Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1680,3,Mod(769,1680)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1680, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1680.769");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1680.bd (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: | \(45.7766844125\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 96 x^{14} - 532 x^{13} + 3236 x^{12} - 12864 x^{11} + 49526 x^{10} - 141436 x^{9} + \cdots + 33750 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 769.16 | ||
Root | \(0.500000 - 4.10071i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1680.769 |
Dual form | 1680.3.bd.a.769.15 |
$q$-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 \(\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(337\) | \(421\) | \(1121\) | \(1471\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 1.73205 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.59769 | + | 1.96501i | 0.919538 | + | 0.393001i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −6.81963 | + | 1.57881i | −0.974233 | + | 0.225545i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 8.15965 | 0.741786 | 0.370893 | − | 0.928676i | \(-0.379052\pi\) | ||||
0.370893 | + | 0.928676i | \(0.379052\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 14.6064 | 1.12357 | 0.561785 | − | 0.827284i | \(-0.310115\pi\) | ||||
0.561785 | + | 0.827284i | \(0.310115\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 7.96343 | + | 3.40349i | 0.530896 | + | 0.226899i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.81421 | 0.342012 | 0.171006 | − | 0.985270i | \(-0.445298\pi\) | ||||
0.171006 | + | 0.985270i | \(0.445298\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 33.7736i | − | 1.77756i | −0.458337 | − | 0.888778i | \(-0.651555\pi\) | ||
0.458337 | − | 0.888778i | \(-0.348445\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −11.8119 | + | 2.73459i | −0.562474 | + | 0.130218i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 37.2576i | − | 1.61989i | −0.586503 | − | 0.809947i | \(-0.699496\pi\) | ||
0.586503 | − | 0.809947i | \(-0.300504\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 17.2775 | + | 18.0690i | 0.691100 | + | 0.722759i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.19615 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9.25305 | −0.319071 | −0.159535 | − | 0.987192i | \(-0.551000\pi\) | ||||
−0.159535 | + | 0.987192i | \(0.551000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 19.2558i | 0.621154i | 0.950548 | + | 0.310577i | \(0.100522\pi\) | ||||
−0.950548 | + | 0.310577i | \(0.899478\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 14.1329 | 0.428270 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −34.4569 | − | 6.14171i | −0.984483 | − | 0.175478i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 63.4350i | − | 1.71446i | −0.514933 | − | 0.857230i | \(-0.672183\pi\) | ||
0.514933 | − | 0.857230i | \(-0.327817\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 25.2990 | 0.648693 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.25880i | 0.201434i | 0.994915 | + | 0.100717i | \(0.0321137\pi\) | ||||
−0.994915 | + | 0.100717i | \(0.967886\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 42.0893i | 0.978822i | 0.872053 | + | 0.489411i | \(0.162788\pi\) | ||||
−0.872053 | + | 0.489411i | \(0.837212\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 13.7931 | + | 5.89502i | 0.306513 | + | 0.131000i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −23.3380 | −0.496552 | −0.248276 | − | 0.968689i | \(-0.579864\pi\) | ||||
−0.248276 | + | 0.968689i | \(0.579864\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 44.0147 | − | 21.5339i | 0.898259 | − | 0.439466i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 10.0705 | 0.197461 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 71.3497i | 1.34622i | 0.739542 | + | 0.673110i | \(0.235042\pi\) | ||||
−0.739542 | + | 0.673110i | \(0.764958\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 37.5155 | + | 16.0337i | 0.682100 | + | 0.291523i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 58.4976i | − | 1.02627i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 42.9350i | 0.727712i | 0.931455 | + | 0.363856i | \(0.118540\pi\) | ||||
−0.931455 | + | 0.363856i | \(0.881460\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 34.2864i | − | 0.562072i | −0.959697 | − | 0.281036i | \(-0.909322\pi\) | ||
0.959697 | − | 0.281036i | \(-0.0906781\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −20.4589 | + | 4.73644i | −0.324744 | + | 0.0751816i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 67.1557 | + | 28.7017i | 1.03316 | + | 0.441564i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.99889i | 0.0746102i | 0.999304 | + | 0.0373051i | \(0.0118773\pi\) | ||||
−0.999304 | + | 0.0373051i | \(0.988123\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 64.5320i | − | 0.935246i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 38.8120 | 0.546648 | 0.273324 | − | 0.961922i | \(-0.411877\pi\) | ||||
0.273324 | + | 0.961922i | \(0.411877\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 124.629 | 1.70725 | 0.853626 | − | 0.520886i | \(-0.174398\pi\) | ||||
0.853626 | + | 0.520886i | \(0.174398\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 29.9255 | + | 31.2964i | 0.399007 | + | 0.417285i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −55.6458 | + | 12.8826i | −0.722672 | + | 0.167306i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 56.1842 | 0.711192 | 0.355596 | − | 0.934640i | \(-0.384278\pi\) | ||||
0.355596 | + | 0.934640i | \(0.384278\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 90.3980 | 1.08913 | 0.544566 | − | 0.838718i | \(-0.316694\pi\) | ||||
0.544566 | + | 0.838718i | \(0.316694\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 26.7319 | + | 11.4249i | 0.314493 | + | 0.134411i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −16.0267 | −0.184215 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 16.2289i | 0.182347i | 0.995835 | + | 0.0911736i | \(0.0290618\pi\) | ||||
−0.995835 | + | 0.0911736i | \(0.970938\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −99.6102 | + | 23.0608i | −1.09462 | + | 0.253415i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 33.3520i | 0.358624i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 66.3653 | − | 155.280i | 0.698582 | − | 1.63453i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 82.7605 | 0.853201 | 0.426601 | − | 0.904440i | \(-0.359711\pi\) | ||||
0.426601 | + | 0.904440i | \(0.359711\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 24.4789 | 0.247262 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 87.2055i | − | 0.863420i | −0.902012 | − | 0.431710i | \(-0.857910\pi\) | ||
0.902012 | − | 0.431710i | \(-0.142090\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 187.567 | 1.82104 | 0.910521 | − | 0.413462i | \(-0.135681\pi\) | ||||
0.910521 | + | 0.413462i | \(0.135681\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −59.6811 | − | 10.6378i | −0.568392 | − | 0.101312i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 157.858i | 1.47531i | 0.675180 | + | 0.737653i | \(0.264066\pi\) | ||||
−0.675180 | + | 0.737653i | \(0.735934\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −112.073 | −1.02819 | −0.514097 | − | 0.857732i | \(-0.671873\pi\) | ||||
−0.514097 | + | 0.857732i | \(0.671873\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 109.873i | − | 0.989844i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 141.987i | − | 1.25653i | −0.778001 | − | 0.628263i | \(-0.783766\pi\) | ||
0.778001 | − | 0.628263i | \(-0.216234\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 73.2113 | − | 171.299i | 0.636620 | − | 1.48955i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 43.8192 | 0.374523 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −39.6507 | + | 9.17955i | −0.333199 | + | 0.0771391i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −54.4202 | −0.449754 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 14.3047i | 0.116298i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 43.9310 | + | 117.026i | 0.351448 | + | 0.936207i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 202.414i | 1.59381i | 0.604104 | + | 0.796905i | \(0.293531\pi\) | ||||
−0.604104 | + | 0.796905i | \(0.706469\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 72.9008i | 0.565123i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 141.260i | − | 1.07832i | −0.842203 | − | 0.539160i | \(-0.818742\pi\) | ||
0.842203 | − | 0.539160i | \(-0.181258\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 53.3222 | + | 230.323i | 0.400919 | + | 1.73175i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 23.8903 | + | 10.2105i | 0.176965 | + | 0.0756331i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 50.6430i | 0.369657i | 0.982771 | + | 0.184829i | \(0.0591730\pi\) | ||||
−0.982771 | + | 0.184829i | \(0.940827\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 74.0256i | − | 0.532559i | −0.963896 | − | 0.266279i | \(-0.914206\pi\) | ||
0.963896 | − | 0.266279i | \(-0.0857943\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −40.4225 | −0.286685 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 119.183 | 0.833448 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −42.5426 | − | 18.1823i | −0.293397 | − | 0.125395i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 76.2357 | − | 37.2977i | 0.518610 | − | 0.253726i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −226.979 | −1.52335 | −0.761676 | − | 0.647958i | \(-0.775623\pi\) | ||||
−0.761676 | + | 0.647958i | \(0.775623\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −294.426 | −1.94984 | −0.974920 | − | 0.222558i | \(-0.928559\pi\) | ||||
−0.974920 | + | 0.222558i | \(0.928559\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 17.4426 | 0.114004 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −37.8377 | + | 88.5321i | −0.244114 | + | 0.571175i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −65.8596 | −0.419488 | −0.209744 | − | 0.977756i | \(-0.567263\pi\) | ||||
−0.209744 | + | 0.977756i | \(0.567263\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 123.581i | 0.777241i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 58.8227 | + | 254.083i | 0.365359 | + | 1.57815i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 28.2075i | 0.173052i | 0.996250 | + | 0.0865260i | \(0.0275766\pi\) | ||||
−0.996250 | + | 0.0865260i | \(0.972423\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 64.9788 | + | 27.7713i | 0.393811 | + | 0.168311i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −128.461 | −0.769227 | −0.384614 | − | 0.923078i | \(-0.625665\pi\) | ||||
−0.384614 | + | 0.923078i | \(0.625665\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 44.3469 | 0.262408 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 101.321i | − | 0.592519i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 112.446 | 0.649976 | 0.324988 | − | 0.945718i | \(-0.394640\pi\) | ||||
0.324988 | + | 0.945718i | \(0.394640\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −146.354 | − | 95.9457i | −0.836307 | − | 0.548261i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 74.3656i | 0.420144i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 68.9019 | 0.384927 | 0.192464 | − | 0.981304i | \(-0.438352\pi\) | ||||
0.192464 | + | 0.981304i | \(0.438352\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 166.537i | − | 0.920094i | −0.887895 | − | 0.460047i | \(-0.847833\pi\) | ||
0.887895 | − | 0.460047i | \(-0.152167\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 59.3858i | − | 0.324513i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 124.650 | − | 291.655i | 0.673785 | − | 1.57651i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 47.4419 | 0.253700 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −35.4358 | + | 8.20376i | −0.187491 | + | 0.0434061i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 148.289 | 0.776382 | 0.388191 | − | 0.921579i | \(-0.373100\pi\) | ||||
0.388191 | + | 0.921579i | \(0.373100\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 35.1886i | 0.182324i | 0.995836 | + | 0.0911622i | \(0.0290582\pi\) | ||||
−0.995836 | + | 0.0911622i | \(0.970942\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 116.317 | + | 49.7127i | 0.596498 | + | 0.254937i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 193.634i | − | 0.982915i | −0.870902 | − | 0.491457i | \(-0.836464\pi\) | ||
0.870902 | − | 0.491457i | \(-0.163536\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 181.838i | − | 0.913759i | −0.889529 | − | 0.456880i | \(-0.848967\pi\) | ||
0.889529 | − | 0.456880i | \(-0.151033\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.65832i | 0.0430762i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 63.1023 | − | 14.6088i | 0.310849 | − | 0.0719647i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −16.2286 | + | 37.9714i | −0.0791638 | + | 0.185226i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 111.773i | − | 0.539965i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 275.580i | − | 1.31857i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −175.914 | −0.833717 | −0.416859 | − | 0.908971i | \(-0.636869\pi\) | ||||
−0.416859 | + | 0.908971i | \(0.636869\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 67.2244 | 0.315607 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −82.7058 | + | 193.514i | −0.384678 | + | 0.900064i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −30.4013 | − | 131.317i | −0.140098 | − | 0.605149i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 215.864 | 0.985683 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 84.9246 | 0.384274 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −20.5675 | −0.0922308 | −0.0461154 | − | 0.998936i | \(-0.514684\pi\) | ||||
−0.0461154 | + | 0.998936i | \(0.514684\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 51.8325 | + | 54.2069i | 0.230367 | + | 0.240920i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 414.087 | 1.82417 | 0.912085 | − | 0.410001i | \(-0.134472\pi\) | ||||
0.912085 | + | 0.410001i | \(0.134472\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 195.520i | 0.853799i | 0.904299 | + | 0.426899i | \(0.140394\pi\) | ||||
−0.904299 | + | 0.426899i | \(0.859606\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −96.3813 | + | 22.3133i | −0.417235 | + | 0.0965942i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 81.3006i | 0.348930i | 0.984663 | + | 0.174465i | \(0.0558195\pi\) | ||||
−0.984663 | + | 0.174465i | \(0.944180\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −107.301 | − | 45.8592i | −0.456599 | − | 0.195146i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 97.3138 | 0.410607 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 249.265 | 1.04295 | 0.521475 | − | 0.853267i | \(-0.325382\pi\) | ||||
0.521475 | + | 0.853267i | \(0.325382\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 262.343i | − | 1.08856i | −0.838904 | − | 0.544280i | \(-0.816803\pi\) | ||
0.838904 | − | 0.544280i | \(-0.183197\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.5885 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 244.680 | − | 12.5169i | 0.998694 | − | 0.0510892i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 493.310i | − | 1.99721i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 156.574 | 0.628811 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 141.917i | 0.565406i | 0.959208 | + | 0.282703i | \(0.0912310\pi\) | ||||
−0.959208 | + | 0.282703i | \(0.908769\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 304.008i | − | 1.20161i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 46.3010 | + | 19.7886i | 0.181573 | + | 0.0776023i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 170.843 | 0.664757 | 0.332379 | − | 0.943146i | \(-0.392149\pi\) | ||||
0.332379 | + | 0.943146i | \(0.392149\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 100.152 | + | 432.604i | 0.386688 | + | 1.67028i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −27.7591 | −0.106357 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 383.417i | 1.45786i | 0.684588 | + | 0.728930i | \(0.259982\pi\) | ||||
−0.684588 | + | 0.728930i | \(0.740018\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −140.203 | + | 328.044i | −0.529066 | + | 1.23790i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 28.1093i | 0.105278i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 154.512i | − | 0.574393i | −0.957872 | − | 0.287196i | \(-0.907277\pi\) | ||
0.957872 | − | 0.287196i | \(-0.0927232\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 320.328i | 1.18202i | 0.806664 | + | 0.591010i | \(0.201271\pi\) | ||||
−0.806664 | + | 0.591010i | \(0.798729\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −172.530 | + | 39.9425i | −0.631978 | + | 0.146309i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 140.978 | + | 147.436i | 0.512648 | + | 0.536132i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 222.854i | 0.804526i | 0.915524 | + | 0.402263i | \(0.131776\pi\) | ||||
−0.915524 | + | 0.402263i | \(0.868224\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 57.7673i | 0.207051i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 218.973 | 0.779263 | 0.389631 | − | 0.920971i | \(-0.372602\pi\) | ||||
0.389631 | + | 0.920971i | \(0.372602\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −36.3957 | −0.128607 | −0.0643034 | − | 0.997930i | \(-0.520483\pi\) | ||||
−0.0643034 | + | 0.997930i | \(0.520483\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 114.948 | − | 268.954i | 0.403326 | − | 0.943697i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −13.0391 | − | 56.3219i | −0.0454324 | − | 0.196244i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −255.195 | −0.883028 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 143.345 | 0.492596 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −168.440 | −0.574882 | −0.287441 | − | 0.957798i | \(-0.592805\pi\) | ||||
−0.287441 | + | 0.957798i | \(0.592805\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −84.3675 | + | 197.402i | −0.285991 | + | 0.669158i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 42.3988 | 0.142757 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 544.199i | − | 1.82006i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −66.4512 | − | 287.034i | −0.220768 | − | 0.953600i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 151.044i | − | 0.498496i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 67.3730 | − | 157.638i | 0.220895 | − | 0.516847i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −223.400 | −0.727688 | −0.363844 | − | 0.931460i | \(-0.618536\pi\) | ||||
−0.363844 | + | 0.931460i | \(0.618536\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 324.876 | 1.05138 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 46.0396i | − | 0.148037i | −0.997257 | − | 0.0740186i | \(-0.976418\pi\) | ||
0.997257 | − | 0.0740186i | \(-0.0235824\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −80.0375 | −0.255711 | −0.127855 | − | 0.991793i | \(-0.540809\pi\) | ||||
−0.127855 | + | 0.991793i | \(0.540809\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −103.371 | − | 18.4251i | −0.328161 | − | 0.0584925i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 185.237i | 0.584343i | 0.956366 | + | 0.292171i | \(0.0943777\pi\) | ||||
−0.956366 | + | 0.292171i | \(0.905622\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −75.5016 | −0.236682 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 273.418i | 0.851768i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 196.367i | − | 0.607946i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 252.362 | + | 263.923i | 0.776499 | + | 0.812070i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −194.116 | −0.593628 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 159.156 | − | 36.8463i | 0.483757 | − | 0.111995i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −61.4686 | −0.185706 | −0.0928529 | − | 0.995680i | \(-0.529599\pi\) | ||||
−0.0928529 | + | 0.995680i | \(0.529599\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 190.305i | − | 0.571487i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −9.82284 | + | 22.9833i | −0.0293219 | + | 0.0686069i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 656.501i | 1.94807i | 0.226387 | + | 0.974037i | \(0.427309\pi\) | ||||
−0.226387 | + | 0.974037i | \(0.572691\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 245.929i | − | 0.725456i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 157.120i | 0.460764i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −266.166 | + | 216.344i | −0.775994 | + | 0.630740i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 126.806 | − | 296.698i | 0.367553 | − | 0.859994i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 321.323i | − | 0.926002i | −0.886358 | − | 0.463001i | \(-0.846773\pi\) | ||
0.886358 | − | 0.463001i | \(-0.153227\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 185.135i | − | 0.530474i | −0.964183 | − | 0.265237i | \(-0.914550\pi\) | ||
0.964183 | − | 0.265237i | \(-0.0854501\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 75.8971 | 0.216231 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 597.338 | 1.69218 | 0.846088 | − | 0.533043i | \(-0.178952\pi\) | ||||
0.846088 | + | 0.533043i | \(0.178952\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 178.446 | + | 76.2658i | 0.502664 | + | 0.214833i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −68.6771 | + | 15.8995i | −0.192373 | + | 0.0445363i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −239.446 | −0.666982 | −0.333491 | − | 0.942753i | \(-0.608227\pi\) | ||||
−0.333491 | + | 0.942753i | \(0.608227\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −779.655 | −2.15971 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −94.2585 | −0.259665 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 573.007 | + | 244.898i | 1.56988 | + | 0.670952i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −398.743 | −1.08649 | −0.543246 | − | 0.839573i | \(-0.682805\pi\) | ||||
−0.543246 | + | 0.839573i | \(0.682805\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 24.7764i | 0.0671447i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −112.648 | − | 486.578i | −0.303633 | − | 1.31153i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 34.7064i | 0.0930466i | 0.998917 | + | 0.0465233i | \(0.0148142\pi\) | ||||
−0.998917 | + | 0.0465233i | \(0.985186\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 76.0907 | + | 202.695i | 0.202908 | + | 0.540520i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −135.154 | −0.358498 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 109.217 | 0.288172 | 0.144086 | − | 0.989565i | \(-0.453976\pi\) | ||||
0.144086 | + | 0.989565i | \(0.453976\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 350.591i | 0.920187i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −336.420 | −0.878381 | −0.439191 | − | 0.898394i | \(-0.644735\pi\) | ||||
−0.439191 | + | 0.898394i | \(0.644735\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −281.156 | − | 50.1142i | −0.730276 | − | 0.130167i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 126.268i | 0.326274i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −311.173 | −0.799930 | −0.399965 | − | 0.916530i | \(-0.630978\pi\) | ||||
−0.399965 | + | 0.916530i | \(0.630978\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 216.623i | − | 0.554023i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 244.669i | − | 0.622568i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 258.317 | + | 110.402i | 0.653968 | + | 0.279499i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −41.2679 | −0.103949 | −0.0519747 | − | 0.998648i | \(-0.516552\pi\) | ||||
−0.0519747 | + | 0.998648i | \(0.516552\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 92.3568 | + | 398.932i | 0.231471 | + | 0.999829i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −495.642 | −1.23601 | −0.618007 | − | 0.786173i | \(-0.712060\pi\) | ||||
−0.618007 | + | 0.786173i | \(0.712060\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 281.258i | 0.697910i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 41.3792 | + | 17.6851i | 0.102171 | + | 0.0436668i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 517.608i | − | 1.27176i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 359.920i | 0.880001i | 0.897998 | + | 0.440000i | \(0.145022\pi\) | ||||
−0.897998 | + | 0.440000i | \(0.854978\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 87.7163i | 0.213422i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −67.7863 | − | 292.801i | −0.164132 | − | 0.708960i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 415.622 | + | 177.633i | 1.00150 | + | 0.428030i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 128.216i | − | 0.307473i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 482.910i | 1.15253i | 0.817263 | + | 0.576265i | \(0.195490\pi\) | ||||
−0.817263 | + | 0.576265i | \(0.804510\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −523.520 | −1.24351 | −0.621757 | − | 0.783210i | \(-0.713581\pi\) | ||||
−0.621757 | + | 0.783210i | \(0.713581\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −70.0139 | −0.165517 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 100.455 | + | 105.057i | 0.236365 | + | 0.247192i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 54.1319 | + | 233.821i | 0.126773 | + | 0.547589i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 206.431 | 0.481191 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −517.027 | −1.19960 | −0.599799 | − | 0.800150i | \(-0.704753\pi\) | ||||
−0.599799 | + | 0.800150i | \(0.704753\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −567.712 | −1.31111 | −0.655557 | − | 0.755146i | \(-0.727566\pi\) | ||||
−0.655557 | + | 0.755146i | \(0.727566\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −73.6860 | − | 31.4926i | −0.169393 | − | 0.0723969i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1258.32 | −2.87945 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 622.875i | − | 1.41885i | −0.704781 | − | 0.709425i | \(-0.748955\pi\) | ||
0.704781 | − | 0.709425i | \(-0.251045\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 132.044 | − | 64.6016i | 0.299420 | − | 0.146489i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 476.699i | − | 1.07607i | −0.842923 | − | 0.538035i | \(-0.819167\pi\) | ||
0.842923 | − | 0.538035i | \(-0.180833\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −31.8899 | + | 74.6154i | −0.0716626 | + | 0.167675i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −393.140 | −0.879507 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 861.931 | 1.91967 | 0.959834 | − | 0.280570i | \(-0.0905233\pi\) | ||||
0.959834 | + | 0.280570i | \(0.0905233\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 67.3889i | 0.149421i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −509.960 | −1.12574 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −503.292 | − | 89.7083i | −1.10614 | − | 0.197161i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 27.5401i | − | 0.0602629i | −0.999546 | − | 0.0301314i | \(-0.990407\pi\) | ||
0.999546 | − | 0.0301314i | \(-0.00959258\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 30.2115 | 0.0658203 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 378.183i | 0.820353i | 0.912006 | + | 0.410176i | \(0.134533\pi\) | ||||
−0.912006 | + | 0.410176i | \(0.865467\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 724.994i | − | 1.56586i | −0.622108 | − | 0.782931i | \(-0.713724\pi\) | ||
0.622108 | − | 0.782931i | \(-0.286276\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −65.5369 | + | 153.342i | −0.140939 | + | 0.329768i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 371.451 | 0.795398 | 0.397699 | − | 0.917516i | \(-0.369809\pi\) | ||||
0.397699 | + | 0.917516i | \(0.369809\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.89231 | − | 34.0905i | −0.0168280 | − | 0.0726877i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −114.072 | −0.242191 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 343.434i | 0.726076i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 610.254 | − | 583.523i | 1.28475 | − | 1.22847i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 214.049i | 0.448740i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 860.650i | 1.79677i | 0.439214 | + | 0.898383i | \(0.355257\pi\) | ||||
−0.439214 | + | 0.898383i | \(0.644743\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 926.558i | − | 1.92632i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 101.884 | + | 440.084i | 0.210940 | + | 0.911147i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 380.507 | + | 162.625i | 0.784551 | + | 0.335309i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 887.173i | 1.82171i | 0.412726 | + | 0.910855i | \(0.364577\pi\) | ||||
−0.412726 | + | 0.910855i | \(0.635423\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 48.8568i | 0.0999116i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 50.1823 | 0.102204 | 0.0511021 | − | 0.998693i | \(-0.483727\pi\) | ||||
0.0511021 | + | 0.998693i | \(0.483727\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −53.7991 | −0.109126 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 112.547 | + | 48.1012i | 0.227367 | + | 0.0971742i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −264.683 | + | 61.2769i | −0.532562 | + | 0.123294i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −160.443 | −0.321529 | −0.160765 | − | 0.986993i | \(-0.551396\pi\) | ||||
−0.160765 | + | 0.986993i | \(0.551396\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −222.501 | −0.444113 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −742.042 | −1.47523 | −0.737616 | − | 0.675220i | \(-0.764049\pi\) | ||||
−0.737616 | + | 0.675220i | \(0.764049\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 171.359 | − | 400.944i | 0.339325 | − | 0.793948i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 76.8111 | 0.151501 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 978.447i | 1.92229i | 0.276038 | + | 0.961147i | \(0.410979\pi\) | ||||
−0.276038 | + | 0.961147i | \(0.589021\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −849.927 | + | 196.767i | −1.66326 | + | 0.385062i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 175.493i | − | 0.342091i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 862.377 | + | 368.571i | 1.67452 | + | 0.715672i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −190.429 | −0.368335 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 194.762 | 0.375264 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 575.650i | − | 1.10489i | −0.833548 | − | 0.552447i | \(-0.813694\pi\) | ||
0.833548 | − | 0.552447i | \(-0.186306\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 339.090 | 0.648355 | 0.324178 | − | 0.945996i | \(-0.394912\pi\) | ||||
0.324178 | + | 0.945996i | \(0.394912\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −253.492 | − | 166.183i | −0.482842 | − | 0.316539i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 111.957i | 0.212442i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −859.125 | −1.62406 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 128.805i | 0.242571i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 120.631i | 0.226325i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −310.191 | + | 725.781i | −0.579797 | + | 1.35660i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 119.342 | 0.222238 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 359.144 | − | 175.709i | 0.666316 | − | 0.325990i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 35.8638 | 0.0662916 | 0.0331458 | − | 0.999451i | \(-0.489447\pi\) | ||||
0.0331458 | + | 0.999451i | \(0.489447\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 288.450i | − | 0.531216i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −515.277 | − | 220.224i | −0.945463 | − | 0.404081i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 700.845i | − | 1.28125i | −0.767853 | − | 0.640626i | \(-0.778675\pi\) | ||
0.767853 | − | 0.640626i | \(-0.221325\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 102.859i | − | 0.187357i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 312.508i | 0.567166i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −383.155 | + | 88.7044i | −0.692867 | + | 0.160406i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 215.901 | − | 505.161i | 0.389010 | − | 0.910200i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 639.349i | − | 1.14784i | −0.818910 | − | 0.573922i | \(-0.805421\pi\) | ||
0.818910 | − | 0.573922i | \(-0.194579\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 614.773i | 1.09977i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 82.1717 | 0.146474 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 227.519 | 0.404120 | 0.202060 | − | 0.979373i | \(-0.435236\pi\) | ||||
0.202060 | + | 0.979373i | \(0.435236\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 279.006 | − | 652.814i | 0.493816 | − | 1.15542i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −61.3767 | + | 14.2093i | −0.108248 | + | 0.0250605i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 613.901 | 1.07891 | 0.539456 | − | 0.842014i | \(-0.318630\pi\) | ||||
0.539456 | + | 0.842014i | \(0.318630\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −366.674 | −0.642161 | −0.321081 | − | 0.947052i | \(-0.604046\pi\) | ||||
−0.321081 | + | 0.947052i | \(0.604046\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 256.844 | 0.448244 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 673.206 | − | 643.718i | 1.17079 | − | 1.11951i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −62.1951 | −0.107790 | −0.0538952 | − | 0.998547i | \(-0.517164\pi\) | ||||
−0.0538952 | + | 0.998547i | \(0.517164\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 60.9485i | 0.105265i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −616.481 | + | 142.722i | −1.06107 | + | 0.245648i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 582.188i | 0.998607i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 201.467 | + | 86.1050i | 0.344388 | + | 0.147188i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 176.872 | 0.301315 | 0.150658 | − | 0.988586i | \(-0.451861\pi\) | ||||
0.150658 | + | 0.988586i | \(0.451861\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 650.337 | 1.10414 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 335.384i | − | 0.567486i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 154.878 | 0.261176 | 0.130588 | − | 0.991437i | \(-0.458313\pi\) | ||||
0.130588 | + | 0.991437i | \(0.458313\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −200.340 | − | 35.7092i | −0.336705 | − | 0.0600154i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 314.953i | − | 0.527559i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −900.825 | −1.50388 | −0.751940 | − | 0.659231i | \(-0.770882\pi\) | ||||
−0.751940 | + | 0.659231i | \(0.770882\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 682.387i | 1.13542i | 0.823229 | + | 0.567710i | \(0.192170\pi\) | ||||
−0.823229 | + | 0.567710i | \(0.807830\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14.9967i | 0.0248701i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −250.207 | − | 106.936i | −0.413566 | − | 0.176754i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −367.814 | −0.605954 | −0.302977 | − | 0.952998i | \(-0.597981\pi\) | ||||
−0.302977 | + | 0.952998i | \(0.597981\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 109.296 | − | 25.3032i | 0.179469 | − | 0.0415488i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −340.883 | −0.557911 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 117.271i | − | 0.191306i | −0.995415 | − | 0.0956532i | \(-0.969506\pi\) | ||
0.995415 | − | 0.0956532i | \(-0.0304940\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −28.1087 | + | 65.7684i | −0.0457053 | + | 0.106940i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 1070.18i | − | 1.73449i | −0.497881 | − | 0.867245i | \(-0.665888\pi\) | ||
0.497881 | − | 0.867245i | \(-0.334112\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 532.192i | − | 0.859761i | −0.902886 | − | 0.429880i | \(-0.858556\pi\) | ||
0.902886 | − | 0.429880i | \(-0.141444\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 193.596i | − | 0.311749i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −25.6224 | − | 110.675i | −0.0411275 | − | 0.177649i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −27.9756 | + | 624.374i | −0.0447610 | + | 0.998998i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 477.319i | − | 0.761275i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 368.825i | − | 0.586366i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −472.933 | −0.749498 | −0.374749 | − | 0.927126i | \(-0.622271\pi\) | ||||
−0.374749 | + | 0.927126i | \(0.622271\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −304.693 | −0.481347 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −397.745 | + | 930.636i | −0.626369 | + | 1.46557i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 642.896 | − | 314.532i | 1.00926 | − | 0.493771i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 116.436 | 0.182216 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −486.990 | −0.759734 | −0.379867 | − | 0.925041i | \(-0.624030\pi\) | ||||
−0.379867 | + | 0.925041i | \(0.624030\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 111.425 | 0.173289 | 0.0866447 | − | 0.996239i | \(-0.472386\pi\) | ||||
0.0866447 | + | 0.996239i | \(0.472386\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −143.251 | + | 335.176i | −0.222094 | + | 0.519652i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −737.696 | −1.14018 | −0.570090 | − | 0.821583i | \(-0.693092\pi\) | ||||
−0.570090 | + | 0.821583i | \(0.693092\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 350.334i | 0.539806i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −52.6566 | − | 227.448i | −0.0808857 | − | 0.349383i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 193.734i | − | 0.296682i | −0.988936 | − | 0.148341i | \(-0.952607\pi\) | ||
0.988936 | − | 0.148341i | \(-0.0473934\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 277.577 | − | 649.469i | 0.423781 | − | 0.991556i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 373.888 | 0.569084 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 823.339 | 1.24938 | 0.624688 | − | 0.780874i | \(-0.285226\pi\) | ||||
0.624688 | + | 0.780874i | \(0.285226\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 657.833i | 0.995208i | 0.867404 | + | 0.497604i | \(0.165787\pi\) | ||||
−0.867404 | + | 0.497604i | \(0.834213\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 147.094 | 0.221861 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −207.428 | + | 1163.73i | −0.311921 | + | 1.74998i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 344.746i | 0.516860i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −35.6239 | −0.0532495 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 279.765i | − | 0.416937i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 727.300i | 1.08068i | 0.841446 | + | 0.540342i | \(0.181705\pi\) | ||||
−0.841446 | + | 0.540342i | \(0.818295\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 89.7766 | + | 93.8891i | 0.133002 | + | 0.139095i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −385.964 | −0.570110 | −0.285055 | − | 0.958511i | \(-0.592012\pi\) | ||||
−0.285055 | + | 0.958511i | \(0.592012\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −564.396 | + | 130.663i | −0.831217 | + | 0.192435i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 717.219 | 1.05319 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 236.488i | 0.346249i | 0.984900 | + | 0.173124i | \(0.0553863\pi\) | ||||
−0.984900 | + | 0.173124i | \(0.944614\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −99.5138 | + | 232.841i | −0.145276 | + | 0.339914i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 338.650i | 0.492941i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1042.16i | 1.51257i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 337.426i | − | 0.488316i | −0.969735 | − | 0.244158i | \(-0.921488\pi\) | ||
0.969735 | − | 0.244158i | \(-0.0785116\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −166.937 | + | 38.6477i | −0.240891 | + | 0.0557687i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 145.461 | − | 340.347i | 0.209296 | − | 0.489708i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 48.0184i | 0.0688929i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 140.817i | 0.201455i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 89.2192 | 0.127274 | 0.0636371 | − | 0.997973i | \(-0.479730\pi\) | ||||
0.0636371 | + | 0.997973i | \(0.479730\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2142.43 | −3.04755 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −185.850 | − | 79.4305i | −0.263617 | − | 0.112667i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 137.681 | + | 594.709i | 0.194740 | + | 0.841172i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 569.646 | 0.803450 | 0.401725 | − | 0.915760i | \(-0.368411\pi\) | ||||
0.401725 | + | 0.915760i | \(0.368411\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 168.552 | 0.237064 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 717.423 | 1.00620 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 547.967 | + | 234.195i | 0.766387 | + | 0.327546i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 431.740 | 0.602147 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 1261.33i | − | 1.75428i | −0.480233 | − | 0.877141i | \(-0.659448\pi\) | ||
0.480233 | − | 0.877141i | \(-0.340552\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1279.14 | + | 296.134i | −1.77412 | + | 0.410727i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 454.391i | − | 0.628481i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −159.870 | − | 167.193i | −0.220510 | − | 0.230611i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 307.746 | 0.423310 | 0.211655 | − | 0.977344i | \(-0.432115\pi\) | ||||
0.211655 | + | 0.977344i | \(0.432115\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 244.716i | 0.334769i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −633.490 | −0.864243 | −0.432121 | − | 0.901815i | \(-0.642235\pi\) | ||||
−0.432121 | + | 0.901815i | \(0.642235\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 423.798 | − | 21.6798i | 0.576596 | − | 0.0294964i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 40.7891i | 0.0553448i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −749.557 | −1.01428 | −0.507142 | − | 0.861862i | \(-0.669298\pi\) | ||||
−0.507142 | + | 0.861862i | \(0.669298\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 854.439i | − | 1.15309i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 145.699i | − | 0.196095i | −0.995182 | − | 0.0980476i | \(-0.968740\pi\) | ||
0.995182 | − | 0.0980476i | \(-0.0312597\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1043.58 | − | 446.016i | −1.40078 | − | 0.598679i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 271.194 | 0.363044 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −249.228 | − | 1076.53i | −0.332748 | − | 1.43729i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −156.811 | −0.208803 | −0.104402 | − | 0.994535i | \(-0.533293\pi\) | ||||
−0.104402 | + | 0.994535i | \(0.533293\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 245.807i | 0.326437i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1353.68 | − | 578.548i | −1.79295 | − | 0.766289i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 296.377i | − | 0.391515i | −0.980652 | − | 0.195758i | \(-0.937283\pi\) | ||
0.980652 | − | 0.195758i | \(-0.0627166\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 526.558i | − | 0.693752i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 312.747i | − | 0.410968i | −0.978660 | − | 0.205484i | \(-0.934123\pi\) | ||
0.978660 | − | 0.205484i | \(-0.0658769\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 764.297 | − | 176.942i | 1.00170 | − | 0.231904i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 80.1958 | + | 34.2748i | 0.104831 | + | 0.0448037i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 627.125i | 0.817634i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 91.1460i | − | 0.118525i | −0.998242 | − | 0.0592627i | \(-0.981125\pi\) | ||
0.998242 | − | 0.0592627i | \(-0.0188750\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 295.908 | 0.383798 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 417.539 | 0.540154 | 0.270077 | − | 0.962839i | \(-0.412951\pi\) | ||||
0.270077 | + | 0.962839i | \(0.412951\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −347.932 | + | 332.692i | −0.448945 | + | 0.429280i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 173.469 | + | 749.291i | 0.223254 | + | 0.964339i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 278.929 | 0.358061 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 316.692 | 0.405496 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −48.0802 | −0.0614052 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −302.802 | − | 129.414i | −0.385735 | − | 0.164859i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −318.111 | −0.404207 | −0.202104 | − | 0.979364i | \(-0.564778\pi\) | ||||
−0.202104 | + | 0.979364i | \(0.564778\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 664.098i | 0.841696i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 224.172 | + | 968.302i | 0.283403 | + | 1.22415i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 500.801i | − | 0.631527i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −242.838 | + | 568.188i | −0.305456 | + | 0.714702i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1188.06 | 1.49067 | 0.745335 | − | 0.666690i | \(-0.232289\pi\) | ||||
0.745335 | + | 0.666690i | \(0.232289\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −135.692 | −0.169827 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 48.6867i | 0.0607824i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1016.93 | 1.26642 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −228.825 | + | 1283.78i | −0.284255 | + | 1.59476i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 267.622i | − | 0.331626i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −223.374 | −0.276111 | −0.138055 | − | 0.990425i | \(-0.544085\pi\) | ||||
−0.138055 | + | 0.990425i | \(0.544085\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 366.185i | − | 0.451523i | −0.974183 | − | 0.225761i | \(-0.927513\pi\) | ||
0.974183 | − | 0.225761i | \(-0.0724870\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 554.824i | 0.682440i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −55.4278 | + | 129.689i | −0.0680096 | + | 0.159128i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1421.51 | 1.73991 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −298.831 | + | 69.1824i | −0.364873 | + | 0.0844718i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1547.39 | −1.88476 | −0.942381 | − | 0.334543i | \(-0.891418\pi\) | ||||
−0.942381 | + | 0.334543i | \(0.891418\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 1284.25i | − | 1.56045i | −0.625499 | − | 0.780225i | \(-0.715105\pi\) | ||
0.625499 | − | 0.780225i | \(-0.284895\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 244.182 | + | 255.367i | 0.295978 | + | 0.309536i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 807.319i | 0.976202i | 0.872787 | + | 0.488101i | \(0.162310\pi\) | ||||
−0.872787 | + | 0.488101i | \(0.837690\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 623.615i | − | 0.752250i | −0.926569 | − | 0.376125i | \(-0.877256\pi\) | ||
0.926569 | − | 0.376125i | \(-0.122744\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 385.994i | 0.464493i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 255.911 | − | 125.202i | 0.307216 | − | 0.150303i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −590.623 | − | 252.426i | −0.707333 | − | 0.302307i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 100.056i | 0.119541i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1146.31i | 1.36628i | 0.730286 | + | 0.683142i | \(0.239387\pi\) | ||||
−0.730286 | + | 0.683142i | \(0.760613\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −755.381 | −0.898194 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 379.272 | 0.449908 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 203.893 | + | 87.1419i | 0.241294 | + | 0.103127i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 371.126 | − | 85.9194i | 0.438165 | − | 0.101440i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −63.0392 | −0.0742511 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2363.43 | −2.77724 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −948.920 | −1.11245 | −0.556225 | − | 0.831032i | \(-0.687751\pi\) | ||||
−0.556225 | + | 0.831032i | \(0.687751\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 199.096 | − | 465.841i | 0.232861 | − | 0.544844i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −868.842 | −1.01382 | −0.506909 | − | 0.862000i | \(-0.669212\pi\) | ||||
−0.506909 | + | 0.862000i | \(0.669212\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 119.981i | 0.139675i | 0.997558 | + | 0.0698377i | \(0.0222482\pi\) | ||||
−0.997558 | + | 0.0698377i | \(0.977752\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −22.5844 | − | 97.5525i | −0.0262304 | − | 0.113301i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 788.430i | 0.913592i | 0.889571 | + | 0.456796i | \(0.151003\pi\) | ||||
−0.889571 | + | 0.456796i | \(0.848997\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 516.991 | + | 220.957i | 0.597678 | + | 0.255441i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −442.011 | −0.509816 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 458.443 | 0.527552 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 73.0157i | 0.0838298i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 248.282 | 0.284400 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −484.355 | − | 728.715i | −0.553549 | − | 0.832817i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 234.663i | − | 0.267574i | −0.991010 | − | 0.133787i | \(-0.957286\pi\) | ||
0.991010 | − | 0.133787i | \(-0.0427139\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −291.747 | −0.331908 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 750.816i | − | 0.852232i | −0.904669 | − | 0.426116i | \(-0.859882\pi\) | ||
0.904669 | − | 0.426116i | \(-0.140118\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1293.79i | 1.46522i | 0.680649 | + | 0.732610i | \(0.261698\pi\) | ||||
−0.680649 | + | 0.732610i | \(0.738302\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −146.129 | + | 341.910i | −0.165117 | + | 0.386339i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −728.248 | −0.821024 | −0.410512 | − | 0.911855i | \(-0.634650\pi\) | ||||
−0.410512 | + | 0.911855i | \(0.634650\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −319.574 | − | 1380.39i | −0.359476 | − | 1.55274i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 73.4368 | 0.0824207 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 788.206i | 0.882650i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 316.790 | + | 135.393i | 0.353955 | + | 0.151277i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 942.580i | − | 1.05081i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 178.175i | − | 0.198192i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 414.842i | 0.460424i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −115.097 | − | 497.157i | −0.127461 | − | 0.550561i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 327.246 | − | 765.685i | 0.361598 | − | 0.846061i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 913.713i | 1.00740i | 0.863878 | + | 0.503700i | \(0.168028\pi\) | ||||
−0.863878 | + | 0.503700i | \(0.831972\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 261.616i | − | 0.287807i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1331.32 | 1.46138 | 0.730690 | − | 0.682709i | \(-0.239198\pi\) | ||||
0.730690 | + | 0.682709i | \(0.239198\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 737.615 | 0.807903 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 116.693 | − | 273.037i | 0.127534 | − | 0.298402i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 223.023 | + | 963.341i | 0.243210 | + | 1.05053i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 111.140 | 0.120936 | 0.0604678 | − | 0.998170i | \(-0.480741\pi\) | ||||
0.0604678 | + | 0.998170i | \(0.480741\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −386.941 | −0.420131 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 566.904 | 0.614197 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1146.21 | − | 1096.00i | 1.23914 | − | 1.18486i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 562.702 | 0.607014 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 571.383i | − | 0.615051i | −0.951540 | − | 0.307526i | \(-0.900499\pi\) | ||
0.951540 | − | 0.307526i | \(-0.0995010\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −727.275 | − | 1486.53i | −0.781176 | − | 1.59671i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 79.7428i | − | 0.0854693i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 218.123 | + | 93.2235i | 0.233287 | + | 0.0997043i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1657.10 | −1.76852 | −0.884259 | − | 0.466997i | \(-0.845336\pi\) | ||||
−0.884259 | + | 0.466997i | \(0.845336\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −138.629 | −0.147635 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 519.083i | − | 0.551629i | −0.961211 | − | 0.275815i | \(-0.911052\pi\) | ||
0.961211 | − | 0.275815i | \(-0.0889476\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 307.703 | 0.326302 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −179.043 | − | 31.9133i | −0.189464 | − | 0.0337707i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 558.258i | 0.589502i | 0.955574 | + | 0.294751i | \(0.0952366\pi\) | ||||
−0.955574 | + | 0.294751i | \(0.904763\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1820.39 | 1.91822 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 320.839i | 0.337370i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 291.413i | − | 0.305784i | −0.988243 | − | 0.152892i | \(-0.951141\pi\) | ||
0.988243 | − | 0.152892i | \(-0.0488587\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 681.786 | + | 291.389i | 0.713912 | + | 0.305119i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −130.773 | −0.136648 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −79.9559 | − | 345.367i | −0.0833742 | − | 0.360132i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 590.215 | 0.614167 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 473.573i | 0.491768i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −69.1458 | + | 161.786i | −0.0716537 | + | 0.167654i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 323.558i | − | 0.334600i | −0.985906 | − | 0.167300i | \(-0.946495\pi\) | ||
0.985906 | − | 0.167300i | \(-0.0535048\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 340.117i | − | 0.350998i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 219.659i | − | 0.226219i | −0.993583 | − | 0.113110i | \(-0.963919\pi\) | ||
0.993583 | − | 0.113110i | \(-0.0360812\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 116.873 | + | 504.827i | 0.120116 | + | 0.518836i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 437.104 | + | 457.127i | 0.448312 | + | 0.468849i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1302.29i | 1.33295i | 0.745527 | + | 0.666475i | \(0.232198\pi\) | ||||
−0.745527 | + | 0.666475i | \(0.767802\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 132.422i | 0.135263i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −336.219 | −0.342731 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 649.905 | 0.661144 | 0.330572 | − | 0.943781i | \(-0.392758\pi\) | ||||
0.330572 | + | 0.943781i | \(0.392758\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 380.492 | − | 890.270i | 0.386287 | − | 0.903827i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 275.667 | − | 63.8196i | 0.279297 | − | 0.0646602i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1568.15 | 1.58559 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 575.568 | 0.580795 | 0.290397 | − | 0.956906i | \(-0.406212\pi\) | ||||
0.290397 | + | 0.956906i | \(0.406212\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −106.467 | −0.107217 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 357.313 | − | 836.035i | 0.359108 | − | 0.840236i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 705.512 | 0.707635 | 0.353817 | − | 0.935315i | \(-0.384883\pi\) | ||||
0.353817 | + | 0.935315i | \(0.384883\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 329.618i | − | 0.329948i |
(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 | 1680.3.bd.a.769.16 | 16 | ||
4.3 | odd | 2 | 210.3.h.a.139.12 | yes | 16 | ||
5.4 | even | 2 | inner | 1680.3.bd.a.769.2 | 16 | ||
7.6 | odd | 2 | inner | 1680.3.bd.a.769.1 | 16 | ||
12.11 | even | 2 | 630.3.h.e.559.2 | 16 | |||
20.3 | even | 4 | 1050.3.f.e.601.10 | 16 | |||
20.7 | even | 4 | 1050.3.f.e.601.7 | 16 | |||
20.19 | odd | 2 | 210.3.h.a.139.5 | yes | 16 | ||
28.27 | even | 2 | 210.3.h.a.139.13 | yes | 16 | ||
35.34 | odd | 2 | inner | 1680.3.bd.a.769.15 | 16 | ||
60.59 | even | 2 | 630.3.h.e.559.15 | 16 | |||
84.83 | odd | 2 | 630.3.h.e.559.7 | 16 | |||
140.27 | odd | 4 | 1050.3.f.e.601.3 | 16 | |||
140.83 | odd | 4 | 1050.3.f.e.601.14 | 16 | |||
140.139 | even | 2 | 210.3.h.a.139.4 | ✓ | 16 | ||
420.419 | odd | 2 | 630.3.h.e.559.10 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.h.a.139.4 | ✓ | 16 | 140.139 | even | 2 | ||
210.3.h.a.139.5 | yes | 16 | 20.19 | odd | 2 | ||
210.3.h.a.139.12 | yes | 16 | 4.3 | odd | 2 | ||
210.3.h.a.139.13 | yes | 16 | 28.27 | even | 2 | ||
630.3.h.e.559.2 | 16 | 12.11 | even | 2 | |||
630.3.h.e.559.7 | 16 | 84.83 | odd | 2 | |||
630.3.h.e.559.10 | 16 | 420.419 | odd | 2 | |||
630.3.h.e.559.15 | 16 | 60.59 | even | 2 | |||
1050.3.f.e.601.3 | 16 | 140.27 | odd | 4 | |||
1050.3.f.e.601.7 | 16 | 20.7 | even | 4 | |||
1050.3.f.e.601.10 | 16 | 20.3 | even | 4 | |||
1050.3.f.e.601.14 | 16 | 140.83 | odd | 4 | |||
1680.3.bd.a.769.1 | 16 | 7.6 | odd | 2 | inner | ||
1680.3.bd.a.769.2 | 16 | 5.4 | even | 2 | inner | ||
1680.3.bd.a.769.15 | 16 | 35.34 | odd | 2 | inner | ||
1680.3.bd.a.769.16 | 16 | 1.1 | even | 1 | trivial |