Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1176,4,Mod(1,1176)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1176, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1176.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1176.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(69.3862461668\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{505}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 126 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 168) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(11.7361\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1176.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −6.73610 | −0.602495 | −0.301248 | − | 0.953546i | \(-0.597403\pi\) | ||||
−0.301248 | + | 0.953546i | \(0.597403\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −53.6805 | −1.47139 | −0.735695 | − | 0.677313i | \(-0.763144\pi\) | ||||
−0.735695 | + | 0.677313i | \(0.763144\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.73610 | 0.0370391 | 0.0185195 | − | 0.999828i | \(-0.494105\pi\) | ||||
0.0185195 | + | 0.999828i | \(0.494105\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 20.2083 | 0.347851 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −46.9444 | −0.669747 | −0.334873 | − | 0.942263i | \(-0.608694\pi\) | ||||
−0.334873 | + | 0.942263i | \(0.608694\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −20.1527 | −0.243334 | −0.121667 | − | 0.992571i | \(-0.538824\pi\) | ||||
−0.121667 | + | 0.992571i | \(0.538824\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 118.944 | 1.07833 | 0.539166 | − | 0.842200i | \(-0.318740\pi\) | ||||
0.539166 | + | 0.842200i | \(0.318740\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −79.6249 | −0.636999 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −103.681 | −0.663896 | −0.331948 | − | 0.943298i | \(-0.607706\pi\) | ||||
−0.331948 | + | 0.943298i | \(0.607706\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −157.528 | −0.912672 | −0.456336 | − | 0.889808i | \(-0.650838\pi\) | ||||
−0.456336 | + | 0.889808i | \(0.650838\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 161.042 | 0.849507 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −37.7361 | −0.167670 | −0.0838348 | − | 0.996480i | \(-0.526717\pi\) | ||||
−0.0838348 | + | 0.996480i | \(0.526717\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.20831 | −0.0213845 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −287.250 | −1.09417 | −0.547084 | − | 0.837078i | \(-0.684262\pi\) | ||||
−0.547084 | + | 0.837078i | \(0.684262\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 504.875 | 1.79053 | 0.895264 | − | 0.445537i | \(-0.146987\pi\) | ||||
0.895264 | + | 0.445537i | \(0.146987\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −60.6249 | −0.200832 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −220.500 | −0.684323 | −0.342162 | − | 0.939641i | \(-0.611159\pi\) | ||||
−0.342162 | + | 0.939641i | \(0.611159\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 140.833 | 0.386678 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 292.319 | 0.757607 | 0.378803 | − | 0.925477i | \(-0.376336\pi\) | ||||
0.378803 | + | 0.925477i | \(0.376336\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 361.597 | 0.886505 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 60.4582 | 0.140489 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −595.875 | −1.31485 | −0.657426 | − | 0.753519i | \(-0.728355\pi\) | ||||
−0.657426 | + | 0.753519i | \(0.728355\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −265.389 | −0.557043 | −0.278521 | − | 0.960430i | \(-0.589844\pi\) | ||||
−0.278521 | + | 0.960430i | \(0.589844\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −11.6946 | −0.0223159 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 936.735 | 1.70807 | 0.854033 | − | 0.520218i | \(-0.174149\pi\) | ||||
0.854033 | + | 0.520218i | \(0.174149\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −356.833 | −0.622575 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −545.944 | −0.912558 | −0.456279 | − | 0.889837i | \(-0.650818\pi\) | ||||
−0.456279 | + | 0.889837i | \(0.650818\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 299.374 | 0.479988 | 0.239994 | − | 0.970774i | \(-0.422855\pi\) | ||||
0.239994 | + | 0.970774i | \(0.422855\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 238.875 | 0.367772 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −940.333 | −1.33919 | −0.669593 | − | 0.742728i | \(-0.733532\pi\) | ||||
−0.669593 | + | 0.742728i | \(0.733532\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 611.319 | 0.808445 | 0.404223 | − | 0.914661i | \(-0.367542\pi\) | ||||
0.404223 | + | 0.914661i | \(0.367542\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 316.222 | 0.403519 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 311.042 | 0.383301 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1176.19 | −1.40086 | −0.700429 | − | 0.713722i | \(-0.747008\pi\) | ||||
−0.700429 | + | 0.713722i | \(0.747008\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 472.583 | 0.526931 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 135.751 | 0.146608 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1482.49 | 1.55179 | 0.775895 | − | 0.630862i | \(-0.217299\pi\) | ||||
0.775895 | + | 0.630862i | \(0.217299\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −483.125 | −0.490463 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 617.944 | 0.608789 | 0.304395 | − | 0.952546i | \(-0.401546\pi\) | ||||
0.304395 | + | 0.952546i | \(0.401546\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −816.764 | −0.781341 | −0.390670 | − | 0.920531i | \(-0.627757\pi\) | ||||
−0.390670 | + | 0.920531i | \(0.627757\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1685.38 | 1.52272 | 0.761361 | − | 0.648328i | \(-0.224531\pi\) | ||||
0.761361 | + | 0.648328i | \(0.224531\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 91.5968 | 0.0804898 | 0.0402449 | − | 0.999190i | \(-0.487186\pi\) | ||||
0.0402449 | + | 0.999190i | \(0.487186\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 113.208 | 0.0968041 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 614.194 | 0.511314 | 0.255657 | − | 0.966767i | \(-0.417708\pi\) | ||||
0.255657 | + | 0.966767i | \(0.417708\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −801.222 | −0.649690 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 15.6249 | 0.0123464 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1550.60 | 1.16499 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 861.750 | 0.631718 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1378.37 | 0.986284 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 234.278 | 0.163691 | 0.0818457 | − | 0.996645i | \(-0.473919\pi\) | ||||
0.0818457 | + | 0.996645i | \(0.473919\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1514.62 | −1.03376 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2664.76 | 1.77726 | 0.888631 | − | 0.458622i | \(-0.151657\pi\) | ||||
0.888631 | + | 0.458622i | \(0.151657\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 181.875 | 0.115950 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1046.31 | −0.652496 | −0.326248 | − | 0.945284i | \(-0.605784\pi\) | ||||
−0.326248 | + | 0.945284i | \(0.605784\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 647.265 | 0.394966 | 0.197483 | − | 0.980306i | \(-0.436723\pi\) | ||||
0.197483 | + | 0.980306i | \(0.436723\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 661.499 | 0.395094 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −93.1949 | −0.0544989 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 698.403 | 0.399994 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1326.81 | 0.729505 | 0.364752 | − | 0.931105i | \(-0.381154\pi\) | ||||
0.364752 | + | 0.931105i | \(0.381154\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3683.24 | 1.98502 | 0.992508 | − | 0.122178i | \(-0.0389879\pi\) | ||||
0.992508 | + | 0.122178i | \(0.0389879\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −422.500 | −0.223249 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1061.12 | 0.549881 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2818.25 | −1.43262 | −0.716308 | − | 0.697784i | \(-0.754169\pi\) | ||||
−0.716308 | + | 0.697784i | \(0.754169\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −876.958 | −0.437405 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4106.61 | 1.97334 | 0.986670 | − | 0.162733i | \(-0.0520308\pi\) | ||||
0.986670 | + | 0.162733i | \(0.0520308\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1084.79 | −0.511824 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1045.56 | 0.484476 | 0.242238 | − | 0.970217i | \(-0.422119\pi\) | ||||
0.242238 | + | 0.970217i | \(0.422119\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2193.99 | −0.998628 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −181.374 | −0.0811114 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1910.31 | −0.839525 | −0.419763 | − | 0.907634i | \(-0.637887\pi\) | ||||
−0.419763 | + | 0.907634i | \(0.637887\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1787.62 | 0.759130 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 231.140 | 0.0965151 | 0.0482576 | − | 0.998835i | \(-0.484633\pi\) | ||||
0.0482576 | + | 0.998835i | \(0.484633\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3308.40 | 1.35863 | 0.679314 | − | 0.733848i | \(-0.262278\pi\) | ||||
0.679314 | + | 0.733848i | \(0.262278\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 796.167 | 0.321609 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 254.194 | 0.101020 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2520.00 | 0.985458 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1800.75 | 0.682187 | 0.341093 | − | 0.940029i | \(-0.389203\pi\) | ||||
0.341093 | + | 0.940029i | \(0.389203\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1283.36 | −0.478644 | −0.239322 | − | 0.970940i | \(-0.576925\pi\) | ||||
−0.239322 | + | 0.970940i | \(0.576925\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 35.0837 | 0.0128841 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 60.7514 | 0.0219714 | 0.0109857 | − | 0.999940i | \(-0.496503\pi\) | ||||
0.0109857 | + | 0.999940i | \(0.496503\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3860.39 | 1.37515 | 0.687577 | − | 0.726112i | \(-0.258675\pi\) | ||||
0.687577 | + | 0.726112i | \(0.258675\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2810.21 | −0.986153 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1934.94 | 0.659231 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1070.50 | 0.359444 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1081.81 | 0.358039 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 491.637 | 0.160406 | 0.0802031 | − | 0.996779i | \(-0.474443\pi\) | ||||
0.0802031 | + | 0.996779i | \(0.474443\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1637.83 | 0.526866 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3400.89 | −1.07878 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −898.123 | −0.277121 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −81.5003 | −0.0248068 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 823.376 | 0.247253 | 0.123626 | − | 0.992329i | \(-0.460548\pi\) | ||||
0.123626 | + | 0.992329i | \(0.460548\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −716.624 | −0.212333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3758.87 | −1.09905 | −0.549527 | − | 0.835476i | \(-0.685192\pi\) | ||||
−0.549527 | + | 0.835476i | \(0.685192\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2440.10 | −0.704132 | −0.352066 | − | 0.935975i | \(-0.614521\pi\) | ||||
−0.352066 | + | 0.935975i | \(0.614521\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1949.86 | −0.548239 | −0.274120 | − | 0.961696i | \(-0.588386\pi\) | ||||
−0.274120 | + | 0.961696i | \(0.588386\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1485.31 | 0.412301 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2821.00 | 0.773180 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2705.64 | 0.732273 | 0.366137 | − | 0.930561i | \(-0.380680\pi\) | ||||
0.366137 | + | 0.930561i | \(0.380680\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 604.211 | 0.161496 | 0.0807482 | − | 0.996735i | \(-0.474269\pi\) | ||||
0.0807482 | + | 0.996735i | \(0.474269\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −34.9872 | −0.00901288 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1833.96 | −0.466756 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1631.82 | −0.410356 | −0.205178 | − | 0.978725i | \(-0.565777\pi\) | ||||
−0.205178 | + | 0.978725i | \(0.565777\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6385.00 | −1.58665 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −948.667 | −0.232972 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7106.55 | −1.72488 | −0.862441 | − | 0.506158i | \(-0.831065\pi\) | ||||
−0.862441 | + | 0.506158i | \(0.831065\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −933.125 | −0.221299 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5570.25 | 1.30599 | 0.652996 | − | 0.757361i | \(-0.273512\pi\) | ||||
0.652996 | + | 0.757361i | \(0.273512\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1969.09 | −0.456455 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3528.58 | 0.808786 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3913.18 | 0.886955 | 0.443477 | − | 0.896286i | \(-0.353745\pi\) | ||||
0.443477 | + | 0.896286i | \(0.353745\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6072.51 | 1.36118 | 0.680588 | − | 0.732666i | \(-0.261724\pi\) | ||||
0.680588 | + | 0.732666i | \(0.261724\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4274.31 | 0.937274 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6140.62 | 1.33196 | 0.665982 | − | 0.745968i | \(-0.268013\pi\) | ||||
0.665982 | + | 0.745968i | \(0.268013\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1417.75 | −0.304224 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −365.751 | −0.0776472 | −0.0388236 | − | 0.999246i | \(-0.512361\pi\) | ||||
−0.0388236 | + | 0.999246i | \(0.512361\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −710.348 | −0.149208 | −0.0746039 | − | 0.997213i | \(-0.523769\pi\) | ||||
−0.0746039 | + | 0.997213i | \(0.523769\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −407.252 | −0.0846440 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2709.22 | −0.551440 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4447.46 | −0.895926 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 296.373 | 0.0590932 | 0.0295466 | − | 0.999563i | \(-0.490594\pi\) | ||||
0.0295466 | + | 0.999563i | \(0.490594\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4013.87 | 0.792192 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1449.37 | 0.283169 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 206.500 | 0.0399404 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1853.83 | −0.351485 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1787.69 | 0.335616 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8596.87 | 1.59821 | 0.799103 | − | 0.601194i | \(-0.205308\pi\) | ||||
0.799103 | + | 0.601194i | \(0.205308\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2450.29 | 0.451107 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10475.3 | −1.90997 | −0.954984 | − | 0.296658i | \(-0.904128\pi\) | ||||
−0.954984 | + | 0.296658i | \(0.904128\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5496.52 | 0.992594 | 0.496297 | − | 0.868153i | \(-0.334693\pi\) | ||||
0.496297 | + | 0.868153i | \(0.334693\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6556.37 | 1.16165 | 0.580824 | − | 0.814029i | \(-0.302730\pi\) | ||||
0.580824 | + | 0.814029i | \(0.302730\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5565.62 | 0.976850 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5056.13 | −0.879145 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 946.057 | 0.162972 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −138.237 | −0.0235939 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −274.790 | −0.0464708 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 102.376 | 0.0170003 | 0.00850017 | − | 0.999964i | \(-0.497294\pi\) | ||||
0.00850017 | + | 0.999964i | \(0.497294\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −339.625 | −0.0558899 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6309.95 | −1.02910 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1333.50 | 0.215549 | 0.107775 | − | 0.994175i | \(-0.465627\pi\) | ||||
0.107775 | + | 0.994175i | \(0.465627\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1842.58 | −0.295208 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8456.17 | 1.34290 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2403.67 | 0.375099 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1101.00 | −0.170331 | −0.0851655 | − | 0.996367i | \(-0.527142\pi\) | ||||
−0.0851655 | + | 0.996367i | \(0.527142\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9467.89 | 1.45216 | 0.726081 | − | 0.687609i | \(-0.241340\pi\) | ||||
0.726081 | + | 0.687609i | \(0.241340\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −46.8748 | −0.00712818 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1684.69 | −0.254015 | −0.127007 | − | 0.991902i | \(-0.540537\pi\) | ||||
−0.127007 | + | 0.991902i | \(0.540537\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3677.53 | 0.549812 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6635.25 | −0.975474 | −0.487737 | − | 0.872991i | \(-0.662177\pi\) | ||||
−0.487737 | + | 0.872991i | \(0.662177\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6452.87 | −0.940788 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4651.79 | −0.672605 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2016.62 | −0.289191 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7121.97 | −1.01298 | −0.506490 | − | 0.862246i | \(-0.669057\pi\) | ||||
−0.506490 | + | 0.862246i | \(0.669057\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2585.25 | −0.364723 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13621.3 | −1.89085 | −0.945424 | − | 0.325843i | \(-0.894352\pi\) | ||||
−0.945424 | + | 0.325843i | \(0.894352\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4135.12 | −0.569432 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −180.000 | −0.0245901 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3331.51 | −0.451525 | −0.225763 | − | 0.974182i | \(-0.572487\pi\) | ||||
−0.225763 | + | 0.974182i | \(0.572487\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −702.834 | −0.0945073 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3275.75 | 0.437031 | 0.218515 | − | 0.975833i | \(-0.429879\pi\) | ||||
0.218515 | + | 0.975833i | \(0.429879\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4543.87 | 0.596842 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14975.4 | −1.95188 | −0.975941 | − | 0.218035i | \(-0.930035\pi\) | ||||
−0.975941 | + | 0.218035i | \(0.930035\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5583.78 | −0.722209 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7994.29 | −1.02610 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6334.18 | 0.806853 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10758.6 | −1.36010 | −0.680050 | − | 0.733166i | \(-0.738042\pi\) | ||||
−0.680050 | + | 0.733166i | \(0.738042\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2607.00 | −0.324657 | −0.162328 | − | 0.986737i | \(-0.551900\pi\) | ||||
−0.162328 | + | 0.986737i | \(0.551900\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −273.484 | −0.0338045 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −545.624 | −0.0669439 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2025.69 | 0.246707 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6214.64 | 0.751330 | 0.375665 | − | 0.926756i | \(-0.377414\pi\) | ||||
0.375665 | + | 0.926756i | \(0.377414\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3138.92 | 0.376719 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4117.91 | −0.487085 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1941.79 | −0.228034 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13111.4 | −1.52872 | −0.764358 | − | 0.644792i | \(-0.776944\pi\) | ||||
−0.764358 | + | 0.644792i | \(0.776944\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8410.12 | −0.973596 | −0.486798 | − | 0.873514i | \(-0.661835\pi\) | ||||
−0.486798 | + | 0.873514i | \(0.661835\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1984.50 | −0.228108 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3737.95 | 0.426628 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 279.585 | 0.0314650 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7783.31 | 0.869858 | 0.434929 | − | 0.900465i | \(-0.356774\pi\) | ||||
0.434929 | + | 0.900465i | \(0.356774\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13870.1 | 1.53939 | 0.769695 | − | 0.638412i | \(-0.220409\pi\) | ||||
0.769695 | + | 0.638412i | \(0.220409\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2095.21 | −0.230937 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2397.05 | −0.262395 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5679.63 | 0.617480 | 0.308740 | − | 0.951146i | \(-0.400093\pi\) | ||||
0.308740 | + | 0.951146i | \(0.400093\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2316.93 | −0.248489 | −0.124245 | − | 0.992252i | \(-0.539651\pi\) | ||||
−0.124245 | + | 0.992252i | \(0.539651\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7922.97 | 0.844010 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3980.42 | −0.421180 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9526.86 | 1.00134 | 0.500669 | − | 0.865639i | \(-0.333088\pi\) | ||||
0.500669 | + | 0.865639i | \(0.333088\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15419.7 | 1.60995 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −11049.7 | −1.14605 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −16627.3 | −1.70195 | −0.850974 | − | 0.525208i | \(-0.823987\pi\) | ||||
−0.850974 | + | 0.525208i | \(0.823987\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1267.50 | 0.128893 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11338.3 | −1.14550 | −0.572749 | − | 0.819730i | \(-0.694123\pi\) | ||||
−0.572749 | + | 0.819730i | \(0.694123\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9207.87 | 0.924246 | 0.462123 | − | 0.886816i | \(-0.347088\pi\) | ||||
0.462123 | + | 0.886816i | \(0.347088\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3183.37 | −0.317474 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −17215.7 | −1.70588 | −0.852941 | − | 0.522007i | \(-0.825184\pi\) | ||||
−0.852941 | + | 0.522007i | \(0.825184\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8454.74 | 0.827121 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −27101.9 | −2.63456 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1604.66 | 0.155004 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2630.88 | 0.252536 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10293.8 | 0.981911 | 0.490956 | − | 0.871185i | \(-0.336648\pi\) | ||||
0.490956 | + | 0.871185i | \(0.336648\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −65.5137 | −0.00621033 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −9986.18 | −0.934946 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11109.0 | 1.03367 | 0.516833 | − | 0.856086i | \(-0.327111\pi\) | ||||
0.516833 | + | 0.856086i | \(0.327111\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −12319.8 | −1.13931 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6573.88 | −0.604226 | −0.302113 | − | 0.953272i | \(-0.597692\pi\) | ||||
−0.302113 | + | 0.953272i | \(0.597692\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4867.22 | 0.444642 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3254.38 | 0.295502 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16841.4 | −1.51087 | −0.755435 | − | 0.655223i | \(-0.772575\pi\) | ||||
−0.755435 | + | 0.655223i | \(0.772575\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3136.67 | −0.279712 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −18436.6 | −1.63429 | −0.817146 | − | 0.576431i | \(-0.804445\pi\) | ||||
−0.817146 | + | 0.576431i | \(0.804445\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4162.53 | −0.366793 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6581.96 | 0.576558 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 20825.2 | 1.81348 | 0.906738 | − | 0.421694i | \(-0.138564\pi\) | ||||
0.906738 | + | 0.421694i | \(0.138564\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 544.123 | 0.0468297 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5501.80 | 0.470754 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11836.5 | 1.00691 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5730.92 | 0.484700 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14384.7 | 1.20961 | 0.604805 | − | 0.796373i | \(-0.293251\pi\) | ||||
0.604805 | + | 0.796373i | \(0.293251\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6487.49 | 0.542405 | 0.271203 | − | 0.962522i | \(-0.412579\pi\) | ||||
0.271203 | + | 0.962522i | \(0.412579\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7395.05 | 0.611259 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1980.77 | 0.162799 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5362.87 | −0.438284 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −498.695 | −0.0405270 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11352.9 | −0.917433 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −693.420 | −0.0557230 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14416.6 | 1.14569 | 0.572844 | − | 0.819664i | \(-0.305840\pi\) | ||||
0.572844 | + | 0.819664i | \(0.305840\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −9925.21 | −0.784404 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −617.006 | −0.0484947 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4881.38 | −0.381559 | −0.190780 | − | 0.981633i | \(-0.561102\pi\) | ||||
−0.190780 | + | 0.981633i | \(0.561102\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2388.50 | −0.185681 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2089.44 | 0.161549 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −762.583 | −0.0583240 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3153.13 | −0.239860 | −0.119930 | − | 0.992782i | \(-0.538267\pi\) | ||||
−0.119930 | + | 0.992782i | \(0.538267\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 876.514 | 0.0663195 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7560.00 | −0.568954 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6795.87 | 0.508724 | 0.254362 | − | 0.967109i | \(-0.418134\pi\) | ||||
0.254362 | + | 0.967109i | \(0.418134\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4137.28 | −0.308065 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −10708.3 | −0.788955 | −0.394477 | − | 0.918906i | \(-0.629074\pi\) | ||||
−0.394477 | + | 0.918906i | \(0.629074\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6531.66 | 0.478706 | 0.239353 | − | 0.970933i | \(-0.423065\pi\) | ||||
0.239353 | + | 0.970933i | \(0.423065\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5402.25 | −0.393861 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9470.94 | −0.686896 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17461.9 | 1.25987 | 0.629937 | − | 0.776646i | \(-0.283081\pi\) | ||||
0.629937 | + | 0.776646i | \(0.283081\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3850.08 | 0.276345 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −15691.9 | −1.11473 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −105.251 | −0.00743863 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9254.42 | 0.650717 | 0.325358 | − | 0.945591i | \(-0.394515\pi\) | ||||
0.325358 | + | 0.945591i | \(0.394515\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3174.61 | 0.222084 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −182.254 | −0.0126852 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −21019.2 | −1.45557 | −0.727786 | − | 0.685804i | \(-0.759451\pi\) | ||||
−0.727786 | + | 0.685804i | \(0.759451\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −11581.2 | −0.793945 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −26971.7 | −1.83979 | −0.919894 | − | 0.392167i | \(-0.871725\pi\) | ||||
−0.919894 | + | 0.392167i | \(0.871725\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −26510.3 | −1.79930 | −0.899648 | − | 0.436616i | \(-0.856177\pi\) | ||||
−0.899648 | + | 0.436616i | \(0.856177\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8430.62 | 0.569355 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −10445.0 | −0.701899 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 29412.0 | 1.96671 | 0.983356 | − | 0.181687i | \(-0.0581556\pi\) | ||||
0.983356 | + | 0.181687i | \(0.0581556\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −382.810 | −0.0253467 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6068.64 | −0.399853 | −0.199926 | − | 0.979811i | \(-0.564070\pi\) | ||||
−0.199926 | + | 0.979811i | \(0.564070\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5804.83 | −0.380607 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1904.56 | 0.124270 | 0.0621352 | − | 0.998068i | \(-0.480209\pi\) | ||||
0.0621352 | + | 0.998068i | \(0.480209\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −406.478 | −0.0263937 | −0.0131969 | − | 0.999913i | \(-0.504201\pi\) | ||||
−0.0131969 | + | 0.999913i | \(0.504201\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3211.50 | −0.207525 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 668.244 | 0.0427676 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3245.42 | −0.206714 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1771.50 | 0.112296 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15294.2 | −0.964903 | −0.482452 | − | 0.875923i | \(-0.660254\pi\) | ||||
−0.482452 | + | 0.875923i | \(0.660254\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1474.91 | −0.0926105 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1578.12 | −0.0986233 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4913.49 | −0.304186 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −15722.2 | −0.968782 | −0.484391 | − | 0.874852i | \(-0.660959\pi\) | ||||
−0.484391 | + | 0.874852i | \(0.660959\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18529.9 | 1.13646 | 0.568232 | − | 0.822868i | \(-0.307628\pi\) | ||||
0.568232 | + | 0.822868i | \(0.307628\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 10202.7 | 0.622836 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8638.95 | −0.524934 | −0.262467 | − | 0.964941i | \(-0.584536\pi\) | ||||
−0.262467 | + | 0.964941i | \(0.584536\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 31986.9 | 1.93466 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 27884.4 | 1.67106 | 0.835528 | − | 0.549448i | \(-0.185162\pi\) | ||||
0.835528 | + | 0.549448i | \(0.185162\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −17950.1 | −1.07079 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2694.37 | 0.159996 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5767.55 | −0.340928 | −0.170464 | − | 0.985364i | \(-0.554527\pi\) | ||||
−0.170464 | + | 0.985364i | \(0.554527\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4090.12 | 0.240677 | 0.120338 | − | 0.992733i | \(-0.461602\pi\) | ||||
0.120338 | + | 0.992733i | \(0.461602\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 244.501 | 0.0143222 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12332.2 | −0.715900 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2470.13 | −0.142751 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 14246.2 | 0.819627 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21667.7 | −1.24106 | −0.620528 | − | 0.784185i | \(-0.713082\pi\) | ||||
−0.620528 | + | 0.784185i | \(0.713082\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2149.87 | 0.122591 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −15318.9 | −0.869648 | −0.434824 | − | 0.900515i | \(-0.643189\pi\) | ||||
−0.434824 | + | 0.900515i | \(0.643189\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11276.6 | 0.634539 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9981.36 | 0.559189 | 0.279595 | − | 0.960118i | \(-0.409800\pi\) | ||||
0.279595 | + | 0.960118i | \(0.409800\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7048.02 | 0.393126 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7320.29 | 0.406531 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 507.497 | 0.0280611 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23243.1 | 1.27961 | 0.639805 | − | 0.768537i | \(-0.279015\pi\) | ||||
0.639805 | + | 0.768537i | \(0.279015\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4360.04 | −0.237965 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13484.8 | 0.732815 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5849.59 | 0.316526 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −11295.6 | −0.608598 | −0.304299 | − | 0.952577i | \(-0.598422\pi\) | ||||
−0.304299 | + | 0.952577i | \(0.598422\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 760.485 | 0.0407998 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4455.93 | −0.238042 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6868.11 | 0.363804 | 0.181902 | − | 0.983317i | \(-0.441775\pi\) | ||||
0.181902 | + | 0.983317i | \(0.441775\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8463.00 | −0.446395 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −18737.1 | −0.984163 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 627.770 | 0.0328353 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −8116.92 | −0.422778 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −31479.5 | −1.63281 | −0.816404 | − | 0.577481i | \(-0.804036\pi\) | ||||
−0.816404 | + | 0.577481i | \(0.804036\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1812.63 | −0.0932400 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8255.55 | 0.422901 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26045.8 | 1.32873 | 0.664363 | − | 0.747410i | \(-0.268703\pi\) | ||||
0.664363 | + | 0.747410i | \(0.268703\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −23701.0 | −1.19920 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3538.40 | −0.178300 | −0.0891499 | − | 0.996018i | \(-0.528415\pi\) | ||||
−0.0891499 | + | 0.996018i | \(0.528415\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −50284.4 | −2.51323 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10426.9 | 0.519024 | 0.259512 | − | 0.965740i | \(-0.416438\pi\) | ||||
0.259512 | + | 0.965740i | \(0.416438\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 104.962 | 0.00520359 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2518.88 | 0.124372 | 0.0621862 | − | 0.998065i | \(-0.480193\pi\) | ||||
0.0621862 | + | 0.998065i | \(0.480193\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8937.50 | −0.439523 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5501.87 | 0.269482 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14820.3 | 0.720105 | 0.360053 | − | 0.932932i | \(-0.382759\pi\) | ||||
0.360053 | + | 0.932932i | \(0.382759\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4895.46 | 0.236919 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −24810.7 | −1.19596 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8892.84 | 0.426969 | 0.213485 | − | 0.976946i | \(-0.431519\pi\) | ||||
0.213485 | + | 0.976946i | \(0.431519\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 19155.0 | 0.916050 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22795.0 | 1.08583 | 0.542916 | − | 0.839787i | \(-0.317320\pi\) | ||||
0.542916 | + | 0.839787i | \(0.317320\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2846.00 | 0.134506 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1034.50 | −0.0487009 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13025.5 | −0.610809 | −0.305405 | − | 0.952223i | \(-0.598792\pi\) | ||||
−0.305405 | + | 0.952223i | \(0.598792\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 21319.7 | 0.995861 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 26467.0 | 1.23150 | 0.615751 | − | 0.787941i | \(-0.288853\pi\) | ||||
0.615751 | + | 0.787941i | \(0.288853\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 12543.1 | 0.581371 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5788.87 | 0.266249 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 29306.5 | 1.34273 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2799.37 | 0.127767 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 18984.0 | 0.863144 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 33216.6 | 1.50450 | 0.752252 | − | 0.658876i | \(-0.228968\pi\) | ||||
0.752252 | + | 0.658876i | \(0.228968\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −16710.7 | −0.754015 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −460.743 | −0.0206324 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5907.28 | 0.263534 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −15363.9 | −0.682830 | −0.341415 | − | 0.939913i | \(-0.610906\pi\) | ||||
−0.341415 | + | 0.939913i | \(0.610906\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10351.2 | 0.458323 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10585.7 | −0.466953 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −16070.6 | −0.706249 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −11739.5 | −0.512083 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 26742.7 | 1.16220 | 0.581102 | − | 0.813831i | \(-0.302622\pi\) | ||||
0.581102 | + | 0.813831i | \(0.302622\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −23651.0 | −1.02404 | −0.512022 | − | 0.858973i | \(-0.671103\pi\) | ||||
−0.512022 | + | 0.858973i | \(0.671103\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −18217.5 | −0.785876 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −27662.5 | −1.18893 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10174.6 | −0.435697 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16974.1 | 0.721558 | 0.360779 | − | 0.932651i | \(-0.382511\pi\) | ||||
0.360779 | + | 0.932651i | \(0.382511\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22328.9 | 0.945730 | 0.472865 | − | 0.881135i | \(-0.343220\pi\) | ||||
0.472865 | + | 0.881135i | \(0.343220\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −12822.9 | −0.541135 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15731.8 | 0.661485 | 0.330743 | − | 0.943721i | \(-0.392701\pi\) | ||||
0.330743 | + | 0.943721i | \(0.392701\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −38025.4 | −1.59309 | −0.796547 | − | 0.604576i | \(-0.793342\pi\) | ||||
−0.796547 | + | 0.604576i | \(0.793342\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −18421.9 | −0.769010 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7042.97 | −0.291895 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4253.25 | 0.175644 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 16546.5 | 0.680868 | 0.340434 | − | 0.940268i | \(-0.389426\pi\) | ||||
0.340434 | + | 0.940268i | \(0.389426\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13639.4 | −0.559242 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1097.25 | 0.0448296 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 14778.9 | 0.601669 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2131.04 | 0.0861452 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4488.50 | −0.180803 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13511.9 | 0.542365 | 0.271182 | − | 0.962528i | \(-0.412585\pi\) | ||||
0.271182 | + | 0.962528i | \(0.412585\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1221.76 | 0.0488692 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 17178.2 | 0.684711 | 0.342355 | − | 0.939570i | \(-0.388775\pi\) | ||||
0.342355 | + | 0.939570i | \(0.388775\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −35914.3 | −1.42652 | −0.713260 | − | 0.700899i | \(-0.752782\pi\) | ||||
−0.713260 | + | 0.700899i | \(0.752782\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −882.508 | −0.0348099 | −0.0174049 | − | 0.999849i | \(-0.505540\pi\) | ||||
−0.0174049 | + | 0.999849i | \(0.505540\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12868.0 | 0.505810 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8127.67 | 0.318374 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 50477.6 | 1.97046 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1626.27 | 0.0632652 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 13342.4 | 0.517263 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17420.1 | 0.670737 | 0.335368 | − | 0.942087i | \(-0.391139\pi\) | ||||
0.335368 | + | 0.942087i | \(0.391139\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −889.120 | −0.0341175 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 38097.8 | 1.45692 | 0.728460 | − | 0.685088i | \(-0.240236\pi\) | ||||
0.728460 | + | 0.685088i | \(0.240236\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −13870.6 | −0.528633 | −0.264317 | − | 0.964436i | \(-0.585146\pi\) | ||||
−0.264317 | + | 0.964436i | \(0.585146\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −12041.6 | −0.457372 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −17467.8 | −0.661230 | −0.330615 | − | 0.943766i | \(-0.607256\pi\) | ||||
−0.330615 | + | 0.943766i | \(0.607256\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4348.12 | −0.163488 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4443.67 | 0.166519 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1556.98 | −0.0581499 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −619.499 | −0.0230596 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 16332.6 | 0.605919 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −13722.8 | −0.507405 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −22285.7 | −0.818567 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −28536.3 | −1.04469 | −0.522344 | − | 0.852735i | \(-0.674942\pi\) | ||||
−0.522344 | + | 0.852735i | \(0.674942\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5561.49 | 0.202930 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −50235.7 | −1.82698 | −0.913492 | − | 0.406857i | \(-0.866625\pi\) | ||||
−0.913492 | + | 0.406857i | \(0.866625\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −32815.9 | −1.18954 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5363.07 | −0.193768 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5317.08 | 0.190854 | 0.0954268 | − | 0.995436i | \(-0.469578\pi\) | ||||
0.0954268 | + | 0.995436i | \(0.469578\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −25790.6 | −0.922725 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −947.814 | −0.0338003 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3004.73 | 0.106805 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7350.87 | −0.260447 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 25493.1 | 0.900325 | 0.450162 | − | 0.892947i | \(-0.351366\pi\) | ||||
0.450162 | + | 0.892947i | \(0.351366\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 31425.9 | 1.10272 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −16975.0 | −0.593734 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 12691.4 | 0.442486 | 0.221243 | − | 0.975219i | \(-0.428989\pi\) | ||||
0.221243 | + | 0.975219i | \(0.428989\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −16489.6 | −0.573074 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −15378.4 | −0.532753 | −0.266377 | − | 0.963869i | \(-0.585826\pi\) | ||||
−0.266377 | + | 0.963869i | \(0.585826\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −34166.8 | −1.17988 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 50442.9 | 1.73091 | 0.865455 | − | 0.500986i | \(-0.167029\pi\) | ||||
0.865455 | + | 0.500986i | \(0.167029\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 519.745 | 0.0177783 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −19669.1 | −0.670678 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 31787.3 | 1.08047 | 0.540237 | − | 0.841513i | \(-0.318335\pi\) | ||||
0.540237 | + | 0.841513i | \(0.318335\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12130.0 | −0.411014 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −16696.9 | −0.563984 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4975.99 | −0.167030 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 15168.4 | 0.507574 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 8644.84 | 0.288381 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1005.61 | 0.0334417 | 0.0167209 | − | 0.999860i | \(-0.494677\pi\) | ||||
0.0167209 | + | 0.999860i | \(0.494677\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2838.17 | −0.0940921 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7070.91 | 0.233693 | 0.116847 | − | 0.993150i | \(-0.462721\pi\) | ||||
0.116847 | + | 0.993150i | \(0.462721\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 414.711 | 0.0136219 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −11097.1 | −0.363384 | −0.181692 | − | 0.983355i | \(-0.558157\pi\) | ||||
−0.181692 | + | 0.983355i | \(0.558157\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 63138.7 | 2.06121 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 824.371 | 0.0268299 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −17775.5 | −0.576755 | −0.288377 | − | 0.957517i | \(-0.593116\pi\) | ||||
−0.288377 | + | 0.957517i | \(0.593116\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −409.228 | −0.0132376 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 60052.0 | 1.93078 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4691.86 | 0.150395 | 0.0751977 | − | 0.997169i | \(-0.476041\pi\) | ||||
0.0751977 | + | 0.997169i | \(0.476041\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −307.129 | −0.00981515 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −26004.0 | −0.828523 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8471.39 | −0.269099 | −0.134549 | − | 0.990907i | \(-0.542959\pi\) | ||||
−0.134549 | + | 0.990907i | \(0.542959\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1018.87 | 0.0322680 |
(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 | 1176.4.a.r.1.1 | 2 | ||
4.3 | odd | 2 | 2352.4.a.cc.1.1 | 2 | |||
7.2 | even | 3 | 168.4.q.d.25.2 | ✓ | 4 | ||
7.4 | even | 3 | 168.4.q.d.121.2 | yes | 4 | ||
7.6 | odd | 2 | 1176.4.a.u.1.2 | 2 | |||
21.2 | odd | 6 | 504.4.s.f.361.1 | 4 | |||
21.11 | odd | 6 | 504.4.s.f.289.1 | 4 | |||
28.11 | odd | 6 | 336.4.q.g.289.2 | 4 | |||
28.23 | odd | 6 | 336.4.q.g.193.2 | 4 | |||
28.27 | even | 2 | 2352.4.a.bo.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.4.q.d.25.2 | ✓ | 4 | 7.2 | even | 3 | ||
168.4.q.d.121.2 | yes | 4 | 7.4 | even | 3 | ||
336.4.q.g.193.2 | 4 | 28.23 | odd | 6 | |||
336.4.q.g.289.2 | 4 | 28.11 | odd | 6 | |||
504.4.s.f.289.1 | 4 | 21.11 | odd | 6 | |||
504.4.s.f.361.1 | 4 | 21.2 | odd | 6 | |||
1176.4.a.r.1.1 | 2 | 1.1 | even | 1 | trivial | ||
1176.4.a.u.1.2 | 2 | 7.6 | odd | 2 | |||
2352.4.a.bo.1.2 | 2 | 28.27 | even | 2 | |||
2352.4.a.cc.1.1 | 2 | 4.3 | odd | 2 |