Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3800,2,Mod(1,3800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3800.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3800 = 2^{3} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3800.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: | \(30.3431527681\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.253565184.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 11x^{4} + 20x^{3} + 22x^{2} - 32x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 760) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-1.59277\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3800.1 |
$q$-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 | ||||||||
\(3\) | 1.59277 | 0.919588 | 0.459794 | − | 0.888026i | \(-0.347923\pi\) | ||||
0.459794 | + | 0.888026i | \(0.347923\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.66290 | −0.628516 | −0.314258 | − | 0.949338i | \(-0.601756\pi\) | ||||
−0.314258 | + | 0.949338i | \(0.601756\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.463073 | −0.154358 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.56511 | 1.67794 | 0.838972 | − | 0.544174i | \(-0.183157\pi\) | ||||
0.838972 | + | 0.544174i | \(0.183157\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.31979 | −1.75280 | −0.876398 | − | 0.481588i | \(-0.840060\pi\) | ||||
−0.876398 | + | 0.481588i | \(0.840060\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.12142 | −0.999592 | −0.499796 | − | 0.866143i | \(-0.666592\pi\) | ||||
−0.499796 | + | 0.866143i | \(0.666592\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.64862 | −0.577976 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.82315 | 0.380154 | 0.190077 | − | 0.981769i | \(-0.439126\pi\) | ||||
0.190077 | + | 0.981769i | \(0.439126\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.51589 | −1.06153 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.08942 | −0.759385 | −0.379693 | − | 0.925113i | \(-0.623970\pi\) | ||||
−0.379693 | + | 0.925113i | \(0.623970\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.61202 | 1.18755 | 0.593777 | − | 0.804630i | \(-0.297636\pi\) | ||||
0.593777 | + | 0.804630i | \(0.297636\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 8.86396 | 1.54302 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.66787 | −1.58939 | −0.794694 | − | 0.607010i | \(-0.792369\pi\) | ||||
−0.794694 | + | 0.607010i | \(0.792369\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −10.0660 | −1.61185 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.61202 | −0.720277 | −0.360138 | − | 0.932899i | \(-0.617271\pi\) | ||||
−0.360138 | + | 0.932899i | \(0.617271\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.75231 | 0.572222 | 0.286111 | − | 0.958196i | \(-0.407637\pi\) | ||||
0.286111 | + | 0.958196i | \(0.407637\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.85299 | 0.562017 | 0.281008 | − | 0.959705i | \(-0.409331\pi\) | ||||
0.281008 | + | 0.959705i | \(0.409331\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.23477 | −0.604967 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.56449 | −0.919213 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.24594 | −0.720585 | −0.360293 | − | 0.932839i | \(-0.617323\pi\) | ||||
−0.360293 | + | 0.932839i | \(0.617323\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.59277 | 0.210968 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −11.5291 | −1.50097 | −0.750483 | − | 0.660890i | \(-0.770179\pi\) | ||||
−0.750483 | + | 0.660890i | \(0.770179\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.02587 | 1.02761 | 0.513804 | − | 0.857908i | \(-0.328236\pi\) | ||||
0.513804 | + | 0.857908i | \(0.328236\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.770043 | 0.0970164 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.155284 | −0.0189710 | −0.00948548 | − | 0.999955i | \(-0.503019\pi\) | ||||
−0.00948548 | + | 0.999955i | \(0.503019\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.90387 | 0.349585 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.1645 | −1.44366 | −0.721831 | − | 0.692069i | \(-0.756699\pi\) | ||||
−0.721831 | + | 0.692069i | \(0.756699\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.795627 | −0.0931211 | −0.0465606 | − | 0.998915i | \(-0.514826\pi\) | ||||
−0.0465606 | + | 0.998915i | \(0.514826\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −9.25422 | −1.05462 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.18555 | −0.808437 | −0.404219 | − | 0.914662i | \(-0.632456\pi\) | ||||
−0.404219 | + | 0.914662i | \(0.632456\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.39634 | −0.821816 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.88500 | −0.645963 | −0.322981 | − | 0.946405i | \(-0.604685\pi\) | ||||
−0.322981 | + | 0.946405i | \(0.604685\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.51351 | −0.698322 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 18.5476 | 1.96604 | 0.983021 | − | 0.183492i | \(-0.0587401\pi\) | ||||
0.983021 | + | 0.183492i | \(0.0587401\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.5092 | 1.10166 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 10.5315 | 1.09206 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.77634 | −0.281894 | −0.140947 | − | 0.990017i | \(-0.545015\pi\) | ||||
−0.140947 | + | 0.990017i | \(0.545015\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.57705 | −0.259004 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.6991 | −1.36311 | −0.681557 | − | 0.731765i | \(-0.738697\pi\) | ||||
−0.681557 | + | 0.731765i | \(0.738697\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.42279 | −0.731389 | −0.365695 | − | 0.930735i | \(-0.619169\pi\) | ||||
−0.365695 | + | 0.930735i | \(0.619169\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.8010 | 1.33419 | 0.667097 | − | 0.744971i | \(-0.267537\pi\) | ||||
0.667097 | + | 0.744971i | \(0.267537\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.7543 | −1.22164 | −0.610818 | − | 0.791771i | \(-0.709159\pi\) | ||||
−0.610818 | + | 0.791771i | \(0.709159\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −15.3987 | −1.46158 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.81913 | −0.735562 | −0.367781 | − | 0.929912i | \(-0.619882\pi\) | ||||
−0.367781 | + | 0.929912i | \(0.619882\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.92653 | 0.270558 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.85351 | 0.628260 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 19.9705 | 1.81550 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −7.34591 | −0.662358 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.07017 | −0.449905 | −0.224952 | − | 0.974370i | \(-0.572223\pi\) | ||||
−0.224952 | + | 0.974370i | \(0.572223\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.97658 | 0.526209 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.8720 | 0.949895 | 0.474947 | − | 0.880014i | \(-0.342467\pi\) | ||||
0.474947 | + | 0.880014i | \(0.342467\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.66290 | −0.144192 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.53861 | −0.644067 | −0.322033 | − | 0.946728i | \(-0.604366\pi\) | ||||
−0.322033 | + | 0.946728i | \(0.604366\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.885954 | −0.0751457 | −0.0375728 | − | 0.999294i | \(-0.511963\pi\) | ||||
−0.0375728 | + | 0.999294i | \(0.511963\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.13694 | 0.516824 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −35.1704 | −2.94109 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.74503 | −0.556321 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.2594 | 1.00433 | 0.502166 | − | 0.864771i | \(-0.332537\pi\) | ||||
0.502166 | + | 0.864771i | \(0.332537\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.95140 | −0.240181 | −0.120091 | − | 0.992763i | \(-0.538319\pi\) | ||||
−0.120091 | + | 0.992763i | \(0.538319\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.90852 | 0.154295 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.7951 | 1.26058 | 0.630292 | − | 0.776358i | \(-0.282935\pi\) | ||||
0.630292 | + | 0.776358i | \(0.282935\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.35559 | −0.662642 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.03172 | −0.238933 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 20.4459 | 1.60144 | 0.800721 | − | 0.599037i | \(-0.204450\pi\) | ||||
0.800721 | + | 0.599037i | \(0.204450\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −14.6083 | −1.13043 | −0.565213 | − | 0.824945i | \(-0.691206\pi\) | ||||
−0.565213 | + | 0.824945i | \(0.691206\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 26.9398 | 2.07229 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.463073 | −0.0354121 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −19.4244 | −1.47681 | −0.738406 | − | 0.674356i | \(-0.764421\pi\) | ||||
−0.738406 | + | 0.674356i | \(0.764421\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −18.3633 | −1.38027 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.21080 | −0.538960 | −0.269480 | − | 0.963006i | \(-0.586852\pi\) | ||||
−0.269480 | + | 0.963006i | \(0.586852\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.1237 | −0.752488 | −0.376244 | − | 0.926521i | \(-0.622785\pi\) | ||||
−0.376244 | + | 0.926521i | \(0.622785\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 12.7834 | 0.944976 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −22.9362 | −1.67726 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 9.17236 | 0.667191 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −24.4017 | −1.76564 | −0.882821 | − | 0.469709i | \(-0.844359\pi\) | ||||
−0.882821 | + | 0.469709i | \(0.844359\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −19.1845 | −1.38093 | −0.690465 | − | 0.723366i | \(-0.742594\pi\) | ||||
−0.690465 | + | 0.723366i | \(0.742594\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.9453 | −0.851066 | −0.425533 | − | 0.904943i | \(-0.639913\pi\) | ||||
−0.425533 | + | 0.904943i | \(0.639913\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.20530 | 0.652546 | 0.326273 | − | 0.945276i | \(-0.394207\pi\) | ||||
0.326273 | + | 0.945276i | \(0.394207\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.247332 | −0.0174455 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.80028 | 0.477286 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.844253 | −0.0586796 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.56511 | 0.384947 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.2971 | 1.25962 | 0.629811 | − | 0.776749i | \(-0.283133\pi\) | ||||
0.629811 | + | 0.776749i | \(0.283133\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −19.3753 | −1.32757 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.9951 | −0.746397 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.26725 | −0.0856331 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 26.0466 | 1.75208 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.57405 | 0.105406 | 0.0527032 | − | 0.998610i | \(-0.483216\pi\) | ||||
0.0527032 | + | 0.998610i | \(0.483216\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 14.6034 | 0.969260 | 0.484630 | − | 0.874719i | \(-0.338954\pi\) | ||||
0.484630 | + | 0.874719i | \(0.338954\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.33328 | 0.616761 | 0.308380 | − | 0.951263i | \(-0.400213\pi\) | ||||
0.308380 | + | 0.951263i | \(0.400213\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −14.7399 | −0.969812 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.02066 | −0.0668658 | −0.0334329 | − | 0.999441i | \(-0.510644\pi\) | ||||
−0.0334329 | + | 0.999441i | \(0.510644\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −11.4449 | −0.743429 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.66778 | 0.237249 | 0.118624 | − | 0.992939i | \(-0.462152\pi\) | ||||
0.118624 | + | 0.992939i | \(0.462152\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −23.1700 | −1.49251 | −0.746254 | − | 0.665661i | \(-0.768150\pi\) | ||||
−0.746254 | + | 0.665661i | \(0.768150\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 4.76697 | 0.305801 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.31979 | −0.402119 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −9.37347 | −0.594020 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −29.6256 | −1.86995 | −0.934977 | − | 0.354709i | \(-0.884580\pi\) | ||||
−0.934977 | + | 0.354709i | \(0.884580\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.1461 | 0.637877 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.9768 | 0.871848 | 0.435924 | − | 0.899984i | \(-0.356422\pi\) | ||||
0.435924 | + | 0.899984i | \(0.356422\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 16.0767 | 0.998956 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.89370 | 0.117217 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.4699 | 0.707264 | 0.353632 | − | 0.935385i | \(-0.384947\pi\) | ||||
0.353632 | + | 0.935385i | \(0.384947\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 29.5421 | 1.80795 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.0864 | 0.980808 | 0.490404 | − | 0.871495i | \(-0.336849\pi\) | ||||
0.490404 | + | 0.871495i | \(0.336849\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.3369 | 0.931649 | 0.465824 | − | 0.884877i | \(-0.345758\pi\) | ||||
0.465824 | + | 0.884877i | \(0.345758\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 16.7387 | 1.01307 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.0546196 | 0.00328177 | 0.00164089 | − | 0.999999i | \(-0.499478\pi\) | ||||
0.00164089 | + | 0.999999i | \(0.499478\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.06185 | −0.183308 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.3315 | 1.21288 | 0.606438 | − | 0.795130i | \(-0.292598\pi\) | ||||
0.606438 | + | 0.795130i | \(0.292598\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 22.3909 | 1.33100 | 0.665501 | − | 0.746397i | \(-0.268218\pi\) | ||||
0.665501 | + | 0.746397i | \(0.268218\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.66932 | 0.452706 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.0138666 | −0.000815685 0 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.42208 | −0.259227 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −13.3983 | −0.782736 | −0.391368 | − | 0.920234i | \(-0.627998\pi\) | ||||
−0.391368 | + | 0.920234i | \(0.627998\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −30.6966 | −1.78119 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −11.5219 | −0.666332 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.23971 | −0.359651 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −21.8196 | −1.25350 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.60404 | −0.433985 | −0.216993 | − | 0.976173i | \(-0.569625\pi\) | ||||
−0.216993 | + | 0.976173i | \(0.569625\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.8228 | −0.672577 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 31.7283 | 1.79915 | 0.899573 | − | 0.436770i | \(-0.143877\pi\) | ||||
0.899573 | + | 0.436770i | \(0.143877\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −26.2396 | −1.48315 | −0.741575 | − | 0.670870i | \(-0.765921\pi\) | ||||
−0.741575 | + | 0.670870i | \(0.765921\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.269210 | −0.0151203 | −0.00756016 | − | 0.999971i | \(-0.502406\pi\) | ||||
−0.00756016 | + | 0.999971i | \(0.502406\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −22.7581 | −1.27421 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 21.9819 | 1.22691 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.12142 | −0.229322 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −20.3146 | −1.12340 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.40713 | −0.353237 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.69472 | −0.532870 | −0.266435 | − | 0.963853i | \(-0.585846\pi\) | ||||
−0.266435 | + | 0.963853i | \(0.585846\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.47693 | 0.245334 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.4219 | 1.00350 | 0.501751 | − | 0.865012i | \(-0.332689\pi\) | ||||
0.501751 | + | 0.865012i | \(0.332689\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −12.4541 | −0.676414 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 36.7967 | 1.99265 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.6823 | 1.00875 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8.85913 | 0.475583 | 0.237791 | − | 0.971316i | \(-0.423577\pi\) | ||||
0.237791 | + | 0.971316i | \(0.423577\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.36382 | −0.340647 | −0.170324 | − | 0.985388i | \(-0.554481\pi\) | ||||
−0.170324 | + | 0.985388i | \(0.554481\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 34.8593 | 1.86065 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 26.4213 | 1.40627 | 0.703133 | − | 0.711058i | \(-0.251784\pi\) | ||||
0.703133 | + | 0.711058i | \(0.251784\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 10.9161 | 0.577740 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.904490 | 0.0477372 | 0.0238686 | − | 0.999715i | \(-0.492402\pi\) | ||||
0.0238686 | + | 0.999715i | \(0.492402\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 31.8085 | 1.66951 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −20.6657 | −1.07874 | −0.539370 | − | 0.842069i | \(-0.681338\pi\) | ||||
−0.539370 | + | 0.842069i | \(0.681338\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.13570 | 0.111180 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.72347 | 0.452900 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −23.7919 | −1.23190 | −0.615949 | − | 0.787786i | \(-0.711227\pi\) | ||||
−0.615949 | + | 0.787786i | \(0.711227\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 25.8443 | 1.33105 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 27.9667 | 1.43655 | 0.718276 | − | 0.695758i | \(-0.244931\pi\) | ||||
0.718276 | + | 0.695758i | \(0.244931\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.07563 | −0.413727 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12.1083 | −0.618707 | −0.309353 | − | 0.950947i | \(-0.600113\pi\) | ||||
−0.309353 | + | 0.950947i | \(0.600113\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.73760 | −0.0883269 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.871634 | 0.0441936 | 0.0220968 | − | 0.999756i | \(-0.492966\pi\) | ||||
0.0220968 | + | 0.999756i | \(0.492966\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.51398 | −0.379998 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 17.3167 | 0.873512 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.7833 | 1.04308 | 0.521542 | − | 0.853226i | \(-0.325357\pi\) | ||||
0.521542 | + | 0.853226i | \(0.325357\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.64862 | −0.132597 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −16.0237 | −0.800184 | −0.400092 | − | 0.916475i | \(-0.631022\pi\) | ||||
−0.400092 | + | 0.916475i | \(0.631022\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −41.7866 | −2.08154 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −53.8028 | −2.66691 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 20.1554 | 0.996621 | 0.498311 | − | 0.866999i | \(-0.333954\pi\) | ||||
0.498311 | + | 0.866999i | \(0.333954\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −12.0073 | −0.592276 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 19.1718 | 0.943382 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.41112 | −0.0691031 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.15507 | 0.251842 | 0.125921 | − | 0.992040i | \(-0.459811\pi\) | ||||
0.125921 | + | 0.992040i | \(0.459811\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.5417 | 1.29356 | 0.646781 | − | 0.762676i | \(-0.276115\pi\) | ||||
0.646781 | + | 0.762676i | \(0.276115\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.78422 | −0.0867516 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13.3462 | −0.645868 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −56.0184 | −2.70460 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −21.2788 | −1.02496 | −0.512481 | − | 0.858699i | \(-0.671274\pi\) | ||||
−0.512481 | + | 0.858699i | \(0.671274\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.44963 | 0.309949 | 0.154975 | − | 0.987918i | \(-0.450470\pi\) | ||||
0.154975 | + | 0.987918i | \(0.450470\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.82315 | 0.0872132 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 22.2324 | 1.06110 | 0.530548 | − | 0.847655i | \(-0.321986\pi\) | ||||
0.530548 | + | 0.847655i | \(0.321986\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.96101 | 0.0933813 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.56611 | −0.359477 | −0.179738 | − | 0.983714i | \(-0.557525\pi\) | ||||
−0.179738 | + | 0.983714i | \(0.557525\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 19.5265 | 0.923571 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 22.5411 | 1.06378 | 0.531891 | − | 0.846813i | \(-0.321482\pi\) | ||||
0.531891 | + | 0.846813i | \(0.321482\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −25.6664 | −1.20858 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.70091 | −0.220868 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −29.9942 | −1.40307 | −0.701536 | − | 0.712634i | \(-0.747502\pi\) | ||||
−0.701536 | + | 0.712634i | \(0.747502\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 22.7333 | 1.06110 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −35.7493 | −1.66501 | −0.832506 | − | 0.554016i | \(-0.813095\pi\) | ||||
−0.832506 | + | 0.554016i | \(0.813095\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.81829 | 0.456295 | 0.228147 | − | 0.973627i | \(-0.426733\pi\) | ||||
0.228147 | + | 0.973627i | \(0.426733\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.96046 | −0.0907194 | −0.0453597 | − | 0.998971i | \(-0.514443\pi\) | ||||
−0.0453597 | + | 0.998971i | \(0.514443\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.258222 | 0.0119236 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 25.1580 | 1.15922 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 20.8821 | 0.960158 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.42925 | 0.111228 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.88045 | −0.451450 | −0.225725 | − | 0.974191i | \(-0.572475\pi\) | ||||
−0.225725 | + | 0.974191i | \(0.572475\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 61.0989 | 2.78587 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.82884 | −0.219720 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.03706 | −0.409508 | −0.204754 | − | 0.978813i | \(-0.565639\pi\) | ||||
−0.204754 | + | 0.978813i | \(0.565639\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 32.5656 | 1.47267 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −20.3715 | −0.919353 | −0.459676 | − | 0.888086i | \(-0.652035\pi\) | ||||
−0.459676 | + | 0.888086i | \(0.652035\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16.8542 | 0.759076 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 20.2283 | 0.907365 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.9386 | −0.623979 | −0.311990 | − | 0.950086i | \(-0.600995\pi\) | ||||
−0.311990 | + | 0.950086i | \(0.600995\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −23.2678 | −1.03953 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 39.7299 | 1.77147 | 0.885735 | − | 0.464192i | \(-0.153655\pi\) | ||||
0.885735 | + | 0.464192i | \(0.153655\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 42.9090 | 1.90566 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −12.5200 | −0.554941 | −0.277471 | − | 0.960734i | \(-0.589496\pi\) | ||||
−0.277471 | + | 0.960734i | \(0.589496\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.32305 | 0.0585282 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.51589 | −0.243533 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 21.4423 | 0.943033 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −30.9387 | −1.35806 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.0426487 | −0.00186847 | −0.000934237 | − | 1.00000i | \(-0.500297\pi\) | ||||
−0.000934237 | 1.00000i | \(0.500297\pi\) | ||||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −29.4459 | −1.28758 | −0.643789 | − | 0.765203i | \(-0.722639\pi\) | ||||
−0.643789 | + | 0.765203i | \(0.722639\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −27.2509 | −1.18707 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.6761 | −0.855483 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.33883 | 0.231686 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 29.1470 | 1.26250 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −11.4852 | −0.495621 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −23.5670 | −1.01510 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20.0558 | −0.862264 | −0.431132 | − | 0.902289i | \(-0.641886\pi\) | ||||
−0.431132 | + | 0.902289i | \(0.641886\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −16.1248 | −0.691979 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.8952 | −0.636874 | −0.318437 | − | 0.947944i | \(-0.603158\pi\) | ||||
−0.318437 | + | 0.947944i | \(0.603158\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.71657 | −0.158619 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.08942 | −0.174215 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.9488 | 0.508116 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9.26068 | −0.392388 | −0.196194 | − | 0.980565i | \(-0.562858\pi\) | ||||
−0.196194 | + | 0.980565i | \(0.562858\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −23.7138 | −1.00299 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −36.5322 | −1.54239 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −12.9472 | −0.545661 | −0.272830 | − | 0.962062i | \(-0.587960\pi\) | ||||
−0.272830 | + | 0.962062i | \(0.587960\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 12.2994 | 0.516525 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 20.0593 | 0.840929 | 0.420464 | − | 0.907309i | \(-0.361867\pi\) | ||||
0.420464 | + | 0.907309i | \(0.361867\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.64571 | −0.236266 | −0.118133 | − | 0.992998i | \(-0.537691\pi\) | ||||
−0.118133 | + | 0.992998i | \(0.537691\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −38.8663 | −1.62366 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −33.5402 | −1.39630 | −0.698148 | − | 0.715953i | \(-0.745992\pi\) | ||||
−0.698148 | + | 0.715953i | \(0.745992\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −30.5566 | −1.26989 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.78616 | 0.405998 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −29.1943 | −1.20910 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 27.5517 | 1.13718 | 0.568591 | − | 0.822621i | \(-0.307489\pi\) | ||||
0.568591 | + | 0.822621i | \(0.307489\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.61202 | 0.272444 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −19.0261 | −0.782630 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 24.4353 | 1.00344 | 0.501719 | − | 0.865031i | \(-0.332701\pi\) | ||||
0.501719 | + | 0.865031i | \(0.332701\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 14.6620 | 0.600074 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.51535 | −0.143633 | −0.0718166 | − | 0.997418i | \(-0.522880\pi\) | ||||
−0.0718166 | + | 0.997418i | \(0.522880\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.21824 | −0.0496932 | −0.0248466 | − | 0.999691i | \(-0.507910\pi\) | ||||
−0.0248466 | + | 0.999691i | \(0.507910\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.0719079 | 0.00292832 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13.1872 | −0.535251 | −0.267625 | − | 0.963523i | \(-0.586239\pi\) | ||||
−0.267625 | + | 0.963523i | \(0.586239\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 10.8313 | 0.438907 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −24.3501 | −0.985100 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.67880 | −0.390923 | −0.195462 | − | 0.980711i | \(-0.562621\pi\) | ||||
−0.195462 | + | 0.980711i | \(0.562621\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10.4077 | 0.418999 | 0.209500 | − | 0.977809i | \(-0.432816\pi\) | ||||
0.209500 | + | 0.977809i | \(0.432816\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −32.7144 | −1.31490 | −0.657452 | − | 0.753496i | \(-0.728366\pi\) | ||||
−0.657452 | + | 0.753496i | \(0.728366\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −10.0563 | −0.403546 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −30.8428 | −1.23569 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8.86396 | 0.353993 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 39.8454 | 1.58874 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −37.2305 | −1.48212 | −0.741061 | − | 0.671438i | \(-0.765677\pi\) | ||||
−0.741061 | + | 0.671438i | \(0.765677\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 29.1431 | 1.15833 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 26.7629 | 1.06038 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.63306 | 0.222840 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 23.3803 | 0.923464 | 0.461732 | − | 0.887019i | \(-0.347228\pi\) | ||||
0.461732 | + | 0.887019i | \(0.347228\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24.6705 | −0.972911 | −0.486455 | − | 0.873705i | \(-0.661710\pi\) | ||||
−0.486455 | + | 0.873705i | \(0.661710\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 47.2591 | 1.85795 | 0.928973 | − | 0.370147i | \(-0.120693\pi\) | ||||
0.928973 | + | 0.370147i | \(0.120693\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −64.1610 | −2.51854 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −17.5127 | −0.686378 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 31.5361 | 1.23410 | 0.617051 | − | 0.786924i | \(-0.288327\pi\) | ||||
0.617051 | + | 0.786924i | \(0.288327\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.368434 | 0.0143740 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −21.3511 | −0.831722 | −0.415861 | − | 0.909428i | \(-0.636520\pi\) | ||||
−0.415861 | + | 0.909428i | \(0.636520\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −31.2161 | −1.21416 | −0.607082 | − | 0.794639i | \(-0.707660\pi\) | ||||
−0.607082 | + | 0.794639i | \(0.707660\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 41.4863 | 1.61119 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.45563 | −0.288683 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.50711 | 0.0969304 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 44.6649 | 1.72427 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.16240 | −0.160449 | −0.0802243 | − | 0.996777i | \(-0.525564\pi\) | ||||
−0.0802243 | + | 0.996777i | \(0.525564\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 35.5734 | 1.36720 | 0.683599 | − | 0.729857i | \(-0.260414\pi\) | ||||
0.683599 | + | 0.729857i | \(0.260414\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.61677 | 0.177175 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 23.2599 | 0.891320 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 26.8628 | 1.02788 | 0.513938 | − | 0.857827i | \(-0.328186\pi\) | ||||
0.513938 | + | 0.857827i | \(0.328186\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14.8658 | 0.567166 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 33.1533 | 1.26304 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 32.0064 | 1.21758 | 0.608791 | − | 0.793331i | \(-0.291655\pi\) | ||||
0.608791 | + | 0.793331i | \(0.291655\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.28538 | 0.162788 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19.0081 | 0.719983 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.62568 | −0.0614890 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −0.822942 | −0.0310821 | −0.0155410 | − | 0.999879i | \(-0.504947\pi\) | ||||
−0.0155410 | + | 0.999879i | \(0.504947\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.66787 | −0.364631 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 22.7802 | 0.856739 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 24.8057 | 0.931599 | 0.465800 | − | 0.884890i | \(-0.345767\pi\) | ||||
0.465800 | + | 0.884890i | \(0.345767\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.32743 | 0.124789 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 12.0547 | 0.451453 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5.84194 | 0.218171 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 13.8765 | 0.517506 | 0.258753 | − | 0.965943i | \(-0.416688\pi\) | ||||
0.258753 | + | 0.965943i | \(0.416688\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.3433 | 0.459690 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −36.9045 | −1.37249 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.7158 | 1.06501 | 0.532506 | − | 0.846426i | \(-0.321251\pi\) | ||||
0.532506 | + | 0.846426i | \(0.321251\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.7817 | 1.10303 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −15.4649 | −0.571989 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 47.1903 | 1.74301 | 0.871506 | − | 0.490384i | \(-0.163144\pi\) | ||||
0.871506 | + | 0.490384i | \(0.163144\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.864174 | −0.0318322 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.61271 | −0.280038 | −0.140019 | − | 0.990149i | \(-0.544716\pi\) | ||||
−0.140019 | + | 0.990149i | \(0.544716\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −10.0660 | −0.369784 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15.8127 | −0.580111 | −0.290055 | − | 0.957010i | \(-0.593674\pi\) | ||||
−0.290055 | + | 0.957010i | \(0.593674\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.72519 | 0.0997093 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −22.9497 | −0.838563 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 35.7516 | 1.30459 | 0.652296 | − | 0.757964i | \(-0.273806\pi\) | ||||
0.652296 | + | 0.757964i | \(0.273806\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −47.1869 | −1.71959 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12.8136 | 0.465717 | 0.232859 | − | 0.972511i | \(-0.425192\pi\) | ||||
0.232859 | + | 0.972511i | \(0.425192\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 16.1604 | 0.586584 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18.8830 | 0.684508 | 0.342254 | − | 0.939608i | \(-0.388810\pi\) | ||||
0.342254 | + | 0.939608i | \(0.388810\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 21.2090 | 0.767818 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 72.8618 | 2.63089 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16.0228 | −0.577798 | −0.288899 | − | 0.957360i | \(-0.593289\pi\) | ||||
−0.288899 | + | 0.957360i | \(0.593289\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 22.2618 | 0.801741 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −9.91039 | −0.356452 | −0.178226 | − | 0.983990i | \(-0.557036\pi\) | ||||
−0.178226 | + | 0.983990i | \(0.557036\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 25.6065 | 0.918628 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.61202 | −0.165243 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −67.6969 | −2.42238 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 22.5568 | 0.806113 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 30.9671 | 1.10386 | 0.551929 | − | 0.833891i | \(-0.313892\pi\) | ||||
0.551929 | + | 0.833891i | \(0.313892\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 18.2689 | 0.650392 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13.0024 | 0.462313 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −50.7219 | −1.80119 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 54.8059 | 1.94132 | 0.970662 | − | 0.240448i | \(-0.0772945\pi\) | ||||
0.970662 | + | 0.240448i | \(0.0772945\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15.8798 | −0.561787 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.58890 | −0.303474 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.42776 | −0.156252 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 25.6221 | 0.901939 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 25.6862 | 0.903080 | 0.451540 | − | 0.892251i | \(-0.350875\pi\) | ||||
0.451540 | + | 0.892251i | \(0.350875\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.01224 | 0.281348 | 0.140674 | − | 0.990056i | \(-0.455073\pi\) | ||||
0.140674 | + | 0.990056i | \(0.455073\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 24.4282 | 0.856733 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.75231 | 0.131277 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.86652 | −0.170050 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −48.8946 | −1.70643 | −0.853217 | − | 0.521555i | \(-0.825352\pi\) | ||||
−0.853217 | + | 0.521555i | \(0.825352\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −39.8314 | −1.38843 | −0.694217 | − | 0.719766i | \(-0.744249\pi\) | ||||
−0.694217 | + | 0.719766i | \(0.744249\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −28.8758 | −1.00411 | −0.502056 | − | 0.864835i | \(-0.667423\pi\) | ||||
−0.502056 | + | 0.864835i | \(0.667423\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.35519 | −0.0817991 | −0.0408995 | − | 0.999163i | \(-0.513022\pi\) | ||||
−0.0408995 | + | 0.999163i | \(0.513022\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.0869966 | 0.00301788 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 17.4533 | 0.604720 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −36.4712 | −1.26063 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 26.0230 | 0.898415 | 0.449207 | − | 0.893428i | \(-0.351706\pi\) | ||||
0.449207 | + | 0.893428i | \(0.351706\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.2767 | −0.423334 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 32.3835 | 1.11535 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −33.2089 | −1.14107 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 35.6636 | 1.22397 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −17.6260 | −0.604211 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −37.7907 | −1.29393 | −0.646964 | − | 0.762520i | \(-0.723962\pi\) | ||||
−0.646964 | + | 0.762520i | \(0.723962\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 19.7796 | 0.675657 | 0.337828 | − | 0.941208i | \(-0.390308\pi\) | ||||
0.337828 | + | 0.941208i | \(0.390308\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22.0641 | 0.752816 | 0.376408 | − | 0.926454i | \(-0.377159\pi\) | ||||
0.376408 | + | 0.926454i | \(0.377159\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 12.2155 | 0.416303 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 32.3505 | 1.10122 | 0.550612 | − | 0.834761i | \(-0.314394\pi\) | ||||
0.550612 | + | 0.834761i | \(0.314394\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.0220864 | −0.000750094 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −39.9884 | −1.35651 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.981363 | 0.0332522 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.28565 | 0.0435126 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 22.5876 | 0.762728 | 0.381364 | − | 0.924425i | \(-0.375454\pi\) | ||||
0.381364 | + | 0.924425i | \(0.375454\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −21.3404 | −0.719794 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31.2658 | 1.05337 | 0.526686 | − | 0.850060i | \(-0.323434\pi\) | ||||
0.526686 | + | 0.850060i | \(0.323434\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −22.4584 | −0.755786 | −0.377893 | − | 0.925849i | \(-0.623351\pi\) | ||||
−0.377893 | + | 0.925849i | \(0.623351\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −14.4883 | −0.486470 | −0.243235 | − | 0.969967i | \(-0.578209\pi\) | ||||
−0.243235 | + | 0.969967i | \(0.578209\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.43117 | 0.282772 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −41.1615 | −1.37896 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.85299 | 0.128935 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −18.3519 | −0.612751 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −27.0393 | −0.901811 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 21.6207 | 0.720291 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −9.93845 | −0.330731 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.58465 | 0.318253 | 0.159127 | − | 0.987258i | \(-0.449132\pi\) | ||||
0.159127 | + | 0.987258i | \(0.449132\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.34370 | 0.210407 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 29.8122 | 0.987721 | 0.493860 | − | 0.869541i | \(-0.335585\pi\) | ||||
0.493860 | + | 0.869541i | \(0.335585\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −32.7507 | −1.08389 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −18.0791 | −0.597025 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −22.0075 | −0.725961 | −0.362981 | − | 0.931797i | \(-0.618241\pi\) | ||||
−0.362981 | + | 0.931797i | \(0.618241\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12.1115 | −0.399088 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 76.8772 | 2.53044 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.43729 | 0.112896 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −22.7036 | −0.744880 | −0.372440 | − | 0.928056i | \(-0.621479\pi\) | ||||
−0.372440 | + | 0.928056i | \(0.621479\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.23477 | −0.138789 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 50.5360 | 1.65447 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10.5567 | −0.344871 | −0.172436 | − | 0.985021i | \(-0.555164\pi\) | ||||
−0.172436 | + | 0.985021i | \(0.555164\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −41.7937 | −1.36389 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24.7961 | −0.808331 | −0.404166 | − | 0.914686i | \(-0.632438\pi\) | ||||
−0.404166 | + | 0.914686i | \(0.632438\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.40842 | −0.273816 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5.83000 | 0.189449 | 0.0947247 | − | 0.995504i | \(-0.469803\pi\) | ||||
0.0947247 | + | 0.995504i | \(0.469803\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.02820 | 0.163222 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.428790 | −0.0139045 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −7.15932 | −0.231913 | −0.115957 | − | 0.993254i | \(-0.536993\pi\) | ||||
−0.115957 | + | 0.993254i | \(0.536993\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −36.2484 | −1.17175 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 12.5359 | 0.404806 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.7188 | 0.410285 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.39088 | −0.205943 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.3120 | 0.331612 | 0.165806 | − | 0.986158i | \(-0.446977\pi\) | ||||
0.165806 | + | 0.986158i | \(0.446977\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.56449 | −0.210882 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 38.2430 | 1.22728 | 0.613639 | − | 0.789587i | \(-0.289705\pi\) | ||||
0.613639 | + | 0.789587i | \(0.289705\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.47325 | 0.0472303 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 18.5114 | 0.592232 | 0.296116 | − | 0.955152i | \(-0.404308\pi\) | ||||
0.296116 | + | 0.955152i | \(0.404308\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 103.220 | 3.29891 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.90615 | 0.188569 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 10.9590 | 0.349539 | 0.174769 | − | 0.984609i | \(-0.444082\pi\) | ||||
0.174769 | + | 0.984609i | \(0.444082\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −10.2051 | −0.324832 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.84104 | 0.217532 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −36.8766 | −1.17142 | −0.585712 | − | 0.810519i | \(-0.699185\pi\) | ||||
−0.585712 | + | 0.810519i | \(0.699185\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −15.4415 | −0.490021 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −36.4988 | −1.15593 | −0.577964 | − | 0.816062i | \(-0.696153\pi\) | ||||
−0.577964 | + | 0.816062i | \(0.696153\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 53.3269 | 1.68719 |
(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 | 3800.2.a.z.1.5 | 6 | ||
4.3 | odd | 2 | 7600.2.a.cn.1.2 | 6 | |||
5.2 | odd | 4 | 760.2.d.e.609.4 | ✓ | 12 | ||
5.3 | odd | 4 | 760.2.d.e.609.9 | yes | 12 | ||
5.4 | even | 2 | 3800.2.a.be.1.2 | 6 | |||
20.3 | even | 4 | 1520.2.d.k.609.4 | 12 | |||
20.7 | even | 4 | 1520.2.d.k.609.9 | 12 | |||
20.19 | odd | 2 | 7600.2.a.cg.1.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
760.2.d.e.609.4 | ✓ | 12 | 5.2 | odd | 4 | ||
760.2.d.e.609.9 | yes | 12 | 5.3 | odd | 4 | ||
1520.2.d.k.609.4 | 12 | 20.3 | even | 4 | |||
1520.2.d.k.609.9 | 12 | 20.7 | even | 4 | |||
3800.2.a.z.1.5 | 6 | 1.1 | even | 1 | trivial | ||
3800.2.a.be.1.2 | 6 | 5.4 | even | 2 | |||
7600.2.a.cg.1.5 | 6 | 20.19 | odd | 2 | |||
7600.2.a.cn.1.2 | 6 | 4.3 | odd | 2 |