Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4864,2,Mod(1,4864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4864, 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("4864.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4864 = 2^{8} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4864.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: | \(38.8392355432\) |
Analytic rank: | \(1\) |
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: | \( x^{10} - 2x^{9} - 23x^{8} + 44x^{7} + 167x^{6} - 266x^{5} - 491x^{4} + 460x^{3} + 546x^{2} + 56x - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 2432) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-2.30294\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4864.1 |
$q$-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 | ||||||||
\(3\) | −0.458177 | −0.264529 | −0.132264 | − | 0.991214i | \(-0.542225\pi\) | ||||
−0.132264 | + | 0.991214i | \(0.542225\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.00397 | 1.34341 | 0.671707 | − | 0.740817i | \(-0.265561\pi\) | ||||
0.671707 | + | 0.740817i | \(0.265561\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.21624 | 0.837660 | 0.418830 | − | 0.908065i | \(-0.362440\pi\) | ||||
0.418830 | + | 0.908065i | \(0.362440\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.79007 | −0.930025 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.02382 | −1.51474 | −0.757369 | − | 0.652987i | \(-0.773516\pi\) | ||||
−0.757369 | + | 0.652987i | \(0.773516\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.22021 | −1.44783 | −0.723913 | − | 0.689892i | \(-0.757658\pi\) | ||||
−0.723913 | + | 0.689892i | \(0.757658\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.37635 | −0.355372 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.73025 | 1.87486 | 0.937430 | − | 0.348174i | \(-0.113198\pi\) | ||||
0.937430 | + | 0.348174i | \(0.113198\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.01543 | −0.221585 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.51613 | −1.35871 | −0.679353 | − | 0.733811i | \(-0.737740\pi\) | ||||
−0.679353 | + | 0.733811i | \(0.737740\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.02382 | 0.804764 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.65288 | 0.510547 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.23562 | 0.415145 | 0.207572 | − | 0.978220i | \(-0.433444\pi\) | ||||
0.207572 | + | 0.978220i | \(0.433444\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.33566 | −0.599103 | −0.299551 | − | 0.954080i | \(-0.596837\pi\) | ||||
−0.299551 | + | 0.954080i | \(0.596837\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.30180 | 0.400692 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.65751 | 1.12533 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.45208 | 0.238720 | 0.119360 | − | 0.992851i | \(-0.461916\pi\) | ||||
0.119360 | + | 0.992851i | \(0.461916\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.39178 | 0.382991 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.16461 | 0.494228 | 0.247114 | − | 0.968986i | \(-0.420518\pi\) | ||||
0.247114 | + | 0.968986i | \(0.420518\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.16101 | 0.329551 | 0.164776 | − | 0.986331i | \(-0.447310\pi\) | ||||
0.164776 | + | 0.986331i | \(0.447310\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −8.38129 | −1.24941 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.95256 | 1.45173 | 0.725865 | − | 0.687837i | \(-0.241440\pi\) | ||||
0.725865 | + | 0.687837i | \(0.241440\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.08828 | −0.298325 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.54182 | −0.495954 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.66810 | −0.915935 | −0.457967 | − | 0.888969i | \(-0.651422\pi\) | ||||
−0.457967 | + | 0.888969i | \(0.651422\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −15.0914 | −2.03492 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.458177 | 0.0606871 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.89126 | 0.506599 | 0.253299 | − | 0.967388i | \(-0.418484\pi\) | ||||
0.253299 | + | 0.967388i | \(0.418484\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.05259 | −0.902991 | −0.451496 | − | 0.892273i | \(-0.649109\pi\) | ||||
−0.451496 | + | 0.892273i | \(0.649109\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.18347 | −0.779044 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −15.6813 | −1.94503 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.2767 | −1.62201 | −0.811004 | − | 0.585041i | \(-0.801078\pi\) | ||||
−0.811004 | + | 0.585041i | \(0.801078\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.98554 | 0.359417 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.72840 | −0.679836 | −0.339918 | − | 0.940455i | \(-0.610399\pi\) | ||||
−0.339918 | + | 0.940455i | \(0.610399\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.89754 | −0.690254 | −0.345127 | − | 0.938556i | \(-0.612164\pi\) | ||||
−0.345127 | + | 0.938556i | \(0.612164\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.84362 | −0.212883 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −11.1340 | −1.26884 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.9369 | −1.79304 | −0.896522 | − | 0.442998i | \(-0.853915\pi\) | ||||
−0.896522 | + | 0.442998i | \(0.853915\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.15473 | 0.794970 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.71734 | −0.956852 | −0.478426 | − | 0.878128i | \(-0.658793\pi\) | ||||
−0.478426 | + | 0.878128i | \(0.658793\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 23.2214 | 2.51871 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.02431 | −0.109818 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.79938 | −0.402734 | −0.201367 | − | 0.979516i | \(-0.564538\pi\) | ||||
−0.201367 | + | 0.979516i | \(0.564538\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −11.5692 | −1.21279 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.52833 | 0.158480 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.00397 | −0.308201 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.94645 | −0.400701 | −0.200351 | − | 0.979724i | \(-0.564208\pi\) | ||||
−0.200351 | + | 0.979724i | \(0.564208\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 14.0168 | 1.40874 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.32025 | 0.628888 | 0.314444 | − | 0.949276i | \(-0.398182\pi\) | ||||
0.314444 | + | 0.949276i | \(0.398182\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.71201 | 0.464288 | 0.232144 | − | 0.972681i | \(-0.425426\pi\) | ||||
0.232144 | + | 0.972681i | \(0.425426\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.05032 | −0.297681 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −18.5550 | −1.79378 | −0.896892 | − | 0.442249i | \(-0.854181\pi\) | ||||
−0.896892 | + | 0.442249i | \(0.854181\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.25995 | 0.886942 | 0.443471 | − | 0.896289i | \(-0.353747\pi\) | ||||
0.443471 | + | 0.896289i | \(0.353747\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.665309 | −0.0631483 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.97386 | −0.750118 | −0.375059 | − | 0.927001i | \(-0.622378\pi\) | ||||
−0.375059 | + | 0.927001i | \(0.622378\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −19.5742 | −1.82531 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 14.5648 | 1.34651 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 17.1321 | 1.57050 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14.2387 | 1.29443 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.44995 | −0.130738 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.93242 | −0.262284 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.32912 | −0.739090 | −0.369545 | − | 0.929213i | \(-0.620486\pi\) | ||||
−0.369545 | + | 0.929213i | \(0.620486\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.990126 | −0.0871758 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.3831 | −1.43140 | −0.715700 | − | 0.698408i | \(-0.753892\pi\) | ||||
−0.715700 | + | 0.698408i | \(0.753892\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.21624 | −0.192172 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 7.96916 | 0.685876 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 16.2267 | 1.38634 | 0.693172 | − | 0.720772i | \(-0.256212\pi\) | ||||
0.693172 | + | 0.720772i | \(0.256212\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.38904 | −0.372273 | −0.186137 | − | 0.982524i | \(-0.559597\pi\) | ||||
−0.186137 | + | 0.982524i | \(0.559597\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.56004 | −0.384024 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 26.2254 | 2.19308 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.71574 | 0.557712 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.956802 | 0.0789157 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.28542 | 0.105306 | 0.0526528 | − | 0.998613i | \(-0.483232\pi\) | ||||
0.0526528 | + | 0.998613i | \(0.483232\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.07295 | −0.738346 | −0.369173 | − | 0.929361i | \(-0.620359\pi\) | ||||
−0.369173 | + | 0.929361i | \(0.620359\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −21.5680 | −1.74367 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −10.0202 | −0.804844 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.13656 | 0.250325 | 0.125162 | − | 0.992136i | \(-0.460055\pi\) | ||||
0.125162 | + | 0.992136i | \(0.460055\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.05517 | 0.242291 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −14.4413 | −1.13813 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14.9640 | −1.17207 | −0.586035 | − | 0.810286i | \(-0.699312\pi\) | ||||
−0.586035 | + | 0.810286i | \(0.699312\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6.91453 | 0.538295 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 21.0799 | 1.63121 | 0.815607 | − | 0.578606i | \(-0.196403\pi\) | ||||
0.815607 | + | 0.578606i | \(0.196403\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 14.2506 | 1.09620 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.79007 | 0.213362 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −23.7808 | −1.80802 | −0.904011 | − | 0.427510i | \(-0.859391\pi\) | ||||
−0.904011 | + | 0.427510i | \(0.859391\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.91775 | 0.674118 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.78289 | −0.134010 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −14.3018 | −1.06897 | −0.534483 | − | 0.845179i | \(-0.679494\pi\) | ||||
−0.534483 | + | 0.845179i | \(0.679494\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.9014 | −1.03328 | −0.516640 | − | 0.856203i | \(-0.672818\pi\) | ||||
−0.516640 | + | 0.856203i | \(0.672818\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.23133 | 0.238867 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.36199 | 0.320700 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −38.8353 | −2.83992 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.87942 | 0.427665 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.17747 | 0.157557 | 0.0787783 | − | 0.996892i | \(-0.474898\pi\) | ||||
0.0787783 | + | 0.996892i | \(0.474898\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 26.6410 | 1.91766 | 0.958831 | − | 0.283978i | \(-0.0916541\pi\) | ||||
0.958831 | + | 0.283978i | \(0.0916541\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 7.18483 | 0.514516 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 20.8500 | 1.48550 | 0.742749 | − | 0.669570i | \(-0.233521\pi\) | ||||
0.742749 | + | 0.669570i | \(0.233521\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.24710 | −0.301069 | −0.150535 | − | 0.988605i | \(-0.548099\pi\) | ||||
−0.150535 | + | 0.988605i | \(0.548099\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.08308 | 0.429068 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.95468 | 0.347750 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.50637 | 0.663954 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 18.1805 | 1.26363 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.02382 | 0.347505 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.1134 | 1.24698 | 0.623488 | − | 0.781833i | \(-0.285715\pi\) | ||||
0.623488 | + | 0.781833i | \(0.285715\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.62462 | 0.179836 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.49161 | 0.442724 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.39263 | −0.501845 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.70212 | 0.182592 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −40.3535 | −2.71447 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.71952 | −0.249078 | −0.124539 | − | 0.992215i | \(-0.539745\pi\) | ||||
−0.124539 | + | 0.992215i | \(0.539745\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −11.2267 | −0.748450 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 17.8318 | 1.18354 | 0.591769 | − | 0.806108i | \(-0.298430\pi\) | ||||
0.591769 | + | 0.806108i | \(0.298430\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.5159 | 0.893158 | 0.446579 | − | 0.894744i | \(-0.352642\pi\) | ||||
0.446579 | + | 0.894744i | \(0.352642\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.10134 | 0.335644 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.5061 | −1.21238 | −0.606189 | − | 0.795321i | \(-0.707302\pi\) | ||||
−0.606189 | + | 0.795321i | \(0.707302\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 29.8972 | 1.95028 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 7.30194 | 0.474312 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.6874 | 0.755995 | 0.377997 | − | 0.925807i | \(-0.376613\pi\) | ||||
0.377997 | + | 0.925807i | \(0.376613\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.2701 | 0.661554 | 0.330777 | − | 0.943709i | \(-0.392689\pi\) | ||||
0.330777 | + | 0.943709i | \(0.392689\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −11.2368 | −0.720839 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.27312 | −0.400775 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.22021 | 0.332154 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.99409 | 0.253115 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −25.1064 | −1.58470 | −0.792350 | − | 0.610066i | \(-0.791143\pi\) | ||||
−0.792350 | + | 0.610066i | \(0.791143\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 32.7358 | 2.05808 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −10.6395 | −0.666273 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12.5905 | 0.785374 | 0.392687 | − | 0.919672i | \(-0.371546\pi\) | ||||
0.392687 | + | 0.919672i | \(0.371546\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.21815 | 0.199966 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.23755 | −0.386095 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −22.7749 | −1.40436 | −0.702181 | − | 0.711999i | \(-0.747790\pi\) | ||||
−0.702181 | + | 0.711999i | \(0.747790\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −20.0308 | −1.23048 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.74079 | 0.106535 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 17.0271 | 1.03816 | 0.519081 | − | 0.854725i | \(-0.326274\pi\) | ||||
0.519081 | + | 0.854725i | \(0.326274\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.19591 | 0.497866 | 0.248933 | − | 0.968521i | \(-0.419920\pi\) | ||||
0.248933 | + | 0.968521i | \(0.419920\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.30076 | 0.320817 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −20.2149 | −1.21901 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.7174 | −1.12462 | −0.562309 | − | 0.826927i | \(-0.690087\pi\) | ||||
−0.562309 | + | 0.826927i | \(0.690087\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 9.30675 | 0.557180 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.189116 | 0.0112817 | 0.00564087 | − | 0.999984i | \(-0.498204\pi\) | ||||
0.00564087 | + | 0.999984i | \(0.498204\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.6357 | −0.632226 | −0.316113 | − | 0.948722i | \(-0.602378\pi\) | ||||
−0.316113 | + | 0.948722i | \(0.602378\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.37635 | 0.0815279 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.01353 | 0.413995 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 42.7567 | 2.51510 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.80817 | 0.105997 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −27.6765 | −1.61688 | −0.808439 | − | 0.588580i | \(-0.799687\pi\) | ||||
−0.808439 | + | 0.588580i | \(0.799687\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.6892 | 0.680572 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −13.3276 | −0.773345 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 34.0155 | 1.96717 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.78932 | 0.276052 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.89579 | −0.166359 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −21.1857 | −1.21309 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.14707 | −0.464978 | −0.232489 | − | 0.972599i | \(-0.574687\pi\) | ||||
−0.232489 | + | 0.972599i | \(0.574687\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.15894 | −0.122818 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.1283 | 0.631030 | 0.315515 | − | 0.948921i | \(-0.397823\pi\) | ||||
0.315515 | + | 0.948921i | \(0.397823\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.2647 | −0.580198 | −0.290099 | − | 0.956997i | \(-0.593688\pi\) | ||||
−0.290099 | + | 0.956997i | \(0.593688\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −18.5750 | −1.04658 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.14866 | 0.401509 | 0.200754 | − | 0.979642i | \(-0.435661\pi\) | ||||
0.200754 | + | 0.979642i | \(0.435661\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −11.2314 | −0.628836 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8.50150 | 0.474508 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.73025 | −0.430122 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −21.0052 | −1.16516 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.24270 | −0.234622 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 22.0573 | 1.21606 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 28.4370 | 1.56304 | 0.781519 | − | 0.623881i | \(-0.214445\pi\) | ||||
0.781519 | + | 0.623881i | \(0.214445\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.05140 | −0.222016 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −39.8828 | −2.17903 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.9197 | −1.03062 | −0.515311 | − | 0.857003i | \(-0.672324\pi\) | ||||
−0.515311 | + | 0.857003i | \(0.672324\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.65344 | 0.198428 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.7578 | 0.907484 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.1418 | −1.08756 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8.96847 | 0.482846 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.34140 | −0.125693 | −0.0628466 | − | 0.998023i | \(-0.520018\pi\) | ||||
−0.0628466 | + | 0.998023i | \(0.520018\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.8506 | −0.794935 | −0.397468 | − | 0.917616i | \(-0.630111\pi\) | ||||
−0.397468 | + | 0.917616i | \(0.630111\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −13.8486 | −0.739183 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −16.9690 | −0.903168 | −0.451584 | − | 0.892229i | \(-0.649141\pi\) | ||||
−0.451584 | + | 0.892229i | \(0.649141\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −17.2079 | −0.913302 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −7.84953 | −0.415441 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 32.2107 | 1.70002 | 0.850008 | − | 0.526770i | \(-0.176597\pi\) | ||||
0.850008 | + | 0.526770i | \(0.176597\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6.52387 | −0.342414 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −17.7160 | −0.927298 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.2366 | 0.534347 | 0.267173 | − | 0.963648i | \(-0.413910\pi\) | ||||
0.267173 | + | 0.963648i | \(0.413910\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.82948 | −0.459644 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −14.7781 | −0.767242 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −30.1908 | −1.56322 | −0.781610 | − | 0.623767i | \(-0.785601\pi\) | ||||
−0.781610 | + | 0.623767i | \(0.785601\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.34357 | 0.0693815 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −11.6704 | −0.601057 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.9865 | 0.821173 | 0.410586 | − | 0.911822i | \(-0.365324\pi\) | ||||
0.410586 | + | 0.911822i | \(0.365324\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.81622 | 0.195511 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 22.6961 | 1.15971 | 0.579857 | − | 0.814718i | \(-0.303108\pi\) | ||||
0.579857 | + | 0.814718i | \(0.303108\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −33.4461 | −1.70457 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.02938 | −0.306491 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12.1956 | 0.618341 | 0.309170 | − | 0.951007i | \(-0.399949\pi\) | ||||
0.309170 | + | 0.951007i | \(0.399949\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −50.3713 | −2.54738 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.50638 | 0.378647 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −47.8740 | −2.40880 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.7422 | 0.539137 | 0.269568 | − | 0.962981i | \(-0.413119\pi\) | ||||
0.269568 | + | 0.962981i | \(0.413119\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.01543 | 0.0508351 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.65983 | −0.282639 | −0.141319 | − | 0.989964i | \(-0.545134\pi\) | ||||
−0.141319 | + | 0.989964i | \(0.545134\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 17.4129 | 0.867396 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 21.4926 | 1.06797 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.29497 | −0.361598 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −27.6645 | −1.36792 | −0.683960 | − | 0.729520i | \(-0.739744\pi\) | ||||
−0.683960 | + | 0.729520i | \(0.739744\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.43473 | −0.366728 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.62396 | 0.424357 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −26.1866 | −1.28545 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.01096 | 0.0984770 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.91763 | 0.337948 | 0.168974 | − | 0.985620i | \(-0.445955\pi\) | ||||
0.168974 | + | 0.985620i | \(0.445955\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.07015 | −0.149630 | −0.0748150 | − | 0.997197i | \(-0.523837\pi\) | ||||
−0.0748150 | + | 0.997197i | \(0.523837\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −27.7684 | −1.35014 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 31.1051 | 1.50882 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −15.6302 | −0.756400 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −12.0159 | −0.580132 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.2015 | −0.635893 | −0.317946 | − | 0.948109i | \(-0.602993\pi\) | ||||
−0.317946 | + | 0.948109i | \(0.602993\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −20.1544 | −0.968559 | −0.484279 | − | 0.874913i | \(-0.660918\pi\) | ||||
−0.484279 | + | 0.874913i | \(0.660918\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.07700 | −0.147531 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.51613 | 0.311709 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.72144 | 0.0821601 | 0.0410800 | − | 0.999156i | \(-0.486920\pi\) | ||||
0.0410800 | + | 0.999156i | \(0.486920\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.82645 | 0.277450 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −38.0168 | −1.80623 | −0.903117 | − | 0.429395i | \(-0.858727\pi\) | ||||
−0.903117 | + | 0.429395i | \(0.858727\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11.4132 | −0.541039 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.588950 | −0.0278564 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −27.1861 | −1.28299 | −0.641496 | − | 0.767127i | \(-0.721686\pi\) | ||||
−0.641496 | + | 0.767127i | \(0.721686\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −15.8984 | −0.748626 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.15702 | 0.195314 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −34.7536 | −1.62927 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.8069 | 0.739415 | 0.369708 | − | 0.929148i | \(-0.379458\pi\) | ||||
0.369708 | + | 0.929148i | \(0.379458\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 20.5074 | 0.957204 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 29.7741 | 1.38672 | 0.693358 | − | 0.720593i | \(-0.256130\pi\) | ||||
0.693358 | + | 0.720593i | \(0.256130\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.8339 | 0.549967 | 0.274984 | − | 0.961449i | \(-0.411328\pi\) | ||||
0.274984 | + | 0.961449i | \(0.411328\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.59104 | 0.212904 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −30.6052 | −1.41624 | −0.708121 | − | 0.706091i | \(-0.750457\pi\) | ||||
−0.708121 | + | 0.706091i | \(0.750457\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −29.4244 | −1.35869 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.43710 | −0.0662181 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −10.8565 | −0.499184 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.02382 | −0.184625 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 18.6045 | 0.851842 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12.3908 | 0.566150 | 0.283075 | − | 0.959098i | \(-0.408645\pi\) | ||||
0.283075 | + | 0.959098i | \(0.408645\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.58015 | −0.345625 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.61668 | 0.301069 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −11.8550 | −0.538308 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.61617 | 0.345122 | 0.172561 | − | 0.984999i | \(-0.444796\pi\) | ||||
0.172561 | + | 0.984999i | \(0.444796\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.85616 | 0.310046 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.09291 | 0.139581 | 0.0697906 | − | 0.997562i | \(-0.477767\pi\) | ||||
0.0697906 | + | 0.997562i | \(0.477767\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 17.2819 | 0.778338 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 42.1061 | 1.89253 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −12.6955 | −0.569472 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.55042 | 0.293237 | 0.146618 | − | 0.989193i | \(-0.453161\pi\) | ||||
0.146618 | + | 0.989193i | \(0.453161\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.65835 | −0.431503 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 34.9332 | 1.55760 | 0.778798 | − | 0.627275i | \(-0.215830\pi\) | ||||
0.778798 | + | 0.627275i | \(0.215830\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.9858 | 0.844858 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.52928 | −0.289976 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10.6461 | −0.471882 | −0.235941 | − | 0.971767i | \(-0.575817\pi\) | ||||
−0.235941 | + | 0.971767i | \(0.575817\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.0704 | −0.578199 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.65288 | −0.117128 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 14.1547 | 0.623732 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −49.9999 | −2.19899 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10.8958 | 0.478274 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −33.7087 | −1.47681 | −0.738403 | − | 0.674359i | \(-0.764420\pi\) | ||||
−0.738403 | + | 0.674359i | \(0.764420\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.61224 | 0.157952 | 0.0789761 | − | 0.996877i | \(-0.474835\pi\) | ||||
0.0789761 | + | 0.996877i | \(0.474835\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.08591 | −0.178324 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −25.7855 | −1.12323 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.4599 | 0.846084 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10.8569 | −0.471149 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −16.5199 | −0.715556 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −55.7388 | −2.40980 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.55276 | 0.282772 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10.4911 | 0.451885 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 45.1835 | 1.94259 | 0.971295 | − | 0.237876i | \(-0.0764513\pi\) | ||||
0.971295 | + | 0.237876i | \(0.0764513\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.36929 | 0.273332 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 27.8166 | 1.19153 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 25.9716 | 1.11047 | 0.555233 | − | 0.831695i | \(-0.312629\pi\) | ||||
0.555233 | + | 0.831695i | \(0.312629\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 19.6772 | 0.839804 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.23562 | −0.0952408 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −35.3201 | −1.50196 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.99857 | −0.0848344 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 27.5515 | 1.16739 | 0.583697 | − | 0.811972i | \(-0.301606\pi\) | ||||
0.583697 | + | 0.811972i | \(0.301606\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11.2809 | −0.477132 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 17.7935 | 0.751241 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 14.8531 | 0.625985 | 0.312992 | − | 0.949756i | \(-0.398669\pi\) | ||||
0.312992 | + | 0.949756i | \(0.398669\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −23.9532 | −1.00772 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 15.8566 | 0.665915 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.86281 | −0.203859 | −0.101930 | − | 0.994792i | \(-0.532502\pi\) | ||||
−0.101930 | + | 0.994792i | \(0.532502\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.6960 | −0.907948 | −0.453974 | − | 0.891015i | \(-0.649994\pi\) | ||||
−0.453974 | + | 0.891015i | \(0.649994\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.997669 | −0.0416782 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −26.2197 | −1.09344 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 28.5083 | 1.18682 | 0.593409 | − | 0.804901i | \(-0.297782\pi\) | ||||
0.593409 | + | 0.804901i | \(0.297782\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −12.2063 | −0.507277 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −19.3197 | −0.801517 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 33.4993 | 1.38740 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 43.7521 | 1.80893 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22.5133 | 0.929224 | 0.464612 | − | 0.885514i | \(-0.346194\pi\) | ||||
0.464612 | + | 0.885514i | \(0.346194\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.33566 | 0.137444 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.55298 | −0.392957 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −11.0209 | −0.452574 | −0.226287 | − | 0.974061i | \(-0.572659\pi\) | ||||
−0.226287 | + | 0.974061i | \(0.572659\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 51.4642 | 2.10983 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.94593 | 0.0796414 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −18.7308 | −0.765319 | −0.382659 | − | 0.923890i | \(-0.624992\pi\) | ||||
−0.382659 | + | 0.923890i | \(0.624992\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.8859 | 0.607209 | 0.303604 | − | 0.952798i | \(-0.401810\pi\) | ||||
0.303604 | + | 0.952798i | \(0.401810\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 37.0430 | 1.50851 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 42.7727 | 1.73896 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 37.9701 | 1.54116 | 0.770579 | − | 0.637345i | \(-0.219967\pi\) | ||||
0.770579 | + | 0.637345i | \(0.219967\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.27012 | −0.0919900 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −51.9544 | −2.10185 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 28.5379 | 1.15264 | 0.576318 | − | 0.817226i | \(-0.304489\pi\) | ||||
0.576318 | + | 0.817226i | \(0.304489\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4.35560 | −0.175635 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.91835 | 0.157747 | 0.0788733 | − | 0.996885i | \(-0.474868\pi\) | ||||
0.0788733 | + | 0.996885i | \(0.474868\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.37059 | 0.215862 | 0.107931 | − | 0.994158i | \(-0.465577\pi\) | ||||
0.107931 | + | 0.994158i | \(0.465577\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −17.2865 | −0.693684 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.42035 | −0.337354 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −28.9280 | −1.15712 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.30180 | −0.0919250 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 11.2249 | 0.447567 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.6483 | 0.742377 | 0.371189 | − | 0.928557i | \(-0.378950\pi\) | ||||
0.371189 | + | 0.928557i | \(0.378950\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.29913 | −0.329861 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −25.0204 | −0.992905 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 10.9012 | 0.431923 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 15.9827 | 0.632264 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 42.2857 | 1.67018 | 0.835092 | − | 0.550111i | \(-0.185415\pi\) | ||||
0.835092 | + | 0.550111i | \(0.185415\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.4426 | 0.727305 | 0.363652 | − | 0.931535i | \(-0.381530\pi\) | ||||
0.363652 | + | 0.931535i | \(0.381530\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.97431 | −0.117113 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.19012 | 0.0861024 | 0.0430512 | − | 0.999073i | \(-0.486292\pi\) | ||||
0.0430512 | + | 0.999073i | \(0.486292\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −19.5490 | −0.767364 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.38714 | 0.132752 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 43.8208 | 1.71484 | 0.857420 | − | 0.514617i | \(-0.172066\pi\) | ||||
0.857420 | + | 0.514617i | \(0.172066\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −49.2144 | −1.92296 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 16.4546 | 0.641954 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11.0297 | 0.429657 | 0.214829 | − | 0.976652i | \(-0.431081\pi\) | ||||
0.214829 | + | 0.976652i | \(0.431081\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.49137 | 0.291381 | 0.145690 | − | 0.989330i | \(-0.453460\pi\) | ||||
0.145690 | + | 0.989330i | \(0.453460\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 18.4890 | 0.718055 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6.65751 | −0.258167 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −14.5676 | −0.564060 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.70420 | 0.0658882 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 35.4309 | 1.36780 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −34.6195 | −1.33448 | −0.667242 | − | 0.744841i | \(-0.732525\pi\) | ||||
−0.667242 | + | 0.744841i | \(0.732525\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 10.6747 | 0.410870 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −29.0201 | −1.11533 | −0.557666 | − | 0.830066i | \(-0.688303\pi\) | ||||
−0.557666 | + | 0.830066i | \(0.688303\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.74629 | −0.335652 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.17012 | −0.313080 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 13.3799 | 0.511966 | 0.255983 | − | 0.966681i | \(-0.417601\pi\) | ||||
0.255983 | + | 0.966681i | \(0.417601\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 48.7446 | 1.86244 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.19269 | −0.236266 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 34.8089 | 1.32611 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 40.7415 | 1.54988 | 0.774940 | − | 0.632035i | \(-0.217780\pi\) | ||||
0.774940 | + | 0.632035i | \(0.217780\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 31.0646 | 1.18005 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −13.1845 | −0.500118 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 24.4632 | 0.926609 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8.47909 | 0.320709 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −43.7760 | −1.65340 | −0.826698 | − | 0.562645i | \(-0.809784\pi\) | ||||
−0.826698 | + | 0.562645i | \(0.809784\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.45208 | −0.0547662 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −13.6982 | −0.515904 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 14.0072 | 0.526795 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 26.0155 | 0.977031 | 0.488516 | − | 0.872555i | \(-0.337538\pi\) | ||||
0.488516 | + | 0.872555i | \(0.337538\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 44.4652 | 1.66758 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 21.7356 | 0.814005 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 78.7801 | 2.94621 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5.35490 | −0.199982 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −31.3051 | −1.16748 | −0.583741 | − | 0.811940i | \(-0.698412\pi\) | ||||
−0.583741 | + | 0.811940i | \(0.698412\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.4430 | 0.388916 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4.70552 | −0.175000 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.99574 | 0.334093 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.31403 | 0.271262 | 0.135631 | − | 0.990759i | \(-0.456694\pi\) | ||||
0.135631 | + | 0.990759i | \(0.456694\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −16.3158 | −0.604287 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 16.7051 | 0.617862 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13.0935 | −0.483620 | −0.241810 | − | 0.970324i | \(-0.577741\pi\) | ||||
−0.241810 | + | 0.970324i | \(0.577741\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.87420 | 0.106016 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 66.6997 | 2.45692 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10.5782 | 0.389124 | 0.194562 | − | 0.980890i | \(-0.437672\pi\) | ||||
0.194562 | + | 0.980890i | \(0.437672\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.39178 | −0.0878642 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 23.6180 | 0.866460 | 0.433230 | − | 0.901283i | \(-0.357374\pi\) | ||||
0.433230 | + | 0.901283i | \(0.357374\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.86136 | 0.141469 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 24.3220 | 0.889896 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −41.1225 | −1.50258 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −24.5994 | −0.897644 | −0.448822 | − | 0.893621i | \(-0.648156\pi\) | ||||
−0.448822 | + | 0.893621i | \(0.648156\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 11.5032 | 0.419199 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −27.2548 | −0.991905 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.03483 | 0.110303 | 0.0551514 | − | 0.998478i | \(-0.482436\pi\) | ||||
0.0551514 | + | 0.998478i | \(0.482436\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −14.9988 | −0.544423 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8.15330 | −0.295557 | −0.147778 | − | 0.989020i | \(-0.547212\pi\) | ||||
−0.147778 | + | 0.989020i | \(0.547212\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 20.5223 | 0.742956 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −64.7894 | −2.34247 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −20.3132 | −0.733466 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.2744 | −0.514747 | −0.257374 | − | 0.966312i | \(-0.582857\pi\) | ||||
−0.257374 | + | 0.966312i | \(0.582857\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.76868 | −0.207754 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −45.2404 | −1.62718 | −0.813591 | − | 0.581437i | \(-0.802491\pi\) | ||||
−0.813591 | + | 0.581437i | \(0.802491\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −13.4221 | −0.482136 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.47448 | −0.0528968 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.16461 | −0.113384 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 28.7784 | 1.02977 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.93084 | 0.211951 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.42212 | 0.336290 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −50.1656 | −1.78821 | −0.894106 | − | 0.447856i | \(-0.852188\pi\) | ||||
−0.894106 | + | 0.447856i | \(0.852188\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 10.4349 | 0.371494 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17.6720 | −0.628344 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 36.8160 | 1.30737 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 9.17764 | 0.325497 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −21.7396 | −0.770056 | −0.385028 | − | 0.922905i | \(-0.625808\pi\) | ||||
−0.385028 | + | 0.922905i | \(0.625808\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 76.9357 | 2.72179 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10.6006 | 0.374552 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 29.6281 | 1.04555 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −43.3812 | −1.52899 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −7.80144 | −0.274624 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −9.48695 | −0.333543 | −0.166772 | − | 0.985996i | \(-0.553334\pi\) | ||||
−0.166772 | + | 0.985996i | \(0.553334\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22.6529 | 0.795450 | 0.397725 | − | 0.917505i | \(-0.369800\pi\) | ||||
0.397725 | + | 0.917505i | \(0.369800\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.75518 | −0.131700 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −44.9513 | −1.57458 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.16101 | −0.0756042 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 32.2790 | 1.12792 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 26.4552 | 0.923292 | 0.461646 | − | 0.887064i | \(-0.347259\pi\) | ||||
0.461646 | + | 0.887064i | \(0.347259\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −35.1129 | −1.22396 | −0.611980 | − | 0.790873i | \(-0.709627\pi\) | ||||
−0.611980 | + | 0.790873i | \(0.709627\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 9.26202 | 0.322462 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −27.4003 | −0.952803 | −0.476402 | − | 0.879228i | \(-0.658059\pi\) | ||||
−0.476402 | + | 0.879228i | \(0.658059\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25.2213 | 0.875972 | 0.437986 | − | 0.898982i | \(-0.355692\pi\) | ||||
0.437986 | + | 0.898982i | \(0.355692\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.57588 | 0.297494 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −16.1429 | −0.559319 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 63.3234 | 2.19140 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.84912 | −0.305870 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −36.8869 | −1.27348 | −0.636738 | − | 0.771080i | \(-0.719717\pi\) | ||||
−0.636738 | + | 0.771080i | \(0.719717\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.0020 | −0.827655 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.0866488 | −0.00298434 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 42.8082 | 1.47265 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 31.5565 | 1.08429 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.87303 | 0.167242 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.46193 | −0.324351 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.36746 | 0.115300 | 0.0576499 | − | 0.998337i | \(-0.481639\pi\) | ||||
0.0576499 | + | 0.998337i | \(0.481639\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.38129 | 0.286634 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −16.0416 | −0.547970 | −0.273985 | − | 0.961734i | \(-0.588342\pi\) | ||||
−0.273985 | + | 0.961734i | \(0.588342\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14.7310 | −0.502614 | −0.251307 | − | 0.967907i | \(-0.580860\pi\) | ||||
−0.251307 | + | 0.967907i | \(0.580860\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.21344 | −0.109514 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 41.3034 | 1.40598 | 0.702991 | − | 0.711198i | \(-0.251847\pi\) | ||||
0.702991 | + | 0.711198i | \(0.251847\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −71.4368 | −2.42892 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −19.5901 | −0.665316 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 80.0642 | 2.71599 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 69.3071 | 2.34838 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 11.0109 | 0.372662 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6.49895 | −0.219704 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.84438 | −0.129815 | −0.0649077 | − | 0.997891i | \(-0.520675\pi\) | ||||
−0.0649077 | + | 0.997891i | \(0.520675\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 12.6807 | 0.427711 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.57677 | −0.154195 | −0.0770976 | − | 0.997024i | \(-0.524565\pi\) | ||||
−0.0770976 | + | 0.997024i | \(0.524565\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.34140 | 0.0787945 | 0.0393972 | − | 0.999224i | \(-0.487456\pi\) | ||||
0.0393972 | + | 0.999224i | \(0.487456\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5.35573 | −0.180031 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 48.1958 | 1.61826 | 0.809129 | − | 0.587631i | \(-0.199939\pi\) | ||||
0.809129 | + | 0.587631i | \(0.199939\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −18.4593 | −0.619106 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −35.9441 | −1.20417 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9.95256 | −0.333050 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −42.9621 | −1.43607 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −15.5851 | −0.520373 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7.45729 | −0.248714 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −51.5461 | −1.71725 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.19436 | −0.0730237 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −41.7593 | −1.38812 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.08133 | 0.135518 | 0.0677592 | − | 0.997702i | \(-0.478415\pi\) | ||||
0.0677592 | + | 0.997702i | \(0.478415\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −17.6340 | −0.584881 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 54.1174 | 1.79299 | 0.896495 | − | 0.443054i | \(-0.146105\pi\) | ||||
0.896495 | + | 0.443054i | \(0.146105\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 43.7943 | 1.44938 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 9.70682 | 0.320898 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −36.3089 | −1.19903 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 32.1252 | 1.05971 | 0.529857 | − | 0.848087i | \(-0.322246\pi\) | ||||
0.529857 | + | 0.848087i | \(0.322246\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.73280 | 0.123000 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 29.9034 | 0.984284 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.84290 | 0.192113 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −13.1469 | −0.431800 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −10.9339 | −0.358730 | −0.179365 | − | 0.983783i | \(-0.557404\pi\) | ||||
−0.179365 | + | 0.983783i | \(0.557404\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.08828 | 0.0684406 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.09875 | −0.166926 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −116.660 | −3.81519 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −46.5172 | −1.51965 | −0.759825 | − | 0.650127i | \(-0.774716\pi\) | ||||
−0.759825 | + | 0.650127i | \(0.774716\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.70307 | 0.153479 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −39.9678 | −1.30291 | −0.651457 | − | 0.758686i | \(-0.725842\pi\) | ||||
−0.651457 | + | 0.758686i | \(0.725842\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −20.6210 | −0.671511 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 17.6616 | 0.574531 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −33.7011 | −1.09514 | −0.547569 | − | 0.836761i | \(-0.684447\pi\) | ||||
−0.547569 | + | 0.836761i | \(0.684447\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 30.7864 | 0.999368 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.27535 | −0.106211 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −30.1472 | −0.976564 | −0.488282 | − | 0.872686i | \(-0.662376\pi\) | ||||
−0.488282 | + | 0.872686i | \(0.662376\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.54106 | 0.211664 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.14596 | 0.166345 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 35.9624 | 1.16129 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.8733 | −0.641076 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 51.7700 | 1.66826 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 80.0287 | 2.57622 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 35.1010 | 1.12877 | 0.564385 | − | 0.825511i | \(-0.309113\pi\) | ||||
0.564385 | + | 0.825511i | \(0.309113\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.54182 | 0.113780 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 38.1884 | 1.22552 | 0.612762 | − | 0.790268i | \(-0.290059\pi\) | ||||
0.612762 | + | 0.790268i | \(0.290059\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.72716 | −0.311839 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 9.62409 | 0.308217 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 22.6596 | 0.724946 | 0.362473 | − | 0.931994i | \(-0.381933\pi\) | ||||
0.362473 | + | 0.931994i | \(0.381933\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 19.0874 | 0.610036 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −25.8359 | −0.824878 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.47180 | 0.0469430 | 0.0234715 | − | 0.999725i | \(-0.492528\pi\) | ||||
0.0234715 | + | 0.999725i | \(0.492528\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 62.6326 | 1.99564 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −10.1061 | −0.321682 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −14.0814 | −0.447763 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −30.6228 | −0.972767 | −0.486383 | − | 0.873746i | \(-0.661684\pi\) | ||||
−0.486383 | + | 0.873746i | \(0.661684\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −13.0292 | −0.413469 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −12.7582 | −0.404461 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.61232 | −0.241085 | −0.120542 | − | 0.992708i | \(-0.538463\pi\) | ||||
−0.120542 | + | 0.992708i | \(0.538463\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.85219 | 0.121878 |
(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 | 4864.2.a.bs.1.6 | 10 | ||
4.3 | odd | 2 | 4864.2.a.bt.1.6 | 10 | |||
8.3 | odd | 2 | inner | 4864.2.a.bs.1.5 | 10 | ||
8.5 | even | 2 | 4864.2.a.bt.1.5 | 10 | |||
16.3 | odd | 4 | 2432.2.c.j.1217.11 | yes | 20 | ||
16.5 | even | 4 | 2432.2.c.j.1217.12 | yes | 20 | ||
16.11 | odd | 4 | 2432.2.c.j.1217.10 | yes | 20 | ||
16.13 | even | 4 | 2432.2.c.j.1217.9 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2432.2.c.j.1217.9 | ✓ | 20 | 16.13 | even | 4 | ||
2432.2.c.j.1217.10 | yes | 20 | 16.11 | odd | 4 | ||
2432.2.c.j.1217.11 | yes | 20 | 16.3 | odd | 4 | ||
2432.2.c.j.1217.12 | yes | 20 | 16.5 | even | 4 | ||
4864.2.a.bs.1.5 | 10 | 8.3 | odd | 2 | inner | ||
4864.2.a.bs.1.6 | 10 | 1.1 | even | 1 | trivial | ||
4864.2.a.bt.1.5 | 10 | 8.5 | even | 2 | |||
4864.2.a.bt.1.6 | 10 | 4.3 | odd | 2 |