Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [400,10,Mod(49,400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(400, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("400.49");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 400 = 2^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 400.c (of order \(2\), degree \(1\), not 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: | \(206.014334466\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 1305x^{4} + 433104x^{2} + 16000000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{8}\cdot 5^{8} \) |
Twist minimal: | no (minimal twist has level 25) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.4 | ||
Root | \(6.48955i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 400.49 |
Dual form | 400.10.c.q.49.3 |
$q$-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 \(\left(\mathbb{Z}/400\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(177\) | \(351\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 30.5073i | 0.217449i | 0.994072 | + | 0.108725i | \(0.0346767\pi\) | ||||
−0.994072 | + | 0.108725i | \(0.965323\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4010.25i | 0.631292i | 0.948877 | + | 0.315646i | \(0.102221\pi\) | ||||
−0.948877 | + | 0.315646i | \(0.897779\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 18752.3 | 0.952716 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 42110.0 | 0.867198 | 0.433599 | − | 0.901106i | \(-0.357243\pi\) | ||||
0.433599 | + | 0.901106i | \(0.357243\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 123743.i | − 1.20165i | −0.799382 | − | 0.600824i | \(-0.794839\pi\) | ||||
0.799382 | − | 0.600824i | \(-0.205161\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 319945.i | 0.929085i | 0.885551 | + | 0.464543i | \(0.153781\pi\) | ||||
−0.885551 | + | 0.464543i | \(0.846219\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.08733e6 | 1.91412 | 0.957059 | − | 0.289893i | \(-0.0936197\pi\) | ||||
0.957059 | + | 0.289893i | \(0.0936197\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −122342. | −0.137274 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.50672e6i | 1.12268i | 0.827585 | + | 0.561341i | \(0.189714\pi\) | ||||
−0.827585 | + | 0.561341i | \(0.810286\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.17256e6i | 0.424617i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.62160e6 | 0.688295 | 0.344148 | − | 0.938916i | \(-0.388168\pi\) | ||||
0.344148 | + | 0.938916i | \(0.388168\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.27023e6 | −0.635991 | −0.317996 | − | 0.948092i | \(-0.603010\pi\) | ||||
−0.317996 | + | 0.948092i | \(0.603010\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.28466e6i | 0.188572i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 2.51034e6i | − 0.220204i | −0.993920 | − | 0.110102i | \(-0.964882\pi\) | ||||
0.993920 | − | 0.110102i | \(-0.0351177\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.77508e6 | 0.261297 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.95349e7 | 1.63233 | 0.816165 | − | 0.577819i | \(-0.196096\pi\) | ||||
0.816165 | + | 0.577819i | \(0.196096\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 1.42413e7i | − 0.635244i | −0.948217 | − | 0.317622i | \(-0.897116\pi\) | ||||
0.948217 | − | 0.317622i | \(-0.102884\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 1.35318e6i | − 0.0404496i | −0.999795 | − | 0.0202248i | \(-0.993562\pi\) | ||||
0.999795 | − | 0.0202248i | \(-0.00643820\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.42715e7 | 0.601470 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9.76067e6 | −0.202029 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 9.73342e7i | − 1.69443i | −0.531249 | − | 0.847216i | \(-0.678277\pi\) | ||||
0.531249 | − | 0.847216i | \(-0.321723\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.31714e7i | 0.416224i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.48924e6 | −0.0804644 | −0.0402322 | − | 0.999190i | \(-0.512810\pi\) | ||||
−0.0402322 | + | 0.999190i | \(0.512810\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.11752e7 | −0.843126 | −0.421563 | − | 0.906799i | \(-0.638518\pi\) | ||||
−0.421563 | + | 0.906799i | \(0.638518\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.52015e7i | 0.601442i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 2.94376e8i | − 1.78470i | −0.451344 | − | 0.892350i | \(-0.649055\pi\) | ||||
0.451344 | − | 0.892350i | \(-0.350945\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.59659e7 | −0.244127 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.56193e8 | −0.729455 | −0.364728 | − | 0.931114i | \(-0.618838\pi\) | ||||
−0.364728 | + | 0.931114i | \(0.618838\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.82539e8i | 1.16446i | 0.813023 | + | 0.582232i | \(0.197820\pi\) | ||||
−0.813023 | + | 0.582232i | \(0.802180\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.68872e8i | 0.547455i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.55294e8 | −1.60399 | −0.801994 | − | 0.597332i | \(-0.796228\pi\) | ||||
−0.801994 | + | 0.597332i | \(0.796228\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.33330e8 | 0.860383 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.48378e6i | 0.0149960i | 0.999972 | + | 0.00749802i | \(0.00238672\pi\) | ||||
−0.999972 | + | 0.00749802i | \(0.997613\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.99778e7i | 0.149669i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.99001e8 | 1.01198 | 0.505990 | − | 0.862539i | \(-0.331127\pi\) | ||||
0.505990 | + | 0.862539i | \(0.331127\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.96242e8 | 0.758591 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 9.97660e7i | − 0.138296i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.25317e8i | 1.06125i | 0.847606 | + | 0.530625i | \(0.178043\pi\) | ||||
−0.847606 | + | 0.530625i | \(0.821957\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.89660e8 | 0.826193 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.58959e8 | 0.916967 | 0.458483 | − | 0.888703i | \(-0.348393\pi\) | ||||
0.458483 | + | 0.888703i | \(0.348393\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.60441e8i | 0.140458i | 0.997531 | + | 0.0702292i | \(0.0223731\pi\) | ||||
−0.997531 | + | 0.0702292i | \(0.977627\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 9.60457e8i | − 0.708355i | −0.935178 | − | 0.354178i | \(-0.884761\pi\) | ||||
0.935178 | − | 0.354178i | \(-0.115239\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.98912e8 | −0.677810 | −0.338905 | − | 0.940821i | \(-0.610057\pi\) | ||||
−0.338905 | + | 0.940821i | \(0.610057\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.65836e7 | 0.0478831 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 2.50705e9i | − 1.44647i | −0.690601 | − | 0.723236i | \(-0.742654\pi\) | ||||
0.690601 | − | 0.723236i | \(-0.257346\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 2.32047e9i | − 1.14483i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.28306e9 | −0.586524 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.84695e8 | −0.247968 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9.01030e8i | 0.354949i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.47541e9i | 0.844364i | 0.906511 | + | 0.422182i | \(0.138736\pi\) | ||||
−0.906511 | + | 0.422182i | \(0.861264\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.34463e8 | 0.138134 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.92402e9 | −0.570808 | −0.285404 | − | 0.958407i | \(-0.592128\pi\) | ||||
−0.285404 | + | 0.958407i | \(0.592128\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.36045e9i | 1.20837i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.48594e8i | 0.108796i | 0.998519 | + | 0.0543978i | \(0.0173239\pi\) | ||||
−0.998519 | + | 0.0543978i | \(0.982676\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.48415e9 | 1.01886 | 0.509429 | − | 0.860513i | \(-0.329857\pi\) | ||||
0.509429 | + | 0.860513i | \(0.329857\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.12818e7 | 0.00879575 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 5.21084e9i | − 1.04207i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.40458e8i | 0.130789i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.20480e9 | 0.366463 | 0.183232 | − | 0.983070i | \(-0.441344\pi\) | ||||
0.183232 | + | 0.983070i | \(0.441344\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.21248e9 | 0.502857 | 0.251428 | − | 0.967876i | \(-0.419100\pi\) | ||||
0.251428 | + | 0.967876i | \(0.419100\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.99971e9i | 0.885154i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 1.08870e10i | − 1.43007i | −0.699088 | − | 0.715036i | \(-0.746410\pi\) | ||||
0.699088 | − | 0.715036i | \(-0.253590\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.96940e9 | 0.368453 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.04232e9 | −0.708740 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.19994e10i | 1.33142i | 0.746212 | + | 0.665708i | \(0.231870\pi\) | ||||
−0.746212 | + | 0.665708i | \(0.768130\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 9.68608e9i | − 0.963660i | −0.876265 | − | 0.481830i | \(-0.839972\pi\) | ||||
0.876265 | − | 0.481830i | \(-0.160028\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.70793e9 | −0.443956 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.03899e10 | 1.82361 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 7.35665e9i | − 0.624414i | −0.950014 | − | 0.312207i | \(-0.898932\pi\) | ||||
0.950014 | − | 0.312207i | \(-0.101068\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 2.28477e8i | − 0.0174969i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.00351e9 | −0.145866 | −0.0729329 | − | 0.997337i | \(-0.523236\pi\) | ||||
−0.0729329 | + | 0.997337i | \(0.523236\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.63414e9 | 0.390188 | 0.195094 | − | 0.980785i | \(-0.437499\pi\) | ||||
0.195094 | + | 0.980785i | \(0.437499\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 2.78151e9i | − 0.183337i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.34729e10i | 0.805701i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.70225e9 | −0.268057 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.16925e9 | −0.498521 | −0.249261 | − | 0.968436i | \(-0.580188\pi\) | ||||
−0.249261 | + | 0.968436i | \(0.580188\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.16327e10i | 1.64107i | 0.571594 | + | 0.820536i | \(0.306325\pi\) | ||||
−0.571594 | + | 0.820536i | \(0.693675\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.59858e10i | 1.22924i | 0.788822 | + | 0.614621i | \(0.210691\pi\) | ||||
−0.788822 | + | 0.614621i | \(0.789309\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.05766e10 | 0.478088 | 0.239044 | − | 0.971009i | \(-0.423166\pi\) | ||||
0.239044 | + | 0.971009i | \(0.423166\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.98061e9 | 0.388082 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.05133e10i | 0.434515i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.82544e10i | 1.06960i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.57873e10 | 1.65992 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.80228e10 | −0.625965 | −0.312983 | − | 0.949759i | \(-0.601328\pi\) | ||||
−0.312983 | + | 0.949759i | \(0.601328\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 4.76502e9i | − 0.158620i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 1.31145e10i | − 0.401496i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.61951e9 | −0.253212 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.95911e10 | 1.11643 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.44522e10i | 1.20371i | 0.798606 | + | 0.601855i | \(0.205571\pi\) | ||||
−0.798606 | + | 0.601855i | \(0.794429\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 5.59677e10i | − 1.39901i | −0.714627 | − | 0.699505i | \(-0.753404\pi\) | ||||
0.714627 | − | 0.699505i | \(-0.246596\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.47705e9 | 0.0354923 | 0.0177462 | − | 0.999843i | \(-0.494351\pi\) | ||||
0.0177462 | + | 0.999843i | \(0.494351\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.15182e9 | −0.119044 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.83279e9i | 0.174106i | 0.996204 | + | 0.0870532i | \(0.0277450\pi\) | ||||
−0.996204 | + | 0.0870532i | \(0.972255\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 1.69405e10i | − 0.348786i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.56371e10 | 1.10300 | 0.551498 | − | 0.834176i | \(-0.314057\pi\) | ||||
0.551498 | + | 0.834176i | \(0.314057\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.16053e10 | −0.221606 | −0.110803 | − | 0.993842i | \(-0.535342\pi\) | ||||
−0.110803 | + | 0.993842i | \(0.535342\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3.32485e10i | 0.611707i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 1.34549e11i | − 2.30009i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.97803e8 | −0.00326088 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.45974e10 | 0.550189 | 0.275094 | − | 0.961417i | \(-0.411291\pi\) | ||||
0.275094 | + | 0.961417i | \(0.411291\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.34479e10i | 0.973587i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 3.67735e10i | − 0.525818i | −0.964821 | − | 0.262909i | \(-0.915318\pi\) | ||||
0.964821 | − | 0.262909i | \(-0.0846820\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.00671e10 | 0.139013 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.91609e10 | 0.655750 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.33758e11i | 1.72392i | 0.506974 | + | 0.861962i | \(0.330764\pi\) | ||||
−0.506974 | + | 0.861962i | \(0.669236\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.82739e10i | 0.220055i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.42461e11 | 1.65886 | 0.829429 | − | 0.558612i | \(-0.188666\pi\) | ||||
0.829429 | + | 0.558612i | \(0.188666\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.11046e11 | 1.25067 | 0.625333 | − | 0.780358i | \(-0.284963\pi\) | ||||
0.625333 | + | 0.780358i | \(0.284963\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.51390e10i | 0.164955i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.80726e10i | 0.286500i | 0.989687 | + | 0.143250i | \(0.0457552\pi\) | ||||
−0.989687 | + | 0.143250i | \(0.954245\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.13244e10 | −0.605919 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.47143e10 | 0.523507 | 0.261753 | − | 0.965135i | \(-0.415699\pi\) | ||||
0.261753 | + | 0.965135i | \(0.415699\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 1.09950e11i | − 1.01895i | −0.860484 | − | 0.509477i | \(-0.829839\pi\) | ||||
0.860484 | − | 0.509477i | \(-0.170161\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.18442e11i | 1.03048i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.62229e10 | 0.136801 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.82289e10 | −0.230768 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.30453e11i | 1.82675i | 0.407124 | + | 0.913373i | \(0.366532\pi\) | ||||
−0.407124 | + | 0.913373i | \(0.633468\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.93764e10i | 0.368227i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.86446e11 | 1.34907 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.71111e10 | 0.401025 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.92552e10i | 0.199394i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 6.85036e10i | − 0.440140i | −0.975484 | − | 0.220070i | \(-0.929371\pi\) | ||||
0.975484 | − | 0.220070i | \(-0.0706286\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.89462e9 | −0.0305426 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.98797e11 | 1.20500 | 0.602502 | − | 0.798118i | \(-0.294171\pi\) | ||||
0.602502 | + | 0.798118i | \(0.294171\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.15202e10i | 0.362300i | 0.983455 | + | 0.181150i | \(0.0579820\pi\) | ||||
−0.983455 | + | 0.181150i | \(0.942018\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 2.25932e11i | − 1.25664i | −0.777955 | − | 0.628320i | \(-0.783743\pi\) | ||||
0.777955 | − | 0.628320i | \(-0.216257\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.10395e11 | 0.596888 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.93010e10 | 0.154031 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.47885e11i | 1.77838i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 3.04741e10i | − 0.147389i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.42658e9 | 0.0255355 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.38825e10 | 0.384101 | 0.192050 | − | 0.981385i | \(-0.438486\pi\) | ||||
0.192050 | + | 0.981385i | \(0.438486\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 4.70746e10i | − 0.209791i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 2.19457e11i | − 0.926862i | −0.886133 | − | 0.463431i | \(-0.846618\pi\) | ||||
0.886133 | − | 0.463431i | \(-0.153382\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.64834e10 | 0.314535 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.37710e11 | −0.551530 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.59163e11i | 1.01100i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.85960e11i | 0.688551i | 0.938869 | + | 0.344276i | \(0.111875\pi\) | ||||
−0.938869 | + | 0.344276i | \(0.888125\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.73237e11 | −0.985881 | −0.492940 | − | 0.870063i | \(-0.664078\pi\) | ||||
−0.492940 | + | 0.870063i | \(0.664078\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.45096e11 | 0.510240 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.02861e11i | 1.03814i | 0.854731 | + | 0.519072i | \(0.173722\pi\) | ||||
−0.854731 | + | 0.519072i | \(0.826278\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 3.91427e10i | − 0.127539i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.47660e11 | 0.786919 | 0.393460 | − | 0.919342i | \(-0.371278\pi\) | ||||
0.393460 | + | 0.919342i | \(0.371278\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.59591e11 | 2.66385 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 1.78375e10i | − 0.0539205i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 2.66354e11i | − 0.766412i | −0.923663 | − | 0.383206i | \(-0.874820\pi\) | ||||
0.923663 | − | 0.383206i | \(-0.125180\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.53847e11 | 1.55515 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.90335e11 | 1.06968 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.20850e11i | 1.39323i | 0.717445 | + | 0.696616i | \(0.245312\pi\) | ||||
−0.717445 | + | 0.696616i | \(0.754688\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 3.24405e11i | − 0.827088i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.28308e10 | 0.0817344 | 0.0408672 | − | 0.999165i | \(-0.486988\pi\) | ||||
0.0408672 | + | 0.999165i | \(0.486988\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.55180e10 | −0.183607 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 7.15293e10i | − 0.169859i | −0.996387 | − | 0.0849297i | \(-0.972933\pi\) | ||||
0.996387 | − | 0.0849297i | \(-0.0270666\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 2.67057e11i | − 0.605207i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.02681e11 | 0.448787 | 0.224394 | − | 0.974499i | \(-0.427960\pi\) | ||||
0.224394 | + | 0.974499i | \(0.427960\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.82067e11 | −1.04307 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 5.86968e10i | − 0.124122i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.63266e10i | 0.0329867i | 0.999864 | + | 0.0164934i | \(0.00525024\pi\) | ||||
−0.999864 | + | 0.0164934i | \(0.994750\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.33026e11 | −0.262759 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.20766e11 | −1.58515 | −0.792574 | − | 0.609776i | \(-0.791259\pi\) | ||||
−0.792574 | + | 0.609776i | \(0.791259\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.04670e11i | 0.764237i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 1.05710e11i | − 0.190960i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.24628e11 | 0.750332 | 0.375166 | − | 0.926958i | \(-0.377586\pi\) | ||||
0.375166 | + | 0.926958i | \(0.377586\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.36854e10 | −0.0236575 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 3.00337e10i | − 0.0507966i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.36799e11i | 0.221550i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.26375e10 | −0.0200308 | −0.0100154 | − | 0.999950i | \(-0.503188\pi\) | ||||
−0.0100154 | + | 0.999950i | \(0.503188\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.04545e10 | −0.0472479 | −0.0236240 | − | 0.999721i | \(-0.507520\pi\) | ||||
−0.0236240 | + | 0.999721i | \(0.507520\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 2.53752e10i | − 0.0385370i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 3.65635e11i | − 0.532259i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.58969e11 | 0.226597 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.05830e11 | −0.566495 | −0.283248 | − | 0.959047i | \(-0.591412\pi\) | ||||
−0.283248 | + | 0.959047i | \(0.591412\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 1.36978e11i | − 0.187265i | −0.995607 | − | 0.0936324i | \(-0.970152\pi\) | ||||
0.995607 | − | 0.0936324i | \(-0.0298478\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.63829e12i | 2.14895i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.84981e11 | 1.00872 | 0.504358 | − | 0.863495i | \(-0.331729\pi\) | ||||
0.504358 | + | 0.863495i | \(0.331729\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.55146e11 | 0.573030 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.87799e11i | 1.09521i | 0.836737 | + | 0.547605i | \(0.184460\pi\) | ||||
−0.836737 | + | 0.547605i | \(0.815540\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6.72624e10i | 0.0796872i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.35477e11 | −0.970122 | −0.485061 | − | 0.874480i | \(-0.661203\pi\) | ||||
−0.485061 | + | 0.874480i | \(0.661203\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.24371e12 | 1.41555 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 9.80041e10i | 0.109346i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.01172e11i | 0.644727i | 0.946616 | + | 0.322364i | \(0.104477\pi\) | ||||
−0.946616 | + | 0.322364i | \(0.895523\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.75154e11 | −0.394505 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.52807e12 | 1.57576 | 0.787879 | − | 0.615829i | \(-0.211179\pi\) | ||||
0.787879 | + | 0.615829i | \(0.211179\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 7.80402e11i | − 0.789231i | −0.918846 | − | 0.394615i | \(-0.870878\pi\) | ||||
0.918846 | − | 0.394615i | \(-0.129122\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.04751e11i | 0.393788i | 0.980425 | + | 0.196894i | \(0.0630855\pi\) | ||||
−0.980425 | + | 0.196894i | \(0.936915\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.18052e12 | 1.12667 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.32132e11 | 0.310968 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 5.99700e11i | − 0.550883i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 1.82524e12i | − 1.61431i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.06972e12 | −1.79640 | −0.898199 | − | 0.439588i | \(-0.855124\pi\) | ||||
−0.898199 | + | 0.439588i | \(0.855124\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.10638e11 | −0.264607 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 1.84335e11i | − 0.154115i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.41184e11i | 0.194298i | 0.995270 | + | 0.0971490i | \(0.0309723\pi\) | ||||
−0.995270 | + | 0.0971490i | \(0.969028\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3.66068e11 | −0.289516 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.27883e12 | −1.76948 | −0.884739 | − | 0.466088i | \(-0.845663\pi\) | ||||
−0.884739 | + | 0.466088i | \(0.845663\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.38767e11i | 0.639485i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 6.26373e11i | − 0.460499i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.88752e11 | 0.713896 | 0.356948 | − | 0.934124i | \(-0.383817\pi\) | ||||
0.356948 | + | 0.934124i | \(0.383817\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.95496e11 | 0.209547 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.22385e12i | 0.852455i | 0.904616 | + | 0.426228i | \(0.140158\pi\) | ||||
−0.904616 | + | 0.426228i | \(0.859842\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 1.43626e11i | − 0.0965380i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.58447e12 | −1.04629 | −0.523146 | − | 0.852243i | \(-0.675242\pi\) | ||||
−0.523146 | + | 0.852243i | \(0.675242\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.13305e12 | −0.735117 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.27495e12i | 0.812767i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 5.69823e10i | − 0.0350778i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.24432e11 | 0.135778 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.71561e12 | −1.61472 | −0.807362 | − | 0.590057i | \(-0.799105\pi\) | ||||
−0.807362 | + | 0.590057i | \(0.799105\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 2.16171e12i | − 1.26340i | −0.775214 | − | 0.631698i | \(-0.782358\pi\) | ||||
0.775214 | − | 0.631698i | \(-0.217642\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 1.04630e12i | − 0.590890i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.69046e11 | −0.260415 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.40441e11 | −0.0766597 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 3.65475e12i | − 1.96149i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 6.11217e10i | − 0.0317184i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.02207e12 | 0.521594 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.29090e12 | −1.14979 | −0.574895 | − | 0.818227i | \(-0.694957\pi\) | ||||
−0.574895 | + | 0.818227i | \(0.694957\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.71882e11i | 0.0848462i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.39447e12i | 1.62117i | 0.585620 | + | 0.810586i | \(0.300851\pi\) | ||||
−0.585620 | + | 0.810586i | \(0.699149\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.70974e12 | −0.803259 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.85053e12 | 1.31748 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 2.22687e12i | − 1.01259i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.74706e12i | 0.769060i | 0.923113 | + | 0.384530i | \(0.125636\pi\) | ||||
−0.923113 | + | 0.384530i | \(0.874364\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.76226e12 | −0.763340 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.11022e11 | −0.175199 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 2.58864e12i | − 1.08588i | −0.839770 | − | 0.542942i | \(-0.817310\pi\) | ||||
0.839770 | − | 0.542942i | \(-0.182690\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.33674e12i | 0.543153i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.99294e12 | 0.797055 | 0.398527 | − | 0.917156i | \(-0.369521\pi\) | ||||
0.398527 | + | 0.917156i | \(0.369521\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.50761e10 | −0.0138086 | −0.00690428 | − | 0.999976i | \(-0.502198\pi\) | ||||
−0.00690428 | + | 0.999976i | \(0.502198\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 2.79729e11i | − 0.108403i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 7.75900e11i | − 0.291417i | −0.989328 | − | 0.145708i | \(-0.953454\pi\) | ||||
0.989328 | − | 0.145708i | \(-0.0465461\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −9.65027e11 | −0.356850 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.60016e10 | −0.00946689 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 4.09874e12i | − 1.46941i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 1.24477e12i | − 0.432730i | −0.976313 | − | 0.216365i | \(-0.930580\pi\) | ||||
0.976313 | − | 0.216365i | \(-0.0694201\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.55581e12 | −1.21736 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.92756e11 | −0.267298 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.57794e11i | 0.0856103i | 0.999083 | + | 0.0428052i | \(0.0136295\pi\) | ||||
−0.999083 | + | 0.0428052i | \(0.986371\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.22664e11i | 0.103960i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.32089e12 | 0.736604 | 0.368302 | − | 0.929706i | \(-0.379939\pi\) | ||||
0.368302 | + | 0.929706i | \(0.379939\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.78665e12 | 0.558605 | 0.279302 | − | 0.960203i | \(-0.409897\pi\) | ||||
0.279302 | + | 0.960203i | \(0.409897\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 5.52022e12i | − 1.70031i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.45787e12i | 0.435883i | 0.975962 | + | 0.217941i | \(0.0699342\pi\) | ||||
−0.975962 | + | 0.217941i | \(0.930066\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.20731e11 | −0.0944851 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.67447e11 | −0.0486062 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 1.42075e12i | − 0.406394i | −0.979138 | − | 0.203197i | \(-0.934867\pi\) | ||||
0.979138 | − | 0.203197i | \(-0.0651331\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.20441e12i | 0.334573i | 0.985908 | + | 0.167286i | \(0.0535004\pi\) | ||||
−0.985908 | + | 0.167286i | \(0.946500\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.91349e12 | −1.34519 | −0.672593 | − | 0.740013i | \(-0.734819\pi\) | ||||
−0.672593 | + | 0.740013i | \(0.734819\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.76671e12 | −0.476710 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.40214e12i | 0.638856i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.39685e12i | 0.360948i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.03171e11 | 0.204588 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.58663e12 | −1.15176 | −0.575879 | − | 0.817535i | \(-0.695340\pi\) | ||||
−0.575879 | + | 0.817535i | \(0.695340\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 5.49826e11i | − 0.136116i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 3.00344e12i | − 0.722755i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.92898e12 | −0.694963 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.30636e12 | −0.539593 | −0.269796 | − | 0.962917i | \(-0.586956\pi\) | ||||
−0.269796 | + | 0.962917i | \(0.586956\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.59493e12i | 0.598654i | 0.954151 | + | 0.299327i | \(0.0967622\pi\) | ||||
−0.954151 | + | 0.299327i | \(0.903238\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 5.14811e12i | − 1.15499i | −0.816394 | − | 0.577495i | \(-0.804030\pi\) | ||||
0.816394 | − | 0.577495i | \(-0.195970\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.15372e11 | −0.0697786 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.00087e11 | 0.0873051 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 4.42559e12i | − 0.952492i | −0.879312 | − | 0.476246i | \(-0.841997\pi\) | ||||
0.879312 | − | 0.476246i | \(-0.158003\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.29826e12i | 1.10940i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.09827e12 | 0.226842 | 0.113421 | − | 0.993547i | \(-0.463819\pi\) | ||||
0.113421 | + | 0.993547i | \(0.463819\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.99232e11 | 0.162842 | 0.0814209 | − | 0.996680i | \(-0.474054\pi\) | ||||
0.0814209 | + | 0.996680i | \(0.474054\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.20782e12i | 0.242768i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.95000e12i | 0.772736i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.35612e12 | −0.261746 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.83939e12 | −0.731157 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 7.68445e12i | − 1.44393i | −0.691931 | − | 0.721963i | \(-0.743240\pi\) | ||||
0.691931 | − | 0.721963i | \(-0.256760\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.28854e12i | 0.235749i | 0.993029 | + | 0.117874i | \(0.0376080\pi\) | ||||
−0.993029 | + | 0.117874i | \(0.962392\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.71076e12 | −0.669959 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.70742e12 | 0.304214 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 8.11444e11i | − 0.142681i | −0.997452 | − | 0.0713404i | \(-0.977272\pi\) | ||||
0.997452 | − | 0.0713404i | \(-0.0227277\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.50607e10i | 0.00771778i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.20445e13 | −2.03611 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.26741e12 | −0.378338 | −0.189169 | − | 0.981945i | \(-0.560579\pi\) | ||||
−0.189169 | + | 0.981945i | \(0.560579\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.16673e12i | 0.521569i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.44955e12i | 1.51657i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.38957e11 | −0.0378594 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.92113e12 | −0.769721 | −0.384861 | − | 0.922975i | \(-0.625751\pi\) | ||||
−0.384861 | + | 0.922975i | \(0.625751\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 2.72956e12i | − 0.421496i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.84566e12i | 0.578874i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.12354e12 | 0.910112 | 0.455056 | − | 0.890463i | \(-0.349619\pi\) | ||||
0.455056 | + | 0.890463i | \(0.349619\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.04130e13 | −1.52815 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 4.92732e12i | − 0.714016i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.69734e12i | 0.239846i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.30376e11 | −0.0321483 | −0.0160741 | − | 0.999871i | \(-0.505117\pi\) | ||||
−0.0160741 | + | 0.999871i | \(0.505117\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.43408e11 | −0.0886702 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 3.54048e11i | − 0.0481880i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 9.25894e12i | − 1.22930i | −0.788801 | − | 0.614648i | \(-0.789298\pi\) | ||||
0.788801 | − | 0.614648i | \(-0.210702\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 5.54661e12 | 0.727368 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.55643e12 | 0.590196 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.22531e12i | 0.924461i | 0.886760 | + | 0.462231i | \(0.152951\pi\) | ||||
−0.886760 | + | 0.462231i | \(0.847049\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 1.23962e13i | − 1.54769i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.24725e13 | −1.53834 | −0.769170 | − | 0.639044i | \(-0.779330\pi\) | ||||
−0.769170 | + | 0.639044i | \(0.779330\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.10474e12 | 0.500154 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 1.15645e13i | − 1.39212i | −0.717986 | − | 0.696058i | \(-0.754936\pi\) | ||||
0.717986 | − | 0.696058i | \(-0.245064\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.21586e11i | 0.0142870i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.85167e12 | 0.447179 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.70732e12 | 0.425285 | 0.212642 | − | 0.977130i | \(-0.431793\pi\) | ||||
0.212642 | + | 0.977130i | \(0.431793\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.05547e12i | 0.119638i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 4.86635e11i | − 0.0538607i | −0.999637 | − | 0.0269303i | \(-0.991427\pi\) | ||||
0.999637 | − | 0.0269303i | \(-0.00857323\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.93562e12 | −0.211706 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.28395e12 | −0.463035 | −0.231518 | − | 0.972831i | \(-0.574369\pi\) | ||||
−0.231518 | + | 0.972831i | \(0.574369\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 4.00589e12i | − 0.427896i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.26745e11i | 0.0966899i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.03625e12 | 0.416207 | 0.208103 | − | 0.978107i | \(-0.433271\pi\) | ||||
0.208103 | + | 0.978107i | \(0.433271\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.12186e12 | 0.114339 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 1.21916e13i | − 1.22815i | −0.789247 | − | 0.614076i | \(-0.789529\pi\) | ||||
0.789247 | − | 0.614076i | \(-0.210471\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.07120e11i | 0.0302282i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.21141e13 | 3.12447 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.57728e12 | −0.632582 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.07397e12i | 0.292262i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.20299e12i | 0.111783i | 0.998437 | + | 0.0558913i | \(0.0178000\pi\) | ||||
−0.998437 | + | 0.0558913i | \(0.982200\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.08059e12 | −0.374866 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.00539e13 | 0.913147 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.12823e13i | 1.01314i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.72611e13i | 1.51533i | 0.652646 | + | 0.757663i | \(0.273659\pi\) | ||||
−0.652646 | + | 0.757663i | \(0.726341\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.32943e11 | 0.0375811 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.12326e13 | 0.964130 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.18977e13i | 1.00982i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.34609e12i | 0.360718i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −7.44408e12 | −0.611002 | −0.305501 | − | 0.952192i | \(-0.598824\pi\) | ||||
−0.305501 | + | 0.952192i | \(0.598824\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.59955e12 | 0.779214 | 0.389607 | − | 0.920981i | \(-0.372611\pi\) | ||||
0.389607 | + | 0.920981i | \(0.372611\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.38772e12i | 0.271957i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 1.54849e13i | − 1.21593i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 9.30568e12 | 0.722721 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.04043e12 | −0.387189 | −0.193595 | − | 0.981082i | \(-0.562015\pi\) | ||||
−0.193595 | + | 0.981082i | \(0.562015\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.62323e13i | 1.23333i | 0.787225 | + | 0.616666i | \(0.211517\pi\) | ||||
−0.787225 | + | 0.616666i | \(0.788483\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.74898e13i | 1.30020i | 0.759850 | + | 0.650099i | \(0.225273\pi\) | ||||
−0.759850 | + | 0.650099i | \(0.774727\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.04102e13 | 0.765535 | 0.382768 | − | 0.923845i | \(-0.374971\pi\) | ||||
0.382768 | + | 0.923845i | \(0.374971\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.56420e11 | −0.0622992 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.76555e12i | 0.558817i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 3.83454e12i | − 0.270053i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.66219e13 | −1.85485 | −0.927426 | − | 0.374006i | \(-0.877984\pi\) | ||||
−0.927426 | + | 0.374006i | \(0.877984\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.63439e12 | −0.526250 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.66919e12i | 0.113836i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 2.34477e12i | − 0.156540i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.35427e12 | 0.221571 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.78237e12 | 0.247219 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.30064e12i | 0.472161i | 0.971734 | + | 0.236080i | \(0.0758629\pi\) | ||||
−0.971734 | + | 0.236080i | \(0.924137\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 1.18598e13i | − 0.751041i | −0.926814 | − | 0.375520i | \(-0.877464\pi\) | ||||
0.926814 | − | 0.375520i | \(-0.122536\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.67692e13 | 1.05085 | 0.525427 | − | 0.850839i | \(-0.323906\pi\) | ||||
0.525427 | + | 0.850839i | \(0.323906\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.61336e12 | −0.224077 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.71596e12i | 0.412154i | 0.978536 | + | 0.206077i | \(0.0660698\pi\) | ||||
−0.978536 | + | 0.206077i | \(0.933930\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.94917e11i | 0.0297472i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.33834e13 | −1.39098 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.64270e13 | −2.14458 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.73518e13i | 1.01107i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 2.79757e13i | − 1.59692i | −0.602051 | − | 0.798458i | \(-0.705649\pi\) | ||||
0.602051 | − | 0.798458i | \(-0.294351\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7.03050e12 | −0.397225 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.06225e13 | 1.15332 | 0.576660 | − | 0.816984i | \(-0.304356\pi\) | ||||
0.576660 | + | 0.816984i | \(0.304356\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 2.02048e13i | − 1.11849i | −0.829003 | − | 0.559244i | \(-0.811091\pi\) | ||||
0.829003 | − | 0.559244i | \(-0.188909\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 3.19954e13i | − 1.73553i | −0.496978 | − | 0.867763i | \(-0.665557\pi\) | ||||
0.496978 | − | 0.867763i | \(-0.334443\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.92701e12 | −0.533041 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.40365e13 | 0.746122 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 1.47135e12i | − 0.0774254i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.68798e12i | 0.293354i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −8.57323e12 | −0.437750 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.11416e13 | 1.57427 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.74231e12i | 0.0872026i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 2.40537e12i | − 0.118018i | −0.998257 | − | 0.0590091i | \(-0.981206\pi\) | ||||
0.998257 | − | 0.0590091i | \(-0.0187941\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.79827e13 | 0.873609 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.11773e13 | 1.49970 | 0.749852 | − | 0.661606i | \(-0.230125\pi\) | ||||
0.749852 | + | 0.661606i | \(0.230125\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.73032e11i | 0.0130045i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 7.71582e12i | − 0.360346i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.42677e13 | 1.58477 | 0.792383 | − | 0.610024i | \(-0.208840\pi\) | ||||
0.792383 | + | 0.610024i | \(0.208840\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.08986e12 | 0.0957082 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.93278e13i | 0.876548i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.00864e12i | 0.133817i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.52782e13 | 1.11346 | 0.556730 | − | 0.830693i | \(-0.312056\pi\) | ||||
0.556730 | + | 0.830693i | \(0.312056\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.63910e13 | 1.15129 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.06476e12i | 0.262027i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.72636e13i | 1.15546i | 0.816227 | + | 0.577731i | \(0.196062\pi\) | ||||
−0.816227 | + | 0.577731i | \(0.803938\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.87682e12 | −0.0787819 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.57383e13 | 0.654340 | 0.327170 | − | 0.944966i | \(-0.393905\pi\) | ||||
0.327170 | + | 0.944966i | \(0.393905\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.45008e13i | 1.83259i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9.71128e12i | 0.392375i | 0.980566 | + | 0.196188i | \(0.0628562\pi\) | ||||
−0.980566 | + | 0.196188i | \(0.937144\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.49624e13 | 1.39927 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.89257e12 | 0.273256 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 4.15385e12i | − 0.163130i | −0.996668 | − | 0.0815648i | \(-0.974008\pi\) | ||||
0.996668 | − | 0.0815648i | \(-0.0259917\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.36787e12i | 0.129793i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.79897e12 | −0.0686818 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.57452e13 | −0.595515 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 1.80108e13i | − 0.674861i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 1.84544e13i | − 0.678706i | −0.940659 | − | 0.339353i | \(-0.889792\pi\) | ||||
0.940659 | − | 0.339353i | \(-0.110208\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.06130e13 | −0.386707 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.95973e12 | 0.106848 | 0.0534238 | − | 0.998572i | \(-0.482987\pi\) | ||||
0.0534238 | + | 0.998572i | \(0.482987\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.79826e13i | 0.643197i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.44178e13i | 1.55967i | 0.625988 | + | 0.779833i | \(0.284696\pi\) | ||||
−0.625988 | + | 0.779833i | \(0.715304\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.52239e13 | 0.877588 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.87319e13 | −0.645761 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.57558e13i | 1.56299i | 0.623914 | + | 0.781493i | \(0.285541\pi\) | ||||
−0.623914 | + | 0.781493i | \(0.714459\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.65550e11i | 0.00555269i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.14576e13 | 0.713177 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.30469e13 | −0.429710 | −0.214855 | − | 0.976646i | \(-0.568928\pi\) | ||||
−0.214855 | + | 0.976646i | \(0.568928\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.55903e12i | 0.0835225i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 5.07578e12i | − 0.162695i | −0.996686 | − | 0.0813476i | \(-0.974078\pi\) | ||||
0.996686 | − | 0.0813476i | \(-0.0259224\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.94352e12 | 0.0935022 |
(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 | 400.10.c.q.49.4 | 6 | ||
4.3 | odd | 2 | 25.10.b.c.24.3 | 6 | |||
5.2 | odd | 4 | 400.10.a.y.1.2 | 3 | |||
5.3 | odd | 4 | 400.10.a.u.1.2 | 3 | |||
5.4 | even | 2 | inner | 400.10.c.q.49.3 | 6 | ||
12.11 | even | 2 | 225.10.b.m.199.4 | 6 | |||
20.3 | even | 4 | 25.10.a.d.1.1 | yes | 3 | ||
20.7 | even | 4 | 25.10.a.c.1.3 | ✓ | 3 | ||
20.19 | odd | 2 | 25.10.b.c.24.4 | 6 | |||
60.23 | odd | 4 | 225.10.a.m.1.3 | 3 | |||
60.47 | odd | 4 | 225.10.a.p.1.1 | 3 | |||
60.59 | even | 2 | 225.10.b.m.199.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
25.10.a.c.1.3 | ✓ | 3 | 20.7 | even | 4 | ||
25.10.a.d.1.1 | yes | 3 | 20.3 | even | 4 | ||
25.10.b.c.24.3 | 6 | 4.3 | odd | 2 | |||
25.10.b.c.24.4 | 6 | 20.19 | odd | 2 | |||
225.10.a.m.1.3 | 3 | 60.23 | odd | 4 | |||
225.10.a.p.1.1 | 3 | 60.47 | odd | 4 | |||
225.10.b.m.199.3 | 6 | 60.59 | even | 2 | |||
225.10.b.m.199.4 | 6 | 12.11 | even | 2 | |||
400.10.a.u.1.2 | 3 | 5.3 | odd | 4 | |||
400.10.a.y.1.2 | 3 | 5.2 | odd | 4 | |||
400.10.c.q.49.3 | 6 | 5.4 | even | 2 | inner | ||
400.10.c.q.49.4 | 6 | 1.1 | even | 1 | trivial |