Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [192,7,Mod(65,192)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(192, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("192.65");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 192 = 2^{6} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 192.e (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: | \(44.1703840550\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-5}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 5 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 12) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 65.1 | ||
Root | \(2.23607i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 192.65 |
Dual form | 192.7.e.d.65.2 |
$q$-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 \(\left(\mathbb{Z}/192\mathbb{Z}\right)^\times\).
\(n\) | \(65\) | \(127\) | \(133\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.00000 | − | 26.8328i | −0.111111 | − | 0.993808i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 160.997i | 1.28798i | 0.765036 | + | 0.643988i | \(0.222721\pi\) | ||||
−0.765036 | + | 0.643988i | \(0.777279\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −242.000 | −0.705539 | −0.352770 | − | 0.935710i | \(-0.614760\pi\) | ||||
−0.352770 | + | 0.935710i | \(0.614760\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −711.000 | + | 160.997i | −0.975309 | + | 0.220846i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1770.97i | 1.33055i | 0.746597 | + | 0.665276i | \(0.231686\pi\) | ||||
−0.746597 | + | 0.665276i | \(0.768314\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2618.00 | −1.19162 | −0.595812 | − | 0.803124i | \(-0.703170\pi\) | ||||
−0.595812 | + | 0.803124i | \(0.703170\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4320.00 | − | 482.991i | 1.28000 | − | 0.143108i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 7083.86i | − | 1.44186i | −0.693007 | − | 0.720931i | \(-0.743715\pi\) | ||
0.693007 | − | 0.720931i | \(-0.256285\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5786.00 | 0.843563 | 0.421782 | − | 0.906697i | \(-0.361405\pi\) | ||||
0.421782 | + | 0.906697i | \(0.361405\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 726.000 | + | 6493.54i | 0.0783933 | + | 0.701171i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 9337.82i | − | 0.767471i | −0.923443 | − | 0.383736i | \(-0.874637\pi\) | ||
0.923443 | − | 0.383736i | \(-0.125363\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −10295.0 | −0.658880 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 6453.00 | + | 18595.1i | 0.327846 | + | 0.944731i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 12396.8i | − | 0.508293i | −0.967166 | − | 0.254147i | \(-0.918205\pi\) | ||
0.967166 | − | 0.254147i | \(-0.0817946\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 20446.0 | 0.686315 | 0.343157 | − | 0.939278i | \(-0.388504\pi\) | ||||
0.343157 | + | 0.939278i | \(0.388504\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 47520.0 | − | 5312.90i | 1.32231 | − | 0.147839i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 38961.2i | − | 0.908717i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 46774.0 | 0.923420 | 0.461710 | − | 0.887031i | \(-0.347236\pi\) | ||||
0.461710 | + | 0.887031i | \(0.347236\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 7854.00 | + | 70248.3i | 0.132403 | + | 1.18425i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 3541.93i | − | 0.0513912i | −0.999670 | − | 0.0256956i | \(-0.991820\pi\) | ||
0.999670 | − | 0.0256956i | \(-0.00818006\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 68618.0 | 0.863044 | 0.431522 | − | 0.902103i | \(-0.357977\pi\) | ||||
0.431522 | + | 0.902103i | \(0.357977\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −25920.0 | − | 114469.i | −0.284444 | − | 1.25617i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 21251.6i | − | 0.204691i | −0.994749 | − | 0.102345i | \(-0.967365\pi\) | ||
0.994749 | − | 0.102345i | \(-0.0326347\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −59085.0 | −0.502214 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −190080. | + | 21251.6i | −1.43293 | + | 0.160207i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 171784.i | − | 1.15386i | −0.816792 | − | 0.576932i | \(-0.804250\pi\) | ||
0.816792 | − | 0.576932i | \(-0.195750\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −285120. | −1.71372 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −17358.0 | − | 155255.i | −0.0937292 | − | 0.838340i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 149566.i | − | 0.728244i | −0.931351 | − | 0.364122i | \(-0.881369\pi\) | ||
0.931351 | − | 0.364122i | \(-0.118631\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −24794.0 | −0.109234 | −0.0546169 | − | 0.998507i | \(-0.517394\pi\) | ||||
−0.0546169 | + | 0.998507i | \(0.517394\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 172062. | − | 38961.2i | 0.688119 | − | 0.155816i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 421490.i | − | 1.53478i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −84358.0 | −0.280480 | −0.140240 | − | 0.990118i | \(-0.544787\pi\) | ||||
−0.140240 | + | 0.990118i | \(0.544787\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −250560. | + | 28013.5i | −0.762719 | + | 0.0852746i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 324248.i | − | 0.905945i | −0.891524 | − | 0.452973i | \(-0.850364\pi\) | ||
0.891524 | − | 0.452973i | \(-0.149636\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −113806. | −0.292548 | −0.146274 | − | 0.989244i | \(-0.546728\pi\) | ||||
−0.146274 | + | 0.989244i | \(0.546728\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 30885.0 | + | 276244.i | 0.0732089 | + | 0.654800i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 428574.i | − | 0.938757i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 159742. | 0.323995 | 0.161997 | − | 0.986791i | \(-0.448206\pi\) | ||||
0.161997 | + | 0.986791i | \(0.448206\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 479601. | − | 228938.i | 0.902454 | − | 0.430786i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 515351.i | 0.901299i | 0.892701 | + | 0.450650i | \(0.148808\pi\) | ||||
−0.892701 | + | 0.450650i | \(0.851192\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.14048e6 | 1.85708 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −332640. | + | 37190.3i | −0.505146 | + | 0.0564770i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 1.25610e6i | − | 1.78178i | −0.454222 | − | 0.890889i | \(-0.650083\pi\) | ||
0.454222 | − | 0.890889i | \(-0.349917\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 633556. | 0.840738 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −61338.0 | − | 548624.i | −0.0762572 | − | 0.682065i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 931528.i | 1.08649i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 899522. | 0.985591 | 0.492795 | − | 0.870145i | \(-0.335975\pi\) | ||||
0.492795 | + | 0.870145i | \(0.335975\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −285120. | − | 1.25916e6i | −0.293848 | − | 1.29770i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 1.19894e6i | − | 1.16368i | −0.813302 | − | 0.581842i | \(-0.802332\pi\) | ||
0.813302 | − | 0.581842i | \(-0.197668\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.59701e6 | 1.46149 | 0.730743 | − | 0.682652i | \(-0.239174\pi\) | ||||
0.730743 | + | 0.682652i | \(0.239174\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.04544e6 | + | 116884.i | −0.903090 | + | 0.100969i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 214287.i | 0.174922i | 0.996168 | + | 0.0874610i | \(0.0278753\pi\) | ||||
−0.996168 | + | 0.0874610i | \(0.972125\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.21811e6 | −1.71278 | −0.856392 | − | 0.516326i | \(-0.827299\pi\) | ||||
−0.856392 | + | 0.516326i | \(0.827299\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −140322. | − | 1.25508e6i | −0.102602 | − | 0.917702i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.01117e6i | 1.39384i | 0.717147 | + | 0.696922i | \(0.245448\pi\) | ||||
−0.717147 | + | 0.696922i | \(0.754552\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.50336e6 | 0.988484 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.86140e6 | − | 421490.i | 1.16220 | − | 0.263166i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.71429e6i | 1.01729i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.36476e6 | −0.770371 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −95040.0 | + | 10625.8i | −0.0510730 | + | 0.00571013i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 858113.i | 0.439354i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −709346. | −0.346296 | −0.173148 | − | 0.984896i | \(-0.555394\pi\) | ||||
−0.173148 | + | 0.984896i | \(0.555394\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −205854. | − | 1.84121e6i | −0.0958937 | − | 0.857700i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 795164.i | − | 0.353706i | −0.984237 | − | 0.176853i | \(-0.943408\pi\) | ||
0.984237 | − | 0.176853i | \(-0.0565917\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.40021e6 | −0.595167 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.99376e6 | + | 1.03891e6i | −1.21679 | + | 0.422258i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 1.46797e6i | − | 0.570894i | −0.958395 | − | 0.285447i | \(-0.907858\pi\) | ||
0.958395 | − | 0.285447i | \(-0.0921420\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.07410e6 | −1.88936 | −0.944680 | − | 0.327993i | \(-0.893628\pi\) | ||||
−0.944680 | + | 0.327993i | \(0.893628\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −570240. | + | 63754.8i | −0.203423 | + | 0.0227434i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 4.63639e6i | − | 1.58552i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.99584e6 | 0.654669 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 177255. | + | 1.58542e6i | 0.0558016 | + | 0.499104i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.32764e6i | 1.00595i | 0.864300 | + | 0.502977i | \(0.167762\pi\) | ||||
−0.864300 | + | 0.502977i | \(0.832238\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.93125e6 | 1.14182 | 0.570912 | − | 0.821011i | \(-0.306590\pi\) | ||||
0.570912 | + | 0.821011i | \(0.306590\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.14048e6 | + | 5.03663e6i | 0.318430 | + | 1.40626i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.29174e6i | 0.883956i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.61188e6 | 0.933328 | 0.466664 | − | 0.884435i | \(-0.345456\pi\) | ||||
0.466664 | + | 0.884435i | \(0.345456\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.60944e6 | + | 515351.i | −1.14672 | + | 0.128207i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.25975e6i | 0.541481i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.76390e6 | 0.869111 | 0.434555 | − | 0.900645i | \(-0.356906\pi\) | ||||
0.434555 | + | 0.900645i | \(0.356906\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 855360. | + | 7.65057e6i | 0.190413 | + | 1.70311i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 478161.i | 0.102666i | 0.998682 | + | 0.0513328i | \(0.0163469\pi\) | ||||
−0.998682 | + | 0.0513328i | \(0.983653\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.02711e6 | 0.419970 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.11385e6 | + | 931528.i | −0.822734 | + | 0.186298i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.01006e6i | 0.967620i | 0.875173 | + | 0.483810i | \(0.160747\pi\) | ||||
−0.875173 | + | 0.483810i | \(0.839253\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.49139e6 | 0.464866 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.01328e6 | + | 448698.i | −0.723735 | + | 0.0809160i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 9.60685e6i | − | 1.67503i | −0.546417 | − | 0.837513i | \(-0.684009\pi\) | ||
0.546417 | − | 0.837513i | \(-0.315991\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.85591e6 | −0.650267 | −0.325133 | − | 0.945668i | \(-0.605409\pi\) | ||||
−0.325133 | + | 0.945668i | \(0.605409\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 74382.0 | + | 665293.i | 0.0121371 | + | 0.108557i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.53047e6i | 1.18934i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.25453e7 | 1.91847 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.56163e6 | − | 4.50002e6i | −0.231309 | − | 0.666545i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 1.36268e6i | − | 0.195566i | −0.995208 | − | 0.0977829i | \(-0.968825\pi\) | ||
0.995208 | − | 0.0977829i | \(-0.0311751\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.53158e6 | −0.630344 | −0.315172 | − | 0.949034i | \(-0.602062\pi\) | ||||
−0.315172 | + | 0.949034i | \(0.602062\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.13098e7 | + | 1.26447e6i | −1.52528 | + | 0.170531i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 6.08681e6i | − | 0.796143i | −0.917354 | − | 0.398071i | \(-0.869680\pi\) | ||
0.917354 | − | 0.398071i | \(-0.130320\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.91777e6 | 0.370248 | 0.185124 | − | 0.982715i | \(-0.440731\pi\) | ||||
0.185124 | + | 0.982715i | \(0.440731\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 253074. | + | 2.26356e6i | 0.0311644 | + | 0.278743i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.00002e6i | 0.358621i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 570240. | 0.0661906 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.50336e6 | + | 6.63919e6i | 0.169493 | + | 0.748521i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.02468e7i | 1.12241i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.12078e7 | 1.19309 | 0.596547 | − | 0.802578i | \(-0.296539\pi\) | ||||
0.596547 | + | 0.802578i | \(0.296539\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −8.70048e6 | + | 972743.i | −0.900336 | + | 0.100661i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.10473e7i | 1.11158i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.94793e6 | −0.484222 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 341418. | + | 3.05374e6i | 0.0325053 | + | 0.290736i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.85456e7i | 1.71816i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.48732e7 | 1.34119 | 0.670593 | − | 0.741825i | \(-0.266040\pi\) | ||||
0.670593 | + | 0.741825i | \(0.266040\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.31974e6 | − | 1.65746e6i | 0.642611 | − | 0.145511i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 2.73614e6i | − | 0.233917i | −0.993137 | − | 0.116958i | \(-0.962686\pi\) | ||
0.993137 | − | 0.116958i | \(-0.0373144\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.96133e6 | 0.746219 | 0.373109 | − | 0.927787i | \(-0.378292\pi\) | ||||
0.373109 | + | 0.927787i | \(0.378292\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.14998e7 | + | 1.28572e6i | −0.932945 | + | 0.104306i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 1.06293e7i | − | 0.840308i | −0.907453 | − | 0.420154i | \(-0.861976\pi\) | ||
0.907453 | − | 0.420154i | \(-0.138024\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.42144e6 | 0.263636 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −479226. | − | 4.28633e6i | −0.0359994 | − | 0.321988i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 2.39080e7i | − | 1.75126i | −0.482984 | − | 0.875629i | \(-0.660447\pi\) | ||
0.482984 | − | 0.875629i | \(-0.339553\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.00217e7 | −0.715964 | −0.357982 | − | 0.933728i | \(-0.616535\pi\) | ||||
−0.357982 | + | 0.933728i | \(0.616535\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −7.58184e6 | − | 1.21822e7i | −0.528392 | − | 0.849001i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 9.51250e6i | − | 0.646839i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.51477e7 | −1.00521 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.38283e7 | − | 1.54605e6i | 0.895718 | − | 0.100144i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.58186e7i | 1.63272i | 0.577544 | + | 0.816359i | \(0.304011\pi\) | ||||
−0.577544 | + | 0.816359i | \(0.695989\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.65370e7 | 1.02116 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.42144e6 | − | 3.06023e7i | −0.206342 | − | 1.84558i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 1.39410e7i | − | 0.821289i | −0.911796 | − | 0.410644i | \(-0.865304\pi\) | ||
0.911796 | − | 0.410644i | \(-0.134696\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.13193e7 | −0.651509 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.99584e6 | + | 8.81410e6i | 0.112255 | + | 0.495743i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.87711e7i | 1.58157i | 0.612092 | + | 0.790787i | \(0.290328\pi\) | ||||
−0.612092 | + | 0.790787i | \(0.709672\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.76566e7 | 1.48615 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.37046e7 | + | 3.76829e6i | −1.77074 | + | 0.197975i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 2.03927e7i | − | 1.04765i | −0.851825 | − | 0.523826i | \(-0.824504\pi\) | ||
0.851825 | − | 0.523826i | \(-0.175496\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.57504e6 | 0.481097 | 0.240548 | − | 0.970637i | \(-0.422673\pi\) | ||||
0.240548 | + | 0.970637i | \(0.422673\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.90067e6 | − | 1.70001e7i | −0.0934154 | − | 0.835532i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 1.82321e7i | − | 0.876675i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.28669e7 | −1.54639 | −0.773196 | − | 0.634167i | \(-0.781343\pi\) | ||||
−0.773196 | + | 0.634167i | \(0.781343\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.45371e7 | + | 3.29174e6i | −0.669369 | + | 0.151570i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 2.37416e7i | − | 1.07002i | −0.844847 | − | 0.535008i | \(-0.820309\pi\) | ||
0.844847 | − | 0.535008i | \(-0.179691\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.93043e7 | 1.73413 | 0.867063 | − | 0.498198i | \(-0.166005\pi\) | ||||
0.867063 | + | 0.498198i | \(0.166005\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.49955e7 | − | 2.79458e6i | 1.07976 | − | 0.120721i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 857147.i | 0.0362585i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.60436e7 | −1.07896 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.69857e6 | − | 2.41367e7i | −0.109510 | − | 0.979488i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 2.32156e7i | − | 0.922947i | −0.887154 | − | 0.461474i | \(-0.847321\pi\) | ||
0.887154 | − | 0.461474i | \(-0.152679\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.40797e7 | 0.937961 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.29314e7 | + | 1.14280e7i | −1.25701 | + | 0.436217i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.44464e7i | 0.914538i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.66056e7 | −0.608911 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.21710e7 | + | 3.59683e6i | −1.15648 | + | 0.129298i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 3.99176e6i | − | 0.140690i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.05148e6 | 0.312827 | 0.156414 | − | 0.987692i | \(-0.450007\pi\) | ||||
0.156414 | + | 0.987692i | \(0.450007\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.79102e6 | − | 4.28522e7i | −0.162387 | − | 1.45244i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.17120e6i | 0.0721804i | 0.999349 | + | 0.0360902i | \(0.0114904\pi\) | ||||
−0.999349 | + | 0.0360902i | \(0.988510\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.08512e7 | 0.353871 | 0.176936 | − | 0.984222i | \(-0.443382\pi\) | ||||
0.176936 | + | 0.984222i | \(0.443382\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.27264e6 | + | 2.77014e7i | 0.200687 | + | 0.886280i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 3.19143e7i | − | 1.00186i | −0.865488 | − | 0.500930i | \(-0.832991\pi\) | ||
0.865488 | − | 0.500930i | \(-0.167009\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.19542e7 | 0.676311 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.74992e6 | − | 642861.i | 0.173839 | − | 0.0194358i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 4.09872e7i | − | 1.21630i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.69523e7 | 0.785138 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.65432e6 | + | 5.95180e7i | 0.190309 | + | 1.70218i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.14288e6i | 0.144417i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.68600e7 | −1.56792 | −0.783958 | − | 0.620814i | \(-0.786802\pi\) | ||||
−0.783958 | + | 0.620814i | \(0.786802\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.32563e7 | + | 7.53047e6i | −0.900620 | + | 0.203934i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 1.35814e7i | − | 0.361251i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.50571e7 | 1.17726 | 0.588632 | − | 0.808401i | \(-0.299667\pi\) | ||||
0.588632 | + | 0.808401i | \(0.299667\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.39654e7 | − | 6.03352e6i | 1.38521 | − | 0.154872i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.62092e7i | 0.913178i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.27696e7 | 1.05987 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.51008e6 | − | 4.03394e7i | −0.109832 | − | 0.982363i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 2.11294e7i | − | 0.505707i | −0.967505 | − | 0.252853i | \(-0.918631\pi\) | ||
0.967505 | − | 0.252853i | \(-0.0813690\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.41108e7 | 0.331953 | 0.165976 | − | 0.986130i | \(-0.446922\pi\) | ||||
0.165976 | + | 0.986130i | \(0.446922\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.68940e7 | − | 4.86821e7i | −0.390670 | − | 1.12577i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 1.60958e7i | − | 0.365923i | −0.983120 | − | 0.182961i | \(-0.941432\pi\) | ||
0.983120 | − | 0.182961i | \(-0.0585683\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.22029e7 | 1.16683 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.59994e7 | − | 5.14288e6i | 1.01099 | − | 0.113032i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 1.11677e7i | − | 0.241369i | −0.992691 | − | 0.120684i | \(-0.961491\pi\) | ||
0.992691 | − | 0.120684i | \(-0.0385089\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.35681e7 | −0.288401 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.09428e6 | + | 3.66203e7i | 0.0855968 | + | 0.765601i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 1.83224e7i | − | 0.376794i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.39616e6 | 0.109166 | 0.0545829 | − | 0.998509i | \(-0.482617\pi\) | ||||
0.0545829 | + | 0.998509i | \(0.482617\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 570240. | + | 2.51831e6i | 0.0113495 | + | 0.0501223i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.15717e7i | 0.814096i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.12151e7 | 0.408807 | 0.204403 | − | 0.978887i | \(-0.434475\pi\) | ||||
0.204403 | + | 0.978887i | \(0.434475\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.30256e7 | − | 2.57434e6i | 0.436634 | − | 0.0488171i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.24547e7i | 0.605695i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.90261e6 | −0.126793 | −0.0633966 | − | 0.997988i | \(-0.520193\pi\) | ||||
−0.0633966 | + | 0.997988i | \(0.520193\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.12804e6 | + | 1.90338e7i | 0.0384773 | + | 0.344151i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 6.12716e7i | − | 1.09059i | −0.838243 | − | 0.545296i | \(-0.816417\pi\) | ||
0.838243 | − | 0.545296i | \(-0.183583\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.89990e7 | 1.20910 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.87874e7 | + | 1.10473e7i | −0.841734 | + | 0.190600i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.49552e7i | 1.27336i | 0.771126 | + | 0.636682i | \(0.219694\pi\) | ||||
−0.771126 | + | 0.636682i | \(0.780306\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.61478e7 | −1.10659 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.13365e7 | + | 2.38549e6i | −0.351516 | + | 0.0393007i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.57180e7i | 0.417297i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.39352e7 | −1.50126 | −0.750631 | − | 0.660721i | \(-0.770251\pi\) | ||||
−0.750631 | + | 0.660721i | \(0.770251\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.20064e6 | + | 3.75716e7i | 0.0661297 | + | 0.591482i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 2.85125e7i | − | 0.442184i | −0.975253 | − | 0.221092i | \(-0.929038\pi\) | ||
0.975253 | − | 0.221092i | \(-0.0709621\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.35276e7 | −0.817830 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.68582e7 | + | 7.72143e7i | 0.554842 | + | 1.16234i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.28352e7i | 1.22866i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.13436e8 | −1.65799 | −0.828996 | − | 0.559255i | \(-0.811087\pi\) | ||||
−0.828996 | + | 0.559255i | \(0.811087\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.93898e7 | + | 4.40391e6i | −0.567359 | + | 0.0634327i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.61950e7i | 0.513805i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.29699e7 | −1.16085 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.52223e7 | + | 1.36152e8i | 0.209929 | + | 1.87766i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 1.15880e8i | − | 1.57531i | −0.616119 | − | 0.787653i | \(-0.711296\pi\) | ||
0.616119 | − | 0.787653i | \(-0.288704\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.58338e7 | −0.882272 | −0.441136 | − | 0.897440i | \(-0.645424\pi\) | ||||
−0.441136 | + | 0.897440i | \(0.645424\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.42144e6 | + | 1.51099e7i | 0.0452051 | + | 0.199636i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.29284e7i | 0.950013i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.00015e6 | 0.0770688 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.24407e8 | + | 1.39092e7i | −1.57570 | + | 0.176169i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 1.15347e8i | − | 1.44070i | −0.693612 | − | 0.720349i | \(-0.743982\pi\) | ||
0.693612 | − | 0.720349i | \(-0.256018\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.17231e7 | −1.12984 | −0.564918 | − | 0.825147i | \(-0.691092\pi\) | ||||
−0.564918 | + | 0.825147i | \(0.691092\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.98752e6 | − | 5.35540e7i | −0.0727410 | − | 0.650615i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 5.40286e7i | − | 0.647410i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.70641e7 | −0.201693 | −0.100847 | − | 0.994902i | \(-0.532155\pi\) | ||||
−0.100847 | + | 0.994902i | \(0.532155\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.20094e7 | − | 9.51250e6i | 0.489814 | − | 0.110912i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.02080e8i | 1.17416i | 0.809528 | + | 0.587081i | \(0.199723\pi\) | ||||
−0.809528 | + | 0.587081i | \(0.800277\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.02228e8 | 2.29488 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.92901e7 | − | 9.98293e6i | 0.999725 | − | 0.111773i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.91565e7i | 0.764002i | 0.924162 | + | 0.382001i | \(0.124765\pi\) | ||||
−0.924162 | + | 0.382001i | \(0.875235\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.27264e6 | 0.0683787 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.17937e7 | − | 1.05486e8i | −0.126869 | − | 1.13475i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.02001e8i | 1.08285i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.98054e7 | 0.521829 | 0.260914 | − | 0.965362i | \(-0.415976\pi\) | ||||
0.260914 | + | 0.965362i | \(0.415976\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.31725e8 | − | 4.57122e7i | 1.36217 | − | 0.472709i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.00776e7i | 0.511141i | 0.966790 | + | 0.255571i | \(0.0822633\pi\) | ||||
−0.966790 | + | 0.255571i | \(0.917737\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.15949e6 | 0.0419080 | 0.0209540 | − | 0.999780i | \(-0.493330\pi\) | ||||
0.0209540 | + | 0.999780i | \(0.493330\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 8.83267e7 | − | 9.87523e6i | 0.878483 | − | 0.0982174i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 1.00127e8i | − | 0.983107i | −0.870847 | − | 0.491553i | \(-0.836429\pi\) | ||
0.870847 | − | 0.491553i | \(-0.163571\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.04146e7 | 0.197890 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.08356e7 | − | 9.69169e7i | −0.103703 | − | 0.927548i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.21520e8i | 1.14832i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.95669e7 | −0.555807 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.76566e7 | + | 1.22138e8i | 0.254826 | + | 1.12537i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.04823e8i | 1.86368i | 0.362867 | + | 0.931841i | \(0.381798\pi\) | ||||
−0.362867 | + | 0.931841i | \(0.618202\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.22454e8 | −1.10037 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.06355e7 | − | 6.77926e6i | 0.538128 | − | 0.0601646i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.44820e8i | 1.26942i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.45737e8 | −1.26178 | −0.630888 | − | 0.775874i | \(-0.717309\pi\) | ||||
−0.630888 | + | 0.775874i | \(0.717309\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.12917e7 | − | 1.00996e8i | −0.0965678 | − | 0.863729i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.01485e8i | 0.857350i | 0.903459 | + | 0.428675i | \(0.141019\pi\) | ||||
−0.903459 | + | 0.428675i | \(0.858981\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.78170e7 | −0.732888 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.02720e8 | − | 4.59034e7i | 1.67140 | − | 0.378468i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.84680e7i | 0.639180i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.42057e7 | −0.758186 | −0.379093 | − | 0.925359i | \(-0.623764\pi\) | ||||
−0.379093 | + | 0.925359i | \(0.623764\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.28304e7 | − | 1.43448e6i | 0.102030 | − | 0.0114073i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 6.54655e7i | − | 0.514409i | −0.966357 | − | 0.257205i | \(-0.917199\pi\) | ||
0.966357 | − | 0.257205i | \(-0.0828014\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.93026e8 | 1.49879 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.08134e6 | − | 5.43932e7i | −0.0466633 | − | 0.417370i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.77803e6i | 0.0665647i | 0.999446 | + | 0.0332823i | \(0.0105961\pi\) | ||||
−0.999446 | + | 0.0332823i | \(0.989404\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.75411e7 | 0.206404 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.73371e7 | + | 1.07591e8i | 0.276559 | + | 0.796940i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.57113e8i | 1.88236i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.76358e7 | 0.272352 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.34434e8 | − | 1.50302e7i | 0.961628 | − | 0.107513i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 1.39544e8i | − | 0.986730i | −0.869822 | − | 0.493365i | \(-0.835767\pi\) | ||
0.869822 | − | 0.493365i | \(-0.164233\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.66441e8 | 1.16347 | 0.581737 | − | 0.813377i | \(-0.302373\pi\) | ||||
0.581737 | + | 0.813377i | \(0.302373\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −7.47417e6 | − | 6.68510e7i | −0.0516518 | − | 0.461987i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 1.44837e8i | − | 0.989570i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.08410e7 | 0.410988 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.40797e7 | + | 1.06342e8i | 0.160830 | + | 0.710263i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.27278e6i | 0.0612390i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.44995e7 | −0.225295 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.57779e8 | + | 2.88205e7i | −1.66465 | + | 0.186114i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 1.04638e8i | − | 0.668223i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.26283e7 | 0.521840 | 0.260920 | − | 0.965360i | \(-0.415974\pi\) | ||||
0.260920 | + | 0.965360i | \(0.415974\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.15677e7 | + | 1.03465e8i | 0.0722519 | + | 0.646240i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 3.57108e8i | − | 2.20602i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.42353e7 | −0.270276 | −0.135138 | − | 0.990827i | \(-0.543148\pi\) | ||||
−0.135138 | + | 0.990827i | \(0.543148\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.76285e7 | − | 3.99176e6i | 0.106537 | − | 0.0241239i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 7.17277e7i | − | 0.428777i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.86576e7 | −0.228591 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.02064e8 | − | 2.25914e7i | 1.18198 | − | 0.132149i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 2.33744e8i | − | 1.35262i | −0.736617 | − | 0.676310i | \(-0.763578\pi\) | ||
0.736617 | − | 0.676310i | \(-0.236422\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.79642e8 | −1.02842 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.76358e7 | − | 3.36625e8i | −0.213164 | − | 1.90659i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 8.34284e7i | − | 0.467508i | −0.972296 | − | 0.233754i | \(-0.924899\pi\) | ||
0.972296 | − | 0.233754i | \(-0.0751010\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.23793e8 | −1.79524 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.16063e8 | + | 5.54029e7i | −0.636717 | + | 0.303937i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 5.02777e7i | − | 0.272922i | −0.990645 | − | 0.136461i | \(-0.956427\pi\) | ||
0.990645 | − | 0.136461i | \(-0.0435729\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.44757e8 | −1.85184 | −0.925922 | − | 0.377716i | \(-0.876710\pi\) | ||||
−0.925922 | + | 0.377716i | \(0.876710\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.65645e7 | + | 4.08803e6i | −0.194355 | + | 0.0217295i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.61329e7i | 0.505671i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.46692e8 | −0.763622 | −0.381811 | − | 0.924240i | \(-0.624699\pi\) | ||||
−0.381811 | + | 0.924240i | \(0.624699\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.35947e7 | + | 1.21595e8i | 0.0700383 | + | 0.626441i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 1.24715e8i | − | 0.635902i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.04223e8 | 1.53528 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6.78586e7 | + | 2.99679e8i | 0.338951 | + | 1.49689i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 3.70598e8i | − | 1.83227i | −0.400875 | − | 0.916133i | \(-0.631294\pi\) | ||
0.400875 | − | 0.916133i | \(-0.368706\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.18301e8 | 0.578950 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.63326e8 | + | 1.82604e7i | −0.791213 | + | 0.0884603i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.20414e8i | 1.05700i | 0.848933 | + | 0.528501i | \(0.177246\pi\) | ||||
−0.848933 | + | 0.528501i | \(0.822754\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.75996e8 | −1.31024 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.75332e6 | − | 7.82921e7i | −0.0411386 | − | 0.367955i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 2.96272e8i | − | 1.37851i | −0.724519 | − | 0.689255i | \(-0.757938\pi\) | ||
0.724519 | − | 0.689255i | \(-0.242062\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.78140e8 | 1.74192 | 0.870962 | − | 0.491350i | \(-0.163496\pi\) | ||||
0.870962 | + | 0.491350i | \(0.163496\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.99785e7 | − | 1.35814e7i | 0.273555 | − | 0.0619429i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 2.19722e8i | − | 0.992219i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.71119e8 | −1.21226 | −0.606128 | − | 0.795367i | \(-0.707278\pi\) | ||||
−0.606128 | + | 0.795367i | \(0.707278\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 8.04989e7 | − | 9.00005e6i | 0.356400 | − | 0.0398468i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.56367e7i | 0.243914i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.95583e7 | 0.388798 | 0.194399 | − | 0.980922i | \(-0.437724\pi\) | ||||
0.194399 | + | 0.980922i | \(0.437724\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.71072e6 | − | 1.53011e7i | −0.00735451 | − | 0.0657807i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 8.35648e7i | − | 0.355769i | −0.984051 | − | 0.177884i | \(-0.943075\pi\) | ||
0.984051 | − | 0.177884i | \(-0.0569253\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.01493e8 | −1.27118 | −0.635588 | − | 0.772028i | \(-0.719242\pi\) | ||||
−0.635588 | + | 0.772028i | \(0.719242\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.73638e8 | − | 6.02570e7i | 0.725054 | − | 0.251613i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.03976e8i | 1.25711i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.99013e8 | −1.22476 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.74951e8 | − | 3.07404e7i | 1.11546 | − | 0.124712i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 3.31341e8i | − | 1.33144i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.78992e8 | −0.712435 | −0.356218 | − | 0.934403i | \(-0.615934\pi\) | ||||
−0.356218 | + | 0.934403i | \(0.615934\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.36235e7 | − | 3.00738e8i | −0.132566 | − | 1.18571i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 1.14203e8i | − | 0.446020i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.54685e8 | 0.598451 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.22029e7 | + | 2.30540e8i | 0.200075 | + | 0.883576i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 2.55168e8i | − | 0.968842i | −0.874835 | − | 0.484421i | \(-0.839030\pi\) | ||
0.874835 | − | 0.484421i | \(-0.160970\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.20260e8 | 1.58083 | 0.790416 | − | 0.612571i | \(-0.209865\pi\) | ||||
0.790416 | + | 0.612571i | \(0.209865\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.96430e8 | − | 3.31419e7i | 1.10470 | − | 0.123509i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.20078e8i | 0.443355i | 0.975120 | + | 0.221677i | \(0.0711532\pi\) | ||||
−0.975120 | + | 0.221677i | \(0.928847\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.64876e8 | 0.968968 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.48438e7 | + | 1.32767e8i | 0.0538024 | + | 0.481224i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.03305e8i | 1.44842i | 0.689581 | + | 0.724209i | \(0.257795\pi\) | ||||
−0.689581 | + | 0.724209i | \(0.742205\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.28019e8 | 0.455565 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.09161e7 | − | 1.83224e7i | 0.285324 | − | 0.0646080i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.33542e8i | 1.16545i | 0.812669 | + | 0.582726i | \(0.198014\pi\) | ||||
−0.812669 | + | 0.582726i | \(0.801986\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.90583e8 | −1.69867 | −0.849334 | − | 0.527856i | \(-0.822996\pi\) | ||||
−0.849334 | + | 0.527856i | \(0.822996\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.97629e8 | − | 5.56367e7i | 1.70752 | − | 0.190906i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 2.25430e8i | − | 0.766560i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.15759e8 | −0.390100 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.46195e7 | − | 3.99089e8i | −0.149021 | − | 1.33288i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 4.39093e7i | − | 0.145341i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.80962e7 | 0.256203 | 0.128102 | − | 0.991761i | \(-0.459112\pi\) | ||||
0.128102 | + | 0.991761i | \(0.459112\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −6.64336e7 | − | 1.91437e8i | −0.216011 | − | 0.622464i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 1.31174e8i | − | 0.422747i | −0.977405 | − | 0.211374i | \(-0.932206\pi\) | ||
0.977405 | − | 0.211374i | \(-0.0677937\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.17684e8 | −0.695373 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.34184e7 | + | 8.20843e6i | −0.232468 | + | 0.0259907i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.37604e6i | 0.00431886i | 0.999998 | + | 0.00215943i | \(0.000687368\pi\) | ||||
−0.999998 | + | 0.00215943i | \(0.999313\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.36339e8 | 0.735297 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.68840e7 | − | 2.40458e8i | −0.0829132 | − | 0.741598i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.49730e8i | 1.37497i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.59620e6 | −0.0169613 | −0.00848065 | − | 0.999964i | \(-0.502700\pi\) | ||||
−0.00848065 | + | 0.999964i | \(0.502700\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.89990e7 | + | 3.04716e8i | 0.207321 | + | 0.915578i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 8.16915e8i | − | 2.43345i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.50906e7 | −0.0740989 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.85215e8 | + | 3.18880e7i | −0.835105 | + | 0.0933675i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.43508e8i | 1.28750i | 0.765235 | + | 0.643751i | \(0.222623\pi\) | ||||
−0.765235 | + | 0.643751i | \(0.777377\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.70634e8 | 0.778963 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.02643e7 | − | 9.18069e7i | −0.0292929 | − | 0.262004i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.90144e8i | 0.821024i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.12264e8 | −0.595576 | −0.297788 | − | 0.954632i | \(-0.596249\pi\) | ||||
−0.297788 | + | 0.954632i | \(0.596249\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.13577e8 | + | 2.57180e7i | −0.315995 | + | 0.0715530i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 1.90921e8i | − | 0.526727i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.46444e8 | 2.04211 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6.41520e8 | + | 7.17241e7i | −1.74041 | + | 0.194584i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.22024e8i | 1.13540i | 0.823234 | + | 0.567702i | \(0.192167\pi\) | ||||
−0.823234 | + | 0.567702i | \(0.807833\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.86475e8 | −1.03114 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.00652e7 | + | 2.68911e8i | 0.0795516 | + | 0.711531i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.27625e8i | 0.334904i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.59541e8 | 1.19597 | 0.597986 | − | 0.801507i | \(-0.295968\pi\) | ||||
0.597986 | + | 0.801507i | \(0.295968\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3.04138e8 | + | 2.39989e8i | −0.785034 | + | 0.619453i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 4.86081e8i | − | 1.24439i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.63121e6 | 0.0193768 | 0.00968838 | − | 0.999953i | \(-0.496916\pi\) | ||||
0.00968838 | + | 0.999953i | \(0.496916\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.55247e8 | + | 2.85375e7i | −0.642834 | + | 0.0718710i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 1.49395e8i | − | 0.373193i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.62220e8 | −0.401949 | −0.200975 | − | 0.979596i | \(-0.564411\pi\) | ||||
−0.200975 | + | 0.979596i | \(0.564411\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.54432e7 | + | 4.06457e8i | 0.111690 | + | 0.998987i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.95948e8i | 1.45292i | 0.687209 | + | 0.726460i | \(0.258836\pi\) | ||||
−0.687209 | + | 0.726460i | \(0.741164\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.35740e8 | −1.29564 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.29699e7 | − | 3.66415e8i | −0.199048 | − | 0.879045i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 5.18574e7i | − | 0.123414i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.72042e7 | −0.111445 | −0.0557225 | − | 0.998446i | \(-0.517746\pi\) | ||||
−0.0557225 | + | 0.998446i | \(0.517746\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.92785e8 | − | 7.74558e7i | 1.62261 | − | 0.181413i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.32918e8i | 1.47064i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.50504e8 | 1.49956 | 0.749778 | − | 0.661690i | \(-0.230160\pi\) | ||||
0.749778 | + | 0.661690i | \(0.230160\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.96109e7 | − | 4.43733e8i | −0.113462 | − | 1.01484i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.49863e8i | 1.47458i | 0.675577 | + | 0.737289i | \(0.263894\pi\) | ||||
−0.675577 | + | 0.737289i | \(0.736106\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.36782e8 | 1.20844 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −8.10881e8 | + | 1.83614e8i | −1.81123 | + | 0.410129i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.91564e8i | 0.867794i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.41673e8 | 0.531433 | 0.265717 | − | 0.964051i | \(-0.414391\pi\) | ||||
0.265717 | + | 0.964051i | \(0.414391\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.74077e8 | + | 4.18231e7i | −0.816203 | + | 0.0912543i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 2.63004e8i | − | 0.569409i | −0.958615 | − | 0.284705i | \(-0.908104\pi\) | ||
0.958615 | − | 0.284705i | \(-0.0918955\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.10492e8 | −0.452199 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.39579e7 | + | 3.03729e8i | 0.0723899 | + | 0.647475i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 2.04936e7i | − | 0.0433517i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.74232e8 | 1.20541 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.30520e8 | − | 7.99963e7i | 0.480200 | − | 0.166642i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.81501e8i | 1.20210i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.26577e8 | −0.669979 | −0.334990 | − | 0.942222i | \(-0.608733\pi\) | ||||
−0.334990 | + | 0.942222i | \(0.608733\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 7.72010e8 | − | 8.63133e7i | 1.57178 | − | 0.175730i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 4.86704e8i | − | 0.983412i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.49107e7 | 0.130166 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8.29699e7 | − | 7.42106e8i | −0.165127 | − | 1.47694i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9.53699e7i | 0.188381i | 0.995554 | + | 0.0941903i | \(0.0300262\pi\) | ||||
−0.995554 | + | 0.0941903i | \(0.969974\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.50543e8 | −0.295135 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.02228e8 | + | 8.93086e8i | 0.393499 | + | 1.73778i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 2.01547e8i | − | 0.389250i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.63813e8 | −0.697414 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5.47193e8 | + | 6.11780e7i | −1.04117 | + | 0.116406i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 2.82791e8i | − | 0.534098i | −0.963683 | − | 0.267049i | \(-0.913952\pi\) | ||
0.963683 | − | 0.267049i | \(-0.0860485\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.15001e8 | −0.403067 | −0.201533 | − | 0.979482i | \(-0.564592\pi\) | ||||
−0.201533 | + | 0.979482i | \(0.564592\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.87251e7 | − | 2.56925e8i | −0.0534552 | − | 0.478118i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.05976e8i | 1.11939i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.97024e8 | 0.728032 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.50458e8 | + | 1.02001e8i | −0.819979 | + | 0.185674i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.97415e8i | 1.44097i | 0.693471 | + | 0.720485i | \(0.256081\pi\) | ||||
−0.693471 | + | 0.720485i | \(0.743919\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.95961e8 | −0.889710 | −0.444855 | − | 0.895603i | \(-0.646745\pi\) | ||||
−0.444855 | + | 0.895603i | \(0.646745\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.89218e8 | + | 5.46963e7i | −0.871246 | + | 0.0974083i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.30031e7i | 0.0406696i | 0.999793 | + | 0.0203348i | \(0.00647321\pi\) | ||||
−0.999793 | + | 0.0203348i | \(0.993527\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.03474e8 | −0.883718 | −0.441859 | − | 0.897085i | \(-0.645681\pi\) | ||||
−0.441859 | + | 0.897085i | \(0.645681\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9.86008e7 | + | 8.81912e8i | 0.171821 | + | 1.53682i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.18550e8i | 0.724123i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.69824e7 | −0.132231 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.31938e8 | + | 3.80196e8i | 0.225006 | + | 0.648383i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 3.06275e8i | − | 0.518592i | −0.965798 | − | 0.259296i | \(-0.916510\pi\) | ||
0.965798 | − | 0.259296i | \(-0.0834905\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.41144e8 | 0.741638 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −6.37053e8 | + | 7.12247e7i | −1.06339 | + | 0.118891i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.26359e8i | 0.540911i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.30272e8 | 0.543527 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.17913e8 | − | 1.05464e9i | −0.192681 | − | 1.72339i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 4.36767e8i | − | 0.708698i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.74562e6 | 0.00442378 | 0.00221189 | − | 0.999998i | \(-0.499296\pi\) | ||||
0.00221189 | + | 0.999998i | \(0.499296\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.49973e8 | − | 6.62316e8i | −0.239947 | − | 1.05966i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.08435e8i | 0.490028i | 0.969520 | + | 0.245014i | \(0.0787926\pi\) | ||||
−0.969520 | + | 0.245014i | \(0.921207\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.04043e9 | 1.64147 | 0.820736 | − | 0.571307i | \(-0.193563\pi\) | ||||
0.820736 | + | 0.571307i | \(0.193563\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.29997e7 | − | 2.57144e6i | 0.0360340 | − | 0.00402872i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 7.72127e8i | − | 1.20131i | −0.799507 | − | 0.600657i | \(-0.794906\pi\) | ||
0.799507 | − | 0.600657i | \(-0.205094\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.06604e8 | −1.24627 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7.81307e7 | + | 6.98822e8i | 0.119885 | + | 1.07228i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.82898e8i | 0.431092i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.20849e8 | 0.334227 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.39560e8 | + | 1.44820e8i | −0.961255 | + | 0.217664i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 2.07663e8i | − | 0.309982i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.17817e8 | 0.471171 | 0.235586 | − | 0.971854i | \(-0.424299\pi\) | ||||
0.235586 | + | 0.971854i | \(0.424299\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.22940e8 | + | 6.96468e7i | −0.917232 | + | 0.102550i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.59366e8i | 0.671786i | 0.941900 | + | 0.335893i | \(0.109038\pi\) | ||||
−0.941900 | + | 0.335893i | \(0.890962\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.77967e8 | 1.13000 | 0.565001 | − | 0.825090i | \(-0.308876\pi\) | ||||
0.565001 | + | 0.825090i | \(0.308876\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7.22390e7 | − | 6.46126e8i | −0.104218 | − | 0.932153i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 6.06049e8i | − | 0.868435i | −0.900808 | − | 0.434217i | \(-0.857025\pi\) | ||
0.900808 | − | 0.434217i | \(-0.142975\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.71662e8 | 0.244325 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.05441e8 | + | 8.49357e8i | 0.573184 | + | 1.20076i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 1.22962e8i | − | 0.172669i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.54667e9 | 2.15739 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.55966e8 | − | 7.33392e7i | 0.908875 | − | 0.101615i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 2.53464e8i | − | 0.348849i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.21689e9 | −1.66371 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.98167e7 | + | 4.45574e8i | 0.0676568 | + | 0.605141i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 6.20790e8i | − | 0.837528i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.52746e8 | −1.00885 | −0.504425 | − | 0.863455i | \(-0.668296\pi\) | ||||
−0.504425 | + | 0.863455i | \(0.668296\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.93026e8 | + | 8.52449e8i | 0.256995 | + | 1.13495i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 8.84130e8i | − | 1.16939i | −0.811252 | − | 0.584697i | \(-0.801213\pi\) | ||
0.811252 | − | 0.584697i | \(-0.198787\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.12669e8 | −1.19923 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.07110e8 | + | 1.19753e7i | −0.139819 | + | 0.0156323i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.92430e8i | 0.249554i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.08334e9 | 1.39578 | 0.697892 | − | 0.716203i | \(-0.254121\pi\) | ||||
0.697892 | + | 0.716203i | \(0.254121\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.71544e7 | − | 2.42877e8i | −0.0347586 | − | 0.310890i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8.48881e8i | 1.07955i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.81538e8 | −0.608423 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.13547e9 | + | 2.57113e8i | −1.42540 | + | 0.322764i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 1.43691e9i | − | 1.79218i | −0.443875 | − | 0.896089i | \(-0.646397\pi\) | ||
0.443875 | − | 0.896089i | \(-0.353603\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.41866e8 | −0.423649 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5.82595e7 | − | 6.51361e6i | 0.0717335 | − | 0.00802005i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.01975e9i | 2.47094i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.12714e9 | 1.37013 | 0.685063 | − | 0.728484i | \(-0.259775\pi\) | ||||
0.685063 | + | 0.728484i | \(0.259775\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.25537e7 | − | 2.91169e8i | −0.0393190 | − | 0.351680i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 1.23121e9i | − | 1.47762i | −0.673913 | − | 0.738810i | \(-0.735388\pi\) | ||
0.673913 | − | 0.738810i | \(-0.264612\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.30739e7 | −0.0394412 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 7.24490e8 | − | 2.51417e8i | 0.858493 | − | 0.297920i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 6.93816e6i | − | 0.00816948i | −0.999992 | − | 0.00408474i | \(-0.998700\pi\) | ||
0.999992 | − | 0.00408474i | \(-0.00130022\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.97944e8 | 0.348607 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.56349e8 | + | 9.57428e7i | −0.995656 | + | 0.111318i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 4.99944e7i | − | 0.0577620i | −0.999583 | − | 0.0288810i | \(-0.990806\pi\) | ||
0.999583 | − | 0.0288810i | \(-0.00919439\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.19387e8 | 0.251884 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −6.58627e7 | − | 5.89094e8i | −0.0751457 | − | 0.672123i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.55249e8i | 0.402788i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.69465e8 | −0.528972 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.44995e7 | − | 1.52358e8i | −0.0386308 | − | 0.170603i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 7.29571e8i | − | 0.811868i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.77551e9 | 1.96356 | 0.981780 | − | 0.190022i | \(-0.0608559\pi\) | ||||
0.981780 | + | 0.190022i | \(0.0608559\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.09980e9 | + | 1.22962e8i | −1.20877 | + | 0.135145i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 4.37887e8i | − | 0.478304i | −0.970982 | − | 0.239152i | \(-0.923131\pi\) | ||
0.970982 | − | 0.239152i | \(-0.0768694\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.22793e9 | 1.33302 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −8.08569e7 | − | 7.23206e8i | −0.0872375 | − | 0.780276i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 1.00202e9i | − | 1.07447i | −0.843433 | − | 0.537235i | \(-0.819469\pi\) | ||
0.843433 | − | 0.537235i | \(-0.180531\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.22451e9 | 2.37075 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.57707e9 | − | 3.57108e8i | 1.67049 | − | 0.378262i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 1.13260e9i | − | 1.19238i | −0.802844 | − | 0.596189i | \(-0.796681\pi\) | ||
0.802844 | − | 0.596189i | \(-0.203319\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.79957e8 | 1.02541 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.37998e8 | − | 1.54287e7i | 0.143523 | − | 0.0160464i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 6.40743e8i | − | 0.662361i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.34604e9 | −1.38305 | −0.691525 | − | 0.722352i | \(-0.743061\pi\) | ||||
−0.691525 | + | 0.722352i | \(0.743061\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.70580e8 | + | 1.52571e9i | 0.174213 | + | 1.55821i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.69753e8i | 0.476870i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.62968e8 | −0.265349 | −0.132675 | − | 0.991160i | \(-0.542357\pi\) | ||||
−0.132675 | + | 0.991160i | \(0.542357\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.01833e8 | + | 8.69769e8i | 0.302740 | + | 0.872384i |
(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 | 192.7.e.d.65.1 | 2 | ||
3.2 | odd | 2 | inner | 192.7.e.d.65.2 | 2 | ||
4.3 | odd | 2 | 192.7.e.e.65.2 | 2 | |||
8.3 | odd | 2 | 12.7.c.a.5.1 | ✓ | 2 | ||
8.5 | even | 2 | 48.7.e.c.17.2 | 2 | |||
12.11 | even | 2 | 192.7.e.e.65.1 | 2 | |||
24.5 | odd | 2 | 48.7.e.c.17.1 | 2 | |||
24.11 | even | 2 | 12.7.c.a.5.2 | yes | 2 | ||
40.3 | even | 4 | 300.7.b.c.149.3 | 4 | |||
40.19 | odd | 2 | 300.7.g.e.101.2 | 2 | |||
40.27 | even | 4 | 300.7.b.c.149.2 | 4 | |||
56.27 | even | 2 | 588.7.c.e.197.2 | 2 | |||
72.11 | even | 6 | 324.7.g.c.53.1 | 4 | |||
72.43 | odd | 6 | 324.7.g.c.53.2 | 4 | |||
72.59 | even | 6 | 324.7.g.c.269.2 | 4 | |||
72.67 | odd | 6 | 324.7.g.c.269.1 | 4 | |||
120.59 | even | 2 | 300.7.g.e.101.1 | 2 | |||
120.83 | odd | 4 | 300.7.b.c.149.1 | 4 | |||
120.107 | odd | 4 | 300.7.b.c.149.4 | 4 | |||
168.83 | odd | 2 | 588.7.c.e.197.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
12.7.c.a.5.1 | ✓ | 2 | 8.3 | odd | 2 | ||
12.7.c.a.5.2 | yes | 2 | 24.11 | even | 2 | ||
48.7.e.c.17.1 | 2 | 24.5 | odd | 2 | |||
48.7.e.c.17.2 | 2 | 8.5 | even | 2 | |||
192.7.e.d.65.1 | 2 | 1.1 | even | 1 | trivial | ||
192.7.e.d.65.2 | 2 | 3.2 | odd | 2 | inner | ||
192.7.e.e.65.1 | 2 | 12.11 | even | 2 | |||
192.7.e.e.65.2 | 2 | 4.3 | odd | 2 | |||
300.7.b.c.149.1 | 4 | 120.83 | odd | 4 | |||
300.7.b.c.149.2 | 4 | 40.27 | even | 4 | |||
300.7.b.c.149.3 | 4 | 40.3 | even | 4 | |||
300.7.b.c.149.4 | 4 | 120.107 | odd | 4 | |||
300.7.g.e.101.1 | 2 | 120.59 | even | 2 | |||
300.7.g.e.101.2 | 2 | 40.19 | odd | 2 | |||
324.7.g.c.53.1 | 4 | 72.11 | even | 6 | |||
324.7.g.c.53.2 | 4 | 72.43 | odd | 6 | |||
324.7.g.c.269.1 | 4 | 72.67 | odd | 6 | |||
324.7.g.c.269.2 | 4 | 72.59 | even | 6 | |||
588.7.c.e.197.1 | 2 | 168.83 | odd | 2 | |||
588.7.c.e.197.2 | 2 | 56.27 | even | 2 |