Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1792,2,Mod(897,1792)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1792, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1792.897");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1792 = 2^{8} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1792.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(14.3091920422\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.399424.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 3x^{4} - 6x^{3} + 6x^{2} - 8x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 896) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 897.1 | ||
Root | \(1.40680 - 0.144584i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1792.897 |
Dual form | 1792.2.b.o.897.6 |
$q$-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 \(\left(\mathbb{Z}/1792\mathbb{Z}\right)^\times\).
\(n\) | \(1023\) | \(1025\) | \(1541\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 3.10278i | − 1.79139i | −0.444671 | − | 0.895694i | \(-0.646679\pi\) | ||||
0.444671 | − | 0.895694i | \(-0.353321\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 2.52444i | − 1.12896i | −0.825446 | − | 0.564481i | \(-0.809076\pi\) | ||||
0.825446 | − | 0.564481i | \(-0.190924\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −6.62721 | −2.20907 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 3.62721i | − 1.09365i | −0.837248 | − | 0.546823i | \(-0.815837\pi\) | ||||
0.837248 | − | 0.546823i | \(-0.184163\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 4.72999i | − 1.31186i | −0.754821 | − | 0.655931i | \(-0.772276\pi\) | ||||
0.754821 | − | 0.655931i | \(-0.227724\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −7.83276 | −2.02241 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.20555 | 1.02000 | 0.509998 | − | 0.860176i | \(-0.329646\pi\) | ||||
0.509998 | + | 0.860176i | \(0.329646\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 7.10278i | − 1.62949i | −0.579821 | − | 0.814744i | \(-0.696877\pi\) | ||||
0.579821 | − | 0.814744i | \(-0.303123\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.10278i | 0.677081i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.578337 | −0.120592 | −0.0602958 | − | 0.998181i | \(-0.519204\pi\) | ||||
−0.0602958 | + | 0.998181i | \(0.519204\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.37279 | −0.274557 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 11.2544i | 2.16592i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.20555i | 1.52373i | 0.647734 | + | 0.761866i | \(0.275717\pi\) | ||||
−0.647734 | + | 0.761866i | \(0.724283\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.04888 | 0.906805 | 0.453402 | − | 0.891306i | \(-0.350210\pi\) | ||||
0.453402 | + | 0.891306i | \(0.350210\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −11.2544 | −1.95914 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.52444i | 0.426708i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.04888i | 0.501232i | 0.968087 | + | 0.250616i | \(0.0806332\pi\) | ||||
−0.968087 | + | 0.250616i | \(0.919367\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −14.6761 | −2.35006 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.205550 | 0.0321015 | 0.0160508 | − | 0.999871i | \(-0.494891\pi\) | ||||
0.0160508 | + | 0.999871i | \(0.494891\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 4.78389i | − 0.729536i | −0.931098 | − | 0.364768i | \(-0.881148\pi\) | ||||
0.931098 | − | 0.364768i | \(-0.118852\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 16.7300i | 2.49396i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.20555 | 0.905173 | 0.452586 | − | 0.891721i | \(-0.350501\pi\) | ||||
0.452586 | + | 0.891721i | \(0.350501\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 13.0489i | − 1.82721i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.00000i | 0.274721i | 0.990521 | + | 0.137361i | \(0.0438619\pi\) | ||||
−0.990521 | + | 0.137361i | \(0.956138\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −9.15667 | −1.23469 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −22.0383 | −2.91905 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 12.5628i | − 1.63553i | −0.575552 | − | 0.817765i | \(-0.695213\pi\) | ||||
0.575552 | − | 0.817765i | \(-0.304787\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.5244i | 1.34752i | 0.738952 | + | 0.673758i | \(0.235321\pi\) | ||||
−0.738952 | + | 0.673758i | \(0.764679\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6.62721 | 0.834950 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −11.9406 | −1.48104 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.57834i | 0.803672i | 0.915712 | + | 0.401836i | \(0.131628\pi\) | ||||
−0.915712 | + | 0.401836i | \(0.868372\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.79445i | 0.216026i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.25443 | 1.08315 | 0.541574 | − | 0.840653i | \(-0.317828\pi\) | ||||
0.541574 | + | 0.840653i | \(0.317828\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.25945i | 0.491839i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.62721i | 0.413359i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.15667 | 0.580171 | 0.290086 | − | 0.957001i | \(-0.406316\pi\) | ||||
0.290086 | + | 0.957001i | \(0.406316\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 15.0383 | 1.67092 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.94610i | 0.652669i | 0.945254 | + | 0.326335i | \(0.105814\pi\) | ||||
−0.945254 | + | 0.326335i | \(0.894186\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 10.6167i | − 1.15154i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 25.4600 | 2.72960 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.4111 | 1.10357 | 0.551787 | − | 0.833985i | \(-0.313946\pi\) | ||||
0.551787 | + | 0.833985i | \(0.313946\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.72999i | 0.495837i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 15.6655i | − 1.62444i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −17.9305 | −1.83963 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.36222 | −0.950590 | −0.475295 | − | 0.879827i | \(-0.657659\pi\) | ||||
−0.475295 | + | 0.879827i | \(0.657659\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 24.0383i | 2.41594i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 4.31889i | − 0.429745i | −0.976642 | − | 0.214873i | \(-0.931066\pi\) | ||||
0.976642 | − | 0.214873i | \(-0.0689337\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.04888 | −0.497481 | −0.248740 | − | 0.968570i | \(-0.580017\pi\) | ||||
−0.248740 | + | 0.968570i | \(0.580017\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 7.83276 | 0.764399 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.83276i | 0.950569i | 0.879832 | + | 0.475285i | \(0.157655\pi\) | ||||
−0.879832 | + | 0.475285i | \(0.842345\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 19.4600i | 1.86393i | 0.362551 | + | 0.931964i | \(0.381906\pi\) | ||||
−0.362551 | + | 0.931964i | \(0.618094\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.45998 | 0.897901 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.78389 | 0.826319 | 0.413159 | − | 0.910659i | \(-0.364425\pi\) | ||||
0.413159 | + | 0.910659i | \(0.364425\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.45998i | 0.136143i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 31.3466i | 2.89800i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.20555 | −0.385522 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.15667 | −0.196061 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 0.637776i | − 0.0575063i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 9.15667i | − 0.818998i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.6761 | 1.30229 | 0.651146 | − | 0.758952i | \(-0.274288\pi\) | ||||
0.651146 | + | 0.758952i | \(0.274288\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −14.8433 | −1.30688 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 4.15165i | − 0.362731i | −0.983416 | − | 0.181366i | \(-0.941948\pi\) | ||||
0.983416 | − | 0.181366i | \(-0.0580518\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.10278i | 0.615889i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 28.4111 | 2.44524 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.25443 | −0.448916 | −0.224458 | − | 0.974484i | \(-0.572061\pi\) | ||||
−0.224458 | + | 0.974484i | \(0.572061\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.89722i | 0.754653i | 0.926080 | + | 0.377326i | \(0.123157\pi\) | ||||
−0.926080 | + | 0.377326i | \(0.876843\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 19.2544i | − 1.62152i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −17.1567 | −1.43471 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 20.7144 | 1.72024 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 3.10278i | − 0.255913i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 21.6655i | − 1.77491i | −0.460895 | − | 0.887455i | \(-0.652472\pi\) | ||||
0.460895 | − | 0.887455i | \(-0.347528\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.98944 | 0.406035 | 0.203017 | − | 0.979175i | \(-0.434925\pi\) | ||||
0.203017 | + | 0.979175i | \(0.434925\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −27.8711 | −2.25324 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 12.7456i | − 1.02375i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.0922i | 1.60353i | 0.597637 | + | 0.801767i | \(0.296106\pi\) | ||||
−0.597637 | + | 0.801767i | \(0.703894\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.20555 | 0.492132 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.578337 | 0.0455793 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 16.0383i | − 1.25622i | −0.778126 | − | 0.628109i | \(-0.783829\pi\) | ||||
0.778126 | − | 0.628109i | \(-0.216171\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 28.4111i | 2.21180i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.79445 | −0.138859 | −0.0694294 | − | 0.997587i | \(-0.522118\pi\) | ||||
−0.0694294 | + | 0.997587i | \(0.522118\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.37279 | −0.720984 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 47.0716i | 3.59966i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 22.8277i | − 1.73556i | −0.496948 | − | 0.867780i | \(-0.665546\pi\) | ||||
0.496948 | − | 0.867780i | \(-0.334454\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.37279 | 0.103773 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −38.9794 | −2.92987 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 3.51941i | − 0.263053i | −0.991313 | − | 0.131527i | \(-0.958012\pi\) | ||||
0.991313 | − | 0.131527i | \(-0.0419879\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.9355i | 0.812832i | 0.913688 | + | 0.406416i | \(0.133222\pi\) | ||||
−0.913688 | + | 0.406416i | \(0.866778\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 32.6550 | 2.41392 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.69670 | 0.565872 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 15.2544i | − 1.11551i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 11.2544i | − 0.818639i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.745574 | −0.0539478 | −0.0269739 | − | 0.999636i | \(-0.508587\pi\) | ||||
−0.0269739 | + | 0.999636i | \(0.508587\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.1361 | −1.01754 | −0.508768 | − | 0.860904i | \(-0.669899\pi\) | ||||
−0.508768 | + | 0.860904i | \(0.669899\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 37.0489i | 2.65313i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.0000i | 0.712470i | 0.934396 | + | 0.356235i | \(0.115940\pi\) | ||||
−0.934396 | + | 0.356235i | \(0.884060\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.637776 | 0.0452107 | 0.0226054 | − | 0.999744i | \(-0.492804\pi\) | ||||
0.0226054 | + | 0.999744i | \(0.492804\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 20.4111 | 1.43969 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 8.20555i | − 0.575917i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 0.518898i | − 0.0362414i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.83276 | 0.266395 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −25.7633 | −1.78208 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.676089i | 0.0465439i | 0.999729 | + | 0.0232719i | \(0.00740836\pi\) | ||||
−0.999729 | + | 0.0232719i | \(0.992592\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −12.0766 | −0.823619 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.04888 | −0.342740 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 28.7144i | − 1.94034i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 19.8922i | − 1.33809i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −23.6655 | −1.58476 | −0.792380 | − | 0.610027i | \(-0.791158\pi\) | ||||
−0.792380 | + | 0.610027i | \(0.791158\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 9.09775 | 0.606517 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.89722i | 0.590530i | 0.955415 | + | 0.295265i | \(0.0954079\pi\) | ||||
−0.955415 | + | 0.295265i | \(0.904592\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 7.68111i | − 0.507582i | −0.967259 | − | 0.253791i | \(-0.918322\pi\) | ||||
0.967259 | − | 0.253791i | \(-0.0816776\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 11.2544 | 0.740487 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.66553 | −0.371161 | −0.185580 | − | 0.982629i | \(-0.559417\pi\) | ||||
−0.185580 | + | 0.982629i | \(0.559417\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 15.6655i | − 1.02191i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 16.0000i | − 1.03931i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.4217 | 0.738806 | 0.369403 | − | 0.929269i | \(-0.379562\pi\) | ||||
0.369403 | + | 0.929269i | \(0.379562\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.5577 | 1.13099 | 0.565496 | − | 0.824751i | \(-0.308685\pi\) | ||||
0.565496 | + | 0.824751i | \(0.308685\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 12.8972i | − 0.827357i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 2.52444i | − 0.161280i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −33.5960 | −2.13766 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 18.4494 | 1.16918 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 12.1517i | − 0.767005i | −0.923540 | − | 0.383503i | \(-0.874718\pi\) | ||||
0.923540 | − | 0.383503i | \(-0.125282\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.09775i | 0.131885i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −32.9411 | −2.06285 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.41110 | 0.399913 | 0.199957 | − | 0.979805i | \(-0.435920\pi\) | ||||
0.199957 | + | 0.979805i | \(0.435920\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 3.04888i | − 0.189448i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 54.3799i | − 3.36603i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.3133 | −0.635948 | −0.317974 | − | 0.948099i | \(-0.603003\pi\) | ||||
−0.317974 | + | 0.948099i | \(0.603003\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.04888 | 0.310150 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 32.3033i | − 1.97693i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 15.6811i | 0.956094i | 0.878334 | + | 0.478047i | \(0.158655\pi\) | ||||
−0.878334 | + | 0.478047i | \(0.841345\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −25.7633 | −1.56501 | −0.782504 | − | 0.622646i | \(-0.786058\pi\) | ||||
−0.782504 | + | 0.622646i | \(0.786058\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 14.6761 | 0.888237 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.97939i | 0.300269i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 17.2544i | − 1.03672i | −0.855163 | − | 0.518359i | \(-0.826543\pi\) | ||||
0.855163 | − | 0.518359i | \(-0.173457\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −33.4600 | −2.00320 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 32.5089 | 1.93932 | 0.969658 | − | 0.244466i | \(-0.0786128\pi\) | ||||
0.969658 | + | 0.244466i | \(0.0786128\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 22.9950i | 1.36691i | 0.729993 | + | 0.683455i | \(0.239523\pi\) | ||||
−0.729993 | + | 0.683455i | \(0.760477\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 55.6344i | 3.29549i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.205550 | −0.0121332 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.686652 | 0.0403913 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 29.0489i | 1.70288i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 8.72999i | − 0.510011i | −0.966940 | − | 0.255006i | \(-0.917923\pi\) | ||||
0.966940 | − | 0.255006i | \(-0.0820773\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −31.7139 | −1.84645 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 40.8222 | 2.36874 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.73553i | 0.158200i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.78389i | 0.275739i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −13.4005 | −0.769841 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 26.5683 | 1.52130 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 26.6605i | − 1.52160i | −0.648989 | − | 0.760798i | \(-0.724808\pi\) | ||||
0.648989 | − | 0.760798i | \(-0.275192\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 15.6655i | 0.891181i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.0978 | −0.572591 | −0.286295 | − | 0.958141i | \(-0.592424\pi\) | ||||
−0.286295 | + | 0.958141i | \(0.592424\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.205550 | 0.0116184 | 0.00580919 | − | 0.999983i | \(-0.498151\pi\) | ||||
0.00580919 | + | 0.999983i | \(0.498151\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 16.7300i | − 0.942628i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 30.4111i | − 1.70806i | −0.520226 | − | 0.854029i | \(-0.674152\pi\) | ||||
0.520226 | − | 0.854029i | \(-0.325848\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 29.7633 | 1.66642 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 30.5089 | 1.70284 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 29.8711i | − 1.66207i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.49327i | 0.360182i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 60.3799 | 3.33902 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.20555 | −0.342123 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 2.47054i | − 0.135793i | −0.997692 | − | 0.0678965i | \(-0.978371\pi\) | ||||
0.997692 | − | 0.0678965i | \(-0.0216288\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 20.2056i | − 1.10726i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 16.6066 | 0.907316 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.2927 | −0.615155 | −0.307577 | − | 0.951523i | \(-0.599518\pi\) | ||||
−0.307577 | + | 0.951523i | \(0.599518\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 27.2544i | − 1.48026i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 18.3133i | − 0.991723i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.52998 | 0.243886 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 2.68614i | − 0.144199i | −0.997397 | − | 0.0720997i | \(-0.977030\pi\) | ||||
0.997397 | − | 0.0720997i | \(-0.0229700\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.4756i | 0.935445i | 0.883875 | + | 0.467723i | \(0.154925\pi\) | ||||
−0.883875 | + | 0.467723i | \(0.845075\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 53.2333 | 2.84138 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.05892 | 0.0563608 | 0.0281804 | − | 0.999603i | \(-0.491029\pi\) | ||||
0.0281804 | + | 0.999603i | \(0.491029\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 13.0489i | 0.690620i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 11.8328 | 0.624509 | 0.312255 | − | 0.949998i | \(-0.398916\pi\) | ||||
0.312255 | + | 0.949998i | \(0.398916\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −31.4494 | −1.65523 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6.69167i | 0.351222i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 23.3622i | − 1.22283i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19.2544 | −1.00507 | −0.502536 | − | 0.864556i | \(-0.667600\pi\) | ||||
−0.502536 | + | 0.864556i | \(0.667600\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.36222 | −0.0709146 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 2.00000i | − 0.103835i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.66553i | 0.500462i | 0.968186 | + | 0.250231i | \(0.0805066\pi\) | ||||
−0.968186 | + | 0.250231i | \(0.919493\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −28.4111 | −1.46714 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 38.8122 | 1.99893 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.0383i | 0.618367i | 0.951002 | + | 0.309183i | \(0.100056\pi\) | ||||
−0.951002 | + | 0.309183i | \(0.899944\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 45.5366i | − 2.33291i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −31.0278 | −1.58544 | −0.792722 | − | 0.609583i | \(-0.791337\pi\) | ||||
−0.792722 | + | 0.609583i | \(0.791337\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.15667 | 0.466667 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 31.7038i | 1.61160i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.1466i | 0.666560i | 0.942828 | + | 0.333280i | \(0.108156\pi\) | ||||
−0.942828 | + | 0.333280i | \(0.891844\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.43223 | −0.123003 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −12.8816 | −0.649793 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 13.0177i | − 0.654992i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.47556i | 0.0740563i | 0.999314 | + | 0.0370282i | \(0.0117891\pi\) | ||||
−0.999314 | + | 0.0370282i | \(0.988211\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 22.0383 | 1.10330 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12.9794 | −0.648160 | −0.324080 | − | 0.946030i | \(-0.605055\pi\) | ||||
−0.324080 | + | 0.946030i | \(0.605055\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 23.8811i | − 1.18960i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 37.9633i | − 1.88641i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.0589 | 0.548170 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.36222 | 0.0673577 | 0.0336788 | − | 0.999433i | \(-0.489278\pi\) | ||||
0.0336788 | + | 0.999433i | \(0.489278\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 16.3033i | 0.804183i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 12.5628i | 0.618173i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15.0106 | 0.736840 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 27.6061 | 1.35188 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 25.3083i | 1.23639i | 0.786024 | + | 0.618196i | \(0.212136\pi\) | ||||
−0.786024 | + | 0.618196i | \(0.787864\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.05892i | 0.0516087i | 0.999667 | + | 0.0258044i | \(0.00821469\pi\) | ||||
−0.999667 | + | 0.0258044i | \(0.991785\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −41.1255 | −1.99959 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.77332 | −0.280047 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 10.5244i | − 0.509313i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 53.2333i | 2.57013i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.2439 | −0.589766 | −0.294883 | − | 0.955533i | \(-0.595281\pi\) | ||||
−0.294883 | + | 0.955533i | \(0.595281\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 37.0278 | 1.77944 | 0.889720 | − | 0.456507i | \(-0.150899\pi\) | ||||
0.889720 | + | 0.456507i | \(0.150899\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 64.2721i | − 3.08161i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.10780i | 0.196503i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.33447 | −0.397783 | −0.198891 | − | 0.980022i | \(-0.563734\pi\) | ||||
−0.198891 | + | 0.980022i | \(0.563734\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.62721 | −0.315582 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 27.5960i | 1.31113i | 0.755140 | + | 0.655564i | \(0.227569\pi\) | ||||
−0.755140 | + | 0.655564i | \(0.772431\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 26.2822i | − 1.24589i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −67.2233 | −3.17955 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.66553 | −0.0786010 | −0.0393005 | − | 0.999227i | \(-0.512513\pi\) | ||||
−0.0393005 | + | 0.999227i | \(0.512513\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 0.745574i | − 0.0351077i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 15.4811i | − 0.727366i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 11.9406 | 0.559782 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −25.7250 | −1.20336 | −0.601682 | − | 0.798736i | \(-0.705502\pi\) | ||||
−0.601682 | + | 0.798736i | \(0.705502\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 47.3311i | 2.20922i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 12.4267i | − 0.578768i | −0.957213 | − | 0.289384i | \(-0.906549\pi\) | ||||
0.957213 | − | 0.289384i | \(-0.0934505\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.33447 | 0.201440 | 0.100720 | − | 0.994915i | \(-0.467885\pi\) | ||||
0.100720 | + | 0.994915i | \(0.467885\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −39.5466 | −1.83393 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 10.6917i | − 0.494752i | −0.968920 | − | 0.247376i | \(-0.920432\pi\) | ||||
0.968920 | − | 0.247376i | \(-0.0795682\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 6.57834i | − 0.303759i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 62.3416 | 2.87255 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −17.3522 | −0.797854 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9.75060i | 0.447388i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 13.2544i | − 0.606878i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.95112 | 0.134840 | 0.0674202 | − | 0.997725i | \(-0.478523\pi\) | ||||
0.0674202 | + | 0.997725i | \(0.478523\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.4211 | 0.657548 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 1.79445i | − 0.0816503i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 23.6344i | 1.07318i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.93051 | 0.268737 | 0.134369 | − | 0.990931i | \(-0.457099\pi\) | ||||
0.134369 | + | 0.990931i | \(0.457099\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −49.7633 | −2.25037 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 21.3028i | 0.961381i | 0.876890 | + | 0.480691i | \(0.159614\pi\) | ||||
−0.876890 | + | 0.480691i | \(0.840386\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 34.5089i | 1.55420i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 60.6832 | 2.72751 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 36.6761i | − 1.64185i | −0.571038 | − | 0.820924i | \(-0.693459\pi\) | ||||
0.571038 | − | 0.820924i | \(-0.306541\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.56777i | 0.248750i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −20.7456 | −0.924999 | −0.462500 | − | 0.886619i | \(-0.653047\pi\) | ||||
−0.462500 | + | 0.886619i | \(0.653047\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.9028 | −0.485167 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 29.0816i | 1.29156i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 21.0333i | − 0.932284i | −0.884710 | − | 0.466142i | \(-0.845644\pi\) | ||||
0.884710 | − | 0.466142i | \(-0.154356\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.25443 | −0.409392 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 79.9377 | 3.52933 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 12.7456i | 0.561637i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 22.5089i | − 0.989938i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −70.8293 | −3.10906 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.7355 | 0.557954 | 0.278977 | − | 0.960298i | \(-0.410005\pi\) | ||||
0.278977 | + | 0.960298i | \(0.410005\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 0.151651i | − 0.00663123i | −0.999995 | − | 0.00331562i | \(-0.998945\pi\) | ||||
0.999995 | − | 0.00331562i | \(-0.00105540\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 4.25945i | − 0.185898i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 21.2333 | 0.924937 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.6655 | −0.985458 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 83.2560i | 3.61300i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 0.972250i | − 0.0421128i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 24.8222 | 1.07316 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −10.9200 | −0.471231 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 3.62721i | − 0.156235i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.5678i | 0.497337i | 0.968589 | + | 0.248669i | \(0.0799930\pi\) | ||||
−0.968589 | + | 0.248669i | \(0.920007\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 33.9305 | 1.45610 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 49.1255 | 2.10431 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.0594i | 0.430111i | 0.976602 | + | 0.215055i | \(0.0689932\pi\) | ||||
−0.976602 | + | 0.215055i | \(0.931007\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 69.7477i | − 2.97676i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 58.2822 | 2.48290 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.15667 | −0.219284 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 23.8811i | − 1.01370i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.50885i | 0.191046i | 0.995427 | + | 0.0955231i | \(0.0304524\pi\) | ||||
−0.995427 | + | 0.0955231i | \(0.969548\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −22.6277 | −0.957051 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −47.3311 | −1.99832 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 24.9739i | − 1.05252i | −0.850323 | − | 0.526261i | \(-0.823593\pi\) | ||||
0.850323 | − | 0.526261i | \(-0.176407\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 22.1744i | − 0.932883i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −15.0383 | −0.631550 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 21.9406 | 0.919796 | 0.459898 | − | 0.887972i | \(-0.347886\pi\) | ||||
0.459898 | + | 0.887972i | \(0.347886\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19.2161i | 0.804169i | 0.915602 | + | 0.402085i | \(0.131714\pi\) | ||||
−0.915602 | + | 0.402085i | \(0.868286\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.31335i | 0.0966415i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.793934 | 0.0331093 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −0.432226 | −0.0179938 | −0.00899689 | − | 0.999960i | \(-0.502864\pi\) | ||||
−0.00899689 | + | 0.999960i | \(0.502864\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 43.8610i | 1.82280i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 5.94610i | − 0.246686i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.25443 | 0.300448 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 79.1326 | 3.27173 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13.3083i | 0.549293i | 0.961545 | + | 0.274647i | \(0.0885609\pi\) | ||||
−0.961545 | + | 0.274647i | \(0.911439\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 35.8610i | − 1.47763i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 31.0278 | 1.27631 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.68665 | 0.315653 | 0.157826 | − | 0.987467i | \(-0.449551\pi\) | ||||
0.157826 | + | 0.987467i | \(0.449551\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.6167i | 0.435240i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 1.97887i | − 0.0809899i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 37.0177 | 1.51250 | 0.756251 | − | 0.654281i | \(-0.227029\pi\) | ||||
0.756251 | + | 0.654281i | \(0.227029\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.78440 | −0.399114 | −0.199557 | − | 0.979886i | \(-0.563950\pi\) | ||||
−0.199557 | + | 0.979886i | \(0.563950\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 43.5960i | − 1.77537i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.44439i | 0.221346i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 40.6066 | 1.64817 | 0.824086 | − | 0.566465i | \(-0.191689\pi\) | ||||
0.824086 | + | 0.566465i | \(0.191689\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −25.4600 | −1.03169 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 29.3522i | − 1.18746i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 24.8122i | − 1.00215i | −0.865403 | − | 0.501077i | \(-0.832937\pi\) | ||||
0.865403 | − | 0.501077i | \(-0.167063\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.61003 | −0.0649225 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 40.4494 | 1.62843 | 0.814216 | − | 0.580562i | \(-0.197167\pi\) | ||||
0.814216 | + | 0.580562i | \(0.197167\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 5.20053i | − 0.209027i | −0.994523 | − | 0.104513i | \(-0.966671\pi\) | ||||
0.994523 | − | 0.104513i | \(-0.0333285\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 6.50885i | − 0.261191i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −10.4111 | −0.417112 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.9794 | −1.19918 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 79.9377i | 3.19240i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 12.8222i | 0.511255i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 43.7422 | 1.74135 | 0.870674 | − | 0.491861i | \(-0.163683\pi\) | ||||
0.870674 | + | 0.491861i | \(0.163683\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.09775 | 0.0833781 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 37.0489i | − 1.47024i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 4.72999i | − 0.187409i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.21611 | 0.285019 | 0.142510 | − | 0.989793i | \(-0.454483\pi\) | ||||
0.142510 | + | 0.989793i | \(0.454483\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 20.3472i | − 0.802413i | −0.915988 | − | 0.401207i | \(-0.868591\pi\) | ||||
0.915988 | − | 0.401207i | \(-0.131409\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 37.4711i | 1.47542i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −11.5577 | −0.454381 | −0.227191 | − | 0.973850i | \(-0.572954\pi\) | ||||
−0.227191 | + | 0.973850i | \(0.572954\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −45.5678 | −1.78869 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 15.6655i | 0.613980i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 14.3033i | − 0.559731i | −0.960039 | − | 0.279866i | \(-0.909710\pi\) | ||||
0.960039 | − | 0.279866i | \(-0.0902900\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.4806 | −0.409510 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −61.3311 | −2.39275 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19.7038i | 0.767553i | 0.923426 | + | 0.383776i | \(0.125377\pi\) | ||||
−0.923426 | + | 0.383776i | \(0.874623\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.7789i | 1.15826i | 0.815234 | + | 0.579132i | \(0.196608\pi\) | ||||
−0.815234 | + | 0.579132i | \(0.803392\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −61.7210 | −2.39705 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 17.9305 | 0.695316 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 4.74557i | − 0.183749i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 73.4288i | 2.83892i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 38.1744 | 1.47371 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 32.9200 | 1.26897 | 0.634485 | − | 0.772935i | \(-0.281212\pi\) | ||||
0.634485 | + | 0.772935i | \(0.281212\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 15.4499i | − 0.594668i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 22.7089i | − 0.872772i | −0.899759 | − | 0.436386i | \(-0.856258\pi\) | ||||
0.899759 | − | 0.436386i | \(-0.143742\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.36222 | 0.359289 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 27.6061 | 1.05787 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 23.5194i | 0.899945i | 0.893042 | + | 0.449973i | \(0.148566\pi\) | ||||
−0.893042 | + | 0.449973i | \(0.851434\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13.2645i | 0.506809i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −23.8328 | −0.909277 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.45998 | 0.360396 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 35.1794i | 1.33829i | 0.743133 | + | 0.669144i | \(0.233339\pi\) | ||||
−0.743133 | + | 0.669144i | \(0.766661\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 24.0383i | − 0.913140i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 22.4605 | 0.851975 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.864451 | 0.0327434 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 17.5789i | 0.664893i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.48110i | 0.0559404i | 0.999609 | + | 0.0279702i | \(0.00890436\pi\) | ||||
−0.999609 | + | 0.0279702i | \(0.991096\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 21.6555 | 0.816752 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −48.6066 | −1.83063 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.31889i | 0.162428i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 29.3622i | 1.10272i | 0.834267 | + | 0.551361i | \(0.185891\pi\) | ||||
−0.834267 | + | 0.551361i | \(0.814109\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −34.1744 | −1.28164 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.91995 | −0.109353 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 43.3110i | 1.61974i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 35.4389i | − 1.32349i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 13.3833 | 0.499115 | 0.249557 | − | 0.968360i | \(-0.419715\pi\) | ||||
0.249557 | + | 0.968360i | \(0.419715\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.04888 | 0.188030 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 54.4777i | − 2.02605i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 11.2645i | − 0.418352i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −21.5366 | −0.798748 | −0.399374 | − | 0.916788i | \(-0.630773\pi\) | ||||
−0.399374 | + | 0.916788i | \(0.630773\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 5.09775 | 0.188806 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 20.1189i | − 0.744124i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 30.2978i | − 1.11907i | −0.828806 | − | 0.559537i | \(-0.810979\pi\) | ||||
0.828806 | − | 0.559537i | \(-0.189021\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −7.83276 | −0.288916 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 23.8610 | 0.878932 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12.9794i | 0.477455i | 0.971087 | + | 0.238727i | \(0.0767302\pi\) | ||||
−0.971087 | + | 0.238727i | \(0.923270\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 104.241i | 3.82939i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −50.0071 | −1.83458 | −0.917292 | − | 0.398215i | \(-0.869630\pi\) | ||||
−0.917292 | + | 0.398215i | \(0.869630\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −54.6933 | −2.00381 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 39.4061i | − 1.44179i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 9.83276i | − 0.359281i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.8917 | 0.835329 | 0.417665 | − | 0.908601i | \(-0.362849\pi\) | ||||
0.417665 | + | 0.908601i | \(0.362849\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −37.7038 | −1.37400 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 12.5955i | − 0.458398i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29.0278i | 1.05503i | 0.849545 | + | 0.527516i | \(0.176876\pi\) | ||||
−0.849545 | + | 0.527516i | \(0.823124\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.50885 | 0.236256 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −36.8122 | −1.33444 | −0.667220 | − | 0.744861i | \(-0.732516\pi\) | ||||
−0.667220 | + | 0.744861i | \(0.732516\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 19.4600i | − 0.704498i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 70.3588i | 2.54383i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −59.4217 | −2.14559 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −47.8711 | −1.72628 | −0.863138 | − | 0.504969i | \(-0.831504\pi\) | ||||
−0.863138 | + | 0.504969i | \(0.831504\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 19.8922i | − 0.716400i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 41.2489i | − 1.48362i | −0.670610 | − | 0.741810i | \(-0.733968\pi\) | ||||
0.670610 | − | 0.741810i | \(-0.266032\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.93103 | −0.248970 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −9.45998 | −0.339375 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 1.45998i | − 0.0523091i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −92.3488 | −3.30028 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 50.7215 | 1.81033 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.79947i | 0.242375i | 0.992630 | + | 0.121188i | \(0.0386702\pi\) | ||||
−0.992630 | + | 0.121188i | \(0.961330\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 32.0000i | 1.13923i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.78389 | −0.312319 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 49.7805 | 1.76776 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 15.6655i | − 0.555599i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6.18996i | 0.219260i | 0.993972 | + | 0.109630i | \(0.0349666\pi\) | ||||
−0.993972 | + | 0.109630i | \(0.965033\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 26.0978 | 0.923272 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −68.9966 | −2.43787 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 33.5678i | − 1.18458i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 1.45998i | − 0.0514574i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 48.6550 | 1.71274 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −30.3517 | −1.06711 | −0.533554 | − | 0.845766i | \(-0.679144\pi\) | ||||
−0.533554 | + | 0.845766i | \(0.679144\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 40.0328i | 1.40574i | 0.711318 | + | 0.702870i | \(0.248099\pi\) | ||||
−0.711318 | + | 0.702870i | \(0.751901\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 79.9377i | 2.80354i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −40.4877 | −1.41822 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −33.9789 | −1.18877 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 31.3466i | − 1.09534i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 51.9789i | 1.81408i | 0.421050 | + | 0.907038i | \(0.361662\pi\) | ||||
−0.421050 | + | 0.907038i | \(0.638338\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −26.9200 | −0.938371 | −0.469185 | − | 0.883100i | \(-0.655452\pi\) | ||||
−0.469185 | + | 0.883100i | \(0.655452\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 15.4499 | 0.537898 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 47.5960i | − 1.65508i | −0.561409 | − | 0.827538i | \(-0.689741\pi\) | ||||
0.561409 | − | 0.827538i | \(-0.310259\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.21109i | 0.285183i | 0.989782 | + | 0.142591i | \(0.0455435\pi\) | ||||
−0.989782 | + | 0.142591i | \(0.954456\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −53.5366 | −1.85716 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.20555 | 0.145714 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.52998i | 0.156766i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 56.8222i | 1.96406i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.04888 | 0.174307 | 0.0871533 | − | 0.996195i | \(-0.472223\pi\) | ||||
0.0871533 | + | 0.996195i | \(0.472223\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −38.3311 | −1.32176 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 100.868i | − 3.47407i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 23.6610i | 0.813964i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.15667 | 0.0741042 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 71.3482 | 2.44867 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 1.76328i | − 0.0604444i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.14109i | 0.0390701i | 0.999809 | + | 0.0195351i | \(0.00621860\pi\) | ||||
−0.999809 | + | 0.0195351i | \(0.993781\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 118.829 | 4.06388 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.45998 | 0.118191 | 0.0590953 | − | 0.998252i | \(-0.481178\pi\) | ||||
0.0590953 | + | 0.998252i | \(0.481178\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 4.15165i | − 0.141653i | −0.997489 | − | 0.0708263i | \(-0.977436\pi\) | ||||
0.997489 | − | 0.0708263i | \(-0.0225636\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.637776i | 0.0217353i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −13.7633 | −0.468507 | −0.234254 | − | 0.972175i | \(-0.575265\pi\) | ||||
−0.234254 | + | 0.972175i | \(0.575265\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −57.6272 | −1.95938 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 2.13053i | − 0.0723564i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 18.7044i | − 0.634502i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 31.1155 | 1.05431 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 62.0455 | 2.09992 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9.15667i | 0.309552i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 53.9688i | − 1.82240i | −0.411967 | − | 0.911199i | \(-0.635158\pi\) | ||||
0.411967 | − | 0.911199i | \(-0.364842\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −27.0872 | −0.913628 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 56.1744 | 1.89256 | 0.946281 | − | 0.323344i | \(-0.104807\pi\) | ||||
0.946281 | + | 0.323344i | \(0.104807\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 52.5371i | 1.76801i | 0.467473 | + | 0.884007i | \(0.345165\pi\) | ||||
−0.467473 | + | 0.884007i | \(0.654835\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 98.4011i | 3.30772i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 44.4988 | 1.49412 | 0.747062 | − | 0.664755i | \(-0.231464\pi\) | ||||
0.747062 | + | 0.664755i | \(0.231464\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −14.6761 | −0.492220 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 54.5472i | − 1.82740i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 44.0766i | − 1.47497i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.88454 | −0.296978 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.48773 | 0.283397 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 41.4288i | 1.38173i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.41110i | 0.280214i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 14.8433 | 0.493955 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 27.6061 | 0.917657 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 44.4182i | 1.47488i | 0.675411 | + | 0.737442i | \(0.263966\pi\) | ||||
−0.675411 | + | 0.737442i | \(0.736034\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 28.6222i | 0.949338i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −48.9894 | −1.62309 | −0.811546 | − | 0.584288i | \(-0.801374\pi\) | ||||
−0.811546 | + | 0.584288i | \(0.801374\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 21.5678 | 0.713789 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 82.4354i | − 2.72523i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.15165i | 0.137100i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −34.9200 | −1.15190 | −0.575951 | − | 0.817484i | \(-0.695368\pi\) | ||||
−0.575951 | + | 0.817484i | \(0.695368\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −82.7215 | −2.72577 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 4.18546i | − 0.137617i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 33.4600 | 1.09897 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.98995 | 0.130906 | 0.0654531 | − | 0.997856i | \(-0.479151\pi\) | ||||
0.0654531 | + | 0.997856i | \(0.479151\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 7.10278i | − 0.232784i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 31.3311i | 1.02573i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −38.5089 | −1.25937 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 47.9789 | 1.56740 | 0.783701 | − | 0.621139i | \(-0.213330\pi\) | ||||
0.783701 | + | 0.621139i | \(0.213330\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 0.637776i | − 0.0208130i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 26.1900i | − 0.853768i | −0.904306 | − | 0.426884i | \(-0.859611\pi\) | ||||
0.904306 | − | 0.426884i | \(-0.140389\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.118877 | −0.00387118 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −28.4111 | −0.924213 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 57.3905i | 1.86494i | 0.361247 | + | 0.932470i | \(0.382351\pi\) | ||||
−0.361247 | + | 0.932470i | \(0.617649\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 43.7733i | − 1.42094i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −94.3588 | −3.05979 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.68665 | 0.119422 | 0.0597112 | − | 0.998216i | \(-0.480982\pi\) | ||||
0.0597112 | + | 0.998216i | \(0.480982\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.88216i | 0.0609051i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 92.3488i | − 2.98521i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.25443 | 0.169674 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.50885 | −0.177705 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 65.1638i | − 2.09987i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 35.6856i | 1.14876i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 27.6172 | 0.888108 | 0.444054 | − | 0.896000i | \(-0.353540\pi\) | ||||
0.444054 | + | 0.896000i | \(0.353540\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −92.6832 | −2.97741 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.94610i | 0.319186i | 0.987183 | + | 0.159593i | \(0.0510181\pi\) | ||||
−0.987183 | + | 0.159593i | \(0.948982\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 8.89722i | − 0.285232i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 20.1471 | 0.645225 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −21.2544 | −0.679989 | −0.339995 | − | 0.940427i | \(-0.610425\pi\) | ||||
−0.339995 | + | 0.940427i | \(0.610425\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 37.7633i | − 1.20692i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 128.965i | − 4.11755i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 16.1844 | 0.516203 | 0.258101 | − | 0.966118i | \(-0.416903\pi\) | ||||
0.258101 | + | 0.966118i | \(0.416903\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 25.2444 | 0.804353 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 19.2544i | 0.612875i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.76670i | 0.0879759i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.0766 | −0.510691 | −0.255345 | − | 0.966850i | \(-0.582189\pi\) | ||||
−0.255345 | + | 0.966850i | \(0.582189\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −7.66553 | −0.243258 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 1.61003i | − 0.0510412i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 29.4444i | − 0.932513i | −0.884650 | − | 0.466257i | \(-0.845602\pi\) | ||||
0.884650 | − | 0.466257i | \(-0.154398\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −34.3133 | −1.08563 |
(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 | 1792.2.b.o.897.1 | 6 | ||
4.3 | odd | 2 | 1792.2.b.p.897.6 | 6 | |||
8.3 | odd | 2 | 1792.2.b.p.897.1 | 6 | |||
8.5 | even | 2 | inner | 1792.2.b.o.897.6 | 6 | ||
16.3 | odd | 4 | 896.2.a.i.1.1 | ✓ | 3 | ||
16.5 | even | 4 | 896.2.a.j.1.1 | yes | 3 | ||
16.11 | odd | 4 | 896.2.a.l.1.3 | yes | 3 | ||
16.13 | even | 4 | 896.2.a.k.1.3 | yes | 3 | ||
48.5 | odd | 4 | 8064.2.a.cb.1.2 | 3 | |||
48.11 | even | 4 | 8064.2.a.bu.1.2 | 3 | |||
48.29 | odd | 4 | 8064.2.a.ch.1.2 | 3 | |||
48.35 | even | 4 | 8064.2.a.ce.1.2 | 3 | |||
112.13 | odd | 4 | 6272.2.a.v.1.1 | 3 | |||
112.27 | even | 4 | 6272.2.a.u.1.1 | 3 | |||
112.69 | odd | 4 | 6272.2.a.w.1.3 | 3 | |||
112.83 | even | 4 | 6272.2.a.x.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
896.2.a.i.1.1 | ✓ | 3 | 16.3 | odd | 4 | ||
896.2.a.j.1.1 | yes | 3 | 16.5 | even | 4 | ||
896.2.a.k.1.3 | yes | 3 | 16.13 | even | 4 | ||
896.2.a.l.1.3 | yes | 3 | 16.11 | odd | 4 | ||
1792.2.b.o.897.1 | 6 | 1.1 | even | 1 | trivial | ||
1792.2.b.o.897.6 | 6 | 8.5 | even | 2 | inner | ||
1792.2.b.p.897.1 | 6 | 8.3 | odd | 2 | |||
1792.2.b.p.897.6 | 6 | 4.3 | odd | 2 | |||
6272.2.a.u.1.1 | 3 | 112.27 | even | 4 | |||
6272.2.a.v.1.1 | 3 | 112.13 | odd | 4 | |||
6272.2.a.w.1.3 | 3 | 112.69 | odd | 4 | |||
6272.2.a.x.1.3 | 3 | 112.83 | even | 4 | |||
8064.2.a.bu.1.2 | 3 | 48.11 | even | 4 | |||
8064.2.a.cb.1.2 | 3 | 48.5 | odd | 4 | |||
8064.2.a.ce.1.2 | 3 | 48.35 | even | 4 | |||
8064.2.a.ch.1.2 | 3 | 48.29 | odd | 4 |