Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4032,2,Mod(575,4032)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4032, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4032.575");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4032.h (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(32.1956820950\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | 12.0.653473922154496.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4x^{10} + 13x^{8} - 28x^{6} + 52x^{4} - 64x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{13} \) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 575.2 | ||
Root | \(-1.35489 + 0.405301i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4032.575 |
Dual form | 4032.2.h.h.575.11 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4032\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(1793\) | \(3781\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 3.31339i | − 1.48179i | −0.671618 | − | 0.740897i | \(-0.734400\pi\) | ||||
0.671618 | − | 0.740897i | \(-0.265600\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.72761 | 1.42543 | 0.712714 | − | 0.701455i | \(-0.247466\pi\) | ||||
0.712714 | + | 0.701455i | \(0.247466\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.97858 | 1.38081 | 0.690404 | − | 0.723424i | \(-0.257433\pi\) | ||||
0.690404 | + | 0.723424i | \(0.257433\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.484966i | 0.117622i | 0.998269 | + | 0.0588108i | \(0.0187309\pi\) | ||||
−0.998269 | + | 0.0588108i | \(0.981269\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 2.29273i | − 0.525989i | −0.964797 | − | 0.262994i | \(-0.915290\pi\) | ||||
0.964797 | − | 0.262994i | \(-0.0847100\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.97002 | 1.66186 | 0.830932 | − | 0.556374i | \(-0.187808\pi\) | ||||
0.830932 | + | 0.556374i | \(0.187808\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.97858 | −1.19572 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 1.41421i | − 0.262613i | −0.991342 | − | 0.131306i | \(-0.958083\pi\) | ||||
0.991342 | − | 0.131306i | \(-0.0419172\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.66442i | 1.37657i | 0.725440 | + | 0.688286i | \(0.241636\pi\) | ||||
−0.725440 | + | 0.688286i | \(0.758364\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.31339 | 0.560066 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.39312 | 0.393426 | 0.196713 | − | 0.980461i | \(-0.436973\pi\) | ||||
0.196713 | + | 0.980461i | \(0.436973\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.55580i | 1.02384i | 0.859032 | + | 0.511922i | \(0.171066\pi\) | ||||
−0.859032 | + | 0.511922i | \(0.828934\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.37169i | 0.819175i | 0.912271 | + | 0.409588i | \(0.134327\pi\) | ||||
−0.912271 | + | 0.409588i | \(0.865673\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.21280 | 0.906230 | 0.453115 | − | 0.891452i | \(-0.350313\pi\) | ||||
0.453115 | + | 0.891452i | \(0.350313\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.00023i | 0.137392i | 0.997638 | + | 0.0686960i | \(0.0218839\pi\) | ||||
−0.997638 | + | 0.0686960i | \(0.978116\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 15.6644i | − 2.11219i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.38392 | −0.180171 | −0.0900853 | − | 0.995934i | \(-0.528714\pi\) | ||||
−0.0900853 | + | 0.995934i | \(0.528714\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.6644 | −1.74955 | −0.874775 | − | 0.484529i | \(-0.838991\pi\) | ||||
−0.874775 | + | 0.484529i | \(0.838991\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 16.4960i | − 2.04608i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.27131i | 0.399654i | 0.979831 | + | 0.199827i | \(0.0640380\pi\) | ||||
−0.979831 | + | 0.199827i | \(0.935962\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.34369 | 0.396823 | 0.198412 | − | 0.980119i | \(-0.436422\pi\) | ||||
0.198412 | + | 0.980119i | \(0.436422\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.10038 | −0.245831 | −0.122916 | − | 0.992417i | \(-0.539224\pi\) | ||||
−0.122916 | + | 0.992417i | \(0.539224\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.72761i | 0.538761i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.0575i | 1.35658i | 0.734795 | + | 0.678290i | \(0.237278\pi\) | ||||
−0.734795 | + | 0.678290i | \(0.762722\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.24241 | 0.355901 | 0.177950 | − | 0.984039i | \(-0.443053\pi\) | ||||
0.177950 | + | 0.984039i | \(0.443053\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.60688 | 0.174291 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.72784i | 0.607149i | 0.952808 | + | 0.303575i | \(0.0981802\pi\) | ||||
−0.952808 | + | 0.303575i | \(0.901820\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.97858i | 0.521897i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7.59672 | −0.779407 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.0575 | 1.22426 | 0.612129 | − | 0.790758i | \(-0.290313\pi\) | ||||
0.612129 | + | 0.790758i | \(0.290313\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.5665i | 1.44942i | 0.689053 | + | 0.724711i | \(0.258027\pi\) | ||||
−0.689053 | + | 0.724711i | \(0.741973\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 5.70727i | − 0.562354i | −0.959656 | − | 0.281177i | \(-0.909275\pi\) | ||||
0.959656 | − | 0.281177i | \(-0.0907248\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.0413 | 1.55077 | 0.775386 | − | 0.631487i | \(-0.217555\pi\) | ||||
0.775386 | + | 0.631487i | \(0.217555\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.37169 | −0.131384 | −0.0656921 | − | 0.997840i | \(-0.520926\pi\) | ||||
−0.0656921 | + | 0.997840i | \(0.520926\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.2834i | 1.06145i | 0.847543 | + | 0.530727i | \(0.178081\pi\) | ||||
−0.847543 | + | 0.530727i | \(0.821919\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 26.4078i | − 2.46254i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.484966 | −0.0444568 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.3503 | 1.03184 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.24241i | 0.290010i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 16.6430i | − 1.47683i | −0.674348 | − | 0.738414i | \(-0.735575\pi\) | ||||
0.674348 | − | 0.738414i | \(-0.264425\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.59672 | −0.663729 | −0.331864 | − | 0.943327i | \(-0.607678\pi\) | ||||
−0.331864 | + | 0.943327i | \(0.607678\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.29273 | 0.198805 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 9.42492i | − 0.805225i | −0.915370 | − | 0.402613i | \(-0.868102\pi\) | ||||
0.915370 | − | 0.402613i | \(-0.131898\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 16.0000i | − 1.35710i | −0.734553 | − | 0.678551i | \(-0.762608\pi\) | ||||
0.734553 | − | 0.678551i | \(-0.237392\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 23.5368 | 1.96824 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.68585 | −0.389138 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 18.4661i | − 1.51281i | −0.654106 | − | 0.756403i | \(-0.726955\pi\) | ||||
0.654106 | − | 0.756403i | \(-0.273045\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 23.3288i | − 1.89847i | −0.314561 | − | 0.949237i | \(-0.601857\pi\) | ||||
0.314561 | − | 0.949237i | \(-0.398143\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 25.3953 | 2.03980 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −22.2499 | −1.77573 | −0.887867 | − | 0.460100i | \(-0.847814\pi\) | ||||
−0.887867 | + | 0.460100i | \(0.847814\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.97002i | 0.628125i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 16.6430i | − 1.30358i | −0.758399 | − | 0.651790i | \(-0.774018\pi\) | ||||
0.758399 | − | 0.651790i | \(-0.225982\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.98064 | −0.694943 | −0.347471 | − | 0.937691i | \(-0.612960\pi\) | ||||
−0.347471 | + | 0.937691i | \(0.612960\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.7862 | 0.906633 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 2.75744i | − 0.209645i | −0.994491 | − | 0.104822i | \(-0.966573\pi\) | ||||
0.994491 | − | 0.104822i | \(-0.0334274\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 5.97858i | − 0.451938i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.72761 | 0.353358 | 0.176679 | − | 0.984269i | \(-0.443465\pi\) | ||||
0.176679 | + | 0.984269i | \(0.443465\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.39312 | 0.623855 | 0.311928 | − | 0.950106i | \(-0.399025\pi\) | ||||
0.311928 | + | 0.950106i | \(0.399025\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 7.92933i | − 0.582976i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.29273i | 0.167661i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.48520 | 0.107465 | 0.0537325 | − | 0.998555i | \(-0.482888\pi\) | ||||
0.0537325 | + | 0.998555i | \(0.482888\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.35027 | −0.601066 | −0.300533 | − | 0.953771i | \(-0.597164\pi\) | ||||
−0.300533 | + | 0.953771i | \(0.597164\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.82866i | 0.272780i | 0.990655 | + | 0.136390i | \(0.0435501\pi\) | ||||
−0.990655 | + | 0.136390i | \(0.956450\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 6.04285i | − 0.428366i | −0.976794 | − | 0.214183i | \(-0.931291\pi\) | ||||
0.976794 | − | 0.214183i | \(-0.0687089\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.41421 | 0.0992583 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 21.7220 | 1.51713 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 10.8391i | − 0.749758i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.95715i | 0.685479i | 0.939431 | + | 0.342739i | \(0.111355\pi\) | ||||
−0.939431 | + | 0.342739i | \(0.888645\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 17.7985 | 1.21385 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.66442 | −0.520295 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.41444i | 0.162413i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 0.786230i | − 0.0526499i | −0.999653 | − | 0.0263249i | \(-0.991620\pi\) | ||||
0.999653 | − | 0.0263249i | \(-0.00838046\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −20.2943 | −1.34698 | −0.673492 | − | 0.739195i | \(-0.735206\pi\) | ||||
−0.673492 | + | 0.739195i | \(0.735206\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.97858 | 0.328994 | 0.164497 | − | 0.986378i | \(-0.447400\pi\) | ||||
0.164497 | + | 0.986378i | \(0.447400\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.383688i | 0.0251362i | 0.999921 | + | 0.0125681i | \(0.00400066\pi\) | ||||
−0.999921 | + | 0.0125681i | \(0.995999\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 20.5855i | − 1.34285i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.48520 | −0.0960693 | −0.0480347 | − | 0.998846i | \(-0.515296\pi\) | ||||
−0.0480347 | + | 0.998846i | \(0.515296\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −23.4721 | −1.51197 | −0.755985 | − | 0.654589i | \(-0.772842\pi\) | ||||
−0.755985 | + | 0.654589i | \(0.772842\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.31339i | 0.211685i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 11.4145i | − 0.726290i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.62633 | −0.292011 | −0.146006 | − | 0.989284i | \(-0.546642\pi\) | ||||
−0.146006 | + | 0.989284i | \(0.546642\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 37.6791 | 2.36887 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 3.78797i | − 0.236287i | −0.992997 | − | 0.118144i | \(-0.962306\pi\) | ||||
0.992997 | − | 0.118144i | \(-0.0376943\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.39312i | 0.148701i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.7989 | 0.789214 | 0.394607 | − | 0.918850i | \(-0.370881\pi\) | ||||
0.394607 | + | 0.918850i | \(0.370881\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.31415 | 0.203587 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 25.4662i | − 1.55270i | −0.630300 | − | 0.776352i | \(-0.717068\pi\) | ||||
0.630300 | − | 0.776352i | \(-0.282932\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.0361i | 1.27785i | 0.769268 | + | 0.638927i | \(0.220621\pi\) | ||||
−0.769268 | + | 0.638927i | \(0.779379\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −28.2644 | −1.70441 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.39312 | −0.504293 | −0.252147 | − | 0.967689i | \(-0.581137\pi\) | ||||
−0.252147 | + | 0.967689i | \(0.581137\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 0.111668i | − 0.00666157i | −0.999994 | − | 0.00333078i | \(-0.998940\pi\) | ||||
0.999994 | − | 0.00333078i | \(-0.00106022\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 11.4637i | − 0.681444i | −0.940164 | − | 0.340722i | \(-0.889329\pi\) | ||||
0.940164 | − | 0.340722i | \(-0.110671\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.55580 | −0.386977 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.7648 | 0.986165 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 17.8089i | − 1.04041i | −0.854042 | − | 0.520204i | \(-0.825856\pi\) | ||||
0.854042 | − | 0.520204i | \(-0.174144\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.58546i | 0.266976i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 39.6794 | 2.29472 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.37169 | −0.309619 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 45.2756i | 2.59247i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.2499i | 1.15572i | 0.816135 | + | 0.577861i | \(0.196112\pi\) | ||||
−0.816135 | + | 0.577861i | \(0.803888\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.38392 | −0.0784747 | −0.0392374 | − | 0.999230i | \(-0.512493\pi\) | ||||
−0.0392374 | + | 0.999230i | \(0.512493\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −30.1151 | −1.70220 | −0.851102 | − | 0.525000i | \(-0.824065\pi\) | ||||
−0.851102 | + | 0.525000i | \(0.824065\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 5.27317i | − 0.296171i | −0.988975 | − | 0.148085i | \(-0.952689\pi\) | ||||
0.988975 | − | 0.148085i | \(-0.0473110\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 6.68585i | − 0.374336i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.11190 | 0.0618676 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −29.7648 | −1.65105 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.21280i | 0.342523i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.95715i | 0.547295i | 0.961830 | + | 0.273647i | \(0.0882301\pi\) | ||||
−0.961830 | + | 0.273647i | \(0.911770\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 10.8391 | 0.592205 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.3717 | −0.728402 | −0.364201 | − | 0.931320i | \(-0.618658\pi\) | ||||
−0.364201 | + | 0.931320i | \(0.618658\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 36.2344i | 1.96220i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 1.00000i | − 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11.2124 | 0.601915 | 0.300957 | − | 0.953638i | \(-0.402694\pi\) | ||||
0.300957 | + | 0.953638i | \(0.402694\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.29273 | 0.229785 | 0.114892 | − | 0.993378i | \(-0.463348\pi\) | ||||
0.114892 | + | 0.993378i | \(0.463348\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 1.78751i | − 0.0951397i | −0.998868 | − | 0.0475698i | \(-0.984852\pi\) | ||||
0.998868 | − | 0.0475698i | \(-0.0151477\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 11.0790i | − 0.588010i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12.7989 | 0.675500 | 0.337750 | − | 0.941236i | \(-0.390334\pi\) | ||||
0.337750 | + | 0.941236i | \(0.390334\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.7434 | 0.723336 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.95940i | 0.364272i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 30.1579i | 1.57423i | 0.616806 | + | 0.787115i | \(0.288426\pi\) | ||||
−0.616806 | + | 0.787115i | \(0.711574\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.00023 | −0.0519293 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.21377 | −0.269959 | −0.134979 | − | 0.990848i | \(-0.543097\pi\) | ||||
−0.134979 | + | 0.990848i | \(0.543097\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 7.04077i | − 0.362618i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 16.7862i | − 0.862251i | −0.902292 | − | 0.431125i | \(-0.858117\pi\) | ||||
0.902292 | − | 0.431125i | \(-0.141883\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −23.7393 | −1.21302 | −0.606511 | − | 0.795075i | \(-0.707431\pi\) | ||||
−0.606511 | + | 0.795075i | \(0.707431\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 15.6644 | 0.798333 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 17.7682i | 0.900885i | 0.892805 | + | 0.450443i | \(0.148734\pi\) | ||||
−0.892805 | + | 0.450443i | \(0.851266\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.86519i | 0.195471i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 39.9514 | 2.01017 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −24.4078 | −1.22499 | −0.612496 | − | 0.790473i | \(-0.709835\pi\) | ||||
−0.612496 | + | 0.790473i | \(0.709835\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 29.1633i | − 1.45635i | −0.685393 | − | 0.728173i | \(-0.740370\pi\) | ||||
0.685393 | − | 0.728173i | \(-0.259630\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 38.1579i | 1.90078i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.3137 | 0.560800 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.4851 | −0.518454 | −0.259227 | − | 0.965816i | \(-0.583468\pi\) | ||||
−0.259227 | + | 0.965816i | \(0.583468\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 1.38392i | − 0.0680981i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 10.7434i | − 0.527372i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 31.1335 | 1.52097 | 0.760485 | − | 0.649356i | \(-0.224961\pi\) | ||||
0.760485 | + | 0.649356i | \(0.224961\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −30.2646 | −1.47501 | −0.737503 | − | 0.675344i | \(-0.763995\pi\) | ||||
−0.737503 | + | 0.675344i | \(0.763995\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 2.89941i | − 0.140642i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 13.6644i | − 0.661268i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.23179 | −0.107502 | −0.0537508 | − | 0.998554i | \(-0.517118\pi\) | ||||
−0.0537508 | + | 0.998554i | \(0.517118\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.54262 | −0.410532 | −0.205266 | − | 0.978706i | \(-0.565806\pi\) | ||||
−0.205266 | + | 0.978706i | \(0.565806\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 18.2731i | − 0.874121i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 1.17092i | − 0.0558851i | −0.999610 | − | 0.0279426i | \(-0.991104\pi\) | ||||
0.999610 | − | 0.0279426i | \(-0.00889556\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.58610 | −0.312915 | −0.156458 | − | 0.987685i | \(-0.550007\pi\) | ||||
−0.156458 | + | 0.987685i | \(0.550007\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 18.9786 | 0.899671 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 11.2228i | − 0.529638i | −0.964298 | − | 0.264819i | \(-0.914688\pi\) | ||||
0.964298 | − | 0.264819i | \(-0.0853121\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 30.9933i | 1.45942i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 16.4960 | 0.773344 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.9143 | 0.557328 | 0.278664 | − | 0.960389i | \(-0.410108\pi\) | ||||
0.278664 | + | 0.960389i | \(0.410108\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.4255i | 0.858159i | 0.903267 | + | 0.429080i | \(0.141162\pi\) | ||||
−0.903267 | + | 0.429080i | \(0.858838\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.47208i | 0.347257i | 0.984811 | + | 0.173628i | \(0.0555492\pi\) | ||||
−0.984811 | + | 0.173628i | \(0.944451\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.57548 | −0.258003 | −0.129001 | − | 0.991644i | \(-0.541177\pi\) | ||||
−0.129001 | + | 0.991644i | \(0.541177\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.27131 | −0.151055 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 25.3953i | 1.16767i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 13.7073i | 0.628933i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −15.9400 | −0.728319 | −0.364159 | − | 0.931337i | \(-0.618644\pi\) | ||||
−0.364159 | + | 0.931337i | \(0.618644\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.9143 | 0.543246 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 39.9514i | − 1.81410i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 34.0722i | 1.54396i | 0.635647 | + | 0.771980i | \(0.280734\pi\) | ||||
−0.635647 | + | 0.771980i | \(0.719266\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −34.0026 | −1.53452 | −0.767258 | − | 0.641339i | \(-0.778379\pi\) | ||||
−0.767258 | + | 0.641339i | \(0.778379\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.685846 | 0.0308890 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.34369i | 0.149985i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.37169i | 0.240470i | 0.992745 | + | 0.120235i | \(0.0383648\pi\) | ||||
−0.992745 | + | 0.120235i | \(0.961635\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 37.3463 | 1.66519 | 0.832594 | − | 0.553884i | \(-0.186855\pi\) | ||||
0.832594 | + | 0.553884i | \(0.186855\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 48.2646 | 2.14775 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 0.403595i | − 0.0178890i | −0.999960 | − | 0.00894451i | \(-0.997153\pi\) | ||||
0.999960 | − | 0.00894451i | \(-0.00284716\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 2.10038i | − 0.0929155i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −18.9104 | −0.833293 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 29.3717 | 1.29177 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 42.9927i | − 1.88355i | −0.336249 | − | 0.941773i | \(-0.609158\pi\) | ||||
0.336249 | − | 0.941773i | \(-0.390842\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 16.0000i | − 0.699631i | −0.936819 | − | 0.349816i | \(-0.886244\pi\) | ||||
0.936819 | − | 0.349816i | \(-0.113756\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.71699 | −0.161915 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 40.5212 | 1.76179 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 32.6386i | 1.41373i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 53.1512i | − 2.29793i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.72761 | −0.203632 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −19.1365 | −0.822742 | −0.411371 | − | 0.911468i | \(-0.634950\pi\) | ||||
−0.411371 | + | 0.911468i | \(0.634950\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.54496i | 0.194685i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.14323i | 0.348179i | 0.984730 | + | 0.174090i | \(0.0556983\pi\) | ||||
−0.984730 | + | 0.174090i | \(0.944302\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.24241 | −0.138131 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.0575 | −0.512739 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 39.0931i | 1.65643i | 0.560412 | + | 0.828214i | \(0.310643\pi\) | ||||
−0.560412 | + | 0.828214i | \(0.689357\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 26.7434i | 1.13112i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −13.6468 | −0.575143 | −0.287572 | − | 0.957759i | \(-0.592848\pi\) | ||||
−0.287572 | + | 0.957759i | \(0.592848\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 37.3864 | 1.57286 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.32355i | 0.0974084i | 0.998813 | + | 0.0487042i | \(0.0155092\pi\) | ||||
−0.998813 | + | 0.0487042i | \(0.984491\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 2.88661i | − 0.120801i | −0.998174 | − | 0.0604005i | \(-0.980762\pi\) | ||||
0.998174 | − | 0.0604005i | \(-0.0192378\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −47.6494 | −1.98712 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.5855 | −0.773723 | −0.386861 | − | 0.922138i | \(-0.626441\pi\) | ||||
−0.386861 | + | 0.922138i | \(0.626441\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.24241i | 0.134518i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.72869i | 0.195842i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.92979 | 0.409846 | 0.204923 | − | 0.978778i | \(-0.434306\pi\) | ||||
0.204923 | + | 0.978778i | \(0.434306\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.5725 | 0.724061 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 24.0823i | − 0.988942i | −0.869194 | − | 0.494471i | \(-0.835362\pi\) | ||||
0.869194 | − | 0.494471i | \(-0.164638\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.60688i | 0.0658759i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 19.2837 | 0.787912 | 0.393956 | − | 0.919129i | \(-0.371106\pi\) | ||||
0.393956 | + | 0.919129i | \(0.371106\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.5855 | 0.431790 | 0.215895 | − | 0.976417i | \(-0.430733\pi\) | ||||
0.215895 | + | 0.976417i | \(0.430733\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 37.6079i | − 1.52898i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 34.0722i | − 1.38295i | −0.722401 | − | 0.691475i | \(-0.756961\pi\) | ||||
0.722401 | − | 0.691475i | \(-0.243039\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 30.9309 | 1.25133 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17.3288 | 0.699906 | 0.349953 | − | 0.936767i | \(-0.386198\pi\) | ||||
0.349953 | + | 0.936767i | \(0.386198\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 1.76760i | − 0.0711611i | −0.999367 | − | 0.0355805i | \(-0.988672\pi\) | ||||
0.999367 | − | 0.0355805i | \(-0.0113280\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 47.0424i | 1.89079i | 0.325922 | + | 0.945397i | \(0.394325\pi\) | ||||
−0.325922 | + | 0.945397i | \(0.605675\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.72784 | −0.229481 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.1495 | −0.765980 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.16058i | 0.0462754i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.0147i | 0.557916i | 0.960303 | + | 0.278958i | \(0.0899890\pi\) | ||||
−0.960303 | + | 0.278958i | \(0.910011\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −55.1448 | −2.18836 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.97858 | −0.197258 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.92956i | 0.352696i | 0.984328 | + | 0.176348i | \(0.0564285\pi\) | ||||
−0.984328 | + | 0.176348i | \(0.943572\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.53635i | 0.178896i | 0.995991 | + | 0.0894480i | \(0.0285103\pi\) | ||||
−0.995991 | + | 0.0894480i | \(0.971490\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.10091 | 0.200537 | 0.100269 | − | 0.994960i | \(-0.468030\pi\) | ||||
0.100269 | + | 0.994960i | \(0.468030\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.54262 | −0.256820 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 26.2535i | 1.02738i | 0.857976 | + | 0.513690i | \(0.171722\pi\) | ||||
−0.857976 | + | 0.513690i | \(0.828278\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 25.1709i | 0.983509i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −16.0413 | −0.624881 | −0.312440 | − | 0.949937i | \(-0.601146\pi\) | ||||
−0.312440 | + | 0.949937i | \(0.601146\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −29.8652 | −1.16162 | −0.580811 | − | 0.814039i | \(-0.697264\pi\) | ||||
−0.580811 | + | 0.814039i | \(0.697264\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 7.59672i | − 0.294588i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 11.2713i | − 0.436427i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −64.6000 | −2.49386 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −35.0080 | −1.34946 | −0.674729 | − | 0.738066i | \(-0.735739\pi\) | ||||
−0.674729 | + | 0.738066i | \(0.735739\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 37.6893i | − 1.44852i | −0.689529 | − | 0.724258i | \(-0.742182\pi\) | ||||
0.689529 | − | 0.724258i | \(-0.257818\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.0575i | 0.462726i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −21.5770 | −0.825620 | −0.412810 | − | 0.910817i | \(-0.635453\pi\) | ||||
−0.412810 | + | 0.910817i | \(0.635453\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −31.2285 | −1.19318 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.97972i | 0.189712i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14.0428i | 0.534215i | 0.963667 | + | 0.267108i | \(0.0860679\pi\) | ||||
−0.963667 | + | 0.267108i | \(0.913932\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −53.0143 | −2.01095 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.17935 | −0.120426 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 27.9214i | − 1.05458i | −0.849687 | − | 0.527288i | \(-0.823209\pi\) | ||||
0.849687 | − | 0.527288i | \(-0.176791\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 5.48677i | − 0.206937i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −14.5665 | −0.547830 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.5426 | 0.395936 | 0.197968 | − | 0.980208i | \(-0.436566\pi\) | ||||
0.197968 | + | 0.980208i | \(0.436566\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 61.0856i | 2.28767i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 77.9865i | − 2.91653i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −31.8801 | −1.18893 | −0.594463 | − | 0.804123i | \(-0.702635\pi\) | ||||
−0.594463 | + | 0.804123i | \(0.702635\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.70727 | 0.212550 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.45498i | 0.314010i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 46.2070i | 1.71372i | 0.515546 | + | 0.856862i | \(0.327589\pi\) | ||||
−0.515546 | + | 0.856862i | \(0.672411\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.60509 | −0.0963528 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −22.4360 | −0.828691 | −0.414346 | − | 0.910120i | \(-0.635990\pi\) | ||||
−0.414346 | + | 0.910120i | \(0.635990\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 15.4655i | 0.569678i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 14.0147i | − 0.515539i | −0.966206 | − | 0.257769i | \(-0.917013\pi\) | ||||
0.966206 | − | 0.257769i | \(-0.0829875\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 25.9313 | 0.951327 | 0.475663 | − | 0.879627i | \(-0.342208\pi\) | ||||
0.475663 | + | 0.879627i | \(0.342208\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −61.1856 | −2.24167 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 16.0413i | 0.586137i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 2.74338i | − 0.100108i | −0.998747 | − | 0.0500538i | \(-0.984061\pi\) | ||||
0.998747 | − | 0.0500538i | \(-0.0159393\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −77.2977 | −2.81315 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.7992 | 0.574233 | 0.287116 | − | 0.957896i | \(-0.407303\pi\) | ||||
0.287116 | + | 0.957896i | \(0.407303\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 27.0527i | 0.980660i | 0.871537 | + | 0.490330i | \(0.163124\pi\) | ||||
−0.871537 | + | 0.490330i | \(0.836876\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 1.37169i | − 0.0496586i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.88994 | −0.248781 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 39.8715 | 1.43780 | 0.718901 | − | 0.695113i | \(-0.244646\pi\) | ||||
0.718901 | + | 0.695113i | \(0.244646\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 34.4261i | − 1.23822i | −0.785304 | − | 0.619110i | \(-0.787493\pi\) | ||||
0.785304 | − | 0.619110i | \(-0.212507\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 45.8223i | − 1.64599i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 15.0307 | 0.538531 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.8077 | 0.565642 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 73.7226i | 2.63127i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 24.1151i | 0.859610i | 0.902922 | + | 0.429805i | \(0.141418\pi\) | ||||
−0.902922 | + | 0.429805i | \(0.858582\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11.2834 | −0.401192 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −68.0294 | −2.41579 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 35.0634i | 1.24201i | 0.783807 | + | 0.621005i | \(0.213275\pi\) | ||||
−0.783807 | + | 0.621005i | \(0.786725\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.01300i | 0.106592i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.92979 | −0.350415 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 26.4078 | 0.930753 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 21.9806i | − 0.772796i | −0.922332 | − | 0.386398i | \(-0.873719\pi\) | ||||
0.922332 | − | 0.386398i | \(-0.126281\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 44.7005i | − 1.56965i | −0.619719 | − | 0.784824i | \(-0.712753\pi\) | ||||
0.619719 | − | 0.784824i | \(-0.287247\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −55.1448 | −1.93164 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.3158 | 0.430877 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 39.3651i | − 1.37385i | −0.726727 | − | 0.686926i | \(-0.758960\pi\) | ||||
0.726727 | − | 0.686926i | \(-0.241040\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 31.9718i | 1.11447i | 0.830355 | + | 0.557234i | \(0.188137\pi\) | ||||
−0.830355 | + | 0.557234i | \(0.811863\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −20.8702 | −0.725728 | −0.362864 | − | 0.931842i | \(-0.618201\pi\) | ||||
−0.362864 | + | 0.931842i | \(0.618201\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 32.2217 | 1.11911 | 0.559554 | − | 0.828794i | \(-0.310973\pi\) | ||||
0.559554 | + | 0.828794i | \(0.310973\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 0.484966i | − 0.0168031i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 29.7564i | 1.02976i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 48.9320 | 1.68932 | 0.844660 | − | 0.535303i | \(-0.179802\pi\) | ||||
0.844660 | + | 0.535303i | \(0.179802\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.0000 | 0.931034 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 39.0524i | − 1.34344i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11.3503i | 0.390000i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 19.0732 | 0.653820 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12.2927 | −0.420895 | −0.210448 | − | 0.977605i | \(-0.567492\pi\) | ||||
−0.210448 | + | 0.977605i | \(0.567492\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 57.1349i | − 1.95169i | −0.218463 | − | 0.975845i | \(-0.570104\pi\) | ||||
0.218463 | − | 0.975845i | \(-0.429896\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21.8223i | 0.744569i | 0.928119 | + | 0.372284i | \(0.121425\pi\) | ||||
−0.928119 | + | 0.372284i | \(0.878575\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −42.2764 | −1.43911 | −0.719553 | − | 0.694437i | \(-0.755653\pi\) | ||||
−0.719553 | + | 0.694437i | \(0.755653\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.13650 | −0.310650 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 57.0033i | 1.93370i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.2865i | 0.551846i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.24241 | −0.109614 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −26.2008 | −0.884737 | −0.442369 | − | 0.896833i | \(-0.645862\pi\) | ||||
−0.442369 | + | 0.896833i | \(0.645862\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 47.4165i | − 1.59750i | −0.601661 | − | 0.798752i | \(-0.705494\pi\) | ||||
0.601661 | − | 0.798752i | \(-0.294506\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.6283i | 0.896114i | 0.894005 | + | 0.448057i | \(0.147884\pi\) | ||||
−0.894005 | + | 0.448057i | \(0.852116\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −6.75684 | −0.226873 | −0.113436 | − | 0.993545i | \(-0.536186\pi\) | ||||
−0.113436 | + | 0.993545i | \(0.536186\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16.6430 | 0.558188 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 14.2443i | − 0.476667i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 15.6644i | − 0.523604i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 10.8391 | 0.361505 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.485078 | −0.0161603 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 27.8097i | − 0.924426i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 25.2860i | − 0.839608i | −0.907615 | − | 0.419804i | \(-0.862099\pi\) | ||||
0.907615 | − | 0.419804i | \(-0.137901\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21.3050 | 0.705865 | 0.352932 | − | 0.935649i | \(-0.385185\pi\) | ||||
0.352932 | + | 0.935649i | \(0.385185\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15.3288 | 0.507311 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 7.59672i | − 0.250866i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 48.4998i | − 1.59986i | −0.600093 | − | 0.799930i | \(-0.704870\pi\) | ||||
0.600093 | − | 0.799930i | \(-0.295130\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 16.6468 | 0.547937 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −14.3074 | −0.470425 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 10.5567i | − 0.346355i | −0.984891 | − | 0.173177i | \(-0.944597\pi\) | ||||
0.984891 | − | 0.173177i | \(-0.0554034\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.29273i | 0.0751412i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.59672 | 0.248439 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −29.5296 | −0.964690 | −0.482345 | − | 0.875981i | \(-0.660215\pi\) | ||||
−0.482345 | + | 0.875981i | \(0.660215\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 6.53503i | − 0.213036i | −0.994311 | − | 0.106518i | \(-0.966030\pi\) | ||||
0.994311 | − | 0.106518i | \(-0.0339701\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 52.2499i | 1.70149i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −43.2951 | −1.40690 | −0.703450 | − | 0.710745i | \(-0.748358\pi\) | ||||
−0.703450 | + | 0.710745i | \(0.748358\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10.4569 | −0.339446 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 19.4848i | 0.631173i | 0.948897 | + | 0.315587i | \(0.102201\pi\) | ||||
−0.948897 | + | 0.315587i | \(0.897799\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 4.92104i | − 0.159241i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.42492 | 0.304346 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.7434 | −0.894948 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 27.6677i | 0.890656i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 28.4422i | − 0.914641i | −0.889302 | − | 0.457320i | \(-0.848809\pi\) | ||||
0.889302 | − | 0.457320i | \(-0.151191\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8.61534 | 0.276479 | 0.138240 | − | 0.990399i | \(-0.455856\pi\) | ||||
0.138240 | + | 0.990399i | \(0.455856\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16.0000 | 0.512936 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 35.8715i | − 1.14763i | −0.818985 | − | 0.573815i | \(-0.805463\pi\) | ||||
0.818985 | − | 0.573815i | \(-0.194537\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 27.0790i | 0.865447i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −41.0633 | −1.30971 | −0.654857 | − | 0.755752i | \(-0.727271\pi\) | ||||
−0.654857 | + | 0.755752i | \(0.727271\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.6858 | 0.404205 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 42.8125i | 1.36136i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 25.6707i | − 0.815456i | −0.913103 | − | 0.407728i | \(-0.866321\pi\) | ||||
0.913103 | − | 0.407728i | \(-0.133679\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −20.0223 | −0.634750 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.45065 | 0.0776130 | 0.0388065 | − | 0.999247i | \(-0.487644\pi\) | ||||
0.0388065 | + | 0.999247i | \(0.487644\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4032.2.h.h.575.2 | 12 | ||
3.2 | odd | 2 | inner | 4032.2.h.h.575.12 | 12 | ||
4.3 | odd | 2 | inner | 4032.2.h.h.575.1 | 12 | ||
8.3 | odd | 2 | 252.2.e.a.71.11 | yes | 12 | ||
8.5 | even | 2 | 252.2.e.a.71.1 | ✓ | 12 | ||
12.11 | even | 2 | inner | 4032.2.h.h.575.11 | 12 | ||
24.5 | odd | 2 | 252.2.e.a.71.12 | yes | 12 | ||
24.11 | even | 2 | 252.2.e.a.71.2 | yes | 12 | ||
56.13 | odd | 2 | 1764.2.e.g.1079.1 | 12 | |||
56.27 | even | 2 | 1764.2.e.g.1079.11 | 12 | |||
168.83 | odd | 2 | 1764.2.e.g.1079.2 | 12 | |||
168.125 | even | 2 | 1764.2.e.g.1079.12 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.2.e.a.71.1 | ✓ | 12 | 8.5 | even | 2 | ||
252.2.e.a.71.2 | yes | 12 | 24.11 | even | 2 | ||
252.2.e.a.71.11 | yes | 12 | 8.3 | odd | 2 | ||
252.2.e.a.71.12 | yes | 12 | 24.5 | odd | 2 | ||
1764.2.e.g.1079.1 | 12 | 56.13 | odd | 2 | |||
1764.2.e.g.1079.2 | 12 | 168.83 | odd | 2 | |||
1764.2.e.g.1079.11 | 12 | 56.27 | even | 2 | |||
1764.2.e.g.1079.12 | 12 | 168.125 | even | 2 | |||
4032.2.h.h.575.1 | 12 | 4.3 | odd | 2 | inner | ||
4032.2.h.h.575.2 | 12 | 1.1 | even | 1 | trivial | ||
4032.2.h.h.575.11 | 12 | 12.11 | even | 2 | inner | ||
4032.2.h.h.575.12 | 12 | 3.2 | odd | 2 | inner |