Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3344,2,Mod(1,3344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("3344.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3344 = 2^{4} \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3344.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: | \(26.7019744359\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.106392688.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{6} - 2x^{5} - 9x^{4} + 12x^{3} + 25x^{2} - 10x - 16 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1672) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-0.870457\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3344.1 |
$q$-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 | ||||||||
\(3\) | 1.87046 | 1.07991 | 0.539955 | − | 0.841694i | \(-0.318441\pi\) | ||||
0.539955 | + | 0.841694i | \(0.318441\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.83301 | 1.26696 | 0.633480 | − | 0.773759i | \(-0.281626\pi\) | ||||
0.633480 | + | 0.773759i | \(0.281626\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.83301 | 1.44874 | 0.724371 | − | 0.689411i | \(-0.242130\pi\) | ||||
0.724371 | + | 0.689411i | \(0.242130\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.498611 | 0.166204 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.12876 | 1.69981 | 0.849906 | − | 0.526934i | \(-0.176659\pi\) | ||||
0.849906 | + | 0.526934i | \(0.176659\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.29902 | 1.36820 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.70874 | −0.899502 | −0.449751 | − | 0.893154i | \(-0.648487\pi\) | ||||
−0.449751 | + | 0.893154i | \(0.648487\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 7.16948 | 1.56451 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.01807 | −0.212282 | −0.106141 | − | 0.994351i | \(-0.533850\pi\) | ||||
−0.106141 | + | 0.994351i | \(0.533850\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.02594 | 0.605188 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.67874 | −0.900424 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.56805 | −0.662571 | −0.331285 | − | 0.943531i | \(-0.607482\pi\) | ||||
−0.331285 | + | 0.943531i | \(0.607482\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.29902 | 0.951733 | 0.475866 | − | 0.879518i | \(-0.342135\pi\) | ||||
0.475866 | + | 0.879518i | \(0.342135\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.87046 | 0.325605 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 10.8590 | 1.83550 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.68789 | 0.277488 | 0.138744 | − | 0.990328i | \(-0.455693\pi\) | ||||
0.138744 | + | 0.990328i | \(0.455693\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 11.4636 | 1.83564 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.71110 | −1.04810 | −0.524049 | − | 0.851688i | \(-0.675579\pi\) | ||||
−0.524049 | + | 0.851688i | \(0.675579\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.59858 | 0.548778 | 0.274389 | − | 0.961619i | \(-0.411524\pi\) | ||||
0.274389 | + | 0.961619i | \(0.411524\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.41257 | 0.210573 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.48461 | 0.945877 | 0.472939 | − | 0.881095i | \(-0.343193\pi\) | ||||
0.472939 | + | 0.881095i | \(0.343193\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.69196 | 1.09885 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.93704 | −0.971380 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.34969 | −0.872197 | −0.436098 | − | 0.899899i | \(-0.643640\pi\) | ||||
−0.436098 | + | 0.899899i | \(0.643640\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.83301 | 0.382003 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.87046 | −0.247748 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.8133 | −1.40777 | −0.703884 | − | 0.710315i | \(-0.748553\pi\) | ||||
−0.703884 | + | 0.710315i | \(0.748553\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.743693 | −0.0952202 | −0.0476101 | − | 0.998866i | \(-0.515160\pi\) | ||||
−0.0476101 | + | 0.998866i | \(0.515160\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.91118 | 0.240786 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 17.3628 | 2.15359 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.07574 | −0.253592 | −0.126796 | − | 0.991929i | \(-0.540469\pi\) | ||||
−0.126796 | + | 0.991929i | \(0.540469\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.90426 | −0.229245 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.65687 | 0.315313 | 0.157656 | − | 0.987494i | \(-0.449606\pi\) | ||||
0.157656 | + | 0.987494i | \(0.449606\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.0837 | −1.29725 | −0.648623 | − | 0.761110i | \(-0.724655\pi\) | ||||
−0.648623 | + | 0.761110i | \(0.724655\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.65990 | 0.653548 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.83301 | 0.436812 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.81581 | 0.204295 | 0.102147 | − | 0.994769i | \(-0.467429\pi\) | ||||
0.102147 | + | 0.994769i | \(0.467429\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.2472 | −1.13858 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.1416 | −1.33272 | −0.666358 | − | 0.745632i | \(-0.732148\pi\) | ||||
−0.666358 | + | 0.745632i | \(0.732148\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.5069 | −1.13963 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.67389 | −0.715516 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.51341 | −0.160421 | −0.0802104 | − | 0.996778i | \(-0.525559\pi\) | ||||
−0.0802104 | + | 0.996778i | \(0.525559\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 23.4916 | 2.46259 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.91160 | 1.02778 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.83301 | −0.290661 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.3901 | −1.35955 | −0.679777 | − | 0.733419i | \(-0.737923\pi\) | ||||
−0.679777 | + | 0.733419i | \(0.737923\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.498611 | 0.0501123 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −18.4417 | −1.83502 | −0.917509 | − | 0.397715i | \(-0.869803\pi\) | ||||
−0.917509 | + | 0.397715i | \(0.869803\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.4662 | 1.32686 | 0.663431 | − | 0.748237i | \(-0.269100\pi\) | ||||
0.663431 | + | 0.748237i | \(0.269100\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 20.3112 | 1.98217 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.3720 | 1.58274 | 0.791370 | − | 0.611338i | \(-0.209368\pi\) | ||||
0.791370 | + | 0.611338i | \(0.209368\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.60741 | 0.728658 | 0.364329 | − | 0.931270i | \(-0.381298\pi\) | ||||
0.364329 | + | 0.931270i | \(0.381298\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.15713 | 0.299662 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.0046 | −0.941150 | −0.470575 | − | 0.882360i | \(-0.655953\pi\) | ||||
−0.470575 | + | 0.882360i | \(0.655953\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.88420 | −0.268953 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.05586 | 0.282515 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −14.2156 | −1.30315 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −12.5528 | −1.13185 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.59253 | −0.500211 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.6361 | 1.83116 | 0.915578 | − | 0.402140i | \(-0.131734\pi\) | ||||
0.915578 | + | 0.402140i | \(0.131734\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.73099 | 0.592630 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.06512 | −0.529912 | −0.264956 | − | 0.964261i | \(-0.585357\pi\) | ||||
−0.264956 | + | 0.964261i | \(0.585357\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.83301 | −0.332364 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −13.2549 | −1.14080 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.2035 | 0.871748 | 0.435874 | − | 0.900008i | \(-0.356439\pi\) | ||||
0.435874 | + | 0.900008i | \(0.356439\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 21.7492 | 1.84474 | 0.922372 | − | 0.386304i | \(-0.126248\pi\) | ||||
0.922372 | + | 0.386304i | \(0.126248\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.1292 | 1.02146 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.12876 | 0.512513 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.1083 | −0.839451 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 14.3875 | 1.18666 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 11.6216 | 0.952075 | 0.476038 | − | 0.879425i | \(-0.342073\pi\) | ||||
0.476038 | + | 0.879425i | \(0.342073\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.2317 | −1.56506 | −0.782528 | − | 0.622616i | \(-0.786070\pi\) | ||||
−0.782528 | + | 0.622616i | \(0.786070\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.84922 | −0.149500 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 15.0122 | 1.20581 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.03393 | −0.401752 | −0.200876 | − | 0.979617i | \(-0.564379\pi\) | ||||
−0.200876 | + | 0.979617i | \(0.564379\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −11.8768 | −0.941893 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.90227 | −0.307542 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.3585 | −1.04632 | −0.523158 | − | 0.852236i | \(-0.675246\pi\) | ||||
−0.523158 | + | 0.852236i | \(0.675246\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.29902 | 0.412528 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.88619 | 0.532869 | 0.266435 | − | 0.963853i | \(-0.414154\pi\) | ||||
0.266435 | + | 0.963853i | \(0.414154\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 24.5617 | 1.88936 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.498611 | −0.0381297 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −14.3759 | −1.09298 | −0.546490 | − | 0.837465i | \(-0.684036\pi\) | ||||
−0.546490 | + | 0.837465i | \(0.684036\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 11.5985 | 0.876761 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −20.2258 | −1.52026 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.40313 | 0.179619 | 0.0898094 | − | 0.995959i | \(-0.471374\pi\) | ||||
0.0898094 | + | 0.995959i | \(0.471374\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.94819 | −0.516455 | −0.258227 | − | 0.966084i | \(-0.583138\pi\) | ||||
−0.258227 | + | 0.966084i | \(0.583138\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.39105 | −0.102829 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.78182 | 0.351566 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.70874 | −0.271210 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −17.9337 | −1.30448 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.1886 | −1.09901 | −0.549504 | − | 0.835491i | \(-0.685183\pi\) | ||||
−0.549504 | + | 0.835491i | \(0.685183\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.9331 | −0.786983 | −0.393491 | − | 0.919328i | \(-0.628733\pi\) | ||||
−0.393491 | + | 0.919328i | \(0.628733\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 32.4764 | 2.32569 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.3440 | −0.879470 | −0.439735 | − | 0.898128i | \(-0.644928\pi\) | ||||
−0.439735 | + | 0.898128i | \(0.644928\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.9921 | −0.920982 | −0.460491 | − | 0.887664i | \(-0.652327\pi\) | ||||
−0.460491 | + | 0.887664i | \(0.652327\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.88258 | −0.273856 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −13.6764 | −0.959894 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −19.0126 | −1.32790 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.507620 | −0.0352820 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.00000 | −0.0691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.42821 | 0.649065 | 0.324532 | − | 0.945875i | \(-0.394793\pi\) | ||||
0.324532 | + | 0.945875i | \(0.394793\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.96957 | 0.340509 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 10.1948 | 0.695280 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 20.3112 | 1.37881 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −20.7316 | −1.40091 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −22.7300 | −1.52898 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.9595 | −0.733900 | −0.366950 | − | 0.930241i | \(-0.619598\pi\) | ||||
−0.366950 | + | 0.930241i | \(0.619598\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.50877 | 0.100584 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 19.1738 | 1.27261 | 0.636306 | − | 0.771437i | \(-0.280462\pi\) | ||||
0.636306 | + | 0.771437i | \(0.280462\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.44137 | 0.293494 | 0.146747 | − | 0.989174i | \(-0.453120\pi\) | ||||
0.146747 | + | 0.989174i | \(0.453120\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7.16948 | 0.471717 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 24.9949 | 1.63747 | 0.818736 | − | 0.574170i | \(-0.194675\pi\) | ||||
0.818736 | + | 0.574170i | \(0.194675\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 18.3710 | 1.19839 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.39640 | 0.220620 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.50862 | 0.550377 | 0.275188 | − | 0.961390i | \(-0.411260\pi\) | ||||
0.275188 | + | 0.961390i | \(0.411260\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.4857 | 1.31960 | 0.659800 | − | 0.751442i | \(-0.270641\pi\) | ||||
0.659800 | + | 0.751442i | \(0.270641\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.13076 | −0.329138 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 21.7914 | 1.39220 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.12876 | −0.389964 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −22.7104 | −1.43921 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.0342 | −0.885828 | −0.442914 | − | 0.896564i | \(-0.646055\pi\) | ||||
−0.442914 | + | 0.896564i | \(0.646055\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.01807 | −0.0640055 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −19.6527 | −1.23070 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 16.4673 | 1.02720 | 0.513601 | − | 0.858029i | \(-0.328311\pi\) | ||||
0.513601 | + | 0.858029i | \(0.328311\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.46971 | 0.402008 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.77907 | −0.110122 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 27.0368 | 1.66716 | 0.833580 | − | 0.552399i | \(-0.186288\pi\) | ||||
0.833580 | + | 0.552399i | \(0.186288\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −17.9887 | −1.10504 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.83076 | −0.173240 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.69523 | 0.164331 | 0.0821657 | − | 0.996619i | \(-0.473816\pi\) | ||||
0.0821657 | + | 0.996619i | \(0.473816\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.753780 | −0.0457889 | −0.0228944 | − | 0.999738i | \(-0.507288\pi\) | ||||
−0.0228944 | + | 0.999738i | \(0.507288\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 43.9400 | 2.65937 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.02594 | 0.182471 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.0493 | 0.723972 | 0.361986 | − | 0.932184i | \(-0.382099\pi\) | ||||
0.361986 | + | 0.932184i | \(0.382099\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.64215 | 0.158181 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 30.3906 | 1.81295 | 0.906475 | − | 0.422258i | \(-0.138763\pi\) | ||||
0.906475 | + | 0.422258i | \(0.138763\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.49645 | −0.564505 | −0.282253 | − | 0.959340i | \(-0.591082\pi\) | ||||
−0.282253 | + | 0.959340i | \(0.591082\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.29902 | −0.313887 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −25.7237 | −1.51842 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.24523 | −0.190896 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −25.0455 | −1.46819 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −17.9766 | −1.05020 | −0.525101 | − | 0.851040i | \(-0.675972\pi\) | ||||
−0.525101 | + | 0.851040i | \(0.675972\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −30.6341 | −1.78359 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.67874 | −0.271488 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.23950 | −0.360840 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 13.7934 | 0.795037 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −34.4944 | −1.98165 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.10689 | −0.120640 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.4216 | −0.651867 | −0.325933 | − | 0.945393i | \(-0.605679\pi\) | ||||
−0.325933 | + | 0.945393i | \(0.605679\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 25.1879 | 1.43289 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −25.6594 | −1.45501 | −0.727507 | − | 0.686101i | \(-0.759321\pi\) | ||||
−0.727507 | + | 0.686101i | \(0.759321\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.6229 | −0.656962 | −0.328481 | − | 0.944511i | \(-0.606537\pi\) | ||||
−0.328481 | + | 0.944511i | \(0.606537\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.41439 | 0.305066 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 30.1542 | 1.69363 | 0.846813 | − | 0.531890i | \(-0.178518\pi\) | ||||
0.846813 | + | 0.531890i | \(0.178518\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.56805 | −0.199773 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 30.6231 | 1.70921 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.70874 | 0.206360 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 18.5453 | 1.02871 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 14.2293 | 0.786884 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 24.8556 | 1.37033 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 25.4171 | 1.39705 | 0.698526 | − | 0.715585i | \(-0.253840\pi\) | ||||
0.698526 | + | 0.715585i | \(0.253840\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.841602 | 0.0461195 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.88058 | −0.321291 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.43868 | −0.514158 | −0.257079 | − | 0.966390i | \(-0.582760\pi\) | ||||
−0.257079 | + | 0.966390i | \(0.582760\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −18.7131 | −1.01636 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.29902 | 0.286958 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.65229 | 0.143210 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.39477 | −0.290445 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 35.1560 | 1.88727 | 0.943636 | − | 0.330985i | \(-0.107381\pi\) | ||||
0.943636 | + | 0.330985i | \(0.107381\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.5526 | 1.15368 | 0.576841 | − | 0.816856i | \(-0.304285\pi\) | ||||
0.576841 | + | 0.816856i | \(0.304285\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −28.6749 | −1.53055 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.48984 | 0.451869 | 0.225934 | − | 0.974143i | \(-0.427457\pi\) | ||||
0.225934 | + | 0.974143i | \(0.427457\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.52695 | 0.399489 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −26.5898 | −1.40728 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.61783 | 0.138164 | 0.0690820 | − | 0.997611i | \(-0.477993\pi\) | ||||
0.0690820 | + | 0.997611i | \(0.477993\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.87046 | 0.0981735 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −31.4002 | −1.64356 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.37102 | 0.228166 | 0.114083 | − | 0.993471i | \(-0.463607\pi\) | ||||
0.114083 | + | 0.993471i | \(0.463607\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.34622 | −0.174197 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −24.3384 | −1.26359 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.66161 | −0.137813 | −0.0689066 | − | 0.997623i | \(-0.521951\pi\) | ||||
−0.0689066 | + | 0.997623i | \(0.521951\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −10.4606 | −0.540182 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −21.8677 | −1.12625 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.7952 | −0.914078 | −0.457039 | − | 0.889447i | \(-0.651090\pi\) | ||||
−0.457039 | + | 0.889447i | \(0.651090\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 38.5989 | 1.97748 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 32.3374 | 1.65236 | 0.826181 | − | 0.563405i | \(-0.190509\pi\) | ||||
0.826181 | + | 0.563405i | \(0.190509\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10.8590 | 0.553423 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.79429 | 0.0912088 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.1909 | 0.668804 | 0.334402 | − | 0.942431i | \(-0.391466\pi\) | ||||
0.334402 | + | 0.942431i | \(0.391466\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.77576 | 0.190948 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −11.3445 | −0.572256 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.14421 | 0.258833 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 30.8885 | 1.55025 | 0.775124 | − | 0.631809i | \(-0.217687\pi\) | ||||
0.775124 | + | 0.631809i | \(0.217687\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7.16948 | −0.358923 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −26.8786 | −1.34225 | −0.671126 | − | 0.741343i | \(-0.734189\pi\) | ||||
−0.671126 | + | 0.741343i | \(0.734189\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 32.4764 | 1.61777 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −29.0305 | −1.44254 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.68789 | 0.0836658 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 28.5926 | 1.41381 | 0.706906 | − | 0.707307i | \(-0.250090\pi\) | ||||
0.706906 | + | 0.707307i | \(0.250090\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 19.0853 | 0.941408 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −41.4474 | −2.03949 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −34.3973 | −1.68850 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 40.6810 | 1.99216 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −17.3779 | −0.848965 | −0.424482 | − | 0.905436i | \(-0.639544\pi\) | ||||
−0.424482 | + | 0.905436i | \(0.639544\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.93888 | 0.435654 | 0.217827 | − | 0.975987i | \(-0.430103\pi\) | ||||
0.217827 | + | 0.975987i | \(0.430103\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.23329 | 0.157208 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −11.2224 | −0.544368 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.85058 | −0.137949 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 11.4636 | 0.553467 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.0145 | 0.626887 | 0.313444 | − | 0.949607i | \(-0.398517\pi\) | ||||
0.313444 | + | 0.949607i | \(0.398517\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.00494 | −0.240522 | −0.120261 | − | 0.992742i | \(-0.538373\pi\) | ||||
−0.120261 | + | 0.992742i | \(0.538373\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −18.9072 | −0.906531 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.01807 | 0.0487009 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −24.6582 | −1.17687 | −0.588437 | − | 0.808543i | \(-0.700256\pi\) | ||||
−0.588437 | + | 0.808543i | \(0.700256\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.83529 | 0.182633 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.81103 | −0.466136 | −0.233068 | − | 0.972460i | \(-0.574877\pi\) | ||||
−0.233068 | + | 0.972460i | \(0.574877\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.28749 | −0.203247 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 21.7376 | 1.02815 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −19.6064 | −0.925285 | −0.462642 | − | 0.886545i | \(-0.653099\pi\) | ||||
−0.462642 | + | 0.886545i | \(0.653099\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.71110 | −0.316013 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −35.9721 | −1.69012 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 66.5519 | 3.12000 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 25.8767 | 1.21046 | 0.605230 | − | 0.796051i | \(-0.293081\pi\) | ||||
0.605230 | + | 0.796051i | \(0.293081\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 17.3522 | 0.809934 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −34.2353 | −1.59450 | −0.797249 | − | 0.603650i | \(-0.793712\pi\) | ||||
−0.797249 | + | 0.603650i | \(0.793712\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.5544 | 1.00172 | 0.500859 | − | 0.865529i | \(-0.333018\pi\) | ||||
0.500859 | + | 0.865529i | \(0.333018\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 28.0796 | 1.30216 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.66020 | −0.308198 | −0.154099 | − | 0.988055i | \(-0.549247\pi\) | ||||
−0.154099 | + | 0.988055i | \(0.549247\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.95632 | −0.367389 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.41576 | −0.433855 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.59858 | 0.165463 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.02594 | −0.138840 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.16602 | −0.144962 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.06349 | 0.368430 | 0.184215 | − | 0.982886i | \(-0.441026\pi\) | ||||
0.184215 | + | 0.982886i | \(0.441026\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.3447 | 0.471677 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −7.29903 | −0.332117 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −37.9341 | −1.72250 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −23.8768 | −1.08196 | −0.540981 | − | 0.841035i | \(-0.681947\pi\) | ||||
−0.540981 | + | 0.841035i | \(0.681947\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −24.9865 | −1.12993 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.42952 | −0.109643 | −0.0548214 | − | 0.998496i | \(-0.517459\pi\) | ||||
−0.0548214 | + | 0.998496i | \(0.517459\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.2330 | 0.595984 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.41257 | 0.0634902 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10.1838 | 0.456807 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −30.9479 | −1.38542 | −0.692709 | − | 0.721217i | \(-0.743583\pi\) | ||||
−0.692709 | + | 0.721217i | \(0.743583\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12.8803 | 0.575450 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 10.1030 | 0.450472 | 0.225236 | − | 0.974304i | \(-0.427685\pi\) | ||||
0.225236 | + | 0.974304i | \(0.427685\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −52.2455 | −2.32490 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 45.9416 | 2.04034 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 30.0363 | 1.33134 | 0.665668 | − | 0.746248i | \(-0.268147\pi\) | ||||
0.665668 | + | 0.746248i | \(0.268147\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −42.4839 | −1.87937 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.67874 | 0.206572 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 38.1498 | 1.68108 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.48461 | 0.285193 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −26.8895 | −1.18032 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −26.3804 | −1.15574 | −0.577872 | − | 0.816127i | \(-0.696117\pi\) | ||||
−0.577872 | + | 0.816127i | \(0.696117\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −22.2738 | −0.973965 | −0.486982 | − | 0.873412i | \(-0.661902\pi\) | ||||
−0.486982 | + | 0.873412i | \(0.661902\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 21.6944 | 0.946823 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −19.6527 | −0.856085 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.9635 | −0.954936 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.39161 | −0.233976 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −41.1307 | −1.78157 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 46.3820 | 2.00527 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.49496 | 0.193972 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.69196 | 0.331316 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 25.9664 | 1.11638 | 0.558192 | − | 0.829712i | \(-0.311495\pi\) | ||||
0.558192 | + | 0.829712i | \(0.311495\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −12.9963 | −0.557724 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 21.5519 | 0.923180 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.05138 | 0.387009 | 0.193505 | − | 0.981099i | \(-0.438015\pi\) | ||||
0.193505 | + | 0.981099i | \(0.438015\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.370813 | −0.0158259 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.56805 | 0.152004 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.96002 | 0.295970 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8.94419 | 0.379660 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.46486 | 0.401039 | 0.200519 | − | 0.979690i | \(-0.435737\pi\) | ||||
0.200519 | + | 0.979690i | \(0.435737\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 22.0548 | 0.932819 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.93704 | −0.292882 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 14.9480 | 0.629982 | 0.314991 | − | 0.949095i | \(-0.397999\pi\) | ||||
0.314991 | + | 0.949095i | \(0.397999\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −28.3430 | −1.19240 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −39.2777 | −1.64951 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −37.8266 | −1.58577 | −0.792887 | − | 0.609369i | \(-0.791423\pi\) | ||||
−0.792887 | + | 0.609369i | \(0.791423\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.6033 | −0.904071 | −0.452035 | − | 0.892000i | \(-0.649302\pi\) | ||||
−0.452035 | + | 0.892000i | \(0.649302\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −28.4096 | −1.18683 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.08062 | −0.128471 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −27.5079 | −1.14517 | −0.572584 | − | 0.819846i | \(-0.694059\pi\) | ||||
−0.572584 | + | 0.819846i | \(0.694059\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −20.4499 | −0.849870 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −46.5389 | −1.93076 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.34969 | −0.262977 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 8.65729 | 0.357935 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 16.4534 | 0.679106 | 0.339553 | − | 0.940587i | \(-0.389724\pi\) | ||||
0.339553 | + | 0.940587i | \(0.389724\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.29902 | −0.218342 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −23.0888 | −0.949748 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −0.937222 | −0.0384871 | −0.0192435 | − | 0.999815i | \(-0.506126\pi\) | ||||
−0.0192435 | + | 0.999815i | \(0.506126\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −40.2730 | −1.65103 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −24.3011 | −0.994577 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.50619 | −0.388412 | −0.194206 | − | 0.980961i | \(-0.562213\pi\) | ||||
−0.194206 | + | 0.980961i | \(0.562213\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −33.0715 | −1.34901 | −0.674507 | − | 0.738268i | \(-0.735644\pi\) | ||||
−0.674507 | + | 0.738268i | \(0.735644\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.03498 | −0.0421478 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.83301 | 0.115178 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.8867 | 0.685411 | 0.342705 | − | 0.939443i | \(-0.388657\pi\) | ||||
0.342705 | + | 0.939443i | \(0.388657\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −25.5811 | −1.03660 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 39.7426 | 1.60781 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12.5772 | −0.507987 | −0.253993 | − | 0.967206i | \(-0.581744\pi\) | ||||
−0.253993 | + | 0.967206i | \(0.581744\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −35.5623 | −1.43401 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −21.2054 | −0.853696 | −0.426848 | − | 0.904323i | \(-0.640376\pi\) | ||||
−0.426848 | + | 0.904323i | \(0.640376\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.83787 | −0.114064 | −0.0570319 | − | 0.998372i | \(-0.518164\pi\) | ||||
−0.0570319 | + | 0.998372i | \(0.518164\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.76328 | 0.191144 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.80090 | −0.232408 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.9734 | −1.23894 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.87046 | −0.0746989 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.25996 | −0.249601 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21.1498 | −0.841962 | −0.420981 | − | 0.907070i | \(-0.638314\pi\) | ||||
−0.420981 | + | 0.907070i | \(0.638314\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 17.6351 | 0.700931 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 58.4622 | 2.32000 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 47.1422 | 1.86784 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.32475 | 0.0524061 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 35.8882 | 1.41750 | 0.708749 | − | 0.705461i | \(-0.249260\pi\) | ||||
0.708749 | + | 0.705461i | \(0.249260\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.9922 | 0.946162 | 0.473081 | − | 0.881019i | \(-0.343142\pi\) | ||||
0.473081 | + | 0.881019i | \(0.343142\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 19.0689 | 0.750839 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.96962 | −0.156062 | −0.0780310 | − | 0.996951i | \(-0.524863\pi\) | ||||
−0.0780310 | + | 0.996951i | \(0.524863\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.8133 | −0.424458 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 37.9912 | 1.48899 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9.43621 | −0.369268 | −0.184634 | − | 0.982807i | \(-0.559110\pi\) | ||||
−0.184634 | + | 0.982807i | \(0.559110\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −17.1825 | −0.671377 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.52644 | −0.215607 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 31.8841 | 1.24203 | 0.621014 | − | 0.783799i | \(-0.286721\pi\) | ||||
0.621014 | + | 0.783799i | \(0.286721\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −27.9815 | −1.08835 | −0.544177 | − | 0.838970i | \(-0.683158\pi\) | ||||
−0.544177 | + | 0.838970i | \(0.683158\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −42.5155 | −1.65116 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −10.8590 | −0.421092 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.63253 | 0.140652 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −20.4992 | −0.792545 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.743693 | −0.0287100 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 33.3736 | 1.28646 | 0.643228 | − | 0.765675i | \(-0.277595\pi\) | ||||
0.643228 | + | 0.765675i | \(0.277595\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −14.1576 | −0.544926 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18.6319 | 0.716081 | 0.358040 | − | 0.933706i | \(-0.383445\pi\) | ||||
0.358040 | + | 0.933706i | \(0.383445\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −51.3242 | −1.96964 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 35.8638 | 1.37431 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 38.0254 | 1.45500 | 0.727501 | − | 0.686106i | \(-0.240681\pi\) | ||||
0.727501 | + | 0.686106i | \(0.240681\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 28.9067 | 1.10447 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.30739 | 0.316947 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −38.9157 | −1.48257 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.7840 | −0.638495 | −0.319247 | − | 0.947671i | \(-0.603430\pi\) | ||||
−0.319247 | + | 0.947671i | \(0.603430\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.91118 | 0.0725997 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 61.6157 | 2.33722 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 24.8897 | 0.942766 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 46.7520 | 1.76832 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −31.4816 | −1.18904 | −0.594522 | − | 0.804079i | \(-0.702659\pi\) | ||||
−0.594522 | + | 0.804079i | \(0.702659\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.68789 | −0.0636601 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 34.3621 | 1.29415 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −70.6872 | −2.65847 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 38.9461 | 1.46265 | 0.731326 | − | 0.682028i | \(-0.238902\pi\) | ||||
0.731326 | + | 0.682028i | \(0.238902\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.905382 | 0.0339545 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.39477 | −0.202036 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 17.3628 | 0.649333 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 15.9150 | 0.594357 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −28.0860 | −1.04743 | −0.523715 | − | 0.851894i | \(-0.675454\pi\) | ||||
−0.523715 | + | 0.851894i | \(0.675454\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 51.6160 | 1.92228 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 38.3176 | 1.42505 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −10.7967 | −0.400980 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −44.4663 | −1.64916 | −0.824582 | − | 0.565742i | \(-0.808590\pi\) | ||||
−0.824582 | + | 0.565742i | \(0.808590\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 21.1448 | 0.783140 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −13.3462 | −0.493627 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 27.3248 | 1.00926 | 0.504631 | − | 0.863335i | \(-0.331628\pi\) | ||||
0.504631 | + | 0.863335i | \(0.331628\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 40.7599 | 1.50345 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.07574 | −0.0764608 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 32.4957 | 1.19538 | 0.597688 | − | 0.801729i | \(-0.296086\pi\) | ||||
0.597688 | + | 0.801729i | \(0.296086\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −11.4636 | −0.421125 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.71370 | −0.136242 | −0.0681212 | − | 0.997677i | \(-0.521700\pi\) | ||||
−0.0681212 | + | 0.997677i | \(0.521700\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 32.9240 | 1.20624 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.05394 | −0.221502 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 62.7540 | 2.29298 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.8240 | −0.394974 | −0.197487 | − | 0.980305i | \(-0.563278\pi\) | ||||
−0.197487 | + | 0.980305i | \(0.563278\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −26.2503 | −0.956614 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −54.4837 | −1.98286 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16.0604 | 0.583724 | 0.291862 | − | 0.956461i | \(-0.405725\pi\) | ||||
0.291862 | + | 0.956461i | \(0.405725\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.90426 | −0.0691201 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24.4280 | −0.885515 | −0.442757 | − | 0.896641i | \(-0.646000\pi\) | ||||
−0.442757 | + | 0.896641i | \(0.646000\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 29.1593 | 1.05564 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.23885 | −0.189411 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −66.2719 | −2.39294 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −29.2657 | −1.05535 | −0.527674 | − | 0.849447i | \(-0.676936\pi\) | ||||
−0.527674 | + | 0.849447i | \(0.676936\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 30.8014 | 1.10928 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 17.0485 | 0.613194 | 0.306597 | − | 0.951839i | \(-0.400810\pi\) | ||||
0.306597 | + | 0.951839i | \(0.400810\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 16.0345 | 0.575978 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 12.1013 | 0.434132 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.71110 | 0.240450 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.65687 | 0.0950704 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 16.6940 | 0.596595 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −14.2612 | −0.509003 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −37.5808 | −1.33961 | −0.669806 | − | 0.742536i | \(-0.733623\pi\) | ||||
−0.669806 | + | 0.742536i | \(0.733623\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 50.5712 | 1.80038 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −38.3476 | −1.36348 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.55792 | −0.161856 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −33.6472 | −1.19334 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 17.4740 | 0.618959 | 0.309480 | − | 0.950906i | \(-0.399845\pi\) | ||||
0.309480 | + | 0.950906i | \(0.399845\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −24.0497 | −0.850819 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.754600 | −0.0266625 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −11.0837 | −0.391135 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11.0552 | −0.389643 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.04132 | 0.177463 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −36.0380 | −1.26703 | −0.633514 | − | 0.773731i | \(-0.718388\pi\) | ||||
−0.633514 | + | 0.773731i | \(0.718388\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 51.5131 | 1.80887 | 0.904435 | − | 0.426611i | \(-0.140293\pi\) | ||||
0.904435 | + | 0.426611i | \(0.140293\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.40991 | −0.0494478 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −37.8447 | −1.32564 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.59858 | −0.125898 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 11.7132 | 0.409291 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 39.3130 | 1.37203 | 0.686017 | − | 0.727586i | \(-0.259358\pi\) | ||||
0.686017 | + | 0.727586i | \(0.259358\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.3573 | 0.849040 | 0.424520 | − | 0.905418i | \(-0.360443\pi\) | ||||
0.424520 | + | 0.905418i | \(0.360443\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.65990 | 0.197052 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.290693 | 0.0101084 | 0.00505420 | − | 0.999987i | \(-0.498391\pi\) | ||||
0.00505420 | + | 0.999987i | \(0.498391\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −44.2644 | −1.53737 | −0.768684 | − | 0.639629i | \(-0.779088\pi\) | ||||
−0.768684 | + | 0.639629i | \(0.779088\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 22.5377 | 0.781824 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −28.5275 | −0.988419 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 19.5086 | 0.675124 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −24.7928 | −0.856963 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −14.9485 | −0.516080 | −0.258040 | − | 0.966134i | \(-0.583077\pi\) | ||||
−0.258040 | + | 0.966134i | \(0.583077\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.2690 | −0.561000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 56.8443 | 1.95782 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 69.5835 | 2.39374 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.83301 | 0.131704 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −17.7627 | −0.609614 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.71839 | −0.0589058 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.52071 | 0.189026 | 0.0945128 | − | 0.995524i | \(-0.469871\pi\) | ||||
0.0945128 | + | 0.995524i | \(0.469871\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.41257 | −0.0483088 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −30.5165 | −1.04242 | −0.521212 | − | 0.853427i | \(-0.674520\pi\) | ||||
−0.521212 | + | 0.853427i | \(0.674520\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −55.2698 | −1.88578 | −0.942891 | − | 0.333101i | \(-0.891905\pi\) | ||||
−0.942891 | + | 0.333101i | \(0.891905\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −48.1151 | −1.63976 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 21.7474 | 0.740291 | 0.370145 | − | 0.928974i | \(-0.379308\pi\) | ||||
0.370145 | + | 0.928974i | \(0.379308\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −40.7271 | −1.38476 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6.07007 | −0.206150 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.81581 | 0.0615972 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.7217 | −0.431058 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.67642 | −0.225963 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −21.4362 | −0.724676 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −38.7805 | −1.30952 | −0.654762 | − | 0.755835i | \(-0.727231\pi\) | ||||
−0.654762 | + | 0.755835i | \(0.727231\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −33.6244 | −1.13412 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −51.5855 | −1.73796 | −0.868979 | − | 0.494849i | \(-0.835223\pi\) | ||||
−0.868979 | + | 0.494849i | \(0.835223\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.82960 | 0.263487 | 0.131743 | − | 0.991284i | \(-0.457942\pi\) | ||||
0.131743 | + | 0.991284i | \(0.457942\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −57.2998 | −1.92611 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −26.0841 | −0.875820 | −0.437910 | − | 0.899019i | \(-0.644281\pi\) | ||||
−0.437910 | + | 0.899019i | \(0.644281\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 79.0983 | 2.65287 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −10.2472 | −0.343295 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.48461 | −0.216999 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.80810 | 0.227570 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −11.6707 | −0.389674 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −18.9072 | −0.630590 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 23.5494 | 0.784543 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 25.7999 | 0.858568 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −19.6843 | −0.654328 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 52.5096 | 1.74355 | 0.871777 | − | 0.489903i | \(-0.162968\pi\) | ||||
0.871777 | + | 0.489903i | \(0.162968\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −9.19523 | −0.304987 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10.2679 | 0.340190 | 0.170095 | − | 0.985428i | \(-0.445592\pi\) | ||||
0.170095 | + | 0.985428i | \(0.445592\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12.1416 | −0.401829 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.94085 | −0.130280 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −23.2476 | −0.767705 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18.6639 | 0.615665 | 0.307833 | − | 0.951441i | \(-0.400396\pi\) | ||||
0.307833 | + | 0.951441i | \(0.400396\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −21.3637 | −0.703957 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 16.2833 | 0.535973 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.10747 | 0.167933 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.71438 | 0.220529 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −24.0742 | −0.789849 | −0.394925 | − | 0.918713i | \(-0.629229\pi\) | ||||
−0.394925 | + | 0.918713i | \(0.629229\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.69196 | −0.252094 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −47.9949 | −1.57128 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −10.5069 | −0.343612 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.95255 | 0.325136 | 0.162568 | − | 0.986697i | \(-0.448022\pi\) | ||||
0.162568 | + | 0.986697i | \(0.448022\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −21.7400 | −0.709460 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −28.7364 | −0.936779 | −0.468390 | − | 0.883522i | \(-0.655166\pi\) | ||||
−0.468390 | + | 0.883522i | \(0.655166\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.83236 | 0.222492 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −50.8062 | −1.65273 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.35752 | −0.0441135 | −0.0220567 | − | 0.999757i | \(-0.507021\pi\) | ||||
−0.0220567 | + | 0.999757i | \(0.507021\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −67.9292 | −2.20508 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 56.4021 | 1.82896 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −57.1898 | −1.85256 | −0.926280 | − | 0.376835i | \(-0.877012\pi\) | ||||
−0.926280 | + | 0.376835i | \(0.877012\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −43.0294 | −1.39240 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −6.67389 | −0.215736 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 39.1103 | 1.26294 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.92035 | −0.0942050 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.16324 | 0.263057 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −30.9736 | −0.997076 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −31.9125 | −1.02624 | −0.513118 | − | 0.858318i | \(-0.671510\pi\) | ||||
−0.513118 | + | 0.858318i | \(0.671510\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.93704 | 0.222850 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −22.4554 | −0.720627 | −0.360314 | − | 0.932831i | \(-0.617330\pi\) | ||||
−0.360314 | + | 0.932831i | \(0.617330\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 83.3649 | 2.67256 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 34.6881 | 1.11091 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 39.6048 | 1.26707 | 0.633535 | − | 0.773714i | \(-0.281603\pi\) | ||||
0.633535 | + | 0.773714i | \(0.281603\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.51341 | −0.0483687 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.79313 | 0.121105 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 50.2521 | 1.60279 | 0.801396 | − | 0.598134i | \(-0.204091\pi\) | ||||
0.801396 | + | 0.598134i | \(0.204091\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −34.9705 | −1.11425 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 46.4913 | 1.47983 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.66360 | −0.116496 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −35.6965 | −1.13394 | −0.566968 | − | 0.823740i | \(-0.691884\pi\) | ||||
−0.566968 | + | 0.823740i | \(0.691884\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 47.5416 | 1.50869 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −36.8066 | −1.16685 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 42.6983 | 1.35227 | 0.676134 | − | 0.736778i | \(-0.263654\pi\) | ||||
0.676134 | + | 0.736778i | \(0.263654\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7.89722 | −0.249857 |
(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 | 3344.2.a.z.1.4 | 6 | ||
4.3 | odd | 2 | 1672.2.a.i.1.3 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1672.2.a.i.1.3 | ✓ | 6 | 4.3 | odd | 2 | ||
3344.2.a.z.1.4 | 6 | 1.1 | even | 1 | trivial |