Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8400,2,Mod(1,8400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8400, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8400.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8400 = 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8400.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: | \(67.0743376979\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 840) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8400.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.00000 | 0.603023 | 0.301511 | − | 0.953463i | \(-0.402509\pi\) | ||||
0.301511 | + | 0.953463i | \(0.402509\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.47214 | −1.24035 | −0.620174 | − | 0.784465i | \(-0.712938\pi\) | ||||
−0.620174 | + | 0.784465i | \(0.712938\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.47214 | 1.56972 | 0.784862 | − | 0.619671i | \(-0.212734\pi\) | ||||
0.784862 | + | 0.619671i | \(0.212734\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.00000 | −0.458831 | −0.229416 | − | 0.973329i | \(-0.573682\pi\) | ||||
−0.229416 | + | 0.973329i | \(0.573682\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.00000 | −0.834058 | −0.417029 | − | 0.908893i | \(-0.636929\pi\) | ||||
−0.417029 | + | 0.908893i | \(0.636929\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.47214 | −1.57324 | −0.786618 | − | 0.617440i | \(-0.788170\pi\) | ||||
−0.786618 | + | 0.617440i | \(0.788170\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.472136 | 0.0847981 | 0.0423991 | − | 0.999101i | \(-0.486500\pi\) | ||||
0.0423991 | + | 0.999101i | \(0.486500\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.00000 | 0.348155 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.47214 | 0.406417 | 0.203208 | − | 0.979136i | \(-0.434863\pi\) | ||||
0.203208 | + | 0.979136i | \(0.434863\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.47214 | −0.716115 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.52786 | −0.550960 | −0.275480 | − | 0.961307i | \(-0.588837\pi\) | ||||
−0.275480 | + | 0.961307i | \(0.588837\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.47214 | 0.376997 | 0.188499 | − | 0.982073i | \(-0.439638\pi\) | ||||
0.188499 | + | 0.982073i | \(0.439638\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.47214 | −0.944058 | −0.472029 | − | 0.881583i | \(-0.656478\pi\) | ||||
−0.472029 | + | 0.881583i | \(0.656478\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.47214 | 0.906280 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.00000 | 0.274721 | 0.137361 | − | 0.990521i | \(-0.456138\pi\) | ||||
0.137361 | + | 0.990521i | \(0.456138\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.00000 | −0.264906 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.52786 | −0.451697 | −0.225848 | − | 0.974162i | \(-0.572515\pi\) | ||||
−0.225848 | + | 0.974162i | \(0.572515\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.52786 | −0.186658 | −0.0933292 | − | 0.995635i | \(-0.529751\pi\) | ||||
−0.0933292 | + | 0.995635i | \(0.529751\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.00000 | −0.481543 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.4721 | −1.48017 | −0.740085 | − | 0.672513i | \(-0.765215\pi\) | ||||
−0.740085 | + | 0.672513i | \(0.765215\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.52786 | 0.881070 | 0.440535 | − | 0.897735i | \(-0.354789\pi\) | ||||
0.440535 | + | 0.897735i | \(0.354789\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.00000 | −0.227921 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.94427 | −1.00631 | −0.503155 | − | 0.864196i | \(-0.667827\pi\) | ||||
−0.503155 | + | 0.864196i | \(0.667827\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.94427 | 0.542704 | 0.271352 | − | 0.962480i | \(-0.412529\pi\) | ||||
0.271352 | + | 0.962480i | \(0.412529\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.47214 | −0.908308 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −17.4164 | −1.84614 | −0.923068 | − | 0.384637i | \(-0.874327\pi\) | ||||
−0.923068 | + | 0.384637i | \(0.874327\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.47214 | 0.468807 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.472136 | 0.0489582 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.52786 | 0.358200 | 0.179100 | − | 0.983831i | \(-0.442681\pi\) | ||||
0.179100 | + | 0.983831i | \(0.442681\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.00000 | 0.201008 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.47214 | 0.444994 | 0.222497 | − | 0.974933i | \(-0.428579\pi\) | ||||
0.222497 | + | 0.974933i | \(0.428579\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.9443 | −1.27544 | −0.637719 | − | 0.770270i | \(-0.720122\pi\) | ||||
−0.637719 | + | 0.770270i | \(0.720122\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.9443 | 1.43140 | 0.715701 | − | 0.698407i | \(-0.246107\pi\) | ||||
0.715701 | + | 0.698407i | \(0.246107\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.47214 | 0.234645 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.9443 | 1.40584 | 0.702919 | − | 0.711269i | \(-0.251879\pi\) | ||||
0.702919 | + | 0.711269i | \(0.251879\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.47214 | −0.413449 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.47214 | −0.593300 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.52786 | −0.318097 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.00000 | −0.354943 | −0.177471 | − | 0.984126i | \(-0.556792\pi\) | ||||
−0.177471 | + | 0.984126i | \(0.556792\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.47214 | 0.217659 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.8885 | −1.21345 | −0.606724 | − | 0.794913i | \(-0.707517\pi\) | ||||
−0.606724 | + | 0.794913i | \(0.707517\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.00000 | 0.173422 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −19.8885 | −1.69919 | −0.849596 | − | 0.527433i | \(-0.823154\pi\) | ||||
−0.849596 | + | 0.527433i | \(0.823154\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.94427 | 0.249730 | 0.124865 | − | 0.992174i | \(-0.460150\pi\) | ||||
0.124865 | + | 0.992174i | \(0.460150\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.47214 | −0.545052 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.94427 | −0.747958 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.4721 | −1.02176 | −0.510879 | − | 0.859653i | \(-0.670680\pi\) | ||||
−0.510879 | + | 0.859653i | \(0.670680\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.8885 | 1.45575 | 0.727875 | − | 0.685710i | \(-0.240508\pi\) | ||||
0.727875 | + | 0.685710i | \(0.240508\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.47214 | 0.523241 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.41641 | 0.751511 | 0.375756 | − | 0.926719i | \(-0.377383\pi\) | ||||
0.375756 | + | 0.926719i | \(0.377383\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.00000 | 0.158610 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.00000 | 0.315244 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −23.4164 | −1.83411 | −0.917057 | − | 0.398755i | \(-0.869442\pi\) | ||||
−0.917057 | + | 0.398755i | \(0.869442\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −10.4721 | −0.810358 | −0.405179 | − | 0.914237i | \(-0.632791\pi\) | ||||
−0.405179 | + | 0.914237i | \(0.632791\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.00000 | 0.538462 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.00000 | −0.152944 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.0000 | 0.912343 | 0.456172 | − | 0.889892i | \(-0.349220\pi\) | ||||
0.456172 | + | 0.889892i | \(0.349220\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 22.9443 | 1.71494 | 0.857468 | − | 0.514538i | \(-0.172036\pi\) | ||||
0.857468 | + | 0.514538i | \(0.172036\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.4721 | 1.22436 | 0.612182 | − | 0.790717i | \(-0.290292\pi\) | ||||
0.612182 | + | 0.790717i | \(0.290292\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.52786 | −0.260787 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12.9443 | 0.946579 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 17.4164 | 1.26021 | 0.630104 | − | 0.776511i | \(-0.283012\pi\) | ||||
0.630104 | + | 0.776511i | \(0.283012\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.9443 | 0.931749 | 0.465875 | − | 0.884851i | \(-0.345740\pi\) | ||||
0.465875 | + | 0.884851i | \(0.345740\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −19.8885 | −1.41700 | −0.708500 | − | 0.705711i | \(-0.750628\pi\) | ||||
−0.708500 | + | 0.705711i | \(0.750628\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.4721 | −1.45123 | −0.725616 | − | 0.688100i | \(-0.758445\pi\) | ||||
−0.725616 | + | 0.688100i | \(0.758445\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.52786 | −0.107767 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.47214 | 0.594627 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.00000 | −0.278019 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.00000 | −0.276686 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −25.8885 | −1.78224 | −0.891120 | − | 0.453767i | \(-0.850080\pi\) | ||||
−0.891120 | + | 0.453767i | \(0.850080\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −12.4721 | −0.854577 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.472136 | −0.0320507 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7.52786 | 0.508686 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −28.9443 | −1.94700 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −20.9443 | −1.40253 | −0.701266 | − | 0.712900i | \(-0.747382\pi\) | ||||
−0.701266 | + | 0.712900i | \(0.747382\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.88854 | 0.656326 | 0.328163 | − | 0.944621i | \(-0.393571\pi\) | ||||
0.328163 | + | 0.944621i | \(0.393571\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −26.3607 | −1.74196 | −0.870981 | − | 0.491316i | \(-0.836516\pi\) | ||||
−0.870981 | + | 0.491316i | \(0.836516\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.00000 | −0.131590 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.94427 | −0.192886 | −0.0964428 | − | 0.995339i | \(-0.530746\pi\) | ||||
−0.0964428 | + | 0.995339i | \(0.530746\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.94427 | −0.580993 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.5279 | −1.00441 | −0.502207 | − | 0.864747i | \(-0.667478\pi\) | ||||
−0.502207 | + | 0.864747i | \(0.667478\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.8885 | −0.765808 | −0.382904 | − | 0.923788i | \(-0.625076\pi\) | ||||
−0.382904 | + | 0.923788i | \(0.625076\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.94427 | 0.569110 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.94427 | 0.313331 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −24.0000 | −1.51487 | −0.757433 | − | 0.652913i | \(-0.773547\pi\) | ||||
−0.757433 | + | 0.652913i | \(0.773547\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.00000 | −0.502956 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 23.4164 | 1.46068 | 0.730338 | − | 0.683086i | \(-0.239363\pi\) | ||||
0.730338 | + | 0.683086i | \(0.239363\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.47214 | −0.153611 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.47214 | −0.524412 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.00000 | −0.246651 | −0.123325 | − | 0.992366i | \(-0.539356\pi\) | ||||
−0.123325 | + | 0.992366i | \(0.539356\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −17.4164 | −1.06587 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 30.3607 | 1.85112 | 0.925562 | − | 0.378597i | \(-0.123593\pi\) | ||||
0.925562 | + | 0.378597i | \(0.123593\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −24.4721 | −1.48658 | −0.743288 | − | 0.668971i | \(-0.766735\pi\) | ||||
−0.743288 | + | 0.668971i | \(0.766735\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.47214 | 0.270666 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 23.4164 | 1.40696 | 0.703478 | − | 0.710717i | \(-0.251629\pi\) | ||||
0.703478 | + | 0.710717i | \(0.251629\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.472136 | 0.0282660 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.94427 | 0.175641 | 0.0878203 | − | 0.996136i | \(-0.472010\pi\) | ||||
0.0878203 | + | 0.996136i | \(0.472010\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −16.9443 | −1.00723 | −0.503616 | − | 0.863927i | \(-0.667997\pi\) | ||||
−0.503616 | + | 0.863927i | \(0.667997\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.52786 | 0.208243 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 24.8885 | 1.46403 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.52786 | 0.206807 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 24.9443 | 1.45726 | 0.728630 | − | 0.684908i | \(-0.240157\pi\) | ||||
0.728630 | + | 0.684908i | \(0.240157\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.00000 | 0.116052 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 17.8885 | 1.03452 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.47214 | −0.142492 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.47214 | 0.256917 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −20.0000 | −1.14146 | −0.570730 | − | 0.821138i | \(-0.693340\pi\) | ||||
−0.570730 | + | 0.821138i | \(0.693340\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.9443 | −0.736374 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −16.0000 | −0.907277 | −0.453638 | − | 0.891186i | \(-0.649874\pi\) | ||||
−0.453638 | + | 0.891186i | \(0.649874\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −25.4164 | −1.43662 | −0.718310 | − | 0.695723i | \(-0.755084\pi\) | ||||
−0.718310 | + | 0.695723i | \(0.755084\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.94427 | 0.390029 | 0.195015 | − | 0.980800i | \(-0.437525\pi\) | ||||
0.195015 | + | 0.980800i | \(0.437525\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −16.9443 | −0.948697 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12.9443 | −0.720239 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 14.9443 | 0.826420 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.47214 | 0.356820 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −33.8885 | −1.86268 | −0.931341 | − | 0.364147i | \(-0.881361\pi\) | ||||
−0.931341 | + | 0.364147i | \(0.881361\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.47214 | 0.135472 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.0557 | −0.602244 | −0.301122 | − | 0.953586i | \(-0.597361\pi\) | ||||
−0.301122 | + | 0.953586i | \(0.597361\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 14.9443 | 0.811661 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.944272 | 0.0511352 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −30.8328 | −1.65519 | −0.827596 | − | 0.561324i | \(-0.810292\pi\) | ||||
−0.827596 | + | 0.561324i | \(0.810292\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 25.4164 | 1.36051 | 0.680255 | − | 0.732976i | \(-0.261869\pi\) | ||||
0.680255 | + | 0.732976i | \(0.261869\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.47214 | −0.238705 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 17.5279 | 0.932914 | 0.466457 | − | 0.884544i | \(-0.345530\pi\) | ||||
0.466457 | + | 0.884544i | \(0.345530\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.47214 | −0.342542 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −13.4164 | −0.708091 | −0.354045 | − | 0.935228i | \(-0.615194\pi\) | ||||
−0.354045 | + | 0.935228i | \(0.615194\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −7.00000 | −0.367405 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 25.8885 | 1.35137 | 0.675685 | − | 0.737190i | \(-0.263848\pi\) | ||||
0.675685 | + | 0.737190i | \(0.263848\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.52786 | −0.183653 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.00000 | −0.103835 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.3607 | −0.847124 | −0.423562 | − | 0.905867i | \(-0.639220\pi\) | ||||
−0.423562 | + | 0.905867i | \(0.639220\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 37.8885 | 1.95136 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.88854 | 0.302474 | 0.151237 | − | 0.988498i | \(-0.451674\pi\) | ||||
0.151237 | + | 0.988498i | \(0.451674\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.00000 | −0.204926 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 20.3607 | 1.04038 | 0.520191 | − | 0.854050i | \(-0.325861\pi\) | ||||
0.520191 | + | 0.854050i | \(0.325861\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.47214 | 0.125666 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.58359 | −0.130993 | −0.0654967 | − | 0.997853i | \(-0.520863\pi\) | ||||
−0.0654967 | + | 0.997853i | \(0.520863\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −25.8885 | −1.30924 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −13.8885 | −0.700584 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.52786 | −0.377813 | −0.188906 | − | 0.981995i | \(-0.560494\pi\) | ||||
−0.188906 | + | 0.981995i | \(0.560494\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.00000 | 0.100125 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.8885 | −0.793436 | −0.396718 | − | 0.917941i | \(-0.629851\pi\) | ||||
−0.396718 | + | 0.917941i | \(0.629851\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.11146 | −0.105179 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.94427 | 0.245078 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.88854 | −0.390063 | −0.195032 | − | 0.980797i | \(-0.562481\pi\) | ||||
−0.195032 | + | 0.980797i | \(0.562481\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −19.8885 | −0.981030 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.94427 | 0.144182 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.00000 | 0.195413 | 0.0977064 | − | 0.995215i | \(-0.468849\pi\) | ||||
0.0977064 | + | 0.995215i | \(0.468849\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.9443 | −0.533391 | −0.266696 | − | 0.963781i | \(-0.585932\pi\) | ||||
−0.266696 | + | 0.963781i | \(0.585932\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.47214 | −0.314686 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.52786 | 0.170725 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −8.94427 | −0.431834 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 21.4164 | 1.03159 | 0.515796 | − | 0.856711i | \(-0.327496\pi\) | ||||
0.515796 | + | 0.856711i | \(0.327496\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.4164 | 1.02921 | 0.514603 | − | 0.857428i | \(-0.327939\pi\) | ||||
0.514603 | + | 0.857428i | \(0.327939\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.00000 | 0.382692 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −31.5279 | −1.50474 | −0.752371 | − | 0.658739i | \(-0.771090\pi\) | ||||
−0.752371 | + | 0.658739i | \(0.771090\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 36.9443 | 1.75528 | 0.877638 | − | 0.479325i | \(-0.159118\pi\) | ||||
0.877638 | + | 0.479325i | \(0.159118\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −12.4721 | −0.589912 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.05573 | −0.427366 | −0.213683 | − | 0.976903i | \(-0.568546\pi\) | ||||
−0.213683 | + | 0.976903i | \(0.568546\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.05573 | −0.332241 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 17.8885 | 0.840477 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.94427 | −0.418395 | −0.209198 | − | 0.977873i | \(-0.567085\pi\) | ||||
−0.209198 | + | 0.977873i | \(0.567085\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.47214 | 0.302093 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.4721 | −0.580885 | −0.290443 | − | 0.956892i | \(-0.593803\pi\) | ||||
−0.290443 | + | 0.956892i | \(0.593803\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 34.8328 | 1.61882 | 0.809409 | − | 0.587245i | \(-0.199788\pi\) | ||||
0.809409 | + | 0.587245i | \(0.199788\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 19.0557 | 0.881794 | 0.440897 | − | 0.897558i | \(-0.354660\pi\) | ||||
0.440897 | + | 0.897558i | \(0.354660\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.52786 | 0.0705502 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.41641 | 0.433885 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.94427 | 0.227338 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.00000 | 0.0915737 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16.0000 | 0.731059 | 0.365529 | − | 0.930800i | \(-0.380888\pi\) | ||||
0.365529 | + | 0.930800i | \(0.380888\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.0557 | −0.504098 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.00000 | 0.182006 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13.8885 | −0.629350 | −0.314675 | − | 0.949199i | \(-0.601896\pi\) | ||||
−0.314675 | + | 0.949199i | \(0.601896\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −23.4164 | −1.05893 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.05573 | −0.0476443 | −0.0238222 | − | 0.999716i | \(-0.507584\pi\) | ||||
−0.0238222 | + | 0.999716i | \(0.507584\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −54.8328 | −2.46955 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.4721 | 0.559452 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.88854 | 0.263607 | 0.131804 | − | 0.991276i | \(-0.457923\pi\) | ||||
0.131804 | + | 0.991276i | \(0.457923\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10.4721 | −0.467861 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 39.4164 | 1.75749 | 0.878745 | − | 0.477291i | \(-0.158381\pi\) | ||||
0.878745 | + | 0.477291i | \(0.158381\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.00000 | 0.310881 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10.5836 | −0.469109 | −0.234555 | − | 0.972103i | \(-0.575363\pi\) | ||||
−0.234555 | + | 0.972103i | \(0.575363\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.52786 | −0.333013 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.00000 | −0.0883022 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12.9443 | −0.569288 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 12.0000 | 0.526742 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.41641 | −0.412540 | −0.206270 | − | 0.978495i | \(-0.566133\pi\) | ||||
−0.206270 | + | 0.978495i | \(0.566133\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.05573 | 0.308525 | 0.154263 | − | 0.988030i | \(-0.450700\pi\) | ||||
0.154263 | + | 0.988030i | \(0.450700\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.05573 | 0.133110 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 15.7771 | 0.683382 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 22.9443 | 0.990118 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.00000 | 0.0861461 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22.9443 | −0.986451 | −0.493226 | − | 0.869901i | \(-0.664182\pi\) | ||||
−0.493226 | + | 0.869901i | \(0.664182\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 16.4721 | 0.706887 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −37.3050 | −1.59504 | −0.797522 | − | 0.603289i | \(-0.793856\pi\) | ||||
−0.797522 | + | 0.603289i | \(0.793856\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.52786 | −0.150566 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 16.9443 | 0.721850 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.94427 | 0.380349 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.05573 | 0.214218 | 0.107109 | − | 0.994247i | \(-0.465841\pi\) | ||||
0.107109 | + | 0.994247i | \(0.465841\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11.0557 | −0.467607 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.9443 | 0.546508 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −34.8328 | −1.46803 | −0.734014 | − | 0.679134i | \(-0.762355\pi\) | ||||
−0.734014 | + | 0.679134i | \(0.762355\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.00000 | −0.251533 | −0.125767 | − | 0.992060i | \(-0.540139\pi\) | ||||
−0.125767 | + | 0.992060i | \(0.540139\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.1115 | 0.423151 | 0.211576 | − | 0.977362i | \(-0.432141\pi\) | ||||
0.211576 | + | 0.977362i | \(0.432141\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 17.4164 | 0.727581 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 24.4721 | 1.01879 | 0.509394 | − | 0.860533i | \(-0.329870\pi\) | ||||
0.509394 | + | 0.860533i | \(0.329870\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 12.9443 | 0.537946 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.94427 | −0.205123 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.00000 | 0.165663 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 15.0557 | 0.621416 | 0.310708 | − | 0.950505i | \(-0.399434\pi\) | ||||
0.310708 | + | 0.950505i | \(0.399434\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.944272 | −0.0389080 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −19.8885 | −0.818105 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −21.3050 | −0.874890 | −0.437445 | − | 0.899245i | \(-0.644116\pi\) | ||||
−0.437445 | + | 0.899245i | \(0.644116\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −20.4721 | −0.837869 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −18.3607 | −0.750197 | −0.375099 | − | 0.926985i | \(-0.622391\pi\) | ||||
−0.375099 | + | 0.926985i | \(0.622391\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.0000 | 0.897399 | 0.448699 | − | 0.893683i | \(-0.351887\pi\) | ||||
0.448699 | + | 0.893683i | \(0.351887\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.52786 | −0.0622194 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.94427 | 0.200682 | 0.100341 | − | 0.994953i | \(-0.468007\pi\) | ||||
0.100341 | + | 0.994953i | \(0.468007\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 8.47214 | 0.343308 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 28.9443 | 1.17096 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.41641 | −0.299546 | −0.149773 | − | 0.988720i | \(-0.547854\pi\) | ||||
−0.149773 | + | 0.988720i | \(0.547854\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −47.8885 | −1.92792 | −0.963960 | − | 0.266047i | \(-0.914282\pi\) | ||||
−0.963960 | + | 0.266047i | \(0.914282\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.8885 | −0.477841 | −0.238920 | − | 0.971039i | \(-0.576794\pi\) | ||||
−0.238920 | + | 0.971039i | \(0.576794\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.00000 | −0.160514 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 17.4164 | 0.697774 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.00000 | −0.159745 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 16.0000 | 0.637962 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.0557 | −0.917834 | −0.458917 | − | 0.888479i | \(-0.651762\pi\) | ||||
−0.458917 | + | 0.888479i | \(0.651762\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −25.8885 | −1.02898 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.47214 | −0.177192 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −12.4721 | −0.493390 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −42.0000 | −1.65890 | −0.829450 | − | 0.558581i | \(-0.811346\pi\) | ||||
−0.829450 | + | 0.558581i | \(0.811346\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.05573 | 0.278251 | 0.139125 | − | 0.990275i | \(-0.455571\pi\) | ||||
0.139125 | + | 0.990275i | \(0.455571\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 38.2492 | 1.50373 | 0.751866 | − | 0.659316i | \(-0.229154\pi\) | ||||
0.751866 | + | 0.659316i | \(0.229154\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.472136 | −0.0185045 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.05573 | 0.0413138 | 0.0206569 | − | 0.999787i | \(-0.493424\pi\) | ||||
0.0206569 | + | 0.999787i | \(0.493424\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.52786 | 0.293690 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.1115 | 0.471795 | 0.235898 | − | 0.971778i | \(-0.424197\pi\) | ||||
0.235898 | + | 0.971778i | \(0.424197\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 48.2492 | 1.87668 | 0.938339 | − | 0.345717i | \(-0.112364\pi\) | ||||
0.938339 | + | 0.345717i | \(0.112364\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −28.9443 | −1.12410 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 33.8885 | 1.31217 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −20.9443 | −0.809752 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.05573 | −0.272383 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21.8885 | 0.843741 | 0.421871 | − | 0.906656i | \(-0.361374\pi\) | ||||
0.421871 | + | 0.906656i | \(0.361374\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.11146 | 0.0811499 | 0.0405749 | − | 0.999176i | \(-0.487081\pi\) | ||||
0.0405749 | + | 0.999176i | \(0.487081\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.52786 | −0.135387 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.88854 | 0.378930 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 14.1115 | 0.539960 | 0.269980 | − | 0.962866i | \(-0.412983\pi\) | ||||
0.269980 | + | 0.962866i | \(0.412983\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −26.3607 | −1.00572 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8.94427 | −0.340750 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 48.8328 | 1.85769 | 0.928844 | − | 0.370471i | \(-0.120804\pi\) | ||||
0.928844 | + | 0.370471i | \(0.120804\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.00000 | −0.0759737 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −22.8328 | −0.864855 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.94427 | −0.111363 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −0.472136 | −0.0178323 | −0.00891616 | − | 0.999960i | \(-0.502838\pi\) | ||||
−0.00891616 | + | 0.999960i | \(0.502838\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.94427 | −0.186477 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.47214 | −0.168192 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 35.8885 | 1.34782 | 0.673911 | − | 0.738812i | \(-0.264613\pi\) | ||||
0.673911 | + | 0.738812i | \(0.264613\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.94427 | −0.335436 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.88854 | −0.0707265 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −15.5279 | −0.579899 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8.94427 | −0.333565 | −0.166783 | − | 0.985994i | \(-0.553338\pi\) | ||||
−0.166783 | + | 0.985994i | \(0.553338\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.9443 | 0.482070 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −11.8885 | −0.442140 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.0557 | 0.706738 | 0.353369 | − | 0.935484i | \(-0.385036\pi\) | ||||
0.353369 | + | 0.935484i | \(0.385036\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 16.0000 | 0.591781 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.63932 | −0.208293 | −0.104147 | − | 0.994562i | \(-0.533211\pi\) | ||||
−0.104147 | + | 0.994562i | \(0.533211\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.05573 | −0.112559 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.0000 | 0.735712 | 0.367856 | − | 0.929883i | \(-0.380092\pi\) | ||||
0.367856 | + | 0.929883i | \(0.380092\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.94427 | 0.328576 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.83282 | −0.103926 | −0.0519630 | − | 0.998649i | \(-0.516548\pi\) | ||||
−0.0519630 | + | 0.998649i | \(0.516548\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.94427 | 0.180901 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26.8328 | −0.979143 | −0.489572 | − | 0.871963i | \(-0.662847\pi\) | ||||
−0.489572 | + | 0.871963i | \(0.662847\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −24.0000 | −0.874609 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −30.4721 | −1.10753 | −0.553764 | − | 0.832673i | \(-0.686809\pi\) | ||||
−0.553764 | + | 0.832673i | \(0.686809\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −8.00000 | −0.290382 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24.4721 | −0.887114 | −0.443557 | − | 0.896246i | \(-0.646284\pi\) | ||||
−0.443557 | + | 0.896246i | \(0.646284\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14.9443 | −0.541019 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.05573 | 0.0380705 | 0.0190353 | − | 0.999819i | \(-0.493941\pi\) | ||||
0.0190353 | + | 0.999819i | \(0.493941\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 23.4164 | 0.843321 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −16.9443 | −0.609443 | −0.304722 | − | 0.952441i | \(-0.598563\pi\) | ||||
−0.304722 | + | 0.952441i | \(0.598563\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.47214 | −0.0886874 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.05573 | 0.252798 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −24.9443 | −0.892576 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −8.47214 | −0.302769 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −36.0000 | −1.28326 | −0.641631 | − | 0.767014i | \(-0.721742\pi\) | ||||
−0.641631 | + | 0.767014i | \(0.721742\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.00000 | −0.142404 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −14.9443 | −0.531357 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.7771 | 0.560261 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 28.0000 | 0.991811 | 0.495905 | − | 0.868377i | \(-0.334836\pi\) | ||||
0.495905 | + | 0.868377i | \(0.334836\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −41.8885 | −1.48191 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −17.4164 | −0.615379 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 15.0557 | 0.531305 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 30.3607 | 1.06875 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −24.8328 | −0.873075 | −0.436538 | − | 0.899686i | \(-0.643795\pi\) | ||||
−0.436538 | + | 0.899686i | \(0.643795\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.0557 | −0.458449 | −0.229224 | − | 0.973374i | \(-0.573619\pi\) | ||||
−0.229224 | + | 0.973374i | \(0.573619\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −24.4721 | −0.858275 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.94427 | −0.172978 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.47214 | 0.156269 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19.3050 | 0.673747 | 0.336874 | − | 0.941550i | \(-0.390630\pi\) | ||||
0.336874 | + | 0.941550i | \(0.390630\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −15.0557 | −0.524810 | −0.262405 | − | 0.964958i | \(-0.584516\pi\) | ||||
−0.262405 | + | 0.964958i | \(0.584516\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 32.7214 | 1.13783 | 0.568917 | − | 0.822395i | \(-0.307363\pi\) | ||||
0.568917 | + | 0.822395i | \(0.307363\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.52786 | 0.122528 | 0.0612639 | − | 0.998122i | \(-0.480487\pi\) | ||||
0.0612639 | + | 0.998122i | \(0.480487\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 23.4164 | 0.812306 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.47214 | 0.224246 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.472136 | 0.0163194 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −32.9443 | −1.13736 | −0.568681 | − | 0.822558i | \(-0.692546\pi\) | ||||
−0.568681 | + | 0.822558i | \(0.692546\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 42.7771 | 1.47507 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.94427 | 0.101406 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.00000 | 0.240523 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −16.9443 | −0.581526 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.88854 | −0.338975 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −31.5279 | −1.07949 | −0.539747 | − | 0.841827i | \(-0.681480\pi\) | ||||
−0.539747 | + | 0.841827i | \(0.681480\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −16.5836 | −0.566485 | −0.283242 | − | 0.959048i | \(-0.591410\pi\) | ||||
−0.283242 | + | 0.959048i | \(0.591410\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21.0557 | 0.718412 | 0.359206 | − | 0.933258i | \(-0.383048\pi\) | ||||
0.359206 | + | 0.933258i | \(0.383048\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.52786 | 0.120229 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −18.8328 | −0.641077 | −0.320538 | − | 0.947236i | \(-0.603864\pi\) | ||||
−0.320538 | + | 0.947236i | \(0.603864\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 24.8885 | 0.845259 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −17.8885 | −0.606827 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.83282 | 0.231521 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.52786 | 0.119400 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 49.3050 | 1.66491 | 0.832455 | − | 0.554093i | \(-0.186935\pi\) | ||||
0.832455 | + | 0.554093i | \(0.186935\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 24.9443 | 0.841349 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 27.5279 | 0.927437 | 0.463719 | − | 0.885983i | \(-0.346515\pi\) | ||||
0.463719 | + | 0.885983i | \(0.346515\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16.3607 | 0.550581 | 0.275290 | − | 0.961361i | \(-0.411226\pi\) | ||||
0.275290 | + | 0.961361i | \(0.411226\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4.58359 | 0.153902 | 0.0769510 | − | 0.997035i | \(-0.475482\pi\) | ||||
0.0769510 | + | 0.997035i | \(0.475482\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.00000 | 0.134156 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.00000 | 0.0670025 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12.9443 | 0.433164 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 17.8885 | 0.597281 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.00000 | −0.133407 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.9443 | 0.431236 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.47214 | −0.0822675 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16.3607 | 0.543247 | 0.271624 | − | 0.962404i | \(-0.412439\pi\) | ||||
0.271624 | + | 0.962404i | \(0.412439\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.47214 | 0.148331 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25.4164 | 0.842083 | 0.421042 | − | 0.907041i | \(-0.361665\pi\) | ||||
0.421042 | + | 0.907041i | \(0.361665\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.88854 | 0.327263 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 13.8885 | 0.458640 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 36.7214 | 1.21133 | 0.605663 | − | 0.795721i | \(-0.292908\pi\) | ||||
0.605663 | + | 0.795721i | \(0.292908\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −20.0000 | −0.659022 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 55.7771 | 1.83593 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −12.9443 | −0.425146 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 19.3050 | 0.633375 | 0.316687 | − | 0.948530i | \(-0.397429\pi\) | ||||
0.316687 | + | 0.948530i | \(0.397429\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.00000 | −0.0655474 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −16.0000 | −0.523816 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15.3050 | −0.499991 | −0.249995 | − | 0.968247i | \(-0.580429\pi\) | ||||
−0.249995 | + | 0.968247i | \(0.580429\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −25.4164 | −0.829433 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 35.5279 | 1.15818 | 0.579088 | − | 0.815265i | \(-0.303409\pi\) | ||||
0.579088 | + | 0.815265i | \(0.303409\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 14.1115 | 0.459532 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 16.0000 | 0.519930 | 0.259965 | − | 0.965618i | \(-0.416289\pi\) | ||||
0.259965 | + | 0.965618i | \(0.416289\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −33.6656 | −1.09283 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.94427 | 0.225183 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 18.0000 | 0.583077 | 0.291539 | − | 0.956559i | \(-0.405833\pi\) | ||||
0.291539 | + | 0.956559i | \(0.405833\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −16.9443 | −0.547731 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 19.8885 | 0.642235 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.7771 | −0.992809 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −25.8885 | −0.832519 | −0.416260 | − | 0.909246i | \(-0.636659\pi\) | ||||
−0.416260 | + | 0.909246i | \(0.636659\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −12.9443 | −0.415830 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 33.8885 | 1.08754 | 0.543768 | − | 0.839236i | \(-0.316997\pi\) | ||||
0.543768 | + | 0.839236i | \(0.316997\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.94427 | −0.0943890 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −52.8328 | −1.69027 | −0.845136 | − | 0.534552i | \(-0.820480\pi\) | ||||
−0.845136 | + | 0.534552i | \(0.820480\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −34.8328 | −1.11326 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.9443 | 0.477134 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 25.5279 | 0.814212 | 0.407106 | − | 0.913381i | \(-0.366538\pi\) | ||||
0.407106 | + | 0.913381i | \(0.366538\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.47214 | 0.206010 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.88854 | −0.314437 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 56.9443 | 1.80889 | 0.904447 | − | 0.426586i | \(-0.140284\pi\) | ||||
0.904447 | + | 0.426586i | \(0.140284\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −33.8885 | −1.07542 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.63932 | −0.178599 | −0.0892995 | − | 0.996005i | \(-0.528463\pi\) | ||||
−0.0892995 | + | 0.996005i | \(0.528463\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.47214 | 0.0782149 |
(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 | 8400.2.a.db.1.1 | 2 | ||
4.3 | odd | 2 | 4200.2.a.bj.1.1 | 2 | |||
5.2 | odd | 4 | 1680.2.t.h.1009.2 | 4 | |||
5.3 | odd | 4 | 1680.2.t.h.1009.4 | 4 | |||
5.4 | even | 2 | 8400.2.a.cz.1.2 | 2 | |||
15.2 | even | 4 | 5040.2.t.u.1009.1 | 4 | |||
15.8 | even | 4 | 5040.2.t.u.1009.2 | 4 | |||
20.3 | even | 4 | 840.2.t.c.169.2 | ✓ | 4 | ||
20.7 | even | 4 | 840.2.t.c.169.4 | yes | 4 | ||
20.19 | odd | 2 | 4200.2.a.bk.1.2 | 2 | |||
60.23 | odd | 4 | 2520.2.t.f.1009.1 | 4 | |||
60.47 | odd | 4 | 2520.2.t.f.1009.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
840.2.t.c.169.2 | ✓ | 4 | 20.3 | even | 4 | ||
840.2.t.c.169.4 | yes | 4 | 20.7 | even | 4 | ||
1680.2.t.h.1009.2 | 4 | 5.2 | odd | 4 | |||
1680.2.t.h.1009.4 | 4 | 5.3 | odd | 4 | |||
2520.2.t.f.1009.1 | 4 | 60.23 | odd | 4 | |||
2520.2.t.f.1009.2 | 4 | 60.47 | odd | 4 | |||
4200.2.a.bj.1.1 | 2 | 4.3 | odd | 2 | |||
4200.2.a.bk.1.2 | 2 | 20.19 | odd | 2 | |||
5040.2.t.u.1009.1 | 4 | 15.2 | even | 4 | |||
5040.2.t.u.1009.2 | 4 | 15.8 | even | 4 | |||
8400.2.a.cz.1.2 | 2 | 5.4 | even | 2 | |||
8400.2.a.db.1.1 | 2 | 1.1 | even | 1 | trivial |