Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [800,6,Mod(449,800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("800.449");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 800 = 2^{5} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 800.c (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: | \(128.307055850\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.6140289600.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 32x^{4} + 116x^{3} + 256x^{2} + 2778x + 7605 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{16} \) |
Twist minimal: | no (minimal twist has level 160) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 449.2 | ||
Root | \(3.05894 - 4.88658i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 800.449 |
Dual form | 800.6.c.j.449.5 |
$q$-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 \(\left(\mathbb{Z}/800\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(351\) | \(577\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − 18.4715i | − 1.18495i | −0.805590 | − | 0.592474i | \(-0.798151\pi\) | ||||
0.805590 | − | 0.592474i | \(-0.201849\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 121.899i | − 0.940275i | −0.882593 | − | 0.470138i | \(-0.844204\pi\) | ||||
0.882593 | − | 0.470138i | \(-0.155796\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −98.1968 | −0.404102 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −438.282 | −1.09213 | −0.546063 | − | 0.837744i | \(-0.683874\pi\) | ||||
−0.546063 | + | 0.837744i | \(0.683874\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 758.285i | − 1.24444i | −0.782842 | − | 0.622220i | \(-0.786231\pi\) | ||||
0.782842 | − | 0.622220i | \(-0.213769\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1534.86i | 1.28809i | 0.764989 | + | 0.644044i | \(0.222744\pi\) | ||||
−0.764989 | + | 0.644044i | \(0.777256\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −75.8518 | −0.0482039 | −0.0241019 | − | 0.999710i | \(-0.507673\pi\) | ||||
−0.0241019 | + | 0.999710i | \(0.507673\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2251.66 | −1.11418 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3694.27i | 1.45616i | 0.685493 | + | 0.728079i | \(0.259587\pi\) | ||||
−0.685493 | + | 0.728079i | \(0.740413\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 2674.73i | − 0.706108i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6323.09 | −1.39616 | −0.698079 | − | 0.716021i | \(-0.745961\pi\) | ||||
−0.698079 | + | 0.716021i | \(0.745961\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2691.35 | 0.502998 | 0.251499 | − | 0.967857i | \(-0.419076\pi\) | ||||
0.251499 | + | 0.967857i | \(0.419076\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 8095.74i | 1.29411i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7252.19i | 0.870893i | 0.900215 | + | 0.435446i | \(0.143409\pi\) | ||||
−0.900215 | + | 0.435446i | \(0.856591\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −14006.7 | −1.47460 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4913.34 | 0.456475 | 0.228238 | − | 0.973605i | \(-0.426704\pi\) | ||||
0.228238 | + | 0.973605i | \(0.426704\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2533.81i | 0.208979i | 0.994526 | + | 0.104490i | \(0.0333209\pi\) | ||||
−0.994526 | + | 0.104490i | \(0.966679\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 11380.6i | − 0.751487i | −0.926724 | − | 0.375743i | \(-0.877387\pi\) | ||||
0.926724 | − | 0.375743i | \(-0.122613\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1947.64 | 0.115882 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 28351.1 | 1.52632 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 29442.3i | 1.43973i | 0.694113 | + | 0.719866i | \(0.255797\pi\) | ||||
−0.694113 | + | 0.719866i | \(0.744203\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1401.10i | 0.0571191i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5681.08 | 0.212472 | 0.106236 | − | 0.994341i | \(-0.466120\pi\) | ||||
0.106236 | + | 0.994341i | \(0.466120\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −48039.8 | −1.65301 | −0.826507 | − | 0.562926i | \(-0.809676\pi\) | ||||
−0.826507 | + | 0.562926i | \(0.809676\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 11970.1i | 0.379967i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 39570.6i | − 1.07693i | −0.842649 | − | 0.538463i | \(-0.819005\pi\) | ||||
0.842649 | − | 0.538463i | \(-0.180995\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 68238.7 | 1.72547 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12622.3 | 0.297161 | 0.148581 | − | 0.988900i | \(-0.452530\pi\) | ||||
0.148581 | + | 0.988900i | \(0.452530\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 57959.2i | 1.27296i | 0.771292 | + | 0.636481i | \(0.219611\pi\) | ||||
−0.771292 | + | 0.636481i | \(0.780389\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 53426.2i | 1.02690i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 29504.0 | 0.531879 | 0.265939 | − | 0.963990i | \(-0.414318\pi\) | ||||
0.265939 | + | 0.963990i | \(0.414318\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −73268.2 | −1.24080 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 112209.i | 1.78786i | 0.448211 | + | 0.893928i | \(0.352061\pi\) | ||||
−0.448211 | + | 0.893928i | \(0.647939\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 116797.i | 1.65437i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −66969.5 | −0.896194 | −0.448097 | − | 0.893985i | \(-0.647898\pi\) | ||||
−0.448097 | + | 0.893985i | \(0.647898\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −92434.2 | −1.17012 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 49713.4i | − 0.596027i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 131833.i | − 1.42264i | −0.702867 | − | 0.711322i | \(-0.748097\pi\) | ||||
0.702867 | − | 0.711322i | \(-0.251903\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 43037.9 | 0.441330 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −30688.2 | −0.299343 | −0.149671 | − | 0.988736i | \(-0.547822\pi\) | ||||
−0.149671 | + | 0.988736i | \(0.547822\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 140744.i | − 1.30718i | −0.756848 | − | 0.653591i | \(-0.773262\pi\) | ||||
0.756848 | − | 0.653591i | \(-0.226738\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 14196.9i | − 0.119876i | −0.998202 | − | 0.0599381i | \(-0.980910\pi\) | ||||
0.998202 | − | 0.0599381i | \(-0.0190903\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9873.09 | −0.0795952 | −0.0397976 | − | 0.999208i | \(-0.512671\pi\) | ||||
−0.0397976 | + | 0.999208i | \(0.512671\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 133959. | 1.03196 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 245866.i | 1.81135i | 0.423973 | + | 0.905675i | \(0.360635\pi\) | ||||
−0.423973 | + | 0.905675i | \(0.639365\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 74461.2i | 0.502881i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 187097. | 1.21116 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 31040.5 | 0.192737 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 90756.9i | − 0.540900i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 88403.3i | − 0.486361i | −0.969981 | − | 0.243181i | \(-0.921809\pi\) | ||||
0.969981 | − | 0.243181i | \(-0.0781908\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 46803.3 | 0.247630 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −274297. | −1.39651 | −0.698253 | − | 0.715851i | \(-0.746039\pi\) | ||||
−0.698253 | + | 0.715851i | \(0.746039\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9246.26i | 0.0453249i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 309183.i | 1.40739i | 0.710503 | + | 0.703694i | \(0.248467\pi\) | ||||
−0.710503 | + | 0.703694i | \(0.751533\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 381380. | 1.67425 | 0.837125 | − | 0.547011i | \(-0.184235\pi\) | ||||
0.837125 | + | 0.547011i | \(0.184235\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −210217. | −0.890473 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 332343.i | 1.35908i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 35975.8i | − 0.137315i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 101742. | 0.375436 | 0.187718 | − | 0.982223i | \(-0.439891\pi\) | ||||
0.187718 | + | 0.982223i | \(0.439891\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 338843. | 1.20936 | 0.604680 | − | 0.796469i | \(-0.293301\pi\) | ||||
0.604680 | + | 0.796469i | \(0.293301\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 150718.i | − 0.520519i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 101650.i | − 0.329123i | −0.986367 | − | 0.164561i | \(-0.947379\pi\) | ||||
0.986367 | − | 0.164561i | \(-0.0526208\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 543843. | 1.70601 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 450327. | 1.36919 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 214136.i | 0.631279i | 0.948879 | + | 0.315640i | \(0.102219\pi\) | ||||
−0.948879 | + | 0.315640i | \(0.897781\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 606370.i | 1.68247i | 0.540672 | + | 0.841234i | \(0.318170\pi\) | ||||
−0.540672 | + | 0.841234i | \(0.681830\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −203703. | −0.548633 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7448.41 | 0.0194793 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 426958.i | − 1.08460i | −0.840184 | − | 0.542301i | \(-0.817553\pi\) | ||||
0.840184 | − | 0.542301i | \(-0.182447\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 104938.i | − 0.251768i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −682764. | −1.59271 | −0.796357 | − | 0.604826i | \(-0.793243\pi\) | ||||
−0.796357 | + | 0.604826i | \(0.793243\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 725666. | 1.64642 | 0.823209 | − | 0.567738i | \(-0.192181\pi\) | ||||
0.823209 | + | 0.567738i | \(0.192181\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 887368.i | 1.95874i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 672700.i | − 1.40675i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −326047. | −0.663936 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 662000. | 1.31303 | 0.656515 | − | 0.754313i | \(-0.272030\pi\) | ||||
0.656515 | + | 0.754313i | \(0.272030\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 481557.i | − 0.930582i | −0.885158 | − | 0.465291i | \(-0.845950\pi\) | ||||
0.885158 | − | 0.465291i | \(-0.154050\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 569264.i | − 1.04508i | −0.852616 | − | 0.522538i | \(-0.824985\pi\) | ||||
0.852616 | − | 0.522538i | \(-0.175015\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 850151. | 1.52182 | 0.760911 | − | 0.648857i | \(-0.224753\pi\) | ||||
0.760911 | + | 0.648857i | \(0.224753\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −730930. | −1.27610 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 770778.i | 1.31277i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 362765.i | − 0.588437i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 33244.5 | 0.0526447 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 285552. | 0.441548 | 0.220774 | − | 0.975325i | \(-0.429142\pi\) | ||||
0.220774 | + | 0.975325i | \(0.429142\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 233153.i | − 0.352120i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 328073.i | − 0.472957i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.07059e6 | 1.50839 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.16386e6 | 1.60295 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 279669.i | 0.376602i | 0.982111 | + | 0.188301i | \(0.0602981\pi\) | ||||
−0.982111 | + | 0.188301i | \(0.939702\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 1.27295e6i | − 1.63964i | −0.572623 | − | 0.819819i | \(-0.694074\pi\) | ||||
0.572623 | − | 0.819819i | \(-0.305926\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −584351. | −0.736352 | −0.368176 | − | 0.929756i | \(-0.620018\pi\) | ||||
−0.368176 | + | 0.929756i | \(0.620018\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 986863. | 1.21682 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 658722.i | − 0.794900i | −0.917624 | − | 0.397450i | \(-0.869895\pi\) | ||||
0.917624 | − | 0.397450i | \(-0.130105\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 544983.i | − 0.630248i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 664166. | 0.752111 | 0.376055 | − | 0.926597i | \(-0.377280\pi\) | ||||
0.376055 | + | 0.926597i | \(0.377280\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −192140. | −0.213095 | −0.106548 | − | 0.994308i | \(-0.533980\pi\) | ||||
−0.106548 | + | 0.994308i | \(0.533980\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 703414.i | 0.764180i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 57517.3i | 0.0599869i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.07267e6 | 2.11852 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.20021e6 | 1.20246 | 0.601231 | − | 0.799075i | \(-0.294677\pi\) | ||||
0.601231 | + | 0.799075i | \(0.294677\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 1.61913e6i | − 1.59031i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 494440.i | 0.466961i | 0.972361 | + | 0.233481i | \(0.0750115\pi\) | ||||
−0.972361 | + | 0.233481i | \(0.924988\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 884034. | 0.818879 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 620907. | 0.564190 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 535899.i | 0.477742i | 0.971051 | + | 0.238871i | \(0.0767773\pi\) | ||||
−0.971051 | + | 0.238871i | \(0.923223\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.23703e6i | 1.06194i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 886621. | 0.747063 | 0.373532 | − | 0.927617i | \(-0.378147\pi\) | ||||
0.373532 | + | 0.927617i | \(0.378147\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.31305e6 | −1.08607 | −0.543036 | − | 0.839710i | \(-0.682725\pi\) | ||||
−0.543036 | + | 0.839710i | \(0.682725\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.70740e6i | 1.38653i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 175211.i | − 0.137203i | −0.997644 | − | 0.0686013i | \(-0.978146\pi\) | ||||
0.997644 | − | 0.0686013i | \(-0.0218536\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −264282. | −0.203263 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.78398e6 | −1.34779 | −0.673897 | − | 0.738826i | \(-0.735381\pi\) | ||||
−0.673897 | + | 0.738826i | \(0.735381\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.98478e6i | 1.47315i | 0.676358 | + | 0.736573i | \(0.263557\pi\) | ||||
−0.676358 | + | 0.736573i | \(0.736443\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 598931.i | − 0.429212i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −935925. | −0.659168 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.43516e6 | −1.68576 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.44146e6i | 1.66143i | 0.556700 | + | 0.830714i | \(0.312067\pi\) | ||||
−0.556700 | + | 0.830714i | \(0.687933\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.17229e6i | 0.771158i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.80131e6 | 1.81210 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 308869. | 0.196498 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 566858.i | 0.354706i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.53943e6i | 1.53777i | 0.639390 | + | 0.768883i | \(0.279187\pi\) | ||||
−0.639390 | + | 0.768883i | \(0.720813\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.59975e6 | −1.54894 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.86583e6 | 1.09388 | 0.546941 | − | 0.837171i | \(-0.315792\pi\) | ||||
0.546941 | + | 0.837171i | \(0.315792\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.17459e6i | 1.25463i | 0.778765 | + | 0.627316i | \(0.215847\pi\) | ||||
−0.778765 | + | 0.627316i | \(0.784153\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.48421e6i | 0.829557i | 0.909922 | + | 0.414779i | \(0.136141\pi\) | ||||
−0.909922 | + | 0.414779i | \(0.863859\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.77130e6 | 1.52478 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −262238. | −0.142047 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 116422.i | − 0.0620908i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 182371.i | 0.0943162i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.38729e6 | −0.706604 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.02880e6 | 1.01782 | 0.508908 | − | 0.860821i | \(-0.330050\pi\) | ||||
0.508908 | + | 0.860821i | \(0.330050\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 712141.i | − 0.351930i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.34355e6i | 0.644435i | 0.946666 | + | 0.322218i | \(0.104428\pi\) | ||||
−0.946666 | + | 0.322218i | \(0.895572\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.54152e6 | 2.14636 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.17957e6 | −0.549337 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 2.28617e6i | − 1.04924i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 1.52038e6i | − 0.677843i | −0.940815 | − | 0.338921i | \(-0.889938\pi\) | ||||
0.940815 | − | 0.338921i | \(-0.110062\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.80948e6 | 0.795224 | 0.397612 | − | 0.917554i | \(-0.369839\pi\) | ||||
0.397612 | + | 0.917554i | \(0.369839\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.02821e6 | −0.878710 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.48843e6i | 1.06289i | 0.847092 | + | 0.531446i | \(0.178351\pi\) | ||||
−0.847092 | + | 0.531446i | \(0.821649\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 3.45597e6i | − 1.43516i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.44154e6 | −0.590324 | −0.295162 | − | 0.955447i | \(-0.595374\pi\) | ||||
−0.295162 | + | 0.955447i | \(0.595374\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.47035e6 | −0.997676 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 573365.i | − 0.228383i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 257353.i | − 0.0997388i | −0.998756 | − | 0.0498694i | \(-0.984119\pi\) | ||||
0.998756 | − | 0.0498694i | \(-0.0158805\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −482474. | −0.184463 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.58898e6 | 1.35374 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 4.55163e6i | − 1.69393i | −0.531651 | − | 0.846964i | \(-0.678428\pi\) | ||||
0.531651 | − | 0.846964i | \(-0.321572\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.79471e6i | 1.73743i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.96634e6 | −1.06077 | −0.530387 | − | 0.847756i | \(-0.677953\pi\) | ||||
−0.530387 | + | 0.847756i | \(0.677953\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.63294e6 | −0.576313 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.57107e6i | 1.24395i | 0.783039 | + | 0.621973i | \(0.213669\pi\) | ||||
−0.783039 | + | 0.621973i | \(0.786331\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 248812.i | − 0.0844489i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 881685. | 0.295420 | 0.147710 | − | 0.989031i | \(-0.452810\pi\) | ||||
0.147710 | + | 0.989031i | \(0.452810\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.67017e6 | −1.87566 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.06668e6i | 1.65479i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.56117e6i | 0.815570i | 0.913078 | + | 0.407785i | \(0.133699\pi\) | ||||
−0.913078 | + | 0.407785i | \(0.866301\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 170792. | 0.0537077 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.37596e6 | −1.04842 | −0.524211 | − | 0.851589i | \(-0.675640\pi\) | ||||
−0.524211 | + | 0.851589i | \(0.675640\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 2.04081e6i | − 0.625952i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 3.17851e6i | − 0.951124i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.56437e6 | 0.758006 | 0.379003 | − | 0.925395i | \(-0.376267\pi\) | ||||
0.379003 | + | 0.925395i | \(0.376267\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.71107e6 | 1.66768 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 692518.i | − 0.199782i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − 7.04466e6i | − 1.98390i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.64881e6 | −1.85016 | −0.925079 | − | 0.379775i | \(-0.876001\pi\) | ||||
−0.925079 | + | 0.379775i | \(0.876001\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.98840e6 | 1.37169 | 0.685846 | − | 0.727747i | \(-0.259432\pi\) | ||||
0.685846 | + | 0.727747i | \(0.259432\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.11754e6i | 0.303677i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.85600e6i | 1.55429i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.13888e6 | 1.61045 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 802200. | 0.208012 | 0.104006 | − | 0.994577i | \(-0.466834\pi\) | ||||
0.104006 | + | 0.994577i | \(0.466834\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.80978e6i | 1.48916i | 0.667535 | + | 0.744578i | \(0.267349\pi\) | ||||
−0.667535 | + | 0.744578i | \(0.732651\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 280217.i | − 0.0701925i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −585972. | −0.145116 | −0.0725581 | − | 0.997364i | \(-0.523116\pi\) | ||||
−0.0725581 | + | 0.997364i | \(0.523116\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −191252. | −0.0468283 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.41675e6i | 1.06929i | 0.845078 | + | 0.534643i | \(0.179554\pi\) | ||||
−0.845078 | + | 0.534643i | \(0.820446\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 1.87934e6i | − 0.444872i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.28408e6 | −0.534681 | −0.267340 | − | 0.963602i | \(-0.586145\pi\) | ||||
−0.267340 | + | 0.963602i | \(0.586145\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.15343e6 | −0.498528 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 6.25893e6i | − 1.43303i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 3.43086e6i | − 0.768444i | −0.923241 | − | 0.384222i | \(-0.874470\pi\) | ||||
0.923241 | − | 0.384222i | \(-0.125530\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.10533e6 | 0.909529 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 674699. | 0.147862 | 0.0739311 | − | 0.997263i | \(-0.476445\pi\) | ||||
0.0739311 | + | 0.997263i | \(0.476445\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.78627e6i | 1.25443i | 0.778846 | + | 0.627215i | \(0.215805\pi\) | ||||
−0.778846 | + | 0.627215i | \(0.784195\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 6.88097e6i | − 1.46002i | −0.683439 | − | 0.730008i | \(-0.739516\pi\) | ||||
0.683439 | − | 0.730008i | \(-0.260484\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.82362e6 | −1.01261 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.87763e6 | −0.389993 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 1.11052e6i | − 0.228231i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 2.89114e6i | − 0.581798i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.94000e6 | −0.983757 | −0.491879 | − | 0.870664i | \(-0.663690\pi\) | ||||
−0.491879 | + | 0.870664i | \(0.663690\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.49923e6 | 1.08377 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 8.31823e6i | − 1.62242i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 5.21802e6i | − 0.996973i | −0.866897 | − | 0.498487i | \(-0.833889\pi\) | ||||
0.866897 | − | 0.498487i | \(-0.166111\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.95542e6 | 0.748033 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.20805e6 | −0.787730 | −0.393865 | − | 0.919168i | \(-0.628862\pi\) | ||||
−0.393865 | + | 0.919168i | \(0.628862\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 9.70503e6i | − 1.79837i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 1.53864e6i | − 0.279413i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.74013e6 | −1.39154 | −0.695771 | − | 0.718263i | \(-0.744937\pi\) | ||||
−0.695771 | + | 0.718263i | \(0.744937\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.12006e7 | 1.99364 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 6.20893e6i | − 1.09420i | −0.837067 | − | 0.547100i | \(-0.815732\pi\) | ||||
0.837067 | − | 0.547100i | \(-0.184268\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.76271e6i | 0.650101i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8.43892e6 | −1.44375 | −0.721876 | − | 0.692022i | \(-0.756720\pi\) | ||||
−0.721876 | + | 0.692022i | \(0.756720\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.06517e6 | 1.19693 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 202883.i | 0.0340372i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.98793e6i | 0.820717i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.88657e6 | −1.28520 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.61888e6 | −1.06829 | −0.534146 | − | 0.845392i | \(-0.679367\pi\) | ||||
−0.534146 | + | 0.845392i | \(0.679367\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 5.48657e6i | − 0.877095i | −0.898708 | − | 0.438548i | \(-0.855493\pi\) | ||||
0.898708 | − | 0.438548i | \(-0.144507\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.13084e6i | 0.647906i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.21127e6 | −1.12040 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −557864. | −0.0858602 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 3.72571e6i | − 0.568057i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.26117e7i | 1.88728i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −853614. | −0.126558 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −427673. | −0.0628230 | −0.0314115 | − | 0.999507i | \(-0.510000\pi\) | ||||
−0.0314115 | + | 0.999507i | \(0.510000\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 1.34041e7i | − 1.95092i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.94393e6i | 1.27809i | 0.769171 | + | 0.639043i | \(0.220669\pi\) | ||||
−0.769171 | + | 0.639043i | \(0.779331\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.71736e6 | 0.667987 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 479618. | 0.0673002 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 3.59650e6i | − 0.500112i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 7.93887e6i | − 1.08423i | −0.840305 | − | 0.542114i | \(-0.817624\pi\) | ||||
0.840305 | − | 0.542114i | \(-0.182376\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.92135e6 | 0.260062 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.24258e7 | −1.66693 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 1.61543e6i | − 0.214792i | −0.994216 | − | 0.107396i | \(-0.965749\pi\) | ||||
0.994216 | − | 0.107396i | \(-0.0342513\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 8.93132e6i | 1.16670i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.97353e6 | −0.255543 | −0.127771 | − | 0.991804i | \(-0.540782\pi\) | ||||
−0.127771 | + | 0.991804i | \(0.540782\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.18140e6 | −0.921762 | −0.460881 | − | 0.887462i | \(-0.652467\pi\) | ||||
−0.460881 | + | 0.887462i | \(0.652467\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 1.22281e7i | − 1.55587i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.61498e6i | 1.20229i | 0.799140 | + | 0.601145i | \(0.205288\pi\) | ||||
−0.799140 | + | 0.601145i | \(0.794712\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −8.89509e6 | −1.10269 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.36782e7 | 1.68108 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 1.29040e7i | − 1.57237i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 2.66522e6i | − 0.319255i | −0.987177 | − | 0.159627i | \(-0.948971\pi\) | ||||
0.987177 | − | 0.159627i | \(-0.0510293\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −204144. | −0.0242465 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.05152e7 | −1.23836 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.83235e6i | 0.681093i | 0.940228 | + | 0.340547i | \(0.110612\pi\) | ||||
−0.940228 | + | 0.340547i | \(0.889388\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 1.57036e7i | − 1.80328i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.39890e6 | −0.728683 | −0.364341 | − | 0.931265i | \(-0.618706\pi\) | ||||
−0.364341 | + | 0.931265i | \(0.618706\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.00505e7 | 1.13502 | 0.567509 | − | 0.823367i | \(-0.307907\pi\) | ||||
0.567509 | + | 0.823367i | \(0.307907\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.88571e6i | 0.435188i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 1.83636e6i | − 0.202295i | −0.994871 | − | 0.101148i | \(-0.967749\pi\) | ||||
0.994871 | − | 0.101148i | \(-0.0322515\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.42374e7 | 1.55557 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.62976e6 | −0.935181 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.33155e7i | 1.43122i | 0.698499 | + | 0.715611i | \(0.253852\pi\) | ||||
−0.698499 | + | 0.715611i | \(0.746148\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 3.09296e6i | − 0.327085i | −0.986536 | − | 0.163543i | \(-0.947708\pi\) | ||||
0.986536 | − | 0.163543i | \(-0.0522921\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.64802e6 | 1.01207 | 0.506036 | − | 0.862512i | \(-0.331110\pi\) | ||||
0.506036 | + | 0.862512i | \(0.331110\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 9.88118e6 | 1.02821 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.16352e6i | 0.842669i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 614077.i | − 0.0623812i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.11311e7 | −1.12179 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.72048e7 | −1.72019 | −0.860096 | − | 0.510132i | \(-0.829597\pi\) | ||||
−0.860096 | + | 0.510132i | \(0.829597\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 5.27457e6i | − 0.523212i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 1.47686e6i | − 0.144209i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.23947e6 | −0.120083 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.86292e6 | 0.179081 | 0.0895403 | − | 0.995983i | \(-0.471460\pi\) | ||||
0.0895403 | + | 0.995983i | \(0.471460\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 1.39819e7i | − 1.33364i | −0.745218 | − | 0.666821i | \(-0.767655\pi\) | ||||
0.745218 | − | 0.666821i | \(-0.232345\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.28310e7i | 1.20504i | 0.798104 | + | 0.602520i | \(0.205837\pi\) | ||||
−0.798104 | + | 0.602520i | \(0.794163\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.48992e6 | −0.232045 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.06001e6 | −0.560430 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 423926.i | 0.0389051i | 0.999811 | + | 0.0194526i | \(0.00619233\pi\) | ||||
−0.999811 | + | 0.0194526i | \(0.993808\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 5.69141e6i | − 0.514406i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.64781e7 | −1.47807 | −0.739035 | − | 0.673668i | \(-0.764718\pi\) | ||||
−0.739035 | + | 0.673668i | \(0.764718\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.71556e7 | −1.52723 | −0.763613 | − | 0.645674i | \(-0.776577\pi\) | ||||
−0.763613 | + | 0.645674i | \(0.776577\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 2.14982e7i | − 1.89941i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 2.33592e7i | − 2.03303i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.16592e6 | 0.446254 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.10550e7 | 1.80530 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.24172e7i | 1.90785i | 0.300053 | + | 0.953923i | \(0.402996\pi\) | ||||
−0.300053 | + | 0.953923i | \(0.597004\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.63329e6i | 0.472379i | 0.971707 | + | 0.236190i | \(0.0758986\pi\) | ||||
−0.971707 | + | 0.236190i | \(0.924101\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.60704e7 | −1.33768 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.35134e7 | −1.94289 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 1.27876e6i | − 0.104891i | −0.998624 | − | 0.0524453i | \(-0.983298\pi\) | ||||
0.998624 | − | 0.0524453i | \(-0.0167015\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.07939e7i | 0.872539i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.23256e7 | 1.79166 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −712345. | −0.0567539 | −0.0283769 | − | 0.999597i | \(-0.509034\pi\) | ||||
−0.0283769 | + | 0.999597i | \(0.509034\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 5.24628e6i | − 0.414972i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.54127e6i | 0.587980i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.21676e7 | −0.941915 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.89586e6 | 0.606882 | 0.303441 | − | 0.952850i | \(-0.401864\pi\) | ||||
0.303441 | + | 0.952850i | \(0.401864\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 550091.i | − 0.0419804i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.74087e6i | 0.281464i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 812363. | 0.0606924 | 0.0303462 | − | 0.999539i | \(-0.490339\pi\) | ||||
0.0303462 | + | 0.999539i | \(0.490339\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.89719e6 | −0.214933 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.94258e6i | 0.732446i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 1.22681e7i | − 0.891212i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.46975e7 | 1.06028 | 0.530142 | − | 0.847909i | \(-0.322139\pi\) | ||||
0.530142 | + | 0.847909i | \(0.322139\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.71565e7 | −1.22911 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.54911e6i | 0.252507i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 946478.i | − 0.0664163i | −0.999448 | − | 0.0332081i | \(-0.989428\pi\) | ||||
0.999448 | − | 0.0332081i | \(-0.0105724\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −4.81105e6 | −0.335290 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.88903e6 | −0.269183 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.33370e6i | 0.160430i | 0.996778 | + | 0.0802150i | \(0.0255607\pi\) | ||||
−0.996778 | + | 0.0802150i | \(0.974439\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.73431e7i | 1.17614i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.17842e7 | −0.793757 | −0.396878 | − | 0.917871i | \(-0.629906\pi\) | ||||
−0.396878 | + | 0.917871i | \(0.629906\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.06243e6 | 0.0710813 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.02537e7i | 0.681413i | 0.940170 | + | 0.340706i | \(0.110666\pi\) | ||||
−0.940170 | + | 0.340706i | \(0.889334\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 1.10186e7i | − 0.722476i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.73058e6 | −0.112717 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.02684e7 | 1.31135 | 0.655676 | − | 0.755043i | \(-0.272384\pi\) | ||||
0.655676 | + | 0.755043i | \(0.272384\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 2.21696e7i | − 1.42486i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.54478e7i | 0.979776i | 0.871785 | + | 0.489888i | \(0.162962\pi\) | ||||
−0.871785 | + | 0.489888i | \(0.837038\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.99078e7 | −1.88443 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.68238e7 | −1.05308 | −0.526540 | − | 0.850150i | \(-0.676511\pi\) | ||||
−0.526540 | + | 0.850150i | \(0.676511\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.20352e6i | 0.0748414i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 4.30788e6i | − 0.264408i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.25563e7 | −1.37547 | −0.687737 | − | 0.725960i | \(-0.741396\pi\) | ||||
−0.687737 | + | 0.725960i | \(0.741396\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.13305e6 | 0.553325 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 5.87038e6i | − 0.353360i | −0.984268 | − | 0.176680i | \(-0.943464\pi\) | ||||
0.984268 | − | 0.176680i | \(-0.0565358\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 1.63294e7i | − 0.970329i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −372686. | −0.0220039 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.53212e6 | −0.324537 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.69126e7i | 0.985838i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.45154e6i | 0.141092i | 0.997509 | + | 0.0705459i | \(0.0224741\pi\) | ||||
−0.997509 | + | 0.0705459i | \(0.977526\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 9.89886e6 | 0.566099 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.99708e7 | 1.70317 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.64279e7i | 2.05708i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.18622e7i | 1.21913i | 0.792737 | + | 0.609564i | \(0.208655\pi\) | ||||
−0.792737 | + | 0.609564i | \(0.791345\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.74676e7 | 0.967980 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.57619e6 | 0.362154 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 2.54025e7i | − 1.39023i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 1.63772e7i | − 0.885231i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.66048e7 | −1.42919 | −0.714593 | − | 0.699541i | \(-0.753388\pi\) | ||||
−0.714593 | + | 0.699541i | \(0.753388\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.44067e7 | −0.769152 | −0.384576 | − | 0.923093i | \(-0.625652\pi\) | ||||
−0.384576 | + | 0.923093i | \(0.625652\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.42540e7i | 1.28694i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 192194.i | − 0.0100736i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 9.07674e6 | 0.472847 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.88597e6 | 0.0976508 | 0.0488254 | − | 0.998807i | \(-0.484452\pi\) | ||||
0.0488254 | + | 0.998807i | \(0.484452\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.52832e7i | 0.786530i | 0.919425 | + | 0.393265i | \(0.128654\pi\) | ||||
−0.919425 | + | 0.393265i | \(0.871346\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.78935e6i | 0.141821i | 0.997483 | + | 0.0709103i | \(0.0225904\pi\) | ||||
−0.997483 | + | 0.0709103i | \(0.977410\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.87077e6 | 0.0945440 | 0.0472720 | − | 0.998882i | \(-0.484947\pi\) | ||||
0.0472720 | + | 0.998882i | \(0.484947\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.23641e6 | −0.162578 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.98934e6i | 0.149267i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 7.19866e6i | − 0.355171i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.01293e6 | 0.0987244 | 0.0493622 | − | 0.998781i | \(-0.484281\pi\) | ||||
0.0493622 | + | 0.998781i | \(0.484281\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.94703e7 | 0.949255 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.29527e7i | 1.59706i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 3.78381e6i | − 0.181226i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.66618e7 | 1.74560 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.67915e7 | −1.26816 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.09443e7i | 0.515008i | 0.966277 | + | 0.257504i | \(0.0829000\pi\) | ||||
−0.966277 | + | 0.257504i | \(0.917100\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.17692e7i | 1.01249i | 0.862390 | + | 0.506245i | \(0.168967\pi\) | ||||
−0.862390 | + | 0.506245i | \(0.831033\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.86741e6 | 0.317549 | 0.158774 | − | 0.987315i | \(-0.449246\pi\) | ||||
0.158774 | + | 0.987315i | \(0.449246\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.10632e7 | −0.508595 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 1.75635e7i | − 0.802755i | −0.915913 | − | 0.401378i | \(-0.868532\pi\) | ||||
0.915913 | − | 0.401378i | \(-0.131468\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.72880e7i | 0.781080i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.29311e7 | −0.580878 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.00058e7 | −1.34017 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.29456e7i | 0.574893i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.95517e6i | 0.129743i | 0.997894 | + | 0.0648715i | \(0.0206638\pi\) | ||||
−0.997894 | + | 0.0648715i | \(0.979336\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.50975e7 | 1.96870 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.53773e7 | 1.53562 | 0.767811 | − | 0.640676i | \(-0.221346\pi\) | ||||
0.767811 | + | 0.640676i | \(0.221346\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.26106e7i | 0.975912i | 0.872868 | + | 0.487956i | \(0.162257\pi\) | ||||
−0.872868 | + | 0.487956i | \(0.837743\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 8.57410e6i | 0.365914i | 0.983121 | + | 0.182957i | \(0.0585670\pi\) | ||||
−0.983121 | + | 0.182957i | \(0.941433\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.07763e7 | −0.457314 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.21122e7 | 1.35511 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 863241.i | 0.0362246i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 5.17444e7i | − 2.14725i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.70177e7 | −0.702265 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.51896e7 | −1.85450 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 5.70528e6i | − 0.232840i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 1.76363e7i | − 0.711852i | −0.934514 | − | 0.355926i | \(-0.884166\pi\) | ||||
0.934514 | − | 0.355926i | \(-0.115834\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.01349e6 | 0.120965 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.48438e7 | −0.592585 | −0.296292 | − | 0.955097i | \(-0.595750\pi\) | ||||
−0.296292 | + | 0.955097i | \(0.595750\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 4.91792e7i | − 1.95256i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.34365e7i | 1.31310i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 448602. | 0.0175215 | 0.00876077 | − | 0.999962i | \(-0.497211\pi\) | ||||
0.00876077 | + | 0.999962i | \(0.497211\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.69071e7 | 1.82217 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 9.57129e6i | − 0.369799i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.38206e7i | 0.528235i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.11976e6 | −0.0805836 | −0.0402918 | − | 0.999188i | \(-0.512829\pi\) | ||||
−0.0402918 | + | 0.999188i | \(0.512829\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −147732. | −0.00558598 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 3.44647e7i | − 1.29619i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 5.54945e6i | − 0.206491i | −0.994656 | − | 0.103245i | \(-0.967077\pi\) | ||||
0.994656 | − | 0.103245i | \(-0.0329227\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.01680e7 | 1.48667 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.00433e6 | 0.221050 | 0.110525 | − | 0.993873i | \(-0.464747\pi\) | ||||
0.110525 | + | 0.993873i | \(0.464747\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.81512e7i | 0.664701i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.19597e7i | 0.433357i | 0.976243 | + | 0.216679i | \(0.0695224\pi\) | ||||
−0.976243 | + | 0.216679i | \(0.930478\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.39496e7 | 1.58413 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.74156e7 | 0.982982 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 2.84885e7i | − 1.01610i | −0.861327 | − | 0.508051i | \(-0.830366\pi\) | ||||
0.861327 | − | 0.508051i | \(-0.169634\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 5.11901e7i | − 1.80678i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.76891e7 | 1.32333 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.13858e7 | −0.746993 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.39409e6i | 0.0484422i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 2.44173e6i | − 0.0839714i | −0.999118 | − | 0.0419857i | \(-0.986632\pi\) | ||||
0.999118 | − | 0.0419857i | \(-0.0133684\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.15048e6 | −0.0735744 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.63888e7 | 0.898198 | 0.449099 | − | 0.893482i | \(-0.351745\pi\) | ||||
0.449099 | + | 0.893482i | \(0.351745\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 4.64898e7i | − 1.57426i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6.67324e6i | 0.223666i | 0.993727 | + | 0.111833i | \(0.0356722\pi\) | ||||
−0.993727 | + | 0.111833i | \(0.964328\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.93516e7 | 0.978756 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 969506. | 0.0321646 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 1.21646e7i | − 0.401528i | −0.979640 | − | 0.200764i | \(-0.935658\pi\) | ||||
0.979640 | − | 0.200764i | \(-0.0643424\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.56253e7i | 0.837289i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.36057e6 | −0.304307 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.16204e7 | −0.375869 | −0.187935 | − | 0.982182i | \(-0.560179\pi\) | ||||
−0.187935 | + | 0.982182i | \(0.560179\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 3.74750e7i | − 1.20606i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.61789e7i | 1.47132i | 0.677354 | + | 0.735658i | \(0.263127\pi\) | ||||
−0.677354 | + | 0.735658i | \(0.736873\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.93977e7 | 0.614944 |
(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 | 800.6.c.j.449.2 | 6 | ||
4.3 | odd | 2 | 800.6.c.k.449.5 | 6 | |||
5.2 | odd | 4 | 160.6.a.g.1.1 | yes | 3 | ||
5.3 | odd | 4 | 800.6.a.n.1.3 | 3 | |||
5.4 | even | 2 | inner | 800.6.c.j.449.5 | 6 | ||
20.3 | even | 4 | 800.6.a.o.1.1 | 3 | |||
20.7 | even | 4 | 160.6.a.f.1.3 | ✓ | 3 | ||
20.19 | odd | 2 | 800.6.c.k.449.2 | 6 | |||
40.27 | even | 4 | 320.6.a.y.1.1 | 3 | |||
40.37 | odd | 4 | 320.6.a.x.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
160.6.a.f.1.3 | ✓ | 3 | 20.7 | even | 4 | ||
160.6.a.g.1.1 | yes | 3 | 5.2 | odd | 4 | ||
320.6.a.x.1.3 | 3 | 40.37 | odd | 4 | |||
320.6.a.y.1.1 | 3 | 40.27 | even | 4 | |||
800.6.a.n.1.3 | 3 | 5.3 | odd | 4 | |||
800.6.a.o.1.1 | 3 | 20.3 | even | 4 | |||
800.6.c.j.449.2 | 6 | 1.1 | even | 1 | trivial | ||
800.6.c.j.449.5 | 6 | 5.4 | even | 2 | inner | ||
800.6.c.k.449.2 | 6 | 20.19 | odd | 2 | |||
800.6.c.k.449.5 | 6 | 4.3 | odd | 2 |