Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [165,6,Mod(1,165)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(165, 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("165.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 165 = 3 \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 165.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: | \(26.4633302691\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.18257.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{3} - x^{2} - 26x + 8 \)
|
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(5.47894\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 165.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.47894 | −0.791773 | −0.395886 | − | 0.918300i | \(-0.629563\pi\) | ||||
−0.395886 | + | 0.918300i | \(0.629563\pi\) | |||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | −11.9391 | −0.373096 | ||||||||
\(5\) | 25.0000 | 0.447214 | ||||||||
\(6\) | 40.3105 | 0.457130 | ||||||||
\(7\) | −168.818 | −1.30219 | −0.651094 | − | 0.758997i | \(-0.725690\pi\) | ||||
−0.651094 | + | 0.758997i | \(0.725690\pi\) | |||||||
\(8\) | 196.801 | 1.08718 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | −111.974 | −0.354091 | ||||||||
\(11\) | 121.000 | 0.301511 | ||||||||
\(12\) | 107.452 | 0.215407 | ||||||||
\(13\) | 290.259 | 0.476352 | 0.238176 | − | 0.971222i | \(-0.423451\pi\) | ||||
0.238176 | + | 0.971222i | \(0.423451\pi\) | |||||||
\(14\) | 756.126 | 1.03104 | ||||||||
\(15\) | −225.000 | −0.258199 | ||||||||
\(16\) | −499.408 | −0.487703 | ||||||||
\(17\) | 623.964 | 0.523645 | 0.261823 | − | 0.965116i | \(-0.415676\pi\) | ||||
0.261823 | + | 0.965116i | \(0.415676\pi\) | |||||||
\(18\) | −362.794 | −0.263924 | ||||||||
\(19\) | −398.456 | −0.253219 | −0.126609 | − | 0.991953i | \(-0.540409\pi\) | ||||
−0.126609 | + | 0.991953i | \(0.540409\pi\) | |||||||
\(20\) | −298.477 | −0.166854 | ||||||||
\(21\) | 1519.36 | 0.751819 | ||||||||
\(22\) | −541.952 | −0.238728 | ||||||||
\(23\) | 3788.06 | 1.49313 | 0.746565 | − | 0.665312i | \(-0.231702\pi\) | ||||
0.746565 | + | 0.665312i | \(0.231702\pi\) | |||||||
\(24\) | −1771.21 | −0.627684 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | −1300.06 | −0.377162 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | 2015.53 | 0.485841 | ||||||||
\(29\) | 4220.43 | 0.931883 | 0.465941 | − | 0.884816i | \(-0.345716\pi\) | ||||
0.465941 | + | 0.884816i | \(0.345716\pi\) | |||||||
\(30\) | 1007.76 | 0.204435 | ||||||||
\(31\) | −5594.57 | −1.04559 | −0.522797 | − | 0.852457i | \(-0.675111\pi\) | ||||
−0.522797 | + | 0.852457i | \(0.675111\pi\) | |||||||
\(32\) | −4060.80 | −0.701030 | ||||||||
\(33\) | −1089.00 | −0.174078 | ||||||||
\(34\) | −2794.70 | −0.414608 | ||||||||
\(35\) | −4220.45 | −0.582356 | ||||||||
\(36\) | −967.065 | −0.124365 | ||||||||
\(37\) | 301.266 | 0.0361781 | 0.0180890 | − | 0.999836i | \(-0.494242\pi\) | ||||
0.0180890 | + | 0.999836i | \(0.494242\pi\) | |||||||
\(38\) | 1784.66 | 0.200492 | ||||||||
\(39\) | −2612.33 | −0.275022 | ||||||||
\(40\) | 4920.01 | 0.486202 | ||||||||
\(41\) | −14636.2 | −1.35978 | −0.679889 | − | 0.733315i | \(-0.737972\pi\) | ||||
−0.679889 | + | 0.733315i | \(0.737972\pi\) | |||||||
\(42\) | −6805.14 | −0.595269 | ||||||||
\(43\) | 151.418 | 0.0124884 | 0.00624421 | − | 0.999981i | \(-0.498012\pi\) | ||||
0.00624421 | + | 0.999981i | \(0.498012\pi\) | |||||||
\(44\) | −1444.63 | −0.112493 | ||||||||
\(45\) | 2025.00 | 0.149071 | ||||||||
\(46\) | −16966.5 | −1.18222 | ||||||||
\(47\) | −13535.0 | −0.893743 | −0.446872 | − | 0.894598i | \(-0.647462\pi\) | ||||
−0.446872 | + | 0.894598i | \(0.647462\pi\) | |||||||
\(48\) | 4494.67 | 0.281575 | ||||||||
\(49\) | 11692.5 | 0.695694 | ||||||||
\(50\) | −2799.34 | −0.158355 | ||||||||
\(51\) | −5615.68 | −0.302327 | ||||||||
\(52\) | −3465.43 | −0.177725 | ||||||||
\(53\) | −18116.1 | −0.885880 | −0.442940 | − | 0.896551i | \(-0.646065\pi\) | ||||
−0.442940 | + | 0.896551i | \(0.646065\pi\) | |||||||
\(54\) | 3265.15 | 0.152377 | ||||||||
\(55\) | 3025.00 | 0.134840 | ||||||||
\(56\) | −33223.5 | −1.41571 | ||||||||
\(57\) | 3586.10 | 0.146196 | ||||||||
\(58\) | −18903.0 | −0.737839 | ||||||||
\(59\) | −50582.4 | −1.89177 | −0.945887 | − | 0.324495i | \(-0.894806\pi\) | ||||
−0.945887 | + | 0.324495i | \(0.894806\pi\) | |||||||
\(60\) | 2686.29 | 0.0963330 | ||||||||
\(61\) | 5984.35 | 0.205917 | 0.102958 | − | 0.994686i | \(-0.467169\pi\) | ||||
0.102958 | + | 0.994686i | \(0.467169\pi\) | |||||||
\(62\) | 25057.8 | 0.827872 | ||||||||
\(63\) | −13674.3 | −0.434063 | ||||||||
\(64\) | 34169.1 | 1.04276 | ||||||||
\(65\) | 7256.49 | 0.213031 | ||||||||
\(66\) | 4877.57 | 0.137830 | ||||||||
\(67\) | 22450.7 | 0.611002 | 0.305501 | − | 0.952192i | \(-0.401176\pi\) | ||||
0.305501 | + | 0.952192i | \(0.401176\pi\) | |||||||
\(68\) | −7449.56 | −0.195370 | ||||||||
\(69\) | −34092.6 | −0.862059 | ||||||||
\(70\) | 18903.2 | 0.461094 | ||||||||
\(71\) | 10017.6 | 0.235841 | 0.117921 | − | 0.993023i | \(-0.462377\pi\) | ||||
0.117921 | + | 0.993023i | \(0.462377\pi\) | |||||||
\(72\) | 15940.8 | 0.362393 | ||||||||
\(73\) | −476.148 | −0.0104577 | −0.00522883 | − | 0.999986i | \(-0.501664\pi\) | ||||
−0.00522883 | + | 0.999986i | \(0.501664\pi\) | |||||||
\(74\) | −1349.35 | −0.0286448 | ||||||||
\(75\) | −5625.00 | −0.115470 | ||||||||
\(76\) | 4757.19 | 0.0944750 | ||||||||
\(77\) | −20427.0 | −0.392624 | ||||||||
\(78\) | 11700.5 | 0.217755 | ||||||||
\(79\) | −85024.7 | −1.53277 | −0.766386 | − | 0.642380i | \(-0.777947\pi\) | ||||
−0.766386 | + | 0.642380i | \(0.777947\pi\) | |||||||
\(80\) | −12485.2 | −0.218107 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 65554.5 | 1.07663 | ||||||||
\(83\) | −25643.4 | −0.408583 | −0.204292 | − | 0.978910i | \(-0.565489\pi\) | ||||
−0.204292 | + | 0.978910i | \(0.565489\pi\) | |||||||
\(84\) | −18139.8 | −0.280501 | ||||||||
\(85\) | 15599.1 | 0.234181 | ||||||||
\(86\) | −678.194 | −0.00988799 | ||||||||
\(87\) | −37983.8 | −0.538023 | ||||||||
\(88\) | 23812.9 | 0.327797 | ||||||||
\(89\) | 1807.91 | 0.0241937 | 0.0120968 | − | 0.999927i | \(-0.496149\pi\) | ||||
0.0120968 | + | 0.999927i | \(0.496149\pi\) | |||||||
\(90\) | −9069.86 | −0.118030 | ||||||||
\(91\) | −49001.0 | −0.620300 | ||||||||
\(92\) | −45226.0 | −0.557081 | ||||||||
\(93\) | 50351.2 | 0.603674 | ||||||||
\(94\) | 60622.4 | 0.707642 | ||||||||
\(95\) | −9961.39 | −0.113243 | ||||||||
\(96\) | 36547.2 | 0.404740 | ||||||||
\(97\) | 11688.5 | 0.126133 | 0.0630666 | − | 0.998009i | \(-0.479912\pi\) | ||||
0.0630666 | + | 0.998009i | \(0.479912\pi\) | |||||||
\(98\) | −52370.1 | −0.550831 | ||||||||
\(99\) | 9801.00 | 0.100504 | ||||||||
\(100\) | −7461.92 | −0.0746192 | ||||||||
\(101\) | −135573. | −1.32242 | −0.661210 | − | 0.750200i | \(-0.729957\pi\) | ||||
−0.661210 | + | 0.750200i | \(0.729957\pi\) | |||||||
\(102\) | 25152.3 | 0.239374 | ||||||||
\(103\) | −88490.5 | −0.821871 | −0.410935 | − | 0.911664i | \(-0.634798\pi\) | ||||
−0.410935 | + | 0.911664i | \(0.634798\pi\) | |||||||
\(104\) | 57123.2 | 0.517880 | ||||||||
\(105\) | 37984.1 | 0.336224 | ||||||||
\(106\) | 81140.9 | 0.701416 | ||||||||
\(107\) | 218742. | 1.84703 | 0.923514 | − | 0.383564i | \(-0.125304\pi\) | ||||
0.923514 | + | 0.383564i | \(0.125304\pi\) | |||||||
\(108\) | 8703.59 | 0.0718024 | ||||||||
\(109\) | 238399. | 1.92193 | 0.960967 | − | 0.276663i | \(-0.0892287\pi\) | ||||
0.960967 | + | 0.276663i | \(0.0892287\pi\) | |||||||
\(110\) | −13548.8 | −0.106763 | ||||||||
\(111\) | −2711.39 | −0.0208874 | ||||||||
\(112\) | 84309.1 | 0.635081 | ||||||||
\(113\) | 187225. | 1.37933 | 0.689664 | − | 0.724130i | \(-0.257758\pi\) | ||||
0.689664 | + | 0.724130i | \(0.257758\pi\) | |||||||
\(114\) | −16061.9 | −0.115754 | ||||||||
\(115\) | 94701.6 | 0.667748 | ||||||||
\(116\) | −50388.0 | −0.347682 | ||||||||
\(117\) | 23511.0 | 0.158784 | ||||||||
\(118\) | 226556. | 1.49786 | ||||||||
\(119\) | −105336. | −0.681885 | ||||||||
\(120\) | −44280.1 | −0.280709 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | −26803.5 | −0.163039 | ||||||||
\(123\) | 131725. | 0.785068 | ||||||||
\(124\) | 66794.1 | 0.390107 | ||||||||
\(125\) | 15625.0 | 0.0894427 | ||||||||
\(126\) | 61246.2 | 0.343679 | ||||||||
\(127\) | 27727.6 | 0.152547 | 0.0762733 | − | 0.997087i | \(-0.475698\pi\) | ||||
0.0762733 | + | 0.997087i | \(0.475698\pi\) | |||||||
\(128\) | −23096.0 | −0.124598 | ||||||||
\(129\) | −1362.77 | −0.00721019 | ||||||||
\(130\) | −32501.4 | −0.168672 | ||||||||
\(131\) | −324623. | −1.65273 | −0.826363 | − | 0.563138i | \(-0.809594\pi\) | ||||
−0.826363 | + | 0.563138i | \(0.809594\pi\) | |||||||
\(132\) | 13001.7 | 0.0649477 | ||||||||
\(133\) | 67266.5 | 0.329739 | ||||||||
\(134\) | −100555. | −0.483775 | ||||||||
\(135\) | −18225.0 | −0.0860663 | ||||||||
\(136\) | 122797. | 0.569297 | ||||||||
\(137\) | −59748.8 | −0.271974 | −0.135987 | − | 0.990711i | \(-0.543421\pi\) | ||||
−0.135987 | + | 0.990711i | \(0.543421\pi\) | |||||||
\(138\) | 152699. | 0.682555 | ||||||||
\(139\) | −117646. | −0.516462 | −0.258231 | − | 0.966083i | \(-0.583140\pi\) | ||||
−0.258231 | + | 0.966083i | \(0.583140\pi\) | |||||||
\(140\) | 50388.3 | 0.217275 | ||||||||
\(141\) | 121815. | 0.516003 | ||||||||
\(142\) | −44868.5 | −0.186733 | ||||||||
\(143\) | 35121.4 | 0.143626 | ||||||||
\(144\) | −40452.0 | −0.162568 | ||||||||
\(145\) | 105511. | 0.416751 | ||||||||
\(146\) | 2132.64 | 0.00828009 | ||||||||
\(147\) | −105233. | −0.401659 | ||||||||
\(148\) | −3596.84 | −0.0134979 | ||||||||
\(149\) | 52786.3 | 0.194785 | 0.0973925 | − | 0.995246i | \(-0.468950\pi\) | ||||
0.0973925 | + | 0.995246i | \(0.468950\pi\) | |||||||
\(150\) | 25194.0 | 0.0914260 | ||||||||
\(151\) | −430119. | −1.53513 | −0.767567 | − | 0.640969i | \(-0.778533\pi\) | ||||
−0.767567 | + | 0.640969i | \(0.778533\pi\) | |||||||
\(152\) | −78416.3 | −0.275294 | ||||||||
\(153\) | 50541.1 | 0.174548 | ||||||||
\(154\) | 91491.3 | 0.310869 | ||||||||
\(155\) | −139864. | −0.467604 | ||||||||
\(156\) | 31188.9 | 0.102610 | ||||||||
\(157\) | −150989. | −0.488873 | −0.244436 | − | 0.969665i | \(-0.578603\pi\) | ||||
−0.244436 | + | 0.969665i | \(0.578603\pi\) | |||||||
\(158\) | 380821. | 1.21361 | ||||||||
\(159\) | 163045. | 0.511463 | ||||||||
\(160\) | −101520. | −0.313510 | ||||||||
\(161\) | −639493. | −1.94434 | ||||||||
\(162\) | −29386.3 | −0.0879747 | ||||||||
\(163\) | 142404. | 0.419812 | 0.209906 | − | 0.977722i | \(-0.432684\pi\) | ||||
0.209906 | + | 0.977722i | \(0.432684\pi\) | |||||||
\(164\) | 174742. | 0.507328 | ||||||||
\(165\) | −27225.0 | −0.0778499 | ||||||||
\(166\) | 114855. | 0.323505 | ||||||||
\(167\) | 55468.4 | 0.153906 | 0.0769528 | − | 0.997035i | \(-0.475481\pi\) | ||||
0.0769528 | + | 0.997035i | \(0.475481\pi\) | |||||||
\(168\) | 299011. | 0.817362 | ||||||||
\(169\) | −287042. | −0.773089 | ||||||||
\(170\) | −69867.5 | −0.185418 | ||||||||
\(171\) | −32274.9 | −0.0844063 | ||||||||
\(172\) | −1807.80 | −0.00465938 | ||||||||
\(173\) | 133612. | 0.339414 | 0.169707 | − | 0.985495i | \(-0.445718\pi\) | ||||
0.169707 | + | 0.985495i | \(0.445718\pi\) | |||||||
\(174\) | 170127. | 0.425992 | ||||||||
\(175\) | −105511. | −0.260438 | ||||||||
\(176\) | −60428.4 | −0.147048 | ||||||||
\(177\) | 455242. | 1.09222 | ||||||||
\(178\) | −8097.52 | −0.0191559 | ||||||||
\(179\) | −188254. | −0.439150 | −0.219575 | − | 0.975596i | \(-0.570467\pi\) | ||||
−0.219575 | + | 0.975596i | \(0.570467\pi\) | |||||||
\(180\) | −24176.6 | −0.0556179 | ||||||||
\(181\) | −652252. | −1.47986 | −0.739928 | − | 0.672686i | \(-0.765140\pi\) | ||||
−0.739928 | + | 0.672686i | \(0.765140\pi\) | |||||||
\(182\) | 219473. | 0.491136 | ||||||||
\(183\) | −53859.1 | −0.118886 | ||||||||
\(184\) | 745493. | 1.62330 | ||||||||
\(185\) | 7531.65 | 0.0161793 | ||||||||
\(186\) | −225520. | −0.477972 | ||||||||
\(187\) | 75499.7 | 0.157885 | ||||||||
\(188\) | 161595. | 0.333452 | ||||||||
\(189\) | 123068. | 0.250606 | ||||||||
\(190\) | 44616.5 | 0.0896626 | ||||||||
\(191\) | −705620. | −1.39955 | −0.699774 | − | 0.714365i | \(-0.746716\pi\) | ||||
−0.699774 | + | 0.714365i | \(0.746716\pi\) | |||||||
\(192\) | −307522. | −0.602037 | ||||||||
\(193\) | −87143.5 | −0.168400 | −0.0841999 | − | 0.996449i | \(-0.526833\pi\) | ||||
−0.0841999 | + | 0.996449i | \(0.526833\pi\) | |||||||
\(194\) | −52352.1 | −0.0998688 | ||||||||
\(195\) | −65308.4 | −0.122994 | ||||||||
\(196\) | −139598. | −0.259561 | ||||||||
\(197\) | −667596. | −1.22560 | −0.612800 | − | 0.790238i | \(-0.709957\pi\) | ||||
−0.612800 | + | 0.790238i | \(0.709957\pi\) | |||||||
\(198\) | −43898.1 | −0.0795761 | ||||||||
\(199\) | −698609. | −1.25055 | −0.625276 | − | 0.780404i | \(-0.715013\pi\) | ||||
−0.625276 | + | 0.780404i | \(0.715013\pi\) | |||||||
\(200\) | 123000. | 0.217436 | ||||||||
\(201\) | −202056. | −0.352762 | ||||||||
\(202\) | 607224. | 1.04706 | ||||||||
\(203\) | −712484. | −1.21349 | ||||||||
\(204\) | 67046.0 | 0.112797 | ||||||||
\(205\) | −365904. | −0.608111 | ||||||||
\(206\) | 396344. | 0.650735 | ||||||||
\(207\) | 306833. | 0.497710 | ||||||||
\(208\) | −144958. | −0.232318 | ||||||||
\(209\) | −48213.1 | −0.0763484 | ||||||||
\(210\) | −170128. | −0.266213 | ||||||||
\(211\) | −558238. | −0.863203 | −0.431602 | − | 0.902064i | \(-0.642051\pi\) | ||||
−0.431602 | + | 0.902064i | \(0.642051\pi\) | |||||||
\(212\) | 216289. | 0.330518 | ||||||||
\(213\) | −90158.8 | −0.136163 | ||||||||
\(214\) | −979735. | −1.46243 | ||||||||
\(215\) | 3785.46 | 0.00558499 | ||||||||
\(216\) | −143468. | −0.209228 | ||||||||
\(217\) | 944465. | 1.36156 | ||||||||
\(218\) | −1.06778e6 | −1.52173 | ||||||||
\(219\) | 4285.33 | 0.00603773 | ||||||||
\(220\) | −36115.7 | −0.0503083 | ||||||||
\(221\) | 181111. | 0.249440 | ||||||||
\(222\) | 12144.2 | 0.0165381 | ||||||||
\(223\) | −382897. | −0.515608 | −0.257804 | − | 0.966197i | \(-0.582999\pi\) | ||||
−0.257804 | + | 0.966197i | \(0.582999\pi\) | |||||||
\(224\) | 685536. | 0.912873 | ||||||||
\(225\) | 50625.0 | 0.0666667 | ||||||||
\(226\) | −838569. | −1.09211 | ||||||||
\(227\) | −404735. | −0.521322 | −0.260661 | − | 0.965430i | \(-0.583941\pi\) | ||||
−0.260661 | + | 0.965430i | \(0.583941\pi\) | |||||||
\(228\) | −42814.7 | −0.0545452 | ||||||||
\(229\) | 664894. | 0.837845 | 0.418922 | − | 0.908022i | \(-0.362408\pi\) | ||||
0.418922 | + | 0.908022i | \(0.362408\pi\) | |||||||
\(230\) | −424163. | −0.528705 | ||||||||
\(231\) | 183843. | 0.226682 | ||||||||
\(232\) | 830582. | 1.01312 | ||||||||
\(233\) | 61531.4 | 0.0742518 | 0.0371259 | − | 0.999311i | \(-0.488180\pi\) | ||||
0.0371259 | + | 0.999311i | \(0.488180\pi\) | |||||||
\(234\) | −105304. | −0.125721 | ||||||||
\(235\) | −338374. | −0.399694 | ||||||||
\(236\) | 603907. | 0.705814 | ||||||||
\(237\) | 765223. | 0.884946 | ||||||||
\(238\) | 471796. | 0.539898 | ||||||||
\(239\) | 1.71207e6 | 1.93877 | 0.969384 | − | 0.245549i | \(-0.0789682\pi\) | ||||
0.969384 | + | 0.245549i | \(0.0789682\pi\) | |||||||
\(240\) | 112367. | 0.125924 | ||||||||
\(241\) | 1.31915e6 | 1.46302 | 0.731512 | − | 0.681828i | \(-0.238815\pi\) | ||||
0.731512 | + | 0.681828i | \(0.238815\pi\) | |||||||
\(242\) | −65576.2 | −0.0719793 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | −71447.6 | −0.0768268 | ||||||||
\(245\) | 292313. | 0.311124 | ||||||||
\(246\) | −589991. | −0.621595 | ||||||||
\(247\) | −115656. | −0.120621 | ||||||||
\(248\) | −1.10102e6 | −1.13675 | ||||||||
\(249\) | 230791. | 0.235896 | ||||||||
\(250\) | −69983.5 | −0.0708183 | ||||||||
\(251\) | −237992. | −0.238440 | −0.119220 | − | 0.992868i | \(-0.538039\pi\) | ||||
−0.119220 | + | 0.992868i | \(0.538039\pi\) | |||||||
\(252\) | 163258. | 0.161947 | ||||||||
\(253\) | 458356. | 0.450196 | ||||||||
\(254\) | −124190. | −0.120782 | ||||||||
\(255\) | −140392. | −0.135205 | ||||||||
\(256\) | −989967. | −0.944106 | ||||||||
\(257\) | −1.90368e6 | −1.79789 | −0.898943 | − | 0.438066i | \(-0.855664\pi\) | ||||
−0.898943 | + | 0.438066i | \(0.855664\pi\) | |||||||
\(258\) | 6103.75 | 0.00570883 | ||||||||
\(259\) | −50859.1 | −0.0471107 | ||||||||
\(260\) | −86635.7 | −0.0794811 | ||||||||
\(261\) | 341854. | 0.310628 | ||||||||
\(262\) | 1.45397e6 | 1.30858 | ||||||||
\(263\) | −907019. | −0.808588 | −0.404294 | − | 0.914629i | \(-0.632483\pi\) | ||||
−0.404294 | + | 0.914629i | \(0.632483\pi\) | |||||||
\(264\) | −214316. | −0.189254 | ||||||||
\(265\) | −452902. | −0.396178 | ||||||||
\(266\) | −301283. | −0.261078 | ||||||||
\(267\) | −16271.2 | −0.0139682 | ||||||||
\(268\) | −268041. | −0.227963 | ||||||||
\(269\) | 698485. | 0.588541 | 0.294270 | − | 0.955722i | \(-0.404923\pi\) | ||||
0.294270 | + | 0.955722i | \(0.404923\pi\) | |||||||
\(270\) | 81628.7 | 0.0681449 | ||||||||
\(271\) | 1.19097e6 | 0.985098 | 0.492549 | − | 0.870285i | \(-0.336065\pi\) | ||||
0.492549 | + | 0.870285i | \(0.336065\pi\) | |||||||
\(272\) | −311613. | −0.255383 | ||||||||
\(273\) | 441009. | 0.358130 | ||||||||
\(274\) | 267611. | 0.215342 | ||||||||
\(275\) | 75625.0 | 0.0603023 | ||||||||
\(276\) | 407034. | 0.321631 | ||||||||
\(277\) | −1.15110e6 | −0.901392 | −0.450696 | − | 0.892677i | \(-0.648824\pi\) | ||||
−0.450696 | + | 0.892677i | \(0.648824\pi\) | |||||||
\(278\) | 526928. | 0.408921 | ||||||||
\(279\) | −453161. | −0.348531 | ||||||||
\(280\) | −830587. | −0.633126 | ||||||||
\(281\) | −1.54201e6 | −1.16498 | −0.582492 | − | 0.812836i | \(-0.697922\pi\) | ||||
−0.582492 | + | 0.812836i | \(0.697922\pi\) | |||||||
\(282\) | −545601. | −0.408557 | ||||||||
\(283\) | 1.28590e6 | 0.954421 | 0.477211 | − | 0.878789i | \(-0.341648\pi\) | ||||
0.477211 | + | 0.878789i | \(0.341648\pi\) | |||||||
\(284\) | −119601. | −0.0879915 | ||||||||
\(285\) | 89652.5 | 0.0653808 | ||||||||
\(286\) | −157307. | −0.113719 | ||||||||
\(287\) | 2.47085e6 | 1.77069 | ||||||||
\(288\) | −328925. | −0.233677 | ||||||||
\(289\) | −1.03053e6 | −0.725795 | ||||||||
\(290\) | −472576. | −0.329972 | ||||||||
\(291\) | −105196. | −0.0728230 | ||||||||
\(292\) | 5684.77 | 0.00390171 | ||||||||
\(293\) | 1.08802e6 | 0.740404 | 0.370202 | − | 0.928951i | \(-0.379288\pi\) | ||||
0.370202 | + | 0.928951i | \(0.379288\pi\) | |||||||
\(294\) | 471331. | 0.318023 | ||||||||
\(295\) | −1.26456e6 | −0.846027 | ||||||||
\(296\) | 59289.3 | 0.0393321 | ||||||||
\(297\) | −88209.0 | −0.0580259 | ||||||||
\(298\) | −236427. | −0.154225 | ||||||||
\(299\) | 1.09952e6 | 0.711255 | ||||||||
\(300\) | 67157.3 | 0.0430814 | ||||||||
\(301\) | −25562.2 | −0.0162623 | ||||||||
\(302\) | 1.92648e6 | 1.21548 | ||||||||
\(303\) | 1.22016e6 | 0.763500 | ||||||||
\(304\) | 198992. | 0.123496 | ||||||||
\(305\) | 149609. | 0.0920889 | ||||||||
\(306\) | −226371. | −0.138203 | ||||||||
\(307\) | −580340. | −0.351428 | −0.175714 | − | 0.984441i | \(-0.556223\pi\) | ||||
−0.175714 | + | 0.984441i | \(0.556223\pi\) | |||||||
\(308\) | 243879. | 0.146487 | ||||||||
\(309\) | 796414. | 0.474507 | ||||||||
\(310\) | 626444. | 0.370236 | ||||||||
\(311\) | −1.68606e6 | −0.988492 | −0.494246 | − | 0.869322i | \(-0.664556\pi\) | ||||
−0.494246 | + | 0.869322i | \(0.664556\pi\) | |||||||
\(312\) | −514109. | −0.298998 | ||||||||
\(313\) | −1.50328e6 | −0.867319 | −0.433659 | − | 0.901077i | \(-0.642778\pi\) | ||||
−0.433659 | + | 0.901077i | \(0.642778\pi\) | |||||||
\(314\) | 676270. | 0.387076 | ||||||||
\(315\) | −341857. | −0.194119 | ||||||||
\(316\) | 1.01512e6 | 0.571871 | ||||||||
\(317\) | 1.31016e6 | 0.732281 | 0.366140 | − | 0.930560i | \(-0.380679\pi\) | ||||
0.366140 | + | 0.930560i | \(0.380679\pi\) | |||||||
\(318\) | −730269. | −0.404962 | ||||||||
\(319\) | 510671. | 0.280973 | ||||||||
\(320\) | 854228. | 0.466336 | ||||||||
\(321\) | −1.96868e6 | −1.06638 | ||||||||
\(322\) | 2.86425e6 | 1.53947 | ||||||||
\(323\) | −248622. | −0.132597 | ||||||||
\(324\) | −78332.3 | −0.0414551 | ||||||||
\(325\) | 181412. | 0.0952704 | ||||||||
\(326\) | −637821. | −0.332395 | ||||||||
\(327\) | −2.14559e6 | −1.10963 | ||||||||
\(328\) | −2.88041e6 | −1.47832 | ||||||||
\(329\) | 2.28495e6 | 1.16382 | ||||||||
\(330\) | 121939. | 0.0616394 | ||||||||
\(331\) | 2.91035e6 | 1.46007 | 0.730037 | − | 0.683408i | \(-0.239503\pi\) | ||||
0.730037 | + | 0.683408i | \(0.239503\pi\) | |||||||
\(332\) | 306159. | 0.152441 | ||||||||
\(333\) | 24402.5 | 0.0120594 | ||||||||
\(334\) | −248440. | −0.121858 | ||||||||
\(335\) | 561267. | 0.273248 | ||||||||
\(336\) | −758782. | −0.366664 | ||||||||
\(337\) | 2.47133e6 | 1.18538 | 0.592688 | − | 0.805432i | \(-0.298067\pi\) | ||||
0.592688 | + | 0.805432i | \(0.298067\pi\) | |||||||
\(338\) | 1.28565e6 | 0.612111 | ||||||||
\(339\) | −1.68502e6 | −0.796355 | ||||||||
\(340\) | −186239. | −0.0873722 | ||||||||
\(341\) | −676944. | −0.315258 | ||||||||
\(342\) | 144557. | 0.0668306 | ||||||||
\(343\) | 863415. | 0.396264 | ||||||||
\(344\) | 29799.2 | 0.0135772 | ||||||||
\(345\) | −852314. | −0.385525 | ||||||||
\(346\) | −598440. | −0.268739 | ||||||||
\(347\) | 1.75988e6 | 0.784619 | 0.392309 | − | 0.919833i | \(-0.371676\pi\) | ||||
0.392309 | + | 0.919833i | \(0.371676\pi\) | |||||||
\(348\) | 453492. | 0.200734 | ||||||||
\(349\) | −386142. | −0.169700 | −0.0848502 | − | 0.996394i | \(-0.527041\pi\) | ||||
−0.0848502 | + | 0.996394i | \(0.527041\pi\) | |||||||
\(350\) | 472579. | 0.206207 | ||||||||
\(351\) | −211599. | −0.0916740 | ||||||||
\(352\) | −491357. | −0.211368 | ||||||||
\(353\) | −2.44184e6 | −1.04299 | −0.521495 | − | 0.853254i | \(-0.674625\pi\) | ||||
−0.521495 | + | 0.853254i | \(0.674625\pi\) | |||||||
\(354\) | −2.03900e6 | −0.864787 | ||||||||
\(355\) | 250441. | 0.105471 | ||||||||
\(356\) | −21584.8 | −0.00902657 | ||||||||
\(357\) | 948028. | 0.393686 | ||||||||
\(358\) | 843180. | 0.347707 | ||||||||
\(359\) | 3.77524e6 | 1.54600 | 0.772998 | − | 0.634408i | \(-0.218756\pi\) | ||||
0.772998 | + | 0.634408i | \(0.218756\pi\) | |||||||
\(360\) | 398521. | 0.162067 | ||||||||
\(361\) | −2.31733e6 | −0.935880 | ||||||||
\(362\) | 2.92140e6 | 1.17171 | ||||||||
\(363\) | −131769. | −0.0524864 | ||||||||
\(364\) | 585027. | 0.231431 | ||||||||
\(365\) | −11903.7 | −0.00467681 | ||||||||
\(366\) | 241232. | 0.0941309 | ||||||||
\(367\) | −3.98351e6 | −1.54383 | −0.771917 | − | 0.635723i | \(-0.780702\pi\) | ||||
−0.771917 | + | 0.635723i | \(0.780702\pi\) | |||||||
\(368\) | −1.89179e6 | −0.728204 | ||||||||
\(369\) | −1.18553e6 | −0.453259 | ||||||||
\(370\) | −33733.8 | −0.0128104 | ||||||||
\(371\) | 3.05832e6 | 1.15358 | ||||||||
\(372\) | −601147. | −0.225228 | ||||||||
\(373\) | 3.13497e6 | 1.16670 | 0.583352 | − | 0.812219i | \(-0.301741\pi\) | ||||
0.583352 | + | 0.812219i | \(0.301741\pi\) | |||||||
\(374\) | −338159. | −0.125009 | ||||||||
\(375\) | −140625. | −0.0516398 | ||||||||
\(376\) | −2.66369e6 | −0.971660 | ||||||||
\(377\) | 1.22502e6 | 0.443904 | ||||||||
\(378\) | −551216. | −0.198423 | ||||||||
\(379\) | −2.50995e6 | −0.897567 | −0.448784 | − | 0.893640i | \(-0.648143\pi\) | ||||
−0.448784 | + | 0.893640i | \(0.648143\pi\) | |||||||
\(380\) | 118930. | 0.0422505 | ||||||||
\(381\) | −249548. | −0.0880728 | ||||||||
\(382\) | 3.16043e6 | 1.10812 | ||||||||
\(383\) | −4.20287e6 | −1.46403 | −0.732014 | − | 0.681290i | \(-0.761419\pi\) | ||||
−0.732014 | + | 0.681290i | \(0.761419\pi\) | |||||||
\(384\) | 207864. | 0.0719368 | ||||||||
\(385\) | −510675. | −0.175587 | ||||||||
\(386\) | 390311. | 0.133334 | ||||||||
\(387\) | 12264.9 | 0.00416281 | ||||||||
\(388\) | −139550. | −0.0470598 | ||||||||
\(389\) | −1.91171e6 | −0.640543 | −0.320271 | − | 0.947326i | \(-0.603774\pi\) | ||||
−0.320271 | + | 0.947326i | \(0.603774\pi\) | |||||||
\(390\) | 292512. | 0.0973829 | ||||||||
\(391\) | 2.36362e6 | 0.781871 | ||||||||
\(392\) | 2.30110e6 | 0.756344 | ||||||||
\(393\) | 2.92161e6 | 0.954202 | ||||||||
\(394\) | 2.99013e6 | 0.970396 | ||||||||
\(395\) | −2.12562e6 | −0.685477 | ||||||||
\(396\) | −117015. | −0.0374976 | ||||||||
\(397\) | 3.62426e6 | 1.15410 | 0.577049 | − | 0.816709i | \(-0.304204\pi\) | ||||
0.577049 | + | 0.816709i | \(0.304204\pi\) | |||||||
\(398\) | 3.12903e6 | 0.990152 | ||||||||
\(399\) | −605399. | −0.190375 | ||||||||
\(400\) | −312130. | −0.0975406 | ||||||||
\(401\) | −2.22052e6 | −0.689593 | −0.344797 | − | 0.938677i | \(-0.612052\pi\) | ||||
−0.344797 | + | 0.938677i | \(0.612052\pi\) | |||||||
\(402\) | 904998. | 0.279307 | ||||||||
\(403\) | −1.62388e6 | −0.498070 | ||||||||
\(404\) | 1.61862e6 | 0.493390 | ||||||||
\(405\) | 164025. | 0.0496904 | ||||||||
\(406\) | 3.19117e6 | 0.960805 | ||||||||
\(407\) | 36453.2 | 0.0109081 | ||||||||
\(408\) | −1.10517e6 | −0.328684 | ||||||||
\(409\) | 20564.7 | 0.00607876 | 0.00303938 | − | 0.999995i | \(-0.499033\pi\) | ||||
0.00303938 | + | 0.999995i | \(0.499033\pi\) | |||||||
\(410\) | 1.63886e6 | 0.481485 | ||||||||
\(411\) | 537739. | 0.157024 | ||||||||
\(412\) | 1.05649e6 | 0.306637 | ||||||||
\(413\) | 8.53922e6 | 2.46345 | ||||||||
\(414\) | −1.37429e6 | −0.394073 | ||||||||
\(415\) | −641086. | −0.182724 | ||||||||
\(416\) | −1.17869e6 | −0.333937 | ||||||||
\(417\) | 1.05881e6 | 0.298180 | ||||||||
\(418\) | 215944. | 0.0604505 | ||||||||
\(419\) | −2.30684e6 | −0.641923 | −0.320962 | − | 0.947092i | \(-0.604006\pi\) | ||||
−0.320962 | + | 0.947092i | \(0.604006\pi\) | |||||||
\(420\) | −453495. | −0.125444 | ||||||||
\(421\) | 5.00382e6 | 1.37593 | 0.687965 | − | 0.725744i | \(-0.258504\pi\) | ||||
0.687965 | + | 0.725744i | \(0.258504\pi\) | |||||||
\(422\) | 2.50032e6 | 0.683461 | ||||||||
\(423\) | −1.09633e6 | −0.297914 | ||||||||
\(424\) | −3.56526e6 | −0.963111 | ||||||||
\(425\) | 389978. | 0.104729 | ||||||||
\(426\) | 403816. | 0.107810 | ||||||||
\(427\) | −1.01027e6 | −0.268143 | ||||||||
\(428\) | −2.61158e6 | −0.689119 | ||||||||
\(429\) | −316092. | −0.0829222 | ||||||||
\(430\) | −16954.9 | −0.00442204 | ||||||||
\(431\) | −2.70202e6 | −0.700641 | −0.350320 | − | 0.936630i | \(-0.613927\pi\) | ||||
−0.350320 | + | 0.936630i | \(0.613927\pi\) | |||||||
\(432\) | 364068. | 0.0938585 | ||||||||
\(433\) | −3.92321e6 | −1.00559 | −0.502796 | − | 0.864405i | \(-0.667695\pi\) | ||||
−0.502796 | + | 0.864405i | \(0.667695\pi\) | |||||||
\(434\) | −4.23020e6 | −1.07805 | ||||||||
\(435\) | −949596. | −0.240611 | ||||||||
\(436\) | −2.84627e6 | −0.717066 | ||||||||
\(437\) | −1.50938e6 | −0.378089 | ||||||||
\(438\) | −19193.7 | −0.00478051 | ||||||||
\(439\) | −53261.3 | −0.0131902 | −0.00659508 | − | 0.999978i | \(-0.502099\pi\) | ||||
−0.00659508 | + | 0.999978i | \(0.502099\pi\) | |||||||
\(440\) | 595322. | 0.146595 | ||||||||
\(441\) | 947095. | 0.231898 | ||||||||
\(442\) | −811188. | −0.197499 | ||||||||
\(443\) | 3.30457e6 | 0.800029 | 0.400015 | − | 0.916509i | \(-0.369005\pi\) | ||||
0.400015 | + | 0.916509i | \(0.369005\pi\) | |||||||
\(444\) | 32371.5 | 0.00779302 | ||||||||
\(445\) | 45197.7 | 0.0108197 | ||||||||
\(446\) | 1.71497e6 | 0.408244 | ||||||||
\(447\) | −475077. | −0.112459 | ||||||||
\(448\) | −5.76837e6 | −1.35787 | ||||||||
\(449\) | 3.04596e6 | 0.713031 | 0.356516 | − | 0.934289i | \(-0.383965\pi\) | ||||
0.356516 | + | 0.934289i | \(0.383965\pi\) | |||||||
\(450\) | −226746. | −0.0527848 | ||||||||
\(451\) | −1.77098e6 | −0.409988 | ||||||||
\(452\) | −2.23529e6 | −0.514622 | ||||||||
\(453\) | 3.87107e6 | 0.886309 | ||||||||
\(454\) | 1.81279e6 | 0.412769 | ||||||||
\(455\) | −1.22503e6 | −0.277407 | ||||||||
\(456\) | 705747. | 0.158941 | ||||||||
\(457\) | −2.67154e6 | −0.598371 | −0.299186 | − | 0.954195i | \(-0.596715\pi\) | ||||
−0.299186 | + | 0.954195i | \(0.596715\pi\) | |||||||
\(458\) | −2.97802e6 | −0.663382 | ||||||||
\(459\) | −454870. | −0.100776 | ||||||||
\(460\) | −1.13065e6 | −0.249134 | ||||||||
\(461\) | −3.30382e6 | −0.724042 | −0.362021 | − | 0.932170i | \(-0.617913\pi\) | ||||
−0.362021 | + | 0.932170i | \(0.617913\pi\) | |||||||
\(462\) | −823421. | −0.179480 | ||||||||
\(463\) | −7.66989e6 | −1.66279 | −0.831394 | − | 0.555684i | \(-0.812457\pi\) | ||||
−0.831394 | + | 0.555684i | \(0.812457\pi\) | |||||||
\(464\) | −2.10771e6 | −0.454482 | ||||||||
\(465\) | 1.25878e6 | 0.269971 | ||||||||
\(466\) | −275596. | −0.0587905 | ||||||||
\(467\) | −7.91117e6 | −1.67860 | −0.839302 | − | 0.543665i | \(-0.817036\pi\) | ||||
−0.839302 | + | 0.543665i | \(0.817036\pi\) | |||||||
\(468\) | −280700. | −0.0592417 | ||||||||
\(469\) | −3.79008e6 | −0.795640 | ||||||||
\(470\) | 1.51556e6 | 0.316467 | ||||||||
\(471\) | 1.35890e6 | 0.282251 | ||||||||
\(472\) | −9.95465e6 | −2.05670 | ||||||||
\(473\) | 18321.6 | 0.00376540 | ||||||||
\(474\) | −3.42739e6 | −0.700676 | ||||||||
\(475\) | −249035. | −0.0506438 | ||||||||
\(476\) | 1.25762e6 | 0.254409 | ||||||||
\(477\) | −1.46740e6 | −0.295293 | ||||||||
\(478\) | −7.66825e6 | −1.53506 | ||||||||
\(479\) | 5.44099e6 | 1.08352 | 0.541762 | − | 0.840532i | \(-0.317757\pi\) | ||||
0.541762 | + | 0.840532i | \(0.317757\pi\) | |||||||
\(480\) | 913680. | 0.181005 | ||||||||
\(481\) | 87445.3 | 0.0172335 | ||||||||
\(482\) | −5.90840e6 | −1.15838 | ||||||||
\(483\) | 5.75544e6 | 1.12256 | ||||||||
\(484\) | −174800. | −0.0339178 | ||||||||
\(485\) | 292212. | 0.0564085 | ||||||||
\(486\) | 264477. | 0.0507922 | ||||||||
\(487\) | −8.50740e6 | −1.62545 | −0.812727 | − | 0.582645i | \(-0.802018\pi\) | ||||
−0.812727 | + | 0.582645i | \(0.802018\pi\) | |||||||
\(488\) | 1.17772e6 | 0.223869 | ||||||||
\(489\) | −1.28164e6 | −0.242378 | ||||||||
\(490\) | −1.30925e6 | −0.246339 | ||||||||
\(491\) | −334168. | −0.0625549 | −0.0312775 | − | 0.999511i | \(-0.509958\pi\) | ||||
−0.0312775 | + | 0.999511i | \(0.509958\pi\) | |||||||
\(492\) | −1.57268e6 | −0.292906 | ||||||||
\(493\) | 2.63339e6 | 0.487976 | ||||||||
\(494\) | 518014. | 0.0955046 | ||||||||
\(495\) | 245025. | 0.0449467 | ||||||||
\(496\) | 2.79397e6 | 0.509939 | ||||||||
\(497\) | −1.69116e6 | −0.307110 | ||||||||
\(498\) | −1.03370e6 | −0.186776 | ||||||||
\(499\) | −3.50055e6 | −0.629339 | −0.314669 | − | 0.949201i | \(-0.601894\pi\) | ||||
−0.314669 | + | 0.949201i | \(0.601894\pi\) | |||||||
\(500\) | −186548. | −0.0333707 | ||||||||
\(501\) | −499216. | −0.0888574 | ||||||||
\(502\) | 1.06595e6 | 0.188790 | ||||||||
\(503\) | 6.56301e6 | 1.15660 | 0.578300 | − | 0.815824i | \(-0.303716\pi\) | ||||
0.578300 | + | 0.815824i | \(0.303716\pi\) | |||||||
\(504\) | −2.69110e6 | −0.471904 | ||||||||
\(505\) | −3.38932e6 | −0.591405 | ||||||||
\(506\) | −2.05295e6 | −0.356453 | ||||||||
\(507\) | 2.58338e6 | 0.446343 | ||||||||
\(508\) | −331042. | −0.0569146 | ||||||||
\(509\) | 109860. | 0.0187952 | 0.00939760 | − | 0.999956i | \(-0.497009\pi\) | ||||
0.00939760 | + | 0.999956i | \(0.497009\pi\) | |||||||
\(510\) | 628807. | 0.107051 | ||||||||
\(511\) | 80382.3 | 0.0136178 | ||||||||
\(512\) | 5.17308e6 | 0.872115 | ||||||||
\(513\) | 290474. | 0.0487320 | ||||||||
\(514\) | 8.52649e6 | 1.42352 | ||||||||
\(515\) | −2.21226e6 | −0.367552 | ||||||||
\(516\) | 16270.2 | 0.00269010 | ||||||||
\(517\) | −1.63773e6 | −0.269474 | ||||||||
\(518\) | 227795. | 0.0373009 | ||||||||
\(519\) | −1.20251e6 | −0.195961 | ||||||||
\(520\) | 1.42808e6 | 0.231603 | ||||||||
\(521\) | −914334. | −0.147574 | −0.0737872 | − | 0.997274i | \(-0.523509\pi\) | ||||
−0.0737872 | + | 0.997274i | \(0.523509\pi\) | |||||||
\(522\) | −1.53115e6 | −0.245946 | ||||||||
\(523\) | 4.00814e6 | 0.640750 | 0.320375 | − | 0.947291i | \(-0.396191\pi\) | ||||
0.320375 | + | 0.947291i | \(0.396191\pi\) | |||||||
\(524\) | 3.87570e6 | 0.616626 | ||||||||
\(525\) | 949601. | 0.150364 | ||||||||
\(526\) | 4.06249e6 | 0.640218 | ||||||||
\(527\) | −3.49081e6 | −0.547520 | ||||||||
\(528\) | 543855. | 0.0848982 | ||||||||
\(529\) | 7.91308e6 | 1.22944 | ||||||||
\(530\) | 2.02852e6 | 0.313683 | ||||||||
\(531\) | −4.09717e6 | −0.630592 | ||||||||
\(532\) | −803100. | −0.123024 | ||||||||
\(533\) | −4.24829e6 | −0.647732 | ||||||||
\(534\) | 72877.7 | 0.0110597 | ||||||||
\(535\) | 5.46856e6 | 0.826016 | ||||||||
\(536\) | 4.41831e6 | 0.664269 | ||||||||
\(537\) | 1.69429e6 | 0.253543 | ||||||||
\(538\) | −3.12847e6 | −0.465990 | ||||||||
\(539\) | 1.41480e6 | 0.209760 | ||||||||
\(540\) | 217590. | 0.0321110 | ||||||||
\(541\) | −1.87833e6 | −0.275918 | −0.137959 | − | 0.990438i | \(-0.544054\pi\) | ||||
−0.137959 | + | 0.990438i | \(0.544054\pi\) | |||||||
\(542\) | −5.33431e6 | −0.779974 | ||||||||
\(543\) | 5.87027e6 | 0.854395 | ||||||||
\(544\) | −2.53379e6 | −0.367091 | ||||||||
\(545\) | 5.95998e6 | 0.859515 | ||||||||
\(546\) | −1.97525e6 | −0.283558 | ||||||||
\(547\) | 87797.6 | 0.0125463 | 0.00627313 | − | 0.999980i | \(-0.498003\pi\) | ||||
0.00627313 | + | 0.999980i | \(0.498003\pi\) | |||||||
\(548\) | 713346. | 0.101473 | ||||||||
\(549\) | 484732. | 0.0686390 | ||||||||
\(550\) | −338720. | −0.0477457 | ||||||||
\(551\) | −1.68165e6 | −0.235970 | ||||||||
\(552\) | −6.70944e6 | −0.937213 | ||||||||
\(553\) | 1.43537e7 | 1.99596 | ||||||||
\(554\) | 5.15571e6 | 0.713698 | ||||||||
\(555\) | −67784.8 | −0.00934114 | ||||||||
\(556\) | 1.40458e6 | 0.192690 | ||||||||
\(557\) | −3.46548e6 | −0.473288 | −0.236644 | − | 0.971596i | \(-0.576048\pi\) | ||||
−0.236644 | + | 0.971596i | \(0.576048\pi\) | |||||||
\(558\) | 2.02968e6 | 0.275957 | ||||||||
\(559\) | 43950.6 | 0.00594888 | ||||||||
\(560\) | 2.10773e6 | 0.284017 | ||||||||
\(561\) | −679497. | −0.0911550 | ||||||||
\(562\) | 6.90655e6 | 0.922403 | ||||||||
\(563\) | −2.85737e6 | −0.379923 | −0.189961 | − | 0.981792i | \(-0.560836\pi\) | ||||
−0.189961 | + | 0.981792i | \(0.560836\pi\) | |||||||
\(564\) | −1.45436e6 | −0.192519 | ||||||||
\(565\) | 4.68062e6 | 0.616854 | ||||||||
\(566\) | −5.75946e6 | −0.755685 | ||||||||
\(567\) | −1.10762e6 | −0.144688 | ||||||||
\(568\) | 1.97148e6 | 0.256402 | ||||||||
\(569\) | −5.48030e6 | −0.709617 | −0.354808 | − | 0.934939i | \(-0.615454\pi\) | ||||
−0.354808 | + | 0.934939i | \(0.615454\pi\) | |||||||
\(570\) | −401549. | −0.0517667 | ||||||||
\(571\) | 8.81180e6 | 1.13103 | 0.565515 | − | 0.824738i | \(-0.308677\pi\) | ||||
0.565515 | + | 0.824738i | \(0.308677\pi\) | |||||||
\(572\) | −419317. | −0.0535861 | ||||||||
\(573\) | 6.35058e6 | 0.808029 | ||||||||
\(574\) | −1.10668e7 | −1.40198 | ||||||||
\(575\) | 2.36754e6 | 0.298626 | ||||||||
\(576\) | 2.76770e6 | 0.347586 | ||||||||
\(577\) | 502598. | 0.0628465 | 0.0314233 | − | 0.999506i | \(-0.489996\pi\) | ||||
0.0314233 | + | 0.999506i | \(0.489996\pi\) | |||||||
\(578\) | 4.61566e6 | 0.574665 | ||||||||
\(579\) | 784291. | 0.0972257 | ||||||||
\(580\) | −1.25970e6 | −0.155488 | ||||||||
\(581\) | 4.32907e6 | 0.532053 | ||||||||
\(582\) | 471169. | 0.0576593 | ||||||||
\(583\) | −2.19205e6 | −0.267103 | ||||||||
\(584\) | −93706.2 | −0.0113694 | ||||||||
\(585\) | 587775. | 0.0710104 | ||||||||
\(586\) | −4.87319e6 | −0.586232 | ||||||||
\(587\) | −7.45878e6 | −0.893455 | −0.446728 | − | 0.894670i | \(-0.647411\pi\) | ||||
−0.446728 | + | 0.894670i | \(0.647411\pi\) | |||||||
\(588\) | 1.25638e6 | 0.149857 | ||||||||
\(589\) | 2.22919e6 | 0.264764 | ||||||||
\(590\) | 5.66389e6 | 0.669861 | ||||||||
\(591\) | 6.00837e6 | 0.707600 | ||||||||
\(592\) | −150455. | −0.0176442 | ||||||||
\(593\) | 6.69352e6 | 0.781660 | 0.390830 | − | 0.920463i | \(-0.372188\pi\) | ||||
0.390830 | + | 0.920463i | \(0.372188\pi\) | |||||||
\(594\) | 395083. | 0.0459433 | ||||||||
\(595\) | −2.63341e6 | −0.304948 | ||||||||
\(596\) | −630220. | −0.0726736 | ||||||||
\(597\) | 6.28748e6 | 0.722006 | ||||||||
\(598\) | −4.92469e6 | −0.563153 | ||||||||
\(599\) | −1.64186e7 | −1.86968 | −0.934842 | − | 0.355065i | \(-0.884459\pi\) | ||||
−0.934842 | + | 0.355065i | \(0.884459\pi\) | |||||||
\(600\) | −1.10700e6 | −0.125537 | ||||||||
\(601\) | 1.42657e7 | 1.61105 | 0.805523 | − | 0.592564i | \(-0.201884\pi\) | ||||
0.805523 | + | 0.592564i | \(0.201884\pi\) | |||||||
\(602\) | 114491. | 0.0128760 | ||||||||
\(603\) | 1.81851e6 | 0.203667 | ||||||||
\(604\) | 5.13522e6 | 0.572752 | ||||||||
\(605\) | 366025. | 0.0406558 | ||||||||
\(606\) | −5.46501e6 | −0.604518 | ||||||||
\(607\) | 2.38734e6 | 0.262992 | 0.131496 | − | 0.991317i | \(-0.458022\pi\) | ||||
0.131496 | + | 0.991317i | \(0.458022\pi\) | |||||||
\(608\) | 1.61805e6 | 0.177514 | ||||||||
\(609\) | 6.41235e6 | 0.700607 | ||||||||
\(610\) | −670089. | −0.0729134 | ||||||||
\(611\) | −3.92865e6 | −0.425736 | ||||||||
\(612\) | −603414. | −0.0651234 | ||||||||
\(613\) | −1.36125e6 | −0.146314 | −0.0731570 | − | 0.997320i | \(-0.523307\pi\) | ||||
−0.0731570 | + | 0.997320i | \(0.523307\pi\) | |||||||
\(614\) | 2.59931e6 | 0.278251 | ||||||||
\(615\) | 3.29314e6 | 0.351093 | ||||||||
\(616\) | −4.02004e6 | −0.426853 | ||||||||
\(617\) | −1.33759e6 | −0.141453 | −0.0707264 | − | 0.997496i | \(-0.522532\pi\) | ||||
−0.0707264 | + | 0.997496i | \(0.522532\pi\) | |||||||
\(618\) | −3.56709e6 | −0.375702 | ||||||||
\(619\) | 1.70842e7 | 1.79212 | 0.896062 | − | 0.443930i | \(-0.146416\pi\) | ||||
0.896062 | + | 0.443930i | \(0.146416\pi\) | |||||||
\(620\) | 1.66985e6 | 0.174461 | ||||||||
\(621\) | −2.76150e6 | −0.287353 | ||||||||
\(622\) | 7.55179e6 | 0.782661 | ||||||||
\(623\) | −305208. | −0.0315047 | ||||||||
\(624\) | 1.30462e6 | 0.134129 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 6.73310e6 | 0.686719 | ||||||||
\(627\) | 433918. | 0.0440797 | ||||||||
\(628\) | 1.80267e6 | 0.182397 | ||||||||
\(629\) | 187979. | 0.0189445 | ||||||||
\(630\) | 1.53116e6 | 0.153698 | ||||||||
\(631\) | 1.70136e7 | 1.70107 | 0.850534 | − | 0.525920i | \(-0.176279\pi\) | ||||
0.850534 | + | 0.525920i | \(0.176279\pi\) | |||||||
\(632\) | −1.67329e7 | −1.66640 | ||||||||
\(633\) | 5.02414e6 | 0.498371 | ||||||||
\(634\) | −5.86815e6 | −0.579800 | ||||||||
\(635\) | 693189. | 0.0682209 | ||||||||
\(636\) | −1.94661e6 | −0.190825 | ||||||||
\(637\) | 3.39387e6 | 0.331395 | ||||||||
\(638\) | −2.28727e6 | −0.222467 | ||||||||
\(639\) | 811429. | 0.0786138 | ||||||||
\(640\) | −577400. | −0.0557220 | ||||||||
\(641\) | 1.04366e7 | 1.00326 | 0.501632 | − | 0.865081i | \(-0.332733\pi\) | ||||
0.501632 | + | 0.865081i | \(0.332733\pi\) | |||||||
\(642\) | 8.81761e6 | 0.844332 | ||||||||
\(643\) | 1.32098e7 | 1.25999 | 0.629996 | − | 0.776598i | \(-0.283056\pi\) | ||||
0.629996 | + | 0.776598i | \(0.283056\pi\) | |||||||
\(644\) | 7.63496e6 | 0.725424 | ||||||||
\(645\) | −34069.1 | −0.00322450 | ||||||||
\(646\) | 1.11356e6 | 0.104987 | ||||||||
\(647\) | 3.14204e6 | 0.295087 | 0.147544 | − | 0.989056i | \(-0.452863\pi\) | ||||
0.147544 | + | 0.989056i | \(0.452863\pi\) | |||||||
\(648\) | 1.29121e6 | 0.120798 | ||||||||
\(649\) | −6.12047e6 | −0.570391 | ||||||||
\(650\) | −812534. | −0.0754325 | ||||||||
\(651\) | −8.50019e6 | −0.786097 | ||||||||
\(652\) | −1.70018e6 | −0.156630 | ||||||||
\(653\) | 9.82598e6 | 0.901764 | 0.450882 | − | 0.892583i | \(-0.351109\pi\) | ||||
0.450882 | + | 0.892583i | \(0.351109\pi\) | |||||||
\(654\) | 9.60998e6 | 0.878574 | ||||||||
\(655\) | −8.11557e6 | −0.739122 | ||||||||
\(656\) | 7.30942e6 | 0.663167 | ||||||||
\(657\) | −38568.0 | −0.00348589 | ||||||||
\(658\) | −1.02341e7 | −0.921482 | ||||||||
\(659\) | −1.78524e7 | −1.60134 | −0.800670 | − | 0.599105i | \(-0.795523\pi\) | ||||
−0.800670 | + | 0.599105i | \(0.795523\pi\) | |||||||
\(660\) | 325041. | 0.0290455 | ||||||||
\(661\) | 1.02807e7 | 0.915207 | 0.457603 | − | 0.889156i | \(-0.348708\pi\) | ||||
0.457603 | + | 0.889156i | \(0.348708\pi\) | |||||||
\(662\) | −1.30353e7 | −1.15605 | ||||||||
\(663\) | −1.63000e6 | −0.144014 | ||||||||
\(664\) | −5.04664e6 | −0.444204 | ||||||||
\(665\) | 1.68166e6 | 0.147464 | ||||||||
\(666\) | −109298. | −0.00954827 | ||||||||
\(667\) | 1.59872e7 | 1.39142 | ||||||||
\(668\) | −662242. | −0.0574216 | ||||||||
\(669\) | 3.44607e6 | 0.297686 | ||||||||
\(670\) | −2.51388e6 | −0.216351 | ||||||||
\(671\) | 724106. | 0.0620863 | ||||||||
\(672\) | −6.16983e6 | −0.527047 | ||||||||
\(673\) | −2.22873e7 | −1.89679 | −0.948394 | − | 0.317094i | \(-0.897293\pi\) | ||||
−0.948394 | + | 0.317094i | \(0.897293\pi\) | |||||||
\(674\) | −1.10690e7 | −0.938549 | ||||||||
\(675\) | −455625. | −0.0384900 | ||||||||
\(676\) | 3.42702e6 | 0.288436 | ||||||||
\(677\) | −1.56465e7 | −1.31204 | −0.656018 | − | 0.754745i | \(-0.727761\pi\) | ||||
−0.656018 | + | 0.754745i | \(0.727761\pi\) | |||||||
\(678\) | 7.54712e6 | 0.630532 | ||||||||
\(679\) | −1.97323e6 | −0.164249 | ||||||||
\(680\) | 3.06991e6 | 0.254597 | ||||||||
\(681\) | 3.64262e6 | 0.300986 | ||||||||
\(682\) | 3.03199e6 | 0.249613 | ||||||||
\(683\) | −1.82208e7 | −1.49457 | −0.747283 | − | 0.664506i | \(-0.768642\pi\) | ||||
−0.747283 | + | 0.664506i | \(0.768642\pi\) | |||||||
\(684\) | 385333. | 0.0314917 | ||||||||
\(685\) | −1.49372e6 | −0.121631 | ||||||||
\(686\) | −3.86719e6 | −0.313751 | ||||||||
\(687\) | −5.98404e6 | −0.483730 | ||||||||
\(688\) | −75619.5 | −0.00609064 | ||||||||
\(689\) | −5.25837e6 | −0.421991 | ||||||||
\(690\) | 3.81747e6 | 0.305248 | ||||||||
\(691\) | 1.07957e7 | 0.860116 | 0.430058 | − | 0.902801i | \(-0.358493\pi\) | ||||
0.430058 | + | 0.902801i | \(0.358493\pi\) | |||||||
\(692\) | −1.59520e6 | −0.126634 | ||||||||
\(693\) | −1.65459e6 | −0.130875 | ||||||||
\(694\) | −7.88239e6 | −0.621240 | ||||||||
\(695\) | −2.94114e6 | −0.230969 | ||||||||
\(696\) | −7.47524e6 | −0.584927 | ||||||||
\(697\) | −9.13244e6 | −0.712041 | ||||||||
\(698\) | 1.72951e6 | 0.134364 | ||||||||
\(699\) | −553783. | −0.0428693 | ||||||||
\(700\) | 1.25971e6 | 0.0971683 | ||||||||
\(701\) | −7.59781e6 | −0.583973 | −0.291987 | − | 0.956422i | \(-0.594316\pi\) | ||||
−0.291987 | + | 0.956422i | \(0.594316\pi\) | |||||||
\(702\) | 947740. | 0.0725849 | ||||||||
\(703\) | −120041. | −0.00916098 | ||||||||
\(704\) | 4.13447e6 | 0.314404 | ||||||||
\(705\) | 3.04537e6 | 0.230764 | ||||||||
\(706\) | 1.09369e7 | 0.825811 | ||||||||
\(707\) | 2.28872e7 | 1.72204 | ||||||||
\(708\) | −5.43516e6 | −0.407502 | ||||||||
\(709\) | 1.26638e7 | 0.946122 | 0.473061 | − | 0.881030i | \(-0.343149\pi\) | ||||
0.473061 | + | 0.881030i | \(0.343149\pi\) | |||||||
\(710\) | −1.12171e6 | −0.0835094 | ||||||||
\(711\) | −6.88700e6 | −0.510924 | ||||||||
\(712\) | 355798. | 0.0263029 | ||||||||
\(713\) | −2.11926e7 | −1.56121 | ||||||||
\(714\) | −4.24616e6 | −0.311710 | ||||||||
\(715\) | 878035. | 0.0642313 | ||||||||
\(716\) | 2.24758e6 | 0.163845 | ||||||||
\(717\) | −1.54086e7 | −1.11935 | ||||||||
\(718\) | −1.69091e7 | −1.22408 | ||||||||
\(719\) | −8.16704e6 | −0.589172 | −0.294586 | − | 0.955625i | \(-0.595182\pi\) | ||||
−0.294586 | + | 0.955625i | \(0.595182\pi\) | |||||||
\(720\) | −1.01130e6 | −0.0727025 | ||||||||
\(721\) | 1.49388e7 | 1.07023 | ||||||||
\(722\) | 1.03792e7 | 0.741004 | ||||||||
\(723\) | −1.18723e7 | −0.844677 | ||||||||
\(724\) | 7.78729e6 | 0.552128 | ||||||||
\(725\) | 2.63777e6 | 0.186377 | ||||||||
\(726\) | 590186. | 0.0415573 | ||||||||
\(727\) | 1.99934e6 | 0.140298 | 0.0701488 | − | 0.997537i | \(-0.477653\pi\) | ||||
0.0701488 | + | 0.997537i | \(0.477653\pi\) | |||||||
\(728\) | −9.64343e6 | −0.674377 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 53316.0 | 0.00370297 | ||||||||
\(731\) | 94479.6 | 0.00653950 | ||||||||
\(732\) | 643028. | 0.0443560 | ||||||||
\(733\) | 2.26768e7 | 1.55892 | 0.779458 | − | 0.626455i | \(-0.215495\pi\) | ||||
0.779458 | + | 0.626455i | \(0.215495\pi\) | |||||||
\(734\) | 1.78419e7 | 1.22237 | ||||||||
\(735\) | −2.63082e6 | −0.179627 | ||||||||
\(736\) | −1.53826e7 | −1.04673 | ||||||||
\(737\) | 2.71653e6 | 0.184224 | ||||||||
\(738\) | 5.30992e6 | 0.358878 | ||||||||
\(739\) | −1.49990e7 | −1.01030 | −0.505151 | − | 0.863031i | \(-0.668563\pi\) | ||||
−0.505151 | + | 0.863031i | \(0.668563\pi\) | |||||||
\(740\) | −89920.9 | −0.00603645 | ||||||||
\(741\) | 1.04090e6 | 0.0696407 | ||||||||
\(742\) | −1.36981e7 | −0.913375 | ||||||||
\(743\) | −8.72196e6 | −0.579618 | −0.289809 | − | 0.957084i | \(-0.593592\pi\) | ||||
−0.289809 | + | 0.957084i | \(0.593592\pi\) | |||||||
\(744\) | 9.90914e6 | 0.656302 | ||||||||
\(745\) | 1.31966e6 | 0.0871105 | ||||||||
\(746\) | −1.40413e7 | −0.923765 | ||||||||
\(747\) | −2.07712e6 | −0.136194 | ||||||||
\(748\) | −901396. | −0.0589063 | ||||||||
\(749\) | −3.69277e7 | −2.40518 | ||||||||
\(750\) | 629851. | 0.0408870 | ||||||||
\(751\) | 3.03235e7 | 1.96191 | 0.980957 | − | 0.194227i | \(-0.0622198\pi\) | ||||
0.980957 | + | 0.194227i | \(0.0622198\pi\) | |||||||
\(752\) | 6.75947e6 | 0.435881 | ||||||||
\(753\) | 2.14193e6 | 0.137663 | ||||||||
\(754\) | −5.48679e6 | −0.351471 | ||||||||
\(755\) | −1.07530e7 | −0.686532 | ||||||||
\(756\) | −1.46932e6 | −0.0935002 | ||||||||
\(757\) | 999401. | 0.0633870 | 0.0316935 | − | 0.999498i | \(-0.489910\pi\) | ||||
0.0316935 | + | 0.999498i | \(0.489910\pi\) | |||||||
\(758\) | 1.12419e7 | 0.710669 | ||||||||
\(759\) | −4.12520e6 | −0.259921 | ||||||||
\(760\) | −1.96041e6 | −0.123115 | ||||||||
\(761\) | 1.23318e7 | 0.771904 | 0.385952 | − | 0.922519i | \(-0.373873\pi\) | ||||
0.385952 | + | 0.922519i | \(0.373873\pi\) | |||||||
\(762\) | 1.11771e6 | 0.0697336 | ||||||||
\(763\) | −4.02461e7 | −2.50272 | ||||||||
\(764\) | 8.42445e6 | 0.522166 | ||||||||
\(765\) | 1.26353e6 | 0.0780605 | ||||||||
\(766\) | 1.88244e7 | 1.15918 | ||||||||
\(767\) | −1.46820e7 | −0.901150 | ||||||||
\(768\) | 8.90970e6 | 0.545080 | ||||||||
\(769\) | −3.88179e6 | −0.236710 | −0.118355 | − | 0.992971i | \(-0.537762\pi\) | ||||
−0.118355 | + | 0.992971i | \(0.537762\pi\) | |||||||
\(770\) | 2.28728e6 | 0.139025 | ||||||||
\(771\) | 1.71332e7 | 1.03801 | ||||||||
\(772\) | 1.04041e6 | 0.0628293 | ||||||||
\(773\) | 2.35138e7 | 1.41539 | 0.707693 | − | 0.706520i | \(-0.249736\pi\) | ||||
0.707693 | + | 0.706520i | \(0.249736\pi\) | |||||||
\(774\) | −54933.7 | −0.00329600 | ||||||||
\(775\) | −3.49661e6 | −0.209119 | ||||||||
\(776\) | 2.30030e6 | 0.137129 | ||||||||
\(777\) | 457732. | 0.0271994 | ||||||||
\(778\) | 8.56244e6 | 0.507164 | ||||||||
\(779\) | 5.83186e6 | 0.344321 | ||||||||
\(780\) | 779722. | 0.0458884 | ||||||||
\(781\) | 1.21214e6 | 0.0711088 | ||||||||
\(782\) | −1.05865e7 | −0.619064 | ||||||||
\(783\) | −3.07669e6 | −0.179341 | ||||||||
\(784\) | −5.83934e6 | −0.339292 | ||||||||
\(785\) | −3.77472e6 | −0.218631 | ||||||||
\(786\) | −1.30857e7 | −0.755511 | ||||||||
\(787\) | 2.16876e6 | 0.124817 | 0.0624086 | − | 0.998051i | \(-0.480122\pi\) | ||||
0.0624086 | + | 0.998051i | \(0.480122\pi\) | |||||||
\(788\) | 7.97049e6 | 0.457266 | ||||||||
\(789\) | 8.16317e6 | 0.466838 | ||||||||
\(790\) | 9.52052e6 | 0.542742 | ||||||||
\(791\) | −3.16069e7 | −1.79614 | ||||||||
\(792\) | 1.92884e6 | 0.109266 | ||||||||
\(793\) | 1.73701e6 | 0.0980890 | ||||||||
\(794\) | −1.62328e7 | −0.913784 | ||||||||
\(795\) | 4.07612e6 | 0.228733 | ||||||||
\(796\) | 8.34075e6 | 0.466576 | ||||||||
\(797\) | −1.85869e7 | −1.03648 | −0.518241 | − | 0.855235i | \(-0.673413\pi\) | ||||
−0.518241 | + | 0.855235i | \(0.673413\pi\) | |||||||
\(798\) | 2.71155e6 | 0.150733 | ||||||||
\(799\) | −8.44534e6 | −0.468005 | ||||||||
\(800\) | −2.53800e6 | −0.140206 | ||||||||
\(801\) | 146441. | 0.00806456 | ||||||||
\(802\) | 9.94556e6 | 0.546001 | ||||||||
\(803\) | −57613.9 | −0.00315310 | ||||||||
\(804\) | 2.41237e6 | 0.131614 | ||||||||
\(805\) | −1.59873e7 | −0.869534 | ||||||||
\(806\) | 7.27326e6 | 0.394359 | ||||||||
\(807\) | −6.28637e6 | −0.339794 | ||||||||
\(808\) | −2.66808e7 | −1.43771 | ||||||||
\(809\) | 2.99966e7 | 1.61139 | 0.805694 | − | 0.592332i | \(-0.201793\pi\) | ||||
0.805694 | + | 0.592332i | \(0.201793\pi\) | |||||||
\(810\) | −734658. | −0.0393435 | ||||||||
\(811\) | −1.54479e6 | −0.0824740 | −0.0412370 | − | 0.999149i | \(-0.513130\pi\) | ||||
−0.0412370 | + | 0.999149i | \(0.513130\pi\) | |||||||
\(812\) | 8.50640e6 | 0.452747 | ||||||||
\(813\) | −1.07188e7 | −0.568747 | ||||||||
\(814\) | −163272. | −0.00863674 | ||||||||
\(815\) | 3.56011e6 | 0.187746 | ||||||||
\(816\) | 2.80451e6 | 0.147446 | ||||||||
\(817\) | −60333.5 | −0.00316230 | ||||||||
\(818\) | −92108.3 | −0.00481299 | ||||||||
\(819\) | −3.96908e6 | −0.206767 | ||||||||
\(820\) | 4.36856e6 | 0.226884 | ||||||||
\(821\) | −2.60445e7 | −1.34852 | −0.674261 | − | 0.738493i | \(-0.735538\pi\) | ||||
−0.674261 | + | 0.738493i | \(0.735538\pi\) | |||||||
\(822\) | −2.40850e6 | −0.124328 | ||||||||
\(823\) | −9.56891e6 | −0.492451 | −0.246226 | − | 0.969213i | \(-0.579190\pi\) | ||||
−0.246226 | + | 0.969213i | \(0.579190\pi\) | |||||||
\(824\) | −1.74150e7 | −0.893521 | ||||||||
\(825\) | −680625. | −0.0348155 | ||||||||
\(826\) | −3.82467e7 | −1.95049 | ||||||||
\(827\) | 1.07164e7 | 0.544860 | 0.272430 | − | 0.962176i | \(-0.412173\pi\) | ||||
0.272430 | + | 0.962176i | \(0.412173\pi\) | |||||||
\(828\) | −3.66330e6 | −0.185694 | ||||||||
\(829\) | −1.64337e7 | −0.830519 | −0.415259 | − | 0.909703i | \(-0.636309\pi\) | ||||
−0.415259 | + | 0.909703i | \(0.636309\pi\) | |||||||
\(830\) | 2.87139e6 | 0.144676 | ||||||||
\(831\) | 1.03599e7 | 0.520419 | ||||||||
\(832\) | 9.91791e6 | 0.496720 | ||||||||
\(833\) | 7.29572e6 | 0.364297 | ||||||||
\(834\) | −4.74235e6 | −0.236091 | ||||||||
\(835\) | 1.38671e6 | 0.0688287 | ||||||||
\(836\) | 575620. | 0.0284853 | ||||||||
\(837\) | 4.07845e6 | 0.201225 | ||||||||
\(838\) | 1.03322e7 | 0.508257 | ||||||||
\(839\) | 9.64356e6 | 0.472969 | 0.236484 | − | 0.971635i | \(-0.424005\pi\) | ||||
0.236484 | + | 0.971635i | \(0.424005\pi\) | |||||||
\(840\) | 7.47528e6 | 0.365535 | ||||||||
\(841\) | −2.69916e6 | −0.131595 | ||||||||
\(842\) | −2.24118e7 | −1.08942 | ||||||||
\(843\) | 1.38781e7 | 0.672604 | ||||||||
\(844\) | 6.66485e6 | 0.322058 | ||||||||
\(845\) | −7.17606e6 | −0.345736 | ||||||||
\(846\) | 4.91041e6 | 0.235881 | ||||||||
\(847\) | −2.47166e6 | −0.118381 | ||||||||
\(848\) | 9.04732e6 | 0.432046 | ||||||||
\(849\) | −1.15731e7 | −0.551035 | ||||||||
\(850\) | −1.74669e6 | −0.0829216 | ||||||||
\(851\) | 1.14121e6 | 0.0540186 | ||||||||
\(852\) | 1.07641e6 | 0.0508019 | ||||||||
\(853\) | −2.52742e7 | −1.18934 | −0.594669 | − | 0.803971i | \(-0.702717\pi\) | ||||
−0.594669 | + | 0.803971i | \(0.702717\pi\) | |||||||
\(854\) | 4.52492e6 | 0.212308 | ||||||||
\(855\) | −806873. | −0.0377476 | ||||||||
\(856\) | 4.30486e7 | 2.00805 | ||||||||
\(857\) | −262739. | −0.0122200 | −0.00611002 | − | 0.999981i | \(-0.501945\pi\) | ||||
−0.00611002 | + | 0.999981i | \(0.501945\pi\) | |||||||
\(858\) | 1.41576e6 | 0.0656555 | ||||||||
\(859\) | −9.43849e6 | −0.436435 | −0.218218 | − | 0.975900i | \(-0.570024\pi\) | ||||
−0.218218 | + | 0.975900i | \(0.570024\pi\) | |||||||
\(860\) | −45194.9 | −0.00208374 | ||||||||
\(861\) | −2.22376e7 | −1.02231 | ||||||||
\(862\) | 1.21022e7 | 0.554748 | ||||||||
\(863\) | 3.78002e7 | 1.72769 | 0.863847 | − | 0.503754i | \(-0.168048\pi\) | ||||
0.863847 | + | 0.503754i | \(0.168048\pi\) | |||||||
\(864\) | 2.96032e6 | 0.134913 | ||||||||
\(865\) | 3.34030e6 | 0.151791 | ||||||||
\(866\) | 1.75718e7 | 0.796200 | ||||||||
\(867\) | 9.27473e6 | 0.419038 | ||||||||
\(868\) | −1.12760e7 | −0.507993 | ||||||||
\(869\) | −1.02880e7 | −0.462148 | ||||||||
\(870\) | 4.25318e6 | 0.190509 | ||||||||
\(871\) | 6.51653e6 | 0.291052 | ||||||||
\(872\) | 4.69171e7 | 2.08949 | ||||||||
\(873\) | 946768. | 0.0420444 | ||||||||
\(874\) | 6.76041e6 | 0.299360 | ||||||||
\(875\) | −2.63778e6 | −0.116471 | ||||||||
\(876\) | −51162.9 | −0.00225266 | ||||||||
\(877\) | 2.42348e7 | 1.06400 | 0.531999 | − | 0.846745i | \(-0.321441\pi\) | ||||
0.531999 | + | 0.846745i | \(0.321441\pi\) | |||||||
\(878\) | 238554. | 0.0104436 | ||||||||
\(879\) | −9.79220e6 | −0.427472 | ||||||||
\(880\) | −1.51071e6 | −0.0657619 | ||||||||
\(881\) | 1.97060e7 | 0.855377 | 0.427689 | − | 0.903926i | \(-0.359328\pi\) | ||||
0.427689 | + | 0.903926i | \(0.359328\pi\) | |||||||
\(882\) | −4.24198e6 | −0.183610 | ||||||||
\(883\) | −2.09867e7 | −0.905822 | −0.452911 | − | 0.891556i | \(-0.649614\pi\) | ||||
−0.452911 | + | 0.891556i | \(0.649614\pi\) | |||||||
\(884\) | −2.16230e6 | −0.0930649 | ||||||||
\(885\) | 1.13810e7 | 0.488454 | ||||||||
\(886\) | −1.48010e7 | −0.633441 | ||||||||
\(887\) | −3.47934e7 | −1.48487 | −0.742434 | − | 0.669919i | \(-0.766329\pi\) | ||||
−0.742434 | + | 0.669919i | \(0.766329\pi\) | |||||||
\(888\) | −533604. | −0.0227084 | ||||||||
\(889\) | −4.68091e6 | −0.198644 | ||||||||
\(890\) | −202438. | −0.00856677 | ||||||||
\(891\) | 793881. | 0.0335013 | ||||||||
\(892\) | 4.57143e6 | 0.192371 | ||||||||
\(893\) | 5.39309e6 | 0.226313 | ||||||||
\(894\) | 2.12784e6 | 0.0890421 | ||||||||
\(895\) | −4.70636e6 | −0.196394 | ||||||||
\(896\) | 3.89902e6 | 0.162250 | ||||||||
\(897\) | −9.89569e6 | −0.410644 | ||||||||
\(898\) | −1.36427e7 | −0.564559 | ||||||||
\(899\) | −2.36115e7 | −0.974370 | ||||||||
\(900\) | −604416. | −0.0248731 | ||||||||
\(901\) | −1.13038e7 | −0.463887 | ||||||||
\(902\) | 7.93210e6 | 0.324617 | ||||||||
\(903\) | 230059. | 0.00938903 | ||||||||
\(904\) | 3.68460e7 | 1.49958 | ||||||||
\(905\) | −1.63063e7 | −0.661811 | ||||||||
\(906\) | −1.73383e7 | −0.701756 | ||||||||
\(907\) | −4.14396e7 | −1.67262 | −0.836310 | − | 0.548257i | \(-0.815291\pi\) | ||||
−0.836310 | + | 0.548257i | \(0.815291\pi\) | |||||||
\(908\) | 4.83217e6 | 0.194503 | ||||||||
\(909\) | −1.09814e7 | −0.440807 | ||||||||
\(910\) | 5.48682e6 | 0.219643 | ||||||||
\(911\) | −4.55462e7 | −1.81826 | −0.909131 | − | 0.416511i | \(-0.863253\pi\) | ||||
−0.909131 | + | 0.416511i | \(0.863253\pi\) | |||||||
\(912\) | −1.79093e6 | −0.0713002 | ||||||||
\(913\) | −3.10285e6 | −0.123193 | ||||||||
\(914\) | 1.19657e7 | 0.473774 | ||||||||
\(915\) | −1.34648e6 | −0.0531675 | ||||||||
\(916\) | −7.93822e6 | −0.312597 | ||||||||
\(917\) | 5.48022e7 | 2.15216 | ||||||||
\(918\) | 2.03734e6 | 0.0797914 | ||||||||
\(919\) | 8.41097e6 | 0.328517 | 0.164258 | − | 0.986417i | \(-0.447477\pi\) | ||||
0.164258 | + | 0.986417i | \(0.447477\pi\) | |||||||
\(920\) | 1.86373e7 | 0.725962 | ||||||||
\(921\) | 5.22306e6 | 0.202897 | ||||||||
\(922\) | 1.47976e7 | 0.573277 | ||||||||
\(923\) | 2.90772e6 | 0.112343 | ||||||||
\(924\) | −2.19491e6 | −0.0845741 | ||||||||
\(925\) | 188291. | 0.00723562 | ||||||||
\(926\) | 3.43530e7 | 1.31655 | ||||||||
\(927\) | −7.16773e6 | −0.273957 | ||||||||
\(928\) | −1.71383e7 | −0.653278 | ||||||||
\(929\) | 1.89074e6 | 0.0718773 | 0.0359386 | − | 0.999354i | \(-0.488558\pi\) | ||||
0.0359386 | + | 0.999354i | \(0.488558\pi\) | |||||||
\(930\) | −5.63800e6 | −0.213756 | ||||||||
\(931\) | −4.65895e6 | −0.176163 | ||||||||
\(932\) | −734628. | −0.0277031 | ||||||||
\(933\) | 1.51746e7 | 0.570706 | ||||||||
\(934\) | 3.54337e7 | 1.32907 | ||||||||
\(935\) | 1.88749e6 | 0.0706083 | ||||||||
\(936\) | 4.62698e6 | 0.172627 | ||||||||
\(937\) | 3.58861e7 | 1.33530 | 0.667648 | − | 0.744477i | \(-0.267301\pi\) | ||||
0.667648 | + | 0.744477i | \(0.267301\pi\) | |||||||
\(938\) | 1.69756e7 | 0.629966 | ||||||||
\(939\) | 1.35295e7 | 0.500747 | ||||||||
\(940\) | 4.03988e6 | 0.149124 | ||||||||
\(941\) | 3.25537e7 | 1.19847 | 0.599235 | − | 0.800573i | \(-0.295472\pi\) | ||||
0.599235 | + | 0.800573i | \(0.295472\pi\) | |||||||
\(942\) | −6.08643e6 | −0.223478 | ||||||||
\(943\) | −5.54427e7 | −2.03032 | ||||||||
\(944\) | 2.52612e7 | 0.922624 | ||||||||
\(945\) | 3.07671e6 | 0.112075 | ||||||||
\(946\) | −82061.5 | −0.00298134 | ||||||||
\(947\) | 6.44146e6 | 0.233405 | 0.116702 | − | 0.993167i | \(-0.462768\pi\) | ||||
0.116702 | + | 0.993167i | \(0.462768\pi\) | |||||||
\(948\) | −9.13605e6 | −0.330170 | ||||||||
\(949\) | −138206. | −0.00498153 | ||||||||
\(950\) | 1.11541e6 | 0.0400984 | ||||||||
\(951\) | −1.17915e7 | −0.422782 | ||||||||
\(952\) | −2.07303e7 | −0.741332 | ||||||||
\(953\) | 2.40023e7 | 0.856093 | 0.428046 | − | 0.903757i | \(-0.359202\pi\) | ||||
0.428046 | + | 0.903757i | \(0.359202\pi\) | |||||||
\(954\) | 6.57242e6 | 0.233805 | ||||||||
\(955\) | −1.76405e7 | −0.625897 | ||||||||
\(956\) | −2.04405e7 | −0.723347 | ||||||||
\(957\) | −4.59604e6 | −0.162220 | ||||||||
\(958\) | −2.43699e7 | −0.857905 | ||||||||
\(959\) | 1.00867e7 | 0.354162 | ||||||||
\(960\) | −7.68806e6 | −0.269239 | ||||||||
\(961\) | 2.67012e6 | 0.0932656 | ||||||||
\(962\) | −391662. | −0.0136450 | ||||||||
\(963\) | 1.77181e7 | 0.615676 | ||||||||
\(964\) | −1.57494e7 | −0.545849 | ||||||||
\(965\) | −2.17859e6 | −0.0753107 | ||||||||
\(966\) | −2.57783e7 | −0.888815 | ||||||||
\(967\) | 4.13239e7 | 1.42113 | 0.710567 | − | 0.703630i | \(-0.248439\pi\) | ||||
0.710567 | + | 0.703630i | \(0.248439\pi\) | |||||||
\(968\) | 2.88136e6 | 0.0988345 | ||||||||
\(969\) | 2.23760e6 | 0.0765549 | ||||||||
\(970\) | −1.30880e6 | −0.0446627 | ||||||||
\(971\) | 8.46004e6 | 0.287955 | 0.143977 | − | 0.989581i | \(-0.454011\pi\) | ||||
0.143977 | + | 0.989581i | \(0.454011\pi\) | |||||||
\(972\) | 704991. | 0.0239341 | ||||||||
\(973\) | 1.98607e7 | 0.672531 | ||||||||
\(974\) | 3.81042e7 | 1.28699 | ||||||||
\(975\) | −1.63271e6 | −0.0550044 | ||||||||
\(976\) | −2.98863e6 | −0.100426 | ||||||||
\(977\) | 1.33050e7 | 0.445942 | 0.222971 | − | 0.974825i | \(-0.428425\pi\) | ||||
0.222971 | + | 0.974825i | \(0.428425\pi\) | |||||||
\(978\) | 5.74039e6 | 0.191909 | ||||||||
\(979\) | 218757. | 0.00729467 | ||||||||
\(980\) | −3.48995e6 | −0.116079 | ||||||||
\(981\) | 1.93103e7 | 0.640645 | ||||||||
\(982\) | 1.49672e6 | 0.0495293 | ||||||||
\(983\) | 2.90239e7 | 0.958014 | 0.479007 | − | 0.877811i | \(-0.340997\pi\) | ||||
0.479007 | + | 0.877811i | \(0.340997\pi\) | |||||||
\(984\) | 2.59237e7 | 0.853510 | ||||||||
\(985\) | −1.66899e7 | −0.548105 | ||||||||
\(986\) | −1.17948e7 | −0.386366 | ||||||||
\(987\) | −2.05645e7 | −0.671933 | ||||||||
\(988\) | 1.38082e6 | 0.0450033 | ||||||||
\(989\) | 573582. | 0.0186468 | ||||||||
\(990\) | −1.09745e6 | −0.0355875 | ||||||||
\(991\) | −4.88551e7 | −1.58025 | −0.790125 | − | 0.612946i | \(-0.789984\pi\) | ||||
−0.790125 | + | 0.612946i | \(0.789984\pi\) | |||||||
\(992\) | 2.27184e7 | 0.732992 | ||||||||
\(993\) | −2.61931e7 | −0.842974 | ||||||||
\(994\) | 7.57460e6 | 0.243161 | ||||||||
\(995\) | −1.74652e7 | −0.559264 | ||||||||
\(996\) | −2.75543e6 | −0.0880118 | ||||||||
\(997\) | −2.19218e7 | −0.698453 | −0.349227 | − | 0.937038i | \(-0.613556\pi\) | ||||
−0.349227 | + | 0.937038i | \(0.613556\pi\) | |||||||
\(998\) | 1.56787e7 | 0.498293 | ||||||||
\(999\) | −219623. | −0.00696248 |
(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 | 165.6.a.c.1.1 | ✓ | 3 | |
3.2 | odd | 2 | 495.6.a.b.1.3 | 3 | |||
5.4 | even | 2 | 825.6.a.g.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.6.a.c.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
495.6.a.b.1.3 | 3 | 3.2 | odd | 2 | |||
825.6.a.g.1.3 | 3 | 5.4 | even | 2 |