Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [60,6,Mod(17,60)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(60, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("60.17");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 60 = 2^{2} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 60.i (of order \(4\), degree \(2\), 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: | \(9.62302918878\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 2 x^{19} + 2 x^{18} - 382 x^{17} + 117610 x^{16} - 661518 x^{15} + 1160778 x^{14} - 161859774 x^{13} + 12872525097 x^{12} - 60314430972 x^{11} + \cdots + 48\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{23}\cdot 3^{14}\cdot 5^{12} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 17.7 | ||
Root | \(-4.98882 + 11.3442i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 60.17 |
Dual form | 60.6.i.a.53.7 |
$q$-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 \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(37\) | \(41\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | 4.61326 | − | 14.8902i | 0.295941 | − | 0.955206i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −31.2988 | + | 46.3183i | −0.559891 | + | 0.828567i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −91.3999 | − | 91.3999i | −0.705019 | − | 0.705019i | 0.260465 | − | 0.965483i | \(-0.416124\pi\) |
−0.965483 | + | 0.260465i | \(0.916124\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −200.436 | − | 137.385i | −0.824838 | − | 0.565369i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 99.2471i | 0.247307i | 0.992325 | + | 0.123653i | \(0.0394611\pi\) | ||||
−0.992325 | + | 0.123653i | \(0.960539\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −452.655 | + | 452.655i | −0.742863 | + | 0.742863i | −0.973128 | − | 0.230265i | \(-0.926041\pi\) |
0.230265 | + | 0.973128i | \(0.426041\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 545.298 | + | 679.724i | 0.625757 | + | 0.780018i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1264.35 | + | 1264.35i | −1.06107 | + | 1.06107i | −0.0630620 | + | 0.998010i | \(0.520087\pi\) |
−0.998010 | + | 0.0630620i | \(0.979913\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 912.778i | − | 0.580071i | −0.957016 | − | 0.290035i | \(-0.906333\pi\) | ||
0.957016 | − | 0.290035i | \(-0.0936671\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1782.61 | + | 939.311i | −0.882082 | + | 0.464794i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1746.66 | − | 1746.66i | −0.688478 | − | 0.688478i | 0.273418 | − | 0.961895i | \(-0.411846\pi\) |
−0.961895 | + | 0.273418i | \(0.911846\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1165.77 | − | 2899.42i | −0.373045 | − | 0.927813i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2970.35 | + | 2350.73i | −0.784148 | + | 0.620574i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −299.372 | −0.0661023 | −0.0330512 | − | 0.999454i | \(-0.510522\pi\) | ||||
−0.0330512 | + | 0.999454i | \(0.510522\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2593.02 | 0.484620 | 0.242310 | − | 0.970199i | \(-0.422095\pi\) | ||||
0.242310 | + | 0.970199i | \(0.422095\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1477.81 | + | 457.853i | 0.236229 | + | 0.0731882i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 7094.20 | − | 1372.78i | 0.978889 | − | 0.189422i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5912.19 | + | 5912.19i | 0.709977 | + | 0.709977i | 0.966530 | − | 0.256553i | \(-0.0825868\pi\) |
−0.256553 | + | 0.966530i | \(0.582587\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4651.90 | + | 8828.33i | 0.489744 | + | 0.929430i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 19485.6i | − | 1.81032i | −0.425074 | − | 0.905159i | \(-0.639752\pi\) | ||
0.425074 | − | 0.905159i | \(-0.360248\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8602.82 | + | 8602.82i | −0.709528 | + | 0.709528i | −0.966436 | − | 0.256908i | \(-0.917296\pi\) |
0.256908 | + | 0.966436i | \(0.417296\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 12636.8 | − | 4983.85i | 0.930265 | − | 0.366888i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 17376.5 | − | 17376.5i | 1.14741 | − | 1.14741i | 0.160348 | − | 0.987061i | \(-0.448738\pi\) |
0.987061 | − | 0.160348i | \(-0.0512617\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 99.1062i | − | 0.00589672i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 12993.6 | + | 24659.2i | 0.699528 | + | 1.32756i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −19439.8 | − | 19439.8i | −0.950609 | − | 0.950609i | 0.0482276 | − | 0.998836i | \(-0.484643\pi\) |
−0.998836 | + | 0.0482276i | \(0.984643\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4596.96 | − | 3106.32i | −0.204910 | − | 0.138465i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −13591.4 | − | 4210.88i | −0.554087 | − | 0.171667i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −220.999 | −0.00826535 | −0.00413267 | − | 0.999991i | \(-0.501315\pi\) | ||||
−0.00413267 | + | 0.999991i | \(0.501315\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 43926.7 | 1.51149 | 0.755743 | − | 0.654868i | \(-0.227276\pi\) | ||||
0.755743 | + | 0.654868i | \(0.227276\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5762.85 | + | 30876.8i | 0.182930 | + | 0.980122i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6798.62 | − | 35133.7i | −0.199589 | − | 1.03143i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −38693.6 | − | 38693.6i | −1.05306 | − | 1.05306i | −0.998511 | − | 0.0545473i | \(-0.982628\pi\) |
−0.0545473 | − | 0.998511i | \(-0.517372\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −34066.0 | + | 17950.3i | −0.861387 | + | 0.453890i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 61863.4i | 1.45642i | 0.685352 | + | 0.728212i | \(0.259648\pi\) | ||||
−0.685352 | + | 0.728212i | \(0.740352\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14032.3 | + | 14032.3i | −0.308193 | + | 0.308193i | −0.844208 | − | 0.536015i | \(-0.819929\pi\) |
0.536015 | + | 0.844208i | \(0.319929\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −48550.8 | + | 3982.71i | −0.996652 | + | 0.0817570i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9071.18 | − | 9071.18i | 0.174356 | − | 0.174356i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 64815.3i | 1.16845i | 0.811592 | + | 0.584225i | \(0.198601\pi\) | ||||
−0.811592 | + | 0.584225i | \(0.801399\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 21299.9 | + | 55073.6i | 0.360715 | + | 0.932676i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5901.84 | − | 5901.84i | −0.0940355 | − | 0.0940355i | 0.658524 | − | 0.752560i | \(-0.271181\pi\) |
−0.752560 | + | 0.658524i | \(0.771181\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −18989.8 | − | 98135.1i | −0.285084 | − | 1.47325i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1381.08 | + | 4457.71i | −0.0195624 | + | 0.0631413i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −125772. | −1.68310 | −0.841551 | − | 0.540177i | \(-0.818357\pi\) | ||||
−0.841551 | + | 0.540177i | \(0.818357\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 82745.2 | 1.04746 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 11962.3 | − | 38610.5i | 0.143419 | − | 0.462912i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 42278.3 | + | 28568.9i | 0.480627 | + | 0.324776i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −70605.0 | − | 70605.0i | −0.761915 | − | 0.761915i | 0.214754 | − | 0.976668i | \(-0.431105\pi\) |
−0.976668 | + | 0.214754i | \(0.931105\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 13635.0 | − | 19892.7i | 0.139820 | − | 0.203988i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15327.6i | 0.149510i | 0.997202 | + | 0.0747552i | \(0.0238175\pi\) | ||||
−0.997202 | + | 0.0747552i | \(0.976182\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −110125. | + | 110125.i | −1.02280 | + | 1.02280i | −0.0230675 | + | 0.999734i | \(0.507343\pi\) |
−0.999734 | + | 0.0230675i | \(0.992657\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 12286.5 | − | 111967.i | 0.108756 | − | 0.991098i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 44058.7 | − | 44058.7i | 0.372025 | − | 0.372025i | −0.496189 | − | 0.868214i | \(-0.665268\pi\) |
0.868214 | + | 0.496189i | \(0.165268\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 121373.i | 0.978487i | 0.872147 | + | 0.489243i | \(0.162727\pi\) | ||||
−0.872147 | + | 0.489243i | \(0.837273\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 115308. | − | 60759.2i | 0.888286 | − | 0.468063i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5465.09 | + | 5465.09i | 0.0402626 | + | 0.0402626i | 0.726951 | − | 0.686689i | \(-0.240937\pi\) |
−0.686689 | + | 0.726951i | \(0.740937\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 135571. | − | 26233.9i | 0.955922 | − | 0.184977i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 152916. | − | 28540.3i | 1.03273 | − | 0.192750i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 231123. | 1.49615 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 151201. | 0.938839 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −290145. | − | 89892.3i | −1.72923 | − | 0.535747i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 170783. | + | 36752.1i | 0.977619 | + | 0.210381i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 58474.8 | + | 58474.8i | 0.321706 | + | 0.321706i | 0.849421 | − | 0.527715i | \(-0.176951\pi\) |
−0.527715 | + | 0.849421i | \(0.676951\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 88410.5 | + | 167785.i | 0.467767 | + | 0.887724i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 114053.i | 0.580668i | 0.956925 | + | 0.290334i | \(0.0937664\pi\) | ||||
−0.956925 | + | 0.290334i | \(0.906234\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −83427.8 | + | 83427.8i | −0.408961 | + | 0.408961i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −15913.5 | − | 211157.i | −0.0751504 | − | 0.997172i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −219342. | + | 219342.i | −0.998437 | + | 0.998437i | −0.999999 | − | 0.00156166i | \(-0.999503\pi\) |
0.00156166 | + | 0.999999i | \(0.499503\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 334777.i | − | 1.46966i | −0.678249 | − | 0.734832i | \(-0.737261\pi\) | ||
0.678249 | − | 0.734832i | \(-0.262739\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −178577. | − | 338902.i | −0.756447 | − | 1.43558i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −44924.7 | − | 44924.7i | −0.183715 | − | 0.183715i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9370.00 | − | 13866.4i | 0.0370101 | − | 0.0547702i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1475.71 | − | 457.203i | −0.00563259 | − | 0.00174508i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −225318. | −0.831438 | −0.415719 | − | 0.909493i | \(-0.636470\pi\) | ||||
−0.415719 | + | 0.909493i | \(0.636470\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −84670.2 | −0.302196 | −0.151098 | − | 0.988519i | \(-0.548281\pi\) | ||||
−0.151098 | + | 0.988519i | \(0.548281\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 427123. | − | 79718.3i | 1.47511 | − | 0.275315i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −81158.4 | + | 120104.i | −0.271334 | + | 0.401540i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −72732.0 | − | 72732.0i | −0.235492 | − | 0.235492i | 0.579488 | − | 0.814981i | \(-0.303252\pi\) |
−0.814981 | + | 0.579488i | \(0.803252\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −379143. | + | 199781.i | −1.18935 | + | 0.626703i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 319290.i | 0.970780i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −75660.4 | + | 75660.4i | −0.223049 | + | 0.223049i | −0.809781 | − | 0.586732i | \(-0.800414\pi\) |
0.586732 | + | 0.809781i | \(0.300414\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −67460.6 | + | 54119.3i | −0.192904 | + | 0.154754i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −116674. | + | 116674.i | −0.323730 | + | 0.323730i | −0.850196 | − | 0.526466i | \(-0.823517\pi\) |
0.526466 | + | 0.850196i | \(0.323517\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 38499.3i | − | 0.103690i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −125402. | + | 182953.i | −0.327954 | + | 0.478464i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 283207. | + | 283207.i | 0.719431 | + | 0.719431i | 0.968489 | − | 0.249057i | \(-0.0801208\pi\) |
−0.249057 | + | 0.968489i | \(0.580121\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −158456. | + | 371557.i | −0.391122 | + | 0.917130i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1019.53 | + | 3290.72i | −0.00244605 | + | 0.00789511i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 49873.7 | 0.116343 | 0.0581713 | − | 0.998307i | \(-0.481473\pi\) | ||||
0.0581713 | + | 0.998307i | \(0.481473\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −124517. | −0.282509 | −0.141255 | − | 0.989973i | \(-0.545114\pi\) | ||||
−0.141255 | + | 0.989973i | \(0.545114\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 202646. | − | 654077.i | 0.447311 | − | 1.44378i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −458887. | + | 88797.9i | −0.985773 | + | 0.190754i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −125483. | − | 125483.i | −0.262410 | − | 0.262410i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 486346. | + | 56632.7i | 0.990356 | + | 0.115322i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 392746.i | − | 0.778984i | −0.921030 | − | 0.389492i | \(-0.872651\pi\) | ||
0.921030 | − | 0.389492i | \(-0.127349\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −230496. | + | 230496.i | −0.445420 | + | 0.445420i | −0.893829 | − | 0.448409i | \(-0.851991\pi\) |
0.448409 | + | 0.893829i | \(0.351991\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −554512. | − | 60848.4i | −1.04430 | − | 0.114594i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 340304. | − | 340304.i | 0.624743 | − | 0.624743i | −0.321998 | − | 0.946740i | \(-0.604354\pi\) |
0.946740 | + | 0.321998i | \(0.104354\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 1.08977e6i | − | 1.95076i | −0.220535 | − | 0.975379i | \(-0.570780\pi\) | ||
0.220535 | − | 0.975379i | \(-0.429220\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −754659. | + | 397652.i | −1.31753 | + | 0.694245i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 27362.6 | + | 27362.6i | 0.0466034 | + | 0.0466034i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 902541. | + | 609877.i | 1.49997 | + | 1.01358i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 110129. | + | 590059.i | 0.178638 | + | 0.957127i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 90590.6 | 0.143455 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 664266. | 1.02715 | 0.513577 | − | 0.858043i | \(-0.328320\pi\) | ||||
0.513577 | + | 0.858043i | \(0.328320\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 921157. | + | 285392.i | 1.39118 | + | 0.431015i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −129209. | − | 667726.i | −0.190633 | − | 0.985149i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −237002. | − | 237002.i | −0.341666 | − | 0.341666i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 144209. | + | 273679.i | 0.203181 | + | 0.385595i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 1.14463e6i | − | 1.57646i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 252258. | − | 252258.i | 0.339690 | − | 0.339690i | −0.516560 | − | 0.856251i | \(-0.672788\pi\) |
0.856251 | + | 0.516560i | \(0.172788\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −164675. | + | 741305.i | −0.216855 | + | 0.976204i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 887226. | − | 887226.i | 1.14280 | − | 1.14280i | 0.154863 | − | 0.987936i | \(-0.450507\pi\) |
0.987936 | − | 0.154863i | \(-0.0494935\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 333704.i | 0.420507i | 0.977647 | + | 0.210253i | \(0.0674289\pi\) | ||||
−0.977647 | + | 0.210253i | \(0.932571\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −93223.9 | − | 176919.i | −0.114947 | − | 0.218145i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −424519. | − | 424519.i | −0.512280 | − | 0.512280i | 0.402944 | − | 0.915225i | \(-0.367987\pi\) |
−0.915225 | + | 0.402944i | \(0.867987\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 260986. | + | 1.34872e6i | 0.308281 | + | 1.59313i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 965113. | + | 299010.i | 1.11611 | + | 0.345792i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 800931. | 0.906986 | 0.453493 | − | 0.891260i | \(-0.350178\pi\) | ||||
0.453493 | + | 0.891260i | \(0.350178\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.63579e6 | −1.81419 | −0.907097 | − | 0.420922i | \(-0.861707\pi\) | ||||
−0.907097 | + | 0.420922i | \(0.861707\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 918318. | − | 63090.3i | 0.997648 | − | 0.0685404i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4590.43 | + | 3101.91i | 0.00488583 | + | 0.00330152i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 413173. | + | 413173.i | 0.430913 | + | 0.430913i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −115106. | + | 60652.8i | −0.117652 | + | 0.0619944i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 742347.i | − | 0.743742i | −0.928284 | − | 0.371871i | \(-0.878716\pi\) | ||
0.928284 | − | 0.371871i | \(-0.121284\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 173351. | − | 173351.i | 0.170265 | − | 0.170265i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.54886e6 | − | 169961.i | −1.49163 | − | 0.163681i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.02107e6 | + | 1.02107e6i | −0.964326 | + | 0.964326i | −0.999385 | − | 0.0350592i | \(-0.988838\pi\) |
0.0350592 | + | 0.999385i | \(0.488838\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 1.08075e6i | − | 1.00109i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 60004.9 | + | 41129.2i | 0.0545237 | + | 0.0373722i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 540568. | + | 540568.i | 0.481905 | + | 0.481905i | 0.905740 | − | 0.423835i | \(-0.139316\pi\) |
−0.423835 | + | 0.905740i | \(0.639316\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.50886e6 | − | 291975.i | 1.31988 | − | 0.255406i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −580221. | + | 1.87278e6i | −0.498099 | + | 1.60771i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −749271. | −0.631333 | −0.315666 | − | 0.948870i | \(-0.602228\pi\) | ||||
−0.315666 | + | 0.948870i | \(0.602228\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.24923e6 | −1.03329 | −0.516643 | − | 0.856201i | \(-0.672819\pi\) | ||||
−0.516643 | + | 0.856201i | \(0.672819\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 381725. | − | 1.23209e6i | 0.309988 | − | 1.00054i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 287759. | − | 115699.i | 0.229455 | − | 0.0922566i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −785236. | − | 785236.i | −0.614895 | − | 0.614895i | 0.329322 | − | 0.944218i | \(-0.393180\pi\) |
−0.944218 | + | 0.329322i | \(0.893180\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −519733. | − | 356241.i | −0.399733 | − | 0.273989i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 280724.i | − | 0.212087i | −0.994362 | − | 0.106043i | \(-0.966182\pi\) | ||
0.994362 | − | 0.106043i | \(-0.0338182\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.51150e6 | + | 1.51150e6i | −1.12187 | + | 1.12187i | −0.130412 | + | 0.991460i | \(0.541630\pi\) |
−0.991460 | + | 0.130412i | \(0.958370\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 620437. | − | 497736.i | 0.452466 | − | 0.362984i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.78098e6 | + | 1.78098e6i | −1.27631 | + | 1.27631i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 1.77730e6i | − | 1.25175i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.37704e6 | + | 725603.i | −0.953267 | + | 0.502304i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.38666e6 | − | 1.38666e6i | −0.943628 | − | 0.943628i | 0.0548654 | − | 0.998494i | \(-0.482527\pi\) |
−0.998494 | + | 0.0548654i | \(0.982527\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6917.02 | − | 10236.3i | 0.00462769 | − | 0.00684839i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −233303. | − | 294798.i | −0.153472 | − | 0.193925i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.58127e6 | 1.02289 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.57259e6 | 1.00046 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 228231. | + | 70710.3i | 0.142813 | + | 0.0442462i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.37486e6 | + | 2.03461e6i | −0.846267 | + | 1.25237i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −171663. | − | 171663.i | −0.103952 | − | 0.103952i | 0.653218 | − | 0.757170i | \(-0.273418\pi\) |
−0.757170 | + | 0.653218i | \(0.773418\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.13174e6 | + | 2.14781e6i | 0.674297 | + | 1.27968i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.87250e6i | 1.09779i | 0.835890 | + | 0.548897i | \(0.184952\pi\) | ||||
−0.835890 | + | 0.548897i | \(0.815048\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −774463. | + | 774463.i | −0.446828 | + | 0.446828i | −0.894299 | − | 0.447471i | \(-0.852325\pi\) |
0.447471 | + | 0.894299i | \(0.352325\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.61053e6 | − | 699481.i | −0.914518 | − | 0.397191i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.99126e6 | − | 1.99126e6i | 1.11296 | − | 1.11296i | 0.120210 | − | 0.992749i | \(-0.461643\pi\) |
0.992749 | − | 0.120210i | \(-0.0383567\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 29711.8i | − | 0.0163476i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −452788. | − | 859297.i | −0.245263 | − | 0.465458i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.15407e6 | + | 1.15407e6i | 0.615497 | + | 0.615497i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.84012e6 | + | 784745.i | 0.966359 | + | 0.412117i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.80726e6 | + | 559924.i | 0.934657 | + | 0.289574i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.17643e6 | −1.61789 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.68012e6 | 1.84626 | 0.923129 | − | 0.384491i | \(-0.125623\pi\) | ||||
0.923129 | + | 0.384491i | \(0.125623\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −372769. | − | 1.99726e6i | −0.184217 | − | 0.987015i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.00329e6 | − | 581157.i | 1.46213 | − | 0.282931i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.72073e6 | − | 1.72073e6i | −0.825349 | − | 0.825349i | 0.161521 | − | 0.986869i | \(-0.448360\pi\) |
−0.986869 | + | 0.161521i | \(0.948360\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 106588. | − | 56164.4i | 0.0503744 | − | 0.0265437i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 257350.i | 0.119850i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.54522e6 | + | 1.54522e6i | −0.709176 | + | 0.709176i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 234797. | − | 2.13970e6i | 0.106205 | − | 0.967845i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 411386. | − | 411386.i | 0.183411 | − | 0.183411i | −0.609429 | − | 0.792841i | \(-0.708601\pi\) |
0.792841 | + | 0.609429i | \(0.208601\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.33706e6i | 0.587606i | 0.955866 | + | 0.293803i | \(0.0949210\pi\) | ||||
−0.955866 | + | 0.293803i | \(0.905079\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 280471. | − | 2.40861e6i | 0.121512 | − | 1.04352i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.49730e6 | + | 1.49730e6i | 0.639546 | + | 0.639546i | 0.950444 | − | 0.310897i | \(-0.100629\pi\) |
−0.310897 | + | 0.950444i | \(0.600629\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.86540e6 | − | 1.93625e6i | −1.20674 | − | 0.815438i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.06623e6 | − | 3.44146e6i | 0.442772 | − | 1.42913i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 815104. | 0.333793 | 0.166896 | − | 0.985974i | \(-0.446625\pi\) | ||||
0.166896 | + | 0.985974i | \(0.446625\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.64294e6 | 0.663518 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 697530. | − | 2.25141e6i | 0.277841 | − | 0.896785i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −210758. | − | 1.08915e6i | −0.0828041 | − | 0.427913i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 740709. | + | 740709.i | 0.287066 | + | 0.287066i | 0.835919 | − | 0.548853i | \(-0.184935\pi\) |
−0.548853 | + | 0.835919i | \(0.684935\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.67703e6 | + | 3.90561e6i | −1.02350 | + | 1.49322i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.55359e6i | 1.34039i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.31784e6 | + | 1.31784e6i | −0.490446 | + | 0.490446i | −0.908447 | − | 0.418000i | \(-0.862731\pi\) |
0.418000 | + | 0.908447i | \(0.362731\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.33511e6 | − | 2.37345e6i | 0.490275 | − | 0.871568i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 135512. | − | 135512.i | 0.0491049 | − | 0.0491049i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 360145.i | 0.128789i | 0.997925 | + | 0.0643947i | \(0.0205117\pi\) | ||||
−0.997925 | + | 0.0643947i | \(0.979488\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.14046e6 | − | 600941.i | 0.402502 | − | 0.212090i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −877902. | − | 877902.i | −0.305808 | − | 0.305808i | 0.537473 | − | 0.843281i | \(-0.319379\pi\) |
−0.843281 | + | 0.537473i | \(0.819379\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 136244. | + | 704079.i | 0.0468453 | + | 0.242086i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.90621e6 | − | 542415.i | 0.986391 | − | 0.184100i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.46632e6 | 1.16143 | 0.580717 | − | 0.814105i | \(-0.302772\pi\) | ||||
0.580717 | + | 0.814105i | \(0.302772\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.41679e6 | 1.46105 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.69827e6 | + | 526156.i | 0.554658 | + | 0.171843i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.00213e6 | − | 2.02864e6i | −0.968138 | − | 0.654204i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −808667. | − | 808667.i | −0.257510 | − | 0.257510i | 0.566531 | − | 0.824040i | \(-0.308285\pi\) |
−0.824040 | + | 0.566531i | \(0.808285\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 857382. | + | 1.62713e6i | 0.269614 | + | 0.511670i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.47909e6i | 1.08045i | 0.841520 | + | 0.540226i | \(0.181661\pi\) | ||||
−0.841520 | + | 0.540226i | \(0.818339\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.17374e6 | + | 1.17374e6i | −0.360006 | + | 0.360006i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.21757e6 | − | 737166.i | −0.974745 | − | 0.223320i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −586768. | + | 586768.i | −0.175582 | + | 0.175582i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.08607e6i | 0.321033i | 0.987033 | + | 0.160517i | \(0.0513160\pi\) | ||||
−0.987033 | + | 0.160517i | \(0.948684\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.25416e6 | + | 4.27793e6i | 0.658235 | + | 1.24919i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 20199.3 | + | 20199.3i | 0.00582723 | + | 0.00582723i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 458084. | − | 88642.3i | 0.130564 | − | 0.0252651i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.98489e6 | − | 1.54441e6i | −1.40383 | − | 0.434934i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.43635e6 | −1.79104 | −0.895519 | − | 0.445023i | \(-0.853196\pi\) | ||||
−0.895519 | + | 0.445023i | \(0.853196\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.42261e6 | −0.666158 | −0.333079 | − | 0.942899i | \(-0.608088\pi\) | ||||
−0.333079 | + | 0.942899i | \(0.608088\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.87014e6 | + | 1.09561e6i | −1.59514 | + | 0.297717i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.13981e6 | + | 2.19194e6i | 1.38030 | + | 0.588649i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.01490e6 | − | 4.01490e6i | −1.06563 | − | 1.06563i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −876186. | + | 461687.i | −0.229855 | + | 0.121117i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 687785.i | − | 0.178344i | −0.996016 | − | 0.0891722i | \(-0.971578\pi\) | ||
0.996016 | − | 0.0891722i | \(-0.0284221\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 72171.9 | − | 72171.9i | 0.0184990 | − | 0.0184990i | −0.697797 | − | 0.716296i | \(-0.745836\pi\) |
0.716296 | + | 0.697797i | \(0.245836\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −163247. | − | 203491.i | −0.0413640 | − | 0.0515610i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.59432e6 | + | 1.59432e6i | −0.399366 | + | 0.399366i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 5.43596e6i | − | 1.34622i | −0.739544 | − | 0.673108i | \(-0.764959\pi\) | ||
0.739544 | − | 0.673108i | \(-0.235041\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −13615.7 | + | 19864.4i | −0.00333383 | + | 0.00486384i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.76348e6 | − | 1.76348e6i | −0.426934 | − | 0.426934i | 0.460649 | − | 0.887582i | \(-0.347617\pi\) |
−0.887582 | + | 0.460649i | \(0.847617\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.93653e6 | − | 5.82556e6i | 0.942353 | − | 1.39456i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.03945e6 | + | 3.35502e6i | −0.246056 | + | 0.794194i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.66972e6 | −0.859047 | −0.429524 | − | 0.903056i | \(-0.641319\pi\) | ||||
−0.429524 | + | 0.903056i | \(0.641319\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.93389e6 | 0.447704 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −390606. | + | 1.26076e6i | −0.0894321 | + | 0.288659i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.58983e6 | + | 3.83261e6i | −0.586465 | + | 0.867894i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.80763e6 | + | 1.80763e6i | 0.404874 | + | 0.404874i | 0.879947 | − | 0.475073i | \(-0.157578\pi\) |
−0.475073 | + | 0.879947i | \(0.657578\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 783409. | − | 6.72770e6i | 0.173563 | − | 1.49051i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 2.07114e6i | − | 0.453898i | −0.973907 | − | 0.226949i | \(-0.927125\pi\) | ||
0.973907 | − | 0.226949i | \(-0.0728750\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.80388e6 | + | 1.80388e6i | −0.391070 | + | 0.391070i | −0.875069 | − | 0.483999i | \(-0.839184\pi\) |
0.483999 | + | 0.875069i | \(0.339184\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.41397e6 | + | 1.76254e6i | 0.303255 | + | 0.378012i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 329212. | − | 329212.i | 0.0698526 | − | 0.0698526i | −0.671317 | − | 0.741170i | \(-0.734271\pi\) |
0.741170 | + | 0.671317i | \(0.234271\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.07319e6i | 1.48485i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.41853e6 | + | 747462.i | −0.294636 | + | 0.155252i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −853805. | − | 853805.i | −0.175471 | − | 0.175471i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.64652e6 | + | 1.06408e6i | −0.538197 | + | 0.216393i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.22570e6 | + | 6.56716e6i | 0.246653 | + | 1.32154i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.04336e6 | 1.40262 | 0.701311 | − | 0.712855i | \(-0.252598\pi\) | ||||
0.701311 | + | 0.712855i | \(0.252598\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.35236e6 | −1.05483 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.75429e6 | + | 1.47297e6i | 0.927295 | + | 0.287293i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.48016e6 | − | 1.06045e6i | 1.05789 | − | 0.204708i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.49566e6 | + | 1.49566e6i | 0.285765 | + | 0.285765i | 0.835403 | − | 0.549638i | \(-0.185234\pi\) |
−0.549638 | + | 0.835403i | \(0.685234\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 777557. | + | 1.47564e6i | 0.147048 | + | 0.279067i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 8.24705e6i | − | 1.54381i | −0.635735 | − | 0.771907i | \(-0.719303\pi\) | ||
0.635735 | − | 0.771907i | \(-0.280697\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 378511. | − | 378511.i | 0.0701393 | − | 0.0701393i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 494633. | + | 1.25417e6i | 0.0907340 | + | 0.230061i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.65431e6 | − | 5.65431e6i | 1.02681 | − | 1.02681i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.98951e6i | 0.897029i | 0.893776 | + | 0.448514i | \(0.148047\pi\) | ||||
−0.893776 | + | 0.448514i | \(0.851953\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.19905e6 | + | 2.27554e6i | 0.213424 | + | 0.405033i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7.34572e6 | − | 7.34572e6i | −1.29454 | − | 1.29454i | −0.931950 | − | 0.362588i | \(-0.881893\pi\) |
−0.362588 | − | 0.931950i | \(-0.618107\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −709949. | − | 479737.i | −0.123879 | − | 0.0837094i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −573261. | − | 177607.i | −0.0990450 | − | 0.0306860i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.08281e6 | 0.356332 | 0.178166 | − | 0.984000i | \(-0.442984\pi\) | ||||
0.178166 | + | 0.984000i | \(0.442984\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.56511e6 | 0.434564 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.14570e6 | + | 2.71127e6i | 0.359977 | + | 0.454861i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.65401e6 | − | 8.54755e6i | −0.274802 | − | 1.42012i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.72457e6 | + | 1.72457e6i | 0.283762 | + | 0.283762i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.52352e6 | − | 2.91050e6i | 0.900114 | − | 0.474296i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 6.85982e6i | − | 1.10718i | −0.832789 | − | 0.553590i | \(-0.813257\pi\) | ||
0.832789 | − | 0.553590i | \(-0.186743\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.98946e6 | − | 5.98946e6i | 0.957488 | − | 0.957488i | −0.0416441 | − | 0.999133i | \(-0.513260\pi\) |
0.999133 | + | 0.0416441i | \(0.0132596\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.80156e6 | + | 4.07353e6i | 0.760299 | + | 0.645018i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.27848e6 | + | 3.27848e6i | −0.514216 | + | 0.514216i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 334669.i | − | 0.0519967i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 44296.2 | + | 30361.9i | 0.00681757 | + | 0.00467297i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.82026e6 | + | 8.82026e6i | 1.34482 | + | 1.34482i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 661737. | + | 3.41971e6i | 0.0999542 | + | 0.516541i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 230080. | − | 742629.i | 0.0344306 | − | 0.111131i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 9836.01 | 0.00145830 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.12752e6 | −1.19389 | −0.596946 | − | 0.802281i | \(-0.703619\pi\) | ||||
−0.596946 | + | 0.802281i | \(0.703619\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −574431. | + | 1.85409e6i | −0.0836061 | + | 0.269855i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.62178e6 | − | 3.79883e6i | −0.810742 | − | 0.547846i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.39180e6 | + | 4.39180e6i | 0.627587 | + | 0.627587i | 0.947460 | − | 0.319873i | \(-0.103640\pi\) |
−0.319873 | + | 0.947460i | \(0.603640\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8.80448e6 | − | 6.03486e6i | −1.24673 | − | 0.854548i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 273260.i | 0.0383440i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.92412e6 | − | 5.92412e6i | 0.823779 | − | 0.823779i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −794751. | + | 7.24257e6i | −0.109521 | + | 0.998068i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −39334.5 | + | 39334.5i | −0.00537199 | + | 0.00537199i | −0.709788 | − | 0.704416i | \(-0.751209\pi\) |
0.704416 | + | 0.709788i | \(0.251209\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 7.78821e6i | − | 1.05416i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.44735e6 | + | 1.28958e6i | −0.328314 | + | 0.172998i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.42062e6 | − | 3.42062e6i | −0.454814 | − | 0.454814i | 0.442135 | − | 0.896949i | \(-0.354221\pi\) |
−0.896949 | + | 0.442135i | \(0.854221\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −424185. | + | 82082.7i | −0.0559029 | + | 0.0108176i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.08691e6 | − | 6.98053e6i | 0.403243 | − | 0.911865i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.14170e7 | 1.47833 | 0.739163 | − | 0.673526i | \(-0.235221\pi\) | ||||
0.739163 | + | 0.673526i | \(0.235221\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.32685e6 | −0.298661 | −0.149331 | − | 0.988787i | \(-0.547712\pi\) | ||||
−0.149331 | + | 0.988787i | \(0.547712\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.84806e6 | − | 1.81184e6i | −0.744090 | − | 0.230533i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.02811e6 | + | 7.10051e6i | −0.381946 | + | 0.895612i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.42852e6 | + | 1.42852e6i | 0.178627 | + | 0.178627i | 0.790757 | − | 0.612130i | \(-0.209687\pi\) |
−0.612130 | + | 0.790757i | \(0.709687\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.36879e6 | + | 4.49546e6i | 0.293650 | + | 0.557285i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.07885e6i | 0.132594i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.92934e6 | − | 1.92934e6i | 0.235092 | − | 0.235092i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.46415e6 | + | 7.97608e6i | −0.418512 | + | 0.963607i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.13039e6 | − | 5.13039e6i | 0.614546 | − | 0.614546i | −0.329581 | − | 0.944127i | \(-0.606907\pi\) |
0.944127 | + | 0.329581i | \(0.106907\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 2.36685e6i | − | 0.281114i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.49728e6 | − | 6.63710e6i | −0.411871 | − | 0.781645i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.57161e6 | + | 3.57161e6i | 0.417087 | + | 0.417087i | 0.884199 | − | 0.467111i | \(-0.154705\pi\) |
−0.467111 | + | 0.884199i | \(0.654705\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.23388e6 | + | 1.07052e7i | −0.837681 | + | 1.23966i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.62269e7 | − | 5.02741e6i | −1.86338 | − | 0.577309i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.49341e7 | −1.70064 | −0.850320 | − | 0.526266i | \(-0.823592\pi\) | ||||
−0.850320 | + | 0.526266i | \(0.823592\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.58569e6 | −0.743730 | −0.371865 | − | 0.928287i | \(-0.621282\pi\) | ||||
−0.371865 | + | 0.928287i | \(0.621282\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.43967e6 | + | 1.30715e7i | 0.273236 | + | 1.46397i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.73242e6 | + | 7.00337e6i | −0.525647 | + | 0.777891i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.10867e6 | + | 2.10867e6i | 0.232294 | + | 0.232294i | 0.813650 | − | 0.581356i | \(-0.197477\pi\) |
−0.581356 | + | 0.813650i | \(0.697477\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 533665. | − | 281204.i | 0.0583077 | − | 0.0307240i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.57311e7i | 1.70473i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.87357e6 | − | 6.87357e6i | 0.738808 | − | 0.738808i | −0.233540 | − | 0.972347i | \(-0.575031\pi\) |
0.972347 | + | 0.233540i | \(0.0750309\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.32448e7 | − | 1.06255e7i | 1.41208 | − | 1.13282i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.24340e6 | + | 4.24340e6i | −0.448746 | + | 0.448746i | −0.894938 | − | 0.446191i | \(-0.852780\pi\) |
0.446191 | + | 0.894938i | \(0.352780\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 3.15907e6i | − | 0.331385i | −0.986177 | − | 0.165692i | \(-0.947014\pi\) | ||
0.986177 | − | 0.165692i | \(-0.0529859\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 9.29414e6 | + | 1.08226e6i | 0.967120 | + | 0.112616i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.14956e7 | + | 1.14956e7i | 1.18662 | + | 1.18662i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.04761e6 | + | 6.76008e6i | −0.721675 | + | 0.692232i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 417918. | − | 1.34891e6i | 0.0424544 | − | 0.137030i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.49502e7 | −1.50667 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.35027e7 | −1.35004 | −0.675019 | − | 0.737801i | \(-0.735864\pi\) | ||||
−0.675019 | + | 0.737801i | \(0.735864\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.06443e6 | − | 9.89104e6i | 0.303977 | − | 0.981144i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.53864e6 | + | 878258.i | −0.446675 | + | 0.0864347i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 44860.9 | + | 44860.9i | 0.00438046 | + | 0.00438046i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.49908e6 | − | 1.23996e7i | 0.823417 | − | 1.20131i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 9.62559e6i | − | 0.925300i | −0.886541 | − | 0.462650i | \(-0.846899\pi\) | ||
0.886541 | − | 0.462650i | \(-0.153101\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.56761e6 | − | 7.56761e6i | 0.721824 | − | 0.721824i | −0.247153 | − | 0.968976i | \(-0.579495\pi\) |
0.968976 | + | 0.247153i | \(0.0794950\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.05386e7 | − | 1.15644e6i | −0.997437 | − | 0.109452i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.14833e7 | + | 1.14833e7i | −1.07846 | + | 1.07846i | −0.0818142 | + | 0.996648i | \(0.526071\pi\) |
−0.996648 | + | 0.0818142i | \(0.973929\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 21933.6i | − | 0.00204408i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.62235e6 | + | 2.43565e6i | −0.427475 | + | 0.225249i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.08314e6 | − | 1.08314e6i | −0.0994035 | − | 0.0994035i | 0.655656 | − | 0.755060i | \(-0.272392\pi\) |
−0.755060 | + | 0.655656i | \(0.772392\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.28273e6 | − | 3.56972e6i | −0.481122 | − | 0.325111i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.74041e6 | − | 884751.i | 0.428452 | − | 0.0799664i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.50688e7 | 1.35166 | 0.675828 | − | 0.737060i | \(-0.263786\pi\) | ||||
0.675828 | + | 0.737060i | \(0.263786\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.82461e6 | 0.162430 | 0.0812152 | − | 0.996697i | \(-0.474120\pi\) | ||||
0.0812152 | + | 0.996697i | \(0.474120\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.70437e7 | − | 5.28046e6i | −1.50585 | − | 0.466539i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.25304e6 | − | 6.47543e6i | −0.109878 | − | 0.567825i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 522903. | + | 522903.i | 0.0455100 | + | 0.0455100i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.59244e6 | − | 4.91991e6i | −0.223946 | − | 0.425003i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.35960e6i | 0.373801i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.29426e6 | − | 3.29426e6i | 0.280363 | − | 0.280363i | −0.552891 | − | 0.833254i | \(-0.686475\pi\) |
0.833254 | + | 0.552891i | \(0.186475\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.02785e7 | + | 5.87187e6i | 0.868300 | + | 0.496040i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −441807. | + | 441807.i | −0.0370477 | + | 0.0370477i | −0.725388 | − | 0.688340i | \(-0.758340\pi\) |
0.688340 | + | 0.725388i | \(0.258340\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.29066e7i | 1.07433i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.11796e6 | − | 1.73040e7i | −0.753407 | − | 1.42981i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.25040e6 | + | 1.25040e6i | 0.102564 | + | 0.102564i | 0.756527 | − | 0.653963i | \(-0.226895\pi\) |
−0.653963 | + | 0.756527i | \(0.726895\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.29440e6 | − | 1.70247e7i | −0.268256 | − | 1.38629i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.96892e6 | + | 1.53946e6i | 0.401671 | + | 0.124445i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.75990e7 | 1.41234 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.70803e6 | −0.693785 | −0.346892 | − | 0.937905i | \(-0.612763\pi\) | ||||
−0.346892 | + | 0.937905i | \(0.612763\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.06443e6 | + | 571946.i | −0.242391 | + | 0.0452399i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.55063e7 | + | 1.04781e7i | 1.21771 | + | 0.822851i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.46366e7 | + | 2.46366e7i | 1.92088 | + | 1.92088i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8.27960e6 | + | 4.36276e6i | −0.640938 | + | 0.337729i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.69157e6i | 0.591180i | 0.955315 | + | 0.295590i | \(0.0955163\pi\) | ||||
−0.955315 | + | 0.295590i | \(0.904484\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.39652e6 | − | 5.39652e6i | 0.411837 | − | 0.411837i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.12866e7 | + | 2.33585e6i | 1.61300 | + | 0.177000i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.40094e6 | − | 1.40094e6i | 0.105408 | − | 0.105408i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.20245e6i | 0.538102i | 0.963126 | + | 0.269051i | \(0.0867100\pi\) | ||||
−0.963126 | + | 0.269051i | \(0.913290\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.90464e6 | − | 1.29913e7i | 0.660605 | − | 0.963781i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.52913e6 | − | 4.52913e6i | −0.333650 | − | 0.333650i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.48692e6 | − | 674743.i | 0.255080 | − | 0.0493598i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.69491e6 | − | 1.19260e7i | 0.268414 | − | 0.866358i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.82537e6 | 0.492384 | 0.246192 | − | 0.969221i | \(-0.420821\pi\) | ||||
0.246192 | + | 0.969221i | \(0.420821\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.01308e7 | 1.44219 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −7.54631e6 | + | 2.43572e7i | −0.536894 | + | 1.73293i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 348998. | + | 868005.i | 0.0246591 | + | 0.0613306i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.24584e6 | − | 6.24584e6i | −0.438283 | − | 0.438283i | 0.453151 | − | 0.891434i | \(-0.350300\pi\) |
−0.891434 | + | 0.453151i | \(0.850300\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.29702e6 | − | 1.39650e7i | 0.229775 | − | 0.973244i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 2.17539e7i | − | 1.50572i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.01323e7 | + | 1.01323e7i | −0.696545 | + | 0.696545i | −0.963664 | − | 0.267119i | \(-0.913928\pi\) |
0.267119 | + | 0.963664i | \(0.413928\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 67364.9 | − | 54042.5i | 0.00459955 | − | 0.00368992i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.84023e6 | − | 3.84023e6i | 0.260429 | − | 0.260429i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.01149e7i | 1.35490i | 0.735570 | + | 0.677449i | \(0.236914\pi\) | ||||
−0.735570 | + | 0.677449i | \(0.763086\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.05830e6 | − | 4.24615e6i | 0.539135 | − | 0.284086i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.47987e6 | + | 4.47987e6i | 0.297710 | + | 0.297710i | 0.840116 | − | 0.542406i | \(-0.182487\pi\) |
−0.542406 | + | 0.840116i | \(0.682487\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.05218e6 | − | 1.04363e7i | 0.465514 | − | 0.688901i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 372116. | + | 1.99376e6i | 0.0243993 | + | 0.130729i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8.05392e6 | −0.524569 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.55756e6 | −0.553669 | −0.276834 | − | 0.960918i | \(-0.589285\pi\) | ||||
−0.276834 | + | 0.960918i | \(0.589285\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.10537e7 | − | 3.42464e6i | −0.710427 | − | 0.220104i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.65008e6 | − | 3.92178e6i | 0.169197 | − | 0.250389i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.84285e6 | − | 7.84285e6i | −0.497433 | − | 0.497433i | 0.413205 | − | 0.910638i | \(-0.364409\pi\) |
−0.910638 | + | 0.413205i | \(0.864409\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.78152e6 | − | 3.38095e6i | −0.112250 | − | 0.213027i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.13075e7i | 0.707793i | 0.935285 | + | 0.353897i | \(0.115144\pi\) | ||||
−0.935285 | + | 0.353897i | \(0.884856\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.10935e7 | − | 1.10935e7i | 0.689852 | − | 0.689852i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −9.67603e6 | + | 2.22787e7i | −0.597783 | + | 1.37637i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 100036. | − | 100036.i | 0.00614002 | − | 0.00614002i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 2.51981e7i | − | 1.53657i | −0.640109 | − | 0.768284i | \(-0.721111\pi\) | ||
0.640109 | − | 0.768284i | \(-0.278889\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.04935e7 | + | 1.99144e7i | 0.635747 | + | 1.20651i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.15965e7 | − | 2.15965e7i | −1.29997 | − | 1.29997i | −0.928406 | − | 0.371567i | \(-0.878821\pi\) |
−0.371567 | − | 0.928406i | \(-0.621179\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.02285e6 | − | 7.51824e6i | −0.180785 | − | 0.449637i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.60925e7 | − | 4.98578e6i | −0.956252 | − | 0.296265i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.77860e7 | −1.05011 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.13976e6 | −0.360183 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 889240. | − | 703744.i | 0.0518340 | − | 0.0410214i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.64525e6 | − | 1.09239e6i | 0.326971 | − | 0.0632711i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.06749e7 | − | 1.06749e7i | −0.614368 | − | 0.614368i | 0.329713 | − | 0.944081i | \(-0.393048\pi\) |
−0.944081 | + | 0.329713i | \(0.893048\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.05430e7 | − | 5.55538e6i | 0.602934 | − | 0.317703i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 999018.i | − | 0.0567717i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.98836e7 | + | 1.98836e7i | −1.12283 | + | 1.12283i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.61321e6 | − | 2.38142e7i | 0.146641 | − | 1.33634i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −7.49492e6 | + | 7.49492e6i | −0.417947 | + | 0.417947i | −0.884496 | − | 0.466548i | \(-0.845497\pi\) |
0.466548 | + | 0.884496i | \(0.345497\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.39400e7i | 2.43497i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.52093e7 | + | 1.72792e7i | 1.38829 | + | 0.951574i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.39267e6 | − | 1.39267e6i | −0.0762182 | − | 0.0762182i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.47890e7 | − | 9.99341e6i | −0.804356 | − | 0.543530i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.45658e6 | + | 1.11568e7i | −0.186837 | + | 0.603053i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.28460e6 | 0.176446 | 0.0882230 | − | 0.996101i | \(-0.471881\pi\) | ||||
0.0882230 | + | 0.996101i | \(0.471881\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.90925e7 | 1.01932 | 0.509660 | − | 0.860376i | \(-0.329771\pi\) | ||||
0.509660 | + | 0.860376i | \(0.329771\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.76304e6 | + | 1.86013e7i | −0.305792 | + | 0.987001i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.13638e6 | − | 5.87254e6i | −0.0599278 | − | 0.309694i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.85246e6 | + | 7.85246e6i | 0.411576 | + | 0.411576i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.65851e7 | − | 1.13679e7i | −0.863988 | − | 0.592204i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.82252e7i | 1.97921i | 0.143814 | + | 0.989605i | \(0.454063\pi\) | ||||
−0.143814 | + | 0.989605i | \(0.545937\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.78614e7 | − | 1.78614e7i | 0.919212 | − | 0.919212i | −0.0777600 | − | 0.996972i | \(-0.524777\pi\) |
0.996972 | + | 0.0777600i | \(0.0247768\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −395272. | − | 4.81853e6i | −0.0202191 | − | 0.246479i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.31871e7 | − | 1.31871e7i | 0.670479 | − | 0.670479i | −0.287347 | − | 0.957826i | \(-0.592773\pi\) |
0.957826 | + | 0.287347i | \(0.0927734\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.40847e6i | 0.273330i | 0.990617 | + | 0.136665i | \(0.0436385\pi\) | ||||
−0.990617 | + | 0.136665i | \(0.956362\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.53148e7 | + | 8.06982e6i | −0.769324 | + | 0.405379i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 125305. | + | 125305.i | 0.00625685 | + | 0.00625685i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.75238e6 | − | 9.05589e6i | −0.0869784 | − | 0.449485i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.70216e6 | + | 6.09549e6i | −0.380014 | + | 0.300743i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.58334e7 | −1.26700 | −0.633501 | − | 0.773742i | \(-0.718383\pi\) | ||||
−0.633501 | + | 0.773742i | \(0.718383\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.04215e7 | −0.995630 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −4.18003e6 | − | 1.29505e6i | −0.202586 | − | 0.0627651i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.78322e6 | + | 1.20498e6i | 0.0859138 | + | 0.0580549i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.38198e7 | − | 1.38198e7i | −0.661899 | − | 0.661899i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.55336e7 | + | 2.94796e7i | 0.739611 | + | 1.40363i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 2.06532e7i | − | 0.977607i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.49234e6 | + | 6.49234e6i | −0.305512 | + | 0.305512i | −0.843166 | − | 0.537654i | \(-0.819311\pi\) |
0.537654 | + | 0.843166i | \(0.319311\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.54915e6 | − | 1.15346e7i | −0.212821 | − | 0.539620i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.74874e6 | − | 4.74874e6i | 0.220865 | − | 0.220865i | −0.587998 | − | 0.808862i | \(-0.700084\pi\) |
0.808862 | + | 0.587998i | \(0.200084\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 3.44086e6i | − | 0.159105i | −0.996831 | − | 0.0795525i | \(-0.974651\pi\) | ||
0.996831 | − | 0.0795525i | \(-0.0253491\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.83031e7 | + | 3.47354e7i | 0.841426 | + | 1.59685i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.94180e7 | + | 1.94180e7i | 0.887520 | + | 0.887520i | 0.994284 | − | 0.106765i | \(-0.0340491\pi\) |
−0.106765 | + | 0.994284i | \(0.534049\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.19817e7 | + | 4.25362e6i | −0.998900 | + | 0.193294i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.64643e7 | − | 8.19915e6i | −1.19568 | − | 0.370443i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.43273e6 | −0.288966 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.50297e7 | 1.56456 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.45171e6 | + | 2.38518e7i | 0.197693 | + | 1.05922i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.22504e7 | − | 1.89687e7i | −0.540917 | − | 0.837563i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.15752e6 | + | 1.15752e6i | 0.0508192 | + | 0.0508192i | 0.732060 | − | 0.681240i | \(-0.238559\pi\) |
−0.681240 | + | 0.732060i | \(0.738559\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.70447e7 | + | 1.42506e7i | −1.18062 | + | 0.622101i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 3.25507e7i | − | 1.41293i | −0.707748 | − | 0.706465i | \(-0.750289\pi\) | ||
0.707748 | − | 0.706465i | \(-0.249711\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.37239e6 | − | 6.37239e6i | 0.275043 | − | 0.275043i | −0.556083 | − | 0.831127i | \(-0.687696\pi\) |
0.831127 | + | 0.556083i | \(0.187696\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −120511. | − | 150219.i | −0.00517210 | − | 0.00644712i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.01092e7 | − | 2.01092e7i | 0.858196 | − | 0.858196i | −0.132930 | − | 0.991125i | \(-0.542438\pi\) |
0.991125 | + | 0.132930i | \(0.0424385\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 1.06892e7i | − | 0.453618i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.46589e6 | + | 2.11395e6i | −0.230657 | + | 0.0892073i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.58609e7 | − | 1.58609e7i | −0.665578 | − | 0.665578i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.56099e6 | + | 2.31006e6i | −0.0651392 | + | 0.0963976i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7.29482e6 | − | 2.35454e7i | 0.302715 | − | 0.977070i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −776278. | −0.0320345 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.91574e7 | 2.01733 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 7.25479e6 | − | 2.34162e7i | 0.296077 | − | 0.955647i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.89724e6 | − | 5.76742e6i | 0.158174 | − | 0.234078i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.06262e7 | − | 1.06262e7i | −0.428904 | − | 0.428904i | 0.459351 | − | 0.888255i | \(-0.348082\pi\) |
−0.888255 | + | 0.459351i | \(0.848082\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.10578e6 | − | 3.07220e6i | 0.0845286 | − | 0.123322i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.34160e7i | 0.934795i | 0.884047 | + | 0.467397i | \(0.154808\pi\) | ||||
−0.884047 | + | 0.467397i | \(0.845192\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 585740. | − | 585740.i | 0.0232556 | − | 0.0232556i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.39532e7 | + | 2.98581e7i | 0.945824 | + | 1.17899i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.04244e7 | − | 1.04244e7i | 0.409382 | − | 0.409382i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.95298e7i | 0.762796i | 0.924411 | + | 0.381398i | \(0.124557\pi\) | ||||
−0.924411 | + | 0.381398i | \(0.875443\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.34803e6 | + | 1.76417e6i | −0.130059 | + | 0.0685317i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.80027e7 | − | 2.80027e7i | −1.08192 | − | 1.08192i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.02497e7 | − | 2.40341e7i | 0.393873 | − | 0.923580i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.72023e7 | − | 6.94345e6i | 1.42191 | − | 0.265385i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.55210e6 | 0.249081 | 0.124541 | − | 0.992215i | \(-0.460254\pi\) | ||||
0.124541 | + | 0.992215i | \(0.460254\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −90462.0 | −0.00342052 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.78819e7 | + | 8.63834e6i | 1.04862 | + | 0.324882i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 9.73963e6 | − | 1.88468e6i | 0.364345 | − | 0.0705033i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.00402e7 | + | 2.00402e7i | 0.745681 | + | 0.745681i | 0.973665 | − | 0.227984i | \(-0.0732133\pi\) |
−0.227984 | + | 0.973665i | \(0.573213\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.95911e6 | + | 1.51047e7i | 0.294578 | + | 0.559047i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 454846.i | 0.0167452i | 0.999965 | + | 0.00837259i | \(0.00266511\pi\) | ||||
−0.999965 | + | 0.00837259i | \(0.997335\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.40349e7 | + | 3.40349e7i | −1.24636 | + | 1.24636i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.78452e7 | + | 2.07542e7i | −0.650043 | + | 0.756008i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5.99645e6 | − | 5.99645e6i | 0.217280 | − | 0.217280i | −0.590071 | − | 0.807351i | \(-0.700900\pi\) |
0.807351 | + | 0.590071i | \(0.200900\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 1.27036e7i | − | 0.457890i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.04640e7 | − | 3.88364e7i | −0.733735 | − | 1.39247i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.66076e7 | + | 1.66076e7i | 0.592343 | + | 0.592343i | 0.938264 | − | 0.345921i | \(-0.112433\pi\) |
−0.345921 | + | 0.938264i | \(0.612433\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.81913e7 | + | 1.22925e7i | 0.645440 | + | 0.436146i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −442415. | − | 137069.i | −0.0156153 | − | 0.00483791i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.00957e7 | 1.40783 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.19054e7 | −0.765144 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.48839e7 | + | 2.77794e6i | −0.517192 | + | 0.0965288i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.46191e6 | − | 1.78904e7i | −0.119674 | − | 0.618446i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.88785e6 | − | 8.88785e6i | −0.305654 | − | 0.305654i | 0.537567 | − | 0.843221i | \(-0.319344\pi\) |
−0.843221 | + | 0.537567i | \(0.819344\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.25083e7 | − | 1.18603e7i | 0.770077 | − | 0.405776i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1.61689e7i | − | 0.550341i | −0.961395 | − | 0.275171i | \(-0.911266\pi\) | ||
0.961395 | − | 0.275171i | \(-0.0887344\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.05986e7 | + | 3.05986e7i | −1.03614 | + | 1.03614i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.01740e7 | − | 2.37796e7i | 0.679641 | − | 0.801110i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.34892e7 | + | 1.34892e7i | −0.452116 | + | 0.452116i | −0.896056 | − | 0.443941i | \(-0.853580\pi\) |
0.443941 | + | 0.896056i | \(0.353580\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 1.24826e7i | − | 0.416243i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.66748e7 | − | 2.43274e7i | 0.553206 | − | 0.807093i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.33156e7 | − | 1.33156e7i | −0.439517 | − | 0.439517i | 0.452332 | − | 0.891849i | \(-0.350592\pi\) |
−0.891849 | + | 0.452332i | \(0.850592\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.11117e6 | + | 2.64134e7i | 0.167853 | + | 0.867428i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.46537e7 | + | 4.72976e7i | −0.478800 | + | 1.54542i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.00525e7 | 0.976988 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.07932e6 | 0.228985 | 0.114493 | − | 0.993424i | \(-0.463476\pi\) | ||||
0.114493 | + | 0.993424i | \(0.463476\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.69774e7 | − | 5.47977e7i | 0.546383 | − | 1.76356i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.04764e7 | + | 3.41086e7i | 1.61633 | + | 1.09221i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.77833e7 | + | 2.77833e7i | 0.885210 | + | 0.885210i | 0.994058 | − | 0.108848i | \(-0.0347163\pi\) |
−0.108848 | + | 0.994058i | \(0.534716\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.14593e7 | − | 3.66328e6i | −0.997320 | − | 0.116133i |
(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 | 60.6.i.a.17.7 | ✓ | 20 | |
3.2 | odd | 2 | inner | 60.6.i.a.17.9 | yes | 20 | |
5.2 | odd | 4 | 300.6.i.d.293.2 | 20 | |||
5.3 | odd | 4 | inner | 60.6.i.a.53.9 | yes | 20 | |
5.4 | even | 2 | 300.6.i.d.257.4 | 20 | |||
15.2 | even | 4 | 300.6.i.d.293.4 | 20 | |||
15.8 | even | 4 | inner | 60.6.i.a.53.7 | yes | 20 | |
15.14 | odd | 2 | 300.6.i.d.257.2 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.6.i.a.17.7 | ✓ | 20 | 1.1 | even | 1 | trivial | |
60.6.i.a.17.9 | yes | 20 | 3.2 | odd | 2 | inner | |
60.6.i.a.53.7 | yes | 20 | 15.8 | even | 4 | inner | |
60.6.i.a.53.9 | yes | 20 | 5.3 | odd | 4 | inner | |
300.6.i.d.257.2 | 20 | 15.14 | odd | 2 | |||
300.6.i.d.257.4 | 20 | 5.4 | even | 2 | |||
300.6.i.d.293.2 | 20 | 5.2 | odd | 4 | |||
300.6.i.d.293.4 | 20 | 15.2 | even | 4 |