Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [12,11,Mod(7,12)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(12, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 11, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("12.7");
S:= CuspForms(chi, 11);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 12 = 2^{2} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 11 \) |
Character orbit: | \([\chi]\) | \(=\) | 12.d (of order \(2\), degree \(1\), 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: | \(7.62428703208\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2 x^{9} + 198 x^{8} - 1066 x^{7} + 30608 x^{6} - 147714 x^{5} + 2092829 x^{4} + \cdots + 1648684816 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{39}\cdot 3^{18} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 7.2 | ||
Root | \(4.69893 + 8.13879i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 12.7 |
Dual form | 12.11.d.a.7.1 |
$q$-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 \(\left(\mathbb{Z}/12\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(7\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −30.5317 | + | 9.58205i | −0.954115 | + | 0.299439i | ||||
\(3\) | 140.296i | 0.577350i | ||||||||
\(4\) | 840.369 | − | 585.112i | 0.820672 | − | 0.571399i | ||||
\(5\) | 2598.88 | 0.831641 | 0.415820 | − | 0.909447i | \(-0.363495\pi\) | ||||
0.415820 | + | 0.909447i | \(0.363495\pi\) | |||||||
\(6\) | −1344.32 | − | 4283.48i | −0.172881 | − | 0.550859i | ||||
\(7\) | 4231.42i | 0.251765i | 0.992045 | + | 0.125883i | \(0.0401763\pi\) | ||||
−0.992045 | + | 0.125883i | \(0.959824\pi\) | |||||||
\(8\) | −20051.3 | + | 25916.9i | −0.611917 | + | 0.790922i | ||||
\(9\) | −19683.0 | −0.333333 | ||||||||
\(10\) | −79348.1 | + | 24902.6i | −0.793481 | + | 0.249026i | ||||
\(11\) | 275746.i | 1.71217i | 0.516838 | + | 0.856083i | \(0.327109\pi\) | ||||
−0.516838 | + | 0.856083i | \(0.672891\pi\) | |||||||
\(12\) | 82089.0 | + | 117900.i | 0.329897 | + | 0.473815i | ||||
\(13\) | −503390. | −1.35577 | −0.677887 | − | 0.735166i | \(-0.737104\pi\) | ||||
−0.677887 | + | 0.735166i | \(0.737104\pi\) | |||||||
\(14\) | −40545.7 | − | 129192.i | −0.0753883 | − | 0.240213i | ||||
\(15\) | 364612.i | 0.480148i | ||||||||
\(16\) | 363863. | − | 983420.i | 0.347007 | − | 0.937863i | ||||
\(17\) | 796250. | 0.560796 | 0.280398 | − | 0.959884i | \(-0.409534\pi\) | ||||
0.280398 | + | 0.959884i | \(0.409534\pi\) | |||||||
\(18\) | 600955. | − | 188603.i | 0.318038 | − | 0.0998130i | ||||
\(19\) | 659638.i | 0.266402i | 0.991089 | + | 0.133201i | \(0.0425256\pi\) | ||||
−0.991089 | + | 0.133201i | \(0.957474\pi\) | |||||||
\(20\) | 2.18401e6 | − | 1.52064e6i | 0.682505 | − | 0.475199i | ||||
\(21\) | −593652. | −0.145357 | ||||||||
\(22\) | −2.64221e6 | − | 8.41900e6i | −0.512690 | − | 1.63360i | ||||
\(23\) | 9.73033e6i | 1.51178i | 0.654699 | + | 0.755890i | \(0.272795\pi\) | ||||
−0.654699 | + | 0.755890i | \(0.727205\pi\) | |||||||
\(24\) | −3.63604e6 | − | 2.81312e6i | −0.456639 | − | 0.353291i | ||||
\(25\) | −3.01146e6 | −0.308374 | ||||||||
\(26\) | 1.53693e7 | − | 4.82350e6i | 1.29357 | − | 0.405972i | ||||
\(27\) | − | 2.76145e6i | − | 0.192450i | ||||||
\(28\) | 2.47586e6 | + | 3.55595e6i | 0.143858 | + | 0.206617i | ||||
\(29\) | 1.57660e6 | 0.0768657 | 0.0384329 | − | 0.999261i | \(-0.487763\pi\) | ||||
0.0384329 | + | 0.999261i | \(0.487763\pi\) | |||||||
\(30\) | −3.49373e6 | − | 1.11322e7i | −0.143775 | − | 0.458117i | ||||
\(31\) | 2.50977e7i | 0.876647i | 0.898817 | + | 0.438323i | \(0.144428\pi\) | ||||
−0.898817 | + | 0.438323i | \(0.855572\pi\) | |||||||
\(32\) | −1.68617e6 | + | 3.35120e7i | −0.0502517 | + | 0.998737i | ||||
\(33\) | −3.86861e7 | −0.988520 | ||||||||
\(34\) | −2.43109e7 | + | 7.62971e6i | −0.535064 | + | 0.167924i | ||||
\(35\) | 1.09969e7i | 0.209378i | ||||||||
\(36\) | −1.65410e7 | + | 1.15168e7i | −0.273557 | + | 0.190466i | ||||
\(37\) | 1.92346e7 | 0.277380 | 0.138690 | − | 0.990336i | \(-0.455711\pi\) | ||||
0.138690 | + | 0.990336i | \(0.455711\pi\) | |||||||
\(38\) | −6.32068e6 | − | 2.01399e7i | −0.0797712 | − | 0.254178i | ||||
\(39\) | − | 7.06236e7i | − | 0.782757i | ||||||
\(40\) | −5.21109e7 | + | 6.73549e7i | −0.508895 | + | 0.657763i | ||||
\(41\) | 1.55004e8 | 1.33790 | 0.668951 | − | 0.743307i | \(-0.266744\pi\) | ||||
0.668951 | + | 0.743307i | \(0.266744\pi\) | |||||||
\(42\) | 1.81252e7 | − | 5.68840e6i | 0.138687 | − | 0.0435255i | ||||
\(43\) | − | 2.62293e8i | − | 1.78420i | −0.451836 | − | 0.892101i | \(-0.649231\pi\) | ||
0.451836 | − | 0.892101i | \(-0.350769\pi\) | |||||||
\(44\) | 1.61343e8 | + | 2.31728e8i | 0.978330 | + | 1.40513i | ||||
\(45\) | −5.11537e7 | −0.277214 | ||||||||
\(46\) | −9.32365e7 | − | 2.97084e8i | −0.452686 | − | 1.44241i | ||||
\(47\) | − | 1.93022e8i | − | 0.841624i | −0.907148 | − | 0.420812i | \(-0.861745\pi\) | ||
0.907148 | − | 0.420812i | \(-0.138255\pi\) | |||||||
\(48\) | 1.37970e8 | + | 5.10486e7i | 0.541475 | + | 0.200344i | ||||
\(49\) | 2.64570e8 | 0.936614 | ||||||||
\(50\) | 9.19450e7 | − | 2.88560e7i | 0.294224 | − | 0.0923391i | ||||
\(51\) | 1.11711e8i | 0.323776i | ||||||||
\(52\) | −4.23033e8 | + | 2.94539e8i | −1.11265 | + | 0.774688i | ||||
\(53\) | −7.19689e8 | −1.72094 | −0.860470 | − | 0.509501i | \(-0.829830\pi\) | ||||
−0.860470 | + | 0.509501i | \(0.829830\pi\) | |||||||
\(54\) | 2.64603e7 | + | 8.43117e7i | 0.0576271 | + | 0.183620i | ||||
\(55\) | 7.16630e8i | 1.42391i | ||||||||
\(56\) | −1.09665e8 | − | 8.48454e7i | −0.199127 | − | 0.154059i | ||||
\(57\) | −9.25447e7 | −0.153807 | ||||||||
\(58\) | −4.81364e7 | + | 1.51071e7i | −0.0733388 | + | 0.0230166i | ||||
\(59\) | 2.98799e8i | 0.417945i | 0.977922 | + | 0.208972i | \(0.0670118\pi\) | ||||
−0.977922 | + | 0.208972i | \(0.932988\pi\) | |||||||
\(60\) | 2.13339e8 | + | 3.06409e8i | 0.274356 | + | 0.394044i | ||||
\(61\) | 1.22549e9 | 1.45098 | 0.725488 | − | 0.688235i | \(-0.241614\pi\) | ||||
0.725488 | + | 0.688235i | \(0.241614\pi\) | |||||||
\(62\) | −2.40487e8 | − | 7.66274e8i | −0.262502 | − | 0.836422i | ||||
\(63\) | − | 8.32870e7i | − | 0.0839217i | ||||||
\(64\) | −2.69632e8 | − | 1.03934e9i | −0.251115 | − | 0.967957i | ||||
\(65\) | −1.30825e9 | −1.12752 | ||||||||
\(66\) | 1.18115e9 | − | 3.70692e8i | 0.943162 | − | 0.296002i | ||||
\(67\) | 1.97452e9i | 1.46248i | 0.682123 | + | 0.731238i | \(0.261057\pi\) | ||||
−0.682123 | + | 0.731238i | \(0.738943\pi\) | |||||||
\(68\) | 6.69144e8 | − | 4.65896e8i | 0.460230 | − | 0.320438i | ||||
\(69\) | −1.36513e9 | −0.872826 | ||||||||
\(70\) | −1.05373e8 | − | 3.35755e8i | −0.0626960 | − | 0.199771i | ||||
\(71\) | − | 1.31168e9i | − | 0.727005i | −0.931593 | − | 0.363502i | \(-0.881581\pi\) | ||
0.931593 | − | 0.363502i | \(-0.118419\pi\) | |||||||
\(72\) | 3.94670e8 | − | 5.10123e8i | 0.203972 | − | 0.263641i | ||||
\(73\) | 2.74215e9 | 1.32275 | 0.661373 | − | 0.750057i | \(-0.269974\pi\) | ||||
0.661373 | + | 0.750057i | \(0.269974\pi\) | |||||||
\(74\) | −5.87265e8 | + | 1.84307e8i | −0.264652 | + | 0.0830584i | ||||
\(75\) | − | 4.22496e8i | − | 0.178040i | ||||||
\(76\) | 3.85962e8 | + | 5.54339e8i | 0.152222 | + | 0.218629i | ||||
\(77\) | −1.16680e9 | −0.431064 | ||||||||
\(78\) | 6.76719e8 | + | 2.15626e9i | 0.234388 | + | 0.746840i | ||||
\(79\) | − | 2.37006e9i | − | 0.770236i | −0.922867 | − | 0.385118i | \(-0.874161\pi\) | ||
0.922867 | − | 0.385118i | \(-0.125839\pi\) | |||||||
\(80\) | 9.45635e8 | − | 2.55579e9i | 0.288585 | − | 0.779965i | ||||
\(81\) | 3.87420e8 | 0.111111 | ||||||||
\(82\) | −4.73254e9 | + | 1.48526e9i | −1.27651 | + | 0.400620i | ||||
\(83\) | − | 6.01652e8i | − | 0.152741i | −0.997080 | − | 0.0763704i | \(-0.975667\pi\) | ||
0.997080 | − | 0.0763704i | \(-0.0243331\pi\) | |||||||
\(84\) | −4.98886e8 | + | 3.47353e8i | −0.119290 | + | 0.0830567i | ||||
\(85\) | 2.06936e9 | 0.466381 | ||||||||
\(86\) | 2.51330e9 | + | 8.00824e9i | 0.534260 | + | 1.70234i | ||||
\(87\) | 2.21192e8i | 0.0443785i | ||||||||
\(88\) | −7.14649e9 | − | 5.52907e9i | −1.35419 | − | 1.04770i | ||||
\(89\) | 2.09147e9 | 0.374544 | 0.187272 | − | 0.982308i | \(-0.440035\pi\) | ||||
0.187272 | + | 0.982308i | \(0.440035\pi\) | |||||||
\(90\) | 1.56181e9 | − | 4.90157e8i | 0.264494 | − | 0.0830086i | ||||
\(91\) | − | 2.13005e9i | − | 0.341337i | ||||||
\(92\) | 5.69334e9 | + | 8.17707e9i | 0.863829 | + | 1.24068i | ||||
\(93\) | −3.52110e9 | −0.506132 | ||||||||
\(94\) | 1.84955e9 | + | 5.89329e9i | 0.252015 | + | 0.803006i | ||||
\(95\) | 1.71432e9i | 0.221551i | ||||||||
\(96\) | −4.70161e9 | − | 2.36563e8i | −0.576621 | − | 0.0290128i | ||||
\(97\) | −7.68892e9 | −0.895379 | −0.447689 | − | 0.894189i | \(-0.647753\pi\) | ||||
−0.447689 | + | 0.894189i | \(0.647753\pi\) | |||||||
\(98\) | −8.07778e9 | + | 2.53513e9i | −0.893638 | + | 0.280459i | ||||
\(99\) | − | 5.42751e9i | − | 0.570722i | ||||||
\(100\) | −2.53074e9 | + | 1.76204e9i | −0.253074 | + | 0.176204i | ||||
\(101\) | 7.56116e9 | 0.719419 | 0.359709 | − | 0.933064i | \(-0.382876\pi\) | ||||
0.359709 | + | 0.933064i | \(0.382876\pi\) | |||||||
\(102\) | −1.07042e9 | − | 3.41072e9i | −0.0969511 | − | 0.308919i | ||||
\(103\) | − | 4.91916e9i | − | 0.424331i | −0.977234 | − | 0.212166i | \(-0.931948\pi\) | ||
0.977234 | − | 0.212166i | \(-0.0680516\pi\) | |||||||
\(104\) | 1.00936e10 | − | 1.30463e10i | 0.829622 | − | 1.07231i | ||||
\(105\) | −1.54283e9 | −0.120885 | ||||||||
\(106\) | 2.19733e10 | − | 6.89610e9i | 1.64198 | − | 0.515317i | ||||
\(107\) | 5.55479e9i | 0.396049i | 0.980197 | + | 0.198025i | \(0.0634526\pi\) | ||||
−0.980197 | + | 0.198025i | \(0.936547\pi\) | |||||||
\(108\) | −1.61576e9 | − | 2.32063e9i | −0.109966 | − | 0.157938i | ||||
\(109\) | 6.87260e9 | 0.446672 | 0.223336 | − | 0.974742i | \(-0.428305\pi\) | ||||
0.223336 | + | 0.974742i | \(0.428305\pi\) | |||||||
\(110\) | −6.86679e9 | − | 2.18799e10i | −0.426374 | − | 1.35857i | ||||
\(111\) | 2.69854e9i | 0.160145i | ||||||||
\(112\) | 4.16126e9 | + | 1.53966e9i | 0.236121 | + | 0.0873642i | ||||
\(113\) | 9.37463e9 | 0.508818 | 0.254409 | − | 0.967097i | \(-0.418119\pi\) | ||||
0.254409 | + | 0.967097i | \(0.418119\pi\) | |||||||
\(114\) | 2.82555e9 | − | 8.86768e8i | 0.146750 | − | 0.0460559i | ||||
\(115\) | 2.52879e10i | 1.25726i | ||||||||
\(116\) | 1.32493e9 | − | 9.22491e8i | 0.0630816 | − | 0.0439210i | ||||
\(117\) | 9.90822e9 | 0.451925 | ||||||||
\(118\) | −2.86310e9 | − | 9.12283e9i | −0.125149 | − | 0.398767i | ||||
\(119\) | 3.36927e9i | 0.141189i | ||||||||
\(120\) | −9.44963e9 | − | 7.31095e9i | −0.379760 | − | 0.293811i | ||||
\(121\) | −5.00985e10 | −1.93152 | ||||||||
\(122\) | −3.74162e10 | + | 1.17427e10i | −1.38440 | + | 0.434479i | ||||
\(123\) | 2.17465e10i | 0.772438i | ||||||||
\(124\) | 1.46849e10 | + | 2.10913e10i | 0.500915 | + | 0.719440i | ||||
\(125\) | −3.32061e10 | −1.08810 | ||||||||
\(126\) | 7.98060e8 | + | 2.54289e9i | 0.0251294 | + | 0.0800710i | ||||
\(127\) | − | 1.50838e10i | − | 0.456553i | −0.973596 | − | 0.228277i | \(-0.926691\pi\) | ||
0.973596 | − | 0.228277i | \(-0.0733091\pi\) | |||||||
\(128\) | 1.81913e10 | + | 2.91491e10i | 0.529437 | + | 0.848349i | ||||
\(129\) | 3.67987e10 | 1.03011 | ||||||||
\(130\) | 3.99430e10 | − | 1.25357e10i | 1.07578 | − | 0.337623i | ||||
\(131\) | 3.05678e10i | 0.792332i | 0.918179 | + | 0.396166i | \(0.129659\pi\) | ||||
−0.918179 | + | 0.396166i | \(0.870341\pi\) | |||||||
\(132\) | −3.25106e10 | + | 2.26357e10i | −0.811251 | + | 0.564839i | ||||
\(133\) | −2.79120e9 | −0.0670708 | ||||||||
\(134\) | −1.89200e10 | − | 6.02856e10i | −0.437922 | − | 1.39537i | ||||
\(135\) | − | 7.17667e9i | − | 0.160049i | ||||||
\(136\) | −1.59659e10 | + | 2.06364e10i | −0.343161 | + | 0.443546i | ||||
\(137\) | 1.84575e10 | 0.382446 | 0.191223 | − | 0.981547i | \(-0.438755\pi\) | ||||
0.191223 | + | 0.981547i | \(0.438755\pi\) | |||||||
\(138\) | 4.16797e10 | − | 1.30807e10i | 0.832777 | − | 0.261358i | ||||
\(139\) | − | 4.67935e10i | − | 0.901802i | −0.892574 | − | 0.450901i | \(-0.851103\pi\) | ||
0.892574 | − | 0.450901i | \(-0.148897\pi\) | |||||||
\(140\) | 6.43444e9 | + | 9.24148e9i | 0.119638 | + | 0.171831i | ||||
\(141\) | 2.70803e10 | 0.485912 | ||||||||
\(142\) | 1.25686e10 | + | 4.00479e10i | 0.217694 | + | 0.693646i | ||||
\(143\) | − | 1.38808e11i | − | 2.32131i | ||||||
\(144\) | −7.16191e9 | + | 1.93567e10i | −0.115669 | + | 0.312621i | ||||
\(145\) | 4.09740e9 | 0.0639247 | ||||||||
\(146\) | −8.37224e10 | + | 2.62754e10i | −1.26205 | + | 0.396082i | ||||
\(147\) | 3.71182e10i | 0.540754i | ||||||||
\(148\) | 1.61642e10 | − | 1.12544e10i | 0.227638 | − | 0.158495i | ||||
\(149\) | 7.94107e10 | 1.08130 | 0.540652 | − | 0.841246i | \(-0.318178\pi\) | ||||
0.540652 | + | 0.841246i | \(0.318178\pi\) | |||||||
\(150\) | 4.04838e9 | + | 1.28995e10i | 0.0533120 | + | 0.169870i | ||||
\(151\) | − | 6.72800e10i | − | 0.857041i | −0.903532 | − | 0.428520i | \(-0.859035\pi\) | ||
0.903532 | − | 0.428520i | \(-0.140965\pi\) | |||||||
\(152\) | −1.70958e10 | − | 1.32266e10i | −0.210703 | − | 0.163016i | ||||
\(153\) | −1.56726e10 | −0.186932 | ||||||||
\(154\) | 3.56243e10 | − | 1.11803e10i | 0.411285 | − | 0.129077i | ||||
\(155\) | 6.52257e10i | 0.729055i | ||||||||
\(156\) | −4.13227e10 | − | 5.93499e10i | −0.447266 | − | 0.642387i | ||||
\(157\) | −4.18782e10 | −0.439026 | −0.219513 | − | 0.975610i | \(-0.570447\pi\) | ||||
−0.219513 | + | 0.975610i | \(0.570447\pi\) | |||||||
\(158\) | 2.27100e10 | + | 7.23619e10i | 0.230639 | + | 0.734894i | ||||
\(159\) | − | 1.00970e11i | − | 0.993585i | ||||||
\(160\) | −4.38214e9 | + | 8.70937e10i | −0.0417914 | + | 0.830590i | ||||
\(161\) | −4.11731e10 | −0.380614 | ||||||||
\(162\) | −1.18286e10 | + | 3.71228e9i | −0.106013 | + | 0.0332710i | ||||
\(163\) | 1.69873e11i | 1.47634i | 0.674614 | + | 0.738171i | \(0.264310\pi\) | ||||
−0.674614 | + | 0.738171i | \(0.735690\pi\) | |||||||
\(164\) | 1.30261e11 | − | 9.06949e10i | 1.09798 | − | 0.764475i | ||||
\(165\) | −1.00540e11 | −0.822093 | ||||||||
\(166\) | 5.76506e9 | + | 1.83695e10i | 0.0457365 | + | 0.145732i | ||||
\(167\) | 1.08854e11i | 0.838031i | 0.907979 | + | 0.419016i | \(0.137625\pi\) | ||||
−0.907979 | + | 0.419016i | \(0.862375\pi\) | |||||||
\(168\) | 1.19035e10 | − | 1.53856e10i | 0.0889463 | − | 0.114966i | ||||
\(169\) | 1.15543e11 | 0.838124 | ||||||||
\(170\) | −6.31810e10 | + | 1.98287e10i | −0.444981 | + | 0.139653i | ||||
\(171\) | − | 1.29837e10i | − | 0.0888007i | ||||||
\(172\) | −1.53471e11 | − | 2.20423e11i | −1.01949 | − | 1.46425i | ||||
\(173\) | −7.15310e10 | −0.461598 | −0.230799 | − | 0.973001i | \(-0.574134\pi\) | ||||
−0.230799 | + | 0.973001i | \(0.574134\pi\) | |||||||
\(174\) | −2.11947e9 | − | 6.75335e9i | −0.0132886 | − | 0.0423422i | ||||
\(175\) | − | 1.27428e10i | − | 0.0776378i | ||||||
\(176\) | 2.71174e11 | + | 1.00334e11i | 1.60578 | + | 0.594133i | ||||
\(177\) | −4.19203e10 | −0.241300 | ||||||||
\(178\) | −6.38562e10 | + | 2.00406e10i | −0.357358 | + | 0.112153i | ||||
\(179\) | 1.36340e11i | 0.741921i | 0.928649 | + | 0.370960i | \(0.120971\pi\) | ||||
−0.928649 | + | 0.370960i | \(0.879029\pi\) | |||||||
\(180\) | −4.29880e10 | + | 2.99307e10i | −0.227502 | + | 0.158400i | ||||
\(181\) | −8.57199e10 | −0.441254 | −0.220627 | − | 0.975358i | \(-0.570810\pi\) | ||||
−0.220627 | + | 0.975358i | \(0.570810\pi\) | |||||||
\(182\) | 2.04103e10 | + | 6.50341e10i | 0.102210 | + | 0.325675i | ||||
\(183\) | 1.71931e11i | 0.837721i | ||||||||
\(184\) | −2.52180e11 | − | 1.95106e11i | −1.19570 | − | 0.925084i | ||||
\(185\) | 4.99884e10 | 0.230680 | ||||||||
\(186\) | 1.07505e11 | − | 3.37394e10i | 0.482909 | − | 0.151556i | ||||
\(187\) | 2.19563e11i | 0.960177i | ||||||||
\(188\) | −1.12940e11 | − | 1.62210e11i | −0.480903 | − | 0.690697i | ||||
\(189\) | 1.16848e10 | 0.0484522 | ||||||||
\(190\) | −1.64267e10 | − | 5.23410e10i | −0.0663410 | − | 0.211385i | ||||
\(191\) | − | 1.65095e11i | − | 0.649480i | −0.945803 | − | 0.324740i | \(-0.894723\pi\) | ||
0.945803 | − | 0.324740i | \(-0.105277\pi\) | |||||||
\(192\) | 1.45815e11 | − | 3.78284e10i | 0.558850 | − | 0.144981i | ||||
\(193\) | 2.92462e11 | 1.09215 | 0.546076 | − | 0.837736i | \(-0.316121\pi\) | ||||
0.546076 | + | 0.837736i | \(0.316121\pi\) | |||||||
\(194\) | 2.34756e11 | − | 7.36756e10i | 0.854295 | − | 0.268111i | ||||
\(195\) | − | 1.83542e11i | − | 0.650972i | ||||||
\(196\) | 2.22337e11 | − | 1.54803e11i | 0.768654 | − | 0.535180i | ||||
\(197\) | −6.30942e10 | −0.212646 | −0.106323 | − | 0.994332i | \(-0.533908\pi\) | ||||
−0.106323 | + | 0.994332i | \(0.533908\pi\) | |||||||
\(198\) | 5.20067e10 | + | 1.65711e11i | 0.170897 | + | 0.544535i | ||||
\(199\) | − | 5.79322e11i | − | 1.85633i | −0.372172 | − | 0.928164i | \(-0.621387\pi\) | ||
0.372172 | − | 0.928164i | \(-0.378613\pi\) | |||||||
\(200\) | 6.03837e10 | − | 7.80478e10i | 0.188699 | − | 0.243900i | ||||
\(201\) | −2.77018e11 | −0.844360 | ||||||||
\(202\) | −2.30855e11 | + | 7.24514e10i | −0.686408 | + | 0.215422i | ||||
\(203\) | 6.67127e9i | 0.0193521i | ||||||||
\(204\) | 6.53634e10 | + | 9.38783e10i | 0.185005 | + | 0.265714i | ||||
\(205\) | 4.02837e11 | 1.11265 | ||||||||
\(206\) | 4.71356e10 | + | 1.50190e11i | 0.127061 | + | 0.404861i | ||||
\(207\) | − | 1.91522e11i | − | 0.503927i | ||||||
\(208\) | −1.83165e11 | + | 4.95044e11i | −0.470463 | + | 1.27153i | ||||
\(209\) | −1.81893e11 | −0.456125 | ||||||||
\(210\) | 4.71051e10 | − | 1.47835e10i | 0.115338 | − | 0.0361976i | ||||
\(211\) | 4.61897e11i | 1.10442i | 0.833706 | + | 0.552209i | \(0.186215\pi\) | ||||
−0.833706 | + | 0.552209i | \(0.813785\pi\) | |||||||
\(212\) | −6.04804e11 | + | 4.21099e11i | −1.41233 | + | 0.983343i | ||||
\(213\) | 1.84024e11 | 0.419736 | ||||||||
\(214\) | −5.32263e10 | − | 1.69597e11i | −0.118593 | − | 0.377877i | ||||
\(215\) | − | 6.81667e11i | − | 1.48382i | ||||||
\(216\) | 7.15683e10 | + | 5.53706e10i | 0.152213 | + | 0.117764i | ||||
\(217\) | −1.06199e11 | −0.220709 | ||||||||
\(218\) | −2.09832e11 | + | 6.58536e10i | −0.426176 | + | 0.133751i | ||||
\(219\) | 3.84713e11i | 0.763688i | ||||||||
\(220\) | 4.19309e11 | + | 6.02234e11i | 0.813619 | + | 1.16856i | ||||
\(221\) | −4.00824e11 | −0.760313 | ||||||||
\(222\) | −2.58576e10 | − | 8.23910e10i | −0.0479538 | − | 0.152797i | ||||
\(223\) | 4.25211e11i | 0.771046i | 0.922698 | + | 0.385523i | \(0.125979\pi\) | ||||
−0.922698 | + | 0.385523i | \(0.874021\pi\) | |||||||
\(224\) | −1.41803e11 | − | 7.13488e9i | −0.251447 | − | 0.0126516i | ||||
\(225\) | 5.92746e10 | 0.102791 | ||||||||
\(226\) | −2.86223e11 | + | 8.98282e10i | −0.485471 | + | 0.152360i | ||||
\(227\) | 2.30595e10i | 0.0382579i | 0.999817 | + | 0.0191290i | \(0.00608931\pi\) | ||||
−0.999817 | + | 0.0191290i | \(0.993911\pi\) | |||||||
\(228\) | −7.77716e10 | + | 5.41490e10i | −0.126225 | + | 0.0878853i | ||||
\(229\) | 4.06047e11 | 0.644761 | 0.322380 | − | 0.946610i | \(-0.395517\pi\) | ||||
0.322380 | + | 0.946610i | \(0.395517\pi\) | |||||||
\(230\) | −2.42310e11 | − | 7.72084e11i | −0.376472 | − | 1.19957i | ||||
\(231\) | − | 1.63697e11i | − | 0.248875i | ||||||
\(232\) | −3.16130e10 | + | 4.08608e10i | −0.0470355 | + | 0.0607948i | ||||
\(233\) | −3.15665e11 | −0.459670 | −0.229835 | − | 0.973230i | \(-0.573819\pi\) | ||||
−0.229835 | + | 0.973230i | \(0.573819\pi\) | |||||||
\(234\) | −3.02515e11 | + | 9.49410e10i | −0.431188 | + | 0.135324i | ||||
\(235\) | − | 5.01641e11i | − | 0.699929i | ||||||
\(236\) | 1.74831e11 | + | 2.51101e11i | 0.238813 | + | 0.342996i | ||||
\(237\) | 3.32510e11 | 0.444696 | ||||||||
\(238\) | −3.22845e10 | − | 1.02869e11i | −0.0422775 | − | 0.134711i | ||||
\(239\) | − | 2.05486e11i | − | 0.263508i | −0.991282 | − | 0.131754i | \(-0.957939\pi\) | ||
0.991282 | − | 0.131754i | \(-0.0420609\pi\) | |||||||
\(240\) | 3.58567e11 | + | 1.32669e11i | 0.450313 | + | 0.166615i | ||||
\(241\) | 8.16890e10 | 0.100480 | 0.0502399 | − | 0.998737i | \(-0.484001\pi\) | ||||
0.0502399 | + | 0.998737i | \(0.484001\pi\) | |||||||
\(242\) | 1.52959e12 | − | 4.80047e11i | 1.84289 | − | 0.578371i | ||||
\(243\) | 5.43536e10i | 0.0641500i | ||||||||
\(244\) | 1.02986e12 | − | 7.17048e11i | 1.19078 | − | 0.829085i | ||||
\(245\) | 6.87586e11 | 0.778927 | ||||||||
\(246\) | −2.08376e11 | − | 6.63957e11i | −0.231298 | − | 0.736995i | ||||
\(247\) | − | 3.32055e11i | − | 0.361181i | ||||||
\(248\) | −6.50454e11 | − | 5.03241e11i | −0.693359 | − | 0.536435i | ||||
\(249\) | 8.44094e10 | 0.0881849 | ||||||||
\(250\) | 1.01384e12 | − | 3.18182e11i | 1.03817 | − | 0.325819i | ||||
\(251\) | 1.75893e12i | 1.76555i | 0.469792 | + | 0.882777i | \(0.344329\pi\) | ||||
−0.469792 | + | 0.882777i | \(0.655671\pi\) | |||||||
\(252\) | −4.87323e10 | − | 6.99918e10i | −0.0479528 | − | 0.0688723i | ||||
\(253\) | −2.68310e12 | −2.58842 | ||||||||
\(254\) | 1.44534e11 | + | 4.60533e11i | 0.136710 | + | 0.435605i | ||||
\(255\) | 2.90323e11i | 0.269265i | ||||||||
\(256\) | −8.34719e11 | − | 7.15660e11i | −0.759173 | − | 0.650889i | ||||
\(257\) | 1.36308e12 | 1.21578 | 0.607892 | − | 0.794020i | \(-0.292015\pi\) | ||||
0.607892 | + | 0.794020i | \(0.292015\pi\) | |||||||
\(258\) | −1.12353e12 | + | 3.52607e11i | −0.982844 | + | 0.308455i | ||||
\(259\) | 8.13897e10i | 0.0698346i | ||||||||
\(260\) | −1.09941e12 | + | 7.65472e11i | −0.925322 | + | 0.644262i | ||||
\(261\) | −3.10323e10 | −0.0256219 | ||||||||
\(262\) | −2.92902e11 | − | 9.33285e11i | −0.237255 | − | 0.755976i | ||||
\(263\) | 1.05658e12i | 0.839702i | 0.907593 | + | 0.419851i | \(0.137918\pi\) | ||||
−0.907593 | + | 0.419851i | \(0.862082\pi\) | |||||||
\(264\) | 7.75707e11 | − | 1.00263e12i | 0.604892 | − | 0.781842i | ||||
\(265\) | −1.87038e12 | −1.43120 | ||||||||
\(266\) | 8.52202e10 | − | 2.67455e10i | 0.0639933 | − | 0.0200836i | ||||
\(267\) | 2.93426e11i | 0.216243i | ||||||||
\(268\) | 1.15532e12 | + | 1.65933e12i | 0.835657 | + | 1.20021i | ||||
\(269\) | 1.36623e12 | 0.969978 | 0.484989 | − | 0.874520i | \(-0.338824\pi\) | ||||
0.484989 | + | 0.874520i | \(0.338824\pi\) | |||||||
\(270\) | 6.87672e10 | + | 2.19116e11i | 0.0479250 | + | 0.152706i | ||||
\(271\) | 2.09567e11i | 0.143376i | 0.997427 | + | 0.0716882i | \(0.0228386\pi\) | ||||
−0.997427 | + | 0.0716882i | \(0.977161\pi\) | |||||||
\(272\) | 2.89726e11 | − | 7.83049e11i | 0.194600 | − | 0.525950i | ||||
\(273\) | 2.98838e11 | 0.197071 | ||||||||
\(274\) | −5.63539e11 | + | 1.76861e11i | −0.364898 | + | 0.114519i | ||||
\(275\) | − | 8.30399e11i | − | 0.527987i | ||||||
\(276\) | −1.14721e12 | + | 7.98753e11i | −0.716305 | + | 0.498732i | ||||
\(277\) | 1.84008e12 | 1.12834 | 0.564168 | − | 0.825660i | \(-0.309197\pi\) | ||||
0.564168 | + | 0.825660i | \(0.309197\pi\) | |||||||
\(278\) | 4.48377e11 | + | 1.42868e12i | 0.270035 | + | 0.860423i | ||||
\(279\) | − | 4.93997e11i | − | 0.292216i | ||||||
\(280\) | −2.85007e11 | − | 2.20503e11i | −0.165602 | − | 0.128122i | ||||
\(281\) | −4.07837e11 | −0.232785 | −0.116393 | − | 0.993203i | \(-0.537133\pi\) | ||||
−0.116393 | + | 0.993203i | \(0.537133\pi\) | |||||||
\(282\) | −8.26806e11 | + | 2.59484e11i | −0.463616 | + | 0.145501i | ||||
\(283\) | − | 1.48717e12i | − | 0.819272i | −0.912249 | − | 0.409636i | \(-0.865656\pi\) | ||
0.912249 | − | 0.409636i | \(-0.134344\pi\) | |||||||
\(284\) | −7.67482e11 | − | 1.10230e12i | −0.415410 | − | 0.596633i | ||||
\(285\) | −2.40512e11 | −0.127912 | ||||||||
\(286\) | 1.33006e12 | + | 4.23804e12i | 0.695092 | + | 2.21480i | ||||
\(287\) | 6.55887e11i | 0.336837i | ||||||||
\(288\) | 3.31888e10 | − | 6.59617e11i | 0.0167506 | − | 0.332912i | ||||
\(289\) | −1.38198e12 | −0.685508 | ||||||||
\(290\) | −1.25101e11 | + | 3.92615e10i | −0.0609915 | + | 0.0191415i | ||||
\(291\) | − | 1.07873e12i | − | 0.516947i | ||||||
\(292\) | 2.30442e12 | − | 1.60446e12i | 1.08554 | − | 0.755816i | ||||
\(293\) | −1.95687e12 | −0.906200 | −0.453100 | − | 0.891460i | \(-0.649682\pi\) | ||||
−0.453100 | + | 0.891460i | \(0.649682\pi\) | |||||||
\(294\) | −3.55668e11 | − | 1.13328e12i | −0.161923 | − | 0.515942i | ||||
\(295\) | 7.76541e11i | 0.347580i | ||||||||
\(296\) | −3.85679e11 | + | 4.98502e11i | −0.169733 | + | 0.219386i | ||||
\(297\) | 7.61459e11 | 0.329507 | ||||||||
\(298\) | −2.42454e12 | + | 7.60918e11i | −1.03169 | + | 0.323785i | ||||
\(299\) | − | 4.89815e12i | − | 2.04963i | ||||||
\(300\) | −2.47208e11 | − | 3.55053e11i | −0.101732 | − | 0.146112i | ||||
\(301\) | 1.10987e12 | 0.449200 | ||||||||
\(302\) | 6.44680e11 | + | 2.05417e12i | 0.256631 | + | 0.817716i | ||||
\(303\) | 1.06080e12i | 0.415357i | ||||||||
\(304\) | 6.48701e11 | + | 2.40018e11i | 0.249849 | + | 0.0924433i | ||||
\(305\) | 3.18489e12 | 1.20669 | ||||||||
\(306\) | 4.78511e11 | − | 1.50176e11i | 0.178355 | − | 0.0559748i | ||||
\(307\) | − | 2.31841e12i | − | 0.850154i | −0.905157 | − | 0.425077i | \(-0.860247\pi\) | ||
0.905157 | − | 0.425077i | \(-0.139753\pi\) | |||||||
\(308\) | −9.80540e11 | + | 6.82708e11i | −0.353762 | + | 0.246310i | ||||
\(309\) | 6.90139e11 | 0.244988 | ||||||||
\(310\) | −6.24996e11 | − | 1.99145e12i | −0.218308 | − | 0.695603i | ||||
\(311\) | 4.08629e11i | 0.140452i | 0.997531 | + | 0.0702259i | \(0.0223720\pi\) | ||||
−0.997531 | + | 0.0702259i | \(0.977628\pi\) | |||||||
\(312\) | 1.83035e12 | + | 1.41610e12i | 0.619099 | + | 0.478982i | ||||
\(313\) | 3.49333e12 | 1.16283 | 0.581417 | − | 0.813606i | \(-0.302498\pi\) | ||||
0.581417 | + | 0.813606i | \(0.302498\pi\) | |||||||
\(314\) | 1.27861e12 | − | 4.01279e11i | 0.418881 | − | 0.131462i | ||||
\(315\) | − | 2.16453e11i | − | 0.0697927i | ||||||
\(316\) | −1.38675e12 | − | 1.99172e12i | −0.440112 | − | 0.632111i | ||||
\(317\) | −4.96339e12 | −1.55054 | −0.775268 | − | 0.631633i | \(-0.782385\pi\) | ||||
−0.775268 | + | 0.631633i | \(0.782385\pi\) | |||||||
\(318\) | 9.67496e11 | + | 3.08277e12i | 0.297518 | + | 0.947995i | ||||
\(319\) | 4.34743e11i | 0.131607i | ||||||||
\(320\) | −7.00742e11 | − | 2.70111e12i | −0.208837 | − | 0.804993i | ||||
\(321\) | −7.79316e11 | −0.228659 | ||||||||
\(322\) | 1.25708e12 | − | 3.94523e11i | 0.363149 | − | 0.113971i | ||||
\(323\) | 5.25237e11i | 0.149397i | ||||||||
\(324\) | 3.25576e11 | − | 2.26685e11i | 0.0911858 | − | 0.0634888i | ||||
\(325\) | 1.51594e12 | 0.418085 | ||||||||
\(326\) | −1.62773e12 | − | 5.18652e12i | −0.442074 | − | 1.40860i | ||||
\(327\) | 9.64199e11i | 0.257886i | ||||||||
\(328\) | −3.10804e12 | + | 4.01723e12i | −0.818685 | + | 1.05818i | ||||
\(329\) | 8.16758e11 | 0.211892 | ||||||||
\(330\) | 3.06967e12 | − | 9.63384e11i | 0.784372 | − | 0.246167i | ||||
\(331\) | 6.74440e12i | 1.69747i | 0.528815 | + | 0.848737i | \(0.322636\pi\) | ||||
−0.528815 | + | 0.848737i | \(0.677364\pi\) | |||||||
\(332\) | −3.52034e11 | − | 5.05609e11i | −0.0872759 | − | 0.125350i | ||||
\(333\) | −3.78595e11 | −0.0924599 | ||||||||
\(334\) | −1.04304e12 | − | 3.32348e12i | −0.250939 | − | 0.799579i | ||||
\(335\) | 5.13155e12i | 1.21625i | ||||||||
\(336\) | −2.16008e11 | + | 5.83809e11i | −0.0504398 | + | 0.136325i | ||||
\(337\) | −4.68085e12 | −1.07690 | −0.538450 | − | 0.842658i | \(-0.680990\pi\) | ||||
−0.538450 | + | 0.842658i | \(0.680990\pi\) | |||||||
\(338\) | −3.52771e12 | + | 1.10713e12i | −0.799667 | + | 0.250967i | ||||
\(339\) | 1.31522e12i | 0.293766i | ||||||||
\(340\) | 1.73902e12 | − | 1.21081e12i | 0.382746 | − | 0.266490i | ||||
\(341\) | −6.92058e12 | −1.50097 | ||||||||
\(342\) | 1.24410e11 | + | 3.96413e11i | 0.0265904 | + | 0.0847261i | ||||
\(343\) | 2.31478e12i | 0.487572i | ||||||||
\(344\) | 6.79782e12 | + | 5.25931e12i | 1.41116 | + | 1.09178i | ||||
\(345\) | −3.54780e12 | −0.725878 | ||||||||
\(346\) | 2.18396e12 | − | 6.85414e11i | 0.440418 | − | 0.138220i | ||||
\(347\) | − | 9.28917e11i | − | 0.184642i | −0.995729 | − | 0.0923208i | \(-0.970571\pi\) | ||
0.995729 | − | 0.0923208i | \(-0.0294285\pi\) | |||||||
\(348\) | 1.29422e11 | + | 1.85882e11i | 0.0253578 | + | 0.0364202i | ||||
\(349\) | 6.18690e12 | 1.19494 | 0.597470 | − | 0.801891i | \(-0.296173\pi\) | ||||
0.597470 | + | 0.801891i | \(0.296173\pi\) | |||||||
\(350\) | 1.22102e11 | + | 3.89058e11i | 0.0232478 | + | 0.0740754i | ||||
\(351\) | 1.39008e12i | 0.260919i | ||||||||
\(352\) | −9.24082e12 | − | 4.64954e11i | −1.71000 | − | 0.0860393i | ||||
\(353\) | −4.52672e11 | −0.0825866 | −0.0412933 | − | 0.999147i | \(-0.513148\pi\) | ||||
−0.0412933 | + | 0.999147i | \(0.513148\pi\) | |||||||
\(354\) | 1.27990e12 | − | 4.01682e11i | 0.230228 | − | 0.0722548i | ||||
\(355\) | − | 3.40890e12i | − | 0.604607i | ||||||
\(356\) | 1.75761e12 | − | 1.22375e12i | 0.307378 | − | 0.214014i | ||||
\(357\) | −4.72695e11 | −0.0815155 | ||||||||
\(358\) | −1.30642e12 | − | 4.16269e12i | −0.222160 | − | 0.707878i | ||||
\(359\) | − | 1.82070e12i | − | 0.305327i | −0.988278 | − | 0.152664i | \(-0.951215\pi\) | ||
0.988278 | − | 0.152664i | \(-0.0487851\pi\) | |||||||
\(360\) | 1.02570e12 | − | 1.32575e12i | 0.169632 | − | 0.219254i | ||||
\(361\) | 5.69594e12 | 0.929030 | ||||||||
\(362\) | 2.61717e12 | − | 8.21372e11i | 0.421007 | − | 0.132129i | ||||
\(363\) | − | 7.02863e12i | − | 1.11516i | ||||||
\(364\) | −1.24632e12 | − | 1.79003e12i | −0.195040 | − | 0.280126i | ||||
\(365\) | 7.12651e12 | 1.10005 | ||||||||
\(366\) | −1.64745e12 | − | 5.24935e12i | −0.250846 | − | 0.799282i | ||||
\(367\) | 4.66568e12i | 0.700785i | 0.936603 | + | 0.350393i | \(0.113952\pi\) | ||||
−0.936603 | + | 0.350393i | \(0.886048\pi\) | |||||||
\(368\) | 9.56901e12 | + | 3.54051e12i | 1.41784 | + | 0.524598i | ||||
\(369\) | −3.05095e12 | −0.445967 | ||||||||
\(370\) | −1.52623e12 | + | 4.78991e11i | −0.220096 | + | 0.0690747i | ||||
\(371\) | − | 3.04531e12i | − | 0.433273i | ||||||
\(372\) | −2.95902e12 | + | 2.06024e12i | −0.415369 | + | 0.289203i | ||||
\(373\) | 5.69256e12 | 0.788430 | 0.394215 | − | 0.919018i | \(-0.371017\pi\) | ||||
0.394215 | + | 0.919018i | \(0.371017\pi\) | |||||||
\(374\) | −2.10386e12 | − | 6.70363e12i | −0.287514 | − | 0.916119i | ||||
\(375\) | − | 4.65868e12i | − | 0.628213i | ||||||
\(376\) | 5.00254e12 | + | 3.87035e12i | 0.665659 | + | 0.515004i | ||||
\(377\) | −7.93646e11 | −0.104213 | ||||||||
\(378\) | −3.56758e11 | + | 1.11965e11i | −0.0462290 | + | 0.0145085i | ||||
\(379\) | − | 1.23996e13i | − | 1.58566i | −0.609443 | − | 0.792830i | \(-0.708607\pi\) | ||
0.609443 | − | 0.792830i | \(-0.291393\pi\) | |||||||
\(380\) | 1.00307e12 | + | 1.44066e12i | 0.126594 | + | 0.181821i | ||||
\(381\) | 2.11620e12 | 0.263591 | ||||||||
\(382\) | 1.58194e12 | + | 5.04062e12i | 0.194480 | + | 0.619679i | ||||
\(383\) | 7.80655e11i | 0.0947252i | 0.998878 | + | 0.0473626i | \(0.0150816\pi\) | ||||
−0.998878 | + | 0.0473626i | \(0.984918\pi\) | |||||||
\(384\) | −4.08950e12 | + | 2.55217e12i | −0.489795 | + | 0.305670i | ||||
\(385\) | −3.03236e12 | −0.358490 | ||||||||
\(386\) | −8.92936e12 | + | 2.80239e12i | −1.04204 | + | 0.327033i | ||||
\(387\) | 5.16271e12i | 0.594734i | ||||||||
\(388\) | −6.46153e12 | + | 4.49888e12i | −0.734813 | + | 0.511618i | ||||
\(389\) | −7.89399e11 | −0.0886235 | −0.0443117 | − | 0.999018i | \(-0.514109\pi\) | ||||
−0.0443117 | + | 0.999018i | \(0.514109\pi\) | |||||||
\(390\) | 1.75871e12 | + | 5.60385e12i | 0.194927 | + | 0.621103i | ||||
\(391\) | 7.74778e12i | 0.847800i | ||||||||
\(392\) | −5.30498e12 | + | 6.85685e12i | −0.573130 | + | 0.740789i | ||||
\(393\) | −4.28854e12 | −0.457453 | ||||||||
\(394\) | 1.92637e12 | − | 6.04571e11i | 0.202889 | − | 0.0636746i | ||||
\(395\) | − | 6.15949e12i | − | 0.640560i | ||||||
\(396\) | −3.17570e12 | − | 4.56111e12i | −0.326110 | − | 0.468376i | ||||
\(397\) | −1.43209e13 | −1.45217 | −0.726087 | − | 0.687603i | \(-0.758663\pi\) | ||||
−0.726087 | + | 0.687603i | \(0.758663\pi\) | |||||||
\(398\) | 5.55109e12 | + | 1.76877e13i | 0.555857 | + | 1.77115i | ||||
\(399\) | − | 3.91595e11i | − | 0.0387233i | ||||||
\(400\) | −1.09576e12 | + | 2.96153e12i | −0.107008 | + | 0.289212i | ||||
\(401\) | 1.41408e13 | 1.36380 | 0.681900 | − | 0.731445i | \(-0.261154\pi\) | ||||
0.681900 | + | 0.731445i | \(0.261154\pi\) | |||||||
\(402\) | 8.45783e12 | − | 2.65440e12i | 0.805617 | − | 0.252834i | ||||
\(403\) | − | 1.26339e13i | − | 1.18854i | ||||||
\(404\) | 6.35416e12 | − | 4.42413e12i | 0.590407 | − | 0.411075i | ||||
\(405\) | 1.00686e12 | 0.0924045 | ||||||||
\(406\) | −6.39245e10 | − | 2.03685e11i | −0.00579478 | − | 0.0184642i | ||||
\(407\) | 5.30387e12i | 0.474921i | ||||||||
\(408\) | −2.89520e12 | − | 2.23995e12i | −0.256081 | − | 0.198124i | ||||
\(409\) | −8.26321e12 | −0.721991 | −0.360996 | − | 0.932567i | \(-0.617563\pi\) | ||||
−0.360996 | + | 0.932567i | \(0.617563\pi\) | |||||||
\(410\) | −1.22993e13 | + | 3.86000e12i | −1.06160 | + | 0.333172i | ||||
\(411\) | 2.58952e12i | 0.220805i | ||||||||
\(412\) | −2.87826e12 | − | 4.13391e12i | −0.242462 | − | 0.348237i | ||||
\(413\) | −1.26434e12 | −0.105224 | ||||||||
\(414\) | 1.83517e12 | + | 5.84750e12i | 0.150895 | + | 0.480804i | ||||
\(415\) | − | 1.56362e12i | − | 0.127025i | ||||||
\(416\) | 8.48800e11 | − | 1.68696e13i | 0.0681300 | − | 1.35406i | ||||
\(417\) | 6.56494e12 | 0.520656 | ||||||||
\(418\) | 5.55349e12 | − | 1.74290e12i | 0.435196 | − | 0.136582i | ||||
\(419\) | 2.24160e13i | 1.73575i | 0.496779 | + | 0.867877i | \(0.334516\pi\) | ||||
−0.496779 | + | 0.867877i | \(0.665484\pi\) | |||||||
\(420\) | −1.29654e12 | + | 9.02728e11i | −0.0992066 | + | 0.0690733i | ||||
\(421\) | −4.29246e11 | −0.0324561 | −0.0162280 | − | 0.999868i | \(-0.505166\pi\) | ||||
−0.0162280 | + | 0.999868i | \(0.505166\pi\) | |||||||
\(422\) | −4.42592e12 | − | 1.41025e13i | −0.330706 | − | 1.05374i | ||||
\(423\) | 3.79926e12i | 0.280541i | ||||||||
\(424\) | 1.44307e13 | − | 1.86521e13i | 1.05307 | − | 1.36113i | ||||
\(425\) | −2.39788e12 | −0.172935 | ||||||||
\(426\) | −5.61857e12 | + | 1.76333e12i | −0.400477 | + | 0.125685i | ||||
\(427\) | 5.18555e12i | 0.365305i | ||||||||
\(428\) | 3.25018e12 | + | 4.66807e12i | 0.226302 | + | 0.325027i | ||||
\(429\) | 1.94742e13 | 1.34021 | ||||||||
\(430\) | 6.53177e12 | + | 2.08124e13i | 0.444312 | + | 1.41573i | ||||
\(431\) | − | 5.36455e12i | − | 0.360701i | −0.983602 | − | 0.180350i | \(-0.942277\pi\) | ||
0.983602 | − | 0.180350i | \(-0.0577231\pi\) | |||||||
\(432\) | −2.71566e12 | − | 1.00479e12i | −0.180492 | − | 0.0667815i | ||||
\(433\) | −8.22302e12 | −0.540246 | −0.270123 | − | 0.962826i | \(-0.587064\pi\) | ||||
−0.270123 | + | 0.962826i | \(0.587064\pi\) | |||||||
\(434\) | 3.24243e12 | − | 1.01760e12i | 0.210582 | − | 0.0660890i | ||||
\(435\) | 5.74850e11i | 0.0369069i | ||||||||
\(436\) | 5.77552e12 | − | 4.02124e12i | 0.366571 | − | 0.255228i | ||||
\(437\) | −6.41850e12 | −0.402741 | ||||||||
\(438\) | −3.68634e12 | − | 1.17459e13i | −0.228678 | − | 0.728647i | ||||
\(439\) | − | 2.66939e12i | − | 0.163715i | −0.996644 | − | 0.0818577i | \(-0.973915\pi\) | ||
0.996644 | − | 0.0818577i | \(-0.0260853\pi\) | |||||||
\(440\) | −1.85729e13 | − | 1.43694e13i | −1.12620 | − | 0.871314i | ||||
\(441\) | −5.20754e12 | −0.312205 | ||||||||
\(442\) | 1.22378e13 | − | 3.84072e12i | 0.725426 | − | 0.227667i | ||||
\(443\) | − | 2.42917e13i | − | 1.42377i | −0.702296 | − | 0.711885i | \(-0.747841\pi\) | ||
0.702296 | − | 0.711885i | \(-0.252159\pi\) | |||||||
\(444\) | 1.57895e12 | + | 2.26777e12i | 0.0915068 | + | 0.131427i | ||||
\(445\) | 5.43548e12 | 0.311486 | ||||||||
\(446\) | −4.07439e12 | − | 1.29824e13i | −0.230881 | − | 0.735667i | ||||
\(447\) | 1.11410e13i | 0.624291i | ||||||||
\(448\) | 4.39787e12 | − | 1.14093e12i | 0.243698 | − | 0.0632220i | ||||
\(449\) | −4.00357e12 | −0.219389 | −0.109695 | − | 0.993965i | \(-0.534987\pi\) | ||||
−0.109695 | + | 0.993965i | \(0.534987\pi\) | |||||||
\(450\) | −1.80975e12 | + | 5.67972e11i | −0.0980747 | + | 0.0307797i | ||||
\(451\) | 4.27418e13i | 2.29071i | ||||||||
\(452\) | 7.87815e12 | − | 5.48521e12i | 0.417573 | − | 0.290738i | ||||
\(453\) | 9.43913e12 | 0.494813 | ||||||||
\(454\) | −2.20958e11 | − | 7.04047e11i | −0.0114559 | − | 0.0365025i | ||||
\(455\) | − | 5.53574e12i | − | 0.283870i | ||||||
\(456\) | 1.85564e12 | − | 2.39847e12i | 0.0941174 | − | 0.121650i | ||||
\(457\) | −1.15136e12 | −0.0577606 | −0.0288803 | − | 0.999583i | \(-0.509194\pi\) | ||||
−0.0288803 | + | 0.999583i | \(0.509194\pi\) | |||||||
\(458\) | −1.23973e13 | + | 3.89076e12i | −0.615176 | + | 0.193067i | ||||
\(459\) | − | 2.19880e12i | − | 0.107925i | ||||||
\(460\) | 1.47963e13 | + | 2.12512e13i | 0.718396 | + | 1.03180i | ||||
\(461\) | −3.89616e13 | −1.87125 | −0.935625 | − | 0.352995i | \(-0.885163\pi\) | ||||
−0.935625 | + | 0.352995i | \(0.885163\pi\) | |||||||
\(462\) | 1.56855e12 | + | 4.99795e12i | 0.0745229 | + | 0.237455i | ||||
\(463\) | − | 2.46043e13i | − | 1.15640i | −0.815897 | − | 0.578198i | \(-0.803756\pi\) | ||
0.815897 | − | 0.578198i | \(-0.196244\pi\) | |||||||
\(464\) | 5.73668e11 | − | 1.55047e12i | 0.0266729 | − | 0.0720895i | ||||
\(465\) | −9.15092e12 | −0.420920 | ||||||||
\(466\) | 9.63778e12 | − | 3.02472e12i | 0.438579 | − | 0.137643i | ||||
\(467\) | 1.39160e13i | 0.626514i | 0.949668 | + | 0.313257i | \(0.101420\pi\) | ||||
−0.949668 | + | 0.313257i | \(0.898580\pi\) | |||||||
\(468\) | 8.32655e12 | − | 5.79742e12i | 0.370882 | − | 0.258229i | ||||
\(469\) | −8.35504e12 | −0.368200 | ||||||||
\(470\) | 4.80675e12 | + | 1.53159e13i | 0.209586 | + | 0.667813i | ||||
\(471\) | − | 5.87536e12i | − | 0.253472i | ||||||
\(472\) | −7.74394e12 | − | 5.99130e12i | −0.330561 | − | 0.255747i | ||||
\(473\) | 7.23262e13 | 3.05485 | ||||||||
\(474\) | −1.01521e13 | + | 3.18613e12i | −0.424291 | + | 0.133159i | ||||
\(475\) | − | 1.98648e12i | − | 0.0821514i | ||||||
\(476\) | 1.97140e12 | + | 2.83143e12i | 0.0806752 | + | 0.115870i | ||||
\(477\) | 1.41656e13 | 0.573647 | ||||||||
\(478\) | 1.96898e12 | + | 6.27385e12i | 0.0789045 | + | 0.251417i | ||||
\(479\) | 1.26427e13i | 0.501373i | 0.968068 | + | 0.250686i | \(0.0806563\pi\) | ||||
−0.968068 | + | 0.250686i | \(0.919344\pi\) | |||||||
\(480\) | −1.22189e13 | − | 6.14798e11i | −0.479541 | − | 0.0241283i | ||||
\(481\) | −9.68250e12 | −0.376064 | ||||||||
\(482\) | −2.49410e12 | + | 7.82748e11i | −0.0958692 | + | 0.0300875i | ||||
\(483\) | − | 5.77643e12i | − | 0.219747i | ||||||
\(484\) | −4.21012e13 | + | 2.93133e13i | −1.58514 | + | 1.10367i | ||||
\(485\) | −1.99826e13 | −0.744633 | ||||||||
\(486\) | −5.20819e11 | − | 1.65951e12i | −0.0192090 | − | 0.0612065i | ||||
\(487\) | − | 4.57472e13i | − | 1.67001i | −0.550240 | − | 0.835006i | \(-0.685464\pi\) | ||
0.550240 | − | 0.835006i | \(-0.314536\pi\) | |||||||
\(488\) | −2.45726e13 | + | 3.17609e13i | −0.887876 | + | 1.14761i | ||||
\(489\) | −2.38326e13 | −0.852366 | ||||||||
\(490\) | −2.09932e13 | + | 6.58848e12i | −0.743186 | + | 0.233241i | ||||
\(491\) | 2.43725e13i | 0.854069i | 0.904235 | + | 0.427034i | \(0.140442\pi\) | ||||
−0.904235 | + | 0.427034i | \(0.859558\pi\) | |||||||
\(492\) | 1.27241e13 | + | 1.82751e13i | 0.441370 | + | 0.633918i | ||||
\(493\) | 1.25537e12 | 0.0431060 | ||||||||
\(494\) | 3.18177e12 | + | 1.01382e13i | 0.108152 | + | 0.344609i | ||||
\(495\) | − | 1.41054e13i | − | 0.474636i | ||||||
\(496\) | 2.46815e13 | + | 9.13210e12i | 0.822174 | + | 0.304202i | ||||
\(497\) | 5.55028e12 | 0.183035 | ||||||||
\(498\) | −2.57716e12 | + | 8.08815e11i | −0.0841386 | + | 0.0264060i | ||||
\(499\) | 1.05755e13i | 0.341821i | 0.985287 | + | 0.170911i | \(0.0546709\pi\) | ||||
−0.985287 | + | 0.170911i | \(0.945329\pi\) | |||||||
\(500\) | −2.79053e13 | + | 1.94293e13i | −0.892971 | + | 0.621737i | ||||
\(501\) | −1.52717e13 | −0.483838 | ||||||||
\(502\) | −1.68542e13 | − | 5.37033e13i | −0.528676 | − | 1.68454i | ||||
\(503\) | − | 6.27653e13i | − | 1.94930i | −0.223728 | − | 0.974652i | \(-0.571823\pi\) | ||
0.223728 | − | 0.974652i | \(-0.428177\pi\) | |||||||
\(504\) | 2.15854e12 | + | 1.67001e12i | 0.0663755 | + | 0.0513532i | ||||
\(505\) | 1.96505e13 | 0.598298 | ||||||||
\(506\) | 8.19197e13 | − | 2.57096e13i | 2.46965 | − | 0.775074i | ||||
\(507\) | 1.62102e13i | 0.483891i | ||||||||
\(508\) | −8.82571e12 | − | 1.26759e13i | −0.260874 | − | 0.374681i | ||||
\(509\) | 2.93229e13 | 0.858258 | 0.429129 | − | 0.903243i | \(-0.358821\pi\) | ||||
0.429129 | + | 0.903243i | \(0.358821\pi\) | |||||||
\(510\) | −2.78189e12 | − | 8.86404e12i | −0.0806285 | − | 0.256910i | ||||
\(511\) | 1.16032e13i | 0.333022i | ||||||||
\(512\) | 3.23429e13 | + | 1.38520e13i | 0.919240 | + | 0.393698i | ||||
\(513\) | 1.82156e12 | 0.0512691 | ||||||||
\(514\) | −4.16172e13 | + | 1.30611e13i | −1.16000 | + | 0.364053i | ||||
\(515\) | − | 1.27843e13i | − | 0.352891i | ||||||
\(516\) | 3.09244e13 | − | 2.15314e13i | 0.845383 | − | 0.588604i | ||||
\(517\) | 5.32251e13 | 1.44100 | ||||||||
\(518\) | −7.79880e11 | − | 2.48497e12i | −0.0209112 | − | 0.0666303i | ||||
\(519\) | − | 1.00355e13i | − | 0.266504i | ||||||
\(520\) | 2.62321e13 | − | 3.39058e13i | 0.689947 | − | 0.891778i | ||||
\(521\) | −1.19837e12 | −0.0312179 | −0.0156090 | − | 0.999878i | \(-0.504969\pi\) | ||||
−0.0156090 | + | 0.999878i | \(0.504969\pi\) | |||||||
\(522\) | 9.47469e11 | − | 2.97353e11i | 0.0244463 | − | 0.00767220i | ||||
\(523\) | − | 2.99007e13i | − | 0.764140i | −0.924133 | − | 0.382070i | \(-0.875211\pi\) | ||
0.924133 | − | 0.382070i | \(-0.124789\pi\) | |||||||
\(524\) | 1.78856e13 | + | 2.56882e13i | 0.452737 | + | 0.650245i | ||||
\(525\) | 1.78776e12 | 0.0448242 | ||||||||
\(526\) | −1.01242e13 | − | 3.22593e13i | −0.251440 | − | 0.801173i | ||||
\(527\) | 1.99840e13i | 0.491620i | ||||||||
\(528\) | −1.40764e13 | + | 3.80447e13i | −0.343023 | + | 0.927096i | ||||
\(529\) | −5.32529e13 | −1.28548 | ||||||||
\(530\) | 5.71060e13 | − | 1.79221e13i | 1.36553 | − | 0.428558i | ||||
\(531\) | − | 5.88125e12i | − | 0.139315i | ||||||
\(532\) | −2.34564e12 | + | 1.63317e12i | −0.0550432 | + | 0.0383242i | ||||
\(533\) | −7.80275e13 | −1.81389 | ||||||||
\(534\) | −2.81162e12 | − | 8.95878e12i | −0.0647515 | − | 0.206321i | ||||
\(535\) | 1.44362e13i | 0.329371i | ||||||||
\(536\) | −5.11736e13 | − | 3.95918e13i | −1.15670 | − | 0.894914i | ||||
\(537\) | −1.91280e13 | −0.428348 | ||||||||
\(538\) | −4.17133e13 | + | 1.30913e13i | −0.925471 | + | 0.290449i | ||||
\(539\) | 7.29543e13i | 1.60364i | ||||||||
\(540\) | −4.19916e12 | − | 6.03104e12i | −0.0914520 | − | 0.131348i | ||||
\(541\) | 7.26527e13 | 1.56771 | 0.783855 | − | 0.620944i | \(-0.213251\pi\) | ||||
0.783855 | + | 0.620944i | \(0.213251\pi\) | |||||||
\(542\) | −2.00809e12 | − | 6.39845e12i | −0.0429325 | − | 0.136798i | ||||
\(543\) | − | 1.20262e13i | − | 0.254758i | ||||||
\(544\) | −1.34261e12 | + | 2.66840e13i | −0.0281810 | + | 0.560088i | ||||
\(545\) | 1.78610e13 | 0.371470 | ||||||||
\(546\) | −9.12403e12 | + | 2.86348e12i | −0.188028 | + | 0.0590107i | ||||
\(547\) | 6.51735e13i | 1.33087i | 0.746457 | + | 0.665433i | \(0.231753\pi\) | ||||
−0.746457 | + | 0.665433i | \(0.768247\pi\) | |||||||
\(548\) | 1.55111e13 | − | 1.07997e13i | 0.313863 | − | 0.218529i | ||||
\(549\) | −2.41213e13 | −0.483658 | ||||||||
\(550\) | 7.95693e12 | + | 2.53535e13i | 0.158100 | + | 0.503761i | ||||
\(551\) | 1.03999e12i | 0.0204772i | ||||||||
\(552\) | 2.73726e13 | − | 3.53799e13i | 0.534097 | − | 0.690337i | ||||
\(553\) | 1.00287e13 | 0.193919 | ||||||||
\(554\) | −5.61809e13 | + | 1.76318e13i | −1.07656 | + | 0.337868i | ||||
\(555\) | 7.01318e12i | 0.133183i | ||||||||
\(556\) | −2.73794e13 | − | 3.93238e13i | −0.515289 | − | 0.740084i | ||||
\(557\) | −4.72270e13 | −0.880875 | −0.440437 | − | 0.897783i | \(-0.645177\pi\) | ||||
−0.440437 | + | 0.897783i | \(0.645177\pi\) | |||||||
\(558\) | 4.73350e12 | + | 1.50826e13i | 0.0875008 | + | 0.278807i | ||||
\(559\) | 1.32035e14i | 2.41898i | ||||||||
\(560\) | 1.08146e13 | + | 4.00138e12i | 0.196368 | + | 0.0726556i | ||||
\(561\) | −3.08038e13 | −0.554358 | ||||||||
\(562\) | 1.24520e13 | − | 3.90792e12i | 0.222104 | − | 0.0697050i | ||||
\(563\) | − | 1.59848e13i | − | 0.282595i | −0.989967 | − | 0.141297i | \(-0.954873\pi\) | ||
0.989967 | − | 0.141297i | \(-0.0451274\pi\) | |||||||
\(564\) | 2.27574e13 | − | 1.58450e13i | 0.398774 | − | 0.277649i | ||||
\(565\) | 2.43635e13 | 0.423153 | ||||||||
\(566\) | 1.42501e13 | + | 4.54058e13i | 0.245322 | + | 0.781680i | ||||
\(567\) | 1.63934e12i | 0.0279739i | ||||||||
\(568\) | 3.39948e13 | + | 2.63010e13i | 0.575004 | + | 0.444867i | ||||
\(569\) | −3.21721e13 | −0.539408 | −0.269704 | − | 0.962943i | \(-0.586926\pi\) | ||||
−0.269704 | + | 0.962943i | \(0.586926\pi\) | |||||||
\(570\) | 7.34324e12 | − | 2.30460e12i | 0.122043 | − | 0.0383020i | ||||
\(571\) | 4.87497e12i | 0.0803141i | 0.999193 | + | 0.0401570i | \(0.0127858\pi\) | ||||
−0.999193 | + | 0.0401570i | \(0.987214\pi\) | |||||||
\(572\) | −8.12181e13 | − | 1.16650e14i | −1.32640 | − | 1.90504i | ||||
\(573\) | 2.31621e13 | 0.374978 | ||||||||
\(574\) | −6.28475e12 | − | 2.00254e13i | −0.100862 | − | 0.321381i | ||||
\(575\) | − | 2.93025e13i | − | 0.466193i | ||||||
\(576\) | 5.30718e12 | + | 2.04573e13i | 0.0837049 | + | 0.322652i | ||||
\(577\) | 1.06156e13 | 0.165984 | 0.0829921 | − | 0.996550i | \(-0.473552\pi\) | ||||
0.0829921 | + | 0.996550i | \(0.473552\pi\) | |||||||
\(578\) | 4.21942e13 | − | 1.32422e13i | 0.654053 | − | 0.205268i | ||||
\(579\) | 4.10313e13i | 0.630554i | ||||||||
\(580\) | 3.44333e12 | − | 2.39744e12i | 0.0524612 | − | 0.0365265i | ||||
\(581\) | 2.54584e12 | 0.0384548 | ||||||||
\(582\) | 1.03364e13 | + | 3.29353e13i | 0.154794 | + | 0.493227i | ||||
\(583\) | − | 1.98452e14i | − | 2.94654i | ||||||
\(584\) | −5.49836e13 | + | 7.10681e13i | −0.809411 | + | 1.04619i | ||||
\(585\) | 2.57502e13 | 0.375839 | ||||||||
\(586\) | 5.97466e13 | − | 1.87508e13i | 0.864619 | − | 0.271352i | ||||
\(587\) | − | 8.41292e13i | − | 1.20714i | −0.797311 | − | 0.603568i | \(-0.793745\pi\) | ||
0.797311 | − | 0.603568i | \(-0.206255\pi\) | |||||||
\(588\) | 2.17183e13 | + | 3.11930e13i | 0.308987 | + | 0.443782i | ||||
\(589\) | −1.65554e13 | −0.233541 | ||||||||
\(590\) | −7.44086e12 | − | 2.37091e13i | −0.104079 | − | 0.331631i | ||||
\(591\) | − | 8.85186e12i | − | 0.122771i | ||||||
\(592\) | 6.99876e12 | − | 1.89157e13i | 0.0962527 | − | 0.260144i | ||||
\(593\) | 1.09982e14 | 1.49985 | 0.749924 | − | 0.661524i | \(-0.230090\pi\) | ||||
0.749924 | + | 0.661524i | \(0.230090\pi\) | |||||||
\(594\) | −2.32486e13 | + | 7.29634e12i | −0.314387 | + | 0.0986672i | ||||
\(595\) | 8.75631e12i | 0.117418i | ||||||||
\(596\) | 6.67343e13 | − | 4.64642e13i | 0.887397 | − | 0.617856i | ||||
\(597\) | 8.12766e13 | 1.07175 | ||||||||
\(598\) | 4.69343e13 | + | 1.49549e14i | 0.613740 | + | 1.95559i | ||||
\(599\) | − | 6.17623e13i | − | 0.800920i | −0.916314 | − | 0.400460i | \(-0.868850\pi\) | ||
0.916314 | − | 0.400460i | \(-0.131150\pi\) | |||||||
\(600\) | 1.09498e13 | + | 8.47160e12i | 0.140815 | + | 0.108946i | ||||
\(601\) | −1.07868e14 | −1.37569 | −0.687844 | − | 0.725859i | \(-0.741443\pi\) | ||||
−0.687844 | + | 0.725859i | \(0.741443\pi\) | |||||||
\(602\) | −3.38862e13 | + | 1.06348e13i | −0.428589 | + | 0.134508i | ||||
\(603\) | − | 3.88646e13i | − | 0.487492i | ||||||
\(604\) | −3.93664e13 | − | 5.65400e13i | −0.489712 | − | 0.703350i | ||||
\(605\) | −1.30200e14 | −1.60633 | ||||||||
\(606\) | −1.01647e13 | − | 3.23881e13i | −0.124374 | − | 0.396298i | ||||
\(607\) | 1.16266e13i | 0.141094i | 0.997508 | + | 0.0705472i | \(0.0224745\pi\) | ||||
−0.997508 | + | 0.0705472i | \(0.977525\pi\) | |||||||
\(608\) | −2.21058e13 | − | 1.11226e12i | −0.266066 | − | 0.0133872i | ||||
\(609\) | −9.35954e11 | −0.0111730 | ||||||||
\(610\) | −9.72402e13 | + | 3.05178e13i | −1.15132 | + | 0.361330i | ||||
\(611\) | 9.71654e13i | 1.14105i | ||||||||
\(612\) | −1.31708e13 | + | 9.17023e12i | −0.153410 | + | 0.106813i | ||||
\(613\) | 1.10989e14 | 1.28227 | 0.641133 | − | 0.767430i | \(-0.278465\pi\) | ||||
0.641133 | + | 0.767430i | \(0.278465\pi\) | |||||||
\(614\) | 2.22151e13 | + | 7.07848e13i | 0.254569 | + | 0.811145i | ||||
\(615\) | 5.65164e13i | 0.642391i | ||||||||
\(616\) | 2.33958e13 | − | 3.02398e13i | 0.263776 | − | 0.340938i | ||||
\(617\) | 1.12126e14 | 1.25395 | 0.626974 | − | 0.779040i | \(-0.284293\pi\) | ||||
0.626974 | + | 0.779040i | \(0.284293\pi\) | |||||||
\(618\) | −2.10711e13 | + | 6.61295e12i | −0.233747 | + | 0.0733589i | ||||
\(619\) | − | 1.31678e14i | − | 1.44898i | −0.689287 | − | 0.724488i | \(-0.742076\pi\) | ||
0.689287 | − | 0.724488i | \(-0.257924\pi\) | |||||||
\(620\) | 3.81644e13 | + | 5.48136e13i | 0.416581 | + | 0.598316i | ||||
\(621\) | 2.68698e13 | 0.290942 | ||||||||
\(622\) | −3.91551e12 | − | 1.24761e13i | −0.0420568 | − | 0.134007i | ||||
\(623\) | 8.84990e12i | 0.0942970i | ||||||||
\(624\) | −6.94527e13 | − | 2.56973e13i | −0.734118 | − | 0.271622i | ||||
\(625\) | −5.68897e13 | −0.596532 | ||||||||
\(626\) | −1.06657e14 | + | 3.34733e13i | −1.10948 | + | 0.348198i | ||||
\(627\) | − | 2.55188e13i | − | 0.263344i | ||||||
\(628\) | −3.51932e13 | + | 2.45035e13i | −0.360297 | + | 0.250859i | ||||
\(629\) | 1.53156e13 | 0.155554 | ||||||||
\(630\) | 2.07406e12 | + | 6.60867e12i | 0.0208987 | + | 0.0665903i | ||||
\(631\) | 1.16942e13i | 0.116902i | 0.998290 | + | 0.0584510i | \(0.0186162\pi\) | ||||
−0.998290 | + | 0.0584510i | \(0.981384\pi\) | |||||||
\(632\) | 6.14247e13 | + | 4.75228e13i | 0.609196 | + | 0.471321i | ||||
\(633\) | −6.48024e13 | −0.637636 | ||||||||
\(634\) | 1.51541e14 | − | 4.75594e13i | 1.47939 | − | 0.464291i | ||||
\(635\) | − | 3.92009e13i | − | 0.379688i | ||||||
\(636\) | −5.90786e13 | − | 8.48517e13i | −0.567733 | − | 0.815408i | ||||
\(637\) | −1.33182e14 | −1.26984 | ||||||||
\(638\) | −4.16573e12 | − | 1.32734e13i | −0.0394083 | − | 0.125568i | ||||
\(639\) | 2.58179e13i | 0.242335i | ||||||||
\(640\) | 4.72770e13 | + | 7.57548e13i | 0.440301 | + | 0.705522i | ||||
\(641\) | 4.41705e13 | 0.408171 | 0.204086 | − | 0.978953i | \(-0.434578\pi\) | ||||
0.204086 | + | 0.978953i | \(0.434578\pi\) | |||||||
\(642\) | 2.37938e13 | − | 7.46744e12i | 0.218167 | − | 0.0684694i | ||||
\(643\) | 7.21456e13i | 0.656380i | 0.944612 | + | 0.328190i | \(0.106439\pi\) | ||||
−0.944612 | + | 0.328190i | \(0.893561\pi\) | |||||||
\(644\) | −3.46006e13 | + | 2.40909e13i | −0.312359 | + | 0.217482i | ||||
\(645\) | 9.56352e13 | 0.856681 | ||||||||
\(646\) | −5.03285e12 | − | 1.60364e13i | −0.0447354 | − | 0.142542i | ||||
\(647\) | 6.83435e13i | 0.602803i | 0.953497 | + | 0.301402i | \(0.0974545\pi\) | ||||
−0.953497 | + | 0.301402i | \(0.902545\pi\) | |||||||
\(648\) | −7.76828e12 | + | 1.00407e13i | −0.0679908 | + | 0.0878802i | ||||
\(649\) | −8.23926e13 | −0.715591 | ||||||||
\(650\) | −4.62842e13 | + | 1.45258e13i | −0.398902 | + | 0.125191i | ||||
\(651\) | − | 1.48993e13i | − | 0.127427i | ||||||
\(652\) | 9.93949e13 | + | 1.42756e14i | 0.843580 | + | 1.21159i | ||||
\(653\) | 1.21386e14 | 1.02236 | 0.511178 | − | 0.859475i | \(-0.329209\pi\) | ||||
0.511178 | + | 0.859475i | \(0.329209\pi\) | |||||||
\(654\) | −9.23900e12 | − | 2.94386e13i | −0.0772212 | − | 0.246053i | ||||
\(655\) | 7.94418e13i | 0.658935i | ||||||||
\(656\) | 5.64003e13 | − | 1.52434e14i | 0.464261 | − | 1.25477i | ||||
\(657\) | −5.39737e13 | −0.440915 | ||||||||
\(658\) | −2.49370e13 | + | 7.82621e12i | −0.202169 | + | 0.0634486i | ||||
\(659\) | 5.86235e13i | 0.471677i | 0.971792 | + | 0.235839i | \(0.0757836\pi\) | ||||
−0.971792 | + | 0.235839i | \(0.924216\pi\) | |||||||
\(660\) | −8.44911e13 | + | 5.88275e13i | −0.674670 | + | 0.469743i | ||||
\(661\) | −1.55218e14 | −1.23008 | −0.615042 | − | 0.788494i | \(-0.710861\pi\) | ||||
−0.615042 | + | 0.788494i | \(0.710861\pi\) | |||||||
\(662\) | −6.46251e13 | − | 2.05918e14i | −0.508290 | − | 1.61959i | ||||
\(663\) | − | 5.62341e13i | − | 0.438967i | ||||||
\(664\) | 1.55930e13 | + | 1.20639e13i | 0.120806 | + | 0.0934647i | ||||
\(665\) | −7.25400e12 | −0.0557788 | ||||||||
\(666\) | 1.15591e13 | − | 3.62772e12i | 0.0882175 | − | 0.0276861i | ||||
\(667\) | 1.53409e13i | 0.116204i | ||||||||
\(668\) | 6.36916e13 | + | 9.14771e13i | 0.478850 | + | 0.687749i | ||||
\(669\) | −5.96554e13 | −0.445163 | ||||||||
\(670\) | −4.91707e13 | − | 1.56675e14i | −0.364194 | − | 1.16045i | ||||
\(671\) | 3.37924e14i | 2.48431i | ||||||||
\(672\) | 1.00100e12 | − | 1.98945e13i | 0.00730443 | − | 0.145173i | ||||
\(673\) | 3.00810e13 | 0.217879 | 0.108940 | − | 0.994048i | \(-0.465254\pi\) | ||||
0.108940 | + | 0.994048i | \(0.465254\pi\) | |||||||
\(674\) | 1.42914e14 | − | 4.48521e13i | 1.02749 | − | 0.322466i | ||||
\(675\) | 8.31600e12i | 0.0593466i | ||||||||
\(676\) | 9.70983e13 | − | 6.76054e13i | 0.687826 | − | 0.478903i | ||||
\(677\) | −1.70799e14 | −1.20099 | −0.600497 | − | 0.799627i | \(-0.705031\pi\) | ||||
−0.600497 | + | 0.799627i | \(0.705031\pi\) | |||||||
\(678\) | −1.26025e13 | − | 4.01560e13i | −0.0879650 | − | 0.280287i | ||||
\(679\) | − | 3.25350e13i | − | 0.225425i | ||||||
\(680\) | −4.14933e13 | + | 5.36314e13i | −0.285386 | + | 0.368871i | ||||
\(681\) | −3.23516e12 | −0.0220882 | ||||||||
\(682\) | 2.11297e14 | − | 6.63134e13i | 1.43209 | − | 0.449448i | ||||
\(683\) | − | 2.49522e14i | − | 1.67883i | −0.543494 | − | 0.839413i | \(-0.682899\pi\) | ||
0.543494 | − | 0.839413i | \(-0.317101\pi\) | |||||||
\(684\) | −7.59690e12 | − | 1.09111e13i | −0.0507406 | − | 0.0728763i | ||||
\(685\) | 4.79688e13 | 0.318058 | ||||||||
\(686\) | −2.21803e13 | − | 7.06741e13i | −0.145998 | − | 0.465200i | ||||
\(687\) | 5.69668e13i | 0.372253i | ||||||||
\(688\) | −2.57944e14 | − | 9.54386e13i | −1.67334 | − | 0.619130i | ||||
\(689\) | 3.62284e14 | 2.33321 | ||||||||
\(690\) | 1.08320e14 | − | 3.39952e13i | 0.692571 | − | 0.217356i | ||||
\(691\) | 1.37253e13i | 0.0871226i | 0.999051 | + | 0.0435613i | \(0.0138704\pi\) | ||||
−0.999051 | + | 0.0435613i | \(0.986130\pi\) | |||||||
\(692\) | −6.01124e13 | + | 4.18537e13i | −0.378821 | + | 0.263756i | ||||
\(693\) | 2.29661e13 | 0.143688 | ||||||||
\(694\) | 8.90093e12 | + | 2.83614e13i | 0.0552889 | + | 0.176169i | ||||
\(695\) | − | 1.21611e14i | − | 0.749975i | ||||||
\(696\) | −5.73260e12 | − | 4.43518e12i | −0.0350999 | − | 0.0271559i | ||||
\(697\) | 1.23422e14 | 0.750290 | ||||||||
\(698\) | −1.88897e14 | + | 5.92832e13i | −1.14011 | + | 0.357812i | ||||
\(699\) | − | 4.42865e13i | − | 0.265391i | ||||||
\(700\) | −7.45595e12 | − | 1.07086e13i | −0.0443621 | − | 0.0637152i | ||||
\(701\) | −6.39494e13 | −0.377786 | −0.188893 | − | 0.981998i | \(-0.560490\pi\) | ||||
−0.188893 | + | 0.981998i | \(0.560490\pi\) | |||||||
\(702\) | −1.33199e13 | − | 4.24416e13i | −0.0781293 | − | 0.248947i | ||||
\(703\) | 1.26879e13i | 0.0738946i | ||||||||
\(704\) | 2.86593e14 | − | 7.43501e13i | 1.65730 | − | 0.429950i | ||||
\(705\) | 7.03783e13 | 0.404104 | ||||||||
\(706\) | 1.38208e13 | − | 4.33752e12i | 0.0787972 | − | 0.0247297i | ||||
\(707\) | 3.19944e13i | 0.181125i | ||||||||
\(708\) | −3.52285e13 | + | 2.45281e13i | −0.198029 | + | 0.137879i | ||||
\(709\) | −1.61109e13 | −0.0899268 | −0.0449634 | − | 0.998989i | \(-0.514317\pi\) | ||||
−0.0449634 | + | 0.998989i | \(0.514317\pi\) | |||||||
\(710\) | 3.26643e13 | + | 1.04080e14i | 0.181043 | + | 0.576865i | ||||
\(711\) | 4.66499e13i | 0.256745i | ||||||||
\(712\) | −4.19368e13 | + | 5.42046e13i | −0.229190 | + | 0.296235i | ||||
\(713\) | −2.44209e14 | −1.32530 | ||||||||
\(714\) | 1.44322e13 | − | 4.52939e12i | 0.0777752 | − | 0.0244089i | ||||
\(715\) | − | 3.60744e14i | − | 1.93050i | ||||||
\(716\) | 7.97741e13 | + | 1.14576e14i | 0.423933 | + | 0.608874i | ||||
\(717\) | 2.88289e13 | 0.152136 | ||||||||
\(718\) | 1.74460e13 | + | 5.55890e13i | 0.0914270 | + | 0.291318i | ||||
\(719\) | 1.17996e14i | 0.614075i | 0.951697 | + | 0.307038i | \(0.0993378\pi\) | ||||
−0.951697 | + | 0.307038i | \(0.900662\pi\) | |||||||
\(720\) | −1.86129e13 | + | 5.03056e13i | −0.0961950 | + | 0.259988i | ||||
\(721\) | 2.08150e13 | 0.106832 | ||||||||
\(722\) | −1.73907e14 | + | 5.45788e13i | −0.886402 | + | 0.278188i | ||||
\(723\) | 1.14606e13i | 0.0580120i | ||||||||
\(724\) | −7.20363e13 | + | 5.01558e13i | −0.362125 | + | 0.252132i | ||||
\(725\) | −4.74789e12 | −0.0237034 | ||||||||
\(726\) | 6.73487e13 | + | 2.14596e14i | 0.333923 | + | 1.06399i | ||||
\(727\) | 3.63046e14i | 1.78768i | 0.448389 | + | 0.893839i | \(0.351998\pi\) | ||||
−0.448389 | + | 0.893839i | \(0.648002\pi\) | |||||||
\(728\) | 5.52044e13 | + | 4.27103e13i | 0.269971 | + | 0.208870i | ||||
\(729\) | −7.62560e12 | −0.0370370 | ||||||||
\(730\) | −2.17584e14 | + | 6.82865e13i | −1.04957 | + | 0.329398i | ||||
\(731\) | − | 2.08851e14i | − | 1.00057i | ||||||
\(732\) | 1.00599e14 | + | 1.44486e14i | 0.478673 | + | 0.687494i | ||||
\(733\) | 1.15776e14 | 0.547142 | 0.273571 | − | 0.961852i | \(-0.411795\pi\) | ||||
0.273571 | + | 0.961852i | \(0.411795\pi\) | |||||||
\(734\) | −4.47068e13 | − | 1.42451e14i | −0.209842 | − | 0.668630i | ||||
\(735\) | 9.64656e13i | 0.449713i | ||||||||
\(736\) | −3.26083e14 | − | 1.64070e13i | −1.50987 | − | 0.0759695i | ||||
\(737\) | −5.44468e14 | −2.50400 | ||||||||
\(738\) | 9.31506e13 | − | 2.92343e13i | 0.425504 | − | 0.133540i | ||||
\(739\) | − | 1.58874e14i | − | 0.720828i | −0.932792 | − | 0.360414i | \(-0.882635\pi\) | ||
0.932792 | − | 0.360414i | \(-0.117365\pi\) | |||||||
\(740\) | 4.20087e13 | − | 2.92488e13i | 0.189313 | − | 0.131810i | ||||
\(741\) | 4.65860e13 | 0.208528 | ||||||||
\(742\) | 2.91803e13 | + | 9.29784e13i | 0.129739 | + | 0.413392i | ||||
\(743\) | − | 1.65809e14i | − | 0.732258i | −0.930564 | − | 0.366129i | \(-0.880683\pi\) | ||
0.930564 | − | 0.366129i | \(-0.119317\pi\) | |||||||
\(744\) | 7.06027e13 | − | 9.12562e13i | 0.309711 | − | 0.400311i | ||||
\(745\) | 2.06379e14 | 0.899257 | ||||||||
\(746\) | −1.73803e14 | + | 5.45463e13i | −0.752253 | + | 0.236087i | ||||
\(747\) | 1.18423e13i | 0.0509136i | ||||||||
\(748\) | 1.28469e14 | + | 1.84514e14i | 0.548644 | + | 0.787990i | ||||
\(749\) | −2.35047e13 | −0.0997114 | ||||||||
\(750\) | 4.46397e13 | + | 1.42238e14i | 0.188112 | + | 0.599388i | ||||
\(751\) | 2.02794e14i | 0.848899i | 0.905452 | + | 0.424450i | \(0.139532\pi\) | ||||
−0.905452 | + | 0.424450i | \(0.860468\pi\) | |||||||
\(752\) | −1.89822e14 | − | 7.02336e13i | −0.789327 | − | 0.292049i | ||||
\(753\) | −2.46772e14 | −1.01934 | ||||||||
\(754\) | 2.42314e13 | − | 7.60476e12i | 0.0994309 | − | 0.0312053i | ||||
\(755\) | − | 1.74853e14i | − | 0.712750i | ||||||
\(756\) | 9.81958e12 | − | 6.83695e12i | 0.0397634 | − | 0.0276856i | ||||
\(757\) | 1.75219e14 | 0.704859 | 0.352429 | − | 0.935838i | \(-0.385356\pi\) | ||||
0.352429 | + | 0.935838i | \(0.385356\pi\) | |||||||
\(758\) | 1.18813e14 | + | 3.78579e14i | 0.474809 | + | 1.51290i | ||||
\(759\) | − | 3.76429e14i | − | 1.49442i | ||||||
\(760\) | −4.44299e13 | − | 3.43743e13i | −0.175229 | − | 0.135571i | ||||
\(761\) | 3.37202e14 | 1.32120 | 0.660598 | − | 0.750740i | \(-0.270303\pi\) | ||||
0.660598 | + | 0.750740i | \(0.270303\pi\) | |||||||
\(762\) | −6.46110e13 | + | 2.02775e13i | −0.251496 | + | 0.0789295i | ||||
\(763\) | 2.90808e13i | 0.112456i | ||||||||
\(764\) | −9.65989e13 | − | 1.38740e14i | −0.371112 | − | 0.533011i | ||||
\(765\) | −4.07311e13 | −0.155460 | ||||||||
\(766\) | −7.48028e12 | − | 2.38347e13i | −0.0283644 | − | 0.0903787i | ||||
\(767\) | − | 1.50412e14i | − | 0.566639i | ||||||
\(768\) | 1.00404e14 | − | 1.17108e14i | 0.375791 | − | 0.438309i | ||||
\(769\) | 2.91514e14 | 1.08400 | 0.541998 | − | 0.840380i | \(-0.317668\pi\) | ||||
0.541998 | + | 0.840380i | \(0.317668\pi\) | |||||||
\(770\) | 9.25832e13 | − | 2.90563e13i | 0.342041 | − | 0.107346i | ||||
\(771\) | 1.91235e14i | 0.701933i | ||||||||
\(772\) | 2.45776e14 | − | 1.71123e14i | 0.896299 | − | 0.624054i | ||||
\(773\) | 1.98552e14 | 0.719412 | 0.359706 | − | 0.933066i | \(-0.382877\pi\) | ||||
0.359706 | + | 0.933066i | \(0.382877\pi\) | |||||||
\(774\) | −4.94693e13 | − | 1.57626e14i | −0.178087 | − | 0.567445i | ||||
\(775\) | − | 7.55806e13i | − | 0.270335i | ||||||
\(776\) | 1.54173e14 | − | 1.99273e14i | 0.547898 | − | 0.708175i | ||||
\(777\) | −1.14187e13 | −0.0403190 | ||||||||
\(778\) | 2.41017e13 | − | 7.56406e12i | 0.0845570 | − | 0.0265373i | ||||
\(779\) | 1.02247e14i | 0.356420i | ||||||||
\(780\) | −1.07393e14 | − | 1.54243e14i | −0.371965 | − | 0.534235i | ||||
\(781\) | 3.61692e14 | 1.24475 | ||||||||
\(782\) | −7.42396e13 | − | 2.36553e14i | −0.253864 | − | 0.808899i | ||||
\(783\) | − | 4.35371e12i | − | 0.0147928i | ||||||
\(784\) | 9.62673e13 | − | 2.60184e14i | 0.325011 | − | 0.878416i | ||||
\(785\) | −1.08836e14 | −0.365112 | ||||||||
\(786\) | 1.30936e14 | − | 4.10930e13i | 0.436463 | − | 0.136979i | ||||
\(787\) | 3.24206e14i | 1.07386i | 0.843627 | + | 0.536930i | \(0.180416\pi\) | ||||
−0.843627 | + | 0.536930i | \(0.819584\pi\) | |||||||
\(788\) | −5.30223e13 | + | 3.69172e13i | −0.174513 | + | 0.121506i | ||||
\(789\) | −1.48235e14 | −0.484802 | ||||||||
\(790\) | 5.90206e13 | + | 1.88060e14i | 0.191809 | + | 0.611168i | ||||
\(791\) | 3.96680e13i | 0.128103i | ||||||||
\(792\) | 1.40664e14 | + | 1.08829e14i | 0.451397 | + | 0.349235i | ||||
\(793\) | −6.16898e14 | −1.96719 | ||||||||
\(794\) | 4.37242e14 | − | 1.37224e14i | 1.38554 | − | 0.434837i | ||||
\(795\) | − | 2.62408e14i | − | 0.826306i | ||||||
\(796\) | −3.38968e14 | − | 4.86844e14i | −1.06070 | − | 1.52344i | ||||
\(797\) | −3.70687e14 | −1.15270 | −0.576350 | − | 0.817203i | \(-0.695523\pi\) | ||||
−0.576350 | + | 0.817203i | \(0.695523\pi\) | |||||||
\(798\) | 3.75228e12 | + | 1.19561e13i | 0.0115953 | + | 0.0369465i | ||||
\(799\) | − | 1.53694e14i | − | 0.471979i | ||||||
\(800\) | 5.07783e12 | − | 1.00920e14i | 0.0154963 | − | 0.307984i | ||||
\(801\) | −4.11665e13 | −0.124848 | ||||||||
\(802\) | −4.31741e14 | + | 1.35497e14i | −1.30122 | + | 0.408375i | ||||
\(803\) | 7.56137e14i | 2.26476i | ||||||||
\(804\) | −2.32797e14 | + | 1.62087e14i | −0.692943 | + | 0.482467i | ||||
\(805\) | −1.07004e14 | −0.316534 | ||||||||
\(806\) | 1.21059e14 | + | 3.85734e14i | 0.355894 | + | 1.13400i | ||||
\(807\) | 1.91677e14i | 0.560017i | ||||||||
\(808\) | −1.51611e14 | + | 1.95962e14i | −0.440225 | + | 0.569004i | ||||
\(809\) | 1.46930e14 | 0.424003 | 0.212001 | − | 0.977269i | \(-0.432002\pi\) | ||||
0.212001 | + | 0.977269i | \(0.432002\pi\) | |||||||
\(810\) | −3.07411e13 | + | 9.64777e12i | −0.0881646 | + | 0.0276695i | ||||
\(811\) | 7.85922e13i | 0.224014i | 0.993707 | + | 0.112007i | \(0.0357279\pi\) | ||||
−0.993707 | + | 0.112007i | \(0.964272\pi\) | |||||||
\(812\) | 3.90345e12 | + | 5.60633e12i | 0.0110578 | + | 0.0158818i | ||||
\(813\) | −2.94015e13 | −0.0827783 | ||||||||
\(814\) | −5.08220e13 | − | 1.61936e14i | −0.142210 | − | 0.453129i | ||||
\(815\) | 4.41480e14i | 1.22779i | ||||||||
\(816\) | 1.09859e14 | + | 4.06474e13i | 0.303657 | + | 0.112352i | ||||
\(817\) | 1.73018e14 | 0.475315 | ||||||||
\(818\) | 2.52290e14 | − | 7.91785e13i | 0.688863 | − | 0.216192i | ||||
\(819\) | 4.19258e13i | 0.113779i | ||||||||
\(820\) | 3.38531e14 | − | 2.35705e14i | 0.913124 | − | 0.635769i | ||||
\(821\) | −3.00642e13 | −0.0805998 | −0.0402999 | − | 0.999188i | \(-0.512831\pi\) | ||||
−0.0402999 | + | 0.999188i | \(0.512831\pi\) | |||||||
\(822\) | −2.48129e13 | − | 7.90624e13i | −0.0661178 | − | 0.210674i | ||||
\(823\) | − | 8.93705e13i | − | 0.236698i | −0.992972 | − | 0.118349i | \(-0.962240\pi\) | ||
0.992972 | − | 0.118349i | \(-0.0377602\pi\) | |||||||
\(824\) | 1.27490e14 | + | 9.86356e13i | 0.335613 | + | 0.259656i | ||||
\(825\) | 1.16502e14 | 0.304834 | ||||||||
\(826\) | 3.86025e13 | − | 1.21150e13i | 0.100396 | − | 0.0315081i | ||||
\(827\) | − | 6.08161e14i | − | 1.57214i | −0.618138 | − | 0.786070i | \(-0.712113\pi\) | ||
0.618138 | − | 0.786070i | \(-0.287887\pi\) | |||||||
\(828\) | −1.12062e14 | − | 1.60949e14i | −0.287943 | − | 0.413559i | ||||
\(829\) | −4.05649e14 | −1.03604 | −0.518022 | − | 0.855367i | \(-0.673331\pi\) | ||||
−0.518022 | + | 0.855367i | \(0.673331\pi\) | |||||||
\(830\) | 1.49827e13 | + | 4.77400e13i | 0.0380364 | + | 0.121197i | ||||
\(831\) | 2.58157e14i | 0.651445i | ||||||||
\(832\) | 1.35730e14 | + | 5.23191e14i | 0.340455 | + | 1.31233i | ||||
\(833\) | 2.10664e14 | 0.525250 | ||||||||
\(834\) | −2.00439e14 | + | 6.29056e13i | −0.496766 | + | 0.155905i | ||||
\(835\) | 2.82897e14i | 0.696941i | ||||||||
\(836\) | −1.52857e14 | + | 1.06428e14i | −0.374329 | + | 0.260629i | ||||
\(837\) | 6.93059e13 | 0.168711 | ||||||||
\(838\) | −2.14791e14 | − | 6.84399e14i | −0.519753 | − | 1.65611i | ||||
\(839\) | − | 1.18612e14i | − | 0.285311i | −0.989772 | − | 0.142656i | \(-0.954436\pi\) | ||
0.989772 | − | 0.142656i | \(-0.0455641\pi\) | |||||||
\(840\) | 3.09357e13 | − | 3.99853e13i | 0.0739713 | − | 0.0956103i | ||||
\(841\) | −4.18222e14 | −0.994092 | ||||||||
\(842\) | 1.31056e13 | − | 4.11306e12i | 0.0309668 | − | 0.00971862i | ||||
\(843\) | − | 5.72180e13i | − | 0.134399i | ||||||
\(844\) | 2.70262e14 | + | 3.88164e14i | 0.631063 | + | 0.906365i | ||||
\(845\) | 3.00281e14 | 0.697018 | ||||||||
\(846\) | −3.64047e13 | − | 1.15998e14i | −0.0840050 | − | 0.267669i | ||||
\(847\) | − | 2.11988e14i | − | 0.486288i | ||||||
\(848\) | −2.61868e14 | + | 7.07757e14i | −0.597178 | + | 1.61401i | ||||
\(849\) | 2.08644e14 | 0.473007 | ||||||||
\(850\) | 7.32113e13 | − | 2.29766e13i | 0.165000 | − | 0.0517834i | ||||
\(851\) | 1.87159e14i | 0.419337i | ||||||||
\(852\) | 1.54648e14 | − | 1.07675e14i | 0.344466 | − | 0.239837i | ||||
\(853\) | −1.22862e13 | −0.0272065 | −0.0136033 | − | 0.999907i | \(-0.504330\pi\) | ||||
−0.0136033 | + | 0.999907i | \(0.504330\pi\) | |||||||
\(854\) | −4.96882e13 | − | 1.58324e14i | −0.109387 | − | 0.348543i | ||||
\(855\) | − | 3.37429e13i | − | 0.0738503i | ||||||
\(856\) | −1.43963e14 | − | 1.11381e14i | −0.313244 | − | 0.242349i | ||||
\(857\) | 2.16293e14 | 0.467885 | 0.233942 | − | 0.972250i | \(-0.424837\pi\) | ||||
0.233942 | + | 0.972250i | \(0.424837\pi\) | |||||||
\(858\) | −5.94580e14 | + | 1.86603e14i | −1.27872 | + | 0.401311i | ||||
\(859\) | − | 2.31945e14i | − | 0.495928i | −0.968769 | − | 0.247964i | \(-0.920239\pi\) | ||
0.968769 | − | 0.247964i | \(-0.0797615\pi\) | |||||||
\(860\) | −3.98852e14 | − | 5.72851e14i | −0.847850 | − | 1.21773i | ||||
\(861\) | −9.20185e13 | −0.194473 | ||||||||
\(862\) | 5.14034e13 | + | 1.63789e14i | 0.108008 | + | 0.344150i | ||||
\(863\) | 3.85505e14i | 0.805334i | 0.915347 | + | 0.402667i | \(0.131917\pi\) | ||||
−0.915347 | + | 0.402667i | \(0.868083\pi\) | |||||||
\(864\) | 9.25418e13 | + | 4.65627e12i | 0.192207 | + | 0.00967095i | ||||
\(865\) | −1.85900e14 | −0.383884 | ||||||||
\(866\) | 2.51063e14 | − | 7.87934e13i | 0.515457 | − | 0.161771i | ||||
\(867\) | − | 1.93886e14i | − | 0.395778i | ||||||
\(868\) | −8.92460e13 | + | 6.21382e13i | −0.181130 | + | 0.126113i | ||||
\(869\) | 6.53535e14 | 1.31877 | ||||||||
\(870\) | −5.50824e12 | − | 1.75511e13i | −0.0110514 | − | 0.0352135i | ||||
\(871\) | − | 9.93955e14i | − | 1.98279i | ||||||
\(872\) | −1.37805e14 | + | 1.78117e14i | −0.273326 | + | 0.353282i | ||||
\(873\) | 1.51341e14 | 0.298460 | ||||||||
\(874\) | 1.95968e14 | − | 6.15024e13i | 0.384262 | − | 0.120596i | ||||
\(875\) | − | 1.40509e14i | − | 0.273945i | ||||||
\(876\) | 2.25100e14 | + | 3.23301e14i | 0.436370 | + | 0.626738i | ||||
\(877\) | 1.98238e14 | 0.382110 | 0.191055 | − | 0.981579i | \(-0.438809\pi\) | ||||
0.191055 | + | 0.981579i | \(0.438809\pi\) | |||||||
\(878\) | 2.55782e13 | + | 8.15010e13i | 0.0490228 | + | 0.156203i | ||||
\(879\) | − | 2.74541e14i | − | 0.523195i | ||||||
\(880\) | 7.04749e14 | + | 2.60755e14i | 1.33543 | + | 0.494105i | ||||
\(881\) | −5.01864e14 | −0.945598 | −0.472799 | − | 0.881170i | \(-0.656756\pi\) | ||||
−0.472799 | + | 0.881170i | \(0.656756\pi\) | |||||||
\(882\) | 1.58995e14 | − | 4.98989e13i | 0.297879 | − | 0.0934863i | ||||
\(883\) | − | 2.29717e14i | − | 0.427946i | −0.976840 | − | 0.213973i | \(-0.931360\pi\) | ||
0.976840 | − | 0.213973i | \(-0.0686405\pi\) | |||||||
\(884\) | −3.36840e14 | + | 2.34527e14i | −0.623968 | + | 0.434442i | ||||
\(885\) | −1.08946e14 | −0.200675 | ||||||||
\(886\) | 2.32765e14 | + | 7.41668e14i | 0.426333 | + | 1.35844i | ||||
\(887\) | − | 1.05125e15i | − | 1.91465i | −0.289017 | − | 0.957324i | \(-0.593328\pi\) | ||
0.289017 | − | 0.957324i | \(-0.406672\pi\) | |||||||
\(888\) | −6.99379e13 | − | 5.41093e13i | −0.126662 | − | 0.0979957i | ||||
\(889\) | 6.38258e13 | 0.114944 | ||||||||
\(890\) | −1.65954e14 | + | 5.20831e13i | −0.297193 | + | 0.0932710i | ||||
\(891\) | 1.06830e14i | 0.190241i | ||||||||
\(892\) | 2.48796e14 | + | 3.57334e14i | 0.440575 | + | 0.632776i | ||||
\(893\) | 1.27325e14 | 0.224210 | ||||||||
\(894\) | −1.06754e14 | − | 3.40154e14i | −0.186937 | − | 0.595646i | ||||
\(895\) | 3.54331e14i | 0.617012i | ||||||||
\(896\) | −1.23342e14 | + | 7.69750e13i | −0.213585 | + | 0.133294i | ||||
\(897\) | 6.87191e14 | 1.18336 | ||||||||
\(898\) | 1.22236e14 | − | 3.83624e13i | 0.209323 | − | 0.0656938i | ||||
\(899\) | 3.95691e13i | 0.0673841i | ||||||||
\(900\) | 4.98125e13 | − | 3.46823e13i | 0.0843579 | − | 0.0587348i | ||||
\(901\) | −5.73053e14 | −0.965097 | ||||||||
\(902\) | −4.09554e14 | − | 1.30498e15i | −0.685928 | − | 2.18560i | ||||
\(903\) | 1.55711e14i | 0.259346i | ||||||||
\(904\) | −1.87974e14 | + | 2.42962e14i | −0.311354 | + | 0.402435i | ||||
\(905\) | −2.22775e14 | −0.366965 | ||||||||
\(906\) | −2.88192e14 | + | 9.04462e13i | −0.472108 | + | 0.148166i | ||||
\(907\) | 6.65909e14i | 1.08487i | 0.840097 | + | 0.542436i | \(0.182498\pi\) | ||||
−0.840097 | + | 0.542436i | \(0.817502\pi\) | |||||||
\(908\) | 1.34924e13 | + | 1.93785e13i | 0.0218605 | + | 0.0313972i | ||||
\(909\) | −1.48826e14 | −0.239806 | ||||||||
\(910\) | 5.30438e13 | + | 1.69016e14i | 0.0850017 | + | 0.270844i | ||||
\(911\) | − | 9.67849e14i | − | 1.54247i | −0.636553 | − | 0.771233i | \(-0.719640\pi\) | ||
0.636553 | − | 0.771233i | \(-0.280360\pi\) | |||||||
\(912\) | −3.36736e13 | + | 9.10103e13i | −0.0533722 | + | 0.144250i | ||||
\(913\) | 1.65903e14 | 0.261518 | ||||||||
\(914\) | 3.51531e13 | − | 1.10324e13i | 0.0551103 | − | 0.0172958i | ||||
\(915\) | 4.46828e14i | 0.696683i | ||||||||
\(916\) | 3.41229e14 | − | 2.37583e14i | 0.529137 | − | 0.368416i | ||||
\(917\) | −1.29345e14 | −0.199482 | ||||||||
\(918\) | 2.10691e13 | + | 6.71332e13i | 0.0323170 | + | 0.102973i | ||||
\(919\) | − | 9.09280e13i | − | 0.138714i | −0.997592 | − | 0.0693570i | \(-0.977905\pi\) | ||
0.997592 | − | 0.0693570i | \(-0.0220948\pi\) | |||||||
\(920\) | −6.55386e14 | − | 5.07056e14i | −0.994392 | − | 0.769337i | ||||
\(921\) | 3.25263e14 | 0.490837 | ||||||||
\(922\) | 1.18956e15 | − | 3.73332e14i | 1.78539 | − | 0.560325i | ||||
\(923\) | 6.60288e14i | 0.985654i | ||||||||
\(924\) | −9.57812e13 | − | 1.37566e14i | −0.142207 | − | 0.204245i | ||||
\(925\) | −5.79243e13 | −0.0855367 | ||||||||
\(926\) | 2.35760e14 | + | 7.51211e14i | 0.346270 | + | 1.10333i | ||||
\(927\) | 9.68238e13i | 0.141444i | ||||||||
\(928\) | −2.65842e12 | + | 5.28352e13i | −0.00386264 | + | 0.0767686i | ||||
\(929\) | −5.91751e14 | −0.855186 | −0.427593 | − | 0.903971i | \(-0.640638\pi\) | ||||
−0.427593 | + | 0.903971i | \(0.640638\pi\) | |||||||
\(930\) | 2.79393e14 | − | 8.76845e13i | 0.401606 | − | 0.126040i | ||||
\(931\) | 1.74521e14i | 0.249516i | ||||||||
\(932\) | −2.65275e14 | + | 1.84699e14i | −0.377239 | + | 0.262655i | ||||
\(933\) | −5.73291e13 | −0.0810899 | ||||||||
\(934\) | −1.33344e14 | − | 4.24880e14i | −0.187603 | − | 0.597767i | ||||
\(935\) | 5.70617e14i | 0.798522i | ||||||||
\(936\) | −1.98673e14 | + | 2.56791e14i | −0.276541 | + | 0.357437i | ||||
\(937\) | 9.18237e14 | 1.27133 | 0.635663 | − | 0.771967i | \(-0.280727\pi\) | ||||
0.635663 | + | 0.771967i | \(0.280727\pi\) | |||||||
\(938\) | 2.55093e14 | − | 8.00584e13i | 0.351306 | − | 0.110254i | ||||
\(939\) | 4.90101e14i | 0.671363i | ||||||||
\(940\) | −2.93516e14 | − | 4.21563e14i | −0.399938 | − | 0.574412i | ||||
\(941\) | −3.47921e14 | −0.471555 | −0.235777 | − | 0.971807i | \(-0.575764\pi\) | ||||
−0.235777 | + | 0.971807i | \(0.575764\pi\) | |||||||
\(942\) | 5.62979e13 | + | 1.79385e14i | 0.0758993 | + | 0.241841i | ||||
\(943\) | 1.50824e15i | 2.02261i | ||||||||
\(944\) | 2.93845e14 | + | 1.08722e14i | 0.391975 | + | 0.145030i | ||||
\(945\) | 3.03675e13 | 0.0402949 | ||||||||
\(946\) | −2.20824e15 | + | 6.93034e14i | −2.91468 | + | 0.914742i | ||||
\(947\) | 9.59918e14i | 1.26033i | 0.776461 | + | 0.630165i | \(0.217013\pi\) | ||||
−0.776461 | + | 0.630165i | \(0.782987\pi\) | |||||||
\(948\) | 2.79431e14 | − | 1.94556e14i | 0.364950 | − | 0.254099i | ||||
\(949\) | −1.38037e15 | −1.79335 | ||||||||
\(950\) | 1.90345e13 | + | 6.06504e13i | 0.0245993 | + | 0.0783819i | ||||
\(951\) | − | 6.96344e14i | − | 0.895202i | ||||||
\(952\) | −8.73211e13 | − | 6.75582e13i | −0.111669 | − | 0.0863960i | ||||
\(953\) | −2.78204e14 | −0.353915 | −0.176958 | − | 0.984218i | \(-0.556626\pi\) | ||||
−0.176958 | + | 0.984218i | \(0.556626\pi\) | |||||||
\(954\) | −4.32501e14 | + | 1.35736e14i | −0.547325 | + | 0.171772i | ||||
\(955\) | − | 4.29061e14i | − | 0.540134i | ||||||
\(956\) | −1.20233e14 | − | 1.72684e14i | −0.150568 | − | 0.216254i | ||||
\(957\) | −6.09927e13 | −0.0759833 | ||||||||
\(958\) | −1.21143e14 | − | 3.86002e14i | −0.150131 | − | 0.478368i | ||||
\(959\) | 7.81015e13i | 0.0962867i | ||||||||
\(960\) | 3.78955e14 | − | 9.83113e13i | 0.464763 | − | 0.120572i | ||||
\(961\) | 1.89736e14 | 0.231490 | ||||||||
\(962\) | 2.95623e14 | − | 9.27782e13i | 0.358809 | − | 0.112608i | ||||
\(963\) | − | 1.09335e14i | − | 0.132016i | ||||||
\(964\) | 6.86489e13 | − | 4.77972e13i | 0.0824609 | − | 0.0574140i | ||||
\(965\) | 7.60073e14 | 0.908278 | ||||||||
\(966\) | 5.53500e13 | + | 1.76364e14i | 0.0658009 | + | 0.209664i | ||||
\(967\) | − | 1.62153e15i | − | 1.91776i | −0.283816 | − | 0.958879i | \(-0.591600\pi\) | ||
0.283816 | − | 0.958879i | \(-0.408400\pi\) | |||||||
\(968\) | 1.00454e15 | − | 1.29840e15i | 1.18193 | − | 1.52768i | ||||
\(969\) | −7.36887e13 | −0.0862546 | ||||||||
\(970\) | 6.10101e14 | − | 1.91474e14i | 0.710466 | − | 0.222972i | ||||
\(971\) | 7.55933e14i | 0.875765i | 0.899032 | + | 0.437882i | \(0.144271\pi\) | ||||
−0.899032 | + | 0.437882i | \(0.855729\pi\) | |||||||
\(972\) | 3.18030e13 | + | 4.56771e13i | 0.0366553 | + | 0.0526462i | ||||
\(973\) | 1.98003e14 | 0.227042 | ||||||||
\(974\) | 4.38352e14 | + | 1.39674e15i | 0.500067 | + | 1.59338i | ||||
\(975\) | 2.12680e14i | 0.241382i | ||||||||
\(976\) | 4.45910e14 | − | 1.20517e15i | 0.503498 | − | 1.36082i | ||||
\(977\) | −9.93537e14 | −1.11612 | −0.558060 | − | 0.829800i | \(-0.688454\pi\) | ||||
−0.558060 | + | 0.829800i | \(0.688454\pi\) | |||||||
\(978\) | 7.27648e14 | − | 2.28365e14i | 0.813256 | − | 0.255232i | ||||
\(979\) | 5.76716e14i | 0.641281i | ||||||||
\(980\) | 5.77826e14 | − | 4.02315e14i | 0.639244 | − | 0.445078i | ||||
\(981\) | −1.35273e14 | −0.148891 | ||||||||
\(982\) | −2.33539e14 | − | 7.44134e14i | −0.255742 | − | 0.814880i | ||||
\(983\) | − | 3.59751e14i | − | 0.391953i | −0.980609 | − | 0.195976i | \(-0.937212\pi\) | ||
0.980609 | − | 0.195976i | \(-0.0627876\pi\) | |||||||
\(984\) | −5.63602e14 | − | 4.36045e14i | −0.610938 | − | 0.472668i | ||||
\(985\) | −1.63974e14 | −0.176845 | ||||||||
\(986\) | −3.83286e13 | + | 1.20290e13i | −0.0411281 | + | 0.0129076i | ||||
\(987\) | 1.14588e14i | 0.122336i | ||||||||
\(988\) | −1.94289e14 | − | 2.79049e14i | −0.206379 | − | 0.296411i | ||||
\(989\) | 2.55220e15 | 2.69732 | ||||||||
\(990\) | 1.35159e14 | + | 4.30663e14i | 0.142125 | + | 0.452857i | ||||
\(991\) | − | 4.37051e14i | − | 0.457261i | −0.973513 | − | 0.228631i | \(-0.926575\pi\) | ||
0.973513 | − | 0.228631i | \(-0.0734248\pi\) | |||||||
\(992\) | −8.41074e14 | − | 4.23189e13i | −0.875539 | − | 0.0440530i | ||||
\(993\) | −9.46213e14 | −0.980037 | ||||||||
\(994\) | −1.69459e14 | + | 5.31831e13i | −0.174636 | + | 0.0548077i | ||||
\(995\) | − | 1.50559e15i | − | 1.54380i | ||||||
\(996\) | 7.09350e13 | − | 4.93890e13i | 0.0723709 | − | 0.0503888i | ||||
\(997\) | 1.00144e15 | 1.01660 | 0.508299 | − | 0.861181i | \(-0.330275\pi\) | ||||
0.508299 | + | 0.861181i | \(0.330275\pi\) | |||||||
\(998\) | −1.01335e14 | − | 3.22889e14i | −0.102355 | − | 0.326137i | ||||
\(999\) | − | 5.31154e13i | − | 0.0533818i |
(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 | 12.11.d.a.7.2 | yes | 10 | |
3.2 | odd | 2 | 36.11.d.e.19.9 | 10 | |||
4.3 | odd | 2 | inner | 12.11.d.a.7.1 | ✓ | 10 | |
8.3 | odd | 2 | 192.11.g.e.127.7 | 10 | |||
8.5 | even | 2 | 192.11.g.e.127.2 | 10 | |||
12.11 | even | 2 | 36.11.d.e.19.10 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
12.11.d.a.7.1 | ✓ | 10 | 4.3 | odd | 2 | inner | |
12.11.d.a.7.2 | yes | 10 | 1.1 | even | 1 | trivial | |
36.11.d.e.19.9 | 10 | 3.2 | odd | 2 | |||
36.11.d.e.19.10 | 10 | 12.11 | even | 2 | |||
192.11.g.e.127.2 | 10 | 8.5 | even | 2 | |||
192.11.g.e.127.7 | 10 | 8.3 | odd | 2 |