Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [338,8,Mod(1,338)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(338, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("338.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 338 = 2 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 338.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: | \(105.586138614\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 8883x^{3} + 76436x^{2} + 9553604x - 121499328 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 26) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(13.5100\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 338.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −8.00000 | −0.707107 | ||||||||
\(3\) | 18.5100 | 0.395805 | 0.197902 | − | 0.980222i | \(-0.436587\pi\) | ||||
0.197902 | + | 0.980222i | \(0.436587\pi\) | |||||||
\(4\) | 64.0000 | 0.500000 | ||||||||
\(5\) | 6.61448 | 0.0236647 | 0.0118323 | − | 0.999930i | \(-0.496234\pi\) | ||||
0.0118323 | + | 0.999930i | \(0.496234\pi\) | |||||||
\(6\) | −148.080 | −0.279876 | ||||||||
\(7\) | 1604.67 | 1.76824 | 0.884120 | − | 0.467260i | \(-0.154759\pi\) | ||||
0.884120 | + | 0.467260i | \(0.154759\pi\) | |||||||
\(8\) | −512.000 | −0.353553 | ||||||||
\(9\) | −1844.38 | −0.843339 | ||||||||
\(10\) | −52.9158 | −0.0167335 | ||||||||
\(11\) | −1173.55 | −0.265843 | −0.132922 | − | 0.991127i | \(-0.542436\pi\) | ||||
−0.132922 | + | 0.991127i | \(0.542436\pi\) | |||||||
\(12\) | 1184.64 | 0.197902 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −12837.3 | −1.25033 | ||||||||
\(15\) | 122.434 | 0.00936659 | ||||||||
\(16\) | 4096.00 | 0.250000 | ||||||||
\(17\) | 28053.1 | 1.38487 | 0.692437 | − | 0.721478i | \(-0.256537\pi\) | ||||
0.692437 | + | 0.721478i | \(0.256537\pi\) | |||||||
\(18\) | 14755.1 | 0.596330 | ||||||||
\(19\) | −13825.5 | −0.462428 | −0.231214 | − | 0.972903i | \(-0.574270\pi\) | ||||
−0.231214 | + | 0.972903i | \(0.574270\pi\) | |||||||
\(20\) | 423.327 | 0.0118323 | ||||||||
\(21\) | 29702.3 | 0.699878 | ||||||||
\(22\) | 9388.37 | 0.187980 | ||||||||
\(23\) | −94424.9 | −1.61823 | −0.809113 | − | 0.587653i | \(-0.800052\pi\) | ||||
−0.809113 | + | 0.587653i | \(0.800052\pi\) | |||||||
\(24\) | −9477.10 | −0.139938 | ||||||||
\(25\) | −78081.2 | −0.999440 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −74620.7 | −0.729602 | ||||||||
\(28\) | 102699. | 0.884120 | ||||||||
\(29\) | 159421. | 1.21381 | 0.606906 | − | 0.794774i | \(-0.292410\pi\) | ||||
0.606906 | + | 0.794774i | \(0.292410\pi\) | |||||||
\(30\) | −979.470 | −0.00662318 | ||||||||
\(31\) | −113805. | −0.686114 | −0.343057 | − | 0.939315i | \(-0.611462\pi\) | ||||
−0.343057 | + | 0.939315i | \(0.611462\pi\) | |||||||
\(32\) | −32768.0 | −0.176777 | ||||||||
\(33\) | −21722.3 | −0.105222 | ||||||||
\(34\) | −224425. | −0.979254 | ||||||||
\(35\) | 10614.0 | 0.0418448 | ||||||||
\(36\) | −118040. | −0.421669 | ||||||||
\(37\) | −402800. | −1.30732 | −0.653662 | − | 0.756787i | \(-0.726768\pi\) | ||||
−0.653662 | + | 0.756787i | \(0.726768\pi\) | |||||||
\(38\) | 110604. | 0.326986 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3386.61 | −0.00836673 | ||||||||
\(41\) | −583062. | −1.32121 | −0.660604 | − | 0.750734i | \(-0.729700\pi\) | ||||
−0.660604 | + | 0.750734i | \(0.729700\pi\) | |||||||
\(42\) | −237618. | −0.494888 | ||||||||
\(43\) | −88507.4 | −0.169762 | −0.0848809 | − | 0.996391i | \(-0.527051\pi\) | ||||
−0.0848809 | + | 0.996391i | \(0.527051\pi\) | |||||||
\(44\) | −75107.0 | −0.132922 | ||||||||
\(45\) | −12199.6 | −0.0199573 | ||||||||
\(46\) | 755399. | 1.14426 | ||||||||
\(47\) | −112810. | −0.158491 | −0.0792457 | − | 0.996855i | \(-0.525251\pi\) | ||||
−0.0792457 | + | 0.996855i | \(0.525251\pi\) | |||||||
\(48\) | 75816.8 | 0.0989512 | ||||||||
\(49\) | 1.75141e6 | 2.12667 | ||||||||
\(50\) | 624650. | 0.706711 | ||||||||
\(51\) | 519262. | 0.548140 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 548744. | 0.506296 | 0.253148 | − | 0.967428i | \(-0.418534\pi\) | ||||
0.253148 | + | 0.967428i | \(0.418534\pi\) | |||||||
\(54\) | 596966. | 0.515907 | ||||||||
\(55\) | −7762.40 | −0.00629110 | ||||||||
\(56\) | −821589. | −0.625167 | ||||||||
\(57\) | −255910. | −0.183031 | ||||||||
\(58\) | −1.27536e6 | −0.858294 | ||||||||
\(59\) | −1.69495e6 | −1.07442 | −0.537211 | − | 0.843448i | \(-0.680522\pi\) | ||||
−0.537211 | + | 0.843448i | \(0.680522\pi\) | |||||||
\(60\) | 7835.76 | 0.00468330 | ||||||||
\(61\) | 1.33588e6 | 0.753554 | 0.376777 | − | 0.926304i | \(-0.377032\pi\) | ||||
0.376777 | + | 0.926304i | \(0.377032\pi\) | |||||||
\(62\) | 910442. | 0.485156 | ||||||||
\(63\) | −2.95961e6 | −1.49123 | ||||||||
\(64\) | 262144. | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 173778. | 0.0744033 | ||||||||
\(67\) | 719239. | 0.292154 | 0.146077 | − | 0.989273i | \(-0.453335\pi\) | ||||
0.146077 | + | 0.989273i | \(0.453335\pi\) | |||||||
\(68\) | 1.79540e6 | 0.692437 | ||||||||
\(69\) | −1.74780e6 | −0.640501 | ||||||||
\(70\) | −84912.2 | −0.0295888 | ||||||||
\(71\) | −1.85217e6 | −0.614153 | −0.307077 | − | 0.951685i | \(-0.599351\pi\) | ||||
−0.307077 | + | 0.951685i | \(0.599351\pi\) | |||||||
\(72\) | 944323. | 0.298165 | ||||||||
\(73\) | 1.50153e6 | 0.451756 | 0.225878 | − | 0.974156i | \(-0.427475\pi\) | ||||
0.225878 | + | 0.974156i | \(0.427475\pi\) | |||||||
\(74\) | 3.22240e6 | 0.924417 | ||||||||
\(75\) | −1.44528e6 | −0.395583 | ||||||||
\(76\) | −884833. | −0.231214 | ||||||||
\(77\) | −1.88315e6 | −0.470075 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.07672e6 | −1.38667 | −0.693337 | − | 0.720614i | \(-0.743860\pi\) | ||||
−0.693337 | + | 0.720614i | \(0.743860\pi\) | |||||||
\(80\) | 27092.9 | 0.00591617 | ||||||||
\(81\) | 2.65244e6 | 0.554559 | ||||||||
\(82\) | 4.66450e6 | 0.934235 | ||||||||
\(83\) | 661334. | 0.126954 | 0.0634771 | − | 0.997983i | \(-0.479781\pi\) | ||||
0.0634771 | + | 0.997983i | \(0.479781\pi\) | |||||||
\(84\) | 1.90095e6 | 0.349939 | ||||||||
\(85\) | 185557. | 0.0327726 | ||||||||
\(86\) | 708059. | 0.120040 | ||||||||
\(87\) | 2.95087e6 | 0.480432 | ||||||||
\(88\) | 600856. | 0.0939898 | ||||||||
\(89\) | 1.03091e7 | 1.55008 | 0.775041 | − | 0.631910i | \(-0.217729\pi\) | ||||
0.775041 | + | 0.631910i | \(0.217729\pi\) | |||||||
\(90\) | 97597.0 | 0.0141120 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −6.04319e6 | −0.809113 | ||||||||
\(93\) | −2.10653e6 | −0.271567 | ||||||||
\(94\) | 902482. | 0.112070 | ||||||||
\(95\) | −91448.6 | −0.0109432 | ||||||||
\(96\) | −606534. | −0.0699691 | ||||||||
\(97\) | −6.14220e6 | −0.683318 | −0.341659 | − | 0.939824i | \(-0.610989\pi\) | ||||
−0.341659 | + | 0.939824i | \(0.610989\pi\) | |||||||
\(98\) | −1.40113e7 | −1.50379 | ||||||||
\(99\) | 2.16447e6 | 0.224196 | ||||||||
\(100\) | −4.99720e6 | −0.499720 | ||||||||
\(101\) | 5.85424e6 | 0.565387 | 0.282693 | − | 0.959210i | \(-0.408772\pi\) | ||||
0.282693 | + | 0.959210i | \(0.408772\pi\) | |||||||
\(102\) | −4.15410e6 | −0.387593 | ||||||||
\(103\) | −1.80551e6 | −0.162806 | −0.0814031 | − | 0.996681i | \(-0.525940\pi\) | ||||
−0.0814031 | + | 0.996681i | \(0.525940\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 196465. | 0.0165624 | ||||||||
\(106\) | −4.38996e6 | −0.358005 | ||||||||
\(107\) | 1.32024e7 | 1.04186 | 0.520931 | − | 0.853599i | \(-0.325585\pi\) | ||||
0.520931 | + | 0.853599i | \(0.325585\pi\) | |||||||
\(108\) | −4.77572e6 | −0.364801 | ||||||||
\(109\) | −2.36217e7 | −1.74710 | −0.873550 | − | 0.486734i | \(-0.838188\pi\) | ||||
−0.873550 | + | 0.486734i | \(0.838188\pi\) | |||||||
\(110\) | 62099.2 | 0.00444848 | ||||||||
\(111\) | −7.45581e6 | −0.517445 | ||||||||
\(112\) | 6.57271e6 | 0.442060 | ||||||||
\(113\) | 1.03738e7 | 0.676340 | 0.338170 | − | 0.941085i | \(-0.390192\pi\) | ||||
0.338170 | + | 0.941085i | \(0.390192\pi\) | |||||||
\(114\) | 2.04728e6 | 0.129423 | ||||||||
\(115\) | −624571. | −0.0382948 | ||||||||
\(116\) | 1.02029e7 | 0.606906 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.35596e7 | 0.759732 | ||||||||
\(119\) | 4.50159e7 | 2.44879 | ||||||||
\(120\) | −62686.1 | −0.00331159 | ||||||||
\(121\) | −1.81100e7 | −0.929327 | ||||||||
\(122\) | −1.06871e7 | −0.532843 | ||||||||
\(123\) | −1.07925e7 | −0.522941 | ||||||||
\(124\) | −7.28354e6 | −0.343057 | ||||||||
\(125\) | −1.03322e6 | −0.0473161 | ||||||||
\(126\) | 2.36769e7 | 1.05446 | ||||||||
\(127\) | 3.07208e7 | 1.33082 | 0.665409 | − | 0.746479i | \(-0.268257\pi\) | ||||
0.665409 | + | 0.746479i | \(0.268257\pi\) | |||||||
\(128\) | −2.09715e6 | −0.0883883 | ||||||||
\(129\) | −1.63827e6 | −0.0671925 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.62980e7 | 0.633411 | 0.316706 | − | 0.948524i | \(-0.397423\pi\) | ||||
0.316706 | + | 0.948524i | \(0.397423\pi\) | |||||||
\(132\) | −1.39023e6 | −0.0526110 | ||||||||
\(133\) | −2.21853e7 | −0.817683 | ||||||||
\(134\) | −5.75391e6 | −0.206584 | ||||||||
\(135\) | −493577. | −0.0172658 | ||||||||
\(136\) | −1.43632e7 | −0.489627 | ||||||||
\(137\) | −3.22644e7 | −1.07202 | −0.536008 | − | 0.844213i | \(-0.680068\pi\) | ||||
−0.536008 | + | 0.844213i | \(0.680068\pi\) | |||||||
\(138\) | 1.39824e7 | 0.452903 | ||||||||
\(139\) | −3.77383e7 | −1.19188 | −0.595938 | − | 0.803030i | \(-0.703220\pi\) | ||||
−0.595938 | + | 0.803030i | \(0.703220\pi\) | |||||||
\(140\) | 679298. | 0.0209224 | ||||||||
\(141\) | −2.08811e6 | −0.0627317 | ||||||||
\(142\) | 1.48174e7 | 0.434272 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −7.55459e6 | −0.210835 | ||||||||
\(145\) | 1.05448e6 | 0.0287245 | ||||||||
\(146\) | −1.20122e7 | −0.319439 | ||||||||
\(147\) | 3.24185e7 | 0.841748 | ||||||||
\(148\) | −2.57792e7 | −0.653662 | ||||||||
\(149\) | −1.69205e7 | −0.419045 | −0.209523 | − | 0.977804i | \(-0.567191\pi\) | ||||
−0.209523 | + | 0.977804i | \(0.567191\pi\) | |||||||
\(150\) | 1.15622e7 | 0.279720 | ||||||||
\(151\) | 3.87829e7 | 0.916687 | 0.458343 | − | 0.888775i | \(-0.348443\pi\) | ||||
0.458343 | + | 0.888775i | \(0.348443\pi\) | |||||||
\(152\) | 7.07867e6 | 0.163493 | ||||||||
\(153\) | −5.17407e7 | −1.16792 | ||||||||
\(154\) | 1.50652e7 | 0.332393 | ||||||||
\(155\) | −752763. | −0.0162367 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.86546e7 | −1.00340 | −0.501701 | − | 0.865041i | \(-0.667292\pi\) | ||||
−0.501701 | + | 0.865041i | \(0.667292\pi\) | |||||||
\(158\) | 4.86137e7 | 0.980526 | ||||||||
\(159\) | 1.01572e7 | 0.200394 | ||||||||
\(160\) | −216743. | −0.00418336 | ||||||||
\(161\) | −1.51520e8 | −2.86141 | ||||||||
\(162\) | −2.12195e7 | −0.392132 | ||||||||
\(163\) | −8.82607e7 | −1.59629 | −0.798143 | − | 0.602468i | \(-0.794184\pi\) | ||||
−0.798143 | + | 0.602468i | \(0.794184\pi\) | |||||||
\(164\) | −3.73160e7 | −0.660604 | ||||||||
\(165\) | −143682. | −0.00249005 | ||||||||
\(166\) | −5.29067e6 | −0.0897702 | ||||||||
\(167\) | −7.18201e7 | −1.19327 | −0.596634 | − | 0.802513i | \(-0.703496\pi\) | ||||
−0.596634 | + | 0.802513i | \(0.703496\pi\) | |||||||
\(168\) | −1.52076e7 | −0.247444 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −1.48446e6 | −0.0231737 | ||||||||
\(171\) | 2.54995e7 | 0.389983 | ||||||||
\(172\) | −5.66447e6 | −0.0848809 | ||||||||
\(173\) | 6.00357e7 | 0.881553 | 0.440776 | − | 0.897617i | \(-0.354703\pi\) | ||||
0.440776 | + | 0.897617i | \(0.354703\pi\) | |||||||
\(174\) | −2.36069e7 | −0.339717 | ||||||||
\(175\) | −1.25294e8 | −1.76725 | ||||||||
\(176\) | −4.80685e6 | −0.0664609 | ||||||||
\(177\) | −3.13735e7 | −0.425262 | ||||||||
\(178\) | −8.24726e7 | −1.09607 | ||||||||
\(179\) | −1.34440e8 | −1.75203 | −0.876015 | − | 0.482284i | \(-0.839807\pi\) | ||||
−0.876015 | + | 0.482284i | \(0.839807\pi\) | |||||||
\(180\) | −780776. | −0.00997867 | ||||||||
\(181\) | −1.55862e8 | −1.95374 | −0.976868 | − | 0.213843i | \(-0.931402\pi\) | ||||
−0.976868 | + | 0.213843i | \(0.931402\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.47272e7 | 0.298260 | ||||||||
\(184\) | 4.83455e7 | 0.572129 | ||||||||
\(185\) | −2.66431e6 | −0.0309374 | ||||||||
\(186\) | 1.68522e7 | 0.192027 | ||||||||
\(187\) | −3.29217e7 | −0.368160 | ||||||||
\(188\) | −7.21985e6 | −0.0792457 | ||||||||
\(189\) | −1.19741e8 | −1.29011 | ||||||||
\(190\) | 731589. | 0.00773801 | ||||||||
\(191\) | −2.23323e7 | −0.231909 | −0.115954 | − | 0.993255i | \(-0.536993\pi\) | ||||
−0.115954 | + | 0.993255i | \(0.536993\pi\) | |||||||
\(192\) | 4.85227e6 | 0.0494756 | ||||||||
\(193\) | −2.69730e6 | −0.0270072 | −0.0135036 | − | 0.999909i | \(-0.504298\pi\) | ||||
−0.0135036 | + | 0.999909i | \(0.504298\pi\) | |||||||
\(194\) | 4.91376e7 | 0.483179 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.12090e8 | 1.06334 | ||||||||
\(197\) | −7.30124e7 | −0.680401 | −0.340200 | − | 0.940353i | \(-0.610495\pi\) | ||||
−0.340200 | + | 0.940353i | \(0.610495\pi\) | |||||||
\(198\) | −1.73157e7 | −0.158531 | ||||||||
\(199\) | −1.10593e8 | −0.994817 | −0.497409 | − | 0.867516i | \(-0.665715\pi\) | ||||
−0.497409 | + | 0.867516i | \(0.665715\pi\) | |||||||
\(200\) | 3.99776e7 | 0.353355 | ||||||||
\(201\) | 1.33131e7 | 0.115636 | ||||||||
\(202\) | −4.68339e7 | −0.399789 | ||||||||
\(203\) | 2.55817e8 | 2.14631 | ||||||||
\(204\) | 3.32328e7 | 0.274070 | ||||||||
\(205\) | −3.85665e6 | −0.0312660 | ||||||||
\(206\) | 1.44441e7 | 0.115121 | ||||||||
\(207\) | 1.74156e8 | 1.36471 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.62249e7 | 0.122933 | ||||||||
\(210\) | −1.57172e6 | −0.0117114 | ||||||||
\(211\) | −7.79932e7 | −0.571568 | −0.285784 | − | 0.958294i | \(-0.592254\pi\) | ||||
−0.285784 | + | 0.958294i | \(0.592254\pi\) | |||||||
\(212\) | 3.51196e7 | 0.253148 | ||||||||
\(213\) | −3.42836e7 | −0.243085 | ||||||||
\(214\) | −1.05619e8 | −0.736708 | ||||||||
\(215\) | −585430. | −0.00401736 | ||||||||
\(216\) | 3.82058e7 | 0.257953 | ||||||||
\(217\) | −1.82619e8 | −1.21322 | ||||||||
\(218\) | 1.88973e8 | 1.23539 | ||||||||
\(219\) | 2.77932e7 | 0.178807 | ||||||||
\(220\) | −496793. | −0.00314555 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 5.96464e7 | 0.365889 | ||||||||
\(223\) | 2.81334e8 | 1.69885 | 0.849425 | − | 0.527709i | \(-0.176949\pi\) | ||||
0.849425 | + | 0.527709i | \(0.176949\pi\) | |||||||
\(224\) | −5.25817e7 | −0.312584 | ||||||||
\(225\) | 1.44012e8 | 0.842866 | ||||||||
\(226\) | −8.29908e7 | −0.478245 | ||||||||
\(227\) | −2.87156e8 | −1.62940 | −0.814700 | − | 0.579882i | \(-0.803099\pi\) | ||||
−0.814700 | + | 0.579882i | \(0.803099\pi\) | |||||||
\(228\) | −1.63782e7 | −0.0915156 | ||||||||
\(229\) | −1.77698e8 | −0.977819 | −0.488909 | − | 0.872335i | \(-0.662605\pi\) | ||||
−0.488909 | + | 0.872335i | \(0.662605\pi\) | |||||||
\(230\) | 4.99657e6 | 0.0270785 | ||||||||
\(231\) | −3.48570e7 | −0.186058 | ||||||||
\(232\) | −8.16233e7 | −0.429147 | ||||||||
\(233\) | 1.38051e8 | 0.714979 | 0.357490 | − | 0.933917i | \(-0.383633\pi\) | ||||
0.357490 | + | 0.933917i | \(0.383633\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −746181. | −0.00375065 | ||||||||
\(236\) | −1.08477e8 | −0.537211 | ||||||||
\(237\) | −1.12480e8 | −0.548852 | ||||||||
\(238\) | −3.60127e8 | −1.73156 | ||||||||
\(239\) | −6.38380e7 | −0.302473 | −0.151237 | − | 0.988498i | \(-0.548326\pi\) | ||||
−0.151237 | + | 0.988498i | \(0.548326\pi\) | |||||||
\(240\) | 501489. | 0.00234165 | ||||||||
\(241\) | −1.77813e8 | −0.818285 | −0.409143 | − | 0.912470i | \(-0.634172\pi\) | ||||
−0.409143 | + | 0.912470i | \(0.634172\pi\) | |||||||
\(242\) | 1.44880e8 | 0.657134 | ||||||||
\(243\) | 2.12292e8 | 0.949099 | ||||||||
\(244\) | 8.54966e7 | 0.376777 | ||||||||
\(245\) | 1.15846e7 | 0.0503271 | ||||||||
\(246\) | 8.63396e7 | 0.369775 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 5.82683e7 | 0.242578 | ||||||||
\(249\) | 1.22413e7 | 0.0502491 | ||||||||
\(250\) | 8.26578e6 | 0.0334575 | ||||||||
\(251\) | 2.57165e8 | 1.02649 | 0.513244 | − | 0.858243i | \(-0.328444\pi\) | ||||
0.513244 | + | 0.858243i | \(0.328444\pi\) | |||||||
\(252\) | −1.89415e8 | −0.745613 | ||||||||
\(253\) | 1.10812e8 | 0.430195 | ||||||||
\(254\) | −2.45766e8 | −0.941031 | ||||||||
\(255\) | 3.43465e6 | 0.0129716 | ||||||||
\(256\) | 1.67772e7 | 0.0625000 | ||||||||
\(257\) | −2.24906e8 | −0.826486 | −0.413243 | − | 0.910621i | \(-0.635604\pi\) | ||||
−0.413243 | + | 0.910621i | \(0.635604\pi\) | |||||||
\(258\) | 1.31061e7 | 0.0475123 | ||||||||
\(259\) | −6.46359e8 | −2.31166 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.94032e8 | −1.02365 | ||||||||
\(262\) | −1.30384e8 | −0.447890 | ||||||||
\(263\) | 4.78020e8 | 1.62032 | 0.810161 | − | 0.586208i | \(-0.199380\pi\) | ||||
0.810161 | + | 0.586208i | \(0.199380\pi\) | |||||||
\(264\) | 1.11218e7 | 0.0372016 | ||||||||
\(265\) | 3.62966e6 | 0.0119813 | ||||||||
\(266\) | 1.77483e8 | 0.578189 | ||||||||
\(267\) | 1.90821e8 | 0.613530 | ||||||||
\(268\) | 4.60313e7 | 0.146077 | ||||||||
\(269\) | 1.76243e8 | 0.552049 | 0.276025 | − | 0.961151i | \(-0.410983\pi\) | ||||
0.276025 | + | 0.961151i | \(0.410983\pi\) | |||||||
\(270\) | 3.94862e6 | 0.0122088 | ||||||||
\(271\) | 1.88337e8 | 0.574834 | 0.287417 | − | 0.957806i | \(-0.407203\pi\) | ||||
0.287417 | + | 0.957806i | \(0.407203\pi\) | |||||||
\(272\) | 1.14906e8 | 0.346219 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.58115e8 | 0.758030 | ||||||||
\(275\) | 9.16320e7 | 0.265695 | ||||||||
\(276\) | −1.11859e8 | −0.320251 | ||||||||
\(277\) | 3.15057e7 | 0.0890656 | 0.0445328 | − | 0.999008i | \(-0.485820\pi\) | ||||
0.0445328 | + | 0.999008i | \(0.485820\pi\) | |||||||
\(278\) | 3.01907e8 | 0.842784 | ||||||||
\(279\) | 2.09900e8 | 0.578627 | ||||||||
\(280\) | −5.43438e6 | −0.0147944 | ||||||||
\(281\) | −2.67569e8 | −0.719388 | −0.359694 | − | 0.933070i | \(-0.617119\pi\) | ||||
−0.359694 | + | 0.933070i | \(0.617119\pi\) | |||||||
\(282\) | 1.67049e7 | 0.0443580 | ||||||||
\(283\) | −1.31279e8 | −0.344303 | −0.172152 | − | 0.985070i | \(-0.555072\pi\) | ||||
−0.172152 | + | 0.985070i | \(0.555072\pi\) | |||||||
\(284\) | −1.18539e8 | −0.307077 | ||||||||
\(285\) | −1.69271e6 | −0.00433137 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.35620e8 | −2.33621 | ||||||||
\(288\) | 6.04367e7 | 0.149083 | ||||||||
\(289\) | 3.76640e8 | 0.917876 | ||||||||
\(290\) | −8.43587e6 | −0.0203113 | ||||||||
\(291\) | −1.13692e8 | −0.270460 | ||||||||
\(292\) | 9.60978e7 | 0.225878 | ||||||||
\(293\) | 5.02530e8 | 1.16715 | 0.583574 | − | 0.812060i | \(-0.301654\pi\) | ||||
0.583574 | + | 0.812060i | \(0.301654\pi\) | |||||||
\(294\) | −2.59348e8 | −0.595206 | ||||||||
\(295\) | −1.12112e7 | −0.0254259 | ||||||||
\(296\) | 2.06233e8 | 0.462209 | ||||||||
\(297\) | 8.75709e7 | 0.193960 | ||||||||
\(298\) | 1.35364e8 | 0.296310 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −9.24980e7 | −0.197792 | ||||||||
\(301\) | −1.42025e8 | −0.300180 | ||||||||
\(302\) | −3.10263e8 | −0.648196 | ||||||||
\(303\) | 1.08362e8 | 0.223783 | ||||||||
\(304\) | −5.66293e7 | −0.115607 | ||||||||
\(305\) | 8.83618e6 | 0.0178326 | ||||||||
\(306\) | 4.13926e8 | 0.825843 | ||||||||
\(307\) | 4.04464e7 | 0.0797802 | 0.0398901 | − | 0.999204i | \(-0.487299\pi\) | ||||
0.0398901 | + | 0.999204i | \(0.487299\pi\) | |||||||
\(308\) | −1.20522e8 | −0.235038 | ||||||||
\(309\) | −3.34200e7 | −0.0644394 | ||||||||
\(310\) | 6.02210e6 | 0.0114811 | ||||||||
\(311\) | −5.80479e7 | −0.109427 | −0.0547136 | − | 0.998502i | \(-0.517425\pi\) | ||||
−0.0547136 | + | 0.998502i | \(0.517425\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.87305e8 | 0.345259 | 0.172629 | − | 0.984987i | \(-0.444774\pi\) | ||||
0.172629 | + | 0.984987i | \(0.444774\pi\) | |||||||
\(314\) | 3.89237e8 | 0.709513 | ||||||||
\(315\) | −1.95763e7 | −0.0352894 | ||||||||
\(316\) | −3.88910e8 | −0.693337 | ||||||||
\(317\) | −6.09607e7 | −0.107484 | −0.0537419 | − | 0.998555i | \(-0.517115\pi\) | ||||
−0.0537419 | + | 0.998555i | \(0.517115\pi\) | |||||||
\(318\) | −8.12579e7 | −0.141700 | ||||||||
\(319\) | −1.87087e8 | −0.322684 | ||||||||
\(320\) | 1.73395e6 | 0.00295808 | ||||||||
\(321\) | 2.44376e8 | 0.412374 | ||||||||
\(322\) | 1.21216e9 | 2.02332 | ||||||||
\(323\) | −3.87849e8 | −0.640404 | ||||||||
\(324\) | 1.69756e8 | 0.277279 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 7.06085e8 | 1.12874 | ||||||||
\(327\) | −4.37236e8 | −0.691511 | ||||||||
\(328\) | 2.98528e8 | 0.467118 | ||||||||
\(329\) | −1.81023e8 | −0.280251 | ||||||||
\(330\) | 1.14945e6 | 0.00176073 | ||||||||
\(331\) | 4.54468e8 | 0.688820 | 0.344410 | − | 0.938819i | \(-0.388079\pi\) | ||||
0.344410 | + | 0.938819i | \(0.388079\pi\) | |||||||
\(332\) | 4.23254e7 | 0.0634771 | ||||||||
\(333\) | 7.42916e8 | 1.10252 | ||||||||
\(334\) | 5.74561e8 | 0.843769 | ||||||||
\(335\) | 4.75739e6 | 0.00691372 | ||||||||
\(336\) | 1.21661e8 | 0.174969 | ||||||||
\(337\) | 2.05246e8 | 0.292125 | 0.146063 | − | 0.989275i | \(-0.453340\pi\) | ||||
0.146063 | + | 0.989275i | \(0.453340\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.92019e8 | 0.267699 | ||||||||
\(340\) | 1.18756e7 | 0.0163863 | ||||||||
\(341\) | 1.33556e8 | 0.182399 | ||||||||
\(342\) | −2.03996e8 | −0.275760 | ||||||||
\(343\) | 1.48891e9 | 1.99223 | ||||||||
\(344\) | 4.53158e7 | 0.0600198 | ||||||||
\(345\) | −1.15608e7 | −0.0151573 | ||||||||
\(346\) | −4.80286e8 | −0.623352 | ||||||||
\(347\) | 2.99289e8 | 0.384537 | 0.192268 | − | 0.981342i | \(-0.438416\pi\) | ||||
0.192268 | + | 0.981342i | \(0.438416\pi\) | |||||||
\(348\) | 1.88856e8 | 0.240216 | ||||||||
\(349\) | −1.03098e8 | −0.129826 | −0.0649128 | − | 0.997891i | \(-0.520677\pi\) | ||||
−0.0649128 | + | 0.997891i | \(0.520677\pi\) | |||||||
\(350\) | 1.00235e9 | 1.24963 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.84548e7 | 0.0469949 | ||||||||
\(353\) | −3.79231e8 | −0.458873 | −0.229436 | − | 0.973324i | \(-0.573688\pi\) | ||||
−0.229436 | + | 0.973324i | \(0.573688\pi\) | |||||||
\(354\) | 2.50988e8 | 0.300705 | ||||||||
\(355\) | −1.22511e7 | −0.0145337 | ||||||||
\(356\) | 6.59781e8 | 0.775041 | ||||||||
\(357\) | 8.33242e8 | 0.969243 | ||||||||
\(358\) | 1.07552e9 | 1.23887 | ||||||||
\(359\) | −1.29204e9 | −1.47382 | −0.736912 | − | 0.675988i | \(-0.763717\pi\) | ||||
−0.736912 | + | 0.675988i | \(0.763717\pi\) | |||||||
\(360\) | 6.24621e6 | 0.00705598 | ||||||||
\(361\) | −7.02727e8 | −0.786161 | ||||||||
\(362\) | 1.24690e9 | 1.38150 | ||||||||
\(363\) | −3.35215e8 | −0.367832 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.93183e6 | 0.0106907 | ||||||||
\(366\) | −1.97817e8 | −0.210902 | ||||||||
\(367\) | −3.21664e8 | −0.339681 | −0.169841 | − | 0.985472i | \(-0.554325\pi\) | ||||
−0.169841 | + | 0.985472i | \(0.554325\pi\) | |||||||
\(368\) | −3.86764e8 | −0.404556 | ||||||||
\(369\) | 1.07539e9 | 1.11423 | ||||||||
\(370\) | 2.13145e7 | 0.0218760 | ||||||||
\(371\) | 8.80551e8 | 0.895253 | ||||||||
\(372\) | −1.34818e8 | −0.135784 | ||||||||
\(373\) | −5.95386e8 | −0.594043 | −0.297021 | − | 0.954871i | \(-0.595993\pi\) | ||||
−0.297021 | + | 0.954871i | \(0.595993\pi\) | |||||||
\(374\) | 2.63373e8 | 0.260328 | ||||||||
\(375\) | −1.91249e7 | −0.0187279 | ||||||||
\(376\) | 5.77588e7 | 0.0560352 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 9.57930e8 | 0.912247 | ||||||||
\(379\) | −1.84954e9 | −1.74512 | −0.872562 | − | 0.488503i | \(-0.837543\pi\) | ||||
−0.872562 | + | 0.488503i | \(0.837543\pi\) | |||||||
\(380\) | −5.85271e6 | −0.00547160 | ||||||||
\(381\) | 5.68640e8 | 0.526744 | ||||||||
\(382\) | 1.78659e8 | 0.163984 | ||||||||
\(383\) | 1.94010e9 | 1.76453 | 0.882263 | − | 0.470757i | \(-0.156019\pi\) | ||||
0.882263 | + | 0.470757i | \(0.156019\pi\) | |||||||
\(384\) | −3.88182e7 | −0.0349845 | ||||||||
\(385\) | −1.24561e7 | −0.0111242 | ||||||||
\(386\) | 2.15784e7 | 0.0190969 | ||||||||
\(387\) | 1.63241e8 | 0.143167 | ||||||||
\(388\) | −3.93101e8 | −0.341659 | ||||||||
\(389\) | −1.63159e9 | −1.40536 | −0.702680 | − | 0.711506i | \(-0.748014\pi\) | ||||
−0.702680 | + | 0.711506i | \(0.748014\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.64891e9 | −2.24104 | ||||||||
\(392\) | −8.96721e8 | −0.751893 | ||||||||
\(393\) | 3.01676e8 | 0.250707 | ||||||||
\(394\) | 5.84099e8 | 0.481116 | ||||||||
\(395\) | −4.01943e7 | −0.0328152 | ||||||||
\(396\) | 1.38526e8 | 0.112098 | ||||||||
\(397\) | 1.46137e9 | 1.17218 | 0.586090 | − | 0.810246i | \(-0.300666\pi\) | ||||
0.586090 | + | 0.810246i | \(0.300666\pi\) | |||||||
\(398\) | 8.84747e8 | 0.703442 | ||||||||
\(399\) | −4.10650e8 | −0.323643 | ||||||||
\(400\) | −3.19821e8 | −0.249860 | ||||||||
\(401\) | −2.15957e8 | −0.167248 | −0.0836240 | − | 0.996497i | \(-0.526649\pi\) | ||||
−0.0836240 | + | 0.996497i | \(0.526649\pi\) | |||||||
\(402\) | −1.06505e8 | −0.0817669 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 3.74671e8 | 0.282693 | ||||||||
\(405\) | 1.75445e7 | 0.0131234 | ||||||||
\(406\) | −2.04653e9 | −1.51767 | ||||||||
\(407\) | 4.72704e8 | 0.347543 | ||||||||
\(408\) | −2.65862e8 | −0.193797 | ||||||||
\(409\) | −2.10034e9 | −1.51795 | −0.758975 | − | 0.651120i | \(-0.774300\pi\) | ||||
−0.758975 | + | 0.651120i | \(0.774300\pi\) | |||||||
\(410\) | 3.08532e7 | 0.0221084 | ||||||||
\(411\) | −5.97213e8 | −0.424309 | ||||||||
\(412\) | −1.15553e8 | −0.0814031 | ||||||||
\(413\) | −2.71983e9 | −1.89984 | ||||||||
\(414\) | −1.39324e9 | −0.964997 | ||||||||
\(415\) | 4.37438e6 | 0.00300433 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.98535e8 | −0.471750 | ||||||||
\(418\) | −1.29799e8 | −0.0869270 | ||||||||
\(419\) | 4.33365e8 | 0.287809 | 0.143905 | − | 0.989592i | \(-0.454034\pi\) | ||||
0.143905 | + | 0.989592i | \(0.454034\pi\) | |||||||
\(420\) | 1.25738e7 | 0.00828119 | ||||||||
\(421\) | 2.60776e9 | 1.70326 | 0.851629 | − | 0.524145i | \(-0.175615\pi\) | ||||
0.851629 | + | 0.524145i | \(0.175615\pi\) | |||||||
\(422\) | 6.23946e8 | 0.404160 | ||||||||
\(423\) | 2.08065e8 | 0.133662 | ||||||||
\(424\) | −2.80957e8 | −0.179003 | ||||||||
\(425\) | −2.19042e9 | −1.38410 | ||||||||
\(426\) | 2.74269e8 | 0.171887 | ||||||||
\(427\) | 2.14365e9 | 1.33246 | ||||||||
\(428\) | 8.44954e8 | 0.520931 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.68344e6 | 0.00284070 | ||||||||
\(431\) | 6.82317e8 | 0.410503 | 0.205251 | − | 0.978709i | \(-0.434199\pi\) | ||||
0.205251 | + | 0.978709i | \(0.434199\pi\) | |||||||
\(432\) | −3.05646e8 | −0.182401 | ||||||||
\(433\) | 2.49592e9 | 1.47749 | 0.738743 | − | 0.673987i | \(-0.235420\pi\) | ||||
0.738743 | + | 0.673987i | \(0.235420\pi\) | |||||||
\(434\) | 1.46096e9 | 0.857873 | ||||||||
\(435\) | 1.95185e7 | 0.0113693 | ||||||||
\(436\) | −1.51179e9 | −0.873550 | ||||||||
\(437\) | 1.30547e9 | 0.748312 | ||||||||
\(438\) | −2.22346e8 | −0.126436 | ||||||||
\(439\) | −1.51778e9 | −0.856216 | −0.428108 | − | 0.903727i | \(-0.640820\pi\) | ||||
−0.428108 | + | 0.903727i | \(0.640820\pi\) | |||||||
\(440\) | 3.97435e6 | 0.00222424 | ||||||||
\(441\) | −3.23026e9 | −1.79351 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.56533e9 | 1.40194 | 0.700971 | − | 0.713190i | \(-0.252750\pi\) | ||||
0.700971 | + | 0.713190i | \(0.252750\pi\) | |||||||
\(444\) | −4.77172e8 | −0.258722 | ||||||||
\(445\) | 6.81892e7 | 0.0366822 | ||||||||
\(446\) | −2.25067e9 | −1.20127 | ||||||||
\(447\) | −3.13197e8 | −0.165860 | ||||||||
\(448\) | 4.20653e8 | 0.221030 | ||||||||
\(449\) | 2.22454e9 | 1.15978 | 0.579892 | − | 0.814693i | \(-0.303095\pi\) | ||||
0.579892 | + | 0.814693i | \(0.303095\pi\) | |||||||
\(450\) | −1.15209e9 | −0.595996 | ||||||||
\(451\) | 6.84251e8 | 0.351235 | ||||||||
\(452\) | 6.63926e8 | 0.338170 | ||||||||
\(453\) | 7.17870e8 | 0.362829 | ||||||||
\(454\) | 2.29725e9 | 1.15216 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.31026e8 | 0.0647113 | ||||||||
\(457\) | 1.58220e9 | 0.775453 | 0.387726 | − | 0.921775i | \(-0.373261\pi\) | ||||
0.387726 | + | 0.921775i | \(0.373261\pi\) | |||||||
\(458\) | 1.42158e9 | 0.691422 | ||||||||
\(459\) | −2.09335e9 | −1.01041 | ||||||||
\(460\) | −3.99726e7 | −0.0191474 | ||||||||
\(461\) | 1.33292e9 | 0.633652 | 0.316826 | − | 0.948484i | \(-0.397383\pi\) | ||||
0.316826 | + | 0.948484i | \(0.397383\pi\) | |||||||
\(462\) | 2.78856e8 | 0.131563 | ||||||||
\(463\) | −2.03271e9 | −0.951790 | −0.475895 | − | 0.879502i | \(-0.657876\pi\) | ||||
−0.475895 | + | 0.879502i | \(0.657876\pi\) | |||||||
\(464\) | 6.52987e8 | 0.303453 | ||||||||
\(465\) | −1.39336e7 | −0.00642655 | ||||||||
\(466\) | −1.10441e9 | −0.505567 | ||||||||
\(467\) | −3.10675e7 | −0.0141155 | −0.00705777 | − | 0.999975i | \(-0.502247\pi\) | ||||
−0.00705777 | + | 0.999975i | \(0.502247\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.15414e9 | 0.516598 | ||||||||
\(470\) | 5.96945e6 | 0.00265211 | ||||||||
\(471\) | −9.00595e8 | −0.397152 | ||||||||
\(472\) | 8.67815e8 | 0.379866 | ||||||||
\(473\) | 1.03867e8 | 0.0451300 | ||||||||
\(474\) | 8.99838e8 | 0.388097 | ||||||||
\(475\) | 1.07951e9 | 0.462169 | ||||||||
\(476\) | 2.88102e9 | 1.22440 | ||||||||
\(477\) | −1.01209e9 | −0.426979 | ||||||||
\(478\) | 5.10704e8 | 0.213881 | ||||||||
\(479\) | −2.95620e9 | −1.22902 | −0.614512 | − | 0.788908i | \(-0.710647\pi\) | ||||
−0.614512 | + | 0.788908i | \(0.710647\pi\) | |||||||
\(480\) | −4.01191e6 | −0.00165580 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 1.42251e9 | 0.578615 | ||||||||
\(483\) | −2.80464e9 | −1.13256 | ||||||||
\(484\) | −1.15904e9 | −0.464664 | ||||||||
\(485\) | −4.06274e7 | −0.0161705 | ||||||||
\(486\) | −1.69834e9 | −0.671114 | ||||||||
\(487\) | −3.14356e8 | −0.123330 | −0.0616652 | − | 0.998097i | \(-0.519641\pi\) | ||||
−0.0616652 | + | 0.998097i | \(0.519641\pi\) | |||||||
\(488\) | −6.83973e8 | −0.266422 | ||||||||
\(489\) | −1.63370e9 | −0.631817 | ||||||||
\(490\) | −9.26772e7 | −0.0355866 | ||||||||
\(491\) | 1.74300e9 | 0.664525 | 0.332262 | − | 0.943187i | \(-0.392188\pi\) | ||||
0.332262 | + | 0.943187i | \(0.392188\pi\) | |||||||
\(492\) | −6.90717e8 | −0.261470 | ||||||||
\(493\) | 4.47225e9 | 1.68098 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.43168e7 | 0.00530553 | ||||||||
\(496\) | −4.66146e8 | −0.171529 | ||||||||
\(497\) | −2.97211e9 | −1.08597 | ||||||||
\(498\) | −9.79301e7 | −0.0355315 | ||||||||
\(499\) | −3.47846e9 | −1.25324 | −0.626621 | − | 0.779324i | \(-0.715563\pi\) | ||||
−0.626621 | + | 0.779324i | \(0.715563\pi\) | |||||||
\(500\) | −6.61263e7 | −0.0236581 | ||||||||
\(501\) | −1.32939e9 | −0.472302 | ||||||||
\(502\) | −2.05732e9 | −0.725837 | ||||||||
\(503\) | −2.26923e9 | −0.795043 | −0.397521 | − | 0.917593i | \(-0.630130\pi\) | ||||
−0.397521 | + | 0.917593i | \(0.630130\pi\) | |||||||
\(504\) | 1.51532e9 | 0.527228 | ||||||||
\(505\) | 3.87227e7 | 0.0133797 | ||||||||
\(506\) | −8.86496e8 | −0.304194 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.96613e9 | 0.665409 | ||||||||
\(509\) | 3.74316e9 | 1.25813 | 0.629065 | − | 0.777352i | \(-0.283438\pi\) | ||||
0.629065 | + | 0.777352i | \(0.283438\pi\) | |||||||
\(510\) | −2.74772e7 | −0.00917227 | ||||||||
\(511\) | 2.40945e9 | 0.798812 | ||||||||
\(512\) | −1.34218e8 | −0.0441942 | ||||||||
\(513\) | 1.03167e9 | 0.337388 | ||||||||
\(514\) | 1.79925e9 | 0.584414 | ||||||||
\(515\) | −1.19425e7 | −0.00385275 | ||||||||
\(516\) | −1.04849e8 | −0.0335962 | ||||||||
\(517\) | 1.32388e8 | 0.0421339 | ||||||||
\(518\) | 5.17087e9 | 1.63459 | ||||||||
\(519\) | 1.11126e9 | 0.348923 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.68654e9 | −0.522475 | −0.261238 | − | 0.965275i | \(-0.584131\pi\) | ||||
−0.261238 | + | 0.965275i | \(0.584131\pi\) | |||||||
\(522\) | 2.35226e9 | 0.723833 | ||||||||
\(523\) | 4.11403e9 | 1.25751 | 0.628755 | − | 0.777604i | \(-0.283565\pi\) | ||||
0.628755 | + | 0.777604i | \(0.283565\pi\) | |||||||
\(524\) | 1.04307e9 | 0.316706 | ||||||||
\(525\) | −2.31919e9 | −0.699486 | ||||||||
\(526\) | −3.82416e9 | −1.14574 | ||||||||
\(527\) | −3.19260e9 | −0.950182 | ||||||||
\(528\) | −8.89745e7 | −0.0263055 | ||||||||
\(529\) | 5.51124e9 | 1.61865 | ||||||||
\(530\) | −2.90373e7 | −0.00847208 | ||||||||
\(531\) | 3.12614e9 | 0.906102 | ||||||||
\(532\) | −1.41986e9 | −0.408842 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −1.52657e9 | −0.433831 | ||||||||
\(535\) | 8.73271e7 | 0.0246553 | ||||||||
\(536\) | −3.68250e8 | −0.103292 | ||||||||
\(537\) | −2.48847e9 | −0.693462 | ||||||||
\(538\) | −1.40994e9 | −0.390358 | ||||||||
\(539\) | −2.05536e9 | −0.565362 | ||||||||
\(540\) | −3.15889e7 | −0.00863290 | ||||||||
\(541\) | 5.21199e9 | 1.41519 | 0.707593 | − | 0.706620i | \(-0.249781\pi\) | ||||
0.707593 | + | 0.706620i | \(0.249781\pi\) | |||||||
\(542\) | −1.50669e9 | −0.406469 | ||||||||
\(543\) | −2.88500e9 | −0.773298 | ||||||||
\(544\) | −9.19245e8 | −0.244813 | ||||||||
\(545\) | −1.56245e8 | −0.0413446 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.06174e9 | −1.32234 | −0.661172 | − | 0.750235i | \(-0.729941\pi\) | ||||
−0.661172 | + | 0.750235i | \(0.729941\pi\) | |||||||
\(548\) | −2.06492e9 | −0.536008 | ||||||||
\(549\) | −2.46388e9 | −0.635501 | ||||||||
\(550\) | −7.33056e8 | −0.187874 | ||||||||
\(551\) | −2.20407e9 | −0.561300 | ||||||||
\(552\) | 8.94874e8 | 0.226451 | ||||||||
\(553\) | −9.75110e9 | −2.45197 | ||||||||
\(554\) | −2.52046e8 | −0.0629789 | ||||||||
\(555\) | −4.93163e7 | −0.0122452 | ||||||||
\(556\) | −2.41525e9 | −0.595938 | ||||||||
\(557\) | −5.64001e9 | −1.38289 | −0.691444 | − | 0.722430i | \(-0.743025\pi\) | ||||
−0.691444 | + | 0.722430i | \(0.743025\pi\) | |||||||
\(558\) | −1.67920e9 | −0.409151 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 4.34750e7 | 0.0104612 | ||||||||
\(561\) | −6.09379e8 | −0.145719 | ||||||||
\(562\) | 2.14055e9 | 0.508684 | ||||||||
\(563\) | −1.03881e9 | −0.245334 | −0.122667 | − | 0.992448i | \(-0.539145\pi\) | ||||
−0.122667 | + | 0.992448i | \(0.539145\pi\) | |||||||
\(564\) | −1.33639e8 | −0.0313658 | ||||||||
\(565\) | 6.86176e7 | 0.0160054 | ||||||||
\(566\) | 1.05023e9 | 0.243459 | ||||||||
\(567\) | 4.25627e9 | 0.980593 | ||||||||
\(568\) | 9.48311e8 | 0.217136 | ||||||||
\(569\) | 1.36295e9 | 0.310160 | 0.155080 | − | 0.987902i | \(-0.450436\pi\) | ||||
0.155080 | + | 0.987902i | \(0.450436\pi\) | |||||||
\(570\) | 1.35417e7 | 0.00306274 | ||||||||
\(571\) | −7.59504e9 | −1.70727 | −0.853637 | − | 0.520868i | \(-0.825608\pi\) | ||||
−0.853637 | + | 0.520868i | \(0.825608\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.13370e8 | −0.0917906 | ||||||||
\(574\) | 7.48496e9 | 1.65195 | ||||||||
\(575\) | 7.37281e9 | 1.61732 | ||||||||
\(576\) | −4.83494e8 | −0.105417 | ||||||||
\(577\) | 9.14980e8 | 0.198288 | 0.0991439 | − | 0.995073i | \(-0.468390\pi\) | ||||
0.0991439 | + | 0.995073i | \(0.468390\pi\) | |||||||
\(578\) | −3.01312e9 | −0.649036 | ||||||||
\(579\) | −4.99269e7 | −0.0106896 | ||||||||
\(580\) | 6.74870e7 | 0.0143622 | ||||||||
\(581\) | 1.06122e9 | 0.224486 | ||||||||
\(582\) | 9.09534e8 | 0.191244 | ||||||||
\(583\) | −6.43977e8 | −0.134595 | ||||||||
\(584\) | −7.68782e8 | −0.159720 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.02024e9 | −0.825298 | ||||||||
\(587\) | 3.69625e9 | 0.754272 | 0.377136 | − | 0.926158i | \(-0.376909\pi\) | ||||
0.377136 | + | 0.926158i | \(0.376909\pi\) | |||||||
\(588\) | 2.07478e9 | 0.420874 | ||||||||
\(589\) | 1.57342e9 | 0.317278 | ||||||||
\(590\) | 8.96898e7 | 0.0179788 | ||||||||
\(591\) | −1.35146e9 | −0.269306 | ||||||||
\(592\) | −1.64987e9 | −0.326831 | ||||||||
\(593\) | −4.56755e9 | −0.899480 | −0.449740 | − | 0.893159i | \(-0.648483\pi\) | ||||
−0.449740 | + | 0.893159i | \(0.648483\pi\) | |||||||
\(594\) | −7.00567e8 | −0.137150 | ||||||||
\(595\) | 2.97757e8 | 0.0579498 | ||||||||
\(596\) | −1.08291e9 | −0.209523 | ||||||||
\(597\) | −2.04708e9 | −0.393753 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.63940e9 | 0.311668 | 0.155834 | − | 0.987783i | \(-0.450194\pi\) | ||||
0.155834 | + | 0.987783i | \(0.450194\pi\) | |||||||
\(600\) | 7.39984e8 | 0.139860 | ||||||||
\(601\) | −4.92573e9 | −0.925572 | −0.462786 | − | 0.886470i | \(-0.653150\pi\) | ||||
−0.462786 | + | 0.886470i | \(0.653150\pi\) | |||||||
\(602\) | 1.13620e9 | 0.212259 | ||||||||
\(603\) | −1.32655e9 | −0.246384 | ||||||||
\(604\) | 2.48211e9 | 0.458343 | ||||||||
\(605\) | −1.19788e8 | −0.0219922 | ||||||||
\(606\) | −8.66894e8 | −0.158238 | ||||||||
\(607\) | 7.26751e9 | 1.31894 | 0.659470 | − | 0.751731i | \(-0.270781\pi\) | ||||
0.659470 | + | 0.751731i | \(0.270781\pi\) | |||||||
\(608\) | 4.53035e8 | 0.0817464 | ||||||||
\(609\) | 4.73515e9 | 0.849520 | ||||||||
\(610\) | −7.06894e7 | −0.0126096 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −3.31140e9 | −0.583959 | ||||||||
\(613\) | −3.16466e9 | −0.554900 | −0.277450 | − | 0.960740i | \(-0.589489\pi\) | ||||
−0.277450 | + | 0.960740i | \(0.589489\pi\) | |||||||
\(614\) | −3.23571e8 | −0.0564131 | ||||||||
\(615\) | −7.13865e7 | −0.0123752 | ||||||||
\(616\) | 9.64172e8 | 0.166197 | ||||||||
\(617\) | −1.11473e10 | −1.91060 | −0.955301 | − | 0.295634i | \(-0.904469\pi\) | ||||
−0.955301 | + | 0.295634i | \(0.904469\pi\) | |||||||
\(618\) | 2.67360e8 | 0.0455656 | ||||||||
\(619\) | 8.69140e9 | 1.47290 | 0.736449 | − | 0.676493i | \(-0.236501\pi\) | ||||
0.736449 | + | 0.676493i | \(0.236501\pi\) | |||||||
\(620\) | −4.81768e7 | −0.00811834 | ||||||||
\(621\) | 7.04605e9 | 1.18066 | ||||||||
\(622\) | 4.64384e8 | 0.0773767 | ||||||||
\(623\) | 1.65426e10 | 2.74092 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.09326e9 | 0.998320 | ||||||||
\(626\) | −1.49844e9 | −0.244135 | ||||||||
\(627\) | 3.00322e8 | 0.0486576 | ||||||||
\(628\) | −3.11390e9 | −0.501701 | ||||||||
\(629\) | −1.12998e10 | −1.81048 | ||||||||
\(630\) | 1.56610e8 | 0.0249534 | ||||||||
\(631\) | −3.41348e9 | −0.540872 | −0.270436 | − | 0.962738i | \(-0.587168\pi\) | ||||
−0.270436 | + | 0.962738i | \(0.587168\pi\) | |||||||
\(632\) | 3.11128e9 | 0.490263 | ||||||||
\(633\) | −1.44365e9 | −0.226229 | ||||||||
\(634\) | 4.87686e8 | 0.0760025 | ||||||||
\(635\) | 2.03202e8 | 0.0314934 | ||||||||
\(636\) | 6.50063e8 | 0.100197 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.49670e9 | 0.228172 | ||||||||
\(639\) | 3.41611e9 | 0.517939 | ||||||||
\(640\) | −1.38716e7 | −0.00209168 | ||||||||
\(641\) | 1.93523e9 | 0.290221 | 0.145110 | − | 0.989415i | \(-0.453646\pi\) | ||||
0.145110 | + | 0.989415i | \(0.453646\pi\) | |||||||
\(642\) | −1.95501e9 | −0.291592 | ||||||||
\(643\) | −7.98936e9 | −1.18515 | −0.592575 | − | 0.805515i | \(-0.701889\pi\) | ||||
−0.592575 | + | 0.805515i | \(0.701889\pi\) | |||||||
\(644\) | −9.69730e9 | −1.43071 | ||||||||
\(645\) | −1.08363e7 | −0.00159009 | ||||||||
\(646\) | 3.10279e9 | 0.452834 | ||||||||
\(647\) | 8.47178e9 | 1.22973 | 0.614865 | − | 0.788632i | \(-0.289211\pi\) | ||||
0.614865 | + | 0.788632i | \(0.289211\pi\) | |||||||
\(648\) | −1.35805e9 | −0.196066 | ||||||||
\(649\) | 1.98910e9 | 0.285628 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.38028e9 | −0.480196 | ||||||||
\(652\) | −5.64868e9 | −0.798143 | ||||||||
\(653\) | 8.72038e9 | 1.22557 | 0.612787 | − | 0.790248i | \(-0.290048\pi\) | ||||
0.612787 | + | 0.790248i | \(0.290048\pi\) | |||||||
\(654\) | 3.49789e9 | 0.488972 | ||||||||
\(655\) | 1.07803e8 | 0.0149895 | ||||||||
\(656\) | −2.38822e9 | −0.330302 | ||||||||
\(657\) | −2.76939e9 | −0.380983 | ||||||||
\(658\) | 1.44818e9 | 0.198167 | ||||||||
\(659\) | −4.03937e9 | −0.549813 | −0.274907 | − | 0.961471i | \(-0.588647\pi\) | ||||
−0.274907 | + | 0.961471i | \(0.588647\pi\) | |||||||
\(660\) | −9.19563e6 | −0.00124502 | ||||||||
\(661\) | −3.29803e9 | −0.444170 | −0.222085 | − | 0.975027i | \(-0.571286\pi\) | ||||
−0.222085 | + | 0.975027i | \(0.571286\pi\) | |||||||
\(662\) | −3.63575e9 | −0.487069 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.38603e8 | −0.0448851 | ||||||||
\(665\) | −1.46744e8 | −0.0193502 | ||||||||
\(666\) | −5.94333e9 | −0.779597 | ||||||||
\(667\) | −1.50533e10 | −1.96422 | ||||||||
\(668\) | −4.59649e9 | −0.596634 | ||||||||
\(669\) | 5.20748e9 | 0.672413 | ||||||||
\(670\) | −3.80591e7 | −0.00488874 | ||||||||
\(671\) | −1.56772e9 | −0.200327 | ||||||||
\(672\) | −9.73284e8 | −0.123722 | ||||||||
\(673\) | 5.27449e9 | 0.667003 | 0.333502 | − | 0.942750i | \(-0.391770\pi\) | ||||
0.333502 | + | 0.942750i | \(0.391770\pi\) | |||||||
\(674\) | −1.64196e9 | −0.206564 | ||||||||
\(675\) | 5.82648e9 | 0.729194 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.02661e10 | 1.27158 | 0.635791 | − | 0.771861i | \(-0.280674\pi\) | ||||
0.635791 | + | 0.771861i | \(0.280674\pi\) | |||||||
\(678\) | −1.53616e9 | −0.189292 | ||||||||
\(679\) | −9.85617e9 | −1.20827 | ||||||||
\(680\) | −9.50051e7 | −0.0115869 | ||||||||
\(681\) | −5.31525e9 | −0.644925 | ||||||||
\(682\) | −1.06845e9 | −0.128976 | ||||||||
\(683\) | −3.81750e9 | −0.458465 | −0.229233 | − | 0.973372i | \(-0.573622\pi\) | ||||
−0.229233 | + | 0.973372i | \(0.573622\pi\) | |||||||
\(684\) | 1.63197e9 | 0.194992 | ||||||||
\(685\) | −2.13412e8 | −0.0253689 | ||||||||
\(686\) | −1.19113e10 | −1.40872 | ||||||||
\(687\) | −3.28918e9 | −0.387025 | ||||||||
\(688\) | −3.62526e8 | −0.0424404 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 9.24863e7 | 0.0107178 | ||||||||
\(691\) | 1.41493e10 | 1.63140 | 0.815700 | − | 0.578475i | \(-0.196352\pi\) | ||||
0.815700 | + | 0.578475i | \(0.196352\pi\) | |||||||
\(692\) | 3.84229e9 | 0.440776 | ||||||||
\(693\) | 3.47325e9 | 0.396432 | ||||||||
\(694\) | −2.39431e9 | −0.271909 | ||||||||
\(695\) | −2.49619e8 | −0.0282054 | ||||||||
\(696\) | −1.51084e9 | −0.169859 | ||||||||
\(697\) | −1.63567e10 | −1.82971 | ||||||||
\(698\) | 8.24782e8 | 0.0918006 | ||||||||
\(699\) | 2.55532e9 | 0.282992 | ||||||||
\(700\) | −8.01883e9 | −0.883625 | ||||||||
\(701\) | −2.63084e9 | −0.288457 | −0.144228 | − | 0.989544i | \(-0.546070\pi\) | ||||
−0.144228 | + | 0.989544i | \(0.546070\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.56892e9 | 0.604543 | ||||||||
\(704\) | −3.07638e8 | −0.0332304 | ||||||||
\(705\) | −1.38118e7 | −0.00148453 | ||||||||
\(706\) | 3.03385e9 | 0.324472 | ||||||||
\(707\) | 9.39409e9 | 0.999740 | ||||||||
\(708\) | −2.00790e9 | −0.212631 | ||||||||
\(709\) | 1.48321e10 | 1.56293 | 0.781466 | − | 0.623947i | \(-0.214472\pi\) | ||||
0.781466 | + | 0.623947i | \(0.214472\pi\) | |||||||
\(710\) | 9.80092e7 | 0.0102769 | ||||||||
\(711\) | 1.12078e10 | 1.16944 | ||||||||
\(712\) | −5.27825e9 | −0.548037 | ||||||||
\(713\) | 1.07461e10 | 1.11029 | ||||||||
\(714\) | −6.66594e9 | −0.685358 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −8.60413e9 | −0.876015 | ||||||||
\(717\) | −1.18164e9 | −0.119720 | ||||||||
\(718\) | 1.03363e10 | 1.04215 | ||||||||
\(719\) | 4.09811e9 | 0.411180 | 0.205590 | − | 0.978638i | \(-0.434089\pi\) | ||||
0.205590 | + | 0.978638i | \(0.434089\pi\) | |||||||
\(720\) | −4.99697e7 | −0.00498933 | ||||||||
\(721\) | −2.89725e9 | −0.287880 | ||||||||
\(722\) | 5.62181e9 | 0.555899 | ||||||||
\(723\) | −3.29132e9 | −0.323881 | ||||||||
\(724\) | −9.97518e9 | −0.976868 | ||||||||
\(725\) | −1.24478e10 | −1.21313 | ||||||||
\(726\) | 2.68172e9 | 0.260097 | ||||||||
\(727\) | −1.07923e10 | −1.04171 | −0.520853 | − | 0.853646i | \(-0.674386\pi\) | ||||
−0.520853 | + | 0.853646i | \(0.674386\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.87136e9 | −0.178901 | ||||||||
\(730\) | −7.94546e7 | −0.00755943 | ||||||||
\(731\) | −2.48291e9 | −0.235099 | ||||||||
\(732\) | 1.58254e9 | 0.149130 | ||||||||
\(733\) | −4.31755e9 | −0.404924 | −0.202462 | − | 0.979290i | \(-0.564894\pi\) | ||||
−0.202462 | + | 0.979290i | \(0.564894\pi\) | |||||||
\(734\) | 2.57331e9 | 0.240191 | ||||||||
\(735\) | 2.14431e8 | 0.0199197 | ||||||||
\(736\) | 3.09411e9 | 0.286065 | ||||||||
\(737\) | −8.44060e8 | −0.0776671 | ||||||||
\(738\) | −8.60311e9 | −0.787877 | ||||||||
\(739\) | −1.59219e10 | −1.45124 | −0.725619 | − | 0.688097i | \(-0.758446\pi\) | ||||
−0.725619 | + | 0.688097i | \(0.758446\pi\) | |||||||
\(740\) | −1.70516e8 | −0.0154687 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −7.04441e9 | −0.633040 | ||||||||
\(743\) | 7.46206e9 | 0.667418 | 0.333709 | − | 0.942676i | \(-0.391700\pi\) | ||||
0.333709 | + | 0.942676i | \(0.391700\pi\) | |||||||
\(744\) | 1.07854e9 | 0.0960136 | ||||||||
\(745\) | −1.11920e8 | −0.00991657 | ||||||||
\(746\) | 4.76309e9 | 0.420052 | ||||||||
\(747\) | −1.21975e9 | −0.107065 | ||||||||
\(748\) | −2.10699e9 | −0.184080 | ||||||||
\(749\) | 2.11855e10 | 1.84226 | ||||||||
\(750\) | 1.52999e8 | 0.0132427 | ||||||||
\(751\) | 7.78292e9 | 0.670507 | 0.335253 | − | 0.942128i | \(-0.391178\pi\) | ||||
0.335253 | + | 0.942128i | \(0.391178\pi\) | |||||||
\(752\) | −4.62071e8 | −0.0396229 | ||||||||
\(753\) | 4.76011e9 | 0.406289 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.56529e8 | 0.0216931 | ||||||||
\(756\) | −7.66344e9 | −0.645056 | ||||||||
\(757\) | −1.36187e10 | −1.14104 | −0.570518 | − | 0.821285i | \(-0.693257\pi\) | ||||
−0.570518 | + | 0.821285i | \(0.693257\pi\) | |||||||
\(758\) | 1.47963e10 | 1.23399 | ||||||||
\(759\) | 2.05113e9 | 0.170273 | ||||||||
\(760\) | 4.68217e7 | 0.00386901 | ||||||||
\(761\) | −7.93048e9 | −0.652309 | −0.326154 | − | 0.945317i | \(-0.605753\pi\) | ||||
−0.326154 | + | 0.945317i | \(0.605753\pi\) | |||||||
\(762\) | −4.54912e9 | −0.372464 | ||||||||
\(763\) | −3.79049e10 | −3.08929 | ||||||||
\(764\) | −1.42927e9 | −0.115954 | ||||||||
\(765\) | −3.42238e8 | −0.0276384 | ||||||||
\(766\) | −1.55208e10 | −1.24771 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 3.10546e8 | 0.0247378 | ||||||||
\(769\) | −1.80037e10 | −1.42764 | −0.713820 | − | 0.700329i | \(-0.753036\pi\) | ||||
−0.713820 | + | 0.700329i | \(0.753036\pi\) | |||||||
\(770\) | 9.96484e7 | 0.00786598 | ||||||||
\(771\) | −4.16300e9 | −0.327127 | ||||||||
\(772\) | −1.72627e8 | −0.0135036 | ||||||||
\(773\) | 1.79933e10 | 1.40114 | 0.700571 | − | 0.713583i | \(-0.252929\pi\) | ||||
0.700571 | + | 0.713583i | \(0.252929\pi\) | |||||||
\(774\) | −1.30593e9 | −0.101234 | ||||||||
\(775\) | 8.88606e9 | 0.685730 | ||||||||
\(776\) | 3.14480e9 | 0.241589 | ||||||||
\(777\) | −1.19641e10 | −0.914967 | ||||||||
\(778\) | 1.30527e10 | 0.993740 | ||||||||
\(779\) | 8.06114e9 | 0.610963 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.17361e9 | 0.163269 | ||||||||
\(782\) | 2.11913e10 | 1.58465 | ||||||||
\(783\) | −1.18961e10 | −0.885600 | ||||||||
\(784\) | 7.17377e9 | 0.531669 | ||||||||
\(785\) | −3.21825e8 | −0.0237452 | ||||||||
\(786\) | −2.41341e9 | −0.177277 | ||||||||
\(787\) | 4.61318e9 | 0.337356 | 0.168678 | − | 0.985671i | \(-0.446050\pi\) | ||||
0.168678 | + | 0.985671i | \(0.446050\pi\) | |||||||
\(788\) | −4.67279e9 | −0.340200 | ||||||||
\(789\) | 8.84813e9 | 0.641331 | ||||||||
\(790\) | 3.21554e8 | 0.0232038 | ||||||||
\(791\) | 1.66465e10 | 1.19593 | ||||||||
\(792\) | −1.10821e9 | −0.0792653 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −1.16910e10 | −0.828857 | ||||||||
\(795\) | 6.71848e7 | 0.00474227 | ||||||||
\(796\) | −7.07798e9 | −0.497409 | ||||||||
\(797\) | −2.80281e9 | −0.196106 | −0.0980528 | − | 0.995181i | \(-0.531261\pi\) | ||||
−0.0980528 | + | 0.995181i | \(0.531261\pi\) | |||||||
\(798\) | 3.28520e9 | 0.228850 | ||||||||
\(799\) | −3.16468e9 | −0.219491 | ||||||||
\(800\) | 2.55857e9 | 0.176678 | ||||||||
\(801\) | −1.90139e10 | −1.30724 | ||||||||
\(802\) | 1.72765e9 | 0.118262 | ||||||||
\(803\) | −1.76211e9 | −0.120096 | ||||||||
\(804\) | 8.52037e8 | 0.0578179 | ||||||||
\(805\) | −1.00223e9 | −0.0677144 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.26224e9 | 0.218504 | ||||||||
\(808\) | −2.99737e9 | −0.199894 | ||||||||
\(809\) | 8.36628e9 | 0.555537 | 0.277768 | − | 0.960648i | \(-0.410405\pi\) | ||||
0.277768 | + | 0.960648i | \(0.410405\pi\) | |||||||
\(810\) | −1.40356e8 | −0.00927968 | ||||||||
\(811\) | 4.54358e9 | 0.299106 | 0.149553 | − | 0.988754i | \(-0.452217\pi\) | ||||
0.149553 | + | 0.988754i | \(0.452217\pi\) | |||||||
\(812\) | 1.63723e10 | 1.07316 | ||||||||
\(813\) | 3.48611e9 | 0.227522 | ||||||||
\(814\) | −3.78163e9 | −0.245750 | ||||||||
\(815\) | −5.83798e8 | −0.0377756 | ||||||||
\(816\) | 2.12690e9 | 0.137035 | ||||||||
\(817\) | 1.22366e9 | 0.0785025 | ||||||||
\(818\) | 1.68027e10 | 1.07335 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.46826e8 | −0.0156330 | ||||||||
\(821\) | −1.50748e10 | −0.950717 | −0.475358 | − | 0.879792i | \(-0.657682\pi\) | ||||
−0.475358 | + | 0.879792i | \(0.657682\pi\) | |||||||
\(822\) | 4.77770e9 | 0.300032 | ||||||||
\(823\) | −1.67438e10 | −1.04702 | −0.523508 | − | 0.852021i | \(-0.675377\pi\) | ||||
−0.523508 | + | 0.852021i | \(0.675377\pi\) | |||||||
\(824\) | 9.24424e8 | 0.0575607 | ||||||||
\(825\) | 1.69610e9 | 0.105163 | ||||||||
\(826\) | 2.17586e10 | 1.34339 | ||||||||
\(827\) | −1.05833e10 | −0.650656 | −0.325328 | − | 0.945601i | \(-0.605475\pi\) | ||||
−0.325328 | + | 0.945601i | \(0.605475\pi\) | |||||||
\(828\) | 1.11460e10 | 0.682356 | ||||||||
\(829\) | 2.53716e10 | 1.54670 | 0.773352 | − | 0.633976i | \(-0.218578\pi\) | ||||
0.773352 | + | 0.633976i | \(0.218578\pi\) | |||||||
\(830\) | −3.49950e7 | −0.00212438 | ||||||||
\(831\) | 5.83169e8 | 0.0352526 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.91325e10 | 2.94518 | ||||||||
\(834\) | 5.58828e9 | 0.333578 | ||||||||
\(835\) | −4.75053e8 | −0.0282383 | ||||||||
\(836\) | 1.03839e9 | 0.0614667 | ||||||||
\(837\) | 8.49223e9 | 0.500591 | ||||||||
\(838\) | −3.46692e9 | −0.203512 | ||||||||
\(839\) | 8.37014e9 | 0.489290 | 0.244645 | − | 0.969613i | \(-0.421329\pi\) | ||||
0.244645 | + | 0.969613i | \(0.421329\pi\) | |||||||
\(840\) | −1.00590e8 | −0.00585569 | ||||||||
\(841\) | 8.16504e9 | 0.473339 | ||||||||
\(842\) | −2.08621e10 | −1.20439 | ||||||||
\(843\) | −4.95268e9 | −0.284737 | ||||||||
\(844\) | −4.99156e9 | −0.285784 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.66452e9 | −0.0945133 | ||||||||
\(847\) | −2.90604e10 | −1.64327 | ||||||||
\(848\) | 2.24766e9 | 0.126574 | ||||||||
\(849\) | −2.42996e9 | −0.136277 | ||||||||
\(850\) | 1.75234e10 | 0.978705 | ||||||||
\(851\) | 3.80343e10 | 2.11554 | ||||||||
\(852\) | −2.19415e9 | −0.121542 | ||||||||
\(853\) | 8.05268e9 | 0.444241 | 0.222121 | − | 0.975019i | \(-0.428702\pi\) | ||||
0.222121 | + | 0.975019i | \(0.428702\pi\) | |||||||
\(854\) | −1.71492e10 | −0.942195 | ||||||||
\(855\) | 1.68666e8 | 0.00922883 | ||||||||
\(856\) | −6.75964e9 | −0.368354 | ||||||||
\(857\) | 2.21962e10 | 1.20461 | 0.602304 | − | 0.798267i | \(-0.294249\pi\) | ||||
0.602304 | + | 0.798267i | \(0.294249\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.25915e8 | −0.0229270 | −0.0114635 | − | 0.999934i | \(-0.503649\pi\) | ||||
−0.0114635 | + | 0.999934i | \(0.503649\pi\) | |||||||
\(860\) | −3.74675e7 | −0.00200868 | ||||||||
\(861\) | −1.73183e10 | −0.924685 | ||||||||
\(862\) | −5.45854e9 | −0.290269 | ||||||||
\(863\) | 1.84502e10 | 0.977156 | 0.488578 | − | 0.872520i | \(-0.337516\pi\) | ||||
0.488578 | + | 0.872520i | \(0.337516\pi\) | |||||||
\(864\) | 2.44517e9 | 0.128977 | ||||||||
\(865\) | 3.97105e8 | 0.0208617 | ||||||||
\(866\) | −1.99674e10 | −1.04474 | ||||||||
\(867\) | 6.97159e9 | 0.363300 | ||||||||
\(868\) | −1.16876e10 | −0.606608 | ||||||||
\(869\) | 7.13131e9 | 0.368638 | ||||||||
\(870\) | −1.56148e8 | −0.00803930 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 1.20943e10 | 0.617693 | ||||||||
\(873\) | 1.13286e10 | 0.576268 | ||||||||
\(874\) | −1.04438e10 | −0.529137 | ||||||||
\(875\) | −1.65798e9 | −0.0836662 | ||||||||
\(876\) | 1.77877e9 | 0.0894035 | ||||||||
\(877\) | 1.81523e10 | 0.908725 | 0.454363 | − | 0.890817i | \(-0.349867\pi\) | ||||
0.454363 | + | 0.890817i | \(0.349867\pi\) | |||||||
\(878\) | 1.21423e10 | 0.605436 | ||||||||
\(879\) | 9.30182e9 | 0.461962 | ||||||||
\(880\) | −3.17948e7 | −0.00157277 | ||||||||
\(881\) | 2.80509e10 | 1.38207 | 0.691037 | − | 0.722819i | \(-0.257154\pi\) | ||||
0.691037 | + | 0.722819i | \(0.257154\pi\) | |||||||
\(882\) | 2.58421e10 | 1.26820 | ||||||||
\(883\) | 2.12689e9 | 0.103964 | 0.0519819 | − | 0.998648i | \(-0.483446\pi\) | ||||
0.0519819 | + | 0.998648i | \(0.483446\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.07519e8 | −0.0100637 | ||||||||
\(886\) | −2.05226e10 | −0.991323 | ||||||||
\(887\) | 2.61618e10 | 1.25874 | 0.629368 | − | 0.777107i | \(-0.283314\pi\) | ||||
0.629368 | + | 0.777107i | \(0.283314\pi\) | |||||||
\(888\) | 3.81737e9 | 0.182944 | ||||||||
\(889\) | 4.92965e10 | 2.35321 | ||||||||
\(890\) | −5.45514e8 | −0.0259382 | ||||||||
\(891\) | −3.11276e9 | −0.147426 | ||||||||
\(892\) | 1.80054e10 | 0.849425 | ||||||||
\(893\) | 1.55966e9 | 0.0732909 | ||||||||
\(894\) | 2.50558e9 | 0.117281 | ||||||||
\(895\) | −8.89248e8 | −0.0414612 | ||||||||
\(896\) | −3.36523e9 | −0.156292 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.77963e10 | −0.820091 | ||||||||
\(899\) | −1.81429e10 | −0.832814 | ||||||||
\(900\) | 9.21674e9 | 0.421433 | ||||||||
\(901\) | 1.53940e10 | 0.701156 | ||||||||
\(902\) | −5.47400e9 | −0.248360 | ||||||||
\(903\) | −2.62887e9 | −0.118812 | ||||||||
\(904\) | −5.31141e9 | −0.239122 | ||||||||
\(905\) | −1.03095e9 | −0.0462345 | ||||||||
\(906\) | −5.74296e9 | −0.256559 | ||||||||
\(907\) | 1.57121e10 | 0.699213 | 0.349607 | − | 0.936897i | \(-0.386315\pi\) | ||||
0.349607 | + | 0.936897i | \(0.386315\pi\) | |||||||
\(908\) | −1.83780e10 | −0.814700 | ||||||||
\(909\) | −1.07974e10 | −0.476812 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.17054e10 | −1.38937 | −0.694687 | − | 0.719312i | \(-0.744457\pi\) | ||||
−0.694687 | + | 0.719312i | \(0.744457\pi\) | |||||||
\(912\) | −1.04821e9 | −0.0457578 | ||||||||
\(913\) | −7.76106e8 | −0.0337500 | ||||||||
\(914\) | −1.26576e10 | −0.548328 | ||||||||
\(915\) | 1.63557e8 | 0.00705823 | ||||||||
\(916\) | −1.13727e10 | −0.488909 | ||||||||
\(917\) | 2.61529e10 | 1.12002 | ||||||||
\(918\) | 1.67468e10 | 0.714466 | ||||||||
\(919\) | −7.15392e9 | −0.304047 | −0.152023 | − | 0.988377i | \(-0.548579\pi\) | ||||
−0.152023 | + | 0.988377i | \(0.548579\pi\) | |||||||
\(920\) | 3.19781e8 | 0.0135393 | ||||||||
\(921\) | 7.48660e8 | 0.0315774 | ||||||||
\(922\) | −1.06634e10 | −0.448059 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −2.23085e9 | −0.0930290 | ||||||||
\(925\) | 3.14511e10 | 1.30659 | ||||||||
\(926\) | 1.62617e10 | 0.673017 | ||||||||
\(927\) | 3.33006e9 | 0.137301 | ||||||||
\(928\) | −5.22389e9 | −0.214574 | ||||||||
\(929\) | −3.59995e10 | −1.47313 | −0.736566 | − | 0.676365i | \(-0.763554\pi\) | ||||
−0.736566 | + | 0.676365i | \(0.763554\pi\) | |||||||
\(930\) | 1.11469e8 | 0.00454426 | ||||||||
\(931\) | −2.42141e10 | −0.983433 | ||||||||
\(932\) | 8.83526e9 | 0.357490 | ||||||||
\(933\) | −1.07446e9 | −0.0433118 | ||||||||
\(934\) | 2.48540e8 | 0.00998119 | ||||||||
\(935\) | −2.17760e8 | −0.00871238 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.38764e10 | −0.551047 | −0.275523 | − | 0.961294i | \(-0.588851\pi\) | ||||
−0.275523 | + | 0.961294i | \(0.588851\pi\) | |||||||
\(938\) | −9.23310e9 | −0.365290 | ||||||||
\(939\) | 3.46701e9 | 0.136655 | ||||||||
\(940\) | −4.77556e7 | −0.00187532 | ||||||||
\(941\) | 1.24319e9 | 0.0486379 | 0.0243190 | − | 0.999704i | \(-0.492258\pi\) | ||||
0.0243190 | + | 0.999704i | \(0.492258\pi\) | |||||||
\(942\) | 7.20476e9 | 0.280829 | ||||||||
\(943\) | 5.50556e10 | 2.13801 | ||||||||
\(944\) | −6.94252e9 | −0.268606 | ||||||||
\(945\) | −7.92026e8 | −0.0305301 | ||||||||
\(946\) | −8.30940e8 | −0.0319118 | ||||||||
\(947\) | 1.08695e10 | 0.415896 | 0.207948 | − | 0.978140i | \(-0.433321\pi\) | ||||
0.207948 | + | 0.978140i | \(0.433321\pi\) | |||||||
\(948\) | −7.19870e9 | −0.274426 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −8.63611e9 | −0.326803 | ||||||||
\(951\) | −1.12838e9 | −0.0425426 | ||||||||
\(952\) | −2.30481e10 | −0.865778 | ||||||||
\(953\) | 4.97595e9 | 0.186230 | 0.0931152 | − | 0.995655i | \(-0.470318\pi\) | ||||
0.0931152 | + | 0.995655i | \(0.470318\pi\) | |||||||
\(954\) | 8.09675e9 | 0.301920 | ||||||||
\(955\) | −1.47717e8 | −0.00548804 | ||||||||
\(956\) | −4.08563e9 | −0.151237 | ||||||||
\(957\) | −3.46298e9 | −0.127720 | ||||||||
\(958\) | 2.36496e10 | 0.869051 | ||||||||
\(959\) | −5.17736e10 | −1.89558 | ||||||||
\(960\) | 3.20953e7 | 0.00117082 | ||||||||
\(961\) | −1.45610e10 | −0.529247 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.43503e10 | −0.878642 | ||||||||
\(964\) | −1.13801e10 | −0.409143 | ||||||||
\(965\) | −1.78412e7 | −0.000639116 0 | ||||||||
\(966\) | 2.24371e10 | 0.800841 | ||||||||
\(967\) | −1.95659e10 | −0.695838 | −0.347919 | − | 0.937525i | \(-0.613112\pi\) | ||||
−0.347919 | + | 0.937525i | \(0.613112\pi\) | |||||||
\(968\) | 9.27230e9 | 0.328567 | ||||||||
\(969\) | −7.17907e9 | −0.253475 | ||||||||
\(970\) | 3.25019e8 | 0.0114343 | ||||||||
\(971\) | −6.28877e9 | −0.220444 | −0.110222 | − | 0.993907i | \(-0.535156\pi\) | ||||
−0.110222 | + | 0.993907i | \(0.535156\pi\) | |||||||
\(972\) | 1.35867e10 | 0.474550 | ||||||||
\(973\) | −6.05574e10 | −2.10752 | ||||||||
\(974\) | 2.51485e9 | 0.0872078 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.47178e9 | 0.188389 | ||||||||
\(977\) | 1.75153e9 | 0.0600878 | 0.0300439 | − | 0.999549i | \(-0.490435\pi\) | ||||
0.0300439 | + | 0.999549i | \(0.490435\pi\) | |||||||
\(978\) | 1.30696e10 | 0.446762 | ||||||||
\(979\) | −1.20982e10 | −0.412079 | ||||||||
\(980\) | 7.41417e8 | 0.0251635 | ||||||||
\(981\) | 4.35674e10 | 1.47340 | ||||||||
\(982\) | −1.39440e10 | −0.469890 | ||||||||
\(983\) | −3.03137e10 | −1.01789 | −0.508946 | − | 0.860799i | \(-0.669965\pi\) | ||||
−0.508946 | + | 0.860799i | \(0.669965\pi\) | |||||||
\(984\) | 5.52574e9 | 0.184887 | ||||||||
\(985\) | −4.82939e8 | −0.0161015 | ||||||||
\(986\) | −3.57780e10 | −1.18863 | ||||||||
\(987\) | −3.35072e9 | −0.110925 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.35730e9 | 0.274713 | ||||||||
\(990\) | −1.14535e8 | −0.00375157 | ||||||||
\(991\) | 4.08606e10 | 1.33367 | 0.666833 | − | 0.745207i | \(-0.267649\pi\) | ||||
0.666833 | + | 0.745207i | \(0.267649\pi\) | |||||||
\(992\) | 3.72917e9 | 0.121289 | ||||||||
\(993\) | 8.41219e9 | 0.272638 | ||||||||
\(994\) | 2.37769e10 | 0.767897 | ||||||||
\(995\) | −7.31517e8 | −0.0235420 | ||||||||
\(996\) | 7.83441e8 | 0.0251246 | ||||||||
\(997\) | 5.95647e10 | 1.90351 | 0.951757 | − | 0.306853i | \(-0.0992759\pi\) | ||||
0.951757 | + | 0.306853i | \(0.0992759\pi\) | |||||||
\(998\) | 2.78277e10 | 0.886176 | ||||||||
\(999\) | 3.00572e10 | 0.953826 |
(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 | 338.8.a.k.1.3 | 5 | ||
13.5 | odd | 4 | 26.8.b.a.25.8 | yes | 10 | ||
13.8 | odd | 4 | 26.8.b.a.25.3 | ✓ | 10 | ||
13.12 | even | 2 | 338.8.a.l.1.3 | 5 | |||
39.5 | even | 4 | 234.8.b.c.181.3 | 10 | |||
39.8 | even | 4 | 234.8.b.c.181.8 | 10 | |||
52.31 | even | 4 | 208.8.f.c.129.5 | 10 | |||
52.47 | even | 4 | 208.8.f.c.129.6 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
26.8.b.a.25.3 | ✓ | 10 | 13.8 | odd | 4 | ||
26.8.b.a.25.8 | yes | 10 | 13.5 | odd | 4 | ||
208.8.f.c.129.5 | 10 | 52.31 | even | 4 | |||
208.8.f.c.129.6 | 10 | 52.47 | even | 4 | |||
234.8.b.c.181.3 | 10 | 39.5 | even | 4 | |||
234.8.b.c.181.8 | 10 | 39.8 | even | 4 | |||
338.8.a.k.1.3 | 5 | 1.1 | even | 1 | trivial | ||
338.8.a.l.1.3 | 5 | 13.12 | even | 2 |