Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,12,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(135.996742959\) |
Analytic rank: | \(1\) |
Dimension: | \(27\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −68.7593 | −1.51938 | −0.759690 | − | 0.650285i | \(-0.774649\pi\) | ||||
−0.759690 | + | 0.650285i | \(0.774649\pi\) | |||||||
\(3\) | 243.000 | 0.577350 | ||||||||
\(4\) | 2679.84 | 1.30852 | ||||||||
\(5\) | 7324.59 | 1.04821 | 0.524105 | − | 0.851654i | \(-0.324400\pi\) | ||||
0.524105 | + | 0.851654i | \(0.324400\pi\) | |||||||
\(6\) | −16708.5 | −0.877215 | ||||||||
\(7\) | −63928.8 | −1.43766 | −0.718832 | − | 0.695184i | \(-0.755323\pi\) | ||||
−0.718832 | + | 0.695184i | \(0.755323\pi\) | |||||||
\(8\) | −43445.2 | −0.468756 | ||||||||
\(9\) | 59049.0 | 0.333333 | ||||||||
\(10\) | −503634. | −1.59263 | ||||||||
\(11\) | −307718. | −0.576093 | −0.288047 | − | 0.957616i | \(-0.593006\pi\) | ||||
−0.288047 | + | 0.957616i | \(0.593006\pi\) | |||||||
\(12\) | 651202. | 0.755473 | ||||||||
\(13\) | −1.14204e6 | −0.853088 | −0.426544 | − | 0.904467i | \(-0.640269\pi\) | ||||
−0.426544 | + | 0.904467i | \(0.640269\pi\) | |||||||
\(14\) | 4.39570e6 | 2.18436 | ||||||||
\(15\) | 1.77988e6 | 0.605184 | ||||||||
\(16\) | −2.50106e6 | −0.596299 | ||||||||
\(17\) | 1.41880e6 | 0.242356 | 0.121178 | − | 0.992631i | \(-0.461333\pi\) | ||||
0.121178 | + | 0.992631i | \(0.461333\pi\) | |||||||
\(18\) | −4.06017e6 | −0.506460 | ||||||||
\(19\) | 4.00245e6 | 0.370836 | 0.185418 | − | 0.982660i | \(-0.440636\pi\) | ||||
0.185418 | + | 0.982660i | \(0.440636\pi\) | |||||||
\(20\) | 1.96288e7 | 1.37160 | ||||||||
\(21\) | −1.55347e7 | −0.830035 | ||||||||
\(22\) | 2.11585e7 | 0.875305 | ||||||||
\(23\) | 4.77119e7 | 1.54570 | 0.772848 | − | 0.634591i | \(-0.218832\pi\) | ||||
0.772848 | + | 0.634591i | \(0.218832\pi\) | |||||||
\(24\) | −1.05572e7 | −0.270636 | ||||||||
\(25\) | 4.82151e6 | 0.0987445 | ||||||||
\(26\) | 7.85260e7 | 1.29616 | ||||||||
\(27\) | 1.43489e7 | 0.192450 | ||||||||
\(28\) | −1.71319e8 | −1.88121 | ||||||||
\(29\) | 1.63918e8 | 1.48401 | 0.742006 | − | 0.670393i | \(-0.233875\pi\) | ||||
0.742006 | + | 0.670393i | \(0.233875\pi\) | |||||||
\(30\) | −1.22383e8 | −0.919505 | ||||||||
\(31\) | 1.17737e8 | 0.738627 | 0.369314 | − | 0.929305i | \(-0.379593\pi\) | ||||
0.369314 | + | 0.929305i | \(0.379593\pi\) | |||||||
\(32\) | 2.60947e8 | 1.37476 | ||||||||
\(33\) | −7.47754e7 | −0.332608 | ||||||||
\(34\) | −9.75560e7 | −0.368231 | ||||||||
\(35\) | −4.68252e8 | −1.50697 | ||||||||
\(36\) | 1.58242e8 | 0.436173 | ||||||||
\(37\) | −5.45888e8 | −1.29418 | −0.647089 | − | 0.762414i | \(-0.724014\pi\) | ||||
−0.647089 | + | 0.762414i | \(0.724014\pi\) | |||||||
\(38\) | −2.75206e8 | −0.563440 | ||||||||
\(39\) | −2.77516e8 | −0.492530 | ||||||||
\(40\) | −3.18218e8 | −0.491354 | ||||||||
\(41\) | −5.77402e8 | −0.778336 | −0.389168 | − | 0.921167i | \(-0.627237\pi\) | ||||
−0.389168 | + | 0.921167i | \(0.627237\pi\) | |||||||
\(42\) | 1.06815e9 | 1.26114 | ||||||||
\(43\) | −1.16727e9 | −1.21086 | −0.605431 | − | 0.795897i | \(-0.706999\pi\) | ||||
−0.605431 | + | 0.795897i | \(0.706999\pi\) | |||||||
\(44\) | −8.24635e8 | −0.753828 | ||||||||
\(45\) | 4.32510e8 | 0.349403 | ||||||||
\(46\) | −3.28064e9 | −2.34850 | ||||||||
\(47\) | −3.29117e8 | −0.209321 | −0.104660 | − | 0.994508i | \(-0.533376\pi\) | ||||
−0.104660 | + | 0.994508i | \(0.533376\pi\) | |||||||
\(48\) | −6.07758e8 | −0.344274 | ||||||||
\(49\) | 2.10956e9 | 1.06688 | ||||||||
\(50\) | −3.31524e8 | −0.150030 | ||||||||
\(51\) | 3.44769e8 | 0.139924 | ||||||||
\(52\) | −3.06049e9 | −1.11628 | ||||||||
\(53\) | 5.23739e9 | 1.72027 | 0.860137 | − | 0.510063i | \(-0.170378\pi\) | ||||
0.860137 | + | 0.510063i | \(0.170378\pi\) | |||||||
\(54\) | −9.86621e8 | −0.292405 | ||||||||
\(55\) | −2.25391e9 | −0.603867 | ||||||||
\(56\) | 2.77740e9 | 0.673913 | ||||||||
\(57\) | 9.72596e8 | 0.214102 | ||||||||
\(58\) | −1.12709e10 | −2.25478 | ||||||||
\(59\) | −7.14924e8 | −0.130189 | ||||||||
\(60\) | 4.76979e9 | 0.791894 | ||||||||
\(61\) | 6.69141e9 | 1.01439 | 0.507193 | − | 0.861832i | \(-0.330683\pi\) | ||||
0.507193 | + | 0.861832i | \(0.330683\pi\) | |||||||
\(62\) | −8.09555e9 | −1.12226 | ||||||||
\(63\) | −3.77493e9 | −0.479221 | ||||||||
\(64\) | −1.28204e10 | −1.49249 | ||||||||
\(65\) | −8.36499e9 | −0.894215 | ||||||||
\(66\) | 5.14151e9 | 0.505357 | ||||||||
\(67\) | −1.09510e10 | −0.990930 | −0.495465 | − | 0.868628i | \(-0.665002\pi\) | ||||
−0.495465 | + | 0.868628i | \(0.665002\pi\) | |||||||
\(68\) | 3.80217e9 | 0.317127 | ||||||||
\(69\) | 1.15940e10 | 0.892408 | ||||||||
\(70\) | 3.21967e10 | 2.28967 | ||||||||
\(71\) | −1.13733e10 | −0.748109 | −0.374055 | − | 0.927407i | \(-0.622033\pi\) | ||||
−0.374055 | + | 0.927407i | \(0.622033\pi\) | |||||||
\(72\) | −2.56539e9 | −0.156252 | ||||||||
\(73\) | −1.17767e10 | −0.664886 | −0.332443 | − | 0.943123i | \(-0.607873\pi\) | ||||
−0.332443 | + | 0.943123i | \(0.607873\pi\) | |||||||
\(74\) | 3.75349e10 | 1.96635 | ||||||||
\(75\) | 1.17163e9 | 0.0570102 | ||||||||
\(76\) | 1.07259e10 | 0.485245 | ||||||||
\(77\) | 1.96720e10 | 0.828228 | ||||||||
\(78\) | 1.90818e10 | 0.748341 | ||||||||
\(79\) | 4.67627e10 | 1.70982 | 0.854910 | − | 0.518776i | \(-0.173612\pi\) | ||||
0.854910 | + | 0.518776i | \(0.173612\pi\) | |||||||
\(80\) | −1.83192e10 | −0.625047 | ||||||||
\(81\) | 3.48678e9 | 0.111111 | ||||||||
\(82\) | 3.97018e10 | 1.18259 | ||||||||
\(83\) | −4.41617e9 | −0.123060 | −0.0615299 | − | 0.998105i | \(-0.519598\pi\) | ||||
−0.0615299 | + | 0.998105i | \(0.519598\pi\) | |||||||
\(84\) | −4.16305e10 | −1.08612 | ||||||||
\(85\) | 1.03922e10 | 0.254040 | ||||||||
\(86\) | 8.02607e10 | 1.83976 | ||||||||
\(87\) | 3.98320e10 | 0.856795 | ||||||||
\(88\) | 1.33688e10 | 0.270047 | ||||||||
\(89\) | 2.79794e9 | 0.0531121 | 0.0265561 | − | 0.999647i | \(-0.491546\pi\) | ||||
0.0265561 | + | 0.999647i | \(0.491546\pi\) | |||||||
\(90\) | −2.97391e10 | −0.530877 | ||||||||
\(91\) | 7.30093e10 | 1.22645 | ||||||||
\(92\) | 1.27861e11 | 2.02257 | ||||||||
\(93\) | 2.86102e10 | 0.426447 | ||||||||
\(94\) | 2.26299e10 | 0.318038 | ||||||||
\(95\) | 2.93163e10 | 0.388714 | ||||||||
\(96\) | 6.34101e10 | 0.793719 | ||||||||
\(97\) | −1.07713e11 | −1.27357 | −0.636783 | − | 0.771043i | \(-0.719735\pi\) | ||||
−0.636783 | + | 0.771043i | \(0.719735\pi\) | |||||||
\(98\) | −1.45052e11 | −1.62099 | ||||||||
\(99\) | −1.81704e10 | −0.192031 | ||||||||
\(100\) | 1.29209e10 | 0.129209 | ||||||||
\(101\) | 1.21405e11 | 1.14939 | 0.574695 | − | 0.818368i | \(-0.305121\pi\) | ||||
0.574695 | + | 0.818368i | \(0.305121\pi\) | |||||||
\(102\) | −2.37061e10 | −0.212598 | ||||||||
\(103\) | 1.13157e11 | 0.961784 | 0.480892 | − | 0.876780i | \(-0.340313\pi\) | ||||
0.480892 | + | 0.876780i | \(0.340313\pi\) | |||||||
\(104\) | 4.96162e10 | 0.399890 | ||||||||
\(105\) | −1.13785e11 | −0.870051 | ||||||||
\(106\) | −3.60119e11 | −2.61375 | ||||||||
\(107\) | −9.86871e10 | −0.680220 | −0.340110 | − | 0.940386i | \(-0.610464\pi\) | ||||
−0.340110 | + | 0.940386i | \(0.610464\pi\) | |||||||
\(108\) | 3.84528e10 | 0.251824 | ||||||||
\(109\) | −1.67870e11 | −1.04503 | −0.522514 | − | 0.852631i | \(-0.675006\pi\) | ||||
−0.522514 | + | 0.852631i | \(0.675006\pi\) | |||||||
\(110\) | 1.54977e11 | 0.917503 | ||||||||
\(111\) | −1.32651e11 | −0.747194 | ||||||||
\(112\) | 1.59890e11 | 0.857278 | ||||||||
\(113\) | 8.34253e10 | 0.425958 | 0.212979 | − | 0.977057i | \(-0.431683\pi\) | ||||
0.212979 | + | 0.977057i | \(0.431683\pi\) | |||||||
\(114\) | −6.68750e10 | −0.325302 | ||||||||
\(115\) | 3.49470e11 | 1.62021 | ||||||||
\(116\) | 4.39274e11 | 1.94186 | ||||||||
\(117\) | −6.74364e10 | −0.284363 | ||||||||
\(118\) | 4.91577e10 | 0.197807 | ||||||||
\(119\) | −9.07024e10 | −0.348426 | ||||||||
\(120\) | −7.73270e10 | −0.283684 | ||||||||
\(121\) | −1.90621e11 | −0.668117 | ||||||||
\(122\) | −4.60097e11 | −1.54124 | ||||||||
\(123\) | −1.40309e11 | −0.449372 | ||||||||
\(124\) | 3.15518e11 | 0.966506 | ||||||||
\(125\) | −3.22330e11 | −0.944705 | ||||||||
\(126\) | 2.59562e11 | 0.728119 | ||||||||
\(127\) | 3.84746e11 | 1.03336 | 0.516682 | − | 0.856177i | \(-0.327167\pi\) | ||||
0.516682 | + | 0.856177i | \(0.327167\pi\) | |||||||
\(128\) | 3.47100e11 | 0.892894 | ||||||||
\(129\) | −2.83647e11 | −0.699092 | ||||||||
\(130\) | 5.75171e11 | 1.35865 | ||||||||
\(131\) | −4.26964e11 | −0.966939 | −0.483470 | − | 0.875361i | \(-0.660624\pi\) | ||||
−0.483470 | + | 0.875361i | \(0.660624\pi\) | |||||||
\(132\) | −2.00386e11 | −0.435223 | ||||||||
\(133\) | −2.55872e11 | −0.533137 | ||||||||
\(134\) | 7.52985e11 | 1.50560 | ||||||||
\(135\) | 1.05100e11 | 0.201728 | ||||||||
\(136\) | −6.16402e10 | −0.113606 | ||||||||
\(137\) | 3.05982e11 | 0.541668 | 0.270834 | − | 0.962626i | \(-0.412701\pi\) | ||||
0.270834 | + | 0.962626i | \(0.412701\pi\) | |||||||
\(138\) | −7.97196e11 | −1.35591 | ||||||||
\(139\) | −9.62226e11 | −1.57288 | −0.786440 | − | 0.617666i | \(-0.788078\pi\) | ||||
−0.786440 | + | 0.617666i | \(0.788078\pi\) | |||||||
\(140\) | −1.25484e12 | −1.97190 | ||||||||
\(141\) | −7.99755e10 | −0.120851 | ||||||||
\(142\) | 7.82019e11 | 1.13666 | ||||||||
\(143\) | 3.51427e11 | 0.491458 | ||||||||
\(144\) | −1.47685e11 | −0.198766 | ||||||||
\(145\) | 1.20063e12 | 1.55556 | ||||||||
\(146\) | 8.09756e11 | 1.01021 | ||||||||
\(147\) | 5.12623e11 | 0.615961 | ||||||||
\(148\) | −1.46289e12 | −1.69346 | ||||||||
\(149\) | −1.17212e12 | −1.30752 | −0.653761 | − | 0.756701i | \(-0.726810\pi\) | ||||
−0.653761 | + | 0.756701i | \(0.726810\pi\) | |||||||
\(150\) | −8.05602e10 | −0.0866201 | ||||||||
\(151\) | 9.13900e11 | 0.947382 | 0.473691 | − | 0.880691i | \(-0.342921\pi\) | ||||
0.473691 | + | 0.880691i | \(0.342921\pi\) | |||||||
\(152\) | −1.73887e11 | −0.173831 | ||||||||
\(153\) | 8.37790e10 | 0.0807853 | ||||||||
\(154\) | −1.35263e12 | −1.25839 | ||||||||
\(155\) | 8.62378e11 | 0.774236 | ||||||||
\(156\) | −7.43700e11 | −0.644485 | ||||||||
\(157\) | 2.00126e12 | 1.67439 | 0.837193 | − | 0.546908i | \(-0.184195\pi\) | ||||
0.837193 | + | 0.546908i | \(0.184195\pi\) | |||||||
\(158\) | −3.21537e12 | −2.59787 | ||||||||
\(159\) | 1.27269e12 | 0.993201 | ||||||||
\(160\) | 1.91133e12 | 1.44104 | ||||||||
\(161\) | −3.05017e12 | −2.22219 | ||||||||
\(162\) | −2.39749e11 | −0.168820 | ||||||||
\(163\) | −2.90005e12 | −1.97412 | −0.987059 | − | 0.160355i | \(-0.948736\pi\) | ||||
−0.987059 | + | 0.160355i | \(0.948736\pi\) | |||||||
\(164\) | −1.54735e12 | −1.01847 | ||||||||
\(165\) | −5.47699e11 | −0.348643 | ||||||||
\(166\) | 3.03653e11 | 0.186975 | ||||||||
\(167\) | −1.12393e11 | −0.0669577 | −0.0334788 | − | 0.999439i | \(-0.510659\pi\) | ||||
−0.0334788 | + | 0.999439i | \(0.510659\pi\) | |||||||
\(168\) | 6.74907e11 | 0.389084 | ||||||||
\(169\) | −4.87900e11 | −0.272242 | ||||||||
\(170\) | −7.14558e11 | −0.385983 | ||||||||
\(171\) | 2.36341e11 | 0.123612 | ||||||||
\(172\) | −3.12810e12 | −1.58444 | ||||||||
\(173\) | −1.78076e12 | −0.873677 | −0.436839 | − | 0.899540i | \(-0.643902\pi\) | ||||
−0.436839 | + | 0.899540i | \(0.643902\pi\) | |||||||
\(174\) | −2.73882e12 | −1.30180 | ||||||||
\(175\) | −3.08233e11 | −0.141961 | ||||||||
\(176\) | 7.69621e11 | 0.343524 | ||||||||
\(177\) | −1.73727e11 | −0.0751646 | ||||||||
\(178\) | −1.92385e11 | −0.0806976 | ||||||||
\(179\) | −2.97323e12 | −1.20931 | −0.604654 | − | 0.796488i | \(-0.706689\pi\) | ||||
−0.604654 | + | 0.796488i | \(0.706689\pi\) | |||||||
\(180\) | 1.15906e12 | 0.457200 | ||||||||
\(181\) | 2.21255e12 | 0.846568 | 0.423284 | − | 0.905997i | \(-0.360877\pi\) | ||||
0.423284 | + | 0.905997i | \(0.360877\pi\) | |||||||
\(182\) | −5.02007e12 | −1.86345 | ||||||||
\(183\) | 1.62601e12 | 0.585657 | ||||||||
\(184\) | −2.07285e12 | −0.724553 | ||||||||
\(185\) | −3.99841e12 | −1.35657 | ||||||||
\(186\) | −1.96722e12 | −0.647935 | ||||||||
\(187\) | −4.36591e11 | −0.139620 | ||||||||
\(188\) | −8.81983e11 | −0.273900 | ||||||||
\(189\) | −9.17308e11 | −0.276678 | ||||||||
\(190\) | −2.01577e12 | −0.590604 | ||||||||
\(191\) | 9.71854e11 | 0.276642 | 0.138321 | − | 0.990387i | \(-0.455829\pi\) | ||||
0.138321 | + | 0.990387i | \(0.455829\pi\) | |||||||
\(192\) | −3.11535e12 | −0.861687 | ||||||||
\(193\) | −1.87888e12 | −0.505050 | −0.252525 | − | 0.967590i | \(-0.581261\pi\) | ||||
−0.252525 | + | 0.967590i | \(0.581261\pi\) | |||||||
\(194\) | 7.40624e12 | 1.93503 | ||||||||
\(195\) | −2.03269e12 | −0.516275 | ||||||||
\(196\) | 5.65329e12 | 1.39602 | ||||||||
\(197\) | −2.04544e12 | −0.491159 | −0.245579 | − | 0.969376i | \(-0.578978\pi\) | ||||
−0.245579 | + | 0.969376i | \(0.578978\pi\) | |||||||
\(198\) | 1.24939e12 | 0.291768 | ||||||||
\(199\) | 3.90343e12 | 0.886654 | 0.443327 | − | 0.896360i | \(-0.353798\pi\) | ||||
0.443327 | + | 0.896360i | \(0.353798\pi\) | |||||||
\(200\) | −2.09471e11 | −0.0462870 | ||||||||
\(201\) | −2.66110e12 | −0.572114 | ||||||||
\(202\) | −8.34769e12 | −1.74636 | ||||||||
\(203\) | −1.04791e13 | −2.13351 | ||||||||
\(204\) | 9.23928e11 | 0.183093 | ||||||||
\(205\) | −4.22923e12 | −0.815860 | ||||||||
\(206\) | −7.78061e12 | −1.46132 | ||||||||
\(207\) | 2.81734e12 | 0.515232 | ||||||||
\(208\) | 2.85632e12 | 0.508696 | ||||||||
\(209\) | −1.23163e12 | −0.213636 | ||||||||
\(210\) | 7.82380e12 | 1.32194 | ||||||||
\(211\) | 4.79581e12 | 0.789421 | 0.394711 | − | 0.918805i | \(-0.370845\pi\) | ||||
0.394711 | + | 0.918805i | \(0.370845\pi\) | |||||||
\(212\) | 1.40354e13 | 2.25101 | ||||||||
\(213\) | −2.76371e12 | −0.431921 | ||||||||
\(214\) | 6.78566e12 | 1.03351 | ||||||||
\(215\) | −8.54978e12 | −1.26924 | ||||||||
\(216\) | −6.23391e11 | −0.0902121 | ||||||||
\(217\) | −7.52681e12 | −1.06190 | ||||||||
\(218\) | 1.15426e13 | 1.58780 | ||||||||
\(219\) | −2.86173e12 | −0.383872 | ||||||||
\(220\) | −6.04012e12 | −0.790170 | ||||||||
\(221\) | −1.62033e12 | −0.206751 | ||||||||
\(222\) | 9.12098e12 | 1.13527 | ||||||||
\(223\) | −5.10096e12 | −0.619405 | −0.309703 | − | 0.950833i | \(-0.600230\pi\) | ||||
−0.309703 | + | 0.950833i | \(0.600230\pi\) | |||||||
\(224\) | −1.66820e13 | −1.97644 | ||||||||
\(225\) | 2.84705e11 | 0.0329148 | ||||||||
\(226\) | −5.73627e12 | −0.647192 | ||||||||
\(227\) | −1.38386e13 | −1.52387 | −0.761937 | − | 0.647651i | \(-0.775752\pi\) | ||||
−0.761937 | + | 0.647651i | \(0.775752\pi\) | |||||||
\(228\) | 2.60641e12 | 0.280156 | ||||||||
\(229\) | −3.00157e12 | −0.314959 | −0.157479 | − | 0.987522i | \(-0.550337\pi\) | ||||
−0.157479 | + | 0.987522i | \(0.550337\pi\) | |||||||
\(230\) | −2.40293e13 | −2.46172 | ||||||||
\(231\) | 4.78030e12 | 0.478178 | ||||||||
\(232\) | −7.12144e12 | −0.695639 | ||||||||
\(233\) | −2.94172e12 | −0.280636 | −0.140318 | − | 0.990106i | \(-0.544812\pi\) | ||||
−0.140318 | + | 0.990106i | \(0.544812\pi\) | |||||||
\(234\) | 4.63688e12 | 0.432055 | ||||||||
\(235\) | −2.41065e12 | −0.219412 | ||||||||
\(236\) | −1.91589e12 | −0.170354 | ||||||||
\(237\) | 1.13633e13 | 0.987165 | ||||||||
\(238\) | 6.23664e12 | 0.529392 | ||||||||
\(239\) | −1.24328e13 | −1.03129 | −0.515646 | − | 0.856802i | \(-0.672448\pi\) | ||||
−0.515646 | + | 0.856802i | \(0.672448\pi\) | |||||||
\(240\) | −4.45158e12 | −0.360871 | ||||||||
\(241\) | 4.39171e11 | 0.0347969 | 0.0173984 | − | 0.999849i | \(-0.494462\pi\) | ||||
0.0173984 | + | 0.999849i | \(0.494462\pi\) | |||||||
\(242\) | 1.31070e13 | 1.01512 | ||||||||
\(243\) | 8.47289e11 | 0.0641500 | ||||||||
\(244\) | 1.79319e13 | 1.32734 | ||||||||
\(245\) | 1.54517e13 | 1.11831 | ||||||||
\(246\) | 9.64753e12 | 0.682768 | ||||||||
\(247\) | −4.57097e12 | −0.316355 | ||||||||
\(248\) | −5.11512e12 | −0.346236 | ||||||||
\(249\) | −1.07313e12 | −0.0710486 | ||||||||
\(250\) | 2.21632e13 | 1.43537 | ||||||||
\(251\) | 2.10997e13 | 1.33681 | 0.668405 | − | 0.743797i | \(-0.266977\pi\) | ||||
0.668405 | + | 0.743797i | \(0.266977\pi\) | |||||||
\(252\) | −1.01162e13 | −0.627069 | ||||||||
\(253\) | −1.46818e13 | −0.890465 | ||||||||
\(254\) | −2.64548e13 | −1.57007 | ||||||||
\(255\) | 2.52530e12 | 0.146670 | ||||||||
\(256\) | 2.38974e12 | 0.135841 | ||||||||
\(257\) | 9.06650e11 | 0.0504438 | 0.0252219 | − | 0.999682i | \(-0.491971\pi\) | ||||
0.0252219 | + | 0.999682i | \(0.491971\pi\) | |||||||
\(258\) | 1.95034e13 | 1.06219 | ||||||||
\(259\) | 3.48980e13 | 1.86059 | ||||||||
\(260\) | −2.24169e13 | −1.17010 | ||||||||
\(261\) | 9.67919e12 | 0.494671 | ||||||||
\(262\) | 2.93578e13 | 1.46915 | ||||||||
\(263\) | −5.28789e12 | −0.259135 | −0.129567 | − | 0.991571i | \(-0.541359\pi\) | ||||
−0.129567 | + | 0.991571i | \(0.541359\pi\) | |||||||
\(264\) | 3.24863e12 | 0.155912 | ||||||||
\(265\) | 3.83617e13 | 1.80321 | ||||||||
\(266\) | 1.75936e13 | 0.810037 | ||||||||
\(267\) | 6.79900e11 | 0.0306643 | ||||||||
\(268\) | −2.93470e13 | −1.29665 | ||||||||
\(269\) | −6.36340e12 | −0.275455 | −0.137728 | − | 0.990470i | \(-0.543980\pi\) | ||||
−0.137728 | + | 0.990470i | \(0.543980\pi\) | |||||||
\(270\) | −7.22660e12 | −0.306502 | ||||||||
\(271\) | −2.73829e13 | −1.13802 | −0.569008 | − | 0.822332i | \(-0.692673\pi\) | ||||
−0.569008 | + | 0.822332i | \(0.692673\pi\) | |||||||
\(272\) | −3.54852e12 | −0.144517 | ||||||||
\(273\) | 1.77413e13 | 0.708093 | ||||||||
\(274\) | −2.10391e13 | −0.823000 | ||||||||
\(275\) | −1.48366e12 | −0.0568860 | ||||||||
\(276\) | 3.10701e13 | 1.16773 | ||||||||
\(277\) | −1.41836e13 | −0.522573 | −0.261287 | − | 0.965261i | \(-0.584147\pi\) | ||||
−0.261287 | + | 0.965261i | \(0.584147\pi\) | |||||||
\(278\) | 6.61620e13 | 2.38980 | ||||||||
\(279\) | 6.95228e12 | 0.246209 | ||||||||
\(280\) | 2.03433e13 | 0.706402 | ||||||||
\(281\) | 2.12548e13 | 0.723722 | 0.361861 | − | 0.932232i | \(-0.382142\pi\) | ||||
0.361861 | + | 0.932232i | \(0.382142\pi\) | |||||||
\(282\) | 5.49906e12 | 0.183619 | ||||||||
\(283\) | −1.55797e13 | −0.510192 | −0.255096 | − | 0.966916i | \(-0.582107\pi\) | ||||
−0.255096 | + | 0.966916i | \(0.582107\pi\) | |||||||
\(284\) | −3.04786e13 | −0.978914 | ||||||||
\(285\) | 7.12387e12 | 0.224424 | ||||||||
\(286\) | −2.41638e13 | −0.746712 | ||||||||
\(287\) | 3.69126e13 | 1.11898 | ||||||||
\(288\) | 1.54087e13 | 0.458254 | ||||||||
\(289\) | −3.22589e13 | −0.941264 | ||||||||
\(290\) | −8.25546e13 | −2.36348 | ||||||||
\(291\) | −2.61741e13 | −0.735294 | ||||||||
\(292\) | −3.15596e13 | −0.870014 | ||||||||
\(293\) | 6.97384e13 | 1.88669 | 0.943345 | − | 0.331815i | \(-0.107661\pi\) | ||||
0.943345 | + | 0.331815i | \(0.107661\pi\) | |||||||
\(294\) | −3.52476e13 | −0.935879 | ||||||||
\(295\) | −5.23653e12 | −0.136465 | ||||||||
\(296\) | 2.37162e13 | 0.606653 | ||||||||
\(297\) | −4.41541e12 | −0.110869 | ||||||||
\(298\) | 8.05945e13 | 1.98662 | ||||||||
\(299\) | −5.44890e13 | −1.31861 | ||||||||
\(300\) | 3.13978e12 | 0.0745988 | ||||||||
\(301\) | 7.46222e13 | 1.74081 | ||||||||
\(302\) | −6.28391e13 | −1.43943 | ||||||||
\(303\) | 2.95013e13 | 0.663600 | ||||||||
\(304\) | −1.00104e13 | −0.221129 | ||||||||
\(305\) | 4.90118e13 | 1.06329 | ||||||||
\(306\) | −5.76059e12 | −0.122744 | ||||||||
\(307\) | −8.59060e12 | −0.179789 | −0.0898944 | − | 0.995951i | \(-0.528653\pi\) | ||||
−0.0898944 | + | 0.995951i | \(0.528653\pi\) | |||||||
\(308\) | 5.27179e13 | 1.08375 | ||||||||
\(309\) | 2.74972e13 | 0.555286 | ||||||||
\(310\) | −5.92966e13 | −1.17636 | ||||||||
\(311\) | −1.43460e13 | −0.279608 | −0.139804 | − | 0.990179i | \(-0.544647\pi\) | ||||
−0.139804 | + | 0.990179i | \(0.544647\pi\) | |||||||
\(312\) | 1.20567e13 | 0.230876 | ||||||||
\(313\) | −4.78260e13 | −0.899850 | −0.449925 | − | 0.893066i | \(-0.648549\pi\) | ||||
−0.449925 | + | 0.893066i | \(0.648549\pi\) | |||||||
\(314\) | −1.37605e14 | −2.54403 | ||||||||
\(315\) | −2.76498e13 | −0.502324 | ||||||||
\(316\) | 1.25317e14 | 2.23733 | ||||||||
\(317\) | 3.44196e13 | 0.603920 | 0.301960 | − | 0.953321i | \(-0.402359\pi\) | ||||
0.301960 | + | 0.953321i | \(0.402359\pi\) | |||||||
\(318\) | −8.75090e13 | −1.50905 | ||||||||
\(319\) | −5.04404e13 | −0.854929 | ||||||||
\(320\) | −9.39039e13 | −1.56444 | ||||||||
\(321\) | −2.39810e13 | −0.392725 | ||||||||
\(322\) | 2.09727e14 | 3.37635 | ||||||||
\(323\) | 5.67870e12 | 0.0898742 | ||||||||
\(324\) | 9.34404e12 | 0.145391 | ||||||||
\(325\) | −5.50636e12 | −0.0842377 | ||||||||
\(326\) | 1.99405e14 | 2.99944 | ||||||||
\(327\) | −4.07925e13 | −0.603348 | ||||||||
\(328\) | 2.50853e13 | 0.364849 | ||||||||
\(329\) | 2.10401e13 | 0.300933 | ||||||||
\(330\) | 3.76594e13 | 0.529721 | ||||||||
\(331\) | 6.96318e13 | 0.963282 | 0.481641 | − | 0.876369i | \(-0.340041\pi\) | ||||
0.481641 | + | 0.876369i | \(0.340041\pi\) | |||||||
\(332\) | −1.18346e13 | −0.161026 | ||||||||
\(333\) | −3.22341e13 | −0.431393 | ||||||||
\(334\) | 7.72810e12 | 0.101734 | ||||||||
\(335\) | −8.02117e13 | −1.03870 | ||||||||
\(336\) | 3.88532e13 | 0.494949 | ||||||||
\(337\) | −5.62053e13 | −0.704389 | −0.352195 | − | 0.935927i | \(-0.614564\pi\) | ||||
−0.352195 | + | 0.935927i | \(0.614564\pi\) | |||||||
\(338\) | 3.35477e13 | 0.413639 | ||||||||
\(339\) | 2.02723e13 | 0.245927 | ||||||||
\(340\) | 2.78494e13 | 0.332416 | ||||||||
\(341\) | −3.62299e13 | −0.425518 | ||||||||
\(342\) | −1.62506e13 | −0.187813 | ||||||||
\(343\) | −8.45354e12 | −0.0961437 | ||||||||
\(344\) | 5.07123e13 | 0.567599 | ||||||||
\(345\) | 8.49213e13 | 0.935431 | ||||||||
\(346\) | 1.22444e14 | 1.32745 | ||||||||
\(347\) | −4.96603e13 | −0.529904 | −0.264952 | − | 0.964262i | \(-0.585356\pi\) | ||||
−0.264952 | + | 0.964262i | \(0.585356\pi\) | |||||||
\(348\) | 1.06744e14 | 1.12113 | ||||||||
\(349\) | −3.32863e13 | −0.344133 | −0.172066 | − | 0.985085i | \(-0.555044\pi\) | ||||
−0.172066 | + | 0.985085i | \(0.555044\pi\) | |||||||
\(350\) | 2.11939e13 | 0.215693 | ||||||||
\(351\) | −1.63871e13 | −0.164177 | ||||||||
\(352\) | −8.02980e13 | −0.791991 | ||||||||
\(353\) | −1.82488e14 | −1.77204 | −0.886021 | − | 0.463646i | \(-0.846541\pi\) | ||||
−0.886021 | + | 0.463646i | \(0.846541\pi\) | |||||||
\(354\) | 1.19453e13 | 0.114204 | ||||||||
\(355\) | −8.33047e13 | −0.784176 | ||||||||
\(356\) | 7.49805e12 | 0.0694982 | ||||||||
\(357\) | −2.20407e13 | −0.201164 | ||||||||
\(358\) | 2.04437e14 | 1.83740 | ||||||||
\(359\) | −2.06373e14 | −1.82655 | −0.913277 | − | 0.407339i | \(-0.866457\pi\) | ||||
−0.913277 | + | 0.407339i | \(0.866457\pi\) | |||||||
\(360\) | −1.87905e13 | −0.163785 | ||||||||
\(361\) | −1.00471e14 | −0.862481 | ||||||||
\(362\) | −1.52134e14 | −1.28626 | ||||||||
\(363\) | −4.63210e13 | −0.385737 | ||||||||
\(364\) | 1.95654e14 | 1.60483 | ||||||||
\(365\) | −8.62593e13 | −0.696940 | ||||||||
\(366\) | −1.11804e14 | −0.889835 | ||||||||
\(367\) | 8.31297e13 | 0.651768 | 0.325884 | − | 0.945410i | \(-0.394338\pi\) | ||||
0.325884 | + | 0.945410i | \(0.394338\pi\) | |||||||
\(368\) | −1.19330e14 | −0.921697 | ||||||||
\(369\) | −3.40950e13 | −0.259445 | ||||||||
\(370\) | 2.74928e14 | 2.06115 | ||||||||
\(371\) | −3.34820e14 | −2.47317 | ||||||||
\(372\) | 7.66709e13 | 0.558013 | ||||||||
\(373\) | −2.44630e14 | −1.75433 | −0.877164 | − | 0.480192i | \(-0.840567\pi\) | ||||
−0.877164 | + | 0.480192i | \(0.840567\pi\) | |||||||
\(374\) | 3.00197e13 | 0.212135 | ||||||||
\(375\) | −7.83263e13 | −0.545426 | ||||||||
\(376\) | 1.42986e13 | 0.0981203 | ||||||||
\(377\) | −1.87201e14 | −1.26599 | ||||||||
\(378\) | 6.30735e13 | 0.420380 | ||||||||
\(379\) | −9.15400e13 | −0.601306 | −0.300653 | − | 0.953734i | \(-0.597205\pi\) | ||||
−0.300653 | + | 0.953734i | \(0.597205\pi\) | |||||||
\(380\) | 7.85632e13 | 0.508639 | ||||||||
\(381\) | 9.34932e13 | 0.596613 | ||||||||
\(382\) | −6.68240e13 | −0.420324 | ||||||||
\(383\) | −3.80408e13 | −0.235861 | −0.117931 | − | 0.993022i | \(-0.537626\pi\) | ||||
−0.117931 | + | 0.993022i | \(0.537626\pi\) | |||||||
\(384\) | 8.43453e13 | 0.515512 | ||||||||
\(385\) | 1.44089e14 | 0.868157 | ||||||||
\(386\) | 1.29191e14 | 0.767363 | ||||||||
\(387\) | −6.89262e13 | −0.403621 | ||||||||
\(388\) | −2.88653e14 | −1.66648 | ||||||||
\(389\) | 1.69152e14 | 0.962841 | 0.481420 | − | 0.876490i | \(-0.340121\pi\) | ||||
0.481420 | + | 0.876490i | \(0.340121\pi\) | |||||||
\(390\) | 1.39767e14 | 0.784419 | ||||||||
\(391\) | 6.76939e13 | 0.374608 | ||||||||
\(392\) | −9.16502e13 | −0.500104 | ||||||||
\(393\) | −1.03752e14 | −0.558263 | ||||||||
\(394\) | 1.40643e14 | 0.746257 | ||||||||
\(395\) | 3.42518e14 | 1.79225 | ||||||||
\(396\) | −4.86939e13 | −0.251276 | ||||||||
\(397\) | 2.92592e14 | 1.48907 | 0.744535 | − | 0.667583i | \(-0.232671\pi\) | ||||
0.744535 | + | 0.667583i | \(0.232671\pi\) | |||||||
\(398\) | −2.68397e14 | −1.34717 | ||||||||
\(399\) | −6.21769e13 | −0.307807 | ||||||||
\(400\) | −1.20589e13 | −0.0588813 | ||||||||
\(401\) | 1.76860e14 | 0.851798 | 0.425899 | − | 0.904771i | \(-0.359958\pi\) | ||||
0.425899 | + | 0.904771i | \(0.359958\pi\) | |||||||
\(402\) | 1.82975e14 | 0.869259 | ||||||||
\(403\) | −1.34461e14 | −0.630114 | ||||||||
\(404\) | 3.25345e14 | 1.50400 | ||||||||
\(405\) | 2.55393e13 | 0.116468 | ||||||||
\(406\) | 7.20534e14 | 3.24161 | ||||||||
\(407\) | 1.67979e14 | 0.745567 | ||||||||
\(408\) | −1.49786e13 | −0.0655903 | ||||||||
\(409\) | −9.26772e13 | −0.400401 | −0.200200 | − | 0.979755i | \(-0.564159\pi\) | ||||
−0.200200 | + | 0.979755i | \(0.564159\pi\) | |||||||
\(410\) | 2.90799e14 | 1.23960 | ||||||||
\(411\) | 7.43537e13 | 0.312732 | ||||||||
\(412\) | 3.03244e14 | 1.25851 | ||||||||
\(413\) | 4.57042e13 | 0.187168 | ||||||||
\(414\) | −1.93719e14 | −0.782833 | ||||||||
\(415\) | −3.23466e13 | −0.128993 | ||||||||
\(416\) | −2.98012e14 | −1.17279 | ||||||||
\(417\) | −2.33821e14 | −0.908103 | ||||||||
\(418\) | 8.46857e13 | 0.324594 | ||||||||
\(419\) | 3.72528e12 | 0.0140923 | 0.00704614 | − | 0.999975i | \(-0.497757\pi\) | ||||
0.00704614 | + | 0.999975i | \(0.497757\pi\) | |||||||
\(420\) | −3.04927e14 | −1.13848 | ||||||||
\(421\) | 4.18454e14 | 1.54204 | 0.771022 | − | 0.636809i | \(-0.219746\pi\) | ||||
0.771022 | + | 0.636809i | \(0.219746\pi\) | |||||||
\(422\) | −3.29757e14 | −1.19943 | ||||||||
\(423\) | −1.94340e13 | −0.0697736 | ||||||||
\(424\) | −2.27539e14 | −0.806388 | ||||||||
\(425\) | 6.84078e12 | 0.0239313 | ||||||||
\(426\) | 1.90031e14 | 0.656252 | ||||||||
\(427\) | −4.27774e14 | −1.45835 | ||||||||
\(428\) | −2.64466e14 | −0.890080 | ||||||||
\(429\) | 8.53966e13 | 0.283743 | ||||||||
\(430\) | 5.87877e14 | 1.92846 | ||||||||
\(431\) | −3.15215e14 | −1.02090 | −0.510448 | − | 0.859909i | \(-0.670520\pi\) | ||||
−0.510448 | + | 0.859909i | \(0.670520\pi\) | |||||||
\(432\) | −3.58875e13 | −0.114758 | ||||||||
\(433\) | −6.15459e14 | −1.94319 | −0.971596 | − | 0.236644i | \(-0.923953\pi\) | ||||
−0.971596 | + | 0.236644i | \(0.923953\pi\) | |||||||
\(434\) | 5.17538e14 | 1.61343 | ||||||||
\(435\) | 2.91753e14 | 0.898101 | ||||||||
\(436\) | −4.49866e14 | −1.36744 | ||||||||
\(437\) | 1.90965e14 | 0.573199 | ||||||||
\(438\) | 1.96771e14 | 0.583248 | ||||||||
\(439\) | −5.68329e14 | −1.66358 | −0.831792 | − | 0.555087i | \(-0.812685\pi\) | ||||
−0.831792 | + | 0.555087i | \(0.812685\pi\) | |||||||
\(440\) | 9.79213e13 | 0.283066 | ||||||||
\(441\) | 1.24567e14 | 0.355625 | ||||||||
\(442\) | 1.11413e14 | 0.314133 | ||||||||
\(443\) | −1.07083e14 | −0.298195 | −0.149097 | − | 0.988823i | \(-0.547637\pi\) | ||||
−0.149097 | + | 0.988823i | \(0.547637\pi\) | |||||||
\(444\) | −3.55483e14 | −0.977717 | ||||||||
\(445\) | 2.04938e13 | 0.0556727 | ||||||||
\(446\) | 3.50738e14 | 0.941113 | ||||||||
\(447\) | −2.84826e14 | −0.754899 | ||||||||
\(448\) | 8.19590e14 | 2.14569 | ||||||||
\(449\) | −1.43883e14 | −0.372097 | −0.186048 | − | 0.982541i | \(-0.559568\pi\) | ||||
−0.186048 | + | 0.982541i | \(0.559568\pi\) | |||||||
\(450\) | −1.95761e13 | −0.0500102 | ||||||||
\(451\) | 1.77677e14 | 0.448394 | ||||||||
\(452\) | 2.23567e14 | 0.557373 | ||||||||
\(453\) | 2.22078e14 | 0.546971 | ||||||||
\(454\) | 9.51531e14 | 2.31535 | ||||||||
\(455\) | 5.34764e14 | 1.28558 | ||||||||
\(456\) | −4.22546e13 | −0.100362 | ||||||||
\(457\) | −5.29269e14 | −1.24204 | −0.621022 | − | 0.783793i | \(-0.713282\pi\) | ||||
−0.621022 | + | 0.783793i | \(0.713282\pi\) | |||||||
\(458\) | 2.06386e14 | 0.478542 | ||||||||
\(459\) | 2.03583e13 | 0.0466414 | ||||||||
\(460\) | 9.36526e14 | 2.12008 | ||||||||
\(461\) | 3.99873e14 | 0.894473 | 0.447236 | − | 0.894416i | \(-0.352408\pi\) | ||||
0.447236 | + | 0.894416i | \(0.352408\pi\) | |||||||
\(462\) | −3.28690e14 | −0.726534 | ||||||||
\(463\) | −7.10906e14 | −1.55280 | −0.776402 | − | 0.630237i | \(-0.782958\pi\) | ||||
−0.776402 | + | 0.630237i | \(0.782958\pi\) | |||||||
\(464\) | −4.09969e14 | −0.884915 | ||||||||
\(465\) | 2.09558e14 | 0.447006 | ||||||||
\(466\) | 2.02270e14 | 0.426393 | ||||||||
\(467\) | 8.69930e13 | 0.181235 | 0.0906174 | − | 0.995886i | \(-0.471116\pi\) | ||||
0.0906174 | + | 0.995886i | \(0.471116\pi\) | |||||||
\(468\) | −1.80719e14 | −0.372093 | ||||||||
\(469\) | 7.00085e14 | 1.42462 | ||||||||
\(470\) | 1.65755e14 | 0.333371 | ||||||||
\(471\) | 4.86306e14 | 0.966707 | ||||||||
\(472\) | 3.10600e13 | 0.0610268 | ||||||||
\(473\) | 3.59190e14 | 0.697570 | ||||||||
\(474\) | −7.81335e14 | −1.49988 | ||||||||
\(475\) | 1.92979e13 | 0.0366180 | ||||||||
\(476\) | −2.43068e14 | −0.455922 | ||||||||
\(477\) | 3.09263e14 | 0.573425 | ||||||||
\(478\) | 8.54873e14 | 1.56692 | ||||||||
\(479\) | −7.89655e14 | −1.43084 | −0.715422 | − | 0.698693i | \(-0.753765\pi\) | ||||
−0.715422 | + | 0.698693i | \(0.753765\pi\) | |||||||
\(480\) | 4.64453e14 | 0.831984 | ||||||||
\(481\) | 6.23427e14 | 1.10405 | ||||||||
\(482\) | −3.01971e13 | −0.0528697 | ||||||||
\(483\) | −7.41190e14 | −1.28298 | ||||||||
\(484\) | −5.10836e14 | −0.874242 | ||||||||
\(485\) | −7.88950e14 | −1.33497 | ||||||||
\(486\) | −5.82590e13 | −0.0974683 | ||||||||
\(487\) | −6.74215e14 | −1.11529 | −0.557647 | − | 0.830078i | \(-0.688296\pi\) | ||||
−0.557647 | + | 0.830078i | \(0.688296\pi\) | |||||||
\(488\) | −2.90709e14 | −0.475500 | ||||||||
\(489\) | −7.04712e14 | −1.13976 | ||||||||
\(490\) | −1.06245e15 | −1.69914 | ||||||||
\(491\) | −5.64669e14 | −0.892988 | −0.446494 | − | 0.894787i | \(-0.647328\pi\) | ||||
−0.446494 | + | 0.894787i | \(0.647328\pi\) | |||||||
\(492\) | −3.76005e14 | −0.588012 | ||||||||
\(493\) | 2.32567e14 | 0.359659 | ||||||||
\(494\) | 3.14297e14 | 0.480664 | ||||||||
\(495\) | −1.33091e14 | −0.201289 | ||||||||
\(496\) | −2.94468e14 | −0.440443 | ||||||||
\(497\) | 7.27080e14 | 1.07553 | ||||||||
\(498\) | 7.37876e13 | 0.107950 | ||||||||
\(499\) | −4.45620e14 | −0.644780 | −0.322390 | − | 0.946607i | \(-0.604486\pi\) | ||||
−0.322390 | + | 0.946607i | \(0.604486\pi\) | |||||||
\(500\) | −8.63795e14 | −1.23616 | ||||||||
\(501\) | −2.73116e13 | −0.0386580 | ||||||||
\(502\) | −1.45080e15 | −2.03112 | ||||||||
\(503\) | 3.31592e14 | 0.459177 | 0.229588 | − | 0.973288i | \(-0.426262\pi\) | ||||
0.229588 | + | 0.973288i | \(0.426262\pi\) | |||||||
\(504\) | 1.64002e14 | 0.224638 | ||||||||
\(505\) | 8.89238e14 | 1.20480 | ||||||||
\(506\) | 1.00951e15 | 1.35295 | ||||||||
\(507\) | −1.18560e14 | −0.157179 | ||||||||
\(508\) | 1.03106e15 | 1.35217 | ||||||||
\(509\) | −4.37985e14 | −0.568214 | −0.284107 | − | 0.958793i | \(-0.591697\pi\) | ||||
−0.284107 | + | 0.958793i | \(0.591697\pi\) | |||||||
\(510\) | −1.73638e14 | −0.222848 | ||||||||
\(511\) | 7.52868e14 | 0.955881 | ||||||||
\(512\) | −8.75178e14 | −1.09929 | ||||||||
\(513\) | 5.74308e13 | 0.0713673 | ||||||||
\(514\) | −6.23407e13 | −0.0766433 | ||||||||
\(515\) | 8.28830e14 | 1.00815 | ||||||||
\(516\) | −7.60129e14 | −0.914774 | ||||||||
\(517\) | 1.01275e14 | 0.120588 | ||||||||
\(518\) | −2.39956e15 | −2.82695 | ||||||||
\(519\) | −4.32724e14 | −0.504418 | ||||||||
\(520\) | 3.63418e14 | 0.419168 | ||||||||
\(521\) | 1.25952e15 | 1.43746 | 0.718732 | − | 0.695287i | \(-0.244723\pi\) | ||||
0.718732 | + | 0.695287i | \(0.244723\pi\) | |||||||
\(522\) | −6.65534e14 | −0.751593 | ||||||||
\(523\) | −7.52673e14 | −0.841099 | −0.420550 | − | 0.907270i | \(-0.638163\pi\) | ||||
−0.420550 | + | 0.907270i | \(0.638163\pi\) | |||||||
\(524\) | −1.14420e15 | −1.26526 | ||||||||
\(525\) | −7.49006e13 | −0.0819614 | ||||||||
\(526\) | 3.63592e14 | 0.393724 | ||||||||
\(527\) | 1.67046e14 | 0.179011 | ||||||||
\(528\) | 1.87018e14 | 0.198334 | ||||||||
\(529\) | 1.32362e15 | 1.38917 | ||||||||
\(530\) | −2.63773e15 | −2.73976 | ||||||||
\(531\) | −4.22156e13 | −0.0433963 | ||||||||
\(532\) | −6.85697e14 | −0.697619 | ||||||||
\(533\) | 6.59417e14 | 0.663989 | ||||||||
\(534\) | −4.67495e13 | −0.0465908 | ||||||||
\(535\) | −7.22843e14 | −0.713014 | ||||||||
\(536\) | 4.75769e14 | 0.464504 | ||||||||
\(537\) | −7.22495e14 | −0.698194 | ||||||||
\(538\) | 4.37543e14 | 0.418522 | ||||||||
\(539\) | −6.49149e14 | −0.614619 | ||||||||
\(540\) | 2.81651e14 | 0.263965 | ||||||||
\(541\) | −1.77185e15 | −1.64378 | −0.821888 | − | 0.569649i | \(-0.807079\pi\) | ||||
−0.821888 | + | 0.569649i | \(0.807079\pi\) | |||||||
\(542\) | 1.88283e15 | 1.72908 | ||||||||
\(543\) | 5.37651e14 | 0.488766 | ||||||||
\(544\) | 3.70233e14 | 0.333181 | ||||||||
\(545\) | −1.22958e15 | −1.09541 | ||||||||
\(546\) | −1.21988e15 | −1.07586 | ||||||||
\(547\) | 5.08668e14 | 0.444124 | 0.222062 | − | 0.975033i | \(-0.428721\pi\) | ||||
0.222062 | + | 0.975033i | \(0.428721\pi\) | |||||||
\(548\) | 8.19985e14 | 0.708782 | ||||||||
\(549\) | 3.95121e14 | 0.338129 | ||||||||
\(550\) | 1.02016e14 | 0.0864315 | ||||||||
\(551\) | 6.56074e14 | 0.550324 | ||||||||
\(552\) | −5.03703e14 | −0.418321 | ||||||||
\(553\) | −2.98948e15 | −2.45815 | ||||||||
\(554\) | 9.75254e14 | 0.793988 | ||||||||
\(555\) | −9.71613e14 | −0.783217 | ||||||||
\(556\) | −2.57862e15 | −2.05814 | ||||||||
\(557\) | 5.44481e14 | 0.430307 | 0.215154 | − | 0.976580i | \(-0.430975\pi\) | ||||
0.215154 | + | 0.976580i | \(0.430975\pi\) | |||||||
\(558\) | −4.78034e14 | −0.374085 | ||||||||
\(559\) | 1.33307e15 | 1.03297 | ||||||||
\(560\) | 1.17113e15 | 0.898607 | ||||||||
\(561\) | −1.06092e14 | −0.0806094 | ||||||||
\(562\) | −1.46146e15 | −1.09961 | ||||||||
\(563\) | −1.32189e15 | −0.984919 | −0.492459 | − | 0.870335i | \(-0.663902\pi\) | ||||
−0.492459 | + | 0.870335i | \(0.663902\pi\) | |||||||
\(564\) | −2.14322e14 | −0.158136 | ||||||||
\(565\) | 6.11056e14 | 0.446493 | ||||||||
\(566\) | 1.07125e15 | 0.775177 | ||||||||
\(567\) | −2.22906e14 | −0.159740 | ||||||||
\(568\) | 4.94114e14 | 0.350680 | ||||||||
\(569\) | 1.85007e15 | 1.30038 | 0.650191 | − | 0.759771i | \(-0.274689\pi\) | ||||
0.650191 | + | 0.759771i | \(0.274689\pi\) | |||||||
\(570\) | −4.89832e14 | −0.340985 | ||||||||
\(571\) | −1.66054e15 | −1.14486 | −0.572429 | − | 0.819954i | \(-0.693999\pi\) | ||||
−0.572429 | + | 0.819954i | \(0.693999\pi\) | |||||||
\(572\) | 9.41768e14 | 0.643081 | ||||||||
\(573\) | 2.36161e14 | 0.159719 | ||||||||
\(574\) | −2.53809e15 | −1.70016 | ||||||||
\(575\) | 2.30043e14 | 0.152629 | ||||||||
\(576\) | −7.57029e14 | −0.497495 | ||||||||
\(577\) | 2.32812e15 | 1.51544 | 0.757721 | − | 0.652579i | \(-0.226313\pi\) | ||||
0.757721 | + | 0.652579i | \(0.226313\pi\) | |||||||
\(578\) | 2.21810e15 | 1.43014 | ||||||||
\(579\) | −4.56568e14 | −0.291591 | ||||||||
\(580\) | 3.21751e15 | 2.03547 | ||||||||
\(581\) | 2.82320e14 | 0.176919 | ||||||||
\(582\) | 1.79972e15 | 1.11719 | ||||||||
\(583\) | −1.61164e15 | −0.991038 | ||||||||
\(584\) | 5.11640e14 | 0.311669 | ||||||||
\(585\) | −4.93944e14 | −0.298072 | ||||||||
\(586\) | −4.79517e15 | −2.86660 | ||||||||
\(587\) | 1.56510e15 | 0.926898 | 0.463449 | − | 0.886124i | \(-0.346612\pi\) | ||||
0.463449 | + | 0.886124i | \(0.346612\pi\) | |||||||
\(588\) | 1.37375e15 | 0.805995 | ||||||||
\(589\) | 4.71238e14 | 0.273909 | ||||||||
\(590\) | 3.60060e14 | 0.207343 | ||||||||
\(591\) | −4.97041e14 | −0.283571 | ||||||||
\(592\) | 1.36530e15 | 0.771718 | ||||||||
\(593\) | −5.65084e14 | −0.316455 | −0.158227 | − | 0.987403i | \(-0.550578\pi\) | ||||
−0.158227 | + | 0.987403i | \(0.550578\pi\) | |||||||
\(594\) | 3.03601e14 | 0.168452 | ||||||||
\(595\) | −6.64358e14 | −0.365224 | ||||||||
\(596\) | −3.14111e15 | −1.71092 | ||||||||
\(597\) | 9.48533e14 | 0.511910 | ||||||||
\(598\) | 3.74663e15 | 2.00348 | ||||||||
\(599\) | 1.21451e15 | 0.643507 | 0.321753 | − | 0.946824i | \(-0.395728\pi\) | ||||
0.321753 | + | 0.946824i | \(0.395728\pi\) | |||||||
\(600\) | −5.09015e13 | −0.0267238 | ||||||||
\(601\) | −1.08552e15 | −0.564716 | −0.282358 | − | 0.959309i | \(-0.591117\pi\) | ||||
−0.282358 | + | 0.959309i | \(0.591117\pi\) | |||||||
\(602\) | −5.13097e15 | −2.64496 | ||||||||
\(603\) | −6.46647e14 | −0.330310 | ||||||||
\(604\) | 2.44911e15 | 1.23967 | ||||||||
\(605\) | −1.39622e15 | −0.700327 | ||||||||
\(606\) | −2.02849e15 | −1.00826 | ||||||||
\(607\) | −1.50458e15 | −0.741102 | −0.370551 | − | 0.928812i | \(-0.620831\pi\) | ||||
−0.370551 | + | 0.928812i | \(0.620831\pi\) | |||||||
\(608\) | 1.04443e15 | 0.509810 | ||||||||
\(609\) | −2.54641e15 | −1.23178 | ||||||||
\(610\) | −3.37002e15 | −1.61554 | ||||||||
\(611\) | 3.75866e14 | 0.178569 | ||||||||
\(612\) | 2.24515e14 | 0.105709 | ||||||||
\(613\) | −7.91295e14 | −0.369237 | −0.184619 | − | 0.982810i | \(-0.559105\pi\) | ||||
−0.184619 | + | 0.982810i | \(0.559105\pi\) | |||||||
\(614\) | 5.90684e14 | 0.273168 | ||||||||
\(615\) | −1.02770e15 | −0.471037 | ||||||||
\(616\) | −8.54654e14 | −0.388236 | ||||||||
\(617\) | 1.66604e15 | 0.750096 | 0.375048 | − | 0.927005i | \(-0.377626\pi\) | ||||
0.375048 | + | 0.927005i | \(0.377626\pi\) | |||||||
\(618\) | −1.89069e15 | −0.843691 | ||||||||
\(619\) | 3.78034e15 | 1.67198 | 0.835992 | − | 0.548741i | \(-0.184893\pi\) | ||||
0.835992 | + | 0.548741i | \(0.184893\pi\) | |||||||
\(620\) | 2.31104e15 | 1.01310 | ||||||||
\(621\) | 6.84614e14 | 0.297469 | ||||||||
\(622\) | 9.86422e14 | 0.424830 | ||||||||
\(623\) | −1.78869e14 | −0.0763574 | ||||||||
\(624\) | 6.94085e14 | 0.293696 | ||||||||
\(625\) | −2.59636e15 | −1.08899 | ||||||||
\(626\) | 3.28848e15 | 1.36721 | ||||||||
\(627\) | −2.99285e14 | −0.123343 | ||||||||
\(628\) | 5.36306e15 | 2.19096 | ||||||||
\(629\) | −7.74508e14 | −0.313652 | ||||||||
\(630\) | 1.90118e15 | 0.763222 | ||||||||
\(631\) | −9.43582e14 | −0.375507 | −0.187753 | − | 0.982216i | \(-0.560121\pi\) | ||||
−0.187753 | + | 0.982216i | \(0.560121\pi\) | |||||||
\(632\) | −2.03161e15 | −0.801488 | ||||||||
\(633\) | 1.16538e15 | 0.455773 | ||||||||
\(634\) | −2.36667e15 | −0.917585 | ||||||||
\(635\) | 2.81810e15 | 1.08318 | ||||||||
\(636\) | 3.41060e15 | 1.29962 | ||||||||
\(637\) | −2.40921e15 | −0.910138 | ||||||||
\(638\) | 3.46825e15 | 1.29896 | ||||||||
\(639\) | −6.71581e14 | −0.249370 | ||||||||
\(640\) | 2.54237e15 | 0.935940 | ||||||||
\(641\) | 1.91334e15 | 0.698350 | 0.349175 | − | 0.937058i | \(-0.386462\pi\) | ||||
0.349175 | + | 0.937058i | \(0.386462\pi\) | |||||||
\(642\) | 1.64891e15 | 0.596699 | ||||||||
\(643\) | 1.55238e15 | 0.556977 | 0.278489 | − | 0.960440i | \(-0.410167\pi\) | ||||
0.278489 | + | 0.960440i | \(0.410167\pi\) | |||||||
\(644\) | −8.17397e15 | −2.90777 | ||||||||
\(645\) | −2.07760e15 | −0.732795 | ||||||||
\(646\) | −3.90463e14 | −0.136553 | ||||||||
\(647\) | −1.34109e15 | −0.465034 | −0.232517 | − | 0.972592i | \(-0.574696\pi\) | ||||
−0.232517 | + | 0.972592i | \(0.574696\pi\) | |||||||
\(648\) | −1.51484e14 | −0.0520840 | ||||||||
\(649\) | 2.19995e14 | 0.0750009 | ||||||||
\(650\) | 3.78614e14 | 0.127989 | ||||||||
\(651\) | −1.82901e15 | −0.613086 | ||||||||
\(652\) | −7.77168e15 | −2.58317 | ||||||||
\(653\) | −1.19942e15 | −0.395319 | −0.197659 | − | 0.980271i | \(-0.563334\pi\) | ||||
−0.197659 | + | 0.980271i | \(0.563334\pi\) | |||||||
\(654\) | 2.80486e15 | 0.916715 | ||||||||
\(655\) | −3.12734e15 | −1.01356 | ||||||||
\(656\) | 1.44412e15 | 0.464121 | ||||||||
\(657\) | −6.95401e14 | −0.221629 | ||||||||
\(658\) | −1.44670e15 | −0.457231 | ||||||||
\(659\) | −4.29128e15 | −1.34498 | −0.672492 | − | 0.740104i | \(-0.734776\pi\) | ||||
−0.672492 | + | 0.740104i | \(0.734776\pi\) | |||||||
\(660\) | −1.46775e15 | −0.456205 | ||||||||
\(661\) | 2.71996e15 | 0.838406 | 0.419203 | − | 0.907893i | \(-0.362310\pi\) | ||||
0.419203 | + | 0.907893i | \(0.362310\pi\) | |||||||
\(662\) | −4.78783e15 | −1.46359 | ||||||||
\(663\) | −3.93741e14 | −0.119368 | ||||||||
\(664\) | 1.91861e14 | 0.0576850 | ||||||||
\(665\) | −1.87416e15 | −0.558839 | ||||||||
\(666\) | 2.21640e15 | 0.655450 | ||||||||
\(667\) | 7.82084e15 | 2.29383 | ||||||||
\(668\) | −3.01197e14 | −0.0876153 | ||||||||
\(669\) | −1.23953e15 | −0.357614 | ||||||||
\(670\) | 5.51530e15 | 1.57819 | ||||||||
\(671\) | −2.05907e15 | −0.584381 | ||||||||
\(672\) | −4.05373e15 | −1.14110 | ||||||||
\(673\) | 4.33839e15 | 1.21128 | 0.605641 | − | 0.795738i | \(-0.292917\pi\) | ||||
0.605641 | + | 0.795738i | \(0.292917\pi\) | |||||||
\(674\) | 3.86464e15 | 1.07024 | ||||||||
\(675\) | 6.91834e13 | 0.0190034 | ||||||||
\(676\) | −1.30750e15 | −0.356233 | ||||||||
\(677\) | −4.29274e15 | −1.16010 | −0.580052 | − | 0.814580i | \(-0.696968\pi\) | ||||
−0.580052 | + | 0.814580i | \(0.696968\pi\) | |||||||
\(678\) | −1.39391e15 | −0.373656 | ||||||||
\(679\) | 6.88593e15 | 1.83096 | ||||||||
\(680\) | −4.51489e14 | −0.119083 | ||||||||
\(681\) | −3.36277e15 | −0.879809 | ||||||||
\(682\) | 2.49114e15 | 0.646524 | ||||||||
\(683\) | 1.80140e15 | 0.463763 | 0.231881 | − | 0.972744i | \(-0.425512\pi\) | ||||
0.231881 | + | 0.972744i | \(0.425512\pi\) | |||||||
\(684\) | 6.33356e14 | 0.161748 | ||||||||
\(685\) | 2.24119e15 | 0.567782 | ||||||||
\(686\) | 5.81260e14 | 0.146079 | ||||||||
\(687\) | −7.29382e14 | −0.181841 | ||||||||
\(688\) | 2.91941e15 | 0.722037 | ||||||||
\(689\) | −5.98132e15 | −1.46754 | ||||||||
\(690\) | −5.83913e15 | −1.42128 | ||||||||
\(691\) | 5.96668e15 | 1.44080 | 0.720399 | − | 0.693560i | \(-0.243959\pi\) | ||||
0.720399 | + | 0.693560i | \(0.243959\pi\) | |||||||
\(692\) | −4.77215e15 | −1.14322 | ||||||||
\(693\) | 1.16161e15 | 0.276076 | ||||||||
\(694\) | 3.41461e15 | 0.805126 | ||||||||
\(695\) | −7.04791e15 | −1.64871 | ||||||||
\(696\) | −1.73051e15 | −0.401627 | ||||||||
\(697\) | −8.19221e14 | −0.188634 | ||||||||
\(698\) | 2.28875e15 | 0.522869 | ||||||||
\(699\) | −7.14837e14 | −0.162025 | ||||||||
\(700\) | −8.26016e14 | −0.185759 | ||||||||
\(701\) | −4.27057e15 | −0.952876 | −0.476438 | − | 0.879208i | \(-0.658072\pi\) | ||||
−0.476438 | + | 0.879208i | \(0.658072\pi\) | |||||||
\(702\) | 1.12676e15 | 0.249447 | ||||||||
\(703\) | −2.18489e15 | −0.479927 | ||||||||
\(704\) | 3.94505e15 | 0.859811 | ||||||||
\(705\) | −5.85788e14 | −0.126678 | ||||||||
\(706\) | 1.25478e16 | 2.69241 | ||||||||
\(707\) | −7.76124e15 | −1.65244 | ||||||||
\(708\) | −4.65560e14 | −0.0983542 | ||||||||
\(709\) | 6.74401e15 | 1.41372 | 0.706861 | − | 0.707353i | \(-0.250111\pi\) | ||||
0.706861 | + | 0.707353i | \(0.250111\pi\) | |||||||
\(710\) | 5.72797e15 | 1.19146 | ||||||||
\(711\) | 2.76129e15 | 0.569940 | ||||||||
\(712\) | −1.21557e14 | −0.0248966 | ||||||||
\(713\) | 5.61748e15 | 1.14169 | ||||||||
\(714\) | 1.51550e15 | 0.305644 | ||||||||
\(715\) | 2.57406e15 | 0.515151 | ||||||||
\(716\) | −7.96780e15 | −1.58240 | ||||||||
\(717\) | −3.02118e15 | −0.595416 | ||||||||
\(718\) | 1.41900e16 | 2.77523 | ||||||||
\(719\) | 6.94235e15 | 1.34740 | 0.673702 | − | 0.739003i | \(-0.264703\pi\) | ||||
0.673702 | + | 0.739003i | \(0.264703\pi\) | |||||||
\(720\) | −1.08173e15 | −0.208349 | ||||||||
\(721\) | −7.23400e15 | −1.38272 | ||||||||
\(722\) | 6.90829e15 | 1.31044 | ||||||||
\(723\) | 1.06719e14 | 0.0200900 | ||||||||
\(724\) | 5.92930e15 | 1.10775 | ||||||||
\(725\) | 7.90331e14 | 0.146538 | ||||||||
\(726\) | 3.18500e15 | 0.586082 | ||||||||
\(727\) | −1.32393e15 | −0.241783 | −0.120892 | − | 0.992666i | \(-0.538575\pi\) | ||||
−0.120892 | + | 0.992666i | \(0.538575\pi\) | |||||||
\(728\) | −3.17190e15 | −0.574906 | ||||||||
\(729\) | 2.05891e14 | 0.0370370 | ||||||||
\(730\) | 5.93113e15 | 1.05892 | ||||||||
\(731\) | −1.65613e15 | −0.293460 | ||||||||
\(732\) | 4.35746e15 | 0.766342 | ||||||||
\(733\) | 6.09764e15 | 1.06436 | 0.532182 | − | 0.846630i | \(-0.321372\pi\) | ||||
0.532182 | + | 0.846630i | \(0.321372\pi\) | |||||||
\(734\) | −5.71594e15 | −0.990283 | ||||||||
\(735\) | 3.75476e15 | 0.645656 | ||||||||
\(736\) | 1.24503e16 | 2.12496 | ||||||||
\(737\) | 3.36982e15 | 0.570868 | ||||||||
\(738\) | 2.34435e15 | 0.394196 | ||||||||
\(739\) | 3.04358e15 | 0.507972 | 0.253986 | − | 0.967208i | \(-0.418258\pi\) | ||||
0.253986 | + | 0.967208i | \(0.418258\pi\) | |||||||
\(740\) | −1.07151e16 | −1.77510 | ||||||||
\(741\) | −1.11075e15 | −0.182648 | ||||||||
\(742\) | 2.30220e16 | 3.75769 | ||||||||
\(743\) | −1.38530e15 | −0.224442 | −0.112221 | − | 0.993683i | \(-0.535796\pi\) | ||||
−0.112221 | + | 0.993683i | \(0.535796\pi\) | |||||||
\(744\) | −1.24297e15 | −0.199899 | ||||||||
\(745\) | −8.58533e15 | −1.37056 | ||||||||
\(746\) | 1.68206e16 | 2.66549 | ||||||||
\(747\) | −2.60770e14 | −0.0410199 | ||||||||
\(748\) | −1.17000e15 | −0.182695 | ||||||||
\(749\) | 6.30894e15 | 0.977927 | ||||||||
\(750\) | 5.38566e15 | 0.828709 | ||||||||
\(751\) | −3.49866e15 | −0.534419 | −0.267209 | − | 0.963638i | \(-0.586102\pi\) | ||||
−0.267209 | + | 0.963638i | \(0.586102\pi\) | |||||||
\(752\) | 8.23142e14 | 0.124818 | ||||||||
\(753\) | 5.12721e15 | 0.771808 | ||||||||
\(754\) | 1.28718e16 | 1.92352 | ||||||||
\(755\) | 6.69394e15 | 0.993056 | ||||||||
\(756\) | −2.45824e15 | −0.362039 | ||||||||
\(757\) | 7.88002e15 | 1.15213 | 0.576063 | − | 0.817405i | \(-0.304588\pi\) | ||||
0.576063 | + | 0.817405i | \(0.304588\pi\) | |||||||
\(758\) | 6.29423e15 | 0.913612 | ||||||||
\(759\) | −3.56768e15 | −0.514110 | ||||||||
\(760\) | −1.27365e15 | −0.182212 | ||||||||
\(761\) | 8.78969e15 | 1.24841 | 0.624206 | − | 0.781260i | \(-0.285422\pi\) | ||||
0.624206 | + | 0.781260i | \(0.285422\pi\) | |||||||
\(762\) | −6.42853e15 | −0.906482 | ||||||||
\(763\) | 1.07317e16 | 1.50240 | ||||||||
\(764\) | 2.60442e15 | 0.361990 | ||||||||
\(765\) | 6.13647e14 | 0.0846800 | ||||||||
\(766\) | 2.61566e15 | 0.358363 | ||||||||
\(767\) | 8.16474e14 | 0.111063 | ||||||||
\(768\) | 5.80707e14 | 0.0784279 | ||||||||
\(769\) | −6.36504e15 | −0.853505 | −0.426752 | − | 0.904369i | \(-0.640342\pi\) | ||||
−0.426752 | + | 0.904369i | \(0.640342\pi\) | |||||||
\(770\) | −9.90749e15 | −1.31906 | ||||||||
\(771\) | 2.20316e14 | 0.0291237 | ||||||||
\(772\) | −5.03511e15 | −0.660866 | ||||||||
\(773\) | −7.57190e15 | −0.986774 | −0.493387 | − | 0.869810i | \(-0.664241\pi\) | ||||
−0.493387 | + | 0.869810i | \(0.664241\pi\) | |||||||
\(774\) | 4.73932e15 | 0.613254 | ||||||||
\(775\) | 5.67672e14 | 0.0729353 | ||||||||
\(776\) | 4.67959e15 | 0.596991 | ||||||||
\(777\) | 8.48020e15 | 1.07421 | ||||||||
\(778\) | −1.16308e16 | −1.46292 | ||||||||
\(779\) | −2.31102e15 | −0.288635 | ||||||||
\(780\) | −5.44730e15 | −0.675555 | ||||||||
\(781\) | 3.49976e15 | 0.430981 | ||||||||
\(782\) | −4.65459e15 | −0.569173 | ||||||||
\(783\) | 2.35204e15 | 0.285598 | ||||||||
\(784\) | −5.27614e15 | −0.636177 | ||||||||
\(785\) | 1.46584e16 | 1.75511 | ||||||||
\(786\) | 7.13393e15 | 0.848213 | ||||||||
\(787\) | −1.79619e14 | −0.0212075 | −0.0106038 | − | 0.999944i | \(-0.503375\pi\) | ||||
−0.0106038 | + | 0.999944i | \(0.503375\pi\) | |||||||
\(788\) | −5.48145e15 | −0.642690 | ||||||||
\(789\) | −1.28496e15 | −0.149612 | ||||||||
\(790\) | −2.35513e16 | −2.72311 | ||||||||
\(791\) | −5.33328e15 | −0.612383 | ||||||||
\(792\) | 7.89417e14 | 0.0900156 | ||||||||
\(793\) | −7.64187e15 | −0.865361 | ||||||||
\(794\) | −2.01185e16 | −2.26246 | ||||||||
\(795\) | 9.32190e15 | 1.04108 | ||||||||
\(796\) | 1.04606e16 | 1.16020 | ||||||||
\(797\) | 1.68156e15 | 0.185221 | 0.0926106 | − | 0.995702i | \(-0.470479\pi\) | ||||
0.0926106 | + | 0.995702i | \(0.470479\pi\) | |||||||
\(798\) | 4.27524e15 | 0.467675 | ||||||||
\(799\) | −4.66953e14 | −0.0507301 | ||||||||
\(800\) | 1.25816e15 | 0.135750 | ||||||||
\(801\) | 1.65216e14 | 0.0177040 | ||||||||
\(802\) | −1.21608e16 | −1.29420 | ||||||||
\(803\) | 3.62389e15 | 0.383036 | ||||||||
\(804\) | −7.13133e15 | −0.748621 | ||||||||
\(805\) | −2.23412e16 | −2.32932 | ||||||||
\(806\) | 9.24545e15 | 0.957382 | ||||||||
\(807\) | −1.54631e15 | −0.159034 | ||||||||
\(808\) | −5.27444e15 | −0.538783 | ||||||||
\(809\) | −6.94771e15 | −0.704896 | −0.352448 | − | 0.935831i | \(-0.614651\pi\) | ||||
−0.352448 | + | 0.935831i | \(0.614651\pi\) | |||||||
\(810\) | −1.75606e15 | −0.176959 | ||||||||
\(811\) | −5.93624e15 | −0.594151 | −0.297076 | − | 0.954854i | \(-0.596011\pi\) | ||||
−0.297076 | + | 0.954854i | \(0.596011\pi\) | |||||||
\(812\) | −2.80823e16 | −2.79173 | ||||||||
\(813\) | −6.65405e15 | −0.657034 | ||||||||
\(814\) | −1.15502e16 | −1.13280 | ||||||||
\(815\) | −2.12417e16 | −2.06929 | ||||||||
\(816\) | −8.62289e14 | −0.0834367 | ||||||||
\(817\) | −4.67194e15 | −0.449031 | ||||||||
\(818\) | 6.37242e15 | 0.608361 | ||||||||
\(819\) | 4.31113e15 | 0.408818 | ||||||||
\(820\) | −1.13337e16 | −1.06757 | ||||||||
\(821\) | 1.57327e16 | 1.47203 | 0.736015 | − | 0.676965i | \(-0.236705\pi\) | ||||
0.736015 | + | 0.676965i | \(0.236705\pi\) | |||||||
\(822\) | −5.11251e15 | −0.475159 | ||||||||
\(823\) | −1.40061e16 | −1.29306 | −0.646528 | − | 0.762890i | \(-0.723780\pi\) | ||||
−0.646528 | + | 0.762890i | \(0.723780\pi\) | |||||||
\(824\) | −4.91613e15 | −0.450842 | ||||||||
\(825\) | −3.60530e14 | −0.0328432 | ||||||||
\(826\) | −3.14259e15 | −0.284379 | ||||||||
\(827\) | 7.21399e15 | 0.648478 | 0.324239 | − | 0.945975i | \(-0.394892\pi\) | ||||
0.324239 | + | 0.945975i | \(0.394892\pi\) | |||||||
\(828\) | 7.55004e15 | 0.674190 | ||||||||
\(829\) | 1.09885e16 | 0.974739 | 0.487369 | − | 0.873196i | \(-0.337957\pi\) | ||||
0.487369 | + | 0.873196i | \(0.337957\pi\) | |||||||
\(830\) | 2.22413e15 | 0.195989 | ||||||||
\(831\) | −3.44661e15 | −0.301708 | ||||||||
\(832\) | 1.46414e16 | 1.27322 | ||||||||
\(833\) | 2.99305e15 | 0.258563 | ||||||||
\(834\) | 1.60774e16 | 1.37975 | ||||||||
\(835\) | −8.23236e14 | −0.0701857 | ||||||||
\(836\) | −3.30056e15 | −0.279546 | ||||||||
\(837\) | 1.68940e15 | 0.142149 | ||||||||
\(838\) | −2.56148e14 | −0.0214116 | ||||||||
\(839\) | −1.66430e16 | −1.38210 | −0.691051 | − | 0.722806i | \(-0.742852\pi\) | ||||
−0.691051 | + | 0.722806i | \(0.742852\pi\) | |||||||
\(840\) | 4.94342e15 | 0.407841 | ||||||||
\(841\) | 1.46686e16 | 1.20229 | ||||||||
\(842\) | −2.87726e16 | −2.34295 | ||||||||
\(843\) | 5.16491e15 | 0.417841 | ||||||||
\(844\) | 1.28520e16 | 1.03297 | ||||||||
\(845\) | −3.57367e15 | −0.285366 | ||||||||
\(846\) | 1.33627e15 | 0.106013 | ||||||||
\(847\) | 1.21862e16 | 0.960527 | ||||||||
\(848\) | −1.30990e16 | −1.02580 | ||||||||
\(849\) | −3.78587e15 | −0.294560 | ||||||||
\(850\) | −4.70367e14 | −0.0363608 | ||||||||
\(851\) | −2.60454e16 | −2.00041 | ||||||||
\(852\) | −7.40631e15 | −0.565176 | ||||||||
\(853\) | −2.43050e16 | −1.84279 | −0.921394 | − | 0.388630i | \(-0.872948\pi\) | ||||
−0.921394 | + | 0.388630i | \(0.872948\pi\) | |||||||
\(854\) | 2.94134e16 | 2.21578 | ||||||||
\(855\) | 1.73110e15 | 0.129571 | ||||||||
\(856\) | 4.28748e15 | 0.318857 | ||||||||
\(857\) | −1.40484e15 | −0.103808 | −0.0519042 | − | 0.998652i | \(-0.516529\pi\) | ||||
−0.0519042 | + | 0.998652i | \(0.516529\pi\) | |||||||
\(858\) | −5.87182e15 | −0.431114 | ||||||||
\(859\) | −9.01491e15 | −0.657656 | −0.328828 | − | 0.944390i | \(-0.606654\pi\) | ||||
−0.328828 | + | 0.944390i | \(0.606654\pi\) | |||||||
\(860\) | −2.29121e16 | −1.66082 | ||||||||
\(861\) | 8.96976e15 | 0.646046 | ||||||||
\(862\) | 2.16739e16 | 1.55113 | ||||||||
\(863\) | −1.45313e16 | −1.03334 | −0.516672 | − | 0.856183i | \(-0.672829\pi\) | ||||
−0.516672 | + | 0.856183i | \(0.672829\pi\) | |||||||
\(864\) | 3.74430e15 | 0.264573 | ||||||||
\(865\) | −1.30433e16 | −0.915797 | ||||||||
\(866\) | 4.23186e16 | 2.95245 | ||||||||
\(867\) | −7.83891e15 | −0.543439 | ||||||||
\(868\) | −2.01707e16 | −1.38951 | ||||||||
\(869\) | −1.43897e16 | −0.985016 | ||||||||
\(870\) | −2.00608e16 | −1.36456 | ||||||||
\(871\) | 1.25065e16 | 0.845350 | ||||||||
\(872\) | 7.29315e15 | 0.489863 | ||||||||
\(873\) | −6.36032e15 | −0.424522 | ||||||||
\(874\) | −1.31306e16 | −0.870907 | ||||||||
\(875\) | 2.06062e16 | 1.35817 | ||||||||
\(876\) | −7.66899e15 | −0.502303 | ||||||||
\(877\) | −1.53984e16 | −1.00225 | −0.501127 | − | 0.865374i | \(-0.667081\pi\) | ||||
−0.501127 | + | 0.865374i | \(0.667081\pi\) | |||||||
\(878\) | 3.90779e16 | 2.52762 | ||||||||
\(879\) | 1.69464e16 | 1.08928 | ||||||||
\(880\) | 5.63716e15 | 0.360085 | ||||||||
\(881\) | −7.14900e15 | −0.453814 | −0.226907 | − | 0.973916i | \(-0.572861\pi\) | ||||
−0.226907 | + | 0.973916i | \(0.572861\pi\) | |||||||
\(882\) | −8.56517e15 | −0.540330 | ||||||||
\(883\) | −2.60603e16 | −1.63379 | −0.816893 | − | 0.576789i | \(-0.804305\pi\) | ||||
−0.816893 | + | 0.576789i | \(0.804305\pi\) | |||||||
\(884\) | −4.34224e15 | −0.270537 | ||||||||
\(885\) | −1.27248e15 | −0.0787883 | ||||||||
\(886\) | 7.36296e15 | 0.453072 | ||||||||
\(887\) | −1.95473e16 | −1.19538 | −0.597690 | − | 0.801727i | \(-0.703915\pi\) | ||||
−0.597690 | + | 0.801727i | \(0.703915\pi\) | |||||||
\(888\) | 5.76304e15 | 0.350251 | ||||||||
\(889\) | −2.45963e16 | −1.48563 | ||||||||
\(890\) | −1.40914e15 | −0.0845880 | ||||||||
\(891\) | −1.07295e15 | −0.0640103 | ||||||||
\(892\) | −1.36698e16 | −0.810503 | ||||||||
\(893\) | −1.31728e15 | −0.0776236 | ||||||||
\(894\) | 1.95845e16 | 1.14698 | ||||||||
\(895\) | −2.17777e16 | −1.26761 | ||||||||
\(896\) | −2.21897e16 | −1.28368 | ||||||||
\(897\) | −1.32408e16 | −0.761302 | ||||||||
\(898\) | 9.89332e15 | 0.565356 | ||||||||
\(899\) | 1.92993e16 | 1.09613 | ||||||||
\(900\) | 7.62966e14 | 0.0430696 | ||||||||
\(901\) | 7.43083e15 | 0.416918 | ||||||||
\(902\) | −1.22169e16 | −0.681281 | ||||||||
\(903\) | 1.81332e16 | 1.00506 | ||||||||
\(904\) | −3.62443e15 | −0.199670 | ||||||||
\(905\) | 1.62061e16 | 0.887381 | ||||||||
\(906\) | −1.52699e16 | −0.831058 | ||||||||
\(907\) | −8.30930e15 | −0.449495 | −0.224747 | − | 0.974417i | \(-0.572156\pi\) | ||||
−0.224747 | + | 0.974417i | \(0.572156\pi\) | |||||||
\(908\) | −3.70852e16 | −1.99402 | ||||||||
\(909\) | 7.16882e15 | 0.383130 | ||||||||
\(910\) | −3.67700e16 | −1.95329 | ||||||||
\(911\) | 1.50691e16 | 0.795675 | 0.397837 | − | 0.917456i | \(-0.369761\pi\) | ||||
0.397837 | + | 0.917456i | \(0.369761\pi\) | |||||||
\(912\) | −2.43252e15 | −0.127669 | ||||||||
\(913\) | 1.35893e15 | 0.0708939 | ||||||||
\(914\) | 3.63922e16 | 1.88714 | ||||||||
\(915\) | 1.19099e16 | 0.613891 | ||||||||
\(916\) | −8.04374e15 | −0.412129 | ||||||||
\(917\) | 2.72953e16 | 1.39013 | ||||||||
\(918\) | −1.39982e15 | −0.0708660 | ||||||||
\(919\) | 1.38543e16 | 0.697188 | 0.348594 | − | 0.937274i | \(-0.386659\pi\) | ||||
0.348594 | + | 0.937274i | \(0.386659\pi\) | |||||||
\(920\) | −1.51828e16 | −0.759484 | ||||||||
\(921\) | −2.08752e15 | −0.103801 | ||||||||
\(922\) | −2.74950e16 | −1.35904 | ||||||||
\(923\) | 1.29888e16 | 0.638203 | ||||||||
\(924\) | 1.28105e16 | 0.625704 | ||||||||
\(925\) | −2.63200e15 | −0.127793 | ||||||||
\(926\) | 4.88814e16 | 2.35930 | ||||||||
\(927\) | 6.68182e15 | 0.320595 | ||||||||
\(928\) | 4.27739e16 | 2.04016 | ||||||||
\(929\) | −3.12674e16 | −1.48254 | −0.741269 | − | 0.671208i | \(-0.765776\pi\) | ||||
−0.741269 | + | 0.671208i | \(0.765776\pi\) | |||||||
\(930\) | −1.44091e16 | −0.679172 | ||||||||
\(931\) | 8.44342e15 | 0.395635 | ||||||||
\(932\) | −7.88334e15 | −0.367217 | ||||||||
\(933\) | −3.48608e15 | −0.161432 | ||||||||
\(934\) | −5.98158e15 | −0.275365 | ||||||||
\(935\) | −3.19785e15 | −0.146351 | ||||||||
\(936\) | 2.92979e15 | 0.133297 | ||||||||
\(937\) | −3.08797e16 | −1.39671 | −0.698354 | − | 0.715753i | \(-0.746084\pi\) | ||||
−0.698354 | + | 0.715753i | \(0.746084\pi\) | |||||||
\(938\) | −4.81374e16 | −2.16455 | ||||||||
\(939\) | −1.16217e16 | −0.519529 | ||||||||
\(940\) | −6.46016e15 | −0.287105 | ||||||||
\(941\) | 1.21992e16 | 0.538999 | 0.269499 | − | 0.963001i | \(-0.413142\pi\) | ||||
0.269499 | + | 0.963001i | \(0.413142\pi\) | |||||||
\(942\) | −3.34381e16 | −1.46880 | ||||||||
\(943\) | −2.75490e16 | −1.20307 | ||||||||
\(944\) | 1.78807e15 | 0.0776316 | ||||||||
\(945\) | −6.71891e15 | −0.290017 | ||||||||
\(946\) | −2.46976e16 | −1.05987 | ||||||||
\(947\) | −4.47461e15 | −0.190911 | −0.0954554 | − | 0.995434i | \(-0.530431\pi\) | ||||
−0.0954554 | + | 0.995434i | \(0.530431\pi\) | |||||||
\(948\) | 3.04520e16 | 1.29172 | ||||||||
\(949\) | 1.34495e16 | 0.567206 | ||||||||
\(950\) | −1.32691e15 | −0.0556366 | ||||||||
\(951\) | 8.36396e15 | 0.348674 | ||||||||
\(952\) | 3.94058e15 | 0.163327 | ||||||||
\(953\) | 4.43753e16 | 1.82865 | 0.914325 | − | 0.404981i | \(-0.132722\pi\) | ||||
0.914325 | + | 0.404981i | \(0.132722\pi\) | |||||||
\(954\) | −2.12647e16 | −0.871250 | ||||||||
\(955\) | 7.11843e15 | 0.289979 | ||||||||
\(956\) | −3.33180e16 | −1.34946 | ||||||||
\(957\) | −1.22570e16 | −0.493594 | ||||||||
\(958\) | 5.42961e16 | 2.17400 | ||||||||
\(959\) | −1.95611e16 | −0.778736 | ||||||||
\(960\) | −2.28186e16 | −0.903229 | ||||||||
\(961\) | −1.15464e16 | −0.454430 | ||||||||
\(962\) | −4.28664e16 | −1.67747 | ||||||||
\(963\) | −5.82737e15 | −0.226740 | ||||||||
\(964\) | 1.17691e15 | 0.0455323 | ||||||||
\(965\) | −1.37620e16 | −0.529398 | ||||||||
\(966\) | 5.09637e16 | 1.94934 | ||||||||
\(967\) | 3.87053e16 | 1.47206 | 0.736029 | − | 0.676950i | \(-0.236699\pi\) | ||||
0.736029 | + | 0.676950i | \(0.236699\pi\) | |||||||
\(968\) | 8.28158e15 | 0.313183 | ||||||||
\(969\) | 1.37992e15 | 0.0518889 | ||||||||
\(970\) | 5.42477e16 | 2.02832 | ||||||||
\(971\) | 1.17311e16 | 0.436146 | 0.218073 | − | 0.975932i | \(-0.430023\pi\) | ||||
0.218073 | + | 0.975932i | \(0.430023\pi\) | |||||||
\(972\) | 2.27060e15 | 0.0839414 | ||||||||
\(973\) | 6.15139e16 | 2.26127 | ||||||||
\(974\) | 4.63586e16 | 1.69456 | ||||||||
\(975\) | −1.33805e15 | −0.0486347 | ||||||||
\(976\) | −1.67356e16 | −0.604878 | ||||||||
\(977\) | 2.66043e16 | 0.956161 | 0.478081 | − | 0.878316i | \(-0.341333\pi\) | ||||
0.478081 | + | 0.878316i | \(0.341333\pi\) | |||||||
\(978\) | 4.84555e16 | 1.73173 | ||||||||
\(979\) | −8.60977e14 | −0.0305975 | ||||||||
\(980\) | 4.14081e16 | 1.46333 | ||||||||
\(981\) | −9.91257e15 | −0.348343 | ||||||||
\(982\) | 3.88263e16 | 1.35679 | ||||||||
\(983\) | 1.81683e16 | 0.631350 | 0.315675 | − | 0.948867i | \(-0.397769\pi\) | ||||
0.315675 | + | 0.948867i | \(0.397769\pi\) | |||||||
\(984\) | 6.09573e15 | 0.210646 | ||||||||
\(985\) | −1.49820e16 | −0.514838 | ||||||||
\(986\) | −1.59912e16 | −0.546459 | ||||||||
\(987\) | 5.11273e15 | 0.173744 | ||||||||
\(988\) | −1.22495e16 | −0.413956 | ||||||||
\(989\) | −5.56927e16 | −1.87163 | ||||||||
\(990\) | 9.15124e15 | 0.305834 | ||||||||
\(991\) | 2.95832e16 | 0.983196 | 0.491598 | − | 0.870822i | \(-0.336413\pi\) | ||||
0.491598 | + | 0.870822i | \(0.336413\pi\) | |||||||
\(992\) | 3.07232e16 | 1.01544 | ||||||||
\(993\) | 1.69205e16 | 0.556151 | ||||||||
\(994\) | −4.99935e16 | −1.63414 | ||||||||
\(995\) | 2.85910e16 | 0.929400 | ||||||||
\(996\) | −2.87582e15 | −0.0929683 | ||||||||
\(997\) | 2.06404e16 | 0.663582 | 0.331791 | − | 0.943353i | \(-0.392347\pi\) | ||||
0.331791 | + | 0.943353i | \(0.392347\pi\) | |||||||
\(998\) | 3.06405e16 | 0.979667 | ||||||||
\(999\) | −7.83290e15 | −0.249065 |
(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 | 177.12.a.b.1.5 | ✓ | 27 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.12.a.b.1.5 | ✓ | 27 | 1.1 | even | 1 | trivial |