Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [56,6,Mod(1,56)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(56, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("56.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 56 = 2^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 56.a (trivial) |
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: | yes |
Analytic conductor: | \(8.98149390953\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{345}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 86 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-8.78709\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 56.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | 15.5742 | 0.999084 | 0.499542 | − | 0.866290i | \(-0.333502\pi\) | ||||
0.499542 | + | 0.866290i | \(0.333502\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 96.7225 | 1.73023 | 0.865113 | − | 0.501578i | \(-0.167247\pi\) | ||||
0.865113 | + | 0.501578i | \(0.167247\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −49.0000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.445054 | −0.00183150 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 281.445 | 0.701313 | 0.350657 | − | 0.936504i | \(-0.385958\pi\) | ||||
0.350657 | + | 0.936504i | \(0.385958\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −269.393 | −0.442107 | −0.221054 | − | 0.975262i | \(-0.570950\pi\) | ||||
−0.221054 | + | 0.975262i | \(0.570950\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1506.37 | 1.72864 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1719.45 | 1.44300 | 0.721499 | − | 0.692415i | \(-0.243453\pi\) | ||||
0.721499 | + | 0.692415i | \(0.243453\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1172.84 | −0.745339 | −0.372670 | − | 0.927964i | \(-0.621558\pi\) | ||||
−0.372670 | + | 0.927964i | \(0.621558\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −763.135 | −0.377618 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 785.341 | 0.309555 | 0.154778 | − | 0.987949i | \(-0.450534\pi\) | ||||
0.154778 | + | 0.987949i | \(0.450534\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6230.25 | 1.99368 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3791.46 | −1.00091 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6149.46 | 1.35782 | 0.678909 | − | 0.734222i | \(-0.262453\pi\) | ||||
0.678909 | + | 0.734222i | \(0.262453\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7006.58 | −1.30949 | −0.654744 | − | 0.755851i | \(-0.727224\pi\) | ||||
−0.654744 | + | 0.755851i | \(0.727224\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4383.27 | 0.700671 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4739.40 | −0.653964 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −11499.9 | −1.38099 | −0.690495 | − | 0.723337i | \(-0.742607\pi\) | ||||
−0.690495 | + | 0.723337i | \(0.742607\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4195.57 | −0.441702 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −13245.3 | −1.23056 | −0.615279 | − | 0.788310i | \(-0.710957\pi\) | ||||
−0.615279 | + | 0.788310i | \(0.710957\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −19824.2 | −1.63502 | −0.817512 | − | 0.575911i | \(-0.804647\pi\) | ||||
−0.817512 | + | 0.575911i | \(0.804647\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −43.0467 | −0.00316890 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6887.96 | 0.454827 | 0.227413 | − | 0.973798i | \(-0.426973\pi\) | ||||
0.227413 | + | 0.973798i | \(0.426973\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2401.00 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 26778.9 | 1.44168 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8654.97 | 0.423229 | 0.211615 | − | 0.977353i | \(-0.432128\pi\) | ||||
0.211615 | + | 0.977353i | \(0.432128\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 27222.1 | 1.21343 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −18266.0 | −0.744656 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −47856.6 | −1.78983 | −0.894915 | − | 0.446236i | \(-0.852764\pi\) | ||||
−0.894915 | + | 0.446236i | \(0.852764\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 52762.1 | 1.81550 | 0.907752 | − | 0.419507i | \(-0.137797\pi\) | ||||
0.907752 | + | 0.419507i | \(0.137797\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 21.8076 | 0.000692241 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −26056.4 | −0.764945 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −24040.2 | −0.654261 | −0.327130 | − | 0.944979i | \(-0.606082\pi\) | ||||
−0.327130 | + | 0.944979i | \(0.606082\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 12231.0 | 0.309272 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12540.9 | 0.295246 | 0.147623 | − | 0.989044i | \(-0.452838\pi\) | ||||
0.147623 | + | 0.989044i | \(0.452838\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4079.29 | 0.0895936 | 0.0447968 | − | 0.998996i | \(-0.485736\pi\) | ||||
0.0447968 | + | 0.998996i | \(0.485736\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 97031.0 | 1.99185 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −13790.8 | −0.265071 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11919.1 | −0.214870 | −0.107435 | − | 0.994212i | \(-0.534264\pi\) | ||||
−0.107435 | + | 0.994212i | \(0.534264\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −58940.7 | −0.998165 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 81916.2 | 1.30519 | 0.652596 | − | 0.757706i | \(-0.273680\pi\) | ||||
0.652596 | + | 0.757706i | \(0.273680\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 166309. | 2.49671 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 95772.7 | 1.35657 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −96968.7 | −1.29765 | −0.648824 | − | 0.760939i | \(-0.724739\pi\) | ||||
−0.648824 | + | 0.760939i | \(0.724739\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13200.2 | 0.167101 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −109122. | −1.30829 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −113440. | −1.28960 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −26410.7 | −0.285004 | −0.142502 | − | 0.989795i | \(-0.545515\pi\) | ||||
−0.142502 | + | 0.989795i | \(0.545515\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −125.258 | −0.00128445 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −73137.7 | −0.713408 | −0.356704 | − | 0.934217i | \(-0.616099\pi\) | ||||
−0.356704 | + | 0.934217i | \(0.616099\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 87649.5 | 0.814060 | 0.407030 | − | 0.913415i | \(-0.366565\pi\) | ||||
0.407030 | + | 0.913415i | \(0.366565\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −73812.3 | −0.653365 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −115438. | −0.974743 | −0.487372 | − | 0.873195i | \(-0.662044\pi\) | ||||
−0.487372 | + | 0.873195i | \(0.662044\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −117303. | −0.945675 | −0.472837 | − | 0.881150i | \(-0.656770\pi\) | ||||
−0.472837 | + | 0.881150i | \(0.656770\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −179102. | −1.37973 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 181535. | 1.33741 | 0.668705 | − | 0.743528i | \(-0.266849\pi\) | ||||
0.668705 | + | 0.743528i | \(0.266849\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 75960.1 | 0.535601 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 119.894 | 0.000809718 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −84252.8 | −0.545402 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −81839.7 | −0.508160 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −206284. | −1.22943 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 300347. | 1.71929 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 106111. | 0.583780 | 0.291890 | − | 0.956452i | \(-0.405716\pi\) | ||||
0.291890 | + | 0.956452i | \(0.405716\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −308745. | −1.63353 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 300334. | 1.52907 | 0.764534 | − | 0.644584i | \(-0.222969\pi\) | ||||
0.764534 | + | 0.644584i | \(0.222969\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 57469.1 | 0.281712 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −366719. | −1.73181 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −91892.5 | −0.418291 | −0.209146 | − | 0.977885i | \(-0.567068\pi\) | ||||
−0.209146 | + | 0.977885i | \(0.567068\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 153133. | 0.672252 | 0.336126 | − | 0.941817i | \(-0.390883\pi\) | ||||
0.336126 | + | 0.941817i | \(0.390883\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 107274. | 0.454410 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −75819.3 | −0.310056 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 594791. | 2.34933 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 37393.6 | 0.142726 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 498602. | 1.83987 | 0.919937 | − | 0.392066i | \(-0.128240\pi\) | ||||
0.919937 | + | 0.392066i | \(0.128240\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 209609. | 0.748114 | 0.374057 | − | 0.927406i | \(-0.377966\pi\) | ||||
0.374057 | + | 0.927406i | \(0.377966\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −765.245 | −0.00264285 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −677694. | −2.26571 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7381.72 | −0.0239006 | −0.0119503 | − | 0.999929i | \(-0.503804\pi\) | ||||
−0.0119503 | + | 0.999929i | \(0.503804\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 134794. | 0.422842 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −38481.7 | −0.117001 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 388154. | 1.14429 | 0.572144 | − | 0.820153i | \(-0.306112\pi\) | ||||
0.572144 | + | 0.820153i | \(0.306112\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 423961. | 1.21232 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −168240. | −0.466808 | −0.233404 | − | 0.972380i | \(-0.574987\pi\) | ||||
−0.233404 | + | 0.972380i | \(0.574987\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −298720. | −0.804541 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 521.976 | 0.00136509 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 321513. | 0.816740 | 0.408370 | − | 0.912817i | \(-0.366097\pi\) | ||||
0.408370 | + | 0.912817i | \(0.366097\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −305282. | −0.753540 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −745327. | −1.78819 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −611906. | −1.42742 | −0.713710 | − | 0.700441i | \(-0.752987\pi\) | ||||
−0.713710 | + | 0.700441i | \(0.752987\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 261474. | 0.593242 | 0.296621 | − | 0.954995i | \(-0.404140\pi\) | ||||
0.296621 | + | 0.954995i | \(0.404140\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 821726. | 1.81384 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.11230e6 | −2.38943 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 483929. | 1.01199 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 185781. | 0.378310 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 703301. | 1.39495 | 0.697474 | − | 0.716610i | \(-0.254307\pi\) | ||||
0.697474 | + | 0.716610i | \(0.254307\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 516411. | 0.997934 | 0.498967 | − | 0.866621i | \(-0.333713\pi\) | ||||
0.498967 | + | 0.866621i | \(0.333713\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −405806. | −0.764244 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 142579. | 0.261752 | 0.130876 | − | 0.991399i | \(-0.458221\pi\) | ||||
0.130876 | + | 0.991399i | \(0.458221\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 984837. | 1.76292 | 0.881458 | − | 0.472262i | \(-0.156562\pi\) | ||||
0.881458 | + | 0.472262i | \(0.156562\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −374406. | −0.653662 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −301323. | −0.513207 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.28112e6 | −2.12914 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −349.519 | −0.000566950 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −330089. | −0.522716 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −242836. | −0.375497 | −0.187748 | − | 0.982217i | \(-0.560119\pi\) | ||||
−0.187748 | + | 0.982217i | \(0.560119\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 195315. | 0.294976 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.91745e6 | −2.82896 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 343322. | 0.494940 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 63531.5 | 0.0895115 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −463206. | −0.637960 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −797063. | −1.07332 | −0.536661 | − | 0.843798i | \(-0.680315\pi\) | ||||
−0.536661 | + | 0.843798i | \(0.680315\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2772.79 | −0.00365142 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −26121.4 | −0.0336459 | −0.0168229 | − | 0.999858i | \(-0.505355\pi\) | ||||
−0.0168229 | + | 0.999858i | \(0.505355\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −761592. | −0.959695 | −0.479848 | − | 0.877352i | \(-0.659308\pi\) | ||||
−0.479848 | + | 0.877352i | \(0.659308\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −214780. | −0.264829 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 657852. | 0.793850 | 0.396925 | − | 0.917851i | \(-0.370077\pi\) | ||||
0.396925 | + | 0.917851i | \(0.370077\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 666221. | 0.786953 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −185630. | −0.214673 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 965388. | 1.09322 | 0.546609 | − | 0.837388i | \(-0.315918\pi\) | ||||
0.546609 | + | 0.837388i | \(0.315918\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 35064.2 | 0.0388885 | 0.0194443 | − | 0.999811i | \(-0.493810\pi\) | ||||
0.0194443 | + | 0.999811i | \(0.493810\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3371.72 | 0.00366299 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 232231. | 0.247175 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 315954. | 0.329520 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.27578e6 | 1.30400 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.31610e6 | 1.31857 | 0.659286 | − | 0.751892i | \(-0.270859\pi\) | ||||
0.659286 | + | 0.751892i | \(0.270859\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 221030. | 0.217095 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.59013e6 | 2.49443 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −529802. | −0.500358 | −0.250179 | − | 0.968200i | \(-0.580489\pi\) | ||||
−0.250179 | + | 0.968200i | \(0.580489\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 563496. | 0.521966 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2736.84 | −0.00248684 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.29457e6 | −1.15408 | −0.577041 | − | 0.816715i | \(-0.695793\pi\) | ||||
−0.577041 | + | 0.816715i | \(0.695793\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 837130. | 0.732282 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.51021e6 | −1.29646 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −444336. | −0.374396 | −0.187198 | − | 0.982322i | \(-0.559941\pi\) | ||||
−0.187198 | + | 0.982322i | \(0.559941\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 624757. | 0.516759 | 0.258379 | − | 0.966044i | \(-0.416812\pi\) | ||||
0.258379 | + | 0.966044i | \(0.416812\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 205583. | 0.166948 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.75347e6 | 1.39819 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.00202e6 | −1.56772 | −0.783860 | − | 0.620938i | \(-0.786752\pi\) | ||||
−0.783860 | + | 0.620938i | \(0.786752\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3118.30 | 0.00239832 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 249316. | 0.188358 | 0.0941792 | − | 0.995555i | \(-0.469977\pi\) | ||||
0.0941792 | + | 0.995555i | \(0.469977\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 645136. | 0.478835 | 0.239417 | − | 0.970917i | \(-0.423044\pi\) | ||||
0.239417 | + | 0.970917i | \(0.423044\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.76673e6 | −1.28842 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 649019. | 0.465107 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.53663e6 | 1.08225 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −411325. | −0.284743 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.00830e6 | 1.36666 | 0.683328 | − | 0.730112i | \(-0.260532\pi\) | ||||
0.683328 | + | 0.730112i | \(0.260532\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.62881e6 | −3.09681 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.06709e6 | −0.701954 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −211565. | −0.136857 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 971385. | 0.617981 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.13906e6 | −0.712754 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.10328e6 | 3.14123 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.71113e6 | −1.03618 | −0.518092 | − | 0.855325i | \(-0.673358\pi\) | ||||
−0.518092 | + | 0.855325i | \(0.673358\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.36507e6 | 0.813314 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −602050. | −0.352965 | −0.176483 | − | 0.984304i | \(-0.556472\pi\) | ||||
−0.176483 | + | 0.984304i | \(0.556472\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.34208e6 | −0.774318 | −0.387159 | − | 0.922013i | \(-0.626543\pi\) | ||||
−0.387159 | + | 0.922013i | \(0.626543\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2109.29 | 0.00119773 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.01803e6 | 0.569001 | 0.284500 | − | 0.958676i | \(-0.408172\pi\) | ||||
0.284500 | + | 0.958676i | \(0.408172\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.73073e6 | 0.952256 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.79786e6 | −0.973850 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.01663e6 | −1.07552 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.67838e6 | −0.881420 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.82689e6 | −0.944809 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −337510. | −0.171908 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −532371. | −0.267082 | −0.133541 | − | 0.991043i | \(-0.542635\pi\) | ||||
−0.133541 | + | 0.991043i | \(0.542635\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5118.09 | 0.00252928 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.32523e6 | −1.13202 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −234947. | −0.112693 | −0.0563463 | − | 0.998411i | \(-0.517945\pi\) | ||||
−0.0563463 | + | 0.998411i | \(0.517945\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.82726e6 | 1.33618 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.97197e6 | −0.918361 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −117649. | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.18302e6 | 0.535110 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.90054e6 | −0.847330 | −0.423665 | − | 0.905819i | \(-0.639257\pi\) | ||||
−0.423665 | + | 0.905819i | \(0.639257\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 341162. | 0.149933 | 0.0749665 | − | 0.997186i | \(-0.476115\pi\) | ||||
0.0749665 | + | 0.997186i | \(0.476115\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.02139e6 | 0.442511 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 673122. | 0.287513 | 0.143756 | − | 0.989613i | \(-0.454082\pi\) | ||||
0.143756 | + | 0.989613i | \(0.454082\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.21299e6 | 0.510842 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.31217e6 | −0.544903 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.43301e6 | 0.586833 | 0.293417 | − | 0.955985i | \(-0.405208\pi\) | ||||
0.293417 | + | 0.955985i | \(0.405208\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.10055e6 | −0.444469 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.27459e6 | −0.507694 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 394559. | 0.155017 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.04781e6 | −0.793643 | −0.396822 | − | 0.917896i | \(-0.629887\pi\) | ||||
−0.396822 | + | 0.917896i | \(0.629887\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5894.87 | 0.00225376 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −424093. | −0.159966 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.33578e6 | −1.24144 | −0.620719 | − | 0.784033i | \(-0.713159\pi\) | ||||
−0.620719 | + | 0.784033i | \(0.713159\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.67766e6 | 1.71771 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.65662e6 | −0.600301 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.29135e6 | 0.819394 | 0.409697 | − | 0.912222i | \(-0.365634\pi\) | ||||
0.409697 | + | 0.912222i | \(0.365634\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.65258e6 | 0.583245 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.84422e6 | 0.642414 | 0.321207 | − | 0.947009i | \(-0.395911\pi\) | ||||
0.321207 | + | 0.947009i | \(0.395911\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.33388e6 | −0.458633 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8822.83 | 0.00299454 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.66601e6 | 1.22834 | 0.614172 | − | 0.789172i | \(-0.289490\pi\) | ||||
0.614172 | + | 0.789172i | \(0.289490\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.35035e6 | 0.446688 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.67746e6 | 1.52767 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.15284e6 | −0.371773 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.59382e6 | −1.46284 | −0.731421 | − | 0.681926i | \(-0.761142\pi\) | ||||
−0.731421 | + | 0.681926i | \(0.761142\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 895033. | 0.281454 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.10984e6 | −0.344666 | −0.172333 | − | 0.985039i | \(-0.555130\pi\) | ||||
−0.172333 | + | 0.985039i | \(0.555130\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.88752e6 | 0.578934 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −5.70089e6 | −1.72705 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.23660e6 | −0.968507 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.60689e6 | 1.06617 | 0.533083 | − | 0.846063i | \(-0.321033\pi\) | ||||
0.533083 | + | 0.846063i | \(0.321033\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.43115e6 | −0.417908 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.34497e6 | 0.676492 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.92314e6 | 2.25828 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.38492e6 | 0.671636 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.51790e6 | 1.53546 | 0.767731 | − | 0.640773i | \(-0.221386\pi\) | ||||
0.767731 | + | 0.640773i | \(0.221386\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.59092e6 | −0.712440 | −0.356220 | − | 0.934402i | \(-0.615935\pi\) | ||||
−0.356220 | + | 0.934402i | \(0.615935\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3065.51 | −0.000833014 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.07126e7 | 2.87688 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.58534e6 | −0.686196 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.18082e6 | −0.309772 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.45364e6 | −0.895537 | −0.447769 | − | 0.894150i | \(-0.647781\pi\) | ||||
−0.447769 | + | 0.894150i | \(0.647781\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 397522. | 0.101892 | 0.0509461 | − | 0.998701i | \(-0.483776\pi\) | ||||
0.0509461 | + | 0.998701i | \(0.483776\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 9.26338e6 | 2.34718 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −921077. | −0.230724 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.60903e6 | 0.398476 | 0.199238 | − | 0.979951i | \(-0.436153\pi\) | ||||
0.199238 | + | 0.979951i | \(0.436153\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1068.57 | −0.000261642 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.08182e6 | −1.71449 | −0.857246 | − | 0.514906i | \(-0.827827\pi\) | ||||
−0.857246 | + | 0.514906i | \(0.827827\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.37906e6 | −2.24522 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7.76531e6 | 1.83819 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.46156e6 | −1.51259 | −0.756295 | − | 0.654230i | \(-0.772993\pi\) | ||||
−0.756295 | + | 0.654230i | \(0.772993\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.72782e6 | −0.863006 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.26449e6 | 0.747429 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.27676e6 | 0.289122 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.37073e6 | −0.754976 | −0.377488 | − | 0.926015i | \(-0.623212\pi\) | ||||
−0.377488 | + | 0.926015i | \(0.623212\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.51920e6 | −1.44432 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.20821e6 | 1.36055 | 0.680274 | − | 0.732958i | \(-0.261861\pi\) | ||||
0.680274 | + | 0.732958i | \(0.261861\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.82940e6 | −1.26378 | −0.631890 | − | 0.775058i | \(-0.717721\pi\) | ||||
−0.631890 | + | 0.775058i | \(0.717721\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.05545e7 | −2.26363 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −174742. | −0.0370770 | −0.0185385 | − | 0.999828i | \(-0.505901\pi\) | ||||
−0.0185385 | + | 0.999828i | \(0.505901\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.17797e6 | 0.247287 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −114964. | −0.0238787 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.57942e6 | −1.14666 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.30707e6 | −1.48597 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3851.93 | −0.000775143 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 371746. | 0.0740299 | 0.0370150 | − | 0.999315i | \(-0.488215\pi\) | ||||
0.0370150 | + | 0.999315i | \(0.488215\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.09800e6 | 0.610546 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −599321. | −0.116894 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.55451e6 | −0.493121 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.71307e6 | −1.66475 | −0.832375 | − | 0.554213i | \(-0.813019\pi\) | ||||
−0.832375 | + | 0.554213i | \(0.813019\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.04519e6 | 1.14324 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.88530e6 | 1.28890 | 0.644450 | − | 0.764646i | \(-0.277086\pi\) | ||||
0.644450 | + | 0.764646i | \(0.277086\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.05737e7 | 1.95933 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −12115.3 | −0.00222239 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −614506. | −0.111592 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −45442.7 | −0.00816982 | −0.00408491 | − | 0.999992i | \(-0.501300\pi\) | ||||
−0.00408491 | + | 0.999992i | \(0.501300\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.62020e6 | −0.466381 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −623417. | −0.109865 | −0.0549324 | − | 0.998490i | \(-0.517494\pi\) | ||||
−0.0549324 | + | 0.998490i | \(0.517494\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.07406e6 | −1.23436 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.65233e6 | −0.803804 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.69092e6 | 1.31578 | 0.657891 | − | 0.753113i | \(-0.271449\pi\) | ||||
0.657891 | + | 0.753113i | \(0.271449\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −199885. | −0.0338632 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.44676e6 | 0.746020 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.47768e6 | 1.40851 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.93858e6 | 0.318976 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.00730e6 | 0.815991 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.32268e6 | 1.18189 | 0.590943 | − | 0.806713i | \(-0.298756\pi\) | ||||
0.590943 | + | 0.806713i | \(0.298756\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.17976e6 | 0.828047 | 0.414024 | − | 0.910266i | \(-0.364123\pi\) | ||||
0.414024 | + | 0.910266i | \(0.364123\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.75452e6 | −0.752850 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.20474e7 | −1.88959 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.81958e6 | −0.904175 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 21298.8 | 0.00327807 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.56819e6 | 0.544038 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.11655e7 | −1.68653 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9.52993e6 | −1.42611 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 675750. | 0.100188 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.31804e6 | 1.36877 | 0.684387 | − | 0.729119i | \(-0.260070\pi\) | ||||
0.684387 | + | 0.729119i | \(0.260070\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.07224e6 | 0.592698 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.13458e7 | −1.63623 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.26417e7 | 1.80650 | 0.903250 | − | 0.429114i | \(-0.141174\pi\) | ||||
0.903250 | + | 0.429114i | \(0.141174\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −23482.0 | −0.00332509 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.21232e6 | −1.01204 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 584035. | 0.0812131 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.73232e7 | −2.38724 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.84693e6 | −0.525384 | −0.262692 | − | 0.964880i | \(-0.584610\pi\) | ||||
−0.262692 | + | 0.964880i | \(0.584610\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.34050e6 | 0.722856 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.53680e6 | 1.01107 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.69193e6 | 0.490888 | 0.245444 | − | 0.969411i | \(-0.421066\pi\) | ||||
0.245444 | + | 0.969411i | \(0.421066\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.75585e7 | 2.31402 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.88809e6 | 0.377271 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.64173e6 | −0.860005 | −0.430002 | − | 0.902828i | \(-0.641487\pi\) | ||||
−0.430002 | + | 0.902828i | \(0.641487\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 292599. | 0.0375562 | 0.0187781 | − | 0.999824i | \(-0.494022\pi\) | ||||
0.0187781 | + | 0.999824i | \(0.494022\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.09533e7 | 1.39367 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.89287e6 | 0.617154 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.55569e6 | 0.444615 | 0.222307 | − | 0.974977i | \(-0.428641\pi\) | ||||
0.222307 | + | 0.974977i | \(0.428641\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.04267e6 | 0.997020 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.01389e6 | −0.493316 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.43590e6 | 0.296816 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 11596.5 | 0.00140099 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.64810e6 | −0.317204 | −0.158602 | − | 0.987343i | \(-0.550699\pi\) | ||||
−0.158602 | + | 0.987343i | \(0.550699\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.21758e6 | 0.976013 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.22055e6 | 0.261512 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.05356e6 | 0.123034 | 0.0615168 | − | 0.998106i | \(-0.480406\pi\) | ||||
0.0615168 | + | 0.998106i | \(0.480406\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.14914e6 | −0.943669 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.53380e7 | 1.76130 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.19012e6 | 1.04654 | 0.523268 | − | 0.852168i | \(-0.324713\pi\) | ||||
0.523268 | + | 0.852168i | \(0.324713\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.46924e6 | 0.391785 | 0.195893 | − | 0.980625i | \(-0.437240\pi\) | ||||
0.195893 | + | 0.980625i | \(0.437240\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 10699.2 | 0.00119828 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.91574e6 | −0.879231 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −744150. | −0.0819764 | −0.0409882 | − | 0.999160i | \(-0.513051\pi\) | ||||
−0.0409882 | + | 0.999160i | \(0.513051\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.69286e6 | −0.512737 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.85557e6 | −0.201082 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.14578e7 | 1.23154 | 0.615772 | − | 0.787925i | \(-0.288844\pi\) | ||||
0.615772 | + | 0.787925i | \(0.288844\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.99524e7 | −2.12719 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.90052e6 | −0.412486 | −0.206243 | − | 0.978501i | \(-0.566124\pi\) | ||||
−0.206243 | + | 0.978501i | \(0.566124\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.65029e6 | 0.278014 | 0.139007 | − | 0.990291i | \(-0.455609\pi\) | ||||
0.139007 | + | 0.990291i | \(0.455609\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.97758e6 | −0.309838 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.75147e6 | 0.490464 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.58083e6 | 0.981077 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.14087e6 | −0.522237 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.97735e7 | −1.99277 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.97599e6 | −0.897447 | −0.448723 | − | 0.893671i | \(-0.648121\pi\) | ||||
−0.448723 | + | 0.893671i | \(0.648121\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.78197e6 | −0.375153 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.02633e7 | 1.01007 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −646812. | −0.0631582 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5581.39 | −0.000540742 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.87152e6 | −0.276036 | −0.138018 | − | 0.990430i | \(-0.544073\pi\) | ||||
−0.138018 | + | 0.990430i | \(0.544073\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.38761e7 | 1.32354 | 0.661772 | − | 0.749705i | \(-0.269805\pi\) | ||||
0.661772 | + | 0.749705i | \(0.269805\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.98626e7 | −2.82637 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −7.24853e6 | −0.680752 | −0.340376 | − | 0.940289i | \(-0.610554\pi\) | ||||
−0.340376 | + | 0.940289i | \(0.610554\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.34690e7 | −1.25523 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.34696e6 | 0.494487 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.23719e7 | −1.13541 | −0.567706 | − | 0.823231i | \(-0.692169\pi\) | ||||
−0.567706 | + | 0.823231i | \(0.692169\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.90491e7 | 2.64563 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1815.50 | −0.000164090 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −572294. | −0.0513341 | −0.0256670 | − | 0.999671i | \(-0.508171\pi\) | ||||
−0.0256670 | + | 0.999671i | \(0.508171\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.73679e6 | 0.599721 | 0.299861 | − | 0.953983i | \(-0.403060\pi\) | ||||
0.299861 | + | 0.953983i | \(0.403060\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −7.21405e6 | −0.637376 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.55855e6 | 0.487425 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.82942e6 | 0.420320 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.24136e7 | −1.07234 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.48496e7 | 1.27324 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.22608e7 | −1.04348 | −0.521738 | − | 0.853106i | \(-0.674716\pi\) | ||||
−0.521738 | + | 0.853106i | \(0.674716\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.36217e7 | −1.99550 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −462085. | −0.0387481 | −0.0193741 | − | 0.999812i | \(-0.506167\pi\) | ||||
−0.0193741 | + | 0.999812i | \(0.506167\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.29413e6 | 0.107721 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −406819. | −0.0336151 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.15378e7 | −0.946392 | −0.473196 | − | 0.880957i | \(-0.656900\pi\) | ||||
−0.473196 | + | 0.880957i | \(0.656900\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.88807e6 | −0.723738 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.18612e7 | −0.958816 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.33159e6 | −0.187113 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.09921e6 | 0.246920 | 0.123460 | − | 0.992350i | \(-0.460601\pi\) | ||||
0.123460 | + | 0.992350i | \(0.460601\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6137.65 | 0.000485477 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.48114e7 | 1.16315 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.27746e7 | −1.77569 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.02455e7 | 0.793122 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.83889e6 | 0.448782 | 0.224391 | − | 0.974499i | \(-0.427961\pi\) | ||||
0.224391 | + | 0.974499i | \(0.427961\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.34876e7 | 1.02931 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.03758e7 | 0.786232 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.58375e6 | 0.269643 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 75435.7 | 0.00563587 | 0.00281794 | − | 0.999996i | \(-0.499103\pi\) | ||||
0.00281794 | + | 0.999996i | \(0.499103\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5304.63 | 0.000393533 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.50255e6 | −0.405359 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.33343e6 | −0.536466 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.50351e7 | 1.09222 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.30869e7 | −0.944091 | −0.472045 | − | 0.881574i | \(-0.656484\pi\) | ||||
−0.472045 | + | 0.881574i | \(0.656484\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.29482e6 | −0.307686 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 546096. | 0.0388529 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.83126e7 | 2.70705 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.58160e6 | −0.251328 | −0.125664 | − | 0.992073i | \(-0.540106\pi\) | ||||
−0.125664 | + | 0.992073i | \(0.540106\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.43751e7 | 1.00182 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.40866e7 | −2.35934 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.23826e6 | −0.635083 | −0.317541 | − | 0.948244i | \(-0.602857\pi\) | ||||
−0.317541 | + | 0.948244i | \(0.602857\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.61680e6 | 0.246949 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.76599e6 | −0.458842 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.90444e7 | −1.28279 | −0.641397 | − | 0.767210i | \(-0.721645\pi\) | ||||
−0.641397 | + | 0.767210i | \(0.721645\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.92073e6 | 0.329218 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.30669e6 | 0.618477 | 0.309238 | − | 0.950985i | \(-0.399926\pi\) | ||||
0.309238 | + | 0.950985i | \(0.399926\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.82260e7 | 3.18340 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −36457.1 | −0.00239046 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.65647e6 | 0.368418 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.56243e7 | 1.65788 | 0.828939 | − | 0.559339i | \(-0.188945\pi\) | ||||
0.828939 | + | 0.559339i | \(0.188945\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.04971e7 | 1.31736 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.02739e7 | 1.29441 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.60956e6 | 0.355786 | 0.177893 | − | 0.984050i | \(-0.443072\pi\) | ||||
0.177893 | + | 0.984050i | \(0.443072\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.44236e6 | 0.216896 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.83985e7 | −1.77760 | −0.888799 | − | 0.458298i | \(-0.848459\pi\) | ||||
−0.888799 | + | 0.458298i | \(0.848459\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.74783e6 | 0.357432 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −74016.5 | −0.00457272 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.28922e7 | 0.791297 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.41205e6 | −0.147086 | −0.0735429 | − | 0.997292i | \(-0.523431\pi\) | ||||
−0.0735429 | + | 0.997292i | \(0.523431\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.25123e6 | −0.499899 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.93891e6 | 0.357485 | 0.178743 | − | 0.983896i | \(-0.442797\pi\) | ||||
0.178743 | + | 0.983896i | \(0.442797\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.36527e7 | −2.61070 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8.77599e6 | 0.521487 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.55346e7 | 0.917183 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.52958e6 | 0.207060 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.33154e7 | −1.35906 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −713979. | −0.0413534 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.62637e7 | 1.51154 | 0.755769 | − | 0.654839i | \(-0.227263\pi\) | ||||
0.755769 | + | 0.654839i | \(0.227263\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.01619e7 | −1.15302 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.89522e6 | −0.505494 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.42137e7 | −0.802648 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.30376e7 | 0.731611 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −9.33689e6 | −0.520663 | −0.260331 | − | 0.965519i | \(-0.583832\pi\) | ||||
−0.260331 | + | 0.965519i | \(0.583832\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.18435e7 | 0.656315 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 43156.3 | 0.00237664 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.14809e6 | 0.0628332 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.72205e6 | −0.202438 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.92017e6 | −0.374053 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.43772e7 | −1.84671 | −0.923357 | − | 0.383942i | \(-0.874566\pi\) | ||||
−0.923357 | + | 0.383942i | \(0.874566\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.02626e7 | −1.08179 | −0.540896 | − | 0.841090i | \(-0.681915\pi\) | ||||
−0.540896 | + | 0.841090i | \(0.681915\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9.73008e6 | 0.516285 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.75433e7 | 1.97988 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.32506e7 | 1.21865 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5874.82 | −0.000306045 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.73641e7 | 0.899073 | 0.449537 | − | 0.893262i | \(-0.351589\pi\) | ||||
0.449537 | + | 0.893262i | \(0.351589\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.65094e7 | −1.36427 | −0.682136 | − | 0.731226i | \(-0.738949\pi\) | ||||
−0.682136 | + | 0.731226i | \(0.738949\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.73089e7 | 1.39691 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.30816e6 | −0.117355 | −0.0586775 | − | 0.998277i | \(-0.518688\pi\) | ||||
−0.0586775 | + | 0.998277i | \(0.518688\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.14314e6 | −0.310459 | −0.155230 | − | 0.987878i | \(-0.549612\pi\) | ||||
−0.155230 | + | 0.987878i | \(0.549612\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.11798e7 | −1.56628 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.12839e6 | 0.206143 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.62726e7 | −0.807684 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.65651e7 | 1.31068 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.04628e7 | 0.513150 | 0.256575 | − | 0.966524i | \(-0.417406\pi\) | ||||
0.256575 | + | 0.966524i | \(0.417406\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.73047e7 | 0.843671 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.88290e6 | 0.188186 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.88930e7 | −1.39204 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.01014e6 | 0.192066 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.00475e7 | 0.478396 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.03136e6 | −0.427493 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.45134e7 | −1.62411 | −0.812054 | − | 0.583583i | \(-0.801650\pi\) | ||||
−0.812054 | + | 0.583583i | \(0.801650\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 50486.8 | 0.00236191 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.35665e7 | −0.630978 | −0.315489 | − | 0.948929i | \(-0.602169\pi\) | ||||
−0.315489 | + | 0.948929i | \(0.602169\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.12783e7 | 1.44630 | 0.723152 | − | 0.690688i | \(-0.242692\pi\) | ||||
0.723152 | + | 0.690688i | \(0.242692\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.01079e7 | 0.464681 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.98071e7 | −0.905305 | −0.452653 | − | 0.891687i | \(-0.649522\pi\) | ||||
−0.452653 | + | 0.891687i | \(0.649522\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.10976e7 | 1.41314 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.39318e7 | 1.08125 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.35457e6 | −0.150691 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.47626e6 | 0.289254 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 11754.2 | 0.000521984 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.47170e7 | −0.649830 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.74647e6 | −0.0766765 | −0.0383383 | − | 0.999265i | \(-0.512206\pi\) | ||||
−0.0383383 | + | 0.999265i | \(0.512206\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.12776e7 | 1.36540 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.17415e7 | 0.509663 | 0.254832 | − | 0.966985i | \(-0.417980\pi\) | ||||
0.254832 | + | 0.966985i | \(0.417980\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.26514e7 | −1.84091 | −0.920453 | − | 0.390854i | \(-0.872180\pi\) | ||||
−0.920453 | + | 0.390854i | \(0.872180\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7.20899e7 | −3.09397 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4.28737e7 | −1.82971 | −0.914854 | − | 0.403785i | \(-0.867694\pi\) | ||||
−0.914854 | + | 0.403785i | \(0.867694\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.19942e6 | −0.220648 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.65886e7 | −0.700026 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8.07846e6 | −0.339000 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.91851e7 | −2.46976 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.29495e6 | −0.136731 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.30866e7 | −1.77805 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.48817e7 | 0.610719 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.51285e7 | 0.617415 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.52904e7 | 1.02644 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.99065e7 | −0.803482 | −0.401741 | − | 0.915753i | \(-0.631595\pi\) | ||||
−0.401741 | + | 0.915753i | \(0.631595\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 32550.2 | 0.00130660 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.12063e7 | −0.447371 | −0.223685 | − | 0.974661i | \(-0.571809\pi\) | ||||
−0.223685 | + | 0.974661i | \(0.571809\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.30549e7 | 0.915348 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 7.94794e7 | 3.13835 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.47164e7 | −0.577933 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.38620e7 | 1.32259 | 0.661293 | − | 0.750128i | \(-0.270008\pi\) | ||||
0.661293 | + | 0.750128i | \(0.270008\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.66494e7 | −1.03523 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.37844e6 | −0.130530 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.16474e7 | −2.75325 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −39008.7 | −0.00149095 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.29019e7 | −0.870627 | −0.435313 | − | 0.900279i | \(-0.643362\pi\) | ||||
−0.435313 | + | 0.900279i | \(0.643362\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.81598e6 | −0.106477 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −9.37644e6 | −0.352642 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.68069e7 | 1.75098 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.97781e7 | 1.10802 | 0.554011 | − | 0.832510i | \(-0.313097\pi\) | ||||
0.554011 | + | 0.832510i | \(0.313097\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.09019e7 | −0.773608 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.30322e7 | −0.479782 | −0.239891 | − | 0.970800i | \(-0.577112\pi\) | ||||
−0.239891 | + | 0.970800i | \(0.577112\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.04021e7 | −0.380926 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.79692e7 | 0.654561 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.66683e7 | 1.69101 | 0.845506 | − | 0.533966i | \(-0.179299\pi\) | ||||
0.845506 | + | 0.533966i | \(0.179299\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.09893e6 | −0.0396100 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.58550e7 | 0.568480 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.00948e7 | 0.716724 | 0.358362 | − | 0.933583i | \(-0.383335\pi\) | ||||
0.358362 | + | 0.933583i | \(0.383335\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.80251e7 | 2.41357 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.69548e7 | 0.951383 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.50273e6 | 0.158099 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.04630e7 | 0.714760 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 51376.2 | 0.00178524 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.99485e7 | 1.72665 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.33633e6 | 0.252297 | 0.126149 | − | 0.992011i | \(-0.459738\pi\) | ||||
0.126149 | + | 0.992011i | \(0.459738\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.14074e7 | −1.07454 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.01630e7 | 1.36703 | 0.683514 | − | 0.729937i | \(-0.260451\pi\) | ||||
0.683514 | + | 0.729937i | \(0.260451\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.50352e6 | −0.254087 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.61394e7 | −0.880613 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.65602e7 | 0.890216 | 0.445108 | − | 0.895477i | \(-0.353165\pi\) | ||||
0.445108 | + | 0.895477i | \(0.353165\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.72914e7 | −0.910057 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 52206.0 | 0.00173200 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.77362e7 | 0.915510 | 0.457755 | − | 0.889078i | \(-0.348654\pi\) | ||||
0.457755 | + | 0.889078i | \(0.348654\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.37906e7 | 0.452890 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.25644e6 | −0.171751 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.55687e7 | −0.506131 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.35437e7 | −0.761536 | −0.380768 | − | 0.924671i | \(-0.624340\pi\) | ||||
−0.380768 | + | 0.924671i | \(0.624340\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −8.29123e6 | −0.266837 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9.52559e7 | 3.05024 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.05582e7 | −1.29223 | −0.646117 | − | 0.763239i | \(-0.723608\pi\) | ||||
−0.646117 | + | 0.763239i | \(0.723608\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.36015e7 | 1.38225 |
(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 | 56.6.a.e.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 504.6.a.i.1.1 | 2 | |||
4.3 | odd | 2 | 112.6.a.i.1.1 | 2 | |||
7.2 | even | 3 | 392.6.i.j.361.1 | 4 | |||
7.3 | odd | 6 | 392.6.i.i.177.2 | 4 | |||
7.4 | even | 3 | 392.6.i.j.177.1 | 4 | |||
7.5 | odd | 6 | 392.6.i.i.361.2 | 4 | |||
7.6 | odd | 2 | 392.6.a.d.1.1 | 2 | |||
8.3 | odd | 2 | 448.6.a.t.1.2 | 2 | |||
8.5 | even | 2 | 448.6.a.v.1.1 | 2 | |||
12.11 | even | 2 | 1008.6.a.bd.1.1 | 2 | |||
28.27 | even | 2 | 784.6.a.u.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.6.a.e.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
112.6.a.i.1.1 | 2 | 4.3 | odd | 2 | |||
392.6.a.d.1.1 | 2 | 7.6 | odd | 2 | |||
392.6.i.i.177.2 | 4 | 7.3 | odd | 6 | |||
392.6.i.i.361.2 | 4 | 7.5 | odd | 6 | |||
392.6.i.j.177.1 | 4 | 7.4 | even | 3 | |||
392.6.i.j.361.1 | 4 | 7.2 | even | 3 | |||
448.6.a.t.1.2 | 2 | 8.3 | odd | 2 | |||
448.6.a.v.1.1 | 2 | 8.5 | even | 2 | |||
504.6.a.i.1.1 | 2 | 3.2 | odd | 2 | |||
784.6.a.u.1.2 | 2 | 28.27 | even | 2 | |||
1008.6.a.bd.1.1 | 2 | 12.11 | even | 2 |