Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [684,6,Mod(505,684)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(684, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("684.505");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 684.k (of order \(3\), degree \(2\), 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: | \(109.702532752\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Relative dimension: | \(9\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 7 x^{17} + 17616 x^{16} - 456301 x^{15} + 216301789 x^{14} - 6076762674 x^{13} + 1365504992251 x^{12} - 54625271848675 x^{11} + \cdots + 55\!\cdots\!41 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{16}\cdot 3^{7}\cdot 5^{2} \) |
Twist minimal: | no (minimal twist has level 76) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 577.4 | ||
Root | \(-11.6095 + 21.8402i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 684.577 |
Dual form | 684.6.k.f.505.4 |
$q$-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 \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(343\) | \(533\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −12.6095 | − | 21.8402i | −0.225565 | − | 0.390690i | 0.730924 | − | 0.682459i | \(-0.239089\pi\) |
−0.956489 | + | 0.291769i | \(0.905756\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −40.7176 | −0.314078 | −0.157039 | − | 0.987592i | \(-0.550195\pi\) | ||||
−0.157039 | + | 0.987592i | \(0.550195\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −324.832 | −0.809426 | −0.404713 | − | 0.914444i | \(-0.632629\pi\) | ||||
−0.404713 | + | 0.914444i | \(0.632629\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −48.8600 | + | 84.6280i | −0.0801854 | + | 0.138885i | −0.903329 | − | 0.428947i | \(-0.858885\pi\) |
0.823144 | + | 0.567833i | \(0.192218\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1057.36 | + | 1831.41i | 0.887365 | + | 1.53696i | 0.842978 | + | 0.537947i | \(0.180800\pi\) |
0.0443869 | + | 0.999014i | \(0.485867\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 806.259 | − | 1351.31i | 0.512378 | − | 0.858760i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1506.33 | + | 2609.05i | −0.593748 | + | 1.02840i | 0.399975 | + | 0.916526i | \(0.369019\pi\) |
−0.993722 | + | 0.111875i | \(0.964314\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1244.50 | − | 2155.54i | 0.398241 | − | 0.689774i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 527.733 | − | 914.060i | 0.116525 | − | 0.201827i | −0.801863 | − | 0.597507i | \(-0.796158\pi\) |
0.918388 | + | 0.395680i | \(0.129491\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7602.00 | 1.42077 | 0.710385 | − | 0.703813i | \(-0.248521\pi\) | ||||
0.710385 | + | 0.703813i | \(0.248521\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 513.427 | + | 889.282i | 0.0708449 | + | 0.122707i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2057.16 | −0.247037 | −0.123519 | − | 0.992342i | \(-0.539418\pi\) | ||||
−0.123519 | + | 0.992342i | \(0.539418\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −230.415 | − | 399.091i | −0.0214068 | − | 0.0370777i | 0.855124 | − | 0.518424i | \(-0.173481\pi\) |
−0.876530 | + | 0.481347i | \(0.840148\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −188.582 | − | 326.633i | −0.0155535 | − | 0.0269395i | 0.858144 | − | 0.513409i | \(-0.171618\pi\) |
−0.873697 | + | 0.486470i | \(0.838284\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8354.76 | − | 14470.9i | 0.551682 | − | 0.955542i | −0.446471 | − | 0.894798i | \(-0.647319\pi\) |
0.998153 | − | 0.0607440i | \(-0.0193473\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −15149.1 | −0.901355 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5234.06 | + | 9065.67i | −0.255947 | + | 0.443313i | −0.965152 | − | 0.261689i | \(-0.915720\pi\) |
0.709206 | + | 0.705002i | \(0.249054\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4095.96 | + | 7094.41i | 0.182578 | + | 0.316235i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −23733.3 | − | 41107.2i | −0.887621 | − | 1.53740i | −0.842680 | − | 0.538415i | \(-0.819023\pi\) |
−0.0449408 | − | 0.998990i | \(-0.514310\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13715.7 | + | 23756.3i | −0.471948 | + | 0.817438i | −0.999485 | − | 0.0320943i | \(-0.989782\pi\) |
0.527537 | + | 0.849532i | \(0.323116\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2464.39 | 0.0723480 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 17228.2 | − | 29840.0i | 0.468869 | − | 0.812105i | −0.530498 | − | 0.847686i | \(-0.677995\pi\) |
0.999367 | + | 0.0355811i | \(0.0113282\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1879.84 | − | 3255.97i | −0.0442562 | − | 0.0766541i | 0.843049 | − | 0.537837i | \(-0.180758\pi\) |
−0.887305 | + | 0.461183i | \(0.847425\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6145.42 | + | 10644.2i | 0.134972 | + | 0.233779i | 0.925587 | − | 0.378535i | \(-0.123572\pi\) |
−0.790615 | + | 0.612314i | \(0.790239\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 13226.4 | 0.254223 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 26717.1 | + | 46275.4i | 0.481639 | + | 0.834223i | 0.999778 | − | 0.0210731i | \(-0.00670827\pi\) |
−0.518139 | + | 0.855297i | \(0.673375\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1317.09 | 0.0209856 | 0.0104928 | − | 0.999945i | \(-0.496660\pi\) | ||||
0.0104928 | + | 0.999945i | \(0.496660\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 26665.6 | − | 46186.2i | 0.400317 | − | 0.693369i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −51736.4 | + | 89610.0i | −0.692342 | + | 1.19917i | 0.278726 | + | 0.960371i | \(0.410088\pi\) |
−0.971068 | + | 0.238801i | \(0.923245\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1989.46 | − | 3445.85i | 0.0251845 | − | 0.0436208i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −39679.5 | − | 569.563i | −0.451083 | − | 0.00647489i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −52995.4 | − | 91790.7i | −0.571885 | − | 0.990533i | −0.996372 | − | 0.0850998i | \(-0.972879\pi\) |
0.424488 | − | 0.905434i | \(-0.360454\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 34282.4 | − | 59378.8i | 0.334401 | − | 0.579200i | −0.648969 | − | 0.760815i | \(-0.724799\pi\) |
0.983370 | + | 0.181616i | \(0.0581327\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −35253.0 | −0.327419 | −0.163709 | − | 0.986509i | \(-0.552346\pi\) | ||||
−0.163709 | + | 0.986509i | \(0.552346\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −126916. | −1.07166 | −0.535832 | − | 0.844325i | \(-0.680002\pi\) | ||||
−0.535832 | + | 0.844325i | \(0.680002\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −107794. | − | 186705.i | −0.869019 | − | 1.50519i | −0.863000 | − | 0.505204i | \(-0.831417\pi\) |
−0.00601921 | − | 0.999982i | \(-0.501916\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −25767.6 | −0.189835 | −0.0949177 | − | 0.995485i | \(-0.530259\pi\) | ||||
−0.0949177 | + | 0.995485i | \(0.530259\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 75976.3 | 0.535714 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −43053.4 | − | 74570.6i | −0.278702 | − | 0.482726i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −55535.1 | −0.344829 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −141579. | −0.810446 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −59314.9 | + | 102736.i | −0.326328 | + | 0.565216i | −0.981780 | − | 0.190020i | \(-0.939145\pi\) |
0.655452 | + | 0.755237i | \(0.272478\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 27739.5 | + | 48046.2i | 0.141228 | + | 0.244614i | 0.927959 | − | 0.372682i | \(-0.121562\pi\) |
−0.786731 | + | 0.617295i | \(0.788228\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −32829.0 | + | 55022.2i | −0.160927 | + | 0.269717i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 159895. | − | 276946.i | 0.727835 | − | 1.26065i | −0.229962 | − | 0.973200i | \(-0.573860\pi\) |
0.957797 | − | 0.287447i | \(-0.0928066\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −105811. | + | 183269.i | −0.464506 | + | 0.804549i | −0.999179 | − | 0.0405104i | \(-0.987102\pi\) |
0.534673 | + | 0.845059i | \(0.320435\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 15871.3 | − | 27489.9i | 0.0649041 | − | 0.112417i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −26617.7 | −0.105136 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −36052.9 | − | 62445.4i | −0.133037 | − | 0.230428i | 0.791809 | − | 0.610769i | \(-0.209140\pi\) |
−0.924846 | + | 0.380342i | \(0.875806\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 265545. | 0.947753 | 0.473877 | − | 0.880591i | \(-0.342854\pi\) | ||||
0.473877 | + | 0.880591i | \(0.342854\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −95857.2 | − | 166029.i | −0.320476 | − | 0.555080i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −159838. | − | 276848.i | −0.517526 | − | 0.896381i | −0.999793 | − | 0.0203568i | \(-0.993520\pi\) |
0.482267 | − | 0.876024i | \(-0.339814\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 61334.4 | − | 106234.i | 0.186483 | − | 0.322998i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −202591. | −0.597244 | −0.298622 | − | 0.954371i | \(-0.596527\pi\) | ||||
−0.298622 | + | 0.954371i | \(0.596527\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 151820. | − | 262959.i | 0.421247 | − | 0.729621i | −0.574815 | − | 0.818284i | \(-0.694926\pi\) |
0.996062 | + | 0.0886623i | \(0.0282592\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 180872. | + | 313279.i | 0.487141 | + | 0.843752i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −328662. | − | 569260.i | −0.834900 | − | 1.44609i | −0.894112 | − | 0.447844i | \(-0.852192\pi\) |
0.0592118 | − | 0.998245i | \(-0.481141\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −50673.2 | + | 87768.6i | −0.125079 | + | 0.216643i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −265873. | −0.620215 | −0.310108 | − | 0.950701i | \(-0.600365\pi\) | ||||
−0.310108 | + | 0.950701i | \(0.600365\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 75575.2 | − | 130900.i | 0.171468 | − | 0.296991i | −0.767465 | − | 0.641090i | \(-0.778482\pi\) |
0.938933 | + | 0.344099i | \(0.111816\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 25939.6 | + | 44928.7i | 0.0557230 | + | 0.0965150i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −343466. | − | 594901.i | −0.718257 | − | 1.24406i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 120491. | 0.238986 | 0.119493 | − | 0.992835i | \(-0.461873\pi\) | ||||
0.119493 | + | 0.992835i | \(0.461873\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 38385.0 | + | 66484.8i | 0.0741769 | + | 0.128478i | 0.900728 | − | 0.434384i | \(-0.143034\pi\) |
−0.826551 | + | 0.562862i | \(0.809700\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −581905. | −1.06828 | −0.534141 | − | 0.845395i | \(-0.679365\pi\) | ||||
−0.534141 | + | 0.845395i | \(0.679365\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 83536.9 | − | 144690.i | 0.149536 | − | 0.259004i | −0.781520 | − | 0.623880i | \(-0.785555\pi\) |
0.931056 | + | 0.364876i | \(0.118889\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −21488.0 | + | 37218.4i | −0.0365979 | + | 0.0633895i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5810.82 | + | 10064.6i | −0.00965724 | + | 0.0167268i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −261899. | + | 438950.i | −0.414732 | + | 0.695103i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −360222. | − | 623923.i | −0.557011 | − | 0.964772i | −0.997744 | − | 0.0671336i | \(-0.978615\pi\) |
0.440733 | − | 0.897638i | \(-0.354719\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4755.83 | + | 8237.33i | −0.00701665 | + | 0.0121532i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −309536. | −0.446233 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −206651. | −0.284615 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −676428. | − | 1.17161e6i | −0.910876 | − | 1.57768i | −0.812830 | − | 0.582501i | \(-0.802074\pi\) |
−0.0980458 | − | 0.995182i | \(-0.531259\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −944144. | −1.21611 | −0.608056 | − | 0.793894i | \(-0.708050\pi\) | ||||
−0.608056 | + | 0.793894i | \(0.708050\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.23700e6 | 1.55877 | 0.779383 | − | 0.626547i | \(-0.215532\pi\) | ||||
0.779383 | + | 0.626547i | \(0.215532\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −495767. | − | 858694.i | −0.598258 | − | 1.03621i | −0.993078 | − | 0.117454i | \(-0.962527\pi\) |
0.394821 | − | 0.918758i | \(-0.370807\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −421396. | −0.497761 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 256516. | 0.290482 | 0.145241 | − | 0.989396i | \(-0.453604\pi\) | ||||
0.145241 | + | 0.989396i | \(0.453604\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −398215. | + | 689728.i | −0.441646 | + | 0.764954i | −0.997812 | − | 0.0661177i | \(-0.978939\pi\) |
0.556166 | + | 0.831072i | \(0.312272\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 191022. | + | 330859.i | 0.203314 | + | 0.352150i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 74965.1 | + | 134257.i | 0.0781838 | + | 0.140022i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 292660. | − | 506902.i | 0.293210 | − | 0.507855i | −0.681357 | − | 0.731951i | \(-0.738610\pi\) |
0.974567 | + | 0.224097i | \(0.0719431\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 489306. | − | 847503.i | 0.480595 | − | 0.832415i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 436841. | − | 756630.i | 0.412563 | − | 0.714580i | −0.582606 | − | 0.812754i | \(-0.697967\pi\) |
0.995169 | + | 0.0981747i | \(0.0313004\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 83762.5 | 0.0775890 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −146951. | − | 254527.i | −0.131004 | − | 0.226905i | 0.793060 | − | 0.609144i | \(-0.208487\pi\) |
−0.924064 | + | 0.382238i | \(0.875153\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 263995. | 0.230930 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.16327e6 | − | 2.01484e6i | −0.980163 | − | 1.69769i | −0.661722 | − | 0.749749i | \(-0.730174\pi\) |
−0.318440 | − | 0.947943i | \(-0.603159\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 130705. | + | 226387.i | 0.108111 | + | 0.187253i | 0.915005 | − | 0.403443i | \(-0.132187\pi\) |
−0.806894 | + | 0.590696i | \(0.798853\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −404255. | + | 700189.i | −0.322347 | + | 0.558321i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.76335e6 | −1.38083 | −0.690415 | − | 0.723414i | \(-0.742572\pi\) | ||||
−0.690415 | + | 0.723414i | \(0.742572\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 477850. | − | 827661.i | 0.361016 | − | 0.625297i | −0.627113 | − | 0.778929i | \(-0.715763\pi\) |
0.988128 | + | 0.153631i | \(0.0490968\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 172840. | + | 299368.i | 0.128286 | + | 0.222197i | 0.923013 | − | 0.384770i | \(-0.125719\pi\) |
−0.794727 | + | 0.606967i | \(0.792386\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9381.96 | + | 16250.0i | 0.00672340 | + | 0.0116453i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.52611e6 | + | 2.64330e6i | −1.07483 | + | 1.86167i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.17269e6 | −0.798023 | −0.399011 | − | 0.916946i | \(-0.630647\pi\) | ||||
−0.399011 | + | 0.916946i | \(0.630647\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −598527. | + | 1.03668e6i | −0.400432 | + | 0.693569i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −147199. | − | 254956.i | −0.0952198 | − | 0.164925i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7678.60 | + | 13299.7i | 0.00488501 | + | 0.00846109i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 691791. | 0.425819 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −160062. | − | 277235.i | −0.0969264 | − | 0.167881i | 0.813485 | − | 0.581586i | \(-0.197568\pi\) |
−0.910411 | + | 0.413705i | \(0.864234\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.45223e6 | −0.851400 | −0.425700 | − | 0.904864i | \(-0.639972\pi\) | ||||
−0.425700 | + | 0.904864i | \(0.639972\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 965219. | − | 1.67181e6i | 0.556884 | − | 0.964552i | −0.440870 | − | 0.897571i | \(-0.645330\pi\) |
0.997754 | − | 0.0669807i | \(-0.0213366\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −757768. | + | 1.31249e6i | −0.423534 | + | 0.733582i | −0.996282 | − | 0.0861494i | \(-0.972544\pi\) |
0.572749 | + | 0.819731i | \(0.305877\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −171425. | + | 296916.i | −0.0943184 | + | 0.163364i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.32732e6 | + | 47760.6i | 1.77455 | + | 0.0254720i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 121613. | + | 210640.i | 0.0638662 | + | 0.110620i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −340186. | + | 589219.i | −0.173271 | + | 0.300115i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.41462e6 | 1.71306 | 0.856531 | − | 0.516096i | \(-0.172615\pi\) | ||||
0.856531 | + | 0.516096i | \(0.172615\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −868951. | −0.423042 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.59676e6 | − | 2.76567e6i | −0.765888 | − | 1.32656i | −0.939776 | − | 0.341791i | \(-0.888967\pi\) |
0.173889 | − | 0.984765i | \(-0.444367\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.46938e6 | −1.15001 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.30118e6 | 0.597174 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −405681. | − | 702659.i | −0.180868 | − | 0.313272i | 0.761309 | − | 0.648390i | \(-0.224557\pi\) |
−0.942176 | + | 0.335118i | \(0.891224\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −491593. | −0.216044 | −0.108022 | − | 0.994148i | \(-0.534452\pi\) | ||||
−0.108022 | + | 0.994148i | \(0.534452\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.82830e6 | 0.780929 | 0.390465 | − | 0.920618i | \(-0.372314\pi\) | ||||
0.390465 | + | 0.920618i | \(0.372314\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −47407.5 | + | 82112.2i | −0.0199653 | + | 0.0345809i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.35760e6 | + | 2.35143e6i | 0.555950 | + | 0.962934i | 0.997829 | + | 0.0658593i | \(0.0209789\pi\) |
−0.441879 | + | 0.897075i | \(0.645688\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.17599e6 | − | 2.17902e6i | −0.474937 | − | 0.880020i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 154981. | − | 268435.i | 0.0608900 | − | 0.105465i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.32754e6 | − | 2.29937e6i | 0.514498 | − | 0.891136i | −0.485361 | − | 0.874314i | \(-0.661312\pi\) |
0.999858 | − | 0.0168222i | \(-0.00535492\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 213119. | − | 369132.i | 0.0803872 | − | 0.139235i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.33938e6 | 1.61494 | 0.807468 | − | 0.589911i | \(-0.200837\pi\) | ||||
0.807468 | + | 0.589911i | \(0.200837\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 51570.1 | + | 89322.0i | 0.0186872 | + | 0.0323672i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.27824e6 | 1.17231 | 0.586155 | − | 0.810199i | \(-0.300641\pi\) | ||||
0.586155 | + | 0.810199i | \(0.300641\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.41742e6 | − | 2.45505e6i | −0.493745 | − | 0.855191i | 0.506229 | − | 0.862399i | \(-0.331039\pi\) |
−0.999974 | + | 0.00720770i | \(0.997706\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −166778. | − | 288867.i | −0.0573437 | − | 0.0993223i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.39366e6 | + | 2.41389e6i | −0.466963 | + | 0.808804i | −0.999288 | − | 0.0377363i | \(-0.987985\pi\) |
0.532324 | + | 0.846540i | \(0.321319\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.37098e6 | −2.10748 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 673777. | − | 1.16702e6i | 0.217282 | − | 0.376343i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.84860e6 | − | 3.20187e6i | −0.588663 | − | 1.01959i | −0.994408 | − | 0.105607i | \(-0.966321\pi\) |
0.405745 | − | 0.913986i | \(-0.367012\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.13618e6 | + | 3.69998e6i | 0.663404 | + | 1.14905i | 0.979715 | + | 0.200394i | \(0.0642221\pi\) |
−0.316312 | + | 0.948655i | \(0.602445\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −371434. | + | 643343.i | −0.113925 | + | 0.197324i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 668230. | 0.199959 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.89320e6 | + | 5.01117e6i | −0.855205 | + | 1.48126i | 0.0212492 | + | 0.999774i | \(0.493236\pi\) |
−0.876454 | + | 0.481485i | \(0.840098\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 966362. | + | 1.67379e6i | 0.278782 | + | 0.482865i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −16607.8 | − | 28765.6i | −0.00473361 | − | 0.00819885i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.36575e6 | −0.936585 | −0.468293 | − | 0.883573i | \(-0.655131\pi\) | ||||
−0.468293 | + | 0.883573i | \(0.655131\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.36298e6 | + | 4.09279e6i | 0.649761 | + | 1.12542i | 0.983180 | + | 0.182641i | \(0.0584646\pi\) |
−0.333418 | + | 0.942779i | \(0.608202\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.26357e6 | 1.41354 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 558472. | − | 967301.i | 0.148228 | − | 0.256739i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −212460. | + | 367991.i | −0.0550914 | + | 0.0954211i | −0.892256 | − | 0.451530i | \(-0.850878\pi\) |
0.837164 | + | 0.546951i | \(0.184212\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.10444e6 | + | 5.37705e6i | −0.795726 | + | 1.37824i | 0.126651 | + | 0.991947i | \(0.459577\pi\) |
−0.922377 | + | 0.386291i | \(0.873756\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.31114e6 | + | 4.13910e6i | 0.578926 | + | 1.03682i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.48593e6 | + | 6.03781e6i | 0.863291 | + | 1.49526i | 0.868734 | + | 0.495279i | \(0.164934\pi\) |
−0.00544290 | + | 0.999985i | \(0.501733\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.32950e6 | − | 2.30277e6i | 0.321870 | − | 0.557495i | −0.659004 | − | 0.752139i | \(-0.729022\pi\) |
0.980874 | + | 0.194645i | \(0.0623553\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.60947e6 | 0.624672 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 636809. | 0.149071 | 0.0745355 | − | 0.997218i | \(-0.476253\pi\) | ||||
0.0745355 | + | 0.997218i | \(0.476253\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 74846.3 | + | 129638.i | 0.0173272 | + | 0.0300116i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −100344. | −0.0227229 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.62218e6 | −0.363337 | −0.181668 | − | 0.983360i | \(-0.558150\pi\) | ||||
−0.181668 | + | 0.983360i | \(0.558150\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.88236e6 | − | 3.26034e6i | −0.412525 | − | 0.714514i | 0.582640 | − | 0.812730i | \(-0.302020\pi\) |
−0.995165 | + | 0.0982159i | \(0.968686\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.56420e6 | 1.85667 | 0.928334 | − | 0.371748i | \(-0.121241\pi\) | ||||
0.928334 | + | 0.371748i | \(0.121241\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.68072e6 | 1.84189 | 0.920944 | − | 0.389694i | \(-0.127419\pi\) | ||||
0.920944 | + | 0.389694i | \(0.127419\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −701489. | + | 1.21502e6i | −0.147261 | + | 0.255064i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 61257.4 | + | 106101.i | 0.0125894 | + | 0.0218055i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.90942e6 | − | 3.41964e6i | −0.388300 | − | 0.695418i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.82656e6 | − | 8.35985e6i | 0.961167 | − | 1.66479i | 0.241589 | − | 0.970379i | \(-0.422331\pi\) |
0.719578 | − | 0.694412i | \(-0.244335\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 100513. | − | 174093.i | 0.0198088 | − | 0.0343098i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.33649e6 | + | 2.31486e6i | −0.257994 | + | 0.446859i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.07551e6 | −0.587617 | −0.293809 | − | 0.955864i | \(-0.594923\pi\) | ||||
−0.293809 | + | 0.955864i | \(0.594923\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.46681e6 | + | 6.00470e6i | 0.648973 | + | 1.12405i | 0.983368 | + | 0.181622i | \(0.0581347\pi\) |
−0.334395 | + | 0.942433i | \(0.608532\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.23202e6 | 0.413601 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 76542.5 | + | 132576.i | 0.0138999 | + | 0.0240753i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 272382. | + | 471779.i | 0.0489696 | + | 0.0848178i | 0.889471 | − | 0.456991i | \(-0.151073\pi\) |
−0.840502 | + | 0.541809i | \(0.817740\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.01810e6 | + | 5.22751e6i | −0.531880 | + | 0.921244i | 0.467427 | + | 0.884032i | \(0.345181\pi\) |
−0.999307 | + | 0.0372121i | \(0.988152\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.72913e6 | −0.301716 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −292272. | + | 506231.i | −0.0500027 | + | 0.0866072i | −0.889943 | − | 0.456071i | \(-0.849256\pi\) |
0.839941 | + | 0.542678i | \(0.182590\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −250227. | − | 433406.i | −0.0423918 | − | 0.0734247i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 444522. | + | 769934.i | 0.0738542 | + | 0.127919i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.71389e6 | + | 4.70060e6i | −0.446546 | + | 0.773441i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.06982e6 | −0.818272 | −0.409136 | − | 0.912473i | \(-0.634170\pi\) | ||||
−0.409136 | + | 0.912473i | \(0.634170\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.09028e6 | − | 3.62047e6i | 0.334157 | − | 0.578777i | −0.649166 | − | 0.760647i | \(-0.724882\pi\) |
0.983323 | + | 0.181870i | \(0.0582151\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.03809e6 | + | 1.39224e7i | 1.26074 | + | 2.18367i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.31992e6 | − | 2.28617e6i | −0.205073 | − | 0.355196i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 45032.4 | 0.00686605 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.60035e6 | + | 2.77188e6i | 0.241730 | + | 0.418688i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.92091e6 | 0.729580 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.36120e6 | − | 4.08971e6i | 0.346848 | − | 0.600758i | −0.638840 | − | 0.769340i | \(-0.720585\pi\) |
0.985688 | + | 0.168582i | \(0.0539187\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.71845e6 | + | 4.70850e6i | −0.392040 | + | 0.679034i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.59488e6 | + | 4.49447e6i | −0.370808 | + | 0.642259i | −0.989690 | − | 0.143225i | \(-0.954253\pi\) |
0.618882 | + | 0.785484i | \(0.287586\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −809691. | − | 1.45010e6i | −0.113616 | − | 0.203479i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.08786e6 | − | 1.88422e6i | −0.151272 | − | 0.262011i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.55878e6 | + | 6.16399e6i | −0.486030 | + | 0.841829i | −0.999871 | − | 0.0160563i | \(-0.994889\pi\) |
0.513841 | + | 0.857886i | \(0.328222\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 36856.4 | 0.00498866 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.55995e6 | −0.872227 | −0.436114 | − | 0.899892i | \(-0.643645\pi\) | ||||
−0.436114 | + | 0.899892i | \(0.643645\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 324915. | + | 562769.i | 0.0428202 | + | 0.0741668i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.10777e7 | −1.43440 | −0.717200 | − | 0.696868i | \(-0.754576\pi\) | ||||
−0.717200 | + | 0.696868i | \(0.754576\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.64684e6 | −0.724795 | −0.362398 | − | 0.932024i | \(-0.618042\pi\) | ||||
−0.362398 | + | 0.932024i | \(0.618042\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.74928e6 | + | 6.49394e6i | 0.472909 | + | 0.819103i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.99850e6 | 0.374942 | 0.187471 | − | 0.982270i | \(-0.439971\pi\) | ||||
0.187471 | + | 0.982270i | \(0.439971\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −53628.9 | −0.00659110 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.70019e6 | − | 2.94482e6i | 0.207170 | − | 0.358829i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.21676e6 | + | 1.24998e7i | 0.864465 | + | 1.49730i | 0.867578 | + | 0.497301i | \(0.165676\pi\) |
−0.00311341 | + | 0.999995i | \(0.500991\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.12919e6 | − | 1.02727e7i | 0.727972 | − | 1.22010i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.75784e6 | − | 6.50878e6i | 0.438836 | − | 0.760086i | −0.558764 | − | 0.829327i | \(-0.688724\pi\) |
0.997600 | + | 0.0692407i | \(0.0220576\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.08576e6 | + | 1.88059e6i | −0.125731 | + | 0.217772i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.09527e6 | − | 1.40214e7i | 0.921858 | − | 1.59671i | 0.125321 | − | 0.992116i | \(-0.460004\pi\) |
0.796538 | − | 0.604589i | \(-0.206663\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.99094e6 | 0.224839 | 0.112419 | − | 0.993661i | \(-0.464140\pi\) | ||||
0.112419 | + | 0.993661i | \(0.464140\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 700267. | + | 1.21290e6i | 0.0777814 | + | 0.134721i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.47599e6 | 0.162596 | 0.0812982 | − | 0.996690i | \(-0.474093\pi\) | ||||
0.0812982 | + | 0.996690i | \(0.474093\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 816427. | + | 1.41409e6i | 0.0884737 | + | 0.153241i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.12920e6 | + | 1.06161e7i | 0.658798 | + | 1.14107i | 0.980927 | + | 0.194376i | \(0.0622683\pi\) |
−0.322129 | + | 0.946696i | \(0.604398\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.89936e6 | − | 6.75389e6i | 0.412364 | − | 0.714235i | −0.582784 | − | 0.812627i | \(-0.698037\pi\) |
0.995148 | + | 0.0983924i | \(0.0313700\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.39100e6 | 0.880212 | 0.440106 | − | 0.897946i | \(-0.354941\pi\) | ||||
0.440106 | + | 0.897946i | \(0.354941\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.10658e6 | − | 3.64871e6i | 0.217449 | − | 0.376633i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.10384e6 | − | 3.64395e6i | −0.215433 | − | 0.373141i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.17516e6 | − | 3.76749e6i | −0.219212 | − | 0.379687i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 725688. | − | 1.25693e6i | 0.0725565 | − | 0.125672i | −0.827465 | − | 0.561518i | \(-0.810218\pi\) |
0.900021 | + | 0.435846i | \(0.143551\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.99171e6 | 0.294432 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 740184. | − | 1.28204e6i | 0.0722755 | − | 0.125185i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.20230e6 | + | 7.27859e6i | 0.403963 | + | 0.699684i | 0.994200 | − | 0.107545i | \(-0.0342991\pi\) |
−0.590237 | + | 0.807230i | \(0.700966\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.07760e6 | + | 3.59850e6i | 0.198168 | + | 0.343237i | 0.947934 | − | 0.318465i | \(-0.103167\pi\) |
−0.749766 | + | 0.661703i | \(0.769834\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.48842e6 | 0.515450 | 0.257725 | − | 0.966218i | \(-0.417027\pi\) | ||||
0.257725 | + | 0.966218i | \(0.417027\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.70933e6 | + | 1.33529e7i | 0.718464 | + | 1.24442i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.39658e6 | −0.587036 | −0.293518 | − | 0.955954i | \(-0.594826\pi\) | ||||
−0.293518 | + | 0.955954i | \(0.594826\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 699560. | − | 1.21167e6i | 0.0637120 | − | 0.110353i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −891088. | + | 1.54341e6i | −0.0799295 | + | 0.138442i | −0.903219 | − | 0.429179i | \(-0.858803\pi\) |
0.823290 | + | 0.567621i | \(0.192136\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.15028e6 | + | 1.41167e7i | −0.725553 | + | 1.25669i | 0.233193 | + | 0.972430i | \(0.425083\pi\) |
−0.958746 | + | 0.284264i | \(0.908251\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.61565e6 | + | 23191.2i | 0.141675 | + | 0.00203362i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.58988e6 | + | 2.75376e6i | 0.138373 | + | 0.239669i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.45531e6 | − | 7.71682e6i | 0.382007 | − | 0.661656i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.81795e6 | 0.324932 | 0.162466 | − | 0.986714i | \(-0.448055\pi\) | ||||
0.162466 | + | 0.986714i | \(0.448055\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.93449e6 | −0.162216 | −0.0811081 | − | 0.996705i | \(-0.525846\pi\) | ||||
−0.0811081 | + | 0.996705i | \(0.525846\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.15785e6 | + | 3.73750e6i | 0.179616 | + | 0.311105i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −732465. | −0.0600808 | −0.0300404 | − | 0.999549i | \(-0.509564\pi\) | ||||
−0.0300404 | + | 0.999549i | \(0.509564\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.06474e6 | −0.656696 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −511473. | − | 885897.i | −0.0410464 | − | 0.0710944i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.91673e6 | −0.471397 | −0.235698 | − | 0.971826i | \(-0.575738\pi\) | ||||
−0.235698 | + | 0.971826i | \(0.575738\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.33685e6 | 0.419105 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 487266. | − | 843969.i | 0.0379913 | − | 0.0658028i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.07558e6 | − | 1.39873e7i | −0.620696 | − | 1.07508i | −0.989356 | − | 0.145513i | \(-0.953517\pi\) |
0.368661 | − | 0.929564i | \(-0.379816\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.65860e6 | + | 2.77986e6i | −0.126577 | + | 0.212146i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.39590e6 | + | 2.41777e6i | −0.105028 | + | 0.181914i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.50009e6 | − | 6.06234e6i | 0.261495 | − | 0.452923i | −0.705144 | − | 0.709064i | \(-0.749118\pi\) |
0.966640 | + | 0.256141i | \(0.0824510\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.14512e7 | + | 1.98340e7i | −0.843579 | + | 1.46112i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −800514. | −0.0585604 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.55155e6 | − | 1.13476e7i | −0.472630 | − | 0.818620i | 0.526879 | − | 0.849940i | \(-0.323362\pi\) |
−0.999509 | + | 0.0313203i | \(0.990029\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.43542e6 | 0.102835 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.31353e6 | − | 2.27510e6i | −0.0928101 | − | 0.160752i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.15352e6 | − | 1.23903e7i | −0.501977 | − | 0.869449i | −0.999997 | − | 0.00228403i | \(-0.999273\pi\) |
0.498021 | − | 0.867165i | \(-0.334060\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 398799. | − | 690741.i | 0.0276033 | − | 0.0478103i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.46017e7 | −1.69124 | −0.845620 | − | 0.533785i | \(-0.820769\pi\) | ||||
−0.845620 | + | 0.533785i | \(0.820769\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.59626e6 | + | 9.69300e6i | −0.379515 | + | 0.657339i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.19096e6 | + | 5.52691e6i | 0.214937 | + | 0.372281i | 0.953253 | − | 0.302173i | \(-0.0977122\pi\) |
−0.738316 | + | 0.674455i | \(0.764379\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 401987. | + | 696262.i | 0.0267141 | + | 0.0462701i | 0.879073 | − | 0.476686i | \(-0.158162\pi\) |
−0.852359 | + | 0.522957i | \(0.824829\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −909214. | + | 1.57480e6i | −0.0600172 | + | 0.103953i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.16774e6 | 0.336586 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.22115e7 | − | 2.11510e7i | 0.790078 | − | 1.36846i | −0.135839 | − | 0.990731i | \(-0.543373\pi\) |
0.925918 | − | 0.377725i | \(-0.123294\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.34837e6 | − | 5.79956e6i | −0.213780 | − | 0.370277i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.52156e7 | − | 2.63542e7i | −0.965050 | − | 1.67152i | −0.709480 | − | 0.704726i | \(-0.751070\pi\) |
−0.255570 | − | 0.966790i | \(-0.582263\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.72001e6 | −0.420638 | −0.210319 | − | 0.977633i | \(-0.567450\pi\) | ||||
−0.210319 | + | 0.977633i | \(0.567450\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.38913e6 | + | 7.60219e6i | 0.272940 | + | 0.472745i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.63843e6 | 0.284697 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.61439e6 | − | 7.99236e6i | 0.281384 | − | 0.487371i | −0.690342 | − | 0.723483i | \(-0.742540\pi\) |
0.971726 | + | 0.236112i | \(0.0758734\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2207.17 | − | 3822.92i | 0.000132858 | − | 0.000230116i | −0.865959 | − | 0.500115i | \(-0.833291\pi\) |
0.866092 | + | 0.499885i | \(0.166624\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.46072e6 | − | 1.63864e7i | 0.565809 | − | 0.980010i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −725071. | − | 10407.7i | −0.0428092 | − | 0.000614487i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 610632. | + | 1.05765e6i | 0.0358222 | + | 0.0620458i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.03095e6 | + | 6.98181e6i | −0.233471 | + | 0.404384i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.44974e7 | −0.834360 | −0.417180 | − | 0.908824i | \(-0.636982\pi\) | ||||
−0.417180 | + | 0.908824i | \(0.636982\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.04919e6 | 0.0596231 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.34030e6 | − | 2.32147e6i | −0.0756867 | − | 0.131093i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.24082e7 | 0.691929 | 0.345964 | − | 0.938248i | \(-0.387552\pi\) | ||||
0.345964 | + | 0.938248i | \(0.387552\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.53361e7 | 1.95818 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.99623e6 | − | 3.45757e6i | −0.109250 | − | 0.189227i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.09357e6 | −0.168256 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.16700e7 | −1.16409 | −0.582047 | − | 0.813155i | \(-0.697748\pi\) | ||||
−0.582047 | + | 0.813155i | \(0.697748\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.06018e6 | − | 3.56833e6i | 0.109990 | − | 0.190508i | −0.805776 | − | 0.592220i | \(-0.798252\pi\) |
0.915766 | + | 0.401712i | \(0.131585\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.55457e6 | + | 4.42464e6i | 0.134717 | + | 0.233337i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −593429. | − | 8518.14i | −0.0311038 | − | 0.000446467i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.20488e7 | + | 2.08691e7i | −0.623858 | + | 1.08055i | 0.364902 | + | 0.931046i | \(0.381102\pi\) |
−0.988760 | + | 0.149509i | \(0.952231\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.56576e7 | + | 2.71197e7i | −0.805796 | + | 1.39568i | 0.109957 | + | 0.993936i | \(0.464929\pi\) |
−0.915753 | + | 0.401743i | \(0.868405\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.78298e6 | − | 1.17485e7i | 0.344871 | − | 0.597334i | −0.640459 | − | 0.767992i | \(-0.721256\pi\) |
0.985330 | + | 0.170658i | \(0.0545893\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.34177e7 | −1.18347 | −0.591737 | − | 0.806131i | \(-0.701557\pi\) | ||||
−0.591737 | + | 0.806131i | \(0.701557\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.60181e7 | − | 2.77442e7i | −0.799831 | − | 1.38535i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.65746e6 | −0.380074 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.43756e7 | − | 2.48992e7i | −0.705051 | − | 1.22118i | −0.966673 | − | 0.256014i | \(-0.917591\pi\) |
0.261622 | − | 0.965170i | \(-0.415743\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.69857e6 | + | 1.67984e7i | 0.472844 | + | 0.818990i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.56139e6 | − | 7.90056e6i | 0.219764 | − | 0.380642i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.26126e6 | 0.108303 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.09876e6 | − | 5.36722e6i | 0.146678 | − | 0.254054i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.39592e6 | − | 1.45422e7i | −0.395090 | − | 0.684315i | 0.598023 | − | 0.801479i | \(-0.295953\pi\) |
−0.993113 | + | 0.117164i | \(0.962620\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.57351e6 | + | 9.65361e6i | 0.259225 | + | 0.448991i | 0.966035 | − | 0.258413i | \(-0.0831995\pi\) |
−0.706810 | + | 0.707404i | \(0.749866\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.21896e7 | − | 2.11131e7i | 0.563648 | − | 0.976266i | −0.433526 | − | 0.901141i | \(-0.642731\pi\) |
0.997174 | − | 0.0751256i | \(-0.0239358\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.13867e7 | −0.520440 | −0.260220 | − | 0.965549i | \(-0.583795\pi\) | ||||
−0.260220 | + | 0.965549i | \(0.583795\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.28850e6 | + | 1.43561e7i | −0.376648 | + | 0.652374i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.67858e6 | − | 1.50317e7i | −0.389851 | − | 0.675242i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.68354e6 | + | 2.91597e6i | 0.0751929 | + | 0.130238i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5.76477e6 | 0.254543 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.95522e7 | − | 3.38654e7i | −0.858414 | − | 1.48682i | −0.873441 | − | 0.486930i | \(-0.838117\pi\) |
0.0150273 | − | 0.999887i | \(-0.495216\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.09362e7 | −0.474708 | −0.237354 | − | 0.971423i | \(-0.576280\pi\) | ||||
−0.237354 | + | 0.971423i | \(0.576280\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.14771e7 | + | 3.71994e7i | −0.926986 | + | 1.60559i | −0.138651 | + | 0.990341i | \(0.544277\pi\) |
−0.788335 | + | 0.615246i | \(0.789057\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.08256e7 | − | 1.87505e7i | 0.462001 | − | 0.800209i | −0.537060 | − | 0.843544i | \(-0.680465\pi\) |
0.999061 | + | 0.0433353i | \(0.0137984\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.41516e6 | − | 4.18318e6i | 0.102492 | − | 0.177522i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.28186e7 | − | 2.29572e7i | −0.537911 | − | 0.963362i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.35252e6 | + | 5.80673e6i | 0.139899 | + | 0.242312i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.01183e6 | − | 6.94869e6i | 0.165555 | − | 0.286750i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.21373e7 | −0.908473 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.81185e6 | −0.154708 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.14753e6 | + | 1.23799e7i | 0.288495 | + | 0.499687i | 0.973451 | − | 0.228897i | \(-0.0735119\pi\) |
−0.684956 | + | 0.728584i | \(0.740179\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.67784e7 | 0.669816 | 0.334908 | − | 0.942251i | \(-0.391295\pi\) | ||||
0.334908 | + | 0.942251i | \(0.391295\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −427834. | −0.0169863 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.12949e6 | − | 1.95633e6i | −0.0443565 | − | 0.0768278i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.40604e7 | −1.33034 | −0.665168 | − | 0.746694i | \(-0.731640\pi\) | ||||
−0.665168 | + | 0.746694i | \(0.731640\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 367396. | 0.0141948 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.56014e6 | + | 4.43429e6i | −0.0983804 | + | 0.170400i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.16519e7 | − | 2.01817e7i | −0.442953 | − | 0.767216i | 0.554955 | − | 0.831881i | \(-0.312736\pi\) |
−0.997907 | + | 0.0646644i | \(0.979402\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.22141e7 | + | 2.04711e7i | −0.461835 | + | 0.774048i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.66184e6 | + | 1.50027e7i | −0.324027 | + | 0.561231i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.82963e7 | − | 3.16902e7i | 0.680794 | − | 1.17917i | −0.293946 | − | 0.955822i | \(-0.594968\pi\) |
0.974739 | − | 0.223347i | \(-0.0716982\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.27910e7 | − | 2.21547e7i | 0.470902 | − | 0.815626i | −0.528544 | − | 0.848906i | \(-0.677262\pi\) |
0.999446 | + | 0.0332800i | \(0.0105953\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.38833e6 | 0.0508409 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.62172e7 | − | 2.80890e7i | −0.587627 | − | 1.01780i | −0.994542 | − | 0.104333i | \(-0.966729\pi\) |
0.406916 | − | 0.913466i | \(-0.366604\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.20106e6 | −0.0432912 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.43185e7 | + | 4.21208e7i | 0.867369 | + | 1.50233i | 0.864675 | + | 0.502331i | \(0.167524\pi\) |
0.00269410 | + | 0.999996i | \(0.499142\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.51933e6 | − | 2.63156e6i | −0.0539068 | − | 0.0933694i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.51053e6 | + | 1.12766e7i | −0.228597 | + | 0.395941i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.91613e7 | 1.01859 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 968028. | − | 1.67667e6i | 0.0334634 | − | 0.0579603i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.29008e7 | + | 3.96653e7i | 0.787561 | + | 1.36410i | 0.927457 | + | 0.373930i | \(0.121990\pi\) |
−0.139895 | + | 0.990166i | \(0.544677\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.65694e7 | − | 2.86990e7i | −0.563973 | − | 0.976830i | −0.997144 | − | 0.0755181i | \(-0.975939\pi\) |
0.433172 | − | 0.901311i | \(-0.357394\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.30835e6 | − | 7.46229e6i | 0.145891 | − | 0.252691i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.87294e7 | −0.962920 | −0.481460 | − | 0.876468i | \(-0.659893\pi\) | ||||
−0.481460 | + | 0.876468i | \(0.659893\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.68056e7 | − | 2.91082e7i | 0.560400 | − | 0.970641i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.41284e7 | − | 2.44712e7i | −0.466348 | − | 0.807739i | 0.532913 | − | 0.846170i | \(-0.321097\pi\) |
−0.999261 | + | 0.0384309i | \(0.987764\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.33750e6 | + | 1.27089e7i | 0.240967 | + | 0.417367i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.13627e6 | 0.0369395 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.23566e7 | − | 3.87228e7i | −0.723140 | − | 1.25251i | −0.959735 | − | 0.280907i | \(-0.909365\pi\) |
0.236595 | − | 0.971608i | \(-0.423968\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.21342e6 | −0.134920 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.35342e7 | + | 4.07625e7i | −0.749828 | + | 1.29874i | 0.198077 | + | 0.980187i | \(0.436531\pi\) |
−0.947905 | + | 0.318554i | \(0.896803\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 684.6.k.f.577.4 | 18 | ||
3.2 | odd | 2 | 76.6.e.a.45.5 | ✓ | 18 | ||
12.11 | even | 2 | 304.6.i.d.273.5 | 18 | |||
19.11 | even | 3 | inner | 684.6.k.f.505.4 | 18 | ||
57.11 | odd | 6 | 76.6.e.a.49.5 | yes | 18 | ||
228.11 | even | 6 | 304.6.i.d.49.5 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.6.e.a.45.5 | ✓ | 18 | 3.2 | odd | 2 | ||
76.6.e.a.49.5 | yes | 18 | 57.11 | odd | 6 | ||
304.6.i.d.49.5 | 18 | 228.11 | even | 6 | |||
304.6.i.d.273.5 | 18 | 12.11 | even | 2 | |||
684.6.k.f.505.4 | 18 | 19.11 | even | 3 | inner | ||
684.6.k.f.577.4 | 18 | 1.1 | even | 1 | trivial |