Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8100,2,Mod(1,8100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8100, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8100.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8100 = 2^{2} \cdot 3^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8100.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: | \(64.6788256372\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.3981.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 4x^{2} + 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | no (minimal twist has level 900) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-0.318459\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8100.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.40179 | 1.28576 | 0.642878 | − | 0.765969i | \(-0.277740\pi\) | ||||
0.642878 | + | 0.765969i | \(0.277740\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.40179 | 1.32719 | 0.663595 | − | 0.748092i | \(-0.269030\pi\) | ||||
0.663595 | + | 0.748092i | \(0.269030\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.06320 | −0.572229 | −0.286115 | − | 0.958195i | \(-0.592364\pi\) | ||||
−0.286115 | + | 0.958195i | \(0.592364\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.40179 | −0.339984 | −0.169992 | − | 0.985445i | \(-0.554374\pi\) | ||||
−0.169992 | + | 0.985445i | \(0.554374\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.35717 | −1.45843 | −0.729217 | − | 0.684283i | \(-0.760115\pi\) | ||||
−0.729217 | + | 0.684283i | \(0.760115\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.107826 | 0.0224832 | 0.0112416 | − | 0.999937i | \(-0.496422\pi\) | ||||
0.0112416 | + | 0.999937i | \(0.496422\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9.08178 | −1.68644 | −0.843222 | − | 0.537565i | \(-0.819344\pi\) | ||||
−0.843222 | + | 0.537565i | \(0.819344\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.06320 | 0.550167 | 0.275084 | − | 0.961420i | \(-0.411294\pi\) | ||||
0.275084 | + | 0.961420i | \(0.411294\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.95538 | −0.321462 | −0.160731 | − | 0.986998i | \(-0.551385\pi\) | ||||
−0.160731 | + | 0.986998i | \(0.551385\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.69575 | 1.35805 | 0.679024 | − | 0.734116i | \(-0.262403\pi\) | ||||
0.679024 | + | 0.734116i | \(0.262403\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.12641 | 1.08677 | 0.543383 | − | 0.839485i | \(-0.317143\pi\) | ||||
0.543383 | + | 0.839485i | \(0.317143\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.48357 | −1.09159 | −0.545795 | − | 0.837918i | \(-0.683772\pi\) | ||||
−0.545795 | + | 0.837918i | \(0.683772\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.57217 | 0.653167 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13.0975 | 1.79909 | 0.899543 | − | 0.436833i | \(-0.143900\pi\) | ||||
0.899543 | + | 0.436833i | \(0.143900\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 13.1793 | 1.71580 | 0.857901 | − | 0.513815i | \(-0.171768\pi\) | ||||
0.857901 | + | 0.513815i | \(0.171768\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.72462 | −0.220814 | −0.110407 | − | 0.993886i | \(-0.535216\pi\) | ||||
−0.110407 | + | 0.993886i | \(0.535216\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.3757 | 1.51194 | 0.755969 | − | 0.654608i | \(-0.227166\pi\) | ||||
0.755969 | + | 0.654608i | \(0.227166\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.50961 | 0.891227 | 0.445614 | − | 0.895225i | \(-0.352986\pi\) | ||||
0.445614 | + | 0.895225i | \(0.352986\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.42037 | 0.634406 | 0.317203 | − | 0.948358i | \(-0.397256\pi\) | ||||
0.317203 | + | 0.948358i | \(0.397256\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 14.9740 | 1.70644 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.43613 | 1.06165 | 0.530824 | − | 0.847482i | \(-0.321883\pi\) | ||||
0.530824 | + | 0.847482i | \(0.321883\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.97396 | 0.985020 | 0.492510 | − | 0.870307i | \(-0.336080\pi\) | ||||
0.492510 | + | 0.870307i | \(0.336080\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.01576 | −0.425670 | −0.212835 | − | 0.977088i | \(-0.568270\pi\) | ||||
−0.212835 | + | 0.977088i | \(0.568270\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.01858 | −0.735747 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.17103 | −0.220435 | −0.110217 | − | 0.993908i | \(-0.535155\pi\) | ||||
−0.110217 | + | 0.993908i | \(0.535155\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.97396 | −0.295920 | −0.147960 | − | 0.988993i | \(-0.547271\pi\) | ||||
−0.147960 | + | 0.988993i | \(0.547271\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.63537 | −0.653802 | −0.326901 | − | 0.945059i | \(-0.606004\pi\) | ||||
−0.326901 | + | 0.945059i | \(0.606004\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.7878 | 1.33292 | 0.666459 | − | 0.745541i | \(-0.267809\pi\) | ||||
0.666459 | + | 0.745541i | \(0.267809\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −18.1347 | −1.73699 | −0.868495 | − | 0.495699i | \(-0.834912\pi\) | ||||
−0.868495 | + | 0.495699i | \(0.834912\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.0817817 | −0.00769338 | −0.00384669 | − | 0.999993i | \(-0.501224\pi\) | ||||
−0.00384669 | + | 0.999993i | \(0.501224\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.76859 | −0.437136 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.37574 | 0.761431 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −21.5811 | −1.91501 | −0.957507 | − | 0.288410i | \(-0.906873\pi\) | ||||
−0.957507 | + | 0.288410i | \(0.906873\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.7878 | 0.942536 | 0.471268 | − | 0.881990i | \(-0.343796\pi\) | ||||
0.471268 | + | 0.881990i | \(0.343796\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −21.6257 | −1.87519 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.5096 | 1.15420 | 0.577102 | − | 0.816672i | \(-0.304183\pi\) | ||||
0.577102 | + | 0.816672i | \(0.304183\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.6100 | 1.23920 | 0.619601 | − | 0.784917i | \(-0.287294\pi\) | ||||
0.619601 | + | 0.784917i | \(0.287294\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −9.08178 | −0.759457 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.133870 | −0.0109671 | −0.00548353 | − | 0.999985i | \(-0.501745\pi\) | ||||
−0.00548353 | + | 0.999985i | \(0.501745\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.14498 | 0.500072 | 0.250036 | − | 0.968237i | \(-0.419558\pi\) | ||||
0.250036 | + | 0.968237i | \(0.419558\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.7747 | −1.17915 | −0.589575 | − | 0.807713i | \(-0.700705\pi\) | ||||
−0.589575 | + | 0.807713i | \(0.700705\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.366801 | 0.0289079 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.9451 | 1.24892 | 0.624458 | − | 0.781058i | \(-0.285320\pi\) | ||||
0.624458 | + | 0.781058i | \(0.285320\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 20.4993 | 1.58629 | 0.793143 | − | 0.609036i | \(-0.208443\pi\) | ||||
0.793143 | + | 0.609036i | \(0.208443\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.74320 | −0.672553 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 22.5914 | 1.71759 | 0.858796 | − | 0.512318i | \(-0.171213\pi\) | ||||
0.858796 | + | 0.512318i | \(0.171213\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −20.5879 | −1.53881 | −0.769407 | − | 0.638759i | \(-0.779448\pi\) | ||||
−0.769407 | + | 0.638759i | \(0.779448\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.32830 | −0.619038 | −0.309519 | − | 0.950893i | \(-0.600168\pi\) | ||||
−0.309519 | + | 0.950893i | \(0.600168\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.17038 | −0.451223 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.78435 | 0.635613 | 0.317807 | − | 0.948156i | \(-0.397054\pi\) | ||||
0.317807 | + | 0.948156i | \(0.397054\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.23076 | −0.520482 | −0.260241 | − | 0.965544i | \(-0.583802\pi\) | ||||
−0.260241 | + | 0.965544i | \(0.583802\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.17932 | −0.297764 | −0.148882 | − | 0.988855i | \(-0.547568\pi\) | ||||
−0.148882 | + | 0.988855i | \(0.547568\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.6518 | 1.10953 | 0.554763 | − | 0.832009i | \(-0.312809\pi\) | ||||
0.554763 | + | 0.832009i | \(0.312809\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −30.8943 | −2.16836 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −27.9829 | −1.93562 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −24.1539 | −1.66282 | −0.831412 | − | 0.555656i | \(-0.812467\pi\) | ||||
−0.831412 | + | 0.555656i | \(0.812467\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.4204 | 0.707381 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.89217 | 0.194549 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.44641 | −0.0968589 | −0.0484295 | − | 0.998827i | \(-0.515422\pi\) | ||||
−0.0484295 | + | 0.998827i | \(0.515422\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 20.5254 | 1.36232 | 0.681158 | − | 0.732136i | \(-0.261476\pi\) | ||||
0.681158 | + | 0.732136i | \(0.261476\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 20.9486 | 1.38432 | 0.692160 | − | 0.721744i | \(-0.256659\pi\) | ||||
0.692160 | + | 0.721744i | \(0.256659\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.90112 | −0.648644 | −0.324322 | − | 0.945947i | \(-0.605136\pi\) | ||||
−0.324322 | + | 0.945947i | \(0.605136\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.10783 | −0.395082 | −0.197541 | − | 0.980295i | \(-0.563296\pi\) | ||||
−0.197541 | + | 0.980295i | \(0.563296\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.296783 | −0.0191175 | −0.00955875 | − | 0.999954i | \(-0.503043\pi\) | ||||
−0.00955875 | + | 0.999954i | \(0.503043\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.1161 | 0.834559 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.51643 | 0.285075 | 0.142537 | − | 0.989789i | \(-0.454474\pi\) | ||||
0.142537 | + | 0.989789i | \(0.454474\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.474626 | 0.0298395 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.5982 | 0.848233 | 0.424117 | − | 0.905608i | \(-0.360585\pi\) | ||||
0.424117 | + | 0.905608i | \(0.360585\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.65178 | −0.413321 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.12358 | −0.439259 | −0.219630 | − | 0.975583i | \(-0.570485\pi\) | ||||
−0.219630 | + | 0.975583i | \(0.570485\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.80358 | −0.536764 | −0.268382 | − | 0.963313i | \(-0.586489\pi\) | ||||
−0.268382 | + | 0.963313i | \(0.586489\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.95885 | −0.604957 | −0.302478 | − | 0.953156i | \(-0.597814\pi\) | ||||
−0.302478 | + | 0.953156i | \(0.597814\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.92933 | 0.536512 | 0.268256 | − | 0.963348i | \(-0.413553\pi\) | ||||
0.268256 | + | 0.963348i | \(0.413553\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −32.0804 | −1.91376 | −0.956879 | − | 0.290486i | \(-0.906183\pi\) | ||||
−0.956879 | + | 0.290486i | \(0.906183\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.36745 | 0.378506 | 0.189253 | − | 0.981928i | \(-0.439393\pi\) | ||||
0.189253 | + | 0.981928i | \(0.439393\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 29.5811 | 1.74612 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.0350 | −0.884411 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 27.9011 | 1.63000 | 0.815000 | − | 0.579460i | \(-0.196737\pi\) | ||||
0.815000 | + | 0.579460i | \(0.196737\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.222466 | −0.0128656 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 24.2425 | 1.39732 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.2054 | 0.696597 | 0.348299 | − | 0.937384i | \(-0.386760\pi\) | ||||
0.348299 | + | 0.937384i | \(0.386760\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.90246 | 0.277993 | 0.138996 | − | 0.990293i | \(-0.455612\pi\) | ||||
0.138996 | + | 0.990293i | \(0.455612\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.5886 | 0.994165 | 0.497083 | − | 0.867703i | \(-0.334405\pi\) | ||||
0.497083 | + | 0.867703i | \(0.334405\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 19.5722 | 1.09928 | 0.549641 | − | 0.835401i | \(-0.314764\pi\) | ||||
0.549641 | + | 0.835401i | \(0.314764\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −39.9761 | −2.23823 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.91140 | 0.495844 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −25.4575 | −1.40352 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.5907 | 0.801980 | 0.400990 | − | 0.916082i | \(-0.368666\pi\) | ||||
0.400990 | + | 0.916082i | \(0.368666\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.90858 | 0.539755 | 0.269877 | − | 0.962895i | \(-0.413017\pi\) | ||||
0.269877 | + | 0.962895i | \(0.413017\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 13.4836 | 0.730176 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.25897 | −0.445943 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.3200 | 0.554007 | 0.277004 | − | 0.960869i | \(-0.410659\pi\) | ||||
0.277004 | + | 0.960869i | \(0.410659\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.1353 | 0.917234 | 0.458617 | − | 0.888634i | \(-0.348345\pi\) | ||||
0.458617 | + | 0.888634i | \(0.348345\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −13.2611 | −0.705817 | −0.352909 | − | 0.935658i | \(-0.614807\pi\) | ||||
−0.352909 | + | 0.935658i | \(0.614807\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −14.2817 | −0.753758 | −0.376879 | − | 0.926263i | \(-0.623003\pi\) | ||||
−0.376879 | + | 0.926263i | \(0.623003\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 21.4136 | 1.12703 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.58111 | −0.500130 | −0.250065 | − | 0.968229i | \(-0.580452\pi\) | ||||
−0.250065 | + | 0.968229i | \(0.580452\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 44.5551 | 2.31318 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 24.1058 | 1.24815 | 0.624076 | − | 0.781363i | \(-0.285475\pi\) | ||||
0.624076 | + | 0.781363i | \(0.285475\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 18.7376 | 0.965033 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.73973 | 0.140730 | 0.0703651 | − | 0.997521i | \(-0.477584\pi\) | ||||
0.0703651 | + | 0.997521i | \(0.477584\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 21.3532 | 1.09110 | 0.545548 | − | 0.838080i | \(-0.316322\pi\) | ||||
0.545548 | + | 0.838080i | \(0.316322\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 14.6697 | 0.743784 | 0.371892 | − | 0.928276i | \(-0.378709\pi\) | ||||
0.371892 | + | 0.928276i | \(0.378709\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.151149 | −0.00764393 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.43065 | −0.322745 | −0.161373 | − | 0.986894i | \(-0.551592\pi\) | ||||
−0.161373 | + | 0.986894i | \(0.551592\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.0750 | −0.902621 | −0.451310 | − | 0.892367i | \(-0.649043\pi\) | ||||
−0.451310 | + | 0.892367i | \(0.649043\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.32001 | −0.314822 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.60716 | −0.426641 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −18.7906 | −0.929137 | −0.464569 | − | 0.885537i | \(-0.653791\pi\) | ||||
−0.464569 | + | 0.885537i | \(0.653791\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 44.8333 | 2.20610 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −39.6594 | −1.93749 | −0.968745 | − | 0.248060i | \(-0.920207\pi\) | ||||
−0.968745 | + | 0.248060i | \(0.920207\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −37.5365 | −1.82942 | −0.914708 | − | 0.404115i | \(-0.867580\pi\) | ||||
−0.914708 | + | 0.404115i | \(0.867580\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.86678 | −0.283913 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.7357 | −0.806132 | −0.403066 | − | 0.915171i | \(-0.632055\pi\) | ||||
−0.403066 | + | 0.915171i | \(0.632055\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −21.0008 | −1.00924 | −0.504618 | − | 0.863343i | \(-0.668367\pi\) | ||||
−0.504618 | + | 0.863343i | \(0.668367\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.685467 | −0.0327903 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.03152 | −0.287869 | −0.143934 | − | 0.989587i | \(-0.545975\pi\) | ||||
−0.143934 | + | 0.989587i | \(0.545975\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.32548 | 0.300533 | 0.150266 | − | 0.988646i | \(-0.451987\pi\) | ||||
0.150266 | + | 0.988646i | \(0.451987\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.6594 | 0.880593 | 0.440296 | − | 0.897853i | \(-0.354873\pi\) | ||||
0.440296 | + | 0.897853i | \(0.354873\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 38.2769 | 1.80239 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 27.5846 | 1.29035 | 0.645176 | − | 0.764034i | \(-0.276784\pi\) | ||||
0.645176 | + | 0.764034i | \(0.276784\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.5288 | 0.630101 | 0.315051 | − | 0.949075i | \(-0.397979\pi\) | ||||
0.315051 | + | 0.949075i | \(0.397979\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −27.4842 | −1.27730 | −0.638650 | − | 0.769497i | \(-0.720507\pi\) | ||||
−0.638650 | + | 0.769497i | \(0.720507\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 32.7515 | 1.51556 | 0.757779 | − | 0.652511i | \(-0.226284\pi\) | ||||
0.757779 | + | 0.652511i | \(0.226284\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 42.0997 | 1.94398 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 31.3689 | 1.44234 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.85567 | −0.267552 | −0.133776 | − | 0.991012i | \(-0.542710\pi\) | ||||
−0.133776 | + | 0.991012i | \(0.542710\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.03434 | 0.183950 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.4864 | 0.747070 | 0.373535 | − | 0.927616i | \(-0.378146\pi\) | ||||
0.373535 | + | 0.927616i | \(0.378146\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.7060 | 0.618545 | 0.309272 | − | 0.950973i | \(-0.399915\pi\) | ||||
0.309272 | + | 0.950973i | \(0.399915\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.7307 | 0.573364 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 25.5461 | 1.14590 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.46964 | 0.200088 | 0.100044 | − | 0.994983i | \(-0.468102\pi\) | ||||
0.100044 | + | 0.994983i | \(0.468102\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −18.1010 | −0.807084 | −0.403542 | − | 0.914961i | \(-0.632221\pi\) | ||||
−0.403542 | + | 0.914961i | \(0.632221\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 21.2088 | 0.940065 | 0.470033 | − | 0.882649i | \(-0.344242\pi\) | ||||
0.470033 | + | 0.882649i | \(0.344242\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 18.4389 | 0.815691 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −32.9411 | −1.44875 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 28.4507 | 1.24645 | 0.623224 | − | 0.782043i | \(-0.285822\pi\) | ||||
0.623224 | + | 0.782043i | \(0.285822\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −26.5111 | −1.15925 | −0.579625 | − | 0.814884i | \(-0.696801\pi\) | ||||
−0.579625 | + | 0.814884i | \(0.696801\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.29396 | −0.187048 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9884 | −0.999495 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −17.9411 | −0.777115 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 20.1257 | 0.866876 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.3132 | −0.615372 | −0.307686 | − | 0.951488i | \(-0.599555\pi\) | ||||
−0.307686 | + | 0.951488i | \(0.599555\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.6511 | −0.583680 | −0.291840 | − | 0.956467i | \(-0.594267\pi\) | ||||
−0.291840 | + | 0.956467i | \(0.594267\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 57.7344 | 2.45957 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 32.0997 | 1.36502 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −23.4665 | −0.994306 | −0.497153 | − | 0.867663i | \(-0.665621\pi\) | ||||
−0.497153 | + | 0.867663i | \(0.665621\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −14.7032 | −0.621880 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −0.582452 | −0.0245474 | −0.0122737 | − | 0.999925i | \(-0.503907\pi\) | ||||
−0.0122737 | + | 0.999925i | \(0.503907\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.55988 | 0.233082 | 0.116541 | − | 0.993186i | \(-0.462819\pi\) | ||||
0.116541 | + | 0.993186i | \(0.462819\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.7412 | −0.951690 | −0.475845 | − | 0.879529i | \(-0.657858\pi\) | ||||
−0.475845 | + | 0.879529i | \(0.657858\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 30.5522 | 1.27191 | 0.635953 | − | 0.771728i | \(-0.280607\pi\) | ||||
0.635953 | + | 0.771728i | \(0.280607\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 30.5275 | 1.26649 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 57.6526 | 2.38773 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 20.3635 | 0.840490 | 0.420245 | − | 0.907411i | \(-0.361944\pi\) | ||||
0.420245 | + | 0.907411i | \(0.361944\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −19.4733 | −0.802383 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15.5199 | 0.637326 | 0.318663 | − | 0.947868i | \(-0.396766\pi\) | ||||
0.318663 | + | 0.947868i | \(0.396766\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −29.2576 | −1.19543 | −0.597717 | − | 0.801707i | \(-0.703925\pi\) | ||||
−0.597717 | + | 0.801707i | \(0.703925\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18.3051 | −0.746680 | −0.373340 | − | 0.927695i | \(-0.621787\pi\) | ||||
−0.373340 | + | 0.927695i | \(0.621787\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.8407 | −0.683544 | −0.341772 | − | 0.939783i | \(-0.611027\pi\) | ||||
−0.341772 | + | 0.939783i | \(0.611027\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15.4401 | 0.624640 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13.5954 | −0.549113 | −0.274556 | − | 0.961571i | \(-0.588531\pi\) | ||||
−0.274556 | + | 0.961571i | \(0.588531\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −29.3134 | −1.18011 | −0.590056 | − | 0.807362i | \(-0.700894\pi\) | ||||
−0.590056 | + | 0.807362i | \(0.700894\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.1642 | 0.488921 | 0.244461 | − | 0.969659i | \(-0.421389\pi\) | ||||
0.244461 | + | 0.969659i | \(0.421389\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −13.6608 | −0.547307 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.74103 | 0.109292 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.45471 | 0.217148 | 0.108574 | − | 0.994088i | \(-0.465371\pi\) | ||||
0.108574 | + | 0.994088i | \(0.465371\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9.43331 | −0.373761 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.67999 | 0.0663557 | 0.0331779 | − | 0.999449i | \(-0.489437\pi\) | ||||
0.0331779 | + | 0.999449i | \(0.489437\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.68346 | 0.224134 | 0.112067 | − | 0.993701i | \(-0.464253\pi\) | ||||
0.112067 | + | 0.993701i | \(0.464253\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −34.3064 | −1.34872 | −0.674361 | − | 0.738401i | \(-0.735581\pi\) | ||||
−0.674361 | + | 0.738401i | \(0.735581\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 58.0126 | 2.27719 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 12.6297 | 0.494239 | 0.247120 | − | 0.968985i | \(-0.420516\pi\) | ||||
0.247120 | + | 0.968985i | \(0.420516\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.33394 | 0.246735 | 0.123368 | − | 0.992361i | \(-0.460631\pi\) | ||||
0.123368 | + | 0.992361i | \(0.460631\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −37.6896 | −1.46596 | −0.732978 | − | 0.680253i | \(-0.761870\pi\) | ||||
−0.732978 | + | 0.680253i | \(0.761870\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.979251 | −0.0379167 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.59140 | −0.293063 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −30.6546 | −1.18165 | −0.590824 | − | 0.806800i | \(-0.701197\pi\) | ||||
−0.590824 | + | 0.806800i | \(0.701197\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 28.8716 | 1.10963 | 0.554813 | − | 0.831975i | \(-0.312790\pi\) | ||||
0.554813 | + | 0.831975i | \(0.312790\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.38538 | −0.283425 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −47.0352 | −1.79975 | −0.899875 | − | 0.436147i | \(-0.856343\pi\) | ||||
−0.899875 | + | 0.436147i | \(0.856343\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −27.0229 | −1.02949 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.850371 | 0.0323496 | 0.0161748 | − | 0.999869i | \(-0.494851\pi\) | ||||
0.0161748 | + | 0.999869i | \(0.494851\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.1896 | −0.461714 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 35.6821 | 1.34770 | 0.673848 | − | 0.738870i | \(-0.264640\pi\) | ||||
0.673848 | + | 0.738870i | \(0.264640\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.4307 | 0.468831 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −10.1168 | −0.380480 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.3909 | 0.578016 | 0.289008 | − | 0.957327i | \(-0.406675\pi\) | ||||
0.289008 | + | 0.957327i | \(0.406675\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.330292 | 0.0123695 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −25.5846 | −0.954144 | −0.477072 | − | 0.878864i | \(-0.658302\pi\) | ||||
−0.477072 | + | 0.878864i | \(0.658302\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −22.5721 | −0.840630 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.13734 | −0.227621 | −0.113811 | − | 0.993502i | \(-0.536306\pi\) | ||||
−0.113811 | + | 0.993502i | \(0.536306\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.98971 | −0.369483 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.13040 | −0.189496 | −0.0947478 | − | 0.995501i | \(-0.530204\pi\) | ||||
−0.0947478 | + | 0.995501i | \(0.530204\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 54.4754 | 2.00663 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 18.8784 | 0.694454 | 0.347227 | − | 0.937781i | \(-0.387123\pi\) | ||||
0.347227 | + | 0.937781i | \(0.387123\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21.9569 | 0.805519 | 0.402759 | − | 0.915306i | \(-0.368051\pi\) | ||||
0.402759 | + | 0.915306i | \(0.368051\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 46.9032 | 1.71381 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.16074 | −0.115337 | −0.0576686 | − | 0.998336i | \(-0.518367\pi\) | ||||
−0.0576686 | + | 0.998336i | \(0.518367\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −39.1753 | −1.42385 | −0.711926 | − | 0.702255i | \(-0.752177\pi\) | ||||
−0.711926 | + | 0.702255i | \(0.752177\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10.0783 | −0.365339 | −0.182669 | − | 0.983174i | \(-0.558474\pi\) | ||||
−0.182669 | + | 0.983174i | \(0.558474\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −61.6904 | −2.23334 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −27.1916 | −0.981832 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 21.1579 | 0.762974 | 0.381487 | − | 0.924374i | \(-0.375412\pi\) | ||||
0.381487 | + | 0.924374i | \(0.375412\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 43.2543 | 1.55575 | 0.777874 | − | 0.628420i | \(-0.216298\pi\) | ||||
0.777874 | + | 0.628420i | \(0.216298\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −55.2803 | −1.98062 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 33.0557 | 1.18283 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.17997 | 0.0420615 | 0.0210307 | − | 0.999779i | \(-0.493305\pi\) | ||||
0.0210307 | + | 0.999779i | \(0.493305\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.278204 | −0.00989180 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.55823 | 0.126357 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.14281 | −0.0404805 | −0.0202403 | − | 0.999795i | \(-0.506443\pi\) | ||||
−0.0202403 | + | 0.999795i | \(0.506443\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.4904 | 0.371123 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 23.8593 | 0.841977 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11.3723 | 0.399828 | 0.199914 | − | 0.979813i | \(-0.435934\pi\) | ||||
0.199914 | + | 0.979813i | \(0.435934\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.08590 | 0.0732459 | 0.0366230 | − | 0.999329i | \(-0.488340\pi\) | ||||
0.0366230 | + | 0.999329i | \(0.488340\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −45.3037 | −1.58498 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.7913 | −0.551120 | −0.275560 | − | 0.961284i | \(-0.588863\pi\) | ||||
−0.275560 | + | 0.961284i | \(0.588863\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.32084 | −0.255188 | −0.127594 | − | 0.991826i | \(-0.540725\pi\) | ||||
−0.127594 | + | 0.991826i | \(0.540725\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −14.8401 | −0.516040 | −0.258020 | − | 0.966140i | \(-0.583070\pi\) | ||||
−0.258020 | + | 0.966140i | \(0.583070\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23.3346 | −0.810444 | −0.405222 | − | 0.914218i | \(-0.632806\pi\) | ||||
−0.405222 | + | 0.914218i | \(0.632806\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.40921 | −0.222066 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 14.6765 | 0.506690 | 0.253345 | − | 0.967376i | \(-0.418469\pi\) | ||||
0.253345 | + | 0.967376i | \(0.418469\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 53.4788 | 1.84410 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 28.4925 | 0.979014 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.210840 | −0.00722751 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −24.5222 | −0.839624 | −0.419812 | − | 0.907611i | \(-0.637904\pi\) | ||||
−0.419812 | + | 0.907611i | \(0.637904\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.58793 | 0.190880 | 0.0954400 | − | 0.995435i | \(-0.469574\pi\) | ||||
0.0954400 | + | 0.995435i | \(0.469574\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −40.0619 | −1.36689 | −0.683447 | − | 0.730001i | \(-0.739520\pi\) | ||||
−0.683447 | + | 0.730001i | \(0.739520\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −27.2157 | −0.926432 | −0.463216 | − | 0.886246i | \(-0.653305\pi\) | ||||
−0.463216 | + | 0.886246i | \(0.653305\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 41.5358 | 1.40901 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −25.5337 | −0.865175 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.8799 | 0.806366 | 0.403183 | − | 0.915119i | \(-0.367904\pi\) | ||||
0.403183 | + | 0.915119i | \(0.367904\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −28.3585 | −0.955421 | −0.477710 | − | 0.878517i | \(-0.658533\pi\) | ||||
−0.477710 | + | 0.878517i | \(0.658533\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −28.3449 | −0.953881 | −0.476941 | − | 0.878936i | \(-0.658254\pi\) | ||||
−0.476941 | + | 0.878936i | \(0.658254\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0.515088 | 0.0172950 | 0.00864749 | − | 0.999963i | \(-0.497247\pi\) | ||||
0.00864749 | + | 0.999963i | \(0.497247\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −73.4144 | −2.46224 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 47.5743 | 1.59201 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −27.8193 | −0.927827 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18.3600 | −0.611660 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.16421 | −0.0718615 | −0.0359308 | − | 0.999354i | \(-0.511440\pi\) | ||||
−0.0359308 | + | 0.999354i | \(0.511440\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −38.4665 | −1.27445 | −0.637226 | − | 0.770677i | \(-0.719918\pi\) | ||||
−0.637226 | + | 0.770677i | \(0.719918\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 39.5015 | 1.30731 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 36.6979 | 1.21187 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18.6992 | 0.616830 | 0.308415 | − | 0.951252i | \(-0.400201\pi\) | ||||
0.308415 | + | 0.951252i | \(0.400201\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −15.4939 | −0.509986 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.20671 | 0.0723997 | 0.0361999 | − | 0.999345i | \(-0.488475\pi\) | ||||
0.0361999 | + | 0.999345i | \(0.488475\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −29.0660 | −0.952600 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21.3429 | 0.697242 | 0.348621 | − | 0.937264i | \(-0.386650\pi\) | ||||
0.348621 | + | 0.937264i | \(0.386650\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.17932 | 0.0384448 | 0.0192224 | − | 0.999815i | \(-0.493881\pi\) | ||||
0.0192224 | + | 0.999815i | \(0.493881\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.937627 | 0.0305333 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −23.6889 | −0.769787 | −0.384894 | − | 0.922961i | \(-0.625762\pi\) | ||||
−0.384894 | + | 0.922961i | \(0.625762\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −11.1833 | −0.363026 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −12.8125 | −0.415038 | −0.207519 | − | 0.978231i | \(-0.566539\pi\) | ||||
−0.207519 | + | 0.978231i | \(0.566539\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 45.9569 | 1.48402 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.6168 | −0.697316 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.9265 | 0.351373 | 0.175686 | − | 0.984446i | \(-0.443786\pi\) | ||||
0.175686 | + | 0.984446i | \(0.443786\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15.7933 | −0.506831 | −0.253415 | − | 0.967358i | \(-0.581554\pi\) | ||||
−0.253415 | + | 0.967358i | \(0.581554\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 49.7001 | 1.59331 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 37.4980 | 1.19967 | 0.599833 | − | 0.800125i | \(-0.295233\pi\) | ||||
0.599833 | + | 0.800125i | \(0.295233\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −17.6765 | −0.564944 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −23.5322 | −0.750560 | −0.375280 | − | 0.926911i | \(-0.622453\pi\) | ||||
−0.375280 | + | 0.926911i | \(0.622453\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.768410 | 0.0244340 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 46.7019 | 1.48353 | 0.741767 | − | 0.670658i | \(-0.233988\pi\) | ||||
0.741767 | + | 0.670658i | \(0.233988\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 42.8580 | 1.35733 | 0.678663 | − | 0.734450i | \(-0.262560\pi\) | ||||
0.678663 | + | 0.734450i | \(0.262560\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8100.2.a.y.1.4 | 4 | ||
3.2 | odd | 2 | 8100.2.a.x.1.4 | 4 | |||
5.2 | odd | 4 | 8100.2.d.s.649.7 | 8 | |||
5.3 | odd | 4 | 8100.2.d.s.649.2 | 8 | |||
5.4 | even | 2 | 8100.2.a.ba.1.1 | 4 | |||
9.2 | odd | 6 | 900.2.i.d.301.1 | ✓ | 8 | ||
9.4 | even | 3 | 2700.2.i.e.1801.1 | 8 | |||
9.5 | odd | 6 | 900.2.i.d.601.1 | yes | 8 | ||
9.7 | even | 3 | 2700.2.i.e.901.1 | 8 | |||
15.2 | even | 4 | 8100.2.d.q.649.7 | 8 | |||
15.8 | even | 4 | 8100.2.d.q.649.2 | 8 | |||
15.14 | odd | 2 | 8100.2.a.z.1.1 | 4 | |||
45.2 | even | 12 | 900.2.s.d.49.5 | 16 | |||
45.4 | even | 6 | 2700.2.i.d.1801.4 | 8 | |||
45.7 | odd | 12 | 2700.2.s.d.1549.7 | 16 | |||
45.13 | odd | 12 | 2700.2.s.d.2449.7 | 16 | |||
45.14 | odd | 6 | 900.2.i.e.601.4 | yes | 8 | ||
45.22 | odd | 12 | 2700.2.s.d.2449.2 | 16 | |||
45.23 | even | 12 | 900.2.s.d.349.5 | 16 | |||
45.29 | odd | 6 | 900.2.i.e.301.4 | yes | 8 | ||
45.32 | even | 12 | 900.2.s.d.349.4 | 16 | |||
45.34 | even | 6 | 2700.2.i.d.901.4 | 8 | |||
45.38 | even | 12 | 900.2.s.d.49.4 | 16 | |||
45.43 | odd | 12 | 2700.2.s.d.1549.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
900.2.i.d.301.1 | ✓ | 8 | 9.2 | odd | 6 | ||
900.2.i.d.601.1 | yes | 8 | 9.5 | odd | 6 | ||
900.2.i.e.301.4 | yes | 8 | 45.29 | odd | 6 | ||
900.2.i.e.601.4 | yes | 8 | 45.14 | odd | 6 | ||
900.2.s.d.49.4 | 16 | 45.38 | even | 12 | |||
900.2.s.d.49.5 | 16 | 45.2 | even | 12 | |||
900.2.s.d.349.4 | 16 | 45.32 | even | 12 | |||
900.2.s.d.349.5 | 16 | 45.23 | even | 12 | |||
2700.2.i.d.901.4 | 8 | 45.34 | even | 6 | |||
2700.2.i.d.1801.4 | 8 | 45.4 | even | 6 | |||
2700.2.i.e.901.1 | 8 | 9.7 | even | 3 | |||
2700.2.i.e.1801.1 | 8 | 9.4 | even | 3 | |||
2700.2.s.d.1549.2 | 16 | 45.43 | odd | 12 | |||
2700.2.s.d.1549.7 | 16 | 45.7 | odd | 12 | |||
2700.2.s.d.2449.2 | 16 | 45.22 | odd | 12 | |||
2700.2.s.d.2449.7 | 16 | 45.13 | odd | 12 | |||
8100.2.a.x.1.4 | 4 | 3.2 | odd | 2 | |||
8100.2.a.y.1.4 | 4 | 1.1 | even | 1 | trivial | ||
8100.2.a.z.1.1 | 4 | 15.14 | odd | 2 | |||
8100.2.a.ba.1.1 | 4 | 5.4 | even | 2 | |||
8100.2.d.q.649.2 | 8 | 15.8 | even | 4 | |||
8100.2.d.q.649.7 | 8 | 15.2 | even | 4 | |||
8100.2.d.s.649.2 | 8 | 5.3 | odd | 4 | |||
8100.2.d.s.649.7 | 8 | 5.2 | odd | 4 |