Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1575,2,Mod(1,1575)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1575, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1575.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1575.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(12.5764383184\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 35) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1575.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.56155 | 1.10418 | 0.552092 | − | 0.833783i | \(-0.313830\pi\) | ||||
0.552092 | + | 0.833783i | \(0.313830\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.438447 | 0.219224 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −2.43845 | −0.862121 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.56155 | −0.772337 | −0.386169 | − | 0.922428i | \(-0.626202\pi\) | ||||
−0.386169 | + | 0.922428i | \(0.626202\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.56155 | −1.26515 | −0.632574 | − | 0.774500i | \(-0.718001\pi\) | ||||
−0.632574 | + | 0.774500i | \(0.718001\pi\) | |||||||
\(14\) | 1.56155 | 0.417343 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.68466 | −1.17116 | ||||||||
\(17\) | −4.56155 | −1.10634 | −0.553170 | − | 0.833069i | \(-0.686582\pi\) | ||||
−0.553170 | + | 0.833069i | \(0.686582\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.12311 | 0.257658 | 0.128829 | − | 0.991667i | \(-0.458878\pi\) | ||||
0.128829 | + | 0.991667i | \(0.458878\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.00000 | −0.852803 | ||||||||
\(23\) | −5.12311 | −1.06824 | −0.534121 | − | 0.845408i | \(-0.679357\pi\) | ||||
−0.534121 | + | 0.845408i | \(0.679357\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −7.12311 | −1.39696 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.438447 | 0.0828587 | ||||||||
\(29\) | 5.68466 | 1.05561 | 0.527807 | − | 0.849364i | \(-0.323014\pi\) | ||||
0.527807 | + | 0.849364i | \(0.323014\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | −2.43845 | −0.431061 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −7.12311 | −1.22160 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.00000 | −0.986394 | −0.493197 | − | 0.869918i | \(-0.664172\pi\) | ||||
−0.493197 | + | 0.869918i | \(0.664172\pi\) | |||||||
\(38\) | 1.75379 | 0.284502 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.12311 | 0.487747 | 0.243874 | − | 0.969807i | \(-0.421582\pi\) | ||||
0.243874 | + | 0.969807i | \(0.421582\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.12311 | −1.39126 | −0.695630 | − | 0.718400i | \(-0.744875\pi\) | ||||
−0.695630 | + | 0.718400i | \(0.744875\pi\) | |||||||
\(44\) | −1.12311 | −0.169315 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8.00000 | −1.17954 | ||||||||
\(47\) | 3.68466 | 0.537463 | 0.268731 | − | 0.963215i | \(-0.413396\pi\) | ||||
0.268731 | + | 0.963215i | \(0.413396\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.00000 | −0.277350 | ||||||||
\(53\) | 3.12311 | 0.428992 | 0.214496 | − | 0.976725i | \(-0.431189\pi\) | ||||
0.214496 | + | 0.976725i | \(0.431189\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.43845 | −0.325851 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 8.87689 | 1.16559 | ||||||||
\(59\) | 4.00000 | 0.520756 | 0.260378 | − | 0.965507i | \(-0.416153\pi\) | ||||
0.260378 | + | 0.965507i | \(0.416153\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.36932 | −1.19962 | −0.599809 | − | 0.800143i | \(-0.704757\pi\) | ||||
−0.599809 | + | 0.800143i | \(0.704757\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5.56155 | 0.695194 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.24621 | 0.763096 | 0.381548 | − | 0.924349i | \(-0.375391\pi\) | ||||
0.381548 | + | 0.924349i | \(0.375391\pi\) | |||||||
\(68\) | −2.00000 | −0.242536 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.00000 | −0.949425 | −0.474713 | − | 0.880141i | \(-0.657448\pi\) | ||||
−0.474713 | + | 0.880141i | \(0.657448\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.24621 | −0.496981 | −0.248491 | − | 0.968634i | \(-0.579935\pi\) | ||||
−0.248491 | + | 0.968634i | \(0.579935\pi\) | |||||||
\(74\) | −9.36932 | −1.08916 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.492423 | 0.0564847 | ||||||||
\(77\) | −2.56155 | −0.291916 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.56155 | −0.738232 | −0.369116 | − | 0.929383i | \(-0.620340\pi\) | ||||
−0.369116 | + | 0.929383i | \(0.620340\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.87689 | 0.538563 | ||||||||
\(83\) | 4.00000 | 0.439057 | 0.219529 | − | 0.975606i | \(-0.429548\pi\) | ||||
0.219529 | + | 0.975606i | \(0.429548\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −14.2462 | −1.53621 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 6.24621 | 0.665848 | ||||||||
\(89\) | −7.12311 | −0.755048 | −0.377524 | − | 0.926000i | \(-0.623224\pi\) | ||||
−0.377524 | + | 0.926000i | \(0.623224\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.56155 | −0.478181 | ||||||||
\(92\) | −2.24621 | −0.234184 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5.75379 | 0.593458 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.8078 | 1.50350 | 0.751750 | − | 0.659448i | \(-0.229210\pi\) | ||||
0.751750 | + | 0.659448i | \(0.229210\pi\) | |||||||
\(98\) | 1.56155 | 0.157741 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.246211 | −0.0244989 | −0.0122495 | − | 0.999925i | \(-0.503899\pi\) | ||||
−0.0122495 | + | 0.999925i | \(0.503899\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.43845 | −0.141734 | −0.0708672 | − | 0.997486i | \(-0.522577\pi\) | ||||
−0.0708672 | + | 0.997486i | \(0.522577\pi\) | |||||||
\(104\) | 11.1231 | 1.09071 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.87689 | 0.473686 | ||||||||
\(107\) | −11.3693 | −1.09911 | −0.549557 | − | 0.835456i | \(-0.685203\pi\) | ||||
−0.549557 | + | 0.835456i | \(0.685203\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.6847 | 1.69388 | 0.846942 | − | 0.531686i | \(-0.178441\pi\) | ||||
0.846942 | + | 0.531686i | \(0.178441\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.68466 | −0.442659 | ||||||||
\(113\) | −14.0000 | −1.31701 | −0.658505 | − | 0.752577i | \(-0.728811\pi\) | ||||
−0.658505 | + | 0.752577i | \(0.728811\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.49242 | 0.231416 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.24621 | 0.575010 | ||||||||
\(119\) | −4.56155 | −0.418157 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.43845 | −0.403495 | ||||||||
\(122\) | −14.6307 | −1.32460 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.2462 | −0.909204 | −0.454602 | − | 0.890695i | \(-0.650219\pi\) | ||||
−0.454602 | + | 0.890695i | \(0.650219\pi\) | |||||||
\(128\) | 13.5616 | 1.19868 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.12311 | 0.797089 | 0.398545 | − | 0.917149i | \(-0.369515\pi\) | ||||
0.398545 | + | 0.917149i | \(0.369515\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.12311 | 0.0973856 | ||||||||
\(134\) | 9.75379 | 0.842599 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 11.1231 | 0.953798 | ||||||||
\(137\) | −8.87689 | −0.758404 | −0.379202 | − | 0.925314i | \(-0.623801\pi\) | ||||
−0.379202 | + | 0.925314i | \(0.623801\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.87689 | −0.583291 | −0.291645 | − | 0.956527i | \(-0.594203\pi\) | ||||
−0.291645 | + | 0.956527i | \(0.594203\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −12.4924 | −1.04834 | ||||||||
\(143\) | 11.6847 | 0.977120 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −6.63068 | −0.548759 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.63068 | −0.216241 | ||||||||
\(149\) | 4.24621 | 0.347863 | 0.173932 | − | 0.984758i | \(-0.444353\pi\) | ||||
0.173932 | + | 0.984758i | \(0.444353\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 21.9309 | 1.78471 | 0.892354 | − | 0.451335i | \(-0.149052\pi\) | ||||
0.892354 | + | 0.451335i | \(0.149052\pi\) | |||||||
\(152\) | −2.73863 | −0.222133 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.00000 | −0.322329 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.75379 | −0.299585 | −0.149792 | − | 0.988717i | \(-0.547861\pi\) | ||||
−0.149792 | + | 0.988717i | \(0.547861\pi\) | |||||||
\(158\) | −10.2462 | −0.815145 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.12311 | −0.403757 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.12311 | −0.0879684 | −0.0439842 | − | 0.999032i | \(-0.514005\pi\) | ||||
−0.0439842 | + | 0.999032i | \(0.514005\pi\) | |||||||
\(164\) | 1.36932 | 0.106926 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.24621 | 0.484800 | ||||||||
\(167\) | 21.9309 | 1.69706 | 0.848531 | − | 0.529146i | \(-0.177488\pi\) | ||||
0.848531 | + | 0.529146i | \(0.177488\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.80776 | 0.600597 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.00000 | −0.304997 | ||||||||
\(173\) | −8.56155 | −0.650923 | −0.325461 | − | 0.945555i | \(-0.605520\pi\) | ||||
−0.325461 | + | 0.945555i | \(0.605520\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 12.0000 | 0.904534 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −11.1231 | −0.833712 | ||||||||
\(179\) | −20.0000 | −1.49487 | −0.747435 | − | 0.664335i | \(-0.768715\pi\) | ||||
−0.747435 | + | 0.664335i | \(0.768715\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 23.6155 | 1.75533 | 0.877664 | − | 0.479276i | \(-0.159101\pi\) | ||||
0.877664 | + | 0.479276i | \(0.159101\pi\) | |||||||
\(182\) | −7.12311 | −0.528000 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 12.4924 | 0.920954 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.6847 | 0.854467 | ||||||||
\(188\) | 1.61553 | 0.117824 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.43845 | 0.682942 | 0.341471 | − | 0.939892i | \(-0.389075\pi\) | ||||
0.341471 | + | 0.939892i | \(0.389075\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.36932 | 0.386492 | 0.193246 | − | 0.981150i | \(-0.438098\pi\) | ||||
0.193246 | + | 0.981150i | \(0.438098\pi\) | |||||||
\(194\) | 23.1231 | 1.66014 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.438447 | 0.0313177 | ||||||||
\(197\) | −7.12311 | −0.507500 | −0.253750 | − | 0.967270i | \(-0.581664\pi\) | ||||
−0.253750 | + | 0.967270i | \(0.581664\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.2462 | −1.29344 | −0.646720 | − | 0.762728i | \(-0.723860\pi\) | ||||
−0.646720 | + | 0.762728i | \(0.723860\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.384472 | −0.0270513 | ||||||||
\(203\) | 5.68466 | 0.398985 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.24621 | −0.156501 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 21.3693 | 1.48170 | ||||||||
\(209\) | −2.87689 | −0.198999 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.0540 | −1.58710 | −0.793551 | − | 0.608504i | \(-0.791770\pi\) | ||||
−0.793551 | + | 0.608504i | \(0.791770\pi\) | |||||||
\(212\) | 1.36932 | 0.0940451 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −17.7538 | −1.21362 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 27.6155 | 1.87036 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 20.8078 | 1.39968 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.56155 | 0.439394 | 0.219697 | − | 0.975568i | \(-0.429493\pi\) | ||||
0.219697 | + | 0.975568i | \(0.429493\pi\) | |||||||
\(224\) | −2.43845 | −0.162926 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −21.8617 | −1.45422 | ||||||||
\(227\) | 23.6847 | 1.57201 | 0.786003 | − | 0.618223i | \(-0.212147\pi\) | ||||
0.786003 | + | 0.618223i | \(0.212147\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.1231 | 1.26369 | 0.631845 | − | 0.775095i | \(-0.282298\pi\) | ||||
0.631845 | + | 0.775095i | \(0.282298\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −13.8617 | −0.910068 | ||||||||
\(233\) | −3.12311 | −0.204601 | −0.102301 | − | 0.994754i | \(-0.532620\pi\) | ||||
−0.102301 | + | 0.994754i | \(0.532620\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.75379 | 0.114162 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −7.12311 | −0.461722 | ||||||||
\(239\) | 0.807764 | 0.0522499 | 0.0261250 | − | 0.999659i | \(-0.491683\pi\) | ||||
0.0261250 | + | 0.999659i | \(0.491683\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.2462 | 0.788848 | 0.394424 | − | 0.918929i | \(-0.370944\pi\) | ||||
0.394424 | + | 0.918929i | \(0.370944\pi\) | |||||||
\(242\) | −6.93087 | −0.445533 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −4.10795 | −0.262985 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.12311 | −0.325975 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.1231 | 1.08080 | 0.540400 | − | 0.841408i | \(-0.318273\pi\) | ||||
0.540400 | + | 0.841408i | \(0.318273\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 13.1231 | 0.825043 | ||||||||
\(254\) | −16.0000 | −1.00393 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 10.0540 | 0.628373 | ||||||||
\(257\) | 22.4924 | 1.40304 | 0.701519 | − | 0.712650i | \(-0.252505\pi\) | ||||
0.701519 | + | 0.712650i | \(0.252505\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.00000 | −0.372822 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 14.2462 | 0.880134 | ||||||||
\(263\) | −21.1231 | −1.30251 | −0.651253 | − | 0.758860i | \(-0.725756\pi\) | ||||
−0.651253 | + | 0.758860i | \(0.725756\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.75379 | 0.107532 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.73863 | 0.167289 | ||||||||
\(269\) | −28.7386 | −1.75223 | −0.876113 | − | 0.482106i | \(-0.839872\pi\) | ||||
−0.876113 | + | 0.482106i | \(0.839872\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.0000 | −0.971931 | −0.485965 | − | 0.873978i | \(-0.661532\pi\) | ||||
−0.485965 | + | 0.873978i | \(0.661532\pi\) | |||||||
\(272\) | 21.3693 | 1.29571 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −13.8617 | −0.837418 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.2462 | −0.976140 | −0.488070 | − | 0.872804i | \(-0.662299\pi\) | ||||
−0.488070 | + | 0.872804i | \(0.662299\pi\) | |||||||
\(278\) | −10.7386 | −0.644060 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.5616 | −0.987979 | −0.493990 | − | 0.869468i | \(-0.664462\pi\) | ||||
−0.493990 | + | 0.869468i | \(0.664462\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 23.6847 | 1.40791 | 0.703953 | − | 0.710246i | \(-0.251416\pi\) | ||||
0.703953 | + | 0.710246i | \(0.251416\pi\) | |||||||
\(284\) | −3.50758 | −0.208136 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 18.2462 | 1.07892 | ||||||||
\(287\) | 3.12311 | 0.184351 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.80776 | 0.223986 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.86174 | −0.108950 | ||||||||
\(293\) | 9.68466 | 0.565784 | 0.282892 | − | 0.959152i | \(-0.408706\pi\) | ||||
0.282892 | + | 0.959152i | \(0.408706\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 14.6307 | 0.850391 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6.63068 | 0.384105 | ||||||||
\(299\) | 23.3693 | 1.35148 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.12311 | −0.525847 | ||||||||
\(302\) | 34.2462 | 1.97065 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −5.26137 | −0.301760 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 31.6847 | 1.80834 | 0.904169 | − | 0.427174i | \(-0.140491\pi\) | ||||
0.904169 | + | 0.427174i | \(0.140491\pi\) | |||||||
\(308\) | −1.12311 | −0.0639949 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.61553 | 0.545247 | 0.272623 | − | 0.962121i | \(-0.412109\pi\) | ||||
0.272623 | + | 0.962121i | \(0.412109\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −31.3002 | −1.76919 | −0.884596 | − | 0.466359i | \(-0.845566\pi\) | ||||
−0.884596 | + | 0.466359i | \(0.845566\pi\) | |||||||
\(314\) | −5.86174 | −0.330797 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.87689 | −0.161838 | ||||||||
\(317\) | −22.4924 | −1.26330 | −0.631650 | − | 0.775254i | \(-0.717622\pi\) | ||||
−0.631650 | + | 0.775254i | \(0.717622\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −14.5616 | −0.815290 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −8.00000 | −0.445823 | ||||||||
\(323\) | −5.12311 | −0.285057 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.75379 | −0.0971334 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −7.61553 | −0.420497 | ||||||||
\(329\) | 3.68466 | 0.203142 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.0000 | 0.659580 | 0.329790 | − | 0.944054i | \(-0.393022\pi\) | ||||
0.329790 | + | 0.944054i | \(0.393022\pi\) | |||||||
\(332\) | 1.75379 | 0.0962517 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 34.2462 | 1.87387 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 34.4924 | 1.87892 | 0.939461 | − | 0.342656i | \(-0.111326\pi\) | ||||
0.939461 | + | 0.342656i | \(0.111326\pi\) | |||||||
\(338\) | 12.1922 | 0.663170 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 22.2462 | 1.19944 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −13.3693 | −0.718739 | ||||||||
\(347\) | −1.12311 | −0.0602915 | −0.0301457 | − | 0.999546i | \(-0.509597\pi\) | ||||
−0.0301457 | + | 0.999546i | \(0.509597\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.4924 | −1.20399 | −0.601996 | − | 0.798499i | \(-0.705628\pi\) | ||||
−0.601996 | + | 0.798499i | \(0.705628\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6.24621 | 0.332924 | ||||||||
\(353\) | −14.8078 | −0.788138 | −0.394069 | − | 0.919081i | \(-0.628933\pi\) | ||||
−0.394069 | + | 0.919081i | \(0.628933\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −3.12311 | −0.165524 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −31.2311 | −1.65061 | ||||||||
\(359\) | −8.00000 | −0.422224 | −0.211112 | − | 0.977462i | \(-0.567708\pi\) | ||||
−0.211112 | + | 0.977462i | \(0.567708\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.7386 | −0.933612 | ||||||||
\(362\) | 36.8769 | 1.93821 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.00000 | −0.104828 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.68466 | −0.192338 | −0.0961688 | − | 0.995365i | \(-0.530659\pi\) | ||||
−0.0961688 | + | 0.995365i | \(0.530659\pi\) | |||||||
\(368\) | 24.0000 | 1.25109 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.12311 | 0.162144 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −29.3693 | −1.52069 | −0.760343 | − | 0.649522i | \(-0.774969\pi\) | ||||
−0.760343 | + | 0.649522i | \(0.774969\pi\) | |||||||
\(374\) | 18.2462 | 0.943489 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −8.98485 | −0.463358 | ||||||||
\(377\) | −25.9309 | −1.33551 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.4924 | 0.847159 | 0.423579 | − | 0.905859i | \(-0.360773\pi\) | ||||
0.423579 | + | 0.905859i | \(0.360773\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 14.7386 | 0.754094 | ||||||||
\(383\) | −10.2462 | −0.523557 | −0.261778 | − | 0.965128i | \(-0.584309\pi\) | ||||
−0.261778 | + | 0.965128i | \(0.584309\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.38447 | 0.426758 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 6.49242 | 0.329603 | ||||||||
\(389\) | −3.93087 | −0.199303 | −0.0996515 | − | 0.995022i | \(-0.531773\pi\) | ||||
−0.0996515 | + | 0.995022i | \(0.531773\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 23.3693 | 1.18184 | ||||||||
\(392\) | −2.43845 | −0.123160 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −11.1231 | −0.560374 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −23.4384 | −1.17634 | −0.588171 | − | 0.808737i | \(-0.700152\pi\) | ||||
−0.588171 | + | 0.808737i | \(0.700152\pi\) | |||||||
\(398\) | −28.4924 | −1.42820 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −27.4384 | −1.37021 | −0.685105 | − | 0.728444i | \(-0.740244\pi\) | ||||
−0.685105 | + | 0.728444i | \(0.740244\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −0.107951 | −0.00537074 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.87689 | 0.440553 | ||||||||
\(407\) | 15.3693 | 0.761829 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −26.4924 | −1.30997 | −0.654983 | − | 0.755644i | \(-0.727324\pi\) | ||||
−0.654983 | + | 0.755644i | \(0.727324\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −0.630683 | −0.0310715 | ||||||||
\(413\) | 4.00000 | 0.196827 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 11.1231 | 0.545355 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −4.49242 | −0.219732 | ||||||||
\(419\) | −9.75379 | −0.476504 | −0.238252 | − | 0.971203i | \(-0.576574\pi\) | ||||
−0.238252 | + | 0.971203i | \(0.576574\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.68466 | 0.472001 | 0.236001 | − | 0.971753i | \(-0.424163\pi\) | ||||
0.236001 | + | 0.971753i | \(0.424163\pi\) | |||||||
\(422\) | −36.0000 | −1.75245 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −7.61553 | −0.369843 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.36932 | −0.453413 | ||||||||
\(428\) | −4.98485 | −0.240952 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.807764 | −0.0389086 | −0.0194543 | − | 0.999811i | \(-0.506193\pi\) | ||||
−0.0194543 | + | 0.999811i | \(0.506193\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.24621 | 0.396288 | 0.198144 | − | 0.980173i | \(-0.436509\pi\) | ||||
0.198144 | + | 0.980173i | \(0.436509\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7.75379 | 0.371339 | ||||||||
\(437\) | −5.75379 | −0.275241 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.3693 | −0.733537 | −0.366769 | − | 0.930312i | \(-0.619536\pi\) | ||||
−0.366769 | + | 0.930312i | \(0.619536\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 32.4924 | 1.54551 | ||||||||
\(443\) | −27.3693 | −1.30036 | −0.650178 | − | 0.759782i | \(-0.725306\pi\) | ||||
−0.650178 | + | 0.759782i | \(0.725306\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 10.2462 | 0.485172 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 5.56155 | 0.262759 | ||||||||
\(449\) | −18.8078 | −0.887593 | −0.443797 | − | 0.896128i | \(-0.646369\pi\) | ||||
−0.443797 | + | 0.896128i | \(0.646369\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.00000 | −0.376705 | ||||||||
\(452\) | −6.13826 | −0.288719 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 36.9848 | 1.73578 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.87689 | 0.415244 | 0.207622 | − | 0.978209i | \(-0.433428\pi\) | ||||
0.207622 | + | 0.978209i | \(0.433428\pi\) | |||||||
\(458\) | 29.8617 | 1.39535 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.87689 | 0.227140 | 0.113570 | − | 0.993530i | \(-0.463771\pi\) | ||||
0.113570 | + | 0.993530i | \(0.463771\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.4924 | 0.952364 | 0.476182 | − | 0.879347i | \(-0.342020\pi\) | ||||
0.476182 | + | 0.879347i | \(0.342020\pi\) | |||||||
\(464\) | −26.6307 | −1.23630 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.87689 | −0.225918 | ||||||||
\(467\) | 26.5616 | 1.22912 | 0.614561 | − | 0.788869i | \(-0.289333\pi\) | ||||
0.614561 | + | 0.788869i | \(0.289333\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.24621 | 0.288423 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −9.75379 | −0.448955 | ||||||||
\(473\) | 23.3693 | 1.07452 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2.00000 | −0.0916698 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.26137 | 0.0576935 | ||||||||
\(479\) | −13.1231 | −0.599610 | −0.299805 | − | 0.954001i | \(-0.596922\pi\) | ||||
−0.299805 | + | 0.954001i | \(0.596922\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 27.3693 | 1.24793 | ||||||||
\(482\) | 19.1231 | 0.871034 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.94602 | −0.0884557 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.12311 | −0.232150 | −0.116075 | − | 0.993240i | \(-0.537031\pi\) | ||||
−0.116075 | + | 0.993240i | \(0.537031\pi\) | |||||||
\(488\) | 22.8466 | 1.03422 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.17708 | −0.188509 | −0.0942545 | − | 0.995548i | \(-0.530047\pi\) | ||||
−0.0942545 | + | 0.995548i | \(0.530047\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −25.9309 | −1.16787 | ||||||||
\(494\) | −8.00000 | −0.359937 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8.00000 | −0.358849 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.17708 | −0.186992 | −0.0934959 | − | 0.995620i | \(-0.529804\pi\) | ||||
−0.0934959 | + | 0.995620i | \(0.529804\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 26.7386 | 1.19340 | ||||||||
\(503\) | 10.0691 | 0.448960 | 0.224480 | − | 0.974479i | \(-0.427932\pi\) | ||||
0.224480 | + | 0.974479i | \(0.427932\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 20.4924 | 0.910999 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.49242 | −0.199319 | ||||||||
\(509\) | 28.2462 | 1.25199 | 0.625996 | − | 0.779827i | \(-0.284693\pi\) | ||||
0.625996 | + | 0.779827i | \(0.284693\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.24621 | −0.187841 | ||||||||
\(512\) | −11.4233 | −0.504843 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 35.1231 | 1.54921 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.43845 | −0.415102 | ||||||||
\(518\) | −9.36932 | −0.411664 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.0000 | −0.438108 | −0.219054 | − | 0.975713i | \(-0.570297\pi\) | ||||
−0.219054 | + | 0.975713i | \(0.570297\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.50758 | −0.328283 | −0.164142 | − | 0.986437i | \(-0.552485\pi\) | ||||
−0.164142 | + | 0.986437i | \(0.552485\pi\) | |||||||
\(524\) | 4.00000 | 0.174741 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −32.9848 | −1.43821 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.24621 | 0.141140 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.492423 | 0.0213492 | ||||||||
\(533\) | −14.2462 | −0.617072 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −15.2311 | −0.657881 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −44.8769 | −1.93478 | ||||||||
\(539\) | −2.56155 | −0.110334 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.1922 | −0.739152 | −0.369576 | − | 0.929201i | \(-0.620497\pi\) | ||||
−0.369576 | + | 0.929201i | \(0.620497\pi\) | |||||||
\(542\) | −24.9848 | −1.07319 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 11.1231 | 0.476899 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.2462 | −0.609124 | −0.304562 | − | 0.952493i | \(-0.598510\pi\) | ||||
−0.304562 | + | 0.952493i | \(0.598510\pi\) | |||||||
\(548\) | −3.89205 | −0.166260 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.38447 | 0.271988 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.56155 | −0.279026 | ||||||||
\(554\) | −25.3693 | −1.07784 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.01515 | −0.127871 | ||||||||
\(557\) | −4.87689 | −0.206641 | −0.103320 | − | 0.994648i | \(-0.532947\pi\) | ||||
−0.103320 | + | 0.994648i | \(0.532947\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 41.6155 | 1.76015 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −25.8617 | −1.09091 | ||||||||
\(563\) | −28.0000 | −1.18006 | −0.590030 | − | 0.807382i | \(-0.700884\pi\) | ||||
−0.590030 | + | 0.807382i | \(0.700884\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 36.9848 | 1.55459 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 19.5076 | 0.818520 | ||||||||
\(569\) | −34.9848 | −1.46664 | −0.733320 | − | 0.679883i | \(-0.762031\pi\) | ||||
−0.733320 | + | 0.679883i | \(0.762031\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.50758 | 0.314182 | 0.157091 | − | 0.987584i | \(-0.449788\pi\) | ||||
0.157091 | + | 0.987584i | \(0.449788\pi\) | |||||||
\(572\) | 5.12311 | 0.214208 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 4.87689 | 0.203558 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13.0540 | −0.543444 | −0.271722 | − | 0.962376i | \(-0.587593\pi\) | ||||
−0.271722 | + | 0.962376i | \(0.587593\pi\) | |||||||
\(578\) | 5.94602 | 0.247322 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.00000 | 0.165948 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.00000 | −0.331326 | ||||||||
\(584\) | 10.3542 | 0.428458 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 15.1231 | 0.624730 | ||||||||
\(587\) | −9.75379 | −0.402582 | −0.201291 | − | 0.979531i | \(-0.564514\pi\) | ||||
−0.201291 | + | 0.979531i | \(0.564514\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 28.1080 | 1.15523 | ||||||||
\(593\) | −23.4384 | −0.962502 | −0.481251 | − | 0.876583i | \(-0.659817\pi\) | ||||
−0.481251 | + | 0.876583i | \(0.659817\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.86174 | 0.0762598 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 36.4924 | 1.49229 | ||||||||
\(599\) | −8.80776 | −0.359875 | −0.179938 | − | 0.983678i | \(-0.557590\pi\) | ||||
−0.179938 | + | 0.983678i | \(0.557590\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −26.4924 | −1.08065 | −0.540324 | − | 0.841457i | \(-0.681698\pi\) | ||||
−0.540324 | + | 0.841457i | \(0.681698\pi\) | |||||||
\(602\) | −14.2462 | −0.580632 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 9.61553 | 0.391250 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.94602 | 0.200753 | 0.100376 | − | 0.994950i | \(-0.467995\pi\) | ||||
0.100376 | + | 0.994950i | \(0.467995\pi\) | |||||||
\(608\) | −2.73863 | −0.111066 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −16.8078 | −0.679969 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.73863 | 0.352950 | 0.176475 | − | 0.984305i | \(-0.443531\pi\) | ||||
0.176475 | + | 0.984305i | \(0.443531\pi\) | |||||||
\(614\) | 49.4773 | 1.99674 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.24621 | 0.251667 | ||||||||
\(617\) | 15.7538 | 0.634224 | 0.317112 | − | 0.948388i | \(-0.397287\pi\) | ||||
0.317112 | + | 0.948388i | \(0.397287\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −42.1080 | −1.69246 | −0.846231 | − | 0.532817i | \(-0.821134\pi\) | ||||
−0.846231 | + | 0.532817i | \(0.821134\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 15.0152 | 0.602053 | ||||||||
\(623\) | −7.12311 | −0.285381 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −48.8769 | −1.95351 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.64584 | −0.0656761 | ||||||||
\(629\) | 27.3693 | 1.09129 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.80776 | 0.350632 | 0.175316 | − | 0.984512i | \(-0.443905\pi\) | ||||
0.175316 | + | 0.984512i | \(0.443905\pi\) | |||||||
\(632\) | 16.0000 | 0.636446 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −35.1231 | −1.39492 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.56155 | −0.180735 | ||||||||
\(638\) | −22.7386 | −0.900231 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.00000 | −0.0789953 | −0.0394976 | − | 0.999220i | \(-0.512576\pi\) | ||||
−0.0394976 | + | 0.999220i | \(0.512576\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.56155 | 0.101018 | 0.0505089 | − | 0.998724i | \(-0.483916\pi\) | ||||
0.0505089 | + | 0.998724i | \(0.483916\pi\) | |||||||
\(644\) | −2.24621 | −0.0885131 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.00000 | −0.314756 | ||||||||
\(647\) | 3.50758 | 0.137897 | 0.0689486 | − | 0.997620i | \(-0.478036\pi\) | ||||
0.0689486 | + | 0.997620i | \(0.478036\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.2462 | −0.402199 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.492423 | −0.0192848 | ||||||||
\(653\) | 49.2311 | 1.92656 | 0.963280 | − | 0.268499i | \(-0.0865275\pi\) | ||||
0.963280 | + | 0.268499i | \(0.0865275\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −14.6307 | −0.571232 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 5.75379 | 0.224306 | ||||||||
\(659\) | 36.1771 | 1.40926 | 0.704629 | − | 0.709575i | \(-0.251113\pi\) | ||||
0.704629 | + | 0.709575i | \(0.251113\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.12311 | 0.121475 | 0.0607374 | − | 0.998154i | \(-0.480655\pi\) | ||||
0.0607374 | + | 0.998154i | \(0.480655\pi\) | |||||||
\(662\) | 18.7386 | 0.728298 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −9.75379 | −0.378520 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −29.1231 | −1.12765 | ||||||||
\(668\) | 9.61553 | 0.372036 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 24.0000 | 0.926510 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 25.8617 | 0.996897 | 0.498448 | − | 0.866919i | \(-0.333903\pi\) | ||||
0.498448 | + | 0.866919i | \(0.333903\pi\) | |||||||
\(674\) | 53.8617 | 2.07468 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.42329 | 0.131665 | ||||||||
\(677\) | −23.9309 | −0.919738 | −0.459869 | − | 0.887987i | \(-0.652104\pi\) | ||||
−0.459869 | + | 0.887987i | \(0.652104\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14.8078 | 0.568270 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 42.7386 | 1.63535 | 0.817674 | − | 0.575681i | \(-0.195263\pi\) | ||||
0.817674 | + | 0.575681i | \(0.195263\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.56155 | 0.0596204 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 42.7386 | 1.62940 | ||||||||
\(689\) | −14.2462 | −0.542737 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.49242 | 0.323067 | 0.161533 | − | 0.986867i | \(-0.448356\pi\) | ||||
0.161533 | + | 0.986867i | \(0.448356\pi\) | |||||||
\(692\) | −3.75379 | −0.142698 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.75379 | −0.0665729 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −14.2462 | −0.539614 | ||||||||
\(698\) | −35.1231 | −1.32943 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −0.0691303 | −0.00261102 | −0.00130551 | − | 0.999999i | \(-0.500416\pi\) | ||||
−0.00130551 | + | 0.999999i | \(0.500416\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.73863 | −0.254152 | ||||||||
\(704\) | −14.2462 | −0.536924 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −23.1231 | −0.870250 | ||||||||
\(707\) | −0.246211 | −0.00925973 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18.1771 | −0.682655 | −0.341327 | − | 0.939945i | \(-0.610876\pi\) | ||||
−0.341327 | + | 0.939945i | \(0.610876\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 17.3693 | 0.650943 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −8.76894 | −0.327711 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −12.4924 | −0.466213 | ||||||||
\(719\) | −49.6155 | −1.85035 | −0.925173 | − | 0.379544i | \(-0.876081\pi\) | ||||
−0.925173 | + | 0.379544i | \(0.876081\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.43845 | −0.0535706 | ||||||||
\(722\) | −27.6998 | −1.03088 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 10.3542 | 0.384809 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19.5076 | −0.723496 | −0.361748 | − | 0.932276i | \(-0.617820\pi\) | ||||
−0.361748 | + | 0.932276i | \(0.617820\pi\) | |||||||
\(728\) | 11.1231 | 0.412250 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 41.6155 | 1.53921 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.68466 | 0.209968 | 0.104984 | − | 0.994474i | \(-0.466521\pi\) | ||||
0.104984 | + | 0.994474i | \(0.466521\pi\) | |||||||
\(734\) | −5.75379 | −0.212376 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 12.4924 | 0.460477 | ||||||||
\(737\) | −16.0000 | −0.589368 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.06913 | 0.223257 | 0.111628 | − | 0.993750i | \(-0.464393\pi\) | ||||
0.111628 | + | 0.993750i | \(0.464393\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4.87689 | 0.179036 | ||||||||
\(743\) | 32.9848 | 1.21010 | 0.605048 | − | 0.796189i | \(-0.293154\pi\) | ||||
0.605048 | + | 0.796189i | \(0.293154\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −45.8617 | −1.67912 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 5.12311 | 0.187319 | ||||||||
\(749\) | −11.3693 | −0.415426 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 45.9309 | 1.67604 | 0.838021 | − | 0.545639i | \(-0.183713\pi\) | ||||
0.838021 | + | 0.545639i | \(0.183713\pi\) | |||||||
\(752\) | −17.2614 | −0.629457 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −40.4924 | −1.47465 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.6307 | −0.531761 | −0.265881 | − | 0.964006i | \(-0.585663\pi\) | ||||
−0.265881 | + | 0.964006i | \(0.585663\pi\) | |||||||
\(758\) | 25.7538 | 0.935420 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −31.7538 | −1.15107 | −0.575537 | − | 0.817776i | \(-0.695207\pi\) | ||||
−0.575537 | + | 0.817776i | \(0.695207\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 17.6847 | 0.640228 | ||||||||
\(764\) | 4.13826 | 0.149717 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −16.0000 | −0.578103 | ||||||||
\(767\) | −18.2462 | −0.658833 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.50758 | −0.342852 | −0.171426 | − | 0.985197i | \(-0.554837\pi\) | ||||
−0.171426 | + | 0.985197i | \(0.554837\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.35416 | 0.0847281 | ||||||||
\(773\) | 8.06913 | 0.290226 | 0.145113 | − | 0.989415i | \(-0.453645\pi\) | ||||
0.145113 | + | 0.989415i | \(0.453645\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −36.1080 | −1.29620 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −6.13826 | −0.220067 | ||||||||
\(779\) | 3.50758 | 0.125672 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20.4924 | 0.733277 | ||||||||
\(782\) | 36.4924 | 1.30497 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.68466 | −0.167309 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.82292 | 0.136272 | 0.0681362 | − | 0.997676i | \(-0.478295\pi\) | ||||
0.0681362 | + | 0.997676i | \(0.478295\pi\) | |||||||
\(788\) | −3.12311 | −0.111256 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −14.0000 | −0.497783 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 42.7386 | 1.51769 | ||||||||
\(794\) | −36.6004 | −1.29890 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8.00000 | −0.283552 | ||||||||
\(797\) | −13.0540 | −0.462396 | −0.231198 | − | 0.972907i | \(-0.574264\pi\) | ||||
−0.231198 | + | 0.972907i | \(0.574264\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −16.8078 | −0.594616 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −42.8466 | −1.51297 | ||||||||
\(803\) | 10.8769 | 0.383837 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0.600373 | 0.0211211 | ||||||||
\(809\) | 53.5464 | 1.88259 | 0.941296 | − | 0.337584i | \(-0.109610\pi\) | ||||
0.941296 | + | 0.337584i | \(0.109610\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.6155 | −0.759024 | −0.379512 | − | 0.925187i | \(-0.623908\pi\) | ||||
−0.379512 | + | 0.925187i | \(0.623908\pi\) | |||||||
\(812\) | 2.49242 | 0.0874669 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 24.0000 | 0.841200 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.2462 | −0.358470 | ||||||||
\(818\) | −41.3693 | −1.44644 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −40.4233 | −1.41078 | −0.705391 | − | 0.708818i | \(-0.749229\pi\) | ||||
−0.705391 | + | 0.708818i | \(0.749229\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.50758 | 0.122266 | 0.0611332 | − | 0.998130i | \(-0.480529\pi\) | ||||
0.0611332 | + | 0.998130i | \(0.480529\pi\) | |||||||
\(824\) | 3.50758 | 0.122192 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.24621 | 0.217333 | ||||||||
\(827\) | 19.3693 | 0.673537 | 0.336769 | − | 0.941587i | \(-0.390666\pi\) | ||||
0.336769 | + | 0.941587i | \(0.390666\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 43.1231 | 1.49773 | 0.748864 | − | 0.662724i | \(-0.230600\pi\) | ||||
0.748864 | + | 0.662724i | \(0.230600\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −25.3693 | −0.879523 | ||||||||
\(833\) | −4.56155 | −0.158048 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.26137 | −0.0436253 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −15.2311 | −0.526148 | ||||||||
\(839\) | 37.1231 | 1.28163 | 0.640816 | − | 0.767695i | \(-0.278596\pi\) | ||||
0.640816 | + | 0.767695i | \(0.278596\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.31534 | 0.114322 | ||||||||
\(842\) | 15.1231 | 0.521177 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −10.1080 | −0.347930 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.43845 | −0.152507 | ||||||||
\(848\) | −14.6307 | −0.502420 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 30.7386 | 1.05371 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 56.7386 | 1.94269 | 0.971347 | − | 0.237666i | \(-0.0763824\pi\) | ||||
0.971347 | + | 0.237666i | \(0.0763824\pi\) | |||||||
\(854\) | −14.6307 | −0.500652 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 27.7235 | 0.947569 | ||||||||
\(857\) | −32.2462 | −1.10151 | −0.550755 | − | 0.834667i | \(-0.685660\pi\) | ||||
−0.550755 | + | 0.834667i | \(0.685660\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.4924 | 0.562714 | 0.281357 | − | 0.959603i | \(-0.409215\pi\) | ||||
0.281357 | + | 0.959603i | \(0.409215\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.26137 | −0.0429623 | ||||||||
\(863\) | −42.2462 | −1.43808 | −0.719039 | − | 0.694970i | \(-0.755418\pi\) | ||||
−0.719039 | + | 0.694970i | \(0.755418\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 12.8769 | 0.437575 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 16.8078 | 0.570164 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −28.4924 | −0.965429 | ||||||||
\(872\) | −43.1231 | −1.46033 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −8.98485 | −0.303917 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.7538 | 0.802108 | 0.401054 | − | 0.916054i | \(-0.368644\pi\) | ||||
0.401054 | + | 0.916054i | \(0.368644\pi\) | |||||||
\(878\) | −24.0000 | −0.809961 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −45.8617 | −1.54512 | −0.772561 | − | 0.634941i | \(-0.781024\pi\) | ||||
−0.772561 | + | 0.634941i | \(0.781024\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24.4924 | −0.824236 | −0.412118 | − | 0.911131i | \(-0.635211\pi\) | ||||
−0.412118 | + | 0.911131i | \(0.635211\pi\) | |||||||
\(884\) | 9.12311 | 0.306843 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −42.7386 | −1.43583 | ||||||||
\(887\) | −12.4924 | −0.419454 | −0.209727 | − | 0.977760i | \(-0.567258\pi\) | ||||
−0.209727 | + | 0.977760i | \(0.567258\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.2462 | −0.343647 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2.87689 | 0.0963255 | ||||||||
\(893\) | 4.13826 | 0.138482 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 13.5616 | 0.453060 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −29.3693 | −0.980067 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.2462 | −0.474610 | ||||||||
\(902\) | −12.4924 | −0.415952 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 34.1383 | 1.13542 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −50.1080 | −1.66381 | −0.831904 | − | 0.554920i | \(-0.812749\pi\) | ||||
−0.831904 | + | 0.554920i | \(0.812749\pi\) | |||||||
\(908\) | 10.3845 | 0.344621 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.49242 | −0.148841 | −0.0744203 | − | 0.997227i | \(-0.523711\pi\) | ||||
−0.0744203 | + | 0.997227i | \(0.523711\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.2462 | −0.339100 | ||||||||
\(914\) | 13.8617 | 0.458506 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.38447 | 0.277031 | ||||||||
\(917\) | 9.12311 | 0.301271 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −13.3002 | −0.438733 | −0.219366 | − | 0.975643i | \(-0.570399\pi\) | ||||
−0.219366 | + | 0.975643i | \(0.570399\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 7.61553 | 0.250804 | ||||||||
\(923\) | 36.4924 | 1.20116 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 32.0000 | 1.05159 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −13.8617 | −0.455034 | ||||||||
\(929\) | 52.1080 | 1.70961 | 0.854803 | − | 0.518952i | \(-0.173678\pi\) | ||||
0.854803 | + | 0.518952i | \(0.173678\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.12311 | 0.0368083 | ||||||||
\(932\) | −1.36932 | −0.0448535 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 41.4773 | 1.35718 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −22.6695 | −0.740580 | −0.370290 | − | 0.928916i | \(-0.620742\pi\) | ||||
−0.370290 | + | 0.928916i | \(0.620742\pi\) | |||||||
\(938\) | 9.75379 | 0.318472 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 13.8617 | 0.451880 | 0.225940 | − | 0.974141i | \(-0.427455\pi\) | ||||
0.225940 | + | 0.974141i | \(0.427455\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −16.0000 | −0.521032 | ||||||||
\(944\) | −18.7386 | −0.609891 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 36.4924 | 1.18647 | ||||||||
\(947\) | 4.00000 | 0.129983 | 0.0649913 | − | 0.997886i | \(-0.479298\pi\) | ||||
0.0649913 | + | 0.997886i | \(0.479298\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 19.3693 | 0.628755 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 11.1231 | 0.360502 | ||||||||
\(953\) | −24.8769 | −0.805842 | −0.402921 | − | 0.915235i | \(-0.632005\pi\) | ||||
−0.402921 | + | 0.915235i | \(0.632005\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0.354162 | 0.0114544 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −20.4924 | −0.662080 | ||||||||
\(959\) | −8.87689 | −0.286650 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | 42.7386 | 1.37795 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 5.36932 | 0.172934 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 26.8769 | 0.864303 | 0.432151 | − | 0.901801i | \(-0.357755\pi\) | ||||
0.432151 | + | 0.901801i | \(0.357755\pi\) | |||||||
\(968\) | 10.8229 | 0.347862 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 49.4773 | 1.58780 | 0.793901 | − | 0.608048i | \(-0.208047\pi\) | ||||
0.793901 | + | 0.608048i | \(0.208047\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.87689 | −0.220463 | ||||||||
\(974\) | −8.00000 | −0.256337 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 43.8920 | 1.40495 | ||||||||
\(977\) | −49.2311 | −1.57504 | −0.787521 | − | 0.616288i | \(-0.788636\pi\) | ||||
−0.787521 | + | 0.616288i | \(0.788636\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18.2462 | 0.583151 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −6.52273 | −0.208149 | ||||||||
\(983\) | −10.4233 | −0.332451 | −0.166226 | − | 0.986088i | \(-0.553158\pi\) | ||||
−0.166226 | + | 0.986088i | \(0.553158\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −40.4924 | −1.28954 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.24621 | −0.0714615 | ||||||||
\(989\) | 46.7386 | 1.48620 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20.4924 | −0.650963 | −0.325482 | − | 0.945548i | \(-0.605526\pi\) | ||||
−0.325482 | + | 0.945548i | \(0.605526\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −12.4924 | −0.396236 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9.68466 | −0.306716 | −0.153358 | − | 0.988171i | \(-0.549009\pi\) | ||||
−0.153358 | + | 0.988171i | \(0.549009\pi\) | |||||||
\(998\) | −6.52273 | −0.206473 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1575.2.a.p.1.2 | 2 | ||
3.2 | odd | 2 | 175.2.a.f.1.1 | 2 | |||
5.2 | odd | 4 | 1575.2.d.e.1324.3 | 4 | |||
5.3 | odd | 4 | 1575.2.d.e.1324.2 | 4 | |||
5.4 | even | 2 | 315.2.a.e.1.1 | 2 | |||
12.11 | even | 2 | 2800.2.a.bi.1.1 | 2 | |||
15.2 | even | 4 | 175.2.b.b.99.2 | 4 | |||
15.8 | even | 4 | 175.2.b.b.99.3 | 4 | |||
15.14 | odd | 2 | 35.2.a.b.1.2 | ✓ | 2 | ||
20.19 | odd | 2 | 5040.2.a.bt.1.2 | 2 | |||
21.20 | even | 2 | 1225.2.a.s.1.1 | 2 | |||
35.34 | odd | 2 | 2205.2.a.x.1.1 | 2 | |||
60.23 | odd | 4 | 2800.2.g.t.449.1 | 4 | |||
60.47 | odd | 4 | 2800.2.g.t.449.4 | 4 | |||
60.59 | even | 2 | 560.2.a.i.1.2 | 2 | |||
105.44 | odd | 6 | 245.2.e.i.116.1 | 4 | |||
105.59 | even | 6 | 245.2.e.h.226.1 | 4 | |||
105.62 | odd | 4 | 1225.2.b.f.99.2 | 4 | |||
105.74 | odd | 6 | 245.2.e.i.226.1 | 4 | |||
105.83 | odd | 4 | 1225.2.b.f.99.3 | 4 | |||
105.89 | even | 6 | 245.2.e.h.116.1 | 4 | |||
105.104 | even | 2 | 245.2.a.d.1.2 | 2 | |||
120.29 | odd | 2 | 2240.2.a.bh.1.2 | 2 | |||
120.59 | even | 2 | 2240.2.a.bd.1.1 | 2 | |||
165.164 | even | 2 | 4235.2.a.m.1.1 | 2 | |||
195.194 | odd | 2 | 5915.2.a.l.1.1 | 2 | |||
420.419 | odd | 2 | 3920.2.a.bs.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.2.a.b.1.2 | ✓ | 2 | 15.14 | odd | 2 | ||
175.2.a.f.1.1 | 2 | 3.2 | odd | 2 | |||
175.2.b.b.99.2 | 4 | 15.2 | even | 4 | |||
175.2.b.b.99.3 | 4 | 15.8 | even | 4 | |||
245.2.a.d.1.2 | 2 | 105.104 | even | 2 | |||
245.2.e.h.116.1 | 4 | 105.89 | even | 6 | |||
245.2.e.h.226.1 | 4 | 105.59 | even | 6 | |||
245.2.e.i.116.1 | 4 | 105.44 | odd | 6 | |||
245.2.e.i.226.1 | 4 | 105.74 | odd | 6 | |||
315.2.a.e.1.1 | 2 | 5.4 | even | 2 | |||
560.2.a.i.1.2 | 2 | 60.59 | even | 2 | |||
1225.2.a.s.1.1 | 2 | 21.20 | even | 2 | |||
1225.2.b.f.99.2 | 4 | 105.62 | odd | 4 | |||
1225.2.b.f.99.3 | 4 | 105.83 | odd | 4 | |||
1575.2.a.p.1.2 | 2 | 1.1 | even | 1 | trivial | ||
1575.2.d.e.1324.2 | 4 | 5.3 | odd | 4 | |||
1575.2.d.e.1324.3 | 4 | 5.2 | odd | 4 | |||
2205.2.a.x.1.1 | 2 | 35.34 | odd | 2 | |||
2240.2.a.bd.1.1 | 2 | 120.59 | even | 2 | |||
2240.2.a.bh.1.2 | 2 | 120.29 | odd | 2 | |||
2800.2.a.bi.1.1 | 2 | 12.11 | even | 2 | |||
2800.2.g.t.449.1 | 4 | 60.23 | odd | 4 | |||
2800.2.g.t.449.4 | 4 | 60.47 | odd | 4 | |||
3920.2.a.bs.1.1 | 2 | 420.419 | odd | 2 | |||
4235.2.a.m.1.1 | 2 | 165.164 | even | 2 | |||
5040.2.a.bt.1.2 | 2 | 20.19 | odd | 2 | |||
5915.2.a.l.1.1 | 2 | 195.194 | odd | 2 |