Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8016,2,Mod(1,8016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8016, 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("8016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8016 = 2^{4} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8016.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: | \(64.0080822603\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.36497.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 3x^{3} + 5x^{2} + x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 501) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.410375\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8016.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.19483 | −0.981556 | −0.490778 | − | 0.871285i | \(-0.663287\pi\) | ||||
−0.490778 | + | 0.871285i | \(0.663287\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.52759 | 1.71127 | 0.855633 | − | 0.517582i | \(-0.173168\pi\) | ||||
0.855633 | + | 0.517582i | \(0.173168\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.62592 | 0.791746 | 0.395873 | − | 0.918305i | \(-0.370442\pi\) | ||||
0.395873 | + | 0.918305i | \(0.370442\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.50686 | 1.24998 | 0.624989 | − | 0.780633i | \(-0.285103\pi\) | ||||
0.624989 | + | 0.780633i | \(0.285103\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.19483 | 0.566702 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.14478 | 0.520186 | 0.260093 | − | 0.965584i | \(-0.416247\pi\) | ||||
0.260093 | + | 0.965584i | \(0.416247\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.09764 | 1.39889 | 0.699447 | − | 0.714684i | \(-0.253430\pi\) | ||||
0.699447 | + | 0.714684i | \(0.253430\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.52759 | −0.988000 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.18843 | 1.29038 | 0.645189 | − | 0.764023i | \(-0.276779\pi\) | ||||
0.645189 | + | 0.764023i | \(0.276779\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.182739 | −0.0365478 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.84359 | 0.342345 | 0.171173 | − | 0.985241i | \(-0.445244\pi\) | ||||
0.171173 | + | 0.985241i | \(0.445244\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.20401 | −0.216247 | −0.108123 | − | 0.994137i | \(-0.534484\pi\) | ||||
−0.108123 | + | 0.994137i | \(0.534484\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.62592 | −0.457115 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −9.93726 | −1.67970 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.7075 | 1.76030 | 0.880152 | − | 0.474691i | \(-0.157440\pi\) | ||||
0.880152 | + | 0.474691i | \(0.157440\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.50686 | −0.721676 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.353073 | 0.0551407 | 0.0275703 | − | 0.999620i | \(-0.491223\pi\) | ||||
0.0275703 | + | 0.999620i | \(0.491223\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.9236 | 1.81833 | 0.909167 | − | 0.416432i | \(-0.136720\pi\) | ||||
0.909167 | + | 0.416432i | \(0.136720\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.19483 | −0.327185 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.986349 | −0.143874 | −0.0719369 | − | 0.997409i | \(-0.522918\pi\) | ||||
−0.0719369 | + | 0.997409i | \(0.522918\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 13.4990 | 1.92843 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.14478 | −0.300330 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.36740 | −1.01199 | −0.505995 | − | 0.862536i | \(-0.668875\pi\) | ||||
−0.505995 | + | 0.862536i | \(0.668875\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.76345 | −0.777143 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.09764 | −0.807652 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.63958 | 0.604021 | 0.302011 | − | 0.953305i | \(-0.402342\pi\) | ||||
0.302011 | + | 0.953305i | \(0.402342\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.9846 | 1.53447 | 0.767237 | − | 0.641363i | \(-0.221631\pi\) | ||||
0.767237 | + | 0.641363i | \(0.221631\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.52759 | 0.570422 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −9.89178 | −1.22692 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.652622 | 0.0797304 | 0.0398652 | − | 0.999205i | \(-0.487307\pi\) | ||||
0.0398652 | + | 0.999205i | \(0.487307\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.18843 | −0.745000 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.2454 | 1.57194 | 0.785972 | − | 0.618262i | \(-0.212163\pi\) | ||||
0.785972 | + | 0.618262i | \(0.212163\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.23916 | −0.847279 | −0.423640 | − | 0.905831i | \(-0.639248\pi\) | ||||
−0.423640 | + | 0.905831i | \(0.639248\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.182739 | 0.0211009 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 11.8891 | 1.35489 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.65804 | −0.861596 | −0.430798 | − | 0.902448i | \(-0.641768\pi\) | ||||
−0.430798 | + | 0.902448i | \(0.641768\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.48636 | 0.711971 | 0.355985 | − | 0.934491i | \(-0.384145\pi\) | ||||
0.355985 | + | 0.934491i | \(0.384145\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.70742 | −0.510592 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.84359 | −0.197653 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.00336 | −0.636355 | −0.318177 | − | 0.948031i | \(-0.603071\pi\) | ||||
−0.318177 | + | 0.948031i | \(0.603071\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 20.4052 | 2.13905 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.20401 | 0.124850 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −13.3833 | −1.37309 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.29839 | −0.842573 | −0.421287 | − | 0.906928i | \(-0.638421\pi\) | ||||
−0.421287 | + | 0.906928i | \(0.638421\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.62592 | 0.263915 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.2104 | −1.21498 | −0.607489 | − | 0.794328i | \(-0.707823\pi\) | ||||
−0.607489 | + | 0.794328i | \(0.707823\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.8965 | −1.46780 | −0.733898 | − | 0.679260i | \(-0.762301\pi\) | ||||
−0.733898 | + | 0.679260i | \(0.762301\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 9.93726 | 0.969778 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.0613 | −0.972666 | −0.486333 | − | 0.873773i | \(-0.661666\pi\) | ||||
−0.486333 | + | 0.873773i | \(0.661666\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.9585 | −1.04964 | −0.524819 | − | 0.851214i | \(-0.675867\pi\) | ||||
−0.524819 | + | 0.851214i | \(0.675867\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.7075 | −1.01631 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.0220 | −1.13093 | −0.565465 | − | 0.824772i | \(-0.691303\pi\) | ||||
−0.565465 | + | 0.824772i | \(0.691303\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −13.5825 | −1.26658 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.50686 | 0.416660 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 9.71069 | 0.890177 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.10452 | −0.373138 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.353073 | −0.0318355 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.3752 | 1.01743 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.03046 | 0.180174 | 0.0900869 | − | 0.995934i | \(-0.471286\pi\) | ||||
0.0900869 | + | 0.995934i | \(0.471286\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −11.9236 | −1.04982 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.73416 | −0.675737 | −0.337868 | − | 0.941193i | \(-0.609706\pi\) | ||||
−0.337868 | + | 0.941193i | \(0.609706\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 27.6076 | 2.39388 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.19483 | 0.188901 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −19.1222 | −1.63372 | −0.816862 | − | 0.576833i | \(-0.804288\pi\) | ||||
−0.816862 | + | 0.576833i | \(0.804288\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.90796 | 0.246650 | 0.123325 | − | 0.992366i | \(-0.460644\pi\) | ||||
0.123325 | + | 0.992366i | \(0.460644\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.986349 | 0.0830655 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 11.8347 | 0.989666 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.04635 | −0.336031 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −13.4990 | −1.11338 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −13.5856 | −1.11298 | −0.556488 | − | 0.830855i | \(-0.687852\pi\) | ||||
−0.556488 | + | 0.830855i | \(0.687852\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.3253 | −1.40991 | −0.704955 | − | 0.709252i | \(-0.749033\pi\) | ||||
−0.704955 | + | 0.709252i | \(0.749033\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.14478 | 0.173395 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.64259 | 0.212258 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.9268 | 1.19129 | 0.595646 | − | 0.803247i | \(-0.296896\pi\) | ||||
0.595646 | + | 0.803247i | \(0.296896\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.36740 | 0.584273 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 28.0187 | 2.20818 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −18.0795 | −1.41609 | −0.708046 | − | 0.706166i | \(-0.750423\pi\) | ||||
−0.708046 | + | 0.706166i | \(0.750423\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.76345 | 0.448684 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.00000 | −0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.31181 | 0.562447 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.09764 | 0.466298 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −17.2480 | −1.31134 | −0.655671 | − | 0.755047i | \(-0.727614\pi\) | ||||
−0.655671 | + | 0.755047i | \(0.727614\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.827368 | −0.0625431 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.63958 | −0.348732 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.8251 | 1.03334 | 0.516670 | − | 0.856185i | \(-0.327171\pi\) | ||||
0.516670 | + | 0.856185i | \(0.327171\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.887785 | 0.0659886 | 0.0329943 | − | 0.999456i | \(-0.489496\pi\) | ||||
0.0329943 | + | 0.999456i | \(0.489496\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.9846 | −0.885929 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −23.5011 | −1.72784 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.63204 | 0.411855 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.52759 | −0.329333 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.8833 | −0.932200 | −0.466100 | − | 0.884732i | \(-0.654341\pi\) | ||||
−0.466100 | + | 0.884732i | \(0.654341\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.6292 | 1.41294 | 0.706470 | − | 0.707743i | \(-0.250286\pi\) | ||||
0.706470 | + | 0.707743i | \(0.250286\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 9.89178 | 0.708365 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.98382 | −0.355082 | −0.177541 | − | 0.984113i | \(-0.556814\pi\) | ||||
−0.177541 | + | 0.984113i | \(0.556814\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.6453 | 1.03818 | 0.519089 | − | 0.854720i | \(-0.326271\pi\) | ||||
0.519089 | + | 0.854720i | \(0.326271\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.652622 | −0.0460324 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.34700 | 0.585844 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.774933 | −0.0541236 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.18843 | 0.430126 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 16.0119 | 1.10757 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.01322 | −0.207438 | −0.103719 | − | 0.994607i | \(-0.533074\pi\) | ||||
−0.103719 | + | 0.994607i | \(0.533074\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −13.2454 | −0.907563 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −26.1703 | −1.78480 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.45126 | −0.370056 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7.23916 | 0.489177 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.66624 | 0.650222 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.11072 | 0.610099 | 0.305050 | − | 0.952336i | \(-0.401327\pi\) | ||||
0.305050 | + | 0.952336i | \(0.401327\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.182739 | −0.0121826 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 18.3539 | 1.21819 | 0.609097 | − | 0.793096i | \(-0.291532\pi\) | ||||
0.609097 | + | 0.793096i | \(0.291532\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.54404 | 0.366360 | 0.183180 | − | 0.983079i | \(-0.441361\pi\) | ||||
0.183180 | + | 0.983079i | \(0.441361\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −11.8891 | −0.782245 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.85999 | 0.187364 | 0.0936821 | − | 0.995602i | \(-0.470136\pi\) | ||||
0.0936821 | + | 0.995602i | \(0.470136\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.16486 | 0.141220 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 7.65804 | 0.497443 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −25.0961 | −1.62333 | −0.811666 | − | 0.584122i | \(-0.801439\pi\) | ||||
−0.811666 | + | 0.584122i | \(0.801439\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.3872 | −1.18442 | −0.592211 | − | 0.805783i | \(-0.701745\pi\) | ||||
−0.592211 | + | 0.805783i | \(0.701745\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −29.6280 | −1.89287 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 27.4812 | 1.74859 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.48636 | −0.411057 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.0744 | −0.951491 | −0.475745 | − | 0.879583i | \(-0.657822\pi\) | ||||
−0.475745 | + | 0.879583i | \(0.657822\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 16.2504 | 1.02165 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.70742 | 0.294790 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 26.1018 | 1.62819 | 0.814094 | − | 0.580733i | \(-0.197234\pi\) | ||||
0.814094 | + | 0.580733i | \(0.197234\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 48.4792 | 3.01235 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.84359 | 0.114115 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 17.5960 | 1.08502 | 0.542508 | − | 0.840051i | \(-0.317475\pi\) | ||||
0.542508 | + | 0.840051i | \(0.317475\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 16.1702 | 0.993326 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.00336 | 0.367400 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −17.8079 | −1.08577 | −0.542885 | − | 0.839807i | \(-0.682668\pi\) | ||||
−0.542885 | + | 0.839807i | \(0.682668\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.5804 | 1.25017 | 0.625085 | − | 0.780557i | \(-0.285064\pi\) | ||||
0.625085 | + | 0.780557i | \(0.285064\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −20.4052 | −1.23498 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.479860 | −0.0289366 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.86009 | 0.292014 | 0.146007 | − | 0.989284i | \(-0.453358\pi\) | ||||
0.146007 | + | 0.989284i | \(0.453358\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.20401 | −0.0720822 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.340342 | 0.0203031 | 0.0101516 | − | 0.999948i | \(-0.496769\pi\) | ||||
0.0101516 | + | 0.999948i | \(0.496769\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.8080 | 0.642469 | 0.321235 | − | 0.947000i | \(-0.395902\pi\) | ||||
0.321235 | + | 0.947000i | \(0.395902\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 13.3833 | 0.792756 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.59857 | 0.0943604 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.3999 | −0.729406 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.29839 | 0.486460 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 13.0134 | 0.760254 | 0.380127 | − | 0.924934i | \(-0.375880\pi\) | ||||
0.380127 | + | 0.924934i | \(0.375880\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.1831 | −0.592881 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.62592 | −0.152372 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 27.8904 | 1.61294 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 53.9852 | 3.11165 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 12.2104 | 0.701468 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −26.3042 | −1.50617 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.6004 | −0.605000 | −0.302500 | − | 0.953149i | \(-0.597821\pi\) | ||||
−0.302500 | + | 0.953149i | \(0.597821\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.8965 | 0.847432 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −23.2712 | −1.31959 | −0.659795 | − | 0.751446i | \(-0.729357\pi\) | ||||
−0.659795 | + | 0.751446i | \(0.729357\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.59154 | −0.372576 | −0.186288 | − | 0.982495i | \(-0.559646\pi\) | ||||
−0.186288 | + | 0.982495i | \(0.559646\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −9.93726 | −0.559901 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.90860 | 0.500357 | 0.250178 | − | 0.968200i | \(-0.419511\pi\) | ||||
0.250178 | + | 0.968200i | \(0.419511\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.84112 | 0.271051 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.0613 | 0.561569 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.0781 | 0.727686 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.823581 | −0.0456840 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 10.9585 | 0.606008 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.46578 | −0.246206 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.2953 | 0.620845 | 0.310422 | − | 0.950599i | \(-0.399530\pi\) | ||||
0.310422 | + | 0.950599i | \(0.399530\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10.7075 | 0.586768 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.43239 | −0.0782599 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 21.4635 | 1.16919 | 0.584596 | − | 0.811325i | \(-0.301253\pi\) | ||||
0.584596 | + | 0.811325i | \(0.301253\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 12.0220 | 0.652943 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.16164 | −0.171212 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 29.4250 | 1.58880 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 13.5825 | 0.731259 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −23.3110 | −1.25140 | −0.625699 | − | 0.780065i | \(-0.715186\pi\) | ||||
−0.625699 | + | 0.780065i | \(0.715186\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.1588 | −1.18613 | −0.593066 | − | 0.805154i | \(-0.702083\pi\) | ||||
−0.593066 | + | 0.805154i | \(0.702083\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.50686 | −0.240559 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11.5024 | −0.612209 | −0.306105 | − | 0.951998i | \(-0.599026\pi\) | ||||
−0.306105 | + | 0.951998i | \(0.599026\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −29.0714 | −1.54295 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −9.71069 | −0.513944 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −33.4833 | −1.76718 | −0.883590 | − | 0.468262i | \(-0.844880\pi\) | ||||
−0.883590 | + | 0.468262i | \(0.844880\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.1812 | 0.956906 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.10452 | 0.215431 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15.8887 | 0.831652 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.74783 | 0.143436 | 0.0717179 | − | 0.997425i | \(-0.477152\pi\) | ||||
0.0717179 | + | 0.997425i | \(0.477152\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.353073 | 0.0183802 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −33.3566 | −1.73179 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.10471 | 0.419646 | 0.209823 | − | 0.977739i | \(-0.432711\pi\) | ||||
0.209823 | + | 0.977739i | \(0.432711\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −11.3752 | −0.587413 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.30879 | 0.427925 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.29718 | 0.220731 | 0.110366 | − | 0.993891i | \(-0.464798\pi\) | ||||
0.110366 | + | 0.993891i | \(0.464798\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.03046 | −0.104023 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 27.4329 | 1.40176 | 0.700878 | − | 0.713281i | \(-0.252792\pi\) | ||||
0.700878 | + | 0.713281i | \(0.252792\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −26.0945 | −1.32990 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 11.9236 | 0.606111 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.77324 | 0.0899067 | 0.0449534 | − | 0.998989i | \(-0.485686\pi\) | ||||
0.0449534 | + | 0.998989i | \(0.485686\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.2728 | 0.671236 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.73416 | 0.390137 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 16.8081 | 0.845705 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.70497 | −0.286324 | −0.143162 | − | 0.989699i | \(-0.545727\pi\) | ||||
−0.143162 | + | 0.989699i | \(0.545727\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −27.6076 | −1.38211 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −22.7358 | −1.13537 | −0.567686 | − | 0.823245i | \(-0.692161\pi\) | ||||
−0.567686 | + | 0.823245i | \(0.692161\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.42631 | −0.270304 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.19483 | −0.109062 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 28.1171 | 1.39371 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −22.6282 | −1.11889 | −0.559445 | − | 0.828867i | \(-0.688986\pi\) | ||||
−0.559445 | + | 0.828867i | \(0.688986\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 19.1222 | 0.943231 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 21.0061 | 1.03364 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14.2364 | −0.698839 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.90796 | −0.142403 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 24.0907 | 1.17691 | 0.588453 | − | 0.808531i | \(-0.299737\pi\) | ||||
0.588453 | + | 0.808531i | \(0.299737\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.42990 | −0.264637 | −0.132319 | − | 0.991207i | \(-0.542242\pi\) | ||||
−0.132319 | + | 0.991207i | \(0.542242\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.986349 | −0.0479579 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.391936 | −0.0190117 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 54.2614 | 2.62590 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −11.8347 | −0.571384 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.8167 | 0.521024 | 0.260512 | − | 0.965471i | \(-0.416109\pi\) | ||||
0.260512 | + | 0.965471i | \(0.416109\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −17.6776 | −0.849530 | −0.424765 | − | 0.905304i | \(-0.639643\pi\) | ||||
−0.424765 | + | 0.905304i | \(0.639643\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.04635 | 0.194008 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 37.7348 | 1.80510 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.9547 | −0.666023 | −0.333011 | − | 0.942923i | \(-0.608065\pi\) | ||||
−0.333011 | + | 0.942923i | \(0.608065\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 13.4990 | 0.642811 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −41.1782 | −1.95643 | −0.978217 | − | 0.207584i | \(-0.933440\pi\) | ||||
−0.978217 | + | 0.207584i | \(0.933440\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.1763 | 0.624618 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 13.5856 | 0.642577 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 33.9009 | 1.59988 | 0.799942 | − | 0.600077i | \(-0.204863\pi\) | ||||
0.799942 | + | 0.600077i | \(0.204863\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.927142 | 0.0436574 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 17.3253 | 0.814012 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −44.7859 | −2.09959 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.56208 | −0.0730708 | −0.0365354 | − | 0.999332i | \(-0.511632\pi\) | ||||
−0.0365354 | + | 0.999332i | \(0.511632\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.14478 | −0.100110 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.34383 | 0.295462 | 0.147731 | − | 0.989028i | \(-0.452803\pi\) | ||||
0.147731 | + | 0.989028i | \(0.452803\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.7171 | −0.730437 | −0.365218 | − | 0.930922i | \(-0.619006\pi\) | ||||
−0.365218 | + | 0.930922i | \(0.619006\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.64259 | −0.122547 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 41.4281 | 1.91706 | 0.958532 | − | 0.284987i | \(-0.0919891\pi\) | ||||
0.958532 | + | 0.284987i | \(0.0919891\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.95480 | 0.136440 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −14.9268 | −0.687792 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 31.3105 | 1.43966 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.11428 | −0.0511266 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.36740 | −0.337330 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −21.7486 | −0.993720 | −0.496860 | − | 0.867831i | \(-0.665514\pi\) | ||||
−0.496860 | + | 0.867831i | \(0.665514\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 48.2573 | 2.20034 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −28.0187 | −1.27489 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 18.2135 | 0.827033 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.22677 | 0.191533 | 0.0957667 | − | 0.995404i | \(-0.469470\pi\) | ||||
0.0957667 | + | 0.995404i | \(0.469470\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 18.0795 | 0.817581 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.2226 | 0.506469 | 0.253235 | − | 0.967405i | \(-0.418505\pi\) | ||||
0.253235 | + | 0.967405i | \(0.418505\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.95409 | 0.178083 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.76345 | −0.259048 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 59.9699 | 2.69002 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.02996 | −0.359470 | −0.179735 | − | 0.983715i | \(-0.557524\pi\) | ||||
−0.179735 | + | 0.983715i | \(0.557524\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.00000 | 0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −35.0823 | −1.56424 | −0.782121 | − | 0.623127i | \(-0.785862\pi\) | ||||
−0.782121 | + | 0.623127i | \(0.785862\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 26.7997 | 1.19257 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.31181 | −0.324729 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.620513 | −0.0275038 | −0.0137519 | − | 0.999905i | \(-0.504377\pi\) | ||||
−0.0137519 | + | 0.999905i | \(0.504377\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −32.7759 | −1.44992 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.09764 | −0.269217 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 32.6952 | 1.44072 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.59008 | −0.113911 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 17.2480 | 0.757103 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.2556 | 0.755983 | 0.377992 | − | 0.925809i | \(-0.376615\pi\) | ||||
0.377992 | + | 0.925809i | \(0.376615\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −27.4817 | −1.20169 | −0.600845 | − | 0.799366i | \(-0.705169\pi\) | ||||
−0.600845 | + | 0.799366i | \(0.705169\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.827368 | 0.0361093 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.58234 | −0.112488 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.2967 | 0.665074 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.63958 | 0.201340 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.59125 | 0.0689247 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 22.0829 | 0.954727 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −13.8251 | −0.596599 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 35.4475 | 1.52683 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.2636 | 0.613239 | 0.306620 | − | 0.951832i | \(-0.400802\pi\) | ||||
0.306620 | + | 0.951832i | \(0.400802\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.887785 | −0.0380985 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 24.0521 | 1.03028 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −26.1563 | −1.11836 | −0.559182 | − | 0.829045i | \(-0.688885\pi\) | ||||
−0.559182 | + | 0.829045i | \(0.688885\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 11.9846 | 0.511492 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11.2415 | 0.478905 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −34.6724 | −1.47442 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 23.5011 | 0.997568 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −22.0575 | −0.934608 | −0.467304 | − | 0.884097i | \(-0.654775\pi\) | ||||
−0.467304 | + | 0.884097i | \(0.654775\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 53.7381 | 2.27288 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.63204 | −0.237785 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.77511 | −0.201247 | −0.100623 | − | 0.994925i | \(-0.532084\pi\) | ||||
−0.100623 | + | 0.994925i | \(0.532084\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 26.3861 | 1.11007 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.52759 | 0.190141 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −39.2560 | −1.64570 | −0.822850 | − | 0.568259i | \(-0.807617\pi\) | ||||
−0.822850 | + | 0.568259i | \(0.807617\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −27.3668 | −1.14527 | −0.572633 | − | 0.819812i | \(-0.694078\pi\) | ||||
−0.572633 | + | 0.819812i | \(0.694078\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12.8833 | 0.538206 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.13087 | −0.0471605 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 42.7549 | 1.77991 | 0.889954 | − | 0.456050i | \(-0.150736\pi\) | ||||
0.889954 | + | 0.456050i | \(0.150736\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −19.6292 | −0.815762 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 29.3676 | 1.21837 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −19.3462 | −0.801240 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −9.89178 | −0.408975 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 21.8718 | 0.902747 | 0.451374 | − | 0.892335i | \(-0.350934\pi\) | ||||
0.451374 | + | 0.892335i | \(0.350934\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.34162 | −0.302506 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.98382 | 0.205007 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −0.763853 | −0.0313677 | −0.0156839 | − | 0.999877i | \(-0.504993\pi\) | ||||
−0.0156839 | + | 0.999877i | \(0.504993\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −21.3133 | −0.873759 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −14.6453 | −0.599392 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.83490 | −0.156690 | −0.0783450 | − | 0.996926i | \(-0.524964\pi\) | ||||
−0.0783450 | + | 0.996926i | \(0.524964\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −38.9975 | −1.59074 | −0.795370 | − | 0.606124i | \(-0.792723\pi\) | ||||
−0.795370 | + | 0.606124i | \(0.792723\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.652622 | 0.0265768 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.00870 | 0.366256 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −25.1931 | −1.02256 | −0.511279 | − | 0.859415i | \(-0.670828\pi\) | ||||
−0.511279 | + | 0.859415i | \(0.670828\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −8.34700 | −0.338237 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.44534 | −0.179839 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −44.1016 | −1.78125 | −0.890623 | − | 0.454742i | \(-0.849731\pi\) | ||||
−0.890623 | + | 0.454742i | \(0.849731\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.774933 | 0.0312483 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.77330 | 0.151908 | 0.0759538 | − | 0.997111i | \(-0.475800\pi\) | ||||
0.0759538 | + | 0.997111i | \(0.475800\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 35.1811 | 1.41405 | 0.707024 | − | 0.707190i | \(-0.250037\pi\) | ||||
0.707024 | + | 0.707190i | \(0.250037\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.18843 | −0.248333 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −27.1807 | −1.08897 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.0529 | −0.962116 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −16.0119 | −0.639456 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 22.9653 | 0.915686 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.6390 | 0.622579 | 0.311289 | − | 0.950315i | \(-0.399239\pi\) | ||||
0.311289 | + | 0.950315i | \(0.399239\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.01322 | 0.119765 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.45650 | −0.176851 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 60.8383 | 2.41050 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 13.2454 | 0.523981 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 24.1866 | 0.955313 | 0.477657 | − | 0.878547i | \(-0.341486\pi\) | ||||
0.477657 | + | 0.878547i | \(0.341486\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24.7104 | 0.974483 | 0.487242 | − | 0.873267i | \(-0.338003\pi\) | ||||
0.487242 | + | 0.873267i | \(0.338003\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 26.1703 | 1.03045 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.00060 | −0.196594 | −0.0982969 | − | 0.995157i | \(-0.531339\pi\) | ||||
−0.0982969 | + | 0.995157i | \(0.531339\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12.1832 | 0.478232 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.45126 | 0.213652 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 14.9748 | 0.586009 | 0.293005 | − | 0.956111i | \(-0.405345\pi\) | ||||
0.293005 | + | 0.956111i | \(0.405345\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 16.9751 | 0.663273 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −7.23916 | −0.282426 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 33.2094 | 1.29366 | 0.646828 | − | 0.762636i | \(-0.276095\pi\) | ||||
0.646828 | + | 0.762636i | \(0.276095\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.56439 | −0.216430 | −0.108215 | − | 0.994128i | \(-0.534513\pi\) | ||||
−0.108215 | + | 0.994128i | \(0.534513\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −9.66624 | −0.375406 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −60.5939 | −2.34973 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.4089 | 0.441755 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9.11072 | −0.352241 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 31.4707 | 1.21491 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 42.9558 | 1.65582 | 0.827911 | − | 0.560859i | \(-0.189529\pi\) | ||||
0.827911 | + | 0.560859i | \(0.189529\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.182739 | 0.00703364 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −12.7007 | −0.488126 | −0.244063 | − | 0.969759i | \(-0.578480\pi\) | ||||
−0.244063 | + | 0.969759i | \(0.578480\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −37.5717 | −1.44187 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −18.3539 | −0.703324 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 29.4729 | 1.12775 | 0.563874 | − | 0.825861i | \(-0.309310\pi\) | ||||
0.563874 | + | 0.825861i | \(0.309310\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 41.9700 | 1.60359 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.54404 | −0.211518 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −33.2039 | −1.26497 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.4746 | 0.512599 | 0.256300 | − | 0.966597i | \(-0.417497\pi\) | ||||
0.256300 | + | 0.966597i | \(0.417497\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 11.8891 | 0.451630 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.38247 | −0.242101 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.757264 | 0.0286834 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.85999 | −0.108175 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −32.7670 | −1.23759 | −0.618796 | − | 0.785552i | \(-0.712379\pi\) | ||||
−0.618796 | + | 0.785552i | \(0.712379\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 65.2906 | 2.46248 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.16486 | −0.0815335 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −55.2836 | −2.07915 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −34.9670 | −1.31321 | −0.656607 | − | 0.754233i | \(-0.728009\pi\) | ||||
−0.656607 | + | 0.754233i | \(0.728009\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.65804 | −0.287199 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.45094 | −0.279040 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −25.9751 | −0.971413 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 25.0961 | 0.937231 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.48429 | 0.353704 | 0.176852 | − | 0.984237i | \(-0.443409\pi\) | ||||
0.176852 | + | 0.984237i | \(0.443409\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −67.4452 | −2.51179 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 18.3872 | 0.683827 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.336896 | −0.0125120 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.6705 | 0.544098 | 0.272049 | − | 0.962283i | \(-0.412299\pi\) | ||||
0.272049 | + | 0.962283i | \(0.412299\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 25.5736 | 0.945872 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.04809 | 0.0387121 | 0.0193560 | − | 0.999813i | \(-0.493838\pi\) | ||||
0.0193560 | + | 0.999813i | \(0.493838\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 29.6280 | 1.09285 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.71374 | 0.0631263 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −11.8911 | −0.437422 | −0.218711 | − | 0.975790i | \(-0.570185\pi\) | ||||
−0.218711 | + | 0.975790i | \(0.570185\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −27.4812 | −1.00955 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −36.4383 | −1.33679 | −0.668396 | − | 0.743806i | \(-0.733019\pi\) | ||||
−0.668396 | + | 0.743806i | \(0.733019\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 29.8181 | 1.09245 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.48636 | 0.237324 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −45.5536 | −1.66449 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17.9405 | 0.654659 | 0.327330 | − | 0.944910i | \(-0.393851\pi\) | ||||
0.327330 | + | 0.944910i | \(0.393851\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 15.0744 | 0.549343 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 38.0259 | 1.38391 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12.8400 | −0.466679 | −0.233339 | − | 0.972395i | \(-0.574965\pi\) | ||||
−0.233339 | + | 0.972395i | \(0.574965\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −16.2504 | −0.589851 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −51.8862 | −1.88087 | −0.940437 | − | 0.339968i | \(-0.889584\pi\) | ||||
−0.940437 | + | 0.339968i | \(0.889584\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −49.6157 | −1.79621 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.70742 | −0.170197 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 20.9099 | 0.755014 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28.7814 | −1.03789 | −0.518943 | − | 0.854809i | \(-0.673674\pi\) | ||||
−0.518943 | + | 0.854809i | \(0.673674\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −26.1018 | −0.940035 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −6.52345 | −0.234632 | −0.117316 | − | 0.993095i | \(-0.537429\pi\) | ||||
−0.117316 | + | 0.993095i | \(0.537429\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.220020 | 0.00790335 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −48.4792 | −1.73918 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.15291 | 0.0771360 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 34.7815 | 1.24458 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.84359 | −0.0658844 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −32.7618 | −1.16932 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −27.3603 | −0.975290 | −0.487645 | − | 0.873042i | \(-0.662144\pi\) | ||||
−0.487645 | + | 0.873042i | \(0.662144\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −17.5960 | −0.626434 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −54.4304 | −1.93532 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 54.0131 | 1.91806 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −16.1702 | −0.573497 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 16.1698 | 0.572764 | 0.286382 | − | 0.958116i | \(-0.407547\pi\) | ||||
0.286382 | + | 0.958116i | \(0.407547\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.11550 | −0.0748411 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.00336 | −0.212118 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −19.0095 | −0.670830 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −61.4961 | −2.16745 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 17.8079 | 0.626869 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −9.51312 | −0.334464 | −0.167232 | − | 0.985918i | \(-0.553483\pi\) | ||||
−0.167232 | + | 0.985918i | \(0.553483\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.25453 | 0.114282 | 0.0571410 | − | 0.998366i | \(-0.481802\pi\) | ||||
0.0571410 | + | 0.998366i | \(0.481802\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −20.5804 | −0.721786 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 39.6813 | 1.38997 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 72.7059 | 2.54366 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 20.4052 | 0.713016 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 14.1377 | 0.493408 | 0.246704 | − | 0.969091i | \(-0.420652\pi\) | ||||
0.246704 | + | 0.969091i | \(0.420652\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.99950 | 0.174272 | 0.0871358 | − | 0.996196i | \(-0.472229\pi\) | ||||
0.0871358 | + | 0.996196i | \(0.472229\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.479860 | 0.0167066 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 30.7739 | 1.07011 | 0.535056 | − | 0.844816i | \(-0.320290\pi\) | ||||
0.535056 | + | 0.844816i | \(0.320290\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.7810 | 0.409171 | 0.204586 | − | 0.978849i | \(-0.434415\pi\) | ||||
0.204586 | + | 0.978849i | \(0.434415\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.86009 | −0.168595 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 28.9525 | 1.00314 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.19483 | 0.0759551 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.20401 | 0.0416167 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 27.5577 | 0.951398 | 0.475699 | − | 0.879608i | \(-0.342195\pi\) | ||||
0.475699 | + | 0.879608i | \(0.342195\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.6012 | −0.882800 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.340342 | −0.0117220 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −16.0482 | −0.552073 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −18.5836 | −0.638539 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −10.8080 | −0.370930 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 66.2627 | 2.27146 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11.9459 | 0.409020 | 0.204510 | − | 0.978864i | \(-0.434440\pi\) | ||||
0.204510 | + | 0.978864i | \(0.434440\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −13.3833 | −0.457698 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −41.7299 | −1.42547 | −0.712734 | − | 0.701435i | \(-0.752543\pi\) | ||||
−0.712734 | + | 0.701435i | \(0.752543\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24.4056 | −0.832708 | −0.416354 | − | 0.909203i | \(-0.636692\pi\) | ||||
−0.416354 | + | 0.909203i | \(0.636692\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.59857 | −0.0544790 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.92599 | 0.235763 | 0.117882 | − | 0.993028i | \(-0.462390\pi\) | ||||
0.117882 | + | 0.993028i | \(0.462390\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 37.8564 | 1.28715 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 12.3999 | 0.421123 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −20.1094 | −0.682166 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.94128 | 0.0996614 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8.29839 | −0.280858 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 51.5022 | 1.74109 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 28.7443 | 0.970625 | 0.485312 | − | 0.874341i | \(-0.338706\pi\) | ||||
0.485312 | + | 0.874341i | \(0.338706\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −13.0134 | −0.438933 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 39.8532 | 1.34269 | 0.671343 | − | 0.741146i | \(-0.265718\pi\) | ||||
0.671343 | + | 0.741146i | \(0.265718\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 32.7450 | 1.10196 | 0.550979 | − | 0.834519i | \(-0.314255\pi\) | ||||
0.550979 | + | 0.834519i | \(0.314255\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 10.1831 | 0.342300 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −34.6559 | −1.16363 | −0.581815 | − | 0.813321i | \(-0.697657\pi\) | ||||
−0.581815 | + | 0.813321i | \(0.697657\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.19306 | 0.308325 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.62592 | 0.0879718 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.01440 | −0.201264 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −30.3438 | −1.01428 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −27.8904 | −0.931234 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.21970 | −0.0740310 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15.8015 | −0.526423 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −53.9852 | −1.79651 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.94853 | −0.0647715 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.3392 | 0.409717 | 0.204858 | − | 0.978792i | \(-0.434327\pi\) | ||||
0.204858 | + | 0.978792i | \(0.434327\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −12.2104 | −0.404993 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −52.4048 | −1.73625 | −0.868124 | − | 0.496348i | \(-0.834674\pi\) | ||||
−0.868124 | + | 0.496348i | \(0.834674\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 17.0327 | 0.563700 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 26.3042 | 0.869589 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −35.0171 | −1.15637 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 34.8078 | 1.14820 | 0.574101 | − | 0.818784i | \(-0.305352\pi\) | ||||
0.574101 | + | 0.818784i | \(0.305352\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.6004 | 0.349297 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 59.6954 | 1.96490 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.95668 | −0.0643354 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −14.8965 | −0.489265 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 50.9235 | 1.67074 | 0.835372 | − | 0.549685i | \(-0.185252\pi\) | ||||
0.835372 | + | 0.549685i | \(0.185252\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 82.3123 | 2.69768 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 23.2712 | 0.761865 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −12.3613 | −0.404259 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23.9406 | 0.782104 | 0.391052 | − | 0.920369i | \(-0.372111\pi\) | ||||
0.391052 | + | 0.920369i | \(0.372111\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.59154 | 0.215107 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −58.0602 | −1.89271 | −0.946355 | − | 0.323130i | \(-0.895265\pi\) | ||||
−0.946355 | + | 0.323130i | \(0.895265\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.18497 | 0.0711523 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 9.93726 | 0.323259 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −32.0239 | −1.04064 | −0.520319 | − | 0.853972i | \(-0.674187\pi\) | ||||
−0.520319 | + | 0.853972i | \(0.674187\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −32.6259 | −1.05908 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.90860 | −0.288881 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 34.0370 | 1.10257 | 0.551283 | − | 0.834318i | \(-0.314138\pi\) | ||||
0.551283 | + | 0.834318i | \(0.314138\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 28.2765 | 0.915007 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.84112 | −0.156491 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −86.5776 | −2.79574 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.5504 | −0.953237 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −10.0613 | −0.324222 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −43.0827 | −1.38688 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −45.0634 | −1.44914 | −0.724571 | − | 0.689200i | \(-0.757962\pi\) | ||||
−0.724571 | + | 0.689200i | \(0.757962\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −13.0781 | −0.420129 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 47.3027 | 1.51802 | 0.759008 | − | 0.651082i | \(-0.225684\pi\) | ||||
0.759008 | + | 0.651082i | \(0.225684\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 13.1660 | 0.422084 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.823581 | 0.0263757 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −16.0859 | −0.514635 | −0.257317 | − | 0.966327i | \(-0.582839\pi\) | ||||
−0.257317 | + | 0.966327i | \(0.582839\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −15.7644 | −0.503831 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.9585 | −0.349879 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.84308 | 0.186365 | 0.0931826 | − | 0.995649i | \(-0.470296\pi\) | ||||
0.0931826 | + | 0.995649i | \(0.470296\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.9386 | 0.348533 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4.46578 | 0.142147 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 73.7885 | 2.34634 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −14.7445 | −0.468376 | −0.234188 | − | 0.972191i | \(-0.575243\pi\) | ||||
−0.234188 | + | 0.972191i | \(0.575243\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −11.2953 | −0.358445 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −32.1439 | −1.01903 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −41.7942 | −1.32364 | −0.661818 | − | 0.749664i | \(-0.730215\pi\) | ||||
−0.661818 | + | 0.749664i | \(0.730215\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −10.7075 | −0.338771 |
(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 | 8016.2.a.p.1.3 | 5 | ||
4.3 | odd | 2 | 501.2.a.b.1.5 | ✓ | 5 | ||
12.11 | even | 2 | 1503.2.a.d.1.1 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
501.2.a.b.1.5 | ✓ | 5 | 4.3 | odd | 2 | ||
1503.2.a.d.1.1 | 5 | 12.11 | even | 2 | |||
8016.2.a.p.1.3 | 5 | 1.1 | even | 1 | trivial |