Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6348,2,Mod(1,6348)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6348, 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("6348.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6348 = 2^{2} \cdot 3 \cdot 23^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6348.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: | \(50.6890352031\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 4x^{9} - 14x^{8} + 65x^{7} + 57x^{6} - 354x^{5} - 46x^{4} + 714x^{3} - 74x^{2} - 323x - 23 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 276) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.92165\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6348.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.68761 | −1.20194 | −0.600968 | − | 0.799273i | \(-0.705218\pi\) | ||||
−0.600968 | + | 0.799273i | \(0.705218\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.168413 | 0.0636541 | 0.0318270 | − | 0.999493i | \(-0.489867\pi\) | ||||
0.0318270 | + | 0.999493i | \(0.489867\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.32400 | 1.60525 | 0.802623 | − | 0.596487i | \(-0.203437\pi\) | ||||
0.802623 | + | 0.596487i | \(0.203437\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.84191 | 1.06555 | 0.532776 | − | 0.846256i | \(-0.321149\pi\) | ||||
0.532776 | + | 0.846256i | \(0.321149\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.68761 | −0.693938 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.65709 | 1.61458 | 0.807291 | − | 0.590154i | \(-0.200933\pi\) | ||||
0.807291 | + | 0.590154i | \(0.200933\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.89290 | 1.58134 | 0.790669 | − | 0.612243i | \(-0.209733\pi\) | ||||
0.790669 | + | 0.612243i | \(0.209733\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.168413 | 0.0367507 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.22326 | 0.444651 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.569888 | −0.105826 | −0.0529128 | − | 0.998599i | \(-0.516851\pi\) | ||||
−0.0529128 | + | 0.998599i | \(0.516851\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.95948 | −1.24996 | −0.624980 | − | 0.780641i | \(-0.714893\pi\) | ||||
−0.624980 | + | 0.780641i | \(0.714893\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.32400 | 0.926789 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.452628 | −0.0765082 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.85711 | −1.45610 | −0.728050 | − | 0.685524i | \(-0.759573\pi\) | ||||
−0.728050 | + | 0.685524i | \(0.759573\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.84191 | 0.615197 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.86755 | 0.760183 | 0.380092 | − | 0.924949i | \(-0.375892\pi\) | ||||
0.380092 | + | 0.924949i | \(0.375892\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.75736 | 1.03049 | 0.515244 | − | 0.857044i | \(-0.327701\pi\) | ||||
0.515244 | + | 0.857044i | \(0.327701\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.68761 | −0.400645 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.26730 | −0.330720 | −0.165360 | − | 0.986233i | \(-0.552879\pi\) | ||||
−0.165360 | + | 0.986233i | \(0.552879\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.97164 | −0.995948 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.65709 | 0.932179 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.87576 | −0.669737 | −0.334868 | − | 0.942265i | \(-0.608692\pi\) | ||||
−0.334868 | + | 0.942265i | \(0.608692\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −14.3088 | −1.92940 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.89290 | 0.912986 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.28099 | 0.296959 | 0.148480 | − | 0.988915i | \(-0.452562\pi\) | ||||
0.148480 | + | 0.988915i | \(0.452562\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.9609 | 1.78751 | 0.893757 | − | 0.448551i | \(-0.148060\pi\) | ||||
0.893757 | + | 0.448551i | \(0.148060\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.168413 | 0.0212180 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −10.3255 | −1.28073 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.61122 | 0.196842 | 0.0984211 | − | 0.995145i | \(-0.468621\pi\) | ||||
0.0984211 | + | 0.995145i | \(0.468621\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.49666 | −1.12705 | −0.563523 | − | 0.826100i | \(-0.690554\pi\) | ||||
−0.563523 | + | 0.826100i | \(0.690554\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.83123 | 0.448411 | 0.224206 | − | 0.974542i | \(-0.428021\pi\) | ||||
0.224206 | + | 0.974542i | \(0.428021\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.22326 | 0.256719 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.896630 | 0.102180 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.62588 | −0.295435 | −0.147717 | − | 0.989030i | \(-0.547193\pi\) | ||||
−0.147717 | + | 0.989030i | \(0.547193\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.96954 | 0.984535 | 0.492268 | − | 0.870444i | \(-0.336168\pi\) | ||||
0.492268 | + | 0.870444i | \(0.336168\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −17.8917 | −1.94062 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.569888 | −0.0610984 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.28643 | −0.666361 | −0.333180 | − | 0.942863i | \(-0.608122\pi\) | ||||
−0.333180 | + | 0.942863i | \(0.608122\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.647026 | 0.0678268 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.95948 | −0.721665 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −18.5254 | −1.90067 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.2783 | 1.34821 | 0.674105 | − | 0.738635i | \(-0.264529\pi\) | ||||
0.674105 | + | 0.738635i | \(0.264529\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.32400 | 0.535082 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.26663 | −0.723056 | −0.361528 | − | 0.932361i | \(-0.617745\pi\) | ||||
−0.361528 | + | 0.932361i | \(0.617745\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.28252 | 0.421969 | 0.210984 | − | 0.977489i | \(-0.432333\pi\) | ||||
0.210984 | + | 0.977489i | \(0.432333\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.452628 | −0.0441720 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.71161 | −0.938857 | −0.469428 | − | 0.882971i | \(-0.655540\pi\) | ||||
−0.469428 | + | 0.882971i | \(0.655540\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.85005 | 0.847681 | 0.423841 | − | 0.905737i | \(-0.360682\pi\) | ||||
0.423841 | + | 0.905737i | \(0.360682\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.85711 | −0.840679 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.54541 | −0.803884 | −0.401942 | − | 0.915665i | \(-0.631665\pi\) | ||||
−0.401942 | + | 0.915665i | \(0.631665\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.84191 | 0.355184 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.12114 | 0.102775 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 17.3450 | 1.57681 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.86755 | 0.438892 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.46281 | 0.667494 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.1659 | −1.34575 | −0.672877 | − | 0.739755i | \(-0.734942\pi\) | ||||
−0.672877 | + | 0.739755i | \(0.734942\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.75736 | 0.594952 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.75962 | −0.153739 | −0.0768696 | − | 0.997041i | \(-0.524493\pi\) | ||||
−0.0768696 | + | 0.997041i | \(0.524493\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.16085 | 0.100659 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.68761 | −0.231313 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −14.6865 | −1.25475 | −0.627375 | − | 0.778717i | \(-0.715871\pi\) | ||||
−0.627375 | + | 0.778717i | \(0.715871\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 22.3528 | 1.89594 | 0.947972 | − | 0.318355i | \(-0.103130\pi\) | ||||
0.947972 | + | 0.318355i | \(0.103130\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.26730 | −0.190941 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 20.4543 | 1.71047 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.53164 | 0.127196 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.97164 | −0.575011 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.86314 | 0.562250 | 0.281125 | − | 0.959671i | \(-0.409292\pi\) | ||||
0.281125 | + | 0.959671i | \(0.409292\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.51838 | −0.123564 | −0.0617820 | − | 0.998090i | \(-0.519678\pi\) | ||||
−0.0617820 | + | 0.998090i | \(0.519678\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.65709 | 0.538194 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 18.7044 | 1.50237 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.59043 | 0.525974 | 0.262987 | − | 0.964799i | \(-0.415292\pi\) | ||||
0.262987 | + | 0.964799i | \(0.415292\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.87576 | −0.386673 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.45066 | 0.191950 | 0.0959751 | − | 0.995384i | \(-0.469403\pi\) | ||||
0.0959751 | + | 0.995384i | \(0.469403\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −14.3088 | −1.11394 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.3057 | 0.797479 | 0.398740 | − | 0.917064i | \(-0.369448\pi\) | ||||
0.398740 | + | 0.917064i | \(0.369448\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.76024 | 0.135403 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.89290 | 0.527113 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.01452 | −0.229190 | −0.114595 | − | 0.993412i | \(-0.536557\pi\) | ||||
−0.114595 | + | 0.993412i | \(0.536557\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.374425 | 0.0283039 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.28099 | 0.171449 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −13.5122 | −1.00995 | −0.504973 | − | 0.863135i | \(-0.668498\pi\) | ||||
−0.504973 | + | 0.863135i | \(0.668498\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.8996 | −1.03315 | −0.516575 | − | 0.856242i | \(-0.672793\pi\) | ||||
−0.516575 | + | 0.856242i | \(0.672793\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 13.9609 | 1.03202 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 23.8045 | 1.75014 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 35.4423 | 2.59180 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.168413 | 0.0122502 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.7981 | −0.926035 | −0.463018 | − | 0.886349i | \(-0.653233\pi\) | ||||
−0.463018 | + | 0.886349i | \(0.653233\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.1381 | 1.16164 | 0.580822 | − | 0.814031i | \(-0.302731\pi\) | ||||
0.580822 | + | 0.814031i | \(0.302731\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −10.3255 | −0.739428 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.1747 | 0.938661 | 0.469330 | − | 0.883023i | \(-0.344495\pi\) | ||||
0.469330 | + | 0.883023i | \(0.344495\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.25611 | 0.656149 | 0.328074 | − | 0.944652i | \(-0.393600\pi\) | ||||
0.328074 | + | 0.944652i | \(0.393600\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.61122 | 0.113647 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.0959765 | −0.00673623 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −13.0821 | −0.913692 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 36.6978 | 2.53844 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.7860 | −1.01791 | −0.508955 | − | 0.860793i | \(-0.669968\pi\) | ||||
−0.508955 | + | 0.860793i | \(0.669968\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −9.49666 | −0.650700 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −18.1612 | −1.23858 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.17207 | −0.0795650 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.83123 | 0.258890 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 25.5759 | 1.72042 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.9643 | 1.00209 | 0.501043 | − | 0.865422i | \(-0.332950\pi\) | ||||
0.501043 | + | 0.865422i | \(0.332950\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.22326 | 0.148217 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −19.3027 | −1.28117 | −0.640583 | − | 0.767889i | \(-0.721307\pi\) | ||||
−0.640583 | + | 0.767889i | \(0.721307\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 26.6442 | 1.76070 | 0.880349 | − | 0.474326i | \(-0.157308\pi\) | ||||
0.880349 | + | 0.474326i | \(0.157308\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.896630 | 0.0589939 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −14.4481 | −0.946527 | −0.473263 | − | 0.880921i | \(-0.656924\pi\) | ||||
−0.473263 | + | 0.880921i | \(0.656924\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.09362 | 0.397504 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.62588 | −0.170569 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −24.1116 | −1.55965 | −0.779823 | − | 0.626000i | \(-0.784691\pi\) | ||||
−0.779823 | + | 0.626000i | \(0.784691\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.2125 | 0.722259 | 0.361129 | − | 0.932516i | \(-0.382391\pi\) | ||||
0.361129 | + | 0.932516i | \(0.382391\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 18.7371 | 1.19707 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 26.4819 | 1.68500 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.96954 | 0.568422 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 28.6735 | 1.80986 | 0.904929 | − | 0.425563i | \(-0.139924\pi\) | ||||
0.904929 | + | 0.425563i | \(0.139924\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −17.8917 | −1.12042 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 18.6188 | 1.16141 | 0.580705 | − | 0.814114i | \(-0.302777\pi\) | ||||
0.580705 | + | 0.814114i | \(0.302777\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.49165 | −0.0926867 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.569888 | −0.0352752 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 14.3106 | 0.882427 | 0.441214 | − | 0.897402i | \(-0.354548\pi\) | ||||
0.441214 | + | 0.897402i | \(0.354548\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 13.1041 | 0.804981 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.28643 | −0.384724 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.01605 | −0.427776 | −0.213888 | − | 0.976858i | \(-0.568613\pi\) | ||||
−0.213888 | + | 0.976858i | \(0.568613\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.6915 | 0.649462 | 0.324731 | − | 0.945806i | \(-0.394726\pi\) | ||||
0.324731 | + | 0.945806i | \(0.394726\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.647026 | 0.0391598 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 11.8366 | 0.713774 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.1540 | 1.33111 | 0.665553 | − | 0.746351i | \(-0.268196\pi\) | ||||
0.665553 | + | 0.746351i | \(0.268196\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.95948 | −0.416653 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.06273 | −0.421327 | −0.210664 | − | 0.977559i | \(-0.567562\pi\) | ||||
−0.210664 | + | 0.977559i | \(0.567562\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −26.9335 | −1.60103 | −0.800515 | − | 0.599313i | \(-0.795441\pi\) | ||||
−0.800515 | + | 0.599313i | \(0.795441\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −18.5254 | −1.09735 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.819758 | 0.0483888 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 27.3168 | 1.60687 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 13.2783 | 0.778390 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −28.5308 | −1.66679 | −0.833393 | − | 0.552681i | \(-0.813605\pi\) | ||||
−0.833393 | + | 0.552681i | \(0.813605\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.13041 | −0.356926 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.32400 | 0.308930 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.13803 | 0.0655948 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −7.26663 | −0.417457 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −37.5216 | −2.14848 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.6303 | −0.663774 | −0.331887 | − | 0.943319i | \(-0.607685\pi\) | ||||
−0.331887 | + | 0.943319i | \(0.607685\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.28252 | 0.243624 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 26.2524 | 1.48864 | 0.744319 | − | 0.667825i | \(-0.232774\pi\) | ||||
0.744319 | + | 0.667825i | \(0.232774\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.6165 | 1.44793 | 0.723964 | − | 0.689837i | \(-0.242318\pi\) | ||||
0.723964 | + | 0.689837i | \(0.242318\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.452628 | −0.0255027 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 20.1963 | 1.13434 | 0.567169 | − | 0.823602i | \(-0.308039\pi\) | ||||
0.567169 | + | 0.823602i | \(0.308039\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.03408 | −0.169876 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.71161 | −0.542049 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 45.8866 | 2.55320 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.54154 | 0.473799 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.85005 | 0.489409 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.381843 | −0.0210517 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −21.5420 | −1.18406 | −0.592028 | − | 0.805917i | \(-0.701673\pi\) | ||||
−0.592028 | + | 0.805917i | \(0.701673\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8.85711 | −0.485366 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.33034 | −0.236592 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.95917 | −0.106723 | −0.0533615 | − | 0.998575i | \(-0.516994\pi\) | ||||
−0.0533615 | + | 0.998575i | \(0.516994\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8.54541 | −0.464123 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −37.0523 | −2.00649 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.35300 | −0.127050 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.75901 | 0.523891 | 0.261946 | − | 0.965083i | \(-0.415636\pi\) | ||||
0.261946 | + | 0.965083i | \(0.415636\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.3641 | −0.875951 | −0.437975 | − | 0.898987i | \(-0.644304\pi\) | ||||
−0.437975 | + | 0.898987i | \(0.644304\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.84191 | 0.205066 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −18.8249 | −1.00195 | −0.500975 | − | 0.865462i | \(-0.667025\pi\) | ||||
−0.500975 | + | 0.865462i | \(0.667025\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 25.5233 | 1.35464 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.12114 | 0.0593370 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 13.1714 | 0.695158 | 0.347579 | − | 0.937651i | \(-0.387004\pi\) | ||||
0.347579 | + | 0.937651i | \(0.387004\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 28.5120 | 1.50063 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 17.3450 | 0.910374 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −10.2968 | −0.538962 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.2223 | −0.638000 | −0.319000 | − | 0.947755i | \(-0.603347\pi\) | ||||
−0.319000 | + | 0.947755i | \(0.603347\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.86755 | 0.253394 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.821140 | −0.0426315 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 25.7142 | 1.33143 | 0.665715 | − | 0.746206i | \(-0.268127\pi\) | ||||
0.665715 | + | 0.746206i | \(0.268127\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7.46281 | 0.385378 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.18946 | −0.112763 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −19.3168 | −0.992239 | −0.496120 | − | 0.868254i | \(-0.665242\pi\) | ||||
−0.496120 | + | 0.868254i | \(0.665242\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −15.1659 | −0.776971 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −26.7155 | −1.36510 | −0.682548 | − | 0.730840i | \(-0.739128\pi\) | ||||
−0.682548 | + | 0.730840i | \(0.739128\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.40979 | −0.122814 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.75736 | 0.343496 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.66024 | 0.286986 | 0.143493 | − | 0.989651i | \(-0.454167\pi\) | ||||
0.143493 | + | 0.989651i | \(0.454167\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.75962 | −0.0887613 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.05735 | 0.355094 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.82688 | 0.392820 | 0.196410 | − | 0.980522i | \(-0.437072\pi\) | ||||
0.196410 | + | 0.980522i | \(0.437072\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.16085 | 0.0581153 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.86169 | 0.442532 | 0.221266 | − | 0.975214i | \(-0.428981\pi\) | ||||
0.221266 | + | 0.975214i | \(0.428981\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −26.7377 | −1.33190 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.68761 | −0.133548 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −47.1552 | −2.33740 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.5450 | 0.669755 | 0.334878 | − | 0.942262i | \(-0.391305\pi\) | ||||
0.334878 | + | 0.942262i | \(0.391305\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −14.6865 | −0.724430 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.384147 | 0.0189027 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −24.1066 | −1.18335 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 22.3528 | 1.09462 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.44850 | −0.461590 | −0.230795 | − | 0.973002i | \(-0.574133\pi\) | ||||
−0.230795 | + | 0.973002i | \(0.574133\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 31.1359 | 1.51747 | 0.758735 | − | 0.651399i | \(-0.225818\pi\) | ||||
0.758735 | + | 0.651399i | \(0.225818\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.26730 | −0.110240 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 14.8004 | 0.717925 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.35120 | 0.113783 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 20.4543 | 0.987543 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 21.5752 | 1.03924 | 0.519621 | − | 0.854397i | \(-0.326073\pi\) | ||||
0.519621 | + | 0.854397i | \(0.326073\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.528096 | 0.0253787 | 0.0126893 | − | 0.999919i | \(-0.495961\pi\) | ||||
0.0126893 | + | 0.999919i | \(0.495961\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.53164 | 0.0734364 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.6220 | 1.03196 | 0.515980 | − | 0.856601i | \(-0.327428\pi\) | ||||
0.515980 | + | 0.856601i | \(0.327428\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.97164 | −0.331983 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 22.2377 | 1.05654 | 0.528272 | − | 0.849075i | \(-0.322840\pi\) | ||||
0.528272 | + | 0.849075i | \(0.322840\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 16.8955 | 0.800923 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6.86314 | 0.324615 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −41.7152 | −1.96866 | −0.984332 | − | 0.176325i | \(-0.943579\pi\) | ||||
−0.984332 | + | 0.176325i | \(0.943579\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 25.9148 | 1.22028 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.51838 | −0.0713397 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.73896 | −0.0815235 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −19.6407 | −0.918751 | −0.459376 | − | 0.888242i | \(-0.651927\pi\) | ||||
−0.459376 | + | 0.888242i | \(0.651927\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.65709 | 0.310726 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14.8017 | −0.689383 | −0.344692 | − | 0.938716i | \(-0.612017\pi\) | ||||
−0.344692 | + | 0.938716i | \(0.612017\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.2602 | 0.709200 | 0.354600 | − | 0.935018i | \(-0.384617\pi\) | ||||
0.354600 | + | 0.935018i | \(0.384617\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 18.7044 | 0.867395 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −15.4487 | −0.714881 | −0.357440 | − | 0.933936i | \(-0.616350\pi\) | ||||
−0.357440 | + | 0.933936i | \(0.616350\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.271351 | 0.0125298 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.59043 | 0.303671 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 35.9762 | 1.65419 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 15.3247 | 0.703144 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.87576 | −0.223246 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −18.9013 | −0.863622 | −0.431811 | − | 0.901964i | \(-0.642125\pi\) | ||||
−0.431811 | + | 0.901964i | \(0.642125\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −34.0282 | −1.55155 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −35.6870 | −1.62046 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.3167 | 0.467494 | 0.233747 | − | 0.972297i | \(-0.424901\pi\) | ||||
0.233747 | + | 0.972297i | \(0.424901\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.45066 | 0.110822 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.96153 | 0.314170 | 0.157085 | − | 0.987585i | \(-0.449790\pi\) | ||||
0.157085 | + | 0.987585i | \(0.449790\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.79380 | −0.170864 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −14.3088 | −0.643135 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.59936 | −0.0717411 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.02074 | −0.0456945 | −0.0228472 | − | 0.999739i | \(-0.507273\pi\) | ||||
−0.0228472 | + | 0.999739i | \(0.507273\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.3057 | 0.460425 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 14.4196 | 0.642937 | 0.321468 | − | 0.946920i | \(-0.395824\pi\) | ||||
0.321468 | + | 0.946920i | \(0.395824\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 19.5299 | 0.869068 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.76024 | 0.0781750 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −25.0238 | −1.10916 | −0.554580 | − | 0.832131i | \(-0.687121\pi\) | ||||
−0.554580 | + | 0.832131i | \(0.687121\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.645228 | 0.0285432 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.89290 | 0.304329 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11.5097 | −0.507180 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12.0711 | −0.530887 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.01452 | −0.132323 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −34.4792 | −1.51056 | −0.755280 | − | 0.655402i | \(-0.772499\pi\) | ||||
−0.755280 | + | 0.655402i | \(0.772499\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.5663 | 0.549485 | 0.274742 | − | 0.961518i | \(-0.411407\pi\) | ||||
0.274742 | + | 0.961518i | \(0.411407\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.374425 | 0.0163412 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −46.3299 | −2.01816 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0 | 0 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.28099 | 0.0989864 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 18.7007 | 0.810016 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 26.1010 | 1.12845 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −13.5122 | −0.583093 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −37.1170 | −1.59874 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.1406 | −0.564960 | −0.282480 | − | 0.959273i | \(-0.591157\pi\) | ||||
−0.282480 | + | 0.959273i | \(0.591157\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −13.8996 | −0.596489 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −23.7855 | −1.01886 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −35.0838 | −1.50008 | −0.750038 | − | 0.661395i | \(-0.769965\pi\) | ||||
−0.750038 | + | 0.661395i | \(0.769965\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 13.9609 | 0.595838 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.92818 | −0.167346 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.442233 | −0.0188056 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 23.8045 | 1.01044 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0.643547 | 0.0272680 | 0.0136340 | − | 0.999907i | \(-0.495660\pi\) | ||||
0.0136340 | + | 0.999907i | \(0.495660\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 25.9611 | 1.09804 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 35.4423 | 1.49638 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 11.6418 | 0.490644 | 0.245322 | − | 0.969442i | \(-0.421106\pi\) | ||||
0.245322 | + | 0.969442i | \(0.421106\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 22.9667 | 0.966218 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.168413 | 0.00707268 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 35.5814 | 1.49165 | 0.745825 | − | 0.666141i | \(-0.232055\pi\) | ||||
0.745825 | + | 0.666141i | \(0.232055\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.13581 | −0.173078 | −0.0865392 | − | 0.996248i | \(-0.527581\pi\) | ||||
−0.0865392 | + | 0.996248i | \(0.527581\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12.7981 | −0.534647 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.33356 | −0.138778 | −0.0693890 | − | 0.997590i | \(-0.522105\pi\) | ||||
−0.0693890 | + | 0.997590i | \(0.522105\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 16.1381 | 0.670676 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.51059 | 0.0626697 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −25.9585 | −1.07509 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −10.3255 | −0.426909 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13.8017 | 0.569656 | 0.284828 | − | 0.958579i | \(-0.408063\pi\) | ||||
0.284828 | + | 0.958579i | \(0.408063\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −47.9710 | −1.97661 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 13.1747 | 0.541936 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −36.1689 | −1.48528 | −0.742639 | − | 0.669692i | \(-0.766426\pi\) | ||||
−0.742639 | + | 0.669692i | \(0.766426\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.01319 | −0.123529 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9.25611 | 0.378828 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18.8219 | 0.769041 | 0.384520 | − | 0.923117i | \(-0.374367\pi\) | ||||
0.384520 | + | 0.923117i | \(0.374367\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −44.4453 | −1.81296 | −0.906481 | − | 0.422247i | \(-0.861241\pi\) | ||||
−0.906481 | + | 0.422247i | \(0.861241\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.61122 | 0.0656140 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −46.6165 | −1.89523 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24.5329 | −0.995760 | −0.497880 | − | 0.867246i | \(-0.665888\pi\) | ||||
−0.497880 | + | 0.867246i | \(0.665888\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.0959765 | −0.00388917 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.71075 | −0.352399 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.27696 | 0.0919657 | 0.0459829 | − | 0.998942i | \(-0.485358\pi\) | ||||
0.0459829 | + | 0.998942i | \(0.485358\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −13.0821 | −0.527520 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.3066 | 0.495445 | 0.247722 | − | 0.968831i | \(-0.420318\pi\) | ||||
0.247722 | + | 0.968831i | \(0.420318\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.92236 | −0.358620 | −0.179310 | − | 0.983793i | \(-0.557387\pi\) | ||||
−0.179310 | + | 0.983793i | \(0.557387\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.05872 | −0.0424166 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.1734 | −1.24694 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 36.6978 | 1.46557 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −58.9625 | −2.35099 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.0833 | 1.31702 | 0.658512 | − | 0.752570i | \(-0.271186\pi\) | ||||
0.658512 | + | 0.752570i | \(0.271186\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −14.7860 | −0.587691 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 40.7600 | 1.61751 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −26.7844 | −1.06124 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.49666 | −0.375682 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −45.5559 | −1.79935 | −0.899675 | − | 0.436560i | \(-0.856197\pi\) | ||||
−0.899675 | + | 0.436560i | \(0.856197\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.72806 | 0.265329 | 0.132664 | − | 0.991161i | \(-0.457647\pi\) | ||||
0.132664 | + | 0.991161i | \(0.457647\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −18.1612 | −0.715095 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.78380 | −0.188070 | −0.0940352 | − | 0.995569i | \(-0.529977\pi\) | ||||
−0.0940352 | + | 0.995569i | \(0.529977\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12.1440 | 0.476692 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.17207 | −0.0459369 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 31.3121 | 1.22534 | 0.612668 | − | 0.790340i | \(-0.290096\pi\) | ||||
0.612668 | + | 0.790340i | \(0.290096\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.72919 | 0.184785 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.83123 | 0.149470 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.80466 | 0.304026 | 0.152013 | − | 0.988378i | \(-0.451424\pi\) | ||||
0.152013 | + | 0.988378i | \(0.451424\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −46.7053 | −1.81663 | −0.908313 | − | 0.418291i | \(-0.862629\pi\) | ||||
−0.908313 | + | 0.418291i | \(0.862629\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 25.5759 | 0.993286 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.11992 | −0.120985 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 14.9643 | 0.578555 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 74.3280 | 2.86940 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −43.8070 | −1.68864 | −0.844318 | − | 0.535842i | \(-0.819994\pi\) | ||||
−0.844318 | + | 0.535842i | \(0.819994\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.22326 | 0.0855731 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −26.0495 | −1.00116 | −0.500582 | − | 0.865689i | \(-0.666881\pi\) | ||||
−0.500582 | + | 0.865689i | \(0.666881\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.23624 | 0.0858191 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −19.3027 | −0.739682 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.0695 | 0.461826 | 0.230913 | − | 0.972974i | \(-0.425829\pi\) | ||||
0.230913 | + | 0.972974i | \(0.425829\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 39.4715 | 1.50813 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 26.6442 | 1.01654 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −18.7322 | −0.713640 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −41.2368 | −1.56872 | −0.784360 | − | 0.620305i | \(-0.787009\pi\) | ||||
−0.784360 | + | 0.620305i | \(0.787009\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.896630 | 0.0340602 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −60.0758 | −2.27880 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 32.4037 | 1.22738 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −14.4481 | −0.546477 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15.9467 | 0.602299 | 0.301149 | − | 0.953577i | \(-0.402630\pi\) | ||||
0.301149 | + | 0.953577i | \(0.402630\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −61.0511 | −2.30259 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.09362 | 0.229499 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.22379 | −0.0460255 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.43912 | 0.204270 | 0.102135 | − | 0.994771i | \(-0.467433\pi\) | ||||
0.102135 | + | 0.994771i | \(0.467433\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.62588 | −0.0984783 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −54.9732 | −2.05588 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −24.1116 | −0.900463 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −5.60236 | −0.208933 | −0.104466 | − | 0.994528i | \(-0.533313\pi\) | ||||
−0.104466 | + | 0.994528i | \(0.533313\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.721231 | 0.0268600 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 11.2125 | 0.416996 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.26701 | −0.0470555 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −39.2481 | −1.45563 | −0.727815 | − | 0.685773i | \(-0.759464\pi\) | ||||
−0.727815 | + | 0.685773i | \(0.759464\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 44.9844 | 1.66381 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 30.2116 | 1.11589 | 0.557946 | − | 0.829877i | \(-0.311590\pi\) | ||||
0.557946 | + | 0.829877i | \(0.311590\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 18.7371 | 0.691127 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.57814 | 0.315980 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.6068 | −0.500534 | −0.250267 | − | 0.968177i | \(-0.580518\pi\) | ||||
−0.250267 | + | 0.968177i | \(0.580518\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 26.4819 | 0.972835 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.28957 | 0.120683 | 0.0603413 | − | 0.998178i | \(-0.480781\pi\) | ||||
0.0603413 | + | 0.998178i | \(0.480781\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −18.4454 | −0.675789 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8.96954 | 0.328178 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.63556 | −0.0597621 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.4896 | 0.747675 | 0.373837 | − | 0.927494i | \(-0.378042\pi\) | ||||
0.373837 | + | 0.927494i | \(0.378042\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 28.6735 | 1.04492 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.08082 | 0.148516 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 47.7612 | 1.73591 | 0.867955 | − | 0.496643i | \(-0.165434\pi\) | ||||
0.867955 | + | 0.496643i | \(0.165434\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14.1657 | 0.513505 | 0.256753 | − | 0.966477i | \(-0.417347\pi\) | ||||
0.256753 | + | 0.966477i | \(0.417347\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.49046 | 0.0539584 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −17.8917 | −0.646875 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.76333 | 0.316426 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 44.9704 | 1.62167 | 0.810836 | − | 0.585273i | \(-0.199013\pi\) | ||||
0.810836 | + | 0.585273i | \(0.199013\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.6188 | 0.670540 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −31.2256 | −1.12311 | −0.561553 | − | 0.827441i | \(-0.689796\pi\) | ||||
−0.561553 | + | 0.827441i | \(0.689796\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −15.4727 | −0.555796 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.49165 | −0.0535127 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 33.5515 | 1.20211 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −50.5602 | −1.80919 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.569888 | −0.0203661 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −17.7125 | −0.632187 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.98462 | 0.248975 | 0.124487 | − | 0.992221i | \(-0.460271\pi\) | ||||
0.124487 | + | 0.992221i | \(0.460271\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 14.3106 | 0.509470 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.43916 | −0.0511705 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 53.6366 | 1.90469 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 13.1041 | 0.464756 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.28738 | −0.116445 | −0.0582225 | − | 0.998304i | \(-0.518543\pi\) | ||||
−0.0582225 | + | 0.998304i | \(0.518543\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15.0936 | −0.533974 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.28643 | −0.222120 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 20.3974 | 0.719810 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −7.01605 | −0.246977 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −36.3906 | −1.27942 | −0.639712 | − | 0.768614i | \(-0.720946\pi\) | ||||
−0.639712 | + | 0.768614i | \(0.720946\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −50.9938 | −1.79063 | −0.895317 | − | 0.445430i | \(-0.853051\pi\) | ||||
−0.895317 | + | 0.445430i | \(0.853051\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 10.6915 | 0.374967 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.58641 | −0.230712 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 46.5778 | 1.62955 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.647026 | 0.0226089 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16.5463 | 0.577469 | 0.288734 | − | 0.957409i | \(-0.406766\pi\) | ||||
0.288734 | + | 0.957409i | \(0.406766\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.22811 | 0.286814 | 0.143407 | − | 0.989664i | \(-0.454194\pi\) | ||||
0.143407 | + | 0.989664i | \(0.454194\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 11.8366 | 0.412098 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −22.7771 | −0.792036 | −0.396018 | − | 0.918243i | \(-0.629608\pi\) | ||||
−0.396018 | + | 0.918243i | \(0.629608\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.13824 | −0.178459 | −0.0892293 | − | 0.996011i | \(-0.528440\pi\) | ||||
−0.0892293 | + | 0.996011i | \(0.528440\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 22.1540 | 0.768514 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −46.4108 | −1.60804 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −27.6977 | −0.958519 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.95948 | −0.240555 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 10.2732 | 0.354671 | 0.177336 | − | 0.984150i | \(-0.443252\pi\) | ||||
0.177336 | + | 0.984150i | \(0.443252\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.6752 | −0.988801 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −7.06273 | −0.243253 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.73084 | −0.162746 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.92111 | 0.100371 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −26.9335 | −0.924355 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −31.2764 | −1.07089 | −0.535443 | − | 0.844572i | \(-0.679855\pi\) | ||||
−0.535443 | + | 0.844572i | \(0.679855\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −18.5254 | −0.633556 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 18.7082 | 0.639060 | 0.319530 | − | 0.947576i | \(-0.396475\pi\) | ||||
0.319530 | + | 0.947576i | \(0.396475\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 41.3968 | 1.41244 | 0.706221 | − | 0.707991i | \(-0.250398\pi\) | ||||
0.706221 | + | 0.707991i | \(0.250398\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.819758 | 0.0279373 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −7.83474 | −0.266698 | −0.133349 | − | 0.991069i | \(-0.542573\pi\) | ||||
−0.133349 | + | 0.991069i | \(0.542573\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.10187 | 0.275472 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 27.3168 | 0.927729 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −13.9802 | −0.474246 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.19016 | 0.209746 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 13.2783 | 0.449404 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.25683 | 0.0424887 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 38.0372 | 1.28443 | 0.642213 | − | 0.766526i | \(-0.278016\pi\) | ||||
0.642213 | + | 0.766526i | \(0.278016\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −28.5308 | −0.962320 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −12.6784 | −0.427147 | −0.213573 | − | 0.976927i | \(-0.568510\pi\) | ||||
−0.213573 | + | 0.976927i | \(0.568510\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.53058 | 0.118813 | 0.0594067 | − | 0.998234i | \(-0.481079\pi\) | ||||
0.0594067 | + | 0.998234i | \(0.481079\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.13041 | −0.206071 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 40.2404 | 1.35114 | 0.675569 | − | 0.737296i | \(-0.263898\pi\) | ||||
0.675569 | + | 0.737296i | \(0.263898\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.55413 | −0.0856627 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.32400 | 0.178361 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −15.6283 | −0.522980 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 36.3154 | 1.21389 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.96613 | 0.132278 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −32.4584 | −1.08134 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.13803 | 0.0378712 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 37.3568 | 1.24178 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 25.8219 | 0.857403 | 0.428701 | − | 0.903446i | \(-0.358971\pi\) | ||||
0.428701 | + | 0.903446i | \(0.358971\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7.26663 | −0.241019 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.8460 | 0.491870 | 0.245935 | − | 0.969286i | \(-0.420905\pi\) | ||||
0.245935 | + | 0.969286i | \(0.420905\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 47.7538 | 1.58042 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −37.5216 | −1.24043 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.296343 | −0.00978612 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25.3485 | 0.836171 | 0.418085 | − | 0.908408i | \(-0.362701\pi\) | ||||
0.418085 | + | 0.908408i | \(0.362701\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11.6303 | −0.383230 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −36.4853 | −1.20093 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −19.6916 | −0.647456 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.28252 | 0.140656 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 45.2024 | 1.48304 | 0.741521 | − | 0.670929i | \(-0.234105\pi\) | ||||
0.741521 | + | 0.670929i | \(0.234105\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −48.0548 | −1.57493 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 26.2524 | 0.859465 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −95.2552 | −3.11518 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −52.7763 | −1.72413 | −0.862064 | − | 0.506800i | \(-0.830828\pi\) | ||||
−0.862064 | + | 0.506800i | \(0.830828\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 25.6165 | 0.835962 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 35.3014 | 1.15079 | 0.575396 | − | 0.817875i | \(-0.304848\pi\) | ||||
0.575396 | + | 0.817875i | \(0.304848\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.452628 | −0.0147240 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 59.7208 | 1.94066 | 0.970332 | − | 0.241775i | \(-0.0777296\pi\) | ||||
0.970332 | + | 0.241775i | \(0.0777296\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14.7192 | 0.477806 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 20.1963 | 0.654910 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −54.1571 | −1.75432 | −0.877161 | − | 0.480197i | \(-0.840565\pi\) | ||||
−0.877161 | + | 0.480197i | \(0.840565\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 34.3962 | 1.11304 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.03408 | −0.0980780 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.47339 | −0.0798700 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 17.4344 | 0.562399 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −9.71161 | −0.312952 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −43.3729 | −1.39622 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.5723 | −0.436457 | −0.218229 | − | 0.975898i | \(-0.570028\pi\) | ||||
−0.218229 | + | 0.975898i | \(0.570028\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 45.8866 | 1.47409 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.68048 | 0.118112 | 0.0590561 | − | 0.998255i | \(-0.481191\pi\) | ||||
0.0590561 | + | 0.998255i | \(0.481191\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.76451 | 0.120685 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 8.54154 | 0.273548 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −22.0511 | −0.705477 | −0.352738 | − | 0.935722i | \(-0.614749\pi\) | ||||
−0.352738 | + | 0.935722i | \(0.614749\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −33.4690 | −1.06967 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.85005 | 0.282560 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 27.2107 | 0.867887 | 0.433944 | − | 0.900940i | \(-0.357122\pi\) | ||||
0.433944 | + | 0.900940i | \(0.357122\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −35.4086 | −1.12821 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.381843 | −0.0121542 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.5200 | 0.461244 | 0.230622 | − | 0.973043i | \(-0.425924\pi\) | ||||
0.230622 | + | 0.973043i | \(0.425924\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −21.5420 | −0.683616 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −24.8768 | −0.788649 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.08045 | −0.160899 | −0.0804497 | − | 0.996759i | \(-0.525636\pi\) | ||||
−0.0804497 | + | 0.996759i | \(0.525636\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.85711 | −0.280226 |
(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 | 6348.2.a.t.1.2 | 10 | ||
23.17 | odd | 22 | 276.2.i.a.13.2 | ✓ | 20 | ||
23.19 | odd | 22 | 276.2.i.a.85.2 | yes | 20 | ||
23.22 | odd | 2 | 6348.2.a.s.1.9 | 10 | |||
69.17 | even | 22 | 828.2.q.c.289.1 | 20 | |||
69.65 | even | 22 | 828.2.q.c.361.1 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
276.2.i.a.13.2 | ✓ | 20 | 23.17 | odd | 22 | ||
276.2.i.a.85.2 | yes | 20 | 23.19 | odd | 22 | ||
828.2.q.c.289.1 | 20 | 69.17 | even | 22 | |||
828.2.q.c.361.1 | 20 | 69.65 | even | 22 | |||
6348.2.a.s.1.9 | 10 | 23.22 | odd | 2 | |||
6348.2.a.t.1.2 | 10 | 1.1 | even | 1 | trivial |