Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3584,2,Mod(1,3584)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3584, 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("3584.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3584 = 2^{9} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3584.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: | \(28.6183840844\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.18857984.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 9x^{4} + 16x^{3} + 6x^{2} - 12x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-2.79169\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3584.1 |
$q$-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 | 0 | ||||||||
\(3\) | 3.22299 | 1.86079 | 0.930397 | − | 0.366554i | \(-0.119462\pi\) | ||||
0.930397 | + | 0.366554i | \(0.119462\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.725063 | −0.324258 | −0.162129 | − | 0.986770i | \(-0.551836\pi\) | ||||
−0.162129 | + | 0.986770i | \(0.551836\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.38766 | 2.46255 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.21848 | 0.668898 | 0.334449 | − | 0.942414i | \(-0.391450\pi\) | ||||
0.334449 | + | 0.942414i | \(0.391450\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.75046 | 0.485490 | 0.242745 | − | 0.970090i | \(-0.421952\pi\) | ||||
0.242745 | + | 0.970090i | \(0.421952\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.33687 | −0.603378 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.69102 | 0.410132 | 0.205066 | − | 0.978748i | \(-0.434259\pi\) | ||||
0.205066 | + | 0.978748i | \(0.434259\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.80241 | 0.413500 | 0.206750 | − | 0.978394i | \(-0.433711\pi\) | ||||
0.206750 | + | 0.978394i | \(0.433711\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.22299 | −0.703314 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.47013 | 1.76615 | 0.883073 | − | 0.469236i | \(-0.155471\pi\) | ||||
0.883073 | + | 0.469236i | \(0.155471\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.47428 | −0.894857 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 14.1414 | 2.72151 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.704174 | 0.130762 | 0.0653809 | − | 0.997860i | \(-0.479174\pi\) | ||||
0.0653809 | + | 0.997860i | \(0.479174\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.28756 | −1.12928 | −0.564640 | − | 0.825337i | \(-0.690985\pi\) | ||||
−0.564640 | + | 0.825337i | \(0.690985\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 7.15015 | 1.24468 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.725063 | 0.122558 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.75496 | −1.11051 | −0.555255 | − | 0.831680i | \(-0.687379\pi\) | ||||
−0.555255 | + | 0.831680i | \(0.687379\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.64171 | 0.903396 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.72453 | 1.36254 | 0.681272 | − | 0.732031i | \(-0.261427\pi\) | ||||
0.681272 | + | 0.732031i | \(0.261427\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.33448 | −1.11850 | −0.559249 | − | 0.829000i | \(-0.688910\pi\) | ||||
−0.559249 | + | 0.829000i | \(0.688910\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.35652 | −0.798503 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.1709 | −1.48358 | −0.741791 | − | 0.670631i | \(-0.766023\pi\) | ||||
−0.741791 | + | 0.670631i | \(0.766023\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.45013 | 0.763170 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13.2440 | 1.81920 | 0.909600 | − | 0.415485i | \(-0.136388\pi\) | ||||
0.909600 | + | 0.415485i | \(0.136388\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.60854 | −0.216896 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.80913 | 0.769438 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.86761 | 1.15446 | 0.577232 | − | 0.816580i | \(-0.304133\pi\) | ||||
0.577232 | + | 0.816580i | \(0.304133\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.4417 | −1.33692 | −0.668462 | − | 0.743746i | \(-0.733047\pi\) | ||||
−0.668462 | + | 0.743746i | \(0.733047\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.38766 | −0.930758 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.26919 | −0.157424 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.71940 | −0.210058 | −0.105029 | − | 0.994469i | \(-0.533494\pi\) | ||||
−0.105029 | + | 0.994469i | \(0.533494\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 27.2992 | 3.28643 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.47808 | 0.175416 | 0.0877079 | − | 0.996146i | \(-0.472046\pi\) | ||||
0.0877079 | + | 0.996146i | \(0.472046\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.52472 | 0.997743 | 0.498872 | − | 0.866676i | \(-0.333748\pi\) | ||||
0.498872 | + | 0.866676i | \(0.333748\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −14.4206 | −1.66514 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.21848 | −0.252820 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.6421 | 1.19733 | 0.598663 | − | 0.801001i | \(-0.295699\pi\) | ||||
0.598663 | + | 0.801001i | \(0.295699\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 23.4146 | 2.60162 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.8440 | −1.19029 | −0.595144 | − | 0.803619i | \(-0.702905\pi\) | ||||
−0.595144 | + | 0.803619i | \(0.702905\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.22609 | −0.132989 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.26954 | 0.243321 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.13326 | −0.226125 | −0.113063 | − | 0.993588i | \(-0.536066\pi\) | ||||
−0.113063 | + | 0.993588i | \(0.536066\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.75046 | −0.183498 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −20.2648 | −2.10136 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.30686 | −0.134081 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.73933 | −0.582740 | −0.291370 | − | 0.956610i | \(-0.594111\pi\) | ||||
−0.291370 | + | 0.956610i | \(0.594111\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 16.3894 | 1.64720 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.40731 | 0.737055 | 0.368528 | − | 0.929617i | \(-0.379862\pi\) | ||||
0.368528 | + | 0.929617i | \(0.379862\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.6714 | 1.64268 | 0.821342 | − | 0.570436i | \(-0.193226\pi\) | ||||
0.821342 | + | 0.570436i | \(0.193226\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.33687 | 0.228055 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.4492 | −1.20351 | −0.601755 | − | 0.798680i | \(-0.705532\pi\) | ||||
−0.601755 | + | 0.798680i | \(0.705532\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.53093 | 0.242419 | 0.121210 | − | 0.992627i | \(-0.461323\pi\) | ||||
0.121210 | + | 0.992627i | \(0.461323\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −21.7712 | −2.06643 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.16568 | 0.109658 | 0.0548291 | − | 0.998496i | \(-0.482539\pi\) | ||||
0.0548291 | + | 0.998496i | \(0.482539\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.14139 | −0.572687 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 12.9318 | 1.19554 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.69102 | −0.155015 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.07833 | −0.552575 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 28.1191 | 2.53541 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.86946 | 0.614423 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.248418 | −0.0220435 | −0.0110218 | − | 0.999939i | \(-0.503508\pi\) | ||||
−0.0110218 | + | 0.999939i | \(0.503508\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −23.6389 | −2.08129 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 18.0997 | 1.58138 | 0.790690 | − | 0.612216i | \(-0.209722\pi\) | ||||
0.790690 | + | 0.612216i | \(0.209722\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.80241 | −0.156288 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −10.2534 | −0.882472 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −17.7633 | −1.51762 | −0.758812 | − | 0.651310i | \(-0.774220\pi\) | ||||
−0.758812 | + | 0.651310i | \(0.774220\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.7027 | 1.07743 | 0.538713 | − | 0.842490i | \(-0.318911\pi\) | ||||
0.538713 | + | 0.842490i | \(0.318911\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −32.7808 | −2.76064 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.88336 | 0.324743 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.510571 | −0.0424006 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.22299 | 0.265828 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.98106 | −0.653834 | −0.326917 | − | 0.945053i | \(-0.606010\pi\) | ||||
−0.326917 | + | 0.945053i | \(0.606010\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.6055 | 1.51409 | 0.757047 | − | 0.653361i | \(-0.226641\pi\) | ||||
0.757047 | + | 0.653361i | \(0.226641\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 12.4927 | 1.00997 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.55888 | 0.366178 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.3166 | 0.982970 | 0.491485 | − | 0.870886i | \(-0.336454\pi\) | ||||
0.491485 | + | 0.870886i | \(0.336454\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 42.6852 | 3.38516 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.47013 | −0.667540 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 24.8444 | 1.94596 | 0.972982 | − | 0.230882i | \(-0.0741610\pi\) | ||||
0.972982 | + | 0.230882i | \(0.0741610\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.18431 | −0.403598 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −10.4042 | −0.805101 | −0.402551 | − | 0.915398i | \(-0.631876\pi\) | ||||
−0.402551 | + | 0.915398i | \(0.631876\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.93590 | −0.764300 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 13.3156 | 1.01827 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13.1678 | 1.00113 | 0.500565 | − | 0.865699i | \(-0.333126\pi\) | ||||
0.500565 | + | 0.865699i | \(0.333126\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.47428 | 0.338224 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 28.5802 | 2.14822 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.59431 | −0.119164 | −0.0595821 | − | 0.998223i | \(-0.518977\pi\) | ||||
−0.0595821 | + | 0.998223i | \(0.518977\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.93385 | 0.441060 | 0.220530 | − | 0.975380i | \(-0.429221\pi\) | ||||
0.220530 | + | 0.975380i | \(0.429221\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −33.6535 | −2.48774 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.89778 | 0.360092 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.75149 | 0.274336 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −14.1414 | −1.02863 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.2217 | −1.17376 | −0.586881 | − | 0.809673i | \(-0.699644\pi\) | ||||
−0.586881 | + | 0.809673i | \(0.699644\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.805434 | 0.0579764 | 0.0289882 | − | 0.999580i | \(-0.490771\pi\) | ||||
0.0289882 | + | 0.999580i | \(0.490771\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.09060 | −0.292934 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.93905 | −0.708128 | −0.354064 | − | 0.935221i | \(-0.615200\pi\) | ||||
−0.354064 | + | 0.935221i | \(0.615200\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −19.4280 | −1.37722 | −0.688608 | − | 0.725134i | \(-0.741778\pi\) | ||||
−0.688608 | + | 0.725134i | \(0.741778\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.54161 | −0.390875 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.704174 | −0.0494233 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.32584 | −0.441816 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 62.5745 | 4.34923 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.99861 | 0.276590 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.4252 | 1.26844 | 0.634222 | − | 0.773151i | \(-0.281321\pi\) | ||||
0.634222 | + | 0.773151i | \(0.281321\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.76384 | 0.326413 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.31796 | 0.362682 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.28756 | 0.426828 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 27.4751 | 1.85659 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.96005 | 0.199115 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.60025 | −0.241090 | −0.120545 | − | 0.992708i | \(-0.538464\pi\) | ||||
−0.120545 | + | 0.992708i | \(0.538464\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −33.0545 | −2.20363 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.9011 | −0.723531 | −0.361765 | − | 0.932269i | \(-0.617826\pi\) | ||||
−0.361765 | + | 0.932269i | \(0.617826\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.3147 | 0.879863 | 0.439932 | − | 0.898031i | \(-0.355003\pi\) | ||||
0.439932 | + | 0.898031i | \(0.355003\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.15015 | −0.470446 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −22.3624 | −1.46501 | −0.732506 | − | 0.680760i | \(-0.761650\pi\) | ||||
−0.732506 | + | 0.680760i | \(0.761650\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.37457 | 0.481064 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 34.2992 | 2.22798 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −18.1505 | −1.17406 | −0.587029 | − | 0.809566i | \(-0.699703\pi\) | ||||
−0.587029 | + | 0.809566i | \(0.699703\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.7278 | −1.27078 | −0.635388 | − | 0.772193i | \(-0.719160\pi\) | ||||
−0.635388 | + | 0.772193i | \(0.719160\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 33.0407 | 2.11956 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.725063 | −0.0463226 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.15503 | 0.200750 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −34.9502 | −2.21488 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.38794 | −0.466322 | −0.233161 | − | 0.972438i | \(-0.574907\pi\) | ||||
−0.233161 | + | 0.972438i | \(0.574907\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 18.7909 | 1.18137 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.95169 | −0.247464 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.13863 | −0.507674 | −0.253837 | − | 0.967247i | \(-0.581693\pi\) | ||||
−0.253837 | + | 0.967247i | \(0.581693\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.75496 | 0.419733 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.20220 | 0.322008 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 18.0689 | 1.11418 | 0.557088 | − | 0.830453i | \(-0.311919\pi\) | ||||
0.557088 | + | 0.830453i | \(0.311919\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.60272 | −0.589891 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.87548 | −0.420773 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −28.5831 | −1.74274 | −0.871371 | − | 0.490624i | \(-0.836769\pi\) | ||||
−0.871371 | + | 0.490624i | \(0.836769\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.6073 | −1.19106 | −0.595528 | − | 0.803335i | \(-0.703057\pi\) | ||||
−0.595528 | + | 0.803335i | \(0.703057\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5.64171 | −0.341452 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −9.92613 | −0.598568 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −23.1932 | −1.39354 | −0.696772 | − | 0.717293i | \(-0.745381\pi\) | ||||
−0.696772 | + | 0.717293i | \(0.745381\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −46.4504 | −2.78091 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.51739 | −0.567760 | −0.283880 | − | 0.958860i | \(-0.591622\pi\) | ||||
−0.283880 | + | 0.958860i | \(0.591622\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.09510 | 0.302872 | 0.151436 | − | 0.988467i | \(-0.451610\pi\) | ||||
0.151436 | + | 0.988467i | \(0.451610\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.21199 | −0.249497 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.72453 | −0.514993 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.1405 | −0.831792 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −18.4978 | −1.08436 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.71074 | −0.158363 | −0.0791815 | − | 0.996860i | \(-0.525231\pi\) | ||||
−0.0791815 | + | 0.996860i | \(0.525231\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.42958 | −0.374344 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 31.3724 | 1.82041 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 14.8266 | 0.857445 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.33448 | 0.422752 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 23.8737 | 1.37151 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.57091 | 0.433509 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.04975 | −0.0599121 | −0.0299561 | − | 0.999551i | \(-0.509537\pi\) | ||||
−0.0299561 | + | 0.999551i | \(0.509537\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 53.7318 | 3.05670 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.41330 | −0.0801410 | −0.0400705 | − | 0.999197i | \(-0.512758\pi\) | ||||
−0.0400705 | + | 0.999197i | \(0.512758\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −26.5463 | −1.50049 | −0.750244 | − | 0.661161i | \(-0.770064\pi\) | ||||
−0.750244 | + | 0.661161i | \(0.770064\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.35652 | 0.301806 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −24.5350 | −1.37802 | −0.689011 | − | 0.724751i | \(-0.741955\pi\) | ||||
−0.689011 | + | 0.724751i | \(0.741955\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.56220 | 0.0874663 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −40.1237 | −2.23949 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.04790 | 0.169589 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.83204 | −0.434444 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.15716 | 0.451092 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 10.1709 | 0.560741 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.6727 | 1.19124 | 0.595619 | − | 0.803267i | \(-0.296907\pi\) | ||||
0.595619 | + | 0.803267i | \(0.296907\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −49.9034 | −2.73469 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.24667 | 0.0681131 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.42780 | −0.459092 | −0.229546 | − | 0.973298i | \(-0.573724\pi\) | ||||
−0.229546 | + | 0.973298i | \(0.573724\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.75698 | 0.204051 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −13.9489 | −0.755373 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −19.7936 | −1.06565 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −32.4126 | −1.74000 | −0.869999 | − | 0.493053i | \(-0.835881\pi\) | ||||
−0.869999 | + | 0.493053i | \(0.835881\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −27.3672 | −1.46493 | −0.732467 | − | 0.680803i | \(-0.761631\pi\) | ||||
−0.732467 | + | 0.680803i | \(0.761631\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 24.7539 | 1.32127 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.81238 | −0.469035 | −0.234518 | − | 0.972112i | \(-0.575351\pi\) | ||||
−0.234518 | + | 0.972112i | \(0.575351\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.07170 | −0.0568800 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5.45013 | −0.288451 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.54142 | 0.239687 | 0.119844 | − | 0.992793i | \(-0.461761\pi\) | ||||
0.119844 | + | 0.992793i | \(0.461761\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.7513 | −0.829018 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −19.5904 | −1.02823 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.18096 | −0.323526 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −15.7472 | −0.821996 | −0.410998 | − | 0.911636i | \(-0.634820\pi\) | ||||
−0.410998 | + | 0.911636i | \(0.634820\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 64.4539 | 3.35534 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −13.2440 | −0.687593 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.3575 | 0.536289 | 0.268144 | − | 0.963379i | \(-0.413590\pi\) | ||||
0.268144 | + | 0.963379i | \(0.413590\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 22.1402 | 1.14331 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.23263 | 0.0634835 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.7152 | −0.909967 | −0.454983 | − | 0.890500i | \(-0.650355\pi\) | ||||
−0.454983 | + | 0.890500i | \(0.650355\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.800648 | −0.0410184 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 27.1645 | 1.38804 | 0.694020 | − | 0.719956i | \(-0.255838\pi\) | ||||
0.694020 | + | 0.719956i | \(0.255838\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.60854 | 0.0819789 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −54.1846 | −2.75436 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 20.7629 | 1.05272 | 0.526361 | − | 0.850261i | \(-0.323556\pi\) | ||||
0.526361 | + | 0.850261i | \(0.323556\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.3231 | 0.724352 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 58.3352 | 2.94262 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.71617 | −0.388243 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 31.0965 | 1.56069 | 0.780345 | − | 0.625350i | \(-0.215044\pi\) | ||||
0.780345 | + | 0.625350i | \(0.215044\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5.80913 | −0.290820 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −21.6415 | −1.08072 | −0.540362 | − | 0.841433i | \(-0.681713\pi\) | ||||
−0.540362 | + | 0.841433i | \(0.681713\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −11.0061 | −0.548254 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −16.9770 | −0.843596 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −14.9858 | −0.742818 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −18.1632 | −0.898111 | −0.449056 | − | 0.893504i | \(-0.648239\pi\) | ||||
−0.449056 | + | 0.893504i | \(0.648239\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −57.2510 | −2.82398 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8.86761 | −0.436346 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.86262 | 0.385961 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 40.9405 | 2.00487 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 24.1668 | 1.18062 | 0.590312 | − | 0.807175i | \(-0.299005\pi\) | ||||
0.590312 | + | 0.807175i | \(0.299005\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −23.7262 | −1.15635 | −0.578173 | − | 0.815914i | \(-0.696234\pi\) | ||||
−0.578173 | + | 0.815914i | \(0.696234\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −75.1394 | −3.65340 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.56608 | −0.367009 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.4417 | 0.505310 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 12.5160 | 0.604280 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 21.8343 | 1.05172 | 0.525861 | − | 0.850571i | \(-0.323743\pi\) | ||||
0.525861 | + | 0.850571i | \(0.323743\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −35.6444 | −1.71296 | −0.856480 | − | 0.516181i | \(-0.827353\pi\) | ||||
−0.856480 | + | 0.516181i | \(0.827353\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.64556 | −0.0788987 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 15.2666 | 0.730301 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.0557759 | 0.00266204 | 0.00133102 | − | 0.999999i | \(-0.499576\pi\) | ||||
0.00133102 | + | 0.999999i | \(0.499576\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.38766 | 0.351793 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14.7541 | −0.700991 | −0.350495 | − | 0.936564i | \(-0.613987\pi\) | ||||
−0.350495 | + | 0.936564i | \(0.613987\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.54675 | 0.0733230 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −25.7229 | −1.21665 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11.0183 | −0.519986 | −0.259993 | − | 0.965611i | \(-0.583720\pi\) | ||||
−0.259993 | + | 0.965611i | \(0.583720\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19.3552 | 0.911403 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 59.9653 | 2.81742 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.26919 | 0.0595007 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 30.5056 | 1.42699 | 0.713495 | − | 0.700660i | \(-0.247111\pi\) | ||||
0.713495 | + | 0.700660i | \(0.247111\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 23.9133 | 1.11618 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.76890 | −0.454983 | −0.227492 | − | 0.973780i | \(-0.573052\pi\) | ||||
−0.227492 | + | 0.973780i | \(0.573052\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.0301 | −0.977352 | −0.488676 | − | 0.872465i | \(-0.662520\pi\) | ||||
−0.488676 | + | 0.872465i | \(0.662520\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 14.6932 | 0.681382 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.67899 | −0.262792 | −0.131396 | − | 0.991330i | \(-0.541946\pi\) | ||||
−0.131396 | + | 0.991330i | \(0.541946\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.71940 | 0.0793945 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 39.6962 | 1.82910 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −16.2714 | −0.748161 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.06447 | −0.370023 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 97.8420 | 4.47988 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −30.3538 | −1.38690 | −0.693449 | − | 0.720505i | \(-0.743910\pi\) | ||||
−0.693449 | + | 0.720505i | \(0.743910\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.8243 | −0.539141 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −27.2992 | −1.24215 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.16138 | 0.188958 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.6275 | 0.572206 | 0.286103 | − | 0.958199i | \(-0.407640\pi\) | ||||
0.286103 | + | 0.958199i | \(0.407640\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 80.0732 | 3.62104 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 27.5915 | 1.24519 | 0.622594 | − | 0.782545i | \(-0.286079\pi\) | ||||
0.622594 | + | 0.782545i | \(0.286079\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.19077 | 0.0536295 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −11.8834 | −0.534118 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.47808 | −0.0663009 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.82017 | −0.394845 | −0.197423 | − | 0.980318i | \(-0.563257\pi\) | ||||
−0.197423 | + | 0.980318i | \(0.563257\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −33.5326 | −1.49813 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 30.2244 | 1.34764 | 0.673819 | − | 0.738896i | \(-0.264653\pi\) | ||||
0.673819 | + | 0.738896i | \(0.264653\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.37077 | −0.238996 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −32.0233 | −1.42220 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.45130 | 0.285949 | 0.142974 | − | 0.989726i | \(-0.454333\pi\) | ||||
0.142974 | + | 0.989726i | \(0.454333\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.52472 | −0.377111 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 25.4885 | 1.12535 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −12.0878 | −0.532654 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −22.5640 | −0.992366 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 42.4397 | 1.86290 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −29.9742 | −1.31319 | −0.656596 | − | 0.754242i | \(-0.728004\pi\) | ||||
−0.656596 | + | 0.754242i | \(0.728004\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.07881 | 0.309535 | 0.154767 | − | 0.987951i | \(-0.450537\pi\) | ||||
0.154767 | + | 0.987951i | \(0.450537\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 14.4206 | 0.629365 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −10.6324 | −0.463153 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 48.7432 | 2.11927 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 65.5109 | 2.84293 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 15.2719 | 0.661501 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.02647 | 0.390248 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.13844 | −0.221740 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.21848 | 0.0955569 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21.6394 | 0.930351 | 0.465175 | − | 0.885218i | \(-0.345991\pi\) | ||||
0.465175 | + | 0.885218i | \(0.345991\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 19.1247 | 0.820721 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.83508 | −0.0786064 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.8782 | −0.636145 | −0.318073 | − | 0.948066i | \(-0.603036\pi\) | ||||
−0.318073 | + | 0.948066i | \(0.603036\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −77.1399 | −3.29225 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.26921 | 0.0540700 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.6421 | −0.452546 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 15.7855 | 0.670056 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −18.1723 | −0.769986 | −0.384993 | − | 0.922920i | \(-0.625796\pi\) | ||||
−0.384993 | + | 0.922920i | \(0.625796\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12.8387 | −0.543019 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.0910 | 0.510483 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.41059 | 0.228029 | 0.114015 | − | 0.993479i | \(-0.463629\pi\) | ||||
0.114015 | + | 0.993479i | \(0.463629\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.845193 | −0.0355575 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −23.4146 | −0.983319 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 23.6309 | 0.990660 | 0.495330 | − | 0.868705i | \(-0.335047\pi\) | ||||
0.495330 | + | 0.868705i | \(0.335047\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.9091 | 0.665773 | 0.332887 | − | 0.942967i | \(-0.391977\pi\) | ||||
0.332887 | + | 0.942967i | \(0.391977\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −52.2824 | −2.18413 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −37.8978 | −1.58045 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.9906 | 0.457544 | 0.228772 | − | 0.973480i | \(-0.426529\pi\) | ||||
0.228772 | + | 0.973480i | \(0.426529\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.59591 | 0.107882 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.8440 | 0.449887 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 29.3816 | 1.21686 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −9.37637 | −0.387665 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −19.7045 | −0.813291 | −0.406646 | − | 0.913586i | \(-0.633302\pi\) | ||||
−0.406646 | + | 0.913586i | \(0.633302\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11.3327 | −0.466957 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −32.0334 | −1.31768 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.05691 | 0.289792 | 0.144896 | − | 0.989447i | \(-0.453715\pi\) | ||||
0.144896 | + | 0.989447i | \(0.453715\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.22609 | 0.0502650 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −62.6163 | −2.56272 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.03378 | 0.246534 | 0.123267 | − | 0.992374i | \(-0.460663\pi\) | ||||
0.123267 | + | 0.992374i | \(0.460663\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 26.3735 | 1.07580 | 0.537900 | − | 0.843009i | \(-0.319218\pi\) | ||||
0.537900 | + | 0.843009i | \(0.319218\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −12.7023 | −0.517280 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.40717 | 0.179177 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.38950 | 0.299930 | 0.149965 | − | 0.988691i | \(-0.452084\pi\) | ||||
0.149965 | + | 0.988691i | \(0.452084\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.26954 | −0.0919666 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −17.8038 | −0.720264 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −38.9532 | −1.57330 | −0.786652 | − | 0.617397i | \(-0.788187\pi\) | ||||
−0.786652 | + | 0.617397i | \(0.788187\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −20.3881 | −0.822128 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.2102 | −0.491563 | −0.245781 | − | 0.969325i | \(-0.579045\pi\) | ||||
−0.245781 | + | 0.969325i | \(0.579045\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 47.9001 | 1.92527 | 0.962634 | − | 0.270804i | \(-0.0872896\pi\) | ||||
0.962634 | + | 0.270804i | \(0.0872896\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 119.779 | 4.80658 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.13326 | 0.0854674 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.3906 | 0.695625 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 12.8875 | 0.514676 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −11.4228 | −0.455455 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.8111 | 0.549810 | 0.274905 | − | 0.961471i | \(-0.411354\pi\) | ||||
0.274905 | + | 0.961471i | \(0.411354\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 59.3843 | 2.36031 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.180119 | 0.00714779 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.75046 | 0.0693557 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 10.9196 | 0.431971 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.42340 | 0.214212 | 0.107106 | − | 0.994248i | \(-0.465842\pi\) | ||||
0.107106 | + | 0.994248i | \(0.465842\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 29.1749 | 1.15054 | 0.575272 | − | 0.817962i | \(-0.304896\pi\) | ||||
0.575272 | + | 0.817962i | \(0.304896\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 17.1397 | 0.674876 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.72718 | 0.382415 | 0.191207 | − | 0.981550i | \(-0.438760\pi\) | ||||
0.191207 | + | 0.981550i | \(0.438760\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 19.6726 | 0.772219 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 20.2648 | 0.794238 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 22.5984 | 0.884346 | 0.442173 | − | 0.896930i | \(-0.354208\pi\) | ||||
0.442173 | + | 0.896930i | \(0.354208\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −13.1235 | −0.512776 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 62.9777 | 2.45700 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −21.0888 | −0.821502 | −0.410751 | − | 0.911748i | \(-0.634733\pi\) | ||||
−0.410751 | + | 0.911748i | \(0.634733\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.3835 | −0.831722 | −0.415861 | − | 0.909428i | \(-0.636520\pi\) | ||||
−0.415861 | + | 0.909428i | \(0.636520\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 9.54022 | 0.370511 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.30686 | 0.0506778 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.96445 | 0.230944 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −11.6036 | −0.448619 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −23.1648 | −0.894267 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.99170 | −0.385152 | −0.192576 | − | 0.981282i | \(-0.561684\pi\) | ||||
−0.192576 | + | 0.981282i | \(0.561684\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −63.2726 | −2.43536 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.11871 | 0.158295 | 0.0791475 | − | 0.996863i | \(-0.474780\pi\) | ||||
0.0791475 | + | 0.996863i | \(0.474780\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.73933 | 0.220255 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −35.1341 | −1.34634 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.28787 | −0.0875429 | −0.0437714 | − | 0.999042i | \(-0.513937\pi\) | ||||
−0.0437714 | + | 0.999042i | \(0.513937\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.8795 | 0.492102 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 42.9133 | 1.63724 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 23.1830 | 0.883203 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.67099 | 0.367902 | 0.183951 | − | 0.982935i | \(-0.441111\pi\) | ||||
0.183951 | + | 0.982935i | \(0.441111\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −16.3894 | −0.622582 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −9.21023 | −0.349364 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.7533 | 0.558822 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −72.0739 | −2.72609 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 51.4462 | 1.94310 | 0.971549 | − | 0.236840i | \(-0.0761116\pi\) | ||||
0.971549 | + | 0.236840i | \(0.0761116\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12.1752 | −0.459196 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 23.7682 | 0.895161 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7.40731 | −0.278581 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.65849 | −0.362732 | −0.181366 | − | 0.983416i | \(-0.558052\pi\) | ||||
−0.181366 | + | 0.983416i | \(0.558052\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 78.6199 | 2.94848 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −53.2565 | −1.99447 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.81569 | −0.105301 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −58.4989 | −2.18468 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 19.5159 | 0.727820 | 0.363910 | − | 0.931434i | \(-0.381441\pi\) | ||||
0.363910 | + | 0.931434i | \(0.381441\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.6714 | −0.620876 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −63.5824 | −2.36465 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.15067 | −0.117013 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −15.5192 | −0.575575 | −0.287787 | − | 0.957694i | \(-0.592920\pi\) | ||||
−0.287787 | + | 0.957694i | \(0.592920\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 36.2462 | 1.34245 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.4027 | −0.458731 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.95395 | 0.146042 | 0.0730212 | − | 0.997330i | \(-0.476736\pi\) | ||||
0.0730212 | + | 0.997330i | \(0.476736\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.33687 | −0.0861968 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.81446 | −0.140508 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 45.5632 | 1.67607 | 0.838034 | − | 0.545617i | \(-0.183705\pi\) | ||||
0.838034 | + | 0.545617i | \(0.183705\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 10.1686 | 0.373554 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −22.6814 | −0.832100 | −0.416050 | − | 0.909342i | \(-0.636586\pi\) | ||||
−0.416050 | + | 0.909342i | \(0.636586\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.78677 | 0.212011 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −80.1121 | −2.93115 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12.4492 | 0.454884 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −39.5036 | −1.44151 | −0.720753 | − | 0.693192i | \(-0.756204\pi\) | ||||
−0.720753 | + | 0.693192i | \(0.756204\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −23.8112 | −0.867730 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −13.4902 | −0.490957 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.75169 | 0.100012 | 0.0500059 | − | 0.998749i | \(-0.484076\pi\) | ||||
0.0500059 | + | 0.998749i | \(0.484076\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 60.5628 | 2.19829 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.0780 | 0.546576 | 0.273288 | − | 0.961932i | \(-0.411889\pi\) | ||||
0.273288 | + | 0.961932i | \(0.411889\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.53093 | −0.0916258 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −9.05797 | −0.327491 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 15.5224 | 0.560480 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −23.1596 | −0.835158 | −0.417579 | − | 0.908641i | \(-0.637121\pi\) | ||||
−0.417579 | + | 0.908641i | \(0.637121\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −26.2307 | −0.944677 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 14.7575 | 0.530790 | 0.265395 | − | 0.964140i | \(-0.414498\pi\) | ||||
0.265395 | + | 0.964140i | \(0.414498\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 28.1323 | 1.01054 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 21.7712 | 0.781037 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 15.7251 | 0.563412 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.27910 | 0.117335 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.95799 | 0.355870 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.93030 | −0.318736 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12.3963 | −0.441879 | −0.220940 | − | 0.975287i | \(-0.570912\pi\) | ||||
−0.220940 | + | 0.975287i | \(0.570912\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 58.2359 | 2.07325 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.16568 | −0.0414469 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −18.2778 | −0.649063 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −30.9495 | −1.09766 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −18.9843 | −0.672457 | −0.336229 | − | 0.941780i | \(-0.609152\pi\) | ||||
−0.336229 | + | 0.941780i | \(0.609152\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −17.1992 | −0.608464 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −15.7598 | −0.556846 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 18.9120 | 0.667389 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.14139 | 0.216455 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −92.1230 | −3.24288 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.90560 | 0.242788 | 0.121394 | − | 0.992604i | \(-0.461264\pi\) | ||||
0.121394 | + | 0.992604i | \(0.461264\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.8566 | −0.486572 | −0.243286 | − | 0.969955i | \(-0.578225\pi\) | ||||
−0.243286 | + | 0.969955i | \(0.578225\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −63.1940 | −2.21631 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −18.0138 | −0.630995 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −13.2197 | −0.462499 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −12.9318 | −0.451873 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 30.6552 | 1.06987 | 0.534936 | − | 0.844892i | \(-0.320336\pi\) | ||||
0.534936 | + | 0.844892i | \(0.320336\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −22.9379 | −0.799564 | −0.399782 | − | 0.916610i | \(-0.630914\pi\) | ||||
−0.399782 | + | 0.916610i | \(0.630914\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −31.9918 | −1.11381 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12.7310 | −0.442701 | −0.221350 | − | 0.975194i | \(-0.571046\pi\) | ||||
−0.221350 | + | 0.975194i | \(0.571046\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19.3666 | 0.672630 | 0.336315 | − | 0.941750i | \(-0.390819\pi\) | ||||
0.336315 | + | 0.941750i | \(0.390819\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −74.7514 | −2.59310 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.69102 | 0.0585902 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.54370 | 0.261061 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −88.9149 | −3.07335 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 26.7513 | 0.923558 | 0.461779 | − | 0.886995i | \(-0.347211\pi\) | ||||
0.461779 | + | 0.886995i | \(0.347211\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.5041 | −0.982901 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −30.6744 | −1.05648 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7.20416 | 0.247830 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.07833 | 0.208854 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 16.4214 | 0.563582 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −57.2154 | −1.96132 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −48.1783 | −1.64959 | −0.824796 | − | 0.565430i | \(-0.808710\pi\) | ||||
−0.824796 | + | 0.565430i | \(0.808710\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −9.65462 | −0.330181 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 26.2828 | 0.897802 | 0.448901 | − | 0.893581i | \(-0.351816\pi\) | ||||
0.448901 | + | 0.893581i | \(0.351816\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15.3098 | −0.522363 | −0.261181 | − | 0.965290i | \(-0.584112\pi\) | ||||
−0.261181 | + | 0.965290i | \(0.584112\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −28.1191 | −0.958296 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 25.5692 | 0.870386 | 0.435193 | − | 0.900337i | \(-0.356680\pi\) | ||||
0.435193 | + | 0.900337i | \(0.356680\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.54750 | −0.324625 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −45.5746 | −1.54779 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 23.6092 | 0.800889 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.00974 | −0.101981 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −42.4002 | −1.43503 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6.86946 | −0.232230 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 47.6643 | 1.60951 | 0.804755 | − | 0.593607i | \(-0.202297\pi\) | ||||
0.804755 | + | 0.593607i | \(0.202297\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −8.73668 | −0.294681 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −57.2434 | −1.92858 | −0.964290 | − | 0.264850i | \(-0.914678\pi\) | ||||
−0.964290 | + | 0.264850i | \(0.914678\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −25.8202 | −0.868919 | −0.434460 | − | 0.900691i | \(-0.643061\pi\) | ||||
−0.434460 | + | 0.900691i | \(0.643061\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −20.7225 | −0.696578 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 34.1175 | 1.14555 | 0.572777 | − | 0.819711i | \(-0.305866\pi\) | ||||
0.572777 | + | 0.819711i | \(0.305866\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.248418 | 0.00833167 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 51.9448 | 1.74022 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −18.3321 | −0.613461 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.15597 | 0.0386400 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 47.7860 | 1.59553 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.42754 | −0.147667 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 22.3958 | 0.746111 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 23.6389 | 0.786655 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.30242 | −0.143017 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.87794 | 0.294787 | 0.147394 | − | 0.989078i | \(-0.452912\pi\) | ||||
0.147394 | + | 0.989078i | \(0.452912\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 54.7227 | 1.81504 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.33134 | 0.143504 | 0.0717519 | − | 0.997423i | \(-0.477141\pi\) | ||||
0.0717519 | + | 0.997423i | \(0.477141\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −24.0573 | −0.796182 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 24.4010 | 0.806671 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −18.0997 | −0.597706 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.08794 | 0.266796 | 0.133398 | − | 0.991063i | \(-0.457411\pi\) | ||||
0.133398 | + | 0.991063i | \(0.457411\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.38332 | −0.111484 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.58732 | 0.0851626 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 30.2236 | 0.993746 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 123.163 | 4.04520 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −21.9875 | −0.721387 | −0.360694 | − | 0.932684i | \(-0.617460\pi\) | ||||
−0.360694 | + | 0.932684i | \(0.617460\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.80241 | 0.0590714 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4.55506 | −0.149126 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.72007 | −0.0889558 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 37.5410 | 1.22641 | 0.613205 | − | 0.789924i | \(-0.289880\pi\) | ||||
0.613205 | + | 0.789924i | \(0.289880\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −85.5586 | −2.79210 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.15697 | −0.135513 | −0.0677567 | − | 0.997702i | \(-0.521584\pi\) | ||||
−0.0677567 | + | 0.997702i | \(0.521584\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 73.8980 | 2.40645 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 10.2534 | 0.333543 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −0.495081 | −0.0160880 | −0.00804399 | − | 0.999968i | \(-0.502561\pi\) | ||||
−0.00804399 | + | 0.999968i | \(0.502561\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14.9222 | 0.484394 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −79.0760 | −2.56421 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.51461 | 0.113849 | 0.0569246 | − | 0.998378i | \(-0.481871\pi\) | ||||
0.0569246 | + | 0.998378i | \(0.481871\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 11.7618 | 0.380602 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.03495 | 0.162757 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 17.7633 | 0.573608 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.53346 | 0.275273 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −91.9706 | −2.96371 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.583991 | −0.0187993 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15.3243 | −0.492795 | −0.246398 | − | 0.969169i | \(-0.579247\pi\) | ||||
−0.246398 | + | 0.969169i | \(0.579247\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9.82334 | 0.315571 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.7915 | −0.603049 | −0.301524 | − | 0.953458i | \(-0.597495\pi\) | ||||
−0.301524 | + | 0.953458i | \(0.597495\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.7027 | −0.407229 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −25.2426 | −0.808410 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.16324 | 0.0372154 | 0.0186077 | − | 0.999827i | \(-0.494077\pi\) | ||||
0.0186077 | + | 0.999827i | \(0.494077\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.73261 | −0.151255 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 18.6977 | 0.596970 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0.537086 | 0.0171304 | 0.00856519 | − | 0.999963i | \(-0.497274\pi\) | ||||
0.00856519 | + | 0.999963i | \(0.497274\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.20644 | 0.229616 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 32.7808 | 1.04342 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −62.1240 | −1.97543 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.63276 | 0.242463 | 0.121231 | − | 0.992624i | \(-0.461316\pi\) | ||||
0.121231 | + | 0.992624i | \(0.461316\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 69.8508 | 2.21665 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 14.0866 | 0.446574 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 33.0138 | 1.04556 | 0.522779 | − | 0.852468i | \(-0.324895\pi\) | ||||
0.522779 | + | 0.852468i | \(0.324895\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −95.5245 | −3.02226 |
(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 | 3584.2.a.k.1.6 | yes | 6 | |
4.3 | odd | 2 | 3584.2.a.f.1.1 | yes | 6 | ||
8.3 | odd | 2 | 3584.2.a.l.1.6 | yes | 6 | ||
8.5 | even | 2 | 3584.2.a.e.1.1 | ✓ | 6 | ||
16.3 | odd | 4 | 3584.2.b.i.1793.1 | 12 | |||
16.5 | even | 4 | 3584.2.b.k.1793.1 | 12 | |||
16.11 | odd | 4 | 3584.2.b.i.1793.12 | 12 | |||
16.13 | even | 4 | 3584.2.b.k.1793.12 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3584.2.a.e.1.1 | ✓ | 6 | 8.5 | even | 2 | ||
3584.2.a.f.1.1 | yes | 6 | 4.3 | odd | 2 | ||
3584.2.a.k.1.6 | yes | 6 | 1.1 | even | 1 | trivial | |
3584.2.a.l.1.6 | yes | 6 | 8.3 | odd | 2 | ||
3584.2.b.i.1793.1 | 12 | 16.3 | odd | 4 | |||
3584.2.b.i.1793.12 | 12 | 16.11 | odd | 4 | |||
3584.2.b.k.1793.1 | 12 | 16.5 | even | 4 | |||
3584.2.b.k.1793.12 | 12 | 16.13 | even | 4 |