Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [450,3,Mod(307,450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(450, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("450.307");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 450.g (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: | \(12.2616118962\) |
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 50) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 343.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 450.343 |
Dual form | 450.3.g.e.307.1 |
$q$-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 \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 | 0.500000 | − | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | − | 2.00000i | − | 0.500000i | ||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.00000 | + | 3.00000i | −0.428571 | + | 0.428571i | −0.888142 | − | 0.459570i | \(-0.848004\pi\) |
0.459570 | + | 0.888142i | \(0.348004\pi\) | |||||||
\(8\) | −2.00000 | − | 2.00000i | −0.250000 | − | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −12.0000 | −1.09091 | −0.545455 | − | 0.838140i | \(-0.683643\pi\) | ||||
−0.545455 | + | 0.838140i | \(0.683643\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −12.0000 | − | 12.0000i | −0.923077 | − | 0.923077i | 0.0741688 | − | 0.997246i | \(-0.476370\pi\) |
−0.997246 | + | 0.0741688i | \(0.976370\pi\) | |||||||
\(14\) | 6.00000i | 0.428571i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | −12.0000 | + | 12.0000i | −0.705882 | + | 0.705882i | −0.965667 | − | 0.259784i | \(-0.916349\pi\) |
0.259784 | + | 0.965667i | \(0.416349\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 20.0000i | − | 1.05263i | −0.850289 | − | 0.526316i | \(-0.823573\pi\) | ||
0.850289 | − | 0.526316i | \(-0.176427\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −12.0000 | + | 12.0000i | −0.545455 | + | 0.545455i | ||||
\(23\) | −3.00000 | − | 3.00000i | −0.130435 | − | 0.130435i | 0.638875 | − | 0.769310i | \(-0.279400\pi\) |
−0.769310 | + | 0.638875i | \(0.779400\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −24.0000 | −0.923077 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 6.00000 | + | 6.00000i | 0.214286 | + | 0.214286i | ||||
\(29\) | − | 30.0000i | − | 1.03448i | −0.855840 | − | 0.517241i | \(-0.826959\pi\) | ||
0.855840 | − | 0.517241i | \(-0.173041\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.00000 | −0.258065 | −0.129032 | − | 0.991640i | \(-0.541187\pi\) | ||||
−0.129032 | + | 0.991640i | \(0.541187\pi\) | |||||||
\(32\) | −4.00000 | + | 4.00000i | −0.125000 | + | 0.125000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 24.0000i | 0.705882i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −48.0000 | + | 48.0000i | −1.29730 | + | 1.29730i | −0.367126 | + | 0.930171i | \(0.619658\pi\) |
−0.930171 | + | 0.367126i | \(0.880342\pi\) | |||||||
\(38\) | −20.0000 | − | 20.0000i | −0.526316 | − | 0.526316i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 48.0000 | 1.17073 | 0.585366 | − | 0.810769i | \(-0.300951\pi\) | ||||
0.585366 | + | 0.810769i | \(0.300951\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −27.0000 | − | 27.0000i | −0.627907 | − | 0.627907i | 0.319634 | − | 0.947541i | \(-0.396440\pi\) |
−0.947541 | + | 0.319634i | \(0.896440\pi\) | |||||||
\(44\) | 24.0000i | 0.545455i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.00000 | −0.130435 | ||||||||
\(47\) | −27.0000 | + | 27.0000i | −0.574468 | + | 0.574468i | −0.933374 | − | 0.358906i | \(-0.883150\pi\) |
0.358906 | + | 0.933374i | \(0.383150\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 31.0000i | 0.632653i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −24.0000 | + | 24.0000i | −0.461538 | + | 0.461538i | ||||
\(53\) | 12.0000 | + | 12.0000i | 0.226415 | + | 0.226415i | 0.811193 | − | 0.584778i | \(-0.198818\pi\) |
−0.584778 | + | 0.811193i | \(0.698818\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 12.0000 | 0.214286 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −30.0000 | − | 30.0000i | −0.517241 | − | 0.517241i | ||||
\(59\) | − | 60.0000i | − | 1.01695i | −0.861077 | − | 0.508475i | \(-0.830210\pi\) | ||
0.861077 | − | 0.508475i | \(-0.169790\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 32.0000 | 0.524590 | 0.262295 | − | 0.964988i | \(-0.415521\pi\) | ||||
0.262295 | + | 0.964988i | \(0.415521\pi\) | |||||||
\(62\) | −8.00000 | + | 8.00000i | −0.129032 | + | 0.129032i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000i | 0.125000i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.00000 | + | 3.00000i | −0.0447761 | + | 0.0447761i | −0.729140 | − | 0.684364i | \(-0.760080\pi\) |
0.684364 | + | 0.729140i | \(0.260080\pi\) | |||||||
\(68\) | 24.0000 | + | 24.0000i | 0.352941 | + | 0.352941i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 48.0000 | 0.676056 | 0.338028 | − | 0.941136i | \(-0.390240\pi\) | ||||
0.338028 | + | 0.941136i | \(0.390240\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.0000 | − | 12.0000i | −0.164384 | − | 0.164384i | 0.620122 | − | 0.784505i | \(-0.287083\pi\) |
−0.784505 | + | 0.620122i | \(0.787083\pi\) | |||||||
\(74\) | 96.0000i | 1.29730i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −40.0000 | −0.526316 | ||||||||
\(77\) | 36.0000 | − | 36.0000i | 0.467532 | − | 0.467532i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 40.0000i | − | 0.506329i | −0.967423 | − | 0.253165i | \(-0.918529\pi\) | ||
0.967423 | − | 0.253165i | \(-0.0814714\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 48.0000 | − | 48.0000i | 0.585366 | − | 0.585366i | ||||
\(83\) | −93.0000 | − | 93.0000i | −1.12048 | − | 1.12048i | −0.991669 | − | 0.128813i | \(-0.958883\pi\) |
−0.128813 | − | 0.991669i | \(-0.541117\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −54.0000 | −0.627907 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 24.0000 | + | 24.0000i | 0.272727 | + | 0.272727i | ||||
\(89\) | 30.0000i | 0.337079i | 0.985695 | + | 0.168539i | \(0.0539050\pi\) | ||||
−0.985695 | + | 0.168539i | \(0.946095\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 72.0000 | 0.791209 | ||||||||
\(92\) | −6.00000 | + | 6.00000i | −0.0652174 | + | 0.0652174i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 54.0000i | 0.574468i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.0000 | − | 12.0000i | 0.123711 | − | 0.123711i | −0.642540 | − | 0.766252i | \(-0.722120\pi\) |
0.766252 | + | 0.642540i | \(0.222120\pi\) | |||||||
\(98\) | 31.0000 | + | 31.0000i | 0.316327 | + | 0.316327i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 78.0000 | 0.772277 | 0.386139 | − | 0.922441i | \(-0.373809\pi\) | ||||
0.386139 | + | 0.922441i | \(0.373809\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 93.0000 | + | 93.0000i | 0.902913 | + | 0.902913i | 0.995687 | − | 0.0927745i | \(-0.0295736\pi\) |
−0.0927745 | + | 0.995687i | \(0.529574\pi\) | |||||||
\(104\) | 48.0000i | 0.461538i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 24.0000 | 0.226415 | ||||||||
\(107\) | −27.0000 | + | 27.0000i | −0.252336 | + | 0.252336i | −0.821928 | − | 0.569591i | \(-0.807101\pi\) |
0.569591 | + | 0.821928i | \(0.307101\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 160.000i | − | 1.46789i | −0.679209 | − | 0.733945i | \(-0.737677\pi\) | ||
0.679209 | − | 0.733945i | \(-0.262323\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 12.0000 | − | 12.0000i | 0.107143 | − | 0.107143i | ||||
\(113\) | 72.0000 | + | 72.0000i | 0.637168 | + | 0.637168i | 0.949856 | − | 0.312688i | \(-0.101229\pi\) |
−0.312688 | + | 0.949856i | \(0.601229\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −60.0000 | −0.517241 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −60.0000 | − | 60.0000i | −0.508475 | − | 0.508475i | ||||
\(119\) | − | 72.0000i | − | 0.605042i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 23.0000 | 0.190083 | ||||||||
\(122\) | 32.0000 | − | 32.0000i | 0.262295 | − | 0.262295i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 16.0000i | 0.129032i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 117.000 | − | 117.000i | 0.921260 | − | 0.921260i | −0.0758587 | − | 0.997119i | \(-0.524170\pi\) |
0.997119 | + | 0.0758587i | \(0.0241698\pi\) | |||||||
\(128\) | 8.00000 | + | 8.00000i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −132.000 | −1.00763 | −0.503817 | − | 0.863811i | \(-0.668071\pi\) | ||||
−0.503817 | + | 0.863811i | \(0.668071\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 60.0000 | + | 60.0000i | 0.451128 | + | 0.451128i | ||||
\(134\) | 6.00000i | 0.0447761i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 48.0000 | 0.352941 | ||||||||
\(137\) | 168.000 | − | 168.000i | 1.22628 | − | 1.22628i | 0.260916 | − | 0.965362i | \(-0.415975\pi\) |
0.965362 | − | 0.260916i | \(-0.0840245\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 100.000i | 0.719424i | 0.933063 | + | 0.359712i | \(0.117125\pi\) | ||||
−0.933063 | + | 0.359712i | \(0.882875\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 48.0000 | − | 48.0000i | 0.338028 | − | 0.338028i | ||||
\(143\) | 144.000 | + | 144.000i | 1.00699 | + | 1.00699i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −24.0000 | −0.164384 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 96.0000 | + | 96.0000i | 0.648649 | + | 0.648649i | ||||
\(149\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −248.000 | −1.64238 | −0.821192 | − | 0.570652i | \(-0.806691\pi\) | ||||
−0.821192 | + | 0.570652i | \(0.806691\pi\) | |||||||
\(152\) | −40.0000 | + | 40.0000i | −0.263158 | + | 0.263158i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | − | 72.0000i | − | 0.467532i | ||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 72.0000 | − | 72.0000i | 0.458599 | − | 0.458599i | −0.439597 | − | 0.898195i | \(-0.644879\pi\) |
0.898195 | + | 0.439597i | \(0.144879\pi\) | |||||||
\(158\) | −40.0000 | − | 40.0000i | −0.253165 | − | 0.253165i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 18.0000 | 0.111801 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 93.0000 | + | 93.0000i | 0.570552 | + | 0.570552i | 0.932283 | − | 0.361731i | \(-0.117814\pi\) |
−0.361731 | + | 0.932283i | \(0.617814\pi\) | |||||||
\(164\) | − | 96.0000i | − | 0.585366i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −186.000 | −1.12048 | ||||||||
\(167\) | 3.00000 | − | 3.00000i | 0.0179641 | − | 0.0179641i | −0.698068 | − | 0.716032i | \(-0.745957\pi\) |
0.716032 | + | 0.698068i | \(0.245957\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 119.000i | 0.704142i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −54.0000 | + | 54.0000i | −0.313953 | + | 0.313953i | ||||
\(173\) | −168.000 | − | 168.000i | −0.971098 | − | 0.971098i | 0.0284957 | − | 0.999594i | \(-0.490928\pi\) |
−0.999594 | + | 0.0284957i | \(0.990928\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 48.0000 | 0.272727 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 30.0000 | + | 30.0000i | 0.168539 | + | 0.168539i | ||||
\(179\) | − | 300.000i | − | 1.67598i | −0.545687 | − | 0.837989i | \(-0.683731\pi\) | ||
0.545687 | − | 0.837989i | \(-0.316269\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 142.000 | 0.784530 | 0.392265 | − | 0.919852i | \(-0.371692\pi\) | ||||
0.392265 | + | 0.919852i | \(0.371692\pi\) | |||||||
\(182\) | 72.0000 | − | 72.0000i | 0.395604 | − | 0.395604i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 12.0000i | 0.0652174i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 144.000 | − | 144.000i | 0.770053 | − | 0.770053i | ||||
\(188\) | 54.0000 | + | 54.0000i | 0.287234 | + | 0.287234i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −192.000 | −1.00524 | −0.502618 | − | 0.864509i | \(-0.667630\pi\) | ||||
−0.502618 | + | 0.864509i | \(0.667630\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −132.000 | − | 132.000i | −0.683938 | − | 0.683938i | 0.276947 | − | 0.960885i | \(-0.410677\pi\) |
−0.960885 | + | 0.276947i | \(0.910677\pi\) | |||||||
\(194\) | − | 24.0000i | − | 0.123711i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 62.0000 | 0.316327 | ||||||||
\(197\) | −132.000 | + | 132.000i | −0.670051 | + | 0.670051i | −0.957728 | − | 0.287677i | \(-0.907117\pi\) |
0.287677 | + | 0.957728i | \(0.407117\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 160.000i | − | 0.804020i | −0.915635 | − | 0.402010i | \(-0.868312\pi\) | ||
0.915635 | − | 0.402010i | \(-0.131688\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 78.0000 | − | 78.0000i | 0.386139 | − | 0.386139i | ||||
\(203\) | 90.0000 | + | 90.0000i | 0.443350 | + | 0.443350i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 186.000 | 0.902913 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 48.0000 | + | 48.0000i | 0.230769 | + | 0.230769i | ||||
\(209\) | 240.000i | 1.14833i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −28.0000 | −0.132701 | −0.0663507 | − | 0.997796i | \(-0.521136\pi\) | ||||
−0.0663507 | + | 0.997796i | \(0.521136\pi\) | |||||||
\(212\) | 24.0000 | − | 24.0000i | 0.113208 | − | 0.113208i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 54.0000i | 0.252336i | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 24.0000 | − | 24.0000i | 0.110599 | − | 0.110599i | ||||
\(218\) | −160.000 | − | 160.000i | −0.733945 | − | 0.733945i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 288.000 | 1.30317 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −117.000 | − | 117.000i | −0.524664 | − | 0.524664i | 0.394313 | − | 0.918976i | \(-0.370983\pi\) |
−0.918976 | + | 0.394313i | \(0.870983\pi\) | |||||||
\(224\) | − | 24.0000i | − | 0.107143i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 144.000 | 0.637168 | ||||||||
\(227\) | 93.0000 | − | 93.0000i | 0.409692 | − | 0.409692i | −0.471939 | − | 0.881631i | \(-0.656446\pi\) |
0.881631 | + | 0.471939i | \(0.156446\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 370.000i | 1.61572i | 0.589374 | + | 0.807860i | \(0.299374\pi\) | ||||
−0.589374 | + | 0.807860i | \(0.700626\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −60.0000 | + | 60.0000i | −0.258621 | + | 0.258621i | ||||
\(233\) | 252.000 | + | 252.000i | 1.08155 | + | 1.08155i | 0.996366 | + | 0.0851794i | \(0.0271464\pi\) |
0.0851794 | + | 0.996366i | \(0.472854\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −120.000 | −0.508475 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −72.0000 | − | 72.0000i | −0.302521 | − | 0.302521i | ||||
\(239\) | 360.000i | 1.50628i | 0.657862 | + | 0.753138i | \(0.271461\pi\) | ||||
−0.657862 | + | 0.753138i | \(0.728539\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 32.0000 | 0.132780 | 0.0663900 | − | 0.997794i | \(-0.478852\pi\) | ||||
0.0663900 | + | 0.997794i | \(0.478852\pi\) | |||||||
\(242\) | 23.0000 | − | 23.0000i | 0.0950413 | − | 0.0950413i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 64.0000i | − | 0.262295i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −240.000 | + | 240.000i | −0.971660 | + | 0.971660i | ||||
\(248\) | 16.0000 | + | 16.0000i | 0.0645161 | + | 0.0645161i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −252.000 | −1.00398 | −0.501992 | − | 0.864872i | \(-0.667399\pi\) | ||||
−0.501992 | + | 0.864872i | \(0.667399\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 36.0000 | + | 36.0000i | 0.142292 | + | 0.142292i | ||||
\(254\) | − | 234.000i | − | 0.921260i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | −192.000 | + | 192.000i | −0.747082 | + | 0.747082i | −0.973930 | − | 0.226848i | \(-0.927158\pi\) |
0.226848 | + | 0.973930i | \(0.427158\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 288.000i | − | 1.11197i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −132.000 | + | 132.000i | −0.503817 | + | 0.503817i | ||||
\(263\) | −333.000 | − | 333.000i | −1.26616 | − | 1.26616i | −0.948056 | − | 0.318104i | \(-0.896954\pi\) |
−0.318104 | − | 0.948056i | \(-0.603046\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 120.000 | 0.451128 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6.00000 | + | 6.00000i | 0.0223881 | + | 0.0223881i | ||||
\(269\) | 480.000i | 1.78439i | 0.451654 | + | 0.892193i | \(0.350834\pi\) | ||||
−0.451654 | + | 0.892193i | \(0.649166\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −88.0000 | −0.324723 | −0.162362 | − | 0.986731i | \(-0.551911\pi\) | ||||
−0.162362 | + | 0.986731i | \(0.551911\pi\) | |||||||
\(272\) | 48.0000 | − | 48.0000i | 0.176471 | − | 0.176471i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 336.000i | − | 1.22628i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −288.000 | + | 288.000i | −1.03971 | + | 1.03971i | −0.0405330 | + | 0.999178i | \(0.512906\pi\) |
−0.999178 | + | 0.0405330i | \(0.987094\pi\) | |||||||
\(278\) | 100.000 | + | 100.000i | 0.359712 | + | 0.359712i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 288.000 | 1.02491 | 0.512456 | − | 0.858714i | \(-0.328736\pi\) | ||||
0.512456 | + | 0.858714i | \(0.328736\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −117.000 | − | 117.000i | −0.413428 | − | 0.413428i | 0.469503 | − | 0.882931i | \(-0.344433\pi\) |
−0.882931 | + | 0.469503i | \(0.844433\pi\) | |||||||
\(284\) | − | 96.0000i | − | 0.338028i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 288.000 | 1.00699 | ||||||||
\(287\) | −144.000 | + | 144.000i | −0.501742 | + | 0.501742i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000i | 0.00346021i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −24.0000 | + | 24.0000i | −0.0821918 | + | 0.0821918i | ||||
\(293\) | −168.000 | − | 168.000i | −0.573379 | − | 0.573379i | 0.359692 | − | 0.933071i | \(-0.382882\pi\) |
−0.933071 | + | 0.359692i | \(0.882882\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 192.000 | 0.648649 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 72.0000i | 0.240803i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 162.000 | 0.538206 | ||||||||
\(302\) | −248.000 | + | 248.000i | −0.821192 | + | 0.821192i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 80.0000i | 0.263158i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −243.000 | + | 243.000i | −0.791531 | + | 0.791531i | −0.981743 | − | 0.190212i | \(-0.939082\pi\) |
0.190212 | + | 0.981743i | \(0.439082\pi\) | |||||||
\(308\) | −72.0000 | − | 72.0000i | −0.233766 | − | 0.233766i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −552.000 | −1.77492 | −0.887460 | − | 0.460885i | \(-0.847532\pi\) | ||||
−0.887460 | + | 0.460885i | \(0.847532\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 48.0000 | + | 48.0000i | 0.153355 | + | 0.153355i | 0.779614 | − | 0.626260i | \(-0.215415\pi\) |
−0.626260 | + | 0.779614i | \(0.715415\pi\) | |||||||
\(314\) | − | 144.000i | − | 0.458599i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −80.0000 | −0.253165 | ||||||||
\(317\) | 228.000 | − | 228.000i | 0.719243 | − | 0.719243i | −0.249207 | − | 0.968450i | \(-0.580170\pi\) |
0.968450 | + | 0.249207i | \(0.0801700\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 360.000i | 1.12853i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 18.0000 | − | 18.0000i | 0.0559006 | − | 0.0559006i | ||||
\(323\) | 240.000 | + | 240.000i | 0.743034 | + | 0.743034i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 186.000 | 0.570552 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −96.0000 | − | 96.0000i | −0.292683 | − | 0.292683i | ||||
\(329\) | − | 162.000i | − | 0.492401i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −148.000 | −0.447130 | −0.223565 | − | 0.974689i | \(-0.571769\pi\) | ||||
−0.223565 | + | 0.974689i | \(0.571769\pi\) | |||||||
\(332\) | −186.000 | + | 186.000i | −0.560241 | + | 0.560241i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 6.00000i | − | 0.0179641i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 192.000 | − | 192.000i | 0.569733 | − | 0.569733i | −0.362321 | − | 0.932054i | \(-0.618015\pi\) |
0.932054 | + | 0.362321i | \(0.118015\pi\) | |||||||
\(338\) | 119.000 | + | 119.000i | 0.352071 | + | 0.352071i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 96.0000 | 0.281525 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −240.000 | − | 240.000i | −0.699708 | − | 0.699708i | ||||
\(344\) | 108.000i | 0.313953i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −336.000 | −0.971098 | ||||||||
\(347\) | −117.000 | + | 117.000i | −0.337176 | + | 0.337176i | −0.855303 | − | 0.518128i | \(-0.826629\pi\) |
0.518128 | + | 0.855303i | \(0.326629\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 130.000i | 0.372493i | 0.982503 | + | 0.186246i | \(0.0596323\pi\) | ||||
−0.982503 | + | 0.186246i | \(0.940368\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 48.0000 | − | 48.0000i | 0.136364 | − | 0.136364i | ||||
\(353\) | −288.000 | − | 288.000i | −0.815864 | − | 0.815864i | 0.169642 | − | 0.985506i | \(-0.445739\pi\) |
−0.985506 | + | 0.169642i | \(0.945739\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 60.0000 | 0.168539 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −300.000 | − | 300.000i | −0.837989 | − | 0.837989i | ||||
\(359\) | − | 120.000i | − | 0.334262i | −0.985935 | − | 0.167131i | \(-0.946550\pi\) | ||
0.985935 | − | 0.167131i | \(-0.0534503\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −39.0000 | −0.108033 | ||||||||
\(362\) | 142.000 | − | 142.000i | 0.392265 | − | 0.392265i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | − | 144.000i | − | 0.395604i | ||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −213.000 | + | 213.000i | −0.580381 | + | 0.580381i | −0.935008 | − | 0.354627i | \(-0.884608\pi\) |
0.354627 | + | 0.935008i | \(0.384608\pi\) | |||||||
\(368\) | 12.0000 | + | 12.0000i | 0.0326087 | + | 0.0326087i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −72.0000 | −0.194070 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 168.000 | + | 168.000i | 0.450402 | + | 0.450402i | 0.895488 | − | 0.445086i | \(-0.146827\pi\) |
−0.445086 | + | 0.895488i | \(0.646827\pi\) | |||||||
\(374\) | − | 288.000i | − | 0.770053i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 108.000 | 0.287234 | ||||||||
\(377\) | −360.000 | + | 360.000i | −0.954907 | + | 0.954907i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 20.0000i | − | 0.0527704i | −0.999652 | − | 0.0263852i | \(-0.991600\pi\) | ||
0.999652 | − | 0.0263852i | \(-0.00839965\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −192.000 | + | 192.000i | −0.502618 | + | 0.502618i | ||||
\(383\) | −123.000 | − | 123.000i | −0.321149 | − | 0.321149i | 0.528059 | − | 0.849208i | \(-0.322920\pi\) |
−0.849208 | + | 0.528059i | \(0.822920\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −264.000 | −0.683938 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −24.0000 | − | 24.0000i | −0.0618557 | − | 0.0618557i | ||||
\(389\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 72.0000 | 0.184143 | ||||||||
\(392\) | 62.0000 | − | 62.0000i | 0.158163 | − | 0.158163i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 264.000i | 0.670051i | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −108.000 | + | 108.000i | −0.272040 | + | 0.272040i | −0.829921 | − | 0.557881i | \(-0.811615\pi\) |
0.557881 | + | 0.829921i | \(0.311615\pi\) | |||||||
\(398\) | −160.000 | − | 160.000i | −0.402010 | − | 0.402010i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 18.0000 | 0.0448878 | 0.0224439 | − | 0.999748i | \(-0.492855\pi\) | ||||
0.0224439 | + | 0.999748i | \(0.492855\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 96.0000 | + | 96.0000i | 0.238213 | + | 0.238213i | ||||
\(404\) | − | 156.000i | − | 0.386139i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 180.000 | 0.443350 | ||||||||
\(407\) | 576.000 | − | 576.000i | 1.41523 | − | 1.41523i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 80.0000i | − | 0.195599i | −0.995206 | − | 0.0977995i | \(-0.968820\pi\) | ||
0.995206 | − | 0.0977995i | \(-0.0311804\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 186.000 | − | 186.000i | 0.451456 | − | 0.451456i | ||||
\(413\) | 180.000 | + | 180.000i | 0.435835 | + | 0.435835i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 96.0000 | 0.230769 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 240.000 | + | 240.000i | 0.574163 | + | 0.574163i | ||||
\(419\) | − | 540.000i | − | 1.28878i | −0.764696 | − | 0.644391i | \(-0.777111\pi\) | ||
0.764696 | − | 0.644391i | \(-0.222889\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −608.000 | −1.44418 | −0.722090 | − | 0.691799i | \(-0.756818\pi\) | ||||
−0.722090 | + | 0.691799i | \(0.756818\pi\) | |||||||
\(422\) | −28.0000 | + | 28.0000i | −0.0663507 | + | 0.0663507i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 48.0000i | − | 0.113208i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −96.0000 | + | 96.0000i | −0.224824 | + | 0.224824i | ||||
\(428\) | 54.0000 | + | 54.0000i | 0.126168 | + | 0.126168i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −312.000 | −0.723898 | −0.361949 | − | 0.932198i | \(-0.617889\pi\) | ||||
−0.361949 | + | 0.932198i | \(0.617889\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −252.000 | − | 252.000i | −0.581986 | − | 0.581986i | 0.353463 | − | 0.935449i | \(-0.385004\pi\) |
−0.935449 | + | 0.353463i | \(0.885004\pi\) | |||||||
\(434\) | − | 48.0000i | − | 0.110599i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −320.000 | −0.733945 | ||||||||
\(437\) | −60.0000 | + | 60.0000i | −0.137300 | + | 0.137300i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 40.0000i | − | 0.0911162i | −0.998962 | − | 0.0455581i | \(-0.985493\pi\) | ||
0.998962 | − | 0.0455581i | \(-0.0145066\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 288.000 | − | 288.000i | 0.651584 | − | 0.651584i | ||||
\(443\) | −213.000 | − | 213.000i | −0.480813 | − | 0.480813i | 0.424578 | − | 0.905391i | \(-0.360422\pi\) |
−0.905391 | + | 0.424578i | \(0.860422\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −234.000 | −0.524664 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −24.0000 | − | 24.0000i | −0.0535714 | − | 0.0535714i | ||||
\(449\) | 480.000i | 1.06904i | 0.845155 | + | 0.534521i | \(0.179508\pi\) | ||||
−0.845155 | + | 0.534521i | \(0.820492\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −576.000 | −1.27716 | ||||||||
\(452\) | 144.000 | − | 144.000i | 0.318584 | − | 0.318584i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 186.000i | − | 0.409692i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 432.000 | − | 432.000i | 0.945295 | − | 0.945295i | −0.0532840 | − | 0.998579i | \(-0.516969\pi\) |
0.998579 | + | 0.0532840i | \(0.0169689\pi\) | |||||||
\(458\) | 370.000 | + | 370.000i | 0.807860 | + | 0.807860i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −222.000 | −0.481562 | −0.240781 | − | 0.970579i | \(-0.577404\pi\) | ||||
−0.240781 | + | 0.970579i | \(0.577404\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 213.000 | + | 213.000i | 0.460043 | + | 0.460043i | 0.898670 | − | 0.438626i | \(-0.144535\pi\) |
−0.438626 | + | 0.898670i | \(0.644535\pi\) | |||||||
\(464\) | 120.000i | 0.258621i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 504.000 | 1.08155 | ||||||||
\(467\) | 3.00000 | − | 3.00000i | 0.00642398 | − | 0.00642398i | −0.703887 | − | 0.710311i | \(-0.748554\pi\) |
0.710311 | + | 0.703887i | \(0.248554\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 18.0000i | − | 0.0383795i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −120.000 | + | 120.000i | −0.254237 | + | 0.254237i | ||||
\(473\) | 324.000 | + | 324.000i | 0.684989 | + | 0.684989i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −144.000 | −0.302521 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 360.000 | + | 360.000i | 0.753138 | + | 0.753138i | ||||
\(479\) | − | 240.000i | − | 0.501044i | −0.968111 | − | 0.250522i | \(-0.919398\pi\) | ||
0.968111 | − | 0.250522i | \(-0.0806022\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1152.00 | 2.39501 | ||||||||
\(482\) | 32.0000 | − | 32.0000i | 0.0663900 | − | 0.0663900i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 46.0000i | − | 0.0950413i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 627.000 | − | 627.000i | 1.28747 | − | 1.28747i | 0.351158 | − | 0.936316i | \(-0.385788\pi\) |
0.936316 | − | 0.351158i | \(-0.114212\pi\) | |||||||
\(488\) | −64.0000 | − | 64.0000i | −0.131148 | − | 0.131148i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 588.000 | 1.19756 | 0.598778 | − | 0.800915i | \(-0.295653\pi\) | ||||
0.598778 | + | 0.800915i | \(0.295653\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 360.000 | + | 360.000i | 0.730223 | + | 0.730223i | ||||
\(494\) | 480.000i | 0.971660i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 32.0000 | 0.0645161 | ||||||||
\(497\) | −144.000 | + | 144.000i | −0.289738 | + | 0.289738i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 460.000i | − | 0.921844i | −0.887441 | − | 0.460922i | \(-0.847519\pi\) | ||
0.887441 | − | 0.460922i | \(-0.152481\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −252.000 | + | 252.000i | −0.501992 | + | 0.501992i | ||||
\(503\) | 627.000 | + | 627.000i | 1.24652 | + | 1.24652i | 0.957246 | + | 0.289275i | \(0.0934141\pi\) |
0.289275 | + | 0.957246i | \(0.406586\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 72.0000 | 0.142292 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −234.000 | − | 234.000i | −0.460630 | − | 0.460630i | ||||
\(509\) | 450.000i | 0.884086i | 0.896994 | + | 0.442043i | \(0.145746\pi\) | ||||
−0.896994 | + | 0.442043i | \(0.854254\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 72.0000 | 0.140900 | ||||||||
\(512\) | 16.0000 | − | 16.0000i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 384.000i | 0.747082i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 324.000 | − | 324.000i | 0.626692 | − | 0.626692i | ||||
\(518\) | −288.000 | − | 288.000i | −0.555985 | − | 0.555985i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 558.000 | 1.07102 | 0.535509 | − | 0.844530i | \(-0.320120\pi\) | ||||
0.535509 | + | 0.844530i | \(0.320120\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 123.000 | + | 123.000i | 0.235182 | + | 0.235182i | 0.814851 | − | 0.579670i | \(-0.196818\pi\) |
−0.579670 | + | 0.814851i | \(0.696818\pi\) | |||||||
\(524\) | 264.000i | 0.503817i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −666.000 | −1.26616 | ||||||||
\(527\) | 96.0000 | − | 96.0000i | 0.182163 | − | 0.182163i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 511.000i | − | 0.965974i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 120.000 | − | 120.000i | 0.225564 | − | 0.225564i | ||||
\(533\) | −576.000 | − | 576.000i | −1.08068 | − | 1.08068i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 12.0000 | 0.0223881 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 480.000 | + | 480.000i | 0.892193 | + | 0.892193i | ||||
\(539\) | − | 372.000i | − | 0.690167i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 542.000 | 1.00185 | 0.500924 | − | 0.865491i | \(-0.332994\pi\) | ||||
0.500924 | + | 0.865491i | \(0.332994\pi\) | |||||||
\(542\) | −88.0000 | + | 88.0000i | −0.162362 | + | 0.162362i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 96.0000i | − | 0.176471i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 147.000 | − | 147.000i | 0.268739 | − | 0.268739i | −0.559853 | − | 0.828592i | \(-0.689142\pi\) |
0.828592 | + | 0.559853i | \(0.189142\pi\) | |||||||
\(548\) | −336.000 | − | 336.000i | −0.613139 | − | 0.613139i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −600.000 | −1.08893 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 120.000 | + | 120.000i | 0.216998 | + | 0.216998i | ||||
\(554\) | 576.000i | 1.03971i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 200.000 | 0.359712 | ||||||||
\(557\) | 288.000 | − | 288.000i | 0.517056 | − | 0.517056i | −0.399624 | − | 0.916679i | \(-0.630859\pi\) |
0.916679 | + | 0.399624i | \(0.130859\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 648.000i | 1.15921i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 288.000 | − | 288.000i | 0.512456 | − | 0.512456i | ||||
\(563\) | 477.000 | + | 477.000i | 0.847247 | + | 0.847247i | 0.989789 | − | 0.142542i | \(-0.0455276\pi\) |
−0.142542 | + | 0.989789i | \(0.545528\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −234.000 | −0.413428 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −96.0000 | − | 96.0000i | −0.169014 | − | 0.169014i | ||||
\(569\) | − | 240.000i | − | 0.421793i | −0.977508 | − | 0.210896i | \(-0.932362\pi\) | ||
0.977508 | − | 0.210896i | \(-0.0676382\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 692.000 | 1.21191 | 0.605954 | − | 0.795499i | \(-0.292791\pi\) | ||||
0.605954 | + | 0.795499i | \(0.292791\pi\) | |||||||
\(572\) | 288.000 | − | 288.000i | 0.503497 | − | 0.503497i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 288.000i | 0.501742i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −168.000 | + | 168.000i | −0.291161 | + | 0.291161i | −0.837539 | − | 0.546378i | \(-0.816006\pi\) |
0.546378 | + | 0.837539i | \(0.316006\pi\) | |||||||
\(578\) | 1.00000 | + | 1.00000i | 0.00173010 | + | 0.00173010i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 558.000 | 0.960413 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −144.000 | − | 144.000i | −0.246998 | − | 0.246998i | ||||
\(584\) | 48.0000i | 0.0821918i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −336.000 | −0.573379 | ||||||||
\(587\) | 213.000 | − | 213.000i | 0.362862 | − | 0.362862i | −0.502004 | − | 0.864866i | \(-0.667404\pi\) |
0.864866 | + | 0.502004i | \(0.167404\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 160.000i | 0.271647i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 192.000 | − | 192.000i | 0.324324 | − | 0.324324i | ||||
\(593\) | 312.000 | + | 312.000i | 0.526138 | + | 0.526138i | 0.919419 | − | 0.393280i | \(-0.128660\pi\) |
−0.393280 | + | 0.919419i | \(0.628660\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 72.0000 | + | 72.0000i | 0.120401 | + | 0.120401i | ||||
\(599\) | 240.000i | 0.400668i | 0.979728 | + | 0.200334i | \(0.0642027\pi\) | ||||
−0.979728 | + | 0.200334i | \(0.935797\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −608.000 | −1.01165 | −0.505824 | − | 0.862637i | \(-0.668811\pi\) | ||||
−0.505824 | + | 0.862637i | \(0.668811\pi\) | |||||||
\(602\) | 162.000 | − | 162.000i | 0.269103 | − | 0.269103i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 496.000i | 0.821192i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 267.000 | − | 267.000i | 0.439868 | − | 0.439868i | −0.452099 | − | 0.891968i | \(-0.649325\pi\) |
0.891968 | + | 0.452099i | \(0.149325\pi\) | |||||||
\(608\) | 80.0000 | + | 80.0000i | 0.131579 | + | 0.131579i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 648.000 | 1.06056 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 228.000 | + | 228.000i | 0.371941 | + | 0.371941i | 0.868184 | − | 0.496243i | \(-0.165287\pi\) |
−0.496243 | + | 0.868184i | \(0.665287\pi\) | |||||||
\(614\) | 486.000i | 0.791531i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −144.000 | −0.233766 | ||||||||
\(617\) | 348.000 | − | 348.000i | 0.564019 | − | 0.564019i | −0.366427 | − | 0.930447i | \(-0.619419\pi\) |
0.930447 | + | 0.366427i | \(0.119419\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 940.000i | − | 1.51858i | −0.650753 | − | 0.759289i | \(-0.725547\pi\) | ||
0.650753 | − | 0.759289i | \(-0.274453\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −552.000 | + | 552.000i | −0.887460 | + | 0.887460i | ||||
\(623\) | −90.0000 | − | 90.0000i | −0.144462 | − | 0.144462i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 96.0000 | 0.153355 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −144.000 | − | 144.000i | −0.229299 | − | 0.229299i | ||||
\(629\) | − | 1152.00i | − | 1.83148i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −808.000 | −1.28051 | −0.640254 | − | 0.768164i | \(-0.721171\pi\) | ||||
−0.640254 | + | 0.768164i | \(0.721171\pi\) | |||||||
\(632\) | −80.0000 | + | 80.0000i | −0.126582 | + | 0.126582i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 456.000i | − | 0.719243i | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 372.000 | − | 372.000i | 0.583987 | − | 0.583987i | ||||
\(638\) | 360.000 | + | 360.000i | 0.564263 | + | 0.564263i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 768.000 | 1.19813 | 0.599064 | − | 0.800701i | \(-0.295540\pi\) | ||||
0.599064 | + | 0.800701i | \(0.295540\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −477.000 | − | 477.000i | −0.741835 | − | 0.741835i | 0.231096 | − | 0.972931i | \(-0.425769\pi\) |
−0.972931 | + | 0.231096i | \(0.925769\pi\) | |||||||
\(644\) | − | 36.0000i | − | 0.0559006i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 480.000 | 0.743034 | ||||||||
\(647\) | −627.000 | + | 627.000i | −0.969088 | + | 0.969088i | −0.999536 | − | 0.0304482i | \(-0.990307\pi\) |
0.0304482 | + | 0.999536i | \(0.490307\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 720.000i | 1.10940i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 186.000 | − | 186.000i | 0.285276 | − | 0.285276i | ||||
\(653\) | 12.0000 | + | 12.0000i | 0.0183767 | + | 0.0183767i | 0.716235 | − | 0.697859i | \(-0.245864\pi\) |
−0.697859 | + | 0.716235i | \(0.745864\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −192.000 | −0.292683 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −162.000 | − | 162.000i | −0.246201 | − | 0.246201i | ||||
\(659\) | − | 540.000i | − | 0.819423i | −0.912215 | − | 0.409712i | \(-0.865629\pi\) | ||
0.912215 | − | 0.409712i | \(-0.134371\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 352.000 | 0.532526 | 0.266263 | − | 0.963900i | \(-0.414211\pi\) | ||||
0.266263 | + | 0.963900i | \(0.414211\pi\) | |||||||
\(662\) | −148.000 | + | 148.000i | −0.223565 | + | 0.223565i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 372.000i | 0.560241i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −90.0000 | + | 90.0000i | −0.134933 | + | 0.134933i | ||||
\(668\) | −6.00000 | − | 6.00000i | −0.00898204 | − | 0.00898204i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −384.000 | −0.572280 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −732.000 | − | 732.000i | −1.08767 | − | 1.08767i | −0.995768 | − | 0.0918988i | \(-0.970706\pi\) |
−0.0918988 | − | 0.995768i | \(-0.529294\pi\) | |||||||
\(674\) | − | 384.000i | − | 0.569733i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 238.000 | 0.352071 | ||||||||
\(677\) | 108.000 | − | 108.000i | 0.159527 | − | 0.159527i | −0.622830 | − | 0.782357i | \(-0.714017\pi\) |
0.782357 | + | 0.622830i | \(0.214017\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 72.0000i | 0.106038i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 96.0000 | − | 96.0000i | 0.140762 | − | 0.140762i | ||||
\(683\) | −933.000 | − | 933.000i | −1.36603 | − | 1.36603i | −0.866016 | − | 0.500016i | \(-0.833327\pi\) |
−0.500016 | − | 0.866016i | \(-0.666673\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −480.000 | −0.699708 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 108.000 | + | 108.000i | 0.156977 | + | 0.156977i | ||||
\(689\) | − | 288.000i | − | 0.417997i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −68.0000 | −0.0984081 | −0.0492041 | − | 0.998789i | \(-0.515668\pi\) | ||||
−0.0492041 | + | 0.998789i | \(0.515668\pi\) | |||||||
\(692\) | −336.000 | + | 336.000i | −0.485549 | + | 0.485549i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 234.000i | 0.337176i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −576.000 | + | 576.000i | −0.826399 | + | 0.826399i | ||||
\(698\) | 130.000 | + | 130.000i | 0.186246 | + | 0.186246i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −192.000 | −0.273894 | −0.136947 | − | 0.990578i | \(-0.543729\pi\) | ||||
−0.136947 | + | 0.990578i | \(0.543729\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 960.000 | + | 960.000i | 1.36558 | + | 1.36558i | ||||
\(704\) | − | 96.0000i | − | 0.136364i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −576.000 | −0.815864 | ||||||||
\(707\) | −234.000 | + | 234.000i | −0.330976 | + | 0.330976i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 50.0000i | − | 0.0705219i | −0.999378 | − | 0.0352609i | \(-0.988774\pi\) | ||
0.999378 | − | 0.0352609i | \(-0.0112262\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 60.0000 | − | 60.0000i | 0.0842697 | − | 0.0842697i | ||||
\(713\) | 24.0000 | + | 24.0000i | 0.0336606 | + | 0.0336606i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −600.000 | −0.837989 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −120.000 | − | 120.000i | −0.167131 | − | 0.167131i | ||||
\(719\) | 840.000i | 1.16829i | 0.811650 | + | 0.584145i | \(0.198570\pi\) | ||||
−0.811650 | + | 0.584145i | \(0.801430\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −558.000 | −0.773925 | ||||||||
\(722\) | −39.0000 | + | 39.0000i | −0.0540166 | + | 0.0540166i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 284.000i | − | 0.392265i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −963.000 | + | 963.000i | −1.32462 | + | 1.32462i | −0.414633 | + | 0.909989i | \(0.636090\pi\) |
−0.909989 | + | 0.414633i | \(0.863910\pi\) | |||||||
\(728\) | −144.000 | − | 144.000i | −0.197802 | − | 0.197802i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 648.000 | 0.886457 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −72.0000 | − | 72.0000i | −0.0982265 | − | 0.0982265i | 0.656286 | − | 0.754512i | \(-0.272127\pi\) |
−0.754512 | + | 0.656286i | \(0.772127\pi\) | |||||||
\(734\) | 426.000i | 0.580381i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 24.0000 | 0.0326087 | ||||||||
\(737\) | 36.0000 | − | 36.0000i | 0.0488467 | − | 0.0488467i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 20.0000i | − | 0.0270636i | −0.999908 | − | 0.0135318i | \(-0.995693\pi\) | ||
0.999908 | − | 0.0135318i | \(-0.00430744\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −72.0000 | + | 72.0000i | −0.0970350 | + | 0.0970350i | ||||
\(743\) | −243.000 | − | 243.000i | −0.327052 | − | 0.327052i | 0.524412 | − | 0.851465i | \(-0.324285\pi\) |
−0.851465 | + | 0.524412i | \(0.824285\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 336.000 | 0.450402 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −288.000 | − | 288.000i | −0.385027 | − | 0.385027i | ||||
\(749\) | − | 162.000i | − | 0.216288i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1072.00 | 1.42743 | 0.713715 | − | 0.700436i | \(-0.247011\pi\) | ||||
0.713715 | + | 0.700436i | \(0.247011\pi\) | |||||||
\(752\) | 108.000 | − | 108.000i | 0.143617 | − | 0.143617i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 720.000i | 0.954907i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −408.000 | + | 408.000i | −0.538970 | + | 0.538970i | −0.923226 | − | 0.384257i | \(-0.874458\pi\) |
0.384257 | + | 0.923226i | \(0.374458\pi\) | |||||||
\(758\) | −20.0000 | − | 20.0000i | −0.0263852 | − | 0.0263852i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1362.00 | −1.78975 | −0.894875 | − | 0.446317i | \(-0.852736\pi\) | ||||
−0.894875 | + | 0.446317i | \(0.852736\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 480.000 | + | 480.000i | 0.629096 | + | 0.629096i | ||||
\(764\) | 384.000i | 0.502618i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −246.000 | −0.321149 | ||||||||
\(767\) | −720.000 | + | 720.000i | −0.938722 | + | 0.938722i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 370.000i | − | 0.481144i | −0.970631 | − | 0.240572i | \(-0.922665\pi\) | ||
0.970631 | − | 0.240572i | \(-0.0773351\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −264.000 | + | 264.000i | −0.341969 | + | 0.341969i | ||||
\(773\) | 132.000 | + | 132.000i | 0.170763 | + | 0.170763i | 0.787315 | − | 0.616551i | \(-0.211471\pi\) |
−0.616551 | + | 0.787315i | \(0.711471\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −48.0000 | −0.0618557 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 960.000i | − | 1.23235i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −576.000 | −0.737516 | ||||||||
\(782\) | 72.0000 | − | 72.0000i | 0.0920716 | − | 0.0920716i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 124.000i | − | 0.158163i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −93.0000 | + | 93.0000i | −0.118170 | + | 0.118170i | −0.763719 | − | 0.645549i | \(-0.776629\pi\) |
0.645549 | + | 0.763719i | \(0.276629\pi\) | |||||||
\(788\) | 264.000 | + | 264.000i | 0.335025 |