Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4032,2,Mod(1583,4032)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4032, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4032.1583");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4032.v (of order \(4\), degree \(2\), 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: | \(36\) |
Relative dimension: | \(18\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 1008) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1583.9 | ||
Character | \(\chi\) | \(=\) | 4032.1583 |
Dual form | 4032.2.v.d.3599.9 |
$q$-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 \(\left(\mathbb{Z}/4032\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(1793\) | \(3781\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.270063 | − | 0.270063i | −0.120776 | − | 0.120776i | 0.644136 | − | 0.764911i | \(-0.277217\pi\) |
−0.764911 | + | 0.644136i | \(0.777217\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.03491 | − | 3.03491i | 0.915060 | − | 0.915060i | −0.0816051 | − | 0.996665i | \(-0.526005\pi\) |
0.996665 | + | 0.0816051i | \(0.0260046\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.28727 | + | 1.28727i | 0.357025 | + | 0.357025i | 0.862715 | − | 0.505690i | \(-0.168762\pi\) |
−0.505690 | + | 0.862715i | \(0.668762\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 5.15741i | − | 1.25086i | −0.780282 | − | 0.625428i | \(-0.784924\pi\) | ||
0.780282 | − | 0.625428i | \(-0.215076\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.55077 | − | 5.55077i | 1.27343 | − | 1.27343i | 0.329161 | − | 0.944274i | \(-0.393234\pi\) |
0.944274 | − | 0.329161i | \(-0.106766\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.69943i | 1.18841i | 0.804313 | + | 0.594206i | \(0.202534\pi\) | ||||
−0.804313 | + | 0.594206i | \(0.797466\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 4.85413i | − | 0.970826i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.94351 | + | 1.94351i | −0.360900 | + | 0.360900i | −0.864144 | − | 0.503244i | \(-0.832140\pi\) |
0.503244 | + | 0.864144i | \(0.332140\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 0.936219i | − | 0.168150i | −0.996459 | − | 0.0840750i | \(-0.973206\pi\) | ||
0.996459 | − | 0.0840750i | \(-0.0267935\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.270063 | − | 0.270063i | −0.0456490 | − | 0.0456490i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.52927 | + | 1.52927i | −0.251411 | + | 0.251411i | −0.821549 | − | 0.570138i | \(-0.806890\pi\) |
0.570138 | + | 0.821549i | \(0.306890\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −12.4273 | −1.94082 | −0.970412 | − | 0.241457i | \(-0.922375\pi\) | ||||
−0.970412 | + | 0.241457i | \(0.922375\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.346427 | + | 0.346427i | 0.0528296 | + | 0.0528296i | 0.733028 | − | 0.680198i | \(-0.238106\pi\) |
−0.680198 | + | 0.733028i | \(0.738106\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.71825 | 1.41755 | 0.708776 | − | 0.705433i | \(-0.249248\pi\) | ||||
0.708776 | + | 0.705433i | \(0.249248\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.69522 | − | 7.69522i | −1.05702 | − | 1.05702i | −0.998273 | − | 0.0587471i | \(-0.981289\pi\) |
−0.0587471 | − | 0.998273i | \(-0.518711\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.63923 | −0.221034 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.03405 | + | 2.03405i | −0.264810 | + | 0.264810i | −0.827005 | − | 0.562195i | \(-0.809957\pi\) |
0.562195 | + | 0.827005i | \(0.309957\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.86902 | + | 5.86902i | 0.751451 | + | 0.751451i | 0.974750 | − | 0.223299i | \(-0.0716826\pi\) |
−0.223299 | + | 0.974750i | \(0.571683\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 0.695288i | − | 0.0862399i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.7316 | + | 10.7316i | −1.31107 | + | 1.31107i | −0.390439 | + | 0.920629i | \(0.627677\pi\) |
−0.920629 | + | 0.390439i | \(0.872323\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 12.5046i | − | 1.48402i | −0.670389 | − | 0.742010i | \(-0.733873\pi\) | ||
0.670389 | − | 0.742010i | \(-0.266127\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.37743i | 0.863463i | 0.902002 | + | 0.431732i | \(0.142097\pi\) | ||||
−0.902002 | + | 0.431732i | \(0.857903\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.03491 | − | 3.03491i | 0.345860 | − | 0.345860i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 13.0724i | − | 1.47076i | −0.677658 | − | 0.735378i | \(-0.737005\pi\) | ||
0.677658 | − | 0.735378i | \(-0.262995\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.53806 | − | 2.53806i | −0.278588 | − | 0.278588i | 0.553957 | − | 0.832545i | \(-0.313117\pi\) |
−0.832545 | + | 0.553957i | \(0.813117\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.39283 | + | 1.39283i | −0.151073 | + | 0.151073i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.04518 | 0.746787 | 0.373394 | − | 0.927673i | \(-0.378194\pi\) | ||||
0.373394 | + | 0.927673i | \(0.378194\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.28727 | + | 1.28727i | 0.134943 | + | 0.134943i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.99812 | −0.307600 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.334289 | 0.0339419 | 0.0169710 | − | 0.999856i | \(-0.494598\pi\) | ||||
0.0169710 | + | 0.999856i | \(0.494598\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.38370 | − | 7.38370i | −0.734706 | − | 0.734706i | 0.236842 | − | 0.971548i | \(-0.423888\pi\) |
−0.971548 | + | 0.236842i | \(0.923888\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.6297 | 1.44151 | 0.720755 | − | 0.693190i | \(-0.243795\pi\) | ||||
0.720755 | + | 0.693190i | \(0.243795\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.13731 | − | 4.13731i | 0.399969 | − | 0.399969i | −0.478253 | − | 0.878222i | \(-0.658730\pi\) |
0.878222 | + | 0.478253i | \(0.158730\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.4525 | + | 10.4525i | 1.00117 | + | 1.00117i | 0.999999 | + | 0.00116943i | \(0.000372243\pi\) |
0.00116943 | + | 0.999999i | \(0.499628\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 8.90575i | − | 0.837782i | −0.908036 | − | 0.418891i | \(-0.862419\pi\) | ||
0.908036 | − | 0.418891i | \(-0.137581\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.53920 | − | 1.53920i | 0.143532 | − | 0.143532i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 5.15741i | − | 0.472779i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 7.42135i | − | 0.674668i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.66124 | + | 2.66124i | −0.238028 | + | 0.238028i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 13.8060i | − | 1.22509i | −0.790437 | − | 0.612543i | \(-0.790147\pi\) | ||
0.790437 | − | 0.612543i | \(-0.209853\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.53288 | − | 8.53288i | −0.745521 | − | 0.745521i | 0.228113 | − | 0.973635i | \(-0.426744\pi\) |
−0.973635 | + | 0.228113i | \(0.926744\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.55077 | − | 5.55077i | 0.481313 | − | 0.481313i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.08397 | 0.348917 | 0.174459 | − | 0.984664i | \(-0.444182\pi\) | ||||
0.174459 | + | 0.984664i | \(0.444182\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.52222 | + | 2.52222i | 0.213932 | + | 0.213932i | 0.805935 | − | 0.592003i | \(-0.201663\pi\) |
−0.592003 | + | 0.805935i | \(0.701663\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.81350 | 0.653397 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.04974 | 0.0871760 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.47402 | + | 4.47402i | 0.366526 | + | 0.366526i | 0.866208 | − | 0.499683i | \(-0.166550\pi\) |
−0.499683 | + | 0.866208i | \(0.666550\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.6642 | 1.51887 | 0.759434 | − | 0.650584i | \(-0.225476\pi\) | ||||
0.759434 | + | 0.650584i | \(0.225476\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.252838 | + | 0.252838i | −0.0203085 | + | 0.0203085i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.517468 | − | 0.517468i | −0.0412985 | − | 0.0412985i | 0.686156 | − | 0.727454i | \(-0.259297\pi\) |
−0.727454 | + | 0.686156i | \(0.759297\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.69943i | 0.449178i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.16031 | + | 2.16031i | −0.169209 | + | 0.169209i | −0.786632 | − | 0.617423i | \(-0.788177\pi\) |
0.617423 | + | 0.786632i | \(0.288177\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 1.45631i | − | 0.112693i | −0.998411 | − | 0.0563465i | \(-0.982055\pi\) | ||
0.998411 | − | 0.0563465i | \(-0.0179451\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 9.68587i | − | 0.745067i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −15.6519 | + | 15.6519i | −1.18999 | + | 1.18999i | −0.212922 | + | 0.977069i | \(0.568298\pi\) |
−0.977069 | + | 0.212922i | \(0.931702\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 4.85413i | − | 0.366938i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.3258 | − | 10.3258i | −0.771788 | − | 0.771788i | 0.206631 | − | 0.978419i | \(-0.433750\pi\) |
−0.978419 | + | 0.206631i | \(0.933750\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.01856 | − | 9.01856i | 0.670344 | − | 0.670344i | −0.287451 | − | 0.957795i | \(-0.592808\pi\) |
0.957795 | + | 0.287451i | \(0.0928078\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.825999 | 0.0607287 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −15.6523 | − | 15.6523i | −1.14461 | − | 1.14461i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.73439 | −0.704356 | −0.352178 | − | 0.935933i | \(-0.614559\pi\) | ||||
−0.352178 | + | 0.935933i | \(0.614559\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.44692 | −0.248115 | −0.124057 | − | 0.992275i | \(-0.539591\pi\) | ||||
−0.124057 | + | 0.992275i | \(0.539591\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.585435 | − | 0.585435i | −0.0417105 | − | 0.0417105i | 0.685944 | − | 0.727654i | \(-0.259390\pi\) |
−0.727654 | + | 0.685944i | \(0.759390\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.57428 | 0.182486 | 0.0912429 | − | 0.995829i | \(-0.470916\pi\) | ||||
0.0912429 | + | 0.995829i | \(0.470916\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.94351 | + | 1.94351i | −0.136407 | + | 0.136407i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.35616 | + | 3.35616i | 0.234405 | + | 0.234405i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 33.6922i | − | 2.33054i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.3783 | − | 11.3783i | 0.783317 | − | 0.783317i | −0.197072 | − | 0.980389i | \(-0.563143\pi\) |
0.980389 | + | 0.197072i | \(0.0631432\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 0.187114i | − | 0.0127611i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 0.936219i | − | 0.0635547i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.63898 | − | 6.63898i | 0.446586 | − | 0.446586i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.26410i | 0.419475i | 0.977758 | + | 0.209738i | \(0.0672610\pi\) | ||||
−0.977758 | + | 0.209738i | \(0.932739\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.38594 | + | 4.38594i | 0.291105 | + | 0.291105i | 0.837517 | − | 0.546412i | \(-0.184007\pi\) |
−0.546412 | + | 0.837517i | \(0.684007\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.8540 | + | 17.8540i | −1.17982 | + | 1.17982i | −0.200034 | + | 0.979789i | \(0.564105\pi\) |
−0.979789 | + | 0.200034i | \(0.935895\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.0142 | 0.983614 | 0.491807 | − | 0.870704i | \(-0.336336\pi\) | ||||
0.491807 | + | 0.870704i | \(0.336336\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.62454 | − | 2.62454i | −0.171206 | − | 0.171206i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.62807 | 0.105311 | 0.0526554 | − | 0.998613i | \(-0.483232\pi\) | ||||
0.0526554 | + | 0.998613i | \(0.483232\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −22.7132 | −1.46308 | −0.731542 | − | 0.681797i | \(-0.761199\pi\) | ||||
−0.731542 | + | 0.681797i | \(0.761199\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.270063 | − | 0.270063i | −0.0172537 | − | 0.0172537i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 14.2907 | 0.909295 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.1734 | − | 16.1734i | 1.02085 | − | 1.02085i | 0.0210767 | − | 0.999778i | \(-0.493291\pi\) |
0.999778 | − | 0.0210767i | \(-0.00670942\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 17.2972 | + | 17.2972i | 1.08747 | + | 1.08747i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 23.1675i | − | 1.44515i | −0.691293 | − | 0.722574i | \(-0.742959\pi\) | ||
0.691293 | − | 0.722574i | \(-0.257041\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.52927 | + | 1.52927i | −0.0950243 | + | 0.0950243i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.643221i | 0.0396627i | 0.999803 | + | 0.0198314i | \(0.00631293\pi\) | ||||
−0.999803 | + | 0.0198314i | \(0.993687\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.15639i | 0.255325i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.72444 | + | 7.72444i | −0.470967 | + | 0.470967i | −0.902228 | − | 0.431260i | \(-0.858069\pi\) |
0.431260 | + | 0.902228i | \(0.358069\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 20.3731i | − | 1.23758i | −0.785558 | − | 0.618788i | \(-0.787624\pi\) | ||
0.785558 | − | 0.618788i | \(-0.212376\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −14.7319 | − | 14.7319i | −0.888364 | − | 0.888364i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 21.6135 | − | 21.6135i | 1.29863 | − | 1.29863i | 0.369336 | − | 0.929296i | \(-0.379585\pi\) |
0.929296 | − | 0.369336i | \(-0.120415\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.42826 | 0.443133 | 0.221566 | − | 0.975145i | \(-0.428883\pi\) | ||||
0.221566 | + | 0.975145i | \(0.428883\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.92425 | + | 8.92425i | 0.530492 | + | 0.530492i | 0.920719 | − | 0.390227i | \(-0.127603\pi\) |
−0.390227 | + | 0.920719i | \(0.627603\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.4273 | −0.733562 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.59890 | −0.564641 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9.06945 | − | 9.06945i | −0.529843 | − | 0.529843i | 0.390682 | − | 0.920526i | \(-0.372239\pi\) |
−0.920526 | + | 0.390682i | \(0.872239\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.09864 | 0.0639654 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −7.33670 | + | 7.33670i | −0.424293 | + | 0.424293i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.346427 | + | 0.346427i | 0.0199677 | + | 0.0199677i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 3.17001i | − | 0.181514i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.2349 | + | 15.2349i | −0.869504 | + | 0.869504i | −0.992417 | − | 0.122913i | \(-0.960776\pi\) |
0.122913 | + | 0.992417i | \(0.460776\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 21.1899i | 1.20157i | 0.799410 | + | 0.600785i | \(0.205145\pi\) | ||||
−0.799410 | + | 0.600785i | \(0.794855\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.4334i | 0.872347i | 0.899863 | + | 0.436173i | \(0.143667\pi\) | ||||
−0.899863 | + | 0.436173i | \(0.856333\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.23380 | − | 8.23380i | 0.462456 | − | 0.462456i | −0.437003 | − | 0.899460i | \(-0.643960\pi\) |
0.899460 | + | 0.437003i | \(0.143960\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.7967i | 0.660490i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −28.6276 | − | 28.6276i | −1.59288 | − | 1.59288i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.24858 | − | 6.24858i | 0.346609 | − | 0.346609i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 9.71825 | 0.535784 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.1815 | + | 18.1815i | 0.999344 | + | 0.999344i | 1.00000 | 0.000656172i | \(-0.000208866\pi\) | |
−0.000656172 | 1.00000i | \(0.500209\pi\) | ||||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.79639 | 0.316691 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.4267 | 1.11271 | 0.556357 | − | 0.830943i | \(-0.312199\pi\) | ||||
0.556357 | + | 0.830943i | \(0.312199\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.84134 | − | 2.84134i | −0.153867 | − | 0.153867i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.37130 | − | 1.37130i | 0.0736154 | − | 0.0736154i | −0.669340 | − | 0.742956i | \(-0.733423\pi\) |
0.742956 | + | 0.669340i | \(0.233423\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.10409 | + | 5.10409i | 0.273216 | + | 0.273216i | 0.830393 | − | 0.557178i | \(-0.188116\pi\) |
−0.557178 | + | 0.830393i | \(0.688116\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 32.0190i | 1.70420i | 0.523378 | + | 0.852101i | \(0.324672\pi\) | ||||
−0.523378 | + | 0.852101i | \(0.675328\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.37702 | + | 3.37702i | −0.179234 | + | 0.179234i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 10.8950i | − | 0.575018i | −0.957778 | − | 0.287509i | \(-0.907173\pi\) | ||
0.957778 | − | 0.287509i | \(-0.0928272\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 42.6222i | − | 2.24327i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.99237 | − | 1.99237i | 0.104286 | − | 0.104286i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.57323i | 0.186521i | 0.995642 | + | 0.0932605i | \(0.0297290\pi\) | ||||
−0.995642 | + | 0.0932605i | \(0.970271\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.69522 | − | 7.69522i | −0.399516 | − | 0.399516i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.40095 | + | 8.40095i | −0.434985 | + | 0.434985i | −0.890320 | − | 0.455335i | \(-0.849519\pi\) |
0.455335 | + | 0.890320i | \(0.349519\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.00363 | −0.257700 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.51287 | + | 7.51287i | 0.385910 | + | 0.385910i | 0.873226 | − | 0.487316i | \(-0.162024\pi\) |
−0.487316 | + | 0.873226i | \(0.662024\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 28.9165 | 1.47757 | 0.738783 | − | 0.673944i | \(-0.235401\pi\) | ||||
0.738783 | + | 0.673944i | \(0.235401\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.63923 | −0.0835431 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.26758 | − | 1.26758i | −0.0642689 | − | 0.0642689i | 0.674242 | − | 0.738511i | \(-0.264471\pi\) |
−0.738511 | + | 0.674242i | \(0.764471\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 29.3943 | 1.48653 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.53036 | + | 3.53036i | −0.177632 | + | 0.177632i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.08140 | − | 2.08140i | −0.104463 | − | 0.104463i | 0.652944 | − | 0.757406i | \(-0.273534\pi\) |
−0.757406 | + | 0.652944i | \(0.773534\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.64862i | 0.381954i | 0.981595 | + | 0.190977i | \(0.0611656\pi\) | ||||
−0.981595 | + | 0.190977i | \(0.938834\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.20517 | − | 1.20517i | 0.0600336 | − | 0.0600336i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.28240i | 0.460111i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 36.0331i | − | 1.78172i | −0.454275 | − | 0.890862i | \(-0.650102\pi\) | ||
0.454275 | − | 0.890862i | \(-0.349898\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.03405 | + | 2.03405i | −0.100089 | + | 0.100089i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.37087i | 0.0672934i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.27031 | + | 4.27031i | 0.208618 | + | 0.208618i | 0.803680 | − | 0.595062i | \(-0.202872\pi\) |
−0.595062 | + | 0.803680i | \(0.702872\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.30843 | + | 6.30843i | −0.307454 | + | 0.307454i | −0.843921 | − | 0.536467i | \(-0.819759\pi\) |
0.536467 | + | 0.843921i | \(0.319759\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −25.0348 | −1.21436 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.86902 | + | 5.86902i | 0.284022 | + | 0.284022i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.7409 | −0.613708 | −0.306854 | − | 0.951757i | \(-0.599276\pi\) | ||||
−0.306854 | + | 0.951757i | \(0.599276\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.89975 | 0.139353 | 0.0696764 | − | 0.997570i | \(-0.477803\pi\) | ||||
0.0696764 | + | 0.997570i | \(0.477803\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 31.6362 | + | 31.6362i | 1.51337 | + | 1.51337i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.1968 | −0.868487 | −0.434243 | − | 0.900796i | \(-0.642984\pi\) | ||||
−0.434243 | + | 0.900796i | \(0.642984\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.90248 | + | 5.90248i | −0.280435 | + | 0.280435i | −0.833283 | − | 0.552847i | \(-0.813541\pi\) |
0.552847 | + | 0.833283i | \(0.313541\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.90264 | − | 1.90264i | −0.0901938 | − | 0.0901938i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 13.5014i | − | 0.637172i | −0.947894 | − | 0.318586i | \(-0.896792\pi\) | ||
0.947894 | − | 0.318586i | \(-0.103208\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −37.7158 | + | 37.7158i | −1.77597 | + | 1.77597i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 0.695288i | − | 0.0325956i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 24.4732i | − | 1.14481i | −0.819972 | − | 0.572403i | \(-0.806011\pi\) | ||
0.819972 | − | 0.572403i | \(-0.193989\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.52778 | + | 5.52778i | −0.257455 | + | 0.257455i | −0.824018 | − | 0.566563i | \(-0.808273\pi\) |
0.566563 | + | 0.824018i | \(0.308273\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 8.48501i | − | 0.394332i | −0.980370 | − | 0.197166i | \(-0.936826\pi\) | ||
0.980370 | − | 0.197166i | \(-0.0631738\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.61601 | + | 1.61601i | 0.0747800 | + | 0.0747800i | 0.743508 | − | 0.668728i | \(-0.233161\pi\) |
−0.668728 | + | 0.743508i | \(0.733161\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.7316 | + | 10.7316i | −0.495537 | + | 0.495537i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.10275 | 0.0966844 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −26.9442 | − | 26.9442i | −1.23628 | − | 1.23628i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −16.9452 | −0.774247 | −0.387123 | − | 0.922028i | \(-0.626531\pi\) | ||||
−0.387123 | + | 0.922028i | \(0.626531\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.93717 | −0.179520 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.0902791 | − | 0.0902791i | −0.00409936 | − | 0.00409936i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.48781 | −0.293991 | −0.146995 | − | 0.989137i | \(-0.546960\pi\) | ||||
−0.146995 | + | 0.989137i | \(0.546960\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.03691 | + | 3.03691i | −0.137054 | + | 0.137054i | −0.772305 | − | 0.635251i | \(-0.780896\pi\) |
0.635251 | + | 0.772305i | \(0.280896\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.0235 | + | 10.0235i | 0.451434 | + | 0.451434i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 12.5046i | − | 0.560907i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −29.0548 | + | 29.0548i | −1.30067 | + | 1.30067i | −0.372735 | + | 0.927938i | \(0.621580\pi\) |
−0.927938 | + | 0.372735i | \(0.878420\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 24.3803i | 1.08706i | 0.839388 | + | 0.543532i | \(0.182913\pi\) | ||||
−0.839388 | + | 0.543532i | \(0.817087\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.98813i | 0.177469i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.39973 | − | 6.39973i | 0.283663 | − | 0.283663i | −0.550905 | − | 0.834568i | \(-0.685717\pi\) |
0.834568 | + | 0.550905i | \(0.185717\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.37743i | 0.326359i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.95095 | − | 3.95095i | −0.174100 | − | 0.174100i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 29.4940 | − | 29.4940i | 1.29715 | − | 1.29715i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 24.3522 | 1.06689 | 0.533444 | − | 0.845835i | \(-0.320897\pi\) | ||||
0.533444 | + | 0.845835i | \(0.320897\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.4483 | + | 13.4483i | 0.588054 | + | 0.588054i | 0.937104 | − | 0.349050i | \(-0.113496\pi\) |
−0.349050 | + | 0.937104i | \(0.613496\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.82847 | −0.210331 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.48348 | −0.412325 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −15.9973 | − | 15.9973i | −0.692921 | − | 0.692921i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.23467 | −0.0966131 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.03491 | − | 3.03491i | 0.130723 | − | 0.130723i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.15117 | + | 2.15117i | 0.0924861 | + | 0.0924861i | 0.751836 | − | 0.659350i | \(-0.229168\pi\) |
−0.659350 | + | 0.751836i | \(0.729168\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 5.64567i | − | 0.241834i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.10155 | + | 5.10155i | −0.218126 | + | 0.218126i | −0.807708 | − | 0.589582i | \(-0.799292\pi\) |
0.589582 | + | 0.807708i | \(0.299292\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 21.5759i | 0.919165i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 13.0724i | − | 0.555893i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −16.0391 | + | 16.0391i | −0.679599 | + | 0.679599i | −0.959909 | − | 0.280310i | \(-0.909563\pi\) |
0.280310 | + | 0.959909i | \(0.409563\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.891890i | 0.0377229i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 20.3434 | + | 20.3434i | 0.857370 | + | 0.857370i | 0.991028 | − | 0.133657i | \(-0.0426721\pi\) |
−0.133657 | + | 0.991028i | \(0.542672\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.40511 | + | 2.40511i | −0.101184 | + | 0.101184i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 34.6243 | 1.45152 | 0.725762 | − | 0.687945i | \(-0.241487\pi\) | ||||
0.725762 | + | 0.687945i | \(0.241487\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 30.1046 | + | 30.1046i | 1.25984 | + | 1.25984i | 0.951170 | + | 0.308667i | \(0.0998828\pi\) |
0.308667 | + | 0.951170i | \(0.400117\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 27.6658 | 1.15374 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.97393 | −0.207067 | −0.103534 | − | 0.994626i | \(-0.533015\pi\) | ||||
−0.103534 | + | 0.994626i | \(0.533015\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.53806 | − | 2.53806i | −0.105296 | − | 0.105296i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −46.7086 | −1.93447 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.50154 | − | 4.50154i | 0.185798 | − | 0.185798i | −0.608079 | − | 0.793877i | \(-0.708059\pi\) |
0.793877 | + | 0.608079i | \(0.208059\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.19674 | − | 5.19674i | −0.214128 | − | 0.214128i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 38.9459i | 1.59931i | 0.600457 | + | 0.799657i | \(0.294985\pi\) | ||||
−0.600457 | + | 0.799657i | \(0.705015\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.39283 | + | 1.39283i | −0.0571003 | + | 0.0571003i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 12.5162i | − | 0.511398i | −0.966756 | − | 0.255699i | \(-0.917694\pi\) | ||
0.966756 | − | 0.255699i | \(-0.0823056\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 25.5234i | − | 1.04112i | −0.853825 | − | 0.520561i | \(-0.825723\pi\) | ||
0.853825 | − | 0.520561i | \(-0.174277\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.00423 | + | 2.00423i | −0.0814836 | + | 0.0814836i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 14.1652i | − | 0.574949i | −0.957788 | − | 0.287475i | \(-0.907184\pi\) | ||
0.957788 | − | 0.287475i | \(-0.0928157\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.5100 | + | 12.5100i | 0.506101 | + | 0.506101i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 28.9735 | − | 28.9735i | 1.17023 | − | 1.17023i | 0.188071 | − | 0.982155i | \(-0.439776\pi\) |
0.982155 | − | 0.188071i | \(-0.0602236\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.73722 | 0.230972 | 0.115486 | − | 0.993309i | \(-0.463157\pi\) | ||||
0.115486 | + | 0.993309i | \(0.463157\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −27.3596 | − | 27.3596i | −1.09968 | − | 1.09968i | −0.994448 | − | 0.105229i | \(-0.966442\pi\) |
−0.105229 | − | 0.994448i | \(-0.533558\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.04518 | 0.282259 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −22.8333 | −0.913330 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.88708 | + | 7.88708i | 0.314479 | + | 0.314479i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 39.5537 | 1.57461 | 0.787303 | − | 0.616566i | \(-0.211477\pi\) | ||||
0.787303 | + | 0.616566i | \(0.211477\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.72850 | + | 3.72850i | −0.147961 | + | 0.147961i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.28727 | + | 1.28727i | 0.0510035 | + | 0.0510035i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 42.5474i | − | 1.68052i | −0.542182 | − | 0.840261i | \(-0.682402\pi\) | ||
0.542182 | − | 0.840261i | \(-0.317598\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.6174 | − | 13.6174i | 0.537017 | − | 0.537017i | −0.385635 | − | 0.922652i | \(-0.626017\pi\) |
0.922652 | + | 0.385635i | \(0.126017\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 29.7806i | 1.17080i | 0.810746 | + | 0.585398i | \(0.199062\pi\) | ||||
−0.810746 | + | 0.585398i | \(0.800938\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12.3463i | 0.484635i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13.9493 | + | 13.9493i | −0.545880 | + | 0.545880i | −0.925246 | − | 0.379367i | \(-0.876142\pi\) |
0.379367 | + | 0.925246i | \(0.376142\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.60883i | 0.180082i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.9096 | + | 12.9096i | 0.502888 | + | 0.502888i | 0.912334 | − | 0.409446i | \(-0.134278\pi\) |
−0.409446 | + | 0.912334i | \(0.634278\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.0427 | + | 19.0427i | −0.740674 | + | 0.740674i | −0.972708 | − | 0.232033i | \(-0.925462\pi\) |
0.232033 | + | 0.972708i | \(0.425462\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.99812 | −0.116262 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −11.0769 | − | 11.0769i | −0.428898 | − | 0.428898i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 35.6239 | 1.37524 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20.4420 | −0.787983 | −0.393991 | − | 0.919114i | \(-0.628906\pi\) | ||||
−0.393991 | + | 0.919114i | \(0.628906\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.78059 | − | 4.78059i | −0.183733 | − | 0.183733i | 0.609247 | − | 0.792980i | \(-0.291472\pi\) |
−0.792980 | + | 0.609247i | \(0.791472\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.334289 | 0.0128288 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.19706 | − | 1.19706i | 0.0458041 | − | 0.0458041i | −0.683834 | − | 0.729638i | \(-0.739689\pi\) |
0.729638 | + | 0.683834i | \(0.239689\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.10293 | − | 1.10293i | −0.0421408 | − | 0.0421408i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 19.8117i | − | 0.754764i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.98198 | − | 2.98198i | 0.113440 | − | 0.113440i | −0.648108 | − | 0.761548i | \(-0.724440\pi\) |
0.761548 | + | 0.648108i | \(0.224440\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 1.36232i | − | 0.0516757i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 64.0929i | 2.42769i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −25.9008 | + | 25.9008i | −0.978261 | + | 0.978261i | −0.999769 | − | 0.0215079i | \(-0.993153\pi\) |
0.0215079 | + | 0.999769i | \(0.493153\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.9773i | 0.640310i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7.38370 | − | 7.38370i | −0.277693 | − | 0.277693i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.86472 | + | 2.86472i | −0.107587 | + | 0.107587i | −0.758851 | − | 0.651264i | \(-0.774239\pi\) |
0.651264 | + | 0.758851i | \(0.274239\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.33591 | 0.199832 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.11014 | − | 2.11014i | −0.0789146 | − | 0.0789146i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.64941 | −0.0615126 | −0.0307563 | − | 0.999527i | \(-0.509792\pi\) | ||||
−0.0307563 | + | 0.999527i | \(0.509792\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.6297 | 0.544839 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.43403 | + | 9.43403i | 0.350371 | + | 0.350371i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 30.5976 | 1.13480 | 0.567400 | − | 0.823442i | \(-0.307949\pi\) | ||||
0.567400 | + | 0.823442i | \(0.307949\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.78667 | − | 1.78667i | 0.0660822 | − | 0.0660822i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 36.9502 | + | 36.9502i | 1.36479 | + | 1.36479i | 0.867704 | + | 0.497082i | \(0.165595\pi\) |
0.497082 | + | 0.867704i | \(0.334405\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 65.1386i | 2.39941i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.0208 | − | 16.0208i | 0.589335 | − | 0.589335i | −0.348116 | − | 0.937451i | \(-0.613179\pi\) |
0.937451 | + | 0.348116i | \(0.113179\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 34.0911i | − | 1.25068i | −0.780352 | − | 0.625341i | \(-0.784960\pi\) | ||
0.780352 | − | 0.625341i | \(-0.215040\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 2.41653i | − | 0.0885349i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.13731 | − | 4.13731i | 0.151174 | − | 0.151174i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 37.9956i | 1.38648i | 0.720708 | + | 0.693239i | \(0.243817\pi\) | ||||
−0.720708 | + | 0.693239i | \(0.756183\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.04050 | − | 5.04050i | −0.183443 | − | 0.183443i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −36.2650 | + | 36.2650i | −1.31807 | + | 1.31807i | −0.402774 | + | 0.915300i | \(0.631954\pi\) |
−0.915300 | + | 0.402774i | \(0.868046\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16.8705 | 0.611556 | 0.305778 | − | 0.952103i | \(-0.401084\pi\) | ||||
0.305778 | + | 0.952103i | \(0.401084\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.4525 | + | 10.4525i | 0.378406 | + | 0.378406i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.23674 | −0.189088 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −46.7971 | −1.68755 | −0.843774 | − | 0.536698i | \(-0.819671\pi\) | ||||
−0.843774 | + | 0.536698i | \(0.819671\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 28.7793 | + | 28.7793i | 1.03512 | + | 1.03512i | 0.999360 | + | 0.0357608i | \(0.0113854\pi\) |
0.0357608 | + | 0.999360i | \(0.488615\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.54453 | −0.163244 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −68.9813 | + | 68.9813i | −2.47151 | + | 2.47151i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −37.9502 | − | 37.9502i | −1.35797 | − | 1.35797i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.279498i | 0.00997571i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −29.7259 | + | 29.7259i | −1.05961 | + | 1.05961i | −0.0615057 | + | 0.998107i | \(0.519590\pi\) |
−0.998107 | + | 0.0615057i | \(0.980410\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 8.90575i | − | 0.316652i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.1100i | 0.536573i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −21.6739 | + | 21.6739i | −0.767728 | + | 0.767728i | −0.977706 | − | 0.209978i | \(-0.932661\pi\) |
0.209978 | + | 0.977706i | \(0.432661\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 50.1210i | − | 1.77315i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 22.3898 | + | 22.3898i | 0.790121 | + | 0.790121i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.53920 | − | 1.53920i | 0.0542498 | − | 0.0542498i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −27.6371 | −0.971669 | −0.485834 | − | 0.874051i | \(-0.661484\pi\) | ||||
−0.485834 | + | 0.874051i | \(0.661484\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20.6941 | − | 20.6941i | −0.726668 | − | 0.726668i | 0.243286 | − | 0.969955i | \(-0.421775\pi\) |
−0.969955 | + | 0.243286i | \(0.921775\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.16684 | 0.0408727 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.84587 | 0.134550 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.30451 | + | 8.30451i | 0.289829 | + | 0.289829i | 0.837013 | − | 0.547183i | \(-0.184300\pi\) |
−0.547183 | + | 0.837013i | \(0.684300\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.77989 | −0.201474 | −0.100737 | − | 0.994913i | \(-0.532120\pi\) | ||||
−0.100737 | + | 0.994913i | \(0.532120\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 8.49162 | − | 8.49162i | 0.295282 | − | 0.295282i | −0.543880 | − | 0.839163i | \(-0.683045\pi\) |
0.839163 | + | 0.543880i | \(0.183045\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −22.2746 | − | 22.2746i | −0.773629 | − | 0.773629i | 0.205110 | − | 0.978739i | \(-0.434245\pi\) |
−0.978739 | + | 0.205110i | \(0.934245\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 5.15741i | − | 0.178694i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.393296 | + | 0.393296i | −0.0136106 | + | 0.0136106i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 31.0889i | 1.07331i | 0.843803 | + | 0.536653i | \(0.180312\pi\) | ||||
−0.843803 | + | 0.536653i | \(0.819688\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.4456i | 0.739502i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.61580 | + | 2.61580i | −0.0899861 | + | 0.0899861i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 7.42135i | − | 0.255001i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.71597 | − | 8.71597i | −0.298780 | − | 0.298780i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −13.2899 | + | 13.2899i | −0.455037 | + | 0.455037i | −0.897022 | − | 0.441985i | \(-0.854274\pi\) |
0.441985 | + | 0.897022i | \(0.354274\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 19.3573 | 0.661234 | 0.330617 | − | 0.943765i | \(-0.392743\pi\) | ||||
0.330617 | + | 0.943765i | \(0.392743\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.21680 | + | 1.21680i | 0.0415165 | + | 0.0415165i | 0.727560 | − | 0.686044i | \(-0.240654\pi\) |
−0.686044 | + | 0.727560i | \(0.740654\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 34.8956 | 1.18786 | 0.593929 | − | 0.804517i | \(-0.297576\pi\) | ||||
0.593929 | + | 0.804517i | \(0.297576\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.45399 | 0.287444 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −39.6734 | − | 39.6734i | −1.34583 | − | 1.34583i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −27.6288 | −0.936167 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.66124 | + | 2.66124i | −0.0899662 | + | 0.0899662i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11.2180 | − | 11.2180i | −0.378804 | − | 0.378804i | 0.491866 | − | 0.870671i | \(-0.336315\pi\) |
−0.870671 | + | 0.491866i | \(0.836315\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.79230i | 0.127766i | 0.997957 | + | 0.0638829i | \(0.0203484\pi\) | ||||
−0.997957 | + | 0.0638829i | \(0.979652\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.66911 | + | 7.66911i | −0.258086 | + | 0.258086i | −0.824275 | − | 0.566189i | \(-0.808417\pi\) |
0.566189 | + | 0.824275i | \(0.308417\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 15.3130i | − | 0.514161i | −0.966390 | − | 0.257081i | \(-0.917239\pi\) | ||
0.966390 | − | 0.257081i | \(-0.0827606\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 13.8060i | − | 0.463039i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 53.9438 | − | 53.9438i | 1.80516 | − | 1.80516i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.57724i | 0.186427i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.81955 | + | 1.81955i | 0.0606853 | + | 0.0606853i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −39.6874 | + | 39.6874i | −1.32218 | + | 1.32218i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.87116 | −0.161923 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −32.8167 | − | 32.8167i | −1.08966 | − | 1.08966i | −0.995563 | − | 0.0940982i | \(-0.970003\pi\) |
−0.0940982 | − | 0.995563i | \(-0.529997\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −26.8385 | −0.889200 | −0.444600 | − | 0.895729i | \(-0.646654\pi\) | ||||
−0.444600 | + | 0.895729i | \(0.646654\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −15.4055 | −0.509849 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8.53288 | − | 8.53288i | −0.281781 | − | 0.281781i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −19.8195 | −0.653785 | −0.326893 | − | 0.945061i | \(-0.606002\pi\) | ||||
−0.326893 | + | 0.945061i | \(0.606002\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 16.0968 | − | 16.0968i | 0.529831 | − | 0.529831i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.42329 | + | 7.42329i | 0.244076 | + | 0.244076i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 38.2590i | 1.25524i | 0.778521 | + | 0.627619i | \(0.215970\pi\) | ||||
−0.778521 | + | 0.627619i | \(0.784030\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.55077 | − | 5.55077i | 0.181919 | − | 0.181919i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8.45420i | 0.276482i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 41.1963i | 1.34582i | 0.739722 | + | 0.672912i | \(0.234957\pi\) | ||||
−0.739722 | + | 0.672912i | \(0.765043\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14.9904 | + | 14.9904i | −0.488673 | + | 0.488673i | −0.907887 | − | 0.419214i | \(-0.862306\pi\) |
0.419214 | + | 0.907887i | \(0.362306\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 70.8287i | − | 2.30650i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.55196 | + | 2.55196i | 0.0829275 | + | 0.0829275i | 0.747354 | − | 0.664426i | \(-0.231324\pi\) |
−0.664426 | + | 0.747354i | \(0.731324\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.49675 | + | 9.49675i | −0.308278 | + | 0.308278i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −16.1058 | −0.521719 | −0.260859 | − | 0.965377i | \(-0.584006\pi\) | ||||
−0.260859 | + | 0.965377i | \(0.584006\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.62890 | + | 2.62890i | 0.0850692 | + | 0.0850692i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.08397 | 0.131878 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.1235 | 0.971726 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.930886 | + | 0.930886i | 0.0299663 | + | 0.0299663i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −21.1491 | −0.680110 | −0.340055 | − | 0.940406i | \(-0.610446\pi\) | ||||
−0.340055 | + | 0.940406i | \(0.610446\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 43.0192 | − | 43.0192i | 1.38055 | − | 1.38055i | 0.536915 | − | 0.843636i | \(-0.319590\pi\) |
0.843636 | − | 0.536915i | \(-0.180410\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.52222 | + | 2.52222i | 0.0808587 | + | 0.0808587i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 2.96367i | − | 0.0948161i | −0.998876 | − | 0.0474081i | \(-0.984904\pi\) | ||
0.998876 | − | 0.0474081i | \(-0.0150961\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 21.3815 | − | 21.3815i | 0.683355 | − | 0.683355i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 29.5904i | 0.943787i | 0.881655 | + | 0.471894i | \(0.156429\pi\) | ||||
−0.881655 | + | 0.471894i | \(0.843571\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.316209i | 0.0100752i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.97443 | + | 1.97443i | −0.0627834 | + | 0.0627834i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25.3741i | 0.806035i | 0.915192 | + | 0.403017i | \(0.132039\pi\) | ||||
−0.915192 | + | 0.403017i | \(0.867961\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.695217 | − | 0.695217i | −0.0220399 | − | 0.0220399i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.08066 | + | 3.08066i | −0.0975654 | + | 0.0975654i | −0.754205 | − | 0.656639i | \(-0.771977\pi\) |
0.656639 | + | 0.754205i | \(0.271977\pi\) | |||||||
\(998\) | 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.v.d.1583.9 | 36 | ||
3.2 | odd | 2 | inner | 4032.2.v.d.1583.10 | 36 | ||
4.3 | odd | 2 | 1008.2.v.d.323.13 | yes | 36 | ||
12.11 | even | 2 | 1008.2.v.d.323.6 | ✓ | 36 | ||
16.5 | even | 4 | 1008.2.v.d.827.6 | yes | 36 | ||
16.11 | odd | 4 | inner | 4032.2.v.d.3599.10 | 36 | ||
48.5 | odd | 4 | 1008.2.v.d.827.13 | yes | 36 | ||
48.11 | even | 4 | inner | 4032.2.v.d.3599.9 | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1008.2.v.d.323.6 | ✓ | 36 | 12.11 | even | 2 | ||
1008.2.v.d.323.13 | yes | 36 | 4.3 | odd | 2 | ||
1008.2.v.d.827.6 | yes | 36 | 16.5 | even | 4 | ||
1008.2.v.d.827.13 | yes | 36 | 48.5 | odd | 4 | ||
4032.2.v.d.1583.9 | 36 | 1.1 | even | 1 | trivial | ||
4032.2.v.d.1583.10 | 36 | 3.2 | odd | 2 | inner | ||
4032.2.v.d.3599.9 | 36 | 48.11 | even | 4 | inner | ||
4032.2.v.d.3599.10 | 36 | 16.11 | odd | 4 | inner |