Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,22,Mod(49,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.49");
S:= CuspForms(chi, 22);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.b (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: | \(209.608008215\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{649})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} + 325x^{2} + 26244 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{4}\cdot 7^{2} \) |
Twist minimal: | no (minimal twist has level 3) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.3 | ||
Root | \(13.2377i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 75.49 |
Dual form | 75.22.b.d.49.2 |
$q$-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 \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).
\(n\) | \(26\) | \(52\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1271.96i | 0.878328i | 0.898407 | + | 0.439164i | \(0.144725\pi\) | ||||
−0.898407 | + | 0.439164i | \(0.855275\pi\) | |||||||
\(3\) | 59049.0i | 0.577350i | ||||||||
\(4\) | 479282. | 0.228540 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −7.51077e7 | −0.507103 | ||||||||
\(7\) | − 6.32076e8i | − 0.845745i | −0.906189 | − | 0.422873i | \(-0.861022\pi\) | ||||
0.906189 | − | 0.422873i | \(-0.138978\pi\) | |||||||
\(8\) | 3.27711e9i | 1.07906i | ||||||||
\(9\) | −3.48678e9 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.97585e10 | 0.694666 | 0.347333 | − | 0.937742i | \(-0.387087\pi\) | ||||
0.347333 | + | 0.937742i | \(0.387087\pi\) | |||||||
\(12\) | 2.83011e10i | 0.131947i | ||||||||
\(13\) | 7.38499e11i | 1.48575i | 0.669432 | + | 0.742874i | \(0.266538\pi\) | ||||
−0.669432 | + | 0.742874i | \(0.733462\pi\) | |||||||
\(14\) | 8.03972e11 | 0.742842 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.16321e12 | −0.719230 | ||||||||
\(17\) | 8.35876e12i | 1.00561i | 0.864401 | + | 0.502804i | \(0.167698\pi\) | ||||
−0.864401 | + | 0.502804i | \(0.832302\pi\) | |||||||
\(18\) | − 4.43503e12i | − 0.292776i | ||||||||
\(19\) | −4.19061e13 | −1.56807 | −0.784034 | − | 0.620718i | \(-0.786841\pi\) | ||||
−0.784034 | + | 0.620718i | \(0.786841\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.73234e13 | 0.488291 | ||||||||
\(22\) | 7.60101e13i | 0.610145i | ||||||||
\(23\) | 4.48926e13i | 0.225961i | 0.993597 | + | 0.112980i | \(0.0360397\pi\) | ||||
−0.993597 | + | 0.112980i | \(0.963960\pi\) | |||||||
\(24\) | −1.93510e14 | −0.622996 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −9.39338e14 | −1.30497 | ||||||||
\(27\) | − 2.05891e14i | − 0.192450i | ||||||||
\(28\) | − 3.02943e14i | − 0.193286i | ||||||||
\(29\) | 2.76669e15 | 1.22119 | 0.610593 | − | 0.791945i | \(-0.290931\pi\) | ||||
0.610593 | + | 0.791945i | \(0.290931\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.36452e15 | 1.83292 | 0.916459 | − | 0.400128i | \(-0.131034\pi\) | ||||
0.916459 | + | 0.400128i | \(0.131034\pi\) | |||||||
\(32\) | 2.84914e15i | 0.447341i | ||||||||
\(33\) | 3.52868e15i | 0.401066i | ||||||||
\(34\) | −1.06320e16 | −0.883253 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.67115e15 | −0.0761798 | ||||||||
\(37\) | 1.77675e16i | 0.607447i | 0.952760 | + | 0.303724i | \(0.0982299\pi\) | ||||
−0.952760 | + | 0.303724i | \(0.901770\pi\) | |||||||
\(38\) | − 5.33027e16i | − 1.37728i | ||||||||
\(39\) | −4.36077e16 | −0.857797 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.45253e17 | 1.69003 | 0.845013 | − | 0.534745i | \(-0.179592\pi\) | ||||
0.845013 | + | 0.534745i | \(0.179592\pi\) | |||||||
\(42\) | 4.74737e16i | 0.428880i | ||||||||
\(43\) | 1.24744e17i | 0.880239i | 0.897939 | + | 0.440119i | \(0.145064\pi\) | ||||
−0.897939 | + | 0.440119i | \(0.854936\pi\) | |||||||
\(44\) | 2.86412e16 | 0.158759 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.71014e16 | −0.198468 | ||||||||
\(47\) | − 4.28566e17i | − 1.18847i | −0.804290 | − | 0.594237i | \(-0.797454\pi\) | ||||
0.804290 | − | 0.594237i | \(-0.202546\pi\) | |||||||
\(48\) | − 1.86784e17i | − 0.415248i | ||||||||
\(49\) | 1.59026e17 | 0.284715 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.93577e17 | −0.580588 | ||||||||
\(52\) | 3.53950e17i | 0.339552i | ||||||||
\(53\) | − 4.77017e17i | − 0.374660i | −0.982297 | − | 0.187330i | \(-0.940017\pi\) | ||||
0.982297 | − | 0.187330i | \(-0.0599834\pi\) | |||||||
\(54\) | 2.61884e17 | 0.169034 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.07138e18 | 0.912611 | ||||||||
\(57\) | − 2.47452e18i | − 0.905324i | ||||||||
\(58\) | 3.51911e18i | 1.07260i | ||||||||
\(59\) | −1.61959e18 | −0.412533 | −0.206267 | − | 0.978496i | \(-0.566131\pi\) | ||||
−0.206267 | + | 0.978496i | \(0.566131\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.76882e18 | −0.676461 | −0.338230 | − | 0.941063i | \(-0.609828\pi\) | ||||
−0.338230 | + | 0.941063i | \(0.609828\pi\) | |||||||
\(62\) | 1.06393e19i | 1.60990i | ||||||||
\(63\) | 2.20391e18i | 0.281915i | ||||||||
\(64\) | −1.02577e19 | −1.11214 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4.48832e18 | −0.352267 | ||||||||
\(67\) | 2.81797e18i | 0.188865i | 0.995531 | + | 0.0944324i | \(0.0301036\pi\) | ||||
−0.995531 | + | 0.0944324i | \(0.969896\pi\) | |||||||
\(68\) | 4.00621e18i | 0.229821i | ||||||||
\(69\) | −2.65086e18 | −0.130458 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.00228e19 | 0.365407 | 0.182704 | − | 0.983168i | \(-0.441515\pi\) | ||||
0.182704 | + | 0.983168i | \(0.441515\pi\) | |||||||
\(72\) | − 1.14266e19i | − 0.359687i | ||||||||
\(73\) | − 1.72739e19i | − 0.470435i | −0.971943 | − | 0.235218i | \(-0.924420\pi\) | ||||
0.971943 | − | 0.235218i | \(-0.0755803\pi\) | |||||||
\(74\) | −2.25995e19 | −0.533538 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.00849e19 | −0.358365 | ||||||||
\(77\) | − 3.77719e19i | − 0.587511i | ||||||||
\(78\) | − 5.54670e19i | − 0.753427i | ||||||||
\(79\) | 3.28276e19 | 0.390080 | 0.195040 | − | 0.980795i | \(-0.437516\pi\) | ||||
0.195040 | + | 0.980795i | \(0.437516\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.21577e19 | 0.111111 | ||||||||
\(82\) | 1.84755e20i | 1.48440i | ||||||||
\(83\) | 3.05240e17i | 0.00215934i | 0.999999 | + | 0.00107967i | \(0.000343670\pi\) | ||||
−0.999999 | + | 0.00107967i | \(0.999656\pi\) | |||||||
\(84\) | 1.78885e19 | 0.111594 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.58669e20 | −0.773139 | ||||||||
\(87\) | 1.63370e20i | 0.705052i | ||||||||
\(88\) | 1.95835e20i | 0.749587i | ||||||||
\(89\) | −2.34593e20 | −0.797480 | −0.398740 | − | 0.917064i | \(-0.630552\pi\) | ||||
−0.398740 | + | 0.917064i | \(0.630552\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.66787e20 | 1.25656 | ||||||||
\(92\) | 2.15162e19i | 0.0516409i | ||||||||
\(93\) | 4.93917e20i | 1.05824i | ||||||||
\(94\) | 5.45116e20 | 1.04387 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.68239e20 | −0.258272 | ||||||||
\(97\) | 5.92086e20i | 0.815233i | 0.913153 | + | 0.407616i | \(0.133640\pi\) | ||||
−0.913153 | + | 0.407616i | \(0.866360\pi\) | |||||||
\(98\) | 2.02274e20i | 0.250073i | ||||||||
\(99\) | −2.08365e20 | −0.231555 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.66229e21 | −1.49739 | −0.748693 | − | 0.662917i | \(-0.769318\pi\) | ||||
−0.748693 | + | 0.662917i | \(0.769318\pi\) | |||||||
\(102\) | − 6.27807e20i | − 0.509946i | ||||||||
\(103\) | 1.17919e21i | 0.864552i | 0.901741 | + | 0.432276i | \(0.142289\pi\) | ||||
−0.901741 | + | 0.432276i | \(0.857711\pi\) | |||||||
\(104\) | −2.42014e21 | −1.60321 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.06745e20 | 0.329075 | ||||||||
\(107\) | 8.69160e20i | 0.427140i | 0.976928 | + | 0.213570i | \(0.0685091\pi\) | ||||
−0.976928 | + | 0.213570i | \(0.931491\pi\) | |||||||
\(108\) | − 9.86799e19i | − 0.0439825i | ||||||||
\(109\) | −4.12021e20 | −0.166702 | −0.0833510 | − | 0.996520i | \(-0.526562\pi\) | ||||
−0.0833510 | + | 0.996520i | \(0.526562\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.04915e21 | −0.350710 | ||||||||
\(112\) | 1.99939e21i | 0.608286i | ||||||||
\(113\) | 2.45943e21i | 0.681569i | 0.940141 | + | 0.340785i | \(0.110693\pi\) | ||||
−0.940141 | + | 0.340785i | \(0.889307\pi\) | |||||||
\(114\) | 3.14747e21 | 0.795172 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.32602e21 | 0.279089 | ||||||||
\(117\) | − 2.57499e21i | − 0.495249i | ||||||||
\(118\) | − 2.06005e21i | − 0.362340i | ||||||||
\(119\) | 5.28337e21 | 0.850487 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.82917e21 | −0.517439 | ||||||||
\(122\) | − 4.79378e21i | − 0.594155i | ||||||||
\(123\) | 8.57702e21i | 0.975737i | ||||||||
\(124\) | 4.00896e21 | 0.418894 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.80328e21 | −0.247614 | ||||||||
\(127\) | − 5.53783e21i | − 0.450195i | −0.974336 | − | 0.225097i | \(-0.927730\pi\) | ||||
0.974336 | − | 0.225097i | \(-0.0722700\pi\) | |||||||
\(128\) | − 7.07226e21i | − 0.529485i | ||||||||
\(129\) | −7.36600e21 | −0.508206 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.54630e22 | −1.49472 | −0.747362 | − | 0.664417i | \(-0.768680\pi\) | ||||
−0.747362 | + | 0.664417i | \(0.768680\pi\) | |||||||
\(132\) | 1.69123e21i | 0.0916594i | ||||||||
\(133\) | 2.64878e22i | 1.32619i | ||||||||
\(134\) | −3.58433e21 | −0.165885 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.73926e22 | −1.08511 | ||||||||
\(137\) | 4.82088e22i | 1.76832i | 0.467188 | + | 0.884158i | \(0.345267\pi\) | ||||
−0.467188 | + | 0.884158i | \(0.654733\pi\) | |||||||
\(138\) | − 3.37178e21i | − 0.114585i | ||||||||
\(139\) | 2.18194e22 | 0.687363 | 0.343682 | − | 0.939086i | \(-0.388326\pi\) | ||||
0.343682 | + | 0.939086i | \(0.388326\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.53064e22 | 0.686166 | ||||||||
\(142\) | 1.27486e22i | 0.320948i | ||||||||
\(143\) | 4.41316e22i | 1.03210i | ||||||||
\(144\) | 1.10294e22 | 0.239743 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.19716e22 | 0.413197 | ||||||||
\(147\) | 9.39035e21i | 0.164380i | ||||||||
\(148\) | 8.51565e21i | 0.138826i | ||||||||
\(149\) | −4.84140e22 | −0.735386 | −0.367693 | − | 0.929947i | \(-0.619852\pi\) | ||||
−0.367693 | + | 0.929947i | \(0.619852\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.22948e23 | −1.62354 | −0.811770 | − | 0.583977i | \(-0.801496\pi\) | ||||
−0.811770 | + | 0.583977i | \(0.801496\pi\) | |||||||
\(152\) | − 1.37331e23i | − 1.69204i | ||||||||
\(153\) | − 2.91452e22i | − 0.335202i | ||||||||
\(154\) | 4.80441e22 | 0.516027 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.09004e22 | −0.196040 | ||||||||
\(157\) | − 5.89828e22i | − 0.517344i | −0.965965 | − | 0.258672i | \(-0.916715\pi\) | ||||
0.965965 | − | 0.258672i | \(-0.0832848\pi\) | |||||||
\(158\) | 4.17552e22i | 0.342619i | ||||||||
\(159\) | 2.81674e22 | 0.216310 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.83755e22 | 0.191105 | ||||||||
\(162\) | 1.54640e22i | 0.0975920i | ||||||||
\(163\) | − 3.18244e22i | − 0.188274i | −0.995559 | − | 0.0941369i | \(-0.969991\pi\) | ||||
0.995559 | − | 0.0941369i | \(-0.0300091\pi\) | |||||||
\(164\) | 6.96170e22 | 0.386238 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.88252e20 | −0.00189661 | ||||||||
\(167\) | 3.62822e22i | 0.166407i | 0.996533 | + | 0.0832033i | \(0.0265151\pi\) | ||||
−0.996533 | + | 0.0832033i | \(0.973485\pi\) | |||||||
\(168\) | 1.22313e23i | 0.526896i | ||||||||
\(169\) | −2.98317e23 | −1.20744 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.46118e23 | 0.522689 | ||||||||
\(172\) | 5.97875e22i | 0.201169i | ||||||||
\(173\) | 3.21510e23i | 1.01791i | 0.860792 | + | 0.508956i | \(0.169969\pi\) | ||||
−0.860792 | + | 0.508956i | \(0.830031\pi\) | |||||||
\(174\) | −2.07800e23 | −0.619267 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.89028e23 | −0.499625 | ||||||||
\(177\) | − 9.56351e22i | − 0.238176i | ||||||||
\(178\) | − 2.98392e23i | − 0.700449i | ||||||||
\(179\) | 1.80418e23 | 0.399321 | 0.199661 | − | 0.979865i | \(-0.436016\pi\) | ||||
0.199661 | + | 0.979865i | \(0.436016\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.36646e21 | −0.0125393 | −0.00626965 | − | 0.999980i | \(-0.501996\pi\) | ||||
−0.00626965 | + | 0.999980i | \(0.501996\pi\) | |||||||
\(182\) | 5.93733e23i | 1.10368i | ||||||||
\(183\) | − 2.22545e23i | − 0.390555i | ||||||||
\(184\) | −1.47118e23 | −0.243825 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −6.28240e23 | −0.929479 | ||||||||
\(187\) | 4.99507e23i | 0.698561i | ||||||||
\(188\) | − 2.05404e23i | − 0.271613i | ||||||||
\(189\) | −1.30139e23 | −0.162764 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.17882e23 | 0.915883 | 0.457942 | − | 0.888982i | \(-0.348587\pi\) | ||||
0.457942 | + | 0.888982i | \(0.348587\pi\) | |||||||
\(192\) | − 6.05707e23i | − 0.642096i | ||||||||
\(193\) | − 1.80064e23i | − 0.180748i | −0.995908 | − | 0.0903742i | \(-0.971194\pi\) | ||||
0.995908 | − | 0.0903742i | \(-0.0288063\pi\) | |||||||
\(194\) | −7.53107e23 | −0.716042 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 7.62185e22 | 0.0650686 | ||||||||
\(197\) | − 1.65216e24i | − 1.33708i | −0.743675 | − | 0.668541i | \(-0.766919\pi\) | ||||
0.743675 | − | 0.668541i | \(-0.233081\pi\) | |||||||
\(198\) | − 2.65031e23i | − 0.203382i | ||||||||
\(199\) | 1.52537e24 | 1.11024 | 0.555120 | − | 0.831770i | \(-0.312672\pi\) | ||||
0.555120 | + | 0.831770i | \(0.312672\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.66398e23 | −0.109041 | ||||||||
\(202\) | − 2.11436e24i | − 1.31520i | ||||||||
\(203\) | − 1.74876e24i | − 1.03281i | ||||||||
\(204\) | −2.36562e23 | −0.132687 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.49987e24 | −0.759361 | ||||||||
\(207\) | − 1.56531e23i | − 0.0753202i | ||||||||
\(208\) | − 2.33603e24i | − 1.06859i | ||||||||
\(209\) | −2.50425e24 | −1.08928 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.35748e24 | 0.534277 | 0.267138 | − | 0.963658i | \(-0.413922\pi\) | ||||
0.267138 | + | 0.963658i | \(0.413922\pi\) | |||||||
\(212\) | − 2.28626e23i | − 0.0856247i | ||||||||
\(213\) | 5.91838e23i | 0.210968i | ||||||||
\(214\) | −1.10553e24 | −0.375169 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 6.74728e23 | 0.207665 | ||||||||
\(217\) | − 5.28701e24i | − 1.55018i | ||||||||
\(218\) | − 5.24072e23i | − 0.146419i | ||||||||
\(219\) | 1.02001e24 | 0.271606 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.17294e24 | −1.49408 | ||||||||
\(222\) | − 1.33448e24i | − 0.308038i | ||||||||
\(223\) | 4.73192e24i | 1.04192i | 0.853580 | + | 0.520962i | \(0.174427\pi\) | ||||
−0.853580 | + | 0.520962i | \(0.825573\pi\) | |||||||
\(224\) | 1.80087e24 | 0.378336 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.12828e24 | −0.598642 | ||||||||
\(227\) | − 8.00226e24i | − 1.46198i | −0.682389 | − | 0.730989i | \(-0.739059\pi\) | ||||
0.682389 | − | 0.730989i | \(-0.260941\pi\) | |||||||
\(228\) | − 1.18599e24i | − 0.206902i | ||||||||
\(229\) | −2.72111e24 | −0.453391 | −0.226696 | − | 0.973966i | \(-0.572792\pi\) | ||||
−0.226696 | + | 0.973966i | \(0.572792\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.23039e24 | 0.339200 | ||||||||
\(232\) | 9.06674e24i | 1.31773i | ||||||||
\(233\) | − 6.60115e24i | − 0.917028i | −0.888687 | − | 0.458514i | \(-0.848382\pi\) | ||||
0.888687 | − | 0.458514i | \(-0.151618\pi\) | |||||||
\(234\) | 3.27527e24 | 0.434991 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −7.76240e23 | −0.0942801 | ||||||||
\(237\) | 1.93843e24i | 0.225213i | ||||||||
\(238\) | 6.72021e24i | 0.747007i | ||||||||
\(239\) | −9.92224e24 | −1.05544 | −0.527718 | − | 0.849420i | \(-0.676952\pi\) | ||||
−0.527718 | + | 0.849420i | \(0.676952\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.54177e25 | −1.50259 | −0.751295 | − | 0.659966i | \(-0.770571\pi\) | ||||
−0.751295 | + | 0.659966i | \(0.770571\pi\) | |||||||
\(242\) | − 4.87054e24i | − 0.454481i | ||||||||
\(243\) | 7.17898e23i | 0.0641500i | ||||||||
\(244\) | −1.80633e24 | −0.154598 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.09096e25 | −0.857018 | ||||||||
\(247\) | − 3.09477e25i | − 2.32975i | ||||||||
\(248\) | 2.74114e25i | 1.97783i | ||||||||
\(249\) | −1.80241e22 | −0.00124670 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.00009e25 | −0.636014 | −0.318007 | − | 0.948088i | \(-0.603014\pi\) | ||||
−0.318007 | + | 0.948088i | \(0.603014\pi\) | |||||||
\(252\) | 1.05630e24i | 0.0644287i | ||||||||
\(253\) | 2.68271e24i | 0.156967i | ||||||||
\(254\) | 7.04387e24 | 0.395419 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.25164e25 | −0.647080 | ||||||||
\(257\) | 3.06596e25i | 1.52149i | 0.649052 | + | 0.760744i | \(0.275166\pi\) | ||||
−0.649052 | + | 0.760744i | \(0.724834\pi\) | |||||||
\(258\) | − 9.36923e24i | − 0.446372i | ||||||||
\(259\) | 1.12304e25 | 0.513746 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.64685e24 | −0.407062 | ||||||||
\(262\) | − 3.23878e25i | − 1.31286i | ||||||||
\(263\) | − 2.33455e25i | − 0.909216i | −0.890692 | − | 0.454608i | \(-0.849779\pi\) | ||||
0.890692 | − | 0.454608i | \(-0.150221\pi\) | |||||||
\(264\) | −1.15639e25 | −0.432775 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −3.36914e25 | −1.16483 | ||||||||
\(267\) | − 1.38525e25i | − 0.460425i | ||||||||
\(268\) | 1.35060e24i | 0.0431631i | ||||||||
\(269\) | −2.29737e25 | −0.706043 | −0.353022 | − | 0.935615i | \(-0.614846\pi\) | ||||
−0.353022 | + | 0.935615i | \(0.614846\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.02085e25 | −1.14325 | −0.571624 | − | 0.820516i | \(-0.693686\pi\) | ||||
−0.571624 | + | 0.820516i | \(0.693686\pi\) | |||||||
\(272\) | − 2.64405e25i | − 0.723263i | ||||||||
\(273\) | 2.75633e25i | 0.725477i | ||||||||
\(274\) | −6.13194e25 | −1.55316 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.27051e24 | −0.0298149 | ||||||||
\(277\) | 4.48722e25i | 1.01377i | 0.862013 | + | 0.506886i | \(0.169203\pi\) | ||||
−0.862013 | + | 0.506886i | \(0.830797\pi\) | |||||||
\(278\) | 2.77532e25i | 0.603731i | ||||||||
\(279\) | −2.91653e25 | −0.610973 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.06489e25 | −1.17871 | −0.589355 | − | 0.807874i | \(-0.700618\pi\) | ||||
−0.589355 | + | 0.807874i | \(0.700618\pi\) | |||||||
\(282\) | 3.21886e25i | 0.602679i | ||||||||
\(283\) | 1.04229e26i | 1.88032i | 0.340739 | + | 0.940158i | \(0.389323\pi\) | ||||
−0.340739 | + | 0.940158i | \(0.610677\pi\) | |||||||
\(284\) | 4.80376e24 | 0.0835100 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5.61334e25 | −0.906521 | ||||||||
\(287\) | − 9.18107e25i | − 1.42933i | ||||||||
\(288\) | − 9.93433e24i | − 0.149114i | ||||||||
\(289\) | −7.76980e23 | −0.0112456 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.49621e25 | −0.470675 | ||||||||
\(292\) | − 8.27907e24i | − 0.107513i | ||||||||
\(293\) | 6.24634e25i | 0.782556i | 0.920273 | + | 0.391278i | \(0.127967\pi\) | ||||
−0.920273 | + | 0.391278i | \(0.872033\pi\) | |||||||
\(294\) | −1.19441e25 | −0.144380 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −5.82261e25 | −0.655472 | ||||||||
\(297\) | − 1.23037e25i | − 0.133689i | ||||||||
\(298\) | − 6.15805e25i | − 0.645911i | ||||||||
\(299\) | −3.31532e25 | −0.335720 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.88476e25 | 0.744458 | ||||||||
\(302\) | − 1.56384e26i | − 1.42600i | ||||||||
\(303\) | − 9.81568e25i | − 0.864516i | ||||||||
\(304\) | 1.32558e26 | 1.12780 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 3.70714e25 | 0.294418 | ||||||||
\(307\) | − 7.14411e25i | − 0.548271i | −0.961691 | − | 0.274135i | \(-0.911608\pi\) | ||||
0.961691 | − | 0.274135i | \(-0.0883917\pi\) | |||||||
\(308\) | − 1.81034e25i | − 0.134269i | ||||||||
\(309\) | −6.96297e25 | −0.499150 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.01915e25 | −0.403228 | −0.201614 | − | 0.979465i | \(-0.564619\pi\) | ||||
−0.201614 | + | 0.979465i | \(0.564619\pi\) | |||||||
\(312\) | − 1.42907e26i | − 0.925615i | ||||||||
\(313\) | − 1.69049e26i | − 1.05876i | −0.848385 | − | 0.529379i | \(-0.822425\pi\) | ||||
0.848385 | − | 0.529379i | \(-0.177575\pi\) | |||||||
\(314\) | 7.50235e25 | 0.454398 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.57337e25 | 0.0891488 | ||||||||
\(317\) | 5.71691e25i | 0.313357i | 0.987650 | + | 0.156678i | \(0.0500786\pi\) | ||||
−0.987650 | + | 0.156678i | \(0.949921\pi\) | |||||||
\(318\) | 3.58277e25i | 0.189991i | ||||||||
\(319\) | 1.65333e26 | 0.848316 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.13230e25 | −0.246609 | ||||||||
\(322\) | 3.60924e25i | 0.167853i | ||||||||
\(323\) | − 3.50283e26i | − 1.57686i | ||||||||
\(324\) | 5.82695e24 | 0.0253933 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4.04792e25 | 0.165366 | ||||||||
\(327\) | − 2.43294e25i | − 0.0962454i | ||||||||
\(328\) | 4.76009e26i | 1.82364i | ||||||||
\(329\) | −2.70886e26 | −1.00515 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.67957e25 | 0.232571 | 0.116285 | − | 0.993216i | \(-0.462901\pi\) | ||||
0.116285 | + | 0.993216i | \(0.462901\pi\) | |||||||
\(332\) | 1.46296e23i | 0 0.000493495i | ||||||||
\(333\) | − 6.19515e25i | − 0.202482i | ||||||||
\(334\) | −4.61493e25 | −0.146160 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.18062e26 | −0.351194 | ||||||||
\(337\) | − 3.55365e26i | − 1.02461i | −0.858802 | − | 0.512307i | \(-0.828791\pi\) | ||||
0.858802 | − | 0.512307i | \(-0.171209\pi\) | |||||||
\(338\) | − 3.79446e26i | − 1.06053i | ||||||||
\(339\) | −1.45227e26 | −0.393504 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.99851e26 | 1.27327 | ||||||||
\(342\) | 1.85855e26i | 0.459093i | ||||||||
\(343\) | − 4.53560e26i | − 1.08654i | ||||||||
\(344\) | −4.08799e26 | −0.949832 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.08947e26 | −0.894062 | ||||||||
\(347\) | 3.94238e25i | 0.0836179i | 0.999126 | + | 0.0418090i | \(0.0133121\pi\) | ||||
−0.999126 | + | 0.0418090i | \(0.986688\pi\) | |||||||
\(348\) | 7.83004e25i | 0.161132i | ||||||||
\(349\) | 5.84299e26 | 1.16672 | 0.583362 | − | 0.812212i | \(-0.301737\pi\) | ||||
0.583362 | + | 0.812212i | \(0.301737\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.52050e26 | 0.285932 | ||||||||
\(352\) | 1.70260e26i | 0.310753i | ||||||||
\(353\) | 4.96062e26i | 0.878823i | 0.898286 | + | 0.439412i | \(0.144813\pi\) | ||||
−0.898286 | + | 0.439412i | \(0.855187\pi\) | |||||||
\(354\) | 1.21644e26 | 0.209197 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.12436e26 | −0.182256 | ||||||||
\(357\) | 3.11978e26i | 0.491029i | ||||||||
\(358\) | 2.29483e26i | 0.350735i | ||||||||
\(359\) | 3.35136e26 | 0.497426 | 0.248713 | − | 0.968577i | \(-0.419992\pi\) | ||||
0.248713 | + | 0.968577i | \(0.419992\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.04192e27 | 1.45884 | ||||||||
\(362\) | − 8.09785e24i | − 0.0110136i | ||||||||
\(363\) | − 2.26109e26i | − 0.298743i | ||||||||
\(364\) | 2.23723e26 | 0.287174 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2.83068e26 | 0.343035 | ||||||||
\(367\) | − 9.70198e25i | − 0.114253i | −0.998367 | − | 0.0571264i | \(-0.981806\pi\) | ||||
0.998367 | − | 0.0571264i | \(-0.0181938\pi\) | |||||||
\(368\) | − 1.42005e26i | − 0.162518i | ||||||||
\(369\) | −5.06465e26 | −0.563342 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.01511e26 | −0.316867 | ||||||||
\(372\) | 2.36725e26i | 0.241849i | ||||||||
\(373\) | 1.03252e27i | 1.02554i | 0.858525 | + | 0.512771i | \(0.171381\pi\) | ||||
−0.858525 | + | 0.512771i | \(0.828619\pi\) | |||||||
\(374\) | −6.35350e26 | −0.613566 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.40446e27 | 1.28244 | ||||||||
\(377\) | 2.04320e27i | 1.81437i | ||||||||
\(378\) | − 1.65531e26i | − 0.142960i | ||||||||
\(379\) | −2.20881e26 | −0.185544 | −0.0927721 | − | 0.995687i | \(-0.529573\pi\) | ||||
−0.0927721 | + | 0.995687i | \(0.529573\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.27003e26 | 0.259920 | ||||||||
\(382\) | 1.04031e27i | 0.804446i | ||||||||
\(383\) | − 1.59547e27i | − 1.20033i | −0.799876 | − | 0.600165i | \(-0.795101\pi\) | ||||
0.799876 | − | 0.600165i | \(-0.204899\pi\) | |||||||
\(384\) | 4.17610e26 | 0.305698 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.29033e26 | 0.158756 | ||||||||
\(387\) | − 4.34955e26i | − 0.293413i | ||||||||
\(388\) | 2.83776e26i | 0.186313i | ||||||||
\(389\) | 3.60474e26 | 0.230358 | 0.115179 | − | 0.993345i | \(-0.463256\pi\) | ||||
0.115179 | + | 0.993345i | \(0.463256\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.75247e26 | −0.227228 | ||||||||
\(392\) | 5.21147e26i | 0.307225i | ||||||||
\(393\) | − 1.50357e27i | − 0.862980i | ||||||||
\(394\) | 2.10148e27 | 1.17440 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −9.98656e25 | −0.0529196 | ||||||||
\(397\) | 1.47191e27i | 0.759595i | 0.925070 | + | 0.379798i | \(0.124006\pi\) | ||||
−0.925070 | + | 0.379798i | \(0.875994\pi\) | |||||||
\(398\) | 1.94020e27i | 0.975156i | ||||||||
\(399\) | −1.56408e27 | −0.765674 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.00401e27 | 0.466360 | 0.233180 | − | 0.972434i | \(-0.425087\pi\) | ||||
0.233180 | + | 0.972434i | \(0.425087\pi\) | |||||||
\(402\) | − 2.11651e26i | − 0.0957740i | ||||||||
\(403\) | 6.17719e27i | 2.72325i | ||||||||
\(404\) | −7.96708e26 | −0.342212 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.22434e27 | 0.907148 | ||||||||
\(407\) | 1.06176e27i | 0.421973i | ||||||||
\(408\) | − 1.61750e27i | − 0.626489i | ||||||||
\(409\) | 4.41838e27 | 1.66789 | 0.833947 | − | 0.551845i | \(-0.186076\pi\) | ||||
0.833947 | + | 0.551845i | \(0.186076\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.84668e27 | −1.02094 | ||||||||
\(412\) | 5.65163e26i | 0.197584i | ||||||||
\(413\) | 1.02370e27i | 0.348898i | ||||||||
\(414\) | 1.99100e26 | 0.0661559 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.10409e27 | −0.664635 | ||||||||
\(417\) | 1.28841e27i | 0.396849i | ||||||||
\(418\) | − 3.18529e27i | − 0.956749i | ||||||||
\(419\) | 2.36639e27 | 0.693169 | 0.346584 | − | 0.938019i | \(-0.387341\pi\) | ||||
0.346584 | + | 0.938019i | \(0.387341\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.72067e27 | 0.758078 | 0.379039 | − | 0.925381i | \(-0.376255\pi\) | ||||
0.379039 | + | 0.925381i | \(0.376255\pi\) | |||||||
\(422\) | 1.72665e27i | 0.469271i | ||||||||
\(423\) | 1.49432e27i | 0.396158i | ||||||||
\(424\) | 1.56324e27 | 0.404281 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −7.52791e26 | −0.185299 | ||||||||
\(427\) | 2.38218e27i | 0.572114i | ||||||||
\(428\) | 4.16573e26i | 0.0976183i | ||||||||
\(429\) | −2.60593e27 | −0.595883 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.87397e27 | 1.93244 | 0.966222 | − | 0.257713i | \(-0.0829688\pi\) | ||||
0.966222 | + | 0.257713i | \(0.0829688\pi\) | |||||||
\(432\) | 6.51276e26i | 0.138416i | ||||||||
\(433\) | − 3.39994e27i | − 0.705258i | −0.935763 | − | 0.352629i | \(-0.885288\pi\) | ||||
0.935763 | − | 0.352629i | \(-0.114712\pi\) | |||||||
\(434\) | 6.72484e27 | 1.36157 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.97474e26 | −0.0380980 | ||||||||
\(437\) | − 1.88128e27i | − 0.354322i | ||||||||
\(438\) | 1.29740e27i | 0.238559i | ||||||||
\(439\) | −2.29516e27 | −0.412037 | −0.206018 | − | 0.978548i | \(-0.566051\pi\) | ||||
−0.206018 | + | 0.978548i | \(0.566051\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.54491e26 | −0.0949050 | ||||||||
\(442\) | − 7.85170e27i | − 1.31229i | ||||||||
\(443\) | − 5.65265e27i | − 0.922599i | −0.887245 | − | 0.461299i | \(-0.847383\pi\) | ||||
0.887245 | − | 0.461299i | \(-0.152617\pi\) | |||||||
\(444\) | −5.02841e26 | −0.0801510 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −6.01879e27 | −0.915152 | ||||||||
\(447\) | − 2.85880e27i | − 0.424576i | ||||||||
\(448\) | 6.48364e27i | 0.940589i | ||||||||
\(449\) | −1.23324e28 | −1.74768 | −0.873839 | − | 0.486216i | \(-0.838377\pi\) | ||||
−0.873839 | + | 0.486216i | \(0.838377\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.68008e27 | 1.17400 | ||||||||
\(452\) | 1.17876e27i | 0.155766i | ||||||||
\(453\) | − 7.25995e27i | − 0.937351i | ||||||||
\(454\) | 1.01785e28 | 1.28410 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 8.10926e27 | 0.976900 | ||||||||
\(457\) | 7.62646e27i | 0.897848i | 0.893570 | + | 0.448924i | \(0.148193\pi\) | ||||
−0.893570 | + | 0.448924i | \(0.851807\pi\) | |||||||
\(458\) | − 3.46113e27i | − 0.398226i | ||||||||
\(459\) | 1.72100e27 | 0.193529 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.04851e26 | −0.0972114 | −0.0486057 | − | 0.998818i | \(-0.515478\pi\) | ||||
−0.0486057 | + | 0.998818i | \(0.515478\pi\) | |||||||
\(462\) | 2.83696e27i | 0.297929i | ||||||||
\(463\) | − 1.19705e27i | − 0.122889i | −0.998111 | − | 0.0614443i | \(-0.980429\pi\) | ||||
0.998111 | − | 0.0614443i | \(-0.0195707\pi\) | |||||||
\(464\) | −8.75161e27 | −0.878313 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 8.39637e27 | 0.805452 | ||||||||
\(467\) | 1.16951e28i | 1.09693i | 0.836174 | + | 0.548464i | \(0.184787\pi\) | ||||
−0.836174 | + | 0.548464i | \(0.815213\pi\) | |||||||
\(468\) | − 1.23415e27i | − 0.113184i | ||||||||
\(469\) | 1.78117e27 | 0.159732 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.48288e27 | 0.298689 | ||||||||
\(472\) | − 5.30757e27i | − 0.445148i | ||||||||
\(473\) | 7.45451e27i | 0.611472i | ||||||||
\(474\) | −2.46560e27 | −0.197811 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2.53222e27 | 0.194370 | ||||||||
\(477\) | 1.66326e27i | 0.124887i | ||||||||
\(478\) | − 1.26206e28i | − 0.927019i | ||||||||
\(479\) | −2.04856e28 | −1.47206 | −0.736029 | − | 0.676950i | \(-0.763301\pi\) | ||||
−0.736029 | + | 0.676950i | \(0.763301\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.31213e28 | −0.902513 | ||||||||
\(482\) | − 1.96106e28i | − 1.31977i | ||||||||
\(483\) | 1.67555e27i | 0.110335i | ||||||||
\(484\) | −1.83525e27 | −0.118255 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −9.13134e26 | −0.0563448 | ||||||||
\(487\) | 3.75693e27i | 0.226871i | 0.993545 | + | 0.113436i | \(0.0361856\pi\) | ||||
−0.993545 | + | 0.113436i | \(0.963814\pi\) | |||||||
\(488\) | − 1.23508e28i | − 0.729942i | ||||||||
\(489\) | 1.87920e27 | 0.108700 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.53173e28 | −0.848841 | −0.424420 | − | 0.905465i | \(-0.639522\pi\) | ||||
−0.424420 | + | 0.905465i | \(0.639522\pi\) | |||||||
\(492\) | 4.11081e27i | 0.222995i | ||||||||
\(493\) | 2.31261e28i | 1.22803i | ||||||||
\(494\) | 3.93640e28 | 2.04629 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.64587e28 | −1.31829 | ||||||||
\(497\) | − 6.33518e27i | − 0.309042i | ||||||||
\(498\) | − 2.29259e25i | − 0.00109501i | ||||||||
\(499\) | −3.84836e27 | −0.179978 | −0.0899890 | − | 0.995943i | \(-0.528683\pi\) | ||||
−0.0899890 | + | 0.995943i | \(0.528683\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.14243e27 | −0.0960749 | ||||||||
\(502\) | − 1.27208e28i | − 0.558629i | ||||||||
\(503\) | − 2.25177e28i | − 0.968411i | −0.874954 | − | 0.484205i | \(-0.839109\pi\) | ||||
0.874954 | − | 0.484205i | \(-0.160891\pi\) | |||||||
\(504\) | −7.22246e27 | −0.304204 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −3.41229e27 | −0.137869 | ||||||||
\(507\) | − 1.76153e28i | − 0.697119i | ||||||||
\(508\) | − 2.65418e27i | − 0.102887i | ||||||||
\(509\) | −2.09122e27 | −0.0794078 | −0.0397039 | − | 0.999211i | \(-0.512641\pi\) | ||||
−0.0397039 | + | 0.999211i | \(0.512641\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.09184e28 | −0.397869 | ||||||||
\(512\) | − 3.07519e28i | − 1.09783i | ||||||||
\(513\) | 8.62810e27i | 0.301775i | ||||||||
\(514\) | −3.89976e28 | −1.33637 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −3.53039e27 | −0.116145 | ||||||||
\(517\) | − 2.56104e28i | − 0.825594i | ||||||||
\(518\) | 1.42846e28i | 0.451237i | ||||||||
\(519\) | −1.89849e28 | −0.587692 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.76486e27 | −0.111932 | −0.0559659 | − | 0.998433i | \(-0.517824\pi\) | ||||
−0.0559659 | + | 0.998433i | \(0.517824\pi\) | |||||||
\(522\) | − 1.22704e28i | − 0.357534i | ||||||||
\(523\) | − 1.74944e28i | − 0.499611i | −0.968296 | − | 0.249806i | \(-0.919633\pi\) | ||||
0.968296 | − | 0.249806i | \(-0.0803667\pi\) | |||||||
\(524\) | −1.22040e28 | −0.341604 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.96944e28 | 0.798590 | ||||||||
\(527\) | 6.99170e28i | 1.84320i | ||||||||
\(528\) | − 1.11619e28i | − 0.288459i | ||||||||
\(529\) | 3.74562e28 | 0.948942 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.64716e27 | 0.137511 | ||||||||
\(532\) | 1.26952e28i | 0.303086i | ||||||||
\(533\) | 1.07269e29i | 2.51095i | ||||||||
\(534\) | 1.76197e28 | 0.404404 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −9.23480e27 | −0.203797 | ||||||||
\(537\) | 1.06535e28i | 0.230548i | ||||||||
\(538\) | − 2.92215e28i | − 0.620138i | ||||||||
\(539\) | 9.50317e27 | 0.197782 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.99960e28 | −1.40121 | −0.700603 | − | 0.713552i | \(-0.747085\pi\) | ||||
−0.700603 | + | 0.713552i | \(0.747085\pi\) | |||||||
\(542\) | − 5.11434e28i | − 1.00415i | ||||||||
\(543\) | − 3.75933e26i | − 0.00723956i | ||||||||
\(544\) | −2.38153e28 | −0.449849 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −3.50593e28 | −0.637207 | ||||||||
\(547\) | − 3.00896e28i | − 0.536476i | −0.963353 | − | 0.268238i | \(-0.913559\pi\) | ||||
0.963353 | − | 0.268238i | \(-0.0864413\pi\) | |||||||
\(548\) | 2.31056e28i | 0.404130i | ||||||||
\(549\) | 1.31411e28 | 0.225487 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.15941e29 | −1.91490 | ||||||||
\(552\) | − 8.68717e27i | − 0.140773i | ||||||||
\(553\) | − 2.07495e28i | − 0.329909i | ||||||||
\(554\) | −5.70754e28 | −0.890424 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.04576e28 | 0.157090 | ||||||||
\(557\) | − 1.17263e29i | − 1.72855i | −0.503017 | − | 0.864277i | \(-0.667777\pi\) | ||||
0.503017 | − | 0.864277i | \(-0.332223\pi\) | |||||||
\(558\) | − 3.70969e28i | − 0.536635i | ||||||||
\(559\) | −9.21233e28 | −1.30781 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.94954e28 | −0.403315 | ||||||||
\(562\) | − 7.71427e28i | − 1.03529i | ||||||||
\(563\) | 6.46986e28i | 0.852230i | 0.904669 | + | 0.426115i | \(0.140118\pi\) | ||||
−0.904669 | + | 0.426115i | \(0.859882\pi\) | |||||||
\(564\) | 1.21289e28 | 0.156816 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.32575e29 | −1.65153 | ||||||||
\(567\) | − 7.68456e27i | − 0.0939717i | ||||||||
\(568\) | 3.28459e28i | 0.394297i | ||||||||
\(569\) | 1.35009e29 | 1.59105 | 0.795527 | − | 0.605918i | \(-0.207194\pi\) | ||||
0.795527 | + | 0.605918i | \(0.207194\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.55750e28 | 0.290494 | 0.145247 | − | 0.989395i | \(-0.453602\pi\) | ||||
0.145247 | + | 0.989395i | \(0.453602\pi\) | |||||||
\(572\) | 2.11515e28i | 0.235875i | ||||||||
\(573\) | 4.82951e28i | 0.528786i | ||||||||
\(574\) | 1.16779e29 | 1.25542 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 3.57664e28 | 0.370714 | ||||||||
\(577\) | 1.52580e29i | 1.55293i | 0.630160 | + | 0.776465i | \(0.282989\pi\) | ||||
−0.630160 | + | 0.776465i | \(0.717011\pi\) | |||||||
\(578\) | − 9.88284e26i | − 0.00987733i | ||||||||
\(579\) | 1.06326e28 | 0.104355 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.92935e26 | 0.00182625 | ||||||||
\(582\) | − 4.44702e28i | − 0.413407i | ||||||||
\(583\) | − 2.85058e28i | − 0.260264i | ||||||||
\(584\) | 5.66084e28 | 0.507629 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.94506e28 | −0.687341 | ||||||||
\(587\) | 1.08485e29i | 0.921868i | 0.887434 | + | 0.460934i | \(0.152486\pi\) | ||||
−0.887434 | + | 0.460934i | \(0.847514\pi\) | |||||||
\(588\) | 4.50063e27i | 0.0375674i | ||||||||
\(589\) | −3.50525e29 | −2.87414 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.75587e28 | 0.771965 | ||||||||
\(592\) | − 5.62023e28i | − 0.436894i | ||||||||
\(593\) | 8.82363e28i | 0.673865i | 0.941529 | + | 0.336933i | \(0.109389\pi\) | ||||
−0.941529 | + | 0.336933i | \(0.890611\pi\) | |||||||
\(594\) | 1.56498e28 | 0.117422 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.32040e28 | −0.168065 | ||||||||
\(597\) | 9.00714e28i | 0.640998i | ||||||||
\(598\) | − 4.21694e28i | − 0.294873i | ||||||||
\(599\) | −9.23342e28 | −0.634426 | −0.317213 | − | 0.948354i | \(-0.602747\pi\) | ||||
−0.317213 | + | 0.948354i | \(0.602747\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.30699e28 | −0.484793 | −0.242397 | − | 0.970177i | \(-0.577934\pi\) | ||||
−0.242397 | + | 0.970177i | \(0.577934\pi\) | |||||||
\(602\) | 1.00291e29i | 0.653878i | ||||||||
\(603\) | − 9.82566e27i | − 0.0629550i | ||||||||
\(604\) | −5.89267e28 | −0.371043 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1.24851e29 | 0.759329 | ||||||||
\(607\) | − 8.07544e28i | − 0.482709i | −0.970437 | − | 0.241354i | \(-0.922408\pi\) | ||||
0.970437 | − | 0.241354i | \(-0.0775916\pi\) | |||||||
\(608\) | − 1.19396e29i | − 0.701461i | ||||||||
\(609\) | 1.03262e29 | 0.596294 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.16496e29 | 1.76577 | ||||||||
\(612\) | − 1.39688e28i | − 0.0766070i | ||||||||
\(613\) | − 2.21326e29i | − 1.19316i | −0.802555 | − | 0.596578i | \(-0.796527\pi\) | ||||
0.802555 | − | 0.596578i | \(-0.203473\pi\) | |||||||
\(614\) | 9.08699e28 | 0.481562 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.23783e29 | 0.633960 | ||||||||
\(617\) | 2.16026e29i | 1.08771i | 0.839180 | + | 0.543854i | \(0.183035\pi\) | ||||
−0.839180 | + | 0.543854i | \(0.816965\pi\) | |||||||
\(618\) | − 8.85659e28i | − 0.438417i | ||||||||
\(619\) | 2.09908e29 | 1.02159 | 0.510795 | − | 0.859702i | \(-0.329351\pi\) | ||||
0.510795 | + | 0.859702i | \(0.329351\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 9.24299e27 | 0.0434861 | ||||||||
\(622\) | − 7.65609e28i | − 0.354167i | ||||||||
\(623\) | 1.48280e29i | 0.674465i | ||||||||
\(624\) | 1.37940e29 | 0.616953 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 2.15023e29 | 0.929938 | ||||||||
\(627\) | − 1.47873e29i | − 0.628899i | ||||||||
\(628\) | − 2.82694e28i | − 0.118234i | ||||||||
\(629\) | −1.48514e29 | −0.610853 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.81094e28 | 0.191391 | 0.0956955 | − | 0.995411i | \(-0.469492\pi\) | ||||
0.0956955 | + | 0.995411i | \(0.469492\pi\) | |||||||
\(632\) | 1.07580e29i | 0.420921i | ||||||||
\(633\) | 8.01576e28i | 0.308465i | ||||||||
\(634\) | −7.27166e28 | −0.275230 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1.35001e28 | 0.0494354 | ||||||||
\(637\) | 1.17441e29i | 0.423014i | ||||||||
\(638\) | 2.10296e29i | 0.745100i | ||||||||
\(639\) | −3.49474e28 | −0.121802 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.04867e28 | −0.170282 | −0.0851408 | − | 0.996369i | \(-0.527134\pi\) | ||||
−0.0851408 | + | 0.996369i | \(0.527134\pi\) | |||||||
\(642\) | − 6.52806e28i | − 0.216604i | ||||||||
\(643\) | − 3.93930e29i | − 1.28589i | −0.765912 | − | 0.642945i | \(-0.777712\pi\) | ||||
0.765912 | − | 0.642945i | \(-0.222288\pi\) | |||||||
\(644\) | 1.35999e28 | 0.0436751 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.45545e29 | 1.38500 | ||||||||
\(647\) | 1.38475e29i | 0.423523i | 0.977321 | + | 0.211762i | \(0.0679201\pi\) | ||||
−0.977321 | + | 0.211762i | \(0.932080\pi\) | |||||||
\(648\) | 3.98420e28i | 0.119896i | ||||||||
\(649\) | −9.67842e28 | −0.286573 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.12193e29 | 0.894998 | ||||||||
\(652\) | − 1.52528e28i | − 0.0430280i | ||||||||
\(653\) | 1.16655e29i | 0.323830i | 0.986805 | + | 0.161915i | \(0.0517670\pi\) | ||||
−0.986805 | + | 0.161915i | \(0.948233\pi\) | |||||||
\(654\) | 3.09459e28 | 0.0845350 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −4.59464e29 | −1.21552 | ||||||||
\(657\) | 6.02303e28i | 0.156812i | ||||||||
\(658\) | − 3.44555e29i | − 0.882849i | ||||||||
\(659\) | 3.36819e29 | 0.849377 | 0.424688 | − | 0.905340i | \(-0.360384\pi\) | ||||
0.424688 | + | 0.905340i | \(0.360384\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.31449e29 | 1.05394 | 0.526968 | − | 0.849885i | \(-0.323329\pi\) | ||||
0.526968 | + | 0.849885i | \(0.323329\pi\) | |||||||
\(662\) | 8.49612e28i | 0.204273i | ||||||||
\(663\) | − 3.64506e29i | − 0.862606i | ||||||||
\(664\) | −1.00030e27 | −0.00233006 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 7.87995e28 | 0.177846 | ||||||||
\(667\) | 1.24204e29i | 0.275940i | ||||||||
\(668\) | 1.73894e28i | 0.0380305i | ||||||||
\(669\) | −2.79415e29 | −0.601555 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.25219e29 | −0.469915 | ||||||||
\(672\) | 1.06340e29i | 0.218433i | ||||||||
\(673\) | − 1.19710e29i | − 0.242088i | −0.992647 | − | 0.121044i | \(-0.961376\pi\) | ||||
0.992647 | − | 0.121044i | \(-0.0386243\pi\) | |||||||
\(674\) | 4.52008e29 | 0.899948 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.42978e29 | −0.275949 | ||||||||
\(677\) | − 7.71503e29i | − 1.46608i | −0.680188 | − | 0.733038i | \(-0.738102\pi\) | ||||
0.680188 | − | 0.733038i | \(-0.261898\pi\) | |||||||
\(678\) | − 1.84722e29i | − 0.345626i | ||||||||
\(679\) | 3.74243e29 | 0.689479 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.72525e29 | 0.844074 | ||||||||
\(682\) | 6.35788e29i | 1.11835i | ||||||||
\(683\) | 6.40488e29i | 1.10941i | 0.832046 | + | 0.554707i | \(0.187170\pi\) | ||||
−0.832046 | + | 0.554707i | \(0.812830\pi\) | |||||||
\(684\) | 7.00316e28 | 0.119455 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 5.76908e29 | 0.954340 | ||||||||
\(687\) | − 1.60679e29i | − 0.261766i | ||||||||
\(688\) | − 3.94591e29i | − 0.633094i | ||||||||
\(689\) | 3.52277e29 | 0.556650 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.07309e30 | 1.64482 | 0.822408 | − | 0.568898i | \(-0.192630\pi\) | ||||
0.822408 | + | 0.568898i | \(0.192630\pi\) | |||||||
\(692\) | 1.54094e29i | 0.232633i | ||||||||
\(693\) | 1.31702e29i | 0.195837i | ||||||||
\(694\) | −5.01454e28 | −0.0734440 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −5.35382e29 | −0.760794 | ||||||||
\(697\) | 1.21413e30i | 1.69950i | ||||||||
\(698\) | 7.43202e29i | 1.02477i | ||||||||
\(699\) | 3.89791e29 | 0.529446 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.18115e29 | −0.946574 | −0.473287 | − | 0.880908i | \(-0.656933\pi\) | ||||
−0.473287 | + | 0.880908i | \(0.656933\pi\) | |||||||
\(702\) | 1.93401e29i | 0.251142i | ||||||||
\(703\) | − 7.44568e29i | − 0.952518i | ||||||||
\(704\) | −6.12985e29 | −0.772568 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6.30969e29 | −0.771895 | ||||||||
\(707\) | 1.05070e30i | 1.26641i | ||||||||
\(708\) | − 4.58362e28i | − 0.0544327i | ||||||||
\(709\) | −4.24360e29 | −0.496534 | −0.248267 | − | 0.968692i | \(-0.579861\pi\) | ||||
−0.248267 | + | 0.968692i | \(0.579861\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.14463e29 | −0.130027 | ||||||||
\(712\) | − 7.68786e29i | − 0.860529i | ||||||||
\(713\) | 3.75505e29i | 0.414167i | ||||||||
\(714\) | −3.96822e29 | −0.431285 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 8.64710e28 | 0.0912607 | ||||||||
\(717\) | − 5.85898e29i | − 0.609356i | ||||||||
\(718\) | 4.26277e29i | 0.436904i | ||||||||
\(719\) | 5.73272e29 | 0.579038 | 0.289519 | − | 0.957172i | \(-0.406505\pi\) | ||||
0.289519 | + | 0.957172i | \(0.406505\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.45334e29 | 0.731191 | ||||||||
\(722\) | 1.32527e30i | 1.28134i | ||||||||
\(723\) | − 9.10400e29i | − 0.867521i | ||||||||
\(724\) | −3.05133e27 | −0.00286572 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 2.87600e29 | 0.262395 | ||||||||
\(727\) | − 1.42987e30i | − 1.28583i | −0.765937 | − | 0.642916i | \(-0.777725\pi\) | ||||
0.765937 | − | 0.642916i | \(-0.222275\pi\) | |||||||
\(728\) | 1.52971e30i | 1.35591i | ||||||||
\(729\) | −4.23912e28 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.04270e30 | −0.885175 | ||||||||
\(732\) | − 1.06662e29i | − 0.0892572i | ||||||||
\(733\) | 1.99143e30i | 1.64276i | 0.570381 | + | 0.821380i | \(0.306795\pi\) | ||||
−0.570381 | + | 0.821380i | \(0.693205\pi\) | |||||||
\(734\) | 1.23405e29 | 0.100351 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.27905e29 | −0.101081 | ||||||||
\(737\) | 1.68398e29i | 0.131198i | ||||||||
\(738\) | − 6.44200e29i | − 0.494799i | ||||||||
\(739\) | 2.11124e30 | 1.59872 | 0.799359 | − | 0.600854i | \(-0.205173\pi\) | ||||
0.799359 | + | 0.600854i | \(0.205173\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.82743e30 | 1.34508 | ||||||||
\(742\) | − 3.83509e29i | − 0.278313i | ||||||||
\(743\) | 1.11538e30i | 0.798067i | 0.916936 | + | 0.399033i | \(0.130654\pi\) | ||||
−0.916936 | + | 0.399033i | \(0.869346\pi\) | |||||||
\(744\) | −1.61862e30 | −1.14190 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.31331e30 | −0.900763 | ||||||||
\(747\) | − 1.06431e27i | 0 0.000719781i | ||||||||
\(748\) | 2.39405e29i | 0.159649i | ||||||||
\(749\) | 5.49375e29 | 0.361251 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.28371e30 | −1.46023 | −0.730116 | − | 0.683323i | \(-0.760534\pi\) | ||||
−0.730116 | + | 0.683323i | \(0.760534\pi\) | |||||||
\(752\) | 1.35564e30i | 0.854787i | ||||||||
\(753\) | − 5.90546e29i | − 0.367203i | ||||||||
\(754\) | −2.59886e30 | −1.59361 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −6.23732e28 | −0.0371980 | ||||||||
\(757\) | − 9.73411e29i | − 0.572519i | −0.958152 | − | 0.286259i | \(-0.907588\pi\) | ||||
0.958152 | − | 0.286259i | \(-0.0924119\pi\) | |||||||
\(758\) | − 2.80951e29i | − 0.162969i | ||||||||
\(759\) | −1.58412e29 | −0.0906251 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.06985e30 | −1.70836 | −0.854179 | − | 0.519979i | \(-0.825940\pi\) | ||||
−0.854179 | + | 0.519979i | \(0.825940\pi\) | |||||||
\(762\) | 4.15933e29i | 0.228295i | ||||||||
\(763\) | 2.60428e29i | 0.140987i | ||||||||
\(764\) | 3.91996e29 | 0.209316 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.02936e30 | 1.05428 | ||||||||
\(767\) | − 1.19607e30i | − 0.612920i | ||||||||
\(768\) | − 7.39078e29i | − 0.373592i | ||||||||
\(769\) | 7.51816e29 | 0.374874 | 0.187437 | − | 0.982277i | \(-0.439982\pi\) | ||||
0.187437 | + | 0.982277i | \(0.439982\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.81042e30 | −0.878432 | ||||||||
\(772\) | − 8.63013e28i | − 0.0413081i | ||||||||
\(773\) | 1.23771e30i | 0.584434i | 0.956352 | + | 0.292217i | \(0.0943930\pi\) | ||||
−0.956352 | + | 0.292217i | \(0.905607\pi\) | |||||||
\(774\) | 5.53243e29 | 0.257713 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1.94033e30 | −0.879686 | ||||||||
\(777\) | 6.63144e29i | 0.296611i | ||||||||
\(778\) | 4.58507e29i | 0.202330i | ||||||||
\(779\) | −6.08698e30 | −2.65008 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.98949e29 | 0.253836 | ||||||||
\(782\) | − 4.77297e29i | − 0.199580i | ||||||||
\(783\) | − 5.69637e29i | − 0.235017i | ||||||||
\(784\) | −5.03033e29 | −0.204776 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.91247e30 | 0.757979 | ||||||||
\(787\) | − 2.14352e30i | − 0.838288i | −0.907920 | − | 0.419144i | \(-0.862330\pi\) | ||||
0.907920 | − | 0.419144i | \(-0.137670\pi\) | |||||||
\(788\) | − 7.91853e29i | − 0.305576i | ||||||||
\(789\) | 1.37853e30 | 0.524936 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.55454e30 | 0.576434 | ||||||||
\(792\) | − 6.82834e29i | − 0.249862i | ||||||||
\(793\) | − 2.78327e30i | − 1.00505i | ||||||||
\(794\) | −1.87221e30 | −0.667174 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7.31081e29 | 0.253734 | ||||||||
\(797\) | − 3.01280e30i | − 1.03195i | −0.856605 | − | 0.515974i | \(-0.827430\pi\) | ||||
0.856605 | − | 0.515974i | \(-0.172570\pi\) | |||||||
\(798\) | − 1.98944e30i | − 0.672513i | ||||||||
\(799\) | 3.58228e30 | 1.19514 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.17975e29 | 0.265827 | ||||||||
\(802\) | 1.27705e30i | 0.409617i | ||||||||
\(803\) | − 1.03226e30i | − 0.326796i | ||||||||
\(804\) | −7.97518e28 | −0.0249202 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −7.85711e30 | −2.39191 | ||||||||
\(807\) | − 1.35657e30i | − 0.407634i | ||||||||
\(808\) | − 5.44752e30i | − 1.61577i | ||||||||
\(809\) | 5.76883e30 | 1.68900 | 0.844498 | − | 0.535559i | \(-0.179899\pi\) | ||||
0.844498 | + | 0.535559i | \(0.179899\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.98728e30 | 1.13752 | 0.568759 | − | 0.822504i | \(-0.307424\pi\) | ||||
0.568759 | + | 0.822504i | \(0.307424\pi\) | |||||||
\(812\) | − 8.38148e29i | − 0.236038i | ||||||||
\(813\) | − 2.37427e30i | − 0.660055i | ||||||||
\(814\) | −1.35051e30 | −0.370631 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.56129e30 | 0.417576 | ||||||||
\(817\) | − 5.22754e30i | − 1.38027i | ||||||||
\(818\) | 5.61998e30i | 1.46496i | ||||||||
\(819\) | −1.62759e30 | −0.418855 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.09615e30 | −1.02748 | −0.513739 | − | 0.857946i | \(-0.671740\pi\) | ||||
−0.513739 | + | 0.857946i | \(0.671740\pi\) | |||||||
\(822\) | − 3.62085e30i | − 0.896719i | ||||||||
\(823\) | 1.43384e30i | 0.350592i | 0.984516 | + | 0.175296i | \(0.0560882\pi\) | ||||
−0.984516 | + | 0.175296i | \(0.943912\pi\) | |||||||
\(824\) | −3.86432e30 | −0.932905 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.30210e30 | −0.306447 | ||||||||
\(827\) | 3.13142e30i | 0.727668i | 0.931464 | + | 0.363834i | \(0.118532\pi\) | ||||
−0.931464 | + | 0.363834i | \(0.881468\pi\) | |||||||
\(828\) | − 7.50225e28i | − 0.0172136i | ||||||||
\(829\) | 4.44329e30 | 1.00666 | 0.503329 | − | 0.864095i | \(-0.332108\pi\) | ||||
0.503329 | + | 0.864095i | \(0.332108\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.64966e30 | −0.585301 | ||||||||
\(832\) | − 7.57531e30i | − 1.65236i | ||||||||
\(833\) | 1.32926e30i | 0.286311i | ||||||||
\(834\) | −1.63880e30 | −0.348564 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.20024e30 | −0.248944 | ||||||||
\(837\) | − 1.72218e30i | − 0.352745i | ||||||||
\(838\) | 3.00994e30i | 0.608829i | ||||||||
\(839\) | 9.30057e29 | 0.185784 | 0.0928922 | − | 0.995676i | \(-0.470389\pi\) | ||||
0.0928922 | + | 0.995676i | \(0.470389\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.52173e30 | 0.491293 | ||||||||
\(842\) | 3.46057e30i | 0.665842i | ||||||||
\(843\) | − 3.58126e30i | − 0.680528i | ||||||||
\(844\) | 6.50614e29 | 0.122103 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.90070e30 | −0.347957 | ||||||||
\(847\) | 2.42033e30i | 0.437621i | ||||||||
\(848\) | 1.50891e30i | 0.269467i | ||||||||
\(849\) | −6.15462e30 | −1.08560 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.97630e29 | −0.137259 | ||||||||
\(852\) | 2.83657e29i | 0.0482145i | ||||||||
\(853\) | − 2.27471e30i | − 0.381911i | −0.981599 | − | 0.190955i | \(-0.938841\pi\) | ||||
0.981599 | − | 0.190955i | \(-0.0611586\pi\) | |||||||
\(854\) | −3.03003e30 | −0.502503 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.84833e30 | −0.460910 | ||||||||
\(857\) | − 3.05003e30i | − 0.487534i | −0.969834 | − | 0.243767i | \(-0.921617\pi\) | ||||
0.969834 | − | 0.243767i | \(-0.0783832\pi\) | |||||||
\(858\) | − 3.31462e30i | − 0.523380i | ||||||||
\(859\) | −1.34073e30 | −0.209128 | −0.104564 | − | 0.994518i | \(-0.533345\pi\) | ||||
−0.104564 | + | 0.994518i | \(0.533345\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.42133e30 | 0.825225 | ||||||||
\(862\) | 1.12873e31i | 1.69732i | ||||||||
\(863\) | 1.14916e31i | 1.70713i | 0.520985 | + | 0.853566i | \(0.325565\pi\) | ||||
−0.520985 | + | 0.853566i | \(0.674435\pi\) | |||||||
\(864\) | 5.86612e29 | 0.0860908 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 4.32457e30 | 0.619448 | ||||||||
\(867\) | − 4.58799e28i | − 0.00649265i | ||||||||
\(868\) | − 2.53397e30i | − 0.354278i | ||||||||
\(869\) | 1.96173e30 | 0.270976 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.08107e30 | −0.280606 | ||||||||
\(872\) | − 1.35024e30i | − 0.179882i | ||||||||
\(873\) | − 2.06448e30i | − 0.271744i | ||||||||
\(874\) | 2.39290e30 | 0.311211 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4.88871e29 | 0.0620727 | ||||||||
\(877\) | − 9.06320e30i | − 1.13707i | −0.822660 | − | 0.568533i | \(-0.807511\pi\) | ||||
0.822660 | − | 0.568533i | \(-0.192489\pi\) | |||||||
\(878\) | − 2.91934e30i | − 0.361904i | ||||||||
\(879\) | −3.68840e30 | −0.451809 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6.50767e30 | −0.778356 | −0.389178 | − | 0.921163i | \(-0.627241\pi\) | ||||
−0.389178 | + | 0.921163i | \(0.627241\pi\) | |||||||
\(882\) | − 7.05287e29i | − 0.0833577i | ||||||||
\(883\) | 5.90742e30i | 0.689939i | 0.938614 | + | 0.344969i | \(0.112111\pi\) | ||||
−0.938614 | + | 0.344969i | \(0.887889\pi\) | |||||||
\(884\) | −2.95858e30 | −0.341456 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 7.18992e30 | 0.810344 | ||||||||
\(887\) | 3.42312e30i | 0.381263i | 0.981662 | + | 0.190632i | \(0.0610536\pi\) | ||||
−0.981662 | + | 0.190632i | \(0.938946\pi\) | |||||||
\(888\) | − 3.43819e30i | − 0.378437i | ||||||||
\(889\) | −3.50032e30 | −0.380750 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 7.26524e29 | 0.0771852 | ||||||||
\(892\) | 2.26792e30i | 0.238121i | ||||||||
\(893\) | 1.79595e31i | 1.86361i | ||||||||
\(894\) | 3.63627e30 | 0.372917 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −4.47020e30 | −0.447810 | ||||||||
\(897\) | − 1.95766e30i | − 0.193828i | ||||||||
\(898\) | − 1.56863e31i | − 1.53503i | ||||||||
\(899\) | 2.31420e31 | 2.23833 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.98728e30 | 0.376761 | ||||||||
\(902\) | 1.10407e31i | 1.03116i | ||||||||
\(903\) | 4.65587e30i | 0.429813i | ||||||||
\(904\) | −8.05980e30 | −0.735455 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 9.23433e30 | 0.823302 | ||||||||
\(907\) | 1.16251e31i | 1.02452i | 0.858829 | + | 0.512262i | \(0.171192\pi\) | ||||
−0.858829 | + | 0.512262i | \(0.828808\pi\) | |||||||
\(908\) | − 3.83534e30i | − 0.334120i | ||||||||
\(909\) | 5.79606e30 | 0.499128 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.34510e31 | −1.13191 | −0.565957 | − | 0.824435i | \(-0.691493\pi\) | ||||
−0.565957 | + | 0.824435i | \(0.691493\pi\) | |||||||
\(912\) | 7.82741e30i | 0.651137i | ||||||||
\(913\) | 1.82407e28i | 0.00150002i | ||||||||
\(914\) | −9.70051e30 | −0.788605 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.30418e30 | −0.103618 | ||||||||
\(917\) | 1.60945e31i | 1.26416i | ||||||||
\(918\) | 2.18903e30i | 0.169982i | ||||||||
\(919\) | 8.55562e30 | 0.656808 | 0.328404 | − | 0.944537i | \(-0.393489\pi\) | ||||
0.328404 | + | 0.944537i | \(0.393489\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.21853e30 | 0.316544 | ||||||||
\(922\) | − 1.15093e30i | − 0.0853835i | ||||||||
\(923\) | 7.40185e30i | 0.542903i | ||||||||
\(924\) | 1.06899e30 | 0.0775205 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1.52259e30 | 0.107937 | ||||||||
\(927\) | − 4.11157e30i | − 0.288184i | ||||||||
\(928\) | 7.88268e30i | 0.546286i | ||||||||
\(929\) | −9.93712e30 | −0.680919 | −0.340460 | − | 0.940259i | \(-0.610583\pi\) | ||||
−0.340460 | + | 0.940259i | \(0.610583\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.66418e30 | −0.446452 | ||||||||
\(932\) | − 3.16381e30i | − 0.209577i | ||||||||
\(933\) | − 3.55425e30i | − 0.232804i | ||||||||
\(934\) | −1.48757e31 | −0.963462 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 8.43852e30 | 0.534404 | ||||||||
\(937\) | 2.14272e30i | 0.134183i | 0.997747 | + | 0.0670917i | \(0.0213720\pi\) | ||||
−0.997747 | + | 0.0670917i | \(0.978628\pi\) | |||||||
\(938\) | 2.26557e30i | 0.140297i | ||||||||
\(939\) | 9.98217e30 | 0.611275 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.69148e31 | 1.01292 | 0.506459 | − | 0.862264i | \(-0.330954\pi\) | ||||
0.506459 | + | 0.862264i | \(0.330954\pi\) | |||||||
\(942\) | 4.43006e30i | 0.262347i | ||||||||
\(943\) | 6.52077e30i | 0.381879i | ||||||||
\(944\) | 5.12310e30 | 0.296706 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.48180e30 | −0.537074 | ||||||||
\(947\) | 1.96530e31i | 1.10092i | 0.834862 | + | 0.550459i | \(0.185547\pi\) | ||||
−0.834862 | + | 0.550459i | \(0.814453\pi\) | |||||||
\(948\) | 9.29057e29i | 0.0514701i | ||||||||
\(949\) | 1.27568e31 | 0.698948 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.37578e30 | −0.180917 | ||||||||
\(952\) | 1.73142e31i | 0.917728i | ||||||||
\(953\) | 2.39001e31i | 1.25292i | 0.779452 | + | 0.626462i | \(0.215498\pi\) | ||||
−0.779452 | + | 0.626462i | \(0.784502\pi\) | |||||||
\(954\) | −2.11559e30 | −0.109692 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −4.75555e30 | −0.241209 | ||||||||
\(957\) | 9.76276e30i | 0.489776i | ||||||||
\(958\) | − 2.60567e31i | − 1.29295i | ||||||||
\(959\) | 3.04716e31 | 1.49555 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.91397e31 | 2.35959 | ||||||||
\(962\) | − 1.66897e31i | − 0.792703i | ||||||||
\(963\) | − 3.03057e30i | − 0.142380i | ||||||||
\(964\) | −7.38943e30 | −0.343401 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −2.13122e30 | −0.0969100 | ||||||||
\(967\) | − 1.63072e31i | − 0.733504i | −0.930319 | − | 0.366752i | \(-0.880470\pi\) | ||||
0.930319 | − | 0.366752i | \(-0.119530\pi\) | |||||||
\(968\) | − 1.25486e31i | − 0.558348i | ||||||||
\(969\) | 2.06839e31 | 0.910401 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.09343e31 | 1.33241 | 0.666207 | − | 0.745767i | \(-0.267917\pi\) | ||||
0.666207 | + | 0.745767i | \(0.267917\pi\) | |||||||
\(972\) | 3.44076e29i | 0.0146608i | ||||||||
\(973\) | − 1.37915e31i | − 0.581334i | ||||||||
\(974\) | −4.77865e30 | −0.199267 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.19216e31 | 0.486531 | ||||||||
\(977\) | − 1.98044e31i | − 0.799592i | −0.916604 | − | 0.399796i | \(-0.869081\pi\) | ||||
0.916604 | − | 0.399796i | \(-0.130919\pi\) | |||||||
\(978\) | 2.39025e30i | 0.0954742i | ||||||||
\(979\) | −1.40189e31 | −0.553982 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.43663e30 | 0.0555673 | ||||||||
\(982\) | − 1.94829e31i | − 0.745561i | ||||||||
\(983\) | − 4.34284e30i | − 0.164423i | −0.996615 | − | 0.0822114i | \(-0.973802\pi\) | ||||
0.996615 | − | 0.0822114i | \(-0.0261983\pi\) | |||||||
\(984\) | −2.81078e31 | −1.05288 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −2.94154e31 | −1.07862 | ||||||||
\(987\) | − 1.59955e31i | − 0.580322i | ||||||||
\(988\) | − 1.48327e31i | − 0.532441i | ||||||||
\(989\) | −5.60008e30 | −0.198899 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.70795e30 | 0.163704 | 0.0818518 | − | 0.996645i | \(-0.473917\pi\) | ||||
0.0818518 | + | 0.996645i | \(0.473917\pi\) | |||||||
\(992\) | 2.38317e31i | 0.819939i | ||||||||
\(993\) | 3.94422e30i | 0.134275i | ||||||||
\(994\) | 8.05807e30 | 0.271440 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −8.63864e27 | −0.000284920 0 | ||||||||
\(997\) | 1.58934e31i | 0.518700i | 0.965783 | + | 0.259350i | \(0.0835084\pi\) | ||||
−0.965783 | + | 0.259350i | \(0.916492\pi\) | |||||||
\(998\) | − 4.89494e30i | − 0.158080i | ||||||||
\(999\) | 3.65817e30 | 0.116903 |
(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 | 75.22.b.d.49.3 | 4 | ||
5.2 | odd | 4 | 3.22.a.c.1.1 | ✓ | 2 | ||
5.3 | odd | 4 | 75.22.a.d.1.2 | 2 | |||
5.4 | even | 2 | inner | 75.22.b.d.49.2 | 4 | ||
15.2 | even | 4 | 9.22.a.e.1.2 | 2 | |||
20.7 | even | 4 | 48.22.a.g.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.22.a.c.1.1 | ✓ | 2 | 5.2 | odd | 4 | ||
9.22.a.e.1.2 | 2 | 15.2 | even | 4 | |||
48.22.a.g.1.1 | 2 | 20.7 | even | 4 | |||
75.22.a.d.1.2 | 2 | 5.3 | odd | 4 | |||
75.22.b.d.49.2 | 4 | 5.4 | even | 2 | inner | ||
75.22.b.d.49.3 | 4 | 1.1 | even | 1 | trivial |