Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3675,2,Mod(1,3675)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3675, 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("3675.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3675 = 3 \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3675.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: | \(29.3450227428\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 105) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.48119\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3675.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.193937 | 0.137134 | 0.0685669 | − | 0.997647i | \(-0.478157\pi\) | ||||
0.0685669 | + | 0.997647i | \(0.478157\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.96239 | −0.981194 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.193937 | 0.0791743 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −0.768452 | −0.271689 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.00000 | 0.603023 | 0.301511 | − | 0.953463i | \(-0.402509\pi\) | ||||
0.301511 | + | 0.953463i | \(0.402509\pi\) | |||||||
\(12\) | −1.96239 | −0.566493 | ||||||||
\(13\) | −1.35026 | −0.374495 | −0.187248 | − | 0.982313i | \(-0.559957\pi\) | ||||
−0.187248 | + | 0.982313i | \(0.559957\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.77575 | 0.943937 | ||||||||
\(17\) | 3.35026 | 0.812558 | 0.406279 | − | 0.913749i | \(-0.366826\pi\) | ||||
0.406279 | + | 0.913749i | \(0.366826\pi\) | |||||||
\(18\) | 0.193937 | 0.0457113 | ||||||||
\(19\) | −5.35026 | −1.22743 | −0.613717 | − | 0.789526i | \(-0.710326\pi\) | ||||
−0.613717 | + | 0.789526i | \(0.710326\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.387873 | 0.0826948 | ||||||||
\(23\) | 4.96239 | 1.03473 | 0.517365 | − | 0.855765i | \(-0.326913\pi\) | ||||
0.517365 | + | 0.855765i | \(0.326913\pi\) | |||||||
\(24\) | −0.768452 | −0.156860 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.261865 | −0.0513560 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.92478 | 1.47159 | 0.735797 | − | 0.677202i | \(-0.236808\pi\) | ||||
0.735797 | + | 0.677202i | \(0.236808\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.57452 | −0.821607 | −0.410804 | − | 0.911724i | \(-0.634752\pi\) | ||||
−0.410804 | + | 0.911724i | \(0.634752\pi\) | |||||||
\(32\) | 2.26916 | 0.401134 | ||||||||
\(33\) | 2.00000 | 0.348155 | ||||||||
\(34\) | 0.649738 | 0.111429 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.96239 | −0.327065 | ||||||||
\(37\) | −0.775746 | −0.127532 | −0.0637660 | − | 0.997965i | \(-0.520311\pi\) | ||||
−0.0637660 | + | 0.997965i | \(0.520311\pi\) | |||||||
\(38\) | −1.03761 | −0.168323 | ||||||||
\(39\) | −1.35026 | −0.216215 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.73813 | −0.583799 | −0.291899 | − | 0.956449i | \(-0.594287\pi\) | ||||
−0.291899 | + | 0.956449i | \(0.594287\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −12.6253 | −1.92534 | −0.962670 | − | 0.270677i | \(-0.912752\pi\) | ||||
−0.962670 | + | 0.270677i | \(0.912752\pi\) | |||||||
\(44\) | −3.92478 | −0.591682 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.962389 | 0.141896 | ||||||||
\(47\) | −9.92478 | −1.44768 | −0.723839 | − | 0.689969i | \(-0.757624\pi\) | ||||
−0.723839 | + | 0.689969i | \(0.757624\pi\) | |||||||
\(48\) | 3.77575 | 0.544982 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.35026 | 0.469130 | ||||||||
\(52\) | 2.64974 | 0.367453 | ||||||||
\(53\) | 8.57452 | 1.17780 | 0.588900 | − | 0.808206i | \(-0.299561\pi\) | ||||
0.588900 | + | 0.808206i | \(0.299561\pi\) | |||||||
\(54\) | 0.193937 | 0.0263914 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.35026 | −0.708659 | ||||||||
\(58\) | 1.53690 | 0.201805 | ||||||||
\(59\) | 8.62530 | 1.12292 | 0.561459 | − | 0.827504i | \(-0.310240\pi\) | ||||
0.561459 | + | 0.827504i | \(0.310240\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.70052 | 1.11399 | 0.556994 | − | 0.830517i | \(-0.311955\pi\) | ||||
0.556994 | + | 0.830517i | \(0.311955\pi\) | |||||||
\(62\) | −0.887166 | −0.112670 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.11142 | −0.888927 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.387873 | 0.0477439 | ||||||||
\(67\) | 9.92478 | 1.21250 | 0.606252 | − | 0.795272i | \(-0.292672\pi\) | ||||
0.606252 | + | 0.795272i | \(0.292672\pi\) | |||||||
\(68\) | −6.57452 | −0.797277 | ||||||||
\(69\) | 4.96239 | 0.597401 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.00000 | 0.237356 | 0.118678 | − | 0.992933i | \(-0.462134\pi\) | ||||
0.118678 | + | 0.992933i | \(0.462134\pi\) | |||||||
\(72\) | −0.768452 | −0.0905629 | ||||||||
\(73\) | 9.35026 | 1.09437 | 0.547183 | − | 0.837013i | \(-0.315700\pi\) | ||||
0.547183 | + | 0.837013i | \(0.315700\pi\) | |||||||
\(74\) | −0.150446 | −0.0174889 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 10.4993 | 1.20435 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.261865 | −0.0296504 | ||||||||
\(79\) | 10.7005 | 1.20390 | 0.601951 | − | 0.798533i | \(-0.294390\pi\) | ||||
0.601951 | + | 0.798533i | \(0.294390\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.724961 | −0.0800586 | ||||||||
\(83\) | −3.22425 | −0.353908 | −0.176954 | − | 0.984219i | \(-0.556624\pi\) | ||||
−0.176954 | + | 0.984219i | \(0.556624\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.44851 | −0.264029 | ||||||||
\(87\) | 7.92478 | 0.849625 | ||||||||
\(88\) | −1.53690 | −0.163835 | ||||||||
\(89\) | −1.03761 | −0.109987 | −0.0549933 | − | 0.998487i | \(-0.517514\pi\) | ||||
−0.0549933 | + | 0.998487i | \(0.517514\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −9.73813 | −1.01527 | ||||||||
\(93\) | −4.57452 | −0.474355 | ||||||||
\(94\) | −1.92478 | −0.198526 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.26916 | 0.231595 | ||||||||
\(97\) | 18.4993 | 1.87832 | 0.939159 | − | 0.343482i | \(-0.111606\pi\) | ||||
0.939159 | + | 0.343482i | \(0.111606\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.00000 | 0.201008 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 17.6629 | 1.75753 | 0.878763 | − | 0.477259i | \(-0.158370\pi\) | ||||
0.878763 | + | 0.477259i | \(0.158370\pi\) | |||||||
\(102\) | 0.649738 | 0.0643337 | ||||||||
\(103\) | −6.70052 | −0.660222 | −0.330111 | − | 0.943942i | \(-0.607086\pi\) | ||||
−0.330111 | + | 0.943942i | \(0.607086\pi\) | |||||||
\(104\) | 1.03761 | 0.101746 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.66291 | 0.161516 | ||||||||
\(107\) | 13.7381 | 1.32812 | 0.664058 | − | 0.747681i | \(-0.268833\pi\) | ||||
0.664058 | + | 0.747681i | \(0.268833\pi\) | |||||||
\(108\) | −1.96239 | −0.188831 | ||||||||
\(109\) | −2.77575 | −0.265868 | −0.132934 | − | 0.991125i | \(-0.542440\pi\) | ||||
−0.132934 | + | 0.991125i | \(0.542440\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.775746 | −0.0736306 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.0508 | 1.13364 | 0.566821 | − | 0.823841i | \(-0.308173\pi\) | ||||
0.566821 | + | 0.823841i | \(0.308173\pi\) | |||||||
\(114\) | −1.03761 | −0.0971812 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −15.5515 | −1.44392 | ||||||||
\(117\) | −1.35026 | −0.124832 | ||||||||
\(118\) | 1.67276 | 0.153990 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 1.68735 | 0.152765 | ||||||||
\(123\) | −3.73813 | −0.337056 | ||||||||
\(124\) | 8.97698 | 0.806156 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.70052 | 0.239633 | 0.119816 | − | 0.992796i | \(-0.461769\pi\) | ||||
0.119816 | + | 0.992796i | \(0.461769\pi\) | |||||||
\(128\) | −5.91748 | −0.523037 | ||||||||
\(129\) | −12.6253 | −1.11160 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −20.6253 | −1.80204 | −0.901020 | − | 0.433777i | \(-0.857181\pi\) | ||||
−0.901020 | + | 0.433777i | \(0.857181\pi\) | |||||||
\(132\) | −3.92478 | −0.341608 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.92478 | 0.166275 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.57452 | −0.220763 | ||||||||
\(137\) | 22.4993 | 1.92224 | 0.961122 | − | 0.276124i | \(-0.0890499\pi\) | ||||
0.961122 | + | 0.276124i | \(0.0890499\pi\) | |||||||
\(138\) | 0.962389 | 0.0819240 | ||||||||
\(139\) | 3.27504 | 0.277785 | 0.138893 | − | 0.990307i | \(-0.455646\pi\) | ||||
0.138893 | + | 0.990307i | \(0.455646\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.92478 | −0.835817 | ||||||||
\(142\) | 0.387873 | 0.0325496 | ||||||||
\(143\) | −2.70052 | −0.225829 | ||||||||
\(144\) | 3.77575 | 0.314646 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.81336 | 0.150075 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.52232 | 0.125134 | ||||||||
\(149\) | −4.44851 | −0.364436 | −0.182218 | − | 0.983258i | \(-0.558328\pi\) | ||||
−0.182218 | + | 0.983258i | \(0.558328\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.29948 | 0.105750 | 0.0528749 | − | 0.998601i | \(-0.483162\pi\) | ||||
0.0528749 | + | 0.998601i | \(0.483162\pi\) | |||||||
\(152\) | 4.11142 | 0.333480 | ||||||||
\(153\) | 3.35026 | 0.270853 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.64974 | 0.212149 | ||||||||
\(157\) | 2.64974 | 0.211472 | 0.105736 | − | 0.994394i | \(-0.466280\pi\) | ||||
0.105736 | + | 0.994394i | \(0.466280\pi\) | |||||||
\(158\) | 2.07522 | 0.165096 | ||||||||
\(159\) | 8.57452 | 0.680003 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.193937 | 0.0152371 | ||||||||
\(163\) | 5.29948 | 0.415087 | 0.207544 | − | 0.978226i | \(-0.433453\pi\) | ||||
0.207544 | + | 0.978226i | \(0.433453\pi\) | |||||||
\(164\) | 7.33567 | 0.572820 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.625301 | −0.0485327 | ||||||||
\(167\) | 14.5501 | 1.12592 | 0.562959 | − | 0.826485i | \(-0.309663\pi\) | ||||
0.562959 | + | 0.826485i | \(0.309663\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.1768 | −0.859753 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.35026 | −0.409145 | ||||||||
\(172\) | 24.7757 | 1.88913 | ||||||||
\(173\) | 4.49929 | 0.342075 | 0.171037 | − | 0.985265i | \(-0.445288\pi\) | ||||
0.171037 | + | 0.985265i | \(0.445288\pi\) | |||||||
\(174\) | 1.53690 | 0.116512 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 7.55149 | 0.569215 | ||||||||
\(177\) | 8.62530 | 0.648317 | ||||||||
\(178\) | −0.201231 | −0.0150829 | ||||||||
\(179\) | 10.0000 | 0.747435 | 0.373718 | − | 0.927543i | \(-0.378083\pi\) | ||||
0.373718 | + | 0.927543i | \(0.378083\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.6253 | −0.789772 | −0.394886 | − | 0.918730i | \(-0.629216\pi\) | ||||
−0.394886 | + | 0.918730i | \(0.629216\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.70052 | 0.643161 | ||||||||
\(184\) | −3.81336 | −0.281124 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.887166 | −0.0650502 | ||||||||
\(187\) | 6.70052 | 0.489991 | ||||||||
\(188\) | 19.4763 | 1.42045 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.8496 | −1.00212 | −0.501059 | − | 0.865413i | \(-0.667056\pi\) | ||||
−0.501059 | + | 0.865413i | \(0.667056\pi\) | |||||||
\(192\) | −7.11142 | −0.513222 | ||||||||
\(193\) | 15.3258 | 1.10318 | 0.551588 | − | 0.834116i | \(-0.314022\pi\) | ||||
0.551588 | + | 0.834116i | \(0.314022\pi\) | |||||||
\(194\) | 3.58769 | 0.257581 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.574515 | −0.0409325 | −0.0204663 | − | 0.999791i | \(-0.506515\pi\) | ||||
−0.0204663 | + | 0.999791i | \(0.506515\pi\) | |||||||
\(198\) | 0.387873 | 0.0275649 | ||||||||
\(199\) | 0.201231 | 0.0142649 | 0.00713244 | − | 0.999975i | \(-0.497730\pi\) | ||||
0.00713244 | + | 0.999975i | \(0.497730\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.92478 | 0.700040 | ||||||||
\(202\) | 3.42548 | 0.241016 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −6.57452 | −0.460308 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.29948 | −0.0905388 | ||||||||
\(207\) | 4.96239 | 0.344910 | ||||||||
\(208\) | −5.09825 | −0.353500 | ||||||||
\(209\) | −10.7005 | −0.740171 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.44851 | 0.443934 | 0.221967 | − | 0.975054i | \(-0.428752\pi\) | ||||
0.221967 | + | 0.975054i | \(0.428752\pi\) | |||||||
\(212\) | −16.8265 | −1.15565 | ||||||||
\(213\) | 2.00000 | 0.137038 | ||||||||
\(214\) | 2.66433 | 0.182130 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.768452 | −0.0522865 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −0.538319 | −0.0364595 | ||||||||
\(219\) | 9.35026 | 0.631832 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.52373 | −0.304299 | ||||||||
\(222\) | −0.150446 | −0.0100972 | ||||||||
\(223\) | −1.55149 | −0.103896 | −0.0519478 | − | 0.998650i | \(-0.516543\pi\) | ||||
−0.0519478 | + | 0.998650i | \(0.516543\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.33709 | 0.155461 | ||||||||
\(227\) | 13.1490 | 0.872732 | 0.436366 | − | 0.899769i | \(-0.356265\pi\) | ||||
0.436366 | + | 0.899769i | \(0.356265\pi\) | |||||||
\(228\) | 10.4993 | 0.695333 | ||||||||
\(229\) | −2.77575 | −0.183426 | −0.0917132 | − | 0.995785i | \(-0.529234\pi\) | ||||
−0.0917132 | + | 0.995785i | \(0.529234\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.08981 | −0.399816 | ||||||||
\(233\) | −0.0507852 | −0.00332705 | −0.00166353 | − | 0.999999i | \(-0.500530\pi\) | ||||
−0.00166353 | + | 0.999999i | \(0.500530\pi\) | |||||||
\(234\) | −0.261865 | −0.0171187 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −16.9262 | −1.10180 | ||||||||
\(237\) | 10.7005 | 0.695074 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.84955 | 0.378376 | 0.189188 | − | 0.981941i | \(-0.439414\pi\) | ||||
0.189188 | + | 0.981941i | \(0.439414\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.0752228 | 0.00484553 | 0.00242276 | − | 0.999997i | \(-0.499229\pi\) | ||||
0.00242276 | + | 0.999997i | \(0.499229\pi\) | |||||||
\(242\) | −1.35756 | −0.0872670 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −17.0738 | −1.09304 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.724961 | −0.0462218 | ||||||||
\(247\) | 7.22425 | 0.459668 | ||||||||
\(248\) | 3.51530 | 0.223222 | ||||||||
\(249\) | −3.22425 | −0.204329 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −19.2243 | −1.21342 | −0.606712 | − | 0.794922i | \(-0.707512\pi\) | ||||
−0.606712 | + | 0.794922i | \(0.707512\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.92478 | 0.623965 | ||||||||
\(254\) | 0.523730 | 0.0328618 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 13.0752 | 0.817201 | ||||||||
\(257\) | −7.35026 | −0.458497 | −0.229248 | − | 0.973368i | \(-0.573627\pi\) | ||||
−0.229248 | + | 0.973368i | \(0.573627\pi\) | |||||||
\(258\) | −2.44851 | −0.152437 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.92478 | 0.490531 | ||||||||
\(262\) | −4.00000 | −0.247121 | ||||||||
\(263\) | −12.9624 | −0.799295 | −0.399648 | − | 0.916669i | \(-0.630867\pi\) | ||||
−0.399648 | + | 0.916669i | \(0.630867\pi\) | |||||||
\(264\) | −1.53690 | −0.0945899 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.03761 | −0.0635008 | ||||||||
\(268\) | −19.4763 | −1.18970 | ||||||||
\(269\) | −4.11142 | −0.250678 | −0.125339 | − | 0.992114i | \(-0.540002\pi\) | ||||
−0.125339 | + | 0.992114i | \(0.540002\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.4241 | 0.997691 | 0.498846 | − | 0.866691i | \(-0.333757\pi\) | ||||
0.498846 | + | 0.866691i | \(0.333757\pi\) | |||||||
\(272\) | 12.6497 | 0.767003 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.36344 | 0.263605 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −9.73813 | −0.586167 | ||||||||
\(277\) | −11.0738 | −0.665361 | −0.332680 | − | 0.943040i | \(-0.607953\pi\) | ||||
−0.332680 | + | 0.943040i | \(0.607953\pi\) | |||||||
\(278\) | 0.635150 | 0.0380938 | ||||||||
\(279\) | −4.57452 | −0.273869 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.3733 | 0.857438 | 0.428719 | − | 0.903438i | \(-0.358965\pi\) | ||||
0.428719 | + | 0.903438i | \(0.358965\pi\) | |||||||
\(282\) | −1.92478 | −0.114619 | ||||||||
\(283\) | −1.14903 | −0.0683028 | −0.0341514 | − | 0.999417i | \(-0.510873\pi\) | ||||
−0.0341514 | + | 0.999417i | \(0.510873\pi\) | |||||||
\(284\) | −3.92478 | −0.232893 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.523730 | −0.0309688 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 2.26916 | 0.133711 | ||||||||
\(289\) | −5.77575 | −0.339750 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 18.4993 | 1.08445 | ||||||||
\(292\) | −18.3488 | −1.07379 | ||||||||
\(293\) | −0.649738 | −0.0379581 | −0.0189791 | − | 0.999820i | \(-0.506042\pi\) | ||||
−0.0189791 | + | 0.999820i | \(0.506042\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0.596124 | 0.0346490 | ||||||||
\(297\) | 2.00000 | 0.116052 | ||||||||
\(298\) | −0.862728 | −0.0499765 | ||||||||
\(299\) | −6.70052 | −0.387501 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0.252016 | 0.0145019 | ||||||||
\(303\) | 17.6629 | 1.01471 | ||||||||
\(304\) | −20.2012 | −1.15862 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.649738 | 0.0371431 | ||||||||
\(307\) | −24.1016 | −1.37555 | −0.687775 | − | 0.725924i | \(-0.741412\pi\) | ||||
−0.687775 | + | 0.725924i | \(0.741412\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.70052 | −0.381179 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.25202 | −0.467929 | −0.233964 | − | 0.972245i | \(-0.575170\pi\) | ||||
−0.233964 | + | 0.972245i | \(0.575170\pi\) | |||||||
\(312\) | 1.03761 | 0.0587432 | ||||||||
\(313\) | 14.9018 | 0.842297 | 0.421148 | − | 0.906992i | \(-0.361627\pi\) | ||||
0.421148 | + | 0.906992i | \(0.361627\pi\) | |||||||
\(314\) | 0.513881 | 0.0290000 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −20.9986 | −1.18126 | ||||||||
\(317\) | 10.1260 | 0.568733 | 0.284367 | − | 0.958716i | \(-0.408217\pi\) | ||||
0.284367 | + | 0.958716i | \(0.408217\pi\) | |||||||
\(318\) | 1.66291 | 0.0932515 | ||||||||
\(319\) | 15.8496 | 0.887405 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 13.7381 | 0.766788 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −17.9248 | −0.997361 | ||||||||
\(324\) | −1.96239 | −0.109022 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.02776 | 0.0569225 | ||||||||
\(327\) | −2.77575 | −0.153499 | ||||||||
\(328\) | 2.87258 | 0.158612 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 27.8496 | 1.53075 | 0.765375 | − | 0.643585i | \(-0.222554\pi\) | ||||
0.765375 | + | 0.643585i | \(0.222554\pi\) | |||||||
\(332\) | 6.32724 | 0.347252 | ||||||||
\(333\) | −0.775746 | −0.0425106 | ||||||||
\(334\) | 2.82179 | 0.154402 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.84955 | −0.209699 | −0.104849 | − | 0.994488i | \(-0.533436\pi\) | ||||
−0.104849 | + | 0.994488i | \(0.533436\pi\) | |||||||
\(338\) | −2.16759 | −0.117901 | ||||||||
\(339\) | 12.0508 | 0.654509 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.14903 | −0.495448 | ||||||||
\(342\) | −1.03761 | −0.0561076 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 9.70194 | 0.523093 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.872577 | 0.0469101 | ||||||||
\(347\) | 9.58769 | 0.514694 | 0.257347 | − | 0.966319i | \(-0.417152\pi\) | ||||
0.257347 | + | 0.966319i | \(0.417152\pi\) | |||||||
\(348\) | −15.5515 | −0.833648 | ||||||||
\(349\) | 15.1490 | 0.810909 | 0.405455 | − | 0.914115i | \(-0.367113\pi\) | ||||
0.405455 | + | 0.914115i | \(0.367113\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.35026 | −0.0720716 | ||||||||
\(352\) | 4.53832 | 0.241893 | ||||||||
\(353\) | 20.3488 | 1.08306 | 0.541530 | − | 0.840681i | \(-0.317845\pi\) | ||||
0.541530 | + | 0.840681i | \(0.317845\pi\) | |||||||
\(354\) | 1.67276 | 0.0889063 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2.03620 | 0.107918 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.93937 | 0.102499 | ||||||||
\(359\) | −31.4010 | −1.65728 | −0.828642 | − | 0.559779i | \(-0.810886\pi\) | ||||
−0.828642 | + | 0.559779i | \(0.810886\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.62530 | 0.506595 | ||||||||
\(362\) | −2.06063 | −0.108305 | ||||||||
\(363\) | −7.00000 | −0.367405 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.68735 | 0.0881992 | ||||||||
\(367\) | 29.4010 | 1.53472 | 0.767361 | − | 0.641215i | \(-0.221569\pi\) | ||||
0.767361 | + | 0.641215i | \(0.221569\pi\) | |||||||
\(368\) | 18.7367 | 0.976719 | ||||||||
\(369\) | −3.73813 | −0.194600 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 8.97698 | 0.465435 | ||||||||
\(373\) | 16.0000 | 0.828449 | 0.414224 | − | 0.910175i | \(-0.364053\pi\) | ||||
0.414224 | + | 0.910175i | \(0.364053\pi\) | |||||||
\(374\) | 1.29948 | 0.0671943 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.62672 | 0.393318 | ||||||||
\(377\) | −10.7005 | −0.551105 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.7005 | 0.549649 | 0.274824 | − | 0.961494i | \(-0.411380\pi\) | ||||
0.274824 | + | 0.961494i | \(0.411380\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.70052 | 0.138352 | ||||||||
\(382\) | −2.68594 | −0.137424 | ||||||||
\(383\) | 16.7757 | 0.857201 | 0.428600 | − | 0.903494i | \(-0.359007\pi\) | ||||
0.428600 | + | 0.903494i | \(0.359007\pi\) | |||||||
\(384\) | −5.91748 | −0.301975 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.97224 | 0.151283 | ||||||||
\(387\) | −12.6253 | −0.641780 | ||||||||
\(388\) | −36.3028 | −1.84300 | ||||||||
\(389\) | −29.3258 | −1.48688 | −0.743439 | − | 0.668804i | \(-0.766807\pi\) | ||||
−0.743439 | + | 0.668804i | \(0.766807\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.6253 | 0.840778 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −20.6253 | −1.04041 | ||||||||
\(394\) | −0.111420 | −0.00561324 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −3.92478 | −0.197227 | ||||||||
\(397\) | −18.3488 | −0.920902 | −0.460451 | − | 0.887685i | \(-0.652312\pi\) | ||||
−0.460451 | + | 0.887685i | \(0.652312\pi\) | |||||||
\(398\) | 0.0390260 | 0.00195620 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −37.3258 | −1.86396 | −0.931981 | − | 0.362506i | \(-0.881921\pi\) | ||||
−0.931981 | + | 0.362506i | \(0.881921\pi\) | |||||||
\(402\) | 1.92478 | 0.0959992 | ||||||||
\(403\) | 6.17679 | 0.307688 | ||||||||
\(404\) | −34.6615 | −1.72447 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.55149 | −0.0769046 | ||||||||
\(408\) | −2.57452 | −0.127458 | ||||||||
\(409\) | 22.3733 | 1.10629 | 0.553144 | − | 0.833086i | \(-0.313428\pi\) | ||||
0.553144 | + | 0.833086i | \(0.313428\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 22.4993 | 1.10981 | ||||||||
\(412\) | 13.1490 | 0.647806 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0.962389 | 0.0472988 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −3.06396 | −0.150223 | ||||||||
\(417\) | 3.27504 | 0.160379 | ||||||||
\(418\) | −2.07522 | −0.101502 | ||||||||
\(419\) | −23.4763 | −1.14689 | −0.573445 | − | 0.819244i | \(-0.694394\pi\) | ||||
−0.573445 | + | 0.819244i | \(0.694394\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.2243 | −1.22935 | −0.614677 | − | 0.788779i | \(-0.710714\pi\) | ||||
−0.614677 | + | 0.788779i | \(0.710714\pi\) | |||||||
\(422\) | 1.25060 | 0.0608783 | ||||||||
\(423\) | −9.92478 | −0.482559 | ||||||||
\(424\) | −6.58910 | −0.319995 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0.387873 | 0.0187925 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −26.9596 | −1.30314 | ||||||||
\(429\) | −2.70052 | −0.130383 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −19.4010 | −0.934516 | −0.467258 | − | 0.884121i | \(-0.654758\pi\) | ||||
−0.467258 | + | 0.884121i | \(0.654758\pi\) | |||||||
\(432\) | 3.77575 | 0.181661 | ||||||||
\(433\) | −6.49929 | −0.312336 | −0.156168 | − | 0.987731i | \(-0.549914\pi\) | ||||
−0.156168 | + | 0.987731i | \(0.549914\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.44709 | 0.260868 | ||||||||
\(437\) | −26.5501 | −1.27006 | ||||||||
\(438\) | 1.81336 | 0.0866456 | ||||||||
\(439\) | 14.6497 | 0.699194 | 0.349597 | − | 0.936900i | \(-0.386319\pi\) | ||||
0.349597 | + | 0.936900i | \(0.386319\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.877317 | −0.0417297 | ||||||||
\(443\) | 19.1392 | 0.909330 | 0.454665 | − | 0.890663i | \(-0.349759\pi\) | ||||
0.454665 | + | 0.890663i | \(0.349759\pi\) | |||||||
\(444\) | 1.52232 | 0.0722459 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −0.300891 | −0.0142476 | ||||||||
\(447\) | −4.44851 | −0.210407 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −32.8021 | −1.54803 | −0.774013 | − | 0.633169i | \(-0.781754\pi\) | ||||
−0.774013 | + | 0.633169i | \(0.781754\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.47627 | −0.352044 | ||||||||
\(452\) | −23.6483 | −1.11232 | ||||||||
\(453\) | 1.29948 | 0.0610547 | ||||||||
\(454\) | 2.55008 | 0.119681 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4.11142 | 0.192535 | ||||||||
\(457\) | −18.7005 | −0.874774 | −0.437387 | − | 0.899273i | \(-0.644096\pi\) | ||||
−0.437387 | + | 0.899273i | \(0.644096\pi\) | |||||||
\(458\) | −0.538319 | −0.0251540 | ||||||||
\(459\) | 3.35026 | 0.156377 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.96239 | 0.324271 | 0.162135 | − | 0.986769i | \(-0.448162\pi\) | ||||
0.162135 | + | 0.986769i | \(0.448162\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.29948 | 0.246288 | 0.123144 | − | 0.992389i | \(-0.460702\pi\) | ||||
0.123144 | + | 0.992389i | \(0.460702\pi\) | |||||||
\(464\) | 29.9219 | 1.38909 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.00984911 | −0.000456251 0 | ||||||||
\(467\) | 13.1490 | 0.608465 | 0.304232 | − | 0.952598i | \(-0.401600\pi\) | ||||
0.304232 | + | 0.952598i | \(0.401600\pi\) | |||||||
\(468\) | 2.64974 | 0.122484 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.64974 | 0.122093 | ||||||||
\(472\) | −6.62813 | −0.305084 | ||||||||
\(473\) | −25.2506 | −1.16102 | ||||||||
\(474\) | 2.07522 | 0.0953181 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.57452 | 0.392600 | ||||||||
\(478\) | 1.13444 | 0.0518882 | ||||||||
\(479\) | −5.14903 | −0.235265 | −0.117633 | − | 0.993057i | \(-0.537531\pi\) | ||||
−0.117633 | + | 0.993057i | \(0.537531\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.04746 | 0.0477601 | ||||||||
\(482\) | 0.0145884 | 0.000664486 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 13.7367 | 0.624396 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.193937 | 0.00879714 | ||||||||
\(487\) | −22.1768 | −1.00493 | −0.502463 | − | 0.864599i | \(-0.667573\pi\) | ||||
−0.502463 | + | 0.864599i | \(0.667573\pi\) | |||||||
\(488\) | −6.68594 | −0.302658 | ||||||||
\(489\) | 5.29948 | 0.239651 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.00000 | 0.0902587 | 0.0451294 | − | 0.998981i | \(-0.485630\pi\) | ||||
0.0451294 | + | 0.998981i | \(0.485630\pi\) | |||||||
\(492\) | 7.33567 | 0.330718 | ||||||||
\(493\) | 26.5501 | 1.19576 | ||||||||
\(494\) | 1.40105 | 0.0630361 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −17.2722 | −0.775545 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −0.625301 | −0.0280204 | ||||||||
\(499\) | −6.55008 | −0.293222 | −0.146611 | − | 0.989194i | \(-0.546837\pi\) | ||||
−0.146611 | + | 0.989194i | \(0.546837\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 14.5501 | 0.650050 | ||||||||
\(502\) | −3.72829 | −0.166402 | ||||||||
\(503\) | −8.77575 | −0.391291 | −0.195646 | − | 0.980675i | \(-0.562680\pi\) | ||||
−0.195646 | + | 0.980675i | \(0.562680\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.92478 | 0.0855668 | ||||||||
\(507\) | −11.1768 | −0.496379 | ||||||||
\(508\) | −5.29948 | −0.235126 | ||||||||
\(509\) | −13.1392 | −0.582384 | −0.291192 | − | 0.956665i | \(-0.594052\pi\) | ||||
−0.291192 | + | 0.956665i | \(0.594052\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 14.3707 | 0.635103 | ||||||||
\(513\) | −5.35026 | −0.236220 | ||||||||
\(514\) | −1.42548 | −0.0628754 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 24.7757 | 1.09069 | ||||||||
\(517\) | −19.8496 | −0.872982 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.49929 | 0.197497 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 37.6629 | 1.65004 | 0.825021 | − | 0.565102i | \(-0.191163\pi\) | ||||
0.825021 | + | 0.565102i | \(0.191163\pi\) | |||||||
\(522\) | 1.53690 | 0.0672685 | ||||||||
\(523\) | 4.00000 | 0.174908 | 0.0874539 | − | 0.996169i | \(-0.472127\pi\) | ||||
0.0874539 | + | 0.996169i | \(0.472127\pi\) | |||||||
\(524\) | 40.4749 | 1.76815 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.51388 | −0.109610 | ||||||||
\(527\) | −15.3258 | −0.667603 | ||||||||
\(528\) | 7.55149 | 0.328637 | ||||||||
\(529\) | 1.62530 | 0.0706652 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.62530 | 0.374306 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.04746 | 0.218630 | ||||||||
\(534\) | −0.201231 | −0.00870811 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −7.62672 | −0.329424 | ||||||||
\(537\) | 10.0000 | 0.431532 | ||||||||
\(538\) | −0.797355 | −0.0343764 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22.4749 | −0.966269 | −0.483135 | − | 0.875546i | \(-0.660502\pi\) | ||||
−0.483135 | + | 0.875546i | \(0.660502\pi\) | |||||||
\(542\) | 3.18523 | 0.136817 | ||||||||
\(543\) | −10.6253 | −0.455975 | ||||||||
\(544\) | 7.60228 | 0.325945 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −25.9248 | −1.10846 | −0.554232 | − | 0.832362i | \(-0.686988\pi\) | ||||
−0.554232 | + | 0.832362i | \(0.686988\pi\) | |||||||
\(548\) | −44.1524 | −1.88610 | ||||||||
\(549\) | 8.70052 | 0.371329 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −42.3996 | −1.80629 | ||||||||
\(552\) | −3.81336 | −0.162307 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −2.14762 | −0.0912435 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.42690 | −0.272561 | ||||||||
\(557\) | −28.5256 | −1.20867 | −0.604335 | − | 0.796730i | \(-0.706561\pi\) | ||||
−0.604335 | + | 0.796730i | \(0.706561\pi\) | |||||||
\(558\) | −0.887166 | −0.0375567 | ||||||||
\(559\) | 17.0475 | 0.721031 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.70052 | 0.282896 | ||||||||
\(562\) | 2.78751 | 0.117584 | ||||||||
\(563\) | 11.6267 | 0.490008 | 0.245004 | − | 0.969522i | \(-0.421211\pi\) | ||||
0.245004 | + | 0.969522i | \(0.421211\pi\) | |||||||
\(564\) | 19.4763 | 0.820099 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −0.222839 | −0.00936663 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.53690 | −0.0644871 | ||||||||
\(569\) | 9.32582 | 0.390959 | 0.195479 | − | 0.980708i | \(-0.437374\pi\) | ||||
0.195479 | + | 0.980708i | \(0.437374\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.6991 | −0.824382 | −0.412191 | − | 0.911097i | \(-0.635236\pi\) | ||||
−0.412191 | + | 0.911097i | \(0.635236\pi\) | |||||||
\(572\) | 5.29948 | 0.221582 | ||||||||
\(573\) | −13.8496 | −0.578573 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −7.11142 | −0.296309 | ||||||||
\(577\) | −32.7974 | −1.36537 | −0.682686 | − | 0.730712i | \(-0.739188\pi\) | ||||
−0.682686 | + | 0.730712i | \(0.739188\pi\) | |||||||
\(578\) | −1.12013 | −0.0465912 | ||||||||
\(579\) | 15.3258 | 0.636920 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 3.58769 | 0.148715 | ||||||||
\(583\) | 17.1490 | 0.710240 | ||||||||
\(584\) | −7.18523 | −0.297327 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.126008 | −0.00520534 | ||||||||
\(587\) | −18.8218 | −0.776859 | −0.388429 | − | 0.921479i | \(-0.626982\pi\) | ||||
−0.388429 | + | 0.921479i | \(0.626982\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 24.4749 | 1.00847 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.574515 | −0.0236324 | ||||||||
\(592\) | −2.92902 | −0.120382 | ||||||||
\(593\) | −33.7499 | −1.38594 | −0.692971 | − | 0.720965i | \(-0.743699\pi\) | ||||
−0.692971 | + | 0.720965i | \(0.743699\pi\) | |||||||
\(594\) | 0.387873 | 0.0159146 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 8.72970 | 0.357582 | ||||||||
\(597\) | 0.201231 | 0.00823583 | ||||||||
\(598\) | −1.29948 | −0.0531395 | ||||||||
\(599\) | −20.2981 | −0.829356 | −0.414678 | − | 0.909968i | \(-0.636106\pi\) | ||||
−0.414678 | + | 0.909968i | \(0.636106\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.8496 | 0.564935 | 0.282468 | − | 0.959277i | \(-0.408847\pi\) | ||||
0.282468 | + | 0.959277i | \(0.408847\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.92478 | 0.404168 | ||||||||
\(604\) | −2.55008 | −0.103761 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 3.42548 | 0.139151 | ||||||||
\(607\) | 25.2506 | 1.02489 | 0.512445 | − | 0.858720i | \(-0.328740\pi\) | ||||
0.512445 | + | 0.858720i | \(0.328740\pi\) | |||||||
\(608\) | −12.1406 | −0.492366 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13.4010 | 0.542148 | ||||||||
\(612\) | −6.57452 | −0.265759 | ||||||||
\(613\) | −9.14903 | −0.369526 | −0.184763 | − | 0.982783i | \(-0.559152\pi\) | ||||
−0.184763 | + | 0.982783i | \(0.559152\pi\) | |||||||
\(614\) | −4.67418 | −0.188634 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.9492 | 0.642091 | 0.321046 | − | 0.947064i | \(-0.395966\pi\) | ||||
0.321046 | + | 0.947064i | \(0.395966\pi\) | |||||||
\(618\) | −1.29948 | −0.0522726 | ||||||||
\(619\) | −11.1735 | −0.449100 | −0.224550 | − | 0.974463i | \(-0.572091\pi\) | ||||
−0.224550 | + | 0.974463i | \(0.572091\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.96239 | 0.199134 | ||||||||
\(622\) | −1.60037 | −0.0641689 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −5.09825 | −0.204093 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 2.89000 | 0.115507 | ||||||||
\(627\) | −10.7005 | −0.427338 | ||||||||
\(628\) | −5.19982 | −0.207495 | ||||||||
\(629\) | −2.59895 | −0.103627 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.5501 | −0.579229 | −0.289615 | − | 0.957143i | \(-0.593527\pi\) | ||||
−0.289615 | + | 0.957143i | \(0.593527\pi\) | |||||||
\(632\) | −8.22284 | −0.327087 | ||||||||
\(633\) | 6.44851 | 0.256305 | ||||||||
\(634\) | 1.96380 | 0.0779926 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −16.8265 | −0.667215 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 3.07381 | 0.121693 | ||||||||
\(639\) | 2.00000 | 0.0791188 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −38.7269 | −1.52962 | −0.764810 | − | 0.644256i | \(-0.777167\pi\) | ||||
−0.764810 | + | 0.644256i | \(0.777167\pi\) | |||||||
\(642\) | 2.66433 | 0.105153 | ||||||||
\(643\) | 11.9511 | 0.471306 | 0.235653 | − | 0.971837i | \(-0.424277\pi\) | ||||
0.235653 | + | 0.971837i | \(0.424277\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.47627 | −0.136772 | ||||||||
\(647\) | 14.5501 | 0.572023 | 0.286011 | − | 0.958226i | \(-0.407671\pi\) | ||||
0.286011 | + | 0.958226i | \(0.407671\pi\) | |||||||
\(648\) | −0.768452 | −0.0301876 | ||||||||
\(649\) | 17.2506 | 0.677145 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −10.3996 | −0.407281 | ||||||||
\(653\) | 49.9756 | 1.95569 | 0.977847 | − | 0.209319i | \(-0.0671247\pi\) | ||||
0.977847 | + | 0.209319i | \(0.0671247\pi\) | |||||||
\(654\) | −0.538319 | −0.0210499 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −14.1142 | −0.551069 | ||||||||
\(657\) | 9.35026 | 0.364788 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −16.9525 | −0.660377 | −0.330189 | − | 0.943915i | \(-0.607112\pi\) | ||||
−0.330189 | + | 0.943915i | \(0.607112\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.6531 | 0.608834 | 0.304417 | − | 0.952539i | \(-0.401538\pi\) | ||||
0.304417 | + | 0.952539i | \(0.401538\pi\) | |||||||
\(662\) | 5.40105 | 0.209918 | ||||||||
\(663\) | −4.52373 | −0.175687 | ||||||||
\(664\) | 2.47768 | 0.0961528 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.150446 | −0.00582965 | ||||||||
\(667\) | 39.3258 | 1.52270 | ||||||||
\(668\) | −28.5529 | −1.10475 | ||||||||
\(669\) | −1.55149 | −0.0599842 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 17.4010 | 0.671760 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 26.0263 | 1.00324 | 0.501621 | − | 0.865088i | \(-0.332737\pi\) | ||||
0.501621 | + | 0.865088i | \(0.332737\pi\) | |||||||
\(674\) | −0.746569 | −0.0287568 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 21.9332 | 0.843585 | ||||||||
\(677\) | 35.4518 | 1.36252 | 0.681262 | − | 0.732039i | \(-0.261431\pi\) | ||||
0.681262 | + | 0.732039i | \(0.261431\pi\) | |||||||
\(678\) | 2.33709 | 0.0897553 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13.1490 | 0.503872 | ||||||||
\(682\) | −1.77433 | −0.0679427 | ||||||||
\(683\) | −23.6629 | −0.905436 | −0.452718 | − | 0.891654i | \(-0.649546\pi\) | ||||
−0.452718 | + | 0.891654i | \(0.649546\pi\) | |||||||
\(684\) | 10.4993 | 0.401450 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.77575 | −0.105901 | ||||||||
\(688\) | −47.6699 | −1.81740 | ||||||||
\(689\) | −11.5778 | −0.441081 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.574515 | 0.0218556 | 0.0109278 | − | 0.999940i | \(-0.496522\pi\) | ||||
0.0109278 | + | 0.999940i | \(0.496522\pi\) | |||||||
\(692\) | −8.82936 | −0.335642 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.85940 | 0.0705820 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −6.08981 | −0.230834 | ||||||||
\(697\) | −12.5237 | −0.474370 | ||||||||
\(698\) | 2.93795 | 0.111203 | ||||||||
\(699\) | −0.0507852 | −0.00192087 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 42.7269 | 1.61377 | 0.806886 | − | 0.590707i | \(-0.201151\pi\) | ||||
0.806886 | + | 0.590707i | \(0.201151\pi\) | |||||||
\(702\) | −0.261865 | −0.00988346 | ||||||||
\(703\) | 4.15045 | 0.156537 | ||||||||
\(704\) | −14.2228 | −0.536043 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.94639 | 0.148524 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −16.9262 | −0.636125 | ||||||||
\(709\) | 27.2506 | 1.02342 | 0.511709 | − | 0.859159i | \(-0.329013\pi\) | ||||
0.511709 | + | 0.859159i | \(0.329013\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 10.7005 | 0.401301 | ||||||||
\(712\) | 0.797355 | 0.0298821 | ||||||||
\(713\) | −22.7005 | −0.850141 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −19.6239 | −0.733379 | ||||||||
\(717\) | 5.84955 | 0.218456 | ||||||||
\(718\) | −6.08981 | −0.227270 | ||||||||
\(719\) | 10.7005 | 0.399062 | 0.199531 | − | 0.979891i | \(-0.436058\pi\) | ||||
0.199531 | + | 0.979891i | \(0.436058\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 1.86670 | 0.0694713 | ||||||||
\(723\) | 0.0752228 | 0.00279757 | ||||||||
\(724\) | 20.8510 | 0.774920 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.35756 | −0.0503836 | ||||||||
\(727\) | −39.9511 | −1.48171 | −0.740853 | − | 0.671668i | \(-0.765578\pi\) | ||||
−0.740853 | + | 0.671668i | \(0.765578\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −42.2981 | −1.56445 | ||||||||
\(732\) | −17.0738 | −0.631066 | ||||||||
\(733\) | 30.3488 | 1.12096 | 0.560480 | − | 0.828168i | \(-0.310617\pi\) | ||||
0.560480 | + | 0.828168i | \(0.310617\pi\) | |||||||
\(734\) | 5.70194 | 0.210462 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 11.2605 | 0.415066 | ||||||||
\(737\) | 19.8496 | 0.731168 | ||||||||
\(738\) | −0.724961 | −0.0266862 | ||||||||
\(739\) | 37.2506 | 1.37029 | 0.685143 | − | 0.728409i | \(-0.259740\pi\) | ||||
0.685143 | + | 0.728409i | \(0.259740\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.22425 | 0.265390 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 26.3634 | 0.967181 | 0.483590 | − | 0.875294i | \(-0.339332\pi\) | ||||
0.483590 | + | 0.875294i | \(0.339332\pi\) | |||||||
\(744\) | 3.51530 | 0.128877 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 3.10299 | 0.113608 | ||||||||
\(747\) | −3.22425 | −0.117969 | ||||||||
\(748\) | −13.1490 | −0.480776 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 50.6516 | 1.84830 | 0.924152 | − | 0.382024i | \(-0.124773\pi\) | ||||
0.924152 | + | 0.382024i | \(0.124773\pi\) | |||||||
\(752\) | −37.4734 | −1.36652 | ||||||||
\(753\) | −19.2243 | −0.700571 | ||||||||
\(754\) | −2.07522 | −0.0755752 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 38.9525 | 1.41575 | 0.707877 | − | 0.706336i | \(-0.249653\pi\) | ||||
0.707877 | + | 0.706336i | \(0.249653\pi\) | |||||||
\(758\) | 2.07522 | 0.0753755 | ||||||||
\(759\) | 9.92478 | 0.360247 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −48.2130 | −1.74772 | −0.873860 | − | 0.486178i | \(-0.838391\pi\) | ||||
−0.873860 | + | 0.486178i | \(0.838391\pi\) | |||||||
\(762\) | 0.523730 | 0.0189727 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 27.1782 | 0.983273 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.25343 | 0.117551 | ||||||||
\(767\) | −11.6464 | −0.420528 | ||||||||
\(768\) | 13.0752 | 0.471811 | ||||||||
\(769\) | −4.44851 | −0.160417 | −0.0802086 | − | 0.996778i | \(-0.525559\pi\) | ||||
−0.0802086 | + | 0.996778i | \(0.525559\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.35026 | −0.264713 | ||||||||
\(772\) | −30.0752 | −1.08243 | ||||||||
\(773\) | −39.3014 | −1.41357 | −0.706786 | − | 0.707427i | \(-0.749856\pi\) | ||||
−0.706786 | + | 0.707427i | \(0.749856\pi\) | |||||||
\(774\) | −2.44851 | −0.0880098 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −14.2158 | −0.510318 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −5.68735 | −0.203901 | ||||||||
\(779\) | 20.0000 | 0.716574 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.00000 | 0.143131 | ||||||||
\(782\) | 3.22425 | 0.115299 | ||||||||
\(783\) | 7.92478 | 0.283208 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −4.00000 | −0.142675 | ||||||||
\(787\) | −0.897015 | −0.0319751 | −0.0159876 | − | 0.999872i | \(-0.505089\pi\) | ||||
−0.0159876 | + | 0.999872i | \(0.505089\pi\) | |||||||
\(788\) | 1.12742 | 0.0401628 | ||||||||
\(789\) | −12.9624 | −0.461473 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −1.53690 | −0.0546115 | ||||||||
\(793\) | −11.7480 | −0.417183 | ||||||||
\(794\) | −3.55851 | −0.126287 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.394893 | −0.0139966 | ||||||||
\(797\) | −3.19982 | −0.113343 | −0.0566717 | − | 0.998393i | \(-0.518049\pi\) | ||||
−0.0566717 | + | 0.998393i | \(0.518049\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −33.2506 | −1.17632 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.03761 | −0.0366622 | ||||||||
\(802\) | −7.23884 | −0.255612 | ||||||||
\(803\) | 18.7005 | 0.659927 | ||||||||
\(804\) | −19.4763 | −0.686875 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.19791 | 0.0421944 | ||||||||
\(807\) | −4.11142 | −0.144729 | ||||||||
\(808\) | −13.5731 | −0.477500 | ||||||||
\(809\) | 4.44851 | 0.156401 | 0.0782006 | − | 0.996938i | \(-0.475083\pi\) | ||||
0.0782006 | + | 0.996938i | \(0.475083\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −37.6747 | −1.32294 | −0.661468 | − | 0.749973i | \(-0.730066\pi\) | ||||
−0.661468 | + | 0.749973i | \(0.730066\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 16.4241 | 0.576017 | ||||||||
\(814\) | −0.300891 | −0.0105462 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 12.6497 | 0.442829 | ||||||||
\(817\) | 67.5487 | 2.36323 | ||||||||
\(818\) | 4.33900 | 0.151710 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −0.749399 | −0.0261542 | −0.0130771 | − | 0.999914i | \(-0.504163\pi\) | ||||
−0.0130771 | + | 0.999914i | \(0.504163\pi\) | |||||||
\(822\) | 4.36344 | 0.152192 | ||||||||
\(823\) | −26.3996 | −0.920233 | −0.460117 | − | 0.887858i | \(-0.652192\pi\) | ||||
−0.460117 | + | 0.887858i | \(0.652192\pi\) | |||||||
\(824\) | 5.14903 | 0.179375 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.43724 | 0.189071 | 0.0945357 | − | 0.995521i | \(-0.469863\pi\) | ||||
0.0945357 | + | 0.995521i | \(0.469863\pi\) | |||||||
\(828\) | −9.73813 | −0.338424 | ||||||||
\(829\) | −22.7757 | −0.791034 | −0.395517 | − | 0.918459i | \(-0.629435\pi\) | ||||
−0.395517 | + | 0.918459i | \(0.629435\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −11.0738 | −0.384146 | ||||||||
\(832\) | 9.60228 | 0.332899 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0.635150 | 0.0219934 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 20.9986 | 0.726251 | ||||||||
\(837\) | −4.57452 | −0.158118 | ||||||||
\(838\) | −4.55291 | −0.157278 | ||||||||
\(839\) | −15.8496 | −0.547187 | −0.273594 | − | 0.961845i | \(-0.588212\pi\) | ||||
−0.273594 | + | 0.961845i | \(0.588212\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 33.8021 | 1.16559 | ||||||||
\(842\) | −4.89191 | −0.168586 | ||||||||
\(843\) | 14.3733 | 0.495042 | ||||||||
\(844\) | −12.6545 | −0.435585 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.92478 | −0.0661752 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 32.3752 | 1.11177 | ||||||||
\(849\) | −1.14903 | −0.0394346 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.84955 | −0.131961 | ||||||||
\(852\) | −3.92478 | −0.134461 | ||||||||
\(853\) | 21.0494 | 0.720717 | 0.360358 | − | 0.932814i | \(-0.382654\pi\) | ||||
0.360358 | + | 0.932814i | \(0.382654\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −10.5571 | −0.360834 | ||||||||
\(857\) | −50.1524 | −1.71317 | −0.856586 | − | 0.516004i | \(-0.827419\pi\) | ||||
−0.856586 | + | 0.516004i | \(0.827419\pi\) | |||||||
\(858\) | −0.523730 | −0.0178799 | ||||||||
\(859\) | 5.35026 | 0.182549 | 0.0912743 | − | 0.995826i | \(-0.470906\pi\) | ||||
0.0912743 | + | 0.995826i | \(0.470906\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3.76257 | −0.128154 | ||||||||
\(863\) | −33.6893 | −1.14680 | −0.573398 | − | 0.819277i | \(-0.694375\pi\) | ||||
−0.573398 | + | 0.819277i | \(0.694375\pi\) | |||||||
\(864\) | 2.26916 | 0.0771984 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.26045 | −0.0428319 | ||||||||
\(867\) | −5.77575 | −0.196155 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 21.4010 | 0.725981 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13.4010 | −0.454077 | ||||||||
\(872\) | 2.13303 | 0.0722334 | ||||||||
\(873\) | 18.4993 | 0.626106 | ||||||||
\(874\) | −5.14903 | −0.174169 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −18.3488 | −0.619950 | ||||||||
\(877\) | −21.5026 | −0.726092 | −0.363046 | − | 0.931771i | \(-0.618263\pi\) | ||||
−0.363046 | + | 0.931771i | \(0.618263\pi\) | |||||||
\(878\) | 2.84112 | 0.0958832 | ||||||||
\(879\) | −0.649738 | −0.0219151 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −32.3634 | −1.09035 | −0.545176 | − | 0.838322i | \(-0.683537\pi\) | ||||
−0.545176 | + | 0.838322i | \(0.683537\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.59895 | −0.0874617 | −0.0437309 | − | 0.999043i | \(-0.513924\pi\) | ||||
−0.0437309 | + | 0.999043i | \(0.513924\pi\) | |||||||
\(884\) | 8.87732 | 0.298576 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.71179 | 0.124700 | ||||||||
\(887\) | −38.2784 | −1.28526 | −0.642631 | − | 0.766176i | \(-0.722157\pi\) | ||||
−0.642631 | + | 0.766176i | \(0.722157\pi\) | |||||||
\(888\) | 0.596124 | 0.0200046 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.00000 | 0.0670025 | ||||||||
\(892\) | 3.04463 | 0.101942 | ||||||||
\(893\) | 53.1002 | 1.77693 | ||||||||
\(894\) | −0.862728 | −0.0288539 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.70052 | −0.223724 | ||||||||
\(898\) | −6.36153 | −0.212287 | ||||||||
\(899\) | −36.2520 | −1.20907 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 28.7269 | 0.957031 | ||||||||
\(902\) | −1.44992 | −0.0482771 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −9.26045 | −0.307998 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0.252016 | 0.00837267 | ||||||||
\(907\) | −49.9972 | −1.66013 | −0.830064 | − | 0.557668i | \(-0.811696\pi\) | ||||
−0.830064 | + | 0.557668i | \(0.811696\pi\) | |||||||
\(908\) | −25.8035 | −0.856320 | ||||||||
\(909\) | 17.6629 | 0.585842 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.9525 | −0.826715 | −0.413357 | − | 0.910569i | \(-0.635644\pi\) | ||||
−0.413357 | + | 0.910569i | \(0.635644\pi\) | |||||||
\(912\) | −20.2012 | −0.668930 | ||||||||
\(913\) | −6.44851 | −0.213414 | ||||||||
\(914\) | −3.62672 | −0.119961 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.44709 | 0.179977 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0.649738 | 0.0214446 | ||||||||
\(919\) | −11.6991 | −0.385918 | −0.192959 | − | 0.981207i | \(-0.561808\pi\) | ||||
−0.192959 | + | 0.981207i | \(0.561808\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −24.1016 | −0.794174 | ||||||||
\(922\) | 1.35026 | 0.0444685 | ||||||||
\(923\) | −2.70052 | −0.0888888 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1.02776 | 0.0337744 | ||||||||
\(927\) | −6.70052 | −0.220074 | ||||||||
\(928\) | 17.9826 | 0.590307 | ||||||||
\(929\) | −23.7090 | −0.777866 | −0.388933 | − | 0.921266i | \(-0.627156\pi\) | ||||
−0.388933 | + | 0.921266i | \(0.627156\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0.0996603 | 0.00326448 | ||||||||
\(933\) | −8.25202 | −0.270159 | ||||||||
\(934\) | 2.55008 | 0.0834411 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.03761 | 0.0339154 | ||||||||
\(937\) | 19.9003 | 0.650116 | 0.325058 | − | 0.945694i | \(-0.394616\pi\) | ||||
0.325058 | + | 0.945694i | \(0.394616\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14.9018 | 0.486300 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.28821 | 0.204990 | 0.102495 | − | 0.994734i | \(-0.467317\pi\) | ||||
0.102495 | + | 0.994734i | \(0.467317\pi\) | |||||||
\(942\) | 0.513881 | 0.0167432 | ||||||||
\(943\) | −18.5501 | −0.604074 | ||||||||
\(944\) | 32.5669 | 1.05996 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.89701 | −0.159216 | ||||||||
\(947\) | −40.0362 | −1.30100 | −0.650501 | − | 0.759506i | \(-0.725441\pi\) | ||||
−0.650501 | + | 0.759506i | \(0.725441\pi\) | |||||||
\(948\) | −20.9986 | −0.682002 | ||||||||
\(949\) | −12.6253 | −0.409835 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10.1260 | 0.328358 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 40.9478 | 1.32643 | 0.663215 | − | 0.748429i | \(-0.269192\pi\) | ||||
0.663215 | + | 0.748429i | \(0.269192\pi\) | |||||||
\(954\) | 1.66291 | 0.0538388 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −11.4791 | −0.371261 | ||||||||
\(957\) | 15.8496 | 0.512343 | ||||||||
\(958\) | −0.998585 | −0.0322628 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10.0738 | −0.324962 | ||||||||
\(962\) | 0.203141 | 0.00654953 | ||||||||
\(963\) | 13.7381 | 0.442705 | ||||||||
\(964\) | −0.147616 | −0.00475440 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 38.2784 | 1.23095 | 0.615475 | − | 0.788157i | \(-0.288964\pi\) | ||||
0.615475 | + | 0.788157i | \(0.288964\pi\) | |||||||
\(968\) | 5.37916 | 0.172893 | ||||||||
\(969\) | −17.9248 | −0.575827 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 28.7269 | 0.921889 | 0.460945 | − | 0.887429i | \(-0.347511\pi\) | ||||
0.460945 | + | 0.887429i | \(0.347511\pi\) | |||||||
\(972\) | −1.96239 | −0.0629436 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −4.30089 | −0.137809 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 32.8510 | 1.05153 | ||||||||
\(977\) | −41.3014 | −1.32135 | −0.660674 | − | 0.750673i | \(-0.729730\pi\) | ||||
−0.660674 | + | 0.750673i | \(0.729730\pi\) | |||||||
\(978\) | 1.02776 | 0.0328642 | ||||||||
\(979\) | −2.07522 | −0.0663244 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.77575 | −0.0886228 | ||||||||
\(982\) | 0.387873 | 0.0123775 | ||||||||
\(983\) | 24.0000 | 0.765481 | 0.382741 | − | 0.923856i | \(-0.374980\pi\) | ||||
0.382741 | + | 0.923856i | \(0.374980\pi\) | |||||||
\(984\) | 2.87258 | 0.0915744 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 5.14903 | 0.163979 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −14.1768 | −0.451024 | ||||||||
\(989\) | −62.6516 | −1.99221 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25.1002 | 0.797333 | 0.398666 | − | 0.917096i | \(-0.369473\pi\) | ||||
0.398666 | + | 0.917096i | \(0.369473\pi\) | |||||||
\(992\) | −10.3803 | −0.329575 | ||||||||
\(993\) | 27.8496 | 0.883779 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 6.32724 | 0.200486 | ||||||||
\(997\) | −32.7974 | −1.03870 | −0.519351 | − | 0.854561i | \(-0.673826\pi\) | ||||
−0.519351 | + | 0.854561i | \(0.673826\pi\) | |||||||
\(998\) | −1.27030 | −0.0402106 | ||||||||
\(999\) | −0.775746 | −0.0245435 |
(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 | 3675.2.a.bj.1.2 | 3 | ||
5.2 | odd | 4 | 735.2.d.b.589.4 | 6 | |||
5.3 | odd | 4 | 735.2.d.b.589.3 | 6 | |||
5.4 | even | 2 | 3675.2.a.bi.1.2 | 3 | |||
7.6 | odd | 2 | 525.2.a.k.1.2 | 3 | |||
15.2 | even | 4 | 2205.2.d.l.1324.3 | 6 | |||
15.8 | even | 4 | 2205.2.d.l.1324.4 | 6 | |||
21.20 | even | 2 | 1575.2.a.w.1.2 | 3 | |||
28.27 | even | 2 | 8400.2.a.dj.1.3 | 3 | |||
35.2 | odd | 12 | 735.2.q.f.214.4 | 12 | |||
35.3 | even | 12 | 735.2.q.e.79.4 | 12 | |||
35.12 | even | 12 | 735.2.q.e.214.4 | 12 | |||
35.13 | even | 4 | 105.2.d.b.64.3 | ✓ | 6 | ||
35.17 | even | 12 | 735.2.q.e.79.3 | 12 | |||
35.18 | odd | 12 | 735.2.q.f.79.4 | 12 | |||
35.23 | odd | 12 | 735.2.q.f.214.3 | 12 | |||
35.27 | even | 4 | 105.2.d.b.64.4 | yes | 6 | ||
35.32 | odd | 12 | 735.2.q.f.79.3 | 12 | |||
35.33 | even | 12 | 735.2.q.e.214.3 | 12 | |||
35.34 | odd | 2 | 525.2.a.j.1.2 | 3 | |||
105.62 | odd | 4 | 315.2.d.e.64.3 | 6 | |||
105.83 | odd | 4 | 315.2.d.e.64.4 | 6 | |||
105.104 | even | 2 | 1575.2.a.x.1.2 | 3 | |||
140.27 | odd | 4 | 1680.2.t.k.1009.1 | 6 | |||
140.83 | odd | 4 | 1680.2.t.k.1009.4 | 6 | |||
140.139 | even | 2 | 8400.2.a.dg.1.1 | 3 | |||
420.83 | even | 4 | 5040.2.t.v.1009.6 | 6 | |||
420.167 | even | 4 | 5040.2.t.v.1009.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.d.b.64.3 | ✓ | 6 | 35.13 | even | 4 | ||
105.2.d.b.64.4 | yes | 6 | 35.27 | even | 4 | ||
315.2.d.e.64.3 | 6 | 105.62 | odd | 4 | |||
315.2.d.e.64.4 | 6 | 105.83 | odd | 4 | |||
525.2.a.j.1.2 | 3 | 35.34 | odd | 2 | |||
525.2.a.k.1.2 | 3 | 7.6 | odd | 2 | |||
735.2.d.b.589.3 | 6 | 5.3 | odd | 4 | |||
735.2.d.b.589.4 | 6 | 5.2 | odd | 4 | |||
735.2.q.e.79.3 | 12 | 35.17 | even | 12 | |||
735.2.q.e.79.4 | 12 | 35.3 | even | 12 | |||
735.2.q.e.214.3 | 12 | 35.33 | even | 12 | |||
735.2.q.e.214.4 | 12 | 35.12 | even | 12 | |||
735.2.q.f.79.3 | 12 | 35.32 | odd | 12 | |||
735.2.q.f.79.4 | 12 | 35.18 | odd | 12 | |||
735.2.q.f.214.3 | 12 | 35.23 | odd | 12 | |||
735.2.q.f.214.4 | 12 | 35.2 | odd | 12 | |||
1575.2.a.w.1.2 | 3 | 21.20 | even | 2 | |||
1575.2.a.x.1.2 | 3 | 105.104 | even | 2 | |||
1680.2.t.k.1009.1 | 6 | 140.27 | odd | 4 | |||
1680.2.t.k.1009.4 | 6 | 140.83 | odd | 4 | |||
2205.2.d.l.1324.3 | 6 | 15.2 | even | 4 | |||
2205.2.d.l.1324.4 | 6 | 15.8 | even | 4 | |||
3675.2.a.bi.1.2 | 3 | 5.4 | even | 2 | |||
3675.2.a.bj.1.2 | 3 | 1.1 | even | 1 | trivial | ||
5040.2.t.v.1009.5 | 6 | 420.167 | even | 4 | |||
5040.2.t.v.1009.6 | 6 | 420.83 | even | 4 | |||
8400.2.a.dg.1.1 | 3 | 140.139 | even | 2 | |||
8400.2.a.dj.1.3 | 3 | 28.27 | even | 2 |