Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7600,2,Mod(1,7600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7600, 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("7600.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7600 = 2^{4} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7600.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: | \(60.6863055362\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 760) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7600.1 |
$q$-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 | ||||||||
\(3\) | 2.41421 | 1.39385 | 0.696923 | − | 0.717146i | \(-0.254552\pi\) | ||||
0.696923 | + | 0.717146i | \(0.254552\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.41421 | −0.912487 | −0.456243 | − | 0.889855i | \(-0.650805\pi\) | ||||
−0.456243 | + | 0.889855i | \(0.650805\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.82843 | 0.942809 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.41421 | −0.426401 | −0.213201 | − | 0.977008i | \(-0.568389\pi\) | ||||
−0.213201 | + | 0.977008i | \(0.568389\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.82843 | −0.507114 | −0.253557 | − | 0.967320i | \(-0.581601\pi\) | ||||
−0.253557 | + | 0.967320i | \(0.581601\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.00000 | −0.242536 | −0.121268 | − | 0.992620i | \(-0.538696\pi\) | ||||
−0.121268 | + | 0.992620i | \(0.538696\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.82843 | −1.27187 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.24264 | 1.09317 | 0.546583 | − | 0.837405i | \(-0.315928\pi\) | ||||
0.546583 | + | 0.837405i | \(0.315928\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.414214 | −0.0797154 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.82843 | 0.710921 | 0.355461 | − | 0.934691i | \(-0.384324\pi\) | ||||
0.355461 | + | 0.934691i | \(0.384324\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.41421 | −0.613211 | −0.306605 | − | 0.951837i | \(-0.599193\pi\) | ||||
−0.306605 | + | 0.951837i | \(0.599193\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.41421 | −0.594338 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.17157 | −0.850201 | −0.425101 | − | 0.905146i | \(-0.639761\pi\) | ||||
−0.425101 | + | 0.905146i | \(0.639761\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.41421 | −0.706840 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.07107 | −1.10432 | −0.552158 | − | 0.833740i | \(-0.686195\pi\) | ||||
−0.552158 | + | 0.833740i | \(0.686195\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.24264 | 0.341999 | 0.171000 | − | 0.985271i | \(-0.445300\pi\) | ||||
0.171000 | + | 0.985271i | \(0.445300\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.00000 | 1.16692 | 0.583460 | − | 0.812142i | \(-0.301699\pi\) | ||||
0.583460 | + | 0.812142i | \(0.301699\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.17157 | −0.167368 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.41421 | −0.338058 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.82843 | 0.251154 | 0.125577 | − | 0.992084i | \(-0.459922\pi\) | ||||
0.125577 | + | 0.992084i | \(0.459922\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.41421 | 0.319770 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −14.4142 | −1.87657 | −0.938285 | − | 0.345862i | \(-0.887587\pi\) | ||||
−0.938285 | + | 0.345862i | \(0.887587\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.41421 | 0.437145 | 0.218573 | − | 0.975821i | \(-0.429860\pi\) | ||||
0.218573 | + | 0.975821i | \(0.429860\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.82843 | −0.860301 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.07107 | −0.741699 | −0.370849 | − | 0.928693i | \(-0.620933\pi\) | ||||
−0.370849 | + | 0.928693i | \(0.620933\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 12.6569 | 1.52371 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.07107 | −0.364469 | −0.182234 | − | 0.983255i | \(-0.558333\pi\) | ||||
−0.182234 | + | 0.983255i | \(0.558333\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −13.8284 | −1.61849 | −0.809247 | − | 0.587468i | \(-0.800125\pi\) | ||||
−0.809247 | + | 0.587468i | \(0.800125\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.41421 | 0.389086 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.828427 | 0.0932053 | 0.0466027 | − | 0.998914i | \(-0.485161\pi\) | ||||
0.0466027 | + | 0.998914i | \(0.485161\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.48528 | −1.05392 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.48528 | −0.272795 | −0.136398 | − | 0.990654i | \(-0.543552\pi\) | ||||
−0.136398 | + | 0.990654i | \(0.543552\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.24264 | 0.990915 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.75736 | −0.398279 | −0.199140 | − | 0.979971i | \(-0.563815\pi\) | ||||
−0.199140 | + | 0.979971i | \(0.563815\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.41421 | 0.462735 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.24264 | −0.854722 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.65685 | −0.777436 | −0.388718 | − | 0.921357i | \(-0.627082\pi\) | ||||
−0.388718 | + | 0.921357i | \(0.627082\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.00000 | −0.402015 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.8995 | 1.58206 | 0.791029 | − | 0.611778i | \(-0.209545\pi\) | ||||
0.791029 | + | 0.611778i | \(0.209545\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.89949 | −0.975426 | −0.487713 | − | 0.873004i | \(-0.662169\pi\) | ||||
−0.487713 | + | 0.873004i | \(0.662169\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.41421 | −0.233391 | −0.116695 | − | 0.993168i | \(-0.537230\pi\) | ||||
−0.116695 | + | 0.993168i | \(0.537230\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.00000 | −0.478913 | −0.239457 | − | 0.970907i | \(-0.576969\pi\) | ||||
−0.239457 | + | 0.970907i | \(0.576969\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −12.4853 | −1.18505 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.0711 | 1.22962 | 0.614811 | − | 0.788674i | \(-0.289232\pi\) | ||||
0.614811 | + | 0.788674i | \(0.289232\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.17157 | −0.478112 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.41421 | 0.221311 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.00000 | −0.818182 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −17.0711 | −1.53925 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.1716 | 0.991317 | 0.495658 | − | 0.868518i | \(-0.334927\pi\) | ||||
0.495658 | + | 0.868518i | \(0.334927\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.41421 | 0.476695 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −21.6569 | −1.89217 | −0.946084 | − | 0.323921i | \(-0.894999\pi\) | ||||
−0.946084 | + | 0.323921i | \(0.894999\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.41421 | −0.209339 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −16.3137 | −1.39377 | −0.696887 | − | 0.717181i | \(-0.745432\pi\) | ||||
−0.696887 | + | 0.717181i | \(0.745432\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.00000 | 0.339276 | 0.169638 | − | 0.985506i | \(-0.445740\pi\) | ||||
0.169638 | + | 0.985506i | \(0.445740\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 19.3137 | 1.62651 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.58579 | 0.216234 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.82843 | −0.233285 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −17.6569 | −1.44651 | −0.723253 | − | 0.690583i | \(-0.757354\pi\) | ||||
−0.723253 | + | 0.690583i | \(0.757354\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.1716 | −0.909130 | −0.454565 | − | 0.890714i | \(-0.650205\pi\) | ||||
−0.454565 | + | 0.890714i | \(0.650205\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.82843 | −0.228665 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.343146 | −0.0273860 | −0.0136930 | − | 0.999906i | \(-0.504359\pi\) | ||||
−0.0136930 | + | 0.999906i | \(0.504359\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.41421 | 0.350070 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −12.6569 | −0.997500 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.92893 | 0.229412 | 0.114706 | − | 0.993400i | \(-0.463407\pi\) | ||||
0.114706 | + | 0.993400i | \(0.463407\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 23.2132 | 1.79629 | 0.898146 | − | 0.439698i | \(-0.144914\pi\) | ||||
0.898146 | + | 0.439698i | \(0.144914\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.65685 | −0.742835 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.82843 | 0.216295 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −18.8284 | −1.43150 | −0.715749 | − | 0.698357i | \(-0.753915\pi\) | ||||
−0.715749 | + | 0.698357i | \(0.753915\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −34.7990 | −2.61565 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 22.9706 | 1.71690 | 0.858450 | − | 0.512897i | \(-0.171428\pi\) | ||||
0.858450 | + | 0.512897i | \(0.171428\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.485281 | 0.0360707 | 0.0180353 | − | 0.999837i | \(-0.494259\pi\) | ||||
0.0180353 | + | 0.999837i | \(0.494259\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.24264 | 0.609314 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.41421 | 0.103418 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.2426 | 0.813489 | 0.406744 | − | 0.913542i | \(-0.366664\pi\) | ||||
0.406744 | + | 0.913542i | \(0.366664\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.65685 | −0.551152 | −0.275576 | − | 0.961279i | \(-0.588869\pi\) | ||||
−0.275576 | + | 0.961279i | \(0.588869\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −20.7279 | −1.47680 | −0.738402 | − | 0.674361i | \(-0.764419\pi\) | ||||
−0.738402 | + | 0.674361i | \(0.764419\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.0711 | −1.13925 | −0.569624 | − | 0.821905i | \(-0.692911\pi\) | ||||
−0.569624 | + | 0.821905i | \(0.692911\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −14.6569 | −1.03381 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −9.24264 | −0.648706 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 14.8284 | 1.03065 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.41421 | −0.0978232 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.8995 | 1.71415 | 0.857076 | − | 0.515190i | \(-0.172279\pi\) | ||||
0.857076 | + | 0.515190i | \(0.172279\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −7.41421 | −0.508014 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.24264 | 0.559547 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −33.3848 | −2.25593 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.82843 | 0.122993 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.17157 | 0.212384 | 0.106192 | − | 0.994346i | \(-0.466134\pi\) | ||||
0.106192 | + | 0.994346i | \(0.466134\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −17.2426 | −1.14443 | −0.572217 | − | 0.820102i | \(-0.693917\pi\) | ||||
−0.572217 | + | 0.820102i | \(0.693917\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −26.9706 | −1.78226 | −0.891132 | − | 0.453743i | \(-0.850088\pi\) | ||||
−0.891132 | + | 0.453743i | \(0.850088\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.24264 | 0.542326 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.34315 | 0.153505 | 0.0767523 | − | 0.997050i | \(-0.475545\pi\) | ||||
0.0767523 | + | 0.997050i | \(0.475545\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.00000 | 0.129914 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.27208 | −0.146969 | −0.0734843 | − | 0.997296i | \(-0.523412\pi\) | ||||
−0.0734843 | + | 0.997296i | \(0.523412\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.65685 | 0.364390 | 0.182195 | − | 0.983262i | \(-0.441680\pi\) | ||||
0.182195 | + | 0.983262i | \(0.441680\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −21.6569 | −1.38929 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.82843 | −0.116340 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.00000 | −0.380235 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 27.5563 | 1.73934 | 0.869671 | − | 0.493632i | \(-0.164331\pi\) | ||||
0.869671 | + | 0.493632i | \(0.164331\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.41421 | −0.466128 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.27208 | −0.204107 | −0.102053 | − | 0.994779i | \(-0.532541\pi\) | ||||
−0.102053 | + | 0.994779i | \(0.532541\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 12.4853 | 0.775798 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.8284 | 0.670263 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.34315 | −0.267810 | −0.133905 | − | 0.990994i | \(-0.542752\pi\) | ||||
−0.133905 | + | 0.990994i | \(0.542752\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9.07107 | −0.555140 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.0000 | −0.609711 | −0.304855 | − | 0.952399i | \(-0.598608\pi\) | ||||
−0.304855 | + | 0.952399i | \(0.598608\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.3848 | 1.29903 | 0.649516 | − | 0.760348i | \(-0.274971\pi\) | ||||
0.649516 | + | 0.760348i | \(0.274971\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 10.6569 | 0.644982 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −19.3137 | −1.16045 | −0.580224 | − | 0.814457i | \(-0.697035\pi\) | ||||
−0.580224 | + | 0.814457i | \(0.697035\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9.65685 | −0.578141 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.2426 | −0.730335 | −0.365167 | − | 0.930942i | \(-0.618988\pi\) | ||||
−0.365167 | + | 0.930942i | \(0.618988\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 26.4853 | 1.57439 | 0.787193 | − | 0.616706i | \(-0.211533\pi\) | ||||
0.787193 | + | 0.616706i | \(0.211533\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 17.0711 | 1.00767 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.0000 | −0.941176 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −18.4853 | −1.08363 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 28.7990 | 1.68245 | 0.841227 | − | 0.540681i | \(-0.181834\pi\) | ||||
0.841227 | + | 0.540681i | \(0.181834\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.585786 | 0.0339908 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −9.58579 | −0.554360 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.41421 | −0.312070 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 38.3848 | 2.20515 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −24.2843 | −1.38598 | −0.692988 | − | 0.720949i | \(-0.743706\pi\) | ||||
−0.692988 | + | 0.720949i | \(0.743706\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −23.8995 | −1.35959 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −14.7574 | −0.836813 | −0.418407 | − | 0.908260i | \(-0.637411\pi\) | ||||
−0.418407 | + | 0.908260i | \(0.637411\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.65685 | 0.263221 | 0.131610 | − | 0.991302i | \(-0.457985\pi\) | ||||
0.131610 | + | 0.991302i | \(0.457985\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 32.7990 | 1.84217 | 0.921087 | − | 0.389356i | \(-0.127302\pi\) | ||||
0.921087 | + | 0.389356i | \(0.127302\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.41421 | −0.303138 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.82843 | −0.325311 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.00000 | −0.0556415 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −12.0711 | −0.667532 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −19.3137 | −1.06480 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.3848 | 0.955554 | 0.477777 | − | 0.878481i | \(-0.341443\pi\) | ||||
0.477777 | + | 0.878481i | \(0.341443\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −14.6274 | −0.801578 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.7279 | 0.693334 | 0.346667 | − | 0.937988i | \(-0.387313\pi\) | ||||
0.346667 | + | 0.937988i | \(0.387313\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 31.5563 | 1.71391 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.82843 | 0.261474 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.7279 | 1.06521 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 20.8284 | 1.11813 | 0.559064 | − | 0.829124i | \(-0.311160\pi\) | ||||
0.559064 | + | 0.829124i | \(0.311160\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.6274 | −0.890045 | −0.445023 | − | 0.895519i | \(-0.646804\pi\) | ||||
−0.445023 | + | 0.895519i | \(0.646804\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.757359 | 0.0404248 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 26.1127 | 1.38984 | 0.694919 | − | 0.719088i | \(-0.255440\pi\) | ||||
0.694919 | + | 0.719088i | \(0.255440\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.82843 | 0.308473 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.07107 | −0.425975 | −0.212987 | − | 0.977055i | \(-0.568319\pi\) | ||||
−0.212987 | + | 0.977055i | \(0.568319\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −21.7279 | −1.14042 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.4558 | 0.911188 | 0.455594 | − | 0.890188i | \(-0.349427\pi\) | ||||
0.455594 | + | 0.890188i | \(0.349427\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −20.0000 | −1.04116 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.41421 | −0.229175 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.97056 | −0.309144 | −0.154572 | − | 0.987982i | \(-0.549400\pi\) | ||||
−0.154572 | + | 0.987982i | \(0.549400\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7.00000 | −0.360518 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −33.3848 | −1.71486 | −0.857430 | − | 0.514600i | \(-0.827940\pi\) | ||||
−0.857430 | + | 0.514600i | \(0.827940\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 26.9706 | 1.38174 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.72792 | 0.241586 | 0.120793 | − | 0.992678i | \(-0.461456\pi\) | ||||
0.120793 | + | 0.992678i | \(0.461456\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.34315 | 0.322440 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −11.8995 | −0.603328 | −0.301664 | − | 0.953414i | \(-0.597542\pi\) | ||||
−0.301664 | + | 0.953414i | \(0.597542\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.24264 | −0.265132 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −52.2843 | −2.63739 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.6274 | 1.13564 | 0.567819 | − | 0.823154i | \(-0.307787\pi\) | ||||
0.567819 | + | 0.823154i | \(0.307787\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5.82843 | −0.291786 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −25.8995 | −1.29336 | −0.646680 | − | 0.762762i | \(-0.723843\pi\) | ||||
−0.646680 | + | 0.762762i | \(0.723843\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.24264 | 0.310968 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.31371 | 0.362527 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.41421 | 0.267716 | 0.133858 | − | 0.991001i | \(-0.457263\pi\) | ||||
0.133858 | + | 0.991001i | \(0.457263\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −39.3848 | −1.94271 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 34.7990 | 1.71235 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.65685 | 0.472898 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15.2132 | −0.743214 | −0.371607 | − | 0.928390i | \(-0.621193\pi\) | ||||
−0.371607 | + | 0.928390i | \(0.621193\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.1421 | −0.737983 | −0.368991 | − | 0.929433i | \(-0.620297\pi\) | ||||
−0.368991 | + | 0.929433i | \(0.620297\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 22.6274 | 1.10018 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.24264 | −0.398889 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.24264 | 0.301398 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.58579 | 0.124553 | 0.0622765 | − | 0.998059i | \(-0.480164\pi\) | ||||
0.0622765 | + | 0.998059i | \(0.480164\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.07107 | 0.435928 | 0.217964 | − | 0.975957i | \(-0.430059\pi\) | ||||
0.217964 | + | 0.975957i | \(0.430059\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.24264 | 0.250790 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.27208 | 0.251623 | 0.125811 | − | 0.992054i | \(-0.459847\pi\) | ||||
0.125811 | + | 0.992054i | \(0.459847\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.31371 | −0.157796 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15.5563 | −0.739104 | −0.369552 | − | 0.929210i | \(-0.620489\pi\) | ||||
−0.369552 | + | 0.929210i | \(0.620489\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −42.6274 | −2.01621 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 31.9411 | 1.50739 | 0.753697 | − | 0.657222i | \(-0.228268\pi\) | ||||
0.753697 | + | 0.657222i | \(0.228268\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.0000 | 0.470882 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −26.9706 | −1.26719 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.31371 | 0.295343 | 0.147671 | − | 0.989036i | \(-0.452822\pi\) | ||||
0.147671 | + | 0.989036i | \(0.452822\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.414214 | 0.0193338 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −32.7279 | −1.52429 | −0.762146 | − | 0.647406i | \(-0.775854\pi\) | ||||
−0.762146 | + | 0.647406i | \(0.775854\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.14214 | −0.285449 | −0.142725 | − | 0.989762i | \(-0.545586\pi\) | ||||
−0.142725 | + | 0.989762i | \(0.545586\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.10051 | −0.0971998 | −0.0485999 | − | 0.998818i | \(-0.515476\pi\) | ||||
−0.0485999 | + | 0.998818i | \(0.515476\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14.6569 | 0.676791 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.828427 | −0.0381719 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.17157 | −0.145829 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.17157 | 0.236790 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 17.4558 | 0.797578 | 0.398789 | − | 0.917043i | \(-0.369431\pi\) | ||||
0.398789 | + | 0.917043i | \(0.369431\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.45584 | 0.431149 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −30.5563 | −1.39036 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.8284 | 0.581312 | 0.290656 | − | 0.956828i | \(-0.406127\pi\) | ||||
0.290656 | + | 0.956828i | \(0.406127\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.07107 | 0.319765 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −26.2426 | −1.18431 | −0.592157 | − | 0.805823i | \(-0.701723\pi\) | ||||
−0.592157 | + | 0.805823i | \(0.701723\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.82843 | −0.172424 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.41421 | 0.332573 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −33.0711 | −1.48046 | −0.740232 | − | 0.672351i | \(-0.765284\pi\) | ||||
−0.740232 | + | 0.672351i | \(0.765284\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 56.0416 | 2.50376 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 13.1005 | 0.584123 | 0.292061 | − | 0.956400i | \(-0.405659\pi\) | ||||
0.292061 | + | 0.956400i | \(0.405659\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −23.3137 | −1.03540 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.65685 | −0.0734388 | −0.0367194 | − | 0.999326i | \(-0.511691\pi\) | ||||
−0.0367194 | + | 0.999326i | \(0.511691\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 33.3848 | 1.47686 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.414214 | −0.0182880 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −11.3137 | −0.497576 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −45.4558 | −1.99529 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −28.0000 | −1.22670 | −0.613351 | − | 0.789810i | \(-0.710179\pi\) | ||||
−0.613351 | + | 0.789810i | \(0.710179\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 22.2132 | 0.971316 | 0.485658 | − | 0.874149i | \(-0.338580\pi\) | ||||
0.485658 | + | 0.874149i | \(0.338580\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.41421 | 0.148725 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.48528 | 0.195012 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −40.7696 | −1.76925 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.9289 | 0.560014 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 55.4558 | 2.39310 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.65685 | 0.0713658 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.0416 | −0.775670 | −0.387835 | − | 0.921729i | \(-0.626777\pi\) | ||||
−0.387835 | + | 0.921729i | \(0.626777\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.17157 | 0.0502770 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 43.9411 | 1.87879 | 0.939393 | − | 0.342841i | \(-0.111389\pi\) | ||||
0.939393 | + | 0.342841i | \(0.111389\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9.65685 | 0.412144 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.82843 | 0.163096 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.00000 | −0.0850487 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 20.6863 | 0.876506 | 0.438253 | − | 0.898852i | \(-0.355597\pi\) | ||||
0.438253 | + | 0.898852i | \(0.355597\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.10051 | −0.173433 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.41421 | 0.144148 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −11.0294 | −0.464835 | −0.232418 | − | 0.972616i | \(-0.574664\pi\) | ||||
−0.232418 | + | 0.972616i | \(0.574664\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 22.8995 | 0.961688 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 24.9706 | 1.04682 | 0.523410 | − | 0.852081i | \(-0.324660\pi\) | ||||
0.523410 | + | 0.852081i | \(0.324660\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.6985 | 0.489566 | 0.244783 | − | 0.969578i | \(-0.421283\pi\) | ||||
0.244783 | + | 0.969578i | \(0.421283\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 27.1421 | 1.13388 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 25.0000 | 1.04076 | 0.520382 | − | 0.853934i | \(-0.325790\pi\) | ||||
0.520382 | + | 0.853934i | \(0.325790\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −18.4853 | −0.768222 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.00000 | 0.248922 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.58579 | −0.107092 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.38478 | 0.180979 | 0.0904895 | − | 0.995897i | \(-0.471157\pi\) | ||||
0.0904895 | + | 0.995897i | \(0.471157\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.41421 | −0.140680 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −50.0416 | −2.05844 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 42.0000 | 1.72473 | 0.862367 | − | 0.506284i | \(-0.168981\pi\) | ||||
0.862367 | + | 0.506284i | \(0.168981\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −38.7990 | −1.58794 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.44365 | 0.0998449 | 0.0499224 | − | 0.998753i | \(-0.484103\pi\) | ||||
0.0499224 | + | 0.998753i | \(0.484103\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 31.5563 | 1.28721 | 0.643605 | − | 0.765358i | \(-0.277438\pi\) | ||||
0.643605 | + | 0.765358i | \(0.277438\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −17.1716 | −0.699281 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.5147 | 0.548546 | 0.274273 | − | 0.961652i | \(-0.411563\pi\) | ||||
0.274273 | + | 0.961652i | \(0.411563\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −22.3137 | −0.904197 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −14.6274 | −0.591762 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −22.7279 | −0.917972 | −0.458986 | − | 0.888443i | \(-0.651787\pi\) | ||||
−0.458986 | + | 0.888443i | \(0.651787\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.79899 | −0.313976 | −0.156988 | − | 0.987601i | \(-0.550178\pi\) | ||||
−0.156988 | + | 0.987601i | \(0.550178\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 30.3848 | 1.22127 | 0.610634 | − | 0.791913i | \(-0.290915\pi\) | ||||
0.610634 | + | 0.791913i | \(0.290915\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.17157 | −0.0871422 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9.07107 | 0.363425 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.41421 | −0.136351 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.17157 | 0.206204 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 38.9706 | 1.55139 | 0.775697 | − | 0.631106i | \(-0.217399\pi\) | ||||
0.775697 | + | 0.631106i | \(0.217399\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 60.1127 | 2.38927 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.14214 | 0.0848745 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.68629 | −0.343624 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −39.2132 | −1.54883 | −0.774414 | − | 0.632679i | \(-0.781955\pi\) | ||||
−0.774414 | + | 0.632679i | \(0.781955\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 31.1716 | 1.22929 | 0.614643 | − | 0.788805i | \(-0.289300\pi\) | ||||
0.614643 | + | 0.788805i | \(0.289300\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.0711 | 0.474563 | 0.237281 | − | 0.971441i | \(-0.423744\pi\) | ||||
0.237281 | + | 0.971441i | \(0.423744\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 20.3848 | 0.800172 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 19.8995 | 0.779923 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 32.2843 | 1.26338 | 0.631691 | − | 0.775221i | \(-0.282361\pi\) | ||||
0.631691 | + | 0.775221i | \(0.282361\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −39.1127 | −1.52593 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.89949 | 0.346675 | 0.173338 | − | 0.984862i | \(-0.444545\pi\) | ||||
0.173338 | + | 0.984862i | \(0.444545\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 43.4853 | 1.69138 | 0.845691 | − | 0.533673i | \(-0.179189\pi\) | ||||
0.845691 | + | 0.533673i | \(0.179189\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.41421 | 0.171434 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 20.0711 | 0.777155 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7.65685 | 0.296031 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.82843 | −0.186399 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28.0000 | −1.07932 | −0.539660 | − | 0.841883i | \(-0.681447\pi\) | ||||
−0.539660 | + | 0.841883i | \(0.681447\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 21.3431 | 0.820284 | 0.410142 | − | 0.912022i | \(-0.365479\pi\) | ||||
0.410142 | + | 0.912022i | \(0.365479\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 18.4853 | 0.709400 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −41.6274 | −1.59517 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 23.3137 | 0.892074 | 0.446037 | − | 0.895014i | \(-0.352835\pi\) | ||||
0.446037 | + | 0.895014i | \(0.352835\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −65.1127 | −2.48420 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.34315 | −0.127364 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.45584 | −0.283634 | −0.141817 | − | 0.989893i | \(-0.545294\pi\) | ||||
−0.141817 | + | 0.989893i | \(0.545294\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 9.65685 | 0.366834 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.07107 | 0.267836 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.65685 | 0.213962 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 32.9706 | 1.24528 | 0.622640 | − | 0.782508i | \(-0.286060\pi\) | ||||
0.622640 | + | 0.782508i | \(0.286060\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.17157 | −0.195050 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −38.3848 | −1.44361 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.6863 | 0.401332 | 0.200666 | − | 0.979660i | \(-0.435689\pi\) | ||||
0.200666 | + | 0.979660i | \(0.435689\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.34315 | 0.0878748 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −17.8995 | −0.670341 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5.48528 | −0.204852 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −30.4142 | −1.13426 | −0.567129 | − | 0.823629i | \(-0.691946\pi\) | ||||
−0.567129 | + | 0.823629i | \(0.691946\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 23.8995 | 0.890064 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 13.6569 | 0.507904 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.78680 | −0.0662686 | −0.0331343 | − | 0.999451i | \(-0.510549\pi\) | ||||
−0.0331343 | + | 0.999451i | \(0.510549\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −23.8284 | −0.882534 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.24264 | −0.0829471 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.6274 | 0.392533 | 0.196266 | − | 0.980551i | \(-0.437118\pi\) | ||||
0.196266 | + | 0.980551i | \(0.437118\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.58579 | 0.316262 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.41421 | −0.272736 | −0.136368 | − | 0.990658i | \(-0.543543\pi\) | ||||
−0.136368 | + | 0.990658i | \(0.543543\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.41421 | −0.162160 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14.2426 | 0.522512 | 0.261256 | − | 0.965270i | \(-0.415863\pi\) | ||||
0.261256 | + | 0.965270i | \(0.415863\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7.02944 | −0.257194 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.82843 | 0.212966 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29.7574 | −1.08586 | −0.542931 | − | 0.839777i | \(-0.682685\pi\) | ||||
−0.542931 | + | 0.839777i | \(0.682685\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 66.5269 | 2.42438 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16.3431 | 0.594002 | 0.297001 | − | 0.954877i | \(-0.404014\pi\) | ||||
0.297001 | + | 0.954877i | \(0.404014\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −17.8995 | −0.649711 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.02944 | −0.146067 | −0.0730335 | − | 0.997329i | \(-0.523268\pi\) | ||||
−0.0730335 | + | 0.997329i | \(0.523268\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.0711 | 0.437002 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 26.3553 | 0.951636 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −30.7990 | −1.11064 | −0.555320 | − | 0.831637i | \(-0.687404\pi\) | ||||
−0.555320 | + | 0.831637i | \(0.687404\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.89949 | −0.284493 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −9.00000 | −0.323708 | −0.161854 | − | 0.986815i | \(-0.551747\pi\) | ||||
−0.161854 | + | 0.986815i | \(0.551747\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 30.1421 | 1.08134 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −7.07107 | −0.253347 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.34315 | 0.155410 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.58579 | −0.0566714 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22.7574 | −0.811212 | −0.405606 | − | 0.914048i | \(-0.632940\pi\) | ||||
−0.405606 | + | 0.914048i | \(0.632940\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −10.4853 | −0.373286 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −31.5563 | −1.12201 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.24264 | −0.221683 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −35.1421 | −1.24480 | −0.622399 | − | 0.782700i | \(-0.713842\pi\) | ||||
−0.622399 | + | 0.782700i | \(0.713842\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.00000 | −0.283020 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10.6274 | −0.375501 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 19.5563 | 0.690129 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −24.1421 | −0.849843 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −8.51472 | −0.299362 | −0.149681 | − | 0.988734i | \(-0.547825\pi\) | ||||
−0.149681 | + | 0.988734i | \(0.547825\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 42.0122 | 1.47525 | 0.737624 | − | 0.675212i | \(-0.235948\pi\) | ||||
0.737624 | + | 0.675212i | \(0.235948\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 51.6274 | 1.81065 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.24264 | 0.0784601 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 12.4853 | 0.436271 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −51.5980 | −1.80078 | −0.900391 | − | 0.435082i | \(-0.856719\pi\) | ||||
−0.900391 | + | 0.435082i | \(0.856719\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −47.5269 | −1.65668 | −0.828342 | − | 0.560223i | \(-0.810716\pi\) | ||||
−0.828342 | + | 0.560223i | \(0.810716\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −33.8701 | −1.17778 | −0.588889 | − | 0.808214i | \(-0.700434\pi\) | ||||
−0.588889 | + | 0.808214i | \(0.700434\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25.7696 | 0.895014 | 0.447507 | − | 0.894281i | \(-0.352312\pi\) | ||||
0.447507 | + | 0.894281i | \(0.352312\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −46.6274 | −1.61749 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.17157 | 0.0405926 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.41421 | 0.0488824 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 49.9411 | 1.72416 | 0.862080 | − | 0.506773i | \(-0.169162\pi\) | ||||
0.862080 | + | 0.506773i | \(0.169162\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.3431 | −0.494591 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −29.5563 | −1.01797 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 21.7279 | 0.746580 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 63.9411 | 2.19445 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −27.1127 | −0.929411 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 19.9411 | 0.682771 | 0.341386 | − | 0.939923i | \(-0.389104\pi\) | ||||
0.341386 | + | 0.939923i | \(0.389104\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −16.0000 | −0.546550 | −0.273275 | − | 0.961936i | \(-0.588107\pi\) | ||||
−0.273275 | + | 0.961936i | \(0.588107\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.21320 | −0.177872 | −0.0889361 | − | 0.996037i | \(-0.528347\pi\) | ||||
−0.0889361 | + | 0.996037i | \(0.528347\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 41.2132 | 1.40454 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −35.0711 | −1.19383 | −0.596917 | − | 0.802303i | \(-0.703608\pi\) | ||||
−0.596917 | + | 0.802303i | \(0.703608\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −38.6274 | −1.31186 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.17157 | −0.0397429 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.1005 | 0.376126 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −21.6569 | −0.732973 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 29.4853 | 0.995647 | 0.497824 | − | 0.867278i | \(-0.334133\pi\) | ||||
0.497824 | + | 0.867278i | \(0.334133\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 69.5269 | 2.34508 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.2843 | 0.413868 | 0.206934 | − | 0.978355i | \(-0.433652\pi\) | ||||
0.206934 | + | 0.978355i | \(0.433652\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 15.4558 | 0.520131 | 0.260065 | − | 0.965591i | \(-0.416256\pi\) | ||||
0.260065 | + | 0.965591i | \(0.416256\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0.928932 | 0.0311905 | 0.0155952 | − | 0.999878i | \(-0.495036\pi\) | ||||
0.0155952 | + | 0.999878i | \(0.495036\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −26.9706 | −0.904564 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 13.4142 | 0.449393 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.00000 | 0.267710 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −23.1421 | −0.772693 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −13.0711 | −0.435945 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.82843 | −0.0609137 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −13.0711 | −0.434978 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.55635 | 0.284109 | 0.142054 | − | 0.989859i | \(-0.454629\pi\) | ||||
0.142054 | + | 0.989859i | \(0.454629\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 44.9706 | 1.49158 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.65685 | 0.319946 | 0.159973 | − | 0.987121i | \(-0.448859\pi\) | ||||
0.159973 | + | 0.987121i | \(0.448859\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.51472 | 0.116320 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 52.2843 | 1.72658 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −46.8406 | −1.54513 | −0.772565 | − | 0.634936i | \(-0.781026\pi\) | ||||
−0.772565 | + | 0.634936i | \(0.781026\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −58.6274 | −1.93184 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.61522 | 0.184827 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −28.0000 | −0.919641 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 25.4853 | 0.836145 | 0.418072 | − | 0.908414i | \(-0.362706\pi\) | ||||
0.418072 | + | 0.908414i | \(0.362706\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.17157 | −0.0383968 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −35.6274 | −1.16639 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −22.3137 | −0.728957 | −0.364479 | − | 0.931212i | \(-0.618753\pi\) | ||||
−0.364479 | + | 0.931212i | \(0.618753\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 11.2426 | 0.366890 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 57.1421 | 1.86278 | 0.931390 | − | 0.364022i | \(-0.118597\pi\) | ||||
0.931390 | + | 0.364022i | \(0.118597\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −37.0711 | −1.20720 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −41.2548 | −1.34060 | −0.670301 | − | 0.742089i | \(-0.733835\pi\) | ||||
−0.670301 | + | 0.742089i | \(0.733835\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 25.2843 | 0.820762 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 79.1838 | 2.56771 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −19.2132 | −0.622377 | −0.311188 | − | 0.950348i | \(-0.600727\pi\) | ||||
−0.311188 | + | 0.950348i | \(0.600727\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −13.0711 | −0.422528 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 39.3848 | 1.27180 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.3431 | −0.623972 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.82843 | −0.220043 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 50.1421 | 1.61246 | 0.806231 | − | 0.591601i | \(-0.201504\pi\) | ||||
0.806231 | + | 0.591601i | \(0.201504\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.41421 | −0.0775557 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 35.5980 | 1.14239 | 0.571197 | − | 0.820813i | \(-0.306479\pi\) | ||||
0.571197 | + | 0.820813i | \(0.306479\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.65685 | −0.309585 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.61522 | 0.0516756 | 0.0258378 | − | 0.999666i | \(-0.491775\pi\) | ||||
0.0258378 | + | 0.999666i | \(0.491775\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.31371 | 0.169827 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14.1421 | −0.451524 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −53.7990 | −1.71592 | −0.857961 | − | 0.513715i | \(-0.828269\pi\) | ||||
−0.857961 | + | 0.513715i | \(0.828269\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −46.6274 | −1.48417 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.7574 | 0.373862 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10.5269 | −0.334398 | −0.167199 | − | 0.985923i | \(-0.553472\pi\) | ||||
−0.167199 | + | 0.985923i | \(0.553472\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 41.9706 | 1.33190 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −27.5563 | −0.872718 | −0.436359 | − | 0.899773i | \(-0.643732\pi\) | ||||
−0.436359 | + | 0.899773i | \(0.643732\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.14214 | 0.0677742 |
(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 | 7600.2.a.bc.1.2 | 2 | ||
4.3 | odd | 2 | 3800.2.a.l.1.1 | 2 | |||
5.2 | odd | 4 | 1520.2.d.d.609.1 | 4 | |||
5.3 | odd | 4 | 1520.2.d.d.609.4 | 4 | |||
5.4 | even | 2 | 7600.2.a.x.1.1 | 2 | |||
20.3 | even | 4 | 760.2.d.c.609.1 | ✓ | 4 | ||
20.7 | even | 4 | 760.2.d.c.609.4 | yes | 4 | ||
20.19 | odd | 2 | 3800.2.a.p.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
760.2.d.c.609.1 | ✓ | 4 | 20.3 | even | 4 | ||
760.2.d.c.609.4 | yes | 4 | 20.7 | even | 4 | ||
1520.2.d.d.609.1 | 4 | 5.2 | odd | 4 | |||
1520.2.d.d.609.4 | 4 | 5.3 | odd | 4 | |||
3800.2.a.l.1.1 | 2 | 4.3 | odd | 2 | |||
3800.2.a.p.1.2 | 2 | 20.19 | odd | 2 | |||
7600.2.a.x.1.1 | 2 | 5.4 | even | 2 | |||
7600.2.a.bc.1.2 | 2 | 1.1 | even | 1 | trivial |