 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.81132 | 0.0750173 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 30.0610 | 1.24075 | 0.620376 | − | 0.784304i | \(-0.286980\pi\) | ||||
0.620376 | + | 0.784304i | \(0.286980\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.73651 | 0.277573 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.11204 | −0.0456661 | −0.0228330 | − | 0.999739i | \(-0.507269\pi\) | ||||
−0.0228330 | + | 0.999739i | \(0.507269\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.96232 | 0.0804473 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −20.6799 | −0.844959 | −0.422480 | − | 0.906372i | \(-0.638840\pi\) | ||||
−0.422480 | + | 0.906372i | \(0.638840\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.3801 | −0.423415 | −0.211707 | − | 0.977333i | \(-0.567902\pi\) | ||||
−0.211707 | + | 0.977333i | \(0.567902\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.87851 | −0.0763725 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.51460 | −0.0614758 | −0.0307379 | − | 0.999527i | \(-0.509786\pi\) | ||||
−0.0307379 | + | 0.999527i | \(0.509786\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.32754 | 0.296441 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 47.5024 | 1.91860 | 0.959301 | − | 0.282385i | \(-0.0911256\pi\) | ||||
0.959301 | + | 0.282385i | \(0.0911256\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.5169 | 0.624686 | 0.312343 | − | 0.949969i | \(-0.398886\pi\) | ||||
0.312343 | + | 0.949969i | \(0.398886\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19.3528 | 0.777857 | 0.388928 | − | 0.921268i | \(-0.372845\pi\) | ||||
0.388928 | + | 0.921268i | \(0.372845\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 38.2517 | 1.53252 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.5611 | 0.982442 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 26.9600 | 1.07497 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.0573 | 0.957705 | 0.478852 | − | 0.877895i | \(-0.341053\pi\) | ||||
0.478852 | + | 0.877895i | \(0.341053\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.77345 | 0.0703772 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.17093 | −0.204880 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.13349 | −0.281756 | −0.140878 | − | 0.990027i | \(-0.544993\pi\) | ||||
−0.140878 | + | 0.990027i | \(0.544993\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −13.5006 | −0.532411 | −0.266205 | − | 0.963916i | \(-0.585770\pi\) | ||||
−0.266205 | + | 0.963916i | \(0.585770\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −46.7829 | −1.83923 | −0.919613 | − | 0.392825i | \(-0.871498\pi\) | ||||
−0.919613 | + | 0.392825i | \(0.871498\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.323374 | 0.0126935 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10.3435 | 0.404772 | 0.202386 | − | 0.979306i | \(-0.435130\pi\) | ||||
0.202386 | + | 0.979306i | \(0.435130\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.42013 | −0.0554890 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −29.6392 | −1.15458 | −0.577289 | − | 0.816540i | \(-0.695889\pi\) | ||||
−0.577289 | + | 0.816540i | \(0.695889\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.65561 | 0.181082 | 0.0905412 | − | 0.995893i | \(-0.471140\pi\) | ||||
0.0905412 | + | 0.995893i | \(0.471140\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.91228 | −0.112933 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −21.0120 | −0.813587 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.59586 | 0.0616075 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 33.2261 | 1.28077 | 0.640387 | − | 0.768053i | \(-0.278774\pi\) | ||||
0.640387 | + | 0.768053i | \(0.278774\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 35.0466 | 1.34695 | 0.673475 | − | 0.739210i | \(-0.264801\pi\) | ||||
0.673475 | + | 0.739210i | \(0.264801\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −38.6859 | −1.48463 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3.83934 | −0.146908 | −0.0734542 | − | 0.997299i | \(-0.523402\pi\) | ||||
−0.0734542 | + | 0.997299i | \(0.523402\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.67459 | 0.102191 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 34.8897 | 1.32919 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 35.1473 | 1.33707 | 0.668534 | − | 0.743682i | \(-0.266922\pi\) | ||||
0.668534 | + | 0.743682i | \(0.266922\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.07008 | 0.0785225 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 27.1556 | 1.02859 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.0199 | 0.453986 | 0.226993 | − | 0.973896i | \(-0.427111\pi\) | ||||
0.226993 | + | 0.973896i | \(0.427111\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −40.0114 | −1.50906 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 27.2691 | 1.02556 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −30.8183 | −1.15741 | −0.578703 | − | 0.815538i | \(-0.696441\pi\) | ||||
−0.578703 | + | 0.815538i | \(0.696441\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.73231 | −0.102326 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.0967041 | 0.00361653 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −35.2346 | −1.31403 | −0.657015 | − | 0.753878i | \(-0.728181\pi\) | ||||
−0.657015 | + | 0.753878i | \(0.728181\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.9194 | −0.406658 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 44.3170 | 1.64589 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −43.9229 | −1.62901 | −0.814505 | − | 0.580156i | \(-0.802991\pi\) | ||||
−0.814505 | + | 0.580156i | \(0.802991\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −43.8004 | −1.62002 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 43.1615 | 1.59421 | 0.797103 | − | 0.603844i | \(-0.206365\pi\) | ||||
0.797103 | + | 0.603844i | \(0.206365\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.20701 | −0.0444608 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24.8598 | 0.914481 | 0.457241 | − | 0.889343i | \(-0.348838\pi\) | ||||
0.457241 | + | 0.889343i | \(0.348838\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 33.3742 | 1.22438 | 0.612191 | − | 0.790710i | \(-0.290288\pi\) | ||||
0.612191 | + | 0.790710i | \(0.290288\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.355857 | −0.0130376 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −23.5497 | −0.860487 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.60294 | 0.240945 | 0.120472 | − | 0.992717i | \(-0.461559\pi\) | ||||
0.120472 | + | 0.992717i | \(0.461559\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.36121 | 0.0859334 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.07219 | −0.0753149 | −0.0376575 | − | 0.999291i | \(-0.511990\pi\) | ||||
−0.0376575 | + | 0.999291i | \(0.511990\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.37348 | 0.267288 | 0.133644 | − | 0.991029i | \(-0.457332\pi\) | ||||
0.133644 | + | 0.991029i | \(0.457332\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −35.8022 | −1.29613 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.22884 | 0.224910 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.805300 | 0.0290399 | 0.0145199 | − | 0.999895i | \(-0.495378\pi\) | ||||
0.0145199 | + | 0.999895i | \(0.495378\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −8.43414 | −0.303355 | −0.151678 | − | 0.988430i | \(-0.548468\pi\) | ||||
−0.151678 | + | 0.988430i | \(0.548468\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.76280 | 0.207006 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −40.3016 | −1.44395 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.531374 | 0.0190141 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.03617 | 0.0369823 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19.7383 | 0.703594 | 0.351797 | − | 0.936076i | \(-0.385571\pi\) | ||||
0.351797 | + | 0.936076i | \(0.385571\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 21.0448 | 0.748268 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 30.7395 | 1.09159 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 25.9278 | 0.918408 | 0.459204 | − | 0.888331i | \(-0.348135\pi\) | ||||
0.459204 | + | 0.888331i | \(0.348135\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.69821 | −0.307721 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.88823 | 0.0666342 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.18121 | 0.0416322 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 29.5937 | 1.04046 | 0.520229 | − | 0.854027i | \(-0.325847\pi\) | ||||
0.520229 | + | 0.854027i | \(0.325847\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.59256 | 0.231496 | 0.115748 | − | 0.993279i | \(-0.463073\pi\) | ||||
0.115748 | + | 0.993279i | \(0.463073\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.416993 | −0.0146066 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 65.0041 | 2.27421 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 38.5957 | 1.34700 | 0.673500 | − | 0.739188i | \(-0.264790\pi\) | ||||
0.673500 | + | 0.739188i | \(0.264790\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −29.2512 | −1.01963 | −0.509817 | − | 0.860283i | \(-0.670287\pi\) | ||||
−0.509817 | + | 0.860283i | \(0.670287\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −36.9174 | −1.28374 | −0.641872 | − | 0.766811i | \(-0.721842\pi\) | ||||
−0.641872 | + | 0.766811i | \(0.721842\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.73793 | −0.164555 | −0.0822775 | − | 0.996609i | \(-0.526219\pi\) | ||||
−0.0822775 | + | 0.996609i | \(0.526219\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.13819 | 0.212676 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.171230 | −0.00592567 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 33.1457 | 1.14432 | 0.572158 | − | 0.820143i | \(-0.306106\pi\) | ||||
0.572158 | + | 0.820143i | \(0.306106\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 50.4893 | 1.74101 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.363279 | −0.0124972 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −32.1120 | −1.10338 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 16.2285 | 0.556306 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 19.2882 | 0.660416 | 0.330208 | − | 0.943908i | \(-0.392881\pi\) | ||||
0.330208 | + | 0.943908i | \(0.392881\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −16.3356 | −0.558012 | −0.279006 | − | 0.960289i | \(-0.590005\pi\) | ||||
−0.279006 | + | 0.960289i | \(0.590005\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −37.9235 | −1.29393 | −0.646967 | − | 0.762518i | \(-0.723963\pi\) | ||||
−0.646967 | + | 0.762518i | \(0.723963\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −23.6597 | −0.805385 | −0.402692 | − | 0.915335i | \(-0.631926\pi\) | ||||
−0.402692 | + | 0.915335i | \(0.631926\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.802080 | −0.0272715 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.877790 | 0.0297770 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −23.2494 | −0.787777 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.99735 | −0.168941 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17.8832 | 0.603871 | 0.301936 | − | 0.953328i | \(-0.402367\pi\) | ||||
0.301936 | + | 0.953328i | \(0.402367\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.78045 | −0.161058 | −0.0805288 | − | 0.996752i | \(-0.525661\pi\) | ||||
−0.0805288 | + | 0.996752i | \(0.525661\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 38.3981 | 1.29220 | 0.646100 | − | 0.763253i | \(-0.276399\pi\) | ||||
0.646100 | + | 0.763253i | \(0.276399\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −34.1197 | −1.14563 | −0.572814 | − | 0.819686i | \(-0.694148\pi\) | ||||
−0.572814 | + | 0.819686i | \(0.694148\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 30.3160 | 1.01677 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12.9090 | 0.431984 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.11844 | −0.0373854 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 10.3365 | 0.344740 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −41.4161 | −1.37977 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.54716 | −0.0514292 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −25.9706 | −0.862340 | −0.431170 | − | 0.902271i | \(-0.641899\pi\) | ||||
−0.431170 | + | 0.902271i | \(0.641899\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23.0338 | 0.763145 | 0.381572 | − | 0.924339i | \(-0.375383\pi\) | ||||
0.381572 | + | 0.924339i | \(0.375383\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.959109 | −0.0317419 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −24.2762 | −0.801670 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −47.0032 | −1.55049 | −0.775246 | − | 0.631659i | \(-0.782374\pi\) | ||||
−0.775246 | + | 0.631659i | \(0.782374\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.2353 | 0.336900 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −34.2280 | −1.12541 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 44.1553 | 1.44869 | 0.724344 | − | 0.689439i | \(-0.242143\pi\) | ||||
0.724344 | + | 0.689439i | \(0.242143\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.10969 | −0.298558 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.114793 | −0.00375414 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 12.9269 | 0.422305 | 0.211152 | − | 0.977453i | \(-0.432278\pi\) | ||||
0.211152 | + | 0.977453i | \(0.432278\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 49.8258 | 1.62427 | 0.812137 | − | 0.583467i | \(-0.198304\pi\) | ||||
0.812137 | + | 0.583467i | \(0.198304\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16.3462 | 0.532306 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 25.5458 | 0.830128 | 0.415064 | − | 0.909792i | \(-0.363759\pi\) | ||||
0.415064 | + | 0.909792i | \(0.363759\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 36.3711 | 1.18066 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 48.6379 | 1.57553 | 0.787767 | − | 0.615973i | \(-0.211237\pi\) | ||||
0.787767 | + | 0.615973i | \(0.211237\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.33639 | 0.107963 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 45.7205 | 1.47639 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.6559 | −0.956642 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.96999 | 0.0634161 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.339589 | 0.0109204 | 0.00546022 | − | 0.999985i | \(-0.498262\pi\) | ||||
0.00546022 | + | 0.999985i | \(0.498262\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15.0126 | 0.481777 | 0.240888 | − | 0.970553i | \(-0.422561\pi\) | ||||
0.240888 | + | 0.970553i | \(0.422561\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 35.3867 | 1.13444 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 26.2407 | 0.839515 | 0.419758 | − | 0.907636i | \(-0.362115\pi\) | ||||
0.419758 | + | 0.907636i | \(0.362115\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.23768 | −0.0715165 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −20.5220 | −0.654551 | −0.327275 | − | 0.944929i | \(-0.606130\pi\) | ||||
−0.327275 | + | 0.944929i | \(0.606130\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.23905 | 0.0713422 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −26.3655 | −0.838373 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.1930 | −0.355559 | −0.177779 | − | 0.984070i | \(-0.556891\pi\) | ||||
−0.177779 | + | 0.984070i | \(0.556891\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.23647 | −0.102603 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −18.6207 | −0.589724 | −0.294862 | − | 0.955540i | \(-0.595274\pi\) | ||||
−0.294862 | + | 0.955540i | \(0.595274\pi\) | |||||||
\(998\) | 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 | 6012.2.a.e.1.3 | 5 | ||
3.2 | odd | 2 | 2004.2.a.a.1.3 | ✓ | 5 | ||
12.11 | even | 2 | 8016.2.a.t.1.3 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2004.2.a.a.1.3 | ✓ | 5 | 3.2 | odd | 2 | ||
6012.2.a.e.1.3 | 5 | 1.1 | even | 1 | trivial | ||
8016.2.a.t.1.3 | 5 | 12.11 | even | 2 |