Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [10,24,Mod(1,10)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 24, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("10.1");
S:= CuspForms(chi, 24);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 24 \) |
Character orbit: | \([\chi]\) | \(=\) | 10.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: | \(33.5204037345\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{1492261}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 373065 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{5}\cdot 3\cdot 5 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(611.291\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 10.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2048.00 | 0.707107 | ||||||||
\(3\) | −339122. | −1.10525 | −0.552626 | − | 0.833430i | \(-0.686374\pi\) | ||||
−0.552626 | + | 0.833430i | \(0.686374\pi\) | |||||||
\(4\) | 4.19430e6 | 0.500000 | ||||||||
\(5\) | −4.88281e7 | −0.447214 | ||||||||
\(6\) | −6.94521e8 | −0.781530 | ||||||||
\(7\) | 5.67214e9 | 1.08422 | 0.542112 | − | 0.840306i | \(-0.317625\pi\) | ||||
0.542112 | + | 0.840306i | \(0.317625\pi\) | |||||||
\(8\) | 8.58993e9 | 0.353553 | ||||||||
\(9\) | 2.08602e10 | 0.221580 | ||||||||
\(10\) | −1.00000e11 | −0.316228 | ||||||||
\(11\) | −7.29056e10 | −0.0770451 | −0.0385225 | − | 0.999258i | \(-0.512265\pi\) | ||||
−0.0385225 | + | 0.999258i | \(0.512265\pi\) | |||||||
\(12\) | −1.42238e12 | −0.552626 | ||||||||
\(13\) | 7.50969e12 | 1.16218 | 0.581090 | − | 0.813839i | \(-0.302626\pi\) | ||||
0.581090 | + | 0.813839i | \(0.302626\pi\) | |||||||
\(14\) | 1.16165e13 | 0.766663 | ||||||||
\(15\) | 1.65587e13 | 0.494283 | ||||||||
\(16\) | 1.75922e13 | 0.250000 | ||||||||
\(17\) | −1.22795e14 | −0.868995 | −0.434497 | − | 0.900673i | \(-0.643074\pi\) | ||||
−0.434497 | + | 0.900673i | \(0.643074\pi\) | |||||||
\(18\) | 4.27218e13 | 0.156681 | ||||||||
\(19\) | −6.14006e14 | −1.20922 | −0.604612 | − | 0.796520i | \(-0.706672\pi\) | ||||
−0.604612 | + | 0.796520i | \(0.706672\pi\) | |||||||
\(20\) | −2.04800e14 | −0.223607 | ||||||||
\(21\) | −1.92354e15 | −1.19834 | ||||||||
\(22\) | −1.49311e14 | −0.0544791 | ||||||||
\(23\) | −3.69414e15 | −0.808431 | −0.404216 | − | 0.914664i | \(-0.632455\pi\) | ||||
−0.404216 | + | 0.914664i | \(0.632455\pi\) | |||||||
\(24\) | −2.91303e15 | −0.390765 | ||||||||
\(25\) | 2.38419e15 | 0.200000 | ||||||||
\(26\) | 1.53798e16 | 0.821785 | ||||||||
\(27\) | 2.48518e16 | 0.860350 | ||||||||
\(28\) | 2.37907e16 | 0.542112 | ||||||||
\(29\) | −1.00053e17 | −1.52284 | −0.761419 | − | 0.648260i | \(-0.775497\pi\) | ||||
−0.761419 | + | 0.648260i | \(0.775497\pi\) | |||||||
\(30\) | 3.39122e16 | 0.349511 | ||||||||
\(31\) | −1.10951e17 | −0.784280 | −0.392140 | − | 0.919905i | \(-0.628265\pi\) | ||||
−0.392140 | + | 0.919905i | \(0.628265\pi\) | |||||||
\(32\) | 3.60288e16 | 0.176777 | ||||||||
\(33\) | 2.47238e16 | 0.0851541 | ||||||||
\(34\) | −2.51484e17 | −0.614472 | ||||||||
\(35\) | −2.76960e17 | −0.484880 | ||||||||
\(36\) | 8.74941e16 | 0.110790 | ||||||||
\(37\) | −5.06294e17 | −0.467824 | −0.233912 | − | 0.972258i | \(-0.575153\pi\) | ||||
−0.233912 | + | 0.972258i | \(0.575153\pi\) | |||||||
\(38\) | −1.25749e18 | −0.855050 | ||||||||
\(39\) | −2.54670e18 | −1.28450 | ||||||||
\(40\) | −4.19430e17 | −0.158114 | ||||||||
\(41\) | 5.37240e17 | 0.152459 | 0.0762297 | − | 0.997090i | \(-0.475712\pi\) | ||||
0.0762297 | + | 0.997090i | \(0.475712\pi\) | |||||||
\(42\) | −3.93942e18 | −0.847355 | ||||||||
\(43\) | −3.30420e18 | −0.542225 | −0.271112 | − | 0.962548i | \(-0.587392\pi\) | ||||
−0.271112 | + | 0.962548i | \(0.587392\pi\) | |||||||
\(44\) | −3.05788e17 | −0.0385225 | ||||||||
\(45\) | −1.01857e18 | −0.0990935 | ||||||||
\(46\) | −7.56560e18 | −0.571647 | ||||||||
\(47\) | −2.83871e19 | −1.67492 | −0.837462 | − | 0.546495i | \(-0.815962\pi\) | ||||
−0.837462 | + | 0.546495i | \(0.815962\pi\) | |||||||
\(48\) | −5.96589e18 | −0.276313 | ||||||||
\(49\) | 4.80439e18 | 0.175543 | ||||||||
\(50\) | 4.88281e18 | 0.141421 | ||||||||
\(51\) | 4.16423e19 | 0.960457 | ||||||||
\(52\) | 3.14979e19 | 0.581090 | ||||||||
\(53\) | −4.33879e19 | −0.642978 | −0.321489 | − | 0.946913i | \(-0.604183\pi\) | ||||
−0.321489 | + | 0.946913i | \(0.604183\pi\) | |||||||
\(54\) | 5.08965e19 | 0.608359 | ||||||||
\(55\) | 3.55984e18 | 0.0344556 | ||||||||
\(56\) | 4.87233e19 | 0.383331 | ||||||||
\(57\) | 2.08223e20 | 1.33650 | ||||||||
\(58\) | −2.04909e20 | −1.07681 | ||||||||
\(59\) | −1.82553e20 | −0.788118 | −0.394059 | − | 0.919085i | \(-0.628930\pi\) | ||||
−0.394059 | + | 0.919085i | \(0.628930\pi\) | |||||||
\(60\) | 6.94521e19 | 0.247142 | ||||||||
\(61\) | 5.31488e20 | 1.56387 | 0.781934 | − | 0.623361i | \(-0.214233\pi\) | ||||
0.781934 | + | 0.623361i | \(0.214233\pi\) | |||||||
\(62\) | −2.27227e20 | −0.554570 | ||||||||
\(63\) | 1.18322e20 | 0.240242 | ||||||||
\(64\) | 7.37870e19 | 0.125000 | ||||||||
\(65\) | −3.66684e20 | −0.519743 | ||||||||
\(66\) | 5.06344e19 | 0.0602131 | ||||||||
\(67\) | 1.46349e21 | 1.46396 | 0.731982 | − | 0.681323i | \(-0.238595\pi\) | ||||
0.731982 | + | 0.681323i | \(0.238595\pi\) | |||||||
\(68\) | −5.15038e20 | −0.434497 | ||||||||
\(69\) | 1.25276e21 | 0.893520 | ||||||||
\(70\) | −5.67214e20 | −0.342862 | ||||||||
\(71\) | 3.40628e21 | 1.74908 | 0.874538 | − | 0.484957i | \(-0.161165\pi\) | ||||
0.874538 | + | 0.484957i | \(0.161165\pi\) | |||||||
\(72\) | 1.79188e20 | 0.0783403 | ||||||||
\(73\) | −1.21932e21 | −0.454889 | −0.227444 | − | 0.973791i | \(-0.573037\pi\) | ||||
−0.227444 | + | 0.973791i | \(0.573037\pi\) | |||||||
\(74\) | −1.03689e21 | −0.330802 | ||||||||
\(75\) | −8.08529e20 | −0.221050 | ||||||||
\(76\) | −2.57533e21 | −0.604612 | ||||||||
\(77\) | −4.13530e20 | −0.0835342 | ||||||||
\(78\) | −5.21564e21 | −0.908279 | ||||||||
\(79\) | −3.86872e21 | −0.581909 | −0.290955 | − | 0.956737i | \(-0.593973\pi\) | ||||
−0.290955 | + | 0.956737i | \(0.593973\pi\) | |||||||
\(80\) | −8.58993e20 | −0.111803 | ||||||||
\(81\) | −1.03916e22 | −1.17248 | ||||||||
\(82\) | 1.10027e21 | 0.107805 | ||||||||
\(83\) | −1.91453e22 | −1.63179 | −0.815893 | − | 0.578203i | \(-0.803754\pi\) | ||||
−0.815893 | + | 0.578203i | \(0.803754\pi\) | |||||||
\(84\) | −8.06793e21 | −0.599170 | ||||||||
\(85\) | 5.99584e21 | 0.388626 | ||||||||
\(86\) | −6.76701e21 | −0.383411 | ||||||||
\(87\) | 3.39302e22 | 1.68312 | ||||||||
\(88\) | −6.26254e20 | −0.0272395 | ||||||||
\(89\) | 1.38166e22 | 0.527737 | 0.263868 | − | 0.964559i | \(-0.415002\pi\) | ||||
0.263868 | + | 0.964559i | \(0.415002\pi\) | |||||||
\(90\) | −2.08602e21 | −0.0700697 | ||||||||
\(91\) | 4.25960e22 | 1.26006 | ||||||||
\(92\) | −1.54943e22 | −0.404216 | ||||||||
\(93\) | 3.76258e22 | 0.866827 | ||||||||
\(94\) | −5.81367e22 | −1.18435 | ||||||||
\(95\) | 2.99808e22 | 0.540781 | ||||||||
\(96\) | −1.22181e22 | −0.195383 | ||||||||
\(97\) | 3.39080e21 | 0.0481312 | 0.0240656 | − | 0.999710i | \(-0.492339\pi\) | ||||
0.0240656 | + | 0.999710i | \(0.492339\pi\) | |||||||
\(98\) | 9.83938e21 | 0.124128 | ||||||||
\(99\) | −1.52083e21 | −0.0170716 | ||||||||
\(100\) | 1.00000e22 | 0.100000 | ||||||||
\(101\) | −6.91624e22 | −0.616842 | −0.308421 | − | 0.951250i | \(-0.599801\pi\) | ||||
−0.308421 | + | 0.951250i | \(0.599801\pi\) | |||||||
\(102\) | 8.52835e22 | 0.679146 | ||||||||
\(103\) | 2.42869e23 | 1.72880 | 0.864398 | − | 0.502809i | \(-0.167700\pi\) | ||||
0.864398 | + | 0.502809i | \(0.167700\pi\) | |||||||
\(104\) | 6.45077e22 | 0.410893 | ||||||||
\(105\) | 9.39230e22 | 0.535914 | ||||||||
\(106\) | −8.88584e22 | −0.454654 | ||||||||
\(107\) | −3.44606e22 | −0.158274 | −0.0791371 | − | 0.996864i | \(-0.525216\pi\) | ||||
−0.0791371 | + | 0.996864i | \(0.525216\pi\) | |||||||
\(108\) | 1.04236e23 | 0.430175 | ||||||||
\(109\) | −4.80102e23 | −1.78209 | −0.891043 | − | 0.453918i | \(-0.850026\pi\) | ||||
−0.891043 | + | 0.453918i | \(0.850026\pi\) | |||||||
\(110\) | 7.29056e21 | 0.0243638 | ||||||||
\(111\) | 1.71695e23 | 0.517063 | ||||||||
\(112\) | 9.97853e22 | 0.271056 | ||||||||
\(113\) | −6.76991e23 | −1.66028 | −0.830139 | − | 0.557556i | \(-0.811739\pi\) | ||||
−0.830139 | + | 0.557556i | \(0.811739\pi\) | |||||||
\(114\) | 4.26440e23 | 0.945045 | ||||||||
\(115\) | 1.80378e23 | 0.361541 | ||||||||
\(116\) | −4.19653e23 | −0.761419 | ||||||||
\(117\) | 1.56654e23 | 0.257516 | ||||||||
\(118\) | −3.73869e23 | −0.557284 | ||||||||
\(119\) | −6.96509e23 | −0.942185 | ||||||||
\(120\) | 1.42238e23 | 0.174756 | ||||||||
\(121\) | −8.90115e23 | −0.994064 | ||||||||
\(122\) | 1.08849e24 | 1.10582 | ||||||||
\(123\) | −1.82190e23 | −0.168506 | ||||||||
\(124\) | −4.65362e23 | −0.392140 | ||||||||
\(125\) | −1.16415e23 | −0.0894427 | ||||||||
\(126\) | 2.42324e23 | 0.169877 | ||||||||
\(127\) | −6.00234e23 | −0.384218 | −0.192109 | − | 0.981374i | \(-0.561533\pi\) | ||||
−0.192109 | + | 0.981374i | \(0.561533\pi\) | |||||||
\(128\) | 1.51116e23 | 0.0883883 | ||||||||
\(129\) | 1.12053e24 | 0.599294 | ||||||||
\(130\) | −7.50969e23 | −0.367514 | ||||||||
\(131\) | 1.78064e24 | 0.797914 | 0.398957 | − | 0.916970i | \(-0.369372\pi\) | ||||
0.398957 | + | 0.916970i | \(0.369372\pi\) | |||||||
\(132\) | 1.03699e23 | 0.0425771 | ||||||||
\(133\) | −3.48273e24 | −1.31107 | ||||||||
\(134\) | 2.99724e24 | 1.03518 | ||||||||
\(135\) | −1.21347e24 | −0.384760 | ||||||||
\(136\) | −1.05480e24 | −0.307236 | ||||||||
\(137\) | −3.22877e24 | −0.864471 | −0.432236 | − | 0.901761i | \(-0.642275\pi\) | ||||
−0.432236 | + | 0.901761i | \(0.642275\pi\) | |||||||
\(138\) | 2.56566e24 | 0.631814 | ||||||||
\(139\) | −3.01015e23 | −0.0682210 | −0.0341105 | − | 0.999418i | \(-0.510860\pi\) | ||||
−0.0341105 | + | 0.999418i | \(0.510860\pi\) | |||||||
\(140\) | −1.16165e24 | −0.242440 | ||||||||
\(141\) | 9.62667e24 | 1.85121 | ||||||||
\(142\) | 6.97605e24 | 1.23678 | ||||||||
\(143\) | −5.47498e23 | −0.0895402 | ||||||||
\(144\) | 3.66977e23 | 0.0553950 | ||||||||
\(145\) | 4.88541e24 | 0.681034 | ||||||||
\(146\) | −2.49717e24 | −0.321655 | ||||||||
\(147\) | −1.62927e24 | −0.194019 | ||||||||
\(148\) | −2.12355e24 | −0.233912 | ||||||||
\(149\) | 1.49284e25 | 1.52185 | 0.760925 | − | 0.648840i | \(-0.224746\pi\) | ||||
0.760925 | + | 0.648840i | \(0.224746\pi\) | |||||||
\(150\) | −1.65587e24 | −0.156306 | ||||||||
\(151\) | 2.25537e24 | 0.197235 | 0.0986173 | − | 0.995125i | \(-0.468558\pi\) | ||||
0.0986173 | + | 0.995125i | \(0.468558\pi\) | |||||||
\(152\) | −5.27427e24 | −0.427525 | ||||||||
\(153\) | −2.56153e24 | −0.192552 | ||||||||
\(154\) | −8.46910e23 | −0.0590676 | ||||||||
\(155\) | 5.41752e24 | 0.350741 | ||||||||
\(156\) | −1.06816e25 | −0.642250 | ||||||||
\(157\) | −2.00139e25 | −1.11812 | −0.559058 | − | 0.829129i | \(-0.688837\pi\) | ||||
−0.559058 | + | 0.829129i | \(0.688837\pi\) | |||||||
\(158\) | −7.92313e24 | −0.411472 | ||||||||
\(159\) | 1.47138e25 | 0.710652 | ||||||||
\(160\) | −1.75922e24 | −0.0790569 | ||||||||
\(161\) | −2.09537e25 | −0.876521 | ||||||||
\(162\) | −2.12821e25 | −0.829070 | ||||||||
\(163\) | −5.04020e24 | −0.182932 | −0.0914661 | − | 0.995808i | \(-0.529155\pi\) | ||||
−0.0914661 | + | 0.995808i | \(0.529155\pi\) | |||||||
\(164\) | 2.25335e24 | 0.0762297 | ||||||||
\(165\) | −1.20722e24 | −0.0380821 | ||||||||
\(166\) | −3.92095e25 | −1.15385 | ||||||||
\(167\) | −4.08368e25 | −1.12153 | −0.560767 | − | 0.827974i | \(-0.689494\pi\) | ||||
−0.560767 | + | 0.827974i | \(0.689494\pi\) | |||||||
\(168\) | −1.65231e25 | −0.423677 | ||||||||
\(169\) | 1.46415e25 | 0.350663 | ||||||||
\(170\) | 1.22795e25 | 0.274800 | ||||||||
\(171\) | −1.28083e25 | −0.267939 | ||||||||
\(172\) | −1.38588e25 | −0.271112 | ||||||||
\(173\) | 8.79177e25 | 1.60896 | 0.804482 | − | 0.593978i | \(-0.202443\pi\) | ||||
0.804482 | + | 0.593978i | \(0.202443\pi\) | |||||||
\(174\) | 6.94890e25 | 1.19014 | ||||||||
\(175\) | 1.35234e25 | 0.216845 | ||||||||
\(176\) | −1.28257e24 | −0.0192613 | ||||||||
\(177\) | 6.19077e25 | 0.871069 | ||||||||
\(178\) | 2.82965e25 | 0.373166 | ||||||||
\(179\) | 6.44672e25 | 0.797129 | 0.398565 | − | 0.917140i | \(-0.369508\pi\) | ||||
0.398565 | + | 0.917140i | \(0.369508\pi\) | |||||||
\(180\) | −4.27218e24 | −0.0495468 | ||||||||
\(181\) | −4.53664e25 | −0.493663 | −0.246832 | − | 0.969058i | \(-0.579389\pi\) | ||||
−0.246832 | + | 0.969058i | \(0.579389\pi\) | |||||||
\(182\) | 8.72366e25 | 0.891000 | ||||||||
\(183\) | −1.80239e26 | −1.72847 | ||||||||
\(184\) | −3.17324e25 | −0.285824 | ||||||||
\(185\) | 2.47214e25 | 0.209217 | ||||||||
\(186\) | 7.70577e25 | 0.612939 | ||||||||
\(187\) | 8.95242e24 | 0.0669518 | ||||||||
\(188\) | −1.19064e26 | −0.837462 | ||||||||
\(189\) | 1.40963e26 | 0.932812 | ||||||||
\(190\) | 6.14006e25 | 0.382390 | ||||||||
\(191\) | 4.01824e25 | 0.235587 | 0.117794 | − | 0.993038i | \(-0.462418\pi\) | ||||
0.117794 | + | 0.993038i | \(0.462418\pi\) | |||||||
\(192\) | −2.50228e25 | −0.138156 | ||||||||
\(193\) | −3.37563e26 | −1.75568 | −0.877841 | − | 0.478952i | \(-0.841017\pi\) | ||||
−0.877841 | + | 0.478952i | \(0.841017\pi\) | |||||||
\(194\) | 6.94435e24 | 0.0340339 | ||||||||
\(195\) | 1.24350e26 | 0.574446 | ||||||||
\(196\) | 2.01511e25 | 0.0877714 | ||||||||
\(197\) | 3.28937e26 | 1.35130 | 0.675649 | − | 0.737223i | \(-0.263863\pi\) | ||||
0.675649 | + | 0.737223i | \(0.263863\pi\) | |||||||
\(198\) | −3.11465e24 | −0.0120715 | ||||||||
\(199\) | 3.82254e26 | 1.39811 | 0.699055 | − | 0.715068i | \(-0.253604\pi\) | ||||
0.699055 | + | 0.715068i | \(0.253604\pi\) | |||||||
\(200\) | 2.04800e25 | 0.0707107 | ||||||||
\(201\) | −4.96302e26 | −1.61805 | ||||||||
\(202\) | −1.41645e26 | −0.436173 | ||||||||
\(203\) | −5.67515e26 | −1.65110 | ||||||||
\(204\) | 1.74661e26 | 0.480229 | ||||||||
\(205\) | −2.62324e25 | −0.0681819 | ||||||||
\(206\) | 4.97395e26 | 1.22244 | ||||||||
\(207\) | −7.70606e25 | −0.179132 | ||||||||
\(208\) | 1.32112e26 | 0.290545 | ||||||||
\(209\) | 4.47645e25 | 0.0931647 | ||||||||
\(210\) | 1.92354e26 | 0.378948 | ||||||||
\(211\) | −1.52630e26 | −0.284703 | −0.142352 | − | 0.989816i | \(-0.545466\pi\) | ||||
−0.142352 | + | 0.989816i | \(0.545466\pi\) | |||||||
\(212\) | −1.81982e26 | −0.321489 | ||||||||
\(213\) | −1.15514e27 | −1.93317 | ||||||||
\(214\) | −7.05754e25 | −0.111917 | ||||||||
\(215\) | 1.61338e26 | 0.242490 | ||||||||
\(216\) | 2.13476e26 | 0.304180 | ||||||||
\(217\) | −6.29329e26 | −0.850336 | ||||||||
\(218\) | −9.83249e26 | −1.26013 | ||||||||
\(219\) | 4.13498e26 | 0.502766 | ||||||||
\(220\) | 1.49311e25 | 0.0172278 | ||||||||
\(221\) | −9.22150e26 | −1.00993 | ||||||||
\(222\) | 3.51632e26 | 0.365619 | ||||||||
\(223\) | 7.09326e26 | 0.700390 | 0.350195 | − | 0.936677i | \(-0.386115\pi\) | ||||
0.350195 | + | 0.936677i | \(0.386115\pi\) | |||||||
\(224\) | 2.04360e26 | 0.191666 | ||||||||
\(225\) | 4.97347e25 | 0.0443160 | ||||||||
\(226\) | −1.38648e27 | −1.17399 | ||||||||
\(227\) | 1.34868e27 | 1.08545 | 0.542727 | − | 0.839909i | \(-0.317392\pi\) | ||||
0.542727 | + | 0.839909i | \(0.317392\pi\) | |||||||
\(228\) | 8.73350e26 | 0.668248 | ||||||||
\(229\) | 1.71030e27 | 1.24441 | 0.622207 | − | 0.782853i | \(-0.286236\pi\) | ||||
0.622207 | + | 0.782853i | \(0.286236\pi\) | |||||||
\(230\) | 3.69414e26 | 0.255648 | ||||||||
\(231\) | 1.40237e26 | 0.0923262 | ||||||||
\(232\) | −8.59450e26 | −0.538404 | ||||||||
\(233\) | 7.74363e26 | 0.461691 | 0.230846 | − | 0.972990i | \(-0.425851\pi\) | ||||
0.230846 | + | 0.972990i | \(0.425851\pi\) | |||||||
\(234\) | 3.20827e26 | 0.182091 | ||||||||
\(235\) | 1.38609e27 | 0.749049 | ||||||||
\(236\) | −7.65684e26 | −0.394059 | ||||||||
\(237\) | 1.31196e27 | 0.643156 | ||||||||
\(238\) | −1.42645e27 | −0.666226 | ||||||||
\(239\) | 2.12271e27 | 0.944744 | 0.472372 | − | 0.881399i | \(-0.343398\pi\) | ||||
0.472372 | + | 0.881399i | \(0.343398\pi\) | |||||||
\(240\) | 2.91303e26 | 0.123571 | ||||||||
\(241\) | −1.93749e27 | −0.783508 | −0.391754 | − | 0.920070i | \(-0.628132\pi\) | ||||
−0.391754 | + | 0.920070i | \(0.628132\pi\) | |||||||
\(242\) | −1.82296e27 | −0.702909 | ||||||||
\(243\) | 1.18440e27 | 0.435537 | ||||||||
\(244\) | 2.22922e27 | 0.781934 | ||||||||
\(245\) | −2.34589e26 | −0.0785051 | ||||||||
\(246\) | −3.73125e26 | −0.119152 | ||||||||
\(247\) | −4.61100e27 | −1.40534 | ||||||||
\(248\) | −9.53061e26 | −0.277285 | ||||||||
\(249\) | 6.49257e27 | 1.80353 | ||||||||
\(250\) | −2.38419e26 | −0.0632456 | ||||||||
\(251\) | 4.58522e27 | 1.16175 | 0.580875 | − | 0.813993i | \(-0.302711\pi\) | ||||
0.580875 | + | 0.813993i | \(0.302711\pi\) | |||||||
\(252\) | 4.96279e26 | 0.120121 | ||||||||
\(253\) | 2.69323e26 | 0.0622856 | ||||||||
\(254\) | −1.22928e27 | −0.271683 | ||||||||
\(255\) | −2.03332e27 | −0.429530 | ||||||||
\(256\) | 3.09485e26 | 0.0625000 | ||||||||
\(257\) | −5.64317e27 | −1.08966 | −0.544832 | − | 0.838545i | \(-0.683407\pi\) | ||||
−0.544832 | + | 0.838545i | \(0.683407\pi\) | |||||||
\(258\) | 2.29484e27 | 0.423765 | ||||||||
\(259\) | −2.87177e27 | −0.507227 | ||||||||
\(260\) | −1.53798e27 | −0.259871 | ||||||||
\(261\) | −2.08713e27 | −0.337430 | ||||||||
\(262\) | 3.64675e27 | 0.564210 | ||||||||
\(263\) | −1.17070e28 | −1.73363 | −0.866813 | − | 0.498633i | \(-0.833836\pi\) | ||||
−0.866813 | + | 0.498633i | \(0.833836\pi\) | |||||||
\(264\) | 2.12376e26 | 0.0301065 | ||||||||
\(265\) | 2.11855e27 | 0.287548 | ||||||||
\(266\) | −7.13263e27 | −0.927066 | ||||||||
\(267\) | −4.68552e27 | −0.583282 | ||||||||
\(268\) | 6.13834e27 | 0.731982 | ||||||||
\(269\) | −1.41632e28 | −1.61812 | −0.809060 | − | 0.587726i | \(-0.800023\pi\) | ||||
−0.809060 | + | 0.587726i | \(0.800023\pi\) | |||||||
\(270\) | −2.48518e27 | −0.272066 | ||||||||
\(271\) | 1.48604e28 | 1.55913 | 0.779566 | − | 0.626320i | \(-0.215439\pi\) | ||||
0.779566 | + | 0.626320i | \(0.215439\pi\) | |||||||
\(272\) | −2.16023e27 | −0.217249 | ||||||||
\(273\) | −1.44452e28 | −1.39269 | ||||||||
\(274\) | −6.61252e27 | −0.611273 | ||||||||
\(275\) | −1.73820e26 | −0.0154090 | ||||||||
\(276\) | 5.25447e27 | 0.446760 | ||||||||
\(277\) | 1.32716e28 | 1.08245 | 0.541223 | − | 0.840879i | \(-0.317962\pi\) | ||||
0.541223 | + | 0.840879i | \(0.317962\pi\) | |||||||
\(278\) | −6.16479e26 | −0.0482395 | ||||||||
\(279\) | −2.31446e27 | −0.173781 | ||||||||
\(280\) | −2.37907e27 | −0.171431 | ||||||||
\(281\) | 1.06254e28 | 0.734892 | 0.367446 | − | 0.930045i | \(-0.380232\pi\) | ||||
0.367446 | + | 0.930045i | \(0.380232\pi\) | |||||||
\(282\) | 1.97154e28 | 1.30900 | ||||||||
\(283\) | 2.71424e28 | 1.73023 | 0.865117 | − | 0.501570i | \(-0.167244\pi\) | ||||
0.865117 | + | 0.501570i | \(0.167244\pi\) | |||||||
\(284\) | 1.42870e28 | 0.874538 | ||||||||
\(285\) | −1.01671e28 | −0.597699 | ||||||||
\(286\) | −1.12128e27 | −0.0633145 | ||||||||
\(287\) | 3.04730e27 | 0.165300 | ||||||||
\(288\) | 7.51569e26 | 0.0391702 | ||||||||
\(289\) | −4.88902e27 | −0.244848 | ||||||||
\(290\) | 1.00053e28 | 0.481564 | ||||||||
\(291\) | −1.14989e27 | −0.0531971 | ||||||||
\(292\) | −5.11420e27 | −0.227444 | ||||||||
\(293\) | −1.41085e27 | −0.0603257 | −0.0301629 | − | 0.999545i | \(-0.509603\pi\) | ||||
−0.0301629 | + | 0.999545i | \(0.509603\pi\) | |||||||
\(294\) | −3.33675e27 | −0.137192 | ||||||||
\(295\) | 8.91373e27 | 0.352457 | ||||||||
\(296\) | −4.34903e27 | −0.165401 | ||||||||
\(297\) | −1.81184e27 | −0.0662857 | ||||||||
\(298\) | 3.05734e28 | 1.07611 | ||||||||
\(299\) | −2.77418e28 | −0.939543 | ||||||||
\(300\) | −3.39122e27 | −0.110525 | ||||||||
\(301\) | −1.87419e28 | −0.587893 | ||||||||
\(302\) | 4.61900e27 | 0.139466 | ||||||||
\(303\) | 2.34544e28 | 0.681765 | ||||||||
\(304\) | −1.08017e28 | −0.302306 | ||||||||
\(305\) | −2.59516e28 | −0.699383 | ||||||||
\(306\) | −5.24601e27 | −0.136155 | ||||||||
\(307\) | 4.70277e28 | 1.17561 | 0.587804 | − | 0.809003i | \(-0.299993\pi\) | ||||
0.587804 | + | 0.809003i | \(0.299993\pi\) | |||||||
\(308\) | −1.73447e27 | −0.0417671 | ||||||||
\(309\) | −8.23620e28 | −1.91075 | ||||||||
\(310\) | 1.10951e28 | 0.248011 | ||||||||
\(311\) | 2.33572e28 | 0.503126 | 0.251563 | − | 0.967841i | \(-0.419055\pi\) | ||||
0.251563 | + | 0.967841i | \(0.419055\pi\) | |||||||
\(312\) | −2.18760e28 | −0.454140 | ||||||||
\(313\) | 3.37396e28 | 0.675119 | 0.337560 | − | 0.941304i | \(-0.390399\pi\) | ||||
0.337560 | + | 0.941304i | \(0.390399\pi\) | |||||||
\(314\) | −4.09886e28 | −0.790627 | ||||||||
\(315\) | −5.77744e27 | −0.107440 | ||||||||
\(316\) | −1.62266e28 | −0.290955 | ||||||||
\(317\) | −2.97844e28 | −0.515000 | −0.257500 | − | 0.966278i | \(-0.582899\pi\) | ||||
−0.257500 | + | 0.966278i | \(0.582899\pi\) | |||||||
\(318\) | 3.01338e28 | 0.502507 | ||||||||
\(319\) | 7.29443e27 | 0.117327 | ||||||||
\(320\) | −3.60288e27 | −0.0559017 | ||||||||
\(321\) | 1.16863e28 | 0.174933 | ||||||||
\(322\) | −4.29131e28 | −0.619794 | ||||||||
\(323\) | 7.53968e28 | 1.05081 | ||||||||
\(324\) | −4.35857e28 | −0.586241 | ||||||||
\(325\) | 1.79045e28 | 0.232436 | ||||||||
\(326\) | −1.03223e28 | −0.129353 | ||||||||
\(327\) | 1.62813e29 | 1.96965 | ||||||||
\(328\) | 4.61486e27 | 0.0539025 | ||||||||
\(329\) | −1.61015e29 | −1.81599 | ||||||||
\(330\) | −2.47238e27 | −0.0269281 | ||||||||
\(331\) | 5.24477e28 | 0.551702 | 0.275851 | − | 0.961200i | \(-0.411040\pi\) | ||||
0.275851 | + | 0.961200i | \(0.411040\pi\) | |||||||
\(332\) | −8.03010e28 | −0.815893 | ||||||||
\(333\) | −1.05614e28 | −0.103660 | ||||||||
\(334\) | −8.36338e28 | −0.793044 | ||||||||
\(335\) | −7.14597e28 | −0.654705 | ||||||||
\(336\) | −3.38393e28 | −0.299585 | ||||||||
\(337\) | −1.64340e29 | −1.40605 | −0.703024 | − | 0.711166i | \(-0.748167\pi\) | ||||
−0.703024 | + | 0.711166i | \(0.748167\pi\) | |||||||
\(338\) | 2.99859e28 | 0.247956 | ||||||||
\(339\) | 2.29582e29 | 1.83502 | ||||||||
\(340\) | 2.51484e28 | 0.194313 | ||||||||
\(341\) | 8.08894e27 | 0.0604249 | ||||||||
\(342\) | −2.62314e28 | −0.189462 | ||||||||
\(343\) | −1.27988e29 | −0.893897 | ||||||||
\(344\) | −2.83829e28 | −0.191705 | ||||||||
\(345\) | −6.11700e28 | −0.399594 | ||||||||
\(346\) | 1.80055e29 | 1.13771 | ||||||||
\(347\) | 2.04136e28 | 0.124776 | 0.0623881 | − | 0.998052i | \(-0.480128\pi\) | ||||
0.0623881 | + | 0.998052i | \(0.480128\pi\) | |||||||
\(348\) | 1.42313e29 | 0.841559 | ||||||||
\(349\) | 2.60772e29 | 1.49200 | 0.745999 | − | 0.665947i | \(-0.231972\pi\) | ||||
0.745999 | + | 0.665947i | \(0.231972\pi\) | |||||||
\(350\) | 2.76960e28 | 0.153333 | ||||||||
\(351\) | 1.86629e29 | 0.999881 | ||||||||
\(352\) | −2.62670e27 | −0.0136198 | ||||||||
\(353\) | −3.17093e29 | −1.59139 | −0.795696 | − | 0.605696i | \(-0.792895\pi\) | ||||
−0.795696 | + | 0.605696i | \(0.792895\pi\) | |||||||
\(354\) | 1.26787e29 | 0.615939 | ||||||||
\(355\) | −1.66322e29 | −0.782211 | ||||||||
\(356\) | 5.79512e28 | 0.263868 | ||||||||
\(357\) | 2.36201e29 | 1.04135 | ||||||||
\(358\) | 1.32029e29 | 0.563656 | ||||||||
\(359\) | 3.06761e27 | 0.0126828 | 0.00634138 | − | 0.999980i | \(-0.497981\pi\) | ||||
0.00634138 | + | 0.999980i | \(0.497981\pi\) | |||||||
\(360\) | −8.74941e27 | −0.0350348 | ||||||||
\(361\) | 1.19174e29 | 0.462221 | ||||||||
\(362\) | −9.29104e28 | −0.349073 | ||||||||
\(363\) | 3.01857e29 | 1.09869 | ||||||||
\(364\) | 1.78661e29 | 0.630032 | ||||||||
\(365\) | 5.95372e28 | 0.203432 | ||||||||
\(366\) | −3.69129e29 | −1.22221 | ||||||||
\(367\) | 1.46745e29 | 0.470874 | 0.235437 | − | 0.971890i | \(-0.424348\pi\) | ||||
0.235437 | + | 0.971890i | \(0.424348\pi\) | |||||||
\(368\) | −6.49880e28 | −0.202108 | ||||||||
\(369\) | 1.12070e28 | 0.0337819 | ||||||||
\(370\) | 5.06294e28 | 0.147939 | ||||||||
\(371\) | −2.46102e29 | −0.697132 | ||||||||
\(372\) | 1.57814e29 | 0.433413 | ||||||||
\(373\) | −5.22732e29 | −1.39196 | −0.695981 | − | 0.718060i | \(-0.745030\pi\) | ||||
−0.695981 | + | 0.718060i | \(0.745030\pi\) | |||||||
\(374\) | 1.83346e28 | 0.0473420 | ||||||||
\(375\) | 3.94789e28 | 0.0988567 | ||||||||
\(376\) | −2.43843e29 | −0.592175 | ||||||||
\(377\) | −7.51368e29 | −1.76981 | ||||||||
\(378\) | 2.88692e29 | 0.659598 | ||||||||
\(379\) | −5.96093e29 | −1.32118 | −0.660592 | − | 0.750745i | \(-0.729694\pi\) | ||||
−0.660592 | + | 0.750745i | \(0.729694\pi\) | |||||||
\(380\) | 1.25749e29 | 0.270391 | ||||||||
\(381\) | 2.03552e29 | 0.424657 | ||||||||
\(382\) | 8.22935e28 | 0.166585 | ||||||||
\(383\) | −4.94929e29 | −0.972203 | −0.486101 | − | 0.873902i | \(-0.661581\pi\) | ||||
−0.486101 | + | 0.873902i | \(0.661581\pi\) | |||||||
\(384\) | −5.12466e28 | −0.0976913 | ||||||||
\(385\) | 2.01919e28 | 0.0373576 | ||||||||
\(386\) | −6.91329e29 | −1.24145 | ||||||||
\(387\) | −6.89264e28 | −0.120146 | ||||||||
\(388\) | 1.42220e28 | 0.0240656 | ||||||||
\(389\) | 5.66942e28 | 0.0931361 | 0.0465681 | − | 0.998915i | \(-0.485172\pi\) | ||||
0.0465681 | + | 0.998915i | \(0.485172\pi\) | |||||||
\(390\) | 2.54670e29 | 0.406195 | ||||||||
\(391\) | 4.53621e29 | 0.702523 | ||||||||
\(392\) | 4.12694e28 | 0.0620638 | ||||||||
\(393\) | −6.03853e29 | −0.881895 | ||||||||
\(394\) | 6.73663e29 | 0.955512 | ||||||||
\(395\) | 1.88902e29 | 0.260238 | ||||||||
\(396\) | −6.37881e27 | −0.00853582 | ||||||||
\(397\) | 3.68342e29 | 0.478807 | 0.239403 | − | 0.970920i | \(-0.423048\pi\) | ||||
0.239403 | + | 0.970920i | \(0.423048\pi\) | |||||||
\(398\) | 7.82856e29 | 0.988613 | ||||||||
\(399\) | 1.18107e30 | 1.44906 | ||||||||
\(400\) | 4.19430e28 | 0.0500000 | ||||||||
\(401\) | −1.21847e30 | −1.41142 | −0.705710 | − | 0.708501i | \(-0.749372\pi\) | ||||
−0.705710 | + | 0.708501i | \(0.749372\pi\) | |||||||
\(402\) | −1.01643e30 | −1.14413 | ||||||||
\(403\) | −8.33207e29 | −0.911475 | ||||||||
\(404\) | −2.90088e29 | −0.308421 | ||||||||
\(405\) | 5.07404e29 | 0.524350 | ||||||||
\(406\) | −1.16227e30 | −1.16750 | ||||||||
\(407\) | 3.69116e28 | 0.0360436 | ||||||||
\(408\) | 3.57705e29 | 0.339573 | ||||||||
\(409\) | 1.47992e30 | 1.36590 | 0.682952 | − | 0.730464i | \(-0.260696\pi\) | ||||
0.682952 | + | 0.730464i | \(0.260696\pi\) | |||||||
\(410\) | −5.37240e28 | −0.0482119 | ||||||||
\(411\) | 1.09495e30 | 0.955458 | ||||||||
\(412\) | 1.01867e30 | 0.864398 | ||||||||
\(413\) | −1.03547e30 | −0.854497 | ||||||||
\(414\) | −1.57820e29 | −0.126666 | ||||||||
\(415\) | 9.34827e29 | 0.729757 | ||||||||
\(416\) | 2.70565e29 | 0.205446 | ||||||||
\(417\) | 1.02081e29 | 0.0754014 | ||||||||
\(418\) | 9.16777e28 | 0.0658774 | ||||||||
\(419\) | 4.36760e29 | 0.305339 | 0.152669 | − | 0.988277i | \(-0.451213\pi\) | ||||
0.152669 | + | 0.988277i | \(0.451213\pi\) | |||||||
\(420\) | 3.93942e29 | 0.267957 | ||||||||
\(421\) | 2.90507e30 | 1.92271 | 0.961353 | − | 0.275319i | \(-0.0887836\pi\) | ||||
0.961353 | + | 0.275319i | \(0.0887836\pi\) | |||||||
\(422\) | −3.12587e29 | −0.201316 | ||||||||
\(423\) | −5.92161e29 | −0.371129 | ||||||||
\(424\) | −3.72699e29 | −0.227327 | ||||||||
\(425\) | −2.92765e29 | −0.173799 | ||||||||
\(426\) | −2.36573e30 | −1.36696 | ||||||||
\(427\) | 3.01467e30 | 1.69558 | ||||||||
\(428\) | −1.44538e29 | −0.0791371 | ||||||||
\(429\) | 1.85668e29 | 0.0989644 | ||||||||
\(430\) | 3.30420e29 | 0.171467 | ||||||||
\(431\) | 5.61010e29 | 0.283454 | 0.141727 | − | 0.989906i | \(-0.454735\pi\) | ||||
0.141727 | + | 0.989906i | \(0.454735\pi\) | |||||||
\(432\) | 4.37198e29 | 0.215087 | ||||||||
\(433\) | −2.91680e30 | −1.39732 | −0.698659 | − | 0.715455i | \(-0.746220\pi\) | ||||
−0.698659 | + | 0.715455i | \(0.746220\pi\) | |||||||
\(434\) | −1.28887e30 | −0.601278 | ||||||||
\(435\) | −1.65675e30 | −0.752713 | ||||||||
\(436\) | −2.01369e30 | −0.891043 | ||||||||
\(437\) | 2.26822e30 | 0.977574 | ||||||||
\(438\) | 8.46844e29 | 0.355509 | ||||||||
\(439\) | 1.03028e30 | 0.421322 | 0.210661 | − | 0.977559i | \(-0.432438\pi\) | ||||
0.210661 | + | 0.977559i | \(0.432438\pi\) | |||||||
\(440\) | 3.05788e28 | 0.0121819 | ||||||||
\(441\) | 1.00221e29 | 0.0388967 | ||||||||
\(442\) | −1.88856e30 | −0.714127 | ||||||||
\(443\) | −2.53393e30 | −0.933582 | −0.466791 | − | 0.884368i | \(-0.654590\pi\) | ||||
−0.466791 | + | 0.884368i | \(0.654590\pi\) | |||||||
\(444\) | 7.20142e29 | 0.258532 | ||||||||
\(445\) | −6.74640e29 | −0.236011 | ||||||||
\(446\) | 1.45270e30 | 0.495250 | ||||||||
\(447\) | −5.06255e30 | −1.68203 | ||||||||
\(448\) | 4.18530e29 | 0.135528 | ||||||||
\(449\) | −4.77953e29 | −0.150852 | −0.0754262 | − | 0.997151i | \(-0.524032\pi\) | ||||
−0.0754262 | + | 0.997151i | \(0.524032\pi\) | |||||||
\(450\) | 1.01857e29 | 0.0313361 | ||||||||
\(451\) | −3.91678e28 | −0.0117462 | ||||||||
\(452\) | −2.83951e30 | −0.830139 | ||||||||
\(453\) | −7.64845e29 | −0.217994 | ||||||||
\(454\) | 2.76209e30 | 0.767531 | ||||||||
\(455\) | −2.07988e30 | −0.563518 | ||||||||
\(456\) | 1.78862e30 | 0.472522 | ||||||||
\(457\) | 5.53212e29 | 0.142513 | 0.0712566 | − | 0.997458i | \(-0.477299\pi\) | ||||
0.0712566 | + | 0.997458i | \(0.477299\pi\) | |||||||
\(458\) | 3.50270e30 | 0.879934 | ||||||||
\(459\) | −3.05167e30 | −0.747639 | ||||||||
\(460\) | 7.56560e29 | 0.180771 | ||||||||
\(461\) | −3.77831e30 | −0.880516 | −0.440258 | − | 0.897871i | \(-0.645113\pi\) | ||||
−0.440258 | + | 0.897871i | \(0.645113\pi\) | |||||||
\(462\) | 2.87205e29 | 0.0652845 | ||||||||
\(463\) | 9.57536e29 | 0.212312 | 0.106156 | − | 0.994350i | \(-0.466146\pi\) | ||||
0.106156 | + | 0.994350i | \(0.466146\pi\) | |||||||
\(464\) | −1.76015e30 | −0.380709 | ||||||||
\(465\) | −1.83720e30 | −0.387657 | ||||||||
\(466\) | 1.58590e30 | 0.326465 | ||||||||
\(467\) | 1.81078e30 | 0.363681 | 0.181841 | − | 0.983328i | \(-0.441795\pi\) | ||||
0.181841 | + | 0.983328i | \(0.441795\pi\) | |||||||
\(468\) | 6.57054e29 | 0.128758 | ||||||||
\(469\) | 8.30114e30 | 1.58727 | ||||||||
\(470\) | 2.83871e30 | 0.529658 | ||||||||
\(471\) | 6.78716e30 | 1.23580 | ||||||||
\(472\) | −1.56812e30 | −0.278642 | ||||||||
\(473\) | 2.40895e29 | 0.0417757 | ||||||||
\(474\) | 2.68690e30 | 0.454780 | ||||||||
\(475\) | −1.46391e30 | −0.241845 | ||||||||
\(476\) | −2.92137e30 | −0.471093 | ||||||||
\(477\) | −9.05081e29 | −0.142471 | ||||||||
\(478\) | 4.34730e30 | 0.668035 | ||||||||
\(479\) | −1.31018e31 | −1.96550 | −0.982751 | − | 0.184936i | \(-0.940792\pi\) | ||||
−0.982751 | + | 0.184936i | \(0.940792\pi\) | |||||||
\(480\) | 5.96589e29 | 0.0873778 | ||||||||
\(481\) | −3.80211e30 | −0.543696 | ||||||||
\(482\) | −3.96798e30 | −0.554024 | ||||||||
\(483\) | 7.10584e30 | 0.968776 | ||||||||
\(484\) | −3.73341e30 | −0.497032 | ||||||||
\(485\) | −1.65566e29 | −0.0215249 | ||||||||
\(486\) | 2.42565e30 | 0.307972 | ||||||||
\(487\) | −7.78763e30 | −0.965656 | −0.482828 | − | 0.875715i | \(-0.660390\pi\) | ||||
−0.482828 | + | 0.875715i | \(0.660390\pi\) | |||||||
\(488\) | 4.56545e30 | 0.552911 | ||||||||
\(489\) | 1.70924e30 | 0.202186 | ||||||||
\(490\) | −4.80439e29 | −0.0555115 | ||||||||
\(491\) | −2.96392e28 | −0.00334526 | −0.00167263 | − | 0.999999i | \(-0.500532\pi\) | ||||
−0.00167263 | + | 0.999999i | \(0.500532\pi\) | |||||||
\(492\) | −7.64159e29 | −0.0842530 | ||||||||
\(493\) | 1.22860e31 | 1.32334 | ||||||||
\(494\) | −9.44332e30 | −0.993722 | ||||||||
\(495\) | 7.42591e28 | 0.00763467 | ||||||||
\(496\) | −1.95187e30 | −0.196070 | ||||||||
\(497\) | 1.93209e31 | 1.89639 | ||||||||
\(498\) | 1.32968e31 | 1.27529 | ||||||||
\(499\) | −1.73299e31 | −1.62420 | −0.812101 | − | 0.583517i | \(-0.801676\pi\) | ||||
−0.812101 | + | 0.583517i | \(0.801676\pi\) | |||||||
\(500\) | −4.88281e29 | −0.0447214 | ||||||||
\(501\) | 1.38486e31 | 1.23958 | ||||||||
\(502\) | 9.39054e30 | 0.821481 | ||||||||
\(503\) | 6.74488e30 | 0.576690 | 0.288345 | − | 0.957527i | \(-0.406895\pi\) | ||||
0.288345 | + | 0.957527i | \(0.406895\pi\) | |||||||
\(504\) | 1.01638e30 | 0.0849385 | ||||||||
\(505\) | 3.37707e30 | 0.275860 | ||||||||
\(506\) | 5.51574e29 | 0.0440426 | ||||||||
\(507\) | −4.96526e30 | −0.387570 | ||||||||
\(508\) | −2.51756e30 | −0.192109 | ||||||||
\(509\) | 1.67540e31 | 1.24987 | 0.624935 | − | 0.780677i | \(-0.285126\pi\) | ||||
0.624935 | + | 0.780677i | \(0.285126\pi\) | |||||||
\(510\) | −4.16423e30 | −0.303723 | ||||||||
\(511\) | −6.91616e30 | −0.493202 | ||||||||
\(512\) | 6.33825e29 | 0.0441942 | ||||||||
\(513\) | −1.52592e31 | −1.04035 | ||||||||
\(514\) | −1.15572e31 | −0.770509 | ||||||||
\(515\) | −1.18588e31 | −0.773141 | ||||||||
\(516\) | 4.69983e30 | 0.299647 | ||||||||
\(517\) | 2.06958e30 | 0.129045 | ||||||||
\(518\) | −5.88138e30 | −0.358663 | ||||||||
\(519\) | −2.98148e31 | −1.77831 | ||||||||
\(520\) | −3.14979e30 | −0.183757 | ||||||||
\(521\) | 9.00283e30 | 0.513742 | 0.256871 | − | 0.966446i | \(-0.417308\pi\) | ||||
0.256871 | + | 0.966446i | \(0.417308\pi\) | |||||||
\(522\) | −4.27444e30 | −0.238599 | ||||||||
\(523\) | −1.06079e31 | −0.579239 | −0.289620 | − | 0.957142i | \(-0.593529\pi\) | ||||
−0.289620 | + | 0.957142i | \(0.593529\pi\) | |||||||
\(524\) | 7.46854e30 | 0.398957 | ||||||||
\(525\) | −4.58609e30 | −0.239668 | ||||||||
\(526\) | −2.39760e31 | −1.22586 | ||||||||
\(527\) | 1.36242e31 | 0.681536 | ||||||||
\(528\) | 4.34947e29 | 0.0212885 | ||||||||
\(529\) | −7.23380e30 | −0.346439 | ||||||||
\(530\) | 4.33879e30 | 0.203327 | ||||||||
\(531\) | −3.80810e30 | −0.174631 | ||||||||
\(532\) | −1.46076e31 | −0.655535 | ||||||||
\(533\) | 4.03451e30 | 0.177185 | ||||||||
\(534\) | −9.59594e30 | −0.412442 | ||||||||
\(535\) | 1.68265e30 | 0.0707823 | ||||||||
\(536\) | 1.25713e31 | 0.517590 | ||||||||
\(537\) | −2.18622e31 | −0.881028 | ||||||||
\(538\) | −2.90063e31 | −1.14418 | ||||||||
\(539\) | −3.50267e29 | −0.0135247 | ||||||||
\(540\) | −5.08965e30 | −0.192380 | ||||||||
\(541\) | 1.12742e31 | 0.417175 | 0.208588 | − | 0.978004i | \(-0.433113\pi\) | ||||
0.208588 | + | 0.978004i | \(0.433113\pi\) | |||||||
\(542\) | 3.04341e31 | 1.10247 | ||||||||
\(543\) | 1.53847e31 | 0.545622 | ||||||||
\(544\) | −4.42415e30 | −0.153618 | ||||||||
\(545\) | 2.34425e31 | 0.796973 | ||||||||
\(546\) | −2.95838e31 | −0.984779 | ||||||||
\(547\) | 4.29561e31 | 1.40014 | 0.700069 | − | 0.714075i | \(-0.253153\pi\) | ||||
0.700069 | + | 0.714075i | \(0.253153\pi\) | |||||||
\(548\) | −1.35424e31 | −0.432236 | ||||||||
\(549\) | 1.10870e31 | 0.346522 | ||||||||
\(550\) | −3.55984e29 | −0.0108958 | ||||||||
\(551\) | 6.14333e31 | 1.84145 | ||||||||
\(552\) | 1.07611e31 | 0.315907 | ||||||||
\(553\) | −2.19439e31 | −0.630920 | ||||||||
\(554\) | 2.71803e31 | 0.765405 | ||||||||
\(555\) | −8.38355e30 | −0.231238 | ||||||||
\(556\) | −1.26255e30 | −0.0341105 | ||||||||
\(557\) | 1.28388e31 | 0.339772 | 0.169886 | − | 0.985464i | \(-0.445660\pi\) | ||||
0.169886 | + | 0.985464i | \(0.445660\pi\) | |||||||
\(558\) | −4.74002e30 | −0.122882 | ||||||||
\(559\) | −2.48135e31 | −0.630163 | ||||||||
\(560\) | −4.87233e30 | −0.121220 | ||||||||
\(561\) | −3.03596e30 | −0.0739985 | ||||||||
\(562\) | 2.17609e31 | 0.519647 | ||||||||
\(563\) | 4.67401e31 | 1.09356 | 0.546780 | − | 0.837276i | \(-0.315853\pi\) | ||||
0.546780 | + | 0.837276i | \(0.315853\pi\) | |||||||
\(564\) | 4.03772e31 | 0.925606 | ||||||||
\(565\) | 3.30562e31 | 0.742499 | ||||||||
\(566\) | 5.55877e31 | 1.22346 | ||||||||
\(567\) | −5.89428e31 | −1.27123 | ||||||||
\(568\) | 2.92597e31 | 0.618392 | ||||||||
\(569\) | −1.56288e31 | −0.323694 | −0.161847 | − | 0.986816i | \(-0.551745\pi\) | ||||
−0.161847 | + | 0.986816i | \(0.551745\pi\) | |||||||
\(570\) | −2.08223e31 | −0.422637 | ||||||||
\(571\) | −3.73702e31 | −0.743378 | −0.371689 | − | 0.928357i | \(-0.621221\pi\) | ||||
−0.371689 | + | 0.928357i | \(0.621221\pi\) | |||||||
\(572\) | −2.29637e30 | −0.0447701 | ||||||||
\(573\) | −1.36267e31 | −0.260383 | ||||||||
\(574\) | 6.24087e30 | 0.116885 | ||||||||
\(575\) | −8.80751e30 | −0.161686 | ||||||||
\(576\) | 1.53921e30 | 0.0276975 | ||||||||
\(577\) | −9.29399e31 | −1.63938 | −0.819692 | − | 0.572805i | \(-0.805855\pi\) | ||||
−0.819692 | + | 0.572805i | \(0.805855\pi\) | |||||||
\(578\) | −1.00127e31 | −0.173134 | ||||||||
\(579\) | 1.14475e32 | 1.94047 | ||||||||
\(580\) | 2.04909e31 | 0.340517 | ||||||||
\(581\) | −1.08595e32 | −1.76922 | ||||||||
\(582\) | −2.35498e30 | −0.0376160 | ||||||||
\(583\) | 3.16322e30 | 0.0495383 | ||||||||
\(584\) | −1.04739e31 | −0.160827 | ||||||||
\(585\) | −7.64911e30 | −0.115165 | ||||||||
\(586\) | −2.88942e30 | −0.0426567 | ||||||||
\(587\) | −4.03960e31 | −0.584791 | −0.292395 | − | 0.956298i | \(-0.594452\pi\) | ||||
−0.292395 | + | 0.956298i | \(0.594452\pi\) | |||||||
\(588\) | −6.83366e30 | −0.0970094 | ||||||||
\(589\) | 6.81246e31 | 0.948370 | ||||||||
\(590\) | 1.82553e31 | 0.249225 | ||||||||
\(591\) | −1.11550e32 | −1.49352 | ||||||||
\(592\) | −8.90681e30 | −0.116956 | ||||||||
\(593\) | 1.98679e31 | 0.255872 | 0.127936 | − | 0.991782i | \(-0.459165\pi\) | ||||
0.127936 | + | 0.991782i | \(0.459165\pi\) | |||||||
\(594\) | −3.71064e30 | −0.0468711 | ||||||||
\(595\) | 3.40092e31 | 0.421358 | ||||||||
\(596\) | 6.26143e31 | 0.760925 | ||||||||
\(597\) | −1.29630e32 | −1.54526 | ||||||||
\(598\) | −5.68153e31 | −0.664357 | ||||||||
\(599\) | −4.06122e30 | −0.0465852 | −0.0232926 | − | 0.999729i | \(-0.507415\pi\) | ||||
−0.0232926 | + | 0.999729i | \(0.507415\pi\) | |||||||
\(600\) | −6.94521e30 | −0.0781530 | ||||||||
\(601\) | −2.13201e31 | −0.235360 | −0.117680 | − | 0.993052i | \(-0.537546\pi\) | ||||
−0.117680 | + | 0.993052i | \(0.537546\pi\) | |||||||
\(602\) | −3.83834e31 | −0.415703 | ||||||||
\(603\) | 3.05288e31 | 0.324385 | ||||||||
\(604\) | 9.45971e30 | 0.0986173 | ||||||||
\(605\) | 4.34626e31 | 0.444559 | ||||||||
\(606\) | 4.80347e31 | 0.482081 | ||||||||
\(607\) | 1.05290e32 | 1.03685 | 0.518425 | − | 0.855123i | \(-0.326519\pi\) | ||||
0.518425 | + | 0.855123i | \(0.326519\pi\) | |||||||
\(608\) | −2.21219e31 | −0.213762 | ||||||||
\(609\) | 1.92457e32 | 1.82488 | ||||||||
\(610\) | −5.31488e31 | −0.494539 | ||||||||
\(611\) | −2.13178e32 | −1.94656 | ||||||||
\(612\) | −1.07438e31 | −0.0962759 | ||||||||
\(613\) | −1.91908e32 | −1.68771 | −0.843855 | − | 0.536572i | \(-0.819719\pi\) | ||||
−0.843855 | + | 0.536572i | \(0.819719\pi\) | |||||||
\(614\) | 9.63128e31 | 0.831281 | ||||||||
\(615\) | 8.89598e30 | 0.0753581 | ||||||||
\(616\) | −3.55220e30 | −0.0295338 | ||||||||
\(617\) | 1.64022e32 | 1.33851 | 0.669256 | − | 0.743032i | \(-0.266613\pi\) | ||||
0.669256 | + | 0.743032i | \(0.266613\pi\) | |||||||
\(618\) | −1.68677e32 | −1.35111 | ||||||||
\(619\) | −9.18518e31 | −0.722180 | −0.361090 | − | 0.932531i | \(-0.617595\pi\) | ||||
−0.361090 | + | 0.932531i | \(0.617595\pi\) | |||||||
\(620\) | 2.27227e31 | 0.175370 | ||||||||
\(621\) | −9.18061e31 | −0.695534 | ||||||||
\(622\) | 4.78356e31 | 0.355764 | ||||||||
\(623\) | 7.83699e31 | 0.572185 | ||||||||
\(624\) | −4.48020e31 | −0.321125 | ||||||||
\(625\) | 5.68434e30 | 0.0400000 | ||||||||
\(626\) | 6.90987e31 | 0.477381 | ||||||||
\(627\) | −1.51806e31 | −0.102970 | ||||||||
\(628\) | −8.39446e31 | −0.559058 | ||||||||
\(629\) | 6.21702e31 | 0.406537 | ||||||||
\(630\) | −1.18322e31 | −0.0759713 | ||||||||
\(631\) | 2.95348e32 | 1.86207 | 0.931035 | − | 0.364930i | \(-0.118907\pi\) | ||||
0.931035 | + | 0.364930i | \(0.118907\pi\) | |||||||
\(632\) | −3.32320e31 | −0.205736 | ||||||||
\(633\) | 5.17602e31 | 0.314669 | ||||||||
\(634\) | −6.09984e31 | −0.364160 | ||||||||
\(635\) | 2.93083e31 | 0.171827 | ||||||||
\(636\) | 6.17140e31 | 0.355326 | ||||||||
\(637\) | 3.60795e31 | 0.204012 | ||||||||
\(638\) | 1.49390e31 | 0.0829628 | ||||||||
\(639\) | 7.10557e31 | 0.387560 | ||||||||
\(640\) | −7.37870e30 | −0.0395285 | ||||||||
\(641\) | −2.62963e31 | −0.138365 | −0.0691826 | − | 0.997604i | \(-0.522039\pi\) | ||||
−0.0691826 | + | 0.997604i | \(0.522039\pi\) | |||||||
\(642\) | 2.39336e31 | 0.123696 | ||||||||
\(643\) | 2.59835e32 | 1.31908 | 0.659541 | − | 0.751668i | \(-0.270751\pi\) | ||||
0.659541 | + | 0.751668i | \(0.270751\pi\) | |||||||
\(644\) | −8.78860e31 | −0.438261 | ||||||||
\(645\) | −5.47132e31 | −0.268013 | ||||||||
\(646\) | 1.54413e32 | 0.743034 | ||||||||
\(647\) | 1.64878e31 | 0.0779403 | 0.0389702 | − | 0.999240i | \(-0.487592\pi\) | ||||
0.0389702 | + | 0.999240i | \(0.487592\pi\) | |||||||
\(648\) | −8.92635e31 | −0.414535 | ||||||||
\(649\) | 1.33091e31 | 0.0607206 | ||||||||
\(650\) | 3.66684e31 | 0.164357 | ||||||||
\(651\) | 2.13419e32 | 0.939835 | ||||||||
\(652\) | −2.11401e31 | −0.0914661 | ||||||||
\(653\) | −2.31883e32 | −0.985751 | −0.492876 | − | 0.870100i | \(-0.664054\pi\) | ||||
−0.492876 | + | 0.870100i | \(0.664054\pi\) | |||||||
\(654\) | 3.33441e32 | 1.39276 | ||||||||
\(655\) | −8.69453e31 | −0.356838 | ||||||||
\(656\) | 9.45123e30 | 0.0381149 | ||||||||
\(657\) | −2.54353e31 | −0.100794 | ||||||||
\(658\) | −3.29759e32 | −1.28410 | ||||||||
\(659\) | −3.55456e32 | −1.36020 | −0.680102 | − | 0.733118i | \(-0.738064\pi\) | ||||
−0.680102 | + | 0.733118i | \(0.738064\pi\) | |||||||
\(660\) | −5.06344e30 | −0.0190410 | ||||||||
\(661\) | −2.00631e32 | −0.741447 | −0.370724 | − | 0.928743i | \(-0.620890\pi\) | ||||
−0.370724 | + | 0.928743i | \(0.620890\pi\) | |||||||
\(662\) | 1.07413e32 | 0.390112 | ||||||||
\(663\) | 3.12721e32 | 1.11622 | ||||||||
\(664\) | −1.64457e32 | −0.576923 | ||||||||
\(665\) | 1.70055e32 | 0.586328 | ||||||||
\(666\) | −2.16298e31 | −0.0732990 | ||||||||
\(667\) | 3.69610e32 | 1.23111 | ||||||||
\(668\) | −1.71282e32 | −0.560767 | ||||||||
\(669\) | −2.40548e32 | −0.774106 | ||||||||
\(670\) | −1.46349e32 | −0.462946 | ||||||||
\(671\) | −3.87484e31 | −0.120488 | ||||||||
\(672\) | −6.93030e31 | −0.211839 | ||||||||
\(673\) | 3.34870e32 | 1.00624 | 0.503122 | − | 0.864215i | \(-0.332185\pi\) | ||||
0.503122 | + | 0.864215i | \(0.332185\pi\) | |||||||
\(674\) | −3.36569e32 | −0.994226 | ||||||||
\(675\) | 5.92514e31 | 0.172070 | ||||||||
\(676\) | 6.14110e31 | 0.175331 | ||||||||
\(677\) | −9.65120e31 | −0.270902 | −0.135451 | − | 0.990784i | \(-0.543248\pi\) | ||||
−0.135451 | + | 0.990784i | \(0.543248\pi\) | |||||||
\(678\) | 4.70184e32 | 1.29756 | ||||||||
\(679\) | 1.92331e31 | 0.0521850 | ||||||||
\(680\) | 5.15038e31 | 0.137400 | ||||||||
\(681\) | −4.57366e32 | −1.19970 | ||||||||
\(682\) | 1.65661e31 | 0.0427269 | ||||||||
\(683\) | −1.74605e32 | −0.442811 | −0.221406 | − | 0.975182i | \(-0.571065\pi\) | ||||
−0.221406 | + | 0.975182i | \(0.571065\pi\) | |||||||
\(684\) | −5.37220e31 | −0.133970 | ||||||||
\(685\) | 1.57655e32 | 0.386603 | ||||||||
\(686\) | −2.62120e32 | −0.632080 | ||||||||
\(687\) | −5.80001e32 | −1.37539 | ||||||||
\(688\) | −5.81281e31 | −0.135556 | ||||||||
\(689\) | −3.25830e32 | −0.747256 | ||||||||
\(690\) | −1.25276e32 | −0.282556 | ||||||||
\(691\) | 4.17873e32 | 0.926931 | 0.463465 | − | 0.886115i | \(-0.346606\pi\) | ||||
0.463465 | + | 0.886115i | \(0.346606\pi\) | |||||||
\(692\) | 3.68754e32 | 0.804482 | ||||||||
\(693\) | −8.62634e30 | −0.0185095 | ||||||||
\(694\) | 4.18071e31 | 0.0882300 | ||||||||
\(695\) | 1.46980e31 | 0.0305094 | ||||||||
\(696\) | 2.91458e32 | 0.595072 | ||||||||
\(697\) | −6.59703e31 | −0.132486 | ||||||||
\(698\) | 5.34061e32 | 1.05500 | ||||||||
\(699\) | −2.62603e32 | −0.510285 | ||||||||
\(700\) | 5.67214e31 | 0.108422 | ||||||||
\(701\) | −5.54616e32 | −1.04288 | −0.521441 | − | 0.853288i | \(-0.674605\pi\) | ||||
−0.521441 | + | 0.853288i | \(0.674605\pi\) | |||||||
\(702\) | 3.82217e32 | 0.707023 | ||||||||
\(703\) | 3.10868e32 | 0.565704 | ||||||||
\(704\) | −5.37948e30 | −0.00963063 | ||||||||
\(705\) | −4.70052e32 | −0.827887 | ||||||||
\(706\) | −6.49406e32 | −1.12528 | ||||||||
\(707\) | −3.92298e32 | −0.668795 | ||||||||
\(708\) | 2.59660e32 | 0.435534 | ||||||||
\(709\) | −9.37126e32 | −1.54656 | −0.773279 | − | 0.634066i | \(-0.781385\pi\) | ||||
−0.773279 | + | 0.634066i | \(0.781385\pi\) | |||||||
\(710\) | −3.40628e32 | −0.553107 | ||||||||
\(711\) | −8.07023e31 | −0.128939 | ||||||||
\(712\) | 1.18684e32 | 0.186583 | ||||||||
\(713\) | 4.09868e32 | 0.634037 | ||||||||
\(714\) | 4.83740e32 | 0.736347 | ||||||||
\(715\) | 2.67333e31 | 0.0400436 | ||||||||
\(716\) | 2.70395e32 | 0.398565 | ||||||||
\(717\) | −7.19855e32 | −1.04418 | ||||||||
\(718\) | 6.28246e30 | 0.00896806 | ||||||||
\(719\) | −7.22362e31 | −0.101478 | −0.0507391 | − | 0.998712i | \(-0.516158\pi\) | ||||
−0.0507391 | + | 0.998712i | \(0.516158\pi\) | |||||||
\(720\) | −1.79188e31 | −0.0247734 | ||||||||
\(721\) | 1.37759e33 | 1.87440 | ||||||||
\(722\) | 2.44069e32 | 0.326839 | ||||||||
\(723\) | 6.57045e32 | 0.865973 | ||||||||
\(724\) | −1.90281e32 | −0.246832 | ||||||||
\(725\) | −2.38545e32 | −0.304568 | ||||||||
\(726\) | 6.18203e32 | 0.776891 | ||||||||
\(727\) | 9.11706e32 | 1.12774 | 0.563870 | − | 0.825863i | \(-0.309312\pi\) | ||||
0.563870 | + | 0.825863i | \(0.309312\pi\) | |||||||
\(728\) | 3.65897e32 | 0.445500 | ||||||||
\(729\) | 5.76647e32 | 0.691104 | ||||||||
\(730\) | 1.21932e32 | 0.143848 | ||||||||
\(731\) | 4.05739e32 | 0.471191 | ||||||||
\(732\) | −7.55977e32 | −0.864234 | ||||||||
\(733\) | 1.25151e33 | 1.40844 | 0.704221 | − | 0.709981i | \(-0.251296\pi\) | ||||
0.704221 | + | 0.709981i | \(0.251296\pi\) | |||||||
\(734\) | 3.00535e32 | 0.332958 | ||||||||
\(735\) | 7.95542e31 | 0.0867679 | ||||||||
\(736\) | −1.33095e32 | −0.142912 | ||||||||
\(737\) | −1.06697e32 | −0.112791 | ||||||||
\(738\) | 2.29518e31 | 0.0238874 | ||||||||
\(739\) | 7.62517e32 | 0.781337 | 0.390669 | − | 0.920531i | \(-0.372244\pi\) | ||||
0.390669 | + | 0.920531i | \(0.372244\pi\) | |||||||
\(740\) | 1.03689e32 | 0.104609 | ||||||||
\(741\) | 1.56369e33 | 1.55325 | ||||||||
\(742\) | −5.04017e32 | −0.492947 | ||||||||
\(743\) | −6.76133e32 | −0.651119 | −0.325560 | − | 0.945521i | \(-0.605553\pi\) | ||||
−0.325560 | + | 0.945521i | \(0.605553\pi\) | |||||||
\(744\) | 3.23203e32 | 0.306470 | ||||||||
\(745\) | −7.28927e32 | −0.680592 | ||||||||
\(746\) | −1.07055e33 | −0.984265 | ||||||||
\(747\) | −3.99375e32 | −0.361571 | ||||||||
\(748\) | 3.75492e31 | 0.0334759 | ||||||||
\(749\) | −1.95465e32 | −0.171605 | ||||||||
\(750\) | 8.08529e31 | 0.0699022 | ||||||||
\(751\) | −9.33180e32 | −0.794522 | −0.397261 | − | 0.917706i | \(-0.630039\pi\) | ||||
−0.397261 | + | 0.917706i | \(0.630039\pi\) | |||||||
\(752\) | −4.99391e32 | −0.418731 | ||||||||
\(753\) | −1.55495e33 | −1.28403 | ||||||||
\(754\) | −1.53880e33 | −1.25145 | ||||||||
\(755\) | −1.10126e32 | −0.0882060 | ||||||||
\(756\) | 5.91241e32 | 0.466406 | ||||||||
\(757\) | 2.41509e33 | 1.87642 | 0.938211 | − | 0.346065i | \(-0.112482\pi\) | ||||
0.938211 | + | 0.346065i | \(0.112482\pi\) | |||||||
\(758\) | −1.22080e33 | −0.934218 | ||||||||
\(759\) | −9.13333e31 | −0.0688413 | ||||||||
\(760\) | 2.57533e32 | 0.191195 | ||||||||
\(761\) | −1.31749e32 | −0.0963435 | −0.0481718 | − | 0.998839i | \(-0.515339\pi\) | ||||
−0.0481718 | + | 0.998839i | \(0.515339\pi\) | |||||||
\(762\) | 4.16875e32 | 0.300278 | ||||||||
\(763\) | −2.72320e33 | −1.93218 | ||||||||
\(764\) | 1.68537e32 | 0.117794 | ||||||||
\(765\) | 1.25075e32 | 0.0861117 | ||||||||
\(766\) | −1.01361e33 | −0.687451 | ||||||||
\(767\) | −1.37092e33 | −0.915935 | ||||||||
\(768\) | −1.04953e32 | −0.0690782 | ||||||||
\(769\) | −7.19550e32 | −0.466561 | −0.233280 | − | 0.972410i | \(-0.574946\pi\) | ||||
−0.233280 | + | 0.972410i | \(0.574946\pi\) | |||||||
\(770\) | 4.13530e31 | 0.0264158 | ||||||||
\(771\) | 1.91372e33 | 1.20435 | ||||||||
\(772\) | −1.41584e33 | −0.877841 | ||||||||
\(773\) | −3.05497e32 | −0.186613 | −0.0933066 | − | 0.995637i | \(-0.529744\pi\) | ||||
−0.0933066 | + | 0.995637i | \(0.529744\pi\) | |||||||
\(774\) | −1.41161e32 | −0.0849561 | ||||||||
\(775\) | −2.64528e32 | −0.156856 | ||||||||
\(776\) | 2.91267e31 | 0.0170170 | ||||||||
\(777\) | 9.73878e32 | 0.560613 | ||||||||
\(778\) | 1.16110e32 | 0.0658572 | ||||||||
\(779\) | −3.29869e32 | −0.184357 | ||||||||
\(780\) | 5.21564e32 | 0.287223 | ||||||||
\(781\) | −2.48336e32 | −0.134758 | ||||||||
\(782\) | 9.29016e32 | 0.496759 | ||||||||
\(783\) | −2.48650e33 | −1.31017 | ||||||||
\(784\) | 8.45197e31 | 0.0438857 | ||||||||
\(785\) | 9.77243e32 | 0.500036 | ||||||||
\(786\) | −1.23669e33 | −0.623594 | ||||||||
\(787\) | −3.70046e32 | −0.183885 | −0.0919426 | − | 0.995764i | \(-0.529308\pi\) | ||||
−0.0919426 | + | 0.995764i | \(0.529308\pi\) | |||||||
\(788\) | 1.37966e33 | 0.675649 | ||||||||
\(789\) | 3.97011e33 | 1.91609 | ||||||||
\(790\) | 3.86872e32 | 0.184016 | ||||||||
\(791\) | −3.83999e33 | −1.80011 | ||||||||
\(792\) | −1.30638e31 | −0.00603573 | ||||||||
\(793\) | 3.99131e33 | 1.81750 | ||||||||
\(794\) | 7.54364e32 | 0.338567 | ||||||||
\(795\) | −7.18446e32 | −0.317813 | ||||||||
\(796\) | 1.60329e33 | 0.699055 | ||||||||
\(797\) | 1.56557e32 | 0.0672823 | 0.0336412 | − | 0.999434i | \(-0.489290\pi\) | ||||
0.0336412 | + | 0.999434i | \(0.489290\pi\) | |||||||
\(798\) | 2.41883e33 | 1.02464 | ||||||||
\(799\) | 3.48578e33 | 1.45550 | ||||||||
\(800\) | 8.58993e31 | 0.0353553 | ||||||||
\(801\) | 2.88218e32 | 0.116936 | ||||||||
\(802\) | −2.49544e33 | −0.998024 | ||||||||
\(803\) | 8.88953e31 | 0.0350469 | ||||||||
\(804\) | −2.08164e33 | −0.809024 | ||||||||
\(805\) | 1.02313e33 | 0.391992 | ||||||||
\(806\) | −1.70641e33 | −0.644510 | ||||||||
\(807\) | 4.80305e33 | 1.78843 | ||||||||
\(808\) | −5.94100e32 | −0.218087 | ||||||||
\(809\) | −3.53778e33 | −1.28033 | −0.640167 | − | 0.768236i | \(-0.721135\pi\) | ||||
−0.640167 | + | 0.768236i | \(0.721135\pi\) | |||||||
\(810\) | 1.03916e33 | 0.370771 | ||||||||
\(811\) | −2.93265e33 | −1.03162 | −0.515811 | − | 0.856702i | \(-0.672509\pi\) | ||||
−0.515811 | + | 0.856702i | \(0.672509\pi\) | |||||||
\(812\) | −2.38033e33 | −0.825549 | ||||||||
\(813\) | −5.03948e33 | −1.72323 | ||||||||
\(814\) | 7.55950e31 | 0.0254866 | ||||||||
\(815\) | 2.46103e32 | 0.0818098 | ||||||||
\(816\) | 7.32580e32 | 0.240114 | ||||||||
\(817\) | 2.02880e33 | 0.655671 | ||||||||
\(818\) | 3.03087e33 | 0.965840 | ||||||||
\(819\) | 8.88562e32 | 0.279205 | ||||||||
\(820\) | −1.10027e32 | −0.0340910 | ||||||||
\(821\) | 2.49297e33 | 0.761677 | 0.380838 | − | 0.924642i | \(-0.375635\pi\) | ||||
0.380838 | + | 0.924642i | \(0.375635\pi\) | |||||||
\(822\) | 2.24245e33 | 0.675611 | ||||||||
\(823\) | −3.98570e33 | −1.18415 | −0.592075 | − | 0.805883i | \(-0.701691\pi\) | ||||
−0.592075 | + | 0.805883i | \(0.701691\pi\) | |||||||
\(824\) | 2.08623e33 | 0.611222 | ||||||||
\(825\) | 5.89463e31 | 0.0170308 | ||||||||
\(826\) | −2.12064e33 | −0.604221 | ||||||||
\(827\) | 1.70726e32 | 0.0479718 | 0.0239859 | − | 0.999712i | \(-0.492364\pi\) | ||||
0.0239859 | + | 0.999712i | \(0.492364\pi\) | |||||||
\(828\) | −3.23216e32 | −0.0895660 | ||||||||
\(829\) | 5.89567e33 | 1.61123 | 0.805613 | − | 0.592443i | \(-0.201836\pi\) | ||||
0.805613 | + | 0.592443i | \(0.201836\pi\) | |||||||
\(830\) | 1.91453e33 | 0.516016 | ||||||||
\(831\) | −4.50069e33 | −1.19637 | ||||||||
\(832\) | 5.54117e32 | 0.145273 | ||||||||
\(833\) | −5.89953e32 | −0.152546 | ||||||||
\(834\) | 2.09061e32 | 0.0533168 | ||||||||
\(835\) | 1.99399e33 | 0.501565 | ||||||||
\(836\) | 1.87756e32 | 0.0465823 | ||||||||
\(837\) | −2.75733e33 | −0.674755 | ||||||||
\(838\) | 8.94485e32 | 0.215907 | ||||||||
\(839\) | 2.81133e33 | 0.669345 | 0.334672 | − | 0.942335i | \(-0.391374\pi\) | ||||
0.334672 | + | 0.942335i | \(0.391374\pi\) | |||||||
\(840\) | 8.06793e32 | 0.189474 | ||||||||
\(841\) | 5.69391e33 | 1.31903 | ||||||||
\(842\) | 5.94959e33 | 1.35956 | ||||||||
\(843\) | −3.60331e33 | −0.812241 | ||||||||
\(844\) | −6.40178e32 | −0.142352 | ||||||||
\(845\) | −7.14919e32 | −0.156821 | ||||||||
\(846\) | −1.21275e33 | −0.262428 | ||||||||
\(847\) | −5.04885e33 | −1.07779 | ||||||||
\(848\) | −7.63288e32 | −0.160744 | ||||||||
\(849\) | −9.20459e33 | −1.91234 | ||||||||
\(850\) | −5.99584e32 | −0.122894 | ||||||||
\(851\) | 1.87032e33 | 0.378204 | ||||||||
\(852\) | −4.84501e33 | −0.966584 | ||||||||
\(853\) | −3.10315e33 | −0.610787 | −0.305393 | − | 0.952226i | \(-0.598788\pi\) | ||||
−0.305393 | + | 0.952226i | \(0.598788\pi\) | |||||||
\(854\) | 6.17405e33 | 1.19896 | ||||||||
\(855\) | 6.25406e32 | 0.119826 | ||||||||
\(856\) | −2.96015e32 | −0.0559584 | ||||||||
\(857\) | −5.09943e33 | −0.951134 | −0.475567 | − | 0.879679i | \(-0.657757\pi\) | ||||
−0.475567 | + | 0.879679i | \(0.657757\pi\) | |||||||
\(858\) | 3.80249e32 | 0.0699784 | ||||||||
\(859\) | 1.31743e33 | 0.239224 | 0.119612 | − | 0.992821i | \(-0.461835\pi\) | ||||
0.119612 | + | 0.992821i | \(0.461835\pi\) | |||||||
\(860\) | 6.76701e32 | 0.121245 | ||||||||
\(861\) | −1.03341e33 | −0.182698 | ||||||||
\(862\) | 1.14895e33 | 0.200432 | ||||||||
\(863\) | −1.29184e33 | −0.222375 | −0.111188 | − | 0.993799i | \(-0.535465\pi\) | ||||
−0.111188 | + | 0.993799i | \(0.535465\pi\) | |||||||
\(864\) | 8.95381e32 | 0.152090 | ||||||||
\(865\) | −4.29286e33 | −0.719550 | ||||||||
\(866\) | −5.97360e33 | −0.988053 | ||||||||
\(867\) | 1.65797e33 | 0.270619 | ||||||||
\(868\) | −2.63960e33 | −0.425168 | ||||||||
\(869\) | 2.82051e32 | 0.0448332 | ||||||||
\(870\) | −3.39302e33 | −0.532249 | ||||||||
\(871\) | 1.09904e34 | 1.70139 | ||||||||
\(872\) | −4.12405e33 | −0.630063 | ||||||||
\(873\) | 7.07328e31 | 0.0106649 | ||||||||
\(874\) | 4.64532e33 | 0.691249 | ||||||||
\(875\) | −6.60324e32 | −0.0969760 | ||||||||
\(876\) | 1.73434e33 | 0.251383 | ||||||||
\(877\) | −1.10353e33 | −0.157866 | −0.0789329 | − | 0.996880i | \(-0.525151\pi\) | ||||
−0.0789329 | + | 0.996880i | \(0.525151\pi\) | |||||||
\(878\) | 2.11002e33 | 0.297920 | ||||||||
\(879\) | 4.78449e32 | 0.0666750 | ||||||||
\(880\) | 6.26254e31 | 0.00861390 | ||||||||
\(881\) | 3.42468e33 | 0.464940 | 0.232470 | − | 0.972604i | \(-0.425319\pi\) | ||||
0.232470 | + | 0.972604i | \(0.425319\pi\) | |||||||
\(882\) | 2.05252e32 | 0.0275042 | ||||||||
\(883\) | −7.33051e33 | −0.969585 | −0.484792 | − | 0.874629i | \(-0.661105\pi\) | ||||
−0.484792 | + | 0.874629i | \(0.661105\pi\) | |||||||
\(884\) | −3.86778e33 | −0.504964 | ||||||||
\(885\) | −3.02284e33 | −0.389554 | ||||||||
\(886\) | −5.18950e33 | −0.660142 | ||||||||
\(887\) | −7.64645e33 | −0.960148 | −0.480074 | − | 0.877228i | \(-0.659390\pi\) | ||||
−0.480074 | + | 0.877228i | \(0.659390\pi\) | |||||||
\(888\) | 1.47485e33 | 0.182809 | ||||||||
\(889\) | −3.40461e33 | −0.416578 | ||||||||
\(890\) | −1.38166e33 | −0.166885 | ||||||||
\(891\) | 7.57608e32 | 0.0903340 | ||||||||
\(892\) | 2.97513e33 | 0.350195 | ||||||||
\(893\) | 1.74298e34 | 2.02536 | ||||||||
\(894\) | −1.03681e34 | −1.18937 | ||||||||
\(895\) | −3.14781e33 | −0.356487 | ||||||||
\(896\) | 8.57149e32 | 0.0958328 | ||||||||
\(897\) | 9.40785e33 | 1.03843 | ||||||||
\(898\) | −9.78848e32 | −0.106669 | ||||||||
\(899\) | 1.11010e34 | 1.19433 | ||||||||
\(900\) | 2.08602e32 | 0.0221580 | ||||||||
\(901\) | 5.32780e33 | 0.558744 | ||||||||
\(902\) | −8.02157e31 | −0.00830585 | ||||||||
\(903\) | 6.35578e33 | 0.649770 | ||||||||
\(904\) | −5.81531e33 | −0.586997 | ||||||||
\(905\) | 2.21516e33 | 0.220773 | ||||||||
\(906\) | −1.56640e33 | −0.154145 | ||||||||
\(907\) | 2.55586e33 | 0.248344 | 0.124172 | − | 0.992261i | \(-0.460373\pi\) | ||||
0.124172 | + | 0.992261i | \(0.460373\pi\) | |||||||
\(908\) | 5.65677e33 | 0.542727 | ||||||||
\(909\) | −1.44274e33 | −0.136680 | ||||||||
\(910\) | −4.25960e33 | −0.398467 | ||||||||
\(911\) | 6.46941e33 | 0.597590 | 0.298795 | − | 0.954317i | \(-0.403415\pi\) | ||||
0.298795 | + | 0.954317i | \(0.403415\pi\) | |||||||
\(912\) | 3.66309e33 | 0.334124 | ||||||||
\(913\) | 1.39580e33 | 0.125721 | ||||||||
\(914\) | 1.13298e33 | 0.100772 | ||||||||
\(915\) | 8.80073e33 | 0.772994 | ||||||||
\(916\) | 7.17353e33 | 0.622207 | ||||||||
\(917\) | 1.01000e34 | 0.865118 | ||||||||
\(918\) | −6.24983e33 | −0.528661 | ||||||||
\(919\) | −5.58007e33 | −0.466134 | −0.233067 | − | 0.972461i | \(-0.574876\pi\) | ||||
−0.233067 | + | 0.972461i | \(0.574876\pi\) | |||||||
\(920\) | 1.54943e33 | 0.127824 | ||||||||
\(921\) | −1.59481e34 | −1.29934 | ||||||||
\(922\) | −7.73798e33 | −0.622619 | ||||||||
\(923\) | 2.55801e34 | 2.03274 | ||||||||
\(924\) | 5.88197e32 | 0.0461631 | ||||||||
\(925\) | −1.20710e33 | −0.0935649 | ||||||||
\(926\) | 1.96103e33 | 0.150127 | ||||||||
\(927\) | 5.06630e33 | 0.383066 | ||||||||
\(928\) | −3.60479e33 | −0.269202 | ||||||||
\(929\) | −1.37312e34 | −1.01281 | −0.506406 | − | 0.862295i | \(-0.669026\pi\) | ||||
−0.506406 | + | 0.862295i | \(0.669026\pi\) | |||||||
\(930\) | −3.76258e33 | −0.274115 | ||||||||
\(931\) | −2.94992e33 | −0.212270 | ||||||||
\(932\) | 3.24791e33 | 0.230846 | ||||||||
\(933\) | −7.92093e33 | −0.556080 | ||||||||
\(934\) | 3.70847e33 | 0.257161 | ||||||||
\(935\) | −4.37130e32 | −0.0299417 | ||||||||
\(936\) | 1.34565e33 | 0.0910455 | ||||||||
\(937\) | −6.15639e33 | −0.411454 | −0.205727 | − | 0.978609i | \(-0.565956\pi\) | ||||
−0.205727 | + | 0.978609i | \(0.565956\pi\) | |||||||
\(938\) | 1.70007e34 | 1.12237 | ||||||||
\(939\) | −1.14418e34 | −0.746176 | ||||||||
\(940\) | 5.81367e33 | 0.374524 | ||||||||
\(941\) | −1.54804e34 | −0.985147 | −0.492574 | − | 0.870271i | \(-0.663944\pi\) | ||||
−0.492574 | + | 0.870271i | \(0.663944\pi\) | |||||||
\(942\) | 1.39001e34 | 0.873841 | ||||||||
\(943\) | −1.98464e33 | −0.123253 | ||||||||
\(944\) | −3.21151e33 | −0.197030 | ||||||||
\(945\) | −6.88296e33 | −0.417166 | ||||||||
\(946\) | 4.93352e32 | 0.0295399 | ||||||||
\(947\) | −1.09161e34 | −0.645720 | −0.322860 | − | 0.946447i | \(-0.604644\pi\) | ||||
−0.322860 | + | 0.946447i | \(0.604644\pi\) | |||||||
\(948\) | 5.50278e33 | 0.321578 | ||||||||
\(949\) | −9.15672e33 | −0.528663 | ||||||||
\(950\) | −2.99808e33 | −0.171010 | ||||||||
\(951\) | 1.01005e34 | 0.569204 | ||||||||
\(952\) | −5.98296e33 | −0.333113 | ||||||||
\(953\) | 3.06171e34 | 1.68421 | 0.842103 | − | 0.539317i | \(-0.181318\pi\) | ||||
0.842103 | + | 0.539317i | \(0.181318\pi\) | |||||||
\(954\) | −1.85361e33 | −0.100742 | ||||||||
\(955\) | −1.96203e33 | −0.105358 | ||||||||
\(956\) | 8.90327e33 | 0.472372 | ||||||||
\(957\) | −2.47370e33 | −0.129676 | ||||||||
\(958\) | −2.68325e34 | −1.38982 | ||||||||
\(959\) | −1.83140e34 | −0.937281 | ||||||||
\(960\) | 1.22181e33 | 0.0617854 | ||||||||
\(961\) | −7.70321e33 | −0.384904 | ||||||||
\(962\) | −7.78672e33 | −0.384451 | ||||||||
\(963\) | −7.18857e32 | −0.0350704 | ||||||||
\(964\) | −8.12642e33 | −0.391754 | ||||||||
\(965\) | 1.64826e34 | 0.785165 | ||||||||
\(966\) | 1.45528e34 | 0.685028 | ||||||||
\(967\) | −1.52535e34 | −0.709519 | −0.354759 | − | 0.934958i | \(-0.615437\pi\) | ||||
−0.354759 | + | 0.934958i | \(0.615437\pi\) | |||||||
\(968\) | −7.64603e33 | −0.351455 | ||||||||
\(969\) | −2.55687e34 | −1.16141 | ||||||||
\(970\) | −3.39080e32 | −0.0152204 | ||||||||
\(971\) | −2.92889e34 | −1.29922 | −0.649610 | − | 0.760268i | \(-0.725068\pi\) | ||||
−0.649610 | + | 0.760268i | \(0.725068\pi\) | |||||||
\(972\) | 4.96773e33 | 0.217769 | ||||||||
\(973\) | −1.70740e33 | −0.0739669 | ||||||||
\(974\) | −1.59491e34 | −0.682822 | ||||||||
\(975\) | −6.07180e33 | −0.256900 | ||||||||
\(976\) | 9.35003e33 | 0.390967 | ||||||||
\(977\) | −6.75647e33 | −0.279211 | −0.139605 | − | 0.990207i | \(-0.544583\pi\) | ||||
−0.139605 | + | 0.990207i | \(0.544583\pi\) | |||||||
\(978\) | 3.50052e33 | 0.142967 | ||||||||
\(979\) | −1.00731e33 | −0.0406595 | ||||||||
\(980\) | −9.83938e32 | −0.0392526 | ||||||||
\(981\) | −1.00150e34 | −0.394874 | ||||||||
\(982\) | −6.07012e31 | −0.00236546 | ||||||||
\(983\) | 2.01524e34 | 0.776178 | 0.388089 | − | 0.921622i | \(-0.373135\pi\) | ||||
0.388089 | + | 0.921622i | \(0.373135\pi\) | |||||||
\(984\) | −1.56500e33 | −0.0595758 | ||||||||
\(985\) | −1.60614e34 | −0.604319 | ||||||||
\(986\) | 2.51617e34 | 0.935741 | ||||||||
\(987\) | 5.46038e34 | 2.00713 | ||||||||
\(988\) | −1.93399e34 | −0.702668 | ||||||||
\(989\) | 1.22062e34 | 0.438352 | ||||||||
\(990\) | 1.52083e32 | 0.00539852 | ||||||||
\(991\) | 6.56935e33 | 0.230502 | 0.115251 | − | 0.993336i | \(-0.463233\pi\) | ||||
0.115251 | + | 0.993336i | \(0.463233\pi\) | |||||||
\(992\) | −3.99743e33 | −0.138642 | ||||||||
\(993\) | −1.77861e34 | −0.609769 | ||||||||
\(994\) | 3.95691e34 | 1.34095 | ||||||||
\(995\) | −1.86647e34 | −0.625254 | ||||||||
\(996\) | 2.72318e34 | 0.901767 | ||||||||
\(997\) | 8.17693e33 | 0.267668 | 0.133834 | − | 0.991004i | \(-0.457271\pi\) | ||||
0.133834 | + | 0.991004i | \(0.457271\pi\) | |||||||
\(998\) | −3.54917e34 | −1.14848 | ||||||||
\(999\) | −1.25823e34 | −0.402493 |
(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 | 10.24.a.c.1.1 | ✓ | 2 | |
5.2 | odd | 4 | 50.24.b.c.49.4 | 4 | |||
5.3 | odd | 4 | 50.24.b.c.49.1 | 4 | |||
5.4 | even | 2 | 50.24.a.b.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.24.a.c.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
50.24.a.b.1.2 | 2 | 5.4 | even | 2 | |||
50.24.b.c.49.1 | 4 | 5.3 | odd | 4 | |||
50.24.b.c.49.4 | 4 | 5.2 | odd | 4 |