Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [495,6,Mod(1,495)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(495, 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("495.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 495 = 3^{2} \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 495.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: | \(79.3899908074\) |
Analytic rank: | \(0\) |
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: | no (minimal twist has level 165) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-4.78415\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 495.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.78415 | −1.02250 | −0.511251 | − | 0.859431i | \(-0.670818\pi\) | ||||
−0.511251 | + | 0.859431i | \(0.670818\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.45634 | 0.0455105 | ||||||||
\(5\) | −25.0000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 17.6498 | 0.136143 | 0.0680713 | − | 0.997680i | \(-0.478315\pi\) | ||||
0.0680713 | + | 0.997680i | \(0.478315\pi\) | |||||||
\(8\) | 176.669 | 0.975968 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 144.604 | 0.457277 | ||||||||
\(11\) | −121.000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 674.396 | 1.10677 | 0.553384 | − | 0.832926i | \(-0.313336\pi\) | ||||
0.553384 | + | 0.832926i | \(0.313336\pi\) | |||||||
\(14\) | −102.089 | −0.139206 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1068.48 | −1.04344 | ||||||||
\(17\) | 2117.62 | 1.77716 | 0.888579 | − | 0.458724i | \(-0.151693\pi\) | ||||
0.888579 | + | 0.458724i | \(0.151693\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2307.79 | −1.46660 | −0.733302 | − | 0.679903i | \(-0.762022\pi\) | ||||
−0.733302 | + | 0.679903i | \(0.762022\pi\) | |||||||
\(20\) | −36.4084 | −0.0203529 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 699.882 | 0.308296 | ||||||||
\(23\) | 3072.47 | 1.21107 | 0.605534 | − | 0.795820i | \(-0.292960\pi\) | ||||
0.605534 | + | 0.795820i | \(0.292960\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | −3900.80 | −1.13167 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 25.7040 | 0.00619591 | ||||||||
\(29\) | 1437.44 | 0.317391 | 0.158696 | − | 0.987328i | \(-0.449271\pi\) | ||||
0.158696 | + | 0.987328i | \(0.449271\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5157.66 | −0.963937 | −0.481969 | − | 0.876188i | \(-0.660078\pi\) | ||||
−0.481969 | + | 0.876188i | \(0.660078\pi\) | |||||||
\(32\) | 526.846 | 0.0909513 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −12248.6 | −1.81715 | ||||||||
\(35\) | −441.244 | −0.0608848 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6928.88 | 0.832067 | 0.416034 | − | 0.909349i | \(-0.363420\pi\) | ||||
0.416034 | + | 0.909349i | \(0.363420\pi\) | |||||||
\(38\) | 13348.6 | 1.49961 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4416.72 | −0.436466 | ||||||||
\(41\) | −2844.78 | −0.264295 | −0.132147 | − | 0.991230i | \(-0.542187\pi\) | ||||
−0.132147 | + | 0.991230i | \(0.542187\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11665.3 | −0.962113 | −0.481057 | − | 0.876689i | \(-0.659747\pi\) | ||||
−0.481057 | + | 0.876689i | \(0.659747\pi\) | |||||||
\(44\) | −176.217 | −0.0137219 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −17771.6 | −1.23832 | ||||||||
\(47\) | −3451.40 | −0.227903 | −0.113952 | − | 0.993486i | \(-0.536351\pi\) | ||||
−0.113952 | + | 0.993486i | \(0.536351\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −16495.5 | −0.981465 | ||||||||
\(50\) | −3615.09 | −0.204500 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 982.146 | 0.0503695 | ||||||||
\(53\) | 18167.6 | 0.888401 | 0.444200 | − | 0.895927i | \(-0.353488\pi\) | ||||
0.444200 | + | 0.895927i | \(0.353488\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3025.00 | 0.134840 | ||||||||
\(56\) | 3118.17 | 0.132871 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −8314.36 | −0.324533 | ||||||||
\(59\) | 8976.88 | 0.335734 | 0.167867 | − | 0.985810i | \(-0.446312\pi\) | ||||
0.167867 | + | 0.985810i | \(0.446312\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −378.820 | −0.0130349 | −0.00651746 | − | 0.999979i | \(-0.502075\pi\) | ||||
−0.00651746 | + | 0.999979i | \(0.502075\pi\) | |||||||
\(62\) | 29832.7 | 0.985628 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 31144.1 | 0.950441 | ||||||||
\(65\) | −16859.9 | −0.494962 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12233.7 | −0.332945 | −0.166473 | − | 0.986046i | \(-0.553238\pi\) | ||||
−0.166473 | + | 0.986046i | \(0.553238\pi\) | |||||||
\(68\) | 3083.97 | 0.0808793 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2552.22 | 0.0622548 | ||||||||
\(71\) | −55867.0 | −1.31525 | −0.657627 | − | 0.753344i | \(-0.728440\pi\) | ||||
−0.657627 | + | 0.753344i | \(0.728440\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 19739.6 | 0.433541 | 0.216771 | − | 0.976223i | \(-0.430448\pi\) | ||||
0.216771 | + | 0.976223i | \(0.430448\pi\) | |||||||
\(74\) | −40077.6 | −0.850791 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3360.92 | −0.0667459 | ||||||||
\(77\) | −2135.62 | −0.0410485 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13495.8 | −0.243293 | −0.121647 | − | 0.992573i | \(-0.538817\pi\) | ||||
−0.121647 | + | 0.992573i | \(0.538817\pi\) | |||||||
\(80\) | 26712.0 | 0.466640 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 16454.6 | 0.270242 | ||||||||
\(83\) | −42078.3 | −0.670444 | −0.335222 | − | 0.942139i | \(-0.608811\pi\) | ||||
−0.335222 | + | 0.942139i | \(0.608811\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −52940.5 | −0.794769 | ||||||||
\(86\) | 67474.0 | 0.983763 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −21376.9 | −0.294265 | ||||||||
\(89\) | 81223.2 | 1.08694 | 0.543469 | − | 0.839429i | \(-0.317110\pi\) | ||||
0.543469 | + | 0.839429i | \(0.317110\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11902.9 | 0.150678 | ||||||||
\(92\) | 4474.55 | 0.0551163 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 19963.4 | 0.233031 | ||||||||
\(95\) | 57694.8 | 0.655885 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 152101. | 1.64136 | 0.820680 | − | 0.571388i | \(-0.193595\pi\) | ||||
0.820680 | + | 0.571388i | \(0.193595\pi\) | |||||||
\(98\) | 95412.3 | 1.00355 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 910.210 | 0.00910210 | ||||||||
\(101\) | −95207.6 | −0.928684 | −0.464342 | − | 0.885656i | \(-0.653709\pi\) | ||||
−0.464342 | + | 0.885656i | \(0.653709\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −150824. | −1.40081 | −0.700403 | − | 0.713748i | \(-0.746996\pi\) | ||||
−0.700403 | + | 0.713748i | \(0.746996\pi\) | |||||||
\(104\) | 119145. | 1.08017 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −105084. | −0.908392 | ||||||||
\(107\) | −192242. | −1.62327 | −0.811633 | − | 0.584168i | \(-0.801421\pi\) | ||||
−0.811633 | + | 0.584168i | \(0.801421\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 96302.8 | 0.776377 | 0.388188 | − | 0.921580i | \(-0.373101\pi\) | ||||
0.388188 | + | 0.921580i | \(0.373101\pi\) | |||||||
\(110\) | −17497.0 | −0.137874 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −18858.5 | −0.142056 | ||||||||
\(113\) | 210371. | 1.54985 | 0.774926 | − | 0.632052i | \(-0.217787\pi\) | ||||
0.774926 | + | 0.632052i | \(0.217787\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −76811.8 | −0.541606 | ||||||||
\(116\) | 2093.39 | 0.0144446 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −51923.6 | −0.343289 | ||||||||
\(119\) | 37375.5 | 0.241947 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | 2191.15 | 0.0133282 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7511.29 | −0.0438692 | ||||||||
\(125\) | −15625.0 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −63529.8 | −0.349517 | −0.174758 | − | 0.984611i | \(-0.555914\pi\) | ||||
−0.174758 | + | 0.984611i | \(0.555914\pi\) | |||||||
\(128\) | −197001. | −1.06278 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 97520.1 | 0.506099 | ||||||||
\(131\) | 88396.0 | 0.450043 | 0.225022 | − | 0.974354i | \(-0.427755\pi\) | ||||
0.225022 | + | 0.974354i | \(0.427755\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −40732.0 | −0.199667 | ||||||||
\(134\) | 70761.8 | 0.340437 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 374118. | 1.73445 | ||||||||
\(137\) | 42642.4 | 0.194106 | 0.0970532 | − | 0.995279i | \(-0.469058\pi\) | ||||
0.0970532 | + | 0.995279i | \(0.469058\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 169503. | 0.744114 | 0.372057 | − | 0.928210i | \(-0.378653\pi\) | ||||
0.372057 | + | 0.928210i | \(0.378653\pi\) | |||||||
\(140\) | −642.599 | −0.00277090 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 323143. | 1.34485 | ||||||||
\(143\) | −81601.9 | −0.333703 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −35936.0 | −0.141942 | ||||||||
\(146\) | −114176. | −0.443297 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 10090.8 | 0.0378678 | ||||||||
\(149\) | 72462.8 | 0.267393 | 0.133696 | − | 0.991022i | \(-0.457315\pi\) | ||||
0.133696 | + | 0.991022i | \(0.457315\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −61316.2 | −0.218843 | −0.109422 | − | 0.993995i | \(-0.534900\pi\) | ||||
−0.109422 | + | 0.993995i | \(0.534900\pi\) | |||||||
\(152\) | −407716. | −1.43136 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 12352.7 | 0.0419722 | ||||||||
\(155\) | 128942. | 0.431086 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 505789. | 1.63765 | 0.818824 | − | 0.574045i | \(-0.194627\pi\) | ||||
0.818824 | + | 0.574045i | \(0.194627\pi\) | |||||||
\(158\) | 78061.5 | 0.248768 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −13171.2 | −0.0406747 | ||||||||
\(161\) | 54228.4 | 0.164878 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 387702. | 1.14295 | 0.571477 | − | 0.820618i | \(-0.306371\pi\) | ||||
0.571477 | + | 0.820618i | \(0.306371\pi\) | |||||||
\(164\) | −4142.95 | −0.0120282 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 243387. | 0.685530 | ||||||||
\(167\) | 635422. | 1.76308 | 0.881538 | − | 0.472113i | \(-0.156509\pi\) | ||||
0.881538 | + | 0.472113i | \(0.156509\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 83516.8 | 0.224935 | ||||||||
\(170\) | 306216. | 0.812653 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −16988.6 | −0.0437862 | ||||||||
\(173\) | 679820. | 1.72695 | 0.863473 | − | 0.504395i | \(-0.168284\pi\) | ||||
0.863473 | + | 0.504395i | \(0.168284\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 11031.1 | 0.0272285 | ||||||||
\(176\) | 129286. | 0.314609 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −469807. | −1.11140 | ||||||||
\(179\) | 63083.3 | 0.147157 | 0.0735787 | − | 0.997289i | \(-0.476558\pi\) | ||||
0.0735787 | + | 0.997289i | \(0.476558\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 523614. | 1.18800 | 0.593998 | − | 0.804466i | \(-0.297549\pi\) | ||||
0.593998 | + | 0.804466i | \(0.297549\pi\) | |||||||
\(182\) | −68848.3 | −0.154069 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 542810. | 1.18196 | ||||||||
\(185\) | −173222. | −0.372112 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −256232. | −0.535833 | ||||||||
\(188\) | −5026.39 | −0.0103720 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −333715. | −0.670644 | ||||||||
\(191\) | 684311. | 1.35728 | 0.678641 | − | 0.734470i | \(-0.262569\pi\) | ||||
0.678641 | + | 0.734470i | \(0.262569\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 527417. | 1.01920 | 0.509601 | − | 0.860411i | \(-0.329793\pi\) | ||||
0.509601 | + | 0.860411i | \(0.329793\pi\) | |||||||
\(194\) | −879777. | −1.67829 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −24023.0 | −0.0446669 | ||||||||
\(197\) | 467139. | 0.857591 | 0.428796 | − | 0.903402i | \(-0.358938\pi\) | ||||
0.428796 | + | 0.903402i | \(0.358938\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −436613. | −0.781563 | −0.390782 | − | 0.920483i | \(-0.627795\pi\) | ||||
−0.390782 | + | 0.920483i | \(0.627795\pi\) | |||||||
\(200\) | 110418. | 0.195194 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 550694. | 0.949581 | ||||||||
\(203\) | 25370.5 | 0.0432104 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 71119.4 | 0.118196 | ||||||||
\(206\) | 872389. | 1.43233 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −720580. | −1.15484 | ||||||||
\(209\) | 279243. | 0.442198 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −747312. | −1.15557 | −0.577785 | − | 0.816189i | \(-0.696083\pi\) | ||||
−0.577785 | + | 0.816189i | \(0.696083\pi\) | |||||||
\(212\) | 26458.2 | 0.0404315 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.11196e6 | 1.65979 | ||||||||
\(215\) | 291634. | 0.430270 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −91031.6 | −0.131233 | ||||||||
\(218\) | −557029. | −0.793847 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4405.41 | 0.00613663 | ||||||||
\(221\) | 1.42812e6 | 1.96690 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 870654. | 1.17242 | 0.586211 | − | 0.810159i | \(-0.300619\pi\) | ||||
0.586211 | + | 0.810159i | \(0.300619\pi\) | |||||||
\(224\) | 9298.71 | 0.0123823 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.21682e6 | −1.58473 | ||||||||
\(227\) | −82323.8 | −0.106038 | −0.0530189 | − | 0.998594i | \(-0.516884\pi\) | ||||
−0.0530189 | + | 0.998594i | \(0.516884\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −340134. | −0.428609 | −0.214305 | − | 0.976767i | \(-0.568748\pi\) | ||||
−0.214305 | + | 0.976767i | \(0.568748\pi\) | |||||||
\(230\) | 444291. | 0.553793 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 253951. | 0.309763 | ||||||||
\(233\) | 248384. | 0.299732 | 0.149866 | − | 0.988706i | \(-0.452116\pi\) | ||||
0.149866 | + | 0.988706i | \(0.452116\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 86284.9 | 0.101921 | ||||||||
\(236\) | 13073.4 | 0.0152794 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −216185. | −0.247391 | ||||||||
\(239\) | 1.37978e6 | 1.56248 | 0.781242 | − | 0.624229i | \(-0.214587\pi\) | ||||
0.781242 | + | 0.624229i | \(0.214587\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.53382e6 | −1.70110 | −0.850552 | − | 0.525891i | \(-0.823732\pi\) | ||||
−0.850552 | + | 0.525891i | \(0.823732\pi\) | |||||||
\(242\) | −84685.7 | −0.0929547 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −551.689 | −0.000593225 0 | ||||||||
\(245\) | 412387. | 0.438925 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.55637e6 | −1.62319 | ||||||||
\(248\) | −911199. | −0.940772 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 90377.3 | 0.0914554 | ||||||||
\(251\) | −338591. | −0.339227 | −0.169614 | − | 0.985511i | \(-0.554252\pi\) | ||||
−0.169614 | + | 0.985511i | \(0.554252\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −371769. | −0.365151 | ||||||||
\(254\) | 367466. | 0.357382 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 142872. | 0.136253 | ||||||||
\(257\) | −1.60985e6 | −1.52038 | −0.760189 | − | 0.649702i | \(-0.774894\pi\) | ||||
−0.760189 | + | 0.649702i | \(0.774894\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 122293. | 0.113280 | ||||||||
\(260\) | −24553.7 | −0.0225259 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −511295. | −0.460170 | ||||||||
\(263\) | −458118. | −0.408402 | −0.204201 | − | 0.978929i | \(-0.565460\pi\) | ||||
−0.204201 | + | 0.978929i | \(0.565460\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −454191. | −0.397305 | ||||||||
\(266\) | 235600. | 0.204160 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −17816.4 | −0.0151525 | ||||||||
\(269\) | 692380. | 0.583397 | 0.291698 | − | 0.956510i | \(-0.405780\pi\) | ||||
0.291698 | + | 0.956510i | \(0.405780\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −486690. | −0.402558 | −0.201279 | − | 0.979534i | \(-0.564510\pi\) | ||||
−0.201279 | + | 0.979534i | \(0.564510\pi\) | |||||||
\(272\) | −2.26264e6 | −1.85436 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −246650. | −0.198474 | ||||||||
\(275\) | −75625.0 | −0.0603023 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.38271e6 | 1.86583 | 0.932915 | − | 0.360098i | \(-0.117257\pi\) | ||||
0.932915 | + | 0.360098i | \(0.117257\pi\) | |||||||
\(278\) | −980428. | −0.760858 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −77954.1 | −0.0594216 | ||||||||
\(281\) | −1.12154e6 | −0.847320 | −0.423660 | − | 0.905821i | \(-0.639255\pi\) | ||||
−0.423660 | + | 0.905821i | \(0.639255\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 965956. | 0.716954 | 0.358477 | − | 0.933539i | \(-0.383296\pi\) | ||||
0.358477 | + | 0.933539i | \(0.383296\pi\) | |||||||
\(284\) | −81361.1 | −0.0598578 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 471997. | 0.341212 | ||||||||
\(287\) | −50209.6 | −0.0359817 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.06446e6 | 2.15829 | ||||||||
\(290\) | 207859. | 0.145136 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 28747.4 | 0.0197307 | ||||||||
\(293\) | −2.20819e6 | −1.50269 | −0.751343 | − | 0.659912i | \(-0.770594\pi\) | ||||
−0.751343 | + | 0.659912i | \(0.770594\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −224422. | −0.150145 | ||||||||
\(296\) | 1.22412e6 | 0.812071 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −419135. | −0.273410 | ||||||||
\(299\) | 2.07206e6 | 1.34037 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −205891. | −0.130985 | ||||||||
\(302\) | 354662. | 0.223768 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.46584e6 | 1.53031 | ||||||||
\(305\) | 9470.49 | 0.00582939 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 805480. | 0.487763 | 0.243881 | − | 0.969805i | \(-0.421579\pi\) | ||||
0.243881 | + | 0.969805i | \(0.421579\pi\) | |||||||
\(308\) | −3110.18 | −0.00186814 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −745817. | −0.440786 | ||||||||
\(311\) | 870766. | 0.510505 | 0.255253 | − | 0.966874i | \(-0.417841\pi\) | ||||
0.255253 | + | 0.966874i | \(0.417841\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.16630e6 | −1.82680 | −0.913400 | − | 0.407063i | \(-0.866553\pi\) | ||||
−0.913400 | + | 0.407063i | \(0.866553\pi\) | |||||||
\(314\) | −2.92556e6 | −1.67450 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −19654.4 | −0.0110724 | ||||||||
\(317\) | −1.72288e6 | −0.962955 | −0.481478 | − | 0.876458i | \(-0.659900\pi\) | ||||
−0.481478 | + | 0.876458i | \(0.659900\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −173930. | −0.0956970 | ||||||||
\(320\) | −778602. | −0.425050 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −313665. | −0.168588 | ||||||||
\(323\) | −4.88703e6 | −2.60639 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 421497. | 0.221354 | ||||||||
\(326\) | −2.24252e6 | −1.16867 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −502584. | −0.257943 | ||||||||
\(329\) | −60916.3 | −0.0310273 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.20493e6 | −1.60786 | −0.803932 | − | 0.594722i | \(-0.797262\pi\) | ||||
−0.803932 | + | 0.594722i | \(0.797262\pi\) | |||||||
\(332\) | −61280.1 | −0.0305122 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3.67537e6 | −1.80275 | ||||||||
\(335\) | 305844. | 0.148898 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.44638e6 | 1.17341 | 0.586703 | − | 0.809802i | \(-0.300425\pi\) | ||||
0.586703 | + | 0.809802i | \(0.300425\pi\) | |||||||
\(338\) | −483073. | −0.229996 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −77099.2 | −0.0361703 | ||||||||
\(341\) | 624077. | 0.290638 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −587781. | −0.269762 | ||||||||
\(344\) | −2.06090e6 | −0.938992 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.93218e6 | −1.76581 | ||||||||
\(347\) | 3.05055e6 | 1.36005 | 0.680025 | − | 0.733189i | \(-0.261969\pi\) | ||||
0.680025 | + | 0.733189i | \(0.261969\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.08755e6 | −1.35691 | −0.678454 | − | 0.734643i | \(-0.737350\pi\) | ||||
−0.678454 | + | 0.734643i | \(0.737350\pi\) | |||||||
\(350\) | −63805.5 | −0.0278412 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −63748.4 | −0.0274228 | ||||||||
\(353\) | −2.98932e6 | −1.27684 | −0.638418 | − | 0.769690i | \(-0.720411\pi\) | ||||
−0.638418 | + | 0.769690i | \(0.720411\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.39668e6 | 0.588200 | ||||||||
\(356\) | 118288. | 0.0494671 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −364883. | −0.150469 | ||||||||
\(359\) | 2.29991e6 | 0.941836 | 0.470918 | − | 0.882177i | \(-0.343923\pi\) | ||||
0.470918 | + | 0.882177i | \(0.343923\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.84981e6 | 1.15093 | ||||||||
\(362\) | −3.02866e6 | −1.21473 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 17334.7 | 0.00685743 | ||||||||
\(365\) | −493489. | −0.193885 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.58207e6 | 1.38825 | 0.694127 | − | 0.719852i | \(-0.255790\pi\) | ||||
0.694127 | + | 0.719852i | \(0.255790\pi\) | |||||||
\(368\) | −3.28288e6 | −1.26368 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.00194e6 | 0.380485 | ||||||||
\(371\) | 320655. | 0.120949 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 511254. | 0.190268 | 0.0951338 | − | 0.995464i | \(-0.469672\pi\) | ||||
0.0951338 | + | 0.995464i | \(0.469672\pi\) | |||||||
\(374\) | 1.48208e6 | 0.547891 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −609755. | −0.222426 | ||||||||
\(377\) | 969404. | 0.351278 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.45209e6 | 0.876877 | 0.438438 | − | 0.898761i | \(-0.355532\pi\) | ||||
0.438438 | + | 0.898761i | \(0.355532\pi\) | |||||||
\(380\) | 84023.0 | 0.0298497 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3.95815e6 | −1.38782 | ||||||||
\(383\) | 1.46315e6 | 0.509674 | 0.254837 | − | 0.966984i | \(-0.417978\pi\) | ||||
0.254837 | + | 0.966984i | \(0.417978\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 53390.5 | 0.0183575 | ||||||||
\(386\) | −3.05065e6 | −1.04214 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 221511. | 0.0746991 | ||||||||
\(389\) | 803978. | 0.269383 | 0.134691 | − | 0.990888i | \(-0.456996\pi\) | ||||
0.134691 | + | 0.990888i | \(0.456996\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.50633e6 | 2.15226 | ||||||||
\(392\) | −2.91424e6 | −0.957878 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.70200e6 | −0.876889 | ||||||||
\(395\) | 337394. | 0.108804 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.87304e6 | −0.914883 | −0.457441 | − | 0.889240i | \(-0.651234\pi\) | ||||
−0.457441 | + | 0.889240i | \(0.651234\pi\) | |||||||
\(398\) | 2.52543e6 | 0.799150 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −667801. | −0.208688 | ||||||||
\(401\) | 3.45072e6 | 1.07164 | 0.535820 | − | 0.844332i | \(-0.320002\pi\) | ||||
0.535820 | + | 0.844332i | \(0.320002\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.47831e6 | −1.06685 | ||||||||
\(404\) | −138654. | −0.0422649 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −146747. | −0.0441827 | ||||||||
\(407\) | −838394. | −0.250878 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.17776e6 | −0.348136 | −0.174068 | − | 0.984734i | \(-0.555691\pi\) | ||||
−0.174068 | + | 0.984734i | \(0.555691\pi\) | |||||||
\(410\) | −411365. | −0.120856 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −219651. | −0.0637513 | ||||||||
\(413\) | 158440. | 0.0457077 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.05196e6 | 0.299832 | ||||||||
\(416\) | 355303. | 0.100662 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.61518e6 | −0.452148 | ||||||||
\(419\) | 443011. | 0.123276 | 0.0616381 | − | 0.998099i | \(-0.480368\pi\) | ||||
0.0616381 | + | 0.998099i | \(0.480368\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.41894e6 | −0.940127 | −0.470063 | − | 0.882633i | \(-0.655769\pi\) | ||||
−0.470063 | + | 0.882633i | \(0.655769\pi\) | |||||||
\(422\) | 4.32256e6 | 1.18157 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.20966e6 | 0.867050 | ||||||||
\(425\) | 1.32351e6 | 0.355432 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6686.08 | −0.00177461 | ||||||||
\(428\) | −279969. | −0.0738756 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.68685e6 | −0.439952 | ||||||||
\(431\) | 4.24640e6 | 1.10110 | 0.550551 | − | 0.834801i | \(-0.314417\pi\) | ||||
0.550551 | + | 0.834801i | \(0.314417\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.03407e6 | −0.265050 | −0.132525 | − | 0.991180i | \(-0.542309\pi\) | ||||
−0.132525 | + | 0.991180i | \(0.542309\pi\) | |||||||
\(434\) | 526540. | 0.134186 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 140249. | 0.0353333 | ||||||||
\(437\) | −7.09063e6 | −1.77616 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.55155e6 | 0.879542 | 0.439771 | − | 0.898110i | \(-0.355060\pi\) | ||||
0.439771 | + | 0.898110i | \(0.355060\pi\) | |||||||
\(440\) | 534424. | 0.131599 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −8.26043e6 | −2.01116 | ||||||||
\(443\) | −2.35135e6 | −0.569257 | −0.284629 | − | 0.958638i | \(-0.591870\pi\) | ||||
−0.284629 | + | 0.958638i | \(0.591870\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.03058e6 | −0.486094 | ||||||||
\(446\) | −5.03599e6 | −1.19880 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 549685. | 0.129395 | ||||||||
\(449\) | −3.01947e6 | −0.706831 | −0.353415 | − | 0.935467i | \(-0.614980\pi\) | ||||
−0.353415 | + | 0.935467i | \(0.614980\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 344218. | 0.0796878 | ||||||||
\(452\) | 306371. | 0.0705345 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 476173. | 0.108424 | ||||||||
\(455\) | −297573. | −0.0673853 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.80671e6 | 0.852626 | 0.426313 | − | 0.904576i | \(-0.359812\pi\) | ||||
0.426313 | + | 0.904576i | \(0.359812\pi\) | |||||||
\(458\) | 1.96738e6 | 0.438254 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −111864. | −0.0246487 | ||||||||
\(461\) | −7.43481e6 | −1.62936 | −0.814680 | − | 0.579910i | \(-0.803088\pi\) | ||||
−0.814680 | + | 0.579910i | \(0.803088\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −108747. | −0.0235757 | −0.0117879 | − | 0.999931i | \(-0.503752\pi\) | ||||
−0.0117879 | + | 0.999931i | \(0.503752\pi\) | |||||||
\(464\) | −1.53588e6 | −0.331178 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.43669e6 | −0.306477 | ||||||||
\(467\) | 6.85473e6 | 1.45445 | 0.727224 | − | 0.686400i | \(-0.240810\pi\) | ||||
0.727224 | + | 0.686400i | \(0.240810\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −215923. | −0.0453280 | ||||||||
\(470\) | −499085. | −0.104215 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.58594e6 | 0.327666 | ||||||||
\(473\) | 1.41151e6 | 0.290088 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.44237e6 | −0.293321 | ||||||||
\(476\) | 54431.3 | 0.0110111 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −7.98085e6 | −1.59764 | ||||||||
\(479\) | 9.48659e6 | 1.88917 | 0.944585 | − | 0.328266i | \(-0.106464\pi\) | ||||
0.944585 | + | 0.328266i | \(0.106464\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.67281e6 | 0.920905 | ||||||||
\(482\) | 8.87182e6 | 1.73938 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 21322.2 | 0.00413732 | ||||||||
\(485\) | −3.80253e6 | −0.734038 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.79771e6 | 1.87198 | 0.935992 | − | 0.352021i | \(-0.114506\pi\) | ||||
0.935992 | + | 0.352021i | \(0.114506\pi\) | |||||||
\(488\) | −66925.7 | −0.0127216 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.38531e6 | −0.448801 | ||||||||
\(491\) | −9.17094e6 | −1.71676 | −0.858381 | − | 0.513012i | \(-0.828530\pi\) | ||||
−0.858381 | + | 0.513012i | \(0.828530\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.04395e6 | 0.564054 | ||||||||
\(494\) | 9.00225e6 | 1.65972 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.51087e6 | 1.00581 | ||||||||
\(497\) | −986040. | −0.179062 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.91031e6 | −0.343441 | −0.171720 | − | 0.985146i | \(-0.554933\pi\) | ||||
−0.171720 | + | 0.985146i | \(0.554933\pi\) | |||||||
\(500\) | −22755.2 | −0.00407058 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.95846e6 | 0.346861 | ||||||||
\(503\) | −7.08413e6 | −1.24844 | −0.624219 | − | 0.781250i | \(-0.714583\pi\) | ||||
−0.624219 | + | 0.781250i | \(0.714583\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.38019e6 | 0.415320 | ||||||||
\(506\) | 2.15037e6 | 0.373367 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −92520.7 | −0.0159067 | ||||||||
\(509\) | 7.51321e6 | 1.28538 | 0.642689 | − | 0.766127i | \(-0.277819\pi\) | ||||
0.642689 | + | 0.766127i | \(0.277819\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 348398. | 0.0590234 | ||||||||
\(512\) | 5.47764e6 | 0.923461 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 9.31158e6 | 1.55459 | ||||||||
\(515\) | 3.77060e6 | 0.626459 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 417619. | 0.0687154 | ||||||||
\(518\) | −707361. | −0.115829 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.97862e6 | −0.483066 | ||||||||
\(521\) | 1.03994e7 | 1.67847 | 0.839235 | − | 0.543770i | \(-0.183003\pi\) | ||||
0.839235 | + | 0.543770i | \(0.183003\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.14037e6 | −1.46120 | −0.730600 | − | 0.682806i | \(-0.760759\pi\) | ||||
−0.730600 | + | 0.682806i | \(0.760759\pi\) | |||||||
\(524\) | 128734. | 0.0204817 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.64982e6 | 0.417592 | ||||||||
\(527\) | −1.09220e7 | −1.71307 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.00374e6 | 0.466684 | ||||||||
\(530\) | 2.62711e6 | 0.406245 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −59319.5 | −0.00908695 | ||||||||
\(533\) | −1.91850e6 | −0.292513 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.80606e6 | 0.725947 | ||||||||
\(536\) | −2.16132e6 | −0.324944 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −4.00483e6 | −0.596524 | ||||||||
\(539\) | 1.99595e6 | 0.295923 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.47380e6 | 0.950969 | 0.475484 | − | 0.879724i | \(-0.342273\pi\) | ||||
0.475484 | + | 0.879724i | \(0.342273\pi\) | |||||||
\(542\) | 2.81508e6 | 0.411617 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.11566e6 | 0.161635 | ||||||||
\(545\) | −2.40757e6 | −0.347206 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −226463. | −0.0323616 | −0.0161808 | − | 0.999869i | \(-0.505151\pi\) | ||||
−0.0161808 | + | 0.999869i | \(0.505151\pi\) | |||||||
\(548\) | 62101.6 | 0.00883388 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 437426. | 0.0616592 | ||||||||
\(551\) | −3.31731e6 | −0.465487 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −238197. | −0.0331226 | ||||||||
\(554\) | −1.37819e7 | −1.90781 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 246853. | 0.0338650 | ||||||||
\(557\) | 5.45555e6 | 0.745076 | 0.372538 | − | 0.928017i | \(-0.378488\pi\) | ||||
0.372538 | + | 0.928017i | \(0.378488\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.86706e6 | −1.06484 | ||||||||
\(560\) | 471461. | 0.0635296 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6.48712e6 | 0.866386 | ||||||||
\(563\) | 1.30266e7 | 1.73205 | 0.866024 | − | 0.500002i | \(-0.166667\pi\) | ||||
0.866024 | + | 0.500002i | \(0.166667\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.25928e6 | −0.693115 | ||||||||
\(566\) | −5.58723e6 | −0.733087 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9.86997e6 | −1.28365 | ||||||||
\(569\) | −3.02736e6 | −0.391998 | −0.195999 | − | 0.980604i | \(-0.562795\pi\) | ||||
−0.195999 | + | 0.980604i | \(0.562795\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.79560e6 | 1.25731 | 0.628653 | − | 0.777686i | \(-0.283607\pi\) | ||||
0.628653 | + | 0.777686i | \(0.283607\pi\) | |||||||
\(572\) | −118840. | −0.0151870 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 290420. | 0.0367914 | ||||||||
\(575\) | 1.92029e6 | 0.242213 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 56282.7 | 0.00703778 | 0.00351889 | − | 0.999994i | \(-0.498880\pi\) | ||||
0.00351889 | + | 0.999994i | \(0.498880\pi\) | |||||||
\(578\) | −1.77253e7 | −2.20686 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −52334.9 | −0.00645983 | ||||||||
\(581\) | −742671. | −0.0912759 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.19829e6 | −0.267863 | ||||||||
\(584\) | 3.48737e6 | 0.423122 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.27725e7 | 1.53650 | ||||||||
\(587\) | 7.92842e6 | 0.949711 | 0.474855 | − | 0.880064i | \(-0.342500\pi\) | ||||
0.474855 | + | 0.880064i | \(0.342500\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.19028e7 | 1.41371 | ||||||||
\(590\) | 1.29809e6 | 0.153523 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −7.40338e6 | −0.868212 | ||||||||
\(593\) | 5.11910e6 | 0.597801 | 0.298900 | − | 0.954284i | \(-0.403380\pi\) | ||||
0.298900 | + | 0.954284i | \(0.403380\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −934388. | −0.108202 | ||||||||
\(596\) | 105530. | 0.0121692 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.19851e7 | −1.37053 | ||||||||
\(599\) | 1.00831e7 | 1.14822 | 0.574110 | − | 0.818778i | \(-0.305348\pi\) | ||||
0.574110 | + | 0.818778i | \(0.305348\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.32233e7 | 1.49332 | 0.746659 | − | 0.665207i | \(-0.231657\pi\) | ||||
0.746659 | + | 0.665207i | \(0.231657\pi\) | |||||||
\(602\) | 1.19090e6 | 0.133932 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −89296.9 | −0.00995965 | ||||||||
\(605\) | −366025. | −0.0406558 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 937160. | 0.103239 | 0.0516193 | − | 0.998667i | \(-0.483562\pi\) | ||||
0.0516193 | + | 0.998667i | \(0.483562\pi\) | |||||||
\(608\) | −1.21585e6 | −0.133390 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −54778.7 | −0.00596056 | ||||||||
\(611\) | −2.32761e6 | −0.252236 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.05919e6 | 0.328818 | 0.164409 | − | 0.986392i | \(-0.447428\pi\) | ||||
0.164409 | + | 0.986392i | \(0.447428\pi\) | |||||||
\(614\) | −4.65901e6 | −0.498738 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −377298. | −0.0400620 | ||||||||
\(617\) | −8.74474e6 | −0.924771 | −0.462385 | − | 0.886679i | \(-0.653006\pi\) | ||||
−0.462385 | + | 0.886679i | \(0.653006\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.14486e6 | −0.434793 | −0.217397 | − | 0.976083i | \(-0.569757\pi\) | ||||
−0.217397 | + | 0.976083i | \(0.569757\pi\) | |||||||
\(620\) | 187782. | 0.0196189 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −5.03664e6 | −0.521993 | ||||||||
\(623\) | 1.43357e6 | 0.147979 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 1.83143e7 | 1.86791 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 736598. | 0.0745301 | ||||||||
\(629\) | 1.46727e7 | 1.47872 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.44508e6 | −0.444433 | −0.222216 | − | 0.974997i | \(-0.571329\pi\) | ||||
−0.222216 | + | 0.974997i | \(0.571329\pi\) | |||||||
\(632\) | −2.38429e6 | −0.237446 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9.96537e6 | 0.984624 | ||||||||
\(635\) | 1.58825e6 | 0.156309 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.11245e7 | −1.08625 | ||||||||
\(638\) | 1.00604e6 | 0.0978504 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 4.92502e6 | 0.475289 | ||||||||
\(641\) | −1.08278e7 | −1.04086 | −0.520432 | − | 0.853903i | \(-0.674229\pi\) | ||||
−0.520432 | + | 0.853903i | \(0.674229\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.23064e7 | −1.17383 | −0.586915 | − | 0.809649i | \(-0.699658\pi\) | ||||
−0.586915 | + | 0.809649i | \(0.699658\pi\) | |||||||
\(644\) | 78974.7 | 0.00750367 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.82673e7 | 2.66504 | ||||||||
\(647\) | 1.26477e7 | 1.18782 | 0.593912 | − | 0.804530i | \(-0.297583\pi\) | ||||
0.593912 | + | 0.804530i | \(0.297583\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.08620e6 | −0.101228 | ||||||||
\(650\) | −2.43800e6 | −0.226334 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 564624. | 0.0520164 | ||||||||
\(653\) | 578855. | 0.0531235 | 0.0265618 | − | 0.999647i | \(-0.491544\pi\) | ||||
0.0265618 | + | 0.999647i | \(0.491544\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.20990e6 | −0.201265 | ||||||||
\(656\) | 3.03959e6 | 0.275775 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 352349. | 0.0317255 | ||||||||
\(659\) | −1.71481e7 | −1.53816 | −0.769081 | − | 0.639151i | \(-0.779286\pi\) | ||||
−0.769081 | + | 0.639151i | \(0.779286\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.99329e6 | 0.622555 | 0.311278 | − | 0.950319i | \(-0.399243\pi\) | ||||
0.311278 | + | 0.950319i | \(0.399243\pi\) | |||||||
\(662\) | 1.85378e7 | 1.64404 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −7.43392e6 | −0.654332 | ||||||||
\(665\) | 1.01830e6 | 0.0892939 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.41649e6 | 0.384382 | ||||||||
\(668\) | 925387. | 0.0802384 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.76904e6 | −0.152248 | ||||||||
\(671\) | 45837.2 | 0.00393017 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.98109e7 | 1.68604 | 0.843018 | − | 0.537885i | \(-0.180777\pi\) | ||||
0.843018 | + | 0.537885i | \(0.180777\pi\) | |||||||
\(674\) | −1.41502e7 | −1.19981 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 121628. | 0.0102369 | ||||||||
\(677\) | 2.85012e6 | 0.238996 | 0.119498 | − | 0.992834i | \(-0.461871\pi\) | ||||
0.119498 | + | 0.992834i | \(0.461871\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.68455e6 | 0.223459 | ||||||||
\(680\) | −9.35295e6 | −0.775669 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3.60975e6 | −0.297178 | ||||||||
\(683\) | −4.58865e6 | −0.376386 | −0.188193 | − | 0.982132i | \(-0.560263\pi\) | ||||
−0.188193 | + | 0.982132i | \(0.560263\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.06606e6 | −0.0868070 | ||||||||
\(686\) | 3.39981e6 | 0.275832 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.24642e7 | 1.00391 | ||||||||
\(689\) | 1.22522e7 | 0.983254 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.65609e6 | −0.211616 | −0.105808 | − | 0.994387i | \(-0.533743\pi\) | ||||
−0.105808 | + | 0.994387i | \(0.533743\pi\) | |||||||
\(692\) | 990046. | 0.0785942 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.76448e7 | −1.39065 | ||||||||
\(695\) | −4.23757e6 | −0.332778 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.02416e6 | −0.469693 | ||||||||
\(698\) | 1.78588e7 | 1.38744 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 16065.0 | 0.00123918 | ||||||||
\(701\) | 7.90907e6 | 0.607898 | 0.303949 | − | 0.952688i | \(-0.401695\pi\) | ||||
0.303949 | + | 0.952688i | \(0.401695\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.59904e7 | −1.22031 | ||||||||
\(704\) | −3.76843e6 | −0.286569 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.72906e7 | 1.30557 | ||||||||
\(707\) | −1.68039e6 | −0.126433 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.38057e7 | −1.77855 | −0.889273 | − | 0.457378i | \(-0.848789\pi\) | ||||
−0.889273 | + | 0.457378i | \(0.848789\pi\) | |||||||
\(710\) | −8.07857e6 | −0.601435 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.43496e7 | 1.06082 | ||||||||
\(713\) | −1.58468e7 | −1.16739 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.04005e6 | 0.149237 | ||||||||
\(716\) | 91870.5 | 0.00669720 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.33030e7 | −0.963029 | ||||||||
\(719\) | 2.00866e7 | 1.44905 | 0.724527 | − | 0.689246i | \(-0.242058\pi\) | ||||
0.724527 | + | 0.689246i | \(0.242058\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.66201e6 | −0.190709 | ||||||||
\(722\) | −1.64837e7 | −1.17683 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 762558. | 0.0540663 | ||||||||
\(725\) | 898400. | 0.0634782 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.00897e7 | −0.708012 | −0.354006 | − | 0.935243i | \(-0.615181\pi\) | ||||
−0.354006 | + | 0.935243i | \(0.615181\pi\) | |||||||
\(728\) | 2.10288e6 | 0.147057 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.85441e6 | 0.198248 | ||||||||
\(731\) | −2.47028e7 | −1.70983 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.48230e7 | −1.01901 | −0.509504 | − | 0.860468i | \(-0.670171\pi\) | ||||
−0.509504 | + | 0.860468i | \(0.670171\pi\) | |||||||
\(734\) | −2.07192e7 | −1.41949 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.61872e6 | 0.110148 | ||||||||
\(737\) | 1.48028e6 | 0.100387 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.85393e7 | −1.24877 | −0.624383 | − | 0.781118i | \(-0.714650\pi\) | ||||
−0.624383 | + | 0.781118i | \(0.714650\pi\) | |||||||
\(740\) | −252269. | −0.0169350 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.85471e6 | −0.123671 | ||||||||
\(743\) | 8.68829e6 | 0.577381 | 0.288690 | − | 0.957423i | \(-0.406780\pi\) | ||||
0.288690 | + | 0.957423i | \(0.406780\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.81157e6 | −0.119582 | ||||||||
\(746\) | −2.95717e6 | −0.194549 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −373160. | −0.0243860 | ||||||||
\(749\) | −3.39303e6 | −0.220995 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.37377e7 | −0.888821 | −0.444411 | − | 0.895823i | \(-0.646587\pi\) | ||||
−0.444411 | + | 0.895823i | \(0.646587\pi\) | |||||||
\(752\) | 3.68776e6 | 0.237803 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −5.60717e6 | −0.359183 | ||||||||
\(755\) | 1.53291e6 | 0.0978696 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.59097e6 | 0.354607 | 0.177304 | − | 0.984156i | \(-0.443263\pi\) | ||||
0.177304 | + | 0.984156i | \(0.443263\pi\) | |||||||
\(758\) | −1.41832e7 | −0.896608 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.01929e7 | 0.640123 | ||||||||
\(761\) | 2.44147e7 | 1.52823 | 0.764117 | − | 0.645078i | \(-0.223175\pi\) | ||||
0.764117 | + | 0.645078i | \(0.223175\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.69972e6 | 0.105698 | ||||||||
\(764\) | 996586. | 0.0617706 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −8.46309e6 | −0.521143 | ||||||||
\(767\) | 6.05397e6 | 0.371580 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.99742e7 | 1.21802 | 0.609008 | − | 0.793164i | \(-0.291568\pi\) | ||||
0.609008 | + | 0.793164i | \(0.291568\pi\) | |||||||
\(770\) | −308819. | −0.0187705 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 768096. | 0.0463844 | ||||||||
\(773\) | 2.64430e7 | 1.59170 | 0.795852 | − | 0.605492i | \(-0.207024\pi\) | ||||
0.795852 | + | 0.605492i | \(0.207024\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.22354e6 | −0.192787 | ||||||||
\(776\) | 2.68716e7 | 1.60191 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.65032e6 | −0.275445 | ||||||||
\(779\) | 6.56515e6 | 0.387616 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.75991e6 | 0.396564 | ||||||||
\(782\) | −3.76336e7 | −2.20069 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.76251e7 | 1.02410 | ||||||||
\(785\) | −1.26447e7 | −0.732378 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.87892e6 | −0.165689 | −0.0828443 | − | 0.996562i | \(-0.526400\pi\) | ||||
−0.0828443 | + | 0.996562i | \(0.526400\pi\) | |||||||
\(788\) | 680310. | 0.0390294 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.95154e6 | −0.111252 | ||||||||
\(791\) | 3.71300e6 | 0.211001 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −255474. | −0.0144266 | ||||||||
\(794\) | 1.66181e7 | 0.935469 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −635855. | −0.0355693 | ||||||||
\(797\) | 2.55634e7 | 1.42552 | 0.712759 | − | 0.701409i | \(-0.247446\pi\) | ||||
0.712759 | + | 0.701409i | \(0.247446\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.30875e6 | −0.405020 | ||||||||
\(800\) | 329279. | 0.0181903 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.99595e7 | −1.09575 | ||||||||
\(803\) | −2.38849e6 | −0.130718 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.35571e6 | −0.0737356 | ||||||||
\(806\) | 2.01190e7 | 1.09086 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.68202e7 | −0.906365 | ||||||||
\(809\) | 2.32458e6 | 0.124874 | 0.0624371 | − | 0.998049i | \(-0.480113\pi\) | ||||
0.0624371 | + | 0.998049i | \(0.480113\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.44240e7 | 0.770076 | 0.385038 | − | 0.922901i | \(-0.374188\pi\) | ||||
0.385038 | + | 0.922901i | \(0.374188\pi\) | |||||||
\(812\) | 36947.9 | 0.00196653 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4.84939e6 | 0.256523 | ||||||||
\(815\) | −9.69255e6 | −0.511145 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.69212e7 | 1.41104 | ||||||||
\(818\) | 6.81233e6 | 0.355969 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 103574. | 0.00537916 | ||||||||
\(821\) | −9.95289e6 | −0.515337 | −0.257668 | − | 0.966233i | \(-0.582954\pi\) | ||||
−0.257668 | + | 0.966233i | \(0.582954\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.46452e7 | 1.26833 | 0.634165 | − | 0.773198i | \(-0.281344\pi\) | ||||
0.634165 | + | 0.773198i | \(0.281344\pi\) | |||||||
\(824\) | −2.66460e7 | −1.36714 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −916439. | −0.0467362 | ||||||||
\(827\) | 2.09014e7 | 1.06270 | 0.531351 | − | 0.847152i | \(-0.321685\pi\) | ||||
0.531351 | + | 0.847152i | \(0.321685\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.31387e6 | −0.420162 | −0.210081 | − | 0.977684i | \(-0.567373\pi\) | ||||
−0.210081 | + | 0.977684i | \(0.567373\pi\) | |||||||
\(830\) | −6.08467e6 | −0.306579 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.10034e7 | 1.05192 | ||||||||
\(833\) | −3.49312e7 | −1.74422 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.58855e7 | −0.788472 | ||||||||
\(836\) | 406671. | 0.0201246 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −2.56244e6 | −0.126050 | ||||||||
\(839\) | 4.03176e7 | 1.97738 | 0.988690 | − | 0.149977i | \(-0.0479198\pi\) | ||||
0.988690 | + | 0.149977i | \(0.0479198\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.84449e7 | −0.899263 | ||||||||
\(842\) | 1.97757e7 | 0.961282 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.08834e6 | −0.0525905 | ||||||||
\(845\) | −2.08792e6 | −0.100594 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 258410. | 0.0123766 | ||||||||
\(848\) | −1.94118e7 | −0.926992 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −7.65539e6 | −0.363430 | ||||||||
\(851\) | 2.12888e7 | 1.00769 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.11646e7 | −0.995951 | −0.497976 | − | 0.867191i | \(-0.665923\pi\) | ||||
−0.497976 | + | 0.867191i | \(0.665923\pi\) | |||||||
\(854\) | 38673.3 | 0.00181454 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.39633e7 | −1.58425 | ||||||||
\(857\) | 1.03622e7 | 0.481946 | 0.240973 | − | 0.970532i | \(-0.422533\pi\) | ||||
0.240973 | + | 0.970532i | \(0.422533\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.77409e7 | −0.820336 | −0.410168 | − | 0.912010i | \(-0.634530\pi\) | ||||
−0.410168 | + | 0.912010i | \(0.634530\pi\) | |||||||
\(860\) | 424716. | 0.0195818 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.45618e7 | −1.12588 | ||||||||
\(863\) | 2.62577e6 | 0.120014 | 0.0600068 | − | 0.998198i | \(-0.480888\pi\) | ||||
0.0600068 | + | 0.998198i | \(0.480888\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.69955e7 | −0.772314 | ||||||||
\(866\) | 5.98118e6 | 0.271014 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −132572. | −0.00597247 | ||||||||
\(869\) | 1.63299e6 | 0.0733557 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.25039e6 | −0.368493 | ||||||||
\(872\) | 1.70137e7 | 0.757718 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 4.10132e7 | 1.81612 | ||||||||
\(875\) | −275778. | −0.0121770 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.30171e6 | 0.320572 | 0.160286 | − | 0.987071i | \(-0.448758\pi\) | ||||
0.160286 | + | 0.987071i | \(0.448758\pi\) | |||||||
\(878\) | −2.05427e7 | −0.899334 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −3.23216e6 | −0.140697 | ||||||||
\(881\) | −6.08524e6 | −0.264142 | −0.132071 | − | 0.991240i | \(-0.542163\pi\) | ||||
−0.132071 | + | 0.991240i | \(0.542163\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.66311e7 | 0.717828 | 0.358914 | − | 0.933371i | \(-0.383147\pi\) | ||||
0.358914 | + | 0.933371i | \(0.383147\pi\) | |||||||
\(884\) | 2.07981e6 | 0.0895146 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.36006e7 | 0.582067 | ||||||||
\(887\) | 1.47741e7 | 0.630511 | 0.315256 | − | 0.949007i | \(-0.397910\pi\) | ||||
0.315256 | + | 0.949007i | \(0.397910\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.12129e6 | −0.0475841 | ||||||||
\(890\) | 1.17452e7 | 0.497032 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.26796e6 | 0.0533574 | ||||||||
\(893\) | 7.96511e6 | 0.334244 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.57708e6 | −0.0658108 | ||||||||
\(896\) | −3.47702e6 | −0.144689 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.74651e7 | 0.722736 | ||||||||
\(899\) | −7.41383e6 | −0.305945 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.84722e7 | 1.57883 | ||||||||
\(902\) | −1.99101e6 | −0.0814810 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.71661e7 | 1.51261 | ||||||||
\(905\) | −1.30904e7 | −0.531288 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9.23123e6 | −0.372599 | −0.186299 | − | 0.982493i | \(-0.559649\pi\) | ||||
−0.186299 | + | 0.982493i | \(0.559649\pi\) | |||||||
\(908\) | −119891. | −0.00482583 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.72121e6 | 0.0689016 | ||||||||
\(911\) | 1.55931e7 | 0.622495 | 0.311247 | − | 0.950329i | \(-0.399253\pi\) | ||||
0.311247 | + | 0.950329i | \(0.399253\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.09147e6 | 0.202146 | ||||||||
\(914\) | −2.20185e7 | −0.871812 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −495349. | −0.0195062 | ||||||||
\(917\) | 1.56017e6 | 0.0612700 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.21091e6 | −0.164470 | −0.0822351 | − | 0.996613i | \(-0.526206\pi\) | ||||
−0.0822351 | + | 0.996613i | \(0.526206\pi\) | |||||||
\(920\) | −1.35703e7 | −0.528590 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 4.30040e7 | 1.66602 | ||||||||
\(923\) | −3.76765e7 | −1.45568 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.33055e6 | 0.166413 | ||||||||
\(926\) | 629009. | 0.0241062 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 757310. | 0.0288671 | ||||||||
\(929\) | −4.10363e7 | −1.56002 | −0.780008 | − | 0.625770i | \(-0.784785\pi\) | ||||
−0.780008 | + | 0.625770i | \(0.784785\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.80682e7 | 1.43942 | ||||||||
\(932\) | 361730. | 0.0136410 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −3.96488e7 | −1.48718 | ||||||||
\(935\) | 6.40581e6 | 0.239632 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.41565e7 | 0.898844 | 0.449422 | − | 0.893320i | \(-0.351630\pi\) | ||||
0.449422 | + | 0.893320i | \(0.351630\pi\) | |||||||
\(938\) | 1.24893e6 | 0.0463479 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 125660. | 0.00463849 | ||||||||
\(941\) | −3.13080e7 | −1.15261 | −0.576304 | − | 0.817236i | \(-0.695505\pi\) | ||||
−0.576304 | + | 0.817236i | \(0.695505\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.74049e6 | −0.320079 | ||||||||
\(944\) | −9.59164e6 | −0.350318 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.16436e6 | −0.296616 | ||||||||
\(947\) | −5699.21 | −0.000206509 0 | −0.000103255 | − | 1.00000i | \(-0.500033\pi\) | ||||
−0.000103255 | 1.00000i | \(0.500033\pi\) | ||||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.33123e7 | 0.479829 | ||||||||
\(950\) | 8.34288e6 | 0.299921 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 6.60310e6 | 0.236132 | ||||||||
\(953\) | 4.24159e7 | 1.51285 | 0.756427 | − | 0.654078i | \(-0.226943\pi\) | ||||
0.756427 | + | 0.654078i | \(0.226943\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.71078e7 | −0.606995 | ||||||||
\(956\) | 2.00942e6 | 0.0711094 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −5.48718e7 | −1.93168 | ||||||||
\(959\) | 752628. | 0.0264261 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.02765e6 | −0.0708247 | ||||||||
\(962\) | −2.70282e7 | −0.941628 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.23375e6 | −0.0774180 | ||||||||
\(965\) | −1.31854e7 | −0.455801 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.43147e7 | 0.492284 | 0.246142 | − | 0.969234i | \(-0.420837\pi\) | ||||
0.246142 | + | 0.969234i | \(0.420837\pi\) | |||||||
\(968\) | 2.58661e6 | 0.0887243 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.19944e7 | 0.750556 | ||||||||
\(971\) | 1.06931e7 | 0.363960 | 0.181980 | − | 0.983302i | \(-0.441749\pi\) | ||||
0.181980 | + | 0.983302i | \(0.441749\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.99168e6 | 0.101306 | ||||||||
\(974\) | −5.66714e7 | −1.91411 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 404762. | 0.0136011 | ||||||||
\(977\) | −5.44429e7 | −1.82476 | −0.912378 | − | 0.409349i | \(-0.865756\pi\) | ||||
−0.912378 | + | 0.409349i | \(0.865756\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.82800e6 | −0.327724 | ||||||||
\(980\) | 600574. | 0.0199757 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 5.30461e7 | 1.75539 | ||||||||
\(983\) | −4.16457e7 | −1.37463 | −0.687316 | − | 0.726359i | \(-0.741211\pi\) | ||||
−0.687316 | + | 0.726359i | \(0.741211\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.16785e7 | −0.383526 | ||||||||
\(986\) | −1.76067e7 | −0.576746 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.26659e6 | −0.0738722 | ||||||||
\(989\) | −3.58414e7 | −1.16518 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.62055e6 | −0.311183 | −0.155591 | − | 0.987821i | \(-0.549728\pi\) | ||||
−0.155591 | + | 0.987821i | \(0.549728\pi\) | |||||||
\(992\) | −2.71730e6 | −0.0876714 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 5.70340e6 | 0.183091 | ||||||||
\(995\) | 1.09153e7 | 0.349526 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.05865e7 | 0.974523 | 0.487262 | − | 0.873256i | \(-0.337996\pi\) | ||||
0.487262 | + | 0.873256i | \(0.337996\pi\) | |||||||
\(998\) | 1.10495e7 | 0.351169 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 495.6.a.b.1.1 | 3 | ||
3.2 | odd | 2 | 165.6.a.c.1.3 | ✓ | 3 | ||
15.14 | odd | 2 | 825.6.a.g.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.6.a.c.1.3 | ✓ | 3 | 3.2 | odd | 2 | ||
495.6.a.b.1.1 | 3 | 1.1 | even | 1 | trivial | ||
825.6.a.g.1.1 | 3 | 15.14 | odd | 2 |