Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [63,6,Mod(62,63)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(63, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("63.62");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 63 = 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 63.c (of order \(2\), degree \(1\), 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: | \(10.1041806482\) |
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: | \( x^{8} - 4x^{7} + 456x^{6} - 612x^{5} + 66744x^{4} + 32004x^{3} + 3729464x^{2} + 2503804x + 66026577 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{10}\cdot 3^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 62.8 | ||
Root | \(-0.822876 + 7.29403i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 63.62 |
Dual form | 63.6.c.b.62.2 |
$q$-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 \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).
\(n\) | \(10\) | \(29\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 7.98430i | 1.41144i | 0.708492 | + | 0.705719i | \(0.249376\pi\) | ||||
−0.708492 | + | 0.705719i | \(0.750624\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −31.7490 | −0.992157 | ||||||||
\(5\) | 67.9227 | 1.21504 | 0.607519 | − | 0.794305i | \(-0.292165\pi\) | ||||
0.607519 | + | 0.794305i | \(0.292165\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 25.6863 | + | 127.072i | 0.198133 | + | 0.980175i | ||||
\(8\) | 2.00393i | 0.0110703i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 542.315i | 1.71495i | ||||||||
\(11\) | − | 181.337i | − | 0.451862i | −0.974143 | − | 0.225931i | \(-0.927458\pi\) | ||
0.974143 | − | 0.225931i | \(-0.0725423\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 796.458i | 1.30709i | 0.756889 | + | 0.653544i | \(0.226718\pi\) | ||||
−0.756889 | + | 0.653544i | \(0.773282\pi\) | |||||||
\(14\) | −1014.58 | + | 205.087i | −1.38346 | + | 0.279652i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1031.97 | −1.00778 | ||||||||
\(17\) | −59.3989 | −0.0498490 | −0.0249245 | − | 0.999689i | \(-0.507935\pi\) | ||||
−0.0249245 | + | 0.999689i | \(0.507935\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 966.599i | − | 0.614274i | −0.951665 | − | 0.307137i | \(-0.900629\pi\) | ||
0.951665 | − | 0.307137i | \(-0.0993710\pi\) | |||||||
\(20\) | −2156.48 | −1.20551 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1447.85 | 0.637774 | ||||||||
\(23\) | − | 2491.36i | − | 0.982014i | −0.871156 | − | 0.491007i | \(-0.836629\pi\) | ||
0.871156 | − | 0.491007i | \(-0.163371\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1488.49 | 0.476317 | ||||||||
\(26\) | −6359.16 | −1.84487 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −815.514 | − | 4034.40i | −0.196579 | − | 0.972487i | ||||
\(29\) | 3787.11i | 0.836205i | 0.908400 | + | 0.418102i | \(0.137305\pi\) | ||||
−0.908400 | + | 0.418102i | \(0.862695\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7424.40i | 1.38758i | 0.720178 | + | 0.693789i | \(0.244060\pi\) | ||||
−0.720178 | + | 0.693789i | \(0.755940\pi\) | |||||||
\(32\) | − | 8175.42i | − | 1.41135i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 474.259i | − | 0.0703587i | ||||||
\(35\) | 1744.68 | + | 8631.05i | 0.240739 | + | 1.19095i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −12638.0 | −1.51766 | −0.758829 | − | 0.651290i | \(-0.774228\pi\) | ||||
−0.758829 | + | 0.651290i | \(0.774228\pi\) | |||||||
\(38\) | 7717.61 | 0.867010 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 136.113i | 0.0134508i | ||||||||
\(41\) | 19790.5 | 1.83865 | 0.919323 | − | 0.393505i | \(-0.128738\pi\) | ||||
0.919323 | + | 0.393505i | \(0.128738\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 13783.1 | 1.13678 | 0.568388 | − | 0.822761i | \(-0.307567\pi\) | ||||
0.568388 | + | 0.822761i | \(0.307567\pi\) | |||||||
\(44\) | 5757.28i | 0.448317i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 19891.8 | 1.38605 | ||||||||
\(47\) | 23475.1 | 1.55011 | 0.775057 | − | 0.631892i | \(-0.217721\pi\) | ||||
0.775057 | + | 0.631892i | \(0.217721\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −15487.4 | + | 6528.00i | −0.921487 | + | 0.388409i | ||||
\(50\) | 11884.5i | 0.672292i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 25286.8i | − | 1.29684i | ||||||
\(53\) | − | 27061.7i | − | 1.32332i | −0.749803 | − | 0.661661i | \(-0.769852\pi\) | ||
0.749803 | − | 0.661661i | \(-0.230148\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 12316.9i | − | 0.549029i | ||||||
\(56\) | −254.643 | + | 51.4736i | −0.0108508 | + | 0.00219338i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −30237.4 | −1.18025 | ||||||||
\(59\) | −9085.13 | −0.339782 | −0.169891 | − | 0.985463i | \(-0.554342\pi\) | ||||
−0.169891 | + | 0.985463i | \(0.554342\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 22432.7i | − | 0.771892i | −0.922521 | − | 0.385946i | \(-0.873875\pi\) | ||
0.922521 | − | 0.385946i | \(-0.126125\pi\) | |||||||
\(62\) | −59278.6 | −1.95848 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 32252.0 | 0.984252 | ||||||||
\(65\) | 54097.6i | 1.58816i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 59524.2 | 1.61997 | 0.809985 | − | 0.586451i | \(-0.199475\pi\) | ||||
0.809985 | + | 0.586451i | \(0.199475\pi\) | |||||||
\(68\) | 1885.86 | 0.0494580 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −68912.9 | + | 13930.0i | −1.68095 | + | 0.339788i | ||||
\(71\) | − | 11632.3i | − | 0.273854i | −0.990581 | − | 0.136927i | \(-0.956277\pi\) | ||
0.990581 | − | 0.136927i | \(-0.0437226\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 38939.3i | − | 0.855227i | −0.903962 | − | 0.427613i | \(-0.859355\pi\) | ||
0.903962 | − | 0.427613i | \(-0.140645\pi\) | |||||||
\(74\) | − | 100905.i | − | 2.14208i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 30688.6i | 0.609456i | ||||||||
\(77\) | 23042.8 | − | 4657.88i | 0.442903 | − | 0.0895285i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15289.7 | 0.275632 | 0.137816 | − | 0.990458i | \(-0.455992\pi\) | ||||
0.137816 | + | 0.990458i | \(0.455992\pi\) | |||||||
\(80\) | −70094.1 | −1.22449 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 158014.i | 2.59513i | ||||||||
\(83\) | 64568.6 | 1.02879 | 0.514395 | − | 0.857554i | \(-0.328017\pi\) | ||||
0.514395 | + | 0.857554i | \(0.328017\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4034.53 | −0.0605684 | ||||||||
\(86\) | 110048.i | 1.60449i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 363.388 | 0.00500223 | ||||||||
\(89\) | −103895. | −1.39034 | −0.695170 | − | 0.718845i | \(-0.744671\pi\) | ||||
−0.695170 | + | 0.718845i | \(0.744671\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −101207. | + | 20458.0i | −1.28117 | + | 0.258977i | ||||
\(92\) | 79098.3i | 0.974311i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 187433.i | 2.18789i | ||||||||
\(95\) | − | 65654.0i | − | 0.746366i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 14530.7i | − | 0.156804i | −0.996922 | − | 0.0784022i | \(-0.975018\pi\) | ||
0.996922 | − | 0.0784022i | \(-0.0249818\pi\) | |||||||
\(98\) | −52121.5 | − | 123656.i | −0.548216 | − | 1.30062i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −47258.1 | −0.472581 | ||||||||
\(101\) | 71877.9 | 0.701119 | 0.350560 | − | 0.936540i | \(-0.385991\pi\) | ||||
0.350560 | + | 0.936540i | \(0.385991\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 199398.i | − | 1.85194i | −0.377597 | − | 0.925970i | \(-0.623250\pi\) | ||
0.377597 | − | 0.925970i | \(-0.376750\pi\) | |||||||
\(104\) | −1596.05 | −0.0144698 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 216069. | 1.86779 | ||||||||
\(107\) | 6187.77i | 0.0522486i | 0.999659 | + | 0.0261243i | \(0.00831657\pi\) | ||||
−0.999659 | + | 0.0261243i | \(0.991683\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2236.70 | 0.0180319 | 0.00901593 | − | 0.999959i | \(-0.497130\pi\) | ||||
0.00901593 | + | 0.999959i | \(0.497130\pi\) | |||||||
\(110\) | 98341.9 | 0.774920 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −26507.4 | − | 131134.i | −0.199674 | − | 0.987803i | ||||
\(113\) | 159158.i | 1.17256i | 0.810110 | + | 0.586278i | \(0.199407\pi\) | ||||
−0.810110 | + | 0.586278i | \(0.800593\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 169220.i | − | 1.19318i | ||||||
\(116\) | − | 120237.i | − | 0.829646i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 72538.4i | − | 0.479582i | ||||||
\(119\) | −1525.74 | − | 7547.92i | −0.00987671 | − | 0.0488607i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 128168. | 0.795821 | ||||||||
\(122\) | 179109. | 1.08948 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 235717.i | − | 1.37669i | ||||||
\(125\) | −111156. | −0.636295 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 50132.9 | 0.275812 | 0.137906 | − | 0.990445i | \(-0.455963\pi\) | ||||
0.137906 | + | 0.990445i | \(0.455963\pi\) | |||||||
\(128\) | − | 4103.93i | − | 0.0221399i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −431931. | −2.24159 | ||||||||
\(131\) | 85756.2 | 0.436604 | 0.218302 | − | 0.975881i | \(-0.429948\pi\) | ||||
0.218302 | + | 0.975881i | \(0.429948\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 122827. | − | 24828.3i | 0.602096 | − | 0.121708i | ||||
\(134\) | 475259.i | 2.28649i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 119.031i | − | 0.000551842i | ||||||
\(137\) | − | 76640.4i | − | 0.348864i | −0.984669 | − | 0.174432i | \(-0.944191\pi\) | ||
0.984669 | − | 0.174432i | \(-0.0558089\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 306446.i | 1.34529i | 0.739963 | + | 0.672647i | \(0.234843\pi\) | ||||
−0.739963 | + | 0.672647i | \(0.765157\pi\) | |||||||
\(140\) | −55391.9 | − | 274027.i | −0.238850 | − | 1.18161i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 92875.6 | 0.386528 | ||||||||
\(143\) | 144428. | 0.590623 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 257230.i | 1.01602i | ||||||||
\(146\) | 310903. | 1.20710 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 401244. | 1.50575 | ||||||||
\(149\) | − | 491067.i | − | 1.81207i | −0.423201 | − | 0.906036i | \(-0.639094\pi\) | ||
0.423201 | − | 0.906036i | \(-0.360906\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −494842. | −1.76614 | −0.883068 | − | 0.469244i | \(-0.844526\pi\) | ||||
−0.883068 | + | 0.469244i | \(0.844526\pi\) | |||||||
\(152\) | 1937.00 | 0.00680018 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 37189.9 | + | 183981.i | 0.126364 | + | 0.625131i | ||||
\(155\) | 504285.i | 1.68596i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 403237.i | 1.30560i | 0.757529 | + | 0.652802i | \(0.226407\pi\) | ||||
−0.757529 | + | 0.652802i | \(0.773593\pi\) | |||||||
\(158\) | 122077.i | 0.389038i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 555296.i | − | 1.71484i | ||||||
\(161\) | 316582. | − | 63993.8i | 0.962545 | − | 0.194569i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 334861. | 0.987179 | 0.493589 | − | 0.869695i | \(-0.335685\pi\) | ||||
0.493589 | + | 0.869695i | \(0.335685\pi\) | |||||||
\(164\) | −628330. | −1.82422 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 515535.i | 1.45207i | ||||||||
\(167\) | −44898.2 | −0.124577 | −0.0622885 | − | 0.998058i | \(-0.519840\pi\) | ||||
−0.0622885 | + | 0.998058i | \(0.519840\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −263053. | −0.708478 | ||||||||
\(170\) | − | 32212.9i | − | 0.0854885i | ||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −437599. | −1.12786 | ||||||||
\(173\) | −462944. | −1.17601 | −0.588007 | − | 0.808856i | \(-0.700087\pi\) | ||||
−0.588007 | + | 0.808856i | \(0.700087\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 38233.8 | + | 189145.i | 0.0943739 | + | 0.466874i | ||||
\(176\) | 187134.i | 0.455378i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 829531.i | − | 1.96238i | ||||||
\(179\) | 51366.8i | 0.119826i | 0.998204 | + | 0.0599128i | \(0.0190823\pi\) | ||||
−0.998204 | + | 0.0599128i | \(0.980918\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 230031.i | 0.521904i | 0.965352 | + | 0.260952i | \(0.0840364\pi\) | ||||
−0.965352 | + | 0.260952i | \(0.915964\pi\) | |||||||
\(182\) | −163343. | − | 808069.i | −0.365529 | − | 1.80830i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 4992.53 | 0.0108712 | ||||||||
\(185\) | −858406. | −1.84401 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10771.2i | 0.0225248i | ||||||||
\(188\) | −745313. | −1.53796 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 524201. | 1.05345 | ||||||||
\(191\) | − | 16387.3i | − | 0.0325031i | −0.999868 | − | 0.0162516i | \(-0.994827\pi\) | ||
0.999868 | − | 0.0162516i | \(-0.00517326\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −649781. | −1.25567 | −0.627833 | − | 0.778348i | \(-0.716058\pi\) | ||||
−0.627833 | + | 0.778348i | \(0.716058\pi\) | |||||||
\(194\) | 116018. | 0.221320 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 491711. | − | 207257.i | 0.914259 | − | 0.385363i | ||||
\(197\) | − | 145238.i | − | 0.266634i | −0.991073 | − | 0.133317i | \(-0.957437\pi\) | ||
0.991073 | − | 0.133317i | \(-0.0425629\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 48399.3i | − | 0.0866375i | −0.999061 | − | 0.0433188i | \(-0.986207\pi\) | ||
0.999061 | − | 0.0433188i | \(-0.0137931\pi\) | |||||||
\(200\) | 2982.83i | 0.00527296i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 573895.i | 0.989586i | ||||||||
\(203\) | −481234. | + | 97276.6i | −0.819627 | + | 0.165679i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.34423e6 | 2.23402 | ||||||||
\(206\) | 1.59205e6 | 2.61390 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 821920.i | − | 1.31726i | ||||||
\(209\) | −175280. | −0.277567 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −658037. | −1.01752 | −0.508761 | − | 0.860908i | \(-0.669896\pi\) | ||||
−0.508761 | + | 0.860908i | \(0.669896\pi\) | |||||||
\(212\) | 859182.i | 1.31294i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −49405.0 | −0.0737457 | ||||||||
\(215\) | 936183. | 1.38123 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −943431. | + | 190705.i | −1.36007 | + | 0.274924i | ||||
\(218\) | 17858.4i | 0.0254509i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 391050.i | 0.544723i | ||||||||
\(221\) | − | 47308.8i | − | 0.0651570i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 732455.i | − | 0.986322i | −0.869938 | − | 0.493161i | \(-0.835841\pi\) | ||
0.869938 | − | 0.493161i | \(-0.164159\pi\) | |||||||
\(224\) | 1.03886e6 | − | 209996.i | 1.38337 | − | 0.279635i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.27077e6 | −1.65499 | ||||||||
\(227\) | 202244. | 0.260502 | 0.130251 | − | 0.991481i | \(-0.458422\pi\) | ||||
0.130251 | + | 0.991481i | \(0.458422\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 321111.i | 0.404637i | 0.979320 | + | 0.202319i | \(0.0648477\pi\) | ||||
−0.979320 | + | 0.202319i | \(0.935152\pi\) | |||||||
\(230\) | 1.35110e6 | 1.68410 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −7589.11 | −0.00925701 | ||||||||
\(233\) | 96874.8i | 0.116902i | 0.998290 | + | 0.0584509i | \(0.0186161\pi\) | ||||
−0.998290 | + | 0.0584509i | \(0.981384\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.59449e6 | 1.88345 | ||||||||
\(236\) | 288444. | 0.337117 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 60264.9 | − | 12181.9i | 0.0689639 | − | 0.0139404i | ||||
\(239\) | − | 434839.i | − | 0.492418i | −0.969217 | − | 0.246209i | \(-0.920815\pi\) | ||
0.969217 | − | 0.246209i | \(-0.0791849\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 812484.i | 0.901098i | 0.892752 | + | 0.450549i | \(0.148772\pi\) | ||||
−0.892752 | + | 0.450549i | \(0.851228\pi\) | |||||||
\(242\) | 1.02333e6i | 1.12325i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 712215.i | 0.765838i | ||||||||
\(245\) | −1.05195e6 | + | 443399.i | −1.11964 | + | 0.471932i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 769856. | 0.802910 | ||||||||
\(248\) | −14878.0 | −0.0153609 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − | 887504.i | − | 0.898091i | ||||||
\(251\) | 679893. | 0.681171 | 0.340585 | − | 0.940214i | \(-0.389375\pi\) | ||||
0.340585 | + | 0.940214i | \(0.389375\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −451777. | −0.443734 | ||||||||
\(254\) | 400276.i | 0.389292i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.06483e6 | 1.01550 | ||||||||
\(257\) | −1.25295e6 | −1.18332 | −0.591658 | − | 0.806189i | \(-0.701526\pi\) | ||||
−0.591658 | + | 0.806189i | \(0.701526\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −324623. | − | 1.60593e6i | −0.300697 | − | 1.48757i | ||||
\(260\) | − | 1.71754e6i | − | 1.57570i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 684703.i | 0.616239i | ||||||||
\(263\) | − | 1.92848e6i | − | 1.71920i | −0.510969 | − | 0.859599i | \(-0.670713\pi\) | ||
0.510969 | − | 0.859599i | \(-0.329287\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 1.83810e6i | − | 1.60789i | ||||||
\(266\) | 198237. | + | 980690.i | 0.171783 | + | 0.849822i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.88984e6 | −1.60726 | ||||||||
\(269\) | 460423. | 0.387951 | 0.193975 | − | 0.981006i | \(-0.437862\pi\) | ||||
0.193975 | + | 0.981006i | \(0.437862\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 72590.5i | − | 0.0600422i | −0.999549 | − | 0.0300211i | \(-0.990443\pi\) | ||
0.999549 | − | 0.0300211i | \(-0.00955745\pi\) | |||||||
\(272\) | 61297.8 | 0.0502369 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 611920. | 0.492400 | ||||||||
\(275\) | − | 269919.i | − | 0.215229i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 331439. | 0.259540 | 0.129770 | − | 0.991544i | \(-0.458576\pi\) | ||||
0.129770 | + | 0.991544i | \(0.458576\pi\) | |||||||
\(278\) | −2.44676e6 | −1.89880 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −17296.0 | + | 3496.22i | −0.0131841 | + | 0.00266504i | ||||
\(281\) | 978539.i | 0.739285i | 0.929174 | + | 0.369643i | \(0.120520\pi\) | ||||
−0.929174 | + | 0.369643i | \(0.879480\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 2.10266e6i | − | 1.56064i | −0.625382 | − | 0.780319i | \(-0.715057\pi\) | ||
0.625382 | − | 0.780319i | \(-0.284943\pi\) | |||||||
\(284\) | 369313.i | 0.271706i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.15315e6i | 0.833627i | ||||||||
\(287\) | 508345. | + | 2.51482e6i | 0.364296 | + | 1.80219i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.41633e6 | −0.997515 | ||||||||
\(290\) | −2.05380e6 | −1.43405 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.23629e6i | 0.848519i | ||||||||
\(293\) | −2.32914e6 | −1.58499 | −0.792495 | − | 0.609878i | \(-0.791218\pi\) | ||||
−0.792495 | + | 0.609878i | \(0.791218\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −617086. | −0.412849 | ||||||||
\(296\) | − | 25325.7i | − | 0.0168009i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.92083e6 | 2.55763 | ||||||||
\(299\) | 1.98427e6 | 1.28358 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 354036. | + | 1.75144e6i | 0.225232 | + | 1.11424i | ||||
\(302\) | − | 3.95097e6i | − | 2.49279i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 997500.i | 0.619054i | ||||||||
\(305\) | − | 1.52369e6i | − | 0.937878i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.81476e6i | 1.09894i | 0.835514 | + | 0.549469i | \(0.185170\pi\) | ||||
−0.835514 | + | 0.549469i | \(0.814830\pi\) | |||||||
\(308\) | −731587. | + | 147883.i | −0.439430 | + | 0.0888263i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4.02636e6 | −2.37963 | ||||||||
\(311\) | 938205. | 0.550043 | 0.275022 | − | 0.961438i | \(-0.411315\pi\) | ||||
0.275022 | + | 0.961438i | \(0.411315\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.33328e6i | 0.769239i | 0.923075 | + | 0.384619i | \(0.125667\pi\) | ||||
−0.923075 | + | 0.384619i | \(0.874333\pi\) | |||||||
\(314\) | −3.21957e6 | −1.84278 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −485432. | −0.273470 | ||||||||
\(317\) | − | 881093.i | − | 0.492463i | −0.969211 | − | 0.246231i | \(-0.920808\pi\) | ||
0.969211 | − | 0.246231i | \(-0.0791923\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 686744. | 0.377849 | ||||||||
\(320\) | 2.19064e6 | 1.19590 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 510946. | + | 2.52768e6i | 0.274622 | + | 1.35857i | ||||
\(323\) | 57414.9i | 0.0306209i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.18552e6i | 0.622588i | ||||||||
\(326\) | 2.67363e6i | 1.39334i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 39658.9i | 0.0203543i | ||||||||
\(329\) | 602989. | + | 2.98303e6i | 0.307128 | + | 1.51938i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.79165e6 | 0.898843 | 0.449421 | − | 0.893320i | \(-0.351630\pi\) | ||||
0.449421 | + | 0.893320i | \(0.351630\pi\) | |||||||
\(332\) | −2.04999e6 | −1.02072 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 358481.i | − | 0.175833i | ||||||
\(335\) | 4.04305e6 | 1.96832 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.78122e6 | −0.854363 | −0.427181 | − | 0.904166i | \(-0.640493\pi\) | ||||
−0.427181 | + | 0.904166i | \(0.640493\pi\) | |||||||
\(338\) | − | 2.10029e6i | − | 0.999972i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 128092. | 0.0600933 | ||||||||
\(341\) | 1.34632e6 | 0.626993 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.22734e6 | − | 1.80033e6i | −0.563286 | − | 0.826262i | ||||
\(344\) | 27620.4i | 0.0125844i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 3.69628e6i | − | 1.65987i | ||||||
\(347\) | 787729.i | 0.351199i | 0.984462 | + | 0.175600i | \(0.0561864\pi\) | ||||
−0.984462 | + | 0.175600i | \(0.943814\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 65065.1i | 0.0285946i | 0.999898 | + | 0.0142973i | \(0.00455113\pi\) | ||||
−0.999898 | + | 0.0142973i | \(0.995449\pi\) | |||||||
\(350\) | −1.51019e6 | + | 305270.i | −0.658964 | + | 0.133203i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.48251e6 | −0.637735 | ||||||||
\(353\) | 1.01928e6 | 0.435370 | 0.217685 | − | 0.976019i | \(-0.430149\pi\) | ||||
0.217685 | + | 0.976019i | \(0.430149\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 790096.i | − | 0.332743i | ||||||
\(356\) | 3.29857e6 | 1.37944 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −410128. | −0.169126 | ||||||||
\(359\) | 510797.i | 0.209176i | 0.994516 | + | 0.104588i | \(0.0333524\pi\) | ||||
−0.994516 | + | 0.104588i | \(0.966648\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.54179e6 | 0.622667 | ||||||||
\(362\) | −1.83664e6 | −0.736635 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.21323e6 | − | 649523.i | 1.27113 | − | 0.256945i | ||||
\(365\) | − | 2.64486e6i | − | 1.03913i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 1.34928e6i | − | 0.522923i | −0.965214 | − | 0.261462i | \(-0.915795\pi\) | ||
0.965214 | − | 0.261462i | \(-0.0842045\pi\) | |||||||
\(368\) | 2.57101e6i | 0.989655i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 6.85377e6i | − | 2.60271i | ||||||
\(371\) | 3.43878e6 | − | 695114.i | 1.29709 | − | 0.262193i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.86645e6 | 1.43893 | 0.719466 | − | 0.694528i | \(-0.244387\pi\) | ||||
0.719466 | + | 0.694528i | \(0.244387\pi\) | |||||||
\(374\) | −86000.8 | −0.0317924 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 47042.6i | 0.0171602i | ||||||||
\(377\) | −3.01627e6 | −1.09299 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.40390e6 | −0.859644 | −0.429822 | − | 0.902914i | \(-0.641424\pi\) | ||||
−0.429822 | + | 0.902914i | \(0.641424\pi\) | |||||||
\(380\) | 2.08445e6i | 0.740512i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 130841. | 0.0458761 | ||||||||
\(383\) | −1.03382e6 | −0.360121 | −0.180061 | − | 0.983656i | \(-0.557629\pi\) | ||||
−0.180061 | + | 0.983656i | \(0.557629\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.56513e6 | − | 316376.i | 0.538144 | − | 0.108781i | ||||
\(386\) | − | 5.18805e6i | − | 1.77229i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 461337.i | 0.155575i | ||||||||
\(389\) | − | 2.43425e6i | − | 0.815628i | −0.913065 | − | 0.407814i | \(-0.866291\pi\) | ||
0.913065 | − | 0.407814i | \(-0.133709\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 147984.i | 0.0489524i | ||||||||
\(392\) | −13081.7 | − | 31035.8i | −0.00429980 | − | 0.0102011i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.15963e6 | 0.376338 | ||||||||
\(395\) | 1.03851e6 | 0.334904 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 1.50463e6i | − | 0.479131i | −0.970880 | − | 0.239566i | \(-0.922995\pi\) | ||
0.970880 | − | 0.239566i | \(-0.0770050\pi\) | |||||||
\(398\) | 386434. | 0.122284 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.53607e6 | −0.480023 | ||||||||
\(401\) | 1.13980e6i | 0.353972i | 0.984213 | + | 0.176986i | \(0.0566348\pi\) | ||||
−0.984213 | + | 0.176986i | \(0.943365\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.91323e6 | −1.81369 | ||||||||
\(404\) | −2.28205e6 | −0.695620 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −776686. | − | 3.84232e6i | −0.233846 | − | 1.15685i | ||||
\(407\) | 2.29174e6i | 0.685771i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.41231e6i | 1.00865i | 0.863514 | + | 0.504325i | \(0.168259\pi\) | ||||
−0.863514 | + | 0.504325i | \(0.831741\pi\) | |||||||
\(410\) | 1.07327e7i | 3.15318i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6.33068e6i | 1.83741i | ||||||||
\(413\) | −233363. | − | 1.15446e6i | −0.0673220 | − | 0.333046i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.38567e6 | 1.25002 | ||||||||
\(416\) | 6.51138e6 | 1.84476 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 1.39949e6i | − | 0.391768i | ||||||
\(419\) | 1.79766e6 | 0.500233 | 0.250116 | − | 0.968216i | \(-0.419531\pi\) | ||||
0.250116 | + | 0.968216i | \(0.419531\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.30245e6 | −0.908095 | −0.454047 | − | 0.890978i | \(-0.650020\pi\) | ||||
−0.454047 | + | 0.890978i | \(0.650020\pi\) | |||||||
\(422\) | − | 5.25396e6i | − | 1.43617i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 54229.8 | 0.0146495 | ||||||||
\(425\) | −88414.7 | −0.0237439 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.85056e6 | − | 576212.i | 0.756589 | − | 0.152937i | ||||
\(428\) | − | 196456.i | − | 0.0518388i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 7.47477e6i | 1.94951i | ||||||||
\(431\) | 3.79786e6i | 0.984794i | 0.870371 | + | 0.492397i | \(0.163879\pi\) | ||||
−0.870371 | + | 0.492397i | \(0.836121\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.80204e6i | 0.718215i | 0.933296 | + | 0.359108i | \(0.116919\pi\) | ||||
−0.933296 | + | 0.359108i | \(0.883081\pi\) | |||||||
\(434\) | −1.52265e6 | − | 7.53264e6i | −0.388039 | − | 1.91965i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −71012.9 | −0.0178904 | ||||||||
\(437\) | −2.40815e6 | −0.603226 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 275441.i | 0.0682131i | 0.999418 | + | 0.0341065i | \(0.0108586\pi\) | ||||
−0.999418 | + | 0.0341065i | \(0.989141\pi\) | |||||||
\(440\) | 24682.3 | 0.00607790 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 377727. | 0.0919650 | ||||||||
\(443\) | 2.82524e6i | 0.683985i | 0.939703 | + | 0.341993i | \(0.111102\pi\) | ||||
−0.939703 | + | 0.341993i | \(0.888898\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.05685e6 | −1.68932 | ||||||||
\(446\) | 5.84814e6 | 1.39213 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 828433. | + | 4.09831e6i | 0.195012 | + | 0.964740i | ||||
\(449\) | − | 3.19212e6i | − | 0.747245i | −0.927581 | − | 0.373622i | \(-0.878116\pi\) | ||
0.927581 | − | 0.373622i | \(-0.121884\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 3.58876e6i | − | 0.830813i | ||||||
\(452\) | − | 5.05312e6i | − | 1.16336i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.61478e6i | 0.367683i | ||||||||
\(455\) | −6.87427e6 | + | 1.38957e6i | −1.55668 | + | 0.314666i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.41224e6 | 0.764273 | 0.382137 | − | 0.924106i | \(-0.375188\pi\) | ||||
0.382137 | + | 0.924106i | \(0.375188\pi\) | |||||||
\(458\) | −2.56384e6 | −0.571120 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 5.37257e6i | 1.18383i | ||||||||
\(461\) | −5.17955e6 | −1.13511 | −0.567557 | − | 0.823334i | \(-0.692111\pi\) | ||||
−0.567557 | + | 0.823334i | \(0.692111\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.95911e6 | 0.641518 | 0.320759 | − | 0.947161i | \(-0.396062\pi\) | ||||
0.320759 | + | 0.947161i | \(0.396062\pi\) | |||||||
\(464\) | − | 3.90817e6i | − | 0.842712i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −773477. | −0.165000 | ||||||||
\(467\) | −4.58858e6 | −0.973612 | −0.486806 | − | 0.873510i | \(-0.661838\pi\) | ||||
−0.486806 | + | 0.873510i | \(0.661838\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.52896e6 | + | 7.56385e6i | 0.320969 | + | 1.58785i | ||||
\(470\) | 1.27309e7i | 2.65837i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 18206.0i | − | 0.00376148i | ||||||
\(473\) | − | 2.49939e6i | − | 0.513665i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 1.43877e6i | − | 0.292589i | ||||||
\(476\) | 48440.6 | + | 239639.i | 0.00979924 | + | 0.0484775i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3.47188e6 | 0.695017 | ||||||||
\(479\) | −8.10226e6 | −1.61349 | −0.806747 | − | 0.590897i | \(-0.798774\pi\) | ||||
−0.806747 | + | 0.590897i | \(0.798774\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 1.00656e7i | − | 1.98371i | ||||||
\(482\) | −6.48711e6 | −1.27184 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.06920e6 | −0.789579 | ||||||||
\(485\) | − | 986967.i | − | 0.190523i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.51573e6 | −1.05385 | −0.526927 | − | 0.849910i | \(-0.676656\pi\) | ||||
−0.526927 | + | 0.849910i | \(0.676656\pi\) | |||||||
\(488\) | 44953.6 | 0.00854505 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3.54023e6 | − | 8.39906e6i | −0.666103 | − | 1.58030i | ||||
\(491\) | − | 6.20893e6i | − | 1.16229i | −0.813801 | − | 0.581143i | \(-0.802606\pi\) | ||
0.813801 | − | 0.581143i | \(-0.197394\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 224950.i | − | 0.0416839i | ||||||
\(494\) | 6.14676e6i | 1.13326i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 7.66175e6i | − | 1.39838i | ||||||
\(497\) | 1.47813e6 | − | 298790.i | 0.268425 | − | 0.0542594i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.86845e6 | −0.335915 | −0.167958 | − | 0.985794i | \(-0.553717\pi\) | ||||
−0.167958 | + | 0.985794i | \(0.553717\pi\) | |||||||
\(500\) | 3.52910e6 | 0.631304 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5.42846e6i | 0.961430i | ||||||||
\(503\) | 1.10682e7 | 1.95055 | 0.975276 | − | 0.220992i | \(-0.0709293\pi\) | ||||
0.975276 | + | 0.220992i | \(0.0709293\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.88214e6 | 0.851887 | ||||||||
\(506\) | − | 3.60712e6i | − | 0.626303i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.59167e6 | −0.273649 | ||||||||
\(509\) | −9.62004e6 | −1.64582 | −0.822910 | − | 0.568171i | \(-0.807651\pi\) | ||||
−0.822910 | + | 0.568171i | \(0.807651\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.94809e6 | − | 1.00021e6i | 0.838272 | − | 0.169448i | ||||
\(512\) | 8.37060e6i | 1.41118i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 1.00039e7i | − | 1.67018i | ||||||
\(515\) | − | 1.35436e7i | − | 2.25018i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 4.25692e6i | − | 0.700437i | ||||||
\(518\) | 1.28222e7 | − | 2.59189e6i | 2.09961 | − | 0.424416i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −108408. | −0.0175814 | ||||||||
\(521\) | 454479. | 0.0733533 | 0.0366766 | − | 0.999327i | \(-0.488323\pi\) | ||||
0.0366766 | + | 0.999327i | \(0.488323\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.69977e6i | 1.07104i | 0.844523 | + | 0.535520i | \(0.179884\pi\) | ||||
−0.844523 | + | 0.535520i | \(0.820116\pi\) | |||||||
\(524\) | −2.72268e6 | −0.433179 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.53976e7 | 2.42654 | ||||||||
\(527\) | − | 441002.i | − | 0.0691693i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 229452. | 0.0356495 | ||||||||
\(530\) | 1.46760e7 | 2.26943 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3.89965e6 | + | 788275.i | −0.597374 | + | 0.120753i | ||||
\(533\) | 1.57623e7i | 2.40327i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 420290.i | 0.0634840i | ||||||||
\(536\) | 119283.i | 0.0179335i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.67616e6i | 0.547569i | ||||||||
\(539\) | 1.18377e6 | + | 2.80845e6i | 0.175507 | + | 0.416385i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.60730e6 | −1.11747 | −0.558737 | − | 0.829345i | \(-0.688714\pi\) | ||||
−0.558737 | + | 0.829345i | \(0.688714\pi\) | |||||||
\(542\) | 579584. | 0.0847459 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 485611.i | 0.0703544i | ||||||||
\(545\) | 151922. | 0.0219094 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.09464e6 | 0.299323 | 0.149662 | − | 0.988737i | \(-0.452182\pi\) | ||||
0.149662 | + | 0.988737i | \(0.452182\pi\) | |||||||
\(548\) | 2.43326e6i | 0.346128i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.15511e6 | 0.303783 | ||||||||
\(551\) | 3.66061e6 | 0.513659 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 392734. | + | 1.94288e6i | 0.0546117 | + | 0.270168i | ||||
\(554\) | 2.64631e6i | 0.366324i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 9.72937e6i | − | 1.33474i | ||||||
\(557\) | − | 5.24643e6i | − | 0.716516i | −0.933623 | − | 0.358258i | \(-0.883371\pi\) | ||
0.933623 | − | 0.358258i | \(-0.116629\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.09776e7i | 1.48587i | ||||||||
\(560\) | −1.80046e6 | − | 8.90697e6i | −0.242612 | − | 1.20022i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −7.81294e6 | −1.04346 | ||||||||
\(563\) | 3.50851e6 | 0.466501 | 0.233250 | − | 0.972417i | \(-0.425064\pi\) | ||||
0.233250 | + | 0.972417i | \(0.425064\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.08105e7i | 1.42470i | ||||||||
\(566\) | 1.67882e7 | 2.20274 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 23310.3 | 0.00303164 | ||||||||
\(569\) | 1.15451e7i | 1.49491i | 0.664310 | + | 0.747457i | \(0.268725\pi\) | ||||
−0.664310 | + | 0.747457i | \(0.731275\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.27200e6 | 0.291620 | 0.145810 | − | 0.989313i | \(-0.453421\pi\) | ||||
0.145810 | + | 0.989313i | \(0.453421\pi\) | |||||||
\(572\) | −4.58543e6 | −0.585990 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.00790e7 | + | 4.05878e6i | −2.54369 | + | 0.514180i | ||||
\(575\) | − | 3.70837e6i | − | 0.467750i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.36093e6i | 0.670349i | 0.942156 | + | 0.335174i | \(0.108795\pi\) | ||||
−0.942156 | + | 0.335174i | \(0.891205\pi\) | |||||||
\(578\) | − | 1.13084e7i | − | 1.40793i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 8.16681e6i | − | 1.00805i | ||||||
\(581\) | 1.65853e6 | + | 8.20484e6i | 0.203837 | + | 1.00839i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.90730e6 | −0.597958 | ||||||||
\(584\) | 78031.8 | 0.00946759 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 1.85966e7i | − | 2.23712i | ||||||
\(587\) | −1.16996e7 | −1.40145 | −0.700725 | − | 0.713431i | \(-0.747140\pi\) | ||||
−0.700725 | + | 0.713431i | \(0.747140\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.17642e6 | 0.852353 | ||||||||
\(590\) | − | 4.92700e6i | − | 0.582710i | ||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.30420e7 | 1.52947 | ||||||||
\(593\) | 1.25302e7 | 1.46326 | 0.731632 | − | 0.681699i | \(-0.238759\pi\) | ||||
0.731632 | + | 0.681699i | \(0.238759\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −103632. | − | 512675.i | −0.0120006 | − | 0.0593676i | ||||
\(596\) | 1.55909e7i | 1.79786i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.58430e7i | 1.81169i | ||||||||
\(599\) | − | 6.68710e6i | − | 0.761502i | −0.924678 | − | 0.380751i | \(-0.875666\pi\) | ||
0.924678 | − | 0.380751i | \(-0.124334\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 1.14251e7i | − | 1.29025i | −0.764077 | − | 0.645125i | \(-0.776805\pi\) | ||
0.764077 | − | 0.645125i | \(-0.223195\pi\) | |||||||
\(602\) | −1.39840e7 | + | 2.82673e6i | −1.57268 | + | 0.317902i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.57108e7 | 1.75228 | ||||||||
\(605\) | 8.70550e6 | 0.966953 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 5.02725e6i | − | 0.553807i | −0.960898 | − | 0.276904i | \(-0.910692\pi\) | ||
0.960898 | − | 0.276904i | \(-0.0893083\pi\) | |||||||
\(608\) | −7.90235e6 | −0.866957 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.21656e7 | 1.32376 | ||||||||
\(611\) | 1.86970e7i | 2.02613i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.15239e6 | −0.661291 | −0.330646 | − | 0.943755i | \(-0.607266\pi\) | ||||
−0.330646 | + | 0.943755i | \(0.607266\pi\) | |||||||
\(614\) | −1.44896e7 | −1.55108 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 9334.08 | + | 46176.3i | 0.000991105 | + | 0.00490306i | ||||
\(617\) | − | 1.45928e7i | − | 1.54321i | −0.636102 | − | 0.771605i | \(-0.719454\pi\) | ||
0.636102 | − | 0.771605i | \(-0.280546\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 204738.i | − | 0.0214770i | −0.999942 | − | 0.0107385i | \(-0.996582\pi\) | ||
0.999942 | − | 0.0107385i | \(-0.00341823\pi\) | |||||||
\(620\) | − | 1.60106e7i | − | 1.67274i | ||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 7.49091e6i | 0.776352i | ||||||||
\(623\) | −2.66868e6 | − | 1.32022e7i | −0.275472 | − | 1.36278i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.22016e7 | −1.24944 | ||||||||
\(626\) | −1.06453e7 | −1.08573 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 1.28024e7i | − | 1.29536i | ||||||
\(629\) | 750683. | 0.0756537 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.28340e6 | −0.528250 | −0.264125 | − | 0.964488i | \(-0.585083\pi\) | ||||
−0.264125 | + | 0.964488i | \(0.585083\pi\) | |||||||
\(632\) | 30639.5i | 0.00305132i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 7.03491e6 | 0.695081 | ||||||||
\(635\) | 3.40516e6 | 0.335122 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.19928e6 | − | 1.23351e7i | −0.507685 | − | 1.20446i | ||||
\(638\) | 5.48317e6i | 0.533310i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − | 278750.i | − | 0.0269008i | ||||||
\(641\) | − | 1.28390e7i | − | 1.23420i | −0.786886 | − | 0.617099i | \(-0.788308\pi\) | ||
0.786886 | − | 0.617099i | \(-0.211692\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.73194e7i | 1.65199i | 0.563681 | + | 0.825993i | \(0.309385\pi\) | ||||
−0.563681 | + | 0.825993i | \(0.690615\pi\) | |||||||
\(644\) | −1.00512e7 | + | 2.03174e6i | −0.954996 | + | 0.193043i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −458418. | −0.0432196 | ||||||||
\(647\) | −1.08785e7 | −1.02166 | −0.510831 | − | 0.859681i | \(-0.670662\pi\) | ||||
−0.510831 | + | 0.859681i | \(0.670662\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.64747e6i | 0.153535i | ||||||||
\(650\) | −9.46555e6 | −0.878744 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.06315e7 | −0.979436 | ||||||||
\(653\) | 1.59790e7i | 1.46645i | 0.679985 | + | 0.733226i | \(0.261986\pi\) | ||||
−0.679985 | + | 0.733226i | \(0.738014\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.82479e6 | 0.530490 | ||||||||
\(656\) | −2.04232e7 | −1.85295 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2.38174e7 | + | 4.81444e6i | −2.14451 | + | 0.433492i | ||||
\(659\) | 3.69348e6i | 0.331300i | 0.986185 | + | 0.165650i | \(0.0529722\pi\) | ||||
−0.986185 | + | 0.165650i | \(0.947028\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 1.23687e6i | − | 0.110109i | −0.998483 | − | 0.0550543i | \(-0.982467\pi\) | ||
0.998483 | − | 0.0550543i | \(-0.0175332\pi\) | |||||||
\(662\) | 1.43051e7i | 1.26866i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 129391.i | 0.0113890i | ||||||||
\(665\) | 8.34276e6 | − | 1.68641e6i | 0.731570 | − | 0.147880i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.43506e6 | 0.821164 | ||||||||
\(668\) | 1.42547e6 | 0.123600 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 3.22809e7i | 2.77817i | ||||||||
\(671\) | −4.06788e6 | −0.348788 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.55042e7 | 1.31951 | 0.659755 | − | 0.751481i | \(-0.270660\pi\) | ||||
0.659755 | + | 0.751481i | \(0.270660\pi\) | |||||||
\(674\) | − | 1.42218e7i | − | 1.20588i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 8.35167e6 | 0.702921 | ||||||||
\(677\) | −5.05302e6 | −0.423721 | −0.211860 | − | 0.977300i | \(-0.567952\pi\) | ||||
−0.211860 | + | 0.977300i | \(0.567952\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.84645e6 | − | 373241.i | 0.153696 | − | 0.0310681i | ||||
\(680\) | − | 8084.94i | − | 0.000670508i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.07494e7i | 0.884962i | ||||||||
\(683\) | − | 896048.i | − | 0.0734986i | −0.999325 | − | 0.0367493i | \(-0.988300\pi\) | ||
0.999325 | − | 0.0367493i | \(-0.0117003\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 5.20562e6i | − | 0.423883i | ||||||
\(686\) | 1.43744e7 | − | 9.79943e6i | 1.16622 | − | 0.795043i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.42237e7 | −1.14562 | ||||||||
\(689\) | 2.15535e7 | 1.72970 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 3.91379e6i | − | 0.311819i | −0.987771 | − | 0.155909i | \(-0.950169\pi\) | ||
0.987771 | − | 0.155909i | \(-0.0498308\pi\) | |||||||
\(692\) | 1.46980e7 | 1.16679 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6.28947e6 | −0.495696 | ||||||||
\(695\) | 2.08146e7i | 1.63458i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.17554e6 | −0.0916546 | ||||||||
\(698\) | −519499. | −0.0403595 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.21388e6 | − | 6.00517e6i | −0.0936337 | − | 0.463212i | ||||
\(701\) | − | 1.89526e7i | − | 1.45671i | −0.685199 | − | 0.728356i | \(-0.740285\pi\) | ||
0.685199 | − | 0.728356i | \(-0.259715\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.22159e7i | 0.932258i | ||||||||
\(704\) | − | 5.84849e6i | − | 0.444746i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.13826e6i | 0.614497i | ||||||||
\(707\) | 1.84628e6 | + | 9.13365e6i | 0.138915 | + | 0.687220i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −890215. | −0.0665088 | −0.0332544 | − | 0.999447i | \(-0.510587\pi\) | ||||
−0.0332544 | + | 0.999447i | \(0.510587\pi\) | |||||||
\(710\) | 6.30836e6 | 0.469646 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 208199.i | − | 0.0153914i | ||||||
\(713\) | 1.84969e7 | 1.36262 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.80991e6 | 0.717629 | ||||||||
\(716\) | − | 1.63084e6i | − | 0.118886i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −4.07835e6 | −0.295239 | ||||||||
\(719\) | 4.20018e6 | 0.303002 | 0.151501 | − | 0.988457i | \(-0.451589\pi\) | ||||
0.151501 | + | 0.988457i | \(0.451589\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.53378e7 | − | 5.12178e6i | 1.81523 | − | 0.366930i | ||||
\(722\) | 1.23101e7i | 0.878856i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 7.30327e6i | − | 0.517810i | ||||||
\(725\) | 5.63707e6i | 0.398298i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 2.34586e7i | − | 1.64614i | −0.567940 | − | 0.823070i | \(-0.692259\pi\) | ||
0.567940 | − | 0.823070i | \(-0.307741\pi\) | |||||||
\(728\) | −40996.6 | − | 202813.i | −0.00286694 | − | 0.0141830i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.11174e7 | 1.46667 | ||||||||
\(731\) | −818700. | −0.0566671 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 1.51434e6i | − | 0.104103i | −0.998644 | − | 0.0520517i | \(-0.983424\pi\) | ||
0.998644 | − | 0.0520517i | \(-0.0165761\pi\) | |||||||
\(734\) | 1.07731e7 | 0.738074 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.03679e7 | −1.38597 | ||||||||
\(737\) | − | 1.07940e7i | − | 0.732002i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.26993e7 | −1.52898 | −0.764488 | − | 0.644638i | \(-0.777008\pi\) | ||||
−0.764488 | + | 0.644638i | \(0.777008\pi\) | |||||||
\(740\) | 2.72536e7 | 1.82955 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5.55000e6 | + | 2.74562e7i | 0.370069 | + | 1.83076i | ||||
\(743\) | − | 4.57793e6i | − | 0.304227i | −0.988363 | − | 0.152113i | \(-0.951392\pi\) | ||
0.988363 | − | 0.152113i | \(-0.0486079\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 3.33546e7i | − | 2.20174i | ||||||
\(746\) | 3.08709e7i | 2.03096i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 341976.i | − | 0.0223482i | ||||||
\(749\) | −786291. | + | 158941.i | −0.0512128 | + | 0.0103522i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.86507e7 | −1.20669 | −0.603346 | − | 0.797480i | \(-0.706166\pi\) | ||||
−0.603346 | + | 0.797480i | \(0.706166\pi\) | |||||||
\(752\) | −2.42256e7 | −1.56218 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 2.40828e7i | − | 1.54269i | ||||||
\(755\) | −3.36110e7 | −2.14592 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.22971e7 | −0.779942 | −0.389971 | − | 0.920827i | \(-0.627515\pi\) | ||||
−0.389971 | + | 0.920827i | \(0.627515\pi\) | |||||||
\(758\) | − | 1.91935e7i | − | 1.21333i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 131566. | 0.00826248 | ||||||||
\(761\) | 2.15406e7 | 1.34833 | 0.674165 | − | 0.738581i | \(-0.264504\pi\) | ||||
0.674165 | + | 0.738581i | \(0.264504\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 57452.4 | + | 284221.i | 0.00357270 | + | 0.0176744i | ||||
\(764\) | 520282.i | 0.0322482i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 8.25434e6i | − | 0.508289i | ||||||
\(767\) | − | 7.23592e6i | − | 0.444125i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 1.68033e7i | − | 1.02466i | −0.858790 | − | 0.512328i | \(-0.828783\pi\) | ||
0.858790 | − | 0.512328i | \(-0.171217\pi\) | |||||||
\(770\) | 2.52604e6 | + | 1.24965e7i | 0.153537 | + | 0.759557i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.06299e7 | 1.24582 | ||||||||
\(773\) | −2.17234e7 | −1.30761 | −0.653805 | − | 0.756663i | \(-0.726828\pi\) | ||||
−0.653805 | + | 0.756663i | \(0.726828\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.10512e7i | 0.660927i | ||||||||
\(776\) | 29118.6 | 0.00173587 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.94358e7 | 1.15121 | ||||||||
\(779\) | − | 1.91295e7i | − | 1.12943i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.10937e6 | −0.123744 | ||||||||
\(782\) | −1.18155e6 | −0.0690932 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.59825e7 | − | 6.73669e6i | 0.928658 | − | 0.391432i | ||||
\(785\) | 2.73889e7i | 1.58636i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 2.36452e7i | − | 1.36084i | −0.732824 | − | 0.680418i | \(-0.761798\pi\) | ||
0.732824 | − | 0.680418i | \(-0.238202\pi\) | |||||||
\(788\) | 4.61117e6i | 0.264543i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 8.29181e6i | 0.472696i | ||||||||
\(791\) | −2.02245e7 | + | 4.08819e6i | −1.14931 | + | 0.232321i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.78667e7 | 1.00893 | ||||||||
\(794\) | 1.20134e7 | 0.676264 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.53663e6i | 0.0859580i | ||||||||
\(797\) | 2.09606e7 | 1.16885 | 0.584425 | − | 0.811448i | \(-0.301320\pi\) | ||||
0.584425 | + | 0.811448i | \(0.301320\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.39440e6 | −0.0772716 | ||||||||
\(800\) | − | 1.21690e7i | − | 0.672250i | ||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −9.10053e6 | −0.499610 | ||||||||
\(803\) | −7.06115e6 | −0.386444 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.15031e7 | − | 4.34663e6i | 1.16953 | − | 0.236409i | ||||
\(806\) | − | 4.72130e7i | − | 2.55990i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 144039.i | 0.00776158i | ||||||||
\(809\) | 2.37033e7i | 1.27332i | 0.771144 | + | 0.636661i | \(0.219685\pi\) | ||||
−0.771144 | + | 0.636661i | \(0.780315\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.53235e6i | 0.241976i | 0.992654 | + | 0.120988i | \(0.0386062\pi\) | ||||
−0.992654 | + | 0.120988i | \(0.961394\pi\) | |||||||
\(812\) | 1.52787e7 | − | 3.08844e6i | 0.813198 | − | 0.164380i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.82979e7 | −0.967923 | ||||||||
\(815\) | 2.27447e7 | 1.19946 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 1.33227e7i | − | 0.698292i | ||||||
\(818\) | −2.72449e7 | −1.42365 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.26779e7 | −2.21650 | ||||||||
\(821\) | − | 1.66553e7i | − | 0.862374i | −0.902263 | − | 0.431187i | \(-0.858095\pi\) | ||
0.902263 | − | 0.431187i | \(-0.141905\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.61928e7 | −0.833339 | −0.416669 | − | 0.909058i | \(-0.636803\pi\) | ||||
−0.416669 | + | 0.909058i | \(0.636803\pi\) | |||||||
\(824\) | 399579. | 0.0205015 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 9.21757e6 | − | 1.86324e6i | 0.470074 | − | 0.0950208i | ||||
\(827\) | − | 1.61246e7i | − | 0.819834i | −0.912123 | − | 0.409917i | \(-0.865558\pi\) | ||
0.912123 | − | 0.409917i | \(-0.134442\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.36056e7i | 1.69834i | 0.528118 | + | 0.849171i | \(0.322898\pi\) | ||||
−0.528118 | + | 0.849171i | \(0.677102\pi\) | |||||||
\(830\) | 3.50165e7i | 1.76432i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.56874e7i | 1.28650i | ||||||||
\(833\) | 919937. | − | 387756.i | 0.0459352 | − | 0.0193618i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.04961e6 | −0.151366 | ||||||||
\(836\) | 5.56498e6 | 0.275390 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1.43530e7i | 0.706047i | ||||||||
\(839\) | 7.40633e6 | 0.363244 | 0.181622 | − | 0.983368i | \(-0.441865\pi\) | ||||
0.181622 | + | 0.983368i | \(0.441865\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.16897e6 | 0.300762 | ||||||||
\(842\) | − | 2.63677e7i | − | 1.28172i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.08920e7 | 1.00954 | ||||||||
\(845\) | −1.78673e7 | −0.860827 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.29215e6 | + | 1.62865e7i | 0.157678 | + | 0.780044i | ||||
\(848\) | 2.79268e7i | 1.33362i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − | 705929.i | − | 0.0335130i | ||||||
\(851\) | 3.14858e7i | 1.49036i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.39804e7i | 0.657880i | 0.944351 | + | 0.328940i | \(0.106691\pi\) | ||||
−0.944351 | + | 0.328940i | \(0.893309\pi\) | |||||||
\(854\) | 4.60065e6 | + | 2.27597e7i | 0.215861 | + | 1.06788i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −12399.9 | −0.000578406 | ||||||||
\(857\) | −6.23872e6 | −0.290164 | −0.145082 | − | 0.989420i | \(-0.546345\pi\) | ||||
−0.145082 | + | 0.989420i | \(0.546345\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.06879e7i | 1.41901i | 0.704701 | + | 0.709504i | \(0.251081\pi\) | ||||
−0.704701 | + | 0.709504i | \(0.748919\pi\) | |||||||
\(860\) | −2.97229e7 | −1.37039 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3.03232e7 | −1.38998 | ||||||||
\(863\) | − | 3.33384e6i | − | 0.152376i | −0.997093 | − | 0.0761882i | \(-0.975725\pi\) | ||
0.997093 | − | 0.0761882i | \(-0.0242750\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.14444e7 | −1.42890 | ||||||||
\(866\) | −2.23723e7 | −1.01372 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.99530e7 | − | 6.05470e6i | 1.34940 | − | 0.272768i | ||||
\(869\) | − | 2.77259e6i | − | 0.124548i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.74086e7i | 2.11744i | ||||||||
\(872\) | 4482.19i | 0.000199618i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 1.92274e7i | − | 0.851415i | ||||||
\(875\) | −2.85519e6 | − | 1.41248e7i | −0.126071 | − | 0.623680i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 389154. | 0.0170853 | 0.00854266 | − | 0.999964i | \(-0.497281\pi\) | ||||
0.00854266 | + | 0.999964i | \(0.497281\pi\) | |||||||
\(878\) | −2.19921e6 | −0.0962785 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.27107e7i | 0.553301i | ||||||||
\(881\) | 2.09290e7 | 0.908465 | 0.454232 | − | 0.890883i | \(-0.349914\pi\) | ||||
0.454232 | + | 0.890883i | \(0.349914\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9.39508e6 | −0.405507 | −0.202754 | − | 0.979230i | \(-0.564989\pi\) | ||||
−0.202754 | + | 0.979230i | \(0.564989\pi\) | |||||||
\(884\) | 1.50201e6i | 0.0646459i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.25576e7 | −0.965402 | ||||||||
\(887\) | −3.01808e7 | −1.28802 | −0.644008 | − | 0.765019i | \(-0.722730\pi\) | ||||
−0.644008 | + | 0.765019i | \(0.722730\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.28773e6 | + | 6.37048e6i | 0.0546474 | + | 0.270344i | ||||
\(890\) | − | 5.63440e7i | − | 2.38436i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2.32547e7i | 0.978586i | ||||||||
\(893\) | − | 2.26910e7i | − | 0.952195i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.48897e6i | 0.145593i | ||||||||
\(896\) | 521493. | − | 105415.i | 0.0217009 | − | 0.00438663i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2.54868e7 | 1.05469 | ||||||||
\(899\) | −2.81170e7 | −1.16030 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.60744e6i | 0.0659662i | ||||||||
\(902\) | 2.86537e7 | 1.17264 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −318943. | −0.0129805 | ||||||||
\(905\) | 1.56243e7i | 0.634133i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.72280e7 | 1.09900 | 0.549499 | − | 0.835494i | \(-0.314819\pi\) | ||||
0.549499 | + | 0.835494i | \(0.314819\pi\) | |||||||
\(908\) | −6.42106e6 | −0.258459 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.10947e7 | − | 5.48862e7i | −0.444132 | − | 2.19715i | ||||
\(911\) | − | 4.64974e7i | − | 1.85623i | −0.372290 | − | 0.928117i | \(-0.621427\pi\) | ||
0.372290 | − | 0.928117i | \(-0.378573\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 1.17087e7i | − | 0.464870i | ||||||
\(914\) | 2.72443e7i | 1.07872i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 1.01949e7i | − | 0.401464i | ||||||
\(917\) | 2.20276e6 | + | 1.08972e7i | 0.0865054 | + | 0.427948i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.94344e7 | 1.14965 | 0.574826 | − | 0.818276i | \(-0.305070\pi\) | ||||
0.574826 | + | 0.818276i | \(0.305070\pi\) | |||||||
\(920\) | 339106. | 0.0132089 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 4.13551e7i | − | 1.60214i | ||||||
\(923\) | 9.26463e6 | 0.357951 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.88115e7 | −0.722886 | ||||||||
\(926\) | 2.36264e7i | 0.905463i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.09612e7 | 1.18018 | ||||||||
\(929\) | 2.33163e7 | 0.886381 | 0.443191 | − | 0.896427i | \(-0.353846\pi\) | ||||
0.443191 | + | 0.896427i | \(0.353846\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.30995e6 | + | 1.49701e7i | 0.238590 | + | 0.566046i | ||||
\(932\) | − | 3.07568e6i | − | 0.115985i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 3.66366e7i | − | 1.37419i | ||||||
\(935\) | 731611.i | 0.0273685i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.49449e7i | 0.928182i | 0.885788 | + | 0.464091i | \(0.153619\pi\) | ||||
−0.885788 | + | 0.464091i | \(0.846381\pi\) | |||||||
\(938\) | −6.03920e7 | + | 1.22076e7i | −2.24116 | + | 0.453028i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −5.06236e7 | −1.86867 | ||||||||
\(941\) | −1.72759e6 | −0.0636013 | −0.0318007 | − | 0.999494i | \(-0.510124\pi\) | ||||
−0.0318007 | + | 0.999494i | \(0.510124\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 4.93054e7i | − | 1.80557i | ||||||
\(944\) | 9.37556e6 | 0.342427 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.99558e7 | 0.725007 | ||||||||
\(947\) | 2.40722e7i | 0.872251i | 0.899886 | + | 0.436126i | \(0.143650\pi\) | ||||
−0.899886 | + | 0.436126i | \(0.856350\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.10135e7 | 1.11786 | ||||||||
\(950\) | 1.14876e7 | 0.412971 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 15125.5 | − | 3057.47i | 0.000540902 | − | 0.000109338i | ||||
\(953\) | 2.66088e7i | 0.949059i | 0.880240 | + | 0.474529i | \(0.157382\pi\) | ||||
−0.880240 | + | 0.474529i | \(0.842618\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 1.11307e6i | − | 0.0394925i | ||||||
\(956\) | 1.38057e7i | 0.488556i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 6.46909e7i | − | 2.27735i | ||||||
\(959\) | 9.73883e6 | − | 1.96861e6i | 0.341948 | − | 0.0691214i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.64926e7 | −0.925372 | ||||||||
\(962\) | 8.03670e7 | 2.79988 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 2.57956e7i | − | 0.894031i | ||||||
\(965\) | −4.41349e7 | −1.52568 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.13663e7 | −1.07869 | −0.539346 | − | 0.842084i | \(-0.681328\pi\) | ||||
−0.539346 | + | 0.842084i | \(0.681328\pi\) | |||||||
\(968\) | 256840.i | 0.00880996i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 7.88024e6 | 0.268912 | ||||||||
\(971\) | 5.86276e6 | 0.199551 | 0.0997756 | − | 0.995010i | \(-0.468188\pi\) | ||||
0.0997756 | + | 0.995010i | \(0.468188\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.89406e7 | + | 7.87146e6i | −1.31862 | + | 0.266547i | ||||
\(974\) | − | 4.40393e7i | − | 1.48745i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.31498e7i | 0.777899i | ||||||||
\(977\) | 7.41259e6i | 0.248447i | 0.992254 | + | 0.124224i | \(0.0396440\pi\) | ||||
−0.992254 | + | 0.124224i | \(0.960356\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.88401e7i | 0.628241i | ||||||||
\(980\) | 3.33983e7 | − | 1.40775e7i | 1.11086 | − | 0.468231i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4.95740e7 | 1.64049 | ||||||||
\(983\) | −7.22864e6 | −0.238601 | −0.119301 | − | 0.992858i | \(-0.538065\pi\) | ||||
−0.119301 | + | 0.992858i | \(0.538065\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 9.86498e6i | − | 0.323971i | ||||||
\(986\) | 1.79607e6 | 0.0588343 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.44422e7 | −0.796613 | ||||||||
\(989\) | − | 3.43386e7i | − | 1.11633i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.40025e7 | 1.42329 | 0.711645 | − | 0.702539i | \(-0.247950\pi\) | ||||
0.711645 | + | 0.702539i | \(0.247950\pi\) | |||||||
\(992\) | 6.06976e7 | 1.95836 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.38563e6 | + | 1.18019e7i | 0.0765838 | + | 0.378865i | ||||
\(995\) | − | 3.28741e6i | − | 0.105268i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 2.90225e7i | − | 0.924690i | −0.886700 | − | 0.462345i | \(-0.847008\pi\) | ||
0.886700 | − | 0.462345i | \(-0.152992\pi\) | |||||||
\(998\) | − | 1.49182e7i | − | 0.474123i | ||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 63.6.c.b.62.8 | yes | 8 | |
3.2 | odd | 2 | inner | 63.6.c.b.62.1 | ✓ | 8 | |
4.3 | odd | 2 | 1008.6.k.b.881.7 | 8 | |||
7.6 | odd | 2 | inner | 63.6.c.b.62.7 | yes | 8 | |
12.11 | even | 2 | 1008.6.k.b.881.1 | 8 | |||
21.20 | even | 2 | inner | 63.6.c.b.62.2 | yes | 8 | |
28.27 | even | 2 | 1008.6.k.b.881.2 | 8 | |||
84.83 | odd | 2 | 1008.6.k.b.881.8 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.6.c.b.62.1 | ✓ | 8 | 3.2 | odd | 2 | inner | |
63.6.c.b.62.2 | yes | 8 | 21.20 | even | 2 | inner | |
63.6.c.b.62.7 | yes | 8 | 7.6 | odd | 2 | inner | |
63.6.c.b.62.8 | yes | 8 | 1.1 | even | 1 | trivial | |
1008.6.k.b.881.1 | 8 | 12.11 | even | 2 | |||
1008.6.k.b.881.2 | 8 | 28.27 | even | 2 | |||
1008.6.k.b.881.7 | 8 | 4.3 | odd | 2 | |||
1008.6.k.b.881.8 | 8 | 84.83 | odd | 2 |