Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [400,6,Mod(1,400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(400, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("400.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 400 = 2^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 400.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.1535279252\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.47217.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 38x - 24 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{4}\cdot 5 \) |
Twist minimal: | no (minimal twist has level 200) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(6.95752\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 400.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.53448 | 0.162587 | 0.0812934 | − | 0.996690i | \(-0.474095\pi\) | ||||
0.0812934 | + | 0.996690i | \(0.474095\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −247.370 | −1.90810 | −0.954050 | − | 0.299647i | \(-0.903131\pi\) | ||||
−0.954050 | + | 0.299647i | \(0.903131\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −236.576 | −0.973566 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −290.180 | −0.723079 | −0.361539 | − | 0.932357i | \(-0.617749\pi\) | ||||
−0.361539 | + | 0.932357i | \(0.617749\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 119.335 | 0.195844 | 0.0979221 | − | 0.995194i | \(-0.468780\pi\) | ||||
0.0979221 | + | 0.995194i | \(0.468780\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1100.71 | −0.923741 | −0.461871 | − | 0.886947i | \(-0.652822\pi\) | ||||
−0.461871 | + | 0.886947i | \(0.652822\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1798.92 | −1.14322 | −0.571609 | − | 0.820526i | \(-0.693681\pi\) | ||||
−0.571609 | + | 0.820526i | \(0.693681\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −626.952 | −0.310232 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3056.46 | 1.20476 | 0.602378 | − | 0.798211i | \(-0.294220\pi\) | ||||
0.602378 | + | 0.798211i | \(0.294220\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1215.47 | −0.320876 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2565.53 | 0.566477 | 0.283239 | − | 0.959049i | \(-0.408591\pi\) | ||||
0.283239 | + | 0.959049i | \(0.408591\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1302.61 | −0.243450 | −0.121725 | − | 0.992564i | \(-0.538843\pi\) | ||||
−0.121725 | + | 0.992564i | \(0.538843\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −735.454 | −0.117563 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 15014.8 | 1.80308 | 0.901542 | − | 0.432691i | \(-0.142436\pi\) | ||||
0.901542 | + | 0.432691i | \(0.142436\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 302.452 | 0.0318417 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 13948.8 | 1.29592 | 0.647961 | − | 0.761674i | \(-0.275622\pi\) | ||||
0.647961 | + | 0.761674i | \(0.275622\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1779.13 | 0.146736 | 0.0733678 | − | 0.997305i | \(-0.476625\pi\) | ||||
0.0733678 | + | 0.997305i | \(0.476625\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3350.75 | −0.221257 | −0.110628 | − | 0.993862i | \(-0.535286\pi\) | ||||
−0.110628 | + | 0.993862i | \(0.535286\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 44384.7 | 2.64085 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2789.72 | −0.150188 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −20874.1 | −1.02075 | −0.510373 | − | 0.859953i | \(-0.670493\pi\) | ||||
−0.510373 | + | 0.859953i | \(0.670493\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4559.33 | −0.185872 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −31645.3 | −1.18353 | −0.591766 | − | 0.806110i | \(-0.701569\pi\) | ||||
−0.591766 | + | 0.806110i | \(0.701569\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −34965.3 | −1.20313 | −0.601565 | − | 0.798824i | \(-0.705456\pi\) | ||||
−0.601565 | + | 0.798824i | \(0.705456\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 58521.8 | 1.85766 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −38022.5 | −1.03479 | −0.517397 | − | 0.855746i | \(-0.673099\pi\) | ||||
−0.517397 | + | 0.855746i | \(0.673099\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7746.52 | 0.195877 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −69549.3 | −1.63737 | −0.818685 | − | 0.574242i | \(-0.805297\pi\) | ||||
−0.818685 | + | 0.574242i | \(0.805297\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 66299.4 | 1.45614 | 0.728069 | − | 0.685504i | \(-0.240418\pi\) | ||||
0.728069 | + | 0.685504i | \(0.240418\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 71781.7 | 1.37971 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −34853.9 | −0.628325 | −0.314162 | − | 0.949369i | \(-0.601724\pi\) | ||||
−0.314162 | + | 0.949369i | \(0.601724\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 54407.5 | 0.921395 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 86638.0 | 1.38043 | 0.690213 | − | 0.723606i | \(-0.257517\pi\) | ||||
0.690213 | + | 0.723606i | \(0.257517\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6502.28 | 0.0921017 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 46305.1 | 0.619660 | 0.309830 | − | 0.950792i | \(-0.399728\pi\) | ||||
0.309830 | + | 0.950792i | \(0.399728\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −29519.9 | −0.373690 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3301.43 | −0.0395817 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16911.9 | 0.182501 | 0.0912503 | − | 0.995828i | \(-0.470914\pi\) | ||||
0.0912503 | + | 0.995828i | \(0.470914\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 68649.7 | 0.703964 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −151350. | −1.47631 | −0.738155 | − | 0.674631i | \(-0.764303\pi\) | ||||
−0.738155 | + | 0.674631i | \(0.764303\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 19867.7 | 0.184525 | 0.0922624 | − | 0.995735i | \(-0.470590\pi\) | ||||
0.0922624 | + | 0.995735i | \(0.470590\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 187685. | 1.58478 | 0.792392 | − | 0.610012i | \(-0.208835\pi\) | ||||
0.792392 | + | 0.610012i | \(0.208835\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 130806. | 1.05454 | 0.527268 | − | 0.849699i | \(-0.323217\pi\) | ||||
0.527268 | + | 0.849699i | \(0.323217\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 38054.7 | 0.293158 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 56375.6 | 0.415332 | 0.207666 | − | 0.978200i | \(-0.433413\pi\) | ||||
0.207666 | + | 0.978200i | \(0.433413\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −28231.9 | −0.190667 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 272282. | 1.76259 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −76846.6 | −0.477157 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 35353.0 | 0.210700 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2888.85 | −0.0158933 | −0.00794667 | − | 0.999968i | \(-0.502530\pi\) | ||||
−0.00794667 | + | 0.999968i | \(0.502530\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4509.15 | 0.0238573 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −212910. | −1.08397 | −0.541985 | − | 0.840388i | \(-0.682327\pi\) | ||||
−0.541985 | + | 0.840388i | \(0.682327\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 444999. | 2.18137 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 173546. | 0.789976 | 0.394988 | − | 0.918686i | \(-0.370749\pi\) | ||||
0.394988 | + | 0.918686i | \(0.370749\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 339914. | 1.49222 | 0.746110 | − | 0.665823i | \(-0.231919\pi\) | ||||
0.746110 | + | 0.665823i | \(0.231919\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8492.38 | −0.0359734 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −34628.7 | −0.141611 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 112492. | 0.429367 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −354534. | −1.30825 | −0.654127 | − | 0.756385i | \(-0.726964\pi\) | ||||
−0.654127 | + | 0.756385i | \(0.726964\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1791.74 | 0.00639487 | 0.00319743 | − | 0.999995i | \(-0.498982\pi\) | ||||
0.00319743 | + | 0.999995i | \(0.498982\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 260402. | 0.899323 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −511537. | −1.65626 | −0.828129 | − | 0.560537i | \(-0.810595\pi\) | ||||
−0.828129 | + | 0.560537i | \(0.810595\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −52904.9 | −0.165960 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −756075. | −2.29879 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 459676. | 1.35514 | 0.677568 | − | 0.735460i | \(-0.263034\pi\) | ||||
0.677568 | + | 0.735460i | \(0.263034\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 259189. | 0.719160 | 0.359580 | − | 0.933114i | \(-0.382920\pi\) | ||||
0.359580 | + | 0.933114i | \(0.382920\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −357052. | −0.961645 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 425583. | 1.11300 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 374220. | 0.950631 | 0.475315 | − | 0.879815i | \(-0.342334\pi\) | ||||
0.475315 | + | 0.879815i | \(0.342334\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −80204.4 | −0.192427 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −200493. | −0.467700 | −0.233850 | − | 0.972273i | \(-0.575132\pi\) | ||||
−0.233850 | + | 0.972273i | \(0.575132\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 705255. | 1.60011 | 0.800055 | − | 0.599927i | \(-0.204804\pi\) | ||||
0.800055 | + | 0.599927i | \(0.204804\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −88618.7 | −0.195613 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 319404. | 0.667938 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 300672. | 0.612263 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −491768. | −0.975386 | −0.487693 | − | 0.873015i | \(-0.662161\pi\) | ||||
−0.487693 | + | 0.873015i | \(0.662161\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −362539. | −0.700585 | −0.350293 | − | 0.936640i | \(-0.613918\pi\) | ||||
−0.350293 | + | 0.936640i | \(0.613918\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 440774. | 0.809190 | 0.404595 | − | 0.914496i | \(-0.367412\pi\) | ||||
0.404595 | + | 0.914496i | \(0.367412\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 985431. | 1.76398 | 0.881990 | − | 0.471269i | \(-0.156204\pi\) | ||||
0.881990 | + | 0.471269i | \(0.156204\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −96367.1 | −0.168244 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −634634. | −1.08090 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −723086. | −1.17291 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 522012. | 0.826637 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −29389.2 | −0.0454445 | −0.0227222 | − | 0.999742i | \(-0.507233\pi\) | ||||
−0.0227222 | + | 0.999742i | \(0.507233\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −176271. | −0.266215 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 322225. | 0.464526 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 168034. | 0.236749 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −131353. | −0.180909 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 167815. | 0.225979 | 0.112990 | − | 0.993596i | \(-0.463957\pi\) | ||||
0.112990 | + | 0.993596i | \(0.463957\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −95840.2 | −0.123448 | −0.0617238 | − | 0.998093i | \(-0.519660\pi\) | ||||
−0.0617238 | + | 0.998093i | \(0.519660\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 557513. | 0.702532 | 0.351266 | − | 0.936276i | \(-0.385751\pi\) | ||||
0.351266 | + | 0.936276i | \(0.385751\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 181929. | 0.224322 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −914906. | −1.10405 | −0.552023 | − | 0.833829i | \(-0.686144\pi\) | ||||
−0.552023 | + | 0.833829i | \(0.686144\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −88336.5 | −0.102157 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.45389e6 | −1.64641 | −0.823203 | − | 0.567747i | \(-0.807815\pi\) | ||||
−0.823203 | + | 0.567747i | \(0.807815\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.06147e6 | 1.17724 | 0.588619 | − | 0.808411i | \(-0.299672\pi\) | ||||
0.588619 | + | 0.808411i | \(0.299672\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 433255. | 0.470682 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −214675. | −0.223893 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 219582. | 0.224439 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 985641. | 0.987494 | 0.493747 | − | 0.869606i | \(-0.335627\pi\) | ||||
0.493747 | + | 0.869606i | \(0.335627\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −886922. | −0.871133 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −317014. | −0.299396 | −0.149698 | − | 0.988732i | \(-0.547830\pi\) | ||||
−0.149698 | + | 0.988732i | \(0.547830\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.71421e6 | −3.44047 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −606944. | −0.551503 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −50112.6 | −0.0446743 | −0.0223371 | − | 0.999750i | \(-0.507111\pi\) | ||||
−0.0223371 | + | 0.999750i | \(0.507111\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 117359. | 0.100749 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.28003e6 | −1.07855 | −0.539274 | − | 0.842130i | \(-0.681301\pi\) | ||||
−0.539274 | + | 0.842130i | \(0.681301\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.43785e6 | −1.18929 | −0.594646 | − | 0.803987i | \(-0.702708\pi\) | ||||
−0.594646 | + | 0.803987i | \(0.702708\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −74817.5 | −0.0607571 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 583518. | 0.456935 | 0.228468 | − | 0.973552i | \(-0.426628\pi\) | ||||
0.228468 | + | 0.973552i | \(0.426628\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 308166. | 0.237014 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.23261e6 | 1.68674 | 0.843368 | − | 0.537336i | \(-0.180569\pi\) | ||||
0.843368 | + | 0.537336i | \(0.180569\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.30526e6 | −0.968792 | −0.484396 | − | 0.874849i | \(-0.660961\pi\) | ||||
−0.484396 | + | 0.874849i | \(0.660961\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.45052e6 | −2.47275 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −208295. | −0.146702 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 42862.9 | 0.0296722 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.30501e6 | −1.56857 | −0.784284 | − | 0.620402i | \(-0.786969\pi\) | ||||
−0.784284 | + | 0.620402i | \(0.786969\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 352706. | 0.232018 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 364743. | 0.235944 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −440101. | −0.279986 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −383592. | −0.240029 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 302646. | 0.183269 | 0.0916346 | − | 0.995793i | \(-0.470791\pi\) | ||||
0.0916346 | + | 0.995793i | \(0.470791\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 50354.2 | 0.0300013 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.41350e6 | 0.828696 | 0.414348 | − | 0.910119i | \(-0.364010\pi\) | ||||
0.414348 | + | 0.910119i | \(0.364010\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 924126. | 0.533176 | 0.266588 | − | 0.963811i | \(-0.414104\pi\) | ||||
0.266588 | + | 0.963811i | \(0.414104\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −113236. | −0.0632903 | −0.0316451 | − | 0.999499i | \(-0.510075\pi\) | ||||
−0.0316451 | + | 0.999499i | \(0.510075\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −744466. | −0.409608 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 475683. | 0.257665 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.98009e6 | 1.05604 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 331524. | 0.171453 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 828872. | 0.422180 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 896472. | 0.449745 | 0.224873 | − | 0.974388i | \(-0.427803\pi\) | ||||
0.224873 | + | 0.974388i | \(0.427803\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.55215e6 | −1.75542 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.26530e6 | −1.56620 | −0.783102 | − | 0.621893i | \(-0.786364\pi\) | ||||
−0.783102 | + | 0.621893i | \(0.786364\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 142883. | 0.0675274 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 377990. | 0.176033 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.82189e6 | −3.13090 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.39262e6 | 1.95839 | 0.979197 | − | 0.202913i | \(-0.0650408\pi\) | ||||
0.979197 | + | 0.202913i | \(0.0650408\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 680341. | 0.298994 | 0.149497 | − | 0.988762i | \(-0.452235\pi\) | ||||
0.149497 | + | 0.988762i | \(0.452235\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −145049. | −0.0628416 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −423316. | −0.180812 | −0.0904062 | − | 0.995905i | \(-0.528817\pi\) | ||||
−0.0904062 | + | 0.995905i | \(0.528817\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 690092. | 0.286574 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.69571e6 | 1.51343 | 0.756715 | − | 0.653745i | \(-0.226803\pi\) | ||||
0.756715 | + | 0.653745i | \(0.226803\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 760032. | 0.306947 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −194766. | −0.0775794 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.42747e6 | −0.553223 | −0.276612 | − | 0.960982i | \(-0.589212\pi\) | ||||
−0.276612 | + | 0.960982i | \(0.589212\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.29997e6 | −1.26166 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.16362e6 | 1.94769 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.36477e6 | 1.25223 | 0.626113 | − | 0.779732i | \(-0.284645\pi\) | ||||
0.626113 | + | 0.779732i | \(0.284645\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 306158. | 0.110941 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 168251. | 0.0601671 | 0.0300835 | − | 0.999547i | \(-0.490423\pi\) | ||||
0.0300835 | + | 0.999547i | \(0.490423\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7321.72 | −0.00258405 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 470292. | 0.163821 | 0.0819106 | − | 0.996640i | \(-0.473898\pi\) | ||||
0.0819106 | + | 0.996640i | \(0.473898\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −420899. | −0.142857 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.85362e6 | −1.62627 | −0.813133 | − | 0.582077i | \(-0.802240\pi\) | ||||
−0.813133 | + | 0.582077i | \(0.802240\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.36427e6 | −1.11288 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −539615. | −0.176239 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.36418e6 | −0.434405 | −0.217202 | − | 0.976127i | \(-0.569693\pi\) | ||||
−0.217202 | + | 0.976127i | \(0.569693\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.12784e6 | 0.354662 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.99367e6 | −0.619145 | −0.309573 | − | 0.950876i | \(-0.600186\pi\) | ||||
−0.309573 | + | 0.950876i | \(0.600186\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −155447. | −0.0476782 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.35700e6 | −1.30377 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.41895e6 | −1.01061 | −0.505305 | − | 0.862941i | \(-0.668620\pi\) | ||||
−0.505305 | + | 0.862941i | \(0.668620\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 439849. | 0.128440 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.82810e6 | 2.25830 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 861505. | 0.242615 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.06851e6 | −0.853871 | −0.426935 | − | 0.904282i | \(-0.640407\pi\) | ||||
−0.426935 | + | 0.904282i | \(0.640407\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.62229e6 | 0.446092 | 0.223046 | − | 0.974808i | \(-0.428400\pi\) | ||||
0.223046 | + | 0.974808i | \(0.428400\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 792707. | 0.215408 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.64935e6 | 2.29569 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −87765.6 | −0.0230240 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 614867. | 0.159437 | 0.0797183 | − | 0.996817i | \(-0.474598\pi\) | ||||
0.0797183 | + | 0.996817i | \(0.474598\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 207106. | 0.0530851 | 0.0265425 | − | 0.999648i | \(-0.491550\pi\) | ||||
0.0265425 | + | 0.999648i | \(0.491550\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.49834e6 | −1.37730 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.93815e6 | 0.975284 | 0.487642 | − | 0.873044i | \(-0.337857\pi\) | ||||
0.487642 | + | 0.873044i | \(0.337857\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.05004e7 | −2.57104 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.09207e6 | 0.748584 | 0.374292 | − | 0.927311i | \(-0.377886\pi\) | ||||
0.374292 | + | 0.927311i | \(0.377886\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −898558. | −0.212705 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.16948e6 | 0.507855 | 0.253927 | − | 0.967223i | \(-0.418278\pi\) | ||||
0.253927 | + | 0.967223i | \(0.418278\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.04767e6 | −0.937053 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4541.11 | 0.00103972 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.38699e6 | −0.982598 | −0.491299 | − | 0.870991i | \(-0.663478\pi\) | ||||
−0.491299 | + | 0.870991i | \(0.663478\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.33788e6 | 0.296406 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.00490e6 | 0.658532 | 0.329266 | − | 0.944237i | \(-0.393199\pi\) | ||||
0.329266 | + | 0.944237i | \(0.393199\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 922183. | 0.199924 | 0.0999619 | − | 0.994991i | \(-0.468128\pi\) | ||||
0.0999619 | + | 0.994991i | \(0.468128\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.45571e6 | 0.733239 | 0.366620 | − | 0.930371i | \(-0.380515\pi\) | ||||
0.366620 | + | 0.930371i | \(0.380515\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.40561e6 | 1.97449 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.29648e6 | −0.269286 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −516266. | −0.106101 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.93832e6 | 0.993764 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.59868e6 | 1.51321 | 0.756605 | − | 0.653872i | \(-0.226857\pi\) | ||||
0.756605 | + | 0.653872i | \(0.226857\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.79180e6 | 0.353123 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.91625e6 | −0.373753 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.60362e6 | −0.879584 | −0.439792 | − | 0.898100i | \(-0.644948\pi\) | ||||
−0.439792 | + | 0.898100i | \(0.644948\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.16504e6 | 0.220327 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.01057e6 | 1.12515 | 0.562577 | − | 0.826745i | \(-0.309810\pi\) | ||||
0.562577 | + | 0.826745i | \(0.309810\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.82391e6 | −0.523278 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.72044e7 | 3.12427 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.29512e6 | −0.232841 | −0.116421 | − | 0.993200i | \(-0.537142\pi\) | ||||
−0.116421 | + | 0.993200i | \(0.537142\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 656908. | 0.116926 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.98765e6 | 0.702744 | 0.351372 | − | 0.936236i | \(-0.385715\pi\) | ||||
0.351372 | + | 0.936236i | \(0.385715\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −904940. | −0.156351 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 479969. | 0.0821142 | 0.0410571 | − | 0.999157i | \(-0.486927\pi\) | ||||
0.0410571 | + | 0.999157i | \(0.486927\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.64004e7 | −2.77846 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.18655e6 | 0.366831 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 972319. | 0.159986 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 948452. | 0.154560 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.49769e6 | −0.241729 | −0.120864 | − | 0.992669i | \(-0.538567\pi\) | ||||
−0.120864 | + | 0.992669i | \(0.538567\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.57897e6 | 1.21159 | 0.605796 | − | 0.795620i | \(-0.292855\pi\) | ||||
0.605796 | + | 0.795620i | \(0.292855\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.43379e6 | 0.224885 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.90559e6 | 0.451435 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.48654e6 | 1.15225 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.66459e6 | 0.253799 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −508146. | −0.0760418 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.28795e7 | −1.90954 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.61980e6 | 0.531730 | 0.265865 | − | 0.964010i | \(-0.414342\pi\) | ||||
0.265865 | + | 0.964010i | \(0.414342\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.78745e6 | 0.260157 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.13597e7 | 1.62330 | 0.811651 | − | 0.584143i | \(-0.198569\pi\) | ||||
0.811651 | + | 0.584143i | \(0.198569\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8.27196e6 | 1.17133 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.61520e6 | −0.647607 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.62180e6 | 1.19891 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.82035e6 | 0.248609 | 0.124305 | − | 0.992244i | \(-0.460330\pi\) | ||||
0.124305 | + | 0.992244i | \(0.460330\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 212312. | 0.0287373 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 809521. | 0.108598 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.21054e7 | 1.60956 | 0.804780 | − | 0.593573i | \(-0.202283\pi\) | ||||
0.804780 | + | 0.593573i | \(0.202283\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.34588e7 | −1.75811 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.71197e6 | 1.25755 | 0.628777 | − | 0.777585i | \(-0.283556\pi\) | ||||
0.628777 | + | 0.777585i | \(0.283556\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.72708e6 | −0.991803 | −0.495901 | − | 0.868379i | \(-0.665162\pi\) | ||||
−0.495901 | + | 0.868379i | \(0.665162\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.24637e6 | −0.158585 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.68085e6 | −1.21053 | −0.605263 | − | 0.796026i | \(-0.706932\pi\) | ||||
−0.605263 | + | 0.796026i | \(0.706932\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −918845. | −0.113906 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.14316e7 | −2.63399 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.05724e6 | 0.738080 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.28718e6 | −0.393757 | −0.196879 | − | 0.980428i | \(-0.563080\pi\) | ||||
−0.196879 | + | 0.980428i | \(0.563080\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.34329e6 | 0.278316 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.11713e6 | 0.131564 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.15399e6 | −0.718655 | −0.359327 | − | 0.933212i | \(-0.616994\pi\) | ||||
−0.359327 | + | 0.933212i | \(0.616994\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.49755e6 | 0.286800 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.73935e6 | −0.881328 | −0.440664 | − | 0.897672i | \(-0.645257\pi\) | ||||
−0.440664 | + | 0.897672i | \(0.645257\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.13857e7 | 1.28580 | 0.642900 | − | 0.765950i | \(-0.277731\pi\) | ||||
0.642900 | + | 0.765950i | \(0.277731\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.99523e6 | 1.00744 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.24328e6 | −0.908089 | −0.454044 | − | 0.890979i | \(-0.650019\pi\) | ||||
−0.454044 | + | 0.890979i | \(0.650019\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.60847e6 | −0.175739 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −399862. | −0.0433319 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.44252e6 | 0.799961 | 0.399980 | − | 0.916524i | \(-0.369017\pi\) | ||||
0.399980 | + | 0.916524i | \(0.369017\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.06327e7 | 1.12443 | 0.562214 | − | 0.826991i | \(-0.309950\pi\) | ||||
0.562214 | + | 0.826991i | \(0.309950\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.90577e6 | −0.829312 | −0.414656 | − | 0.909978i | \(-0.636098\pi\) | ||||
−0.414656 | + | 0.909978i | \(0.636098\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.71505e6 | −0.386576 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.14545e7 | −1.18237 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.32303e6 | 0.134400 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.65270e7 | −1.66558 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.26384e6 | −0.626278 | −0.313139 | − | 0.949707i | \(-0.601381\pi\) | ||||
−0.313139 | + | 0.949707i | \(0.601381\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −74486.1 | −0.00738866 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.29666e6 | 0.517194 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.64537e7 | 1.59409 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.06859e7 | 1.02722 | 0.513611 | − | 0.858023i | \(-0.328307\pi\) | ||||
0.513611 | + | 0.858023i | \(0.328307\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.10617e7 | −1.05510 | −0.527549 | − | 0.849524i | \(-0.676889\pi\) | ||||
−0.527549 | + | 0.849524i | \(0.676889\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.43619e6 | −0.134881 | −0.0674404 | − | 0.997723i | \(-0.521483\pi\) | ||||
−0.0674404 | + | 0.997723i | \(0.521483\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.18284e6 | 0.855786 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 816673. | 0.0755258 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7.84002e6 | −0.719506 | −0.359753 | − | 0.933048i | \(-0.617139\pi\) | ||||
−0.359753 | + | 0.933048i | \(0.617139\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.56849e7 | −1.41764 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.41636e7 | 1.27046 | 0.635230 | − | 0.772323i | \(-0.280905\pi\) | ||||
0.635230 | + | 0.772323i | \(0.280905\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.42312e6 | 0.749842 | 0.374921 | − | 0.927057i | \(-0.377670\pi\) | ||||
0.374921 | + | 0.927057i | \(0.377670\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −332912. | −0.0294135 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.84144e6 | 0.682466 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 425323. | 0.0367412 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.01462e7 | 0.869957 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.43547e6 | 0.803019 | 0.401509 | − | 0.915855i | \(-0.368486\pi\) | ||||
0.401509 | + | 0.915855i | \(0.368486\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.39970e6 | 0.704356 | 0.352178 | − | 0.935933i | \(-0.385441\pi\) | ||||
0.352178 | + | 0.935933i | \(0.385441\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.18350e6 | −0.348229 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −242905. | −0.0200710 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.92821e6 | 0.404238 | 0.202119 | − | 0.979361i | \(-0.435217\pi\) | ||||
0.202119 | + | 0.979361i | \(0.435217\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.41300e6 | 0.114222 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.49102e6 | −0.199907 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.73031e7 | 1.37857 | 0.689285 | − | 0.724490i | \(-0.257925\pi\) | ||||
0.689285 | + | 0.724490i | \(0.257925\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.69819e7 | −1.34323 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.53536e7 | −1.19710 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.31881e6 | −0.179503 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.77146e6 | −0.443599 | −0.221800 | − | 0.975092i | \(-0.571193\pi\) | ||||
−0.221800 | + | 0.975092i | \(0.571193\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.70105e7 | −2.06132 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.74393e7 | 2.81695 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.29358e6 | 0.544911 | 0.272455 | − | 0.962168i | \(-0.412164\pi\) | ||||
0.272455 | + | 0.962168i | \(0.412164\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.24562e6 | 0.611715 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.98136e6 | −0.293297 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.68485e6 | −0.267684 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.70735e6 | 0.700291 | 0.350145 | − | 0.936695i | \(-0.386132\pi\) | ||||
0.350145 | + | 0.936695i | \(0.386132\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.91467e6 | −0.352092 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.69026e6 | 0.191403 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.73733e6 | −0.332428 | −0.166214 | − | 0.986090i | \(-0.553154\pi\) | ||||
−0.166214 | + | 0.986090i | \(0.553154\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.21229e7 | −0.844869 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.95830e6 | −0.135546 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.81524e6 | 0.193533 | 0.0967667 | − | 0.995307i | \(-0.469150\pi\) | ||||
0.0967667 | + | 0.995307i | \(0.469150\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.10334e7 | 0.748237 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.68260e6 | 0.584842 | 0.292421 | − | 0.956290i | \(-0.405539\pi\) | ||||
0.292421 | + | 0.956290i | \(0.405539\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −544089. | −0.0364019 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.09845e6 | 0.272363 | 0.136181 | − | 0.990684i | \(-0.456517\pi\) | ||||
0.136181 | + | 0.990684i | \(0.456517\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.04965e7 | −1.34394 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.64276e7 | −3.02393 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.62828e6 | 0.299447 | 0.149723 | − | 0.988728i | \(-0.452162\pi\) | ||||
0.149723 | + | 0.988728i | \(0.452162\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.49808e6 | 0.160553 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.87265e7 | −1.18773 | −0.593863 | − | 0.804566i | \(-0.702398\pi\) | ||||
−0.593863 | + | 0.804566i | \(0.702398\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.24788e6 | −0.141635 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5.03003e6 | −0.314854 | −0.157427 | − | 0.987531i | \(-0.550320\pi\) | ||||
−0.157427 | + | 0.987531i | \(0.550320\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.23574e7 | −2.01216 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.77641e6 | −0.231788 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.38788e7 | −1.45612 | −0.728060 | − | 0.685513i | \(-0.759578\pi\) | ||||
−0.728060 | + | 0.685513i | \(0.759578\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −803464. | −0.0486778 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.69482e7 | 1.02017 | 0.510086 | − | 0.860123i | \(-0.329613\pi\) | ||||
0.510086 | + | 0.860123i | \(0.329613\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −9.41358e6 | −0.559374 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.50929e7 | −1.48152 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.01818e7 | 1.18395 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.11834e6 | −0.181769 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.60447e7 | −1.49893 | −0.749466 | − | 0.662043i | \(-0.769690\pi\) | ||||
−0.749466 | + | 0.662043i | \(0.769690\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −127009. | −0.00726345 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.39456e7 | −0.792494 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.17259e6 | −0.235626 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.54203e7 | −1.41754 | −0.708769 | − | 0.705441i | \(-0.750749\pi\) | ||||
−0.708769 | + | 0.705441i | \(0.750749\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.68820e6 | 0.204384 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.09547e7 | −0.603280 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.92387e7 | −1.05290 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.24421e6 | −0.175358 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4.37704e6 | −0.235131 | −0.117565 | − | 0.993065i | \(-0.537509\pi\) | ||||
−0.117565 | + | 0.993065i | \(0.537509\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.41629e6 | 0.449333 | 0.224667 | − | 0.974436i | \(-0.427871\pi\) | ||||
0.224667 | + | 0.974436i | \(0.427871\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.64418e6 | −0.193363 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.20051e6 | −0.167751 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.98372e6 | 0.363812 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.43979e7 | 0.745488 | 0.372744 | − | 0.927934i | \(-0.378417\pi\) | ||||
0.372744 | + | 0.927934i | \(0.378417\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.85762e6 | −0.198527 | −0.0992635 | − | 0.995061i | \(-0.531649\pi\) | ||||
−0.0992635 | + | 0.995061i | \(0.531649\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.10270e7 | 0.560653 | 0.280327 | − | 0.959905i | \(-0.409557\pi\) | ||||
0.280327 | + | 0.959905i | \(0.409557\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.64140e7 | 0.829523 | 0.414761 | − | 0.909930i | \(-0.363865\pi\) | ||||
0.414761 | + | 0.909930i | \(0.363865\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.47891e6 | 0.0742916 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.88547e7 | −2.43946 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.58329e6 | 0.0781171 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.86354e7 | −0.913974 | −0.456987 | − | 0.889473i | \(-0.651071\pi\) | ||||
−0.456987 | + | 0.889473i | \(0.651071\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.39292e7 | −0.679104 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.65850e6 | 0.274241 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.90095e7 | 0.910464 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.30815e6 | −0.157513 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.58922e7 | 2.17228 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.28504e6 | −0.107528 | −0.0537639 | − | 0.998554i | \(-0.517122\pi\) | ||||
−0.0537639 | + | 0.998554i | \(0.517122\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.20029e7 | 1.95356 | 0.976781 | − | 0.214241i | \(-0.0687276\pi\) | ||||
0.976781 | + | 0.214241i | \(0.0687276\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.39699e6 | −0.295797 | −0.147898 | − | 0.989003i | \(-0.547251\pi\) | ||||
−0.147898 | + | 0.989003i | \(0.547251\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.74526e6 | −0.402036 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −8.50743e6 | −0.388840 | −0.194420 | − | 0.980918i | \(-0.562283\pi\) | ||||
−0.194420 | + | 0.980918i | \(0.562283\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −527920. | −0.0238517 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.01139e7 | 0.454328 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.53743e6 | −0.202658 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.00097e6 | −0.177676 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.75823e7 | −1.21097 | −0.605483 | − | 0.795858i | \(-0.707020\pi\) | ||||
−0.605483 | + | 0.795858i | \(0.707020\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5.84199e6 | −0.255028 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.10318e7 | 1.34700 | 0.673499 | − | 0.739188i | \(-0.264791\pi\) | ||||
0.673499 | + | 0.739188i | \(0.264791\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.68243e7 | 0.726164 | 0.363082 | − | 0.931757i | \(-0.381724\pi\) | ||||
0.363082 | + | 0.931757i | \(0.381724\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.41735e7 | 0.604879 | 0.302439 | − | 0.953169i | \(-0.402199\pi\) | ||||
0.302439 | + | 0.953169i | \(0.402199\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 714613. | 0.0303261 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.57880e7 | −0.666241 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.02774e6 | 0.252945 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 924433. | 0.0383614 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.34188e6 | −0.137909 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.29763e7 | 0.942906 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.11543e6 | −0.0455220 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.35968e7 | −0.548807 | −0.274404 | − | 0.961615i | \(-0.588480\pi\) | ||||
−0.274404 | + | 0.961615i | \(0.588480\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.58057e7 | 1.43729 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.14453e7 | 1.25534 | 0.627668 | − | 0.778481i | \(-0.284010\pi\) | ||||
0.627668 | + | 0.778481i | \(0.284010\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.51406e7 | −0.998157 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.26674e7 | 2.06832 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.73140e7 | 0.676253 | 0.338127 | − | 0.941101i | \(-0.390207\pi\) | ||||
0.338127 | + | 0.941101i | \(0.390207\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 767050. | 0.0297971 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.29969e6 | −0.320669 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.70023e6 | −0.179647 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.19303e7 | 0.453535 | 0.226767 | − | 0.973949i | \(-0.427184\pi\) | ||||
0.226767 | + | 0.973949i | \(0.427184\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.98448e7 | −3.01906 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.58248e6 | 0.134735 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.88245e7 | 1.07254 | 0.536270 | − | 0.844046i | \(-0.319833\pi\) | ||||
0.536270 | + | 0.844046i | \(0.319833\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.34218e6 | 0.0866873 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.86079e7 | 1.42135 | 0.710676 | − | 0.703519i | \(-0.248389\pi\) | ||||
0.710676 | + | 0.703519i | \(0.248389\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.26341e7 | 1.56127 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −5.06877e7 | −1.83666 | −0.918328 | − | 0.395820i | \(-0.870461\pi\) | ||||
−0.918328 | + | 0.395820i | \(0.870461\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.91186e6 | 0.285176 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −286994. | −0.0102902 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.32695e7 | 1.54330 | 0.771649 | − | 0.636048i | \(-0.219432\pi\) | ||||
0.771649 | + | 0.636048i | \(0.219432\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.88683e6 | −0.0665967 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.29301e7 | −1.50735 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.69324e7 | −0.940732 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.44019e7 | −1.54289 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.77348e7 | −0.953804 | −0.476902 | − | 0.878956i | \(-0.658240\pi\) | ||||
−0.476902 | + | 0.878956i | \(0.658240\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.01850e6 | 0.171698 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.42588e7 | 0.485327 | 0.242664 | − | 0.970111i | \(-0.421979\pi\) | ||||
0.242664 | + | 0.970111i | \(0.421979\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.40845e7 | −2.84730 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.74148e7 | −1.58919 | −0.794597 | − | 0.607137i | \(-0.792318\pi\) | ||||
−0.794597 | + | 0.607137i | \(0.792318\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.34368e7 | −0.448063 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.09456e7 | −1.02666 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.76960e7 | 1.57434 | 0.787169 | − | 0.616738i | \(-0.211546\pi\) | ||||
0.787169 | + | 0.616738i | \(0.211546\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.10076e6 | 0.0686409 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.43782e6 | 0.176780 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.56020e7 | −0.504657 | −0.252328 | − | 0.967642i | \(-0.581196\pi\) | ||||
−0.252328 | + | 0.967642i | \(0.581196\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.27209e6 | 0.0731226 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.28177e7 | −0.408388 | −0.204194 | − | 0.978930i | \(-0.565457\pi\) | ||||
−0.204194 | + | 0.978930i | \(0.565457\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.82501e7 | −0.578566 |
(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 | 400.6.a.x.1.2 | 3 | ||
4.3 | odd | 2 | 200.6.a.i.1.2 | yes | 3 | ||
5.2 | odd | 4 | 400.6.c.p.49.3 | 6 | |||
5.3 | odd | 4 | 400.6.c.p.49.4 | 6 | |||
5.4 | even | 2 | 400.6.a.y.1.2 | 3 | |||
20.3 | even | 4 | 200.6.c.g.49.3 | 6 | |||
20.7 | even | 4 | 200.6.c.g.49.4 | 6 | |||
20.19 | odd | 2 | 200.6.a.h.1.2 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
200.6.a.h.1.2 | ✓ | 3 | 20.19 | odd | 2 | ||
200.6.a.i.1.2 | yes | 3 | 4.3 | odd | 2 | ||
200.6.c.g.49.3 | 6 | 20.3 | even | 4 | |||
200.6.c.g.49.4 | 6 | 20.7 | even | 4 | |||
400.6.a.x.1.2 | 3 | 1.1 | even | 1 | trivial | ||
400.6.a.y.1.2 | 3 | 5.4 | even | 2 | |||
400.6.c.p.49.3 | 6 | 5.2 | odd | 4 | |||
400.6.c.p.49.4 | 6 | 5.3 | odd | 4 |