Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4864,2,Mod(1,4864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4864, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4864.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4864 = 2^{8} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4864.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(38.8392355432\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 13x^{6} + 24x^{5} + 48x^{4} - 68x^{3} - 62x^{2} + 32x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 152) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-2.81542\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4864.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.70663 | 0.985325 | 0.492662 | − | 0.870221i | \(-0.336024\pi\) | ||||
0.492662 | + | 0.870221i | \(0.336024\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.66222 | 0.743367 | 0.371683 | − | 0.928360i | \(-0.378781\pi\) | ||||
0.371683 | + | 0.928360i | \(0.378781\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.99556 | −0.754251 | −0.377125 | − | 0.926162i | \(-0.623087\pi\) | ||||
−0.377125 | + | 0.926162i | \(0.623087\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.0874066 | −0.0291355 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.08741 | 0.629377 | 0.314688 | − | 0.949195i | \(-0.398100\pi\) | ||||
0.314688 | + | 0.949195i | \(0.398100\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.77322 | −1.32385 | −0.661927 | − | 0.749568i | \(-0.730261\pi\) | ||||
−0.661927 | + | 0.749568i | \(0.730261\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.83680 | 0.732457 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.10657 | 0.510917 | 0.255459 | − | 0.966820i | \(-0.417774\pi\) | ||||
0.255459 | + | 0.966820i | \(0.417774\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.40569 | −0.743182 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.84437 | −1.01012 | −0.505061 | − | 0.863084i | \(-0.668530\pi\) | ||||
−0.505061 | + | 0.863084i | \(0.668530\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.23703 | −0.447406 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.26907 | −1.01403 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.695946 | 0.129234 | 0.0646170 | − | 0.997910i | \(-0.479417\pi\) | ||||
0.0646170 | + | 0.997910i | \(0.479417\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.77587 | −1.75580 | −0.877899 | − | 0.478846i | \(-0.841055\pi\) | ||||
−0.877899 | + | 0.478846i | \(0.841055\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.56244 | 0.620140 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.31706 | −0.560685 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.0772780 | −0.0127044 | −0.00635221 | − | 0.999980i | \(-0.502022\pi\) | ||||
−0.00635221 | + | 0.999980i | \(0.502022\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −8.14614 | −1.30443 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.7743 | −1.68267 | −0.841334 | − | 0.540516i | \(-0.818229\pi\) | ||||
−0.841334 | + | 0.540516i | \(0.818229\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.43840 | −0.219354 | −0.109677 | − | 0.993967i | \(-0.534982\pi\) | ||||
−0.109677 | + | 0.993967i | \(0.534982\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.145289 | −0.0216584 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.88133 | 0.420285 | 0.210143 | − | 0.977671i | \(-0.432607\pi\) | ||||
0.210143 | + | 0.977671i | \(0.432607\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.01774 | −0.431106 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.59513 | 0.503419 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.00264 | −1.23661 | −0.618304 | − | 0.785939i | \(-0.712180\pi\) | ||||
−0.618304 | + | 0.785939i | \(0.712180\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.46973 | 0.467858 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.70663 | 0.226049 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.5253 | 1.50046 | 0.750230 | − | 0.661177i | \(-0.229943\pi\) | ||||
0.750230 | + | 0.661177i | \(0.229943\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.82910 | 1.13045 | 0.565225 | − | 0.824937i | \(-0.308789\pi\) | ||||
0.565225 | + | 0.824937i | \(0.308789\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.174425 | 0.0219755 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −7.93414 | −0.984109 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.27859 | 0.156205 | 0.0781023 | − | 0.996945i | \(-0.475114\pi\) | ||||
0.0781023 | + | 0.996945i | \(0.475114\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −8.26756 | −0.995297 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.66655 | −0.553818 | −0.276909 | − | 0.960896i | \(-0.589310\pi\) | ||||
−0.276909 | + | 0.960896i | \(0.589310\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.44578 | −0.520339 | −0.260170 | − | 0.965563i | \(-0.583779\pi\) | ||||
−0.260170 | + | 0.965563i | \(0.583779\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.81779 | −0.440840 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.16555 | −0.474708 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.10044 | −0.123809 | −0.0619044 | − | 0.998082i | \(-0.519717\pi\) | ||||
−0.0619044 | + | 0.998082i | \(0.519717\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.73014 | −0.970016 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.47419 | 0.271578 | 0.135789 | − | 0.990738i | \(-0.456643\pi\) | ||||
0.135789 | + | 0.990738i | \(0.456643\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.50157 | 0.379799 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.18772 | 0.127337 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.8259 | 1.67755 | 0.838773 | − | 0.544481i | \(-0.183273\pi\) | ||||
0.838773 | + | 0.544481i | \(0.183273\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.52526 | 0.998518 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −16.6838 | −1.73003 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.66222 | 0.170540 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.9046 | −1.41180 | −0.705898 | − | 0.708313i | \(-0.749456\pi\) | ||||
−0.705898 | + | 0.708313i | \(0.749456\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.182453 | −0.0183372 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.00493 | −0.0999945 | −0.0499973 | − | 0.998749i | \(-0.515921\pi\) | ||||
−0.0499973 | + | 0.998749i | \(0.515921\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.4581 | 1.22753 | 0.613767 | − | 0.789487i | \(-0.289653\pi\) | ||||
0.613767 | + | 0.789487i | \(0.289653\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.66100 | −0.552457 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.3004 | 1.47915 | 0.739573 | − | 0.673076i | \(-0.235027\pi\) | ||||
0.739573 | + | 0.673076i | \(0.235027\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.65850 | −0.733551 | −0.366775 | − | 0.930309i | \(-0.619538\pi\) | ||||
−0.366775 | + | 0.930309i | \(0.619538\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.131885 | −0.0125180 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.3938 | 1.63627 | 0.818134 | − | 0.575028i | \(-0.195009\pi\) | ||||
0.818134 | + | 0.575028i | \(0.195009\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.05240 | −0.750891 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.417211 | 0.0385712 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.20378 | −0.385360 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.64273 | −0.603885 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −18.3878 | −1.65797 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.0295 | −1.07595 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −18.1488 | −1.61045 | −0.805225 | − | 0.592970i | \(-0.797955\pi\) | ||||
−0.805225 | + | 0.592970i | \(0.797955\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.45482 | −0.216135 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.70500 | −0.847930 | −0.423965 | − | 0.905679i | \(-0.639362\pi\) | ||||
−0.423965 | + | 0.905679i | \(0.639362\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.99556 | −0.173037 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −8.75834 | −0.753798 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 20.2253 | 1.72797 | 0.863983 | − | 0.503521i | \(-0.167962\pi\) | ||||
0.863983 | + | 0.503521i | \(0.167962\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.7746 | −1.42280 | −0.711401 | − | 0.702786i | \(-0.751939\pi\) | ||||
−0.711401 | + | 0.702786i | \(0.751939\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.91737 | 0.414117 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −9.96366 | −0.833203 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.15681 | 0.0960682 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.15017 | −0.424779 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −13.6533 | −1.11853 | −0.559263 | − | 0.828991i | \(-0.688916\pi\) | ||||
−0.559263 | + | 0.828991i | \(0.688916\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.77602 | 0.551425 | 0.275712 | − | 0.961240i | \(-0.411086\pi\) | ||||
0.275712 | + | 0.961240i | \(0.411086\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.184128 | −0.0148858 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −16.2496 | −1.30520 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −23.4178 | −1.86895 | −0.934473 | − | 0.356035i | \(-0.884129\pi\) | ||||
−0.934473 | + | 0.356035i | \(0.884129\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −15.3642 | −1.21846 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.66724 | 0.761885 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.06973 | −0.0837875 | −0.0418938 | − | 0.999122i | \(-0.513339\pi\) | ||||
−0.0418938 | + | 0.999122i | \(0.513339\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.92155 | 0.460992 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13.6217 | 1.05408 | 0.527039 | − | 0.849841i | \(-0.323302\pi\) | ||||
0.527039 | + | 0.849841i | \(0.323302\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.78367 | 0.752590 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.0874066 | −0.00668415 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.5684 | 0.879527 | 0.439763 | − | 0.898114i | \(-0.355062\pi\) | ||||
0.439763 | + | 0.898114i | \(0.355062\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.46413 | 0.337456 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 19.6694 | 1.47844 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 20.4983 | 1.53211 | 0.766057 | − | 0.642772i | \(-0.222216\pi\) | ||||
0.766057 | + | 0.642772i | \(0.222216\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.7745 | −1.39550 | −0.697750 | − | 0.716341i | \(-0.745815\pi\) | ||||
−0.697750 | + | 0.716341i | \(0.745815\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 15.0680 | 1.11386 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.128453 | −0.00944404 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.39726 | 0.321560 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 10.5147 | 0.764835 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.0392 | 1.01584 | 0.507919 | − | 0.861405i | \(-0.330415\pi\) | ||||
0.507919 | + | 0.861405i | \(0.330415\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −23.8700 | −1.71820 | −0.859099 | − | 0.511809i | \(-0.828976\pi\) | ||||
−0.859099 | + | 0.511809i | \(0.828976\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −13.5407 | −0.969667 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.84890 | −0.131729 | −0.0658645 | − | 0.997829i | \(-0.520980\pi\) | ||||
−0.0658645 | + | 0.997829i | \(0.520980\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.3608 | −1.30156 | −0.650781 | − | 0.759266i | \(-0.725558\pi\) | ||||
−0.650781 | + | 0.759266i | \(0.725558\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.18208 | 0.153912 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.38880 | −0.0974748 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −17.9093 | −1.25084 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.423430 | 0.0294304 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.08741 | 0.144389 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.5147 | 1.06808 | 0.534039 | − | 0.845460i | \(-0.320674\pi\) | ||||
0.534039 | + | 0.845460i | \(0.320674\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −7.96409 | −0.545690 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.39094 | −0.163061 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 19.5083 | 1.32431 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.58731 | −0.512703 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.0551 | −0.676380 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.9260 | 0.932553 | 0.466276 | − | 0.884639i | \(-0.345595\pi\) | ||||
0.466276 | + | 0.884639i | \(0.345595\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.195531 | 0.0130354 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.49624 | −0.0993088 | −0.0496544 | − | 0.998766i | \(-0.515812\pi\) | ||||
−0.0496544 | + | 0.998766i | \(0.515812\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.03706 | −0.0685310 | −0.0342655 | − | 0.999413i | \(-0.510909\pi\) | ||||
−0.0342655 | + | 0.999413i | \(0.510909\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.10905 | −0.467741 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4.93372 | −0.323219 | −0.161609 | − | 0.986855i | \(-0.551668\pi\) | ||||
−0.161609 | + | 0.986855i | \(0.551668\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.78940 | 0.312426 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.87804 | −0.121992 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.84533 | 0.248733 | 0.124367 | − | 0.992236i | \(-0.460310\pi\) | ||||
0.124367 | + | 0.992236i | \(0.460310\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.41134 | −0.0909123 | −0.0454562 | − | 0.998966i | \(-0.514474\pi\) | ||||
−0.0454562 | + | 0.998966i | \(0.514474\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.908064 | 0.0582523 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.01614 | −0.320469 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.77322 | −0.303713 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.22253 | 0.267592 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.24640 | −0.520508 | −0.260254 | − | 0.965540i | \(-0.583806\pi\) | ||||
−0.260254 | + | 0.965540i | \(0.583806\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −10.1122 | −0.635747 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.97590 | 0.374225 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.0726 | 0.940200 | 0.470100 | − | 0.882613i | \(-0.344218\pi\) | ||||
0.470100 | + | 0.882613i | \(0.344218\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.154213 | 0.00958232 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.0608303 | −0.00376530 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.49141 | −0.585265 | −0.292633 | − | 0.956225i | \(-0.594531\pi\) | ||||
−0.292633 | + | 0.956225i | \(0.594531\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −14.9644 | −0.919253 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 27.0091 | 1.65293 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.98549 | −0.243000 | −0.121500 | − | 0.992591i | \(-0.538770\pi\) | ||||
−0.121500 | + | 0.992591i | \(0.538770\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.38427 | 0.387817 | 0.193908 | − | 0.981020i | \(-0.437884\pi\) | ||||
0.193908 | + | 0.981020i | \(0.437884\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 16.2561 | 0.983865 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.66959 | −0.281587 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.1758 | −0.911823 | −0.455912 | − | 0.890025i | \(-0.650687\pi\) | ||||
−0.455912 | + | 0.890025i | \(0.650687\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.854475 | 0.0511561 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.9058 | −0.889207 | −0.444603 | − | 0.895728i | \(-0.646655\pi\) | ||||
−0.444603 | + | 0.895728i | \(0.646655\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.9931 | 0.891250 | 0.445625 | − | 0.895220i | \(-0.352981\pi\) | ||||
0.445625 | + | 0.895220i | \(0.352981\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.83680 | 0.168037 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 21.5008 | 1.26915 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.5624 | −0.738963 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −23.7300 | −1.39108 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −21.6983 | −1.26763 | −0.633814 | − | 0.773485i | \(-0.718512\pi\) | ||||
−0.633814 | + | 0.773485i | \(0.718512\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 19.1575 | 1.11539 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −10.9987 | −0.638208 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 23.1233 | 1.33725 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.87042 | 0.165448 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.71505 | −0.0985270 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 14.6759 | 0.840339 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.81449 | −0.445996 | −0.222998 | − | 0.974819i | \(-0.571584\pi\) | ||||
−0.222998 | + | 0.974819i | \(0.571584\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 21.2614 | 1.20952 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.8288 | 0.727455 | 0.363727 | − | 0.931505i | \(-0.381504\pi\) | ||||
0.363727 | + | 0.931505i | \(0.381504\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.07578 | 0.230377 | 0.115188 | − | 0.993344i | \(-0.463253\pi\) | ||||
0.115188 | + | 0.993344i | \(0.463253\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.289933 | 0.0163358 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.26448 | 0.127186 | 0.0635931 | − | 0.997976i | \(-0.479744\pi\) | ||||
0.0635931 | + | 0.997976i | \(0.479744\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.45272 | 0.0813368 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 26.1122 | 1.45744 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.10657 | 0.117212 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.6778 | 0.592300 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −13.0702 | −0.722786 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.74987 | −0.317000 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.31171 | 0.401888 | 0.200944 | − | 0.979603i | \(-0.435599\pi\) | ||||
0.200944 | + | 0.979603i | \(0.435599\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.00675460 | 0.000370150 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.12529 | 0.116117 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.00356 | −0.327035 | −0.163517 | − | 0.986540i | \(-0.552284\pi\) | ||||
−0.163517 | + | 0.986540i | \(0.552284\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 29.6848 | 1.61225 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −20.4062 | −1.10506 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.9910 | 1.07941 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −13.7425 | −0.739871 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.66747 | 0.357929 | 0.178964 | − | 0.983856i | \(-0.442725\pi\) | ||||
0.178964 | + | 0.983856i | \(0.442725\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 35.5072 | 1.90066 | 0.950329 | − | 0.311248i | \(-0.100747\pi\) | ||||
0.950329 | + | 0.311248i | \(0.100747\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 25.1504 | 1.34243 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −27.8315 | −1.48132 | −0.740659 | − | 0.671881i | \(-0.765487\pi\) | ||||
−0.740659 | + | 0.671881i | \(0.765487\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.75683 | −0.411690 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −7.17431 | −0.379705 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10.6778 | 0.563551 | 0.281775 | − | 0.959480i | \(-0.409077\pi\) | ||||
0.281775 | + | 0.959480i | \(0.409077\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −11.3367 | −0.595023 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.38986 | −0.386803 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.8950 | −0.881911 | −0.440956 | − | 0.897529i | \(-0.645360\pi\) | ||||
−0.440956 | + | 0.897529i | \(0.645360\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.941747 | 0.0490254 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 17.9653 | 0.932713 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 33.4640 | 1.73270 | 0.866350 | − | 0.499438i | \(-0.166460\pi\) | ||||
0.866350 | + | 0.499438i | \(0.166460\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −20.5300 | −1.06016 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.32191 | −0.171087 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −37.0251 | −1.90185 | −0.950925 | − | 0.309423i | \(-0.899864\pi\) | ||||
−0.950925 | + | 0.309423i | \(0.899864\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −30.9734 | −1.58682 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 16.2264 | 0.829131 | 0.414566 | − | 0.910019i | \(-0.363934\pi\) | ||||
0.414566 | + | 0.910019i | \(0.363934\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.92405 | −0.352882 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.125726 | 0.00639100 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −11.8131 | −0.598947 | −0.299473 | − | 0.954105i | \(-0.596811\pi\) | ||||
−0.299473 | + | 0.954105i | \(0.596811\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.2050 | −0.516089 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −16.5629 | −0.835486 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.82917 | −0.0920353 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.9654 | −0.550340 | −0.275170 | − | 0.961396i | \(-0.588734\pi\) | ||||
−0.275170 | + | 0.961396i | \(0.588734\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.40569 | −0.170498 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.9479 | 0.596650 | 0.298325 | − | 0.954464i | \(-0.403572\pi\) | ||||
0.298325 | + | 0.954464i | \(0.403572\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 46.6624 | 2.32442 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −14.5114 | −0.721077 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.161311 | −0.00799587 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.28997 | 0.0637848 | 0.0318924 | − | 0.999491i | \(-0.489847\pi\) | ||||
0.0318924 | + | 0.999491i | \(0.489847\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 34.5172 | 1.70261 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −22.9993 | −1.13172 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.11265 | 0.201882 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −28.6281 | −1.40192 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15.6802 | −0.766030 | −0.383015 | − | 0.923742i | \(-0.625114\pi\) | ||||
−0.383015 | + | 0.923742i | \(0.625114\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −26.2544 | −1.27956 | −0.639782 | − | 0.768557i | \(-0.720975\pi\) | ||||
−0.639782 | + | 0.768557i | \(0.720975\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.251847 | −0.0122452 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.71245 | −0.228587 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −17.6190 | −0.852643 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −17.0043 | −0.820975 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 33.4648 | 1.61194 | 0.805972 | − | 0.591954i | \(-0.201643\pi\) | ||||
0.805972 | + | 0.591954i | \(0.201643\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.89119 | 0.283112 | 0.141556 | − | 0.989930i | \(-0.454789\pi\) | ||||
0.141556 | + | 0.989930i | \(0.454789\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.97426 | 0.0946584 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.84437 | −0.231738 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.9770 | 1.23982 | 0.619908 | − | 0.784674i | \(-0.287170\pi\) | ||||
0.619908 | + | 0.784674i | \(0.287170\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.263770 | 0.0125605 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11.0652 | −0.525722 | −0.262861 | − | 0.964834i | \(-0.584666\pi\) | ||||
−0.262861 | + | 0.964834i | \(0.584666\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 26.3062 | 1.24703 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −23.3012 | −1.10211 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.56950 | 0.168455 | 0.0842274 | − | 0.996447i | \(-0.473158\pi\) | ||||
0.0842274 | + | 0.996447i | \(0.473158\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −22.4904 | −1.05903 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11.5642 | 0.543332 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 15.8331 | 0.742265 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 23.3258 | 1.09113 | 0.545567 | − | 0.838067i | \(-0.316314\pi\) | ||||
0.545567 | + | 0.838067i | \(0.316314\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −11.0996 | −0.518087 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.16887 | −0.380462 | −0.190231 | − | 0.981739i | \(-0.560924\pi\) | ||||
−0.190231 | + | 0.981739i | \(0.560924\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.8015 | 0.594936 | 0.297468 | − | 0.954732i | \(-0.403858\pi\) | ||||
0.297468 | + | 0.954732i | \(0.403858\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −27.7321 | −1.28605 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.897425 | 0.0415279 | 0.0207639 | − | 0.999784i | \(-0.493390\pi\) | ||||
0.0207639 | + | 0.999784i | \(0.493390\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.55150 | −0.117817 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −39.9656 | −1.84152 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.00253 | −0.138056 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.23703 | −0.102642 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.786890 | 0.0360292 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12.9960 | −0.593803 | −0.296901 | − | 0.954908i | \(-0.595953\pi\) | ||||
−0.296901 | + | 0.954908i | \(0.595953\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.368865 | 0.0168188 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 16.4984 | 0.750704 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −23.1125 | −1.04948 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.0621 | 0.546588 | 0.273294 | − | 0.961931i | \(-0.411887\pi\) | ||||
0.273294 | + | 0.961931i | \(0.411887\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.82563 | −0.0825579 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −30.5337 | −1.37797 | −0.688983 | − | 0.724778i | \(-0.741942\pi\) | ||||
−0.688983 | + | 0.724778i | \(0.741942\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.46606 | 0.0660279 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.303277 | −0.0136313 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.31239 | 0.417718 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −40.2124 | −1.80015 | −0.900077 | − | 0.435731i | \(-0.856490\pi\) | ||||
−0.900077 | + | 0.435731i | \(0.856490\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 23.2472 | 1.03861 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 35.7181 | 1.59259 | 0.796296 | − | 0.604907i | \(-0.206790\pi\) | ||||
0.796296 | + | 0.604907i | \(0.206790\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.67042 | −0.0743326 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 16.6971 | 0.741545 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −35.3428 | −1.56654 | −0.783270 | − | 0.621681i | \(-0.786450\pi\) | ||||
−0.783270 | + | 0.621681i | \(0.786450\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.87183 | 0.392466 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.26907 | −0.232635 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 20.7081 | 0.912508 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.01450 | 0.264518 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 19.7429 | 0.866619 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.50662 | −0.109817 | −0.0549086 | − | 0.998491i | \(-0.517487\pi\) | ||||
−0.0549086 | + | 0.998491i | \(0.517487\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.95330 | 0.435227 | 0.217614 | − | 0.976035i | \(-0.430173\pi\) | ||||
0.217614 | + | 0.976035i | \(0.430173\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 7.61863 | 0.332504 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −20.5935 | −0.897068 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.467940 | 0.0203452 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.00738 | −0.0437167 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 51.4283 | 2.22761 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 25.4326 | 1.09955 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 34.9831 | 1.50963 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.29925 | −0.271328 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 34.7061 | 1.49213 | 0.746065 | − | 0.665873i | \(-0.231941\pi\) | ||||
0.746065 | + | 0.665873i | \(0.231941\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −32.0412 | −1.37502 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −12.7301 | −0.545297 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.21429 | −0.308461 | −0.154230 | − | 0.988035i | \(-0.549290\pi\) | ||||
−0.154230 | + | 0.988035i | \(0.549290\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.771721 | −0.0329363 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.695946 | 0.0296483 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.19599 | 0.0933829 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.219222 | −0.00930545 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.27230 | 0.181023 | 0.0905116 | − | 0.995895i | \(-0.471150\pi\) | ||||
0.0905116 | + | 0.995895i | \(0.471150\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.86582 | 0.290393 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.50451 | 0.316840 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 23.9662 | 1.01005 | 0.505027 | − | 0.863103i | \(-0.331482\pi\) | ||||
0.505027 | + | 0.863103i | \(0.331482\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 28.9122 | 1.21635 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 17.4215 | 0.731635 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.53074 | −0.273783 | −0.136891 | − | 0.990586i | \(-0.543711\pi\) | ||||
−0.136891 | + | 0.990586i | \(0.543711\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13.8125 | −0.578035 | −0.289017 | − | 0.957324i | \(-0.593329\pi\) | ||||
−0.289017 | + | 0.957324i | \(0.593329\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 23.9597 | 1.00093 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 10.8370 | 0.451934 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.75601 | −0.0731035 | −0.0365517 | − | 0.999332i | \(-0.511637\pi\) | ||||
−0.0365517 | + | 0.999332i | \(0.511637\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −40.7373 | −1.69298 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.93740 | −0.204838 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −18.7922 | −0.778293 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.693496 | 0.0286725 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22.1818 | 0.915540 | 0.457770 | − | 0.889071i | \(-0.348648\pi\) | ||||
0.457770 | + | 0.889071i | \(0.348648\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.77587 | −0.402808 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.15540 | −0.129796 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −14.8347 | −0.609186 | −0.304593 | − | 0.952483i | \(-0.598520\pi\) | ||||
−0.304593 | + | 0.952483i | \(0.598520\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.98760 | −0.286464 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −31.3351 | −1.28246 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −19.9337 | −0.814468 | −0.407234 | − | 0.913324i | \(-0.633507\pi\) | ||||
−0.407234 | + | 0.913324i | \(0.633507\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −31.4765 | −1.28395 | −0.641976 | − | 0.766724i | \(-0.721885\pi\) | ||||
−0.641976 | + | 0.766724i | \(0.721885\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.111757 | −0.00455110 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −11.0417 | −0.448908 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −25.8245 | −1.04818 | −0.524092 | − | 0.851662i | \(-0.675595\pi\) | ||||
−0.524092 | + | 0.851662i | \(0.675595\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.37018 | −0.0960443 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −13.7532 | −0.556396 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.844965 | −0.0341278 | −0.0170639 | − | 0.999854i | \(-0.505432\pi\) | ||||
−0.0170639 | + | 0.999854i | \(0.505432\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −30.5646 | −1.23248 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10.0344 | 0.403970 | 0.201985 | − | 0.979389i | \(-0.435261\pi\) | ||||
0.201985 | + | 0.979389i | \(0.435261\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 29.2896 | 1.17725 | 0.588625 | − | 0.808406i | \(-0.299669\pi\) | ||||
0.588625 | + | 0.808406i | \(0.299669\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 25.5253 | 1.02430 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −31.5816 | −1.26529 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.81055 | −0.352422 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.56244 | 0.142270 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.162791 | −0.00649091 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.02437 | −0.0407796 | −0.0203898 | − | 0.999792i | \(-0.506491\pi\) | ||||
−0.0203898 | + | 0.999792i | \(0.506491\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 26.4779 | 1.05240 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −30.1673 | −1.19715 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 14.4043 | 0.570721 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.407887 | 0.0161358 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −31.8367 | −1.25747 | −0.628737 | − | 0.777618i | \(-0.716428\pi\) | ||||
−0.628737 | + | 0.777618i | \(0.716428\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −34.2996 | −1.35264 | −0.676322 | − | 0.736606i | \(-0.736427\pi\) | ||||
−0.676322 | + | 0.736606i | \(0.736427\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.08045 | −0.160668 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.45559 | 0.371738 | 0.185869 | − | 0.982575i | \(-0.440490\pi\) | ||||
0.185869 | + | 0.982575i | \(0.440490\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 24.0579 | 0.944355 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 33.2936 | 1.30488 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.33451 | 0.247888 | 0.123944 | − | 0.992289i | \(-0.460446\pi\) | ||||
0.123944 | + | 0.992289i | \(0.460446\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −16.1318 | −0.630323 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.388590 | 0.0151604 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.22355 | 0.281390 | 0.140695 | − | 0.990053i | \(-0.455066\pi\) | ||||
0.140695 | + | 0.990053i | \(0.455066\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.529621 | 0.0205999 | 0.0102999 | − | 0.999947i | \(-0.496721\pi\) | ||||
0.0102999 | + | 0.999947i | \(0.496721\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −17.1604 | −0.666454 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.31706 | −0.128630 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.37142 | −0.130542 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 23.7665 | 0.918867 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 18.4299 | 0.711479 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 41.7434 | 1.60909 | 0.804544 | − | 0.593893i | \(-0.202410\pi\) | ||||
0.804544 | + | 0.593893i | \(0.202410\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 11.7871 | 0.453684 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 33.4165 | 1.28430 | 0.642151 | − | 0.766578i | \(-0.278042\pi\) | ||||
0.642151 | + | 0.766578i | \(0.278042\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 27.7474 | 1.06485 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.55353 | −0.0978514 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 30.1765 | 1.15467 | 0.577336 | − | 0.816507i | \(-0.304092\pi\) | ||||
0.577336 | + | 0.816507i | \(0.304092\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 33.6189 | 1.28451 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.76988 | −0.0675252 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 42.9716 | 1.63709 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.6002 | 0.669544 | 0.334772 | − | 0.942299i | \(-0.391341\pi\) | ||||
0.334772 | + | 0.942299i | \(0.391341\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.364096 | 0.0138309 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −27.8830 | −1.05766 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −22.6968 | −0.859704 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8.42005 | −0.318475 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −30.6993 | −1.15950 | −0.579748 | − | 0.814796i | \(-0.696849\pi\) | ||||
−0.579748 | + | 0.814796i | \(0.696849\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.0772780 | −0.00291459 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 8.17374 | 0.307841 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.00540 | 0.0754210 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.79437 | 0.330279 | 0.165140 | − | 0.986270i | \(-0.447193\pi\) | ||||
0.165140 | + | 0.986270i | \(0.447193\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.0961853 | 0.00360723 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 47.3579 | 1.77357 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −16.5618 | −0.619375 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.56256 | 0.245083 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −12.5991 | −0.469867 | −0.234933 | − | 0.972011i | \(-0.575487\pi\) | ||||
−0.234933 | + | 0.972011i | \(0.575487\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −24.8609 | −0.925869 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.40864 | −0.0895781 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.55685 | −0.0578200 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −39.7756 | −1.47519 | −0.737597 | − | 0.675241i | \(-0.764040\pi\) | ||||
−0.737597 | + | 0.675241i | \(0.764040\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.7402 | 1.02741 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.03009 | −0.112072 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.50154 | −0.203204 | −0.101602 | − | 0.994825i | \(-0.532397\pi\) | ||||
−0.101602 | + | 0.994825i | \(0.532397\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −8.56071 | −0.315766 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.66894 | 0.0983115 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −52.6937 | −1.93837 | −0.969185 | − | 0.246335i | \(-0.920774\pi\) | ||||
−0.969185 | + | 0.246335i | \(0.920774\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.14614 | −0.299256 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6.61647 | −0.242735 | −0.121367 | − | 0.992608i | \(-0.538728\pi\) | ||||
−0.121367 | + | 0.992608i | \(0.538728\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −22.6948 | −0.831474 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.216261 | −0.00791256 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −30.5329 | −1.11565 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 39.9062 | 1.45620 | 0.728099 | − | 0.685472i | \(-0.240404\pi\) | ||||
0.728099 | + | 0.685472i | \(0.240404\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −14.0736 | −0.512869 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 11.2632 | 0.409911 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −34.2645 | −1.24537 | −0.622683 | − | 0.782475i | \(-0.713957\pi\) | ||||
−0.622683 | + | 0.782475i | \(0.713957\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −17.2578 | −0.626417 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12.4757 | 0.452243 | 0.226122 | − | 0.974099i | \(-0.427395\pi\) | ||||
0.226122 | + | 0.974099i | \(0.427395\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15.2830 | 0.553281 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.306060 | −0.0110656 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −55.0126 | −1.98639 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.32384 | 0.119861 | 0.0599304 | − | 0.998203i | \(-0.480912\pi\) | ||||
0.0599304 | + | 0.998203i | \(0.480912\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 25.7233 | 0.926402 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 14.4248 | 0.518824 | 0.259412 | − | 0.965767i | \(-0.416471\pi\) | ||||
0.259412 | + | 0.965767i | \(0.416471\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 21.8689 | 0.785555 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.263185 | 0.00944170 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −10.7743 | −0.386030 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.74099 | −0.348560 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.66699 | −0.131047 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −38.9255 | −1.38931 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 38.6403 | 1.37738 | 0.688689 | − | 0.725057i | \(-0.258187\pi\) | ||||
0.688689 | + | 0.725057i | \(0.258187\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −16.1983 | −0.576676 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −34.7103 | −1.23416 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −42.1433 | −1.49655 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −25.5387 | −0.905763 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 30.9316 | 1.09565 | 0.547826 | − | 0.836592i | \(-0.315456\pi\) | ||||
0.547826 | + | 0.836592i | \(0.315456\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.06971 | 0.214731 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.38329 | −0.0488762 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.28015 | −0.327490 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 16.0691 | 0.566360 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.80177 | −0.239434 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −56.7269 | −1.99441 | −0.997206 | − | 0.0747056i | \(-0.976198\pi\) | ||||
−0.997206 | + | 0.0747056i | \(0.976198\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.91800 | 0.172694 | 0.0863472 | − | 0.996265i | \(-0.472481\pi\) | ||||
0.0863472 | + | 0.996265i | \(0.472481\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 10.8956 | 0.382125 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.77812 | −0.0622849 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.43840 | −0.0503233 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.832570 | −0.0290924 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −19.0797 | −0.665886 | −0.332943 | − | 0.942947i | \(-0.608042\pi\) | ||||
−0.332943 | + | 0.942947i | \(0.608042\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −19.6263 | −0.684131 | −0.342066 | − | 0.939676i | \(-0.611127\pi\) | ||||
−0.342066 | + | 0.939676i | \(0.611127\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −7.96928 | −0.277455 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −28.0107 | −0.974029 | −0.487014 | − | 0.873394i | \(-0.661914\pi\) | ||||
−0.487014 | + | 0.873394i | \(0.661914\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 23.1932 | 0.805533 | 0.402766 | − | 0.915303i | \(-0.368049\pi\) | ||||
0.402766 | + | 0.915303i | \(0.368049\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −25.8995 | −0.898442 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.35707 | −0.220259 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 22.6422 | 0.783567 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 51.5097 | 1.78044 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 27.6363 | 0.954110 | 0.477055 | − | 0.878873i | \(-0.341704\pi\) | ||||
0.477055 | + | 0.878873i | \(0.341704\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.5157 | −0.983299 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −25.4388 | −0.876157 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 16.2626 | 0.559450 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 13.2560 | 0.455481 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 25.5878 | 0.878171 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.374363 | 0.0128330 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 53.0502 | 1.81640 | 0.908202 | − | 0.418532i | \(-0.137455\pi\) | ||||
0.908202 | + | 0.418532i | \(0.137455\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.145289 | −0.00496877 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 8.06832 | 0.275609 | 0.137804 | − | 0.990459i | \(-0.455996\pi\) | ||||
0.137804 | + | 0.990459i | \(0.455996\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.1806 | −0.347357 | −0.173679 | − | 0.984802i | \(-0.555565\pi\) | ||||
−0.173679 | + | 0.984802i | \(0.555565\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 36.6940 | 1.25053 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 45.7074 | 1.55590 | 0.777949 | − | 0.628327i | \(-0.216260\pi\) | ||||
0.777949 | + | 0.628327i | \(0.216260\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 19.2292 | 0.653811 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −21.4394 | −0.728119 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.29706 | −0.0779223 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.10299 | −0.206792 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.21535 | 0.0411334 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 24.0056 | 0.811539 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.41970 | 0.284313 | 0.142157 | − | 0.989844i | \(-0.454596\pi\) | ||||
0.142157 | + | 0.989844i | \(0.454596\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −37.0310 | −1.24903 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.33625 | 0.280855 | 0.140428 | − | 0.990091i | \(-0.455152\pi\) | ||||
0.140428 | + | 0.990091i | \(0.455152\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.9797 | 0.907941 | 0.453970 | − | 0.891017i | \(-0.350007\pi\) | ||||
0.453970 | + | 0.891017i | \(0.350007\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 32.6948 | 1.09902 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −25.8570 | −0.868193 | −0.434097 | − | 0.900866i | \(-0.642932\pi\) | ||||
−0.434097 | + | 0.900866i | \(0.642932\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 36.2171 | 1.21468 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −18.2234 | −0.610505 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.88133 | 0.0964200 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 34.0726 | 1.13892 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 39.4629 | 1.31763 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6.80348 | −0.226909 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18.9647 | −0.631805 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.89875 | 0.163020 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −31.2074 | −1.03737 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −21.7649 | −0.722690 | −0.361345 | − | 0.932432i | \(-0.617682\pi\) | ||||
−0.361345 | + | 0.932432i | \(0.617682\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.0878377 | 0.00291339 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 13.3098 | 0.440974 | 0.220487 | − | 0.975390i | \(-0.429235\pi\) | ||||
0.220487 | + | 0.975390i | \(0.429235\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.16464 | 0.170925 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 25.0464 | 0.828007 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 19.3669 | 0.639552 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −29.7421 | −0.981103 | −0.490551 | − | 0.871412i | \(-0.663205\pi\) | ||||
−0.490551 | + | 0.871412i | \(0.663205\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −13.3365 | −0.439451 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 22.2745 | 0.733174 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.172873 | 0.00568403 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.08892 | −0.0357648 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −30.3181 | −0.994705 | −0.497352 | − | 0.867549i | \(-0.665694\pi\) | ||||
−0.497352 | + | 0.867549i | \(0.665694\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.01774 | −0.0989024 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 21.8941 | 0.716779 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.30921 | 0.239037 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.81465 | 0.287962 | 0.143981 | − | 0.989580i | \(-0.454010\pi\) | ||||
0.143981 | + | 0.989580i | \(0.454010\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.95586 | 0.226996 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −42.2936 | −1.37873 | −0.689366 | − | 0.724413i | \(-0.742111\pi\) | ||||
−0.689366 | + | 0.724413i | \(0.742111\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 52.1949 | 1.69970 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 17.4778 | 0.568553 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −30.2387 | −0.982626 | −0.491313 | − | 0.870983i | \(-0.663483\pi\) | ||||
−0.491313 | + | 0.870983i | \(0.663483\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 21.2207 | 0.688853 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.86464 | 0.125320 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.52937 | 0.0495411 | 0.0247706 | − | 0.999693i | \(-0.492114\pi\) | ||||
0.0247706 | + | 0.999693i | \(0.492114\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 23.3362 | 0.755141 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.47926 | 0.0801432 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −40.3609 | −1.30332 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 64.5676 | 2.08283 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.33736 | −0.0430957 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −39.6771 | −1.27725 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.67723 | −0.118252 | −0.0591259 | − | 0.998251i | \(-0.518831\pi\) | ||||
−0.0591259 | + | 0.998251i | \(0.518831\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.59513 | 0.115492 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.89852 | −0.189293 | −0.0946463 | − | 0.995511i | \(-0.530172\pi\) | ||||
−0.0946463 | + | 0.995511i | \(0.530172\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 33.4747 | 1.07315 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 18.2232 | 0.583608 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −19.5003 | −0.623871 | −0.311935 | − | 0.950103i | \(-0.600977\pi\) | ||||
−0.311935 | + | 0.950103i | \(0.600977\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 33.0352 | 1.05581 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.669403 | 0.0213724 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.43384 | −0.0776274 | −0.0388137 | − | 0.999246i | \(-0.512358\pi\) | ||||
−0.0388137 | + | 0.999246i | \(0.512358\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.07328 | −0.0979229 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −9.81291 | −0.312348 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.96815 | 0.221574 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 15.1966 | 0.482736 | 0.241368 | − | 0.970434i | \(-0.422404\pi\) | ||||
0.241368 | + | 0.970434i | \(0.422404\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 12.4784 | 0.395990 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −30.5196 | −0.967537 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 42.5056 | 1.34617 | 0.673083 | − | 0.739567i | \(-0.264970\pi\) | ||||
0.673083 | + | 0.739567i | \(0.264970\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.407183 | 0.0128827 |
(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 | 4864.2.a.bn.1.6 | 8 | ||
4.3 | odd | 2 | 4864.2.a.bo.1.3 | 8 | |||
8.3 | odd | 2 | 4864.2.a.bq.1.6 | 8 | |||
8.5 | even | 2 | 4864.2.a.bp.1.3 | 8 | |||
16.3 | odd | 4 | 152.2.c.b.77.7 | ✓ | 16 | ||
16.5 | even | 4 | 608.2.c.b.305.6 | 16 | |||
16.11 | odd | 4 | 152.2.c.b.77.8 | yes | 16 | ||
16.13 | even | 4 | 608.2.c.b.305.11 | 16 | |||
48.5 | odd | 4 | 5472.2.g.b.2737.6 | 16 | |||
48.11 | even | 4 | 1368.2.g.b.685.9 | 16 | |||
48.29 | odd | 4 | 5472.2.g.b.2737.11 | 16 | |||
48.35 | even | 4 | 1368.2.g.b.685.10 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
152.2.c.b.77.7 | ✓ | 16 | 16.3 | odd | 4 | ||
152.2.c.b.77.8 | yes | 16 | 16.11 | odd | 4 | ||
608.2.c.b.305.6 | 16 | 16.5 | even | 4 | |||
608.2.c.b.305.11 | 16 | 16.13 | even | 4 | |||
1368.2.g.b.685.9 | 16 | 48.11 | even | 4 | |||
1368.2.g.b.685.10 | 16 | 48.35 | even | 4 | |||
4864.2.a.bn.1.6 | 8 | 1.1 | even | 1 | trivial | ||
4864.2.a.bo.1.3 | 8 | 4.3 | odd | 2 | |||
4864.2.a.bp.1.3 | 8 | 8.5 | even | 2 | |||
4864.2.a.bq.1.6 | 8 | 8.3 | odd | 2 | |||
5472.2.g.b.2737.6 | 16 | 48.5 | odd | 4 | |||
5472.2.g.b.2737.11 | 16 | 48.29 | odd | 4 |