Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3680,2,Mod(1,3680)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3680, 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("3680.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3680 = 2^{5} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3680.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: | \(29.3849479438\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.1573.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 7x + 2 \) |
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 | 1.2 | ||
Root | \(0.277754\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3680.1 |
$q$-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 | ||||||||
\(3\) | −0.277754 | −0.160362 | −0.0801808 | − | 0.996780i | \(-0.525550\pi\) | ||||
−0.0801808 | + | 0.996780i | \(0.525550\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.27775 | 0.482946 | 0.241473 | − | 0.970408i | \(-0.422370\pi\) | ||||
0.241473 | + | 0.970408i | \(0.422370\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.92285 | −0.974284 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.277754 | −0.0837461 | −0.0418730 | − | 0.999123i | \(-0.513333\pi\) | ||||
−0.0418730 | + | 0.999123i | \(0.513333\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.92285 | −1.08800 | −0.544002 | − | 0.839084i | \(-0.683092\pi\) | ||||
−0.544002 | + | 0.839084i | \(0.683092\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.277754 | −0.0717159 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.47836 | 1.32870 | 0.664349 | − | 0.747423i | \(-0.268709\pi\) | ||||
0.664349 | + | 0.747423i | \(0.268709\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.92285 | −0.899964 | −0.449982 | − | 0.893038i | \(-0.648570\pi\) | ||||
−0.449982 | + | 0.893038i | \(0.648570\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.354902 | −0.0774459 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.64510 | 0.316599 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.799393 | 0.148444 | 0.0742218 | − | 0.997242i | \(-0.476353\pi\) | ||||
0.0742218 | + | 0.997242i | \(0.476353\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.27775 | 0.947913 | 0.473956 | − | 0.880548i | \(-0.342825\pi\) | ||||
0.473956 | + | 0.880548i | \(0.342825\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.0771475 | 0.0134297 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.27775 | 0.215980 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.75612 | −0.288704 | −0.144352 | − | 0.989526i | \(-0.546110\pi\) | ||||
−0.144352 | + | 0.989526i | \(0.546110\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.08959 | 0.174474 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.0339 | 1.56703 | 0.783514 | − | 0.621375i | \(-0.213425\pi\) | ||||
0.783514 | + | 0.621375i | \(0.213425\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.00000 | −0.609994 | −0.304997 | − | 0.952353i | \(-0.598656\pi\) | ||||
−0.304997 | + | 0.952353i | \(0.598656\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.92285 | −0.435713 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.95672 | −1.30647 | −0.653236 | − | 0.757154i | \(-0.726589\pi\) | ||||
−0.653236 | + | 0.757154i | \(0.726589\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.36734 | −0.766763 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.52164 | −0.213072 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.6451 | 1.46222 | 0.731108 | − | 0.682261i | \(-0.239003\pi\) | ||||
0.731108 | + | 0.682261i | \(0.239003\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.277754 | −0.0374524 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.08959 | 0.144320 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.08959 | 1.05317 | 0.526587 | − | 0.850121i | \(-0.323471\pi\) | ||||
0.526587 | + | 0.850121i | \(0.323471\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 15.0124 | 1.92215 | 0.961073 | − | 0.276294i | \(-0.0891064\pi\) | ||||
0.961073 | + | 0.276294i | \(0.0891064\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.73469 | −0.470526 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.92285 | −0.486570 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.6451 | 1.54484 | 0.772422 | − | 0.635109i | \(-0.219045\pi\) | ||||
0.772422 | + | 0.635109i | \(0.219045\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.277754 | −0.0334377 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.32407 | 1.10656 | 0.553282 | − | 0.832994i | \(-0.313375\pi\) | ||||
0.553282 | + | 0.832994i | \(0.313375\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.55551 | 0.533182 | 0.266591 | − | 0.963810i | \(-0.414103\pi\) | ||||
0.266591 | + | 0.963810i | \(0.414103\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.277754 | −0.0320723 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.354902 | −0.0404448 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.00000 | −0.900070 | −0.450035 | − | 0.893011i | \(-0.648589\pi\) | ||||
−0.450035 | + | 0.893011i | \(0.648589\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.31162 | 0.923514 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.64510 | −0.290337 | −0.145169 | − | 0.989407i | \(-0.546372\pi\) | ||||
−0.145169 | + | 0.989407i | \(0.546372\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.47836 | 0.594212 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.222035 | −0.0238046 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.2902 | 1.40876 | 0.704379 | − | 0.709824i | \(-0.251226\pi\) | ||||
0.704379 | + | 0.709824i | \(0.251226\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.01244 | −0.525447 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.46592 | −0.152009 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.92285 | −0.402476 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.16674 | 0.321533 | 0.160767 | − | 0.986992i | \(-0.448603\pi\) | ||||
0.160767 | + | 0.986992i | \(0.448603\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.811835 | 0.0815925 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.60182 | 0.557402 | 0.278701 | − | 0.960378i | \(-0.410096\pi\) | ||||
0.278701 | + | 0.960378i | \(0.410096\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.83326 | 0.279170 | 0.139585 | − | 0.990210i | \(-0.455423\pi\) | ||||
0.139585 | + | 0.990210i | \(0.455423\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.354902 | −0.0346349 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −19.2006 | −1.85619 | −0.928096 | − | 0.372340i | \(-0.878556\pi\) | ||||
−0.928096 | + | 0.372340i | \(0.878556\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.07715 | −0.390520 | −0.195260 | − | 0.980752i | \(-0.562555\pi\) | ||||
−0.195260 | + | 0.980752i | \(0.562555\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.487769 | 0.0462970 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.7561 | 1.10592 | 0.552961 | − | 0.833207i | \(-0.313498\pi\) | ||||
0.552961 | + | 0.833207i | \(0.313498\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.00000 | 0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 11.4659 | 1.06002 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.00000 | 0.641689 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9229 | −0.992987 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.78695 | −0.251291 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.8457 | −1.58355 | −0.791775 | − | 0.610813i | \(-0.790843\pi\) | ||||
−0.791775 | + | 0.610813i | \(0.790843\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.11102 | 0.0978196 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.4012 | −1.08350 | −0.541750 | − | 0.840540i | \(-0.682238\pi\) | ||||
−0.541750 | + | 0.840540i | \(0.682238\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.01244 | −0.434634 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.64510 | 0.141588 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 15.0339 | 1.28443 | 0.642215 | − | 0.766524i | \(-0.278016\pi\) | ||||
0.642215 | + | 0.766524i | \(0.278016\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −18.0030 | −1.52700 | −0.763499 | − | 0.645809i | \(-0.776520\pi\) | ||||
−0.763499 | + | 0.645809i | \(0.776520\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.48777 | 0.209508 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.08959 | 0.0911160 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.799393 | 0.0663860 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.49080 | 0.122959 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −14.3241 | −1.17347 | −0.586737 | − | 0.809778i | \(-0.699588\pi\) | ||||
−0.586737 | + | 0.809778i | \(0.699588\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 24.1912 | 1.96865 | 0.984326 | − | 0.176359i | \(-0.0564319\pi\) | ||||
0.984326 | + | 0.176359i | \(0.0564319\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −16.0124 | −1.29453 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.27775 | 0.423919 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.7994 | 1.02150 | 0.510751 | − | 0.859728i | \(-0.329367\pi\) | ||||
0.510751 | + | 0.859728i | \(0.329367\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.95672 | −0.234483 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.27775 | 0.100701 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 19.4351 | 1.52227 | 0.761137 | − | 0.648592i | \(-0.224642\pi\) | ||||
0.761137 | + | 0.648592i | \(0.224642\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.0771475 | 0.00600592 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 24.8024 | 1.91927 | 0.959635 | − | 0.281249i | \(-0.0907488\pi\) | ||||
0.959635 | + | 0.281249i | \(0.0907488\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.38877 | 0.183752 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 11.4659 | 0.876821 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −12.6790 | −0.963964 | −0.481982 | − | 0.876181i | \(-0.660083\pi\) | ||||
−0.481982 | + | 0.876181i | \(0.660083\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.27775 | 0.0965892 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.24692 | −0.168889 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.154295 | −0.0115325 | −0.00576627 | − | 0.999983i | \(-0.501835\pi\) | ||||
−0.00576627 | + | 0.999983i | \(0.501835\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.410621 | 0.0305212 | 0.0152606 | − | 0.999884i | \(-0.495142\pi\) | ||||
0.0152606 | + | 0.999884i | \(0.495142\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.16977 | −0.308238 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.75612 | −0.129112 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.52164 | −0.111273 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.10203 | 0.152900 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.44449 | −0.538664 | −0.269332 | − | 0.963047i | \(-0.586803\pi\) | ||||
−0.269332 | + | 0.963047i | \(0.586803\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.06774 | −0.580729 | −0.290364 | − | 0.956916i | \(-0.593776\pi\) | ||||
−0.290364 | + | 0.956916i | \(0.593776\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.08959 | 0.0780271 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.4569 | 1.31500 | 0.657501 | − | 0.753454i | \(-0.271614\pi\) | ||||
0.657501 | + | 0.753454i | \(0.271614\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.29020 | 0.233236 | 0.116618 | − | 0.993177i | \(-0.462795\pi\) | ||||
0.116618 | + | 0.993177i | \(0.462795\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.51223 | −0.247734 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.02143 | 0.0716902 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.0339 | 0.700796 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.92285 | −0.203152 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.08959 | 0.0753685 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −26.3365 | −1.81308 | −0.906540 | − | 0.422120i | \(-0.861286\pi\) | ||||
−0.906540 | + | 0.422120i | \(0.861286\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.58980 | −0.177450 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.00000 | −0.272798 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.74367 | 0.457790 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.26531 | −0.0855019 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −21.4908 | −1.44563 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 25.9134 | 1.73529 | 0.867646 | − | 0.497182i | \(-0.165632\pi\) | ||||
0.867646 | + | 0.497182i | \(0.165632\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.92285 | −0.194857 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.7347 | −0.712486 | −0.356243 | − | 0.934393i | \(-0.615943\pi\) | ||||
−0.356243 | + | 0.934393i | \(0.615943\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.22203 | 0.279000 | 0.139500 | − | 0.990222i | \(-0.455450\pi\) | ||||
0.139500 | + | 0.990222i | \(0.455450\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.0985755 | 0.00648579 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4.55551 | −0.298441 | −0.149221 | − | 0.988804i | \(-0.547676\pi\) | ||||
−0.149221 | + | 0.988804i | \(0.547676\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.95672 | −0.584272 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.22203 | 0.144337 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 24.3365 | 1.57420 | 0.787099 | − | 0.616827i | \(-0.211582\pi\) | ||||
0.787099 | + | 0.616827i | \(0.211582\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.6914 | 1.01077 | 0.505386 | − | 0.862893i | \(-0.331350\pi\) | ||||
0.505386 | + | 0.862893i | \(0.331350\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −7.24388 | −0.464695 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.36734 | −0.342907 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 15.3888 | 0.979164 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.734688 | 0.0465589 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −30.6575 | −1.93509 | −0.967543 | − | 0.252705i | \(-0.918680\pi\) | ||||
−0.967543 | + | 0.252705i | \(0.918680\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.277754 | −0.0174623 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.52164 | −0.0952887 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.24692 | 0.264916 | 0.132458 | − | 0.991189i | \(-0.457713\pi\) | ||||
0.132458 | + | 0.991189i | \(0.457713\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.24388 | −0.139428 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.33651 | −0.144626 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 20.2130 | 1.24639 | 0.623195 | − | 0.782066i | \(-0.285834\pi\) | ||||
0.623195 | + | 0.782066i | \(0.285834\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.6451 | 0.653923 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.69141 | −0.225911 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.08959 | 0.371289 | 0.185644 | − | 0.982617i | \(-0.440563\pi\) | ||||
0.185644 | + | 0.982617i | \(0.440563\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.78999 | 0.533954 | 0.266977 | − | 0.963703i | \(-0.413975\pi\) | ||||
0.266977 | + | 0.963703i | \(0.413975\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.39223 | 0.0842614 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.277754 | −0.0167492 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.8024 | 1.37007 | 0.685033 | − | 0.728512i | \(-0.259788\pi\) | ||||
0.685033 | + | 0.728512i | \(0.259788\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −15.4261 | −0.923536 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −23.3579 | −1.39342 | −0.696709 | − | 0.717354i | \(-0.745353\pi\) | ||||
−0.696709 | + | 0.717354i | \(0.745353\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.2439 | −0.727823 | −0.363912 | − | 0.931433i | \(-0.618559\pi\) | ||||
−0.363912 | + | 0.931433i | \(0.618559\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.08959 | 0.0645417 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 12.8208 | 0.756789 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.0124 | 0.765438 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.879575 | −0.0515616 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 26.1573 | 1.52813 | 0.764064 | − | 0.645141i | \(-0.223201\pi\) | ||||
0.764064 | + | 0.645141i | \(0.223201\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.08959 | 0.470994 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.456933 | −0.0265140 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.92285 | −0.226864 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.11102 | −0.294594 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.55593 | −0.0893859 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 15.0124 | 0.859610 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.38877 | 0.307553 | 0.153777 | − | 0.988106i | \(-0.450856\pi\) | ||||
0.153777 | + | 0.988106i | \(0.450856\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.786951 | −0.0447681 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 26.5804 | 1.50724 | 0.753618 | − | 0.657313i | \(-0.228307\pi\) | ||||
0.753618 | + | 0.657313i | \(0.228307\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.1235 | 1.42006 | 0.710031 | − | 0.704170i | \(-0.248681\pi\) | ||||
0.710031 | + | 0.704170i | \(0.248681\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.73469 | −0.210426 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 19.5894 | 1.10025 | 0.550125 | − | 0.835083i | \(-0.314580\pi\) | ||||
0.550125 | + | 0.835083i | \(0.314580\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.222035 | −0.0124316 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.33305 | 0.297662 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −21.4908 | −1.19578 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.92285 | −0.217601 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.13245 | 0.0626244 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −11.4445 | −0.630955 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 31.1141 | 1.71018 | 0.855091 | − | 0.518477i | \(-0.173501\pi\) | ||||
0.855091 | + | 0.518477i | \(0.173501\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.13287 | 0.281279 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.6451 | 0.690876 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.9229 | 0.976320 | 0.488160 | − | 0.872754i | \(-0.337668\pi\) | ||||
0.488160 | + | 0.872754i | \(0.337668\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.26531 | −0.177347 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.46592 | −0.0793840 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.8024 | −0.853251 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.277754 | −0.0149538 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.16674 | −0.384731 | −0.192365 | − | 0.981323i | \(-0.561616\pi\) | ||||
−0.192365 | + | 0.981323i | \(0.561616\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.93529 | 0.424767 | 0.212383 | − | 0.977186i | \(-0.431877\pi\) | ||||
0.212383 | + | 0.977186i | \(0.431877\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.45348 | −0.344461 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.32407 | 0.494870 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.94428 | −0.102902 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −27.6049 | −1.45693 | −0.728464 | − | 0.685084i | \(-0.759766\pi\) | ||||
−0.728464 | + | 0.685084i | \(0.759766\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.61123 | −0.190065 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.03387 | 0.159237 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.55551 | 0.238446 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.5341 | −0.602074 | −0.301037 | − | 0.953612i | \(-0.597333\pi\) | ||||
−0.301037 | + | 0.953612i | \(0.597333\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −29.3275 | −1.52673 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 13.6018 | 0.706171 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.6237 | −0.601851 | −0.300925 | − | 0.953648i | \(-0.597296\pi\) | ||||
−0.300925 | + | 0.953648i | \(0.597296\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.277754 | −0.0143432 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.13590 | −0.161507 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.2778 | 0.630666 | 0.315333 | − | 0.948981i | \(-0.397884\pi\) | ||||
0.315333 | + | 0.948981i | \(0.397884\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.95672 | 0.253941 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.64510 | −0.237353 | −0.118677 | − | 0.992933i | \(-0.537865\pi\) | ||||
−0.118677 | + | 0.992933i | \(0.537865\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.354902 | −0.0180875 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 11.6914 | 0.594308 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9.90142 | −0.502022 | −0.251011 | − | 0.967984i | \(-0.580763\pi\) | ||||
−0.251011 | + | 0.967984i | \(0.580763\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.47836 | 0.277053 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.44449 | 0.173752 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.00000 | −0.402524 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.34549 | −0.318471 | −0.159236 | − | 0.987241i | \(-0.550903\pi\) | ||||
−0.159236 | + | 0.987241i | \(0.550903\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.39223 | 0.0696986 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.84571 | −0.291921 | −0.145960 | − | 0.989290i | \(-0.546627\pi\) | ||||
−0.145960 | + | 0.989290i | \(0.546627\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −20.7039 | −1.03133 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 8.31162 | 0.413008 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.487769 | 0.0241778 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.52467 | 0.372071 | 0.186036 | − | 0.982543i | \(-0.440436\pi\) | ||||
0.186036 | + | 0.982543i | \(0.440436\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.17572 | −0.205973 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 10.3365 | 0.508626 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.64510 | −0.129843 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.00042 | 0.244872 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14.4012 | 0.703545 | 0.351773 | − | 0.936085i | \(-0.385579\pi\) | ||||
0.351773 | + | 0.936085i | \(0.385579\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −18.4784 | −0.900580 | −0.450290 | − | 0.892882i | \(-0.648679\pi\) | ||||
−0.450290 | + | 0.892882i | \(0.648679\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 26.1792 | 1.27288 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.47836 | 0.265740 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 19.1822 | 0.928292 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.302638 | −0.0146115 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.1359 | −0.632734 | −0.316367 | − | 0.948637i | \(-0.602463\pi\) | ||||
−0.316367 | + | 0.948637i | \(0.602463\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −36.1479 | −1.73716 | −0.868579 | − | 0.495550i | \(-0.834966\pi\) | ||||
−0.868579 | + | 0.495550i | \(0.834966\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.222035 | −0.0106458 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.92285 | −0.187655 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.16977 | −0.389922 | −0.194961 | − | 0.980811i | \(-0.562458\pi\) | ||||
−0.194961 | + | 0.980811i | \(0.562458\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 15.6880 | 0.747045 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.36734 | 0.0649645 | 0.0324822 | − | 0.999472i | \(-0.489659\pi\) | ||||
0.0324822 | + | 0.999472i | \(0.489659\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.2902 | 0.630016 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.97857 | 0.188180 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −0.944281 | −0.0445634 | −0.0222817 | − | 0.999752i | \(-0.507093\pi\) | ||||
−0.0222817 | + | 0.999752i | \(0.507093\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.78695 | −0.131232 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.71921 | −0.315696 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.01244 | −0.234987 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.75612 | −0.362816 | −0.181408 | − | 0.983408i | \(-0.558065\pi\) | ||||
−0.181408 | + | 0.983408i | \(0.558065\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 9.01244 | 0.420665 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.84571 | 0.458560 | 0.229280 | − | 0.973360i | \(-0.426363\pi\) | ||||
0.229280 | + | 0.973360i | \(0.426363\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.29020 | 0.338804 | 0.169402 | − | 0.985547i | \(-0.445816\pi\) | ||||
0.169402 | + | 0.985547i | \(0.445816\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.46592 | −0.0679804 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −37.5153 | −1.73600 | −0.868000 | − | 0.496565i | \(-0.834595\pi\) | ||||
−0.868000 | + | 0.496565i | \(0.834595\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 16.1573 | 0.746076 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.55509 | −0.163810 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.11102 | 0.0510846 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.92285 | −0.179993 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −31.1141 | −1.42461 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −26.1792 | −1.19616 | −0.598079 | − | 0.801437i | \(-0.704069\pi\) | ||||
−0.598079 | + | 0.801437i | \(0.704069\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.88898 | 0.314111 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.354902 | −0.0161486 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.16674 | 0.143794 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.9567 | −0.496496 | −0.248248 | − | 0.968696i | \(-0.579855\pi\) | ||||
−0.248248 | + | 0.968696i | \(0.579855\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5.39818 | −0.244114 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.6884 | −0.888524 | −0.444262 | − | 0.895897i | \(-0.646534\pi\) | ||||
−0.444262 | + | 0.895897i | \(0.646534\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.37936 | 0.197237 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.811835 | 0.0364893 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 11.9139 | 0.534410 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 32.8243 | 1.46942 | 0.734708 | − | 0.678383i | \(-0.237319\pi\) | ||||
0.734708 | + | 0.678383i | \(0.237319\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.88898 | −0.307777 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 17.9010 | 0.798166 | 0.399083 | − | 0.916915i | \(-0.369328\pi\) | ||||
0.399083 | + | 0.916915i | \(0.369328\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.60182 | 0.249278 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.663492 | −0.0294667 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −43.3579 | −1.92181 | −0.960903 | − | 0.276884i | \(-0.910698\pi\) | ||||
−0.960903 | + | 0.276884i | \(0.910698\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.82082 | 0.257498 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.45348 | −0.284928 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.83326 | 0.124848 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.48777 | 0.109412 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.52164 | 0.154583 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −25.5122 | −1.11771 | −0.558856 | − | 0.829265i | \(-0.688759\pi\) | ||||
−0.558856 | + | 0.829265i | \(0.688759\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −24.4012 | −1.06699 | −0.533495 | − | 0.845803i | \(-0.679122\pi\) | ||||
−0.533495 | + | 0.845803i | \(0.679122\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.354902 | −0.0154892 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 28.9134 | 1.25949 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −23.6447 | −1.02609 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −39.3614 | −1.70493 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −19.2006 | −0.830115 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.0428561 | 0.00184938 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.49080 | 0.0642134 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.3147 | −0.701422 | −0.350711 | − | 0.936484i | \(-0.614060\pi\) | ||||
−0.350711 | + | 0.936484i | \(0.614060\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.114052 | −0.00489443 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.07715 | −0.174646 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.1016 | 0.474671 | 0.237335 | − | 0.971428i | \(-0.423726\pi\) | ||||
0.237335 | + | 0.971428i | \(0.423726\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −43.8792 | −1.87272 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.13590 | −0.133594 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.2220 | −0.434685 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.487769 | 0.0207046 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 39.8487 | 1.68845 | 0.844223 | − | 0.535993i | \(-0.180063\pi\) | ||||
0.844223 | + | 0.535993i | \(0.180063\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15.6914 | 0.663676 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.422642 | 0.0178440 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 11.0463 | 0.465547 | 0.232773 | − | 0.972531i | \(-0.425220\pi\) | ||||
0.232773 | + | 0.972531i | \(0.425220\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11.7561 | 0.494584 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 10.6202 | 0.446007 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −38.4938 | −1.61375 | −0.806873 | − | 0.590725i | \(-0.798842\pi\) | ||||
−0.806873 | + | 0.590725i | \(0.798842\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.2778 | −0.848598 | −0.424299 | − | 0.905522i | \(-0.639479\pi\) | ||||
−0.424299 | + | 0.905522i | \(0.639479\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.06774 | 0.0863811 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.00000 | 0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14.8024 | −0.616233 | −0.308117 | − | 0.951349i | \(-0.599699\pi\) | ||||
−0.308117 | + | 0.951349i | \(0.599699\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.24085 | 0.0931265 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.37979 | −0.140217 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.95672 | −0.122455 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 11.4659 | 0.474057 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −36.7716 | −1.51773 | −0.758863 | − | 0.651250i | \(-0.774245\pi\) | ||||
−0.758863 | + | 0.651250i | \(0.774245\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −20.7039 | −0.853087 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.12649 | −0.210876 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8.73469 | −0.358691 | −0.179345 | − | 0.983786i | \(-0.557398\pi\) | ||||
−0.179345 | + | 0.983786i | \(0.557398\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.00000 | 0.286972 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.913866 | −0.0374021 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −20.8581 | −0.852241 | −0.426120 | − | 0.904666i | \(-0.640120\pi\) | ||||
−0.426120 | + | 0.904666i | \(0.640120\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 42.7283 | 1.74292 | 0.871462 | − | 0.490463i | \(-0.163172\pi\) | ||||
0.871462 | + | 0.490463i | \(0.163172\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −36.9598 | −1.50512 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −10.9229 | −0.444077 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.29020 | 0.0523675 | 0.0261837 | − | 0.999657i | \(-0.491665\pi\) | ||||
0.0261837 | + | 0.999657i | \(0.491665\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.283706 | −0.0114964 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 35.1359 | 1.42145 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 42.4938 | 1.71631 | 0.858155 | − | 0.513391i | \(-0.171611\pi\) | ||||
0.858155 | + | 0.513391i | \(0.171611\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.78695 | −0.112381 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.34246 | −0.255338 | −0.127669 | − | 0.991817i | \(-0.540749\pi\) | ||||
−0.127669 | + | 0.991817i | \(0.540749\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.3241 | 0.897280 | 0.448640 | − | 0.893713i | \(-0.351909\pi\) | ||||
0.448640 | + | 0.893713i | \(0.351909\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.64510 | 0.0660155 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 16.9816 | 0.680354 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.302638 | −0.0120862 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −9.62064 | −0.383600 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −30.6481 | −1.22008 | −0.610041 | − | 0.792370i | \(-0.708847\pi\) | ||||
−0.610041 | + | 0.792370i | \(0.708847\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7.31508 | 0.290748 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −17.8457 | −0.708185 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 21.0553 | 0.834241 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −27.2529 | −1.07811 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −24.3147 | −0.960371 | −0.480186 | − | 0.877167i | \(-0.659431\pi\) | ||||
−0.480186 | + | 0.877167i | \(0.659431\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −23.6944 | −0.934418 | −0.467209 | − | 0.884147i | \(-0.654740\pi\) | ||||
−0.467209 | + | 0.884147i | \(0.654740\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.11102 | 0.0437463 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 32.8951 | 1.29324 | 0.646619 | − | 0.762813i | \(-0.276182\pi\) | ||||
0.646619 | + | 0.762813i | \(0.276182\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.24692 | −0.0881993 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.87308 | −0.0734120 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −48.9045 | −1.91378 | −0.956890 | − | 0.290452i | \(-0.906194\pi\) | ||||
−0.956890 | + | 0.290452i | \(0.906194\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12.4012 | −0.484556 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −13.3151 | −0.519471 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21.9134 | 0.853627 | 0.426813 | − | 0.904340i | \(-0.359636\pi\) | ||||
0.426813 | + | 0.904340i | \(0.359636\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.34549 | 0.246811 | 0.123406 | − | 0.992356i | \(-0.460618\pi\) | ||||
0.123406 | + | 0.992356i | \(0.460618\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.96916 | 0.231823 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.01244 | −0.194374 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.799393 | 0.0309526 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7.19757 | −0.278274 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.16977 | −0.160972 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.9816 | 0.885876 | 0.442938 | − | 0.896552i | \(-0.353936\pi\) | ||||
0.442938 | + | 0.896552i | \(0.353936\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.64510 | 0.0633199 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.97815 | −0.383491 | −0.191746 | − | 0.981445i | \(-0.561415\pi\) | ||||
−0.191746 | + | 0.981445i | \(0.561415\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.04631 | 0.155283 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.98161 | 0.114255 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15.1265 | 0.578799 | 0.289400 | − | 0.957208i | \(-0.406544\pi\) | ||||
0.289400 | + | 0.957208i | \(0.406544\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15.0339 | 0.574415 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.17269 | −0.0447409 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −41.7592 | −1.59090 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 35.8457 | 1.36363 | 0.681817 | − | 0.731522i | \(-0.261190\pi\) | ||||
0.681817 | + | 0.731522i | \(0.261190\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.03733 | 0.0394047 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −18.0030 | −0.682894 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 54.9692 | 2.08211 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.26531 | 0.0478585 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −13.0339 | −0.492282 | −0.246141 | − | 0.969234i | \(-0.579163\pi\) | ||||
−0.246141 | + | 0.969234i | \(0.579163\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.88898 | 0.259823 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.48777 | 0.0936948 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7.15775 | 0.269195 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.21001 | −0.0829988 | −0.0414994 | − | 0.999139i | \(-0.513213\pi\) | ||||
−0.0414994 | + | 0.999139i | \(0.513213\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 23.3828 | 0.876924 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.27775 | 0.197653 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.08959 | 0.0407483 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6.75957 | −0.252441 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 37.9259 | 1.41440 | 0.707198 | − | 0.707015i | \(-0.249959\pi\) | ||||
0.707198 | + | 0.707015i | \(0.249959\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.62021 | 0.134824 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4.35836 | −0.162089 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.799393 | 0.0296887 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26.5465 | 0.984556 | 0.492278 | − | 0.870438i | \(-0.336164\pi\) | ||||
0.492278 | + | 0.870438i | \(0.336164\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −22.9229 | −0.848995 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −21.9134 | −0.810498 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.37936 | −0.309499 | −0.154749 | − | 0.987954i | \(-0.549457\pi\) | ||||
−0.154749 | + | 0.987954i | \(0.549457\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.49080 | 0.0549891 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.51223 | −0.129375 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −23.4904 | −0.864108 | −0.432054 | − | 0.901848i | \(-0.642211\pi\) | ||||
−0.432054 | + | 0.901848i | \(0.642211\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.27430 | −0.157020 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 28.7681 | 1.05540 | 0.527700 | − | 0.849431i | \(-0.323054\pi\) | ||||
0.527700 | + | 0.849431i | \(0.323054\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14.3241 | −0.524793 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7.73123 | 0.282871 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −24.5337 | −0.896440 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.13590 | −0.114431 | −0.0572153 | − | 0.998362i | \(-0.518222\pi\) | ||||
−0.0572153 | + | 0.998362i | \(0.518222\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.51527 | 0.310314 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 24.1912 | 0.880408 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.0218495 | −0.000794132 0 | −0.000397066 | − | 1.00000i | \(-0.500126\pi\) | ||||
−0.000397066 | 1.00000i | \(0.500126\pi\) | ||||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.0771475 | 0.00280028 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8.83368 | −0.320221 | −0.160110 | − | 0.987099i | \(-0.551185\pi\) | ||||
−0.160110 | + | 0.987099i | \(0.551185\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.20959 | −0.188600 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −16.0124 | −0.578931 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −31.7343 | −1.14586 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −53.2036 | −1.91857 | −0.959286 | − | 0.282436i | \(-0.908858\pi\) | ||||
−0.959286 | + | 0.282436i | \(0.908858\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.17960 | −0.0424823 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −15.3768 | −0.553063 | −0.276532 | − | 0.961005i | \(-0.589185\pi\) | ||||
−0.276532 | + | 0.961005i | \(0.589185\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.27775 | 0.189583 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.623249 | 0.0223589 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −39.3614 | −1.41027 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.58980 | −0.0926703 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.31508 | 0.0469971 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12.7994 | 0.456830 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −36.0957 | −1.28667 | −0.643336 | − | 0.765584i | \(-0.722450\pi\) | ||||
−0.643336 | + | 0.765584i | \(0.722450\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5.61426 | −0.199873 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 15.0214 | 0.534100 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −58.8916 | −2.09130 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.95672 | −0.104864 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6.13245 | −0.217222 | −0.108611 | − | 0.994084i | \(-0.534640\pi\) | ||||
−0.108611 | + | 0.994084i | \(0.534640\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −49.0682 | −1.73591 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −38.8453 | −1.37253 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.26531 | −0.0446519 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.27775 | 0.0450349 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.69141 | −0.0595405 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −30.7008 | −1.07938 | −0.539692 | − | 0.841863i | \(-0.681459\pi\) | ||||
−0.539692 | + | 0.841863i | \(0.681459\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.490803 | 0.0172344 | 0.00861722 | − | 0.999963i | \(-0.497257\pi\) | ||||
0.00861722 | + | 0.999963i | \(0.497257\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.44146 | −0.0856256 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 19.4351 | 0.680781 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 15.6914 | 0.548973 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 14.6506 | 0.511934 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −18.8024 | −0.656209 | −0.328105 | − | 0.944641i | \(-0.606410\pi\) | ||||
−0.328105 | + | 0.944641i | \(0.606410\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 36.2718 | 1.26436 | 0.632178 | − | 0.774823i | \(-0.282161\pi\) | ||||
0.632178 | + | 0.774823i | \(0.282161\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.0771475 | 0.00268593 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 51.6018 | 1.79437 | 0.897186 | − | 0.441654i | \(-0.145608\pi\) | ||||
0.897186 | + | 0.441654i | \(0.145608\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17.2255 | 0.598266 | 0.299133 | − | 0.954211i | \(-0.403303\pi\) | ||||
0.299133 | + | 0.954211i | \(0.403303\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6.33347 | −0.219706 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −29.4042 | −1.01880 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 24.8024 | 0.858323 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.68242 | 0.300108 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 13.7592 | 0.475019 | 0.237509 | − | 0.971385i | \(-0.423669\pi\) | ||||
0.237509 | + | 0.971385i | \(0.423669\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.3610 | −0.977965 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6.48777 | 0.223451 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.38877 | 0.0821762 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −13.9567 | −0.479559 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.40079 | 0.116715 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.75612 | −0.0601989 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −22.3490 | −0.765213 | −0.382607 | − | 0.923911i | \(-0.624974\pi\) | ||||
−0.382607 | + | 0.923911i | \(0.624974\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 11.4659 | 0.392126 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 35.9134 | 1.22678 | 0.613390 | − | 0.789780i | \(-0.289805\pi\) | ||||
0.613390 | + | 0.789780i | \(0.289805\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.64552 | −0.192623 | −0.0963113 | − | 0.995351i | \(-0.530704\pi\) | ||||
−0.0963113 | + | 0.995351i | \(0.530704\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.56104 | −0.121360 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −36.5616 | −1.24457 | −0.622285 | − | 0.782791i | \(-0.713796\pi\) | ||||
−0.622285 | + | 0.782791i | \(0.713796\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12.6790 | −0.431098 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.61426 | −0.122747 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.22203 | 0.0753774 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −49.6049 | −1.68080 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −9.25590 | −0.313265 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.27775 | 0.0431960 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.45693 | 0.218035 | 0.109018 | − | 0.994040i | \(-0.465230\pi\) | ||||
0.109018 | + | 0.994040i | \(0.465230\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7.26531 | −0.245053 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.3147 | 0.414891 | 0.207446 | − | 0.978247i | \(-0.433485\pi\) | ||||
0.207446 | + | 0.978247i | \(0.433485\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.43508 | −0.250210 | −0.125105 | − | 0.992143i | \(-0.539927\pi\) | ||||
−0.125105 | + | 0.992143i | \(0.539927\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.24692 | −0.0755293 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 23.6914 | 0.795480 | 0.397740 | − | 0.917498i | \(-0.369795\pi\) | ||||
0.397740 | + | 0.917498i | \(0.369795\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −22.8024 | −0.764769 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.30859 | −0.0773407 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 35.1359 | 1.17578 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.154295 | −0.00515751 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.08959 | 0.0363803 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.21900 | 0.140712 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 58.3177 | 1.94284 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.41961 | 0.0472416 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.410621 | 0.0136495 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.5337 | −0.349764 | −0.174882 | − | 0.984589i | \(-0.555954\pi\) | ||||
−0.174882 | + | 0.984589i | \(0.555954\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −16.3733 | −0.543068 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 37.9383 | 1.25695 | 0.628476 | − | 0.777829i | \(-0.283679\pi\) | ||||
0.628476 | + | 0.777829i | \(0.283679\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.734688 | 0.0243146 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4.16977 | −0.137848 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −15.8457 | −0.523271 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 27.2036 | 0.897365 | 0.448683 | − | 0.893691i | \(-0.351893\pi\) | ||||
0.448683 | + | 0.893691i | \(0.351893\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.49675 | −0.0493198 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −36.5769 | −1.20394 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.75612 | −0.0577407 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8.28121 | −0.271991 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.84874 | 0.0606552 | 0.0303276 | − | 0.999540i | \(-0.490345\pi\) | ||||
0.0303276 | + | 0.999540i | \(0.490345\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 21.0553 | 0.690060 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −7.38282 | −0.241703 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.52164 | −0.0497629 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 51.8363 | 1.69342 | 0.846709 | − | 0.532056i | \(-0.178581\pi\) | ||||
0.846709 | + | 0.532056i | \(0.178581\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.97815 | −0.227723 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −30.4569 | −0.992868 | −0.496434 | − | 0.868075i | \(-0.665357\pi\) | ||||
−0.496434 | + | 0.868075i | \(0.665357\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.0339 | 0.326748 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.10203 | 0.0683791 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −38.8118 | −1.26122 | −0.630608 | − | 0.776102i | \(-0.717194\pi\) | ||||
−0.630608 | + | 0.776102i | \(0.717194\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −17.8706 | −0.580104 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.44104 | −0.176438 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.49979 | 0.0809761 | 0.0404881 | − | 0.999180i | \(-0.487109\pi\) | ||||
0.0404881 | + | 0.999180i | \(0.487109\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.44449 | −0.240898 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.0616712 | 0.00199355 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 19.2096 | 0.620310 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.14531 | −0.101462 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 56.1205 | 1.80846 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −8.06774 | −0.259710 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.35794 | 0.0436683 | 0.0218341 | − | 0.999762i | \(-0.493049\pi\) | ||||
0.0218341 | + | 0.999762i | \(0.493049\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.96916 | 0.191757 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.59241 | 0.147378 | 0.0736888 | − | 0.997281i | \(-0.476523\pi\) | ||||
0.0736888 | + | 0.997281i | \(0.476523\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −23.0035 | −0.737457 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.08959 | 0.0348948 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −9.45693 | −0.302554 | −0.151277 | − | 0.988491i | \(-0.548339\pi\) | ||||
−0.151277 | + | 0.988491i | \(0.548339\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.69141 | −0.117978 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11.9169 | 0.380477 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −24.6571 | −0.786440 | −0.393220 | − | 0.919444i | \(-0.628639\pi\) | ||||
−0.393220 | + | 0.919444i | \(0.628639\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 18.4569 | 0.588087 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.17876 | 0.101181 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.00000 | −0.127193 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18.7437 | −0.595412 | −0.297706 | − | 0.954658i | \(-0.596222\pi\) | ||||
−0.297706 | + | 0.954658i | \(0.596222\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −8.64206 | −0.274248 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.29020 | 0.104306 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17.0682 | 0.540554 | 0.270277 | − | 0.962783i | \(-0.412885\pi\) | ||||
0.270277 | + | 0.962783i | \(0.412885\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.88898 | −0.0914034 |
(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 | 3680.2.a.q.1.2 | ✓ | 3 | |
4.3 | odd | 2 | 3680.2.a.r.1.2 | yes | 3 | ||
8.3 | odd | 2 | 7360.2.a.bx.1.2 | 3 | |||
8.5 | even | 2 | 7360.2.a.cd.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3680.2.a.q.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial | |
3680.2.a.r.1.2 | yes | 3 | 4.3 | odd | 2 | ||
7360.2.a.bx.1.2 | 3 | 8.3 | odd | 2 | |||
7360.2.a.cd.1.2 | 3 | 8.5 | even | 2 |