Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,20,Mod(1,1)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 20, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 20);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 20 \) |
Character orbit: | \([\chi]\) | \(=\) | 1.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: | \(2.28816696556\) |
Analytic rank: | \(0\) |
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 | \(\chi\) | \(=\) | 1.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 456.000 | 0.629767 | 0.314883 | − | 0.949130i | \(-0.398035\pi\) | ||||
0.314883 | + | 0.949130i | \(0.398035\pi\) | |||||||
\(3\) | 50652.0 | 1.48575 | 0.742873 | − | 0.669432i | \(-0.233463\pi\) | ||||
0.742873 | + | 0.669432i | \(0.233463\pi\) | |||||||
\(4\) | −316352. | −0.603394 | ||||||||
\(5\) | −2.37741e6 | −0.544364 | −0.272182 | − | 0.962246i | \(-0.587745\pi\) | ||||
−0.272182 | + | 0.962246i | \(0.587745\pi\) | |||||||
\(6\) | 2.30973e7 | 0.935674 | ||||||||
\(7\) | −1.69175e7 | −0.158455 | −0.0792275 | − | 0.996857i | \(-0.525245\pi\) | ||||
−0.0792275 | + | 0.996857i | \(0.525245\pi\) | |||||||
\(8\) | −3.83332e8 | −1.00976 | ||||||||
\(9\) | 1.40336e9 | 1.20744 | ||||||||
\(10\) | −1.08410e9 | −0.342822 | ||||||||
\(11\) | −1.62121e7 | −0.00207305 | −0.00103652 | − | 0.999999i | \(-0.500330\pi\) | ||||
−0.00103652 | + | 0.999999i | \(0.500330\pi\) | |||||||
\(12\) | −1.60239e10 | −0.896490 | ||||||||
\(13\) | 5.04216e10 | 1.31873 | 0.659364 | − | 0.751824i | \(-0.270826\pi\) | ||||
0.659364 | + | 0.751824i | \(0.270826\pi\) | |||||||
\(14\) | −7.71440e9 | −0.0997897 | ||||||||
\(15\) | −1.20421e11 | −0.808786 | ||||||||
\(16\) | −8.93976e9 | −0.0325227 | ||||||||
\(17\) | 2.25070e11 | 0.460313 | 0.230156 | − | 0.973154i | \(-0.426076\pi\) | ||||
0.230156 | + | 0.973154i | \(0.426076\pi\) | |||||||
\(18\) | 6.39934e11 | 0.760407 | ||||||||
\(19\) | −1.71028e12 | −1.21593 | −0.607964 | − | 0.793965i | \(-0.708013\pi\) | ||||
−0.607964 | + | 0.793965i | \(0.708013\pi\) | |||||||
\(20\) | 7.52098e11 | 0.328465 | ||||||||
\(21\) | −8.56907e11 | −0.235424 | ||||||||
\(22\) | −7.39272e9 | −0.00130554 | ||||||||
\(23\) | 1.40365e13 | 1.62497 | 0.812485 | − | 0.582982i | \(-0.198114\pi\) | ||||
0.812485 | + | 0.582982i | \(0.198114\pi\) | |||||||
\(24\) | −1.94165e13 | −1.50025 | ||||||||
\(25\) | −1.34214e13 | −0.703668 | ||||||||
\(26\) | 2.29923e13 | 0.830491 | ||||||||
\(27\) | 1.22123e13 | 0.308207 | ||||||||
\(28\) | 5.35190e12 | 0.0956107 | ||||||||
\(29\) | 1.13784e12 | 0.0145646 | 0.00728230 | − | 0.999973i | \(-0.497682\pi\) | ||||
0.00728230 | + | 0.999973i | \(0.497682\pi\) | |||||||
\(30\) | −5.49118e13 | −0.509347 | ||||||||
\(31\) | −1.04627e14 | −0.710734 | −0.355367 | − | 0.934727i | \(-0.615644\pi\) | ||||
−0.355367 | + | 0.934727i | \(0.615644\pi\) | |||||||
\(32\) | 1.96900e14 | 0.989283 | ||||||||
\(33\) | −8.21176e11 | −0.00308002 | ||||||||
\(34\) | 1.02632e14 | 0.289890 | ||||||||
\(35\) | 4.02199e13 | 0.0862571 | ||||||||
\(36\) | −4.43957e14 | −0.728563 | ||||||||
\(37\) | −1.69392e14 | −0.214278 | −0.107139 | − | 0.994244i | \(-0.534169\pi\) | ||||
−0.107139 | + | 0.994244i | \(0.534169\pi\) | |||||||
\(38\) | −7.79887e14 | −0.765751 | ||||||||
\(39\) | 2.55396e15 | 1.95929 | ||||||||
\(40\) | 9.11337e14 | 0.549679 | ||||||||
\(41\) | −3.30998e15 | −1.57899 | −0.789495 | − | 0.613757i | \(-0.789657\pi\) | ||||
−0.789495 | + | 0.613757i | \(0.789657\pi\) | |||||||
\(42\) | −3.90750e14 | −0.148262 | ||||||||
\(43\) | 1.12791e15 | 0.342236 | 0.171118 | − | 0.985251i | \(-0.445262\pi\) | ||||
0.171118 | + | 0.985251i | \(0.445262\pi\) | |||||||
\(44\) | 5.12873e12 | 0.00125086 | ||||||||
\(45\) | −3.33637e15 | −0.657288 | ||||||||
\(46\) | 6.40066e15 | 1.02335 | ||||||||
\(47\) | 3.49869e15 | 0.456012 | 0.228006 | − | 0.973660i | \(-0.426779\pi\) | ||||
0.228006 | + | 0.973660i | \(0.426779\pi\) | |||||||
\(48\) | −4.52817e14 | −0.0483204 | ||||||||
\(49\) | −1.11127e16 | −0.974892 | ||||||||
\(50\) | −6.12016e15 | −0.443147 | ||||||||
\(51\) | 1.14003e16 | 0.683908 | ||||||||
\(52\) | −1.59510e16 | −0.795711 | ||||||||
\(53\) | 2.99563e16 | 1.24700 | 0.623501 | − | 0.781822i | \(-0.285710\pi\) | ||||
0.623501 | + | 0.781822i | \(0.285710\pi\) | |||||||
\(54\) | 5.56881e15 | 0.194098 | ||||||||
\(55\) | 3.85428e13 | 0.00112849 | ||||||||
\(56\) | 6.48503e15 | 0.160002 | ||||||||
\(57\) | −8.66290e16 | −1.80656 | ||||||||
\(58\) | 5.18853e14 | 0.00917230 | ||||||||
\(59\) | 5.83914e16 | 0.877515 | 0.438758 | − | 0.898605i | \(-0.355419\pi\) | ||||
0.438758 | + | 0.898605i | \(0.355419\pi\) | |||||||
\(60\) | 3.80953e16 | 0.488016 | ||||||||
\(61\) | 2.33737e16 | 0.255914 | 0.127957 | − | 0.991780i | \(-0.459158\pi\) | ||||
0.127957 | + | 0.991780i | \(0.459158\pi\) | |||||||
\(62\) | −4.77099e16 | −0.447597 | ||||||||
\(63\) | −2.37415e16 | −0.191325 | ||||||||
\(64\) | 9.44733e16 | 0.655540 | ||||||||
\(65\) | −1.19873e17 | −0.717867 | ||||||||
\(66\) | −3.74456e14 | −0.00193970 | ||||||||
\(67\) | −2.05103e17 | −0.921002 | −0.460501 | − | 0.887659i | \(-0.652330\pi\) | ||||
−0.460501 | + | 0.887659i | \(0.652330\pi\) | |||||||
\(68\) | −7.12014e16 | −0.277750 | ||||||||
\(69\) | 7.10979e17 | 2.41429 | ||||||||
\(70\) | 1.83403e16 | 0.0543219 | ||||||||
\(71\) | −1.77902e17 | −0.460498 | −0.230249 | − | 0.973132i | \(-0.573954\pi\) | ||||
−0.230249 | + | 0.973132i | \(0.573954\pi\) | |||||||
\(72\) | −5.37954e17 | −1.21923 | ||||||||
\(73\) | 2.99854e17 | 0.596132 | 0.298066 | − | 0.954545i | \(-0.403658\pi\) | ||||
0.298066 | + | 0.954545i | \(0.403658\pi\) | |||||||
\(74\) | −7.72429e16 | −0.134945 | ||||||||
\(75\) | −6.79821e17 | −1.04547 | ||||||||
\(76\) | 5.41050e17 | 0.733683 | ||||||||
\(77\) | 2.74269e14 | 0.000328485 0 | ||||||||
\(78\) | 1.16460e18 | 1.23390 | ||||||||
\(79\) | −9.22271e16 | −0.0865767 | −0.0432884 | − | 0.999063i | \(-0.513783\pi\) | ||||
−0.0432884 | + | 0.999063i | \(0.513783\pi\) | |||||||
\(80\) | 2.12535e16 | 0.0177042 | ||||||||
\(81\) | −1.01250e18 | −0.749525 | ||||||||
\(82\) | −1.50935e18 | −0.994396 | ||||||||
\(83\) | 1.20854e18 | 0.709611 | 0.354805 | − | 0.934940i | \(-0.384547\pi\) | ||||
0.354805 | + | 0.934940i | \(0.384547\pi\) | |||||||
\(84\) | 2.71084e17 | 0.142053 | ||||||||
\(85\) | −5.35084e17 | −0.250578 | ||||||||
\(86\) | 5.14329e17 | 0.215529 | ||||||||
\(87\) | 5.76336e16 | 0.0216393 | ||||||||
\(88\) | 6.21462e15 | 0.00209329 | ||||||||
\(89\) | 4.37120e18 | 1.32250 | 0.661250 | − | 0.750166i | \(-0.270026\pi\) | ||||
0.661250 | + | 0.750166i | \(0.270026\pi\) | |||||||
\(90\) | −1.52139e18 | −0.413938 | ||||||||
\(91\) | −8.53010e17 | −0.208959 | ||||||||
\(92\) | −4.44049e18 | −0.980497 | ||||||||
\(93\) | −5.29956e18 | −1.05597 | ||||||||
\(94\) | 1.59540e18 | 0.287181 | ||||||||
\(95\) | 4.06603e18 | 0.661907 | ||||||||
\(96\) | 9.97337e18 | 1.46982 | ||||||||
\(97\) | −6.35013e17 | −0.0848108 | −0.0424054 | − | 0.999100i | \(-0.513502\pi\) | ||||
−0.0424054 | + | 0.999100i | \(0.513502\pi\) | |||||||
\(98\) | −5.06739e18 | −0.613955 | ||||||||
\(99\) | −2.27515e16 | −0.00250308 | ||||||||
\(100\) | 4.24589e18 | 0.424589 | ||||||||
\(101\) | −1.42252e19 | −1.29421 | −0.647105 | − | 0.762401i | \(-0.724021\pi\) | ||||
−0.647105 | + | 0.762401i | \(0.724021\pi\) | |||||||
\(102\) | 5.19851e18 | 0.430703 | ||||||||
\(103\) | 4.90729e18 | 0.370586 | 0.185293 | − | 0.982683i | \(-0.440677\pi\) | ||||
0.185293 | + | 0.982683i | \(0.440677\pi\) | |||||||
\(104\) | −1.93282e19 | −1.33160 | ||||||||
\(105\) | 2.03722e18 | 0.128156 | ||||||||
\(106\) | 1.36601e19 | 0.785321 | ||||||||
\(107\) | 2.64625e19 | 1.39151 | 0.695753 | − | 0.718281i | \(-0.255071\pi\) | ||||
0.695753 | + | 0.718281i | \(0.255071\pi\) | |||||||
\(108\) | −3.86339e18 | −0.185970 | ||||||||
\(109\) | −1.84178e19 | −0.812242 | −0.406121 | − | 0.913819i | \(-0.633119\pi\) | ||||
−0.406121 | + | 0.913819i | \(0.633119\pi\) | |||||||
\(110\) | 1.75755e16 | 0.000710686 0 | ||||||||
\(111\) | −8.58006e18 | −0.318363 | ||||||||
\(112\) | 1.51239e17 | 0.00515338 | ||||||||
\(113\) | 2.57421e19 | 0.806118 | 0.403059 | − | 0.915174i | \(-0.367947\pi\) | ||||
0.403059 | + | 0.915174i | \(0.367947\pi\) | |||||||
\(114\) | −3.95028e19 | −1.13771 | ||||||||
\(115\) | −3.33706e19 | −0.884575 | ||||||||
\(116\) | −3.59956e17 | −0.00878818 | ||||||||
\(117\) | 7.07599e19 | 1.59229 | ||||||||
\(118\) | 2.66265e19 | 0.552630 | ||||||||
\(119\) | −3.80763e18 | −0.0729389 | ||||||||
\(120\) | 4.61610e19 | 0.816683 | ||||||||
\(121\) | −6.11588e19 | −0.999996 | ||||||||
\(122\) | 1.06584e19 | 0.161166 | ||||||||
\(123\) | −1.67657e20 | −2.34598 | ||||||||
\(124\) | 3.30989e19 | 0.428852 | ||||||||
\(125\) | 7.72537e19 | 0.927415 | ||||||||
\(126\) | −1.08261e19 | −0.120490 | ||||||||
\(127\) | 8.80720e19 | 0.909290 | 0.454645 | − | 0.890673i | \(-0.349766\pi\) | ||||
0.454645 | + | 0.890673i | \(0.349766\pi\) | |||||||
\(128\) | −6.01524e19 | −0.576445 | ||||||||
\(129\) | 5.71311e19 | 0.508476 | ||||||||
\(130\) | −5.46620e19 | −0.452089 | ||||||||
\(131\) | 7.19289e19 | 0.553129 | 0.276564 | − | 0.960995i | \(-0.410804\pi\) | ||||
0.276564 | + | 0.960995i | \(0.410804\pi\) | |||||||
\(132\) | 2.59781e17 | 0.00185846 | ||||||||
\(133\) | 2.89337e19 | 0.192670 | ||||||||
\(134\) | −9.35268e19 | −0.580016 | ||||||||
\(135\) | −2.90337e19 | −0.167776 | ||||||||
\(136\) | −8.62765e19 | −0.464807 | ||||||||
\(137\) | −2.95426e20 | −1.48458 | −0.742290 | − | 0.670079i | \(-0.766260\pi\) | ||||
−0.742290 | + | 0.670079i | \(0.766260\pi\) | |||||||
\(138\) | 3.24206e20 | 1.52044 | ||||||||
\(139\) | 1.38478e20 | 0.606375 | 0.303187 | − | 0.952931i | \(-0.401949\pi\) | ||||
0.303187 | + | 0.952931i | \(0.401949\pi\) | |||||||
\(140\) | −1.27237e19 | −0.0520470 | ||||||||
\(141\) | 1.77216e20 | 0.677518 | ||||||||
\(142\) | −8.11235e19 | −0.290006 | ||||||||
\(143\) | −8.17441e17 | −0.00273378 | ||||||||
\(144\) | −1.25457e19 | −0.0392692 | ||||||||
\(145\) | −2.70510e18 | −0.00792843 | ||||||||
\(146\) | 1.36733e20 | 0.375424 | ||||||||
\(147\) | −5.62880e20 | −1.44844 | ||||||||
\(148\) | 5.35876e19 | 0.129294 | ||||||||
\(149\) | −2.66021e20 | −0.602070 | −0.301035 | − | 0.953613i | \(-0.597332\pi\) | ||||
−0.301035 | + | 0.953613i | \(0.597332\pi\) | |||||||
\(150\) | −3.09998e20 | −0.658404 | ||||||||
\(151\) | 5.75578e20 | 1.14769 | 0.573844 | − | 0.818965i | \(-0.305452\pi\) | ||||
0.573844 | + | 0.818965i | \(0.305452\pi\) | |||||||
\(152\) | 6.55604e20 | 1.22780 | ||||||||
\(153\) | 3.15855e20 | 0.555801 | ||||||||
\(154\) | 1.25067e17 | 0.000206869 0 | ||||||||
\(155\) | 2.48741e20 | 0.386898 | ||||||||
\(156\) | −8.07949e20 | −1.18223 | ||||||||
\(157\) | −1.07238e21 | −1.47673 | −0.738363 | − | 0.674403i | \(-0.764401\pi\) | ||||
−0.738363 | + | 0.674403i | \(0.764401\pi\) | |||||||
\(158\) | −4.20556e19 | −0.0545232 | ||||||||
\(159\) | 1.51735e21 | 1.85273 | ||||||||
\(160\) | −4.68111e20 | −0.538529 | ||||||||
\(161\) | −2.37464e20 | −0.257485 | ||||||||
\(162\) | −4.61699e20 | −0.472026 | ||||||||
\(163\) | −5.80765e20 | −0.560039 | −0.280019 | − | 0.959994i | \(-0.590341\pi\) | ||||
−0.280019 | + | 0.959994i | \(0.590341\pi\) | |||||||
\(164\) | 1.04712e21 | 0.952752 | ||||||||
\(165\) | 1.95227e18 | 0.00167665 | ||||||||
\(166\) | 5.51096e20 | 0.446889 | ||||||||
\(167\) | 2.43392e20 | 0.186423 | 0.0932117 | − | 0.995646i | \(-0.470287\pi\) | ||||
0.0932117 | + | 0.995646i | \(0.470287\pi\) | |||||||
\(168\) | 3.28480e20 | 0.237723 | ||||||||
\(169\) | 1.08042e21 | 0.739041 | ||||||||
\(170\) | −2.43998e20 | −0.157805 | ||||||||
\(171\) | −2.40014e21 | −1.46816 | ||||||||
\(172\) | −3.56818e20 | −0.206503 | ||||||||
\(173\) | −1.19350e21 | −0.653711 | −0.326855 | − | 0.945074i | \(-0.605989\pi\) | ||||
−0.326855 | + | 0.945074i | \(0.605989\pi\) | |||||||
\(174\) | 2.62809e19 | 0.0136277 | ||||||||
\(175\) | 2.27057e20 | 0.111500 | ||||||||
\(176\) | 1.44932e17 | 6.74210e−5 0 | ||||||||
\(177\) | 2.95764e21 | 1.30377 | ||||||||
\(178\) | 1.99327e21 | 0.832867 | ||||||||
\(179\) | −4.14664e21 | −1.64283 | −0.821415 | − | 0.570331i | \(-0.806815\pi\) | ||||
−0.821415 | + | 0.570331i | \(0.806815\pi\) | |||||||
\(180\) | 1.05547e21 | 0.396603 | ||||||||
\(181\) | 3.32364e21 | 1.18486 | 0.592430 | − | 0.805622i | \(-0.298169\pi\) | ||||
0.592430 | + | 0.805622i | \(0.298169\pi\) | |||||||
\(182\) | −3.88973e20 | −0.131595 | ||||||||
\(183\) | 1.18392e21 | 0.380223 | ||||||||
\(184\) | −5.38065e21 | −1.64084 | ||||||||
\(185\) | 4.02715e20 | 0.116645 | ||||||||
\(186\) | −2.41660e21 | −0.665015 | ||||||||
\(187\) | −3.64886e18 | −0.000954250 0 | ||||||||
\(188\) | −1.10682e21 | −0.275155 | ||||||||
\(189\) | −2.06602e20 | −0.0488369 | ||||||||
\(190\) | 1.85411e21 | 0.416847 | ||||||||
\(191\) | 6.19380e21 | 1.32477 | 0.662384 | − | 0.749164i | \(-0.269545\pi\) | ||||
0.662384 | + | 0.749164i | \(0.269545\pi\) | |||||||
\(192\) | 4.78526e21 | 0.973966 | ||||||||
\(193\) | −5.20697e21 | −1.00877 | −0.504383 | − | 0.863480i | \(-0.668280\pi\) | ||||
−0.504383 | + | 0.863480i | \(0.668280\pi\) | |||||||
\(194\) | −2.89566e20 | −0.0534111 | ||||||||
\(195\) | −6.07180e21 | −1.06657 | ||||||||
\(196\) | 3.51552e21 | 0.588244 | ||||||||
\(197\) | 2.42384e21 | 0.386433 | 0.193216 | − | 0.981156i | \(-0.438108\pi\) | ||||
0.193216 | + | 0.981156i | \(0.438108\pi\) | |||||||
\(198\) | −1.03747e19 | −0.00157636 | ||||||||
\(199\) | −1.05907e21 | −0.153399 | −0.0766993 | − | 0.997054i | \(-0.524438\pi\) | ||||
−0.0766993 | + | 0.997054i | \(0.524438\pi\) | |||||||
\(200\) | 5.14485e21 | 0.710539 | ||||||||
\(201\) | −1.03889e22 | −1.36837 | ||||||||
\(202\) | −6.48668e21 | −0.815051 | ||||||||
\(203\) | −1.92494e19 | −0.00230783 | ||||||||
\(204\) | −3.60649e21 | −0.412666 | ||||||||
\(205\) | 7.86919e21 | 0.859545 | ||||||||
\(206\) | 2.23773e21 | 0.233383 | ||||||||
\(207\) | 1.96984e22 | 1.96206 | ||||||||
\(208\) | −4.50757e20 | −0.0428885 | ||||||||
\(209\) | 2.77272e19 | 0.00252067 | ||||||||
\(210\) | 9.28972e20 | 0.0807085 | ||||||||
\(211\) | −1.32424e22 | −1.09972 | −0.549861 | − | 0.835256i | \(-0.685319\pi\) | ||||
−0.549861 | + | 0.835256i | \(0.685319\pi\) | |||||||
\(212\) | −9.47673e21 | −0.752433 | ||||||||
\(213\) | −9.01111e21 | −0.684183 | ||||||||
\(214\) | 1.20669e22 | 0.876325 | ||||||||
\(215\) | −2.68151e21 | −0.186301 | ||||||||
\(216\) | −4.68137e21 | −0.311216 | ||||||||
\(217\) | 1.77003e21 | 0.112619 | ||||||||
\(218\) | −8.39851e21 | −0.511523 | ||||||||
\(219\) | 1.51882e22 | 0.885701 | ||||||||
\(220\) | −1.21931e19 | −0.000680924 0 | ||||||||
\(221\) | 1.13484e22 | 0.607027 | ||||||||
\(222\) | −3.91251e21 | −0.200494 | ||||||||
\(223\) | 2.00921e22 | 0.986575 | 0.493287 | − | 0.869866i | \(-0.335795\pi\) | ||||
0.493287 | + | 0.869866i | \(0.335795\pi\) | |||||||
\(224\) | −3.33106e21 | −0.156757 | ||||||||
\(225\) | −1.88351e22 | −0.849639 | ||||||||
\(226\) | 1.17384e22 | 0.507667 | ||||||||
\(227\) | −2.03494e22 | −0.843929 | −0.421965 | − | 0.906612i | \(-0.638659\pi\) | ||||
−0.421965 | + | 0.906612i | \(0.638659\pi\) | |||||||
\(228\) | 2.74053e22 | 1.09007 | ||||||||
\(229\) | −3.99900e22 | −1.52586 | −0.762930 | − | 0.646481i | \(-0.776240\pi\) | ||||
−0.762930 | + | 0.646481i | \(0.776240\pi\) | |||||||
\(230\) | −1.52170e22 | −0.557076 | ||||||||
\(231\) | 1.38923e19 | 0.000488045 0 | ||||||||
\(232\) | −4.36168e20 | −0.0147068 | ||||||||
\(233\) | 2.42170e22 | 0.783862 | 0.391931 | − | 0.919995i | \(-0.371807\pi\) | ||||
0.391931 | + | 0.919995i | \(0.371807\pi\) | |||||||
\(234\) | 3.22665e22 | 1.00277 | ||||||||
\(235\) | −8.31783e21 | −0.248236 | ||||||||
\(236\) | −1.84722e22 | −0.529487 | ||||||||
\(237\) | −4.67149e21 | −0.128631 | ||||||||
\(238\) | −1.73628e21 | −0.0459345 | ||||||||
\(239\) | 2.62411e22 | 0.667116 | 0.333558 | − | 0.942730i | \(-0.391751\pi\) | ||||
0.333558 | + | 0.942730i | \(0.391751\pi\) | |||||||
\(240\) | 1.07653e21 | 0.0263039 | ||||||||
\(241\) | 7.36445e22 | 1.72973 | 0.864865 | − | 0.502004i | \(-0.167404\pi\) | ||||
0.864865 | + | 0.502004i | \(0.167404\pi\) | |||||||
\(242\) | −2.78884e22 | −0.629764 | ||||||||
\(243\) | −6.54789e22 | −1.42181 | ||||||||
\(244\) | −7.39431e21 | −0.154417 | ||||||||
\(245\) | 2.64194e22 | 0.530696 | ||||||||
\(246\) | −7.64518e22 | −1.47742 | ||||||||
\(247\) | −8.62350e22 | −1.60348 | ||||||||
\(248\) | 4.01068e22 | 0.717674 | ||||||||
\(249\) | 6.12151e22 | 1.05430 | ||||||||
\(250\) | 3.52277e22 | 0.584055 | ||||||||
\(251\) | 7.29309e22 | 1.16416 | 0.582078 | − | 0.813133i | \(-0.302240\pi\) | ||||
0.582078 | + | 0.813133i | \(0.302240\pi\) | |||||||
\(252\) | 7.51066e21 | 0.115444 | ||||||||
\(253\) | −2.27562e20 | −0.00336864 | ||||||||
\(254\) | 4.01608e22 | 0.572641 | ||||||||
\(255\) | −2.71031e22 | −0.372295 | ||||||||
\(256\) | −7.69607e22 | −1.01857 | ||||||||
\(257\) | −6.38120e22 | −0.813838 | −0.406919 | − | 0.913464i | \(-0.633397\pi\) | ||||
−0.406919 | + | 0.913464i | \(0.633397\pi\) | |||||||
\(258\) | 2.60518e22 | 0.320221 | ||||||||
\(259\) | 2.86570e21 | 0.0339534 | ||||||||
\(260\) | 3.79220e22 | 0.433156 | ||||||||
\(261\) | 1.59680e21 | 0.0175859 | ||||||||
\(262\) | 3.27996e22 | 0.348342 | ||||||||
\(263\) | −1.35820e23 | −1.39118 | −0.695590 | − | 0.718439i | \(-0.744857\pi\) | ||||
−0.695590 | + | 0.718439i | \(0.744857\pi\) | |||||||
\(264\) | 3.14783e20 | 0.00311010 | ||||||||
\(265\) | −7.12184e22 | −0.678823 | ||||||||
\(266\) | 1.31938e22 | 0.121337 | ||||||||
\(267\) | 2.21410e23 | 1.96490 | ||||||||
\(268\) | 6.48846e22 | 0.555726 | ||||||||
\(269\) | −1.33672e23 | −1.10508 | −0.552540 | − | 0.833486i | \(-0.686341\pi\) | ||||
−0.552540 | + | 0.833486i | \(0.686341\pi\) | |||||||
\(270\) | −1.32393e22 | −0.105660 | ||||||||
\(271\) | 2.00548e23 | 1.54529 | 0.772643 | − | 0.634840i | \(-0.218934\pi\) | ||||
0.772643 | + | 0.634840i | \(0.218934\pi\) | |||||||
\(272\) | −2.01207e21 | −0.0149706 | ||||||||
\(273\) | −4.32067e22 | −0.310460 | ||||||||
\(274\) | −1.34714e23 | −0.934939 | ||||||||
\(275\) | 2.17589e20 | 0.00145874 | ||||||||
\(276\) | −2.24919e23 | −1.45677 | ||||||||
\(277\) | 2.00223e23 | 1.25301 | 0.626507 | − | 0.779416i | \(-0.284484\pi\) | ||||
0.626507 | + | 0.779416i | \(0.284484\pi\) | |||||||
\(278\) | 6.31461e22 | 0.381875 | ||||||||
\(279\) | −1.46830e23 | −0.858170 | ||||||||
\(280\) | −1.54176e22 | −0.0870994 | ||||||||
\(281\) | −1.19239e23 | −0.651194 | −0.325597 | − | 0.945509i | \(-0.605565\pi\) | ||||
−0.325597 | + | 0.945509i | \(0.605565\pi\) | |||||||
\(282\) | 8.08104e22 | 0.426679 | ||||||||
\(283\) | −3.46108e21 | −0.0176702 | −0.00883509 | − | 0.999961i | \(-0.502812\pi\) | ||||
−0.00883509 | + | 0.999961i | \(0.502812\pi\) | |||||||
\(284\) | 5.62798e22 | 0.277861 | ||||||||
\(285\) | 2.05953e23 | 0.983425 | ||||||||
\(286\) | −3.72753e20 | −0.00172165 | ||||||||
\(287\) | 5.59968e22 | 0.250199 | ||||||||
\(288\) | 2.76322e23 | 1.19450 | ||||||||
\(289\) | −1.88416e23 | −0.788112 | ||||||||
\(290\) | −1.23353e21 | −0.00499307 | ||||||||
\(291\) | −3.21647e22 | −0.126007 | ||||||||
\(292\) | −9.48593e22 | −0.359702 | ||||||||
\(293\) | −2.13236e23 | −0.782739 | −0.391370 | − | 0.920234i | \(-0.627999\pi\) | ||||
−0.391370 | + | 0.920234i | \(0.627999\pi\) | |||||||
\(294\) | −2.56673e23 | −0.912181 | ||||||||
\(295\) | −1.38820e23 | −0.477687 | ||||||||
\(296\) | 6.49335e22 | 0.216370 | ||||||||
\(297\) | −1.97987e20 | −0.000638927 0 | ||||||||
\(298\) | −1.21306e23 | −0.379164 | ||||||||
\(299\) | 7.07745e23 | 2.14289 | ||||||||
\(300\) | 2.15063e23 | 0.630831 | ||||||||
\(301\) | −1.90815e22 | −0.0542290 | ||||||||
\(302\) | 2.62464e23 | 0.722776 | ||||||||
\(303\) | −7.20534e23 | −1.92287 | ||||||||
\(304\) | 1.52895e22 | 0.0395452 | ||||||||
\(305\) | −5.55688e22 | −0.139310 | ||||||||
\(306\) | 1.44030e23 | 0.350025 | ||||||||
\(307\) | 1.91887e23 | 0.452097 | 0.226048 | − | 0.974116i | \(-0.427419\pi\) | ||||
0.226048 | + | 0.974116i | \(0.427419\pi\) | |||||||
\(308\) | −8.67656e19 | −0.000198205 0 | ||||||||
\(309\) | 2.48564e23 | 0.550596 | ||||||||
\(310\) | 1.13426e23 | 0.243655 | ||||||||
\(311\) | −1.54522e23 | −0.321933 | −0.160967 | − | 0.986960i | \(-0.551461\pi\) | ||||
−0.160967 | + | 0.986960i | \(0.551461\pi\) | |||||||
\(312\) | −9.79013e23 | −1.97843 | ||||||||
\(313\) | 2.87408e23 | 0.563413 | 0.281707 | − | 0.959501i | \(-0.409100\pi\) | ||||
0.281707 | + | 0.959501i | \(0.409100\pi\) | |||||||
\(314\) | −4.89003e23 | −0.929994 | ||||||||
\(315\) | 5.64432e22 | 0.104150 | ||||||||
\(316\) | 2.91762e22 | 0.0522398 | ||||||||
\(317\) | 2.63533e22 | 0.0457901 | 0.0228950 | − | 0.999738i | \(-0.492712\pi\) | ||||
0.0228950 | + | 0.999738i | \(0.492712\pi\) | |||||||
\(318\) | 6.91910e23 | 1.16679 | ||||||||
\(319\) | −1.84467e19 | −3.01931e−5 0 | ||||||||
\(320\) | −2.24602e23 | −0.356852 | ||||||||
\(321\) | 1.34038e24 | 2.06743 | ||||||||
\(322\) | −1.08283e23 | −0.162155 | ||||||||
\(323\) | −3.84933e23 | −0.559707 | ||||||||
\(324\) | 3.20306e23 | 0.452259 | ||||||||
\(325\) | −6.76729e23 | −0.927946 | ||||||||
\(326\) | −2.64829e23 | −0.352694 | ||||||||
\(327\) | −9.32897e23 | −1.20679 | ||||||||
\(328\) | 1.26882e24 | 1.59441 | ||||||||
\(329\) | −5.91893e22 | −0.0722574 | ||||||||
\(330\) | 8.90236e20 | 0.00105590 | ||||||||
\(331\) | −1.05338e24 | −1.21400 | −0.606998 | − | 0.794703i | \(-0.707626\pi\) | ||||
−0.606998 | + | 0.794703i | \(0.707626\pi\) | |||||||
\(332\) | −3.82325e23 | −0.428175 | ||||||||
\(333\) | −2.37719e23 | −0.258728 | ||||||||
\(334\) | 1.10987e23 | 0.117403 | ||||||||
\(335\) | 4.87613e23 | 0.501360 | ||||||||
\(336\) | 7.66055e21 | 0.00765661 | ||||||||
\(337\) | 6.76160e23 | 0.657000 | 0.328500 | − | 0.944504i | \(-0.393457\pi\) | ||||
0.328500 | + | 0.944504i | \(0.393457\pi\) | |||||||
\(338\) | 4.92671e23 | 0.465424 | ||||||||
\(339\) | 1.30389e24 | 1.19769 | ||||||||
\(340\) | 1.69275e23 | 0.151197 | ||||||||
\(341\) | 1.69622e21 | 0.00147338 | ||||||||
\(342\) | −1.09447e24 | −0.924600 | ||||||||
\(343\) | 3.80841e23 | 0.312932 | ||||||||
\(344\) | −4.32365e23 | −0.345578 | ||||||||
\(345\) | −1.69029e24 | −1.31425 | ||||||||
\(346\) | −5.44237e23 | −0.411685 | ||||||||
\(347\) | 1.06325e24 | 0.782535 | 0.391268 | − | 0.920277i | \(-0.372037\pi\) | ||||
0.391268 | + | 0.920277i | \(0.372037\pi\) | |||||||
\(348\) | −1.82325e22 | −0.0130570 | ||||||||
\(349\) | −7.14667e23 | −0.498037 | −0.249019 | − | 0.968499i | \(-0.580108\pi\) | ||||
−0.249019 | + | 0.968499i | \(0.580108\pi\) | |||||||
\(350\) | 1.03538e23 | 0.0702189 | ||||||||
\(351\) | 6.15764e23 | 0.406440 | ||||||||
\(352\) | −3.19216e21 | −0.00205083 | ||||||||
\(353\) | −5.07321e23 | −0.317266 | −0.158633 | − | 0.987338i | \(-0.550709\pi\) | ||||
−0.158633 | + | 0.987338i | \(0.550709\pi\) | |||||||
\(354\) | 1.34868e24 | 0.821068 | ||||||||
\(355\) | 4.22947e23 | 0.250678 | ||||||||
\(356\) | −1.38284e24 | −0.797988 | ||||||||
\(357\) | −1.92864e23 | −0.108369 | ||||||||
\(358\) | −1.89087e24 | −1.03460 | ||||||||
\(359\) | 3.32006e24 | 1.76909 | 0.884544 | − | 0.466458i | \(-0.154470\pi\) | ||||
0.884544 | + | 0.466458i | \(0.154470\pi\) | |||||||
\(360\) | 1.27894e24 | 0.663706 | ||||||||
\(361\) | 9.46633e23 | 0.478479 | ||||||||
\(362\) | 1.51558e24 | 0.746186 | ||||||||
\(363\) | −3.09782e24 | −1.48574 | ||||||||
\(364\) | 2.69851e23 | 0.126084 | ||||||||
\(365\) | −7.12875e23 | −0.324512 | ||||||||
\(366\) | 5.39869e23 | 0.239452 | ||||||||
\(367\) | −2.24430e24 | −0.969958 | −0.484979 | − | 0.874526i | \(-0.661173\pi\) | ||||
−0.484979 | + | 0.874526i | \(0.661173\pi\) | |||||||
\(368\) | −1.25483e23 | −0.0528484 | ||||||||
\(369\) | −4.64511e24 | −1.90654 | ||||||||
\(370\) | 1.83638e23 | 0.0734592 | ||||||||
\(371\) | −5.06787e23 | −0.197594 | ||||||||
\(372\) | 1.67653e24 | 0.637166 | ||||||||
\(373\) | 5.10606e24 | 1.89170 | 0.945850 | − | 0.324603i | \(-0.105231\pi\) | ||||
0.945850 | + | 0.324603i | \(0.105231\pi\) | |||||||
\(374\) | −1.66388e21 | −0.000600955 0 | ||||||||
\(375\) | 3.91305e24 | 1.37790 | ||||||||
\(376\) | −1.34116e24 | −0.460465 | ||||||||
\(377\) | 5.73715e22 | 0.0192067 | ||||||||
\(378\) | −9.42106e22 | −0.0307559 | ||||||||
\(379\) | −4.28975e24 | −1.36571 | −0.682857 | − | 0.730552i | \(-0.739263\pi\) | ||||
−0.682857 | + | 0.730552i | \(0.739263\pi\) | |||||||
\(380\) | −1.28630e24 | −0.399390 | ||||||||
\(381\) | 4.46102e24 | 1.35098 | ||||||||
\(382\) | 2.82437e24 | 0.834295 | ||||||||
\(383\) | −1.86803e24 | −0.538264 | −0.269132 | − | 0.963103i | \(-0.586737\pi\) | ||||
−0.269132 | + | 0.963103i | \(0.586737\pi\) | |||||||
\(384\) | −3.04684e24 | −0.856451 | ||||||||
\(385\) | −6.52050e20 | −0.000178815 0 | ||||||||
\(386\) | −2.37438e24 | −0.635288 | ||||||||
\(387\) | 1.58287e24 | 0.413230 | ||||||||
\(388\) | 2.00888e23 | 0.0511743 | ||||||||
\(389\) | −6.47448e24 | −1.60947 | −0.804737 | − | 0.593632i | \(-0.797694\pi\) | ||||
−0.804737 | + | 0.593632i | \(0.797694\pi\) | |||||||
\(390\) | −2.76874e24 | −0.671689 | ||||||||
\(391\) | 3.15920e24 | 0.747995 | ||||||||
\(392\) | 4.25985e24 | 0.984411 | ||||||||
\(393\) | 3.64334e24 | 0.821809 | ||||||||
\(394\) | 1.10527e24 | 0.243363 | ||||||||
\(395\) | 2.19262e23 | 0.0471292 | ||||||||
\(396\) | 7.19748e21 | 0.00151034 | ||||||||
\(397\) | 1.22760e24 | 0.251505 | 0.125752 | − | 0.992062i | \(-0.459866\pi\) | ||||
0.125752 | + | 0.992062i | \(0.459866\pi\) | |||||||
\(398\) | −4.82937e23 | −0.0966054 | ||||||||
\(399\) | 1.46555e24 | 0.286258 | ||||||||
\(400\) | 1.19984e23 | 0.0228852 | ||||||||
\(401\) | −5.17895e23 | −0.0964651 | −0.0482326 | − | 0.998836i | \(-0.515359\pi\) | ||||
−0.0482326 | + | 0.998836i | \(0.515359\pi\) | |||||||
\(402\) | −4.73732e24 | −0.861757 | ||||||||
\(403\) | −5.27546e24 | −0.937264 | ||||||||
\(404\) | 4.50017e24 | 0.780918 | ||||||||
\(405\) | 2.40712e24 | 0.408014 | ||||||||
\(406\) | −8.77772e21 | −0.00145340 | ||||||||
\(407\) | 2.74621e21 | 0.000444208 0 | ||||||||
\(408\) | −4.37008e24 | −0.690586 | ||||||||
\(409\) | 2.81877e24 | 0.435199 | 0.217599 | − | 0.976038i | \(-0.430177\pi\) | ||||
0.217599 | + | 0.976038i | \(0.430177\pi\) | |||||||
\(410\) | 3.58835e24 | 0.541313 | ||||||||
\(411\) | −1.49639e25 | −2.20571 | ||||||||
\(412\) | −1.55243e24 | −0.223609 | ||||||||
\(413\) | −9.87839e23 | −0.139047 | ||||||||
\(414\) | 8.98245e24 | 1.23564 | ||||||||
\(415\) | −2.87320e24 | −0.386286 | ||||||||
\(416\) | 9.92800e24 | 1.30459 | ||||||||
\(417\) | 7.01420e24 | 0.900919 | ||||||||
\(418\) | 1.26436e22 | 0.00158744 | ||||||||
\(419\) | 8.65571e24 | 1.06235 | 0.531177 | − | 0.847261i | \(-0.321750\pi\) | ||||
0.531177 | + | 0.847261i | \(0.321750\pi\) | |||||||
\(420\) | −6.44479e23 | −0.0773286 | ||||||||
\(421\) | −5.21652e24 | −0.611929 | −0.305964 | − | 0.952043i | \(-0.598979\pi\) | ||||
−0.305964 | + | 0.952043i | \(0.598979\pi\) | |||||||
\(422\) | −6.03853e24 | −0.692569 | ||||||||
\(423\) | 4.90994e24 | 0.550608 | ||||||||
\(424\) | −1.14832e25 | −1.25918 | ||||||||
\(425\) | −3.02076e24 | −0.323908 | ||||||||
\(426\) | −4.10907e24 | −0.430876 | ||||||||
\(427\) | −3.95425e23 | −0.0405508 | ||||||||
\(428\) | −8.37147e24 | −0.839626 | ||||||||
\(429\) | −4.14050e22 | −0.00406171 | ||||||||
\(430\) | −1.22277e24 | −0.117326 | ||||||||
\(431\) | 1.04364e25 | 0.979526 | 0.489763 | − | 0.871856i | \(-0.337083\pi\) | ||||
0.489763 | + | 0.871856i | \(0.337083\pi\) | |||||||
\(432\) | −1.09175e23 | −0.0100237 | ||||||||
\(433\) | 1.45110e25 | 1.30335 | 0.651675 | − | 0.758499i | \(-0.274067\pi\) | ||||
0.651675 | + | 0.758499i | \(0.274067\pi\) | |||||||
\(434\) | 8.07134e23 | 0.0709240 | ||||||||
\(435\) | −1.37019e23 | −0.0117796 | ||||||||
\(436\) | 5.82650e24 | 0.490102 | ||||||||
\(437\) | −2.40064e25 | −1.97585 | ||||||||
\(438\) | 6.92582e24 | 0.557785 | ||||||||
\(439\) | 1.79857e25 | 1.41747 | 0.708735 | − | 0.705474i | \(-0.249266\pi\) | ||||
0.708735 | + | 0.705474i | \(0.249266\pi\) | |||||||
\(440\) | −1.47747e22 | −0.00113951 | ||||||||
\(441\) | −1.55951e25 | −1.17713 | ||||||||
\(442\) | 5.17487e24 | 0.382286 | ||||||||
\(443\) | 8.73685e24 | 0.631712 | 0.315856 | − | 0.948807i | \(-0.397708\pi\) | ||||
0.315856 | + | 0.948807i | \(0.397708\pi\) | |||||||
\(444\) | 2.71432e24 | 0.192098 | ||||||||
\(445\) | −1.03921e25 | −0.719921 | ||||||||
\(446\) | 9.16201e24 | 0.621312 | ||||||||
\(447\) | −1.34745e25 | −0.894523 | ||||||||
\(448\) | −1.59826e24 | −0.103874 | ||||||||
\(449\) | −1.60576e25 | −1.02174 | −0.510870 | − | 0.859658i | \(-0.670677\pi\) | ||||
−0.510870 | + | 0.859658i | \(0.670677\pi\) | |||||||
\(450\) | −8.58881e24 | −0.535075 | ||||||||
\(451\) | 5.36618e22 | 0.00327332 | ||||||||
\(452\) | −8.14357e24 | −0.486407 | ||||||||
\(453\) | 2.91542e25 | 1.70517 | ||||||||
\(454\) | −9.27933e24 | −0.531479 | ||||||||
\(455\) | 2.02795e24 | 0.113750 | ||||||||
\(456\) | 3.32077e25 | 1.82420 | ||||||||
\(457\) | −2.67587e24 | −0.143966 | −0.0719831 | − | 0.997406i | \(-0.522933\pi\) | ||||
−0.0719831 | + | 0.997406i | \(0.522933\pi\) | |||||||
\(458\) | −1.82355e25 | −0.960936 | ||||||||
\(459\) | 2.74863e24 | 0.141871 | ||||||||
\(460\) | 1.05569e25 | 0.533747 | ||||||||
\(461\) | 6.96807e24 | 0.345107 | 0.172553 | − | 0.985000i | \(-0.444798\pi\) | ||||
0.172553 | + | 0.985000i | \(0.444798\pi\) | |||||||
\(462\) | 6.33488e21 | 0.000307354 0 | ||||||||
\(463\) | −2.49843e25 | −1.18754 | −0.593770 | − | 0.804635i | \(-0.702361\pi\) | ||||
−0.593770 | + | 0.804635i | \(0.702361\pi\) | |||||||
\(464\) | −1.01720e22 | −0.000473679 0 | ||||||||
\(465\) | 1.25992e25 | 0.574832 | ||||||||
\(466\) | 1.10430e25 | 0.493650 | ||||||||
\(467\) | 1.94531e25 | 0.852075 | 0.426037 | − | 0.904706i | \(-0.359909\pi\) | ||||
0.426037 | + | 0.904706i | \(0.359909\pi\) | |||||||
\(468\) | −2.23850e25 | −0.960776 | ||||||||
\(469\) | 3.46983e24 | 0.145937 | ||||||||
\(470\) | −3.79293e24 | −0.156331 | ||||||||
\(471\) | −5.43180e25 | −2.19404 | ||||||||
\(472\) | −2.23833e25 | −0.886084 | ||||||||
\(473\) | −1.82859e22 | −0.000709471 0 | ||||||||
\(474\) | −2.13020e24 | −0.0810076 | ||||||||
\(475\) | 2.29543e25 | 0.855610 | ||||||||
\(476\) | 1.20455e24 | 0.0440108 | ||||||||
\(477\) | 4.20396e25 | 1.50568 | ||||||||
\(478\) | 1.19659e25 | 0.420128 | ||||||||
\(479\) | 3.34153e25 | 1.15016 | 0.575080 | − | 0.818097i | \(-0.304971\pi\) | ||||
0.575080 | + | 0.818097i | \(0.304971\pi\) | |||||||
\(480\) | −2.37108e25 | −0.800118 | ||||||||
\(481\) | −8.54103e24 | −0.282574 | ||||||||
\(482\) | 3.35819e25 | 1.08933 | ||||||||
\(483\) | −1.20280e25 | −0.382557 | ||||||||
\(484\) | 1.93477e25 | 0.603391 | ||||||||
\(485\) | 1.50969e24 | 0.0461679 | ||||||||
\(486\) | −2.98584e25 | −0.895410 | ||||||||
\(487\) | −4.86181e25 | −1.42979 | −0.714896 | − | 0.699231i | \(-0.753526\pi\) | ||||
−0.714896 | + | 0.699231i | \(0.753526\pi\) | |||||||
\(488\) | −8.95988e24 | −0.258413 | ||||||||
\(489\) | −2.94169e25 | −0.832075 | ||||||||
\(490\) | 1.20473e25 | 0.334215 | ||||||||
\(491\) | 9.86730e24 | 0.268488 | 0.134244 | − | 0.990948i | \(-0.457139\pi\) | ||||
0.134244 | + | 0.990948i | \(0.457139\pi\) | |||||||
\(492\) | 5.30387e25 | 1.41555 | ||||||||
\(493\) | 2.56093e23 | 0.00670427 | ||||||||
\(494\) | −3.93232e25 | −1.00982 | ||||||||
\(495\) | 5.40896e22 | 0.00136259 | ||||||||
\(496\) | 9.35339e23 | 0.0231150 | ||||||||
\(497\) | 3.00967e24 | 0.0729681 | ||||||||
\(498\) | 2.79141e25 | 0.663964 | ||||||||
\(499\) | −3.54150e25 | −0.826481 | −0.413240 | − | 0.910622i | \(-0.635603\pi\) | ||||
−0.413240 | + | 0.910622i | \(0.635603\pi\) | |||||||
\(500\) | −2.44394e25 | −0.559596 | ||||||||
\(501\) | 1.23283e25 | 0.276978 | ||||||||
\(502\) | 3.32565e25 | 0.733147 | ||||||||
\(503\) | 1.47204e25 | 0.318436 | 0.159218 | − | 0.987243i | \(-0.449103\pi\) | ||||
0.159218 | + | 0.987243i | \(0.449103\pi\) | |||||||
\(504\) | 9.10086e24 | 0.193193 | ||||||||
\(505\) | 3.38191e25 | 0.704521 | ||||||||
\(506\) | −1.03768e23 | −0.00212146 | ||||||||
\(507\) | 5.47254e25 | 1.09803 | ||||||||
\(508\) | −2.78618e25 | −0.548660 | ||||||||
\(509\) | −4.88290e25 | −0.943754 | −0.471877 | − | 0.881664i | \(-0.656423\pi\) | ||||
−0.471877 | + | 0.881664i | \(0.656423\pi\) | |||||||
\(510\) | −1.23590e25 | −0.234459 | ||||||||
\(511\) | −5.07279e24 | −0.0944601 | ||||||||
\(512\) | −3.55692e24 | −0.0650143 | ||||||||
\(513\) | −2.08864e25 | −0.374757 | ||||||||
\(514\) | −2.90983e25 | −0.512528 | ||||||||
\(515\) | −1.16667e25 | −0.201733 | ||||||||
\(516\) | −1.80735e25 | −0.306811 | ||||||||
\(517\) | −5.67212e22 | −0.000945334 0 | ||||||||
\(518\) | 1.30676e24 | 0.0213827 | ||||||||
\(519\) | −6.04533e25 | −0.971248 | ||||||||
\(520\) | 4.59511e25 | 0.724876 | ||||||||
\(521\) | 7.14445e25 | 1.10665 | 0.553325 | − | 0.832965i | \(-0.313359\pi\) | ||||
0.553325 | + | 0.832965i | \(0.313359\pi\) | |||||||
\(522\) | 7.28139e23 | 0.0110750 | ||||||||
\(523\) | 8.99895e25 | 1.34408 | 0.672041 | − | 0.740514i | \(-0.265418\pi\) | ||||
0.672041 | + | 0.740514i | \(0.265418\pi\) | |||||||
\(524\) | −2.27548e25 | −0.333754 | ||||||||
\(525\) | 1.15009e25 | 0.165660 | ||||||||
\(526\) | −6.19338e25 | −0.876120 | ||||||||
\(527\) | −2.35484e25 | −0.327160 | ||||||||
\(528\) | 7.34111e21 | 0.000100170 0 | ||||||||
\(529\) | 1.22409e26 | 1.64053 | ||||||||
\(530\) | −3.24756e25 | −0.427500 | ||||||||
\(531\) | 8.19444e25 | 1.05955 | ||||||||
\(532\) | −9.15324e24 | −0.116256 | ||||||||
\(533\) | −1.66895e26 | −2.08226 | ||||||||
\(534\) | 1.00963e26 | 1.23743 | ||||||||
\(535\) | −6.29123e25 | −0.757486 | ||||||||
\(536\) | 7.86223e25 | 0.929995 | ||||||||
\(537\) | −2.10036e26 | −2.44083 | ||||||||
\(538\) | −6.09544e25 | −0.695943 | ||||||||
\(539\) | 1.80160e23 | 0.00202100 | ||||||||
\(540\) | 9.18486e24 | 0.101235 | ||||||||
\(541\) | −9.33602e25 | −1.01109 | −0.505543 | − | 0.862802i | \(-0.668708\pi\) | ||||
−0.505543 | + | 0.862802i | \(0.668708\pi\) | |||||||
\(542\) | 9.14497e25 | 0.973171 | ||||||||
\(543\) | 1.68349e26 | 1.76040 | ||||||||
\(544\) | 4.43162e25 | 0.455379 | ||||||||
\(545\) | 4.37866e25 | 0.442155 | ||||||||
\(546\) | −1.97022e25 | −0.195517 | ||||||||
\(547\) | −2.74670e25 | −0.267875 | −0.133938 | − | 0.990990i | \(-0.542762\pi\) | ||||
−0.133938 | + | 0.990990i | \(0.542762\pi\) | |||||||
\(548\) | 9.34587e25 | 0.895786 | ||||||||
\(549\) | 3.28018e25 | 0.309001 | ||||||||
\(550\) | 9.92207e22 | 0.000918664 0 | ||||||||
\(551\) | −1.94602e24 | −0.0177095 | ||||||||
\(552\) | −2.72541e26 | −2.43787 | ||||||||
\(553\) | 1.56026e24 | 0.0137185 | ||||||||
\(554\) | 9.13016e25 | 0.789106 | ||||||||
\(555\) | 2.03983e25 | 0.173305 | ||||||||
\(556\) | −4.38079e25 | −0.365882 | ||||||||
\(557\) | 1.42589e26 | 1.17074 | 0.585370 | − | 0.810766i | \(-0.300949\pi\) | ||||
0.585370 | + | 0.810766i | \(0.300949\pi\) | |||||||
\(558\) | −6.69543e25 | −0.540447 | ||||||||
\(559\) | 5.68712e25 | 0.451316 | ||||||||
\(560\) | −3.59557e23 | −0.00280531 | ||||||||
\(561\) | −1.84822e23 | −0.00141777 | ||||||||
\(562\) | −5.43732e25 | −0.410100 | ||||||||
\(563\) | −1.72252e26 | −1.27742 | −0.638712 | − | 0.769446i | \(-0.720533\pi\) | ||||
−0.638712 | + | 0.769446i | \(0.720533\pi\) | |||||||
\(564\) | −5.60626e25 | −0.408810 | ||||||||
\(565\) | −6.11995e25 | −0.438821 | ||||||||
\(566\) | −1.57825e24 | −0.0111281 | ||||||||
\(567\) | 1.71290e25 | 0.118766 | ||||||||
\(568\) | 6.81956e25 | 0.464994 | ||||||||
\(569\) | 5.24893e25 | 0.351969 | 0.175984 | − | 0.984393i | \(-0.443689\pi\) | ||||
0.175984 | + | 0.984393i | \(0.443689\pi\) | |||||||
\(570\) | 9.39144e25 | 0.619329 | ||||||||
\(571\) | −3.21674e24 | −0.0208628 | −0.0104314 | − | 0.999946i | \(-0.503320\pi\) | ||||
−0.0104314 | + | 0.999946i | \(0.503320\pi\) | |||||||
\(572\) | 2.58599e23 | 0.00164955 | ||||||||
\(573\) | 3.13728e26 | 1.96827 | ||||||||
\(574\) | 2.55345e25 | 0.157567 | ||||||||
\(575\) | −1.88390e26 | −1.14344 | ||||||||
\(576\) | 1.32580e26 | 0.791527 | ||||||||
\(577\) | 1.17453e26 | 0.689752 | 0.344876 | − | 0.938648i | \(-0.387921\pi\) | ||||
0.344876 | + | 0.938648i | \(0.387921\pi\) | |||||||
\(578\) | −8.59176e25 | −0.496327 | ||||||||
\(579\) | −2.63744e26 | −1.49877 | ||||||||
\(580\) | 8.55764e23 | 0.00478397 | ||||||||
\(581\) | −2.04456e25 | −0.112441 | ||||||||
\(582\) | −1.46671e25 | −0.0793553 | ||||||||
\(583\) | −4.85655e23 | −0.00258509 | ||||||||
\(584\) | −1.14943e26 | −0.601953 | ||||||||
\(585\) | −1.68225e26 | −0.866783 | ||||||||
\(586\) | −9.72354e25 | −0.492943 | ||||||||
\(587\) | 1.86886e24 | 0.00932213 | 0.00466107 | − | 0.999989i | \(-0.498516\pi\) | ||||
0.00466107 | + | 0.999989i | \(0.498516\pi\) | |||||||
\(588\) | 1.78068e26 | 0.873981 | ||||||||
\(589\) | 1.78941e26 | 0.864201 | ||||||||
\(590\) | −6.33021e25 | −0.300832 | ||||||||
\(591\) | 1.22772e26 | 0.574141 | ||||||||
\(592\) | 1.51433e24 | 0.00696889 | ||||||||
\(593\) | −1.50165e26 | −0.680063 | −0.340032 | − | 0.940414i | \(-0.610438\pi\) | ||||
−0.340032 | + | 0.940414i | \(0.610438\pi\) | |||||||
\(594\) | −9.02822e22 | −0.000402375 0 | ||||||||
\(595\) | 9.05231e24 | 0.0397053 | ||||||||
\(596\) | 8.41563e25 | 0.363285 | ||||||||
\(597\) | −5.36441e25 | −0.227911 | ||||||||
\(598\) | 3.22732e26 | 1.34952 | ||||||||
\(599\) | 1.65804e26 | 0.682403 | 0.341201 | − | 0.939990i | \(-0.389166\pi\) | ||||
0.341201 | + | 0.939990i | \(0.389166\pi\) | |||||||
\(600\) | 2.60597e26 | 1.05568 | ||||||||
\(601\) | −2.54795e26 | −1.01598 | −0.507989 | − | 0.861364i | \(-0.669611\pi\) | ||||
−0.507989 | + | 0.861364i | \(0.669611\pi\) | |||||||
\(602\) | −8.70118e24 | −0.0341516 | ||||||||
\(603\) | −2.87833e26 | −1.11206 | ||||||||
\(604\) | −1.82085e26 | −0.692507 | ||||||||
\(605\) | 1.45400e26 | 0.544361 | ||||||||
\(606\) | −3.28564e26 | −1.21096 | ||||||||
\(607\) | 3.14191e26 | 1.13999 | 0.569996 | − | 0.821648i | \(-0.306945\pi\) | ||||
0.569996 | + | 0.821648i | \(0.306945\pi\) | |||||||
\(608\) | −3.36753e26 | −1.20290 | ||||||||
\(609\) | −9.75020e23 | −0.00342885 | ||||||||
\(610\) | −2.53394e25 | −0.0877329 | ||||||||
\(611\) | 1.76410e26 | 0.601355 | ||||||||
\(612\) | −9.99214e25 | −0.335367 | ||||||||
\(613\) | −3.91478e26 | −1.29370 | −0.646848 | − | 0.762619i | \(-0.723913\pi\) | ||||
−0.646848 | + | 0.762619i | \(0.723913\pi\) | |||||||
\(614\) | 8.75005e25 | 0.284715 | ||||||||
\(615\) | 3.98590e26 | 1.27707 | ||||||||
\(616\) | −1.05136e23 | −0.000331692 0 | ||||||||
\(617\) | 4.86066e26 | 1.51003 | 0.755016 | − | 0.655706i | \(-0.227629\pi\) | ||||
0.755016 | + | 0.655706i | \(0.227629\pi\) | |||||||
\(618\) | 1.13345e26 | 0.346747 | ||||||||
\(619\) | −4.51098e26 | −1.35897 | −0.679485 | − | 0.733689i | \(-0.737797\pi\) | ||||
−0.679485 | + | 0.733689i | \(0.737797\pi\) | |||||||
\(620\) | −7.86897e25 | −0.233452 | ||||||||
\(621\) | 1.71418e26 | 0.500827 | ||||||||
\(622\) | −7.04619e25 | −0.202743 | ||||||||
\(623\) | −7.39500e25 | −0.209557 | ||||||||
\(624\) | −2.28318e25 | −0.0637215 | ||||||||
\(625\) | 7.23294e25 | 0.198817 | ||||||||
\(626\) | 1.31058e26 | 0.354819 | ||||||||
\(627\) | 1.40444e24 | 0.00374508 | ||||||||
\(628\) | 3.39248e26 | 0.891047 | ||||||||
\(629\) | −3.81251e25 | −0.0986349 | ||||||||
\(630\) | 2.57381e25 | 0.0655905 | ||||||||
\(631\) | 2.03805e26 | 0.511607 | 0.255803 | − | 0.966729i | \(-0.417660\pi\) | ||||
0.255803 | + | 0.966729i | \(0.417660\pi\) | |||||||
\(632\) | 3.53536e25 | 0.0874221 | ||||||||
\(633\) | −6.70753e26 | −1.63391 | ||||||||
\(634\) | 1.20171e25 | 0.0288371 | ||||||||
\(635\) | −2.09383e26 | −0.494985 | ||||||||
\(636\) | −4.80016e26 | −1.11793 | ||||||||
\(637\) | −5.60320e26 | −1.28562 | ||||||||
\(638\) | −8.41170e21 | −1.90146e−5 0 | ||||||||
\(639\) | −2.49662e26 | −0.556024 | ||||||||
\(640\) | 1.43007e26 | 0.313796 | ||||||||
\(641\) | 5.77927e26 | 1.24946 | 0.624729 | − | 0.780842i | \(-0.285209\pi\) | ||||
0.624729 | + | 0.780842i | \(0.285209\pi\) | |||||||
\(642\) | 6.11213e26 | 1.30200 | ||||||||
\(643\) | 7.72049e26 | 1.62047 | 0.810235 | − | 0.586106i | \(-0.199340\pi\) | ||||
0.810235 | + | 0.586106i | \(0.199340\pi\) | |||||||
\(644\) | 7.51221e25 | 0.155365 | ||||||||
\(645\) | −1.35824e26 | −0.276796 | ||||||||
\(646\) | −1.75529e26 | −0.352485 | ||||||||
\(647\) | −1.39226e24 | −0.00275504 | −0.00137752 | − | 0.999999i | \(-0.500438\pi\) | ||||
−0.00137752 | + | 0.999999i | \(0.500438\pi\) | |||||||
\(648\) | 3.88123e26 | 0.756844 | ||||||||
\(649\) | −9.46648e23 | −0.00181913 | ||||||||
\(650\) | −3.08588e26 | −0.584390 | ||||||||
\(651\) | 8.96556e25 | 0.167324 | ||||||||
\(652\) | 1.83726e26 | 0.337924 | ||||||||
\(653\) | −6.19470e26 | −1.12291 | −0.561455 | − | 0.827507i | \(-0.689758\pi\) | ||||
−0.561455 | + | 0.827507i | \(0.689758\pi\) | |||||||
\(654\) | −4.25401e26 | −0.759994 | ||||||||
\(655\) | −1.71004e26 | −0.301103 | ||||||||
\(656\) | 2.95905e25 | 0.0513530 | ||||||||
\(657\) | 4.20804e26 | 0.719795 | ||||||||
\(658\) | −2.69903e25 | −0.0455053 | ||||||||
\(659\) | −7.96627e25 | −0.132386 | −0.0661932 | − | 0.997807i | \(-0.521085\pi\) | ||||
−0.0661932 | + | 0.997807i | \(0.521085\pi\) | |||||||
\(660\) | −6.17605e23 | −0.00101168 | ||||||||
\(661\) | −1.85436e26 | −0.299420 | −0.149710 | − | 0.988730i | \(-0.547834\pi\) | ||||
−0.149710 | + | 0.988730i | \(0.547834\pi\) | |||||||
\(662\) | −4.80339e26 | −0.764535 | ||||||||
\(663\) | 5.74819e26 | 0.901888 | ||||||||
\(664\) | −4.63273e26 | −0.716540 | ||||||||
\(665\) | −6.87873e25 | −0.104882 | ||||||||
\(666\) | −1.08400e26 | −0.162938 | ||||||||
\(667\) | 1.59713e25 | 0.0236670 | ||||||||
\(668\) | −7.69977e25 | −0.112487 | ||||||||
\(669\) | 1.01771e27 | 1.46580 | ||||||||
\(670\) | 2.22351e26 | 0.315740 | ||||||||
\(671\) | −3.78937e23 | −0.000530521 0 | ||||||||
\(672\) | −1.68725e26 | −0.232901 | ||||||||
\(673\) | 5.91532e26 | 0.805073 | 0.402536 | − | 0.915404i | \(-0.368129\pi\) | ||||
0.402536 | + | 0.915404i | \(0.368129\pi\) | |||||||
\(674\) | 3.08329e26 | 0.413757 | ||||||||
\(675\) | −1.63906e26 | −0.216875 | ||||||||
\(676\) | −3.41793e26 | −0.445933 | ||||||||
\(677\) | −2.97418e26 | −0.382626 | −0.191313 | − | 0.981529i | \(-0.561275\pi\) | ||||
−0.191313 | + | 0.981529i | \(0.561275\pi\) | |||||||
\(678\) | 5.94573e26 | 0.754264 | ||||||||
\(679\) | 1.07429e25 | 0.0134387 | ||||||||
\(680\) | 2.05115e26 | 0.253024 | ||||||||
\(681\) | −1.03074e27 | −1.25387 | ||||||||
\(682\) | 7.73477e23 | 0.000927889 0 | ||||||||
\(683\) | −1.25943e27 | −1.48997 | −0.744983 | − | 0.667084i | \(-0.767542\pi\) | ||||
−0.744983 | + | 0.667084i | \(0.767542\pi\) | |||||||
\(684\) | 7.59290e26 | 0.885880 | ||||||||
\(685\) | 7.02349e26 | 0.808151 | ||||||||
\(686\) | 1.73663e26 | 0.197074 | ||||||||
\(687\) | −2.02558e27 | −2.26704 | ||||||||
\(688\) | −1.00833e25 | −0.0111304 | ||||||||
\(689\) | 1.51044e27 | 1.64446 | ||||||||
\(690\) | −7.70771e26 | −0.827674 | ||||||||
\(691\) | 3.19965e25 | 0.0338891 | 0.0169446 | − | 0.999856i | \(-0.494606\pi\) | ||||
0.0169446 | + | 0.999856i | \(0.494606\pi\) | |||||||
\(692\) | 3.77567e26 | 0.394445 | ||||||||
\(693\) | 3.84899e23 | 0.000396626 0 | ||||||||
\(694\) | 4.84840e26 | 0.492815 | ||||||||
\(695\) | −3.29220e26 | −0.330088 | ||||||||
\(696\) | −2.20928e25 | −0.0218506 | ||||||||
\(697\) | −7.44979e26 | −0.726829 | ||||||||
\(698\) | −3.25888e26 | −0.313648 | ||||||||
\(699\) | 1.22664e27 | 1.16462 | ||||||||
\(700\) | −7.18300e25 | −0.0672782 | ||||||||
\(701\) | 2.06463e27 | 1.90775 | 0.953874 | − | 0.300208i | \(-0.0970562\pi\) | ||||
0.953874 | + | 0.300208i | \(0.0970562\pi\) | |||||||
\(702\) | 2.80788e26 | 0.255963 | ||||||||
\(703\) | 2.89708e26 | 0.260546 | ||||||||
\(704\) | −1.53161e24 | −0.00135897 | ||||||||
\(705\) | −4.21315e26 | −0.368816 | ||||||||
\(706\) | −2.31338e26 | −0.199803 | ||||||||
\(707\) | 2.40655e26 | 0.205074 | ||||||||
\(708\) | −9.35656e26 | −0.786684 | ||||||||
\(709\) | −1.44096e27 | −1.19539 | −0.597697 | − | 0.801722i | \(-0.703918\pi\) | ||||
−0.597697 | + | 0.801722i | \(0.703918\pi\) | |||||||
\(710\) | 1.92864e26 | 0.157869 | ||||||||
\(711\) | −1.29428e26 | −0.104536 | ||||||||
\(712\) | −1.67562e27 | −1.33541 | ||||||||
\(713\) | −1.46860e27 | −1.15492 | ||||||||
\(714\) | −8.79461e25 | −0.0682470 | ||||||||
\(715\) | 1.94339e24 | 0.00148817 | ||||||||
\(716\) | 1.31180e27 | 0.991273 | ||||||||
\(717\) | 1.32916e27 | 0.991165 | ||||||||
\(718\) | 1.51395e27 | 1.11411 | ||||||||
\(719\) | −1.26393e27 | −0.917907 | −0.458953 | − | 0.888460i | \(-0.651776\pi\) | ||||
−0.458953 | + | 0.888460i | \(0.651776\pi\) | |||||||
\(720\) | 2.98264e25 | 0.0213767 | ||||||||
\(721\) | −8.30194e25 | −0.0587211 | ||||||||
\(722\) | 4.31665e26 | 0.301331 | ||||||||
\(723\) | 3.73024e27 | 2.56994 | ||||||||
\(724\) | −1.05144e27 | −0.714937 | ||||||||
\(725\) | −1.52714e25 | −0.0102486 | ||||||||
\(726\) | −1.41260e27 | −0.935670 | ||||||||
\(727\) | 5.54468e26 | 0.362493 | 0.181246 | − | 0.983438i | \(-0.441987\pi\) | ||||
0.181246 | + | 0.983438i | \(0.441987\pi\) | |||||||
\(728\) | 3.26986e26 | 0.210999 | ||||||||
\(729\) | −2.13985e27 | −1.36293 | ||||||||
\(730\) | −3.25071e26 | −0.204367 | ||||||||
\(731\) | 2.53860e26 | 0.157536 | ||||||||
\(732\) | −3.74537e26 | −0.229424 | ||||||||
\(733\) | 8.06563e26 | 0.487698 | 0.243849 | − | 0.969813i | \(-0.421590\pi\) | ||||
0.243849 | + | 0.969813i | \(0.421590\pi\) | |||||||
\(734\) | −1.02340e27 | −0.610848 | ||||||||
\(735\) | 1.33820e27 | 0.788479 | ||||||||
\(736\) | 2.76379e27 | 1.60755 | ||||||||
\(737\) | 3.32514e24 | 0.00190928 | ||||||||
\(738\) | −2.11817e27 | −1.20068 | ||||||||
\(739\) | 6.63850e26 | 0.371490 | 0.185745 | − | 0.982598i | \(-0.440530\pi\) | ||||
0.185745 | + | 0.982598i | \(0.440530\pi\) | |||||||
\(740\) | −1.27400e26 | −0.0703829 | ||||||||
\(741\) | −4.36798e27 | −2.38236 | ||||||||
\(742\) | −2.31095e26 | −0.124438 | ||||||||
\(743\) | −3.64095e27 | −1.93562 | −0.967811 | − | 0.251677i | \(-0.919018\pi\) | ||||
−0.967811 | + | 0.251677i | \(0.919018\pi\) | |||||||
\(744\) | 2.03149e27 | 1.06628 | ||||||||
\(745\) | 6.32441e26 | 0.327745 | ||||||||
\(746\) | 2.32837e27 | 1.19133 | ||||||||
\(747\) | 1.69603e27 | 0.856814 | ||||||||
\(748\) | 1.15432e24 | 0.000575788 0 | ||||||||
\(749\) | −4.47681e26 | −0.220491 | ||||||||
\(750\) | 1.78435e27 | 0.867758 | ||||||||
\(751\) | −1.55458e27 | −0.746505 | −0.373253 | − | 0.927730i | \(-0.621758\pi\) | ||||
−0.373253 | + | 0.927730i | \(0.621758\pi\) | |||||||
\(752\) | −3.12775e25 | −0.0148307 | ||||||||
\(753\) | 3.69410e27 | 1.72964 | ||||||||
\(754\) | 2.61614e25 | 0.0120958 | ||||||||
\(755\) | −1.36839e27 | −0.624759 | ||||||||
\(756\) | 6.53590e25 | 0.0294679 | ||||||||
\(757\) | 1.33406e27 | 0.593970 | 0.296985 | − | 0.954882i | \(-0.404019\pi\) | ||||
0.296985 | + | 0.954882i | \(0.404019\pi\) | |||||||
\(758\) | −1.95613e27 | −0.860081 | ||||||||
\(759\) | −1.15265e25 | −0.00500494 | ||||||||
\(760\) | −1.55864e27 | −0.668370 | ||||||||
\(761\) | −6.89829e25 | −0.0292137 | −0.0146069 | − | 0.999893i | \(-0.504650\pi\) | ||||
−0.0146069 | + | 0.999893i | \(0.504650\pi\) | |||||||
\(762\) | 2.03423e27 | 0.850799 | ||||||||
\(763\) | 3.11584e26 | 0.128704 | ||||||||
\(764\) | −1.95942e27 | −0.799357 | ||||||||
\(765\) | −7.50917e26 | −0.302558 | ||||||||
\(766\) | −8.51822e26 | −0.338981 | ||||||||
\(767\) | 2.94419e27 | 1.15720 | ||||||||
\(768\) | −3.89821e27 | −1.51333 | ||||||||
\(769\) | −8.09673e26 | −0.310463 | −0.155231 | − | 0.987878i | \(-0.549612\pi\) | ||||
−0.155231 | + | 0.987878i | \(0.549612\pi\) | |||||||
\(770\) | −2.97335e23 | −0.000112612 0 | ||||||||
\(771\) | −3.23221e27 | −1.20916 | ||||||||
\(772\) | 1.64724e27 | 0.608683 | ||||||||
\(773\) | 1.00924e27 | 0.368374 | 0.184187 | − | 0.982891i | \(-0.441035\pi\) | ||||
0.184187 | + | 0.982891i | \(0.441035\pi\) | |||||||
\(774\) | 7.21790e26 | 0.260239 | ||||||||
\(775\) | 1.40424e27 | 0.500121 | ||||||||
\(776\) | 2.43421e26 | 0.0856389 | ||||||||
\(777\) | 1.45154e26 | 0.0504461 | ||||||||
\(778\) | −2.95236e27 | −1.01359 | ||||||||
\(779\) | 5.66100e27 | 1.91994 | ||||||||
\(780\) | 1.92083e27 | 0.643560 | ||||||||
\(781\) | 2.88417e24 | 0.000954633 0 | ||||||||
\(782\) | 1.44060e27 | 0.471062 | ||||||||
\(783\) | 1.38956e25 | 0.00448890 | ||||||||
\(784\) | 9.93448e25 | 0.0317061 | ||||||||
\(785\) | 2.54948e27 | 0.803876 | ||||||||
\(786\) | 1.66136e27 | 0.517548 | ||||||||
\(787\) | −4.88307e27 | −1.50291 | −0.751456 | − | 0.659784i | \(-0.770648\pi\) | ||||
−0.751456 | + | 0.659784i | \(0.770648\pi\) | |||||||
\(788\) | −7.66785e26 | −0.233171 | ||||||||
\(789\) | −6.87955e27 | −2.06694 | ||||||||
\(790\) | 9.99833e25 | 0.0296804 | ||||||||
\(791\) | −4.35493e26 | −0.127733 | ||||||||
\(792\) | 8.72137e24 | 0.00252752 | ||||||||
\(793\) | 1.17854e27 | 0.337480 | ||||||||
\(794\) | 5.59784e26 | 0.158389 | ||||||||
\(795\) | −3.60735e27 | −1.00856 | ||||||||
\(796\) | 3.35040e26 | 0.0925598 | ||||||||
\(797\) | 1.18346e27 | 0.323072 | 0.161536 | − | 0.986867i | \(-0.448355\pi\) | ||||
0.161536 | + | 0.986867i | \(0.448355\pi\) | |||||||
\(798\) | 6.68291e26 | 0.180276 | ||||||||
\(799\) | 7.87451e26 | 0.209908 | ||||||||
\(800\) | −2.64267e27 | −0.696127 | ||||||||
\(801\) | 6.13438e27 | 1.59684 | ||||||||
\(802\) | −2.36160e26 | −0.0607506 | ||||||||
\(803\) | −4.86126e24 | −0.00123581 | ||||||||
\(804\) | 3.28653e27 | 0.825669 | ||||||||
\(805\) | 5.64549e26 | 0.140165 | ||||||||
\(806\) | −2.40561e27 | −0.590258 | ||||||||
\(807\) | −6.77075e27 | −1.64187 | ||||||||
\(808\) | 5.45297e27 | 1.30685 | ||||||||
\(809\) | −5.08495e27 | −1.20441 | −0.602207 | − | 0.798340i | \(-0.705712\pi\) | ||||
−0.602207 | + | 0.798340i | \(0.705712\pi\) | |||||||
\(810\) | 1.09765e27 | 0.256954 | ||||||||
\(811\) | −2.72133e25 | −0.00629627 | −0.00314813 | − | 0.999995i | \(-0.501002\pi\) | ||||
−0.00314813 | + | 0.999995i | \(0.501002\pi\) | |||||||
\(812\) | 6.08958e24 | 0.00139253 | ||||||||
\(813\) | 1.01581e28 | 2.29590 | ||||||||
\(814\) | 1.25227e24 | 0.000279748 0 | ||||||||
\(815\) | 1.38072e27 | 0.304865 | ||||||||
\(816\) | −1.01916e26 | −0.0222425 | ||||||||
\(817\) | −1.92905e27 | −0.416134 | ||||||||
\(818\) | 1.28536e27 | 0.274074 | ||||||||
\(819\) | −1.19708e27 | −0.252306 | ||||||||
\(820\) | −2.48943e27 | −0.518644 | ||||||||
\(821\) | −5.16381e26 | −0.106343 | −0.0531716 | − | 0.998585i | \(-0.516933\pi\) | ||||
−0.0531716 | + | 0.998585i | \(0.516933\pi\) | |||||||
\(822\) | −6.82355e27 | −1.38908 | ||||||||
\(823\) | −1.97624e27 | −0.397687 | −0.198843 | − | 0.980031i | \(-0.563718\pi\) | ||||
−0.198843 | + | 0.980031i | \(0.563718\pi\) | |||||||
\(824\) | −1.88112e27 | −0.374204 | ||||||||
\(825\) | 1.10213e25 | 0.00216731 | ||||||||
\(826\) | −4.50455e26 | −0.0875670 | ||||||||
\(827\) | −1.16795e27 | −0.224450 | −0.112225 | − | 0.993683i | \(-0.535798\pi\) | ||||
−0.112225 | + | 0.993683i | \(0.535798\pi\) | |||||||
\(828\) | −6.23162e27 | −1.18389 | ||||||||
\(829\) | 4.20809e27 | 0.790345 | 0.395173 | − | 0.918607i | \(-0.370685\pi\) | ||||
0.395173 | + | 0.918607i | \(0.370685\pi\) | |||||||
\(830\) | −1.31018e27 | −0.243270 | ||||||||
\(831\) | 1.01417e28 | 1.86166 | ||||||||
\(832\) | 4.76350e27 | 0.864479 | ||||||||
\(833\) | −2.50113e27 | −0.448755 | ||||||||
\(834\) | 3.19848e27 | 0.567369 | ||||||||
\(835\) | −5.78644e26 | −0.101482 | ||||||||
\(836\) | −8.77156e24 | −0.00152096 | ||||||||
\(837\) | −1.27774e27 | −0.219053 | ||||||||
\(838\) | 3.94700e27 | 0.669036 | ||||||||
\(839\) | 8.49254e27 | 1.42331 | 0.711654 | − | 0.702530i | \(-0.247947\pi\) | ||||
0.711654 | + | 0.702530i | \(0.247947\pi\) | |||||||
\(840\) | −7.80931e26 | −0.129408 | ||||||||
\(841\) | −6.10197e27 | −0.999788 | ||||||||
\(842\) | −2.37873e27 | −0.385372 | ||||||||
\(843\) | −6.03972e27 | −0.967508 | ||||||||
\(844\) | 4.18926e27 | 0.663565 | ||||||||
\(845\) | −2.56860e27 | −0.402307 | ||||||||
\(846\) | 2.23893e27 | 0.346755 | ||||||||
\(847\) | 1.03466e27 | 0.158454 | ||||||||
\(848\) | −2.67802e26 | −0.0405558 | ||||||||
\(849\) | −1.75311e26 | −0.0262534 | ||||||||
\(850\) | −1.37747e27 | −0.203986 | ||||||||
\(851\) | −2.37768e27 | −0.348195 | ||||||||
\(852\) | 2.85068e27 | 0.412831 | ||||||||
\(853\) | −9.33345e27 | −1.33668 | −0.668338 | − | 0.743857i | \(-0.732994\pi\) | ||||
−0.668338 | + | 0.743857i | \(0.732994\pi\) | |||||||
\(854\) | −1.80314e26 | −0.0255376 | ||||||||
\(855\) | 5.70612e27 | 0.799214 | ||||||||
\(856\) | −1.01439e28 | −1.40509 | ||||||||
\(857\) | −1.11037e28 | −1.52108 | −0.760539 | − | 0.649292i | \(-0.775065\pi\) | ||||
−0.760539 | + | 0.649292i | \(0.775065\pi\) | |||||||
\(858\) | −1.88807e25 | −0.00255793 | ||||||||
\(859\) | 1.11478e28 | 1.49367 | 0.746834 | − | 0.665011i | \(-0.231573\pi\) | ||||
0.746834 | + | 0.665011i | \(0.231573\pi\) | |||||||
\(860\) | 8.48302e26 | 0.112413 | ||||||||
\(861\) | 2.83635e27 | 0.371732 | ||||||||
\(862\) | 4.75899e27 | 0.616873 | ||||||||
\(863\) | 1.15445e28 | 1.48004 | 0.740021 | − | 0.672583i | \(-0.234815\pi\) | ||||
0.740021 | + | 0.672583i | \(0.234815\pi\) | |||||||
\(864\) | 2.40460e27 | 0.304903 | ||||||||
\(865\) | 2.83745e27 | 0.355856 | ||||||||
\(866\) | 6.61699e27 | 0.820806 | ||||||||
\(867\) | −9.54364e27 | −1.17093 | ||||||||
\(868\) | −5.59952e26 | −0.0679538 | ||||||||
\(869\) | 1.49520e24 | 0.000179478 0 | ||||||||
\(870\) | −6.24806e25 | −0.00741843 | ||||||||
\(871\) | −1.03416e28 | −1.21455 | ||||||||
\(872\) | 7.06012e27 | 0.820173 | ||||||||
\(873\) | −8.91154e26 | −0.102404 | ||||||||
\(874\) | −1.09469e28 | −1.24432 | ||||||||
\(875\) | −1.30694e27 | −0.146954 | ||||||||
\(876\) | −4.80482e27 | −0.534426 | ||||||||
\(877\) | 1.55912e28 | 1.71547 | 0.857734 | − | 0.514094i | \(-0.171872\pi\) | ||||
0.857734 | + | 0.514094i | \(0.171872\pi\) | |||||||
\(878\) | 8.20147e27 | 0.892676 | ||||||||
\(879\) | −1.08008e28 | −1.16295 | ||||||||
\(880\) | −3.44564e23 | −3.67015e−5 0 | ||||||||
\(881\) | 3.35920e26 | 0.0353969 | 0.0176985 | − | 0.999843i | \(-0.494366\pi\) | ||||
0.0176985 | + | 0.999843i | \(0.494366\pi\) | |||||||
\(882\) | −7.11139e27 | −0.741315 | ||||||||
\(883\) | −1.34374e26 | −0.0138576 | −0.00692882 | − | 0.999976i | \(-0.502206\pi\) | ||||
−0.00692882 | + | 0.999976i | \(0.502206\pi\) | |||||||
\(884\) | −3.59009e27 | −0.366276 | ||||||||
\(885\) | −7.03153e27 | −0.709722 | ||||||||
\(886\) | 3.98400e27 | 0.397832 | ||||||||
\(887\) | 9.23887e27 | 0.912735 | 0.456367 | − | 0.889791i | \(-0.349150\pi\) | ||||
0.456367 | + | 0.889791i | \(0.349150\pi\) | |||||||
\(888\) | 3.28901e27 | 0.321471 | ||||||||
\(889\) | −1.48996e27 | −0.144082 | ||||||||
\(890\) | −4.73881e27 | −0.453382 | ||||||||
\(891\) | 1.64147e25 | 0.00155380 | ||||||||
\(892\) | −6.35619e27 | −0.595293 | ||||||||
\(893\) | −5.98374e27 | −0.554478 | ||||||||
\(894\) | −6.14437e27 | −0.563341 | ||||||||
\(895\) | 9.85826e27 | 0.894296 | ||||||||
\(896\) | 1.01763e27 | 0.0913406 | ||||||||
\(897\) | 3.58487e28 | 3.18379 | ||||||||
\(898\) | −7.32226e27 | −0.643458 | ||||||||
\(899\) | −1.19048e26 | −0.0103516 | ||||||||
\(900\) | 5.95853e27 | 0.512667 | ||||||||
\(901\) | 6.74227e27 | 0.574011 | ||||||||
\(902\) | 2.44698e25 | 0.00206143 | ||||||||
\(903\) | −9.66517e26 | −0.0805705 | ||||||||
\(904\) | −9.86777e27 | −0.813990 | ||||||||
\(905\) | −7.90165e27 | −0.644995 | ||||||||
\(906\) | 1.32943e28 | 1.07386 | ||||||||
\(907\) | −1.80585e28 | −1.44349 | −0.721743 | − | 0.692161i | \(-0.756659\pi\) | ||||
−0.721743 | + | 0.692161i | \(0.756659\pi\) | |||||||
\(908\) | 6.43758e27 | 0.509222 | ||||||||
\(909\) | −1.99631e28 | −1.56268 | ||||||||
\(910\) | 9.24747e26 | 0.0716357 | ||||||||
\(911\) | −1.99304e28 | −1.52789 | −0.763943 | − | 0.645283i | \(-0.776739\pi\) | ||||
−0.763943 | + | 0.645283i | \(0.776739\pi\) | |||||||
\(912\) | 7.74443e26 | 0.0587541 | ||||||||
\(913\) | −1.95930e25 | −0.00147106 | ||||||||
\(914\) | −1.22020e27 | −0.0906651 | ||||||||
\(915\) | −2.81467e27 | −0.206980 | ||||||||
\(916\) | 1.26509e28 | 0.920694 | ||||||||
\(917\) | −1.21686e27 | −0.0876460 | ||||||||
\(918\) | 1.25337e27 | 0.0893460 | ||||||||
\(919\) | 1.04320e28 | 0.735984 | 0.367992 | − | 0.929829i | \(-0.380045\pi\) | ||||
0.367992 | + | 0.929829i | \(0.380045\pi\) | |||||||
\(920\) | 1.27920e28 | 0.893212 | ||||||||
\(921\) | 9.71946e27 | 0.671701 | ||||||||
\(922\) | 3.17744e27 | 0.217337 | ||||||||
\(923\) | −8.97012e27 | −0.607271 | ||||||||
\(924\) | −4.39485e24 | −0.000294483 0 | ||||||||
\(925\) | 2.27348e27 | 0.150781 | ||||||||
\(926\) | −1.13929e28 | −0.747874 | ||||||||
\(927\) | 6.88672e27 | 0.447461 | ||||||||
\(928\) | 2.24039e26 | 0.0144085 | ||||||||
\(929\) | −5.17736e27 | −0.329578 | −0.164789 | − | 0.986329i | \(-0.552694\pi\) | ||||
−0.164789 | + | 0.986329i | \(0.552694\pi\) | |||||||
\(930\) | 5.74525e27 | 0.362010 | ||||||||
\(931\) | 1.90058e28 | 1.18540 | ||||||||
\(932\) | −7.66111e27 | −0.472977 | ||||||||
\(933\) | −7.82683e27 | −0.478311 | ||||||||
\(934\) | 8.87060e27 | 0.536609 | ||||||||
\(935\) | 8.67484e24 | 0.000519459 0 | ||||||||
\(936\) | −2.71245e28 | −1.60783 | ||||||||
\(937\) | 9.33202e27 | 0.547582 | 0.273791 | − | 0.961789i | \(-0.411722\pi\) | ||||
0.273791 | + | 0.961789i | \(0.411722\pi\) | |||||||
\(938\) | 1.58224e27 | 0.0919065 | ||||||||
\(939\) | 1.45578e28 | 0.837089 | ||||||||
\(940\) | 2.63136e27 | 0.149784 | ||||||||
\(941\) | 4.50115e27 | 0.253642 | 0.126821 | − | 0.991926i | \(-0.459523\pi\) | ||||
0.126821 | + | 0.991926i | \(0.459523\pi\) | |||||||
\(942\) | −2.47690e28 | −1.38173 | ||||||||
\(943\) | −4.64607e28 | −2.56581 | ||||||||
\(944\) | −5.22005e26 | −0.0285391 | ||||||||
\(945\) | 4.91178e26 | 0.0265850 | ||||||||
\(946\) | −8.33835e24 | −0.000446801 0 | ||||||||
\(947\) | 1.76126e28 | 0.934324 | 0.467162 | − | 0.884172i | \(-0.345276\pi\) | ||||
0.467162 | + | 0.884172i | \(0.345276\pi\) | |||||||
\(948\) | 1.47783e27 | 0.0776151 | ||||||||
\(949\) | 1.51191e28 | 0.786135 | ||||||||
\(950\) | 1.04672e28 | 0.538835 | ||||||||
\(951\) | 1.33485e27 | 0.0680325 | ||||||||
\(952\) | 1.45959e27 | 0.0736511 | ||||||||
\(953\) | 5.93730e27 | 0.296624 | 0.148312 | − | 0.988941i | \(-0.452616\pi\) | ||||
0.148312 | + | 0.988941i | \(0.452616\pi\) | |||||||
\(954\) | 1.91700e28 | 0.948230 | ||||||||
\(955\) | −1.47252e28 | −0.721155 | ||||||||
\(956\) | −8.30141e27 | −0.402534 | ||||||||
\(957\) | −9.34363e23 | −4.48593e−5 0 | ||||||||
\(958\) | 1.52374e28 | 0.724333 | ||||||||
\(959\) | 4.99789e27 | 0.235239 | ||||||||
\(960\) | −1.13765e28 | −0.530192 | ||||||||
\(961\) | −1.07239e28 | −0.494857 | ||||||||
\(962\) | −3.89471e27 | −0.177956 | ||||||||
\(963\) | 3.71365e28 | 1.68016 | ||||||||
\(964\) | −2.32976e28 | −1.04371 | ||||||||
\(965\) | 1.23791e28 | 0.549136 | ||||||||
\(966\) | −5.48477e27 | −0.240922 | ||||||||
\(967\) | −2.58489e28 | −1.12432 | −0.562160 | − | 0.827028i | \(-0.690030\pi\) | ||||
−0.562160 | + | 0.827028i | \(0.690030\pi\) | |||||||
\(968\) | 2.34441e28 | 1.00976 | ||||||||
\(969\) | −1.94976e28 | −0.831583 | ||||||||
\(970\) | 6.88417e26 | 0.0290750 | ||||||||
\(971\) | 2.05732e28 | 0.860438 | 0.430219 | − | 0.902725i | \(-0.358436\pi\) | ||||
0.430219 | + | 0.902725i | \(0.358436\pi\) | |||||||
\(972\) | 2.07144e28 | 0.857912 | ||||||||
\(973\) | −2.34271e27 | −0.0960831 | ||||||||
\(974\) | −2.21698e28 | −0.900435 | ||||||||
\(975\) | −3.42777e28 | −1.37869 | ||||||||
\(976\) | −2.08955e26 | −0.00832300 | ||||||||
\(977\) | −2.34524e28 | −0.925099 | −0.462550 | − | 0.886593i | \(-0.653065\pi\) | ||||
−0.462550 | + | 0.886593i | \(0.653065\pi\) | |||||||
\(978\) | −1.34141e28 | −0.524014 | ||||||||
\(979\) | −7.08664e25 | −0.00274160 | ||||||||
\(980\) | −8.35784e27 | −0.320218 | ||||||||
\(981\) | −2.58468e28 | −0.980736 | ||||||||
\(982\) | 4.49949e27 | 0.169085 | ||||||||
\(983\) | 4.25526e28 | 1.58368 | 0.791840 | − | 0.610729i | \(-0.209123\pi\) | ||||
0.791840 | + | 0.610729i | \(0.209123\pi\) | |||||||
\(984\) | 6.42684e28 | 2.36889 | ||||||||
\(985\) | −5.76245e27 | −0.210360 | ||||||||
\(986\) | 1.16778e26 | 0.00422213 | ||||||||
\(987\) | −2.99806e27 | −0.107356 | ||||||||
\(988\) | 2.72806e28 | 0.967527 | ||||||||
\(989\) | 1.58320e28 | 0.556123 | ||||||||
\(990\) | 2.46649e25 | 0.000858113 0 | ||||||||
\(991\) | 5.21472e28 | 1.79693 | 0.898466 | − | 0.439044i | \(-0.144683\pi\) | ||||
0.898466 | + | 0.439044i | \(0.144683\pi\) | |||||||
\(992\) | −2.06010e28 | −0.703117 | ||||||||
\(993\) | −5.33556e28 | −1.80369 | ||||||||
\(994\) | 1.37241e27 | 0.0459529 | ||||||||
\(995\) | 2.51785e27 | 0.0835046 | ||||||||
\(996\) | −1.93655e28 | −0.636159 | ||||||||
\(997\) | −1.61541e27 | −0.0525629 | −0.0262815 | − | 0.999655i | \(-0.508367\pi\) | ||||
−0.0262815 | + | 0.999655i | \(0.508367\pi\) | |||||||
\(998\) | −1.61493e28 | −0.520490 | ||||||||
\(999\) | −2.06867e27 | −0.0660419 |
(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 | 1.20.a.a.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 9.20.a.a.1.1 | 1 | |||
4.3 | odd | 2 | 16.20.a.a.1.1 | 1 | |||
5.2 | odd | 4 | 25.20.b.a.24.2 | 2 | |||
5.3 | odd | 4 | 25.20.b.a.24.1 | 2 | |||
5.4 | even | 2 | 25.20.a.a.1.1 | 1 | |||
7.6 | odd | 2 | 49.20.a.b.1.1 | 1 | |||
8.3 | odd | 2 | 64.20.a.h.1.1 | 1 | |||
8.5 | even | 2 | 64.20.a.b.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.20.a.a.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
9.20.a.a.1.1 | 1 | 3.2 | odd | 2 | |||
16.20.a.a.1.1 | 1 | 4.3 | odd | 2 | |||
25.20.a.a.1.1 | 1 | 5.4 | even | 2 | |||
25.20.b.a.24.1 | 2 | 5.3 | odd | 4 | |||
25.20.b.a.24.2 | 2 | 5.2 | odd | 4 | |||
49.20.a.b.1.1 | 1 | 7.6 | odd | 2 | |||
64.20.a.b.1.1 | 1 | 8.5 | even | 2 | |||
64.20.a.h.1.1 | 1 | 8.3 | odd | 2 |