Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,6,Mod(209,336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(336, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("336.209");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.k (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(53.8889634572\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 484x^{10} + 194194x^{8} - 39867800x^{6} + 5398720873x^{4} - 310089434788x^{2} + 9371104623076 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{10} \) |
Twist minimal: | no (minimal twist has level 21) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 209.10 | ||
Root | \(-6.98672 - 2.99433i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 336.209 |
Dual form | 336.6.k.d.209.9 |
$q$-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 \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 9.94100 | + | 12.0074i | 0.637716 | + | 0.770272i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 61.8023 | 1.10555 | 0.552777 | − | 0.833329i | \(-0.313568\pi\) | ||||
0.552777 | + | 0.833329i | \(0.313568\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −92.4210 | + | 90.9140i | −0.712895 | + | 0.701271i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −45.3530 | + | 238.730i | −0.186638 | + | 0.982429i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 615.301i | 1.53323i | 0.642110 | + | 0.766613i | \(0.278059\pi\) | ||||
−0.642110 | + | 0.766613i | \(0.721941\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 322.895i | 0.529911i | 0.964261 | + | 0.264955i | \(0.0853572\pi\) | ||||
−0.964261 | + | 0.264955i | \(0.914643\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 614.377 | + | 742.083i | 0.705029 | + | 0.851577i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1537.42 | −1.29024 | −0.645120 | − | 0.764081i | \(-0.723193\pi\) | ||||
−0.645120 | + | 0.764081i | \(0.723193\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 2171.63i | − | 1.38007i | −0.723775 | − | 0.690036i | \(-0.757595\pi\) | ||
0.723775 | − | 0.690036i | \(-0.242405\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2010.39 | − | 205.956i | −0.994793 | − | 0.101912i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 793.329i | − | 0.312704i | −0.987701 | − | 0.156352i | \(-0.950027\pi\) | ||
0.987701 | − | 0.156352i | \(-0.0499735\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 694.530 | 0.222250 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3317.37 | + | 1828.65i | −0.875759 | + | 0.482748i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 513.596i | − | 0.113404i | −0.998391 | − | 0.0567018i | \(-0.981942\pi\) | ||
0.998391 | − | 0.0567018i | \(-0.0180584\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 161.215i | − | 0.0301302i | −0.999887 | − | 0.0150651i | \(-0.995204\pi\) | ||
0.999887 | − | 0.0150651i | \(-0.00479555\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −7388.14 | + | 6116.71i | −1.18100 | + | 0.977762i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5711.84 | + | 5618.70i | −0.788144 | + | 0.775293i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8593.37 | −1.03195 | −0.515976 | − | 0.856603i | \(-0.672571\pi\) | ||||
−0.515976 | + | 0.856603i | \(0.672571\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3877.11 | + | 3209.90i | −0.408175 | + | 0.337932i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7004.53 | 0.650758 | 0.325379 | − | 0.945584i | \(-0.394508\pi\) | ||||
0.325379 | + | 0.945584i | \(0.394508\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7726.50 | 0.637253 | 0.318627 | − | 0.947880i | \(-0.396778\pi\) | ||||
0.318627 | + | 0.947880i | \(0.396778\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2802.92 | + | 14754.1i | −0.206338 | + | 1.08613i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 17604.2 | 1.16244 | 0.581221 | − | 0.813745i | \(-0.302575\pi\) | ||||
0.581221 | + | 0.813745i | \(0.302575\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 276.290 | − | 16804.7i | 0.0164390 | − | 0.999865i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −15283.5 | − | 18460.3i | −0.822806 | − | 0.993835i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7345.26i | 0.359184i | 0.983741 | + | 0.179592i | \(0.0574778\pi\) | ||||
−0.983741 | + | 0.179592i | \(0.942522\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 38027.1i | 1.69506i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 26075.5 | − | 21588.2i | 1.06303 | − | 0.880093i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −23416.6 | −0.875779 | −0.437889 | − | 0.899029i | \(-0.644274\pi\) | ||||
−0.437889 | + | 0.899029i | \(0.644274\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13344.8i | 0.459186i | 0.973287 | + | 0.229593i | \(0.0737395\pi\) | ||||
−0.973287 | + | 0.229593i | \(0.926260\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −17512.3 | − | 26186.9i | −0.555895 | − | 0.831252i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 19955.7i | 0.585845i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −14471.1 | −0.393835 | −0.196918 | − | 0.980420i | \(-0.563093\pi\) | ||||
−0.196918 | + | 0.980420i | \(0.563093\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 9525.78 | − | 7886.48i | 0.240867 | − | 0.199416i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 7370.42i | − | 0.173519i | −0.996229 | − | 0.0867593i | \(-0.972349\pi\) | ||
0.996229 | − | 0.0867593i | \(-0.0276511\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9422.68i | 0.206951i | 0.994632 | + | 0.103475i | \(0.0329963\pi\) | ||||
−0.994632 | + | 0.103475i | \(0.967004\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6904.32 | + | 8339.47i | 0.141732 | + | 0.171193i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −55939.5 | − | 56866.8i | −1.07521 | − | 1.09303i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −27229.8 | −0.490882 | −0.245441 | − | 0.969412i | \(-0.578933\pi\) | ||||
−0.245441 | + | 0.969412i | \(0.578933\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −54935.2 | − | 21654.3i | −0.930333 | − | 0.366717i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −15577.0 | −0.248192 | −0.124096 | − | 0.992270i | \(-0.539603\pi\) | ||||
−0.124096 | + | 0.992270i | \(0.539603\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −95016.2 | −1.42643 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6166.93 | − | 5105.66i | 0.0873516 | − | 0.0723192i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 90024.7 | 1.20472 | 0.602361 | − | 0.798224i | \(-0.294227\pi\) | ||||
0.602361 | + | 0.798224i | \(0.294227\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −29355.7 | − | 29842.3i | −0.371611 | − | 0.377771i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1935.77 | − | 1602.64i | 0.0232085 | − | 0.0192145i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 134212.i | − | 1.52574i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 84850.1i | 0.915637i | 0.889046 | + | 0.457818i | \(0.151369\pi\) | ||||
−0.889046 | + | 0.457818i | \(0.848631\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −146891. | − | 27905.8i | −1.50628 | − | 0.286158i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −80893.8 | −0.789063 | −0.394532 | − | 0.918882i | \(-0.629093\pi\) | ||||
−0.394532 | + | 0.918882i | \(0.629093\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 214822.i | 1.99520i | 0.0692543 | + | 0.997599i | \(0.477938\pi\) | ||||
−0.0692543 | + | 0.997599i | \(0.522062\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −124247. | − | 12728.5i | −1.09980 | − | 0.112669i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 120007.i | 1.01332i | 0.862146 | + | 0.506660i | \(0.169120\pi\) | ||||
−0.862146 | + | 0.506660i | \(0.830880\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 29204.1 | 0.235439 | 0.117719 | − | 0.993047i | \(-0.462442\pi\) | ||||
0.117719 | + | 0.993047i | \(0.462442\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −85426.7 | − | 103184.i | −0.658091 | − | 0.794883i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 64313.7i | − | 0.473813i | −0.971532 | − | 0.236907i | \(-0.923866\pi\) | ||
0.971532 | − | 0.236907i | \(-0.0761335\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 49029.6i | − | 0.345711i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −77084.8 | − | 14644.3i | −0.520600 | − | 0.0989014i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 142090. | − | 139773.i | 0.919805 | − | 0.904807i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −217545. | −1.35078 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 69632.0 | + | 84105.8i | 0.414998 | + | 0.501260i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −150209. | −0.859845 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 293422. | 1.61430 | 0.807149 | − | 0.590348i | \(-0.201010\pi\) | ||||
0.807149 | + | 0.590348i | \(0.201010\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 76809.2 | + | 92774.9i | 0.406386 | + | 0.490858i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −159323. | −0.811147 | −0.405573 | − | 0.914063i | \(-0.632928\pi\) | ||||
−0.405573 | + | 0.914063i | \(0.632928\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 197432. | + | 200704.i | 0.967804 | + | 0.983847i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −205021. | + | 113015.i | −0.968199 | + | 0.533704i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 387950.i | − | 1.76593i | −0.469436 | − | 0.882967i | \(-0.655543\pi\) | ||
0.469436 | − | 0.882967i | \(-0.344457\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 324317.i | 1.42375i | 0.702308 | + | 0.711874i | \(0.252153\pi\) | ||||
−0.702308 | + | 0.711874i | \(0.747847\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 175003. | + | 211380.i | 0.741308 | + | 0.895397i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −198678. | −0.812473 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 31741.4i | − | 0.125374i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 204527. | − | 163738.i | 0.780651 | − | 0.624967i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 318945.i | 1.17693i | 0.808523 | + | 0.588464i | \(0.200267\pi\) | ||||
−0.808523 | + | 0.588464i | \(0.799733\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −479410. | −1.71106 | −0.855529 | − | 0.517754i | \(-0.826768\pi\) | ||||
−0.855529 | + | 0.517754i | \(0.826768\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 69726.6 | − | 367029.i | 0.240808 | − | 1.26757i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 9963.49i | − | 0.0333106i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 323801.i | 1.04840i | 0.851594 | + | 0.524202i | \(0.175636\pi\) | ||||
−0.851594 | + | 0.524202i | \(0.824364\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −88197.1 | + | 73019.2i | −0.276670 | + | 0.229057i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 72124.7 | + | 73320.3i | 0.219290 | + | 0.222925i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 21423.8 | 0.0631579 | 0.0315789 | − | 0.999501i | \(-0.489946\pi\) | ||||
0.0315789 | + | 0.999501i | \(0.489946\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −456604. | + | 378027.i | −1.30566 | + | 1.08097i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −436305. | −1.21059 | −0.605297 | − | 0.796000i | \(-0.706946\pi\) | ||||
−0.605297 | + | 0.796000i | \(0.706946\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 267032. | 0.719195 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 518434. | + | 98489.9i | 1.35582 | + | 0.257574i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −185581. | −0.471431 | −0.235715 | − | 0.971822i | \(-0.575743\pi\) | ||||
−0.235715 | + | 0.971822i | \(0.575743\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −64189.2 | + | 63142.5i | −0.158441 | + | 0.155857i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −232785. | − | 281172.i | −0.558498 | − | 0.674588i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 170761.i | − | 0.398341i | −0.979965 | − | 0.199171i | \(-0.936175\pi\) | ||
0.979965 | − | 0.199171i | \(-0.0638248\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 326285.i | − | 0.740289i | −0.928974 | − | 0.370144i | \(-0.879308\pi\) | ||
0.928974 | − | 0.370144i | \(-0.120692\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −160236. | + | 132661.i | −0.353698 | + | 0.292830i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −531090. | −1.14088 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 945977.i | − | 1.97823i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 140345. | − | 470601.i | 0.285787 | − | 0.958293i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 296995.i | 0.589069i | 0.955641 | + | 0.294534i | \(0.0951646\pi\) | ||||
−0.955641 | + | 0.294534i | \(0.904835\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 414092. | 0.800208 | 0.400104 | − | 0.916470i | \(-0.368974\pi\) | ||||
0.400104 | + | 0.916470i | \(0.368974\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −239615. | + | 198379.i | −0.451260 | + | 0.373602i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 216937.i | 0.398262i | 0.979973 | + | 0.199131i | \(0.0638119\pi\) | ||||
−0.979973 | + | 0.199131i | \(0.936188\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 36716.3i | 0.0657244i | 0.999460 | + | 0.0328622i | \(0.0104623\pi\) | ||||
−0.999460 | + | 0.0328622i | \(0.989538\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −143857. | − | 173760.i | −0.251155 | − | 0.303360i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 46693.1 | + | 47467.1i | 0.0795266 | + | 0.0808448i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 432896. | 0.719448 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 189392. | + | 35979.8i | 0.307210 | + | 0.0583624i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.33621e6 | 2.11596 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 587416. | 0.908321 | 0.454161 | − | 0.890920i | \(-0.349939\pi\) | ||||
0.454161 | + | 0.890920i | \(0.349939\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 88499.2 | − | 73269.3i | 0.133657 | − | 0.110656i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 477516. | 0.704518 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 14656.7 | + | 14899.7i | 0.0211294 | + | 0.0214797i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −113141. | + | 93670.8i | −0.159408 | + | 0.131976i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 496425.i | − | 0.683712i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 349812.i | 0.471056i | 0.971868 | + | 0.235528i | \(0.0756819\pi\) | ||||
−0.971868 | + | 0.235528i | \(0.924318\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −31499.0 | + | 165805.i | −0.0414802 | + | 0.218344i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 925060. | 1.19153 | 0.595766 | − | 0.803158i | \(-0.296849\pi\) | ||||
0.595766 | + | 0.803158i | \(0.296849\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 136041.i | − | 0.171428i | −0.996320 | − | 0.0857142i | \(-0.972683\pi\) | ||
0.996320 | − | 0.0857142i | \(-0.0273172\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 126725. | − | 1.23700e6i | 0.156254 | − | 1.52524i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.13764e6i | 1.37283i | 0.727212 | + | 0.686413i | \(0.240816\pi\) | ||||
−0.727212 | + | 0.686413i | \(0.759184\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.08798e6 | 1.28514 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −270692. | − | 326958.i | −0.313043 | − | 0.378113i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.04427e6i | 1.18254i | 0.806473 | + | 0.591271i | \(0.201374\pi\) | ||||
−0.806473 | + | 0.591271i | \(0.798626\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 503492.i | 0.558406i | 0.960232 | + | 0.279203i | \(0.0900702\pi\) | ||||
−0.960232 | + | 0.279203i | \(0.909930\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −286101. | − | 874891.i | −0.310816 | − | 0.950470i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 17075.4 | − | 1.03857e6i | 0.0181742 | − | 1.10540i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 701208. | 0.731315 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −154851. | − | 187038.i | −0.158276 | − | 0.191175i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.68197e6 | 1.68514 | 0.842568 | − | 0.538590i | \(-0.181043\pi\) | ||||
0.842568 | + | 0.538590i | \(0.181043\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 488136. | 0.479446 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −944556. | − | 1.14089e6i | −0.909656 | − | 1.09874i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 953741. | 0.900736 | 0.450368 | − | 0.892843i | \(-0.351293\pi\) | ||||
0.450368 | + | 0.892843i | \(0.351293\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 794208. | − | 781258.i | 0.735673 | − | 0.723677i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 122611. | + | 23293.1i | 0.111411 | + | 0.0211654i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 1.64469e6i | − | 1.46621i | −0.680117 | − | 0.733104i | \(-0.738071\pi\) | ||
0.680117 | − | 0.733104i | \(-0.261929\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 453954.i | 0.397098i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 894935. | + | 1.08096e6i | 0.768269 | + | 0.927963i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 76973.2 | 0.0648573 | 0.0324286 | − | 0.999474i | \(-0.489676\pi\) | ||||
0.0324286 | + | 0.999474i | \(0.489676\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.79795e6i | 1.48715i | 0.668652 | + | 0.743576i | \(0.266872\pi\) | ||||
−0.668652 | + | 0.743576i | \(0.733128\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 66502.0 | − | 649146.i | 0.0540043 | − | 0.527152i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 427345.i | 0.340759i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.16102e6 | 0.909160 | 0.454580 | − | 0.890706i | \(-0.349789\pi\) | ||||
0.454580 | + | 0.890706i | \(0.349789\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 38487.0 | + | 7311.60i | 0.0296008 | + | 0.00562344i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.50031e6i | 1.13348i | 0.823896 | + | 0.566741i | \(0.191796\pi\) | ||||
−0.823896 | + | 0.566741i | \(0.808204\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 775321.i | 0.575460i | 0.957712 | + | 0.287730i | \(0.0929006\pi\) | ||||
−0.957712 | + | 0.287730i | \(0.907099\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.61153e6 | − | 1.33420e6i | 1.17524 | − | 0.972991i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −647366. | + | 636810.i | −0.463922 | + | 0.456357i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 943804. | 0.664718 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.01883e6 | + | 843495.i | −0.705289 | + | 0.583916i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 194034. | 0.132041 | 0.0660206 | − | 0.997818i | \(-0.478970\pi\) | ||||
0.0660206 | + | 0.997818i | \(0.478970\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.44720e6 | −0.968221 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.12517e6 | − | 2.04118e6i | −0.740162 | − | 1.34274i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 256162. | 0.165705 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −714091. | + | 702447.i | −0.454295 | + | 0.446887i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −804165. | − | 971320.i | −0.503198 | − | 0.607793i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 824742.i | 0.507655i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 394659.i | − | 0.238988i | −0.992835 | − | 0.119494i | \(-0.961873\pi\) | ||
0.992835 | − | 0.119494i | \(-0.0381273\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.57945e6 | + | 2.13555e6i | −1.53685 | + | 1.27237i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.29757e6 | −1.34700 | −0.673501 | − | 0.739186i | \(-0.735210\pi\) | ||||
−0.673501 | + | 0.739186i | \(0.735210\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 634859.i | − | 0.366283i | −0.983087 | − | 0.183141i | \(-0.941373\pi\) | ||
0.983087 | − | 0.183141i | \(-0.0586266\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.08230e6 | − | 1.61841e6i | −0.614572 | − | 0.918994i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 192873.i | − | 0.107801i | −0.998546 | − | 0.0539005i | \(-0.982835\pi\) | ||
0.998546 | − | 0.0539005i | \(-0.0171654\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 316016. | 0.173873 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.44096e6 | + | 1.19299e6i | −0.780532 | + | 0.646210i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.33871e6i | 1.78062i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 224260.i | 0.117772i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 290318. | + | 350664.i | 0.150143 | + | 0.181352i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.62700e6 | + | 1.60047e6i | −0.828700 | + | 0.815187i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.85474e6 | 1.43218 | 0.716088 | − | 0.698010i | \(-0.245931\pi\) | ||||
0.716088 | + | 0.698010i | \(0.245931\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 389735. | − | 2.05150e6i | 0.192601 | − | 1.01382i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −894348. | −0.435406 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.37722e6 | 1.61989 | 0.809944 | − | 0.586507i | \(-0.199497\pi\) | ||||
0.809944 | + | 0.586507i | \(0.199497\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 772237. | − | 639342.i | 0.364965 | − | 0.302158i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 99196.0 | 0.0461964 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.50225e6 | + | 1.57823e6i | 0.689457 | + | 0.724327i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 588716. | − | 487403.i | 0.266292 | − | 0.220466i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 547961.i | 0.244301i | 0.992512 | + | 0.122151i | \(0.0389791\pi\) | ||||
−0.992512 | + | 0.122151i | \(0.961021\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1206.49i | 0.000530223i | 1.00000 | 0.000265112i | \(8.43876e-5\pi\) | |||||
−1.00000 | 0.000265112i | \(0.999916\pi\) | ||||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −590461. | − | 1.07116e6i | −0.255813 | − | 0.464074i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.15208e6 | −0.492090 | −0.246045 | − | 0.969258i | \(-0.579131\pi\) | ||||
−0.246045 | + | 0.969258i | \(0.579131\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 455509.i | − | 0.191834i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.09082e6 | + | 316640.i | 1.28352 | + | 0.131491i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 2.10870e6i | − | 0.863531i | −0.901986 | − | 0.431766i | \(-0.857891\pi\) | ||
0.901986 | − | 0.431766i | \(-0.142109\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.23988e6 | −0.904599 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.16261e6 | − | 2.61213e6i | −0.861414 | − | 1.04047i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 582344.i | 0.228795i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.37130e6i | 1.30657i | 0.757113 | + | 0.653284i | \(0.226609\pi\) | ||||
−0.757113 | + | 0.653284i | \(0.773391\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −317676. | + | 1.67219e6i | −0.121456 | + | 0.639323i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −667787. | − | 678856.i | −0.251885 | − | 0.256061i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −65054.8 | −0.0242107 | −0.0121054 | − | 0.999927i | \(-0.503853\pi\) | ||||
−0.0121054 | + | 0.999927i | \(0.503853\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.49323e6 | − | 1.80361e6i | −0.548337 | − | 0.662315i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 165838. | 0.0600938 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 690875. | 0.247059 | 0.123530 | − | 0.992341i | \(-0.460579\pi\) | ||||
0.123530 | + | 0.992341i | \(0.460579\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.91691e6 | + | 3.52322e6i | 1.02946 | + | 1.24345i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.44872e6 | 0.852986 | 0.426493 | − | 0.904491i | \(-0.359749\pi\) | ||||
0.426493 | + | 0.904491i | \(0.359749\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.45719e6 | − | 3.51450e6i | −1.18870 | − | 1.20840i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −350420. | + | 1.84455e6i | −0.118936 | + | 0.626056i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 3.72849e6i | − | 1.24928i | −0.780913 | − | 0.624640i | \(-0.785246\pi\) | ||
0.780913 | − | 0.624640i | \(-0.214754\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.21968e6i | 0.403463i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.58383e6 | − | 1.91304e6i | −0.517281 | − | 0.624803i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.68287e6 | −0.542697 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.19740e6i | 1.01817i | 0.860716 | + | 0.509086i | \(0.170016\pi\) | ||||
−0.860716 | + | 0.509086i | \(0.829984\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −447259. | + | 4.36583e6i | −0.140646 | + | 1.37289i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 6.01416e6i | − | 1.86773i | −0.357627 | − | 0.933865i | \(-0.616414\pi\) | ||
0.357627 | − | 0.933865i | \(-0.383586\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 52055.6 | 0.0159663 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.39512e6 | − | 1.33828e6i | −1.02853 | − | 0.405425i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 5.28751e6i | − | 1.58221i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.69952e6i | 1.68473i | 0.538909 | + | 0.842364i | \(0.318837\pi\) | ||||
−0.538909 | + | 0.842364i | \(0.681163\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.65825e6 | − | 3.85661e6i | 1.36025 | − | 1.12616i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.16419e6 | − | 2.12890e6i | 0.624338 | − | 0.614158i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −962694. | −0.274390 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.89419e6 | + | 3.22404e6i | −1.09667 | + | 0.907946i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.40292e6 | 0.668658 | 0.334329 | − | 0.942456i | \(-0.391490\pi\) | ||||
0.334329 | + | 0.942456i | \(0.391490\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.84926e6 | −0.508501 | −0.254251 | − | 0.967138i | \(-0.581829\pi\) | ||||
−0.254251 | + | 0.967138i | \(0.581829\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −798403. | + | 4.20265e6i | −0.216956 | + | 1.14202i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.06778e6 | −0.286755 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.21323e6 | − | 1.23334e6i | −0.322014 | − | 0.327351i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.97505e6 | − | 2.38559e6i | −0.518127 | − | 0.625825i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 670021.i | − | 0.173738i | −0.996220 | − | 0.0868691i | \(-0.972314\pi\) | ||
0.996220 | − | 0.0868691i | \(-0.0276862\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.18314e6i | 0.815898i | 0.913005 | + | 0.407949i | \(0.133756\pi\) | ||||
−0.913005 | + | 0.407949i | \(0.866244\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 381131. | − | 315542.i | 0.0965719 | − | 0.0799528i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.72282e6 | −0.431554 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 3.04218e6i | − | 0.753396i | −0.926336 | − | 0.376698i | \(-0.877059\pi\) | ||
0.926336 | − | 0.376698i | \(-0.122941\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.99927e6 | + | 828104.i | 0.979228 | + | 0.202763i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 4.06656e6i | − | 0.984505i | −0.870452 | − | 0.492253i | \(-0.836174\pi\) | ||
0.870452 | − | 0.492253i | \(-0.163826\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.56374e6 | 1.33188 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.82969e6 | + | 3.17063e6i | −0.906555 | + | 0.750546i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 3.30712e6i | − | 0.774166i | −0.922045 | − | 0.387083i | \(-0.873483\pi\) | ||
0.922045 | − | 0.387083i | \(-0.126517\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.30990e6i | 0.997758i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.76582e6 | − | 5.75645e6i | −1.09117 | − | 1.31798i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.81425e6 | − | 1.84432e6i | −0.410836 | − | 0.417646i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 797135. | 0.178542 | 0.0892712 | − | 0.996007i | \(-0.471546\pi\) | ||||
0.0892712 | + | 0.996007i | \(0.471546\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.10019e6 | − | 2.81140e6i | 1.12994 | − | 0.622861i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.32869e6 | −0.948646 | −0.474323 | − | 0.880351i | \(-0.657307\pi\) | ||||
−0.474323 | + | 0.880351i | \(0.657307\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.38489e6 | −1.16741 | −0.583706 | − | 0.811965i | \(-0.698398\pi\) | ||||
−0.583706 | + | 0.811965i | \(0.698398\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 119635. | − | 99047.1i | 0.0256582 | − | 0.0212427i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −677568. | −0.143767 | −0.0718837 | − | 0.997413i | \(-0.522901\pi\) | ||||
−0.0718837 | + | 0.997413i | \(0.522901\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.33743e6 | − | 1.31563e6i | 0.280763 | − | 0.276185i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.88799e6 | + | 3.21891e6i | −0.807557 | + | 0.668584i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.75413e6i | 0.977053i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 1.50826e6i | − | 0.306720i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.75353e6 | − | 333130.i | −0.352873 | − | 0.0670374i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.87592e6 | −1.56842 | −0.784210 | − | 0.620495i | \(-0.786932\pi\) | ||||
−0.784210 | + | 0.620495i | \(0.786932\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 2.77476e6i | − | 0.546842i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −163391. | + | 1.59490e6i | −0.0318683 | + | 0.311076i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.24394e6i | 1.01229i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.38336e6 | −1.21963 | −0.609813 | − | 0.792545i | \(-0.708756\pi\) | ||||
−0.609813 | + | 0.792545i | \(0.708756\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 212974. | + | 257243.i | 0.0402768 | + | 0.0486488i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 837734.i | 0.156820i | 0.996921 | + | 0.0784102i | \(0.0249844\pi\) | ||||
−0.996921 | + | 0.0784102i | \(0.975016\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 789613.i | 0.146318i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −9.07821e6 | − | 1.72464e6i | −1.66528 | − | 0.316363i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 670074. | + | 681182.i | 0.121684 | + | 0.123701i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.80919e6 | 0.864611 | 0.432306 | − | 0.901727i | \(-0.357700\pi\) | ||||
0.432306 | + | 0.901727i | \(0.357700\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.33731e6 | − | 5.23886e6i | −0.772015 | − | 0.932487i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.58231e6 | 0.455081 | 0.227540 | − | 0.973769i | \(-0.426932\pi\) | ||||
0.227540 | + | 0.973769i | \(0.426932\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.99943e6 | −0.872352 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.65456e6 | + | 3.20635e6i | 0.458642 | + | 0.553975i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.81775e6 | 0.995315 | 0.497658 | − | 0.867374i | \(-0.334194\pi\) | ||||
0.497658 | + | 0.867374i | \(0.334194\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −856653. | − | 870853.i | −0.145129 | − | 0.147534i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.97115e6 | + | 7.20410e6i | 0.666227 | + | 1.20861i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.32765e7i | 2.20580i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.08319e7i | 1.78229i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.84486e6 | − | 2.22833e6i | −0.300639 | − | 0.363130i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.44578e6 | −1.20175 | −0.600877 | − | 0.799341i | \(-0.705182\pi\) | ||||
−0.600877 | + | 0.799341i | \(0.705182\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.68003e6i | 0.428435i | 0.976786 | + | 0.214218i | \(0.0687202\pi\) | ||||
−0.976786 | + | 0.214218i | \(0.931280\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.39628e6 | − | 143042.i | −0.221092 | − | 0.0226499i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 247856.i | 0.0388752i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.80697e6 | 0.902216 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.06201e6 | − | 5.59026e6i | 0.163453 | − | 0.860390i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.26173e6i | 0.344844i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.41670e6i | 1.12028i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.05038e6 | − | 1.69753e6i | 0.306831 | − | 0.254028i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.03400e7 | + | 170002.i | 1.53302 | + | 0.0252047i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.33897e6 | −1.07806 | −0.539029 | − | 0.842288i | \(-0.681209\pi\) | ||||
−0.539029 | + | 0.842288i | \(0.681209\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.91782e6 | − | 3.24360e6i | 0.570224 | − | 0.472094i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.80488e6 | 0.260290 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.63983e6 | 0.520131 | 0.260066 | − | 0.965591i | \(-0.416256\pi\) | ||||
0.260066 | + | 0.965591i | \(0.416256\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.18582e6 | − | 605228.i | −0.451118 | − | 0.0857015i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.11534e6 | −0.156505 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.51661e6 | − | 2.47557e6i | 0.349947 | − | 0.344241i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5.27957e6 | − | 6.37699e6i | −0.727556 | − | 0.878786i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.12162e7i | 1.53183i | 0.642944 | + | 0.765913i | \(0.277713\pi\) | ||||
−0.642944 | + | 0.765913i | \(0.722287\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.49485e6i | 0.337687i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.13587e7 | − | 9.40395e6i | 1.52377 | − | 1.26155i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.46722e7 | −1.95085 | −0.975426 | − | 0.220326i | \(-0.929288\pi\) | ||||
−0.975426 | + | 0.220326i | \(0.929288\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 3.97474e6i | − | 0.523826i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7.04584e6 | − | 2.99307e6i | 0.920397 | − | 0.390984i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 5.12118e6i | − | 0.663116i | −0.943435 | − | 0.331558i | \(-0.892426\pi\) | ||
0.943435 | − | 0.331558i | \(-0.107574\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.08710e6 | −0.524596 | −0.262298 | − | 0.964987i | \(-0.584480\pi\) | ||||
−0.262298 | + | 0.964987i | \(0.584480\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.56613e6 | + | 2.95243e6i | −0.453743 | + | 0.375658i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 550991.i | − | 0.0694984i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 2.58345e6i | − | 0.323043i | −0.986869 | − | 0.161521i | \(-0.948360\pi\) | ||
0.986869 | − | 0.161521i | \(-0.0516401\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.11648e6 | + | 4.97214e6i | 0.510305 | + | 0.616378i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.43964e6 | − | 1.41617e6i | 0.176935 | − | 0.174050i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.51955e6 | −0.550711 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.76402e6 | − | 905049.i | −0.575551 | − | 0.109341i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.72773e6 | 1.16524 | 0.582621 | − | 0.812744i | \(-0.302027\pi\) | ||||
0.582621 | + | 0.812744i | \(0.302027\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −350100. | −0.0415819 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.60484e6 | + | 2.15657e6i | −0.306770 | + | 0.253978i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9.57397e6 | 1.11803 | 0.559017 | − | 0.829156i | \(-0.311179\pi\) | ||||
0.559017 | + | 0.829156i | \(0.311179\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.78149e6 | − | 8.63830e6i | 1.01689 | − | 1.00031i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −440866. | + | 364997.i | −0.0506257 | + | 0.0419135i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 5.71115e6i | − | 0.650364i | −0.945651 | − | 0.325182i | \(-0.894574\pi\) | ||
0.945651 | − | 0.325182i | \(-0.105426\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 1.49010e6i | − | 0.168279i | −0.996454 | − | 0.0841395i | \(-0.973186\pi\) | ||
0.996454 | − | 0.0841395i | \(-0.0268141\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 656308. | − | 3.45469e6i | 0.0735046 | − | 0.386915i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.34448e7 | −1.49336 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 1.13768e7i | − | 1.25328i | −0.779308 | − | 0.626641i | \(-0.784429\pi\) | ||
0.779308 | − | 0.626641i | \(-0.215571\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −105778. | + | 1.03253e6i | −0.0115572 | + | 0.112813i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.68431e6i | 0.615991i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.50093e6 | 0.913724 | 0.456862 | − | 0.889537i | \(-0.348973\pi\) | ||||
0.456862 | + | 0.889537i | \(0.348973\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.30342e6 | + | 5.19794e6i | 0.458803 | + | 0.554170i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 1.82563e7i | − | 1.93064i | −0.261073 | − | 0.965319i | \(-0.584076\pi\) | ||
0.261073 | − | 0.965319i | \(-0.415924\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 1.24791e7i | − | 1.30905i | −0.756041 | − | 0.654524i | \(-0.772869\pi\) | ||
0.756041 | − | 0.654524i | \(-0.227131\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.45072e6 | + | 2.63177e6i | 0.150957 | + | 0.273854i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.32017e6 | + | 8.18450e6i | −0.858840 | + | 0.844836i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.14537e7 | −1.17285 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.32832e7 | + | 1.60443e7i | 1.34938 | + | 1.62987i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.32116e7 | 1.33146 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.52412e7 | 1.52387 | 0.761933 | − | 0.647656i | \(-0.224251\pi\) | ||||
0.761933 | + | 0.647656i | \(0.224251\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.83950e6 | + | 7.05331e6i | 0.579250 | + | 0.699654i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.81342e7 | 1.78469 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.42616e6 | + | 89212.6i | 0.529839 | + | 0.00871119i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.75954e6 | + | 334271.i | 0.170470 | + | 0.0323852i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.06269e6i | 0.294414i | 0.989106 | + | 0.147207i | \(0.0470283\pi\) | ||||
−0.989106 | + | 0.147207i | \(0.952972\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.16015e6i | 0.396809i | 0.980120 | + | 0.198404i | \(0.0635760\pi\) | ||||
−0.980120 | + | 0.198404i | \(0.936424\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.74699e6 | + | 5.73370e6i | 0.449282 | + | 0.542670i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.44997e7 | 1.36175 | 0.680877 | − | 0.732398i | \(-0.261599\pi\) | ||||
0.680877 | + | 0.732398i | \(0.261599\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 1.44083e7i | − | 1.34277i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −33203.2 | + | 324106.i | −0.00307063 | + | 0.0299733i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.47090e6i | 0.502084i | 0.967976 | + | 0.251042i | \(0.0807732\pi\) | ||||
−0.967976 | + | 0.251042i | \(0.919227\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.84652e6 | −0.896766 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.24948e6 | − | 427347.i | −0.203314 | − | 0.0386249i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 1.88834e7i | − | 1.69381i | −0.531741 | − | 0.846907i | \(-0.678462\pi\) | ||
0.531741 | − | 0.846907i | \(-0.321538\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.64223e6i | 0.413260i | 0.978419 | + | 0.206630i | \(0.0662496\pi\) | ||||
−0.978419 | + | 0.206630i | \(0.933750\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.96075e6 | − | 4.93496e6i | 0.526644 | − | 0.436014i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.22017e7 | + | 1.24040e7i | 1.06996 | + | 1.08770i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −407451. | −0.0354618 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.20031e6 | + | 3.47748e6i | −0.362841 | + | 0.300400i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.21109e6 | −0.704036 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 629529. | 0.0535770 | 0.0267885 | − | 0.999641i | \(-0.491472\pi\) | ||||
0.0267885 | + | 0.999641i | \(0.491472\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.30401e6 | + | 1.27005e6i | −0.194637 | + | 0.107291i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.49528e6 | 0.544661 | 0.272331 | − | 0.962204i | \(-0.412206\pi\) | ||||
0.272331 | + | 0.962204i | \(0.412206\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.71406e6 | − | 7.84193e6i | −0.642109 | − | 0.652753i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.19603e6 | + | 1.11075e7i | 0.759858 | + | 0.917803i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.25581e6i | 0.677186i | 0.940933 | + | 0.338593i | \(0.109951\pi\) | ||||
−0.940933 | + | 0.338593i | \(0.890049\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 2.39762e7i | − | 1.95233i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.63350e6 | − | 1.35239e6i | 0.132046 | − | 0.109322i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.37175e6 | −0.190336 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 2.21202e7i | − | 1.76235i | −0.472787 | − | 0.881177i | \(-0.656752\pi\) | ||
0.472787 | − | 0.881177i | \(-0.343248\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.61128e7 | − | 1.07754e7i | 1.27450 | − | 0.852313i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.00436e7i | 1.57403i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.07689e7 | −0.839633 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.36600e7 | + | 1.13093e7i | −1.05745 | + | 0.875472i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.20151e6i | 0.322932i | 0.986878 | + | 0.161466i | \(0.0516222\pi\) | ||||
−0.986878 | + | 0.161466i | \(0.948378\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.86616e7i | 1.42417i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.08156e7 | + | 1.30638e7i | 0.819556 | + | 0.989910i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7.47629e6 | − | 7.35438e6i | 0.562519 | − | 0.553347i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.27013e7 | 0.948928 | 0.474464 | − | 0.880275i | \(-0.342642\pi\) | ||||
0.474464 | + | 0.880275i | \(0.342642\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.23495e6 | − | 6.50058e6i | 0.0916172 | − | 0.482257i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −127897. | −0.00942185 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.22787e7 | −0.898233 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.25389e7 | + | 1.03810e7i | −0.910879 | + | 0.754125i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.21200e7 | 0.874337 | 0.437169 | − | 0.899380i | \(-0.355981\pi\) | ||||
0.437169 | + | 0.899380i | \(0.355981\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.95303e7 | − | 1.98541e7i | −1.39917 | − | 1.42237i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.04560e6 | + | 5.00521e6i | −0.430124 | + | 0.356104i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 356708.i | − | 0.0252039i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 3.77140e6i | − | 0.264647i | −0.991207 | − | 0.132323i | \(-0.957756\pi\) | ||
0.991207 | − | 0.132323i | \(-0.0422437\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 7.66100e6 | − | 1.21326e7i | 0.533908 | − | 0.845542i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.18789e7 | −0.822209 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 1.16976e7i | − | 0.804148i | −0.915607 | − | 0.402074i | \(-0.868289\pi\) | ||
0.915607 | − | 0.402074i | \(-0.131711\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.26402e7 | − | 1.01194e7i | 0.863052 | − | 0.690935i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 8.90409e6i | − | 0.603838i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.02243e6 | 0.0688689 | 0.0344344 | − | 0.999407i | \(-0.489037\pi\) | ||||
0.0344344 | + | 0.999407i | \(0.489037\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.97071e6 | + | 8.41965e6i | 0.466371 | + | 0.563312i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 1.29463e7i | − | 0.860345i | −0.902747 | − | 0.430173i | \(-0.858453\pi\) | ||
0.902747 | − | 0.430173i | \(-0.141547\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.97116e7i | 1.30116i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 706463. | − | 3.71870e6i | 0.0463221 | − | 0.243831i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.09103e7 | − | 1.10912e7i | −0.710612 | − | 0.722391i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.90253e7 | 1.87792 | 0.938959 | − | 0.344028i | \(-0.111792\pi\) | ||||
0.938959 | + | 0.344028i | \(0.111792\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.67205e7 | + | 2.01960e7i | 1.07464 | + | 1.29801i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.96287e7 | −1.89167 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.29941e7 | −0.824148 | −0.412074 | − | 0.911150i | \(-0.635195\pi\) | ||||
−0.412074 | + | 0.911150i | \(0.635195\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.85256e6 | + | 5.86122e6i | 0.305750 | + | 0.369304i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.68382e7 | −1.05398 | −0.526991 | − | 0.849871i | \(-0.676680\pi\) | ||||
−0.526991 | + | 0.849871i | \(0.676680\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.69908e6 | + | 2.65506e6i | −0.167843 | + | 0.165106i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.30927e6 | − | 2.26832e7i | 0.266226 | − | 1.40137i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 7.56111e6i | − | 0.464085i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 2.53765e7i | − | 1.54745i | −0.633525 | − | 0.773723i | \(-0.718392\pi\) | ||
0.633525 | − | 0.773723i | \(-0.281608\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.48114e6 | + | 1.14519e7i | 0.574413 | + | 0.693812i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.00362e6 | 0.180799 | 0.0903996 | − | 0.995906i | \(-0.471186\pi\) | ||||
0.0903996 | + | 0.995906i | \(0.471186\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 111969.i | − | 0.00669643i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.72761e7 | + | 1.76985e6i | 1.02658 | + | 0.105168i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 1.52112e7i | − | 0.898093i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.53503e6 | 0.266043 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 939186. | + | 1.70379e6i | 0.0547454 | + | 0.0993142i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.00117e7i | 1.15907i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.42926e6i | 0.542676i | 0.962484 | + | 0.271338i | \(0.0874662\pi\) | ||||
−0.962484 | + | 0.271338i | \(0.912534\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.97484e7 | − | 1.63499e7i | 1.12938 | − | 0.935023i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.84701e6 | + | 5.94393e6i | 0.332271 | + | 0.337779i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.30898e6 | −0.243328 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.45079e6 | + | 4.51276e6i | −0.305873 | + | 0.253235i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6.70033e6 | −0.373637 | −0.186819 | − | 0.982394i | \(-0.559818\pi\) | ||||
−0.186819 | + | 0.982394i | \(0.559818\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.70651e7 | −1.49983 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.08289e6 | + | 2.14916e7i | −0.224847 | + | 1.18355i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.79778e6 | −0.317302 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.45748e6 | + | 4.53137e6i | 0.242437 | + | 0.246456i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 765190. | + | 924244.i | 0.0413605 | + | 0.0499577i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 2.51823e7i | − | 1.35277i | −0.736547 | − | 0.676386i | \(-0.763545\pi\) | ||
0.736547 | − | 0.676386i | \(-0.236455\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 2.59174e6i | − | 0.138369i | −0.997604 | − | 0.0691846i | \(-0.977960\pi\) | ||
0.997604 | − | 0.0691846i | \(-0.0220397\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.15887e7 | + | 1.78735e7i | −1.14551 | + | 0.948380i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.32404e6 | 0.0698245 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 1.67791e7i | − | 0.879455i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 8.45562e6 | − | 5.65465e6i | 0.440490 | − | 0.294575i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.39963e7i | 1.24247i | 0.783623 | + | 0.621237i | \(0.213370\pi\) | ||||
−0.783623 | + | 0.621237i | \(0.786630\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.47240e7 | 0.757748 | 0.378874 | − | 0.925448i | \(-0.376311\pi\) | ||||
0.378874 | + | 0.925448i | \(0.376311\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5.13128e6 | + | 4.24824e6i | −0.262477 | + | 0.217307i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.95165e7i | 1.50072i | 0.661028 | + | 0.750361i | \(0.270121\pi\) | ||||
−0.661028 | + | 0.750361i | \(0.729879\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.36080e7i | 1.69846i | 0.528019 | + | 0.849232i | \(0.322935\pi\) | ||||
−0.528019 | + | 0.849232i | \(0.677065\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.15417e7 | + | 1.39408e7i | 0.579785 | + | 0.700300i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −424774. | + | 2.58359e7i | −0.0212102 | + | 1.29007i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.69647e7 | −1.33838 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 294806. | + | 534811.i | 0.0145453 | + | 0.0263868i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −6.45947e6 | −0.316805 | −0.158402 | − | 0.987375i | \(-0.550634\pi\) | ||||
−0.158402 | + | 0.987375i | \(0.550634\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.02474e7 | 0.987140 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.80147e7 | + | 1.49146e7i | −0.873089 | + | 0.722839i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.65032e7 | 0.795108 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.01057e7 | − | 1.97779e7i | 0.962965 | − | 0.947263i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −9.30955e6 | + | 7.70746e6i | −0.443261 | + | 0.366980i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.81737e6i | 0.322696i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.03008e7i | 1.89645i | 0.317602 | + | 0.948224i | \(0.397123\pi\) | ||||
−0.317602 | + | 0.948224i | \(0.602877\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.20404e7 | + | 6.08691e6i | 1.49893 | + | 0.284762i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −9.87862e6 | −0.459456 | −0.229728 | − | 0.973255i | \(-0.573784\pi\) | ||||
−0.229728 | + | 0.973255i | \(0.573784\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.71083e6i | 0.217829i | 0.994051 | + | 0.108914i | \(0.0347374\pi\) | ||||
−0.994051 | + | 0.108914i | \(0.965263\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.40819e7 | − | 1.44262e6i | −0.647369 | − | 0.0663200i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 8.17467e6i | 0.373632i | 0.982395 | + | 0.186816i | \(0.0598167\pi\) | ||||
−0.982395 | + | 0.186816i | \(0.940183\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.14693e7 | −0.521192 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9.38236e6 | + | 1.13326e7i | 0.423901 | + | 0.512014i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 1.67545e7i | − | 0.752633i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 4.67264e6i | − | 0.208698i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.02563e7 | − | 3.84821e6i | −0.899548 | − | 0.170892i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.38824e7 | − | 1.36561e7i | 0.612979 | − | 0.602984i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.16202e7 | −0.510169 | −0.255084 | − | 0.966919i | \(-0.582103\pi\) | ||||
−0.255084 | + | 0.966919i | \(0.582103\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.92889e6 | + | 2.32984e6i | 0.0842047 | + | 0.101708i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.28179e7 | −1.85860 | −0.929300 | − | 0.369327i | \(-0.879588\pi\) | ||||
−0.929300 | + | 0.369327i | \(0.879588\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.20297e7 | −0.950839 | −0.475420 | − | 0.879759i | \(-0.657704\pi\) | ||||
−0.475420 | + | 0.879759i | \(0.657704\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.43866e7 | − | 1.73771e7i | −0.617449 | − | 0.745793i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.86327e7 | −0.795181 | −0.397590 | − | 0.917563i | \(-0.630153\pi\) | ||||
−0.397590 | + | 0.917563i | \(0.630153\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.71184e7 | + | 2.66762e7i | −1.15082 | + | 1.13206i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.33239e7 | − | 3.38017e7i | 0.562260 | − | 1.42641i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 3.82298e7i | − | 1.60426i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 1.05534e7i | − | 0.440388i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.54651e6 | + | 3.07583e6i | 0.105673 | + | 0.127638i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −82799.6 | −0.00341687 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 1.12927e7i | − | 0.463434i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.55333e7 | − | 1.59132e6i | −0.633935 | − | 0.0649437i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 2.01652e7i | − | 0.818429i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.81361e6 | −0.234654 | −0.117327 | − | 0.993093i | \(-0.537433\pi\) | ||||
−0.117327 | + | 0.993093i | \(0.537433\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.66878e6 | − | 1.93118e7i | 0.147269 | − | 0.775198i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.69096e7i | 1.07426i | 0.843498 | + | 0.537132i | \(0.180492\pi\) | ||||
−0.843498 | + | 0.537132i | \(0.819508\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 9.58454e6i | − | 0.380535i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −9.90297e6 | + | 8.19876e6i | −0.391032 | + | 0.323739i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.47248e7 | − | 1.44847e7i | 0.578262 | − | 0.568833i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.86255e7 | −0.727476 | −0.363738 | − | 0.931501i | \(-0.618500\pi\) | ||||
−0.363738 | + | 0.931501i | \(0.618500\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.73881e6 | − | 3.92331e6i | 0.184086 | − | 0.152406i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.37987e6 | 0.0919494 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.96835e6 | −0.229351 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.12845e7 | − | 9.74283e6i | −1.96014 | − | 0.372380i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.43516e7 | 0.925740 | 0.462870 | − | 0.886426i | \(-0.346820\pi\) | ||||
0.462870 | + | 0.886426i | \(0.346820\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.64936e7 | − | 600000.i | −1.37989 | − | 0.0226870i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.28402e7 | − | 2.75878e7i | −0.859004 | − | 1.03756i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 5.84636e7i | − | 2.18704i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 6.06143e6i | − | 0.225541i | −0.993621 | − | 0.112771i | \(-0.964027\pi\) | ||
0.993621 | − | 0.112771i | \(-0.0359725\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.62298e6 | − | 6.31114e6i | 0.282137 | − | 0.233584i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.76788e6 | −0.0650847 | −0.0325424 | − | 0.999470i | \(-0.510360\pi\) | ||||
−0.0325424 | + | 0.999470i | \(0.510360\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 5.55690e6i | − | 0.203495i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 8.67366e6 | − | 2.90842e7i | 0.315953 | − | 1.05944i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 4.74165e7i | − | 1.71812i | −0.511872 | − | 0.859061i | \(-0.671048\pi\) | ||
0.511872 | − | 0.859061i | \(-0.328952\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.04253e6 | −0.109665 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.31589e6 | − | 1.91735e6i | 0.0830362 | − | 0.0687464i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.22073e7i | 1.14874i | 0.818596 | + | 0.574370i | \(0.194753\pi\) | ||||
−0.818596 | + | 0.574370i | \(0.805247\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.83550e7i | 0.651247i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.14152e6 | + | 3.79452e6i | 0.110882 | + | 0.133930i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.52701e7 | + | 3.58547e7i | 1.23840 | + | 1.25893i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.86032e7 | 0.999092 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.86493e7 | − | 5.44267e6i | −0.995515 | − | 0.189124i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.55918e7 | 0.884674 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.97124e7 | −1.02181 | −0.510906 | − | 0.859637i | \(-0.670690\pi\) | ||||
−0.510906 | + | 0.859637i | \(0.670690\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.00890e7 | + | 3.31901e7i | −1.37156 | + | 1.13553i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.54497e7 | −0.525861 | −0.262931 | − | 0.964815i | \(-0.584689\pi\) | ||||
−0.262931 | + | 0.964815i | \(0.584689\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.94850e7 | − | 2.99737e7i | −0.998432 | − | 1.01498i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.69277e6 | + | 2.22937e6i | −0.0907168 | + | 0.0751053i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.78966e7i | 0.935008i | 0.883991 | + | 0.467504i | \(0.154847\pi\) | ||||
−0.883991 | + | 0.467504i | \(0.845153\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.53923e7i | 1.84711i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.32449e6 | + | 6.97191e6i | −0.0439418 | + | 0.231302i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.66294e6 | −0.120905 | −0.0604527 | − | 0.998171i | \(-0.519254\pi\) | ||||
−0.0604527 | + | 0.998171i | \(0.519254\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.34072e7i | 0.440300i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.53914e7 | − | 3.62568e6i | −1.15639 | − | 0.118467i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 6.12966e6i | − | 0.199272i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.89627e6 | −0.190719 | −0.0953594 | − | 0.995443i | \(-0.530400\pi\) | ||||
−0.0953594 | + | 0.995443i | \(0.530400\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.83789e7 | + | 3.42778e7i | 0.913320 | + | 1.10316i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.26916e6i | 0.0726619i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 1.33192e7i | − | 0.424366i | −0.977230 | − | 0.212183i | \(-0.931943\pi\) | ||
0.977230 | − | 0.212183i | \(-0.0680572\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.85074e7 | − | 1.57142e7i | 0.903741 | − | 0.498173i |
(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 | 336.6.k.d.209.10 | 12 | ||
3.2 | odd | 2 | inner | 336.6.k.d.209.4 | 12 | ||
4.3 | odd | 2 | 21.6.c.a.20.7 | yes | 12 | ||
7.6 | odd | 2 | inner | 336.6.k.d.209.3 | 12 | ||
12.11 | even | 2 | 21.6.c.a.20.6 | yes | 12 | ||
21.20 | even | 2 | inner | 336.6.k.d.209.9 | 12 | ||
28.27 | even | 2 | 21.6.c.a.20.8 | yes | 12 | ||
84.83 | odd | 2 | 21.6.c.a.20.5 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.6.c.a.20.5 | ✓ | 12 | 84.83 | odd | 2 | ||
21.6.c.a.20.6 | yes | 12 | 12.11 | even | 2 | ||
21.6.c.a.20.7 | yes | 12 | 4.3 | odd | 2 | ||
21.6.c.a.20.8 | yes | 12 | 28.27 | even | 2 | ||
336.6.k.d.209.3 | 12 | 7.6 | odd | 2 | inner | ||
336.6.k.d.209.4 | 12 | 3.2 | odd | 2 | inner | ||
336.6.k.d.209.9 | 12 | 21.20 | even | 2 | inner | ||
336.6.k.d.209.10 | 12 | 1.1 | even | 1 | trivial |