Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1480,2,Mod(1,1480)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1480, 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("1480.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1480 = 2^{3} \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1480.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: | \(11.8178594991\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.568.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 6x - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(3.12489\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1480.1 |
$q$-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 | ||||||||
\(3\) | 3.12489 | 1.80415 | 0.902077 | − | 0.431576i | \(-0.142042\pi\) | ||||
0.902077 | + | 0.431576i | \(0.142042\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.12489 | −1.18110 | −0.590548 | − | 0.807003i | \(-0.701088\pi\) | ||||
−0.590548 | + | 0.807003i | \(0.701088\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.76491 | 2.25497 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.51514 | 0.456831 | 0.228416 | − | 0.973564i | \(-0.426645\pi\) | ||||
0.228416 | + | 0.973564i | \(0.426645\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.12489 | 0.806842 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.60975 | 1.28696 | 0.643482 | − | 0.765461i | \(-0.277489\pi\) | ||||
0.643482 | + | 0.765461i | \(0.277489\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −9.76491 | −2.13088 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.00000 | 0.834058 | 0.417029 | − | 0.908893i | \(-0.363071\pi\) | ||||
0.417029 | + | 0.908893i | \(0.363071\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 11.7649 | 2.26416 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.03028 | −0.191317 | −0.0956587 | − | 0.995414i | \(-0.530496\pi\) | ||||
−0.0956587 | + | 0.995414i | \(0.530496\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.640023 | −0.114952 | −0.0574758 | − | 0.998347i | \(-0.518305\pi\) | ||||
−0.0574758 | + | 0.998347i | \(0.518305\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.73463 | 0.824194 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.12489 | −0.528202 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.00000 | 0.164399 | ||||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.76491 | −0.900328 | −0.450164 | − | 0.892946i | \(-0.648634\pi\) | ||||
−0.450164 | + | 0.892946i | \(0.648634\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.03028 | 0.462113 | 0.231056 | − | 0.972940i | \(-0.425782\pi\) | ||||
0.231056 | + | 0.972940i | \(0.425782\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.76491 | 1.00845 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.18544 | −0.172914 | −0.0864569 | − | 0.996256i | \(-0.527554\pi\) | ||||
−0.0864569 | + | 0.996256i | \(0.527554\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.76491 | 0.394987 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.79518 | 1.20811 | 0.604056 | − | 0.796942i | \(-0.293550\pi\) | ||||
0.604056 | + | 0.796942i | \(0.293550\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.51514 | 0.204301 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 17.5298 | 2.32188 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.67030 | −0.477832 | −0.238916 | − | 0.971040i | \(-0.576792\pi\) | ||||
−0.238916 | + | 0.971040i | \(0.576792\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14.4995 | −1.85648 | −0.928238 | − | 0.371987i | \(-0.878677\pi\) | ||||
−0.928238 | + | 0.371987i | \(0.878677\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −21.1396 | −2.66333 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.6703 | 1.42575 | 0.712877 | − | 0.701289i | \(-0.247392\pi\) | ||||
0.712877 | + | 0.701289i | \(0.247392\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 12.4995 | 1.50477 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.734633 | −0.0871849 | −0.0435924 | − | 0.999049i | \(-0.513880\pi\) | ||||
−0.0435924 | + | 0.999049i | \(0.513880\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.70436 | 0.901727 | 0.450863 | − | 0.892593i | \(-0.351116\pi\) | ||||
0.450863 | + | 0.892593i | \(0.351116\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.12489 | 0.360831 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.73463 | −0.539561 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.57947 | −0.290213 | −0.145107 | − | 0.989416i | \(-0.546353\pi\) | ||||
−0.145107 | + | 0.989416i | \(0.546353\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 16.4693 | 1.82992 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.5942 | −1.38239 | −0.691194 | − | 0.722669i | \(-0.742915\pi\) | ||||
−0.691194 | + | 0.722669i | \(0.742915\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.21949 | −0.345166 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.56009 | 0.907368 | 0.453684 | − | 0.891163i | \(-0.350109\pi\) | ||||
0.453684 | + | 0.891163i | \(0.350109\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.00000 | −0.207390 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.60975 | 0.575548 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.00000 | 0.609208 | 0.304604 | − | 0.952479i | \(-0.401476\pi\) | ||||
0.304604 | + | 0.952479i | \(0.401476\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 10.2498 | 1.03014 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −15.2947 | −1.52188 | −0.760941 | − | 0.648821i | \(-0.775262\pi\) | ||||
−0.760941 | + | 0.648821i | \(0.775262\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.7493 | −1.45329 | −0.726646 | − | 0.687012i | \(-0.758922\pi\) | ||||
−0.726646 | + | 0.687012i | \(0.758922\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −9.76491 | −0.952958 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.95035 | −0.478568 | −0.239284 | − | 0.970950i | \(-0.576913\pi\) | ||||
−0.239284 | + | 0.970950i | \(0.576913\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −18.4995 | −1.77193 | −0.885967 | − | 0.463748i | \(-0.846504\pi\) | ||||
−0.885967 | + | 0.463748i | \(0.846504\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.12489 | 0.296601 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −17.4693 | −1.64337 | −0.821685 | − | 0.569942i | \(-0.806966\pi\) | ||||
−0.821685 | + | 0.569942i | \(0.806966\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.00000 | 0.373002 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.70436 | −0.791305 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −18.0147 | −1.62433 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.5639 | 1.55854 | 0.779271 | − | 0.626687i | \(-0.215590\pi\) | ||||
0.779271 | + | 0.626687i | \(0.215590\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 9.46927 | 0.833722 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.640023 | 0.0559191 | 0.0279596 | − | 0.999609i | \(-0.491099\pi\) | ||||
0.0279596 | + | 0.999609i | \(0.491099\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −17.5298 | −1.52003 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 11.7649 | 1.01256 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.4995 | −0.897036 | −0.448518 | − | 0.893774i | \(-0.648048\pi\) | ||||
−0.448518 | + | 0.893774i | \(0.648048\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.5601 | −1.23497 | −0.617486 | − | 0.786582i | \(-0.711849\pi\) | ||||
−0.617486 | + | 0.786582i | \(0.711849\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.70436 | −0.311963 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.03028 | −0.0855598 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 8.64002 | 0.712617 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.76491 | 0.636126 | 0.318063 | − | 0.948070i | \(-0.396968\pi\) | ||||
0.318063 | + | 0.948070i | \(0.396968\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 21.7796 | 1.77240 | 0.886199 | − | 0.463305i | \(-0.153337\pi\) | ||||
0.886199 | + | 0.463305i | \(0.153337\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.640023 | −0.0514079 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −19.3553 | −1.54472 | −0.772360 | − | 0.635185i | \(-0.780924\pi\) | ||||
−0.772360 | + | 0.635185i | \(0.780924\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 27.4839 | 2.17962 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −12.4995 | −0.985102 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.2195 | 0.878779 | 0.439389 | − | 0.898297i | \(-0.355195\pi\) | ||||
0.439389 | + | 0.898297i | \(0.355195\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.73463 | 0.368591 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.1892 | −0.943230 | −0.471615 | − | 0.881805i | \(-0.656329\pi\) | ||||
−0.471615 | + | 0.881805i | \(0.656329\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −13.0000 | −1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 37.9494 | 2.90207 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.23509 | 0.474045 | 0.237023 | − | 0.971504i | \(-0.423828\pi\) | ||||
0.237023 | + | 0.971504i | \(0.423828\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.12489 | −0.236219 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −11.4693 | −0.862083 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.450805 | 0.0336947 | 0.0168474 | − | 0.999858i | \(-0.494637\pi\) | ||||
0.0168474 | + | 0.999858i | \(0.494637\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.64380 | −0.568160 | −0.284080 | − | 0.958801i | \(-0.591688\pi\) | ||||
−0.284080 | + | 0.958801i | \(0.591688\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −45.3094 | −3.34937 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.00000 | 0.0735215 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −36.7640 | −2.67419 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.1093 | 1.31034 | 0.655171 | − | 0.755481i | \(-0.272597\pi\) | ||||
0.655171 | + | 0.755481i | \(0.272597\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.5298 | 1.26182 | 0.630912 | − | 0.775854i | \(-0.282681\pi\) | ||||
0.630912 | + | 0.775854i | \(0.282681\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.73463 | −0.479823 | −0.239911 | − | 0.970795i | \(-0.577118\pi\) | ||||
−0.239911 | + | 0.970795i | \(0.577118\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.8595 | 0.840699 | 0.420349 | − | 0.907362i | \(-0.361907\pi\) | ||||
0.420349 | + | 0.907362i | \(0.361907\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 36.4683 | 2.57228 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.21949 | 0.225964 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.76491 | −0.402639 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 27.0596 | 1.88077 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.49954 | 0.587926 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −21.8255 | −1.50253 | −0.751263 | − | 0.660003i | \(-0.770555\pi\) | ||||
−0.751263 | + | 0.660003i | \(0.770555\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.29564 | −0.157295 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.03028 | 0.206663 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.00000 | 0.135769 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 24.0752 | 1.62685 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.62534 | −0.443666 | −0.221833 | − | 0.975085i | \(-0.571204\pi\) | ||||
−0.221833 | + | 0.975085i | \(0.571204\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.76491 | 0.450994 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 17.2800 | 1.14692 | 0.573458 | − | 0.819235i | \(-0.305601\pi\) | ||||
0.573458 | + | 0.819235i | \(0.305601\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.3553 | 0.750378 | 0.375189 | − | 0.926948i | \(-0.377578\pi\) | ||||
0.375189 | + | 0.926948i | \(0.377578\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −14.7952 | −0.973452 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.00000 | −0.393073 | −0.196537 | − | 0.980497i | \(-0.562969\pi\) | ||||
−0.196537 | + | 0.980497i | \(0.562969\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.18544 | −0.0773294 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.06055 | −0.523589 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 23.6997 | 1.53300 | 0.766502 | − | 0.642242i | \(-0.221996\pi\) | ||||
0.766502 | + | 0.642242i | \(0.221996\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −27.5904 | −1.77725 | −0.888626 | − | 0.458633i | \(-0.848339\pi\) | ||||
−0.888626 | + | 0.458633i | \(0.848339\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 16.1698 | 1.03730 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.76491 | 0.176644 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −39.3553 | −2.49404 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.04965 | 0.192492 | 0.0962462 | − | 0.995358i | \(-0.469316\pi\) | ||||
0.0962462 | + | 0.995358i | \(0.469316\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.06055 | 0.381024 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 25.4693 | 1.58873 | 0.794365 | − | 0.607441i | \(-0.207804\pi\) | ||||
0.794365 | + | 0.607441i | \(0.207804\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.12489 | −0.194171 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.96972 | −0.431415 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.0946093 | 0.00583386 | 0.00291693 | − | 0.999996i | \(-0.499072\pi\) | ||||
0.00291693 | + | 0.999996i | \(0.499072\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.79518 | 0.540284 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 26.7493 | 1.63703 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −17.5904 | −1.07250 | −0.536252 | − | 0.844058i | \(-0.680160\pi\) | ||||
−0.536252 | + | 0.844058i | \(0.680160\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.32500 | 0.384217 | 0.192108 | − | 0.981374i | \(-0.438468\pi\) | ||||
0.192108 | + | 0.981374i | \(0.438468\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.51514 | 0.0913663 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.5904 | 0.816566 | 0.408283 | − | 0.912855i | \(-0.366128\pi\) | ||||
0.408283 | + | 0.912855i | \(0.366128\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.32970 | −0.259212 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.9991 | 1.13339 | 0.566695 | − | 0.823928i | \(-0.308222\pi\) | ||||
0.566695 | + | 0.823928i | \(0.308222\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.34060 | 0.436353 | 0.218177 | − | 0.975909i | \(-0.429989\pi\) | ||||
0.218177 | + | 0.975909i | \(0.429989\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 17.5298 | 1.03838 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 18.0147 | 1.06337 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −17.0000 | −1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 18.7493 | 1.09910 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −10.0000 | −0.584206 | −0.292103 | − | 0.956387i | \(-0.594355\pi\) | ||||
−0.292103 | + | 0.956387i | \(0.594355\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.67030 | −0.213693 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 17.8255 | 1.03434 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.46927 | −0.545799 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −47.7943 | −2.74571 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −14.4995 | −0.830241 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.40493 | −0.251403 | −0.125701 | − | 0.992068i | \(-0.540118\pi\) | ||||
−0.125701 | + | 0.992068i | \(0.540118\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −46.0899 | −2.62196 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −24.1698 | −1.37055 | −0.685273 | − | 0.728286i | \(-0.740317\pi\) | ||||
−0.685273 | + | 0.728286i | \(0.740317\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.9991 | 0.847798 | 0.423899 | − | 0.905709i | \(-0.360661\pi\) | ||||
0.423899 | + | 0.905709i | \(0.360661\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −21.1396 | −1.19108 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 24.5601 | 1.37943 | 0.689716 | − | 0.724080i | \(-0.257735\pi\) | ||||
0.689716 | + | 0.724080i | \(0.257735\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.56101 | −0.0873998 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −15.4693 | −0.863410 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −57.8089 | −3.19684 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.70436 | 0.204228 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.1698 | −0.888775 | −0.444387 | − | 0.895835i | \(-0.646579\pi\) | ||||
−0.444387 | + | 0.895835i | \(0.646579\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.76491 | 0.370715 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 11.6703 | 0.637617 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −27.8548 | −1.51735 | −0.758674 | − | 0.651470i | \(-0.774153\pi\) | ||||
−0.758674 | + | 0.651470i | \(0.774153\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −54.5895 | −2.96489 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.969724 | −0.0525135 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.2342 | 0.714578 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 12.4995 | 0.672953 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.49954 | −0.241548 | −0.120774 | − | 0.992680i | \(-0.538538\pi\) | ||||
−0.120774 | + | 0.992680i | \(0.538538\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −35.5298 | −1.90187 | −0.950934 | − | 0.309395i | \(-0.899874\pi\) | ||||
−0.950934 | + | 0.309395i | \(0.899874\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 16.0606 | 0.854817 | 0.427408 | − | 0.904059i | \(-0.359427\pi\) | ||||
0.427408 | + | 0.904059i | \(0.359427\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.734633 | −0.0389903 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.51514 | −0.291078 | −0.145539 | − | 0.989353i | \(-0.546492\pi\) | ||||
−0.145539 | + | 0.989353i | \(0.546492\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.4693 | 0.656277 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −27.2001 | −1.42764 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.70436 | 0.403264 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.60975 | −0.292826 | −0.146413 | − | 0.989224i | \(-0.546773\pi\) | ||||
−0.146413 | + | 0.989224i | \(0.546773\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −38.9991 | −2.03021 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −27.4839 | −1.42690 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19.8255 | −1.02652 | −0.513262 | − | 0.858232i | \(-0.671563\pi\) | ||||
−0.513262 | + | 0.858232i | \(0.671563\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.12489 | 0.161368 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.5151 | 0.899692 | 0.449846 | − | 0.893106i | \(-0.351479\pi\) | ||||
0.449846 | + | 0.893106i | \(0.351479\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 54.8851 | 2.81185 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11.5298 | 0.589146 | 0.294573 | − | 0.955629i | \(-0.404823\pi\) | ||||
0.294573 | + | 0.955629i | \(0.404823\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.73463 | −0.241299 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 20.4995 | 1.04205 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 28.0899 | 1.42422 | 0.712108 | − | 0.702070i | \(-0.247741\pi\) | ||||
0.712108 | + | 0.702070i | \(0.247741\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.00000 | 0.100887 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.57947 | −0.129787 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.26537 | 0.0635070 | 0.0317535 | − | 0.999496i | \(-0.489891\pi\) | ||||
0.0317535 | + | 0.999496i | \(0.489891\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −54.7787 | −2.74236 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.43899 | −0.221673 | −0.110836 | − | 0.993839i | \(-0.535353\pi\) | ||||
−0.110836 | + | 0.993839i | \(0.535353\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 16.4693 | 0.818364 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.51514 | 0.0751026 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.909172 | −0.0449556 | −0.0224778 | − | 0.999747i | \(-0.507156\pi\) | ||||
−0.0224778 | + | 0.999747i | \(0.507156\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −32.8099 | −1.61839 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11.4693 | 0.564366 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.5942 | −0.618223 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −45.4986 | −2.22808 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −19.6050 | −0.957769 | −0.478885 | − | 0.877878i | \(-0.658959\pi\) | ||||
−0.478885 | + | 0.877878i | \(0.658959\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.909172 | 0.0443103 | 0.0221552 | − | 0.999755i | \(-0.492947\pi\) | ||||
0.0221552 | + | 0.999755i | \(0.492947\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8.01938 | −0.389915 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 45.3094 | 2.19268 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.3288 | 0.642025 | 0.321012 | − | 0.947075i | \(-0.395977\pi\) | ||||
0.321012 | + | 0.947075i | \(0.395977\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.8255 | −0.568295 | −0.284148 | − | 0.958781i | \(-0.591711\pi\) | ||||
−0.284148 | + | 0.958781i | \(0.591711\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.21949 | −0.154363 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 22.4390 | 1.07340 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.5492 | −0.742123 | −0.371061 | − | 0.928608i | \(-0.621006\pi\) | ||||
−0.371061 | + | 0.928608i | \(0.621006\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 18.7044 | 0.890684 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 27.4646 | 1.30488 | 0.652441 | − | 0.757840i | \(-0.273745\pi\) | ||||
0.652441 | + | 0.757840i | \(0.273745\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.56009 | 0.405787 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 24.2645 | 1.14767 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.0000 | 0.660701 | 0.330350 | − | 0.943858i | \(-0.392833\pi\) | ||||
0.330350 | + | 0.943858i | \(0.392833\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.73463 | −0.411298 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 68.0587 | 3.19768 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −36.9385 | −1.72791 | −0.863956 | − | 0.503568i | \(-0.832020\pi\) | ||||
−0.863956 | + | 0.503568i | \(0.832020\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −21.1807 | −0.986485 | −0.493243 | − | 0.869892i | \(-0.664189\pi\) | ||||
−0.493243 | + | 0.869892i | \(0.664189\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.08991 | 0.283022 | 0.141511 | − | 0.989937i | \(-0.454804\pi\) | ||||
0.141511 | + | 0.989937i | \(0.454804\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.00000 | −0.0927478 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14.6282 | 0.676913 | 0.338456 | − | 0.940982i | \(-0.390095\pi\) | ||||
0.338456 | + | 0.940982i | \(0.390095\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −36.4683 | −1.68395 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −60.4830 | −2.78691 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.59129 | 0.211108 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.60975 | 0.257393 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 59.4986 | 2.72425 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 19.6703 | 0.898759 | 0.449379 | − | 0.893341i | \(-0.351645\pi\) | ||||
0.449379 | + | 0.893341i | \(0.351645\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −39.0596 | −1.77727 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.00000 | 0.272446 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.65940 | −0.211138 | −0.105569 | − | 0.994412i | \(-0.533666\pi\) | ||||
−0.105569 | + | 0.994412i | \(0.533666\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 35.0596 | 1.58545 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 37.6197 | 1.69775 | 0.848877 | − | 0.528590i | \(-0.177279\pi\) | ||||
0.848877 | + | 0.528590i | \(0.177279\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 10.2498 | 0.460693 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.29564 | 0.102974 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.359060 | −0.0160737 | −0.00803686 | − | 0.999968i | \(-0.502558\pi\) | ||||
−0.00803686 | + | 0.999968i | \(0.502558\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −38.0899 | −1.70173 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.49954 | 0.378976 | 0.189488 | − | 0.981883i | \(-0.439317\pi\) | ||||
0.189488 | + | 0.981883i | \(0.439317\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.2947 | −0.680606 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −40.6235 | −1.80415 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −16.1745 | −0.716924 | −0.358462 | − | 0.933544i | \(-0.616699\pi\) | ||||
−0.358462 | + | 0.933544i | \(0.616699\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −24.0752 | −1.06503 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 65.9982 | 2.91389 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −14.7493 | −0.649932 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.79610 | −0.0789925 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 19.4839 | 0.855250 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.2947 | −0.494831 | −0.247415 | − | 0.968909i | \(-0.579581\pi\) | ||||
−0.247415 | + | 0.968909i | \(0.579581\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.0303 | −0.482320 | −0.241160 | − | 0.970485i | \(-0.577528\pi\) | ||||
−0.241160 | + | 0.970485i | \(0.577528\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −9.76491 | −0.426176 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −24.8292 | −1.07750 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.95035 | −0.214022 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.40871 | 0.0607905 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.18922 | 0.180442 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.9991 | 0.816834 | 0.408417 | − | 0.912795i | \(-0.366081\pi\) | ||||
0.408417 | + | 0.912795i | \(0.366081\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −23.8860 | −1.02505 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −18.4995 | −0.792433 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −33.9982 | −1.45366 | −0.726828 | − | 0.686819i | \(-0.759006\pi\) | ||||
−0.726828 | + | 0.686819i | \(0.759006\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −98.0881 | −4.18630 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.77959 | −0.246219 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.06055 | 0.342770 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.12489 | 0.132644 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 19.8789 | 0.842296 | 0.421148 | − | 0.906992i | \(-0.361627\pi\) | ||||
0.421148 | + | 0.906992i | \(0.361627\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 28.4995 | 1.20111 | 0.600556 | − | 0.799583i | \(-0.294946\pi\) | ||||
0.600556 | + | 0.799583i | \(0.294946\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −17.4693 | −0.734938 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −51.4646 | −2.16131 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 38.4995 | 1.61398 | 0.806992 | − | 0.590562i | \(-0.201094\pi\) | ||||
0.806992 | + | 0.590562i | \(0.201094\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.3553 | 0.893691 | 0.446845 | − | 0.894611i | \(-0.352547\pi\) | ||||
0.446845 | + | 0.894611i | \(0.352547\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 56.5895 | 2.36406 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.00000 | 0.166812 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 26.9385 | 1.12147 | 0.560733 | − | 0.827997i | \(-0.310519\pi\) | ||||
0.560733 | + | 0.827997i | \(0.310519\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 54.7787 | 2.27652 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 39.3553 | 1.63273 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13.3259 | 0.551903 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 24.1505 | 0.996796 | 0.498398 | − | 0.866948i | \(-0.333922\pi\) | ||||
0.498398 | + | 0.866948i | \(0.333922\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.59037 | −0.147939 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −21.0450 | −0.865674 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.58325 | 0.311407 | 0.155703 | − | 0.987804i | \(-0.450236\pi\) | ||||
0.155703 | + | 0.987804i | \(0.450236\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 37.0596 | 1.51675 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −38.5142 | −1.57365 | −0.786824 | − | 0.617177i | \(-0.788276\pi\) | ||||
−0.786824 | + | 0.617177i | \(0.788276\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −23.4087 | −0.954861 | −0.477431 | − | 0.878669i | \(-0.658432\pi\) | ||||
−0.477431 | + | 0.878669i | \(0.658432\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 78.9485 | 3.21503 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −8.70436 | −0.353882 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.5005 | −0.629144 | −0.314572 | − | 0.949234i | \(-0.601861\pi\) | ||||
−0.314572 | + | 0.949234i | \(0.601861\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 10.0606 | 0.407674 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.2645 | 0.899253 | 0.449626 | − | 0.893217i | \(-0.351557\pi\) | ||||
0.449626 | + | 0.893217i | \(0.351557\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −18.0147 | −0.726422 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −46.3232 | −1.86490 | −0.932450 | − | 0.361298i | \(-0.882334\pi\) | ||||
−0.932450 | + | 0.361298i | \(0.882334\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −26.7034 | −1.07330 | −0.536651 | − | 0.843804i | \(-0.680311\pi\) | ||||
−0.536651 | + | 0.843804i | \(0.680311\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 47.0596 | 1.88844 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −26.7493 | −1.07169 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 26.5601 | 1.06071 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.29942 | −0.370204 | −0.185102 | − | 0.982719i | \(-0.559262\pi\) | ||||
−0.185102 | + | 0.982719i | \(0.559262\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −68.2021 | −2.71079 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 17.5639 | 0.697001 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.96972 | −0.196599 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −21.1131 | −0.833916 | −0.416958 | − | 0.908926i | \(-0.636904\pi\) | ||||
−0.416958 | + | 0.908926i | \(0.636904\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17.9007 | −0.705934 | −0.352967 | − | 0.935636i | \(-0.614827\pi\) | ||||
−0.352967 | + | 0.935636i | \(0.614827\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9.46927 | 0.372852 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −32.6500 | −1.28360 | −0.641802 | − | 0.766870i | \(-0.721813\pi\) | ||||
−0.641802 | + | 0.766870i | \(0.721813\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.56101 | −0.218289 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.24977 | 0.244948 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −42.0587 | −1.64588 | −0.822942 | − | 0.568125i | \(-0.807669\pi\) | ||||
−0.822942 | + | 0.568125i | \(0.807669\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.640023 | 0.0250078 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 52.1193 | 2.03337 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −0.613528 | −0.0238997 | −0.0119498 | − | 0.999929i | \(-0.503804\pi\) | ||||
−0.0119498 | + | 0.999929i | \(0.503804\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −41.6803 | −1.62118 | −0.810588 | − | 0.585617i | \(-0.800852\pi\) | ||||
−0.810588 | + | 0.585617i | \(0.800852\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −17.5298 | −0.679777 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.12110 | −0.159570 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −20.7034 | −0.800441 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −21.9688 | −0.848096 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 36.2039 | 1.39556 | 0.697779 | − | 0.716313i | \(-0.254172\pi\) | ||||
0.697779 | + | 0.716313i | \(0.254172\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 11.7649 | 0.452832 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 41.6732 | 1.60163 | 0.800815 | − | 0.598912i | \(-0.204400\pi\) | ||||
0.800815 | + | 0.598912i | \(0.204400\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −18.7493 | −0.719533 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 53.9982 | 2.06921 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −11.5005 | −0.440053 | −0.220026 | − | 0.975494i | \(-0.570614\pi\) | ||||
−0.220026 | + | 0.975494i | \(0.570614\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10.4995 | −0.401167 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 35.4839 | 1.35380 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 44.7181 | 1.70116 | 0.850579 | − | 0.525848i | \(-0.176252\pi\) | ||||
0.850579 | + | 0.525848i | \(0.176252\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −32.0294 | −1.21669 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −14.5601 | −0.552296 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −18.7493 | −0.709164 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 41.9083 | 1.58285 | 0.791426 | − | 0.611264i | \(-0.209339\pi\) | ||||
0.791426 | + | 0.611264i | \(0.209339\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.60975 | 0.211576 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.70436 | −0.139514 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 47.7943 | 1.79749 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 35.0284 | 1.31552 | 0.657760 | − | 0.753227i | \(-0.271504\pi\) | ||||
0.657760 | + | 0.753227i | \(0.271504\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −17.4499 | −0.654422 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.56009 | −0.0958763 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 74.0587 | 2.76577 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 13.8936 | 0.518143 | 0.259071 | − | 0.965858i | \(-0.416583\pi\) | ||||
0.259071 | + | 0.965858i | \(0.416583\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 46.0899 | 1.71648 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −86.2167 | −3.20644 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.03028 | −0.0382635 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25.0284 | 0.928254 | 0.464127 | − | 0.885769i | \(-0.346368\pi\) | ||||
0.464127 | + | 0.885769i | \(0.346368\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.12110 | 0.0415224 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17.7649 | 0.656162 | 0.328081 | − | 0.944650i | \(-0.393598\pi\) | ||||
0.328081 | + | 0.944650i | \(0.393598\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 8.64002 | 0.318692 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 17.6821 | 0.651329 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 43.7943 | 1.61100 | 0.805499 | − | 0.592597i | \(-0.201897\pi\) | ||||
0.805499 | + | 0.592597i | \(0.201897\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 19.4646 | 0.714086 | 0.357043 | − | 0.934088i | \(-0.383785\pi\) | ||||
0.357043 | + | 0.934088i | \(0.383785\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.76491 | 0.284484 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −85.1983 | −3.11724 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 15.4693 | 0.565235 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.5151 | −0.493174 | −0.246587 | − | 0.969121i | \(-0.579309\pi\) | ||||
−0.246587 | + | 0.969121i | \(0.579309\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 9.52982 | 0.347286 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 21.7796 | 0.792640 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 40.7106 | 1.47965 | 0.739825 | − | 0.672799i | \(-0.234908\pi\) | ||||
0.739825 | + | 0.672799i | \(0.234908\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 18.9385 | 0.687425 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.17454 | −0.151327 | −0.0756635 | − | 0.997133i | \(-0.524107\pi\) | ||||
−0.0756635 | + | 0.997133i | \(0.524107\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 57.8089 | 2.09282 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.09083 | −0.255702 | −0.127851 | − | 0.991793i | \(-0.540808\pi\) | ||||
−0.127851 | + | 0.991793i | \(0.540808\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 79.5885 | 2.86631 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.26537 | 0.0455121 | 0.0227560 | − | 0.999741i | \(-0.492756\pi\) | ||||
0.0227560 | + | 0.999741i | \(0.492756\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.640023 | −0.0229903 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −9.76491 | −0.350314 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −32.3397 | −1.15869 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.11307 | −0.0398288 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −12.1211 | −0.433173 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −19.3553 | −0.690820 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 27.3141 | 0.973643 | 0.486821 | − | 0.873502i | \(-0.338156\pi\) | ||||
0.486821 | + | 0.873502i | \(0.338156\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.295643 | 0.0105252 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 54.5895 | 1.94098 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 27.4839 | 0.974755 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 24.9991 | 0.885513 | 0.442756 | − | 0.896642i | \(-0.354001\pi\) | ||||
0.442756 | + | 0.896642i | \(0.354001\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 57.9083 | 2.04609 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 11.6732 | 0.411937 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −12.4995 | −0.440551 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −54.9679 | −1.93496 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11.4693 | 0.403238 | 0.201619 | − | 0.979464i | \(-0.435380\pi\) | ||||
0.201619 | + | 0.979464i | \(0.435380\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20.8851 | −0.733375 | −0.366687 | − | 0.930344i | \(-0.619508\pi\) | ||||
−0.366687 | + | 0.930344i | \(0.619508\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 19.7649 | 0.693186 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 11.2195 | 0.393002 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16.9991 | 0.594723 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.7034 | 0.443353 | 0.221677 | − | 0.975120i | \(-0.428847\pi\) | ||||
0.221677 | + | 0.975120i | \(0.428847\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.2909 | −0.707298 | −0.353649 | − | 0.935378i | \(-0.615059\pi\) | ||||
−0.353649 | + | 0.935378i | \(0.615059\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.73463 | 0.164839 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 23.7190 | 0.824792 | 0.412396 | − | 0.911005i | \(-0.364692\pi\) | ||||
0.412396 | + | 0.911005i | \(0.364692\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 52.5895 | 1.82651 | 0.913254 | − | 0.407392i | \(-0.133562\pi\) | ||||
0.913254 | + | 0.407392i | \(0.133562\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 42.4683 | 1.47321 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12.1892 | −0.421825 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.52982 | −0.260269 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 34.5601 | 1.19315 | 0.596573 | − | 0.802558i | \(-0.296528\pi\) | ||||
0.596573 | + | 0.802558i | \(0.296528\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.9385 | −0.963398 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 59.3700 | 2.04481 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −13.0000 | −0.447214 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 27.2001 | 0.934607 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 22.9385 | 0.787248 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.00000 | 0.137118 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −31.7115 | −1.08578 | −0.542890 | − | 0.839804i | \(-0.682670\pi\) | ||||
−0.542890 | + | 0.839804i | \(0.682670\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 37.9494 | 1.29784 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.93945 | 0.271206 | 0.135603 | − | 0.990763i | \(-0.456703\pi\) | ||||
0.135603 | + | 0.990763i | \(0.456703\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 30.8898 | 1.05395 | 0.526973 | − | 0.849882i | \(-0.323327\pi\) | ||||
0.526973 | + | 0.849882i | \(0.323327\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 56.2938 | 1.91849 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −20.7081 | −0.704913 | −0.352457 | − | 0.935828i | \(-0.614654\pi\) | ||||
−0.352457 | + | 0.935828i | \(0.614654\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.23509 | 0.211999 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −53.1231 | −1.80415 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.90826 | −0.132578 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 40.5895 | 1.37374 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.12489 | −0.105640 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −39.1202 | −1.32099 | −0.660497 | − | 0.750828i | \(-0.729655\pi\) | ||||
−0.660497 | + | 0.750828i | \(0.729655\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −31.2489 | −1.05400 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.3491 | 0.416051 | 0.208026 | − | 0.978123i | \(-0.433296\pi\) | ||||
0.208026 | + | 0.978123i | \(0.433296\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 35.2195 | 1.18523 | 0.592615 | − | 0.805486i | \(-0.298096\pi\) | ||||
0.592615 | + | 0.805486i | \(0.298096\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −11.4693 | −0.385535 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 51.8043 | 1.73942 | 0.869708 | − | 0.493566i | \(-0.164307\pi\) | ||||
0.869708 | + | 0.493566i | \(0.164307\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −54.8851 | −1.84079 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 24.9532 | 0.835964 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.65001 | −0.222534 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.450805 | 0.0150687 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.659401 | 0.0219923 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −29.5904 | −0.984706 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −7.64380 | −0.254089 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 55.8695 | 1.85512 | 0.927558 | − | 0.373679i | \(-0.121904\pi\) | ||||
0.927558 | + | 0.373679i | \(0.121904\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −103.467 | −3.43180 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 33.2607 | 1.10198 | 0.550988 | − | 0.834513i | \(-0.314251\pi\) | ||||
0.550988 | + | 0.834513i | \(0.314251\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −19.0819 | −0.631518 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −45.3094 | −1.49788 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.00000 | −0.0660458 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.98910 | 0.164575 | 0.0822876 | − | 0.996609i | \(-0.473777\pi\) | ||||
0.0822876 | + | 0.996609i | \(0.473777\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −13.7649 | −0.453569 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.00000 | 0.0328798 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −99.7778 | −3.27713 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 30.0000 | 0.984268 | 0.492134 | − | 0.870519i | \(-0.336217\pi\) | ||||
0.492134 | + | 0.870519i | \(0.336217\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15.5104 | 0.508334 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −75.5280 | −2.47268 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −58.8851 | −1.92369 | −0.961846 | − | 0.273591i | \(-0.911789\pi\) | ||||
−0.961846 | + | 0.273591i | \(0.911789\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 46.8704 | 1.52956 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 19.6509 | 0.640602 | 0.320301 | − | 0.947316i | \(-0.396216\pi\) | ||||
0.320301 | + | 0.947316i | \(0.396216\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −23.0596 | −0.750925 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −36.7640 | −1.19593 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −32.3397 | −1.05090 | −0.525449 | − | 0.850825i | \(-0.676103\pi\) | ||||
−0.525449 | + | 0.850825i | \(0.676103\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 76.7475 | 2.48871 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −48.8245 | −1.58158 | −0.790791 | − | 0.612086i | \(-0.790331\pi\) | ||||
−0.790791 | + | 0.612086i | \(0.790331\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 18.1093 | 0.586003 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.87798 | −0.157683 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 32.8099 | 1.05949 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.5904 | −0.986786 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −33.4886 | −1.07916 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 17.5298 | 0.564305 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −14.9915 | −0.482095 | −0.241047 | − | 0.970513i | \(-0.577491\pi\) | ||||
−0.241047 | + | 0.970513i | \(0.577491\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.4390 | −0.591735 | −0.295868 | − | 0.955229i | \(-0.595609\pi\) | ||||
−0.295868 | + | 0.955229i | \(0.595609\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 45.4986 | 1.45862 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 29.5298 | 0.944743 | 0.472371 | − | 0.881400i | \(-0.343398\pi\) | ||||
0.472371 | + | 0.881400i | \(0.343398\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.9697 | 0.414514 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −125.148 | −3.99566 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −27.9348 | −0.890980 | −0.445490 | − | 0.895287i | \(-0.646971\pi\) | ||||
−0.445490 | + | 0.895287i | \(0.646971\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.73463 | −0.214583 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 11.5757 | 0.368458 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12.1211 | 0.385429 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.85952 | −0.122602 | −0.0613008 | − | 0.998119i | \(-0.519525\pi\) | ||||
−0.0613008 | + | 0.998119i | \(0.519525\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −50.5289 | −1.60349 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11.8595 | 0.375972 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18.6500 | 0.590652 | 0.295326 | − | 0.955397i | \(-0.404572\pi\) | ||||
0.295326 | + | 0.955397i | \(0.404572\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 11.7649 | 0.372225 |
(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 | 1480.2.a.f.1.3 | ✓ | 3 | |
4.3 | odd | 2 | 2960.2.a.s.1.1 | 3 | |||
5.4 | even | 2 | 7400.2.a.m.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1480.2.a.f.1.3 | ✓ | 3 | 1.1 | even | 1 | trivial | |
2960.2.a.s.1.1 | 3 | 4.3 | odd | 2 | |||
7400.2.a.m.1.1 | 3 | 5.4 | even | 2 |