Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [10,15,Mod(3,10)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3]))
N = Newforms(chi, 15, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("10.3");
S:= CuspForms(chi, 15);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 15 \) |
Character orbit: | \([\chi]\) | \(=\) | 10.c (of order \(4\), degree \(2\), minimal) |
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: | no |
Analytic conductor: | \(12.4328968152\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 513401x^{6} + 81983771116x^{4} + 4511941511282436x^{2} + 65023716741123799296 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{14}\cdot 3^{4}\cdot 5^{9} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 7.3 | ||
Root | \(394.425i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 10.7 |
Dual form | 10.15.c.b.3.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/10\mathbb{Z}\right)^\times\).
\(n\) | \(7\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 64.0000 | + | 64.0000i | 0.500000 | + | 0.500000i | ||||
\(3\) | 803.510 | − | 803.510i | 0.367403 | − | 0.367403i | −0.499126 | − | 0.866529i | \(-0.666346\pi\) |
0.866529 | + | 0.499126i | \(0.166346\pi\) | |||||||
\(4\) | 8192.00i | 0.500000i | ||||||||
\(5\) | −66844.3 | − | 40439.5i | −0.855607 | − | 0.517626i | ||||
\(6\) | 102849. | 0.367403 | ||||||||
\(7\) | −657264. | − | 657264.i | −0.798093 | − | 0.798093i | 0.184701 | − | 0.982795i | \(-0.440868\pi\) |
−0.982795 | + | 0.184701i | \(0.940868\pi\) | |||||||
\(8\) | −524288. | + | 524288.i | −0.250000 | + | 0.250000i | ||||
\(9\) | 3.49171e6i | 0.730030i | ||||||||
\(10\) | −1.68991e6 | − | 6.86616e6i | −0.168991 | − | 0.686616i | ||||
\(11\) | −3.22749e7 | −1.65621 | −0.828106 | − | 0.560572i | \(-0.810581\pi\) | ||||
−0.828106 | + | 0.560572i | \(0.810581\pi\) | |||||||
\(12\) | 6.58235e6 | + | 6.58235e6i | 0.183701 | + | 0.183701i | ||||
\(13\) | 6.03964e7 | − | 6.03964e7i | 0.962515 | − | 0.962515i | −0.0368076 | − | 0.999322i | \(-0.511719\pi\) |
0.999322 | + | 0.0368076i | \(0.0117189\pi\) | |||||||
\(14\) | − | 8.41298e7i | − | 0.798093i | ||||||
\(15\) | −8.62036e7 | + | 2.12165e7i | −0.504529 | + | 0.124175i | ||||
\(16\) | −6.71089e7 | −0.250000 | ||||||||
\(17\) | −4.71953e8 | − | 4.71953e8i | −1.15015 | − | 1.15015i | −0.986521 | − | 0.163634i | \(-0.947679\pi\) |
−0.163634 | − | 0.986521i | \(-0.552321\pi\) | |||||||
\(18\) | −2.23470e8 | + | 2.23470e8i | −0.365015 | + | 0.365015i | ||||
\(19\) | − | 1.04276e8i | − | 0.116657i | −0.998297 | − | 0.0583285i | \(-0.981423\pi\) | ||
0.998297 | − | 0.0583285i | \(-0.0185771\pi\) | |||||||
\(20\) | 3.31280e8 | − | 5.47589e8i | 0.258813 | − | 0.427804i | ||||
\(21\) | −1.05624e9 | −0.586443 | ||||||||
\(22\) | −2.06559e9 | − | 2.06559e9i | −0.828106 | − | 0.828106i | ||||
\(23\) | 1.62414e8 | − | 1.62414e8i | 0.0477011 | − | 0.0477011i | −0.682854 | − | 0.730555i | \(-0.739261\pi\) |
0.730555 | + | 0.682854i | \(0.239261\pi\) | |||||||
\(24\) | 8.42541e8i | 0.183701i | ||||||||
\(25\) | 2.83281e9 | + | 5.40630e9i | 0.464128 | + | 0.885768i | ||||
\(26\) | 7.73074e9 | 0.962515 | ||||||||
\(27\) | 6.64879e9 | + | 6.64879e9i | 0.635618 | + | 0.635618i | ||||
\(28\) | 5.38431e9 | − | 5.38431e9i | 0.399047 | − | 0.399047i | ||||
\(29\) | 1.93503e10i | 1.12176i | 0.827896 | + | 0.560882i | \(0.189538\pi\) | ||||
−0.827896 | + | 0.560882i | \(0.810462\pi\) | |||||||
\(30\) | −6.87489e9 | − | 4.15917e9i | −0.314352 | − | 0.190177i | ||||
\(31\) | 2.02592e10 | 0.736360 | 0.368180 | − | 0.929754i | \(-0.379981\pi\) | ||||
0.368180 | + | 0.929754i | \(0.379981\pi\) | |||||||
\(32\) | −4.29497e9 | − | 4.29497e9i | −0.125000 | − | 0.125000i | ||||
\(33\) | −2.59332e10 | + | 2.59332e10i | −0.608497 | + | 0.608497i | ||||
\(34\) | − | 6.04100e10i | − | 1.15015i | ||||||
\(35\) | 1.73549e10 | + | 7.05138e10i | 0.269741 | + | 1.09597i | ||||
\(36\) | −2.86041e10 | −0.365015 | ||||||||
\(37\) | −5.96741e10 | − | 5.96741e10i | −0.628599 | − | 0.628599i | 0.319116 | − | 0.947716i | \(-0.396614\pi\) |
−0.947716 | + | 0.319116i | \(0.896614\pi\) | |||||||
\(38\) | 6.67369e9 | − | 6.67369e9i | 0.0583285 | − | 0.0583285i | ||||
\(39\) | − | 9.70582e10i | − | 0.707261i | ||||||
\(40\) | 5.62476e10 | − | 1.38437e10i | 0.343308 | − | 0.0844954i | ||||
\(41\) | 5.92311e9 | 0.0304133 | 0.0152066 | − | 0.999884i | \(-0.495159\pi\) | ||||
0.0152066 | + | 0.999884i | \(0.495159\pi\) | |||||||
\(42\) | −6.75991e10 | − | 6.75991e10i | −0.293222 | − | 0.293222i | ||||
\(43\) | −2.19515e11 | + | 2.19515e11i | −0.807579 | + | 0.807579i | −0.984267 | − | 0.176688i | \(-0.943462\pi\) |
0.176688 | + | 0.984267i | \(0.443462\pi\) | |||||||
\(44\) | − | 2.64396e11i | − | 0.828106i | ||||||
\(45\) | 1.41203e11 | − | 2.33401e11i | 0.377882 | − | 0.624619i | ||||
\(46\) | 2.07890e10 | 0.0477011 | ||||||||
\(47\) | 8.05628e10 | + | 8.05628e10i | 0.159019 | + | 0.159019i | 0.782132 | − | 0.623113i | \(-0.214132\pi\) |
−0.623113 | + | 0.782132i | \(0.714132\pi\) | |||||||
\(48\) | −5.39226e10 | + | 5.39226e10i | −0.0918507 | + | 0.0918507i | ||||
\(49\) | 1.85769e11i | 0.273906i | ||||||||
\(50\) | −1.64703e11 | + | 5.27303e11i | −0.210820 | + | 0.674948i | ||||
\(51\) | −7.58438e11 | −0.845140 | ||||||||
\(52\) | 4.94767e11 | + | 4.94767e11i | 0.481257 | + | 0.481257i | ||||
\(53\) | 8.11926e11 | − | 8.11926e11i | 0.691171 | − | 0.691171i | −0.271319 | − | 0.962490i | \(-0.587460\pi\) |
0.962490 | + | 0.271319i | \(0.0874597\pi\) | |||||||
\(54\) | 8.51045e11i | 0.635618i | ||||||||
\(55\) | 2.15739e12 | + | 1.30518e12i | 1.41707 | + | 0.857298i | ||||
\(56\) | 6.89191e11 | 0.399047 | ||||||||
\(57\) | −8.37871e10 | − | 8.37871e10i | −0.0428601 | − | 0.0428601i | ||||
\(58\) | −1.23842e12 | + | 1.23842e12i | −0.560882 | + | 0.560882i | ||||
\(59\) | − | 2.98543e12i | − | 1.19962i | −0.800144 | − | 0.599808i | \(-0.795244\pi\) | ||
0.800144 | − | 0.599808i | \(-0.204756\pi\) | |||||||
\(60\) | −1.73806e11 | − | 7.06180e11i | −0.0620877 | − | 0.252265i | ||||
\(61\) | −1.20995e12 | −0.384997 | −0.192499 | − | 0.981297i | \(-0.561659\pi\) | ||||
−0.192499 | + | 0.981297i | \(0.561659\pi\) | |||||||
\(62\) | 1.29659e12 | + | 1.29659e12i | 0.368180 | + | 0.368180i | ||||
\(63\) | 2.29498e12 | − | 2.29498e12i | 0.582632 | − | 0.582632i | ||||
\(64\) | − | 5.49756e11i | − | 0.125000i | ||||||
\(65\) | −6.47955e12 | + | 1.59476e12i | −1.32176 | + | 0.325312i | ||||
\(66\) | −3.31945e12 | −0.608497 | ||||||||
\(67\) | −2.14532e12 | − | 2.14532e12i | −0.353971 | − | 0.353971i | 0.507614 | − | 0.861585i | \(-0.330528\pi\) |
−0.861585 | + | 0.507614i | \(0.830528\pi\) | |||||||
\(68\) | 3.86624e12 | − | 3.86624e12i | 0.575077 | − | 0.575077i | ||||
\(69\) | − | 2.61002e11i | − | 0.0350510i | ||||||
\(70\) | −3.40217e12 | + | 5.62360e12i | −0.413113 | + | 0.682854i | ||||
\(71\) | −1.46929e13 | −1.61547 | −0.807737 | − | 0.589543i | \(-0.799308\pi\) | ||||
−0.807737 | + | 0.589543i | \(0.799308\pi\) | |||||||
\(72\) | −1.83066e12 | − | 1.83066e12i | −0.182508 | − | 0.182508i | ||||
\(73\) | 1.07590e13 | − | 1.07590e13i | 0.973897 | − | 0.973897i | −0.0257706 | − | 0.999668i | \(-0.508204\pi\) |
0.999668 | + | 0.0257706i | \(0.00820395\pi\) | |||||||
\(74\) | − | 7.63829e12i | − | 0.628599i | ||||||
\(75\) | 6.62021e12 | + | 2.06783e12i | 0.495955 | + | 0.154912i | ||||
\(76\) | 8.54232e11 | 0.0583285 | ||||||||
\(77\) | 2.12131e13 | + | 2.12131e13i | 1.32181 | + | 1.32181i | ||||
\(78\) | 6.21172e12 | − | 6.21172e12i | 0.353631 | − | 0.353631i | ||||
\(79\) | 1.48621e13i | 0.773908i | 0.922099 | + | 0.386954i | \(0.126473\pi\) | ||||
−0.922099 | + | 0.386954i | \(0.873527\pi\) | |||||||
\(80\) | 4.48585e12 | + | 2.71385e12i | 0.213902 | + | 0.129406i | ||||
\(81\) | −6.01602e12 | −0.262975 | ||||||||
\(82\) | 3.79079e11 | + | 3.79079e11i | 0.0152066 | + | 0.0152066i | ||||
\(83\) | −4.77351e12 | + | 4.77351e12i | −0.175910 | + | 0.175910i | −0.789570 | − | 0.613660i | \(-0.789697\pi\) |
0.613660 | + | 0.789570i | \(0.289697\pi\) | |||||||
\(84\) | − | 8.65269e12i | − | 0.293222i | ||||||
\(85\) | 1.24618e13 | + | 5.06329e13i | 0.388731 | + | 1.57943i | ||||
\(86\) | −2.80979e13 | −0.807579 | ||||||||
\(87\) | 1.55481e13 | + | 1.55481e13i | 0.412139 | + | 0.412139i | ||||
\(88\) | 1.69213e13 | − | 1.69213e13i | 0.414053 | − | 0.414053i | ||||
\(89\) | − | 6.04797e13i | − | 1.36735i | −0.729787 | − | 0.683675i | \(-0.760381\pi\) | ||
0.729787 | − | 0.683675i | \(-0.239619\pi\) | |||||||
\(90\) | 2.39747e13 | − | 5.90068e12i | 0.501251 | − | 0.123368i | ||||
\(91\) | −7.93927e13 | −1.53635 | ||||||||
\(92\) | 1.33050e12 | + | 1.33050e12i | 0.0238506 | + | 0.0238506i | ||||
\(93\) | 1.62785e13 | − | 1.62785e13i | 0.270541 | − | 0.270541i | ||||
\(94\) | 1.03120e13i | 0.159019i | ||||||||
\(95\) | −4.21689e12 | + | 6.97029e12i | −0.0603847 | + | 0.0998126i | ||||
\(96\) | −6.90210e12 | −0.0918507 | ||||||||
\(97\) | 3.52779e12 | + | 3.52779e12i | 0.0436617 | + | 0.0436617i | 0.728601 | − | 0.684939i | \(-0.240171\pi\) |
−0.684939 | + | 0.728601i | \(0.740171\pi\) | |||||||
\(98\) | −1.18892e13 | + | 1.18892e13i | −0.136953 | + | 0.136953i | ||||
\(99\) | − | 1.12695e14i | − | 1.20909i | ||||||
\(100\) | −4.42884e13 | + | 2.32064e13i | −0.442884 | + | 0.232064i | ||||
\(101\) | −2.44883e13 | −0.228406 | −0.114203 | − | 0.993457i | \(-0.536432\pi\) | ||||
−0.114203 | + | 0.993457i | \(0.536432\pi\) | |||||||
\(102\) | −4.85400e13 | − | 4.85400e13i | −0.422570 | − | 0.422570i | ||||
\(103\) | 2.49581e13 | − | 2.49581e13i | 0.202932 | − | 0.202932i | −0.598323 | − | 0.801255i | \(-0.704166\pi\) |
0.801255 | + | 0.598323i | \(0.204166\pi\) | |||||||
\(104\) | 6.33302e13i | 0.481257i | ||||||||
\(105\) | 7.06034e13 | + | 4.27137e13i | 0.501765 | + | 0.303558i | ||||
\(106\) | 1.03927e14 | 0.691171 | ||||||||
\(107\) | −4.22212e13 | − | 4.22212e13i | −0.262932 | − | 0.262932i | 0.563312 | − | 0.826244i | \(-0.309527\pi\) |
−0.826244 | + | 0.563312i | \(0.809527\pi\) | |||||||
\(108\) | −5.44669e13 | + | 5.44669e13i | −0.317809 | + | 0.317809i | ||||
\(109\) | − | 2.61457e14i | − | 1.43026i | −0.698993 | − | 0.715128i | \(-0.746368\pi\) | ||
0.698993 | − | 0.715128i | \(-0.253632\pi\) | |||||||
\(110\) | 5.45416e13 | + | 2.21605e14i | 0.279885 | + | 1.13718i | ||||
\(111\) | −9.58975e13 | −0.461898 | ||||||||
\(112\) | 4.41082e13 | + | 4.41082e13i | 0.199523 | + | 0.199523i | ||||
\(113\) | −7.69947e13 | + | 7.69947e13i | −0.327274 | + | 0.327274i | −0.851549 | − | 0.524275i | \(-0.824336\pi\) |
0.524275 | + | 0.851549i | \(0.324336\pi\) | |||||||
\(114\) | − | 1.07248e13i | − | 0.0428601i | ||||||
\(115\) | −1.74244e13 | + | 4.28851e12i | −0.0655047 | + | 0.0161221i | ||||
\(116\) | −1.58518e14 | −0.560882 | ||||||||
\(117\) | 2.10887e14 | + | 2.10887e14i | 0.702665 | + | 0.702665i | ||||
\(118\) | 1.91067e14 | − | 1.91067e14i | 0.599808 | − | 0.599808i | ||||
\(119\) | 6.20395e14i | 1.83586i | ||||||||
\(120\) | 3.40719e13 | − | 5.63191e13i | 0.0950885 | − | 0.157176i | ||||
\(121\) | 6.61918e14 | 1.74304 | ||||||||
\(122\) | −7.74367e13 | − | 7.74367e13i | −0.192499 | − | 0.192499i | ||||
\(123\) | 4.75928e12 | − | 4.75928e12i | 0.0111739 | − | 0.0111739i | ||||
\(124\) | 1.65963e14i | 0.368180i | ||||||||
\(125\) | 2.92708e13 | − | 4.75938e14i | 0.0613854 | − | 0.998114i | ||||
\(126\) | 2.93757e14 | 0.582632 | ||||||||
\(127\) | −3.49275e14 | − | 3.49275e14i | −0.655454 | − | 0.655454i | 0.298847 | − | 0.954301i | \(-0.403398\pi\) |
−0.954301 | + | 0.298847i | \(0.903398\pi\) | |||||||
\(128\) | 3.51844e13 | − | 3.51844e13i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | 3.52765e14i | 0.593413i | ||||||||
\(130\) | −5.16756e14 | − | 3.12627e14i | −0.823535 | − | 0.498222i | ||||
\(131\) | −1.18659e15 | −1.79227 | −0.896133 | − | 0.443786i | \(-0.853635\pi\) | ||||
−0.896133 | + | 0.443786i | \(0.853635\pi\) | |||||||
\(132\) | −2.12445e14 | − | 2.12445e14i | −0.304248 | − | 0.304248i | ||||
\(133\) | −6.85371e13 | + | 6.85371e13i | −0.0931032 | + | 0.0931032i | ||||
\(134\) | − | 2.74600e14i | − | 0.353971i | ||||||
\(135\) | −1.75560e14 | − | 7.13307e14i | −0.214827 | − | 0.872851i | ||||
\(136\) | 4.94879e14 | 0.575077 | ||||||||
\(137\) | 8.96275e14 | + | 8.96275e14i | 0.989457 | + | 0.989457i | 0.999945 | − | 0.0104876i | \(-0.00333838\pi\) |
−0.0104876 | + | 0.999945i | \(0.503338\pi\) | |||||||
\(138\) | 1.67042e13 | − | 1.67042e13i | 0.0175255 | − | 0.0175255i | ||||
\(139\) | − | 6.49657e14i | − | 0.648008i | −0.946056 | − | 0.324004i | \(-0.894971\pi\) | ||
0.946056 | − | 0.324004i | \(-0.105029\pi\) | |||||||
\(140\) | −5.77649e14 | + | 1.42172e14i | −0.547984 | + | 0.134870i | ||||
\(141\) | 1.29466e14 | 0.116848 | ||||||||
\(142\) | −9.40348e14 | − | 9.40348e14i | −0.807737 | − | 0.807737i | ||||
\(143\) | −1.94929e15 | + | 1.94929e15i | −1.59413 | + | 1.59413i | ||||
\(144\) | − | 2.34325e14i | − | 0.182508i | ||||||
\(145\) | 7.82516e14 | − | 1.29346e15i | 0.580653 | − | 0.959789i | ||||
\(146\) | 1.37716e15 | 0.973897 | ||||||||
\(147\) | 1.49267e14 | + | 1.49267e14i | 0.100634 | + | 0.100634i | ||||
\(148\) | 4.88850e14 | − | 4.88850e14i | 0.314300 | − | 0.314300i | ||||
\(149\) | 2.17503e15i | 1.33402i | 0.745050 | + | 0.667008i | \(0.232425\pi\) | ||||
−0.745050 | + | 0.667008i | \(0.767575\pi\) | |||||||
\(150\) | 2.91352e14 | + | 5.56034e14i | 0.170522 | + | 0.325434i | ||||
\(151\) | 2.45470e15 | 1.37139 | 0.685693 | − | 0.727891i | \(-0.259499\pi\) | ||||
0.685693 | + | 0.727891i | \(0.259499\pi\) | |||||||
\(152\) | 5.46709e13 | + | 5.46709e13i | 0.0291643 | + | 0.0291643i | ||||
\(153\) | 1.64792e15 | − | 1.64792e15i | 0.839648 | − | 0.839648i | ||||
\(154\) | 2.71528e15i | 1.32181i | ||||||||
\(155\) | −1.35421e15 | − | 8.19272e14i | −0.630035 | − | 0.381159i | ||||
\(156\) | 7.95100e14 | 0.353631 | ||||||||
\(157\) | 6.05092e14 | + | 6.05092e14i | 0.257350 | + | 0.257350i | 0.823975 | − | 0.566626i | \(-0.191751\pi\) |
−0.566626 | + | 0.823975i | \(0.691751\pi\) | |||||||
\(158\) | −9.51172e14 | + | 9.51172e14i | −0.386954 | + | 0.386954i | ||||
\(159\) | − | 1.30478e15i | − | 0.507876i | ||||||
\(160\) | 1.13408e14 | + | 4.60780e14i | 0.0422477 | + | 0.171654i | ||||
\(161\) | −2.13498e14 | −0.0761399 | ||||||||
\(162\) | −3.85026e14 | − | 3.85026e14i | −0.131487 | − | 0.131487i | ||||
\(163\) | −2.75781e15 | + | 2.75781e15i | −0.902091 | + | 0.902091i | −0.995617 | − | 0.0935255i | \(-0.970186\pi\) |
0.0935255 | + | 0.995617i | \(0.470186\pi\) | |||||||
\(164\) | 4.85221e13i | 0.0152066i | ||||||||
\(165\) | 2.78221e15 | − | 6.84761e14i | 0.835608 | − | 0.205661i | ||||
\(166\) | −6.11010e14 | −0.175910 | ||||||||
\(167\) | −2.23202e15 | − | 2.23202e15i | −0.616145 | − | 0.616145i | 0.328395 | − | 0.944540i | \(-0.393492\pi\) |
−0.944540 | + | 0.328395i | \(0.893492\pi\) | |||||||
\(168\) | 5.53772e14 | − | 5.53772e14i | 0.146611 | − | 0.146611i | ||||
\(169\) | − | 3.35807e15i | − | 0.852870i | ||||||
\(170\) | −2.44295e15 | + | 4.03806e15i | −0.595350 | + | 0.984081i | ||||
\(171\) | 3.64103e14 | 0.0851632 | ||||||||
\(172\) | −1.79827e15 | − | 1.79827e15i | −0.403789 | − | 0.403789i | ||||
\(173\) | −2.01216e15 | + | 2.01216e15i | −0.433851 | + | 0.433851i | −0.889936 | − | 0.456085i | \(-0.849251\pi\) |
0.456085 | + | 0.889936i | \(0.349251\pi\) | |||||||
\(174\) | 1.99016e15i | 0.412139i | ||||||||
\(175\) | 1.69146e15 | − | 5.41527e15i | 0.336509 | − | 1.07734i | ||||
\(176\) | 2.16593e15 | 0.414053 | ||||||||
\(177\) | −2.39882e15 | − | 2.39882e15i | −0.440742 | − | 0.440742i | ||||
\(178\) | 3.87070e15 | − | 3.87070e15i | 0.683675 | − | 0.683675i | ||||
\(179\) | − | 3.89718e15i | − | 0.661879i | −0.943652 | − | 0.330940i | \(-0.892634\pi\) | ||
0.943652 | − | 0.330940i | \(-0.107366\pi\) | |||||||
\(180\) | 1.91202e15 | + | 1.15674e15i | 0.312310 | + | 0.188941i | ||||
\(181\) | −5.53039e15 | −0.868973 | −0.434486 | − | 0.900678i | \(-0.643070\pi\) | ||||
−0.434486 | + | 0.900678i | \(0.643070\pi\) | |||||||
\(182\) | −5.08114e15 | − | 5.08114e15i | −0.768177 | − | 0.768177i | ||||
\(183\) | −9.72205e14 | + | 9.72205e14i | −0.141449 | + | 0.141449i | ||||
\(184\) | 1.70303e14i | 0.0238506i | ||||||||
\(185\) | 1.57568e15 | + | 6.40207e15i | 0.212455 | + | 0.863213i | ||||
\(186\) | 2.08364e15 | 0.270541 | ||||||||
\(187\) | 1.52322e16 | + | 1.52322e16i | 1.90490 | + | 1.90490i | ||||
\(188\) | −6.59971e14 | + | 6.59971e14i | −0.0795096 | + | 0.0795096i | ||||
\(189\) | − | 8.74002e15i | − | 1.01456i | ||||||
\(190\) | −7.15979e14 | + | 1.76218e14i | −0.0800986 | + | 0.0197140i | ||||
\(191\) | −1.55732e16 | −1.67936 | −0.839679 | − | 0.543082i | \(-0.817257\pi\) | ||||
−0.839679 | + | 0.543082i | \(0.817257\pi\) | |||||||
\(192\) | −4.41734e14 | − | 4.41734e14i | −0.0459253 | − | 0.0459253i | ||||
\(193\) | 2.69767e15 | − | 2.69767e15i | 0.270450 | − | 0.270450i | −0.558831 | − | 0.829281i | \(-0.688750\pi\) |
0.829281 | + | 0.558831i | \(0.188750\pi\) | |||||||
\(194\) | 4.51557e14i | 0.0436617i | ||||||||
\(195\) | −3.92498e15 | + | 6.48779e15i | −0.366096 | + | 0.605138i | ||||
\(196\) | −1.52182e15 | −0.136953 | ||||||||
\(197\) | 1.36065e16 | + | 1.36065e16i | 1.18163 | + | 1.18163i | 0.979322 | + | 0.202310i | \(0.0648448\pi\) |
0.202310 | + | 0.979322i | \(0.435155\pi\) | |||||||
\(198\) | 7.21246e15 | − | 7.21246e15i | 0.604543 | − | 0.604543i | ||||
\(199\) | 1.18868e16i | 0.961818i | 0.876770 | + | 0.480909i | \(0.159693\pi\) | ||||
−0.876770 | + | 0.480909i | \(0.840307\pi\) | |||||||
\(200\) | −4.31967e15 | − | 1.34925e15i | −0.337474 | − | 0.105410i | ||||
\(201\) | −3.44756e15 | −0.260100 | ||||||||
\(202\) | −1.56725e15 | − | 1.56725e15i | −0.114203 | − | 0.114203i | ||||
\(203\) | 1.27182e16 | − | 1.27182e16i | 0.895272 | − | 0.895272i | ||||
\(204\) | − | 6.21312e15i | − | 0.422570i | ||||||
\(205\) | −3.95926e14 | − | 2.39528e14i | −0.0260218 | − | 0.0157427i | ||||
\(206\) | 3.19463e15 | 0.202932 | ||||||||
\(207\) | 5.67103e14 | + | 5.67103e14i | 0.0348233 | + | 0.0348233i | ||||
\(208\) | −4.05313e15 | + | 4.05313e15i | −0.240629 | + | 0.240629i | ||||
\(209\) | 3.36551e15i | 0.193209i | ||||||||
\(210\) | 1.78494e15 | + | 7.25229e15i | 0.0991035 | + | 0.402662i | ||||
\(211\) | 3.57939e15 | 0.192235 | 0.0961173 | − | 0.995370i | \(-0.469358\pi\) | ||||
0.0961173 | + | 0.995370i | \(0.469358\pi\) | |||||||
\(212\) | 6.65130e15 | + | 6.65130e15i | 0.345585 | + | 0.345585i | ||||
\(213\) | −1.18059e16 | + | 1.18059e16i | −0.593530 | + | 0.593530i | ||||
\(214\) | − | 5.40431e15i | − | 0.262932i | ||||||
\(215\) | 2.35504e16 | − | 5.79625e15i | 1.10899 | − | 0.272947i | ||||
\(216\) | −6.97176e15 | −0.317809 | ||||||||
\(217\) | −1.33156e16 | − | 1.33156e16i | −0.587684 | − | 0.587684i | ||||
\(218\) | 1.67332e16 | − | 1.67332e16i | 0.715128 | − | 0.715128i | ||||
\(219\) | − | 1.72900e16i | − | 0.715625i | ||||||
\(220\) | −1.06920e16 | + | 1.76734e16i | −0.428649 | + | 0.708533i | ||||
\(221\) | −5.70085e16 | −2.21408 | ||||||||
\(222\) | −6.13744e15 | − | 6.13744e15i | −0.230949 | − | 0.230949i | ||||
\(223\) | 1.59754e16 | − | 1.59754e16i | 0.582530 | − | 0.582530i | −0.353068 | − | 0.935598i | \(-0.614862\pi\) |
0.935598 | + | 0.353068i | \(0.114862\pi\) | |||||||
\(224\) | 5.64586e15i | 0.199523i | ||||||||
\(225\) | −1.88773e16 | + | 9.89136e15i | −0.646638 | + | 0.338827i | ||||
\(226\) | −9.85532e15 | −0.327274 | ||||||||
\(227\) | −1.72932e16 | − | 1.72932e16i | −0.556793 | − | 0.556793i | 0.371600 | − | 0.928393i | \(-0.378809\pi\) |
−0.928393 | + | 0.371600i | \(0.878809\pi\) | |||||||
\(228\) | 6.86384e14 | − | 6.86384e14i | 0.0214301 | − | 0.0214301i | ||||
\(229\) | − | 2.08347e16i | − | 0.630868i | −0.948948 | − | 0.315434i | \(-0.897850\pi\) | ||
0.948948 | − | 0.315434i | \(-0.102150\pi\) | |||||||
\(230\) | −1.38963e15 | − | 8.40696e14i | −0.0408134 | − | 0.0246913i | ||||
\(231\) | 3.40899e16 | 0.971274 | ||||||||
\(232\) | −1.01451e16 | − | 1.01451e16i | −0.280441 | − | 0.280441i | ||||
\(233\) | 1.59507e16 | − | 1.59507e16i | 0.427847 | − | 0.427847i | −0.460048 | − | 0.887894i | \(-0.652168\pi\) |
0.887894 | + | 0.460048i | \(0.152168\pi\) | |||||||
\(234\) | 2.69935e16i | 0.702665i | ||||||||
\(235\) | −2.12725e15 | − | 8.64309e15i | −0.0537456 | − | 0.218370i | ||||
\(236\) | 2.44566e16 | 0.599808 | ||||||||
\(237\) | 1.19418e16 | + | 1.19418e16i | 0.284336 | + | 0.284336i | ||||
\(238\) | −3.97053e16 | + | 3.97053e16i | −0.917931 | + | 0.917931i | ||||
\(239\) | 1.56773e16i | 0.351954i | 0.984394 | + | 0.175977i | \(0.0563085\pi\) | ||||
−0.984394 | + | 0.175977i | \(0.943692\pi\) | |||||||
\(240\) | 5.78503e15 | − | 1.42382e15i | 0.126132 | − | 0.0310439i | ||||
\(241\) | 3.45641e16 | 0.731991 | 0.365996 | − | 0.930617i | \(-0.380729\pi\) | ||||
0.365996 | + | 0.930617i | \(0.380729\pi\) | |||||||
\(242\) | 4.23628e16 | + | 4.23628e16i | 0.871519 | + | 0.871519i | ||||
\(243\) | −3.66349e16 | + | 3.66349e16i | −0.732236 | + | 0.732236i | ||||
\(244\) | − | 9.91189e15i | − | 0.192499i | ||||||
\(245\) | 7.51241e15 | − | 1.24176e16i | 0.141780 | − | 0.234356i | ||||
\(246\) | 6.09188e14 | 0.0111739 | ||||||||
\(247\) | −6.29792e15 | − | 6.29792e15i | −0.112284 | − | 0.112284i | ||||
\(248\) | −1.06217e16 | + | 1.06217e16i | −0.184090 | + | 0.184090i | ||||
\(249\) | 7.67113e15i | 0.129260i | ||||||||
\(250\) | 3.23334e16 | − | 2.85867e16i | 0.529750 | − | 0.468364i | ||||
\(251\) | 1.06204e17 | 1.69210 | 0.846051 | − | 0.533102i | \(-0.178974\pi\) | ||||
0.846051 | + | 0.533102i | \(0.178974\pi\) | |||||||
\(252\) | 1.88005e16 | + | 1.88005e16i | 0.291316 | + | 0.291316i | ||||
\(253\) | −5.24189e15 | + | 5.24189e15i | −0.0790031 | + | 0.0790031i | ||||
\(254\) | − | 4.47073e16i | − | 0.655454i | ||||||
\(255\) | 5.06972e16 | + | 3.06708e16i | 0.723108 | + | 0.437466i | ||||
\(256\) | 4.50360e15 | 0.0625000 | ||||||||
\(257\) | −2.42209e16 | − | 2.42209e16i | −0.327084 | − | 0.327084i | 0.524393 | − | 0.851477i | \(-0.324292\pi\) |
−0.851477 | + | 0.524393i | \(0.824292\pi\) | |||||||
\(258\) | −2.25769e16 | + | 2.25769e16i | −0.296707 | + | 0.296707i | ||||
\(259\) | 7.84433e16i | 1.00336i | ||||||||
\(260\) | −1.30642e16 | − | 5.30805e16i | −0.162656 | − | 0.660878i | ||||
\(261\) | −6.75656e16 | −0.818922 | ||||||||
\(262\) | −7.59419e16 | − | 7.59419e16i | −0.896133 | − | 0.896133i | ||||
\(263\) | −5.11732e16 | + | 5.11732e16i | −0.587966 | + | 0.587966i | −0.937080 | − | 0.349114i | \(-0.886483\pi\) |
0.349114 | + | 0.937080i | \(0.386483\pi\) | |||||||
\(264\) | − | 2.71929e16i | − | 0.304248i | ||||||
\(265\) | −8.71065e16 | + | 2.14388e16i | −0.949138 | + | 0.233603i | ||||
\(266\) | −8.77275e15 | −0.0931032 | ||||||||
\(267\) | −4.85960e16 | − | 4.85960e16i | −0.502368 | − | 0.502368i | ||||
\(268\) | 1.75744e16 | − | 1.75744e16i | 0.176985 | − | 0.176985i | ||||
\(269\) | − | 4.55495e16i | − | 0.446908i | −0.974715 | − | 0.223454i | \(-0.928267\pi\) | ||
0.974715 | − | 0.223454i | \(-0.0717332\pi\) | |||||||
\(270\) | 3.44158e16 | − | 5.68875e16i | 0.329012 | − | 0.543839i | ||||
\(271\) | 8.13494e16 | 0.757825 | 0.378913 | − | 0.925432i | \(-0.376298\pi\) | ||||
0.378913 | + | 0.925432i | \(0.376298\pi\) | |||||||
\(272\) | 3.16722e16 | + | 3.16722e16i | 0.287539 | + | 0.287539i | ||||
\(273\) | −6.37928e16 | + | 6.37928e16i | −0.564460 | + | 0.564460i | ||||
\(274\) | 1.14723e17i | 0.989457i | ||||||||
\(275\) | −9.14286e16 | − | 1.74488e17i | −0.768694 | − | 1.46702i | ||||
\(276\) | 2.13813e15 | 0.0175255 | ||||||||
\(277\) | 1.76612e15 | + | 1.76612e15i | 0.0141144 | + | 0.0141144i | 0.714129 | − | 0.700014i | \(-0.246823\pi\) |
−0.700014 | + | 0.714129i | \(0.746823\pi\) | |||||||
\(278\) | 4.15780e16 | − | 4.15780e16i | 0.324004 | − | 0.324004i | ||||
\(279\) | 7.07393e16i | 0.537566i | ||||||||
\(280\) | −4.60685e16 | − | 2.78706e16i | −0.341427 | − | 0.206557i | ||||
\(281\) | 1.55782e17 | 1.12609 | 0.563045 | − | 0.826426i | \(-0.309630\pi\) | ||||
0.563045 | + | 0.826426i | \(0.309630\pi\) | |||||||
\(282\) | 8.28583e15 | + | 8.28583e15i | 0.0584241 | + | 0.0584241i | ||||
\(283\) | 1.10583e17 | − | 1.10583e17i | 0.760647 | − | 0.760647i | −0.215792 | − | 0.976439i | \(-0.569233\pi\) |
0.976439 | + | 0.215792i | \(0.0692333\pi\) | |||||||
\(284\) | − | 1.20365e17i | − | 0.807737i | ||||||
\(285\) | 2.21238e15 | + | 8.98900e15i | 0.0144859 | + | 0.0588569i | ||||
\(286\) | −2.49509e17 | −1.59413 | ||||||||
\(287\) | −3.89305e15 | − | 3.89305e15i | −0.0242726 | − | 0.0242726i | ||||
\(288\) | 1.49968e16 | − | 1.49968e16i | 0.0912538 | − | 0.0912538i | ||||
\(289\) | 2.77101e17i | 1.64571i | ||||||||
\(290\) | 1.32862e17 | − | 3.27002e16i | 0.770221 | − | 0.189568i | ||||
\(291\) | 5.66923e15 | 0.0320828 | ||||||||
\(292\) | 8.81380e16 | + | 8.81380e16i | 0.486949 | + | 0.486949i | ||||
\(293\) | 9.92848e16 | − | 9.92848e16i | 0.535562 | − | 0.535562i | −0.386660 | − | 0.922222i | \(-0.626371\pi\) |
0.922222 | + | 0.386660i | \(0.126371\pi\) | |||||||
\(294\) | 1.91062e16i | 0.100634i | ||||||||
\(295\) | −1.20729e17 | + | 1.99559e17i | −0.620952 | + | 1.02640i | ||||
\(296\) | 6.25728e16 | 0.314300 | ||||||||
\(297\) | −2.14589e17 | − | 2.14589e17i | −1.05272 | − | 1.05272i | ||||
\(298\) | −1.39202e17 | + | 1.39202e17i | −0.667008 | + | 0.667008i | ||||
\(299\) | − | 1.96184e16i | − | 0.0918261i | ||||||
\(300\) | −1.69396e16 | + | 5.42327e16i | −0.0774560 | + | 0.247978i | ||||
\(301\) | 2.88559e17 | 1.28905 | ||||||||
\(302\) | 1.57101e17 | + | 1.57101e17i | 0.685693 | + | 0.685693i | ||||
\(303\) | −1.96766e16 | + | 1.96766e16i | −0.0839172 | + | 0.0839172i | ||||
\(304\) | 6.99787e15i | 0.0291643i | ||||||||
\(305\) | 8.08781e16 | + | 4.89297e16i | 0.329407 | + | 0.199284i | ||||
\(306\) | 2.10934e17 | 0.839648 | ||||||||
\(307\) | 7.50777e16 | + | 7.50777e16i | 0.292107 | + | 0.292107i | 0.837912 | − | 0.545805i | \(-0.183776\pi\) |
−0.545805 | + | 0.837912i | \(0.683776\pi\) | |||||||
\(308\) | −1.73778e17 | + | 1.73778e17i | −0.660906 | + | 0.660906i | ||||
\(309\) | − | 4.01081e16i | − | 0.149115i | ||||||
\(310\) | −3.42362e16 | − | 1.39103e17i | −0.124438 | − | 0.505597i | ||||
\(311\) | −3.72883e17 | −1.32510 | −0.662552 | − | 0.749016i | \(-0.730527\pi\) | ||||
−0.662552 | + | 0.749016i | \(0.730527\pi\) | |||||||
\(312\) | 5.08864e16 | + | 5.08864e16i | 0.176815 | + | 0.176815i | ||||
\(313\) | 2.68205e17 | − | 2.68205e17i | 0.911289 | − | 0.911289i | −0.0850850 | − | 0.996374i | \(-0.527116\pi\) |
0.996374 | + | 0.0850850i | \(0.0271162\pi\) | |||||||
\(314\) | 7.74518e16i | 0.257350i | ||||||||
\(315\) | −2.46214e17 | + | 6.05985e16i | −0.800090 | + | 0.196919i | ||||
\(316\) | −1.21750e17 | −0.386954 | ||||||||
\(317\) | 1.52004e17 | + | 1.52004e17i | 0.472542 | + | 0.472542i | 0.902736 | − | 0.430194i | \(-0.141555\pi\) |
−0.430194 | + | 0.902736i | \(0.641555\pi\) | |||||||
\(318\) | 8.35060e16 | − | 8.35060e16i | 0.253938 | − | 0.253938i | ||||
\(319\) | − | 6.24528e17i | − | 1.85788i | ||||||
\(320\) | −2.22318e16 | + | 3.67481e16i | −0.0647032 | + | 0.106951i | ||||
\(321\) | −6.78503e16 | −0.193204 | ||||||||
\(322\) | −1.36639e16 | − | 1.36639e16i | −0.0380699 | − | 0.0380699i | ||||
\(323\) | −4.92136e16 | + | 4.92136e16i | −0.134174 | + | 0.134174i | ||||
\(324\) | − | 4.92833e16i | − | 0.131487i | ||||||
\(325\) | 4.97612e17 | + | 1.55430e17i | 1.29929 | + | 0.405836i | ||||
\(326\) | −3.52999e17 | −0.902091 | ||||||||
\(327\) | −2.10083e17 | − | 2.10083e17i | −0.525480 | − | 0.525480i | ||||
\(328\) | −3.10542e15 | + | 3.10542e15i | −0.00760331 | + | 0.00760331i | ||||
\(329\) | − | 1.05902e17i | − | 0.253824i | ||||||
\(330\) | 2.21886e17 | + | 1.34237e17i | 0.520634 | + | 0.314973i | ||||
\(331\) | −5.28017e17 | −1.21297 | −0.606487 | − | 0.795093i | \(-0.707422\pi\) | ||||
−0.606487 | + | 0.795093i | \(0.707422\pi\) | |||||||
\(332\) | −3.91046e16 | − | 3.91046e16i | −0.0879552 | − | 0.0879552i | ||||
\(333\) | 2.08365e17 | − | 2.08365e17i | 0.458897 | − | 0.458897i | ||||
\(334\) | − | 2.85699e17i | − | 0.616145i | ||||||
\(335\) | 5.66467e16 | + | 2.30158e17i | 0.119636 | + | 0.486085i | ||||
\(336\) | 7.08828e16 | 0.146611 | ||||||||
\(337\) | 3.24151e16 | + | 3.24151e16i | 0.0656656 | + | 0.0656656i | 0.739177 | − | 0.673511i | \(-0.235215\pi\) |
−0.673511 | + | 0.739177i | \(0.735215\pi\) | |||||||
\(338\) | 2.14916e17 | − | 2.14916e17i | 0.426435 | − | 0.426435i | ||||
\(339\) | 1.23732e17i | 0.240483i | ||||||||
\(340\) | −4.14785e17 | + | 1.02087e17i | −0.789715 | + | 0.194366i | ||||
\(341\) | −6.53863e17 | −1.21957 | ||||||||
\(342\) | 2.33026e16 | + | 2.33026e16i | 0.0425816 | + | 0.0425816i | ||||
\(343\) | −3.23672e17 | + | 3.23672e17i | −0.579491 | + | 0.579491i | ||||
\(344\) | − | 2.30178e17i | − | 0.403789i | ||||||
\(345\) | −1.05548e16 | + | 1.74465e16i | −0.0181433 | + | 0.0299899i | ||||
\(346\) | −2.57557e17 | −0.433851 | ||||||||
\(347\) | −1.72047e17 | − | 1.72047e17i | −0.284015 | − | 0.284015i | 0.550693 | − | 0.834708i | \(-0.314364\pi\) |
−0.834708 | + | 0.550693i | \(0.814364\pi\) | |||||||
\(348\) | −1.27370e17 | + | 1.27370e17i | −0.206069 | + | 0.206069i | ||||
\(349\) | 8.19436e16i | 0.129938i | 0.997887 | + | 0.0649691i | \(0.0206949\pi\) | ||||
−0.997887 | + | 0.0649691i | \(0.979305\pi\) | |||||||
\(350\) | 4.54831e17 | − | 2.38324e17i | 0.706926 | − | 0.370417i | ||||
\(351\) | 8.03125e17 | 1.22358 | ||||||||
\(352\) | 1.38620e17 | + | 1.38620e17i | 0.207026 | + | 0.207026i | ||||
\(353\) | −4.75391e17 | + | 4.75391e17i | −0.696030 | + | 0.696030i | −0.963552 | − | 0.267522i | \(-0.913795\pi\) |
0.267522 | + | 0.963552i | \(0.413795\pi\) | |||||||
\(354\) | − | 3.07049e17i | − | 0.440742i | ||||||
\(355\) | 9.82139e17 | + | 5.94175e17i | 1.38221 | + | 0.836211i | ||||
\(356\) | 4.95450e17 | 0.683675 | ||||||||
\(357\) | 4.98494e17 | + | 4.98494e17i | 0.674500 | + | 0.674500i | ||||
\(358\) | 2.49419e17 | − | 2.49419e17i | 0.330940 | − | 0.330940i | ||||
\(359\) | 6.51435e17i | 0.847637i | 0.905747 | + | 0.423818i | \(0.139311\pi\) | ||||
−0.905747 | + | 0.423818i | \(0.860689\pi\) | |||||||
\(360\) | 4.83383e16 | + | 1.96401e17i | 0.0616842 | + | 0.250625i | ||||
\(361\) | 7.88133e17 | 0.986391 | ||||||||
\(362\) | −3.53945e17 | − | 3.53945e17i | −0.434486 | − | 0.434486i | ||||
\(363\) | 5.31858e17 | − | 5.31858e17i | 0.640397 | − | 0.640397i | ||||
\(364\) | − | 6.50385e17i | − | 0.768177i | ||||||
\(365\) | −1.15427e18 | + | 2.84090e17i | −1.33739 | + | 0.329159i | ||||
\(366\) | −1.24442e17 | −0.141449 | ||||||||
\(367\) | 1.93211e17 | + | 1.93211e17i | 0.215461 | + | 0.215461i | 0.806583 | − | 0.591121i | \(-0.201315\pi\) |
−0.591121 | + | 0.806583i | \(0.701315\pi\) | |||||||
\(368\) | −1.08994e16 | + | 1.08994e16i | −0.0119253 | + | 0.0119253i | ||||
\(369\) | 2.06818e16i | 0.0222026i | ||||||||
\(370\) | −3.08888e17 | + | 5.10576e17i | −0.325379 | + | 0.537834i | ||||
\(371\) | −1.06730e18 | −1.10324 | ||||||||
\(372\) | 1.33353e17 | + | 1.33353e17i | 0.135270 | + | 0.135270i | ||||
\(373\) | 9.45700e17 | − | 9.45700e17i | 0.941438 | − | 0.941438i | −0.0569399 | − | 0.998378i | \(-0.518134\pi\) |
0.998378 | + | 0.0569399i | \(0.0181343\pi\) | |||||||
\(374\) | 1.94973e18i | 1.90490i | ||||||||
\(375\) | −3.58901e17 | − | 4.05940e17i | −0.344157 | − | 0.389263i | ||||
\(376\) | −8.44763e16 | −0.0795096 | ||||||||
\(377\) | 1.16869e18 | + | 1.16869e18i | 1.07971 | + | 1.07971i | ||||
\(378\) | 5.59361e17 | − | 5.59361e17i | 0.507282 | − | 0.507282i | ||||
\(379\) | − | 6.91007e17i | − | 0.615188i | −0.951518 | − | 0.307594i | \(-0.900476\pi\) | ||
0.951518 | − | 0.307594i | \(-0.0995239\pi\) | |||||||
\(380\) | −5.71006e16 | − | 3.45447e16i | −0.0499063 | − | 0.0301923i | ||||
\(381\) | −5.61292e17 | −0.481631 | ||||||||
\(382\) | −9.96683e17 | − | 9.96683e17i | −0.839679 | − | 0.839679i | ||||
\(383\) | −1.04056e18 | + | 1.04056e18i | −0.860750 | + | 0.860750i | −0.991425 | − | 0.130675i | \(-0.958285\pi\) |
0.130675 | + | 0.991425i | \(0.458285\pi\) | |||||||
\(384\) | − | 5.65420e16i | − | 0.0459253i | ||||||
\(385\) | −5.60129e17 | − | 2.27582e18i | −0.446748 | − | 1.81515i | ||||
\(386\) | 3.45302e17 | 0.270450 | ||||||||
\(387\) | −7.66483e17 | − | 7.66483e17i | −0.589557 | − | 0.589557i | ||||
\(388\) | −2.88997e16 | + | 2.88997e16i | −0.0218308 | + | 0.0218308i | ||||
\(389\) | − | 1.61552e18i | − | 1.19858i | −0.800533 | − | 0.599288i | \(-0.795450\pi\) | ||
0.800533 | − | 0.599288i | \(-0.204550\pi\) | |||||||
\(390\) | −6.66417e17 | + | 1.64019e17i | −0.485617 | + | 0.119521i | ||||
\(391\) | −1.53304e17 | −0.109727 | ||||||||
\(392\) | −9.73965e16 | − | 9.73965e16i | −0.0684764 | − | 0.0684764i | ||||
\(393\) | −9.53438e17 | + | 9.53438e17i | −0.658483 | + | 0.658483i | ||||
\(394\) | 1.74163e18i | 1.18163i | ||||||||
\(395\) | 6.01014e17 | − | 9.93445e17i | 0.400595 | − | 0.662162i | ||||
\(396\) | 9.23194e17 | 0.604543 | ||||||||
\(397\) | −1.39748e18 | − | 1.39748e18i | −0.899111 | − | 0.899111i | 0.0962469 | − | 0.995357i | \(-0.469316\pi\) |
−0.995357 | + | 0.0962469i | \(0.969316\pi\) | |||||||
\(398\) | −7.60754e17 | + | 7.60754e17i | −0.480909 | + | 0.480909i | ||||
\(399\) | 1.10141e17i | 0.0684127i | ||||||||
\(400\) | −1.90107e17 | − | 3.62811e17i | −0.116032 | − | 0.221442i | ||||
\(401\) | 3.14384e17 | 0.188560 | 0.0942800 | − | 0.995546i | \(-0.469945\pi\) | ||||
0.0942800 | + | 0.995546i | \(0.469945\pi\) | |||||||
\(402\) | −2.20644e17 | − | 2.20644e17i | −0.130050 | − | 0.130050i | ||||
\(403\) | 1.22358e18 | − | 1.22358e18i | 0.708758 | − | 0.708758i | ||||
\(404\) | − | 2.00608e17i | − | 0.114203i | ||||||
\(405\) | 4.02137e17 | + | 2.43285e17i | 0.225003 | + | 0.136123i | ||||
\(406\) | 1.62794e18 | 0.895272 | ||||||||
\(407\) | 1.92597e18 | + | 1.92597e18i | 1.04109 | + | 1.04109i | ||||
\(408\) | 3.97640e17 | − | 3.97640e17i | 0.211285 | − | 0.211285i | ||||
\(409\) | 2.53540e18i | 1.32429i | 0.749375 | + | 0.662145i | \(0.230354\pi\) | ||||
−0.749375 | + | 0.662145i | \(0.769646\pi\) | |||||||
\(410\) | −1.00095e16 | − | 4.06691e16i | −0.00513956 | − | 0.0208822i | ||||
\(411\) | 1.44033e18 | 0.727059 | ||||||||
\(412\) | 2.04456e17 | + | 2.04456e17i | 0.101466 | + | 0.101466i | ||||
\(413\) | −1.96221e18 | + | 1.96221e18i | −0.957406 | + | 0.957406i | ||||
\(414\) | 7.25892e16i | 0.0348233i | ||||||||
\(415\) | 5.12121e17 | − | 1.26044e17i | 0.241566 | − | 0.0594545i | ||||
\(416\) | −5.18801e17 | −0.240629 | ||||||||
\(417\) | −5.22006e17 | − | 5.22006e17i | −0.238080 | − | 0.238080i | ||||
\(418\) | −2.15393e17 | + | 2.15393e17i | −0.0966044 | + | 0.0966044i | ||||
\(419\) | − | 1.62469e18i | − | 0.716592i | −0.933608 | − | 0.358296i | \(-0.883358\pi\) | ||
0.933608 | − | 0.358296i | \(-0.116642\pi\) | |||||||
\(420\) | −3.49910e17 | + | 5.78383e17i | −0.151779 | + | 0.250883i | ||||
\(421\) | 1.08059e18 | 0.460984 | 0.230492 | − | 0.973074i | \(-0.425966\pi\) | ||||
0.230492 | + | 0.973074i | \(0.425966\pi\) | |||||||
\(422\) | 2.29081e17 | + | 2.29081e17i | 0.0961173 | + | 0.0961173i | ||||
\(423\) | −2.81302e17 | + | 2.81302e17i | −0.116089 | + | 0.116089i | ||||
\(424\) | 8.51366e17i | 0.345585i | ||||||||
\(425\) | 1.21457e18 | − | 3.88847e18i | 0.484952 | − | 1.55259i | ||||
\(426\) | −1.51116e18 | −0.593530 | ||||||||
\(427\) | 7.95255e17 | + | 7.95255e17i | 0.307264 | + | 0.307264i | ||||
\(428\) | 3.45876e17 | − | 3.45876e17i | 0.131466 | − | 0.131466i | ||||
\(429\) | 3.13254e18i | 1.17137i | ||||||||
\(430\) | 1.87819e18 | + | 1.13627e18i | 0.690970 | + | 0.418023i | ||||
\(431\) | 1.22714e18 | 0.444174 | 0.222087 | − | 0.975027i | \(-0.428713\pi\) | ||||
0.222087 | + | 0.975027i | \(0.428713\pi\) | |||||||
\(432\) | −4.46193e17 | − | 4.46193e17i | −0.158904 | − | 0.158904i | ||||
\(433\) | −2.81886e18 | + | 2.81886e18i | −0.987775 | + | 0.987775i | −0.999926 | − | 0.0121513i | \(-0.996132\pi\) |
0.0121513 | + | 0.999926i | \(0.496132\pi\) | |||||||
\(434\) | − | 1.70440e18i | − | 0.587684i | ||||||
\(435\) | −4.10546e17 | − | 1.66806e18i | −0.139295 | − | 0.565963i | ||||
\(436\) | 2.14185e18 | 0.715128 | ||||||||
\(437\) | −1.69359e16 | − | 1.69359e16i | −0.00556467 | − | 0.00556467i | ||||
\(438\) | 1.10656e18 | − | 1.10656e18i | 0.357813 | − | 0.357813i | ||||
\(439\) | 2.69036e18i | 0.856166i | 0.903739 | + | 0.428083i | \(0.140811\pi\) | ||||
−0.903739 | + | 0.428083i | \(0.859189\pi\) | |||||||
\(440\) | −1.81539e18 | + | 4.46805e17i | −0.568591 | + | 0.139942i | ||||
\(441\) | −6.48652e17 | −0.199959 | ||||||||
\(442\) | −3.64854e18 | − | 3.64854e18i | −1.10704 | − | 1.10704i | ||||
\(443\) | −5.80048e17 | + | 5.80048e17i | −0.173236 | + | 0.173236i | −0.788399 | − | 0.615164i | \(-0.789090\pi\) |
0.615164 | + | 0.788399i | \(0.289090\pi\) | |||||||
\(444\) | − | 7.85592e17i | − | 0.230949i | ||||||
\(445\) | −2.44577e18 | + | 4.04272e18i | −0.707775 | + | 1.16991i | ||||
\(446\) | 2.04485e18 | 0.582530 | ||||||||
\(447\) | 1.74766e18 | + | 1.74766e18i | 0.490121 | + | 0.490121i | ||||
\(448\) | −3.61335e17 | + | 3.61335e17i | −0.0997617 | + | 0.0997617i | ||||
\(449\) | − | 4.56796e18i | − | 1.24165i | −0.783951 | − | 0.620823i | \(-0.786799\pi\) | ||
0.783951 | − | 0.620823i | \(-0.213201\pi\) | |||||||
\(450\) | −1.84119e18 | − | 5.75097e17i | −0.492733 | − | 0.153905i | ||||
\(451\) | −1.91168e17 | −0.0503708 | ||||||||
\(452\) | −6.30741e17 | − | 6.30741e17i | −0.163637 | − | 0.163637i | ||||
\(453\) | 1.97238e18 | − | 1.97238e18i | 0.503851 | − | 0.503851i | ||||
\(454\) | − | 2.21353e18i | − | 0.556793i | ||||||
\(455\) | 5.30695e18 | + | 3.21060e18i | 1.31451 | + | 0.795256i | ||||
\(456\) | 8.78572e16 | 0.0214301 | ||||||||
\(457\) | −2.61088e18 | − | 2.61088e18i | −0.627154 | − | 0.627154i | 0.320197 | − | 0.947351i | \(-0.396251\pi\) |
−0.947351 | + | 0.320197i | \(0.896251\pi\) | |||||||
\(458\) | 1.33342e18 | − | 1.33342e18i | 0.315434 | − | 0.315434i | ||||
\(459\) | − | 6.27583e18i | − | 1.46212i | ||||||
\(460\) | −3.51315e16 | − | 1.42741e17i | −0.00806105 | − | 0.0327524i | ||||
\(461\) | −5.14453e18 | −1.16262 | −0.581312 | − | 0.813681i | \(-0.697460\pi\) | ||||
−0.581312 | + | 0.813681i | \(0.697460\pi\) | |||||||
\(462\) | 2.18175e18 | + | 2.18175e18i | 0.485637 | + | 0.485637i | ||||
\(463\) | −3.16003e18 | + | 3.16003e18i | −0.692825 | + | 0.692825i | −0.962853 | − | 0.270027i | \(-0.912967\pi\) |
0.270027 | + | 0.962853i | \(0.412967\pi\) | |||||||
\(464\) | − | 1.29858e18i | − | 0.280441i | ||||||
\(465\) | −1.74642e18 | + | 4.29830e17i | −0.371516 | + | 0.0914378i | ||||
\(466\) | 2.04169e18 | 0.427847 | ||||||||
\(467\) | −3.72214e18 | − | 3.72214e18i | −0.768377 | − | 0.768377i | 0.209444 | − | 0.977821i | \(-0.432835\pi\) |
−0.977821 | + | 0.209444i | \(0.932835\pi\) | |||||||
\(468\) | −1.72758e18 | + | 1.72758e18i | −0.351333 | + | 0.351333i | ||||
\(469\) | 2.82008e18i | 0.565004i | ||||||||
\(470\) | 4.17014e17 | − | 6.89301e17i | 0.0823124 | − | 0.136058i | ||||
\(471\) | 9.72395e17 | 0.189102 | ||||||||
\(472\) | 1.56522e18 | + | 1.56522e18i | 0.299904 | + | 0.299904i | ||||
\(473\) | 7.08482e18 | − | 7.08482e18i | 1.33752 | − | 1.33752i | ||||
\(474\) | 1.52855e18i | 0.284336i | ||||||||
\(475\) | 5.63750e17 | − | 2.95395e17i | 0.103331 | − | 0.0541437i | ||||
\(476\) | −5.08228e18 | −0.917931 | ||||||||
\(477\) | 2.83501e18 | + | 2.83501e18i | 0.504576 | + | 0.504576i | ||||
\(478\) | −1.00335e18 | + | 1.00335e18i | −0.175977 | + | 0.175977i | ||||
\(479\) | 4.65636e18i | 0.804819i | 0.915460 | + | 0.402409i | \(0.131827\pi\) | ||||
−0.915460 | + | 0.402409i | \(0.868173\pi\) | |||||||
\(480\) | 4.61366e17 | + | 2.79117e17i | 0.0785881 | + | 0.0475443i | ||||
\(481\) | −7.20820e18 | −1.21007 | ||||||||
\(482\) | 2.21210e18 | + | 2.21210e18i | 0.365996 | + | 0.365996i | ||||
\(483\) | −1.71548e17 | + | 1.71548e17i | −0.0279740 | + | 0.0279740i | ||||
\(484\) | 5.42243e18i | 0.871519i | ||||||||
\(485\) | −9.31507e16 | − | 3.78475e17i | −0.0147569 | − | 0.0599577i | ||||
\(486\) | −4.68926e18 | −0.732236 | ||||||||
\(487\) | 6.02307e17 | + | 6.02307e17i | 0.0927075 | + | 0.0927075i | 0.751940 | − | 0.659232i | \(-0.229119\pi\) |
−0.659232 | + | 0.751940i | \(0.729119\pi\) | |||||||
\(488\) | 6.34361e17 | − | 6.34361e17i | 0.0962493 | − | 0.0962493i | ||||
\(489\) | 4.43185e18i | 0.662862i | ||||||||
\(490\) | 1.27552e18 | − | 3.13933e17i | 0.188068 | − | 0.0462875i | ||||
\(491\) | 7.52825e18 | 1.09427 | 0.547134 | − | 0.837045i | \(-0.315719\pi\) | ||||
0.547134 | + | 0.837045i | \(0.315719\pi\) | |||||||
\(492\) | 3.89880e16 | + | 3.89880e16i | 0.00558696 | + | 0.00558696i | ||||
\(493\) | 9.13242e18 | − | 9.13242e18i | 1.29020 | − | 1.29020i | ||||
\(494\) | − | 8.06133e17i | − | 0.112284i | ||||||
\(495\) | −4.55731e18 | + | 7.53300e18i | −0.625853 | + | 1.03450i | ||||
\(496\) | −1.35957e18 | −0.184090 | ||||||||
\(497\) | 9.65714e18 | + | 9.65714e18i | 1.28930 | + | 1.28930i | ||||
\(498\) | −4.90952e17 | + | 4.90952e17i | −0.0646300 | + | 0.0646300i | ||||
\(499\) | − | 1.39305e19i | − | 1.80827i | −0.427250 | − | 0.904134i | \(-0.640517\pi\) | ||
0.427250 | − | 0.904134i | \(-0.359483\pi\) | |||||||
\(500\) | 3.89888e18 | + | 2.39787e17i | 0.499057 | + | 0.0306927i | ||||
\(501\) | −3.58690e18 | −0.452747 | ||||||||
\(502\) | 6.79708e18 | + | 6.79708e18i | 0.846051 | + | 0.846051i | ||||
\(503\) | 3.16546e18 | − | 3.16546e18i | 0.388562 | − | 0.388562i | −0.485612 | − | 0.874174i | \(-0.661403\pi\) |
0.874174 | + | 0.485612i | \(0.161403\pi\) | |||||||
\(504\) | 2.40646e18i | 0.291316i | ||||||||
\(505\) | 1.63690e18 | + | 9.90293e17i | 0.195426 | + | 0.118229i | ||||
\(506\) | −6.70962e17 | −0.0790031 | ||||||||
\(507\) | −2.69824e18 | − | 2.69824e18i | −0.313347 | − | 0.313347i | ||||
\(508\) | 2.86126e18 | − | 2.86126e18i | 0.327727 | − | 0.327727i | ||||
\(509\) | − | 5.30902e18i | − | 0.599777i | −0.953974 | − | 0.299889i | \(-0.903050\pi\) | ||
0.953974 | − | 0.299889i | \(-0.0969496\pi\) | |||||||
\(510\) | 1.28169e18 | + | 5.20756e18i | 0.142821 | + | 0.580287i | ||||
\(511\) | −1.41430e19 | −1.55452 | ||||||||
\(512\) | 2.88230e17 | + | 2.88230e17i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | 6.93312e17 | − | 6.93312e17i | 0.0741493 | − | 0.0741493i | ||||
\(514\) | − | 3.10028e18i | − | 0.327084i | ||||||
\(515\) | −2.67760e18 | + | 6.59013e17i | −0.278673 | + | 0.0685872i | ||||
\(516\) | −2.88985e18 | −0.296707 | ||||||||
\(517\) | −2.60016e18 | − | 2.60016e18i | −0.263370 | − | 0.263370i | ||||
\(518\) | −5.02037e18 | + | 5.02037e18i | −0.501681 | + | 0.501681i | ||||
\(519\) | 3.23358e18i | 0.318796i | ||||||||
\(520\) | 2.56104e18 | − | 4.23326e18i | 0.249111 | − | 0.411767i | ||||
\(521\) | 6.72471e18 | 0.645371 | 0.322686 | − | 0.946506i | \(-0.395414\pi\) | ||||
0.322686 | + | 0.946506i | \(0.395414\pi\) | |||||||
\(522\) | −4.32420e18 | − | 4.32420e18i | −0.409461 | − | 0.409461i | ||||
\(523\) | −9.16785e18 | + | 9.16785e18i | −0.856556 | + | 0.856556i | −0.990931 | − | 0.134374i | \(-0.957098\pi\) |
0.134374 | + | 0.990931i | \(0.457098\pi\) | |||||||
\(524\) | − | 9.72056e18i | − | 0.896133i | ||||||
\(525\) | −2.99212e18 | − | 5.71033e18i | −0.272184 | − | 0.519453i | ||||
\(526\) | −6.55017e18 | −0.587966 | ||||||||
\(527\) | −9.56139e18 | − | 9.56139e18i | −0.846928 | − | 0.846928i | ||||
\(528\) | 1.74035e18 | − | 1.74035e18i | 0.152124 | − | 0.152124i | ||||
\(529\) | 1.15401e19i | 0.995449i | ||||||||
\(530\) | −6.94690e18 | − | 4.20274e18i | −0.591371 | − | 0.357768i | ||||
\(531\) | 1.04243e19 | 0.875756 | ||||||||
\(532\) | −5.61456e17 | − | 5.61456e17i | −0.0465516 | − | 0.0465516i | ||||
\(533\) | 3.57735e17 | − | 3.57735e17i | 0.0292732 | − | 0.0292732i | ||||
\(534\) | − | 6.22029e18i | − | 0.502368i | ||||||
\(535\) | 1.11484e18 | + | 4.52965e18i | 0.0888663 | + | 0.361067i | ||||
\(536\) | 2.24953e18 | 0.176985 | ||||||||
\(537\) | −3.13142e18 | − | 3.13142e18i | −0.243176 | − | 0.243176i | ||||
\(538\) | 2.91517e18 | − | 2.91517e18i | 0.223454 | − | 0.223454i | ||||
\(539\) | − | 5.99567e18i | − | 0.453646i | ||||||
\(540\) | 5.84341e18 | − | 1.43819e18i | 0.436426 | − | 0.107414i | ||||
\(541\) | 1.02681e19 | 0.757021 | 0.378511 | − | 0.925597i | \(-0.376436\pi\) | ||||
0.378511 | + | 0.925597i | \(0.376436\pi\) | |||||||
\(542\) | 5.20636e18 | + | 5.20636e18i | 0.378913 | + | 0.378913i | ||||
\(543\) | −4.44373e18 | + | 4.44373e18i | −0.319263 | + | 0.319263i | ||||
\(544\) | 4.05405e18i | 0.287539i | ||||||||
\(545\) | −1.05732e19 | + | 1.74769e19i | −0.740337 | + | 1.22374i | ||||
\(546\) | −8.16548e18 | −0.564460 | ||||||||
\(547\) | −1.37514e19 | − | 1.37514e19i | −0.938504 | − | 0.938504i | 0.0597118 | − | 0.998216i | \(-0.480982\pi\) |
−0.998216 | + | 0.0597118i | \(0.980982\pi\) | |||||||
\(548\) | −7.34228e18 | + | 7.34228e18i | −0.494729 | + | 0.494729i | ||||
\(549\) | − | 4.22479e18i | − | 0.281060i | ||||||
\(550\) | 5.31578e18 | − | 1.70186e19i | 0.349163 | − | 1.11786i | ||||
\(551\) | 2.01778e18 | 0.130862 | ||||||||
\(552\) | 1.36840e17 | + | 1.36840e17i | 0.00876276 | + | 0.00876276i | ||||
\(553\) | 9.76830e18 | − | 9.76830e18i | 0.617651 | − | 0.617651i | ||||
\(554\) | 2.26063e17i | 0.0141144i | ||||||||
\(555\) | 6.41020e18 | + | 3.87804e18i | 0.395203 | + | 0.239090i | ||||
\(556\) | 5.32199e18 | 0.324004 | ||||||||
\(557\) | 1.68618e19 | + | 1.68618e19i | 1.01372 | + | 1.01372i | 0.999905 | + | 0.0138151i | \(0.00439763\pi\) |
0.0138151 | + | 0.999905i | \(0.495602\pi\) | |||||||
\(558\) | −4.52732e18 | + | 4.52732e18i | −0.268783 | + | 0.268783i | ||||
\(559\) | 2.65158e19i | 1.55461i | ||||||||
\(560\) | −1.16467e18 | − | 4.73210e18i | −0.0674352 | − | 0.273992i | ||||
\(561\) | 2.44785e19 | 1.39973 | ||||||||
\(562\) | 9.97005e18 | + | 9.97005e18i | 0.563045 | + | 0.563045i | ||||
\(563\) | 7.75422e17 | − | 7.75422e17i | 0.0432493 | − | 0.0432493i | −0.685151 | − | 0.728401i | \(-0.740264\pi\) |
0.728401 | + | 0.685151i | \(0.240264\pi\) | |||||||
\(564\) | 1.06059e18i | 0.0584241i | ||||||||
\(565\) | 8.26029e18 | − | 2.03303e18i | 0.449424 | − | 0.110613i | ||||
\(566\) | 1.41546e19 | 0.760647 | ||||||||
\(567\) | 3.95412e18 | + | 3.95412e18i | 0.209879 | + | 0.209879i | ||||
\(568\) | 7.70333e18 | − | 7.70333e18i | 0.403869 | − | 0.403869i | ||||
\(569\) | 1.15213e19i | 0.596644i | 0.954465 | + | 0.298322i | \(0.0964269\pi\) | ||||
−0.954465 | + | 0.298322i | \(0.903573\pi\) | |||||||
\(570\) | −4.33704e17 | + | 7.16889e17i | −0.0221855 | + | 0.0366714i | ||||
\(571\) | −5.14309e18 | −0.259879 | −0.129939 | − | 0.991522i | \(-0.541478\pi\) | ||||
−0.129939 | + | 0.991522i | \(0.541478\pi\) | |||||||
\(572\) | −1.59686e19 | − | 1.59686e19i | −0.797064 | − | 0.797064i | ||||
\(573\) | −1.25132e19 | + | 1.25132e19i | −0.617001 | + | 0.617001i | ||||
\(574\) | − | 4.98310e17i | − | 0.0242726i | ||||||
\(575\) | 1.33815e18 | + | 4.17971e17i | 0.0643915 | + | 0.0201127i | ||||
\(576\) | 1.91959e18 | 0.0912538 | ||||||||
\(577\) | −1.54960e19 | − | 1.54960e19i | −0.727761 | − | 0.727761i | 0.242412 | − | 0.970173i | \(-0.422061\pi\) |
−0.970173 | + | 0.242412i | \(0.922061\pi\) | |||||||
\(578\) | −1.77345e19 | + | 1.77345e19i | −0.822856 | + | 0.822856i | ||||
\(579\) | − | 4.33521e18i | − | 0.198728i | ||||||
\(580\) | 1.05960e19 | + | 6.41037e18i | 0.479895 | + | 0.290327i | ||||
\(581\) | 6.27492e18 | 0.280786 | ||||||||
\(582\) | 3.62831e17 | + | 3.62831e17i | 0.0160414 | + | 0.0160414i | ||||
\(583\) | −2.62048e19 | + | 2.62048e19i | −1.14473 | + | 1.14473i | ||||
\(584\) | 1.12817e19i | 0.486949i | ||||||||
\(585\) | −5.56843e18 | − | 2.26247e19i | −0.237488 | − | 0.964923i | ||||
\(586\) | 1.27085e19 | 0.535562 | ||||||||
\(587\) | −3.11856e19 | − | 3.11856e19i | −1.29864 | − | 1.29864i | −0.929294 | − | 0.369342i | \(-0.879583\pi\) |
−0.369342 | − | 0.929294i | \(-0.620417\pi\) | |||||||
\(588\) | −1.22280e18 | + | 1.22280e18i | −0.0503168 | + | 0.0503168i | ||||
\(589\) | − | 2.11256e18i | − | 0.0859016i | ||||||
\(590\) | −2.04984e19 | + | 5.04510e18i | −0.823676 | + | 0.202724i | ||||
\(591\) | 2.18659e19 | 0.868269 | ||||||||
\(592\) | 4.00466e18 | + | 4.00466e18i | 0.157150 | + | 0.157150i | ||||
\(593\) | 1.53125e19 | − | 1.53125e19i | 0.593831 | − | 0.593831i | −0.344833 | − | 0.938664i | \(-0.612064\pi\) |
0.938664 | + | 0.344833i | \(0.112064\pi\) | |||||||
\(594\) | − | 2.74674e19i | − | 1.05272i | ||||||
\(595\) | 2.50885e19 | − | 4.14699e19i | 0.950289 | − | 1.57078i | ||||
\(596\) | −1.78178e19 | −0.667008 | ||||||||
\(597\) | 9.55115e18 | + | 9.55115e18i | 0.353375 | + | 0.353375i | ||||
\(598\) | 1.25558e18 | − | 1.25558e18i | 0.0459130 | − | 0.0459130i | ||||
\(599\) | 1.85841e19i | 0.671667i | 0.941921 | + | 0.335834i | \(0.109018\pi\) | ||||
−0.941921 | + | 0.335834i | \(0.890982\pi\) | |||||||
\(600\) | −4.55503e18 | + | 2.38676e18i | −0.162717 | + | 0.0852609i | ||||
\(601\) | −4.10179e19 | −1.44828 | −0.724139 | − | 0.689654i | \(-0.757763\pi\) | ||||
−0.724139 | + | 0.689654i | \(0.757763\pi\) | |||||||
\(602\) | 1.84677e19 | + | 1.84677e19i | 0.644523 | + | 0.644523i | ||||
\(603\) | 7.49083e18 | − | 7.49083e18i | 0.258410 | − | 0.258410i | ||||
\(604\) | 2.01089e19i | 0.685693i | ||||||||
\(605\) | −4.42455e19 | − | 2.67676e19i | −1.49136 | − | 0.902241i | ||||
\(606\) | −2.51860e18 | −0.0839172 | ||||||||
\(607\) | 1.51335e19 | + | 1.51335e19i | 0.498445 | + | 0.498445i | 0.910954 | − | 0.412508i | \(-0.135347\pi\) |
−0.412508 | + | 0.910954i | \(0.635347\pi\) | |||||||
\(608\) | −4.47864e17 | + | 4.47864e17i | −0.0145821 | + | 0.0145821i | ||||
\(609\) | − | 2.04385e19i | − | 0.657851i | ||||||
\(610\) | 2.04470e18 | + | 8.30770e18i | 0.0650610 | + | 0.264346i | ||||
\(611\) | 9.73141e18 | 0.306117 | ||||||||
\(612\) | 1.34998e19 | + | 1.34998e19i | 0.419824 | + | 0.419824i | ||||
\(613\) | 3.41597e19 | − | 3.41597e19i | 1.05024 | − | 1.05024i | 0.0515757 | − | 0.998669i | \(-0.483576\pi\) |
0.998669 | − | 0.0515757i | \(-0.0164243\pi\) | |||||||
\(614\) | 9.60995e18i | 0.292107i | ||||||||
\(615\) | −5.10594e17 | + | 1.25668e17i | −0.0153444 | + | 0.00377658i | ||||
\(616\) | −2.22436e19 | −0.660906 | ||||||||
\(617\) | 6.90783e17 | + | 6.90783e17i | 0.0202930 | + | 0.0202930i | 0.717180 | − | 0.696888i | \(-0.245432\pi\) |
−0.696888 | + | 0.717180i | \(0.745432\pi\) | |||||||
\(618\) | 2.56692e18 | − | 2.56692e18i | 0.0745577 | − | 0.0745577i | ||||
\(619\) | − | 3.74206e19i | − | 1.07467i | −0.843368 | − | 0.537336i | \(-0.819431\pi\) | ||
0.843368 | − | 0.537336i | \(-0.180569\pi\) | |||||||
\(620\) | 6.71147e18 | − | 1.10937e19i | 0.190579 | − | 0.315018i | ||||
\(621\) | 2.15971e18 | 0.0606394 | ||||||||
\(622\) | −2.38645e19 | − | 2.38645e19i | −0.662552 | − | 0.662552i | ||||
\(623\) | −3.97511e19 | + | 3.97511e19i | −1.09127 | + | 1.09127i | ||||
\(624\) | 6.51346e18i | 0.176815i | ||||||||
\(625\) | −2.12033e19 | + | 3.06300e19i | −0.569171 | + | 0.822219i | ||||
\(626\) | 3.43302e19 | 0.911289 | ||||||||
\(627\) | 2.70422e18 | + | 2.70422e18i | 0.0709854 | + | 0.0709854i | ||||
\(628\) | −4.95691e18 | + | 4.95691e18i | −0.128675 | + | 0.128675i | ||||
\(629\) | 5.63267e19i | 1.44597i | ||||||||
\(630\) | −1.96360e19 | − | 1.18794e19i | −0.498504 | − | 0.301585i | ||||
\(631\) | 5.04599e19 | 1.26690 | 0.633448 | − | 0.773785i | \(-0.281639\pi\) | ||||
0.633448 | + | 0.773785i | \(0.281639\pi\) | |||||||
\(632\) | −7.79200e18 | − | 7.79200e18i | −0.193477 | − | 0.193477i | ||||
\(633\) | 2.87607e18 | − | 2.87607e18i | 0.0706275 | − | 0.0706275i | ||||
\(634\) | 1.94565e19i | 0.472542i | ||||||||
\(635\) | 9.22256e18 | + | 3.74716e19i | 0.221531 | + | 0.900091i | ||||
\(636\) | 1.06888e19 | 0.253938 | ||||||||
\(637\) | 1.12198e19 | + | 1.12198e19i | 0.263638 | + | 0.263638i | ||||
\(638\) | 3.99698e19 | − | 3.99698e19i | 0.928939 | − | 0.928939i | ||||
\(639\) | − | 5.13035e19i | − | 1.17935i | ||||||
\(640\) | −3.77471e18 | + | 9.29037e17i | −0.0858271 | + | 0.0211239i | ||||
\(641\) | −7.11564e19 | −1.60032 | −0.800162 | − | 0.599784i | \(-0.795253\pi\) | ||||
−0.800162 | + | 0.599784i | \(0.795253\pi\) | |||||||
\(642\) | −4.34242e18 | − | 4.34242e18i | −0.0966020 | − | 0.0966020i | ||||
\(643\) | 2.55404e19 | − | 2.55404e19i | 0.562020 | − | 0.562020i | −0.367861 | − | 0.929881i | \(-0.619910\pi\) |
0.929881 | + | 0.367861i | \(0.119910\pi\) | |||||||
\(644\) | − | 1.74897e18i | − | 0.0380699i | ||||||
\(645\) | 1.42656e19 | − | 2.35803e19i | 0.307166 | − | 0.507729i | ||||
\(646\) | −6.29934e18 | −0.134174 | ||||||||
\(647\) | 3.71373e19 | + | 3.71373e19i | 0.782494 | + | 0.782494i | 0.980251 | − | 0.197757i | \(-0.0633658\pi\) |
−0.197757 | + | 0.980251i | \(0.563366\pi\) | |||||||
\(648\) | 3.15413e18 | − | 3.15413e18i | 0.0657437 | − | 0.0657437i | ||||
\(649\) | 9.63543e19i | 1.98682i | ||||||||
\(650\) | 2.18997e19 | + | 4.17947e19i | 0.446730 | + | 0.852565i | ||||
\(651\) | −2.13985e19 | −0.431834 | ||||||||
\(652\) | −2.25919e19 | − | 2.25919e19i | −0.451046 | − | 0.451046i | ||||
\(653\) | −1.57979e19 | + | 1.57979e19i | −0.312038 | + | 0.312038i | −0.845699 | − | 0.533661i | \(-0.820816\pi\) |
0.533661 | + | 0.845699i | \(0.320816\pi\) | |||||||
\(654\) | − | 2.68906e19i | − | 0.525480i | ||||||
\(655\) | 7.93169e19 | + | 4.79852e19i | 1.53348 | + | 0.927722i | ||||
\(656\) | −3.97493e17 | −0.00760331 | ||||||||
\(657\) | 3.75675e19 | + | 3.75675e19i | 0.710975 | + | 0.710975i | ||||
\(658\) | 6.77774e18 | − | 6.77774e18i | 0.126912 | − | 0.126912i | ||||
\(659\) | − | 1.01968e20i | − | 1.88916i | −0.328286 | − | 0.944579i | \(-0.606471\pi\) | ||
0.328286 | − | 0.944579i | \(-0.393529\pi\) | |||||||
\(660\) | 5.60956e18 | + | 2.27919e19i | 0.102830 | + | 0.417804i | ||||
\(661\) | −9.17130e19 | −1.66349 | −0.831746 | − | 0.555157i | \(-0.812658\pi\) | ||||
−0.831746 | + | 0.555157i | \(0.812658\pi\) | |||||||
\(662\) | −3.37931e19 | − | 3.37931e19i | −0.606487 | − | 0.606487i | ||||
\(663\) | −4.58069e19 | + | 4.58069e19i | −0.813460 | + | 0.813460i | ||||
\(664\) | − | 5.00539e18i | − | 0.0879552i | ||||||
\(665\) | 7.35293e18 | − | 1.80971e18i | 0.127852 | − | 0.0314672i | ||||
\(666\) | 2.66707e19 | 0.458897 | ||||||||
\(667\) | 3.14276e18 | + | 3.14276e18i | 0.0535094 | + | 0.0535094i | ||||
\(668\) | 1.82847e19 | − | 1.82847e19i | 0.308073 | − | 0.308073i | ||||
\(669\) | − | 2.56728e19i | − | 0.428046i | ||||||
\(670\) | −1.11047e19 | + | 1.83555e19i | −0.183224 | + | 0.302860i | ||||
\(671\) | 3.90509e19 | 0.637637 | ||||||||
\(672\) | 4.53650e18 | + | 4.53650e18i | 0.0733054 | + | 0.0733054i | ||||
\(673\) | 7.14516e19 | − | 7.14516e19i | 1.14263 | − | 1.14263i | 0.154666 | − | 0.987967i | \(-0.450570\pi\) |
0.987967 | − | 0.154666i | \(-0.0494301\pi\) | |||||||
\(674\) | 4.14913e18i | 0.0656656i | ||||||||
\(675\) | −1.71106e19 | + | 5.47801e19i | −0.268002 | + | 0.858018i | ||||
\(676\) | 2.75093e19 | 0.426435 | ||||||||
\(677\) | 4.33021e18 | + | 4.33021e18i | 0.0664337 | + | 0.0664337i | 0.739543 | − | 0.673109i | \(-0.235042\pi\) |
−0.673109 | + | 0.739543i | \(0.735042\pi\) | |||||||
\(678\) | −7.91885e18 | + | 7.91885e18i | −0.120241 | + | 0.120241i | ||||
\(679\) | − | 4.63738e18i | − | 0.0696922i | ||||||
\(680\) | −3.30798e19 | − | 2.00126e19i | −0.492040 | − | 0.297675i | ||||
\(681\) | −2.77905e19 | −0.409135 | ||||||||
\(682\) | −4.18472e19 | − | 4.18472e19i | −0.609784 | − | 0.609784i | ||||
\(683\) | 1.29755e18 | − | 1.29755e18i | 0.0187145 | − | 0.0187145i | −0.697688 | − | 0.716402i | \(-0.745788\pi\) |
0.716402 | + | 0.697688i | \(0.245788\pi\) | |||||||
\(684\) | 2.98273e18i | 0.0425816i | ||||||||
\(685\) | −2.36660e19 | − | 9.61558e19i | −0.334418 | − | 1.35876i | ||||
\(686\) | −4.14301e19 | −0.579491 | ||||||||
\(687\) | −1.67409e19 | − | 1.67409e19i | −0.231783 | − | 0.231783i | ||||
\(688\) | 1.47314e19 | − | 1.47314e19i | 0.201895 | − | 0.201895i | ||||
\(689\) | − | 9.80748e19i | − | 1.33052i | ||||||
\(690\) | −1.79209e18 | + | 4.41070e17i | −0.0240666 | + | 0.00592331i | ||||
\(691\) | −1.03076e20 | −1.37028 | −0.685140 | − | 0.728411i | \(-0.740259\pi\) | ||||
−0.685140 | + | 0.728411i | \(0.740259\pi\) | |||||||
\(692\) | −1.64836e19 | − | 1.64836e19i | −0.216925 | − | 0.216925i | ||||
\(693\) | −7.40701e19 | + | 7.40701e19i | −0.964963 | + | 0.964963i | ||||
\(694\) | − | 2.20220e19i | − | 0.284015i | ||||||
\(695\) | −2.62718e19 | + | 4.34259e19i | −0.335426 | + | 0.554440i | ||||
\(696\) | −1.63034e19 | −0.206069 | ||||||||
\(697\) | −2.79543e18 | − | 2.79543e18i | −0.0349800 | − | 0.0349800i | ||||
\(698\) | −5.24439e18 | + | 5.24439e18i | −0.0649691 | + | 0.0649691i | ||||
\(699\) | − | 2.56331e19i | − | 0.314384i | ||||||
\(700\) | 4.43619e19 | + | 1.38565e19i | 0.538671 | + | 0.168254i | ||||
\(701\) | 8.07311e19 | 0.970542 | 0.485271 | − | 0.874364i | \(-0.338721\pi\) | ||||
0.485271 | + | 0.874364i | \(0.338721\pi\) | |||||||
\(702\) | 5.14000e19 | + | 5.14000e19i | 0.611792 | + | 0.611792i | ||||
\(703\) | −6.22260e18 | + | 6.22260e18i | −0.0733305 | + | 0.0733305i | ||||
\(704\) | 1.77433e19i | 0.207026i | ||||||||
\(705\) | −8.65407e18 | − | 5.23554e18i | −0.0999762 | − | 0.0604836i | ||||
\(706\) | −6.08500e19 | −0.696030 | ||||||||
\(707\) | 1.60953e19 | + | 1.60953e19i | 0.182290 | + | 0.182290i | ||||
\(708\) | 1.96511e19 | − | 1.96511e19i | 0.220371 | − | 0.220371i | ||||
\(709\) | 4.52131e19i | 0.502043i | 0.967982 | + | 0.251022i | \(0.0807665\pi\) | ||||
−0.967982 | + | 0.251022i | \(0.919234\pi\) | |||||||
\(710\) | 2.48297e19 | + | 1.00884e20i | 0.273000 | + | 1.10921i | ||||
\(711\) | −5.18941e19 | −0.564977 | ||||||||
\(712\) | 3.17088e19 | + | 3.17088e19i | 0.341837 | + | 0.341837i | ||||
\(713\) | 3.29038e18 | − | 3.29038e18i | 0.0351252 | − | 0.0351252i | ||||
\(714\) | 6.38072e19i | 0.674500i | ||||||||
\(715\) | 2.09127e20 | − | 5.14705e19i | 2.18911 | − | 0.538786i | ||||
\(716\) | 3.19257e19 | 0.330940 | ||||||||
\(717\) | 1.25969e19 | + | 1.25969e19i | 0.129309 | + | 0.129309i | ||||
\(718\) | −4.16918e19 | + | 4.16918e19i | −0.423818 | + | 0.423818i | ||||
\(719\) | − | 1.26641e20i | − | 1.27489i | −0.770497 | − | 0.637443i | \(-0.779992\pi\) | ||
0.770497 | − | 0.637443i | \(-0.220008\pi\) | |||||||
\(720\) | −9.47598e18 | + | 1.56633e19i | −0.0944706 | + | 0.156155i | ||||
\(721\) | −3.28081e19 | −0.323917 | ||||||||
\(722\) | 5.04405e19 | + | 5.04405e19i | 0.493196 | + | 0.493196i | ||||
\(723\) | 2.77726e19 | − | 2.77726e19i | 0.268936 | − | 0.268936i | ||||
\(724\) | − | 4.53050e19i | − | 0.434486i | ||||||
\(725\) | −1.04613e20 | + | 5.48157e19i | −0.993623 | + | 0.520641i | ||||
\(726\) | 6.80778e19 | 0.640397 | ||||||||
\(727\) | −4.36485e18 | − | 4.36485e18i | −0.0406657 | − | 0.0406657i | 0.686482 | − | 0.727147i | \(-0.259154\pi\) |
−0.727147 | + | 0.686482i | \(0.759154\pi\) | |||||||
\(728\) | 4.16247e19 | − | 4.16247e19i | 0.384088 | − | 0.384088i | ||||
\(729\) | 3.00985e19i | 0.275076i | ||||||||
\(730\) | −9.20551e19 | − | 5.56915e19i | −0.833274 | − | 0.504114i | ||||
\(731\) | 2.07201e20 | 1.85768 | ||||||||
\(732\) | −7.96430e18 | − | 7.96430e18i | −0.0707245 | − | 0.0707245i | ||||
\(733\) | 5.77817e18 | − | 5.77817e18i | 0.0508233 | − | 0.0508233i | −0.681238 | − | 0.732062i | \(-0.738558\pi\) |
0.732062 | + | 0.681238i | \(0.238558\pi\) | |||||||
\(734\) | 2.47310e19i | 0.215461i | ||||||||
\(735\) | −3.94137e18 | − | 1.60140e19i | −0.0340123 | − | 0.138193i | ||||
\(736\) | −1.39513e18 | −0.0119253 | ||||||||
\(737\) | 6.92398e19 | + | 6.92398e19i | 0.586251 | + | 0.586251i | ||||
\(738\) | −1.32364e18 | + | 1.32364e18i | −0.0111013 | + | 0.0111013i | ||||
\(739\) | 2.29620e20i | 1.90765i | 0.300368 | + | 0.953824i | \(0.402891\pi\) | ||||
−0.300368 | + | 0.953824i | \(0.597109\pi\) | |||||||
\(740\) | −5.24457e19 | + | 1.29080e19i | −0.431607 | + | 0.106228i | ||||
\(741\) | −1.01209e19 | −0.0825070 | ||||||||
\(742\) | −6.83072e19 | − | 6.83072e19i | −0.551619 | − | 0.551619i | ||||
\(743\) | 2.69258e19 | − | 2.69258e19i | 0.215401 | − | 0.215401i | −0.591156 | − | 0.806557i | \(-0.701328\pi\) |
0.806557 | + | 0.591156i | \(0.201328\pi\) | |||||||
\(744\) | 1.70692e19i | 0.135270i | ||||||||
\(745\) | 8.79571e19 | − | 1.45388e20i | 0.690521 | − | 1.14139i | ||||
\(746\) | 1.21050e20 | 0.941438 | ||||||||
\(747\) | −1.66677e19 | − | 1.66677e19i | −0.128420 | − | 0.128420i | ||||
\(748\) | −1.24782e20 | + | 1.24782e20i | −0.952450 | + | 0.952450i | ||||
\(749\) | 5.55009e19i | 0.419689i | ||||||||
\(750\) | 3.01048e18 | − | 4.89499e19i | 0.0225532 | − | 0.366710i | ||||
\(751\) | −1.12909e20 | −0.838010 | −0.419005 | − | 0.907984i | \(-0.637621\pi\) | ||||
−0.419005 | + | 0.907984i | \(0.637621\pi\) | |||||||
\(752\) | −5.40648e18 | − | 5.40648e18i | −0.0397548 | − | 0.0397548i | ||||
\(753\) | 8.53363e19 | − | 8.53363e19i | 0.621683 | − | 0.621683i | ||||
\(754\) | 1.49592e20i | 1.07971i | ||||||||
\(755\) | −1.64083e20 | − | 9.92668e19i | −1.17337 | − | 0.709865i | ||||
\(756\) | 7.15982e19 | 0.507282 | ||||||||
\(757\) | −6.51187e19 | − | 6.51187e19i | −0.457124 | − | 0.457124i | 0.440586 | − | 0.897710i | \(-0.354771\pi\) |
−0.897710 | + | 0.440586i | \(0.854771\pi\) | |||||||
\(758\) | 4.42245e19 | − | 4.42245e19i | 0.307594 | − | 0.307594i | ||||
\(759\) | 8.42382e18i | 0.0580519i | ||||||||
\(760\) | −1.44357e18 | − | 5.86530e18i | −0.00985699 | − | 0.0400493i | ||||
\(761\) | −8.37664e19 | −0.566731 | −0.283366 | − | 0.959012i | \(-0.591451\pi\) | ||||
−0.283366 | + | 0.959012i | \(0.591451\pi\) | |||||||
\(762\) | −3.59227e19 | − | 3.59227e19i | −0.240815 | − | 0.240815i | ||||
\(763\) | −1.71846e20 | + | 1.71846e20i | −1.14148 | + | 1.14148i | ||||
\(764\) | − | 1.27575e20i | − | 0.839679i | ||||||
\(765\) | −1.76796e20 | + | 4.35132e19i | −1.15303 | + | 0.283786i | ||||
\(766\) | −1.33192e20 | −0.860750 | ||||||||
\(767\) | −1.80309e20 | − | 1.80309e20i | −1.15465 | − | 1.15465i | ||||
\(768\) | 3.61869e18 | − | 3.61869e18i | 0.0229627 | − | 0.0229627i | ||||
\(769\) | 1.62320e20i | 1.02068i | 0.859973 | + | 0.510339i | \(0.170480\pi\) | ||||
−0.859973 | + | 0.510339i | \(0.829520\pi\) | |||||||
\(770\) | 1.09805e20 | − | 1.81501e20i | 0.684203 | − | 1.13095i | ||||
\(771\) | −3.89235e19 | −0.240343 | ||||||||
\(772\) | 2.20993e19 | + | 2.20993e19i | 0.135225 | + | 0.135225i | ||||
\(773\) | 2.22705e20 | − | 2.22705e20i | 1.35044 | − | 1.35044i | 0.465263 | − | 0.885172i | \(-0.345960\pi\) |
0.885172 | − | 0.465263i | \(-0.154040\pi\) | |||||||
\(774\) | − | 9.81099e19i | − | 0.589557i | ||||||
\(775\) | 5.73905e19 | + | 1.09527e20i | 0.341765 | + | 0.652245i | ||||
\(776\) | −3.69916e18 | −0.0218308 | ||||||||
\(777\) | 6.30300e19 | + | 6.30300e19i | 0.368638 | + | 0.368638i | ||||
\(778\) | 1.03393e20 | − | 1.03393e20i | 0.599288 | − | 0.599288i | ||||
\(779\) | − | 6.17641e17i | − | 0.00354792i | ||||||
\(780\) | −5.31479e19 | − | 3.21535e19i | −0.302569 | − | 0.183048i | ||||
\(781\) | 4.74213e20 | 2.67557 | ||||||||
\(782\) | −9.81143e18 | − | 9.81143e18i | −0.0548637 | − | 0.0548637i | ||||
\(783\) | −1.28656e20 | + | 1.28656e20i | −0.713013 | + | 0.713013i | ||||
\(784\) | − | 1.24667e19i | − | 0.0684764i | ||||||
\(785\) | −1.59773e19 | − | 6.49166e19i | −0.0869795 | − | 0.353401i | ||||
\(786\) | −1.22040e20 | −0.658483 | ||||||||
\(787\) | −1.43266e20 | − | 1.43266e20i | −0.766161 | − | 0.766161i | 0.211267 | − | 0.977428i | \(-0.432241\pi\) |
−0.977428 | + | 0.211267i | \(0.932241\pi\) | |||||||
\(788\) | −1.11464e20 | + | 1.11464e20i | −0.590816 | + | 0.590816i | ||||
\(789\) | 8.22363e19i | 0.432041i | ||||||||
\(790\) | 1.02045e20 | − | 2.51155e19i | 0.531378 | − | 0.130783i | ||||
\(791\) | 1.01212e20 | 0.522391 | ||||||||
\(792\) | 5.90844e19 | + | 5.90844e19i | 0.302271 | + | 0.302271i | ||||
\(793\) | −7.30765e19 | + | 7.30765e19i | −0.370566 | + | 0.370566i | ||||
\(794\) | − | 1.78878e20i | − | 0.899111i | ||||||
\(795\) | −5.27647e19 | + | 8.72172e19i | −0.262890 | + | 0.434542i | ||||
\(796\) | −9.73766e19 | −0.480909 | ||||||||
\(797\) | 9.23139e19 | + | 9.23139e19i | 0.451917 | + | 0.451917i | 0.895990 | − | 0.444073i | \(-0.146467\pi\) |
−0.444073 | + | 0.895990i | \(0.646467\pi\) | |||||||
\(798\) | −7.04899e18 | + | 7.04899e18i | −0.0342064 | + | 0.0342064i | ||||
\(799\) | − | 7.60437e19i | − | 0.365794i | ||||||
\(800\) | 1.10531e19 | − | 3.53867e19i | 0.0527051 | − | 0.168737i | ||||
\(801\) | 2.11178e20 | 0.998207 | ||||||||
\(802\) | 2.01206e19 | + | 2.01206e19i | 0.0942800 | + | 0.0942800i | ||||
\(803\) | −3.47246e20 | + | 3.47246e20i | −1.61298 | + | 1.61298i | ||||
\(804\) | − | 2.82424e19i | − | 0.130050i | ||||||
\(805\) | 1.42711e19 | + | 8.63374e18i | 0.0651458 | + | 0.0394119i | ||||
\(806\) | 1.56619e20 | 0.708758 | ||||||||
\(807\) | −3.65995e19 | − | 3.65995e19i | −0.164195 | − | 0.164195i | ||||
\(808\) | 1.28389e19 | − | 1.28389e19i | 0.0571016 | − | 0.0571016i | ||||
\(809\) | 1.28441e20i | 0.566323i | 0.959072 | + | 0.283162i | \(0.0913833\pi\) | ||||
−0.959072 | + | 0.283162i | \(0.908617\pi\) | |||||||
\(810\) | 1.01665e19 | + | 4.13070e19i | 0.0444404 | + | 0.180563i | ||||
\(811\) | 1.08142e20 | 0.468651 | 0.234325 | − | 0.972158i | \(-0.424712\pi\) | ||||
0.234325 | + | 0.972158i | \(0.424712\pi\) | |||||||
\(812\) | 1.04188e20 | + | 1.04188e20i | 0.447636 | + | 0.447636i | ||||
\(813\) | 6.53650e19 | − | 6.53650e19i | 0.278427 | − | 0.278427i | ||||
\(814\) | 2.46525e20i | 1.04109i | ||||||||
\(815\) | 2.95868e20 | − | 7.28194e19i | 1.23878 | − | 0.304890i | ||||
\(816\) | 5.08979e19 | 0.211285 | ||||||||
\(817\) | 2.28902e19 | + | 2.28902e19i | 0.0942097 | + | 0.0942097i | ||||
\(818\) | −1.62266e20 | + | 1.62266e20i | −0.662145 | + | 0.662145i | ||||
\(819\) | − | 2.77217e20i | − | 1.12158i | ||||||
\(820\) | 1.96221e18 | − | 3.24343e18i | 0.00787134 | − | 0.0130109i | ||||
\(821\) | −2.31305e20 | −0.919988 | −0.459994 | − | 0.887922i | \(-0.652148\pi\) | ||||
−0.459994 | + | 0.887922i | \(0.652148\pi\) | |||||||
\(822\) | 9.21812e19 | + | 9.21812e19i | 0.363529 | + | 0.363529i | ||||
\(823\) | 1.62824e20 | − | 1.62824e20i | 0.636678 | − | 0.636678i | −0.313057 | − | 0.949734i | \(-0.601353\pi\) |
0.949734 | + | 0.313057i | \(0.101353\pi\) | |||||||
\(824\) | 2.61704e19i | 0.101466i | ||||||||
\(825\) | −2.13666e20 | − | 6.67388e19i | −0.821407 | − | 0.256567i | ||||
\(826\) | −2.51163e20 | −0.957406 | ||||||||
\(827\) | 4.31954e19 | + | 4.31954e19i | 0.163267 | + | 0.163267i | 0.784012 | − | 0.620745i | \(-0.213170\pi\) |
−0.620745 | + | 0.784012i | \(0.713170\pi\) | |||||||
\(828\) | −4.64571e18 | + | 4.64571e18i | −0.0174116 | + | 0.0174116i | ||||
\(829\) | 5.78065e19i | 0.214830i | 0.994214 | + | 0.107415i | \(0.0342574\pi\) | ||||
−0.994214 | + | 0.107415i | \(0.965743\pi\) | |||||||
\(830\) | 4.08425e19 | + | 2.47089e19i | 0.150510 | + | 0.0910557i | ||||
\(831\) | 2.83819e18 | 0.0103713 | ||||||||
\(832\) | −3.32033e19 | − | 3.32033e19i | −0.120314 | − | 0.120314i | ||||
\(833\) | 8.76743e19 | − | 8.76743e19i | 0.315034 | − | 0.315034i | ||||
\(834\) | − | 6.68167e19i | − | 0.238080i | ||||||
\(835\) | 5.89361e19 | + | 2.39460e20i | 0.208246 | + | 0.846111i | ||||
\(836\) | −2.75702e19 | −0.0966044 | ||||||||
\(837\) | 1.34699e20 | + | 1.34699e20i | 0.468044 | + | 0.468044i | ||||
\(838\) | 1.03980e20 | − | 1.03980e20i | 0.358296 | − | 0.358296i | ||||
\(839\) | − | 7.42680e19i | − | 0.253786i | −0.991916 | − | 0.126893i | \(-0.959499\pi\) | ||
0.991916 | − | 0.126893i | \(-0.0405005\pi\) | |||||||
\(840\) | −5.94108e19 | + | 1.46222e19i | −0.201331 | + | 0.0495518i | ||||
\(841\) | −7.68752e19 | −0.258353 | ||||||||
\(842\) | 6.91577e19 | + | 6.91577e19i | 0.230492 | + | 0.230492i | ||||
\(843\) | 1.25172e20 | − | 1.25172e20i | 0.413728 | − | 0.413728i | ||||
\(844\) | 2.93223e19i | 0.0961173i | ||||||||
\(845\) | −1.35799e20 | + | 2.24468e20i | −0.441467 | + | 0.729721i | ||||
\(846\) | −3.60067e19 | −0.116089 | ||||||||
\(847\) | −4.35055e20 | − | 4.35055e20i | −1.39111 | − | 1.39111i | ||||
\(848\) | −5.44874e19 | + | 5.44874e19i | −0.172793 | + | 0.172793i | ||||
\(849\) | − | 1.77709e20i | − | 0.558928i | ||||||
\(850\) | 3.26595e20 | − | 1.71130e20i | 1.01877 | − | 0.533819i | ||||
\(851\) | −1.93838e19 | −0.0599698 | ||||||||
\(852\) | −9.67141e19 | − | 9.67141e19i | −0.296765 | − | 0.296765i | ||||
\(853\) | 1.81274e20 | − | 1.81274e20i | 0.551685 | − | 0.551685i | −0.375242 | − | 0.926927i | \(-0.622440\pi\) |
0.926927 | + | 0.375242i | \(0.122440\pi\) | |||||||
\(854\) | 1.01793e20i | 0.307264i | ||||||||
\(855\) | −2.43382e19 | − | 1.47242e19i | −0.0728662 | − | 0.0440826i | ||||
\(856\) | 4.42721e19 | 0.131466 | ||||||||
\(857\) | −2.03302e20 | − | 2.03302e20i | −0.598793 | − | 0.598793i | 0.341198 | − | 0.939991i | \(-0.389167\pi\) |
−0.939991 | + | 0.341198i | \(0.889167\pi\) | |||||||
\(858\) | −2.00483e20 | + | 2.00483e20i | −0.585687 | + | 0.585687i | ||||
\(859\) | 7.68775e19i | 0.222765i | 0.993778 | + | 0.111383i | \(0.0355279\pi\) | ||||
−0.993778 | + | 0.111383i | \(0.964472\pi\) | |||||||
\(860\) | 4.74829e19 | + | 1.92925e20i | 0.136473 | + | 0.554497i | ||||
\(861\) | −6.25621e18 | −0.0178357 | ||||||||
\(862\) | 7.85370e19 | + | 7.85370e19i | 0.222087 | + | 0.222087i | ||||
\(863\) | −4.01628e18 | + | 4.01628e18i | −0.0112655 | + | 0.0112655i | −0.712717 | − | 0.701452i | \(-0.752536\pi\) |
0.701452 | + | 0.712717i | \(0.252536\pi\) | |||||||
\(864\) | − | 5.71127e19i | − | 0.158904i | ||||||
\(865\) | 2.15872e20 | − | 5.31308e19i | 0.595778 | − | 0.146634i | ||||
\(866\) | −3.60814e20 | −0.987775 | ||||||||
\(867\) | 2.22654e20 | + | 2.22654e20i | 0.604639 | + | 0.604639i | ||||
\(868\) | 1.09082e20 | − | 1.09082e20i | 0.293842 | − | 0.293842i | ||||
\(869\) | − | 4.79671e20i | − | 1.28176i | ||||||
\(870\) | 8.04811e19 | − | 1.33031e20i | 0.213334 | − | 0.352629i | ||||
\(871\) | −2.59139e20 | −0.681405 | ||||||||
\(872\) | 1.37079e20 | + | 1.37079e20i | 0.357564 | + | 0.357564i | ||||
\(873\) | −1.23180e19 | + | 1.23180e19i | −0.0318744 | + | 0.0318744i | ||||
\(874\) | − | 2.16780e18i | − | 0.00556467i | ||||||
\(875\) | −3.32056e20 | + | 2.93578e20i | −0.845579 | + | 0.747597i | ||||
\(876\) | 1.41639e20 | 0.357813 | ||||||||
\(877\) | −2.82852e20 | − | 2.82852e20i | −0.708862 | − | 0.708862i | 0.257434 | − | 0.966296i | \(-0.417123\pi\) |
−0.966296 | + | 0.257434i | \(0.917123\pi\) | |||||||
\(878\) | −1.72183e20 | + | 1.72183e20i | −0.428083 | + | 0.428083i | ||||
\(879\) | − | 1.59553e20i | − | 0.393534i | ||||||
\(880\) | −1.44780e20 | − | 8.75891e19i | −0.354267 | − | 0.214324i | ||||
\(881\) | −5.52031e20 | −1.34009 | −0.670043 | − | 0.742323i | \(-0.733724\pi\) | ||||
−0.670043 | + | 0.742323i | \(0.733724\pi\) | |||||||
\(882\) | −4.15137e19 | − | 4.15137e19i | −0.0999797 | − | 0.0999797i | ||||
\(883\) | 4.89936e20 | − | 4.89936e20i | 1.17062 | − | 1.17062i | 0.188554 | − | 0.982063i | \(-0.439620\pi\) |
0.982063 | − | 0.188554i | \(-0.0603799\pi\) | |||||||
\(884\) | − | 4.67014e20i | − | 1.10704i | ||||||
\(885\) | 6.33404e19 | + | 2.57354e20i | 0.148963 | + | 0.605242i | ||||
\(886\) | −7.42461e19 | −0.173236 | ||||||||
\(887\) | 3.77508e20 | + | 3.77508e20i | 0.873899 | + | 0.873899i | 0.992895 | − | 0.118996i | \(-0.0379676\pi\) |
−0.118996 | + | 0.992895i | \(0.537968\pi\) | |||||||
\(888\) | 5.02779e19 | − | 5.02779e19i | 0.115475 | − | 0.115475i | ||||
\(889\) | 4.59132e20i | 1.04623i | ||||||||
\(890\) | −4.15264e20 | + | 1.02205e20i | −0.938845 | + | 0.231070i | ||||
\(891\) | 1.94166e20 | 0.435542 | ||||||||
\(892\) | 1.30871e20 | + | 1.30871e20i | 0.291265 | + | 0.291265i | ||||
\(893\) | 8.40080e18 | − | 8.40080e18i | 0.0185507 | − | 0.0185507i | ||||
\(894\) | 2.23700e20i | 0.490121i | ||||||||
\(895\) | −1.57600e20 | + | 2.60504e20i | −0.342606 | + | 0.566309i | ||||
\(896\) | −4.62508e19 | −0.0997617 | ||||||||
\(897\) | −1.57636e19 | − | 1.57636e19i | −0.0337371 | − | 0.0337371i | ||||
\(898\) | 2.92349e20 | − | 2.92349e20i | 0.620823 | − | 0.620823i | ||||
\(899\) | 3.92021e20i | 0.826022i | ||||||||
\(900\) | −8.10300e19 | − | 1.54642e20i | −0.169414 | − | 0.323319i | ||||
\(901\) | −7.66382e20 | −1.58991 | ||||||||
\(902\) | −1.22347e19 | − | 1.22347e19i | −0.0251854 | − | 0.0251854i | ||||
\(903\) | 2.31860e20 | − | 2.31860e20i | 0.473599 | − | 0.473599i | ||||
\(904\) | − | 8.07348e19i | − | 0.163637i | ||||||
\(905\) | 3.69675e20 | + | 2.23646e20i | 0.743499 | + | 0.449802i | ||||
\(906\) | 2.52464e20 | 0.503851 | ||||||||
\(907\) | 2.78009e20 | + | 2.78009e20i | 0.550565 | + | 0.550565i | 0.926604 | − | 0.376039i | \(-0.122714\pi\) |
−0.376039 | + | 0.926604i | \(0.622714\pi\) | |||||||
\(908\) | 1.41666e20 | − | 1.41666e20i | 0.278396 | − | 0.278396i | ||||
\(909\) | − | 8.55060e19i | − | 0.166744i | ||||||
\(910\) | 1.34166e20 | + | 5.45124e20i | 0.259630 | + | 1.05489i | ||||
\(911\) | 8.47316e20 | 1.62711 | 0.813555 | − | 0.581488i | \(-0.197529\pi\) | ||||
0.813555 | + | 0.581488i | \(0.197529\pi\) | |||||||
\(912\) | 5.62286e18 | + | 5.62286e18i | 0.0107150 | + | 0.0107150i | ||||
\(913\) | 1.54065e20 | − | 1.54065e20i | 0.291345 | − | 0.291345i | ||||
\(914\) | − | 3.34193e20i | − | 0.627154i | ||||||
\(915\) | 1.04302e20 | − | 2.56709e19i | 0.194243 | − | 0.0478072i | ||||
\(916\) | 1.70678e20 | 0.315434 | ||||||||
\(917\) | 7.79904e20 | + | 7.79904e20i | 1.43039 | + | 1.43039i | ||||
\(918\) | 4.01653e20 | − | 4.01653e20i | 0.731059 | − | 0.731059i | ||||
\(919\) | 4.04823e20i | 0.731234i | 0.930765 | + | 0.365617i | \(0.119142\pi\) | ||||
−0.930765 | + | 0.365617i | \(0.880858\pi\) | |||||||
\(920\) | 6.88698e18 | − | 1.13838e19i | 0.0123457 | − | 0.0204067i | ||||
\(921\) | 1.20651e20 | 0.214642 | ||||||||
\(922\) | −3.29250e20 | − | 3.29250e20i | −0.581312 | − | 0.581312i | ||||
\(923\) | −8.87400e20 | + | 8.87400e20i | −1.55492 | + | 1.55492i | ||||
\(924\) | 2.79264e20i | 0.485637i | ||||||||
\(925\) | 1.53571e20 | − | 4.91662e20i | 0.265043 | − | 0.848544i | ||||
\(926\) | −4.04483e20 | −0.692825 | ||||||||
\(927\) | 8.71464e19 | + | 8.71464e19i | 0.148146 | + | 0.148146i | ||||
\(928\) | 8.31088e19 | − | 8.31088e19i | 0.140220 | − | 0.140220i | ||||
\(929\) | 8.05131e20i | 1.34821i | 0.738637 | + | 0.674104i | \(0.235470\pi\) | ||||
−0.738637 | + | 0.674104i | \(0.764530\pi\) | |||||||
\(930\) | −1.39280e20 | − | 8.42615e19i | −0.231477 | − | 0.140039i | ||||
\(931\) | 1.93713e19 | 0.0319530 | ||||||||
\(932\) | 1.30668e20 | + | 1.30668e20i | 0.213923 | + | 0.213923i | ||||
\(933\) | −2.99615e20 | + | 2.99615e20i | −0.486847 | + | 0.486847i | ||||
\(934\) | − | 4.76434e20i | − | 0.768377i | ||||||
\(935\) | −4.02204e20 | − | 1.63417e21i | −0.643821 | − | 2.61587i | ||||
\(936\) | −2.21131e20 | −0.351333 | ||||||||
\(937\) | −4.71181e20 | − | 4.71181e20i | −0.743037 | − | 0.743037i | 0.230124 | − | 0.973161i | \(-0.426087\pi\) |
−0.973161 | + | 0.230124i | \(0.926087\pi\) | |||||||
\(938\) | −1.80485e20 | + | 1.80485e20i | −0.282502 | + | 0.282502i | ||||
\(939\) | − | 4.31010e20i | − | 0.669620i | ||||||
\(940\) | 7.08042e19 | − | 1.74264e19i | 0.109185 | − | 0.0268728i | ||||
\(941\) | −6.14686e20 | −0.940862 | −0.470431 | − | 0.882437i | \(-0.655902\pi\) | ||||
−0.470431 | + | 0.882437i | \(0.655902\pi\) | |||||||
\(942\) | 6.22333e19 | + | 6.22333e19i | 0.0945510 | + | 0.0945510i | ||||
\(943\) | 9.61996e17 | − | 9.61996e17i | 0.00145075 | − | 0.00145075i | ||||
\(944\) | 2.00349e20i | 0.299904i | ||||||||
\(945\) | −3.53442e20 | + | 5.84221e20i | −0.525165 | + | 0.868069i | ||||
\(946\) | 9.06857e20 | 1.33752 | ||||||||
\(947\) | 5.85232e19 | + | 5.85232e19i | 0.0856797 | + | 0.0856797i | 0.748648 | − | 0.662968i | \(-0.230703\pi\) |
−0.662968 | + | 0.748648i | \(0.730703\pi\) | |||||||
\(948\) | −9.78273e19 | + | 9.78273e19i | −0.142168 | + | 0.142168i | ||||
\(949\) | − | 1.29961e21i | − | 1.87478i | ||||||
\(950\) | 5.49853e19 | + | 1.71747e19i | 0.0787374 | + | 0.0245937i | ||||
\(951\) | 2.44273e20 | 0.347226 | ||||||||
\(952\) | −3.25266e20 | − | 3.25266e20i | −0.458965 | − | 0.458965i | ||||
\(953\) | −2.15777e20 | + | 2.15777e20i | −0.302242 | + | 0.302242i | −0.841890 | − | 0.539649i | \(-0.818557\pi\) |
0.539649 | + | 0.841890i | \(0.318557\pi\) | |||||||
\(954\) | 3.62882e20i | 0.504576i | ||||||||
\(955\) | 1.04098e21 | + | 6.29771e20i | 1.43687 | + | 0.869279i | ||||
\(956\) | −1.28429e20 | −0.175977 | ||||||||
\(957\) | −5.01814e20 | − | 5.01814e20i | −0.682589 | − | 0.682589i | ||||
\(958\) | −2.98007e20 | + | 2.98007e20i | −0.402409 | + | 0.402409i | ||||
\(959\) | − | 1.17818e21i | − | 1.57936i | ||||||
\(960\) | 1.16639e19 | + | 4.73909e19i | 0.0155219 | + | 0.0630662i | ||||
\(961\) | −3.46509e20 | −0.457773 | ||||||||
\(962\) | −4.61325e20 | − | 4.61325e20i | −0.605036 | − | 0.605036i | ||||
\(963\) | 1.47424e20 | − | 1.47424e20i | 0.191949 | − | 0.191949i | ||||
\(964\) | 2.83149e20i | 0.365996i | ||||||||
\(965\) | −2.89416e20 | + | 7.12315e19i | −0.371391 | + | 0.0914073i | ||||
\(966\) | −2.19581e19 | −0.0279740 | ||||||||
\(967\) | −3.29886e20 | − | 3.29886e20i | −0.417232 | − | 0.417232i | 0.467016 | − | 0.884249i | \(-0.345329\pi\) |
−0.884249 | + | 0.467016i | \(0.845329\pi\) | |||||||
\(968\) | −3.47036e20 | + | 3.47036e20i | −0.435759 | + | 0.435759i | ||||
\(969\) | 7.90872e19i | 0.0985915i | ||||||||
\(970\) | 1.82607e19 | − | 3.01840e19i | 0.0226004 | − | 0.0373573i | ||||
\(971\) | −4.04627e20 | −0.497188 | −0.248594 | − | 0.968608i | \(-0.579968\pi\) | ||||
−0.248594 | + | 0.968608i | \(0.579968\pi\) | |||||||
\(972\) | −3.00113e20 | − | 3.00113e20i | −0.366118 | − | 0.366118i | ||||
\(973\) | −4.26996e20 | + | 4.26996e20i | −0.517171 | + | 0.517171i | ||||
\(974\) | 7.70953e19i | 0.0927075i | ||||||||
\(975\) | 5.24726e20 | − | 2.74947e20i | 0.626470 | − | 0.328259i | ||||
\(976\) | 8.11982e19 | 0.0962493 | ||||||||
\(977\) | −1.12448e20 | − | 1.12448e20i | −0.132339 | − | 0.132339i | 0.637834 | − | 0.770174i | \(-0.279830\pi\) |
−0.770174 | + | 0.637834i | \(0.779830\pi\) | |||||||
\(978\) | −2.83638e20 | + | 2.83638e20i | −0.331431 | + | 0.331431i | ||||
\(979\) | 1.95198e21i | 2.26462i | ||||||||
\(980\) | 1.01725e20 | + | 6.15416e19i | 0.117178 | + | 0.0708902i | ||||
\(981\) | 9.12931e20 | 1.04413 | ||||||||
\(982\) | 4.81808e20 | + | 4.81808e20i | 0.547134 | + | 0.547134i | ||||
\(983\) | 9.61422e20 | − | 9.61422e20i | 1.08403 | − | 1.08403i | 0.0878954 | − | 0.996130i | \(-0.471986\pi\) |
0.996130 | − | 0.0878954i | \(-0.0280141\pi\) | |||||||
\(984\) | 4.99047e18i | 0.00558696i | ||||||||
\(985\) | −3.59277e20 | − | 1.45975e21i | −0.399370 | − | 1.62265i | ||||
\(986\) | 1.16895e21 | 1.29020 | ||||||||
\(987\) | −8.50934e19 | − | 8.50934e19i | −0.0932558 | − | 0.0932558i | ||||
\(988\) | 5.15925e19 | − | 5.15925e19i | 0.0561421 | − | 0.0561421i | ||||
\(989\) | 7.13046e19i | 0.0770448i | ||||||||
\(990\) | −7.73780e20 | + | 1.90444e20i | −0.830178 | + | 0.204324i | ||||
\(991\) | −3.45922e20 | −0.368521 | −0.184261 | − | 0.982877i | \(-0.558989\pi\) | ||||
−0.184261 | + | 0.982877i | \(0.558989\pi\) | |||||||
\(992\) | −8.70126e19 | − | 8.70126e19i | −0.0920451 | − | 0.0920451i | ||||
\(993\) | −4.24267e20 | + | 4.24267e20i | −0.445650 | + | 0.445650i | ||||
\(994\) | 1.23611e21i | 1.28930i | ||||||||
\(995\) | 4.80696e20 | − | 7.94564e20i | 0.497862 | − | 0.822939i | ||||
\(996\) | −6.28419e19 | −0.0646300 | ||||||||
\(997\) | 9.86724e20 | + | 9.86724e20i | 1.00770 | + | 1.00770i | 0.999970 | + | 0.00772627i | \(0.00245937\pi\) |
0.00772627 | + | 0.999970i | \(0.497541\pi\) | |||||||
\(998\) | 8.91551e20 | − | 8.91551e20i | 0.904134 | − | 0.904134i | ||||
\(999\) | − | 7.93521e20i | − | 0.799098i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 10.15.c.b.7.3 | yes | 8 | |
3.2 | odd | 2 | 90.15.g.b.37.3 | 8 | |||
4.3 | odd | 2 | 80.15.p.b.17.2 | 8 | |||
5.2 | odd | 4 | 50.15.c.e.43.2 | 8 | |||
5.3 | odd | 4 | inner | 10.15.c.b.3.3 | ✓ | 8 | |
5.4 | even | 2 | 50.15.c.e.7.2 | 8 | |||
15.8 | even | 4 | 90.15.g.b.73.3 | 8 | |||
20.3 | even | 4 | 80.15.p.b.33.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.15.c.b.3.3 | ✓ | 8 | 5.3 | odd | 4 | inner | |
10.15.c.b.7.3 | yes | 8 | 1.1 | even | 1 | trivial | |
50.15.c.e.7.2 | 8 | 5.4 | even | 2 | |||
50.15.c.e.43.2 | 8 | 5.2 | odd | 4 | |||
80.15.p.b.17.2 | 8 | 4.3 | odd | 2 | |||
80.15.p.b.33.2 | 8 | 20.3 | even | 4 | |||
90.15.g.b.37.3 | 8 | 3.2 | odd | 2 | |||
90.15.g.b.73.3 | 8 | 15.8 | even | 4 |