Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,5,Mod(97,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.97");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.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: | \(81.0420510577\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 66x^{6} + 212x^{5} + 2021x^{4} - 4400x^{3} - 25028x^{2} + 27264x + 127778 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2\cdot 7^{6} \) |
Twist minimal: | no (minimal twist has level 49) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 97.1 | ||
Root | \(3.71722 + 0.765367i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 784.97 |
Dual form | 784.5.c.g.97.8 |
$q$-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 \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(687\) | \(689\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − 16.1337i | − 1.79264i | −0.443409 | − | 0.896319i | \(-0.646231\pi\) | ||||
0.443409 | − | 0.896319i | \(-0.353769\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 7.83726i | − 0.313490i | −0.987639 | − | 0.156745i | \(-0.949900\pi\) | ||||
0.987639 | − | 0.156745i | \(-0.0501001\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −179.298 | −2.21355 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −30.5126 | −0.252170 | −0.126085 | − | 0.992019i | \(-0.540241\pi\) | ||||
−0.126085 | + | 0.992019i | \(0.540241\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 162.301i | 0.960361i | 0.877170 | + | 0.480181i | \(0.159429\pi\) | ||||
−0.877170 | + | 0.480181i | \(0.840571\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −126.444 | −0.561975 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 345.619i | 1.19591i | 0.801528 | + | 0.597957i | \(0.204021\pi\) | ||||
−0.801528 | + | 0.597957i | \(0.795979\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 263.892i | − 0.731002i | −0.930811 | − | 0.365501i | \(-0.880898\pi\) | ||||
0.930811 | − | 0.365501i | \(-0.119102\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −213.179 | −0.402985 | −0.201492 | − | 0.979490i | \(-0.564579\pi\) | ||||
−0.201492 | + | 0.979490i | \(0.564579\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 563.577 | 0.901724 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1585.91i | 2.17546i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1011.68 | −1.20295 | −0.601474 | − | 0.798893i | \(-0.705419\pi\) | ||||
−0.601474 | + | 0.798893i | \(0.705419\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 273.802i | 0.284914i | 0.989801 | + | 0.142457i | \(0.0455002\pi\) | ||||
−0.989801 | + | 0.142457i | \(0.954500\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 492.283i | 0.452050i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1546.00 | 1.12929 | 0.564646 | − | 0.825333i | \(-0.309013\pi\) | ||||
0.564646 | + | 0.825333i | \(0.309013\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2618.52 | 1.72158 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 531.628i | 0.316257i | 0.987419 | + | 0.158128i | \(0.0505460\pi\) | ||||
−0.987419 | + | 0.158128i | \(0.949454\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1470.93 | 0.795526 | 0.397763 | − | 0.917488i | \(-0.369787\pi\) | ||||
0.397763 | + | 0.917488i | \(0.369787\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1405.20i | 0.693928i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2383.59i | 1.07903i | 0.841975 | + | 0.539517i | \(0.181393\pi\) | ||||
−0.841975 | + | 0.539517i | \(0.818607\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5576.13 | 2.14384 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3206.62 | 1.14155 | 0.570777 | − | 0.821105i | \(-0.306642\pi\) | ||||
0.570777 | + | 0.821105i | \(0.306642\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 239.135i | 0.0790530i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4257.56 | −1.31042 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 3118.51i | − 0.895865i | −0.894067 | − | 0.447932i | \(-0.852160\pi\) | ||||
0.894067 | − | 0.447932i | \(-0.147840\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3944.63i | 1.06010i | 0.847966 | + | 0.530050i | \(0.177827\pi\) | ||||
−0.847966 | + | 0.530050i | \(0.822173\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1272.00 | 0.301064 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6919.27 | 1.54138 | 0.770692 | − | 0.637208i | \(-0.219911\pi\) | ||||
0.770692 | + | 0.637208i | \(0.219911\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3439.38i | 0.722406i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8580.05 | −1.70205 | −0.851027 | − | 0.525122i | \(-0.824020\pi\) | ||||
−0.851027 | + | 0.525122i | \(0.824020\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 359.285i | 0.0674207i | 0.999432 | + | 0.0337104i | \(0.0107324\pi\) | ||||
−0.999432 | + | 0.0337104i | \(0.989268\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 9092.62i | − 1.61647i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2087.16 | −0.334427 | −0.167214 | − | 0.985921i | \(-0.553477\pi\) | ||||
−0.167214 | + | 0.985921i | \(0.553477\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 11063.6 | 1.68627 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10594.2i | 1.53784i | 0.639344 | + | 0.768921i | \(0.279206\pi\) | ||||
−0.639344 | + | 0.768921i | \(0.720794\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2708.71 | 0.374908 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 16322.2i | 2.15645i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 10431.1i | − 1.31689i | −0.752628 | − | 0.658446i | \(-0.771214\pi\) | ||||
0.752628 | − | 0.658446i | \(-0.228786\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4417.46 | 0.510748 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2068.19 | −0.229162 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1403.85i | 0.149203i | 0.997213 | + | 0.0746016i | \(0.0237685\pi\) | ||||
−0.997213 | + | 0.0746016i | \(0.976231\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5470.85 | 0.558193 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14051.5i | 1.37747i | 0.725014 | + | 0.688734i | \(0.241833\pi\) | ||||
−0.725014 | + | 0.688734i | \(0.758167\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1748.62i | 0.164824i | 0.996598 | + | 0.0824121i | \(0.0262624\pi\) | ||||
−0.996598 | + | 0.0824121i | \(0.973738\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8463.37 | −0.739224 | −0.369612 | − | 0.929186i | \(-0.620509\pi\) | ||||
−0.369612 | + | 0.929186i | \(0.620509\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10952.5 | −0.921852 | −0.460926 | − | 0.887439i | \(-0.652483\pi\) | ||||
−0.460926 | + | 0.887439i | \(0.652483\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 24942.8i | − 2.02441i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5884.58 | 0.460849 | 0.230424 | − | 0.973090i | \(-0.425989\pi\) | ||||
0.230424 | + | 0.973090i | \(0.425989\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1670.74i | 0.126332i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 29100.2i | − 2.12581i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −13710.0 | −0.936410 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8577.15 | 0.566934 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 9315.19i | − 0.596172i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8451.12 | 0.523971 | 0.261985 | − | 0.965072i | \(-0.415623\pi\) | ||||
0.261985 | + | 0.965072i | \(0.415623\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − 23731.6i | − 1.42609i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 801.065i | 0.0466794i | 0.999728 | + | 0.0233397i | \(0.00742993\pi\) | ||||
−0.999728 | + | 0.0233397i | \(0.992570\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 12429.2 | 0.681987 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 22808.9 | 1.21524 | 0.607621 | − | 0.794227i | \(-0.292124\pi\) | ||||
0.607621 | + | 0.794227i | \(0.292124\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 32895.2i | − 1.70256i | −0.524709 | − | 0.851281i | \(-0.675826\pi\) | ||||
0.524709 | − | 0.851281i | \(-0.324174\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 38456.2 | 1.93432 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 4952.23i | − 0.242175i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7928.79i | 0.377112i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 29961.9 | 1.34957 | 0.674786 | − | 0.738013i | \(-0.264236\pi\) | ||||
0.674786 | + | 0.738013i | \(0.264236\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4517.62 | 0.198132 | 0.0990662 | − | 0.995081i | \(-0.468414\pi\) | ||||
0.0990662 | + | 0.995081i | \(0.468414\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 61968.8i | − 2.64722i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2145.86 | 0.0893178 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 31715.2i | 1.28667i | 0.765583 | + | 0.643337i | \(0.222450\pi\) | ||||
−0.765583 | + | 0.643337i | \(0.777550\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − 51734.9i | − 2.04639i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13505.2 | −0.508306 | −0.254153 | − | 0.967164i | \(-0.581797\pi\) | ||||
−0.254153 | + | 0.967164i | \(0.581797\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3858.15 | 0.141713 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 24965.3i | − 0.895168i | −0.894242 | − | 0.447584i | \(-0.852285\pi\) | ||||
0.894242 | − | 0.447584i | \(-0.147715\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2219.36 | 0.0777060 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 47315.2i | 1.61811i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 25428.2i | 0.849618i | 0.905283 | + | 0.424809i | \(0.139659\pi\) | ||||
−0.905283 | + | 0.424809i | \(0.860341\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −50313.2 | −1.60596 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3612.57 | 0.112748 | 0.0563742 | − | 0.998410i | \(-0.482046\pi\) | ||||
0.0563742 | + | 0.998410i | \(0.482046\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 15458.2i | − 0.471847i | −0.971772 | − | 0.235923i | \(-0.924189\pi\) | ||||
0.971772 | − | 0.235923i | \(-0.0758114\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 63641.8 | 1.90038 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 12116.4i | − 0.354022i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 10545.7i | − 0.301574i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13375.6 | −0.366646 | −0.183323 | − | 0.983053i | \(-0.558685\pi\) | ||||
−0.183323 | + | 0.983053i | \(0.558685\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13763.6 | 0.369501 | 0.184751 | − | 0.982785i | \(-0.440852\pi\) | ||||
0.184751 | + | 0.982785i | \(0.440852\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 20522.1i | − 0.539699i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 25150.4 | 0.648057 | 0.324028 | − | 0.946047i | \(-0.394963\pi\) | ||||
0.324028 | + | 0.946047i | \(0.394963\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 42790.6i | − 1.08054i | −0.841491 | − | 0.540271i | \(-0.818322\pi\) | ||||
0.841491 | − | 0.540271i | \(-0.181678\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − 111634.i | − 2.76314i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4166.50 | 0.0991435 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 38222.5 | 0.892028 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8052.02i | 0.184337i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3516.62 | 0.0789879 | 0.0394940 | − | 0.999220i | \(-0.487425\pi\) | ||||
0.0394940 | + | 0.999220i | \(0.487425\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 138428.i | 3.05117i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 11528.0i | − 0.249390i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5796.61 | 0.120861 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −56094.4 | −1.14851 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 67281.8i | 1.35297i | 0.736457 | + | 0.676485i | \(0.236497\pi\) | ||||
−0.736457 | + | 0.676485i | \(0.763503\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −101048. | −1.99601 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 74331.3i | 1.44251i | 0.692667 | + | 0.721257i | \(0.256435\pi\) | ||||
−0.692667 | + | 0.721257i | \(0.743565\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 27965.0i | − 0.533266i | −0.963798 | − | 0.266633i | \(-0.914089\pi\) | ||||
0.963798 | − | 0.266633i | \(-0.0859112\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −39880.8 | −0.734602 | −0.367301 | − | 0.930102i | \(-0.619718\pi\) | ||||
−0.367301 | + | 0.930102i | \(0.619718\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 18680.8 | 0.338267 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 33673.7i | 0.599508i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 29726.5 | 0.520413 | 0.260206 | − | 0.965553i | \(-0.416209\pi\) | ||||
0.260206 | + | 0.965553i | \(0.416209\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 62828.5i | − 1.08174i | −0.841106 | − | 0.540870i | \(-0.818095\pi\) | ||||
0.841106 | − | 0.540870i | \(-0.181905\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 50038.4i | − 0.847405i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 42829.9 | 0.702026 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 170924. | 2.75679 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 62181.9i | 0.986999i | 0.869746 | + | 0.493499i | \(0.164282\pi\) | ||||
−0.869746 | + | 0.493499i | \(0.835718\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6504.64 | 0.101621 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − 43701.6i | − 0.672074i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 114684.i | 1.73634i | 0.496264 | + | 0.868172i | \(0.334705\pi\) | ||||
−0.496264 | + | 0.868172i | \(0.665295\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 181392. | 2.66279 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 83591.6 | 1.20851 | 0.604256 | − | 0.796790i | \(-0.293470\pi\) | ||||
0.604256 | + | 0.796790i | \(0.293470\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − 25131.1i | − 0.357866i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −168293. | −2.36071 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 6858.72i | − 0.0947848i | −0.998876 | − | 0.0473924i | \(-0.984909\pi\) | ||||
0.998876 | − | 0.0473924i | \(-0.0150911\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 50356.0i | 0.685666i | 0.939396 | + | 0.342833i | \(0.111387\pi\) | ||||
−0.939396 | + | 0.342833i | \(0.888613\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −17196.2 | −0.227388 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 84305.6 | 1.09875 | 0.549373 | − | 0.835577i | \(-0.314867\pi\) | ||||
0.549373 | + | 0.835577i | \(0.314867\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − 49092.2i | − 0.630672i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9852.07 | 0.124771 | 0.0623857 | − | 0.998052i | \(-0.480129\pi\) | ||||
0.0623857 | + | 0.998052i | \(0.480129\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 31733.2i | − 0.396225i | −0.980179 | − | 0.198112i | \(-0.936519\pi\) | ||||
0.980179 | − | 0.198112i | \(-0.0634811\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 33367.6i | 0.410805i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −35931.6 | −0.430211 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 22649.4 | 0.267468 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 17750.9i | 0.206769i | 0.994641 | + | 0.103384i | \(0.0329672\pi\) | ||||
−0.994641 | + | 0.103384i | \(0.967033\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −24440.5 | −0.280845 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 48390.3i | − 0.548587i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 34599.2i | − 0.387011i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 226704. | 2.46930 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 30915.1 | 0.332331 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5360.84i | 0.0568795i | 0.999596 | + | 0.0284398i | \(0.00905388\pi\) | ||||
−0.999596 | + | 0.0284398i | \(0.990946\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 28211.8 | 0.295470 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 138382.i | 1.43073i | 0.698751 | + | 0.715365i | \(0.253740\pi\) | ||||
−0.698751 | + | 0.715365i | \(0.746260\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 45760.7i | − 0.467094i | −0.972346 | − | 0.233547i | \(-0.924967\pi\) | ||||
0.972346 | − | 0.233547i | \(-0.0750333\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 39438.7 | 0.392468 | 0.196234 | − | 0.980557i | \(-0.437129\pi\) | ||||
0.196234 | + | 0.980557i | \(0.437129\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 30868.9 | 0.303348 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 136546.i | 1.32516i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 91206.0 | 0.874215 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 91469.2i | 0.865981i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 176705.i | 1.65255i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −39807.2 | −0.363333 | −0.181667 | − | 0.983360i | \(-0.558149\pi\) | ||||
−0.181667 | + | 0.983360i | \(0.558149\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −277195. | −2.49975 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 54228.1i | − 0.483209i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −71094.3 | −0.626001 | −0.313001 | − | 0.949753i | \(-0.601334\pi\) | ||||
−0.313001 | + | 0.949753i | \(0.601334\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 94940.3i | − 0.826136i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 8354.42i | − 0.0718468i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 26955.3 | 0.226467 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −66258.0 | −0.550275 | −0.275137 | − | 0.961405i | \(-0.588723\pi\) | ||||
−0.275137 | + | 0.961405i | \(0.588723\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 225684.i | 1.85289i | 0.376429 | + | 0.926445i | \(0.377152\pi\) | ||||
−0.376429 | + | 0.926445i | \(0.622848\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −257395. | −2.08923 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 132999.i | − 1.06733i | −0.845697 | − | 0.533664i | \(-0.820815\pi\) | ||||
0.845697 | − | 0.533664i | \(-0.179185\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 67244.1i | 0.533578i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −232730. | −1.80578 | −0.902888 | − | 0.429875i | \(-0.858557\pi\) | ||||
−0.902888 | + | 0.429875i | \(0.858557\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 60682.2 | 0.465636 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 221193.i | 1.67865i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2815.81 | 0.0211357 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 108571.i | 0.806084i | 0.915181 | + | 0.403042i | \(0.132047\pi\) | ||||
−0.915181 | + | 0.403042i | \(0.867953\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − 95319.7i | − 0.700052i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −169883. | −1.22105 | −0.610523 | − | 0.791999i | \(-0.709041\pi\) | ||||
−0.610523 | + | 0.791999i | \(0.709041\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −150289. | −1.06872 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 164197.i | − 1.15526i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 224839. | 1.56528 | 0.782641 | − | 0.622474i | \(-0.213872\pi\) | ||||
0.782641 | + | 0.622474i | \(0.213872\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 136348.i | − 0.939290i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 24577.7i | 0.167550i | 0.996485 | + | 0.0837750i | \(0.0266977\pi\) | ||||
−0.996485 | + | 0.0837750i | \(0.973302\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −263734. | −1.76094 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 144136. | 0.952520 | 0.476260 | − | 0.879305i | \(-0.341992\pi\) | ||||
0.476260 | + | 0.879305i | \(0.341992\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 73678.7i | − 0.481935i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12924.2 | 0.0836793 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 16357.6i | 0.104840i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 153247.i | 0.972327i | 0.873868 | + | 0.486164i | \(0.161604\pi\) | ||||
−0.873868 | + | 0.486164i | \(0.838396\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −45426.3 | −0.282500 | −0.141250 | − | 0.989974i | \(-0.545112\pi\) | ||||
−0.141250 | + | 0.989974i | \(0.545112\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −44438.4 | −0.273620 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 86708.3i | − 0.528629i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −47172.5 | −0.284774 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10421.7i | 0.0623003i | 0.999515 | + | 0.0311502i | \(0.00991701\pi\) | ||||
−0.999515 | + | 0.0311502i | \(0.990083\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 367993.i | − 2.17849i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 83029.4 | 0.482099 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −530723. | −3.05208 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 148730.i | 0.847167i | 0.905857 | + | 0.423584i | \(0.139228\pi\) | ||||
−0.905857 | + | 0.423584i | \(0.860772\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 238275. | 1.34436 | 0.672178 | − | 0.740389i | \(-0.265359\pi\) | ||||
0.672178 | + | 0.740389i | \(0.265359\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 427372.i | − 2.38850i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 194783.i | 1.07838i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −79898.0 | −0.434132 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −280105. | −1.50788 | −0.753938 | − | 0.656945i | \(-0.771848\pi\) | ||||
−0.753938 | + | 0.656945i | \(0.771848\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 78101.0i | − 0.416563i | −0.978069 | − | 0.208281i | \(-0.933213\pi\) | ||||
0.978069 | − | 0.208281i | \(-0.0667870\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 127921. | 0.676026 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 56256.1i | 0.294583i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 310618.i | 1.61175i | 0.592087 | + | 0.805874i | \(0.298304\pi\) | ||||
−0.592087 | + | 0.805874i | \(0.701696\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5382.84 | 0.0274286 | 0.0137143 | − | 0.999906i | \(-0.495634\pi\) | ||||
0.0137143 | + | 0.999906i | \(0.495634\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −81751.3 | −0.412833 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 483397.i | − 2.41930i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 167992. | 0.833292 | 0.416646 | − | 0.909069i | \(-0.363206\pi\) | ||||
0.416646 | + | 0.909069i | \(0.363206\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 16221.3i | − 0.0797506i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 72886.1i | − 0.355180i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −195647. | −0.936787 | −0.468394 | − | 0.883520i | \(-0.655167\pi\) | ||||
−0.468394 | + | 0.883520i | \(0.655167\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −548122. | −2.60167 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 355715.i | − 1.67379i | −0.547365 | − | 0.836894i | \(-0.684369\pi\) | ||||
0.547365 | − | 0.836894i | \(-0.315631\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 103798. | 0.484205 | 0.242102 | − | 0.970251i | \(-0.422163\pi\) | ||||
0.242102 | + | 0.970251i | \(0.422163\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − 34620.8i | − 0.160114i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 294112.i | 1.34859i | 0.738463 | + | 0.674295i | \(0.235552\pi\) | ||||
−0.738463 | + | 0.674295i | \(0.764448\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 511685. | 2.30654 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −44881.8 | −0.200608 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 148723.i | − 0.659162i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −574941. | −2.52689 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 367747.i | − 1.60279i | −0.598133 | − | 0.801397i | \(-0.704091\pi\) | ||||
0.598133 | − | 0.801397i | \(-0.295909\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 250918.i | 1.08453i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 11002.4 | 0.0467738 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 342314. | 1.44333 | 0.721667 | − | 0.692240i | \(-0.243376\pi\) | ||||
0.721667 | + | 0.692240i | \(0.243376\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 217889.i | 0.911209i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −41579.7 | −0.172472 | −0.0862360 | − | 0.996275i | \(-0.527484\pi\) | ||||
−0.0862360 | + | 0.996275i | \(0.527484\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 349655.i | − 1.43862i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − 42876.4i | − 0.174988i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −355975. | −1.42961 | −0.714807 | − | 0.699322i | \(-0.753485\pi\) | ||||
−0.714807 | + | 0.699322i | \(0.753485\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −402785. | −1.60471 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 196448.i | 0.776446i | 0.921566 | + | 0.388223i | \(0.126911\pi\) | ||||
−0.921566 | + | 0.388223i | \(0.873089\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 110126. | 0.431823 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 35806.6i | − 0.139299i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 133569.i | 0.515551i | 0.966205 | + | 0.257776i | \(0.0829895\pi\) | ||||
−0.966205 | + | 0.257776i | \(0.917010\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 418509. | 1.59027 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 13704.4 | 0.0516708 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 72729.4i | − 0.272100i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 410253. | 1.52306 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 359413.i | 1.32409i | 0.749463 | + | 0.662046i | \(0.230312\pi\) | ||||
−0.749463 | + | 0.662046i | \(0.769688\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 149926.i | − 0.548119i | −0.961713 | − | 0.274060i | \(-0.911633\pi\) | ||||
0.961713 | − | 0.274060i | \(-0.0883665\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −94631.3 | −0.340733 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −234396. | −0.837603 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 559142.i | 1.98305i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −86283.7 | −0.303721 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 66329.6i | 0.231739i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 58284.3i | − 0.202117i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −168242. | −0.574830 | −0.287415 | − | 0.957806i | \(-0.592796\pi\) | ||||
−0.287415 | + | 0.957806i | \(0.592796\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −249398. | −0.845851 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 85837.7i | 0.288992i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −297422. | −0.994027 | −0.497013 | − | 0.867743i | \(-0.665570\pi\) | ||||
−0.497013 | + | 0.867743i | \(0.665570\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 707265.i | − 2.34659i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 266974.i | 0.879357i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −195483. | −0.634634 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 451666. | 1.45582 | 0.727909 | − | 0.685674i | \(-0.240492\pi\) | ||||
0.727909 | + | 0.685674i | \(0.240492\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 238733.i | 0.763992i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −170142. | −0.540613 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 550994.i | 1.73832i | 0.494531 | + | 0.869160i | \(0.335340\pi\) | ||||
−0.494531 | + | 0.869160i | \(0.664660\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 46119.0i | − 0.144472i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 143742. | 0.443975 | 0.221988 | − | 0.975049i | \(-0.428746\pi\) | ||||
0.221988 | + | 0.975049i | \(0.428746\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −118245. | −0.362668 | −0.181334 | − | 0.983422i | \(-0.558042\pi\) | ||||
−0.181334 | + | 0.983422i | \(0.558042\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 215799.i | 0.657264i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −120143. | −0.363381 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 451941.i | 1.35747i | 0.734383 | + | 0.678735i | \(0.237471\pi\) | ||||
−0.734383 | + | 0.678735i | \(0.762529\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 222058.i | − 0.662383i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −97842.4 | −0.287866 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −228066. | −0.666422 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 59990.7i | − 0.174104i | −0.996204 | − | 0.0870518i | \(-0.972255\pi\) | ||||
0.996204 | − | 0.0870518i | \(-0.0277446\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 72254.1 | 0.208273 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − 405771.i | − 1.16173i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 77447.2i | 0.220240i | 0.993918 | + | 0.110120i | \(0.0351235\pi\) | ||||
−0.993918 | + | 0.110120i | \(0.964876\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −690372. | −1.93702 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 407051. | 1.13448 | 0.567238 | − | 0.823554i | \(-0.308012\pi\) | ||||
0.567238 | + | 0.823554i | \(0.308012\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 681741.i | 1.88743i | 0.330761 | + | 0.943715i | \(0.392695\pi\) | ||||
−0.330761 | + | 0.943715i | \(0.607305\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.24061e6 | −3.41193 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 107449.i | 0.293556i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 96785.6i | − 0.262684i | −0.991337 | − | 0.131342i | \(-0.958071\pi\) | ||||
0.991337 | − | 0.131342i | \(-0.0419286\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −386858. | −1.03626 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 478095. | 1.27231 | 0.636156 | − | 0.771561i | \(-0.280524\pi\) | ||||
0.636156 | + | 0.771561i | \(0.280524\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − 67221.3i | − 0.177728i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −55323.0 | −0.145323 | −0.0726617 | − | 0.997357i | \(-0.523149\pi\) | ||||
−0.0726617 | + | 0.997357i | \(0.523149\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 142719.i | − 0.372479i | −0.982504 | − | 0.186239i | \(-0.940370\pi\) | ||||
0.982504 | − | 0.186239i | \(-0.0596300\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 338083.i | − 0.876679i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 279230. | 0.714830 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 129909. | 0.330450 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 534328.i | 1.35054i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 667428. | 1.67628 | 0.838138 | − | 0.545459i | \(-0.183644\pi\) | ||||
0.838138 | + | 0.545459i | \(0.183644\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 56736.3i | − 0.141597i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 66233.6i | − 0.164260i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.53839e6 | 3.76759 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11099.0 | 0.0270127 | 0.0135063 | − | 0.999909i | \(-0.495701\pi\) | ||||
0.0135063 | + | 0.999909i | \(0.495701\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 136149.i | 0.329300i | 0.986352 | + | 0.164650i | \(0.0526494\pi\) | ||||
−0.986352 | + | 0.164650i | \(0.947351\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −185991. | −0.447066 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 110825.i | 0.264746i | 0.991200 | + | 0.132373i | \(0.0422597\pi\) | ||||
−0.991200 | + | 0.132373i | \(0.957740\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 95153.7i | 0.225911i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −88318.2 | −0.207121 | −0.103560 | − | 0.994623i | \(-0.533024\pi\) | ||||
−0.103560 | + | 0.994623i | \(0.533024\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6278.16 | 0.0146335 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 64419.0i | − 0.149239i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −136014. | −0.313194 | −0.156597 | − | 0.987663i | \(-0.550052\pi\) | ||||
−0.156597 | + | 0.987663i | \(0.550052\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 138133.i | − 0.316150i | −0.987427 | − | 0.158075i | \(-0.949471\pi\) | ||||
0.987427 | − | 0.158075i | \(-0.0505288\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 905012.i | 2.05886i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 215669. | 0.484769 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.08551e6 | 2.42539 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 120361.i | − 0.267326i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 752500. | 1.66141 | 0.830704 | − | 0.556714i | \(-0.187938\pi\) | ||||
0.830704 | + | 0.556714i | \(0.187938\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 893785.i | 1.96167i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 774498.i | 1.68983i | 0.534901 | + | 0.844914i | \(0.320349\pi\) | ||||
−0.534901 | + | 0.844914i | \(0.679651\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.19924e6 | 2.58591 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 330088. | 0.707600 | 0.353800 | − | 0.935321i | \(-0.384889\pi\) | ||||
0.353800 | + | 0.935321i | \(0.384889\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 178759.i | − 0.380967i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −451181. | −0.955954 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 520438.i | 1.09630i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 705962.i | 1.47851i | 0.673424 | + | 0.739257i | \(0.264823\pi\) | ||||
−0.673424 | + | 0.739257i | \(0.735177\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −257808. | −0.533737 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −183741. | −0.378216 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 643427.i | 1.31688i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −387191. | −0.787933 | −0.393966 | − | 0.919125i | \(-0.628897\pi\) | ||||
−0.393966 | + | 0.919125i | \(0.628897\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 407977.i | − 0.825515i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − 301391.i | − 0.606390i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 650735. | 1.29453 | 0.647264 | − | 0.762266i | \(-0.275913\pi\) | ||||
0.647264 | + | 0.762266i | \(0.275913\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 374224. | 0.740273 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 58368.9i | − 0.114816i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −38811.9 | −0.0759194 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 479600.i | − 0.932912i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 84700.1i | − 0.163842i | −0.996639 | − | 0.0819212i | \(-0.973894\pi\) | ||||
0.996639 | − | 0.0819212i | \(-0.0261056\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.01366e6 | −1.93917 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −570159. | −1.08473 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 602305.i | − 1.13959i | −0.821788 | − | 0.569794i | \(-0.807023\pi\) | ||||
0.821788 | − | 0.569794i | \(-0.192977\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 88844.8 | 0.167177 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 508381.i | 0.951381i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 471815.i | − 0.878140i | −0.898453 | − | 0.439070i | \(-0.855308\pi\) | ||||
0.898453 | − | 0.439070i | \(-0.144692\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −211125. | −0.388691 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 328102. | 0.600786 | 0.300393 | − | 0.953815i | \(-0.402882\pi\) | ||||
0.300393 | + | 0.953815i | \(0.402882\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 691007.i | − 1.25848i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 237585. | 0.430370 | 0.215185 | − | 0.976573i | \(-0.430965\pi\) | ||||
0.215185 | + | 0.976573i | \(0.430965\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − 234819.i | − 0.423078i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 1.89952e6i | − 3.40410i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 364285. | 0.645894 | 0.322947 | − | 0.946417i | \(-0.395326\pi\) | ||||
0.322947 | + | 0.946417i | \(0.395326\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.00323e6 | 1.76933 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 35405.7i | − 0.0621126i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −590661. | −1.03073 | −0.515367 | − | 0.856969i | \(-0.672345\pi\) | ||||
−0.515367 | + | 0.856969i | \(0.672345\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − 104944.i | − 0.182169i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 272715.i | 0.470912i | 0.971885 | + | 0.235456i | \(0.0756584\pi\) | ||||
−0.971885 | + | 0.235456i | \(0.924342\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −485665. | −0.829878 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 506137. | 0.860354 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − 725929.i | − 1.22756i | −0.789478 | − | 0.613778i | \(-0.789649\pi\) | ||||
0.789478 | − | 0.613778i | \(-0.210351\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.85028e6 | 3.11264 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 392620.i | − 0.657073i | −0.944491 | − | 0.328536i | \(-0.893445\pi\) | ||||
0.944491 | − | 0.328536i | \(-0.106555\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 154309.i | 0.256914i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 140292. | 0.231184 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 261800. | 0.429207 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 1.60443e6i | − 2.61697i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 248560. | 0.403360 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 324279.i | − 0.523563i | −0.965127 | − | 0.261782i | \(-0.915690\pi\) | ||||
0.965127 | − | 0.261782i | \(-0.0843100\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 1.34865e6i | − 2.16643i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −640218. | −1.01808 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −405459. | −0.641524 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 179577.i | − 0.282706i | −0.989959 | − | 0.141353i | \(-0.954855\pi\) | ||||
0.989959 | − | 0.141353i | \(-0.0451453\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −823813. | −1.29043 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.87027e6i | 2.91501i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 10962.7i | − 0.0170015i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −110657. | −0.169915 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −982618. | −1.50137 | −0.750685 | − | 0.660660i | \(-0.770276\pi\) | ||||
−0.750685 | + | 0.660660i | \(0.770276\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 994497.i | 1.51203i | 0.654552 | + | 0.756017i | \(0.272857\pi\) | ||||
−0.654552 | + | 0.756017i | \(0.727143\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 812431. | 1.22915 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 105844.i | 0.159349i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 388166.i | − 0.581531i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.02275e6 | −1.51734 | −0.758668 | − | 0.651477i | \(-0.774150\pi\) | ||||
−0.758668 | + | 0.651477i | \(0.774150\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −317711. | −0.469065 | −0.234532 | − | 0.972108i | \(-0.575356\pi\) | ||||
−0.234532 | + | 0.972108i | \(0.575356\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 277439.i | 0.407624i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 50540.8 | 0.0738977 | 0.0369489 | − | 0.999317i | \(-0.488236\pi\) | ||||
0.0369489 | + | 0.999317i | \(0.488236\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.07529e6i | 1.56465i | 0.622868 | + | 0.782327i | \(0.285967\pi\) | ||||
−0.622868 | + | 0.782327i | \(0.714033\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − 1.36017e6i | − 1.96965i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −195660. | −0.280627 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −434227. | −0.619820 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 966211.i | − 1.37261i | −0.727312 | − | 0.686307i | \(-0.759231\pi\) | ||||
0.727312 | − | 0.686307i | \(-0.240769\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 316212. | 0.447082 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 158951.i | − 0.223670i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 17393.7i | − 0.0243601i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −511976. | −0.710288 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −329575. | −0.455088 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 395709.i | 0.543848i | 0.962319 | + | 0.271924i | \(0.0876600\pi\) | ||||
−0.962319 | + | 0.271924i | \(0.912340\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 370822. | 0.507263 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 787067.i | − 1.07164i | −0.844331 | − | 0.535822i | \(-0.820002\pi\) | ||||
0.844331 | − | 0.535822i | \(-0.179998\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 1.32116e6i | − 1.79047i | −0.445592 | − | 0.895236i | \(-0.647007\pi\) | ||||
0.445592 | − | 0.895236i | \(-0.352993\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 648112. | 0.870219 | 0.435110 | − | 0.900377i | \(-0.356710\pi\) | ||||
0.435110 | + | 0.900377i | \(0.356710\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 199288. | 0.266347 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 579712.i | 0.771212i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 63684.7 | 0.0843327 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.12300e6i | 1.48028i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 251708.i | − 0.330270i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 35839.1 | 0.0465969 | 0.0232985 | − | 0.999729i | \(-0.492583\pi\) | ||||
0.0232985 | + | 0.999729i | \(0.492583\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 286389. | 0.370662 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 830960.i | − 1.07060i | −0.844661 | − | 0.535302i | \(-0.820198\pi\) | ||||
0.844661 | − | 0.535302i | \(-0.179802\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.54585e6 | 1.98265 | 0.991327 | − | 0.131415i | \(-0.0419522\pi\) | ||||
0.991327 | + | 0.131415i | \(0.0419522\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 394318.i | 0.503454i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 853705.i | 1.08508i | 0.840031 | + | 0.542539i | \(0.182537\pi\) | ||||
−0.840031 | + | 0.542539i | \(0.817463\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −337579. | −0.425227 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 629008. | 0.788776 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 28312.7i | − 0.0353455i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −558214. | −0.693771 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 277000.i | − 0.342736i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.10827e6i | 1.36520i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −121150. | −0.147919 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −194393. | −0.236302 | −0.118151 | − | 0.992996i | \(-0.537697\pi\) | ||||
−0.118151 | + | 0.992996i | \(0.537697\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 2.51941e6i | − 3.04910i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −433279. | −0.522072 | −0.261036 | − | 0.965329i | \(-0.584064\pi\) | ||||
−0.261036 | + | 0.965329i | \(0.584064\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 323256.i | − 0.387798i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 498777.i | − 0.595750i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −935259. | −1.10739 | −0.553695 | − | 0.832719i | \(-0.686783\pi\) | ||||
−0.553695 | + | 0.832719i | \(0.686783\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 86490.4 | 0.101964 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 1.39255e6i | − 1.63459i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 871291. | 1.01831 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 313524.i | − 0.364847i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 1.16877e6i | − 1.35425i | −0.735867 | − | 0.677126i | \(-0.763225\pi\) | ||||
0.735867 | − | 0.677126i | \(-0.236775\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.23262e6 | 2.56478 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −82649.7 | −0.0945405 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 695595.i | − 0.792277i | −0.918191 | − | 0.396139i | \(-0.870350\pi\) | ||||
0.918191 | − | 0.396139i | \(-0.129650\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −738292. | −0.837331 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.55308e6i | 1.75394i | 0.480543 | + | 0.876971i | \(0.340440\pi\) | ||||
−0.480543 | + | 0.876971i | \(0.659560\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 113332.i | − 0.127447i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.04501e6 | −1.16525 | −0.582627 | − | 0.812740i | \(-0.697975\pi\) | ||||
−0.582627 | + | 0.812740i | \(0.697975\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −58312.3 | −0.0647482 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − 636294.i | − 0.703553i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −855805. | −0.942300 | −0.471150 | − | 0.882053i | \(-0.656161\pi\) | ||||
−0.471150 | + | 0.882053i | \(0.656161\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 104828.i | 0.114940i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 498032.i | − 0.543793i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 848553. | 0.918824 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.51746e6 | 1.63631 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 107869.i | − 0.115835i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.73940e6 | 1.86015 | 0.930074 | − | 0.367371i | \(-0.119742\pi\) | ||||
0.930074 | + | 0.367371i | \(0.119742\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − 1.47150e6i | − 1.56715i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 93336.5i | 0.0989950i | 0.998774 | + | 0.0494975i | \(0.0157620\pi\) | ||||
−0.998774 | + | 0.0494975i | \(0.984238\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.47574e6 | 1.55239 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.05190e6 | 1.10201 | 0.551004 | − | 0.834503i | \(-0.314245\pi\) | ||||
0.551004 | + | 0.834503i | \(0.314245\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 318280.i | 0.332081i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.96376e6 | 2.04057 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 32971.7i | − 0.0341219i | −0.999854 | − | 0.0170610i | \(-0.994569\pi\) | ||||
0.999854 | − | 0.0170610i | \(-0.00543094\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − 197110.i | − 0.203159i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −313571. | −0.320585 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −638020. | −0.649661 | −0.324831 | − | 0.945772i | \(-0.605307\pi\) | ||||
−0.324831 | + | 0.945772i | \(0.605307\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 642239.i | 0.651325i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −335361. | −0.338740 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 1.72164e6i | − 1.73202i | −0.500026 | − | 0.866010i | \(-0.666676\pi\) | ||||
0.500026 | − | 0.866010i | \(-0.333324\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.45182e6i | 2.45674i |
(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 | 784.5.c.g.97.1 | 8 | ||
4.3 | odd | 2 | 49.5.b.b.48.6 | yes | 8 | ||
7.6 | odd | 2 | inner | 784.5.c.g.97.8 | 8 | ||
12.11 | even | 2 | 441.5.d.g.244.4 | 8 | |||
28.3 | even | 6 | 49.5.d.c.19.3 | 16 | |||
28.11 | odd | 6 | 49.5.d.c.19.4 | 16 | |||
28.19 | even | 6 | 49.5.d.c.31.4 | 16 | |||
28.23 | odd | 6 | 49.5.d.c.31.3 | 16 | |||
28.27 | even | 2 | 49.5.b.b.48.5 | ✓ | 8 | ||
84.83 | odd | 2 | 441.5.d.g.244.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
49.5.b.b.48.5 | ✓ | 8 | 28.27 | even | 2 | ||
49.5.b.b.48.6 | yes | 8 | 4.3 | odd | 2 | ||
49.5.d.c.19.3 | 16 | 28.3 | even | 6 | |||
49.5.d.c.19.4 | 16 | 28.11 | odd | 6 | |||
49.5.d.c.31.3 | 16 | 28.23 | odd | 6 | |||
49.5.d.c.31.4 | 16 | 28.19 | even | 6 | |||
441.5.d.g.244.3 | 8 | 84.83 | odd | 2 | |||
441.5.d.g.244.4 | 8 | 12.11 | even | 2 | |||
784.5.c.g.97.1 | 8 | 1.1 | even | 1 | trivial | ||
784.5.c.g.97.8 | 8 | 7.6 | odd | 2 | inner |