Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [936,2,Mod(469,936)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(936, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("936.469");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 936 = 2^{3} \cdot 3^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 936.g (of order \(2\), degree \(1\), 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: | \(7.47399762919\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 104) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 469.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 936.469 |
Dual form | 936.2.g.a.469.2 |
$q$-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 \(\left(\mathbb{Z}/936\mathbb{Z}\right)^\times\).
\(n\) | \(145\) | \(209\) | \(469\) | \(703\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | − | 1.00000i | 0.707107 | − | 0.707107i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | − | 2.00000i | − | 1.00000i | ||||||
\(5\) | − | 3.00000i | − | 1.34164i | −0.741620 | − | 0.670820i | \(-0.765942\pi\) | ||
0.741620 | − | 0.670820i | \(-0.234058\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.00000 | 1.13389 | 0.566947 | − | 0.823754i | \(-0.308125\pi\) | ||||
0.566947 | + | 0.823754i | \(0.308125\pi\) | |||||||
\(8\) | −2.00000 | − | 2.00000i | −0.707107 | − | 0.707107i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.00000 | − | 3.00000i | −0.948683 | − | 0.948683i | ||||
\(11\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000i | 0.277350i | ||||||||
\(14\) | 3.00000 | − | 3.00000i | 0.801784 | − | 0.801784i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.00000 | −1.00000 | ||||||||
\(17\) | 7.00000 | 1.69775 | 0.848875 | − | 0.528594i | \(-0.177281\pi\) | ||||
0.848875 | + | 0.528594i | \(0.177281\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 4.00000i | − | 0.917663i | −0.888523 | − | 0.458831i | \(-0.848268\pi\) | ||
0.888523 | − | 0.458831i | \(-0.151732\pi\) | |||||||
\(20\) | −6.00000 | −1.34164 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.00000 | −0.834058 | −0.417029 | − | 0.908893i | \(-0.636929\pi\) | ||||
−0.417029 | + | 0.908893i | \(0.636929\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.00000 | −0.800000 | ||||||||
\(26\) | 1.00000 | + | 1.00000i | 0.196116 | + | 0.196116i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − | 6.00000i | − | 1.13389i | ||||||
\(29\) | 4.00000i | 0.742781i | 0.928477 | + | 0.371391i | \(0.121119\pi\) | ||||
−0.928477 | + | 0.371391i | \(0.878881\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.00000 | −1.43684 | −0.718421 | − | 0.695608i | \(-0.755135\pi\) | ||||
−0.718421 | + | 0.695608i | \(0.755135\pi\) | |||||||
\(32\) | −4.00000 | + | 4.00000i | −0.707107 | + | 0.707107i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 7.00000 | − | 7.00000i | 1.20049 | − | 1.20049i | ||||
\(35\) | − | 9.00000i | − | 1.52128i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.00000i | 1.15079i | 0.817875 | + | 0.575396i | \(0.195152\pi\) | ||||
−0.817875 | + | 0.575396i | \(0.804848\pi\) | |||||||
\(38\) | −4.00000 | − | 4.00000i | −0.648886 | − | 0.648886i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −6.00000 | + | 6.00000i | −0.948683 | + | 0.948683i | ||||
\(41\) | −2.00000 | −0.312348 | −0.156174 | − | 0.987730i | \(-0.549916\pi\) | ||||
−0.156174 | + | 0.987730i | \(0.549916\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 1.00000i | − | 0.152499i | −0.997089 | − | 0.0762493i | \(-0.975706\pi\) | ||
0.997089 | − | 0.0762493i | \(-0.0242945\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.00000 | + | 4.00000i | −0.589768 | + | 0.589768i | ||||
\(47\) | 7.00000 | 1.02105 | 0.510527 | − | 0.859861i | \(-0.329450\pi\) | ||||
0.510527 | + | 0.859861i | \(0.329450\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.00000 | 0.285714 | ||||||||
\(50\) | −4.00000 | + | 4.00000i | −0.565685 | + | 0.565685i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.00000 | 0.277350 | ||||||||
\(53\) | − | 4.00000i | − | 0.549442i | −0.961524 | − | 0.274721i | \(-0.911414\pi\) | ||
0.961524 | − | 0.274721i | \(-0.0885855\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −6.00000 | − | 6.00000i | −0.801784 | − | 0.801784i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.00000 | + | 4.00000i | 0.525226 | + | 0.525226i | ||||
\(59\) | 14.0000i | 1.82264i | 0.411693 | + | 0.911322i | \(0.364937\pi\) | ||||
−0.411693 | + | 0.911322i | \(0.635063\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 10.0000i | − | 1.28037i | −0.768221 | − | 0.640184i | \(-0.778858\pi\) | ||
0.768221 | − | 0.640184i | \(-0.221142\pi\) | |||||||
\(62\) | −8.00000 | + | 8.00000i | −1.01600 | + | 1.01600i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000i | 1.00000i | ||||||||
\(65\) | 3.00000 | 0.372104 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.00000i | 0.244339i | 0.992509 | + | 0.122169i | \(0.0389851\pi\) | ||||
−0.992509 | + | 0.122169i | \(0.961015\pi\) | |||||||
\(68\) | − | 14.0000i | − | 1.69775i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −9.00000 | − | 9.00000i | −1.07571 | − | 1.07571i | ||||
\(71\) | 3.00000 | 0.356034 | 0.178017 | − | 0.984027i | \(-0.443032\pi\) | ||||
0.178017 | + | 0.984027i | \(0.443032\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.0000 | 1.63858 | 0.819288 | − | 0.573382i | \(-0.194369\pi\) | ||||
0.819288 | + | 0.573382i | \(0.194369\pi\) | |||||||
\(74\) | 7.00000 | + | 7.00000i | 0.813733 | + | 0.813733i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −8.00000 | −0.917663 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.0000 | −1.12509 | −0.562544 | − | 0.826767i | \(-0.690177\pi\) | ||||
−0.562544 | + | 0.826767i | \(0.690177\pi\) | |||||||
\(80\) | 12.0000i | 1.34164i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.00000 | + | 2.00000i | −0.220863 | + | 0.220863i | ||||
\(83\) | − | 14.0000i | − | 1.53670i | −0.640030 | − | 0.768350i | \(-0.721078\pi\) | ||
0.640030 | − | 0.768350i | \(-0.278922\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 21.0000i | − | 2.27777i | ||||||
\(86\) | −1.00000 | − | 1.00000i | −0.107833 | − | 0.107833i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.00000i | 0.314485i | ||||||||
\(92\) | 8.00000i | 0.834058i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 7.00000 | − | 7.00000i | 0.721995 | − | 0.721995i | ||||
\(95\) | −12.0000 | −1.23117 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.00000 | 0.812277 | 0.406138 | − | 0.913812i | \(-0.366875\pi\) | ||||
0.406138 | + | 0.913812i | \(0.366875\pi\) | |||||||
\(98\) | 2.00000 | − | 2.00000i | 0.202031 | − | 0.202031i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 8.00000i | 0.800000i | ||||||||
\(101\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.00000 | −0.591198 | −0.295599 | − | 0.955312i | \(-0.595519\pi\) | ||||
−0.295599 | + | 0.955312i | \(0.595519\pi\) | |||||||
\(104\) | 2.00000 | − | 2.00000i | 0.196116 | − | 0.196116i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.00000 | − | 4.00000i | −0.388514 | − | 0.388514i | ||||
\(107\) | 8.00000i | 0.773389i | 0.922208 | + | 0.386695i | \(0.126383\pi\) | ||||
−0.922208 | + | 0.386695i | \(0.873617\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.00000i | 0.0957826i | 0.998853 | + | 0.0478913i | \(0.0152501\pi\) | ||||
−0.998853 | + | 0.0478913i | \(0.984750\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −12.0000 | −1.13389 | ||||||||
\(113\) | 6.00000 | 0.564433 | 0.282216 | − | 0.959351i | \(-0.408930\pi\) | ||||
0.282216 | + | 0.959351i | \(0.408930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.0000i | 1.11901i | ||||||||
\(116\) | 8.00000 | 0.742781 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 14.0000 | + | 14.0000i | 1.28880 | + | 1.28880i | ||||
\(119\) | 21.0000 | 1.92507 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.0000 | 1.00000 | ||||||||
\(122\) | −10.0000 | − | 10.0000i | −0.905357 | − | 0.905357i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 16.0000i | 1.43684i | ||||||||
\(125\) | − | 3.00000i | − | 0.268328i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.00000 | 0.709885 | 0.354943 | − | 0.934888i | \(-0.384500\pi\) | ||||
0.354943 | + | 0.934888i | \(0.384500\pi\) | |||||||
\(128\) | 8.00000 | + | 8.00000i | 0.707107 | + | 0.707107i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 3.00000 | − | 3.00000i | 0.263117 | − | 0.263117i | ||||
\(131\) | 15.0000i | 1.31056i | 0.755388 | + | 0.655278i | \(0.227449\pi\) | ||||
−0.755388 | + | 0.655278i | \(0.772551\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 12.0000i | − | 1.04053i | ||||||
\(134\) | 2.00000 | + | 2.00000i | 0.172774 | + | 0.172774i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −14.0000 | − | 14.0000i | −1.20049 | − | 1.20049i | ||||
\(137\) | 12.0000 | 1.02523 | 0.512615 | − | 0.858619i | \(-0.328677\pi\) | ||||
0.512615 | + | 0.858619i | \(0.328677\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.0000i | 0.933008i | 0.884519 | + | 0.466504i | \(0.154487\pi\) | ||||
−0.884519 | + | 0.466504i | \(0.845513\pi\) | |||||||
\(140\) | −18.0000 | −1.52128 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.00000 | − | 3.00000i | 0.251754 | − | 0.251754i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 12.0000 | 0.996546 | ||||||||
\(146\) | 14.0000 | − | 14.0000i | 1.15865 | − | 1.15865i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 14.0000 | 1.15079 | ||||||||
\(149\) | − | 6.00000i | − | 0.491539i | −0.969328 | − | 0.245770i | \(-0.920959\pi\) | ||
0.969328 | − | 0.245770i | \(-0.0790407\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.0000 | 1.38344 | 0.691720 | − | 0.722166i | \(-0.256853\pi\) | ||||
0.691720 | + | 0.722166i | \(0.256853\pi\) | |||||||
\(152\) | −8.00000 | + | 8.00000i | −0.648886 | + | 0.648886i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 24.0000i | 1.92773i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.00000i | 0.159617i | 0.996810 | + | 0.0798087i | \(0.0254309\pi\) | ||||
−0.996810 | + | 0.0798087i | \(0.974569\pi\) | |||||||
\(158\) | −10.0000 | + | 10.0000i | −0.795557 | + | 0.795557i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 12.0000 | + | 12.0000i | 0.948683 | + | 0.948683i | ||||
\(161\) | −12.0000 | −0.945732 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 24.0000i | 1.87983i | 0.341415 | + | 0.939913i | \(0.389094\pi\) | ||||
−0.341415 | + | 0.939913i | \(0.610906\pi\) | |||||||
\(164\) | 4.00000i | 0.312348i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −14.0000 | − | 14.0000i | −1.08661 | − | 1.08661i | ||||
\(167\) | 12.0000 | 0.928588 | 0.464294 | − | 0.885681i | \(-0.346308\pi\) | ||||
0.464294 | + | 0.885681i | \(0.346308\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | −21.0000 | − | 21.0000i | −1.61063 | − | 1.61063i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.00000 | −0.152499 | ||||||||
\(173\) | 6.00000i | 0.456172i | 0.973641 | + | 0.228086i | \(0.0732467\pi\) | ||||
−0.973641 | + | 0.228086i | \(0.926753\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −12.0000 | −0.907115 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 21.0000i | − | 1.56961i | −0.619740 | − | 0.784807i | \(-0.712762\pi\) | ||
0.619740 | − | 0.784807i | \(-0.287238\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.0000i | 0.743294i | 0.928374 | + | 0.371647i | \(0.121207\pi\) | ||||
−0.928374 | + | 0.371647i | \(0.878793\pi\) | |||||||
\(182\) | 3.00000 | + | 3.00000i | 0.222375 | + | 0.222375i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 8.00000 | + | 8.00000i | 0.589768 | + | 0.589768i | ||||
\(185\) | 21.0000 | 1.54395 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | − | 14.0000i | − | 1.02105i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −12.0000 | + | 12.0000i | −0.870572 | + | 0.870572i | ||||
\(191\) | −12.0000 | −0.868290 | −0.434145 | − | 0.900843i | \(-0.642949\pi\) | ||||
−0.434145 | + | 0.900843i | \(0.642949\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.00000 | −0.431889 | −0.215945 | − | 0.976406i | \(-0.569283\pi\) | ||||
−0.215945 | + | 0.976406i | \(0.569283\pi\) | |||||||
\(194\) | 8.00000 | − | 8.00000i | 0.574367 | − | 0.574367i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | − | 4.00000i | − | 0.285714i | ||||||
\(197\) | − | 17.0000i | − | 1.21120i | −0.795769 | − | 0.605600i | \(-0.792933\pi\) | ||
0.795769 | − | 0.605600i | \(-0.207067\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.0000 | −0.708881 | −0.354441 | − | 0.935079i | \(-0.615329\pi\) | ||||
−0.354441 | + | 0.935079i | \(0.615329\pi\) | |||||||
\(200\) | 8.00000 | + | 8.00000i | 0.565685 | + | 0.565685i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 12.0000i | 0.842235i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.00000i | 0.419058i | ||||||||
\(206\) | −6.00000 | + | 6.00000i | −0.418040 | + | 0.418040i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 4.00000i | − | 0.277350i | ||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 15.0000i | − | 1.03264i | −0.856395 | − | 0.516321i | \(-0.827301\pi\) | ||
0.856395 | − | 0.516321i | \(-0.172699\pi\) | |||||||
\(212\) | −8.00000 | −0.549442 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 8.00000 | + | 8.00000i | 0.546869 | + | 0.546869i | ||||
\(215\) | −3.00000 | −0.204598 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −24.0000 | −1.62923 | ||||||||
\(218\) | 1.00000 | + | 1.00000i | 0.0677285 | + | 0.0677285i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.00000i | 0.470871i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.00000 | −0.0669650 | −0.0334825 | − | 0.999439i | \(-0.510660\pi\) | ||||
−0.0334825 | + | 0.999439i | \(0.510660\pi\) | |||||||
\(224\) | −12.0000 | + | 12.0000i | −0.801784 | + | 0.801784i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.00000 | − | 6.00000i | 0.399114 | − | 0.399114i | ||||
\(227\) | 18.0000i | 1.19470i | 0.801980 | + | 0.597351i | \(0.203780\pi\) | ||||
−0.801980 | + | 0.597351i | \(0.796220\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.0000i | 1.38772i | 0.720110 | + | 0.693860i | \(0.244091\pi\) | ||||
−0.720110 | + | 0.693860i | \(0.755909\pi\) | |||||||
\(230\) | 12.0000 | + | 12.0000i | 0.791257 | + | 0.791257i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8.00000 | − | 8.00000i | 0.525226 | − | 0.525226i | ||||
\(233\) | −19.0000 | −1.24473 | −0.622366 | − | 0.782727i | \(-0.713828\pi\) | ||||
−0.622366 | + | 0.782727i | \(0.713828\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 21.0000i | − | 1.36989i | ||||||
\(236\) | 28.0000 | 1.82264 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 21.0000 | − | 21.0000i | 1.36123 | − | 1.36123i | ||||
\(239\) | −5.00000 | −0.323423 | −0.161712 | − | 0.986838i | \(-0.551701\pi\) | ||||
−0.161712 | + | 0.986838i | \(0.551701\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.00000 | −0.515325 | −0.257663 | − | 0.966235i | \(-0.582952\pi\) | ||||
−0.257663 | + | 0.966235i | \(0.582952\pi\) | |||||||
\(242\) | 11.0000 | − | 11.0000i | 0.707107 | − | 0.707107i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −20.0000 | −1.28037 | ||||||||
\(245\) | − | 6.00000i | − | 0.383326i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.00000 | 0.254514 | ||||||||
\(248\) | 16.0000 | + | 16.0000i | 1.01600 | + | 1.01600i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −3.00000 | − | 3.00000i | −0.189737 | − | 0.189737i | ||||
\(251\) | − | 20.0000i | − | 1.26239i | −0.775625 | − | 0.631194i | \(-0.782565\pi\) | ||
0.775625 | − | 0.631194i | \(-0.217435\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 8.00000 | − | 8.00000i | 0.501965 | − | 0.501965i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 1.00000 | ||||||||
\(257\) | 7.00000 | 0.436648 | 0.218324 | − | 0.975876i | \(-0.429941\pi\) | ||||
0.218324 | + | 0.975876i | \(0.429941\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 21.0000i | 1.30488i | ||||||||
\(260\) | − | 6.00000i | − | 0.372104i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 15.0000 | + | 15.0000i | 0.926703 | + | 0.926703i | ||||
\(263\) | −14.0000 | −0.863277 | −0.431638 | − | 0.902047i | \(-0.642064\pi\) | ||||
−0.431638 | + | 0.902047i | \(0.642064\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.0000 | −0.737154 | ||||||||
\(266\) | −12.0000 | − | 12.0000i | −0.735767 | − | 0.735767i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.00000 | 0.244339 | ||||||||
\(269\) | − | 6.00000i | − | 0.365826i | −0.983129 | − | 0.182913i | \(-0.941447\pi\) | ||
0.983129 | − | 0.182913i | \(-0.0585527\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.00000 | −0.182237 | −0.0911185 | − | 0.995840i | \(-0.529044\pi\) | ||||
−0.0911185 | + | 0.995840i | \(0.529044\pi\) | |||||||
\(272\) | −28.0000 | −1.69775 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 12.0000 | − | 12.0000i | 0.724947 | − | 0.724947i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 18.0000i | − | 1.08152i | −0.841178 | − | 0.540758i | \(-0.818138\pi\) | ||
0.841178 | − | 0.540758i | \(-0.181862\pi\) | |||||||
\(278\) | 11.0000 | + | 11.0000i | 0.659736 | + | 0.659736i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −18.0000 | + | 18.0000i | −1.07571 | + | 1.07571i | ||||
\(281\) | 8.00000 | 0.477240 | 0.238620 | − | 0.971113i | \(-0.423305\pi\) | ||||
0.238620 | + | 0.971113i | \(0.423305\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.00000i | 0.237775i | 0.992908 | + | 0.118888i | \(0.0379328\pi\) | ||||
−0.992908 | + | 0.118888i | \(0.962067\pi\) | |||||||
\(284\) | − | 6.00000i | − | 0.356034i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.00000 | −0.354169 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 32.0000 | 1.88235 | ||||||||
\(290\) | 12.0000 | − | 12.0000i | 0.704664 | − | 0.704664i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 28.0000i | − | 1.63858i | ||||||
\(293\) | 1.00000i | 0.0584206i | 0.999573 | + | 0.0292103i | \(0.00929925\pi\) | ||||
−0.999573 | + | 0.0292103i | \(0.990701\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 42.0000 | 2.44533 | ||||||||
\(296\) | 14.0000 | − | 14.0000i | 0.813733 | − | 0.813733i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −6.00000 | − | 6.00000i | −0.347571 | − | 0.347571i | ||||
\(299\) | − | 4.00000i | − | 0.231326i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 3.00000i | − | 0.172917i | ||||||
\(302\) | 17.0000 | − | 17.0000i | 0.978240 | − | 0.978240i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 16.0000i | 0.917663i | ||||||||
\(305\) | −30.0000 | −1.71780 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.00000i | 0.114146i | 0.998370 | + | 0.0570730i | \(0.0181768\pi\) | ||||
−0.998370 | + | 0.0570730i | \(0.981823\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 24.0000 | + | 24.0000i | 1.36311 | + | 1.36311i | ||||
\(311\) | −32.0000 | −1.81455 | −0.907277 | − | 0.420534i | \(-0.861843\pi\) | ||||
−0.907277 | + | 0.420534i | \(0.861843\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 29.0000 | 1.63918 | 0.819588 | − | 0.572953i | \(-0.194202\pi\) | ||||
0.819588 | + | 0.572953i | \(0.194202\pi\) | |||||||
\(314\) | 2.00000 | + | 2.00000i | 0.112867 | + | 0.112867i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 20.0000i | 1.12509i | ||||||||
\(317\) | 18.0000i | 1.01098i | 0.862832 | + | 0.505490i | \(0.168688\pi\) | ||||
−0.862832 | + | 0.505490i | \(0.831312\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 24.0000 | 1.34164 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −12.0000 | + | 12.0000i | −0.668734 | + | 0.668734i | ||||
\(323\) | − | 28.0000i | − | 1.55796i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 4.00000i | − | 0.221880i | ||||||
\(326\) | 24.0000 | + | 24.0000i | 1.32924 | + | 1.32924i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4.00000 | + | 4.00000i | 0.220863 | + | 0.220863i | ||||
\(329\) | 21.0000 | 1.15777 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.0000i | 0.549650i | 0.961494 | + | 0.274825i | \(0.0886199\pi\) | ||||
−0.961494 | + | 0.274825i | \(0.911380\pi\) | |||||||
\(332\) | −28.0000 | −1.53670 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 12.0000 | − | 12.0000i | 0.656611 | − | 0.656611i | ||||
\(335\) | 6.00000 | 0.327815 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.0000 | −0.926049 | −0.463025 | − | 0.886345i | \(-0.653236\pi\) | ||||
−0.463025 | + | 0.886345i | \(0.653236\pi\) | |||||||
\(338\) | −1.00000 | + | 1.00000i | −0.0543928 | + | 0.0543928i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −42.0000 | −2.27777 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.0000 | −0.809924 | ||||||||
\(344\) | −2.00000 | + | 2.00000i | −0.107833 | + | 0.107833i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.00000 | + | 6.00000i | 0.322562 | + | 0.322562i | ||||
\(347\) | − | 7.00000i | − | 0.375780i | −0.982190 | − | 0.187890i | \(-0.939835\pi\) | ||
0.982190 | − | 0.187890i | \(-0.0601648\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 19.0000i | − | 1.01705i | −0.861048 | − | 0.508523i | \(-0.830192\pi\) | ||
0.861048 | − | 0.508523i | \(-0.169808\pi\) | |||||||
\(350\) | −12.0000 | + | 12.0000i | −0.641427 | + | 0.641427i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.00000 | 0.319348 | 0.159674 | − | 0.987170i | \(-0.448956\pi\) | ||||
0.159674 | + | 0.987170i | \(0.448956\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 9.00000i | − | 0.477670i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −21.0000 | − | 21.0000i | −1.10988 | − | 1.10988i | ||||
\(359\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.00000 | 0.157895 | ||||||||
\(362\) | 10.0000 | + | 10.0000i | 0.525588 | + | 0.525588i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 6.00000 | 0.314485 | ||||||||
\(365\) | − | 42.0000i | − | 2.19838i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −22.0000 | −1.14839 | −0.574195 | − | 0.818718i | \(-0.694685\pi\) | ||||
−0.574195 | + | 0.818718i | \(0.694685\pi\) | |||||||
\(368\) | 16.0000 | 0.834058 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 21.0000 | − | 21.0000i | 1.09174 | − | 1.09174i | ||||
\(371\) | − | 12.0000i | − | 0.623009i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 36.0000i | − | 1.86401i | −0.362446 | − | 0.932005i | \(-0.618058\pi\) | ||
0.362446 | − | 0.932005i | \(-0.381942\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −14.0000 | − | 14.0000i | −0.721995 | − | 0.721995i | ||||
\(377\) | −4.00000 | −0.206010 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 4.00000i | − | 0.205466i | −0.994709 | − | 0.102733i | \(-0.967241\pi\) | ||
0.994709 | − | 0.102733i | \(-0.0327588\pi\) | |||||||
\(380\) | 24.0000i | 1.23117i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −12.0000 | + | 12.0000i | −0.613973 | + | 0.613973i | ||||
\(383\) | 1.00000 | 0.0510976 | 0.0255488 | − | 0.999674i | \(-0.491867\pi\) | ||||
0.0255488 | + | 0.999674i | \(0.491867\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6.00000 | + | 6.00000i | −0.305392 | + | 0.305392i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 16.0000i | − | 0.812277i | ||||||
\(389\) | 34.0000i | 1.72387i | 0.507020 | + | 0.861934i | \(0.330747\pi\) | ||||
−0.507020 | + | 0.861934i | \(0.669253\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −28.0000 | −1.41602 | ||||||||
\(392\) | −4.00000 | − | 4.00000i | −0.202031 | − | 0.202031i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −17.0000 | − | 17.0000i | −0.856448 | − | 0.856448i | ||||
\(395\) | 30.0000i | 1.50946i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.0000i | 1.10415i | 0.833795 | + | 0.552074i | \(0.186163\pi\) | ||||
−0.833795 | + | 0.552074i | \(0.813837\pi\) | |||||||
\(398\) | −10.0000 | + | 10.0000i | −0.501255 | + | 0.501255i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 16.0000 | 0.800000 | ||||||||
\(401\) | −32.0000 | −1.59800 | −0.799002 | − | 0.601329i | \(-0.794638\pi\) | ||||
−0.799002 | + | 0.601329i | \(0.794638\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 8.00000i | − | 0.398508i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 12.0000 | + | 12.0000i | 0.595550 | + | 0.595550i | ||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(410\) | 6.00000 | + | 6.00000i | 0.296319 | + | 0.296319i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 12.0000i | 0.591198i | ||||||||
\(413\) | 42.0000i | 2.06668i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −42.0000 | −2.06170 | ||||||||
\(416\) | −4.00000 | − | 4.00000i | −0.196116 | − | 0.196116i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 11.0000i | − | 0.537385i | −0.963226 | − | 0.268693i | \(-0.913408\pi\) | ||
0.963226 | − | 0.268693i | \(-0.0865916\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.0000i | 0.731055i | 0.930800 | + | 0.365528i | \(0.119111\pi\) | ||||
−0.930800 | + | 0.365528i | \(0.880889\pi\) | |||||||
\(422\) | −15.0000 | − | 15.0000i | −0.730189 | − | 0.730189i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −8.00000 | + | 8.00000i | −0.388514 | + | 0.388514i | ||||
\(425\) | −28.0000 | −1.35820 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 30.0000i | − | 1.45180i | ||||||
\(428\) | 16.0000 | 0.773389 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.00000 | + | 3.00000i | −0.144673 | + | 0.144673i | ||||
\(431\) | 3.00000 | 0.144505 | 0.0722525 | − | 0.997386i | \(-0.476981\pi\) | ||||
0.0722525 | + | 0.997386i | \(0.476981\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.00000 | −0.0480569 | −0.0240285 | − | 0.999711i | \(-0.507649\pi\) | ||||
−0.0240285 | + | 0.999711i | \(0.507649\pi\) | |||||||
\(434\) | −24.0000 | + | 24.0000i | −1.15204 | + | 1.15204i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.00000 | 0.0957826 | ||||||||
\(437\) | 16.0000i | 0.765384i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.0000 | −0.477274 | −0.238637 | − | 0.971109i | \(-0.576701\pi\) | ||||
−0.238637 | + | 0.971109i | \(0.576701\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 7.00000 | + | 7.00000i | 0.332956 | + | 0.332956i | ||||
\(443\) | − | 9.00000i | − | 0.427603i | −0.976877 | − | 0.213801i | \(-0.931415\pi\) | ||
0.976877 | − | 0.213801i | \(-0.0685846\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1.00000 | + | 1.00000i | −0.0473514 | + | 0.0473514i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 24.0000i | 1.13389i | ||||||||
\(449\) | 20.0000 | 0.943858 | 0.471929 | − | 0.881636i | \(-0.343558\pi\) | ||||
0.471929 | + | 0.881636i | \(0.343558\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | − | 12.0000i | − | 0.564433i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 18.0000 | + | 18.0000i | 0.844782 | + | 0.844782i | ||||
\(455\) | 9.00000 | 0.421927 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −32.0000 | −1.49690 | −0.748448 | − | 0.663193i | \(-0.769201\pi\) | ||||
−0.748448 | + | 0.663193i | \(0.769201\pi\) | |||||||
\(458\) | 21.0000 | + | 21.0000i | 0.981266 | + | 0.981266i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 24.0000 | 1.11901 | ||||||||
\(461\) | − | 5.00000i | − | 0.232873i | −0.993198 | − | 0.116437i | \(-0.962853\pi\) | ||
0.993198 | − | 0.116437i | \(-0.0371472\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.0000 | −0.743583 | −0.371792 | − | 0.928316i | \(-0.621256\pi\) | ||||
−0.371792 | + | 0.928316i | \(0.621256\pi\) | |||||||
\(464\) | − | 16.0000i | − | 0.742781i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −19.0000 | + | 19.0000i | −0.880158 | + | 0.880158i | ||||
\(467\) | − | 12.0000i | − | 0.555294i | −0.960683 | − | 0.277647i | \(-0.910445\pi\) | ||
0.960683 | − | 0.277647i | \(-0.0895545\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.00000i | 0.277054i | ||||||||
\(470\) | −21.0000 | − | 21.0000i | −0.968658 | − | 0.968658i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 28.0000 | − | 28.0000i | 1.28880 | − | 1.28880i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 16.0000i | 0.734130i | ||||||||
\(476\) | − | 42.0000i | − | 1.92507i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −5.00000 | + | 5.00000i | −0.228695 | + | 0.228695i | ||||
\(479\) | −5.00000 | −0.228456 | −0.114228 | − | 0.993455i | \(-0.536439\pi\) | ||||
−0.114228 | + | 0.993455i | \(0.536439\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.00000 | −0.319173 | ||||||||
\(482\) | −8.00000 | + | 8.00000i | −0.364390 | + | 0.364390i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 22.0000i | − | 1.00000i | ||||||
\(485\) | − | 24.0000i | − | 1.08978i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.00000 | 0.362515 | 0.181257 | − | 0.983436i | \(-0.441983\pi\) | ||||
0.181257 | + | 0.983436i | \(0.441983\pi\) | |||||||
\(488\) | −20.0000 | + | 20.0000i | −0.905357 | + | 0.905357i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −6.00000 | − | 6.00000i | −0.271052 | − | 0.271052i | ||||
\(491\) | − | 15.0000i | − | 0.676941i | −0.940977 | − | 0.338470i | \(-0.890091\pi\) | ||
0.940977 | − | 0.338470i | \(-0.109909\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 28.0000i | 1.26106i | ||||||||
\(494\) | 4.00000 | − | 4.00000i | 0.179969 | − | 0.179969i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 32.0000 | 1.43684 | ||||||||
\(497\) | 9.00000 | 0.403705 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.00000i | 0.268597i | 0.990941 | + | 0.134298i | \(0.0428781\pi\) | ||||
−0.990941 | + | 0.134298i | \(0.957122\pi\) | |||||||
\(500\) | −6.00000 | −0.268328 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −20.0000 | − | 20.0000i | −0.892644 | − | 0.892644i | ||||
\(503\) | −4.00000 | −0.178351 | −0.0891756 | − | 0.996016i | \(-0.528423\pi\) | ||||
−0.0891756 | + | 0.996016i | \(0.528423\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − | 16.0000i | − | 0.709885i | ||||||
\(509\) | 14.0000i | 0.620539i | 0.950649 | + | 0.310270i | \(0.100419\pi\) | ||||
−0.950649 | + | 0.310270i | \(0.899581\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 42.0000 | 1.85797 | ||||||||
\(512\) | 16.0000 | − | 16.0000i | 0.707107 | − | 0.707107i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 7.00000 | − | 7.00000i | 0.308757 | − | 0.308757i | ||||
\(515\) | 18.0000i | 0.793175i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 21.0000 | + | 21.0000i | 0.922687 | + | 0.922687i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −6.00000 | − | 6.00000i | −0.263117 | − | 0.263117i | ||||
\(521\) | 3.00000 | 0.131432 | 0.0657162 | − | 0.997838i | \(-0.479067\pi\) | ||||
0.0657162 | + | 0.997838i | \(0.479067\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 44.0000i | 1.92399i | 0.273075 | + | 0.961993i | \(0.411959\pi\) | ||||
−0.273075 | + | 0.961993i | \(0.588041\pi\) | |||||||
\(524\) | 30.0000 | 1.31056 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −14.0000 | + | 14.0000i | −0.610429 | + | 0.610429i | ||||
\(527\) | −56.0000 | −2.43940 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | −12.0000 | + | 12.0000i | −0.521247 | + | 0.521247i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −24.0000 | −1.04053 | ||||||||
\(533\) | − | 2.00000i | − | 0.0866296i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 24.0000 | 1.03761 | ||||||||
\(536\) | 4.00000 | − | 4.00000i | 0.172774 | − | 0.172774i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −6.00000 | − | 6.00000i | −0.258678 | − | 0.258678i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 25.0000i | − | 1.07483i | −0.843317 | − | 0.537417i | \(-0.819400\pi\) | ||
0.843317 | − | 0.537417i | \(-0.180600\pi\) | |||||||
\(542\) | −3.00000 | + | 3.00000i | −0.128861 | + | 0.128861i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −28.0000 | + | 28.0000i | −1.20049 | + | 1.20049i | ||||
\(545\) | 3.00000 | 0.128506 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 13.0000i | − | 0.555840i | −0.960604 | − | 0.277920i | \(-0.910355\pi\) | ||
0.960604 | − | 0.277920i | \(-0.0896450\pi\) | |||||||
\(548\) | − | 24.0000i | − | 1.02523i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 16.0000 | 0.681623 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −30.0000 | −1.27573 | ||||||||
\(554\) | −18.0000 | − | 18.0000i | −0.764747 | − | 0.764747i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 22.0000 | 0.933008 | ||||||||
\(557\) | 13.0000i | 0.550828i | 0.961326 | + | 0.275414i | \(0.0888149\pi\) | ||||
−0.961326 | + | 0.275414i | \(0.911185\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.00000 | 0.0422955 | ||||||||
\(560\) | 36.0000i | 1.52128i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8.00000 | − | 8.00000i | 0.337460 | − | 0.337460i | ||||
\(563\) | 31.0000i | 1.30649i | 0.757145 | + | 0.653247i | \(0.226594\pi\) | ||||
−0.757145 | + | 0.653247i | \(0.773406\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 18.0000i | − | 0.757266i | ||||||
\(566\) | 4.00000 | + | 4.00000i | 0.168133 | + | 0.168133i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6.00000 | − | 6.00000i | −0.251754 | − | 0.251754i | ||||
\(569\) | −25.0000 | −1.04805 | −0.524027 | − | 0.851701i | \(-0.675571\pi\) | ||||
−0.524027 | + | 0.851701i | \(0.675571\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.00000i | 0.209243i | 0.994512 | + | 0.104622i | \(0.0333632\pi\) | ||||
−0.994512 | + | 0.104622i | \(0.966637\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −6.00000 | + | 6.00000i | −0.250435 | + | 0.250435i | ||||
\(575\) | 16.0000 | 0.667246 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.00000 | −0.0832611 | −0.0416305 | − | 0.999133i | \(-0.513255\pi\) | ||||
−0.0416305 | + | 0.999133i | \(0.513255\pi\) | |||||||
\(578\) | 32.0000 | − | 32.0000i | 1.33102 | − | 1.33102i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 24.0000i | − | 0.996546i | ||||||
\(581\) | − | 42.0000i | − | 1.74245i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −28.0000 | − | 28.0000i | −1.15865 | − | 1.15865i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.00000 | + | 1.00000i | 0.0413096 | + | 0.0413096i | ||||
\(587\) | 28.0000i | 1.15568i | 0.816149 | + | 0.577842i | \(0.196105\pi\) | ||||
−0.816149 | + | 0.577842i | \(0.803895\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 32.0000i | 1.31854i | ||||||||
\(590\) | 42.0000 | − | 42.0000i | 1.72911 | − | 1.72911i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 28.0000i | − | 1.15079i | ||||||
\(593\) | −24.0000 | −0.985562 | −0.492781 | − | 0.870153i | \(-0.664020\pi\) | ||||
−0.492781 | + | 0.870153i | \(0.664020\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 63.0000i | − | 2.58275i | ||||||
\(596\) | −12.0000 | −0.491539 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4.00000 | − | 4.00000i | −0.163572 | − | 0.163572i | ||||
\(599\) | −10.0000 | −0.408589 | −0.204294 | − | 0.978909i | \(-0.565490\pi\) | ||||
−0.204294 | + | 0.978909i | \(0.565490\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 27.0000 | 1.10135 | 0.550676 | − | 0.834719i | \(-0.314370\pi\) | ||||
0.550676 | + | 0.834719i | \(0.314370\pi\) | |||||||
\(602\) | −3.00000 | − | 3.00000i | −0.122271 | − | 0.122271i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 34.0000i | − | 1.38344i | ||||||
\(605\) | − | 33.0000i | − | 1.34164i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22.0000 | −0.892952 | −0.446476 | − | 0.894795i | \(-0.647321\pi\) | ||||
−0.446476 | + | 0.894795i | \(0.647321\pi\) | |||||||
\(608\) | 16.0000 | + | 16.0000i | 0.648886 | + | 0.648886i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −30.0000 | + | 30.0000i | −1.21466 | + | 1.21466i | ||||
\(611\) | 7.00000i | 0.283190i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.0000i | 0.565455i | 0.959200 | + | 0.282727i | \(0.0912392\pi\) | ||||
−0.959200 | + | 0.282727i | \(0.908761\pi\) | |||||||
\(614\) | 2.00000 | + | 2.00000i | 0.0807134 | + | 0.0807134i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.0000 | 0.483102 | 0.241551 | − | 0.970388i | \(-0.422344\pi\) | ||||
0.241551 | + | 0.970388i | \(0.422344\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.00000i | 0.241160i | 0.992704 | + | 0.120580i | \(0.0384755\pi\) | ||||
−0.992704 | + | 0.120580i | \(0.961525\pi\) | |||||||
\(620\) | 48.0000 | 1.92773 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −32.0000 | + | 32.0000i | −1.28308 | + | 1.28308i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.0000 | −1.16000 | ||||||||
\(626\) | 29.0000 | − | 29.0000i | 1.15907 | − | 1.15907i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.00000 | 0.159617 | ||||||||
\(629\) | 49.0000i | 1.95376i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.0000 | −0.915616 | −0.457808 | − | 0.889051i | \(-0.651365\pi\) | ||||
−0.457808 | + | 0.889051i | \(0.651365\pi\) | |||||||
\(632\) | 20.0000 | + | 20.0000i | 0.795557 | + | 0.795557i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 18.0000 | + | 18.0000i | 0.714871 | + | 0.714871i | ||||
\(635\) | − | 24.0000i | − | 0.952411i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.00000i | 0.0792429i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 24.0000 | − | 24.0000i | 0.948683 | − | 0.948683i | ||||
\(641\) | −2.00000 | −0.0789953 | −0.0394976 | − | 0.999220i | \(-0.512576\pi\) | ||||
−0.0394976 | + | 0.999220i | \(0.512576\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 26.0000i | − | 1.02534i | −0.858586 | − | 0.512670i | \(-0.828656\pi\) | ||
0.858586 | − | 0.512670i | \(-0.171344\pi\) | |||||||
\(644\) | 24.0000i | 0.945732i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −28.0000 | − | 28.0000i | −1.10165 | − | 1.10165i | ||||
\(647\) | −18.0000 | −0.707653 | −0.353827 | − | 0.935311i | \(-0.615120\pi\) | ||||
−0.353827 | + | 0.935311i | \(0.615120\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −4.00000 | − | 4.00000i | −0.156893 | − | 0.156893i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 48.0000 | 1.87983 | ||||||||
\(653\) | − | 44.0000i | − | 1.72185i | −0.508729 | − | 0.860927i | \(-0.669885\pi\) | ||
0.508729 | − | 0.860927i | \(-0.330115\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 45.0000 | 1.75830 | ||||||||
\(656\) | 8.00000 | 0.312348 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 21.0000 | − | 21.0000i | 0.818665 | − | 0.818665i | ||||
\(659\) | 4.00000i | 0.155818i | 0.996960 | + | 0.0779089i | \(0.0248243\pi\) | ||||
−0.996960 | + | 0.0779089i | \(0.975176\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30.0000i | 1.16686i | 0.812162 | + | 0.583432i | \(0.198291\pi\) | ||||
−0.812162 | + | 0.583432i | \(0.801709\pi\) | |||||||
\(662\) | 10.0000 | + | 10.0000i | 0.388661 | + | 0.388661i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −28.0000 | + | 28.0000i | −1.08661 | + | 1.08661i | ||||
\(665\) | −36.0000 | −1.39602 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 16.0000i | − | 0.619522i | ||||||
\(668\) | − | 24.0000i | − | 0.928588i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 6.00000 | − | 6.00000i | 0.231800 | − | 0.231800i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 29.0000 | 1.11787 | 0.558934 | − | 0.829212i | \(-0.311211\pi\) | ||||
0.558934 | + | 0.829212i | \(0.311211\pi\) | |||||||
\(674\) | −17.0000 | + | 17.0000i | −0.654816 | + | 0.654816i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.00000i | 0.0769231i | ||||||||
\(677\) | − | 22.0000i | − | 0.845529i | −0.906240 | − | 0.422764i | \(-0.861060\pi\) | ||
0.906240 | − | 0.422764i | \(-0.138940\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 24.0000 | 0.921035 | ||||||||
\(680\) | −42.0000 | + | 42.0000i | −1.61063 | + | 1.61063i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 26.0000i | 0.994862i | 0.867503 | + | 0.497431i | \(0.165723\pi\) | ||||
−0.867503 | + | 0.497431i | \(0.834277\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 36.0000i | − | 1.37549i | ||||||
\(686\) | −15.0000 | + | 15.0000i | −0.572703 | + | 0.572703i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.00000i | 0.152499i | ||||||||
\(689\) | 4.00000 | 0.152388 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 20.0000i | − | 0.760836i | −0.924815 | − | 0.380418i | \(-0.875780\pi\) | ||
0.924815 | − | 0.380418i | \(-0.124220\pi\) | |||||||
\(692\) | 12.0000 | 0.456172 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7.00000 | − | 7.00000i | −0.265716 | − | 0.265716i | ||||
\(695\) | 33.0000 | 1.25176 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −14.0000 | −0.530288 | ||||||||
\(698\) | −19.0000 | − | 19.0000i | −0.719161 | − | 0.719161i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 24.0000i | 0.907115i | ||||||||
\(701\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 28.0000 | 1.05604 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.00000 | − | 6.00000i | 0.225813 | − | 0.225813i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.00000i | 0.225335i | 0.993633 | + | 0.112667i | \(0.0359394\pi\) | ||||
−0.993633 | + | 0.112667i | \(0.964061\pi\) | |||||||
\(710\) | −9.00000 | − | 9.00000i | −0.337764 | − | 0.337764i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 32.0000 | 1.19841 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −42.0000 | −1.56961 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 30.0000 | 1.11881 | 0.559406 | − | 0.828894i | \(-0.311029\pi\) | ||||
0.559406 | + | 0.828894i | \(0.311029\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −18.0000 | −0.670355 | ||||||||
\(722\) | 3.00000 | − | 3.00000i | 0.111648 | − | 0.111648i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 20.0000 | 0.743294 | ||||||||
\(725\) | − | 16.0000i | − | 0.594225i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.00000 | 0.296704 | 0.148352 | − | 0.988935i | \(-0.452603\pi\) | ||||
0.148352 | + | 0.988935i | \(0.452603\pi\) | |||||||
\(728\) | 6.00000 | − | 6.00000i | 0.222375 | − | 0.222375i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −42.0000 | − | 42.0000i | −1.55449 | − | 1.55449i | ||||
\(731\) | − | 7.00000i | − | 0.258904i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 1.00000i | − | 0.0369358i | −0.999829 | − | 0.0184679i | \(-0.994121\pi\) | ||
0.999829 | − | 0.0184679i | \(-0.00587886\pi\) | |||||||
\(734\) | −22.0000 | + | 22.0000i | −0.812035 | + | 0.812035i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 16.0000 | − | 16.0000i | 0.589768 | − | 0.589768i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 34.0000i | − | 1.25071i | −0.780340 | − | 0.625355i | \(-0.784954\pi\) | ||
0.780340 | − | 0.625355i | \(-0.215046\pi\) | |||||||
\(740\) | − | 42.0000i | − | 1.54395i | ||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −12.0000 | − | 12.0000i | −0.440534 | − | 0.440534i | ||||
\(743\) | 21.0000 | 0.770415 | 0.385208 | − | 0.922830i | \(-0.374130\pi\) | ||||
0.385208 | + | 0.922830i | \(0.374130\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −18.0000 | −0.659469 | ||||||||
\(746\) | −36.0000 | − | 36.0000i | −1.31805 | − | 1.31805i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 24.0000i | 0.876941i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.00000 | 0.0729810 | 0.0364905 | − | 0.999334i | \(-0.488382\pi\) | ||||
0.0364905 | + | 0.999334i | \(0.488382\pi\) | |||||||
\(752\) | −28.0000 | −1.02105 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −4.00000 | + | 4.00000i | −0.145671 | + | 0.145671i | ||||
\(755\) | − | 51.0000i | − | 1.85608i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32.0000i | 1.16306i | 0.813525 | + | 0.581530i | \(0.197546\pi\) | ||||
−0.813525 | + | 0.581530i | \(0.802454\pi\) | |||||||
\(758\) | −4.00000 | − | 4.00000i | −0.145287 | − | 0.145287i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 24.0000 | + | 24.0000i | 0.870572 | + | 0.870572i | ||||
\(761\) | −22.0000 | −0.797499 | −0.398750 | − | 0.917060i | \(-0.630556\pi\) | ||||
−0.398750 | + | 0.917060i | \(0.630556\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.00000i | 0.108607i | ||||||||
\(764\) | 24.0000i | 0.868290i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.00000 | − | 1.00000i | 0.0361315 | − | 0.0361315i | ||||
\(767\) | −14.0000 | −0.505511 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −20.0000 | −0.721218 | −0.360609 | − | 0.932717i | \(-0.617431\pi\) | ||||
−0.360609 | + | 0.932717i | \(0.617431\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 12.0000i | 0.431889i | ||||||||
\(773\) | 21.0000i | 0.755318i | 0.925945 | + | 0.377659i | \(0.123271\pi\) | ||||
−0.925945 | + | 0.377659i | \(0.876729\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 32.0000 | 1.14947 | ||||||||
\(776\) | −16.0000 | − | 16.0000i | −0.574367 | − | 0.574367i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 34.0000 | + | 34.0000i | 1.21896 | + | 1.21896i | ||||
\(779\) | 8.00000i | 0.286630i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −28.0000 | + | 28.0000i | −1.00128 | + | 1.00128i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −8.00000 | −0.285714 | ||||||||
\(785\) | 6.00000 | 0.214149 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 22.0000i | 0.784215i | 0.919919 | + | 0.392108i | \(0.128254\pi\) | ||||
−0.919919 | + | 0.392108i | \(0.871746\pi\) | |||||||
\(788\) | −34.0000 | −1.21120 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(79 |