Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6003,2,Mod(1,6003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6003, 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("6003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6003 = 3^{2} \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6003.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: | \(47.9341963334\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 2 x^{13} - 18 x^{12} + 34 x^{11} + 124 x^{10} - 216 x^{9} - 420 x^{8} + 647 x^{7} + 750 x^{6} + \cdots - 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 2001) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(1.35292\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6003.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.35292 | 0.956661 | 0.478330 | − | 0.878180i | \(-0.341242\pi\) | ||||
0.478330 | + | 0.878180i | \(0.341242\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.169600 | −0.0848002 | ||||||||
\(5\) | 0.738177 | 0.330123 | 0.165061 | − | 0.986283i | \(-0.447218\pi\) | ||||
0.165061 | + | 0.986283i | \(0.447218\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.44152 | 1.30077 | 0.650385 | − | 0.759604i | \(-0.274607\pi\) | ||||
0.650385 | + | 0.759604i | \(0.274607\pi\) | |||||||
\(8\) | −2.93530 | −1.03779 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.998696 | 0.315816 | ||||||||
\(11\) | −1.17333 | −0.353771 | −0.176886 | − | 0.984231i | \(-0.556602\pi\) | ||||
−0.176886 | + | 0.984231i | \(0.556602\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.89875 | −0.803969 | −0.401984 | − | 0.915646i | \(-0.631679\pi\) | ||||
−0.401984 | + | 0.915646i | \(0.631679\pi\) | |||||||
\(14\) | 4.65611 | 1.24440 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.63203 | −0.908009 | ||||||||
\(17\) | 3.96681 | 0.962092 | 0.481046 | − | 0.876695i | \(-0.340257\pi\) | ||||
0.481046 | + | 0.876695i | \(0.340257\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.02566 | −0.694134 | −0.347067 | − | 0.937840i | \(-0.612822\pi\) | ||||
−0.347067 | + | 0.937840i | \(0.612822\pi\) | |||||||
\(20\) | −0.125195 | −0.0279945 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.58742 | −0.338439 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.45509 | −0.891019 | ||||||||
\(26\) | −3.92179 | −0.769126 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.583682 | −0.110306 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.3766 | 1.86369 | 0.931847 | − | 0.362852i | \(-0.118197\pi\) | ||||
0.931847 | + | 0.362852i | \(0.118197\pi\) | |||||||
\(32\) | 0.956741 | 0.169129 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5.36678 | 0.920396 | ||||||||
\(35\) | 2.54045 | 0.429414 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.14877 | 0.517654 | 0.258827 | − | 0.965924i | \(-0.416664\pi\) | ||||
0.258827 | + | 0.965924i | \(0.416664\pi\) | |||||||
\(38\) | −4.09349 | −0.664051 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.16677 | −0.342597 | ||||||||
\(41\) | 7.62266 | 1.19046 | 0.595230 | − | 0.803556i | \(-0.297061\pi\) | ||||
0.595230 | + | 0.803556i | \(0.297061\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.17008 | 0.940928 | 0.470464 | − | 0.882419i | \(-0.344086\pi\) | ||||
0.470464 | + | 0.882419i | \(0.344086\pi\) | |||||||
\(44\) | 0.198997 | 0.0299999 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.35292 | 0.199478 | ||||||||
\(47\) | −11.0057 | −1.60535 | −0.802673 | − | 0.596419i | \(-0.796590\pi\) | ||||
−0.802673 | + | 0.596419i | \(0.796590\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.84403 | 0.692005 | ||||||||
\(50\) | −6.02740 | −0.852403 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.491629 | 0.0681767 | ||||||||
\(53\) | 12.0907 | 1.66079 | 0.830395 | − | 0.557176i | \(-0.188115\pi\) | ||||
0.830395 | + | 0.557176i | \(0.188115\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.866122 | −0.116788 | ||||||||
\(56\) | −10.1019 | −1.34992 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.35292 | 0.177647 | ||||||||
\(59\) | −1.75699 | −0.228741 | −0.114371 | − | 0.993438i | \(-0.536485\pi\) | ||||
−0.114371 | + | 0.993438i | \(0.536485\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.90124 | 0.371466 | 0.185733 | − | 0.982600i | \(-0.440534\pi\) | ||||
0.185733 | + | 0.982600i | \(0.440534\pi\) | |||||||
\(62\) | 14.0387 | 1.78292 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.55847 | 1.06981 | ||||||||
\(65\) | −2.13979 | −0.265408 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.65474 | 1.05735 | 0.528673 | − | 0.848826i | \(-0.322690\pi\) | ||||
0.528673 | + | 0.848826i | \(0.322690\pi\) | |||||||
\(68\) | −0.672772 | −0.0815856 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3.43703 | 0.410804 | ||||||||
\(71\) | 8.41446 | 0.998613 | 0.499306 | − | 0.866425i | \(-0.333588\pi\) | ||||
0.499306 | + | 0.866425i | \(0.333588\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.23211 | 0.144207 | 0.0721037 | − | 0.997397i | \(-0.477029\pi\) | ||||
0.0721037 | + | 0.997397i | \(0.477029\pi\) | |||||||
\(74\) | 4.26004 | 0.495219 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.513153 | 0.0588627 | ||||||||
\(77\) | −4.03802 | −0.460175 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.7529 | −1.77234 | −0.886169 | − | 0.463363i | \(-0.846643\pi\) | ||||
−0.886169 | + | 0.463363i | \(0.846643\pi\) | |||||||
\(80\) | −2.68108 | −0.299754 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 10.3129 | 1.13887 | ||||||||
\(83\) | 9.53737 | 1.04686 | 0.523431 | − | 0.852068i | \(-0.324652\pi\) | ||||
0.523431 | + | 0.852068i | \(0.324652\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.92821 | 0.317609 | ||||||||
\(86\) | 8.34764 | 0.900149 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.44407 | 0.367139 | ||||||||
\(89\) | 10.0938 | 1.06994 | 0.534971 | − | 0.844871i | \(-0.320323\pi\) | ||||
0.534971 | + | 0.844871i | \(0.320323\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.97610 | −1.04578 | ||||||||
\(92\) | −0.169600 | −0.0176821 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −14.8899 | −1.53577 | ||||||||
\(95\) | −2.23347 | −0.229150 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.9789 | −1.31780 | −0.658902 | − | 0.752229i | \(-0.728979\pi\) | ||||
−0.658902 | + | 0.752229i | \(0.728979\pi\) | |||||||
\(98\) | 6.55360 | 0.662014 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.755586 | 0.0755586 | ||||||||
\(101\) | 6.44364 | 0.641166 | 0.320583 | − | 0.947220i | \(-0.396121\pi\) | ||||
0.320583 | + | 0.947220i | \(0.396121\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.18324 | 0.412187 | 0.206094 | − | 0.978532i | \(-0.433925\pi\) | ||||
0.206094 | + | 0.978532i | \(0.433925\pi\) | |||||||
\(104\) | 8.50871 | 0.834348 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 16.3578 | 1.58881 | ||||||||
\(107\) | 5.35867 | 0.518042 | 0.259021 | − | 0.965872i | \(-0.416600\pi\) | ||||
0.259021 | + | 0.965872i | \(0.416600\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.3099 | 1.08329 | 0.541647 | − | 0.840606i | \(-0.317801\pi\) | ||||
0.541647 | + | 0.840606i | \(0.317801\pi\) | |||||||
\(110\) | −1.17180 | −0.111726 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −12.4997 | −1.18111 | ||||||||
\(113\) | 5.42973 | 0.510786 | 0.255393 | − | 0.966837i | \(-0.417795\pi\) | ||||
0.255393 | + | 0.966837i | \(0.417795\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.738177 | 0.0688354 | ||||||||
\(116\) | −0.169600 | −0.0157470 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.37708 | −0.218828 | ||||||||
\(119\) | 13.6518 | 1.25146 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.62331 | −0.874846 | ||||||||
\(122\) | 3.92516 | 0.355367 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.75988 | −0.158042 | ||||||||
\(125\) | −6.97953 | −0.624268 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.48395 | −0.841564 | −0.420782 | − | 0.907162i | \(-0.638244\pi\) | ||||
−0.420782 | + | 0.907162i | \(0.638244\pi\) | |||||||
\(128\) | 9.66546 | 0.854314 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.89497 | −0.253906 | ||||||||
\(131\) | 0.643336 | 0.0562085 | 0.0281042 | − | 0.999605i | \(-0.491053\pi\) | ||||
0.0281042 | + | 0.999605i | \(0.491053\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −10.4129 | −0.902910 | ||||||||
\(134\) | 11.7092 | 1.01152 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −11.6438 | −0.998446 | ||||||||
\(137\) | 15.3086 | 1.30790 | 0.653951 | − | 0.756536i | \(-0.273110\pi\) | ||||
0.653951 | + | 0.756536i | \(0.273110\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.30209 | 0.704174 | 0.352087 | − | 0.935967i | \(-0.385472\pi\) | ||||
0.352087 | + | 0.935967i | \(0.385472\pi\) | |||||||
\(140\) | −0.430861 | −0.0364144 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 11.3841 | 0.955334 | ||||||||
\(143\) | 3.40118 | 0.284421 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.738177 | 0.0613023 | ||||||||
\(146\) | 1.66695 | 0.137958 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.534032 | −0.0438972 | ||||||||
\(149\) | −17.6570 | −1.44652 | −0.723258 | − | 0.690578i | \(-0.757356\pi\) | ||||
−0.723258 | + | 0.690578i | \(0.757356\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.23676 | 0.670298 | 0.335149 | − | 0.942165i | \(-0.391213\pi\) | ||||
0.335149 | + | 0.942165i | \(0.391213\pi\) | |||||||
\(152\) | 8.88123 | 0.720363 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −5.46313 | −0.440232 | ||||||||
\(155\) | 7.65977 | 0.615248 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.2680 | 1.37814 | 0.689068 | − | 0.724696i | \(-0.258020\pi\) | ||||
0.689068 | + | 0.724696i | \(0.258020\pi\) | |||||||
\(158\) | −21.3124 | −1.69553 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.706244 | 0.0558335 | ||||||||
\(161\) | 3.44152 | 0.271229 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −21.4179 | −1.67758 | −0.838791 | − | 0.544454i | \(-0.816737\pi\) | ||||
−0.838791 | + | 0.544454i | \(0.816737\pi\) | |||||||
\(164\) | −1.29281 | −0.100951 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 12.9033 | 1.00149 | ||||||||
\(167\) | −1.86970 | −0.144682 | −0.0723409 | − | 0.997380i | \(-0.523047\pi\) | ||||
−0.0723409 | + | 0.997380i | \(0.523047\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.59724 | −0.353634 | ||||||||
\(170\) | 3.96164 | 0.303844 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.04645 | −0.0797909 | ||||||||
\(173\) | 8.89523 | 0.676292 | 0.338146 | − | 0.941094i | \(-0.390200\pi\) | ||||
0.338146 | + | 0.941094i | \(0.390200\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −15.3323 | −1.15901 | ||||||||
\(176\) | 4.26156 | 0.321227 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 13.6561 | 1.02357 | ||||||||
\(179\) | −11.5346 | −0.862136 | −0.431068 | − | 0.902319i | \(-0.641863\pi\) | ||||
−0.431068 | + | 0.902319i | \(0.641863\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.24247 | 0.315340 | 0.157670 | − | 0.987492i | \(-0.449602\pi\) | ||||
0.157670 | + | 0.987492i | \(0.449602\pi\) | |||||||
\(182\) | −13.4969 | −1.00046 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.93530 | −0.216393 | ||||||||
\(185\) | 2.32435 | 0.170889 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.65436 | −0.340360 | ||||||||
\(188\) | 1.86657 | 0.136134 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.02172 | −0.219218 | ||||||||
\(191\) | 21.9527 | 1.58844 | 0.794222 | − | 0.607628i | \(-0.207879\pi\) | ||||
0.794222 | + | 0.607628i | \(0.207879\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.4290 | −1.18258 | −0.591292 | − | 0.806457i | \(-0.701382\pi\) | ||||
−0.591292 | + | 0.806457i | \(0.701382\pi\) | |||||||
\(194\) | −17.5594 | −1.26069 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.821550 | −0.0586821 | ||||||||
\(197\) | −22.2164 | −1.58285 | −0.791426 | − | 0.611266i | \(-0.790661\pi\) | ||||
−0.791426 | + | 0.611266i | \(0.790661\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.1955 | −1.14807 | −0.574033 | − | 0.818832i | \(-0.694622\pi\) | ||||
−0.574033 | + | 0.818832i | \(0.694622\pi\) | |||||||
\(200\) | 13.0770 | 0.924687 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 8.71775 | 0.613379 | ||||||||
\(203\) | 3.44152 | 0.241547 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.62687 | 0.392998 | ||||||||
\(206\) | 5.65960 | 0.394323 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 10.5284 | 0.730011 | ||||||||
\(209\) | 3.55009 | 0.245565 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.9907 | 1.37621 | 0.688107 | − | 0.725609i | \(-0.258442\pi\) | ||||
0.688107 | + | 0.725609i | \(0.258442\pi\) | |||||||
\(212\) | −2.05059 | −0.140835 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 7.24987 | 0.495591 | ||||||||
\(215\) | 4.55461 | 0.310622 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 35.7113 | 2.42424 | ||||||||
\(218\) | 15.3014 | 1.03634 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.146895 | 0.00990364 | ||||||||
\(221\) | −11.4988 | −0.773492 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.34982 | 0.559145 | 0.279573 | − | 0.960125i | \(-0.409807\pi\) | ||||
0.279573 | + | 0.960125i | \(0.409807\pi\) | |||||||
\(224\) | 3.29264 | 0.219999 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7.34600 | 0.488649 | ||||||||
\(227\) | 7.28325 | 0.483406 | 0.241703 | − | 0.970350i | \(-0.422294\pi\) | ||||
0.241703 | + | 0.970350i | \(0.422294\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.3948 | −1.08340 | −0.541700 | − | 0.840572i | \(-0.682219\pi\) | ||||
−0.541700 | + | 0.840572i | \(0.682219\pi\) | |||||||
\(230\) | 0.998696 | 0.0658521 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.93530 | −0.192712 | ||||||||
\(233\) | −17.6144 | −1.15396 | −0.576980 | − | 0.816758i | \(-0.695769\pi\) | ||||
−0.576980 | + | 0.816758i | \(0.695769\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.12416 | −0.529962 | ||||||||
\(236\) | 0.297987 | 0.0193973 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 18.4699 | 1.19722 | ||||||||
\(239\) | 20.3195 | 1.31436 | 0.657178 | − | 0.753735i | \(-0.271750\pi\) | ||||
0.657178 | + | 0.753735i | \(0.271750\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.51402 | 0.161942 | 0.0809712 | − | 0.996716i | \(-0.474198\pi\) | ||||
0.0809712 | + | 0.996716i | \(0.474198\pi\) | |||||||
\(242\) | −13.0196 | −0.836931 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −0.492052 | −0.0315004 | ||||||||
\(245\) | 3.57575 | 0.228447 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.77064 | 0.558062 | ||||||||
\(248\) | −30.4585 | −1.93411 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −9.44277 | −0.597213 | ||||||||
\(251\) | 4.97478 | 0.314005 | 0.157003 | − | 0.987598i | \(-0.449817\pi\) | ||||
0.157003 | + | 0.987598i | \(0.449817\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.17333 | −0.0737664 | ||||||||
\(254\) | −12.8310 | −0.805092 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4.04031 | −0.252519 | ||||||||
\(257\) | 14.1760 | 0.884275 | 0.442137 | − | 0.896947i | \(-0.354220\pi\) | ||||
0.442137 | + | 0.896947i | \(0.354220\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.8365 | 0.673349 | ||||||||
\(260\) | 0.362909 | 0.0225067 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0.870383 | 0.0537725 | ||||||||
\(263\) | 18.3150 | 1.12935 | 0.564675 | − | 0.825313i | \(-0.309002\pi\) | ||||
0.564675 | + | 0.825313i | \(0.309002\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.92510 | 0.548264 | ||||||||
\(266\) | −14.0878 | −0.863778 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.46785 | −0.0896631 | ||||||||
\(269\) | 12.3846 | 0.755103 | 0.377551 | − | 0.925989i | \(-0.376766\pi\) | ||||
0.377551 | + | 0.925989i | \(0.376766\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.0474151 | 0.00288026 | 0.00144013 | − | 0.999999i | \(-0.499542\pi\) | ||||
0.00144013 | + | 0.999999i | \(0.499542\pi\) | |||||||
\(272\) | −14.4076 | −0.873588 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 20.7114 | 1.25122 | ||||||||
\(275\) | 5.22728 | 0.315217 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.5455 | 0.934039 | 0.467020 | − | 0.884247i | \(-0.345328\pi\) | ||||
0.467020 | + | 0.884247i | \(0.345328\pi\) | |||||||
\(278\) | 11.2321 | 0.673655 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −7.45698 | −0.445640 | ||||||||
\(281\) | 24.5204 | 1.46277 | 0.731383 | − | 0.681967i | \(-0.238875\pi\) | ||||
0.731383 | + | 0.681967i | \(0.238875\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 24.5260 | 1.45792 | 0.728961 | − | 0.684556i | \(-0.240004\pi\) | ||||
0.728961 | + | 0.684556i | \(0.240004\pi\) | |||||||
\(284\) | −1.42710 | −0.0846826 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.60153 | 0.272094 | ||||||||
\(287\) | 26.2335 | 1.54851 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.26444 | −0.0743786 | ||||||||
\(290\) | 0.998696 | 0.0586455 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.208966 | −0.0122288 | ||||||||
\(293\) | 28.1398 | 1.64394 | 0.821972 | − | 0.569528i | \(-0.192874\pi\) | ||||
0.821972 | + | 0.569528i | \(0.192874\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.29697 | −0.0755127 | ||||||||
\(296\) | −9.24258 | −0.537214 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −23.8885 | −1.38383 | ||||||||
\(299\) | −2.89875 | −0.167639 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 21.2344 | 1.22393 | ||||||||
\(302\) | 11.1437 | 0.641247 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 10.9893 | 0.630280 | ||||||||
\(305\) | 2.14163 | 0.122629 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −20.2600 | −1.15630 | −0.578149 | − | 0.815931i | \(-0.696225\pi\) | ||||
−0.578149 | + | 0.815931i | \(0.696225\pi\) | |||||||
\(308\) | 0.684850 | 0.0390229 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 10.3631 | 0.588583 | ||||||||
\(311\) | −19.5818 | −1.11038 | −0.555191 | − | 0.831723i | \(-0.687355\pi\) | ||||
−0.555191 | + | 0.831723i | \(0.687355\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −32.6842 | −1.84742 | −0.923710 | − | 0.383092i | \(-0.874859\pi\) | ||||
−0.923710 | + | 0.383092i | \(0.874859\pi\) | |||||||
\(314\) | 23.3623 | 1.31841 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.67169 | 0.150295 | ||||||||
\(317\) | 13.2909 | 0.746493 | 0.373247 | − | 0.927732i | \(-0.378245\pi\) | ||||
0.373247 | + | 0.927732i | \(0.378245\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.17333 | −0.0656936 | ||||||||
\(320\) | 6.31766 | 0.353168 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 4.65611 | 0.259475 | ||||||||
\(323\) | −12.0022 | −0.667821 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.9142 | 0.716352 | ||||||||
\(326\) | −28.9768 | −1.60488 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −22.3748 | −1.23544 | ||||||||
\(329\) | −37.8763 | −2.08819 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.6966 | −1.35745 | −0.678724 | − | 0.734394i | \(-0.737467\pi\) | ||||
−0.678724 | + | 0.734394i | \(0.737467\pi\) | |||||||
\(332\) | −1.61754 | −0.0887742 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.52956 | −0.138411 | ||||||||
\(335\) | 6.38873 | 0.349054 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −28.3431 | −1.54395 | −0.771974 | − | 0.635654i | \(-0.780731\pi\) | ||||
−0.771974 | + | 0.635654i | \(0.780731\pi\) | |||||||
\(338\) | −6.21971 | −0.338308 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.496625 | −0.0269333 | ||||||||
\(341\) | −12.1751 | −0.659321 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.41979 | −0.400631 | ||||||||
\(344\) | −18.1110 | −0.976482 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 12.0346 | 0.646982 | ||||||||
\(347\) | 7.12832 | 0.382668 | 0.191334 | − | 0.981525i | \(-0.438719\pi\) | ||||
0.191334 | + | 0.981525i | \(0.438719\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −20.1149 | −1.07673 | −0.538364 | − | 0.842713i | \(-0.680957\pi\) | ||||
−0.538364 | + | 0.842713i | \(0.680957\pi\) | |||||||
\(350\) | −20.7434 | −1.10878 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.12257 | −0.0598331 | ||||||||
\(353\) | 5.22872 | 0.278297 | 0.139148 | − | 0.990272i | \(-0.455563\pi\) | ||||
0.139148 | + | 0.990272i | \(0.455563\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.21136 | 0.329665 | ||||||||
\(356\) | −1.71191 | −0.0907312 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −15.6054 | −0.824772 | ||||||||
\(359\) | 6.09563 | 0.321715 | 0.160857 | − | 0.986978i | \(-0.448574\pi\) | ||||
0.160857 | + | 0.986978i | \(0.448574\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.84537 | −0.518178 | ||||||||
\(362\) | 5.73973 | 0.301674 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.69195 | 0.0886823 | ||||||||
\(365\) | 0.909514 | 0.0476061 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 24.0718 | 1.25654 | 0.628268 | − | 0.777997i | \(-0.283764\pi\) | ||||
0.628268 | + | 0.777997i | \(0.283764\pi\) | |||||||
\(368\) | −3.63203 | −0.189333 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3.14466 | 0.163483 | ||||||||
\(371\) | 41.6104 | 2.16031 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.81626 | 0.456488 | 0.228244 | − | 0.973604i | \(-0.426702\pi\) | ||||
0.228244 | + | 0.973604i | \(0.426702\pi\) | |||||||
\(374\) | −6.29699 | −0.325609 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 32.3051 | 1.66601 | ||||||||
\(377\) | −2.89875 | −0.149293 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.9793 | 0.872169 | 0.436085 | − | 0.899906i | \(-0.356365\pi\) | ||||
0.436085 | + | 0.899906i | \(0.356365\pi\) | |||||||
\(380\) | 0.378798 | 0.0194319 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 29.7003 | 1.51960 | ||||||||
\(383\) | −20.0054 | −1.02223 | −0.511114 | − | 0.859513i | \(-0.670767\pi\) | ||||
−0.511114 | + | 0.859513i | \(0.670767\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.98077 | −0.151914 | ||||||||
\(386\) | −22.2271 | −1.13133 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.20122 | 0.111750 | ||||||||
\(389\) | −2.36742 | −0.120033 | −0.0600164 | − | 0.998197i | \(-0.519115\pi\) | ||||
−0.0600164 | + | 0.998197i | \(0.519115\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.96681 | 0.200610 | ||||||||
\(392\) | −14.2187 | −0.718153 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −30.0570 | −1.51425 | ||||||||
\(395\) | −11.6284 | −0.585089 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.4601 | −1.12724 | −0.563619 | − | 0.826035i | \(-0.690591\pi\) | ||||
−0.563619 | + | 0.826035i | \(0.690591\pi\) | |||||||
\(398\) | −21.9112 | −1.09831 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 16.1811 | 0.809053 | ||||||||
\(401\) | 38.1990 | 1.90757 | 0.953783 | − | 0.300498i | \(-0.0971528\pi\) | ||||
0.953783 | + | 0.300498i | \(0.0971528\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −30.0792 | −1.49835 | ||||||||
\(404\) | −1.09284 | −0.0543710 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.65611 | 0.231079 | ||||||||
\(407\) | −3.69453 | −0.183131 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −26.4483 | −1.30778 | −0.653892 | − | 0.756588i | \(-0.726865\pi\) | ||||
−0.653892 | + | 0.756588i | \(0.726865\pi\) | |||||||
\(410\) | 7.61272 | 0.375965 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −0.709480 | −0.0349536 | ||||||||
\(413\) | −6.04672 | −0.297540 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.04027 | 0.345593 | ||||||||
\(416\) | −2.77335 | −0.135975 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 4.80299 | 0.234922 | ||||||||
\(419\) | 18.1958 | 0.888925 | 0.444462 | − | 0.895798i | \(-0.353395\pi\) | ||||
0.444462 | + | 0.895798i | \(0.353395\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.3568 | 0.845920 | 0.422960 | − | 0.906148i | \(-0.360991\pi\) | ||||
0.422960 | + | 0.906148i | \(0.360991\pi\) | |||||||
\(422\) | 27.0458 | 1.31657 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −35.4899 | −1.72354 | ||||||||
\(425\) | −17.6725 | −0.857242 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.98468 | 0.483192 | ||||||||
\(428\) | −0.908833 | −0.0439301 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 6.16204 | 0.297160 | ||||||||
\(431\) | −6.91304 | −0.332990 | −0.166495 | − | 0.986042i | \(-0.553245\pi\) | ||||
−0.166495 | + | 0.986042i | \(0.553245\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.4908 | 0.696383 | 0.348192 | − | 0.937423i | \(-0.386796\pi\) | ||||
0.348192 | + | 0.937423i | \(0.386796\pi\) | |||||||
\(434\) | 48.3146 | 2.31917 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.91817 | −0.0918635 | ||||||||
\(437\) | −3.02566 | −0.144737 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −23.0948 | −1.10225 | −0.551127 | − | 0.834421i | \(-0.685802\pi\) | ||||
−0.551127 | + | 0.834421i | \(0.685802\pi\) | |||||||
\(440\) | 2.54233 | 0.121201 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −15.5570 | −0.739970 | ||||||||
\(443\) | −3.39253 | −0.161184 | −0.0805920 | − | 0.996747i | \(-0.525681\pi\) | ||||
−0.0805920 | + | 0.996747i | \(0.525681\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.45102 | 0.353212 | ||||||||
\(446\) | 11.2967 | 0.534912 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 29.4541 | 1.39158 | ||||||||
\(449\) | 8.19587 | 0.386787 | 0.193394 | − | 0.981121i | \(-0.438051\pi\) | ||||
0.193394 | + | 0.981121i | \(0.438051\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.94386 | −0.421150 | ||||||||
\(452\) | −0.920884 | −0.0433147 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 9.85367 | 0.462456 | ||||||||
\(455\) | −7.36413 | −0.345236 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 39.5184 | 1.84859 | 0.924297 | − | 0.381674i | \(-0.124652\pi\) | ||||
0.924297 | + | 0.381674i | \(0.124652\pi\) | |||||||
\(458\) | −22.1809 | −1.03645 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.125195 | −0.00583725 | ||||||||
\(461\) | −25.3442 | −1.18040 | −0.590200 | − | 0.807257i | \(-0.700951\pi\) | ||||
−0.590200 | + | 0.807257i | \(0.700951\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.3101 | 0.850943 | 0.425471 | − | 0.904972i | \(-0.360108\pi\) | ||||
0.425471 | + | 0.904972i | \(0.360108\pi\) | |||||||
\(464\) | −3.63203 | −0.168613 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −23.8310 | −1.10395 | ||||||||
\(467\) | 4.56418 | 0.211205 | 0.105603 | − | 0.994408i | \(-0.466323\pi\) | ||||
0.105603 | + | 0.994408i | \(0.466323\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 29.7854 | 1.37536 | ||||||||
\(470\) | −10.9914 | −0.506993 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5.15731 | 0.237384 | ||||||||
\(473\) | −7.23952 | −0.332873 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 13.4796 | 0.618487 | ||||||||
\(476\) | −2.31536 | −0.106124 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 27.4907 | 1.25739 | ||||||||
\(479\) | −15.6660 | −0.715797 | −0.357898 | − | 0.933761i | \(-0.616507\pi\) | ||||
−0.357898 | + | 0.933761i | \(0.616507\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.12749 | −0.416178 | ||||||||
\(482\) | 3.40128 | 0.154924 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.63212 | 0.0741871 | ||||||||
\(485\) | −9.58070 | −0.435037 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.9794 | 0.633468 | 0.316734 | − | 0.948514i | \(-0.397414\pi\) | ||||
0.316734 | + | 0.948514i | \(0.397414\pi\) | |||||||
\(488\) | −8.51603 | −0.385502 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 4.83772 | 0.218546 | ||||||||
\(491\) | 41.1904 | 1.85890 | 0.929449 | − | 0.368951i | \(-0.120283\pi\) | ||||
0.929449 | + | 0.368951i | \(0.120283\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.96681 | 0.178656 | ||||||||
\(494\) | 11.8660 | 0.533876 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −37.6882 | −1.69225 | ||||||||
\(497\) | 28.9585 | 1.29897 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −41.4979 | −1.85770 | −0.928851 | − | 0.370454i | \(-0.879202\pi\) | ||||
−0.928851 | + | 0.370454i | \(0.879202\pi\) | |||||||
\(500\) | 1.18373 | 0.0529381 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 6.73050 | 0.300397 | ||||||||
\(503\) | −16.9864 | −0.757384 | −0.378692 | − | 0.925523i | \(-0.623626\pi\) | ||||
−0.378692 | + | 0.925523i | \(0.623626\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.75655 | 0.211664 | ||||||||
\(506\) | −1.58742 | −0.0705694 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.60848 | 0.0713648 | ||||||||
\(509\) | −27.3370 | −1.21169 | −0.605846 | − | 0.795582i | \(-0.707165\pi\) | ||||
−0.605846 | + | 0.795582i | \(0.707165\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.24032 | 0.187581 | ||||||||
\(512\) | −24.7972 | −1.09589 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 19.1790 | 0.845951 | ||||||||
\(515\) | 3.08797 | 0.136072 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.9133 | 0.567925 | ||||||||
\(518\) | 14.6610 | 0.644167 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 6.28093 | 0.275437 | ||||||||
\(521\) | 11.3336 | 0.496535 | 0.248268 | − | 0.968691i | \(-0.420139\pi\) | ||||
0.248268 | + | 0.968691i | \(0.420139\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.81341 | −0.166749 | −0.0833743 | − | 0.996518i | \(-0.526570\pi\) | ||||
−0.0833743 | + | 0.996518i | \(0.526570\pi\) | |||||||
\(524\) | −0.109110 | −0.00476649 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 24.7787 | 1.08040 | ||||||||
\(527\) | 41.1620 | 1.79304 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 12.0750 | 0.524503 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.76603 | 0.0765669 | ||||||||
\(533\) | −22.0962 | −0.957092 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.95565 | 0.171018 | ||||||||
\(536\) | −25.4043 | −1.09730 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 16.7554 | 0.722377 | ||||||||
\(539\) | −5.68363 | −0.244811 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.8352 | −0.551827 | −0.275913 | − | 0.961183i | \(-0.588980\pi\) | ||||
−0.275913 | + | 0.961183i | \(0.588980\pi\) | |||||||
\(542\) | 0.0641489 | 0.00275543 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.79521 | 0.162718 | ||||||||
\(545\) | 8.34872 | 0.357620 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 25.7312 | 1.10019 | 0.550094 | − | 0.835103i | \(-0.314592\pi\) | ||||
0.550094 | + | 0.835103i | \(0.314592\pi\) | |||||||
\(548\) | −2.59635 | −0.110910 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 7.07210 | 0.301556 | ||||||||
\(551\) | −3.02566 | −0.128898 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −54.2138 | −2.30540 | ||||||||
\(554\) | 21.0319 | 0.893559 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.40804 | −0.0597141 | ||||||||
\(557\) | −34.7825 | −1.47378 | −0.736890 | − | 0.676012i | \(-0.763707\pi\) | ||||
−0.736890 | + | 0.676012i | \(0.763707\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −17.8855 | −0.756477 | ||||||||
\(560\) | −9.22700 | −0.389912 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 33.1742 | 1.39937 | ||||||||
\(563\) | −16.3561 | −0.689326 | −0.344663 | − | 0.938727i | \(-0.612007\pi\) | ||||
−0.344663 | + | 0.938727i | \(0.612007\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.00810 | 0.168622 | ||||||||
\(566\) | 33.1818 | 1.39474 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −24.6990 | −1.03635 | ||||||||
\(569\) | −10.5054 | −0.440407 | −0.220204 | − | 0.975454i | \(-0.570672\pi\) | ||||
−0.220204 | + | 0.975454i | \(0.570672\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.7569 | −0.910498 | −0.455249 | − | 0.890364i | \(-0.650450\pi\) | ||||
−0.455249 | + | 0.890364i | \(0.650450\pi\) | |||||||
\(572\) | −0.576841 | −0.0241190 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 35.4919 | 1.48140 | ||||||||
\(575\) | −4.45509 | −0.185790 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 31.5980 | 1.31544 | 0.657721 | − | 0.753262i | \(-0.271521\pi\) | ||||
0.657721 | + | 0.753262i | \(0.271521\pi\) | |||||||
\(578\) | −1.71068 | −0.0711551 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.125195 | −0.00519844 | ||||||||
\(581\) | 32.8230 | 1.36173 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −14.1864 | −0.587539 | ||||||||
\(584\) | −3.61661 | −0.149656 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 38.0710 | 1.57270 | ||||||||
\(587\) | −38.0454 | −1.57030 | −0.785151 | − | 0.619304i | \(-0.787415\pi\) | ||||
−0.785151 | + | 0.619304i | \(0.787415\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −31.3961 | −1.29365 | ||||||||
\(590\) | −1.75470 | −0.0722400 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −11.4364 | −0.470034 | ||||||||
\(593\) | −18.4978 | −0.759612 | −0.379806 | − | 0.925066i | \(-0.624009\pi\) | ||||
−0.379806 | + | 0.925066i | \(0.624009\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.0775 | 0.413136 | ||||||||
\(596\) | 2.99463 | 0.122665 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.92179 | −0.160374 | ||||||||
\(599\) | 0.949485 | 0.0387949 | 0.0193975 | − | 0.999812i | \(-0.493825\pi\) | ||||
0.0193975 | + | 0.999812i | \(0.493825\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 30.9918 | 1.26418 | 0.632091 | − | 0.774894i | \(-0.282197\pi\) | ||||
0.632091 | + | 0.774894i | \(0.282197\pi\) | |||||||
\(602\) | 28.7285 | 1.17089 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.39696 | −0.0568414 | ||||||||
\(605\) | −7.10370 | −0.288807 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −23.3743 | −0.948734 | −0.474367 | − | 0.880327i | \(-0.657323\pi\) | ||||
−0.474367 | + | 0.880327i | \(0.657323\pi\) | |||||||
\(608\) | −2.89477 | −0.117399 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.89746 | 0.117315 | ||||||||
\(611\) | 31.9028 | 1.29065 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.83570 | −0.316481 | −0.158241 | − | 0.987401i | \(-0.550582\pi\) | ||||
−0.158241 | + | 0.987401i | \(0.550582\pi\) | |||||||
\(614\) | −27.4102 | −1.10618 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 11.8528 | 0.477563 | ||||||||
\(617\) | −1.46753 | −0.0590806 | −0.0295403 | − | 0.999564i | \(-0.509404\pi\) | ||||
−0.0295403 | + | 0.999564i | \(0.509404\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 27.2490 | 1.09523 | 0.547614 | − | 0.836731i | \(-0.315536\pi\) | ||||
0.547614 | + | 0.836731i | \(0.315536\pi\) | |||||||
\(620\) | −1.29910 | −0.0521731 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −26.4927 | −1.06226 | ||||||||
\(623\) | 34.7380 | 1.39175 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.1233 | 0.684934 | ||||||||
\(626\) | −44.2192 | −1.76735 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.92866 | −0.116866 | ||||||||
\(629\) | 12.4906 | 0.498031 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.06096 | −0.201474 | −0.100737 | − | 0.994913i | \(-0.532120\pi\) | ||||
−0.100737 | + | 0.994913i | \(0.532120\pi\) | |||||||
\(632\) | 46.2394 | 1.83931 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 17.9816 | 0.714141 | ||||||||
\(635\) | −7.00083 | −0.277820 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −14.0416 | −0.556350 | ||||||||
\(638\) | −1.58742 | −0.0628465 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 7.13482 | 0.282029 | ||||||||
\(641\) | −10.4401 | −0.412358 | −0.206179 | − | 0.978514i | \(-0.566103\pi\) | ||||
−0.206179 | + | 0.978514i | \(0.566103\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.1008 | 0.477209 | 0.238605 | − | 0.971117i | \(-0.423310\pi\) | ||||
0.238605 | + | 0.971117i | \(0.423310\pi\) | |||||||
\(644\) | −0.583682 | −0.0230003 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −16.2381 | −0.638878 | ||||||||
\(647\) | −34.6932 | −1.36393 | −0.681966 | − | 0.731384i | \(-0.738875\pi\) | ||||
−0.681966 | + | 0.731384i | \(0.738875\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.06153 | 0.0809220 | ||||||||
\(650\) | 17.4719 | 0.685305 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.63249 | 0.142259 | ||||||||
\(653\) | −10.2303 | −0.400342 | −0.200171 | − | 0.979761i | \(-0.564150\pi\) | ||||
−0.200171 | + | 0.979761i | \(0.564150\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.474896 | 0.0185557 | ||||||||
\(656\) | −27.6858 | −1.08095 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −51.2437 | −1.99769 | ||||||||
\(659\) | 13.9869 | 0.544853 | 0.272427 | − | 0.962177i | \(-0.412174\pi\) | ||||
0.272427 | + | 0.962177i | \(0.412174\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 35.3316 | 1.37424 | 0.687120 | − | 0.726544i | \(-0.258875\pi\) | ||||
0.687120 | + | 0.726544i | \(0.258875\pi\) | |||||||
\(662\) | −33.4126 | −1.29862 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −27.9951 | −1.08642 | ||||||||
\(665\) | −7.68654 | −0.298071 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | 0.317102 | 0.0122690 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 8.64346 | 0.333926 | ||||||||
\(671\) | −3.40411 | −0.131414 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 35.8417 | 1.38160 | 0.690799 | − | 0.723047i | \(-0.257259\pi\) | ||||
0.690799 | + | 0.723047i | \(0.257259\pi\) | |||||||
\(674\) | −38.3461 | −1.47703 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.779694 | 0.0299882 | ||||||||
\(677\) | −18.3954 | −0.706992 | −0.353496 | − | 0.935436i | \(-0.615007\pi\) | ||||
−0.353496 | + | 0.935436i | \(0.615007\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −44.6670 | −1.71416 | ||||||||
\(680\) | −8.59517 | −0.329610 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −16.4720 | −0.630746 | ||||||||
\(683\) | −14.3777 | −0.550146 | −0.275073 | − | 0.961423i | \(-0.588702\pi\) | ||||
−0.275073 | + | 0.961423i | \(0.588702\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11.3005 | 0.431769 | ||||||||
\(686\) | −10.0384 | −0.383268 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −22.4099 | −0.854371 | ||||||||
\(689\) | −35.0480 | −1.33522 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −35.0831 | −1.33462 | −0.667311 | − | 0.744779i | \(-0.732555\pi\) | ||||
−0.667311 | + | 0.744779i | \(0.732555\pi\) | |||||||
\(692\) | −1.50864 | −0.0573497 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 9.64406 | 0.366084 | ||||||||
\(695\) | 6.12841 | 0.232464 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 30.2376 | 1.14533 | ||||||||
\(698\) | −27.2139 | −1.03006 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.60036 | 0.0982844 | ||||||||
\(701\) | 30.9498 | 1.16896 | 0.584480 | − | 0.811408i | \(-0.301299\pi\) | ||||
0.584480 | + | 0.811408i | \(0.301299\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.52710 | −0.359322 | ||||||||
\(704\) | −10.0419 | −0.378467 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7.07406 | 0.266236 | ||||||||
\(707\) | 22.1759 | 0.834010 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.5484 | −0.433708 | −0.216854 | − | 0.976204i | \(-0.569580\pi\) | ||||
−0.216854 | + | 0.976204i | \(0.569580\pi\) | |||||||
\(710\) | 8.40349 | 0.315377 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −29.6284 | −1.11037 | ||||||||
\(713\) | 10.3766 | 0.388607 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.51067 | 0.0938939 | ||||||||
\(716\) | 1.95627 | 0.0731093 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 8.24691 | 0.307772 | ||||||||
\(719\) | −21.9392 | −0.818192 | −0.409096 | − | 0.912491i | \(-0.634156\pi\) | ||||
−0.409096 | + | 0.912491i | \(0.634156\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.3967 | 0.536161 | ||||||||
\(722\) | −13.3200 | −0.495720 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −0.719524 | −0.0267409 | ||||||||
\(725\) | −4.45509 | −0.165458 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.989895 | −0.0367132 | −0.0183566 | − | 0.999832i | \(-0.505843\pi\) | ||||
−0.0183566 | + | 0.999832i | \(0.505843\pi\) | |||||||
\(728\) | 29.2829 | 1.08529 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.23050 | 0.0455429 | ||||||||
\(731\) | 24.4755 | 0.905260 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17.2010 | −0.635334 | −0.317667 | − | 0.948202i | \(-0.602899\pi\) | ||||
−0.317667 | + | 0.948202i | \(0.602899\pi\) | |||||||
\(734\) | 32.5672 | 1.20208 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.956741 | 0.0352659 | ||||||||
\(737\) | −10.1548 | −0.374058 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −50.3396 | −1.85177 | −0.925885 | − | 0.377804i | \(-0.876679\pi\) | ||||
−0.925885 | + | 0.377804i | \(0.876679\pi\) | |||||||
\(740\) | −0.394210 | −0.0144915 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 56.2957 | 2.06668 | ||||||||
\(743\) | −19.7654 | −0.725123 | −0.362562 | − | 0.931960i | \(-0.618098\pi\) | ||||
−0.362562 | + | 0.931960i | \(0.618098\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −13.0340 | −0.477528 | ||||||||
\(746\) | 11.9277 | 0.436705 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.789381 | 0.0288626 | ||||||||
\(749\) | 18.4420 | 0.673854 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.73724 | 0.209355 | 0.104677 | − | 0.994506i | \(-0.466619\pi\) | ||||
0.104677 | + | 0.994506i | \(0.466619\pi\) | |||||||
\(752\) | 39.9731 | 1.45767 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −3.92179 | −0.142823 | ||||||||
\(755\) | 6.08018 | 0.221281 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16.1728 | −0.587811 | −0.293905 | − | 0.955834i | \(-0.594955\pi\) | ||||
−0.293905 | + | 0.955834i | \(0.594955\pi\) | |||||||
\(758\) | 22.9717 | 0.834370 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6.55592 | 0.237808 | ||||||||
\(761\) | −47.5884 | −1.72508 | −0.862538 | − | 0.505992i | \(-0.831127\pi\) | ||||
−0.862538 | + | 0.505992i | \(0.831127\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 38.9233 | 1.40912 | ||||||||
\(764\) | −3.72319 | −0.134700 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −27.0657 | −0.977925 | ||||||||
\(767\) | 5.09309 | 0.183901 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −26.6504 | −0.961038 | −0.480519 | − | 0.876984i | \(-0.659552\pi\) | ||||
−0.480519 | + | 0.876984i | \(0.659552\pi\) | |||||||
\(770\) | −4.03276 | −0.145330 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.78636 | 0.100283 | ||||||||
\(773\) | 12.8708 | 0.462932 | 0.231466 | − | 0.972843i | \(-0.425648\pi\) | ||||
0.231466 | + | 0.972843i | \(0.425648\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −46.2288 | −1.66059 | ||||||||
\(776\) | 38.0969 | 1.36760 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −3.20293 | −0.114831 | ||||||||
\(779\) | −23.0636 | −0.826338 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.87291 | −0.353280 | ||||||||
\(782\) | 5.36678 | 0.191916 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −17.5937 | −0.628346 | ||||||||
\(785\) | 12.7468 | 0.454954 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 45.1481 | 1.60936 | 0.804678 | − | 0.593712i | \(-0.202338\pi\) | ||||
0.804678 | + | 0.593712i | \(0.202338\pi\) | |||||||
\(788\) | 3.76791 | 0.134226 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −15.7323 | −0.559732 | ||||||||
\(791\) | 18.6865 | 0.664415 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.40999 | −0.298647 | ||||||||
\(794\) | −30.3867 | −1.07838 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.74676 | 0.0973562 | ||||||||
\(797\) | −53.6633 | −1.90085 | −0.950427 | − | 0.310949i | \(-0.899353\pi\) | ||||
−0.950427 | + | 0.310949i | \(0.899353\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −43.6575 | −1.54449 | ||||||||
\(800\) | −4.26237 | −0.150698 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 51.6802 | 1.82489 | ||||||||
\(803\) | −1.44566 | −0.0510164 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.54045 | 0.0895390 | ||||||||
\(806\) | −40.6948 | −1.43341 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −18.9140 | −0.665393 | ||||||||
\(809\) | 1.77290 | 0.0623319 | 0.0311660 | − | 0.999514i | \(-0.490078\pi\) | ||||
0.0311660 | + | 0.999514i | \(0.490078\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.70116 | −0.0597359 | −0.0298680 | − | 0.999554i | \(-0.509509\pi\) | ||||
−0.0298680 | + | 0.999554i | \(0.509509\pi\) | |||||||
\(812\) | −0.583682 | −0.0204832 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −4.99841 | −0.175194 | ||||||||
\(815\) | −15.8102 | −0.553808 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −18.6686 | −0.653131 | ||||||||
\(818\) | −35.7825 | −1.25111 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.954319 | −0.0333263 | ||||||||
\(821\) | 43.2876 | 1.51075 | 0.755374 | − | 0.655294i | \(-0.227455\pi\) | ||||
0.755374 | + | 0.655294i | \(0.227455\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −40.8222 | −1.42297 | −0.711485 | − | 0.702701i | \(-0.751977\pi\) | ||||
−0.711485 | + | 0.702701i | \(0.751977\pi\) | |||||||
\(824\) | −12.2791 | −0.427762 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.18075 | −0.284645 | ||||||||
\(827\) | −40.1223 | −1.39519 | −0.697595 | − | 0.716493i | \(-0.745746\pi\) | ||||
−0.697595 | + | 0.716493i | \(0.745746\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.4375 | −0.501437 | −0.250718 | − | 0.968060i | \(-0.580667\pi\) | ||||
−0.250718 | + | 0.968060i | \(0.580667\pi\) | |||||||
\(830\) | 9.52494 | 0.330616 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −24.8089 | −0.860093 | ||||||||
\(833\) | 19.2153 | 0.665772 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.38017 | −0.0477627 | ||||||||
\(836\) | −0.602096 | −0.0208239 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 24.6176 | 0.850399 | ||||||||
\(839\) | 50.2263 | 1.73401 | 0.867003 | − | 0.498303i | \(-0.166043\pi\) | ||||
0.867003 | + | 0.498303i | \(0.166043\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 23.4824 | 0.809258 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −3.39042 | −0.116703 | ||||||||
\(845\) | −3.39358 | −0.116743 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −33.1188 | −1.13797 | ||||||||
\(848\) | −43.9139 | −1.50801 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −23.9095 | −0.820090 | ||||||||
\(851\) | 3.14877 | 0.107938 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −29.4488 | −1.00831 | −0.504154 | − | 0.863614i | \(-0.668196\pi\) | ||||
−0.504154 | + | 0.863614i | \(0.668196\pi\) | |||||||
\(854\) | 13.5085 | 0.462251 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −15.7293 | −0.537617 | ||||||||
\(857\) | −3.87360 | −0.132320 | −0.0661598 | − | 0.997809i | \(-0.521075\pi\) | ||||
−0.0661598 | + | 0.997809i | \(0.521075\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24.7385 | 0.844068 | 0.422034 | − | 0.906580i | \(-0.361316\pi\) | ||||
0.422034 | + | 0.906580i | \(0.361316\pi\) | |||||||
\(860\) | −0.772464 | −0.0263408 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −9.35281 | −0.318558 | ||||||||
\(863\) | 14.4203 | 0.490873 | 0.245437 | − | 0.969413i | \(-0.421069\pi\) | ||||
0.245437 | + | 0.969413i | \(0.421069\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.56626 | 0.223259 | ||||||||
\(866\) | 19.6049 | 0.666202 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −6.05664 | −0.205576 | ||||||||
\(869\) | 18.4833 | 0.627002 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −25.0879 | −0.850073 | ||||||||
\(872\) | −33.1980 | −1.12423 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −4.09349 | −0.138464 | ||||||||
\(875\) | −24.0202 | −0.812030 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 24.0202 | 0.811103 | 0.405552 | − | 0.914072i | \(-0.367079\pi\) | ||||
0.405552 | + | 0.914072i | \(0.367079\pi\) | |||||||
\(878\) | −31.2455 | −1.05448 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3.14579 | 0.106044 | ||||||||
\(881\) | −37.0159 | −1.24710 | −0.623549 | − | 0.781785i | \(-0.714310\pi\) | ||||
−0.623549 | + | 0.781785i | \(0.714310\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −23.0023 | −0.774089 | −0.387045 | − | 0.922061i | \(-0.626504\pi\) | ||||
−0.387045 | + | 0.922061i | \(0.626504\pi\) | |||||||
\(884\) | 1.95020 | 0.0655923 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.58983 | −0.154198 | ||||||||
\(887\) | −41.1958 | −1.38322 | −0.691610 | − | 0.722271i | \(-0.743098\pi\) | ||||
−0.691610 | + | 0.722271i | \(0.743098\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −32.6392 | −1.09468 | ||||||||
\(890\) | 10.0806 | 0.337904 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.41613 | −0.0474156 | ||||||||
\(893\) | 33.2995 | 1.11433 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.51457 | −0.284611 | ||||||||
\(896\) | 33.2638 | 1.11127 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 11.0884 | 0.370024 | ||||||||
\(899\) | 10.3766 | 0.346079 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 47.9616 | 1.59783 | ||||||||
\(902\) | −12.1004 | −0.402898 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −15.9379 | −0.530086 | ||||||||
\(905\) | 3.13169 | 0.104101 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19.8581 | −0.659379 | −0.329689 | − | 0.944089i | \(-0.606944\pi\) | ||||
−0.329689 | + | 0.944089i | \(0.606944\pi\) | |||||||
\(908\) | −1.23524 | −0.0409929 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −9.96309 | −0.330273 | ||||||||
\(911\) | −0.186985 | −0.00619509 | −0.00309755 | − | 0.999995i | \(-0.500986\pi\) | ||||
−0.00309755 | + | 0.999995i | \(0.500986\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.1904 | −0.370350 | ||||||||
\(914\) | 53.4654 | 1.76848 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.78057 | 0.0918725 | ||||||||
\(917\) | 2.21405 | 0.0731144 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10.2250 | 0.337293 | 0.168646 | − | 0.985677i | \(-0.446060\pi\) | ||||
0.168646 | + | 0.985677i | \(0.446060\pi\) | |||||||
\(920\) | −2.16677 | −0.0714364 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −34.2888 | −1.12924 | ||||||||
\(923\) | −24.3914 | −0.802854 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −14.0281 | −0.461240 | ||||||||
\(926\) | 24.7722 | 0.814064 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0.956741 | 0.0314065 | ||||||||
\(929\) | 5.47909 | 0.179763 | 0.0898815 | − | 0.995952i | \(-0.471351\pi\) | ||||
0.0898815 | + | 0.995952i | \(0.471351\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −14.6564 | −0.480344 | ||||||||
\(932\) | 2.98741 | 0.0978560 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 6.17498 | 0.202052 | ||||||||
\(935\) | −3.43574 | −0.112361 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12.6673 | −0.413822 | −0.206911 | − | 0.978360i | \(-0.566341\pi\) | ||||
−0.206911 | + | 0.978360i | \(0.566341\pi\) | |||||||
\(938\) | 40.2974 | 1.31576 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.37786 | 0.0449408 | ||||||||
\(941\) | 29.4280 | 0.959325 | 0.479663 | − | 0.877453i | \(-0.340759\pi\) | ||||
0.479663 | + | 0.877453i | \(0.340759\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.62266 | 0.248228 | ||||||||
\(944\) | 6.38146 | 0.207699 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.79451 | −0.318447 | ||||||||
\(947\) | 26.1468 | 0.849656 | 0.424828 | − | 0.905274i | \(-0.360335\pi\) | ||||
0.424828 | + | 0.905274i | \(0.360335\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.57158 | −0.115938 | ||||||||
\(950\) | 18.2369 | 0.591682 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −40.0722 | −1.29875 | ||||||||
\(953\) | −8.31667 | −0.269403 | −0.134702 | − | 0.990886i | \(-0.543008\pi\) | ||||
−0.134702 | + | 0.990886i | \(0.543008\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 16.2050 | 0.524381 | ||||||||
\(956\) | −3.44619 | −0.111458 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −21.1949 | −0.684775 | ||||||||
\(959\) | 52.6848 | 1.70128 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 76.6739 | 2.47335 | ||||||||
\(962\) | −12.3488 | −0.398141 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −0.426379 | −0.0137327 | ||||||||
\(965\) | −12.1275 | −0.390398 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −53.2301 | −1.71176 | −0.855882 | − | 0.517171i | \(-0.826985\pi\) | ||||
−0.855882 | + | 0.517171i | \(0.826985\pi\) | |||||||
\(968\) | 28.2473 | 0.907903 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −12.9619 | −0.416183 | ||||||||
\(971\) | 59.8856 | 1.92182 | 0.960910 | − | 0.276861i | \(-0.0892942\pi\) | ||||
0.960910 | + | 0.276861i | \(0.0892942\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 28.5718 | 0.915969 | ||||||||
\(974\) | 18.9131 | 0.606014 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −10.5374 | −0.337295 | ||||||||
\(977\) | 22.6380 | 0.724253 | 0.362126 | − | 0.932129i | \(-0.382051\pi\) | ||||
0.362126 | + | 0.932129i | \(0.382051\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −11.8433 | −0.378514 | ||||||||
\(980\) | −0.606449 | −0.0193723 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 55.7275 | 1.77833 | ||||||||
\(983\) | 6.36352 | 0.202965 | 0.101482 | − | 0.994837i | \(-0.467641\pi\) | ||||
0.101482 | + | 0.994837i | \(0.467641\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −16.3996 | −0.522535 | ||||||||
\(986\) | 5.36678 | 0.170913 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.48750 | −0.0473238 | ||||||||
\(989\) | 6.17008 | 0.196197 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.24797 | −0.230239 | −0.115120 | − | 0.993352i | \(-0.536725\pi\) | ||||
−0.115120 | + | 0.993352i | \(0.536725\pi\) | |||||||
\(992\) | 9.92772 | 0.315205 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 39.1786 | 1.24267 | ||||||||
\(995\) | −11.9551 | −0.379003 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 32.7559 | 1.03739 | 0.518694 | − | 0.854960i | \(-0.326418\pi\) | ||||
0.518694 | + | 0.854960i | \(0.326418\pi\) | |||||||
\(998\) | −56.1435 | −1.77719 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6003.2.a.p.1.10 | 14 | ||
3.2 | odd | 2 | 2001.2.a.m.1.5 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2001.2.a.m.1.5 | ✓ | 14 | 3.2 | odd | 2 | ||
6003.2.a.p.1.10 | 14 | 1.1 | even | 1 | trivial |