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: | \(0\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 23.0914 | 0.510252 | 0.255126 | − | 0.966908i | \(-0.417883\pi\) | ||||
0.255126 | + | 0.966908i | \(0.417883\pi\) | |||||||
\(3\) | 243.000 | 0.577350 | ||||||||
\(4\) | −1514.79 | −0.739643 | ||||||||
\(5\) | 32.6758 | 0.00467617 | 0.00233809 | − | 0.999997i | \(-0.499256\pi\) | ||||
0.00233809 | + | 0.999997i | \(0.499256\pi\) | |||||||
\(6\) | 5611.21 | 0.294594 | ||||||||
\(7\) | −80813.9 | −1.81739 | −0.908693 | − | 0.417466i | \(-0.862918\pi\) | ||||
−0.908693 | + | 0.417466i | \(0.862918\pi\) | |||||||
\(8\) | −82269.7 | −0.887657 | ||||||||
\(9\) | 59049.0 | 0.333333 | ||||||||
\(10\) | 754.528 | 0.00238603 | ||||||||
\(11\) | −196616. | −0.368094 | −0.184047 | − | 0.982917i | \(-0.558920\pi\) | ||||
−0.184047 | + | 0.982917i | \(0.558920\pi\) | |||||||
\(12\) | −368093. | −0.427033 | ||||||||
\(13\) | −2.11622e6 | −1.58078 | −0.790392 | − | 0.612602i | \(-0.790123\pi\) | ||||
−0.790392 | + | 0.612602i | \(0.790123\pi\) | |||||||
\(14\) | −1.86611e6 | −0.927325 | ||||||||
\(15\) | 7940.21 | 0.00269979 | ||||||||
\(16\) | 1.20256e6 | 0.286714 | ||||||||
\(17\) | −4.62145e6 | −0.789422 | −0.394711 | − | 0.918805i | \(-0.629155\pi\) | ||||
−0.394711 | + | 0.918805i | \(0.629155\pi\) | |||||||
\(18\) | 1.36352e6 | 0.170084 | ||||||||
\(19\) | 4.04501e6 | 0.374779 | 0.187389 | − | 0.982286i | \(-0.439997\pi\) | ||||
0.187389 | + | 0.982286i | \(0.439997\pi\) | |||||||
\(20\) | −49496.8 | −0.00345870 | ||||||||
\(21\) | −1.96378e7 | −1.04927 | ||||||||
\(22\) | −4.54013e6 | −0.187821 | ||||||||
\(23\) | −2.90999e7 | −0.942732 | −0.471366 | − | 0.881938i | \(-0.656239\pi\) | ||||
−0.471366 | + | 0.881938i | \(0.656239\pi\) | |||||||
\(24\) | −1.99915e7 | −0.512489 | ||||||||
\(25\) | −4.88271e7 | −0.999978 | ||||||||
\(26\) | −4.88664e7 | −0.806598 | ||||||||
\(27\) | 1.43489e7 | 0.192450 | ||||||||
\(28\) | 1.22416e8 | 1.34422 | ||||||||
\(29\) | 1.75499e8 | 1.58886 | 0.794432 | − | 0.607353i | \(-0.207769\pi\) | ||||
0.794432 | + | 0.607353i | \(0.207769\pi\) | |||||||
\(30\) | 183350. | 0.00137757 | ||||||||
\(31\) | −2.81038e8 | −1.76309 | −0.881547 | − | 0.472095i | \(-0.843498\pi\) | ||||
−0.881547 | + | 0.472095i | \(0.843498\pi\) | |||||||
\(32\) | 1.96257e8 | 1.03395 | ||||||||
\(33\) | −4.77776e7 | −0.212519 | ||||||||
\(34\) | −1.06716e8 | −0.402804 | ||||||||
\(35\) | −2.64066e6 | −0.00849841 | ||||||||
\(36\) | −8.94467e7 | −0.246548 | ||||||||
\(37\) | −3.05876e8 | −0.725163 | −0.362581 | − | 0.931952i | \(-0.618105\pi\) | ||||
−0.362581 | + | 0.931952i | \(0.618105\pi\) | |||||||
\(38\) | 9.34049e7 | 0.191232 | ||||||||
\(39\) | −5.14241e8 | −0.912666 | ||||||||
\(40\) | −2.68822e6 | −0.00415084 | ||||||||
\(41\) | −1.04911e9 | −1.41420 | −0.707100 | − | 0.707113i | \(-0.749997\pi\) | ||||
−0.707100 | + | 0.707113i | \(0.749997\pi\) | |||||||
\(42\) | −4.53464e8 | −0.535391 | ||||||||
\(43\) | 8.82678e8 | 0.915642 | 0.457821 | − | 0.889044i | \(-0.348630\pi\) | ||||
0.457821 | + | 0.889044i | \(0.348630\pi\) | |||||||
\(44\) | 2.97831e8 | 0.272258 | ||||||||
\(45\) | 1.92947e6 | 0.00155872 | ||||||||
\(46\) | −6.71957e8 | −0.481031 | ||||||||
\(47\) | 2.35478e9 | 1.49766 | 0.748828 | − | 0.662764i | \(-0.230617\pi\) | ||||
0.748828 | + | 0.662764i | \(0.230617\pi\) | |||||||
\(48\) | 2.92223e8 | 0.165534 | ||||||||
\(49\) | 4.55357e9 | 2.30289 | ||||||||
\(50\) | −1.12748e9 | −0.510241 | ||||||||
\(51\) | −1.12301e9 | −0.455773 | ||||||||
\(52\) | 3.20562e9 | 1.16921 | ||||||||
\(53\) | −2.72305e9 | −0.894413 | −0.447206 | − | 0.894431i | \(-0.647581\pi\) | ||||
−0.447206 | + | 0.894431i | \(0.647581\pi\) | |||||||
\(54\) | 3.31336e8 | 0.0981981 | ||||||||
\(55\) | −6.42457e6 | −0.00172127 | ||||||||
\(56\) | 6.64854e9 | 1.61321 | ||||||||
\(57\) | 9.82937e8 | 0.216378 | ||||||||
\(58\) | 4.05252e9 | 0.810721 | ||||||||
\(59\) | 7.14924e8 | 0.130189 | ||||||||
\(60\) | −1.20277e7 | −0.00199688 | ||||||||
\(61\) | −7.46101e9 | −1.13106 | −0.565528 | − | 0.824729i | \(-0.691327\pi\) | ||||
−0.565528 | + | 0.824729i | \(0.691327\pi\) | |||||||
\(62\) | −6.48956e9 | −0.899623 | ||||||||
\(63\) | −4.77198e9 | −0.605795 | ||||||||
\(64\) | 2.06900e9 | 0.240863 | ||||||||
\(65\) | −6.91491e7 | −0.00739202 | ||||||||
\(66\) | −1.10325e9 | −0.108438 | ||||||||
\(67\) | −1.03666e9 | −0.0938051 | −0.0469025 | − | 0.998899i | \(-0.514935\pi\) | ||||
−0.0469025 | + | 0.998899i | \(0.514935\pi\) | |||||||
\(68\) | 7.00052e9 | 0.583890 | ||||||||
\(69\) | −7.07128e9 | −0.544287 | ||||||||
\(70\) | −6.09764e7 | −0.00433633 | ||||||||
\(71\) | 2.41936e9 | 0.159140 | 0.0795702 | − | 0.996829i | \(-0.474645\pi\) | ||||
0.0795702 | + | 0.996829i | \(0.474645\pi\) | |||||||
\(72\) | −4.85794e9 | −0.295886 | ||||||||
\(73\) | 2.86219e10 | 1.61593 | 0.807966 | − | 0.589229i | \(-0.200569\pi\) | ||||
0.807966 | + | 0.589229i | \(0.200569\pi\) | |||||||
\(74\) | −7.06309e9 | −0.370016 | ||||||||
\(75\) | −1.18650e10 | −0.577338 | ||||||||
\(76\) | −6.12733e9 | −0.277202 | ||||||||
\(77\) | 1.58893e10 | 0.668968 | ||||||||
\(78\) | −1.18745e10 | −0.465690 | ||||||||
\(79\) | 6.54301e9 | 0.239237 | 0.119619 | − | 0.992820i | \(-0.461833\pi\) | ||||
0.119619 | + | 0.992820i | \(0.461833\pi\) | |||||||
\(80\) | 3.92947e7 | 0.00134072 | ||||||||
\(81\) | 3.48678e9 | 0.111111 | ||||||||
\(82\) | −2.42255e10 | −0.721599 | ||||||||
\(83\) | −5.44336e10 | −1.51683 | −0.758416 | − | 0.651770i | \(-0.774027\pi\) | ||||
−0.758416 | + | 0.651770i | \(0.774027\pi\) | |||||||
\(84\) | 2.97471e10 | 0.776083 | ||||||||
\(85\) | −1.51009e8 | −0.00369147 | ||||||||
\(86\) | 2.03823e10 | 0.467209 | ||||||||
\(87\) | 4.26463e10 | 0.917331 | ||||||||
\(88\) | 1.61755e10 | 0.326741 | ||||||||
\(89\) | 4.77033e10 | 0.905531 | 0.452765 | − | 0.891630i | \(-0.350438\pi\) | ||||
0.452765 | + | 0.891630i | \(0.350438\pi\) | |||||||
\(90\) | 4.45542e7 | 0.000795343 0 | ||||||||
\(91\) | 1.71020e11 | 2.87289 | ||||||||
\(92\) | 4.40802e10 | 0.697285 | ||||||||
\(93\) | −6.82922e10 | −1.01792 | ||||||||
\(94\) | 5.43751e10 | 0.764183 | ||||||||
\(95\) | 1.32174e8 | 0.00175253 | ||||||||
\(96\) | 4.76905e10 | 0.596953 | ||||||||
\(97\) | 6.19173e10 | 0.732095 | 0.366048 | − | 0.930596i | \(-0.380711\pi\) | ||||
0.366048 | + | 0.930596i | \(0.380711\pi\) | |||||||
\(98\) | 1.05148e11 | 1.17505 | ||||||||
\(99\) | −1.16100e10 | −0.122698 | ||||||||
\(100\) | 7.39626e10 | 0.739626 | ||||||||
\(101\) | −1.48326e11 | −1.40427 | −0.702133 | − | 0.712046i | \(-0.747769\pi\) | ||||
−0.702133 | + | 0.712046i | \(0.747769\pi\) | |||||||
\(102\) | −2.59319e10 | −0.232559 | ||||||||
\(103\) | −1.07904e11 | −0.917136 | −0.458568 | − | 0.888659i | \(-0.651638\pi\) | ||||
−0.458568 | + | 0.888659i | \(0.651638\pi\) | |||||||
\(104\) | 1.74101e11 | 1.40319 | ||||||||
\(105\) | −6.41680e8 | −0.00490656 | ||||||||
\(106\) | −6.28789e10 | −0.456376 | ||||||||
\(107\) | −1.79873e9 | −0.0123981 | −0.00619906 | − | 0.999981i | \(-0.501973\pi\) | ||||
−0.00619906 | + | 0.999981i | \(0.501973\pi\) | |||||||
\(108\) | −2.17356e10 | −0.142344 | ||||||||
\(109\) | 2.47694e11 | 1.54195 | 0.770975 | − | 0.636865i | \(-0.219769\pi\) | ||||
0.770975 | + | 0.636865i | \(0.219769\pi\) | |||||||
\(110\) | −1.48352e8 | −0.000878282 0 | ||||||||
\(111\) | −7.43278e10 | −0.418673 | ||||||||
\(112\) | −9.71839e10 | −0.521069 | ||||||||
\(113\) | −1.33748e10 | −0.0682899 | −0.0341450 | − | 0.999417i | \(-0.510871\pi\) | ||||
−0.0341450 | + | 0.999417i | \(0.510871\pi\) | |||||||
\(114\) | 2.26974e10 | 0.110408 | ||||||||
\(115\) | −9.50861e8 | −0.00440838 | ||||||||
\(116\) | −2.65844e11 | −1.17519 | ||||||||
\(117\) | −1.24961e11 | −0.526928 | ||||||||
\(118\) | 1.65086e10 | 0.0664292 | ||||||||
\(119\) | 3.73478e11 | 1.43468 | ||||||||
\(120\) | −6.53239e8 | −0.00239649 | ||||||||
\(121\) | −2.46654e11 | −0.864507 | ||||||||
\(122\) | −1.72285e11 | −0.577124 | ||||||||
\(123\) | −2.54934e11 | −0.816489 | ||||||||
\(124\) | 4.25713e11 | 1.30406 | ||||||||
\(125\) | −3.19096e9 | −0.00935224 | ||||||||
\(126\) | −1.10192e11 | −0.309108 | ||||||||
\(127\) | 7.43211e11 | 1.99614 | 0.998072 | − | 0.0620676i | \(-0.0197694\pi\) | ||||
0.998072 | + | 0.0620676i | \(0.0197694\pi\) | |||||||
\(128\) | −3.54159e11 | −0.911052 | ||||||||
\(129\) | 2.14491e11 | 0.528646 | ||||||||
\(130\) | −1.59675e9 | −0.00377179 | ||||||||
\(131\) | −7.58634e11 | −1.71807 | −0.859034 | − | 0.511919i | \(-0.828935\pi\) | ||||
−0.859034 | + | 0.511919i | \(0.828935\pi\) | |||||||
\(132\) | 7.23729e10 | 0.157188 | ||||||||
\(133\) | −3.26893e11 | −0.681117 | ||||||||
\(134\) | −2.39380e10 | −0.0478643 | ||||||||
\(135\) | 4.68861e8 | 0.000899930 0 | ||||||||
\(136\) | 3.80205e11 | 0.700736 | ||||||||
\(137\) | −6.77878e11 | −1.20002 | −0.600010 | − | 0.799993i | \(-0.704837\pi\) | ||||
−0.600010 | + | 0.799993i | \(0.704837\pi\) | |||||||
\(138\) | −1.63286e11 | −0.277724 | ||||||||
\(139\) | −8.19489e11 | −1.33956 | −0.669779 | − | 0.742560i | \(-0.733611\pi\) | ||||
−0.669779 | + | 0.742560i | \(0.733611\pi\) | |||||||
\(140\) | 4.00003e9 | 0.00628579 | ||||||||
\(141\) | 5.72212e11 | 0.864672 | ||||||||
\(142\) | 5.58665e10 | 0.0812017 | ||||||||
\(143\) | 4.16082e11 | 0.581876 | ||||||||
\(144\) | 7.10102e10 | 0.0955712 | ||||||||
\(145\) | 5.73457e9 | 0.00742980 | ||||||||
\(146\) | 6.60920e11 | 0.824533 | ||||||||
\(147\) | 1.10652e12 | 1.32957 | ||||||||
\(148\) | 4.63337e11 | 0.536361 | ||||||||
\(149\) | 7.79795e11 | 0.869873 | 0.434937 | − | 0.900461i | \(-0.356771\pi\) | ||||
0.434937 | + | 0.900461i | \(0.356771\pi\) | |||||||
\(150\) | −2.73979e11 | −0.294588 | ||||||||
\(151\) | −2.00521e11 | −0.207867 | −0.103934 | − | 0.994584i | \(-0.533143\pi\) | ||||
−0.103934 | + | 0.994584i | \(0.533143\pi\) | |||||||
\(152\) | −3.32782e11 | −0.332675 | ||||||||
\(153\) | −2.72892e11 | −0.263141 | ||||||||
\(154\) | 3.66906e11 | 0.341343 | ||||||||
\(155\) | −9.18313e9 | −0.00824454 | ||||||||
\(156\) | 7.78967e11 | 0.675046 | ||||||||
\(157\) | 1.61750e11 | 0.135330 | 0.0676652 | − | 0.997708i | \(-0.478445\pi\) | ||||
0.0676652 | + | 0.997708i | \(0.478445\pi\) | |||||||
\(158\) | 1.51087e11 | 0.122071 | ||||||||
\(159\) | −6.61700e11 | −0.516389 | ||||||||
\(160\) | 6.41285e9 | 0.00483494 | ||||||||
\(161\) | 2.35168e12 | 1.71331 | ||||||||
\(162\) | 8.05147e10 | 0.0566947 | ||||||||
\(163\) | −1.89658e12 | −1.29104 | −0.645519 | − | 0.763744i | \(-0.723359\pi\) | ||||
−0.645519 | + | 0.763744i | \(0.723359\pi\) | |||||||
\(164\) | 1.58918e12 | 1.04600 | ||||||||
\(165\) | −1.56117e9 | −0.000993776 0 | ||||||||
\(166\) | −1.25695e12 | −0.773968 | ||||||||
\(167\) | −7.97901e11 | −0.475344 | −0.237672 | − | 0.971345i | \(-0.576384\pi\) | ||||
−0.237672 | + | 0.971345i | \(0.576384\pi\) | |||||||
\(168\) | 1.61559e12 | 0.931390 | ||||||||
\(169\) | 2.68623e12 | 1.49888 | ||||||||
\(170\) | −3.48702e9 | −0.00188358 | ||||||||
\(171\) | 2.38854e11 | 0.124926 | ||||||||
\(172\) | −1.33707e12 | −0.677248 | ||||||||
\(173\) | 3.52739e12 | 1.73061 | 0.865307 | − | 0.501242i | \(-0.167123\pi\) | ||||
0.865307 | + | 0.501242i | \(0.167123\pi\) | |||||||
\(174\) | 9.84763e11 | 0.468070 | ||||||||
\(175\) | 3.94591e12 | 1.81735 | ||||||||
\(176\) | −2.36443e11 | −0.105537 | ||||||||
\(177\) | 1.73727e11 | 0.0751646 | ||||||||
\(178\) | 1.10153e12 | 0.462049 | ||||||||
\(179\) | −2.73949e12 | −1.11424 | −0.557120 | − | 0.830432i | \(-0.688094\pi\) | ||||
−0.557120 | + | 0.830432i | \(0.688094\pi\) | |||||||
\(180\) | −2.92274e9 | −0.00115290 | ||||||||
\(181\) | 1.78794e12 | 0.684101 | 0.342050 | − | 0.939682i | \(-0.388879\pi\) | ||||
0.342050 | + | 0.939682i | \(0.388879\pi\) | |||||||
\(182\) | 3.94909e12 | 1.46590 | ||||||||
\(183\) | −1.81303e12 | −0.653015 | ||||||||
\(184\) | 2.39404e12 | 0.836823 | ||||||||
\(185\) | −9.99472e9 | −0.00339099 | ||||||||
\(186\) | −1.57696e12 | −0.519398 | ||||||||
\(187\) | 9.08650e11 | 0.290581 | ||||||||
\(188\) | −3.56699e12 | −1.10773 | ||||||||
\(189\) | −1.15959e12 | −0.349756 | ||||||||
\(190\) | 3.05207e9 | 0.000894232 0 | ||||||||
\(191\) | 3.55645e12 | 1.01236 | 0.506178 | − | 0.862429i | \(-0.331058\pi\) | ||||
0.506178 | + | 0.862429i | \(0.331058\pi\) | |||||||
\(192\) | 5.02767e11 | 0.139062 | ||||||||
\(193\) | −1.22933e12 | −0.330447 | −0.165224 | − | 0.986256i | \(-0.552835\pi\) | ||||
−0.165224 | + | 0.986256i | \(0.552835\pi\) | |||||||
\(194\) | 1.42976e12 | 0.373553 | ||||||||
\(195\) | −1.68032e10 | −0.00426778 | ||||||||
\(196\) | −6.89769e12 | −1.70332 | ||||||||
\(197\) | 1.01555e12 | 0.243859 | 0.121930 | − | 0.992539i | \(-0.461092\pi\) | ||||
0.121930 | + | 0.992539i | \(0.461092\pi\) | |||||||
\(198\) | −2.68090e11 | −0.0626069 | ||||||||
\(199\) | 6.19152e12 | 1.40639 | 0.703194 | − | 0.710998i | \(-0.251756\pi\) | ||||
0.703194 | + | 0.710998i | \(0.251756\pi\) | |||||||
\(200\) | 4.01699e12 | 0.887637 | ||||||||
\(201\) | −2.51909e11 | −0.0541584 | ||||||||
\(202\) | −3.42505e12 | −0.716530 | ||||||||
\(203\) | −1.41828e13 | −2.88758 | ||||||||
\(204\) | 1.70113e12 | 0.337109 | ||||||||
\(205\) | −3.42806e10 | −0.00661305 | ||||||||
\(206\) | −2.49166e12 | −0.467971 | ||||||||
\(207\) | −1.71832e12 | −0.314244 | ||||||||
\(208\) | −2.54489e12 | −0.453232 | ||||||||
\(209\) | −7.95312e11 | −0.137954 | ||||||||
\(210\) | −1.48173e10 | −0.00250358 | ||||||||
\(211\) | 2.52523e12 | 0.415668 | 0.207834 | − | 0.978164i | \(-0.433359\pi\) | ||||
0.207834 | + | 0.978164i | \(0.433359\pi\) | |||||||
\(212\) | 4.12484e12 | 0.661546 | ||||||||
\(213\) | 5.87905e11 | 0.0918797 | ||||||||
\(214\) | −4.15352e10 | −0.00632617 | ||||||||
\(215\) | 2.88422e10 | 0.00428170 | ||||||||
\(216\) | −1.18048e12 | −0.170830 | ||||||||
\(217\) | 2.27118e13 | 3.20422 | ||||||||
\(218\) | 5.71960e12 | 0.786784 | ||||||||
\(219\) | 6.95513e12 | 0.932959 | ||||||||
\(220\) | 9.73185e9 | 0.00127312 | ||||||||
\(221\) | 9.78000e12 | 1.24791 | ||||||||
\(222\) | −1.71633e12 | −0.213629 | ||||||||
\(223\) | 1.21374e13 | 1.47384 | 0.736918 | − | 0.675983i | \(-0.236281\pi\) | ||||
0.736918 | + | 0.675983i | \(0.236281\pi\) | |||||||
\(224\) | −1.58603e13 | −1.87909 | ||||||||
\(225\) | −2.88319e12 | −0.333326 | ||||||||
\(226\) | −3.08843e11 | −0.0348451 | ||||||||
\(227\) | 4.34287e12 | 0.478227 | 0.239114 | − | 0.970992i | \(-0.423143\pi\) | ||||
0.239114 | + | 0.970992i | \(0.423143\pi\) | |||||||
\(228\) | −1.48894e12 | −0.160043 | ||||||||
\(229\) | 1.10467e13 | 1.15914 | 0.579572 | − | 0.814921i | \(-0.303220\pi\) | ||||
0.579572 | + | 0.814921i | \(0.303220\pi\) | |||||||
\(230\) | −2.19567e10 | −0.00224939 | ||||||||
\(231\) | 3.86110e12 | 0.386229 | ||||||||
\(232\) | −1.44383e13 | −1.41037 | ||||||||
\(233\) | 1.16025e13 | 1.10687 | 0.553433 | − | 0.832894i | \(-0.313318\pi\) | ||||
0.553433 | + | 0.832894i | \(0.313318\pi\) | |||||||
\(234\) | −2.88551e12 | −0.268866 | ||||||||
\(235\) | 7.69442e10 | 0.00700330 | ||||||||
\(236\) | −1.08296e12 | −0.0962933 | ||||||||
\(237\) | 1.58995e12 | 0.138124 | ||||||||
\(238\) | 8.62412e12 | 0.732051 | ||||||||
\(239\) | −1.88821e13 | −1.56625 | −0.783127 | − | 0.621862i | \(-0.786377\pi\) | ||||
−0.783127 | + | 0.621862i | \(0.786377\pi\) | |||||||
\(240\) | 9.54861e9 | 0.000774067 0 | ||||||||
\(241\) | −1.27106e13 | −1.00710 | −0.503548 | − | 0.863967i | \(-0.667972\pi\) | ||||
−0.503548 | + | 0.863967i | \(0.667972\pi\) | |||||||
\(242\) | −5.69558e12 | −0.441117 | ||||||||
\(243\) | 8.47289e11 | 0.0641500 | ||||||||
\(244\) | 1.13019e13 | 0.836576 | ||||||||
\(245\) | 1.48791e11 | 0.0107687 | ||||||||
\(246\) | −5.88679e12 | −0.416615 | ||||||||
\(247\) | −8.56013e12 | −0.592444 | ||||||||
\(248\) | 2.31209e13 | 1.56502 | ||||||||
\(249\) | −1.32274e13 | −0.875744 | ||||||||
\(250\) | −7.36836e10 | −0.00477200 | ||||||||
\(251\) | −7.60243e12 | −0.481667 | −0.240833 | − | 0.970566i | \(-0.577421\pi\) | ||||
−0.240833 | + | 0.970566i | \(0.577421\pi\) | |||||||
\(252\) | 7.22854e12 | 0.448072 | ||||||||
\(253\) | 5.72150e12 | 0.347014 | ||||||||
\(254\) | 1.71618e13 | 1.01854 | ||||||||
\(255\) | −3.66953e10 | −0.00213127 | ||||||||
\(256\) | −1.24153e13 | −0.705730 | ||||||||
\(257\) | −8.58575e10 | −0.00477690 | −0.00238845 | − | 0.999997i | \(-0.500760\pi\) | ||||
−0.00238845 | + | 0.999997i | \(0.500760\pi\) | |||||||
\(258\) | 4.95289e12 | 0.269743 | ||||||||
\(259\) | 2.47190e13 | 1.31790 | ||||||||
\(260\) | 1.04746e11 | 0.00546745 | ||||||||
\(261\) | 1.03631e13 | 0.529621 | ||||||||
\(262\) | −1.75179e13 | −0.876648 | ||||||||
\(263\) | 8.70407e12 | 0.426546 | 0.213273 | − | 0.976993i | \(-0.431588\pi\) | ||||
0.213273 | + | 0.976993i | \(0.431588\pi\) | |||||||
\(264\) | 3.93065e12 | 0.188644 | ||||||||
\(265\) | −8.89776e10 | −0.00418243 | ||||||||
\(266\) | −7.54841e12 | −0.347542 | ||||||||
\(267\) | 1.15919e13 | 0.522808 | ||||||||
\(268\) | 1.57033e12 | 0.0693822 | ||||||||
\(269\) | −3.50062e13 | −1.51533 | −0.757664 | − | 0.652644i | \(-0.773660\pi\) | ||||
−0.757664 | + | 0.652644i | \(0.773660\pi\) | |||||||
\(270\) | 1.08267e10 | 0.000459191 0 | ||||||||
\(271\) | 1.26831e13 | 0.527100 | 0.263550 | − | 0.964646i | \(-0.415107\pi\) | ||||
0.263550 | + | 0.964646i | \(0.415107\pi\) | |||||||
\(272\) | −5.55759e12 | −0.226338 | ||||||||
\(273\) | 4.15579e13 | 1.65867 | ||||||||
\(274\) | −1.56531e13 | −0.612313 | ||||||||
\(275\) | 9.60016e12 | 0.368086 | ||||||||
\(276\) | 1.07115e13 | 0.402578 | ||||||||
\(277\) | −1.18944e13 | −0.438230 | −0.219115 | − | 0.975699i | \(-0.570317\pi\) | ||||
−0.219115 | + | 0.975699i | \(0.570317\pi\) | |||||||
\(278\) | −1.89231e13 | −0.683513 | ||||||||
\(279\) | −1.65950e13 | −0.587698 | ||||||||
\(280\) | 2.17246e11 | 0.00754367 | ||||||||
\(281\) | −4.97437e13 | −1.69376 | −0.846882 | − | 0.531781i | \(-0.821523\pi\) | ||||
−0.846882 | + | 0.531781i | \(0.821523\pi\) | |||||||
\(282\) | 1.32132e13 | 0.441201 | ||||||||
\(283\) | 7.59641e11 | 0.0248762 | 0.0124381 | − | 0.999923i | \(-0.496041\pi\) | ||||
0.0124381 | + | 0.999923i | \(0.496041\pi\) | |||||||
\(284\) | −3.66482e12 | −0.117707 | ||||||||
\(285\) | 3.21182e10 | 0.00101182 | ||||||||
\(286\) | 9.60791e12 | 0.296904 | ||||||||
\(287\) | 8.47829e13 | 2.57015 | ||||||||
\(288\) | 1.15888e13 | 0.344651 | ||||||||
\(289\) | −1.29141e13 | −0.376813 | ||||||||
\(290\) | 1.32419e11 | 0.00379107 | ||||||||
\(291\) | 1.50459e13 | 0.422675 | ||||||||
\(292\) | −4.33561e13 | −1.19521 | ||||||||
\(293\) | 8.39756e12 | 0.227186 | 0.113593 | − | 0.993527i | \(-0.463764\pi\) | ||||
0.113593 | + | 0.993527i | \(0.463764\pi\) | |||||||
\(294\) | 2.55510e13 | 0.678418 | ||||||||
\(295\) | 2.33607e10 | 0.000608786 0 | ||||||||
\(296\) | 2.51643e13 | 0.643696 | ||||||||
\(297\) | −2.82122e12 | −0.0708397 | ||||||||
\(298\) | 1.80065e13 | 0.443855 | ||||||||
\(299\) | 6.15818e13 | 1.49026 | ||||||||
\(300\) | 1.79729e13 | 0.427023 | ||||||||
\(301\) | −7.13327e13 | −1.66407 | ||||||||
\(302\) | −4.63030e12 | −0.106065 | ||||||||
\(303\) | −3.60432e13 | −0.810753 | ||||||||
\(304\) | 4.86438e12 | 0.107454 | ||||||||
\(305\) | −2.43794e11 | −0.00528901 | ||||||||
\(306\) | −6.30146e12 | −0.134268 | ||||||||
\(307\) | −3.01401e13 | −0.630787 | −0.315394 | − | 0.948961i | \(-0.602137\pi\) | ||||
−0.315394 | + | 0.948961i | \(0.602137\pi\) | |||||||
\(308\) | −2.40689e13 | −0.494797 | ||||||||
\(309\) | −2.62207e13 | −0.529509 | ||||||||
\(310\) | −2.12051e11 | −0.00420679 | ||||||||
\(311\) | 5.01933e13 | 0.978281 | 0.489140 | − | 0.872205i | \(-0.337311\pi\) | ||||
0.489140 | + | 0.872205i | \(0.337311\pi\) | |||||||
\(312\) | 4.23065e13 | 0.810134 | ||||||||
\(313\) | −4.47804e13 | −0.842547 | −0.421274 | − | 0.906934i | \(-0.638417\pi\) | ||||
−0.421274 | + | 0.906934i | \(0.638417\pi\) | |||||||
\(314\) | 3.73503e12 | 0.0690527 | ||||||||
\(315\) | −1.55928e11 | −0.00283280 | ||||||||
\(316\) | −9.91127e12 | −0.176950 | ||||||||
\(317\) | −7.52336e13 | −1.32004 | −0.660018 | − | 0.751250i | \(-0.729451\pi\) | ||||
−0.660018 | + | 0.751250i | \(0.729451\pi\) | |||||||
\(318\) | −1.52796e13 | −0.263489 | ||||||||
\(319\) | −3.45059e13 | −0.584851 | ||||||||
\(320\) | 6.76061e10 | 0.00112632 | ||||||||
\(321\) | −4.37092e11 | −0.00715805 | ||||||||
\(322\) | 5.43035e13 | 0.874220 | ||||||||
\(323\) | −1.86938e13 | −0.295858 | ||||||||
\(324\) | −5.28174e12 | −0.0821825 | ||||||||
\(325\) | 1.03329e14 | 1.58075 | ||||||||
\(326\) | −4.37946e13 | −0.658755 | ||||||||
\(327\) | 6.01897e13 | 0.890245 | ||||||||
\(328\) | 8.63102e13 | 1.25532 | ||||||||
\(329\) | −1.90299e14 | −2.72182 | ||||||||
\(330\) | −3.60496e10 | −0.000507076 0 | ||||||||
\(331\) | 3.77022e13 | 0.521571 | 0.260785 | − | 0.965397i | \(-0.416019\pi\) | ||||
0.260785 | + | 0.965397i | \(0.416019\pi\) | |||||||
\(332\) | 8.24554e13 | 1.12191 | ||||||||
\(333\) | −1.80617e13 | −0.241721 | ||||||||
\(334\) | −1.84246e13 | −0.242546 | ||||||||
\(335\) | −3.38738e10 | −0.000438649 0 | ||||||||
\(336\) | −2.36157e13 | −0.300839 | ||||||||
\(337\) | −7.70482e13 | −0.965602 | −0.482801 | − | 0.875730i | \(-0.660381\pi\) | ||||
−0.482801 | + | 0.875730i | \(0.660381\pi\) | |||||||
\(338\) | 6.20287e13 | 0.764805 | ||||||||
\(339\) | −3.25008e12 | −0.0394272 | ||||||||
\(340\) | 2.28747e11 | 0.00273037 | ||||||||
\(341\) | 5.52565e13 | 0.648984 | ||||||||
\(342\) | 5.51546e12 | 0.0637439 | ||||||||
\(343\) | −2.08196e14 | −2.36785 | ||||||||
\(344\) | −7.26177e13 | −0.812776 | ||||||||
\(345\) | −2.31059e11 | −0.00254518 | ||||||||
\(346\) | 8.14524e13 | 0.883050 | ||||||||
\(347\) | −1.50757e14 | −1.60867 | −0.804334 | − | 0.594177i | \(-0.797478\pi\) | ||||
−0.804334 | + | 0.594177i | \(0.797478\pi\) | |||||||
\(348\) | −6.46002e13 | −0.678497 | ||||||||
\(349\) | 8.88573e13 | 0.918657 | 0.459329 | − | 0.888266i | \(-0.348090\pi\) | ||||
0.459329 | + | 0.888266i | \(0.348090\pi\) | |||||||
\(350\) | 9.11165e13 | 0.927305 | ||||||||
\(351\) | −3.03654e13 | −0.304222 | ||||||||
\(352\) | −3.85872e13 | −0.380592 | ||||||||
\(353\) | 1.96988e13 | 0.191284 | 0.0956420 | − | 0.995416i | \(-0.469510\pi\) | ||||
0.0956420 | + | 0.995416i | \(0.469510\pi\) | |||||||
\(354\) | 4.01159e12 | 0.0383529 | ||||||||
\(355\) | 7.90545e10 | 0.000744168 0 | ||||||||
\(356\) | −7.22603e13 | −0.669769 | ||||||||
\(357\) | 9.07551e13 | 0.828315 | ||||||||
\(358\) | −6.32587e13 | −0.568543 | ||||||||
\(359\) | −1.26180e14 | −1.11679 | −0.558393 | − | 0.829577i | \(-0.688582\pi\) | ||||
−0.558393 | + | 0.829577i | \(0.688582\pi\) | |||||||
\(360\) | −1.58737e11 | −0.00138361 | ||||||||
\(361\) | −1.00128e14 | −0.859541 | ||||||||
\(362\) | 4.12859e13 | 0.349064 | ||||||||
\(363\) | −5.99369e13 | −0.499123 | ||||||||
\(364\) | −2.59059e14 | −2.12491 | ||||||||
\(365\) | 9.35243e11 | 0.00755638 | ||||||||
\(366\) | −4.18653e13 | −0.333202 | ||||||||
\(367\) | −2.20870e14 | −1.73170 | −0.865851 | − | 0.500301i | \(-0.833223\pi\) | ||||
−0.865851 | + | 0.500301i | \(0.833223\pi\) | |||||||
\(368\) | −3.49945e13 | −0.270294 | ||||||||
\(369\) | −6.19491e13 | −0.471400 | ||||||||
\(370\) | −2.30792e11 | −0.00173026 | ||||||||
\(371\) | 2.20060e14 | 1.62549 | ||||||||
\(372\) | 1.03448e14 | 0.752899 | ||||||||
\(373\) | 9.05981e13 | 0.649711 | 0.324856 | − | 0.945764i | \(-0.394684\pi\) | ||||
0.324856 | + | 0.945764i | \(0.394684\pi\) | |||||||
\(374\) | 2.09820e13 | 0.148270 | ||||||||
\(375\) | −7.75403e11 | −0.00539952 | ||||||||
\(376\) | −1.93727e14 | −1.32940 | ||||||||
\(377\) | −3.71395e14 | −2.51165 | ||||||||
\(378\) | −2.67766e13 | −0.178464 | ||||||||
\(379\) | −1.24245e14 | −0.816135 | −0.408067 | − | 0.912952i | \(-0.633797\pi\) | ||||
−0.408067 | + | 0.912952i | \(0.633797\pi\) | |||||||
\(380\) | −2.00215e11 | −0.00129625 | ||||||||
\(381\) | 1.80600e14 | 1.15247 | ||||||||
\(382\) | 8.21233e13 | 0.516557 | ||||||||
\(383\) | 1.28435e14 | 0.796326 | 0.398163 | − | 0.917315i | \(-0.369648\pi\) | ||||
0.398163 | + | 0.917315i | \(0.369648\pi\) | |||||||
\(384\) | −8.60606e13 | −0.525996 | ||||||||
\(385\) | 5.19194e11 | 0.00312821 | ||||||||
\(386\) | −2.83869e13 | −0.168611 | ||||||||
\(387\) | 5.21212e13 | 0.305214 | ||||||||
\(388\) | −9.37916e13 | −0.541489 | ||||||||
\(389\) | −2.45451e14 | −1.39714 | −0.698572 | − | 0.715539i | \(-0.746181\pi\) | ||||
−0.698572 | + | 0.715539i | \(0.746181\pi\) | |||||||
\(390\) | −3.88010e11 | −0.00217765 | ||||||||
\(391\) | 1.34484e14 | 0.744214 | ||||||||
\(392\) | −3.74621e14 | −2.04418 | ||||||||
\(393\) | −1.84348e14 | −0.991927 | ||||||||
\(394\) | 2.34506e13 | 0.124430 | ||||||||
\(395\) | 2.13798e11 | 0.00111871 | ||||||||
\(396\) | 1.75866e13 | 0.0907526 | ||||||||
\(397\) | 2.08288e14 | 1.06003 | 0.530013 | − | 0.847989i | \(-0.322187\pi\) | ||||
0.530013 | + | 0.847989i | \(0.322187\pi\) | |||||||
\(398\) | 1.42971e14 | 0.717613 | ||||||||
\(399\) | −7.94350e13 | −0.393243 | ||||||||
\(400\) | −5.87177e13 | −0.286707 | ||||||||
\(401\) | −1.25727e14 | −0.605528 | −0.302764 | − | 0.953066i | \(-0.597909\pi\) | ||||
−0.302764 | + | 0.953066i | \(0.597909\pi\) | |||||||
\(402\) | −5.81693e12 | −0.0276344 | ||||||||
\(403\) | 5.94738e14 | 2.78707 | ||||||||
\(404\) | 2.24682e14 | 1.03865 | ||||||||
\(405\) | 1.13933e11 | 0.000519575 0 | ||||||||
\(406\) | −3.27500e14 | −1.47339 | ||||||||
\(407\) | 6.01399e13 | 0.266928 | ||||||||
\(408\) | 9.23899e13 | 0.404570 | ||||||||
\(409\) | −1.28206e14 | −0.553899 | −0.276950 | − | 0.960884i | \(-0.589323\pi\) | ||||
−0.276950 | + | 0.960884i | \(0.589323\pi\) | |||||||
\(410\) | −7.91585e11 | −0.00337432 | ||||||||
\(411\) | −1.64724e14 | −0.692831 | ||||||||
\(412\) | 1.63452e14 | 0.678353 | ||||||||
\(413\) | −5.77758e13 | −0.236603 | ||||||||
\(414\) | −3.96784e13 | −0.160344 | ||||||||
\(415\) | −1.77866e12 | −0.00709297 | ||||||||
\(416\) | −4.15323e14 | −1.63446 | ||||||||
\(417\) | −1.99136e14 | −0.773394 | ||||||||
\(418\) | −1.83649e13 | −0.0703911 | ||||||||
\(419\) | −2.42222e14 | −0.916296 | −0.458148 | − | 0.888876i | \(-0.651487\pi\) | ||||
−0.458148 | + | 0.888876i | \(0.651487\pi\) | |||||||
\(420\) | 9.72008e11 | 0.00362910 | ||||||||
\(421\) | −4.87087e14 | −1.79496 | −0.897481 | − | 0.441053i | \(-0.854605\pi\) | ||||
−0.897481 | + | 0.441053i | \(0.854605\pi\) | |||||||
\(422\) | 5.83110e13 | 0.212096 | ||||||||
\(423\) | 1.39047e14 | 0.499219 | ||||||||
\(424\) | 2.24024e14 | 0.793931 | ||||||||
\(425\) | 2.25652e14 | 0.789405 | ||||||||
\(426\) | 1.35756e13 | 0.0468818 | ||||||||
\(427\) | 6.02954e14 | 2.05556 | ||||||||
\(428\) | 2.72470e12 | 0.00917017 | ||||||||
\(429\) | 1.01108e14 | 0.335946 | ||||||||
\(430\) | 6.66006e11 | 0.00218475 | ||||||||
\(431\) | 5.99881e13 | 0.194286 | 0.0971428 | − | 0.995270i | \(-0.469030\pi\) | ||||
0.0971428 | + | 0.995270i | \(0.469030\pi\) | |||||||
\(432\) | 1.72555e13 | 0.0551781 | ||||||||
\(433\) | 3.38430e14 | 1.06853 | 0.534264 | − | 0.845318i | \(-0.320589\pi\) | ||||
0.534264 | + | 0.845318i | \(0.320589\pi\) | |||||||
\(434\) | 5.24447e14 | 1.63496 | ||||||||
\(435\) | 1.39350e12 | 0.00428960 | ||||||||
\(436\) | −3.75204e14 | −1.14049 | ||||||||
\(437\) | −1.17709e14 | −0.353316 | ||||||||
\(438\) | 1.60604e14 | 0.476044 | ||||||||
\(439\) | −8.87244e13 | −0.259710 | −0.129855 | − | 0.991533i | \(-0.541451\pi\) | ||||
−0.129855 | + | 0.991533i | \(0.541451\pi\) | |||||||
\(440\) | 5.28547e11 | 0.00152790 | ||||||||
\(441\) | 2.68883e14 | 0.767630 | ||||||||
\(442\) | 2.25834e14 | 0.636747 | ||||||||
\(443\) | 4.91192e14 | 1.36782 | 0.683912 | − | 0.729564i | \(-0.260277\pi\) | ||||
0.683912 | + | 0.729564i | \(0.260277\pi\) | |||||||
\(444\) | 1.12591e14 | 0.309668 | ||||||||
\(445\) | 1.55874e12 | 0.00423442 | ||||||||
\(446\) | 2.80269e14 | 0.752028 | ||||||||
\(447\) | 1.89490e14 | 0.502221 | ||||||||
\(448\) | −1.67204e14 | −0.437741 | ||||||||
\(449\) | 8.30943e13 | 0.214890 | 0.107445 | − | 0.994211i | \(-0.465733\pi\) | ||||
0.107445 | + | 0.994211i | \(0.465733\pi\) | |||||||
\(450\) | −6.65768e13 | −0.170080 | ||||||||
\(451\) | 2.06272e14 | 0.520558 | ||||||||
\(452\) | 2.02600e13 | 0.0505101 | ||||||||
\(453\) | −4.87265e13 | −0.120012 | ||||||||
\(454\) | 1.00283e14 | 0.244017 | ||||||||
\(455\) | 5.58821e12 | 0.0134341 | ||||||||
\(456\) | −8.08660e13 | −0.192070 | ||||||||
\(457\) | −6.65893e14 | −1.56266 | −0.781332 | − | 0.624116i | \(-0.785459\pi\) | ||||
−0.781332 | + | 0.624116i | \(0.785459\pi\) | |||||||
\(458\) | 2.55084e14 | 0.591456 | ||||||||
\(459\) | −6.63128e13 | −0.151924 | ||||||||
\(460\) | 1.44035e12 | 0.00326063 | ||||||||
\(461\) | 1.15391e14 | 0.258116 | 0.129058 | − | 0.991637i | \(-0.458805\pi\) | ||||
0.129058 | + | 0.991637i | \(0.458805\pi\) | |||||||
\(462\) | 8.91581e13 | 0.197074 | ||||||||
\(463\) | −6.74287e14 | −1.47282 | −0.736409 | − | 0.676536i | \(-0.763480\pi\) | ||||
−0.736409 | + | 0.676536i | \(0.763480\pi\) | |||||||
\(464\) | 2.11049e14 | 0.455549 | ||||||||
\(465\) | −2.23150e12 | −0.00475999 | ||||||||
\(466\) | 2.67918e14 | 0.564780 | ||||||||
\(467\) | 2.62842e14 | 0.547586 | 0.273793 | − | 0.961789i | \(-0.411722\pi\) | ||||
0.273793 | + | 0.961789i | \(0.411722\pi\) | |||||||
\(468\) | 1.89289e14 | 0.389738 | ||||||||
\(469\) | 8.37769e13 | 0.170480 | ||||||||
\(470\) | 1.77675e12 | 0.00357345 | ||||||||
\(471\) | 3.93052e13 | 0.0781331 | ||||||||
\(472\) | −5.88166e13 | −0.115563 | ||||||||
\(473\) | −1.73548e14 | −0.337042 | ||||||||
\(474\) | 3.67142e13 | 0.0704779 | ||||||||
\(475\) | −1.97506e14 | −0.374770 | ||||||||
\(476\) | −5.65739e14 | −1.06115 | ||||||||
\(477\) | −1.60793e14 | −0.298138 | ||||||||
\(478\) | −4.36014e14 | −0.799185 | ||||||||
\(479\) | 1.35085e14 | 0.244772 | 0.122386 | − | 0.992483i | \(-0.460945\pi\) | ||||
0.122386 | + | 0.992483i | \(0.460945\pi\) | |||||||
\(480\) | 1.55832e12 | 0.00279146 | ||||||||
\(481\) | 6.47300e14 | 1.14633 | ||||||||
\(482\) | −2.93504e14 | −0.513873 | ||||||||
\(483\) | 5.71458e14 | 0.989179 | ||||||||
\(484\) | 3.73628e14 | 0.639426 | ||||||||
\(485\) | 2.02319e12 | 0.00342340 | ||||||||
\(486\) | 1.95651e13 | 0.0327327 | ||||||||
\(487\) | 2.99730e14 | 0.495817 | 0.247908 | − | 0.968783i | \(-0.420257\pi\) | ||||
0.247908 | + | 0.968783i | \(0.420257\pi\) | |||||||
\(488\) | 6.13815e14 | 1.00399 | ||||||||
\(489\) | −4.60869e14 | −0.745381 | ||||||||
\(490\) | 3.43579e12 | 0.00549476 | ||||||||
\(491\) | 9.64896e14 | 1.52592 | 0.762961 | − | 0.646445i | \(-0.223745\pi\) | ||||
0.762961 | + | 0.646445i | \(0.223745\pi\) | |||||||
\(492\) | 3.86172e14 | 0.603910 | ||||||||
\(493\) | −8.11062e14 | −1.25428 | ||||||||
\(494\) | −1.97665e14 | −0.302296 | ||||||||
\(495\) | −3.79364e11 | −0.000573757 0 | ||||||||
\(496\) | −3.37966e14 | −0.505503 | ||||||||
\(497\) | −1.95518e14 | −0.289219 | ||||||||
\(498\) | −3.05438e14 | −0.446850 | ||||||||
\(499\) | 8.18754e14 | 1.18468 | 0.592339 | − | 0.805689i | \(-0.298204\pi\) | ||||
0.592339 | + | 0.805689i | \(0.298204\pi\) | |||||||
\(500\) | 4.83362e12 | 0.00691732 | ||||||||
\(501\) | −1.93890e14 | −0.274440 | ||||||||
\(502\) | −1.75551e14 | −0.245772 | ||||||||
\(503\) | 7.25668e14 | 1.00488 | 0.502440 | − | 0.864612i | \(-0.332436\pi\) | ||||
0.502440 | + | 0.864612i | \(0.332436\pi\) | |||||||
\(504\) | 3.92590e14 | 0.537738 | ||||||||
\(505\) | −4.84666e12 | −0.00656659 | ||||||||
\(506\) | 1.32117e14 | 0.177065 | ||||||||
\(507\) | 6.52753e14 | 0.865376 | ||||||||
\(508\) | −1.12581e15 | −1.47643 | ||||||||
\(509\) | −1.69377e14 | −0.219739 | −0.109870 | − | 0.993946i | \(-0.535043\pi\) | ||||
−0.109870 | + | 0.993946i | \(0.535043\pi\) | |||||||
\(510\) | −8.47345e11 | −0.00108749 | ||||||||
\(511\) | −2.31305e15 | −2.93677 | ||||||||
\(512\) | 4.38630e14 | 0.550952 | ||||||||
\(513\) | 5.80415e13 | 0.0721262 | ||||||||
\(514\) | −1.98257e12 | −0.00243742 | ||||||||
\(515\) | −3.52585e12 | −0.00428869 | ||||||||
\(516\) | −3.24908e14 | −0.391009 | ||||||||
\(517\) | −4.62987e14 | −0.551278 | ||||||||
\(518\) | 5.70796e14 | 0.672462 | ||||||||
\(519\) | 8.57157e14 | 0.999171 | ||||||||
\(520\) | 5.68887e12 | 0.00656157 | ||||||||
\(521\) | −7.53695e14 | −0.860178 | −0.430089 | − | 0.902787i | \(-0.641518\pi\) | ||||
−0.430089 | + | 0.902787i | \(0.641518\pi\) | |||||||
\(522\) | 2.39297e14 | 0.270240 | ||||||||
\(523\) | −1.10013e15 | −1.22938 | −0.614689 | − | 0.788770i | \(-0.710718\pi\) | ||||
−0.614689 | + | 0.788770i | \(0.710718\pi\) | |||||||
\(524\) | 1.14917e15 | 1.27076 | ||||||||
\(525\) | 9.58855e14 | 1.04925 | ||||||||
\(526\) | 2.00989e14 | 0.217646 | ||||||||
\(527\) | 1.29880e15 | 1.39183 | ||||||||
\(528\) | −5.74556e13 | −0.0609321 | ||||||||
\(529\) | −1.06005e14 | −0.111255 | ||||||||
\(530\) | −2.05462e12 | −0.00213409 | ||||||||
\(531\) | 4.22156e13 | 0.0433963 | ||||||||
\(532\) | 4.95174e14 | 0.503783 | ||||||||
\(533\) | 2.22015e15 | 2.23554 | ||||||||
\(534\) | 2.67673e14 | 0.266764 | ||||||||
\(535\) | −5.87749e10 | −5.79757e−5 0 | ||||||||
\(536\) | 8.52860e13 | 0.0832667 | ||||||||
\(537\) | −6.65697e14 | −0.643306 | ||||||||
\(538\) | −8.08341e14 | −0.773200 | ||||||||
\(539\) | −8.95302e14 | −0.847679 | ||||||||
\(540\) | −7.10226e11 | −0.000665627 0 | ||||||||
\(541\) | −2.13492e14 | −0.198060 | −0.0990298 | − | 0.995084i | \(-0.531574\pi\) | ||||
−0.0990298 | + | 0.995084i | \(0.531574\pi\) | |||||||
\(542\) | 2.92869e14 | 0.268954 | ||||||||
\(543\) | 4.34469e14 | 0.394966 | ||||||||
\(544\) | −9.06993e14 | −0.816225 | ||||||||
\(545\) | 8.09360e12 | 0.00721043 | ||||||||
\(546\) | 9.59629e14 | 0.846338 | ||||||||
\(547\) | 9.40079e14 | 0.820793 | 0.410397 | − | 0.911907i | \(-0.365390\pi\) | ||||
0.410397 | + | 0.911907i | \(0.365390\pi\) | |||||||
\(548\) | 1.02684e15 | 0.887585 | ||||||||
\(549\) | −4.40565e14 | −0.377018 | ||||||||
\(550\) | 2.21681e14 | 0.187817 | ||||||||
\(551\) | 7.09897e14 | 0.595472 | ||||||||
\(552\) | 5.81752e14 | 0.483140 | ||||||||
\(553\) | −5.28766e14 | −0.434786 | ||||||||
\(554\) | −2.74657e14 | −0.223608 | ||||||||
\(555\) | −2.42872e12 | −0.00195779 | ||||||||
\(556\) | 1.24135e15 | 0.990794 | ||||||||
\(557\) | 1.26663e15 | 1.00103 | 0.500513 | − | 0.865729i | \(-0.333145\pi\) | ||||
0.500513 | + | 0.865729i | \(0.333145\pi\) | |||||||
\(558\) | −3.83202e14 | −0.299874 | ||||||||
\(559\) | −1.86794e15 | −1.44743 | ||||||||
\(560\) | −3.17556e12 | −0.00243661 | ||||||||
\(561\) | 2.20802e14 | 0.167767 | ||||||||
\(562\) | −1.14865e15 | −0.864247 | ||||||||
\(563\) | 6.71361e14 | 0.500219 | 0.250109 | − | 0.968218i | \(-0.419533\pi\) | ||||
0.250109 | + | 0.968218i | \(0.419533\pi\) | |||||||
\(564\) | −8.66779e14 | −0.639548 | ||||||||
\(565\) | −4.37033e11 | −0.000319336 0 | ||||||||
\(566\) | 1.75412e13 | 0.0126931 | ||||||||
\(567\) | −2.81781e14 | −0.201932 | ||||||||
\(568\) | −1.99040e14 | −0.141262 | ||||||||
\(569\) | 7.24889e14 | 0.509512 | 0.254756 | − | 0.967005i | \(-0.418005\pi\) | ||||
0.254756 | + | 0.967005i | \(0.418005\pi\) | |||||||
\(570\) | 7.41654e11 | 0.000516285 0 | ||||||||
\(571\) | −2.62128e15 | −1.80724 | −0.903619 | − | 0.428338i | \(-0.859099\pi\) | ||||
−0.903619 | + | 0.428338i | \(0.859099\pi\) | |||||||
\(572\) | −6.30276e14 | −0.430380 | ||||||||
\(573\) | 8.64217e14 | 0.584484 | ||||||||
\(574\) | 1.95776e15 | 1.31142 | ||||||||
\(575\) | 1.42086e15 | 0.942712 | ||||||||
\(576\) | 1.22172e14 | 0.0802878 | ||||||||
\(577\) | −5.30497e14 | −0.345315 | −0.172658 | − | 0.984982i | \(-0.555235\pi\) | ||||
−0.172658 | + | 0.984982i | \(0.555235\pi\) | |||||||
\(578\) | −2.98204e14 | −0.192270 | ||||||||
\(579\) | −2.98726e14 | −0.190784 | ||||||||
\(580\) | −8.68666e12 | −0.00549540 | ||||||||
\(581\) | 4.39900e15 | 2.75667 | ||||||||
\(582\) | 3.47431e14 | 0.215671 | ||||||||
\(583\) | 5.35394e14 | 0.329228 | ||||||||
\(584\) | −2.35472e15 | −1.43439 | ||||||||
\(585\) | −4.08318e12 | −0.00246401 | ||||||||
\(586\) | 1.93911e14 | 0.115922 | ||||||||
\(587\) | 1.76214e15 | 1.04359 | 0.521795 | − | 0.853071i | \(-0.325262\pi\) | ||||
0.521795 | + | 0.853071i | \(0.325262\pi\) | |||||||
\(588\) | −1.67614e15 | −0.983409 | ||||||||
\(589\) | −1.13680e15 | −0.660770 | ||||||||
\(590\) | 5.39431e11 | 0.000310634 0 | ||||||||
\(591\) | 2.46780e14 | 0.140792 | ||||||||
\(592\) | −3.67835e14 | −0.207914 | ||||||||
\(593\) | −2.25566e15 | −1.26320 | −0.631600 | − | 0.775294i | \(-0.717601\pi\) | ||||
−0.631600 | + | 0.775294i | \(0.717601\pi\) | |||||||
\(594\) | −6.51459e13 | −0.0361461 | ||||||||
\(595\) | 1.22037e13 | 0.00670883 | ||||||||
\(596\) | −1.18122e15 | −0.643395 | ||||||||
\(597\) | 1.50454e15 | 0.811979 | ||||||||
\(598\) | 1.42201e15 | 0.760406 | ||||||||
\(599\) | 3.85161e14 | 0.204078 | 0.102039 | − | 0.994780i | \(-0.467463\pi\) | ||||
0.102039 | + | 0.994780i | \(0.467463\pi\) | |||||||
\(600\) | 9.76128e14 | 0.512478 | ||||||||
\(601\) | 3.23146e14 | 0.168109 | 0.0840543 | − | 0.996461i | \(-0.473213\pi\) | ||||
0.0840543 | + | 0.996461i | \(0.473213\pi\) | |||||||
\(602\) | −1.64717e15 | −0.849098 | ||||||||
\(603\) | −6.12139e13 | −0.0312684 | ||||||||
\(604\) | 3.03746e14 | 0.153747 | ||||||||
\(605\) | −8.05960e12 | −0.00404259 | ||||||||
\(606\) | −8.32287e14 | −0.413689 | ||||||||
\(607\) | 2.70154e15 | 1.33068 | 0.665339 | − | 0.746541i | \(-0.268287\pi\) | ||||
0.665339 | + | 0.746541i | \(0.268287\pi\) | |||||||
\(608\) | 7.93862e14 | 0.387503 | ||||||||
\(609\) | −3.44642e15 | −1.66714 | ||||||||
\(610\) | −5.62955e12 | −0.00269873 | ||||||||
\(611\) | −4.98323e15 | −2.36747 | ||||||||
\(612\) | 4.13374e14 | 0.194630 | ||||||||
\(613\) | 2.58621e15 | 1.20679 | 0.603394 | − | 0.797443i | \(-0.293815\pi\) | ||||
0.603394 | + | 0.797443i | \(0.293815\pi\) | |||||||
\(614\) | −6.95976e14 | −0.321861 | ||||||||
\(615\) | −8.33017e12 | −0.00381804 | ||||||||
\(616\) | −1.30721e15 | −0.593814 | ||||||||
\(617\) | 4.09511e15 | 1.84373 | 0.921864 | − | 0.387514i | \(-0.126666\pi\) | ||||
0.921864 | + | 0.387514i | \(0.126666\pi\) | |||||||
\(618\) | −6.05473e14 | −0.270183 | ||||||||
\(619\) | −1.43141e15 | −0.633092 | −0.316546 | − | 0.948577i | \(-0.602523\pi\) | ||||
−0.316546 | + | 0.948577i | \(0.602523\pi\) | |||||||
\(620\) | 1.39105e13 | 0.00609801 | ||||||||
\(621\) | −4.17552e14 | −0.181429 | ||||||||
\(622\) | 1.15903e15 | 0.499170 | ||||||||
\(623\) | −3.85509e15 | −1.64570 | ||||||||
\(624\) | −6.18408e14 | −0.261674 | ||||||||
\(625\) | 2.38403e15 | 0.999934 | ||||||||
\(626\) | −1.03404e15 | −0.429912 | ||||||||
\(627\) | −1.93261e14 | −0.0796475 | ||||||||
\(628\) | −2.45017e14 | −0.100096 | ||||||||
\(629\) | 1.41359e15 | 0.572459 | ||||||||
\(630\) | −3.60060e12 | −0.00144544 | ||||||||
\(631\) | 2.98660e15 | 1.18854 | 0.594272 | − | 0.804264i | \(-0.297440\pi\) | ||||
0.594272 | + | 0.804264i | \(0.297440\pi\) | |||||||
\(632\) | −5.38291e14 | −0.212360 | ||||||||
\(633\) | 6.13630e14 | 0.239986 | ||||||||
\(634\) | −1.73725e15 | −0.673552 | ||||||||
\(635\) | 2.42850e13 | 0.00933432 | ||||||||
\(636\) | 1.00234e15 | 0.381943 | ||||||||
\(637\) | −9.63635e15 | −3.64037 | ||||||||
\(638\) | −7.96790e14 | −0.298421 | ||||||||
\(639\) | 1.42861e14 | 0.0530468 | ||||||||
\(640\) | −1.15724e13 | −0.00426024 | ||||||||
\(641\) | −3.24322e15 | −1.18374 | −0.591871 | − | 0.806032i | \(-0.701611\pi\) | ||||
−0.591871 | + | 0.806032i | \(0.701611\pi\) | |||||||
\(642\) | −1.00931e13 | −0.00365241 | ||||||||
\(643\) | −7.11517e14 | −0.255285 | −0.127642 | − | 0.991820i | \(-0.540741\pi\) | ||||
−0.127642 | + | 0.991820i | \(0.540741\pi\) | |||||||
\(644\) | −3.56229e15 | −1.26724 | ||||||||
\(645\) | 7.00865e12 | 0.00247204 | ||||||||
\(646\) | −4.31666e14 | −0.150962 | ||||||||
\(647\) | 2.83929e15 | 0.984546 | 0.492273 | − | 0.870441i | \(-0.336166\pi\) | ||||
0.492273 | + | 0.870441i | \(0.336166\pi\) | |||||||
\(648\) | −2.86857e14 | −0.0986285 | ||||||||
\(649\) | −1.40565e14 | −0.0479217 | ||||||||
\(650\) | 2.38600e15 | 0.806581 | ||||||||
\(651\) | 5.51896e15 | 1.84996 | ||||||||
\(652\) | 2.87292e15 | 0.954907 | ||||||||
\(653\) | 2.12909e15 | 0.701733 | 0.350866 | − | 0.936425i | \(-0.385887\pi\) | ||||
0.350866 | + | 0.936425i | \(0.385887\pi\) | |||||||
\(654\) | 1.38986e15 | 0.454250 | ||||||||
\(655\) | −2.47889e13 | −0.00803398 | ||||||||
\(656\) | −1.26163e15 | −0.405471 | ||||||||
\(657\) | 1.69010e15 | 0.538644 | ||||||||
\(658\) | −4.39427e15 | −1.38881 | ||||||||
\(659\) | −3.01446e15 | −0.944799 | −0.472399 | − | 0.881385i | \(-0.656612\pi\) | ||||
−0.472399 | + | 0.881385i | \(0.656612\pi\) | |||||||
\(660\) | 2.36484e12 | 0.000735039 0 | ||||||||
\(661\) | −6.64300e14 | −0.204765 | −0.102383 | − | 0.994745i | \(-0.532647\pi\) | ||||
−0.102383 | + | 0.994745i | \(0.532647\pi\) | |||||||
\(662\) | 8.70597e14 | 0.266133 | ||||||||
\(663\) | 2.37654e15 | 0.720478 | ||||||||
\(664\) | 4.47824e15 | 1.34643 | ||||||||
\(665\) | −1.06815e13 | −0.00318502 | ||||||||
\(666\) | −4.17069e14 | −0.123339 | ||||||||
\(667\) | −5.10702e15 | −1.49787 | ||||||||
\(668\) | 1.20865e15 | 0.351585 | ||||||||
\(669\) | 2.94939e15 | 0.850919 | ||||||||
\(670\) | −7.82192e11 | −0.000223822 0 | ||||||||
\(671\) | 1.46695e15 | 0.416334 | ||||||||
\(672\) | −3.85406e15 | −1.08489 | ||||||||
\(673\) | 3.38199e15 | 0.944257 | 0.472128 | − | 0.881530i | \(-0.343486\pi\) | ||||
0.472128 | + | 0.881530i | \(0.343486\pi\) | |||||||
\(674\) | −1.77915e15 | −0.492701 | ||||||||
\(675\) | −7.00615e14 | −0.192446 | ||||||||
\(676\) | −4.06906e15 | −1.10863 | ||||||||
\(677\) | 3.81617e15 | 1.03131 | 0.515656 | − | 0.856796i | \(-0.327548\pi\) | ||||
0.515656 | + | 0.856796i | \(0.327548\pi\) | |||||||
\(678\) | −7.50489e13 | −0.0201178 | ||||||||
\(679\) | −5.00378e15 | −1.33050 | ||||||||
\(680\) | 1.24235e13 | 0.00327676 | ||||||||
\(681\) | 1.05532e15 | 0.276105 | ||||||||
\(682\) | 1.27595e15 | 0.331146 | ||||||||
\(683\) | −2.73376e14 | −0.0703796 | −0.0351898 | − | 0.999381i | \(-0.511204\pi\) | ||||
−0.0351898 | + | 0.999381i | \(0.511204\pi\) | |||||||
\(684\) | −3.61813e14 | −0.0924007 | ||||||||
\(685\) | −2.21502e13 | −0.00561150 | ||||||||
\(686\) | −4.80753e15 | −1.20820 | ||||||||
\(687\) | 2.68435e15 | 0.669232 | ||||||||
\(688\) | 1.06148e15 | 0.262527 | ||||||||
\(689\) | 5.76257e15 | 1.41387 | ||||||||
\(690\) | −5.33548e12 | −0.00129868 | ||||||||
\(691\) | 7.82046e14 | 0.188844 | 0.0944219 | − | 0.995532i | \(-0.469900\pi\) | ||||
0.0944219 | + | 0.995532i | \(0.469900\pi\) | |||||||
\(692\) | −5.34325e15 | −1.28004 | ||||||||
\(693\) | 9.38246e14 | 0.222989 | ||||||||
\(694\) | −3.48120e15 | −0.820827 | ||||||||
\(695\) | −2.67774e13 | −0.00626401 | ||||||||
\(696\) | −3.50850e15 | −0.814275 | ||||||||
\(697\) | 4.84842e15 | 1.11640 | ||||||||
\(698\) | 2.05184e15 | 0.468747 | ||||||||
\(699\) | 2.81941e15 | 0.639049 | ||||||||
\(700\) | −5.97721e15 | −1.34419 | ||||||||
\(701\) | 4.73443e15 | 1.05638 | 0.528189 | − | 0.849127i | \(-0.322871\pi\) | ||||
0.528189 | + | 0.849127i | \(0.322871\pi\) | |||||||
\(702\) | −7.01180e14 | −0.155230 | ||||||||
\(703\) | −1.23727e15 | −0.271775 | ||||||||
\(704\) | −4.06798e14 | −0.0886603 | ||||||||
\(705\) | 1.86974e13 | 0.00404336 | ||||||||
\(706\) | 4.54872e14 | 0.0976031 | ||||||||
\(707\) | 1.19868e16 | 2.55209 | ||||||||
\(708\) | −2.63159e14 | −0.0555949 | ||||||||
\(709\) | −3.55437e15 | −0.745089 | −0.372544 | − | 0.928014i | \(-0.621515\pi\) | ||||
−0.372544 | + | 0.928014i | \(0.621515\pi\) | |||||||
\(710\) | 1.82548e12 | 0.000379713 0 | ||||||||
\(711\) | 3.86358e14 | 0.0797457 | ||||||||
\(712\) | −3.92453e15 | −0.803800 | ||||||||
\(713\) | 8.17818e15 | 1.66213 | ||||||||
\(714\) | 2.09566e15 | 0.422650 | ||||||||
\(715\) | 1.35958e13 | 0.00272095 | ||||||||
\(716\) | 4.14975e15 | 0.824139 | ||||||||
\(717\) | −4.58835e15 | −0.904277 | ||||||||
\(718\) | −2.91366e15 | −0.569842 | ||||||||
\(719\) | 4.65529e15 | 0.903520 | 0.451760 | − | 0.892140i | \(-0.350796\pi\) | ||||
0.451760 | + | 0.892140i | \(0.350796\pi\) | |||||||
\(720\) | 2.32031e12 | 0.000446908 0 | ||||||||
\(721\) | 8.72017e15 | 1.66679 | ||||||||
\(722\) | −2.31210e15 | −0.438583 | ||||||||
\(723\) | −3.08867e15 | −0.581447 | ||||||||
\(724\) | −2.70834e15 | −0.505990 | ||||||||
\(725\) | −8.56912e15 | −1.58883 | ||||||||
\(726\) | −1.38403e15 | −0.254679 | ||||||||
\(727\) | 1.70435e15 | 0.311257 | 0.155628 | − | 0.987816i | \(-0.450260\pi\) | ||||
0.155628 | + | 0.987816i | \(0.450260\pi\) | |||||||
\(728\) | −1.40698e16 | −2.55014 | ||||||||
\(729\) | 2.05891e14 | 0.0370370 | ||||||||
\(730\) | 2.15961e13 | 0.00385566 | ||||||||
\(731\) | −4.07925e15 | −0.722828 | ||||||||
\(732\) | 2.74635e15 | 0.482998 | ||||||||
\(733\) | 2.90878e15 | 0.507737 | 0.253869 | − | 0.967239i | \(-0.418297\pi\) | ||||
0.253869 | + | 0.967239i | \(0.418297\pi\) | |||||||
\(734\) | −5.10019e15 | −0.883605 | ||||||||
\(735\) | 3.61563e13 | 0.00621732 | ||||||||
\(736\) | −5.71107e15 | −0.974741 | ||||||||
\(737\) | 2.03824e14 | 0.0345291 | ||||||||
\(738\) | −1.43049e15 | −0.240533 | ||||||||
\(739\) | −8.19566e15 | −1.36785 | −0.683926 | − | 0.729551i | \(-0.739729\pi\) | ||||
−0.683926 | + | 0.729551i | \(0.739729\pi\) | |||||||
\(740\) | 1.51399e13 | 0.00250812 | ||||||||
\(741\) | −2.08011e15 | −0.342047 | ||||||||
\(742\) | 5.08149e15 | 0.829411 | ||||||||
\(743\) | 5.72916e15 | 0.928223 | 0.464111 | − | 0.885777i | \(-0.346374\pi\) | ||||
0.464111 | + | 0.885777i | \(0.346374\pi\) | |||||||
\(744\) | 5.61838e15 | 0.903566 | ||||||||
\(745\) | 2.54804e13 | 0.00406768 | ||||||||
\(746\) | 2.09204e15 | 0.331517 | ||||||||
\(747\) | −3.21425e15 | −0.505611 | ||||||||
\(748\) | −1.37641e15 | −0.214926 | ||||||||
\(749\) | 1.45363e14 | 0.0225322 | ||||||||
\(750\) | −1.79051e13 | −0.00275512 | ||||||||
\(751\) | −1.03765e16 | −1.58501 | −0.792504 | − | 0.609866i | \(-0.791223\pi\) | ||||
−0.792504 | + | 0.609866i | \(0.791223\pi\) | |||||||
\(752\) | 2.83177e15 | 0.429398 | ||||||||
\(753\) | −1.84739e15 | −0.278090 | ||||||||
\(754\) | −8.57603e15 | −1.28157 | ||||||||
\(755\) | −6.55217e12 | −0.000972024 0 | ||||||||
\(756\) | 1.75654e15 | 0.258694 | ||||||||
\(757\) | −4.55421e15 | −0.665864 | −0.332932 | − | 0.942951i | \(-0.608038\pi\) | ||||
−0.332932 | + | 0.942951i | \(0.608038\pi\) | |||||||
\(758\) | −2.86898e15 | −0.416435 | ||||||||
\(759\) | 1.39032e15 | 0.200349 | ||||||||
\(760\) | −1.08739e13 | −0.00155564 | ||||||||
\(761\) | −6.12924e15 | −0.870544 | −0.435272 | − | 0.900299i | \(-0.643348\pi\) | ||||
−0.435272 | + | 0.900299i | \(0.643348\pi\) | |||||||
\(762\) | 4.17031e15 | 0.588053 | ||||||||
\(763\) | −2.00172e16 | −2.80232 | ||||||||
\(764\) | −5.38727e15 | −0.748781 | ||||||||
\(765\) | −8.91695e12 | −0.00123049 | ||||||||
\(766\) | 2.96575e15 | 0.406327 | ||||||||
\(767\) | −1.51294e15 | −0.205800 | ||||||||
\(768\) | −3.01692e15 | −0.407453 | ||||||||
\(769\) | −5.25841e14 | −0.0705115 | −0.0352557 | − | 0.999378i | \(-0.511225\pi\) | ||||
−0.0352557 | + | 0.999378i | \(0.511225\pi\) | |||||||
\(770\) | 1.19889e13 | 0.00159618 | ||||||||
\(771\) | −2.08634e13 | −0.00275794 | ||||||||
\(772\) | 1.86217e15 | 0.244413 | ||||||||
\(773\) | −4.59777e14 | −0.0599184 | −0.0299592 | − | 0.999551i | \(-0.509538\pi\) | ||||
−0.0299592 | + | 0.999551i | \(0.509538\pi\) | |||||||
\(774\) | 1.20355e15 | 0.155736 | ||||||||
\(775\) | 1.37223e16 | 1.76306 | ||||||||
\(776\) | −5.09392e15 | −0.649849 | ||||||||
\(777\) | 6.00672e15 | 0.760890 | ||||||||
\(778\) | −5.66780e15 | −0.712896 | ||||||||
\(779\) | −4.24367e15 | −0.530012 | ||||||||
\(780\) | 2.54533e13 | 0.00315663 | ||||||||
\(781\) | −4.75685e14 | −0.0585785 | ||||||||
\(782\) | 3.10542e15 | 0.379737 | ||||||||
\(783\) | 2.51822e15 | 0.305777 | ||||||||
\(784\) | 5.47595e15 | 0.660270 | ||||||||
\(785\) | 5.28530e12 | 0.000632829 0 | ||||||||
\(786\) | −4.25685e15 | −0.506133 | ||||||||
\(787\) | 1.58443e16 | 1.87074 | 0.935369 | − | 0.353674i | \(-0.115068\pi\) | ||||
0.935369 | + | 0.353674i | \(0.115068\pi\) | |||||||
\(788\) | −1.53835e15 | −0.180369 | ||||||||
\(789\) | 2.11509e15 | 0.246267 | ||||||||
\(790\) | 4.93689e12 | 0.000570827 0 | ||||||||
\(791\) | 1.08087e15 | 0.124109 | ||||||||
\(792\) | 9.55148e14 | 0.108914 | ||||||||
\(793\) | 1.57891e16 | 1.78795 | ||||||||
\(794\) | 4.80966e15 | 0.540881 | ||||||||
\(795\) | −2.16216e13 | −0.00241473 | ||||||||
\(796\) | −9.37884e15 | −1.04022 | ||||||||
\(797\) | 1.10469e16 | 1.21680 | 0.608400 | − | 0.793631i | \(-0.291812\pi\) | ||||
0.608400 | + | 0.793631i | \(0.291812\pi\) | |||||||
\(798\) | −1.83426e15 | −0.200653 | ||||||||
\(799\) | −1.08825e16 | −1.18228 | ||||||||
\(800\) | −9.58266e15 | −1.03393 | ||||||||
\(801\) | 2.81683e15 | 0.301844 | ||||||||
\(802\) | −2.90321e15 | −0.308972 | ||||||||
\(803\) | −5.62752e15 | −0.594814 | ||||||||
\(804\) | 3.81589e14 | 0.0400578 | ||||||||
\(805\) | 7.68429e13 | 0.00801173 | ||||||||
\(806\) | 1.37333e16 | 1.42211 | ||||||||
\(807\) | −8.50650e15 | −0.874876 | ||||||||
\(808\) | 1.22027e16 | 1.24651 | ||||||||
\(809\) | −1.65576e16 | −1.67989 | −0.839947 | − | 0.542669i | \(-0.817414\pi\) | ||||
−0.839947 | + | 0.542669i | \(0.817414\pi\) | |||||||
\(810\) | 2.63088e12 | 0.000265114 0 | ||||||||
\(811\) | −4.97584e15 | −0.498025 | −0.249013 | − | 0.968500i | \(-0.580106\pi\) | ||||
−0.249013 | + | 0.968500i | \(0.580106\pi\) | |||||||
\(812\) | 2.14839e16 | 2.13578 | ||||||||
\(813\) | 3.08198e15 | 0.304321 | ||||||||
\(814\) | 1.38871e15 | 0.136201 | ||||||||
\(815\) | −6.19722e13 | −0.00603712 | ||||||||
\(816\) | −1.35049e15 | −0.130676 | ||||||||
\(817\) | 3.57044e15 | 0.343163 | ||||||||
\(818\) | −2.96046e15 | −0.282628 | ||||||||
\(819\) | 1.00986e16 | 0.957631 | ||||||||
\(820\) | 5.19278e13 | 0.00489129 | ||||||||
\(821\) | −1.06268e16 | −0.994295 | −0.497147 | − | 0.867666i | \(-0.665619\pi\) | ||||
−0.497147 | + | 0.867666i | \(0.665619\pi\) | |||||||
\(822\) | −3.80371e15 | −0.353519 | ||||||||
\(823\) | 4.84440e15 | 0.447240 | 0.223620 | − | 0.974676i | \(-0.428213\pi\) | ||||
0.223620 | + | 0.974676i | \(0.428213\pi\) | |||||||
\(824\) | 8.87725e15 | 0.814102 | ||||||||
\(825\) | 2.33284e15 | 0.212514 | ||||||||
\(826\) | −1.33412e15 | −0.120727 | ||||||||
\(827\) | −1.28296e16 | −1.15327 | −0.576636 | − | 0.817001i | \(-0.695635\pi\) | ||||
−0.576636 | + | 0.817001i | \(0.695635\pi\) | |||||||
\(828\) | 2.60289e15 | 0.232428 | ||||||||
\(829\) | −4.09240e15 | −0.363018 | −0.181509 | − | 0.983389i | \(-0.558098\pi\) | ||||
−0.181509 | + | 0.983389i | \(0.558098\pi\) | |||||||
\(830\) | −4.10717e13 | −0.00361921 | ||||||||
\(831\) | −2.89033e15 | −0.253012 | ||||||||
\(832\) | −4.37846e15 | −0.380753 | ||||||||
\(833\) | −2.10441e16 | −1.81795 | ||||||||
\(834\) | −4.59832e15 | −0.394626 | ||||||||
\(835\) | −2.60720e13 | −0.00222279 | ||||||||
\(836\) | 1.20473e15 | 0.102036 | ||||||||
\(837\) | −4.03259e15 | −0.339308 | ||||||||
\(838\) | −5.59323e15 | −0.467542 | ||||||||
\(839\) | −2.34497e13 | −0.00194736 | −0.000973681 | − | 1.00000i | \(-0.500310\pi\) | ||||
−0.000973681 | 1.00000i | \(0.500310\pi\) | ||||||||
\(840\) | 5.27908e13 | 0.00435534 | ||||||||
\(841\) | 1.85995e16 | 1.52449 | ||||||||
\(842\) | −1.12475e16 | −0.915883 | ||||||||
\(843\) | −1.20877e16 | −0.977895 | ||||||||
\(844\) | −3.82518e15 | −0.307446 | ||||||||
\(845\) | 8.77745e13 | 0.00700900 | ||||||||
\(846\) | 3.21080e15 | 0.254728 | ||||||||
\(847\) | 1.99331e16 | 1.57114 | ||||||||
\(848\) | −3.27464e15 | −0.256440 | ||||||||
\(849\) | 1.84593e14 | 0.0143623 | ||||||||
\(850\) | 5.21061e15 | 0.402796 | ||||||||
\(851\) | 8.90095e15 | 0.683634 | ||||||||
\(852\) | −8.90552e14 | −0.0679581 | ||||||||
\(853\) | 1.55756e16 | 1.18094 | 0.590468 | − | 0.807061i | \(-0.298943\pi\) | ||||
0.590468 | + | 0.807061i | \(0.298943\pi\) | |||||||
\(854\) | 1.39230e16 | 1.04886 | ||||||||
\(855\) | 7.80473e12 | 0.000584176 0 | ||||||||
\(856\) | 1.47981e14 | 0.0110053 | ||||||||
\(857\) | −5.14979e15 | −0.380535 | −0.190268 | − | 0.981732i | \(-0.560936\pi\) | ||||
−0.190268 | + | 0.981732i | \(0.560936\pi\) | |||||||
\(858\) | 2.33472e15 | 0.171417 | ||||||||
\(859\) | 1.33478e16 | 0.973748 | 0.486874 | − | 0.873472i | \(-0.338137\pi\) | ||||
0.486874 | + | 0.873472i | \(0.338137\pi\) | |||||||
\(860\) | −4.36898e13 | −0.00316693 | ||||||||
\(861\) | 2.06023e16 | 1.48388 | ||||||||
\(862\) | 1.38521e15 | 0.0991347 | ||||||||
\(863\) | −1.56635e16 | −1.11386 | −0.556929 | − | 0.830560i | \(-0.688020\pi\) | ||||
−0.556929 | + | 0.830560i | \(0.688020\pi\) | |||||||
\(864\) | 2.81608e15 | 0.198984 | ||||||||
\(865\) | 1.15260e14 | 0.00809265 | ||||||||
\(866\) | 7.81482e15 | 0.545219 | ||||||||
\(867\) | −3.13812e15 | −0.217553 | ||||||||
\(868\) | −3.44035e16 | −2.36998 | ||||||||
\(869\) | −1.28646e15 | −0.0880617 | ||||||||
\(870\) | 3.21779e13 | 0.00218878 | ||||||||
\(871\) | 2.19381e15 | 0.148285 | ||||||||
\(872\) | −2.03777e16 | −1.36872 | ||||||||
\(873\) | 3.65615e15 | 0.244032 | ||||||||
\(874\) | −2.71807e15 | −0.180280 | ||||||||
\(875\) | 2.57874e14 | 0.0169966 | ||||||||
\(876\) | −1.05355e16 | −0.690056 | ||||||||
\(877\) | 2.79689e15 | 0.182045 | 0.0910223 | − | 0.995849i | \(-0.470987\pi\) | ||||
0.0910223 | + | 0.995849i | \(0.470987\pi\) | |||||||
\(878\) | −2.04877e15 | −0.132518 | ||||||||
\(879\) | 2.04061e15 | 0.131166 | ||||||||
\(880\) | −7.72595e12 | −0.000493512 0 | ||||||||
\(881\) | 2.21053e16 | 1.40323 | 0.701615 | − | 0.712556i | \(-0.252462\pi\) | ||||
0.701615 | + | 0.712556i | \(0.252462\pi\) | |||||||
\(882\) | 6.20889e15 | 0.391685 | ||||||||
\(883\) | 1.88831e16 | 1.18383 | 0.591916 | − | 0.805999i | \(-0.298372\pi\) | ||||
0.591916 | + | 0.805999i | \(0.298372\pi\) | |||||||
\(884\) | −1.48146e16 | −0.923004 | ||||||||
\(885\) | 5.67665e12 | 0.000351483 0 | ||||||||
\(886\) | 1.13423e16 | 0.697936 | ||||||||
\(887\) | −6.82286e15 | −0.417240 | −0.208620 | − | 0.977997i | \(-0.566897\pi\) | ||||
−0.208620 | + | 0.977997i | \(0.566897\pi\) | |||||||
\(888\) | 6.11493e15 | 0.371638 | ||||||||
\(889\) | −6.00618e16 | −3.62776 | ||||||||
\(890\) | 3.59935e13 | 0.00216062 | ||||||||
\(891\) | −6.85556e14 | −0.0408993 | ||||||||
\(892\) | −1.83856e16 | −1.09011 | ||||||||
\(893\) | 9.52511e15 | 0.561289 | ||||||||
\(894\) | 4.37559e15 | 0.256260 | ||||||||
\(895\) | −8.95150e13 | −0.00521038 | ||||||||
\(896\) | 2.86210e16 | 1.65573 | ||||||||
\(897\) | 1.49644e16 | 0.860400 | ||||||||
\(898\) | 1.91876e15 | 0.109648 | ||||||||
\(899\) | −4.93220e16 | −2.80132 | ||||||||
\(900\) | 4.36742e15 | 0.246542 | ||||||||
\(901\) | 1.25844e16 | 0.706069 | ||||||||
\(902\) | 4.76311e15 | 0.265616 | ||||||||
\(903\) | −1.73338e16 | −0.960754 | ||||||||
\(904\) | 1.10034e15 | 0.0606180 | ||||||||
\(905\) | 5.84222e13 | 0.00319897 | ||||||||
\(906\) | −1.12516e15 | −0.0612365 | ||||||||
\(907\) | 3.32482e16 | 1.79857 | 0.899285 | − | 0.437362i | \(-0.144087\pi\) | ||||
0.899285 | + | 0.437362i | \(0.144087\pi\) | |||||||
\(908\) | −6.57852e15 | −0.353717 | ||||||||
\(909\) | −8.75849e15 | −0.468088 | ||||||||
\(910\) | 1.29039e14 | 0.00685480 | ||||||||
\(911\) | 3.33817e16 | 1.76261 | 0.881307 | − | 0.472544i | \(-0.156664\pi\) | ||||
0.881307 | + | 0.472544i | \(0.156664\pi\) | |||||||
\(912\) | 1.18205e15 | 0.0620387 | ||||||||
\(913\) | 1.07025e16 | 0.558337 | ||||||||
\(914\) | −1.53764e16 | −0.797353 | ||||||||
\(915\) | −5.92420e13 | −0.00305361 | ||||||||
\(916\) | −1.67334e16 | −0.857353 | ||||||||
\(917\) | 6.13082e16 | 3.12239 | ||||||||
\(918\) | −1.53125e15 | −0.0775198 | ||||||||
\(919\) | −3.87899e15 | −0.195201 | −0.0976007 | − | 0.995226i | \(-0.531117\pi\) | ||||
−0.0976007 | + | 0.995226i | \(0.531117\pi\) | |||||||
\(920\) | 7.82271e13 | 0.00391313 | ||||||||
\(921\) | −7.32403e15 | −0.364185 | ||||||||
\(922\) | 2.66453e15 | 0.131705 | ||||||||
\(923\) | −5.11991e15 | −0.251566 | ||||||||
\(924\) | −5.84874e15 | −0.285671 | ||||||||
\(925\) | 1.49350e16 | 0.725147 | ||||||||
\(926\) | −1.55702e16 | −0.751509 | ||||||||
\(927\) | −6.37164e15 | −0.305712 | ||||||||
\(928\) | 3.44430e16 | 1.64281 | ||||||||
\(929\) | 2.71315e16 | 1.28643 | 0.643217 | − | 0.765684i | \(-0.277599\pi\) | ||||
0.643217 | + | 0.765684i | \(0.277599\pi\) | |||||||
\(930\) | −5.15284e13 | −0.00242879 | ||||||||
\(931\) | 1.84192e16 | 0.863074 | ||||||||
\(932\) | −1.75754e16 | −0.818684 | ||||||||
\(933\) | 1.21970e16 | 0.564811 | ||||||||
\(934\) | 6.06940e15 | 0.279407 | ||||||||
\(935\) | 2.96908e13 | 0.00135881 | ||||||||
\(936\) | 1.02805e16 | 0.467731 | ||||||||
\(937\) | −1.07760e15 | −0.0487404 | −0.0243702 | − | 0.999703i | \(-0.507758\pi\) | ||||
−0.0243702 | + | 0.999703i | \(0.507758\pi\) | |||||||
\(938\) | 1.93452e15 | 0.0869878 | ||||||||
\(939\) | −1.08816e16 | −0.486445 | ||||||||
\(940\) | −1.16554e14 | −0.00517994 | ||||||||
\(941\) | 3.70173e16 | 1.63554 | 0.817771 | − | 0.575544i | \(-0.195210\pi\) | ||||
0.817771 | + | 0.575544i | \(0.195210\pi\) | |||||||
\(942\) | 9.07611e14 | 0.0398676 | ||||||||
\(943\) | 3.05291e16 | 1.33321 | ||||||||
\(944\) | 8.59742e14 | 0.0373269 | ||||||||
\(945\) | −3.78905e13 | −0.00163552 | ||||||||
\(946\) | −4.00747e15 | −0.171977 | ||||||||
\(947\) | −1.04889e16 | −0.447513 | −0.223756 | − | 0.974645i | \(-0.571832\pi\) | ||||
−0.223756 | + | 0.974645i | \(0.571832\pi\) | |||||||
\(948\) | −2.40844e15 | −0.102162 | ||||||||
\(949\) | −6.05703e16 | −2.55444 | ||||||||
\(950\) | −4.56068e15 | −0.191227 | ||||||||
\(951\) | −1.82818e16 | −0.762123 | ||||||||
\(952\) | −3.07259e16 | −1.27351 | ||||||||
\(953\) | 3.94046e15 | 0.162381 | 0.0811906 | − | 0.996699i | \(-0.474128\pi\) | ||||
0.0811906 | + | 0.996699i | \(0.474128\pi\) | |||||||
\(954\) | −3.71294e15 | −0.152125 | ||||||||
\(955\) | 1.16210e14 | 0.00473395 | ||||||||
\(956\) | 2.86024e16 | 1.15847 | ||||||||
\(957\) | −8.38494e15 | −0.337664 | ||||||||
\(958\) | 3.11930e15 | 0.124896 | ||||||||
\(959\) | 5.47820e16 | 2.18090 | ||||||||
\(960\) | 1.64283e13 | 0.000650280 0 | ||||||||
\(961\) | 5.35739e16 | 2.10850 | ||||||||
\(962\) | 1.49471e16 | 0.584915 | ||||||||
\(963\) | −1.06213e14 | −0.00413270 | ||||||||
\(964\) | 1.92538e16 | 0.744891 | ||||||||
\(965\) | −4.01692e13 | −0.00154523 | ||||||||
\(966\) | 1.31958e16 | 0.504731 | ||||||||
\(967\) | −1.48756e16 | −0.565756 | −0.282878 | − | 0.959156i | \(-0.591289\pi\) | ||||
−0.282878 | + | 0.959156i | \(0.591289\pi\) | |||||||
\(968\) | 2.02921e16 | 0.767385 | ||||||||
\(969\) | −4.54260e15 | −0.170814 | ||||||||
\(970\) | 4.67184e13 | 0.00174680 | ||||||||
\(971\) | 1.88583e16 | 0.701126 | 0.350563 | − | 0.936539i | \(-0.385990\pi\) | ||||
0.350563 | + | 0.936539i | \(0.385990\pi\) | |||||||
\(972\) | −1.28346e15 | −0.0474481 | ||||||||
\(973\) | 6.62261e16 | 2.43449 | ||||||||
\(974\) | 6.92119e15 | 0.252992 | ||||||||
\(975\) | 2.51089e16 | 0.912646 | ||||||||
\(976\) | −8.97235e15 | −0.324289 | ||||||||
\(977\) | −1.93781e16 | −0.696450 | −0.348225 | − | 0.937411i | \(-0.613216\pi\) | ||||
−0.348225 | + | 0.937411i | \(0.613216\pi\) | |||||||
\(978\) | −1.06421e16 | −0.380333 | ||||||||
\(979\) | −9.37921e15 | −0.333320 | ||||||||
\(980\) | −2.25387e14 | −0.00796500 | ||||||||
\(981\) | 1.46261e16 | 0.513983 | ||||||||
\(982\) | 2.22808e16 | 0.778605 | ||||||||
\(983\) | 4.98162e16 | 1.73112 | 0.865558 | − | 0.500809i | \(-0.166964\pi\) | ||||
0.865558 | + | 0.500809i | \(0.166964\pi\) | |||||||
\(984\) | 2.09734e16 | 0.724762 | ||||||||
\(985\) | 3.31840e13 | 0.00114033 | ||||||||
\(986\) | −1.87285e16 | −0.640001 | ||||||||
\(987\) | −4.62427e16 | −1.57144 | ||||||||
\(988\) | 1.29668e16 | 0.438197 | ||||||||
\(989\) | −2.56858e16 | −0.863206 | ||||||||
\(990\) | −8.76004e12 | −0.000292761 0 | ||||||||
\(991\) | −9.60040e15 | −0.319069 | −0.159534 | − | 0.987192i | \(-0.550999\pi\) | ||||
−0.159534 | + | 0.987192i | \(0.550999\pi\) | |||||||
\(992\) | −5.51557e16 | −1.82296 | ||||||||
\(993\) | 9.16164e15 | 0.301129 | ||||||||
\(994\) | −4.51479e15 | −0.147575 | ||||||||
\(995\) | 2.02313e14 | 0.00657652 | ||||||||
\(996\) | 2.00367e16 | 0.647737 | ||||||||
\(997\) | 2.54447e16 | 0.818039 | 0.409020 | − | 0.912526i | \(-0.365871\pi\) | ||||
0.409020 | + | 0.912526i | \(0.365871\pi\) | |||||||
\(998\) | 1.89062e16 | 0.604485 | ||||||||
\(999\) | −4.38898e15 | −0.139558 |
(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.d.1.16 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.12.a.d.1.16 | ✓ | 28 | 1.1 | even | 1 | trivial |