Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [378,6,Mod(1,378)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(378, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("378.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 378 = 2 \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 378.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: | \(60.6250838893\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 378.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | −91.0000 | −1.62786 | −0.813929 | − | 0.580965i | \(-0.802675\pi\) | ||||
−0.813929 | + | 0.580965i | \(0.802675\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −49.0000 | −0.377964 | ||||||||
\(8\) | −64.0000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 364.000 | 1.15107 | ||||||||
\(11\) | 61.0000 | 0.152002 | 0.0760008 | − | 0.997108i | \(-0.475785\pi\) | ||||
0.0760008 | + | 0.997108i | \(0.475785\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 156.000 | 0.256015 | 0.128008 | − | 0.991773i | \(-0.459142\pi\) | ||||
0.128008 | + | 0.991773i | \(0.459142\pi\) | |||||||
\(14\) | 196.000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | −614.000 | −0.515283 | −0.257642 | − | 0.966241i | \(-0.582945\pi\) | ||||
−0.257642 | + | 0.966241i | \(0.582945\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2207.00 | 1.40255 | 0.701275 | − | 0.712891i | \(-0.252615\pi\) | ||||
0.701275 | + | 0.712891i | \(0.252615\pi\) | |||||||
\(20\) | −1456.00 | −0.813929 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −244.000 | −0.107481 | ||||||||
\(23\) | 3139.00 | 1.23729 | 0.618645 | − | 0.785670i | \(-0.287682\pi\) | ||||
0.618645 | + | 0.785670i | \(0.287682\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5156.00 | 1.64992 | ||||||||
\(26\) | −624.000 | −0.181030 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −784.000 | −0.188982 | ||||||||
\(29\) | −3424.00 | −0.756030 | −0.378015 | − | 0.925800i | \(-0.623393\pi\) | ||||
−0.378015 | + | 0.925800i | \(0.623393\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6435.00 | 1.20266 | 0.601332 | − | 0.798999i | \(-0.294637\pi\) | ||||
0.601332 | + | 0.798999i | \(0.294637\pi\) | |||||||
\(32\) | −1024.00 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2456.00 | 0.364360 | ||||||||
\(35\) | 4459.00 | 0.615272 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6199.00 | −0.744419 | −0.372209 | − | 0.928149i | \(-0.621400\pi\) | ||||
−0.372209 | + | 0.928149i | \(0.621400\pi\) | |||||||
\(38\) | −8828.00 | −0.991753 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 5824.00 | 0.575535 | ||||||||
\(41\) | −4929.00 | −0.457930 | −0.228965 | − | 0.973435i | \(-0.573534\pi\) | ||||
−0.228965 | + | 0.973435i | \(0.573534\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4222.00 | −0.348215 | −0.174107 | − | 0.984727i | \(-0.555704\pi\) | ||||
−0.174107 | + | 0.984727i | \(0.555704\pi\) | |||||||
\(44\) | 976.000 | 0.0760008 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −12556.0 | −0.874897 | ||||||||
\(47\) | −5142.00 | −0.339537 | −0.169769 | − | 0.985484i | \(-0.554302\pi\) | ||||
−0.169769 | + | 0.985484i | \(0.554302\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2401.00 | 0.142857 | ||||||||
\(50\) | −20624.0 | −1.16667 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2496.00 | 0.128008 | ||||||||
\(53\) | −5724.00 | −0.279905 | −0.139952 | − | 0.990158i | \(-0.544695\pi\) | ||||
−0.139952 | + | 0.990158i | \(0.544695\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5551.00 | −0.247437 | ||||||||
\(56\) | 3136.00 | 0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 13696.0 | 0.534594 | ||||||||
\(59\) | 15902.0 | 0.594733 | 0.297366 | − | 0.954763i | \(-0.403892\pi\) | ||||
0.297366 | + | 0.954763i | \(0.403892\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 18624.0 | 0.640838 | 0.320419 | − | 0.947276i | \(-0.396176\pi\) | ||||
0.320419 | + | 0.947276i | \(0.396176\pi\) | |||||||
\(62\) | −25740.0 | −0.850412 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | −14196.0 | −0.416757 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11884.0 | 0.323427 | 0.161713 | − | 0.986838i | \(-0.448298\pi\) | ||||
0.161713 | + | 0.986838i | \(0.448298\pi\) | |||||||
\(68\) | −9824.00 | −0.257642 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −17836.0 | −0.435063 | ||||||||
\(71\) | 55879.0 | 1.31554 | 0.657768 | − | 0.753221i | \(-0.271501\pi\) | ||||
0.657768 | + | 0.753221i | \(0.271501\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −42494.0 | −0.933298 | −0.466649 | − | 0.884443i | \(-0.654539\pi\) | ||||
−0.466649 | + | 0.884443i | \(0.654539\pi\) | |||||||
\(74\) | 24796.0 | 0.526384 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 35312.0 | 0.701275 | ||||||||
\(77\) | −2989.00 | −0.0574512 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −23622.0 | −0.425842 | −0.212921 | − | 0.977069i | \(-0.568298\pi\) | ||||
−0.212921 | + | 0.977069i | \(0.568298\pi\) | |||||||
\(80\) | −23296.0 | −0.406964 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 19716.0 | 0.323805 | ||||||||
\(83\) | −79400.0 | −1.26510 | −0.632551 | − | 0.774519i | \(-0.717992\pi\) | ||||
−0.632551 | + | 0.774519i | \(0.717992\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 55874.0 | 0.838808 | ||||||||
\(86\) | 16888.0 | 0.246225 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3904.00 | −0.0537407 | ||||||||
\(89\) | −12201.0 | −0.163275 | −0.0816376 | − | 0.996662i | \(-0.526015\pi\) | ||||
−0.0816376 | + | 0.996662i | \(0.526015\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7644.00 | −0.0967648 | ||||||||
\(92\) | 50224.0 | 0.618645 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 20568.0 | 0.240089 | ||||||||
\(95\) | −200837. | −2.28315 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 104080. | 1.12315 | 0.561575 | − | 0.827426i | \(-0.310196\pi\) | ||||
0.561575 | + | 0.827426i | \(0.310196\pi\) | |||||||
\(98\) | −9604.00 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 82496.0 | 0.824960 | ||||||||
\(101\) | −190102. | −1.85431 | −0.927157 | − | 0.374673i | \(-0.877755\pi\) | ||||
−0.927157 | + | 0.374673i | \(0.877755\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 142211. | 1.32081 | 0.660405 | − | 0.750910i | \(-0.270385\pi\) | ||||
0.660405 | + | 0.750910i | \(0.270385\pi\) | |||||||
\(104\) | −9984.00 | −0.0905151 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 22896.0 | 0.197922 | ||||||||
\(107\) | −57972.0 | −0.489507 | −0.244753 | − | 0.969585i | \(-0.578707\pi\) | ||||
−0.244753 | + | 0.969585i | \(0.578707\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −100181. | −0.807642 | −0.403821 | − | 0.914838i | \(-0.632318\pi\) | ||||
−0.403821 | + | 0.914838i | \(0.632318\pi\) | |||||||
\(110\) | 22204.0 | 0.174964 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −12544.0 | −0.0944911 | ||||||||
\(113\) | −206026. | −1.51784 | −0.758920 | − | 0.651184i | \(-0.774273\pi\) | ||||
−0.758920 | + | 0.651184i | \(0.774273\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −285649. | −2.01413 | ||||||||
\(116\) | −54784.0 | −0.378015 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −63608.0 | −0.420539 | ||||||||
\(119\) | 30086.0 | 0.194759 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −157330. | −0.976896 | ||||||||
\(122\) | −74496.0 | −0.453141 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 102960. | 0.601332 | ||||||||
\(125\) | −184821. | −1.05798 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 205668. | 1.13151 | 0.565754 | − | 0.824574i | \(-0.308585\pi\) | ||||
0.565754 | + | 0.824574i | \(0.308585\pi\) | |||||||
\(128\) | −16384.0 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 56784.0 | 0.294691 | ||||||||
\(131\) | 202250. | 1.02970 | 0.514850 | − | 0.857281i | \(-0.327848\pi\) | ||||
0.514850 | + | 0.857281i | \(0.327848\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −108143. | −0.530114 | ||||||||
\(134\) | −47536.0 | −0.228697 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 39296.0 | 0.182180 | ||||||||
\(137\) | −282868. | −1.28760 | −0.643802 | − | 0.765192i | \(-0.722644\pi\) | ||||
−0.643802 | + | 0.765192i | \(0.722644\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −376796. | −1.65413 | −0.827064 | − | 0.562107i | \(-0.809991\pi\) | ||||
−0.827064 | + | 0.562107i | \(0.809991\pi\) | |||||||
\(140\) | 71344.0 | 0.307636 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −223516. | −0.930224 | ||||||||
\(143\) | 9516.00 | 0.0389148 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 311584. | 1.23071 | ||||||||
\(146\) | 169976. | 0.659942 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −99184.0 | −0.372209 | ||||||||
\(149\) | 41574.0 | 0.153411 | 0.0767054 | − | 0.997054i | \(-0.475560\pi\) | ||||
0.0767054 | + | 0.997054i | \(0.475560\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −552182. | −1.97079 | −0.985394 | − | 0.170290i | \(-0.945529\pi\) | ||||
−0.985394 | + | 0.170290i | \(0.945529\pi\) | |||||||
\(152\) | −141248. | −0.495876 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 11956.0 | 0.0406241 | ||||||||
\(155\) | −585585. | −1.95777 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −323692. | −1.04805 | −0.524026 | − | 0.851702i | \(-0.675571\pi\) | ||||
−0.524026 | + | 0.851702i | \(0.675571\pi\) | |||||||
\(158\) | 94488.0 | 0.301116 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 93184.0 | 0.287767 | ||||||||
\(161\) | −153811. | −0.467652 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −278416. | −0.820777 | −0.410389 | − | 0.911911i | \(-0.634607\pi\) | ||||
−0.410389 | + | 0.911911i | \(0.634607\pi\) | |||||||
\(164\) | −78864.0 | −0.228965 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 317600. | 0.894562 | ||||||||
\(167\) | 503066. | 1.39583 | 0.697917 | − | 0.716179i | \(-0.254110\pi\) | ||||
0.697917 | + | 0.716179i | \(0.254110\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −346957. | −0.934456 | ||||||||
\(170\) | −223496. | −0.593127 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −67552.0 | −0.174107 | ||||||||
\(173\) | −470029. | −1.19401 | −0.597007 | − | 0.802236i | \(-0.703644\pi\) | ||||
−0.597007 | + | 0.802236i | \(0.703644\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −252644. | −0.623611 | ||||||||
\(176\) | 15616.0 | 0.0380004 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 48804.0 | 0.115453 | ||||||||
\(179\) | 708456. | 1.65265 | 0.826324 | − | 0.563195i | \(-0.190428\pi\) | ||||
0.826324 | + | 0.563195i | \(0.190428\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 585378. | 1.32813 | 0.664064 | − | 0.747676i | \(-0.268830\pi\) | ||||
0.664064 | + | 0.747676i | \(0.268830\pi\) | |||||||
\(182\) | 30576.0 | 0.0684230 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −200896. | −0.437448 | ||||||||
\(185\) | 564109. | 1.21181 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −37454.0 | −0.0783239 | ||||||||
\(188\) | −82272.0 | −0.169769 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 803348. | 1.61443 | ||||||||
\(191\) | 160881. | 0.319096 | 0.159548 | − | 0.987190i | \(-0.448996\pi\) | ||||
0.159548 | + | 0.987190i | \(0.448996\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −828802. | −1.60161 | −0.800806 | − | 0.598923i | \(-0.795595\pi\) | ||||
−0.800806 | + | 0.598923i | \(0.795595\pi\) | |||||||
\(194\) | −416320. | −0.794187 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 38416.0 | 0.0714286 | ||||||||
\(197\) | −531242. | −0.975274 | −0.487637 | − | 0.873046i | \(-0.662141\pi\) | ||||
−0.487637 | + | 0.873046i | \(0.662141\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 527519. | 0.944290 | 0.472145 | − | 0.881521i | \(-0.343480\pi\) | ||||
0.472145 | + | 0.881521i | \(0.343480\pi\) | |||||||
\(200\) | −329984. | −0.583335 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 760408. | 1.31120 | ||||||||
\(203\) | 167776. | 0.285752 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 448539. | 0.745445 | ||||||||
\(206\) | −568844. | −0.933953 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 39936.0 | 0.0640039 | ||||||||
\(209\) | 134627. | 0.213190 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 535970. | 0.828771 | 0.414385 | − | 0.910102i | \(-0.363997\pi\) | ||||
0.414385 | + | 0.910102i | \(0.363997\pi\) | |||||||
\(212\) | −91584.0 | −0.139952 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 231888. | 0.346134 | ||||||||
\(215\) | 384202. | 0.566844 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −315315. | −0.454564 | ||||||||
\(218\) | 400724. | 0.571089 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −88816.0 | −0.123718 | ||||||||
\(221\) | −95784.0 | −0.131920 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 43385.0 | 0.0584221 | 0.0292111 | − | 0.999573i | \(-0.490701\pi\) | ||||
0.0292111 | + | 0.999573i | \(0.490701\pi\) | |||||||
\(224\) | 50176.0 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 824104. | 1.07327 | ||||||||
\(227\) | 1.21268e6 | 1.56200 | 0.781000 | − | 0.624531i | \(-0.214710\pi\) | ||||
0.781000 | + | 0.624531i | \(0.214710\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 568828. | 0.716791 | 0.358395 | − | 0.933570i | \(-0.383324\pi\) | ||||
0.358395 | + | 0.933570i | \(0.383324\pi\) | |||||||
\(230\) | 1.14260e6 | 1.42421 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 219136. | 0.267297 | ||||||||
\(233\) | 353470. | 0.426543 | 0.213271 | − | 0.976993i | \(-0.431588\pi\) | ||||
0.213271 | + | 0.976993i | \(0.431588\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 467922. | 0.552718 | ||||||||
\(236\) | 254432. | 0.297366 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −120344. | −0.137715 | ||||||||
\(239\) | 1.07506e6 | 1.21741 | 0.608704 | − | 0.793397i | \(-0.291690\pi\) | ||||
0.608704 | + | 0.793397i | \(0.291690\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.50741e6 | −1.67182 | −0.835911 | − | 0.548865i | \(-0.815060\pi\) | ||||
−0.835911 | + | 0.548865i | \(0.815060\pi\) | |||||||
\(242\) | 629320. | 0.690769 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 297984. | 0.320419 | ||||||||
\(245\) | −218491. | −0.232551 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 344292. | 0.359074 | ||||||||
\(248\) | −411840. | −0.425206 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 739284. | 0.748103 | ||||||||
\(251\) | −50040.0 | −0.0501341 | −0.0250670 | − | 0.999686i | \(-0.507980\pi\) | ||||
−0.0250670 | + | 0.999686i | \(0.507980\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 191479. | 0.188070 | ||||||||
\(254\) | −822672. | −0.800097 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | 958947. | 0.905653 | 0.452826 | − | 0.891599i | \(-0.350416\pi\) | ||||
0.452826 | + | 0.891599i | \(0.350416\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 303751. | 0.281364 | ||||||||
\(260\) | −227136. | −0.208378 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −809000. | −0.728107 | ||||||||
\(263\) | −1.70706e6 | −1.52180 | −0.760902 | − | 0.648867i | \(-0.775243\pi\) | ||||
−0.760902 | + | 0.648867i | \(0.775243\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 520884. | 0.455645 | ||||||||
\(266\) | 432572. | 0.374847 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 190144. | 0.161713 | ||||||||
\(269\) | −353479. | −0.297840 | −0.148920 | − | 0.988849i | \(-0.547580\pi\) | ||||
−0.148920 | + | 0.988849i | \(0.547580\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.27774e6 | −1.88400 | −0.942002 | − | 0.335608i | \(-0.891058\pi\) | ||||
−0.942002 | + | 0.335608i | \(0.891058\pi\) | |||||||
\(272\) | −157184. | −0.128821 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.13147e6 | 0.910474 | ||||||||
\(275\) | 314516. | 0.250790 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.42376e6 | −1.11490 | −0.557451 | − | 0.830210i | \(-0.688221\pi\) | ||||
−0.557451 | + | 0.830210i | \(0.688221\pi\) | |||||||
\(278\) | 1.50718e6 | 1.16965 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −285376. | −0.217532 | ||||||||
\(281\) | −1.15324e6 | −0.871271 | −0.435635 | − | 0.900123i | \(-0.643476\pi\) | ||||
−0.435635 | + | 0.900123i | \(0.643476\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −75980.0 | −0.0563940 | −0.0281970 | − | 0.999602i | \(-0.508977\pi\) | ||||
−0.0281970 | + | 0.999602i | \(0.508977\pi\) | |||||||
\(284\) | 894064. | 0.657768 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −38064.0 | −0.0275169 | ||||||||
\(287\) | 241521. | 0.173081 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.04286e6 | −0.734483 | ||||||||
\(290\) | −1.24634e6 | −0.870242 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −679904. | −0.466649 | ||||||||
\(293\) | 1.94248e6 | 1.32187 | 0.660934 | − | 0.750444i | \(-0.270160\pi\) | ||||
0.660934 | + | 0.750444i | \(0.270160\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.44708e6 | −0.968140 | ||||||||
\(296\) | 396736. | 0.263192 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −166296. | −0.108478 | ||||||||
\(299\) | 489684. | 0.316766 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 206878. | 0.131613 | ||||||||
\(302\) | 2.20873e6 | 1.39356 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 564992. | 0.350637 | ||||||||
\(305\) | −1.69478e6 | −1.04319 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.78930e6 | −1.08352 | −0.541761 | − | 0.840533i | \(-0.682242\pi\) | ||||
−0.541761 | + | 0.840533i | \(0.682242\pi\) | |||||||
\(308\) | −47824.0 | −0.0287256 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.34234e6 | 1.38435 | ||||||||
\(311\) | 3.29078e6 | 1.92929 | 0.964646 | − | 0.263550i | \(-0.0848933\pi\) | ||||
0.964646 | + | 0.263550i | \(0.0848933\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.28470e6 | 0.741209 | 0.370605 | − | 0.928791i | \(-0.379150\pi\) | ||||
0.370605 | + | 0.928791i | \(0.379150\pi\) | |||||||
\(314\) | 1.29477e6 | 0.741085 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −377952. | −0.212921 | ||||||||
\(317\) | 1.80779e6 | 1.01042 | 0.505209 | − | 0.862997i | \(-0.331416\pi\) | ||||
0.505209 | + | 0.862997i | \(0.331416\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −208864. | −0.114918 | ||||||||
\(320\) | −372736. | −0.203482 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 615244. | 0.330680 | ||||||||
\(323\) | −1.35510e6 | −0.722711 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 804336. | 0.422405 | ||||||||
\(326\) | 1.11366e6 | 0.580377 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 315456. | 0.161903 | ||||||||
\(329\) | 251958. | 0.128333 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.18148e6 | 1.09441 | 0.547206 | − | 0.836998i | \(-0.315692\pi\) | ||||
0.547206 | + | 0.836998i | \(0.315692\pi\) | |||||||
\(332\) | −1.27040e6 | −0.632551 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.01226e6 | −0.987004 | ||||||||
\(335\) | −1.08144e6 | −0.526492 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −463293. | −0.222219 | −0.111109 | − | 0.993808i | \(-0.535440\pi\) | ||||
−0.111109 | + | 0.993808i | \(0.535440\pi\) | |||||||
\(338\) | 1.38783e6 | 0.660760 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 893984. | 0.419404 | ||||||||
\(341\) | 392535. | 0.182807 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −117649. | −0.0539949 | ||||||||
\(344\) | 270208. | 0.123112 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.88012e6 | 0.844295 | ||||||||
\(347\) | −1.63248e6 | −0.727822 | −0.363911 | − | 0.931434i | \(-0.618559\pi\) | ||||
−0.363911 | + | 0.931434i | \(0.618559\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.46267e6 | 1.52176 | 0.760882 | − | 0.648890i | \(-0.224766\pi\) | ||||
0.760882 | + | 0.648890i | \(0.224766\pi\) | |||||||
\(350\) | 1.01058e6 | 0.440960 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −62464.0 | −0.0268703 | ||||||||
\(353\) | 1.07462e6 | 0.459006 | 0.229503 | − | 0.973308i | \(-0.426290\pi\) | ||||
0.229503 | + | 0.973308i | \(0.426290\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.08499e6 | −2.14151 | ||||||||
\(356\) | −195216. | −0.0816376 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.83382e6 | −1.16860 | ||||||||
\(359\) | 1.45320e6 | 0.595097 | 0.297549 | − | 0.954707i | \(-0.403831\pi\) | ||||
0.297549 | + | 0.954707i | \(0.403831\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.39475e6 | 0.967146 | ||||||||
\(362\) | −2.34151e6 | −0.939128 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −122304. | −0.0483824 | ||||||||
\(365\) | 3.86695e6 | 1.51928 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.04242e6 | −0.791555 | −0.395777 | − | 0.918346i | \(-0.629525\pi\) | ||||
−0.395777 | + | 0.918346i | \(0.629525\pi\) | |||||||
\(368\) | 803584. | 0.309323 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2.25644e6 | −0.856877 | ||||||||
\(371\) | 280476. | 0.105794 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.67184e6 | 0.994349 | 0.497175 | − | 0.867651i | \(-0.334371\pi\) | ||||
0.497175 | + | 0.867651i | \(0.334371\pi\) | |||||||
\(374\) | 149816. | 0.0553833 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 329088. | 0.120045 | ||||||||
\(377\) | −534144. | −0.193555 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.09525e6 | 0.749268 | 0.374634 | − | 0.927173i | \(-0.377768\pi\) | ||||
0.374634 | + | 0.927173i | \(0.377768\pi\) | |||||||
\(380\) | −3.21339e6 | −1.14158 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −643524. | −0.225635 | ||||||||
\(383\) | −718154. | −0.250162 | −0.125081 | − | 0.992147i | \(-0.539919\pi\) | ||||
−0.125081 | + | 0.992147i | \(0.539919\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 271999. | 0.0935224 | ||||||||
\(386\) | 3.31521e6 | 1.13251 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.66528e6 | 0.561575 | ||||||||
\(389\) | −2.49082e6 | −0.834581 | −0.417290 | − | 0.908773i | \(-0.637020\pi\) | ||||
−0.417290 | + | 0.908773i | \(0.637020\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.92735e6 | −0.637555 | ||||||||
\(392\) | −153664. | −0.0505076 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.12497e6 | 0.689623 | ||||||||
\(395\) | 2.14960e6 | 0.693211 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.18576e6 | −1.65134 | −0.825669 | − | 0.564155i | \(-0.809202\pi\) | ||||
−0.825669 | + | 0.564155i | \(0.809202\pi\) | |||||||
\(398\) | −2.11008e6 | −0.667714 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.31994e6 | 0.412480 | ||||||||
\(401\) | 2.05462e6 | 0.638072 | 0.319036 | − | 0.947743i | \(-0.396641\pi\) | ||||
0.319036 | + | 0.947743i | \(0.396641\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.00386e6 | 0.307901 | ||||||||
\(404\) | −3.04163e6 | −0.927157 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −671104. | −0.202057 | ||||||||
\(407\) | −378139. | −0.113153 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.79285e6 | −1.41672 | −0.708362 | − | 0.705849i | \(-0.750566\pi\) | ||||
−0.708362 | + | 0.705849i | \(0.750566\pi\) | |||||||
\(410\) | −1.79416e6 | −0.527109 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.27538e6 | 0.660405 | ||||||||
\(413\) | −779198. | −0.224788 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.22540e6 | 2.05940 | ||||||||
\(416\) | −159744. | −0.0452576 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −538508. | −0.150748 | ||||||||
\(419\) | −4.84279e6 | −1.34760 | −0.673799 | − | 0.738915i | \(-0.735339\pi\) | ||||
−0.673799 | + | 0.738915i | \(0.735339\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.84008e6 | −1.60588 | −0.802941 | − | 0.596059i | \(-0.796732\pi\) | ||||
−0.802941 | + | 0.596059i | \(0.796732\pi\) | |||||||
\(422\) | −2.14388e6 | −0.586029 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 366336. | 0.0989612 | ||||||||
\(425\) | −3.16578e6 | −0.850176 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −912576. | −0.242214 | ||||||||
\(428\) | −927552. | −0.244753 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.53681e6 | −0.400819 | ||||||||
\(431\) | −2.40485e6 | −0.623584 | −0.311792 | − | 0.950150i | \(-0.600929\pi\) | ||||
−0.311792 | + | 0.950150i | \(0.600929\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.08008e6 | −0.789482 | −0.394741 | − | 0.918792i | \(-0.629166\pi\) | ||||
−0.394741 | + | 0.918792i | \(0.629166\pi\) | |||||||
\(434\) | 1.26126e6 | 0.321425 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.60290e6 | −0.403821 | ||||||||
\(437\) | 6.92777e6 | 1.73536 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.47711e6 | −1.35641 | −0.678204 | − | 0.734874i | \(-0.737241\pi\) | ||||
−0.678204 | + | 0.734874i | \(0.737241\pi\) | |||||||
\(440\) | 355264. | 0.0874822 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 383136. | 0.0932819 | ||||||||
\(443\) | −3.32792e6 | −0.805681 | −0.402841 | − | 0.915270i | \(-0.631977\pi\) | ||||
−0.402841 | + | 0.915270i | \(0.631977\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.11029e6 | 0.265789 | ||||||||
\(446\) | −173540. | −0.0413107 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −200704. | −0.0472456 | ||||||||
\(449\) | 2.43221e6 | 0.569358 | 0.284679 | − | 0.958623i | \(-0.408113\pi\) | ||||
0.284679 | + | 0.958623i | \(0.408113\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −300669. | −0.0696061 | ||||||||
\(452\) | −3.29642e6 | −0.758920 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −4.85071e6 | −1.10450 | ||||||||
\(455\) | 695604. | 0.157519 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.05921e6 | 1.80510 | 0.902552 | − | 0.430581i | \(-0.141691\pi\) | ||||
0.902552 | + | 0.430581i | \(0.141691\pi\) | |||||||
\(458\) | −2.27531e6 | −0.506847 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −4.57038e6 | −1.00707 | ||||||||
\(461\) | 1.94668e6 | 0.426620 | 0.213310 | − | 0.976985i | \(-0.431576\pi\) | ||||
0.213310 | + | 0.976985i | \(0.431576\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.44786e6 | −0.964270 | −0.482135 | − | 0.876097i | \(-0.660139\pi\) | ||||
−0.482135 | + | 0.876097i | \(0.660139\pi\) | |||||||
\(464\) | −876544. | −0.189007 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.41388e6 | −0.301611 | ||||||||
\(467\) | −5.21753e6 | −1.10706 | −0.553532 | − | 0.832828i | \(-0.686720\pi\) | ||||
−0.553532 | + | 0.832828i | \(0.686720\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −582316. | −0.122244 | ||||||||
\(470\) | −1.87169e6 | −0.390831 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.01773e6 | −0.210270 | ||||||||
\(473\) | −257542. | −0.0529292 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.13793e7 | 2.31410 | ||||||||
\(476\) | 481376. | 0.0973794 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4.30022e6 | −0.860838 | ||||||||
\(479\) | −1.93410e6 | −0.385158 | −0.192579 | − | 0.981281i | \(-0.561685\pi\) | ||||
−0.192579 | + | 0.981281i | \(0.561685\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −967044. | −0.190583 | ||||||||
\(482\) | 6.02966e6 | 1.18216 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.51728e6 | −0.488448 | ||||||||
\(485\) | −9.47128e6 | −1.82833 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.82693e6 | 0.540122 | 0.270061 | − | 0.962843i | \(-0.412956\pi\) | ||||
0.270061 | + | 0.962843i | \(0.412956\pi\) | |||||||
\(488\) | −1.19194e6 | −0.226571 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 873964. | 0.164438 | ||||||||
\(491\) | −8.52446e6 | −1.59574 | −0.797871 | − | 0.602828i | \(-0.794041\pi\) | ||||
−0.797871 | + | 0.602828i | \(0.794041\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.10234e6 | 0.389569 | ||||||||
\(494\) | −1.37717e6 | −0.253904 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.64736e6 | 0.300666 | ||||||||
\(497\) | −2.73807e6 | −0.497226 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −459146. | −0.0825466 | −0.0412733 | − | 0.999148i | \(-0.513141\pi\) | ||||
−0.0412733 | + | 0.999148i | \(0.513141\pi\) | |||||||
\(500\) | −2.95714e6 | −0.528989 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 200160. | 0.0354501 | ||||||||
\(503\) | 6.68198e6 | 1.17757 | 0.588783 | − | 0.808291i | \(-0.299607\pi\) | ||||
0.588783 | + | 0.808291i | \(0.299607\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.72993e7 | 3.01856 | ||||||||
\(506\) | −765916. | −0.132986 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.29069e6 | 0.565754 | ||||||||
\(509\) | 3.37000e6 | 0.576548 | 0.288274 | − | 0.957548i | \(-0.406919\pi\) | ||||
0.288274 | + | 0.957548i | \(0.406919\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.08221e6 | 0.352754 | ||||||||
\(512\) | −262144. | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3.83579e6 | −0.640393 | ||||||||
\(515\) | −1.29412e7 | −2.15009 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −313662. | −0.0516102 | ||||||||
\(518\) | −1.21500e6 | −0.198954 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 908544. | 0.147346 | ||||||||
\(521\) | −1.36876e6 | −0.220919 | −0.110459 | − | 0.993881i | \(-0.535232\pi\) | ||||
−0.110459 | + | 0.993881i | \(0.535232\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.10535e6 | 0.176704 | 0.0883522 | − | 0.996089i | \(-0.471840\pi\) | ||||
0.0883522 | + | 0.996089i | \(0.471840\pi\) | |||||||
\(524\) | 3.23600e6 | 0.514850 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.82823e6 | 1.07608 | ||||||||
\(527\) | −3.95109e6 | −0.619713 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.41698e6 | 0.530888 | ||||||||
\(530\) | −2.08354e6 | −0.322189 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.73029e6 | −0.265057 | ||||||||
\(533\) | −768924. | −0.117237 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.27545e6 | 0.796848 | ||||||||
\(536\) | −760576. | −0.114349 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.41392e6 | 0.210605 | ||||||||
\(539\) | 146461. | 0.0217145 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.78908e6 | 0.556597 | 0.278298 | − | 0.960495i | \(-0.410230\pi\) | ||||
0.278298 | + | 0.960495i | \(0.410230\pi\) | |||||||
\(542\) | 9.11098e6 | 1.33219 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 628736. | 0.0910901 | ||||||||
\(545\) | 9.11647e6 | 1.31473 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.38407e7 | −1.97783 | −0.988914 | − | 0.148486i | \(-0.952560\pi\) | ||||
−0.988914 | + | 0.148486i | \(0.952560\pi\) | |||||||
\(548\) | −4.52589e6 | −0.643802 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.25806e6 | −0.177336 | ||||||||
\(551\) | −7.55677e6 | −1.06037 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.15748e6 | 0.160953 | ||||||||
\(554\) | 5.69504e6 | 0.788355 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.02874e6 | −0.827064 | ||||||||
\(557\) | −1.24182e7 | −1.69598 | −0.847991 | − | 0.530011i | \(-0.822188\pi\) | ||||
−0.847991 | + | 0.530011i | \(0.822188\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −658632. | −0.0891483 | ||||||||
\(560\) | 1.14150e6 | 0.153818 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4.61295e6 | 0.616081 | ||||||||
\(563\) | −4.10598e6 | −0.545941 | −0.272970 | − | 0.962022i | \(-0.588006\pi\) | ||||
−0.272970 | + | 0.962022i | \(0.588006\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.87484e7 | 2.47083 | ||||||||
\(566\) | 303920. | 0.0398766 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.57626e6 | −0.465112 | ||||||||
\(569\) | −4.34685e6 | −0.562852 | −0.281426 | − | 0.959583i | \(-0.590807\pi\) | ||||
−0.281426 | + | 0.959583i | \(0.590807\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.57428e6 | −0.843836 | −0.421918 | − | 0.906634i | \(-0.638643\pi\) | ||||
−0.421918 | + | 0.906634i | \(0.638643\pi\) | |||||||
\(572\) | 152256. | 0.0194574 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −966084. | −0.122387 | ||||||||
\(575\) | 1.61847e7 | 2.04143 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.22885e7 | 1.53660 | 0.768300 | − | 0.640090i | \(-0.221103\pi\) | ||||
0.768300 | + | 0.640090i | \(0.221103\pi\) | |||||||
\(578\) | 4.17144e6 | 0.519358 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4.98534e6 | 0.615354 | ||||||||
\(581\) | 3.89060e6 | 0.478163 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −349164. | −0.0425459 | ||||||||
\(584\) | 2.71962e6 | 0.329971 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.76993e6 | −0.934702 | ||||||||
\(587\) | −3.47921e6 | −0.416759 | −0.208380 | − | 0.978048i | \(-0.566819\pi\) | ||||
−0.208380 | + | 0.978048i | \(0.566819\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.42020e7 | 1.68680 | ||||||||
\(590\) | 5.78833e6 | 0.684578 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.58694e6 | −0.186105 | ||||||||
\(593\) | −1.10998e7 | −1.29622 | −0.648109 | − | 0.761547i | \(-0.724440\pi\) | ||||
−0.648109 | + | 0.761547i | \(0.724440\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.73783e6 | −0.317040 | ||||||||
\(596\) | 665184. | 0.0767054 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.95874e6 | −0.223987 | ||||||||
\(599\) | 1.13402e7 | 1.29138 | 0.645688 | − | 0.763601i | \(-0.276571\pi\) | ||||
0.645688 | + | 0.763601i | \(0.276571\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.21989e6 | 0.137764 | 0.0688819 | − | 0.997625i | \(-0.478057\pi\) | ||||
0.0688819 | + | 0.997625i | \(0.478057\pi\) | |||||||
\(602\) | −827512. | −0.0930643 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −8.83491e6 | −0.985394 | ||||||||
\(605\) | 1.43170e7 | 1.59025 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.71749e6 | 1.07049 | 0.535245 | − | 0.844697i | \(-0.320219\pi\) | ||||
0.535245 | + | 0.844697i | \(0.320219\pi\) | |||||||
\(608\) | −2.25997e6 | −0.247938 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6.77914e6 | 0.737649 | ||||||||
\(611\) | −802152. | −0.0869268 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.77080e6 | −0.942732 | −0.471366 | − | 0.881938i | \(-0.656239\pi\) | ||||
−0.471366 | + | 0.881938i | \(0.656239\pi\) | |||||||
\(614\) | 7.15720e6 | 0.766165 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 191296. | 0.0203121 | ||||||||
\(617\) | 6.26430e6 | 0.662460 | 0.331230 | − | 0.943550i | \(-0.392536\pi\) | ||||
0.331230 | + | 0.943550i | \(0.392536\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.13527e7 | −1.19089 | −0.595445 | − | 0.803396i | \(-0.703024\pi\) | ||||
−0.595445 | + | 0.803396i | \(0.703024\pi\) | |||||||
\(620\) | −9.36936e6 | −0.978883 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.31631e7 | −1.36422 | ||||||||
\(623\) | 597849. | 0.0617123 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 706211. | 0.0723160 | ||||||||
\(626\) | −5.13880e6 | −0.524114 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −5.17907e6 | −0.524026 | ||||||||
\(629\) | 3.80619e6 | 0.383587 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.62718e6 | 0.162690 | 0.0813452 | − | 0.996686i | \(-0.474078\pi\) | ||||
0.0813452 | + | 0.996686i | \(0.474078\pi\) | |||||||
\(632\) | 1.51181e6 | 0.150558 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −7.23118e6 | −0.714473 | ||||||||
\(635\) | −1.87158e7 | −1.84193 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 374556. | 0.0365736 | ||||||||
\(638\) | 835456. | 0.0812591 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.49094e6 | 0.143884 | ||||||||
\(641\) | −1.09340e7 | −1.05108 | −0.525538 | − | 0.850770i | \(-0.676136\pi\) | ||||
−0.525538 | + | 0.850770i | \(0.676136\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.62540e6 | −0.631953 | −0.315977 | − | 0.948767i | \(-0.602332\pi\) | ||||
−0.315977 | + | 0.948767i | \(0.602332\pi\) | |||||||
\(644\) | −2.46098e6 | −0.233826 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.42039e6 | 0.511034 | ||||||||
\(647\) | 1.00420e7 | 0.943105 | 0.471553 | − | 0.881838i | \(-0.343694\pi\) | ||||
0.471553 | + | 0.881838i | \(0.343694\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 970022. | 0.0904003 | ||||||||
\(650\) | −3.21734e6 | −0.298685 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.45466e6 | −0.410389 | ||||||||
\(653\) | −1.70284e7 | −1.56276 | −0.781379 | − | 0.624057i | \(-0.785483\pi\) | ||||
−0.781379 | + | 0.624057i | \(0.785483\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.84048e7 | −1.67620 | ||||||||
\(656\) | −1.26182e6 | −0.114483 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1.00783e6 | −0.0907451 | ||||||||
\(659\) | 2.81993e6 | 0.252944 | 0.126472 | − | 0.991970i | \(-0.459635\pi\) | ||||
0.126472 | + | 0.991970i | \(0.459635\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.37419e6 | −0.834507 | −0.417254 | − | 0.908790i | \(-0.637007\pi\) | ||||
−0.417254 | + | 0.908790i | \(0.637007\pi\) | |||||||
\(662\) | −8.72590e6 | −0.773865 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5.08160e6 | 0.447281 | ||||||||
\(665\) | 9.84101e6 | 0.862950 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.07479e7 | −0.935428 | ||||||||
\(668\) | 8.04906e6 | 0.697917 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 4.32578e6 | 0.372286 | ||||||||
\(671\) | 1.13606e6 | 0.0974084 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.42917e7 | −1.21632 | −0.608158 | − | 0.793816i | \(-0.708091\pi\) | ||||
−0.608158 | + | 0.793816i | \(0.708091\pi\) | |||||||
\(674\) | 1.85317e6 | 0.157132 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.55131e6 | −0.467228 | ||||||||
\(677\) | 917127. | 0.0769056 | 0.0384528 | − | 0.999260i | \(-0.487757\pi\) | ||||
0.0384528 | + | 0.999260i | \(0.487757\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.09992e6 | −0.424511 | ||||||||
\(680\) | −3.57594e6 | −0.296563 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.57014e6 | −0.129264 | ||||||||
\(683\) | −8.63528e6 | −0.708312 | −0.354156 | − | 0.935186i | \(-0.615232\pi\) | ||||
−0.354156 | + | 0.935186i | \(0.615232\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.57410e7 | 2.09604 | ||||||||
\(686\) | 470596. | 0.0381802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.08083e6 | −0.0870537 | ||||||||
\(689\) | −892944. | −0.0716599 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.31114e7 | 1.04461 | 0.522306 | − | 0.852758i | \(-0.325072\pi\) | ||||
0.522306 | + | 0.852758i | \(0.325072\pi\) | |||||||
\(692\) | −7.52046e6 | −0.597007 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6.52993e6 | 0.514648 | ||||||||
\(695\) | 3.42884e7 | 2.69269 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.02641e6 | 0.235964 | ||||||||
\(698\) | −1.38507e7 | −1.07605 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −4.04230e6 | −0.311806 | ||||||||
\(701\) | 1.24314e7 | 0.955490 | 0.477745 | − | 0.878499i | \(-0.341454\pi\) | ||||
0.477745 | + | 0.878499i | \(0.341454\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.36812e7 | −1.04408 | ||||||||
\(704\) | 249856. | 0.0190002 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4.29848e6 | −0.324566 | ||||||||
\(707\) | 9.31500e6 | 0.700865 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.35949e6 | −0.699256 | −0.349628 | − | 0.936889i | \(-0.613692\pi\) | ||||
−0.349628 | + | 0.936889i | \(0.613692\pi\) | |||||||
\(710\) | 2.03400e7 | 1.51427 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 780864. | 0.0577265 | ||||||||
\(713\) | 2.01995e7 | 1.48804 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −865956. | −0.0633477 | ||||||||
\(716\) | 1.13353e7 | 0.826324 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −5.81278e6 | −0.420797 | ||||||||
\(719\) | 3.73119e6 | 0.269169 | 0.134585 | − | 0.990902i | \(-0.457030\pi\) | ||||
0.134585 | + | 0.990902i | \(0.457030\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.96834e6 | −0.499219 | ||||||||
\(722\) | −9.57900e6 | −0.683876 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 9.36605e6 | 0.664064 | ||||||||
\(725\) | −1.76541e7 | −1.24739 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.99543e6 | 0.420712 | 0.210356 | − | 0.977625i | \(-0.432538\pi\) | ||||
0.210356 | + | 0.977625i | \(0.432538\pi\) | |||||||
\(728\) | 489216. | 0.0342115 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.54678e7 | −1.07429 | ||||||||
\(731\) | 2.59231e6 | 0.179429 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.97288e6 | −0.135625 | −0.0678126 | − | 0.997698i | \(-0.521602\pi\) | ||||
−0.0678126 | + | 0.997698i | \(0.521602\pi\) | |||||||
\(734\) | 8.16970e6 | 0.559714 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.21434e6 | −0.218724 | ||||||||
\(737\) | 724924. | 0.0491613 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.97822e6 | 0.335323 | 0.167661 | − | 0.985845i | \(-0.446379\pi\) | ||||
0.167661 | + | 0.985845i | \(0.446379\pi\) | |||||||
\(740\) | 9.02574e6 | 0.605904 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.12190e6 | −0.0748076 | ||||||||
\(743\) | 3.88689e6 | 0.258303 | 0.129152 | − | 0.991625i | \(-0.458775\pi\) | ||||
0.129152 | + | 0.991625i | \(0.458775\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.78323e6 | −0.249731 | ||||||||
\(746\) | −1.06874e7 | −0.703111 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −599264. | −0.0391619 | ||||||||
\(749\) | 2.84063e6 | 0.185016 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.67681e6 | 0.108489 | 0.0542444 | − | 0.998528i | \(-0.482725\pi\) | ||||
0.0542444 | + | 0.998528i | \(0.482725\pi\) | |||||||
\(752\) | −1.31635e6 | −0.0848843 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.13658e6 | 0.136864 | ||||||||
\(755\) | 5.02486e7 | 3.20816 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.75632e7 | 1.11395 | 0.556973 | − | 0.830530i | \(-0.311963\pi\) | ||||
0.556973 | + | 0.830530i | \(0.311963\pi\) | |||||||
\(758\) | −8.38098e6 | −0.529812 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.28536e7 | 0.807216 | ||||||||
\(761\) | 2.18506e7 | 1.36773 | 0.683866 | − | 0.729607i | \(-0.260297\pi\) | ||||
0.683866 | + | 0.729607i | \(0.260297\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.90887e6 | 0.305260 | ||||||||
\(764\) | 2.57410e6 | 0.159548 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.87262e6 | 0.176891 | ||||||||
\(767\) | 2.48071e6 | 0.152261 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.12233e6 | −0.251378 | −0.125689 | − | 0.992070i | \(-0.540114\pi\) | ||||
−0.125689 | + | 0.992070i | \(0.540114\pi\) | |||||||
\(770\) | −1.08800e6 | −0.0661303 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.32608e7 | −0.800806 | ||||||||
\(773\) | −1.84891e7 | −1.11293 | −0.556463 | − | 0.830872i | \(-0.687842\pi\) | ||||
−0.556463 | + | 0.830872i | \(0.687842\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.31789e7 | 1.98430 | ||||||||
\(776\) | −6.66112e6 | −0.397094 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 9.96328e6 | 0.590138 | ||||||||
\(779\) | −1.08783e7 | −0.642270 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.40862e6 | 0.199964 | ||||||||
\(782\) | 7.70938e6 | 0.450820 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 614656. | 0.0357143 | ||||||||
\(785\) | 2.94560e7 | 1.70608 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.75980e7 | −1.01280 | −0.506402 | − | 0.862298i | \(-0.669025\pi\) | ||||
−0.506402 | + | 0.862298i | \(0.669025\pi\) | |||||||
\(788\) | −8.49987e6 | −0.487637 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −8.59841e6 | −0.490174 | ||||||||
\(791\) | 1.00953e7 | 0.573690 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.90534e6 | 0.164064 | ||||||||
\(794\) | 2.07430e7 | 1.16767 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.44030e6 | 0.472145 | ||||||||
\(797\) | −2.67358e7 | −1.49090 | −0.745448 | − | 0.666564i | \(-0.767764\pi\) | ||||
−0.745448 | + | 0.666564i | \(0.767764\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.15719e6 | 0.174958 | ||||||||
\(800\) | −5.27974e6 | −0.291667 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −8.21846e6 | −0.451185 | ||||||||
\(803\) | −2.59213e6 | −0.141863 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.39968e7 | 0.761271 | ||||||||
\(806\) | −4.01544e6 | −0.217719 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.21665e7 | 0.655599 | ||||||||
\(809\) | −1.57538e7 | −0.846279 | −0.423140 | − | 0.906065i | \(-0.639072\pi\) | ||||
−0.423140 | + | 0.906065i | \(0.639072\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.93811e7 | 1.03473 | 0.517364 | − | 0.855765i | \(-0.326913\pi\) | ||||
0.517364 | + | 0.855765i | \(0.326913\pi\) | |||||||
\(812\) | 2.68442e6 | 0.142876 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.51256e6 | 0.0800111 | ||||||||
\(815\) | 2.53359e7 | 1.33611 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.31795e6 | −0.488388 | ||||||||
\(818\) | 1.91714e7 | 1.00178 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 7.17662e6 | 0.372722 | ||||||||
\(821\) | −1.75374e6 | −0.0908046 | −0.0454023 | − | 0.998969i | \(-0.514457\pi\) | ||||
−0.0454023 | + | 0.998969i | \(0.514457\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.28736e7 | −1.69180 | −0.845898 | − | 0.533344i | \(-0.820935\pi\) | ||||
−0.845898 | + | 0.533344i | \(0.820935\pi\) | |||||||
\(824\) | −9.10150e6 | −0.466977 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.11679e6 | 0.158949 | ||||||||
\(827\) | 148647. | 0.00755775 | 0.00377887 | − | 0.999993i | \(-0.498797\pi\) | ||||
0.00377887 | + | 0.999993i | \(0.498797\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.57770e7 | 1.30270 | 0.651352 | − | 0.758776i | \(-0.274202\pi\) | ||||
0.651352 | + | 0.758776i | \(0.274202\pi\) | |||||||
\(830\) | −2.89016e7 | −1.45622 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 638976. | 0.0320019 | ||||||||
\(833\) | −1.47421e6 | −0.0736119 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.57790e7 | −2.27222 | ||||||||
\(836\) | 2.15403e6 | 0.106595 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1.93711e7 | 0.952895 | ||||||||
\(839\) | 2.35917e7 | 1.15706 | 0.578528 | − | 0.815662i | \(-0.303627\pi\) | ||||
0.578528 | + | 0.815662i | \(0.303627\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.78737e6 | −0.428419 | ||||||||
\(842\) | 2.33603e7 | 1.13553 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 8.57552e6 | 0.414385 | ||||||||
\(845\) | 3.15731e7 | 1.52116 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.70917e6 | 0.369232 | ||||||||
\(848\) | −1.46534e6 | −0.0699761 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.26631e7 | 0.601165 | ||||||||
\(851\) | −1.94587e7 | −0.921062 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.08230e6 | 0.286217 | 0.143109 | − | 0.989707i | \(-0.454290\pi\) | ||||
0.143109 | + | 0.989707i | \(0.454290\pi\) | |||||||
\(854\) | 3.65030e6 | 0.171271 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.71021e6 | 0.173067 | ||||||||
\(857\) | −1.31230e7 | −0.610352 | −0.305176 | − | 0.952296i | \(-0.598715\pi\) | ||||
−0.305176 | + | 0.952296i | \(0.598715\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.31280e7 | −0.607039 | −0.303519 | − | 0.952825i | \(-0.598162\pi\) | ||||
−0.303519 | + | 0.952825i | \(0.598162\pi\) | |||||||
\(860\) | 6.14723e6 | 0.283422 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 9.61940e6 | 0.440941 | ||||||||
\(863\) | −1.43530e7 | −0.656020 | −0.328010 | − | 0.944674i | \(-0.606378\pi\) | ||||
−0.328010 | + | 0.944674i | \(0.606378\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.27726e7 | 1.94368 | ||||||||
\(866\) | 1.23203e7 | 0.558248 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −5.04504e6 | −0.227282 | ||||||||
\(869\) | −1.44094e6 | −0.0647287 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.85390e6 | 0.0828022 | ||||||||
\(872\) | 6.41158e6 | 0.285545 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.77111e7 | −1.22709 | ||||||||
\(875\) | 9.05623e6 | 0.399878 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.46782e7 | 0.644427 | 0.322214 | − | 0.946667i | \(-0.395573\pi\) | ||||
0.322214 | + | 0.946667i | \(0.395573\pi\) | |||||||
\(878\) | 2.19084e7 | 0.959125 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.42106e6 | −0.0618592 | ||||||||
\(881\) | −6.50392e6 | −0.282316 | −0.141158 | − | 0.989987i | \(-0.545083\pi\) | ||||
−0.141158 | + | 0.989987i | \(0.545083\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.32985e7 | −1.43722 | −0.718609 | − | 0.695414i | \(-0.755221\pi\) | ||||
−0.718609 | + | 0.695414i | \(0.755221\pi\) | |||||||
\(884\) | −1.53254e6 | −0.0659602 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.33117e7 | 0.569703 | ||||||||
\(887\) | −4.26864e7 | −1.82171 | −0.910857 | − | 0.412722i | \(-0.864578\pi\) | ||||
−0.910857 | + | 0.412722i | \(0.864578\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.00777e7 | −0.427670 | ||||||||
\(890\) | −4.44116e6 | −0.187941 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 694160. | 0.0292111 | ||||||||
\(893\) | −1.13484e7 | −0.476218 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.44695e7 | −2.69028 | ||||||||
\(896\) | 802816. | 0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −9.72884e6 | −0.402597 | ||||||||
\(899\) | −2.20334e7 | −0.909250 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.51454e6 | 0.144230 | ||||||||
\(902\) | 1.20268e6 | 0.0492189 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.31857e7 | 0.536637 | ||||||||
\(905\) | −5.32694e7 | −2.16200 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.06295e7 | 0.832667 | 0.416334 | − | 0.909212i | \(-0.363315\pi\) | ||||
0.416334 | + | 0.909212i | \(0.363315\pi\) | |||||||
\(908\) | 1.94028e7 | 0.781000 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.78242e6 | −0.111383 | ||||||||
\(911\) | 3.06892e7 | 1.22515 | 0.612575 | − | 0.790412i | \(-0.290134\pi\) | ||||
0.612575 | + | 0.790412i | \(0.290134\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.84340e6 | −0.192297 | ||||||||
\(914\) | −3.22369e7 | −1.27640 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9.10125e6 | 0.358395 | ||||||||
\(917\) | −9.91025e6 | −0.389190 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.94223e6 | 0.193034 | 0.0965170 | − | 0.995331i | \(-0.469230\pi\) | ||||
0.0965170 | + | 0.995331i | \(0.469230\pi\) | |||||||
\(920\) | 1.82815e7 | 0.712103 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −7.78670e6 | −0.301666 | ||||||||
\(923\) | 8.71712e6 | 0.336798 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.19620e7 | −1.22823 | ||||||||
\(926\) | 1.77914e7 | 0.681842 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.50618e6 | 0.133648 | ||||||||
\(929\) | −3.50874e7 | −1.33386 | −0.666932 | − | 0.745119i | \(-0.732393\pi\) | ||||
−0.666932 | + | 0.745119i | \(0.732393\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.29901e6 | 0.200364 | ||||||||
\(932\) | 5.65552e6 | 0.213271 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2.08701e7 | 0.782812 | ||||||||
\(935\) | 3.40831e6 | 0.127500 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.12272e7 | −0.417757 | −0.208878 | − | 0.977942i | \(-0.566981\pi\) | ||||
−0.208878 | + | 0.977942i | \(0.566981\pi\) | |||||||
\(938\) | 2.32926e6 | 0.0864394 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 7.48675e6 | 0.276359 | ||||||||
\(941\) | 3.58550e6 | 0.132000 | 0.0660002 | − | 0.997820i | \(-0.478976\pi\) | ||||
0.0660002 | + | 0.997820i | \(0.478976\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.54721e7 | −0.566593 | ||||||||
\(944\) | 4.07091e6 | 0.148683 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.03017e6 | 0.0374266 | ||||||||
\(947\) | 2.44504e7 | 0.885954 | 0.442977 | − | 0.896533i | \(-0.353922\pi\) | ||||
0.442977 | + | 0.896533i | \(0.353922\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.62906e6 | −0.238939 | ||||||||
\(950\) | −4.55172e7 | −1.63631 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.92550e6 | −0.0688576 | ||||||||
\(953\) | −6.77017e6 | −0.241472 | −0.120736 | − | 0.992685i | \(-0.538525\pi\) | ||||
−0.120736 | + | 0.992685i | \(0.538525\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.46402e7 | −0.519443 | ||||||||
\(956\) | 1.72009e7 | 0.608704 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 7.73638e6 | 0.272348 | ||||||||
\(959\) | 1.38605e7 | 0.486669 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.27801e7 | 0.446401 | ||||||||
\(962\) | 3.86818e6 | 0.134762 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.41186e7 | −0.835911 | ||||||||
\(965\) | 7.54210e7 | 2.60720 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.96428e7 | −0.675518 | −0.337759 | − | 0.941233i | \(-0.609669\pi\) | ||||
−0.337759 | + | 0.941233i | \(0.609669\pi\) | |||||||
\(968\) | 1.00691e7 | 0.345385 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3.78851e7 | 1.29282 | ||||||||
\(971\) | −4.91321e7 | −1.67231 | −0.836156 | − | 0.548491i | \(-0.815202\pi\) | ||||
−0.836156 | + | 0.548491i | \(0.815202\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.84630e7 | 0.625202 | ||||||||
\(974\) | −1.13077e7 | −0.381924 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.76774e6 | 0.160210 | ||||||||
\(977\) | −3.86953e7 | −1.29694 | −0.648472 | − | 0.761238i | \(-0.724592\pi\) | ||||
−0.648472 | + | 0.761238i | \(0.724592\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −744261. | −0.0248181 | ||||||||
\(980\) | −3.49586e6 | −0.116276 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 3.40978e7 | 1.12836 | ||||||||
\(983\) | 3.11692e7 | 1.02883 | 0.514413 | − | 0.857542i | \(-0.328010\pi\) | ||||
0.514413 | + | 0.857542i | \(0.328010\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.83430e7 | 1.58761 | ||||||||
\(986\) | −8.40934e6 | −0.275467 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5.50867e6 | 0.179537 | ||||||||
\(989\) | −1.32529e7 | −0.430843 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.64590e7 | −0.532379 | −0.266189 | − | 0.963921i | \(-0.585765\pi\) | ||||
−0.266189 | + | 0.963921i | \(0.585765\pi\) | |||||||
\(992\) | −6.58944e6 | −0.212603 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.09523e7 | 0.351592 | ||||||||
\(995\) | −4.80042e7 | −1.53717 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.30534e7 | 1.69035 | 0.845173 | − | 0.534493i | \(-0.179497\pi\) | ||||
0.845173 | + | 0.534493i | \(0.179497\pi\) | |||||||
\(998\) | 1.83658e6 | 0.0583693 | ||||||||
\(999\) | 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 | 378.6.a.a.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 378.6.a.d.1.1 | yes | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
378.6.a.a.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
378.6.a.d.1.1 | yes | 1 | 3.2 | odd | 2 |