Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8008,2,Mod(1,8008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8008.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: | \(63.9442019386\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} - 17 x^{10} + 79 x^{9} + 80 x^{8} - 536 x^{7} - 4 x^{6} + 1484 x^{5} - 682 x^{4} - 1431 x^{3} + 1069 x^{2} - 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.54910\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8008.1 |
$q$-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 | ||||||||
\(3\) | −1.54910 | −0.894375 | −0.447187 | − | 0.894440i | \(-0.647574\pi\) | ||||
−0.447187 | + | 0.894440i | \(0.647574\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.31877 | −1.48420 | −0.742099 | − | 0.670290i | \(-0.766170\pi\) | ||||
−0.742099 | + | 0.670290i | \(0.766170\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.600281 | −0.200094 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.14111 | 1.32743 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.21891 | 1.50831 | 0.754153 | − | 0.656698i | \(-0.228048\pi\) | ||||
0.754153 | + | 0.656698i | \(0.228048\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.02163 | −0.234379 | −0.117190 | − | 0.993110i | \(-0.537388\pi\) | ||||
−0.117190 | + | 0.993110i | \(0.537388\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.54910 | −0.338042 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.37831 | 1.32997 | 0.664985 | − | 0.746857i | \(-0.268438\pi\) | ||||
0.664985 | + | 0.746857i | \(0.268438\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.01423 | 1.20285 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.57720 | 1.07333 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.00023 | −1.29991 | −0.649955 | − | 0.759973i | \(-0.725212\pi\) | ||||
−0.649955 | + | 0.759973i | \(0.725212\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.53675 | 0.276008 | 0.138004 | − | 0.990432i | \(-0.455931\pi\) | ||||
0.138004 | + | 0.990432i | \(0.455931\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.54910 | −0.269664 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.31877 | −0.560974 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.743700 | 0.122264 | 0.0611318 | − | 0.998130i | \(-0.480529\pi\) | ||||
0.0611318 | + | 0.998130i | \(0.480529\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.54910 | −0.248055 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.0378083 | −0.00590466 | −0.00295233 | − | 0.999996i | \(-0.500940\pi\) | ||||
−0.00295233 | + | 0.999996i | \(0.500940\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.82955 | −0.279004 | −0.139502 | − | 0.990222i | \(-0.544550\pi\) | ||||
−0.139502 | + | 0.990222i | \(0.544550\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.99219 | 0.296979 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.30648 | −0.190570 | −0.0952849 | − | 0.995450i | \(-0.530376\pi\) | ||||
−0.0952849 | + | 0.995450i | \(0.530376\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9.63373 | −1.34899 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.95351 | −1.09250 | −0.546250 | − | 0.837622i | \(-0.683945\pi\) | ||||
−0.546250 | + | 0.837622i | \(0.683945\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.31877 | −0.447503 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.58262 | 0.209623 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.85219 | 0.371323 | 0.185661 | − | 0.982614i | \(-0.440557\pi\) | ||||
0.185661 | + | 0.982614i | \(0.440557\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.21055 | 0.283031 | 0.141516 | − | 0.989936i | \(-0.454802\pi\) | ||||
0.141516 | + | 0.989936i | \(0.454802\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.600281 | −0.0756282 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.31877 | −0.411643 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.93967 | −1.21432 | −0.607162 | − | 0.794578i | \(-0.707692\pi\) | ||||
−0.607162 | + | 0.794578i | \(0.707692\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −9.88066 | −1.18949 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.309613 | −0.0367443 | −0.0183722 | − | 0.999831i | \(-0.505848\pi\) | ||||
−0.0183722 | + | 0.999831i | \(0.505848\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.99410 | −0.350433 | −0.175216 | − | 0.984530i | \(-0.556063\pi\) | ||||
−0.175216 | + | 0.984530i | \(0.556063\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −9.31666 | −1.07580 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.6124 | 1.53152 | 0.765759 | − | 0.643127i | \(-0.222363\pi\) | ||||
0.765759 | + | 0.643127i | \(0.222363\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.83882 | −0.759869 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −11.3950 | −1.25076 | −0.625379 | − | 0.780321i | \(-0.715056\pi\) | ||||
−0.625379 | + | 0.780321i | \(0.715056\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −20.6391 | −2.23863 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 10.8441 | 1.16261 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.23084 | 0.130469 | 0.0652346 | − | 0.997870i | \(-0.479220\pi\) | ||||
0.0652346 | + | 0.997870i | \(0.479220\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.00000 | 0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.38058 | −0.246855 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.39057 | 0.347865 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.03876 | −0.613143 | −0.306571 | − | 0.951848i | \(-0.599182\pi\) | ||||
−0.306571 | + | 0.951848i | \(0.599182\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.600281 | −0.0603305 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.62869 | 0.460572 | 0.230286 | − | 0.973123i | \(-0.426034\pi\) | ||||
0.230286 | + | 0.973123i | \(0.426034\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.85531 | −0.872540 | −0.436270 | − | 0.899816i | \(-0.643701\pi\) | ||||
−0.436270 | + | 0.899816i | \(0.643701\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.14111 | 0.501721 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.6277 | 1.51079 | 0.755393 | − | 0.655272i | \(-0.227446\pi\) | ||||
0.755393 | + | 0.655272i | \(0.227446\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.98139 | −0.860261 | −0.430130 | − | 0.902767i | \(-0.641532\pi\) | ||||
−0.430130 | + | 0.902767i | \(0.641532\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.15207 | −0.109349 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.54415 | −0.803766 | −0.401883 | − | 0.915691i | \(-0.631644\pi\) | ||||
−0.401883 | + | 0.915691i | \(0.631644\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −21.1681 | −1.97394 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.600281 | −0.0554960 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.21891 | 0.570086 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.0585689 | 0.00528098 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.36599 | −0.301063 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.68676 | −0.593354 | −0.296677 | − | 0.954978i | \(-0.595878\pi\) | ||||
−0.296677 | + | 0.954978i | \(0.595878\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.83417 | 0.249534 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.15291 | 0.799694 | 0.399847 | − | 0.916582i | \(-0.369063\pi\) | ||||
0.399847 | + | 0.916582i | \(0.369063\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.02163 | −0.0885870 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −18.5095 | −1.59304 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.97359 | 0.254051 | 0.127026 | − | 0.991899i | \(-0.459457\pi\) | ||||
0.127026 | + | 0.991899i | \(0.459457\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.8417 | −0.919582 | −0.459791 | − | 0.888027i | \(-0.652076\pi\) | ||||
−0.459791 | + | 0.888027i | \(0.652076\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.02387 | 0.170441 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.00000 | 0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 23.2321 | 1.92932 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.54910 | −0.127768 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 14.2660 | 1.16872 | 0.584358 | − | 0.811496i | \(-0.301346\pi\) | ||||
0.584358 | + | 0.811496i | \(0.301346\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.49421 | 0.691249 | 0.345625 | − | 0.938373i | \(-0.387667\pi\) | ||||
0.345625 | + | 0.938373i | \(0.387667\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.73309 | −0.301802 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.10012 | −0.409651 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.2953 | 1.06108 | 0.530541 | − | 0.847659i | \(-0.321989\pi\) | ||||
0.530541 | + | 0.847659i | \(0.321989\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 12.3208 | 0.977104 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.37831 | 0.502682 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −15.5141 | −1.21516 | −0.607580 | − | 0.794259i | \(-0.707860\pi\) | ||||
−0.607580 | + | 0.794259i | \(0.707860\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.14111 | 0.400235 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.21029 | 0.325802 | 0.162901 | − | 0.986642i | \(-0.447915\pi\) | ||||
0.162901 | + | 0.986642i | \(0.447915\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.613267 | 0.0468977 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.86188 | 0.597728 | 0.298864 | − | 0.954296i | \(-0.403392\pi\) | ||||
0.298864 | + | 0.954296i | \(0.403392\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.01423 | 0.454633 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.41833 | −0.332102 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −22.0749 | −1.64995 | −0.824976 | − | 0.565168i | \(-0.808811\pi\) | ||||
−0.824976 | + | 0.565168i | \(0.808811\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.90681 | 0.141732 | 0.0708662 | − | 0.997486i | \(-0.477424\pi\) | ||||
0.0708662 | + | 0.997486i | \(0.477424\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.42436 | −0.253136 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.46817 | −0.181463 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.21891 | 0.454772 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.57720 | 0.405682 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.57689 | 0.403530 | 0.201765 | − | 0.979434i | \(-0.435332\pi\) | ||||
0.201765 | + | 0.979434i | \(0.435332\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.148948 | 0.0107215 | 0.00536076 | − | 0.999986i | \(-0.498294\pi\) | ||||
0.00536076 | + | 0.999986i | \(0.498294\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.14111 | 0.368163 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.60967 | 0.470919 | 0.235460 | − | 0.971884i | \(-0.424340\pi\) | ||||
0.235460 | + | 0.971884i | \(0.424340\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.89725 | −0.701598 | −0.350799 | − | 0.936451i | \(-0.614090\pi\) | ||||
−0.350799 | + | 0.936451i | \(0.614090\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 15.3976 | 1.08606 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.00023 | −0.491320 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.125477 | 0.00876370 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.82878 | −0.266118 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.02163 | −0.0706679 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.30926 | 0.640876 | 0.320438 | − | 0.947269i | \(-0.396170\pi\) | ||||
0.320438 | + | 0.947269i | \(0.396170\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.479623 | 0.0328632 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.07186 | 0.414098 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.53675 | 0.104321 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.63817 | 0.313418 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.21891 | 0.418329 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 24.4444 | 1.63692 | 0.818459 | − | 0.574564i | \(-0.194829\pi\) | ||||
0.818459 | + | 0.574564i | \(0.194829\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.61022 | −0.240682 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.8024 | 0.849727 | 0.424863 | − | 0.905257i | \(-0.360322\pi\) | ||||
0.424863 | + | 0.905257i | \(0.360322\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.37385 | −0.619442 | −0.309721 | − | 0.950828i | \(-0.600236\pi\) | ||||
−0.309721 | + | 0.950828i | \(0.600236\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.54910 | −0.101923 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.72252 | 0.440407 | 0.220203 | − | 0.975454i | \(-0.429328\pi\) | ||||
0.220203 | + | 0.975454i | \(0.429328\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.33591 | 0.282843 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −21.0871 | −1.36975 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.6728 | 0.755049 | 0.377524 | − | 0.926000i | \(-0.376775\pi\) | ||||
0.377524 | + | 0.926000i | \(0.376775\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.42583 | 0.349508 | 0.174754 | − | 0.984612i | \(-0.444087\pi\) | ||||
0.174754 | + | 0.984612i | \(0.444087\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −6.13758 | −0.393726 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.31877 | −0.212028 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.02163 | −0.0650051 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 17.6520 | 1.11865 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 28.5344 | 1.80108 | 0.900539 | − | 0.434775i | \(-0.143172\pi\) | ||||
0.900539 | + | 0.434775i | \(0.143172\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.37831 | 0.401001 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 31.9721 | 2.00217 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 16.3385 | 1.01916 | 0.509582 | − | 0.860422i | \(-0.329800\pi\) | ||||
0.509582 | + | 0.860422i | \(0.329800\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.743700 | 0.0462113 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.20210 | 0.260104 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.5084 | −0.647977 | −0.323989 | − | 0.946061i | \(-0.605024\pi\) | ||||
−0.323989 | + | 0.946061i | \(0.605024\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 26.3959 | 1.62149 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.90670 | −0.116688 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 26.8012 | 1.63410 | 0.817048 | − | 0.576570i | \(-0.195609\pi\) | ||||
0.817048 | + | 0.576570i | \(0.195609\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.10670 | −0.431701 | −0.215851 | − | 0.976426i | \(-0.569252\pi\) | ||||
−0.215851 | + | 0.976426i | \(0.569252\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.54910 | −0.0937560 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.01423 | 0.362672 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.13705 | −0.488908 | −0.244454 | − | 0.969661i | \(-0.578609\pi\) | ||||
−0.244454 | + | 0.969661i | \(0.578609\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.922481 | −0.0552275 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −30.9310 | −1.84519 | −0.922594 | − | 0.385771i | \(-0.873935\pi\) | ||||
−0.922594 | + | 0.385771i | \(0.873935\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −17.2695 | −1.02657 | −0.513284 | − | 0.858219i | \(-0.671571\pi\) | ||||
−0.513284 | + | 0.858219i | \(0.671571\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.25234 | −0.311122 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.0378083 | −0.00223175 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 21.6748 | 1.27499 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.35466 | 0.548380 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.47772 | −0.436853 | −0.218427 | − | 0.975853i | \(-0.570092\pi\) | ||||
−0.218427 | + | 0.975853i | \(0.570092\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.46574 | −0.551117 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.57720 | 0.323622 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.37831 | 0.368867 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.82955 | −0.105454 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −7.17032 | −0.411924 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.33629 | −0.420075 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.4902 | −0.884070 | −0.442035 | − | 0.896998i | \(-0.645743\pi\) | ||||
−0.442035 | + | 0.896998i | \(0.645743\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 13.7178 | 0.780377 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.4377 | 0.875393 | 0.437696 | − | 0.899123i | \(-0.355795\pi\) | ||||
0.437696 | + | 0.899123i | \(0.355795\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 35.0431 | 1.98075 | 0.990377 | − | 0.138395i | \(-0.0441943\pi\) | ||||
0.990377 | + | 0.138395i | \(0.0441943\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.99219 | 0.112247 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −14.4070 | −0.809175 | −0.404587 | − | 0.914499i | \(-0.632585\pi\) | ||||
−0.404587 | + | 0.914499i | \(0.632585\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.00023 | −0.391938 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −24.2089 | −1.35121 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.35345 | −0.353515 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.01423 | 0.333609 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 13.9131 | 0.769396 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.30648 | −0.0720286 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.2853 | −0.620294 | −0.310147 | − | 0.950689i | \(-0.600378\pi\) | ||||
−0.310147 | + | 0.950689i | \(0.600378\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.446429 | −0.0244641 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 32.9875 | 1.80230 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −21.6167 | −1.17754 | −0.588769 | − | 0.808301i | \(-0.700387\pi\) | ||||
−0.588769 | + | 0.808301i | \(0.700387\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 13.2358 | 0.718868 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.53675 | 0.0832197 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 32.7916 | 1.76544 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.96522 | −0.212864 | −0.106432 | − | 0.994320i | \(-0.533943\pi\) | ||||
−0.106432 | + | 0.994320i | \(0.533943\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 27.0076 | 1.44569 | 0.722843 | − | 0.691013i | \(-0.242835\pi\) | ||||
0.722843 | + | 0.691013i | \(0.242835\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.57720 | 0.297689 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.5211 | 0.985779 | 0.492890 | − | 0.870092i | \(-0.335941\pi\) | ||||
0.492890 | + | 0.870092i | \(0.335941\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.02754 | 0.0545359 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −9.63373 | −0.509871 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −21.2727 | −1.12273 | −0.561364 | − | 0.827569i | \(-0.689723\pi\) | ||||
−0.561364 | + | 0.827569i | \(0.689723\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.9563 | −0.945066 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.54910 | −0.0813068 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.93672 | 0.520112 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.65798 | −0.138745 | −0.0693727 | − | 0.997591i | \(-0.522100\pi\) | ||||
−0.0693727 | + | 0.997591i | \(0.522100\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.0226956 | 0.00118149 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.95351 | −0.412926 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 26.1344 | 1.35319 | 0.676593 | − | 0.736357i | \(-0.263456\pi\) | ||||
0.676593 | + | 0.736357i | \(0.263456\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.21427 | 0.269264 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7.00023 | −0.360530 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.00213 | −0.102843 | −0.0514213 | − | 0.998677i | \(-0.516375\pi\) | ||||
−0.0514213 | + | 0.998677i | \(0.516375\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10.3585 | 0.530681 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10.3948 | −0.531149 | −0.265574 | − | 0.964090i | \(-0.585562\pi\) | ||||
−0.265574 | + | 0.964090i | \(0.585562\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.31877 | −0.169140 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.09825 | 0.0558269 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −31.3009 | −1.58702 | −0.793510 | − | 0.608558i | \(-0.791748\pi\) | ||||
−0.793510 | + | 0.608558i | \(0.791748\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 39.6661 | 2.00600 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −14.1788 | −0.715226 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −45.1765 | −2.27308 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 23.3595 | 1.17238 | 0.586190 | − | 0.810174i | \(-0.300627\pi\) | ||||
0.586190 | + | 0.810174i | \(0.300627\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.58262 | 0.0792299 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 33.3811 | 1.66697 | 0.833485 | − | 0.552542i | \(-0.186342\pi\) | ||||
0.833485 | + | 0.552542i | \(0.186342\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.53675 | 0.0765510 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 22.6965 | 1.12780 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.743700 | 0.0368638 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 25.5848 | 1.26509 | 0.632543 | − | 0.774525i | \(-0.282011\pi\) | ||||
0.632543 | + | 0.774525i | \(0.282011\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.60640 | −0.227217 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.85219 | 0.140347 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 37.8172 | 1.85637 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 16.7949 | 0.822451 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.09521 | −0.346624 | −0.173312 | − | 0.984867i | \(-0.555447\pi\) | ||||
−0.173312 | + | 0.984867i | \(0.555447\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.1596 | 0.982519 | 0.491260 | − | 0.871013i | \(-0.336537\pi\) | ||||
0.491260 | + | 0.871013i | \(0.336537\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.784255 | 0.0381318 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 37.4019 | 1.81426 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.21055 | 0.106976 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.54910 | −0.0747914 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.245405 | 0.0118208 | 0.00591038 | − | 0.999983i | \(-0.498119\pi\) | ||||
0.00591038 | + | 0.999983i | \(0.498119\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.7873 | 0.614519 | 0.307260 | − | 0.951626i | \(-0.400588\pi\) | ||||
0.307260 | + | 0.951626i | \(0.400588\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −35.9890 | −1.72554 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.51631 | −0.311717 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.63337 | 0.268866 | 0.134433 | − | 0.990923i | \(-0.457079\pi\) | ||||
0.134433 | + | 0.990923i | \(0.457079\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.600281 | −0.0285848 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.46289 | 0.449596 | 0.224798 | − | 0.974405i | \(-0.427828\pi\) | ||||
0.224798 | + | 0.974405i | \(0.427828\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.08489 | −0.193642 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −22.0995 | −1.04527 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 17.0017 | 0.802359 | 0.401180 | − | 0.915999i | \(-0.368600\pi\) | ||||
0.401180 | + | 0.915999i | \(0.368600\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.0378083 | −0.00178032 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −13.1584 | −0.618236 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.31877 | −0.155586 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.86138 | 0.320962 | 0.160481 | − | 0.987039i | \(-0.448696\pi\) | ||||
0.160481 | + | 0.987039i | \(0.448696\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 34.6841 | 1.61892 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.45887 | −0.254245 | −0.127123 | − | 0.991887i | \(-0.540574\pi\) | ||||
−0.127123 | + | 0.991887i | \(0.540574\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −35.8728 | −1.66715 | −0.833575 | − | 0.552406i | \(-0.813710\pi\) | ||||
−0.833575 | + | 0.552406i | \(0.813710\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 7.90061 | 0.366382 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.35921 | 0.340544 | 0.170272 | − | 0.985397i | \(-0.445535\pi\) | ||||
0.170272 | + | 0.985397i | \(0.445535\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.93967 | −0.458971 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −20.5958 | −0.949005 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.82955 | −0.0841229 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.14434 | −0.281922 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.77434 | 0.218602 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −21.2874 | −0.972646 | −0.486323 | − | 0.873779i | \(-0.661662\pi\) | ||||
−0.486323 | + | 0.873779i | \(0.661662\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.743700 | 0.0339098 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −9.88066 | −0.449586 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 20.0412 | 0.910026 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.86941 | −0.401911 | −0.200956 | − | 0.979600i | \(-0.564405\pi\) | ||||
−0.200956 | + | 0.979600i | \(0.564405\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 24.0330 | 1.08681 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.85321 | 0.309281 | 0.154640 | − | 0.987971i | \(-0.450578\pi\) | ||||
0.154640 | + | 0.987971i | \(0.450578\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −43.5338 | −1.96066 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.99219 | 0.0895424 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.309613 | −0.0138881 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.1193 | −0.453002 | −0.226501 | − | 0.974011i | \(-0.572729\pi\) | ||||
−0.226501 | + | 0.974011i | \(0.572729\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.52217 | −0.291389 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 37.4867 | 1.67145 | 0.835726 | − | 0.549147i | \(-0.185047\pi\) | ||||
0.835726 | + | 0.549147i | \(0.185047\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.3616 | −0.683580 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.54910 | −0.0687981 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 40.1767 | 1.78080 | 0.890401 | − | 0.455176i | \(-0.150424\pi\) | ||||
0.890401 | + | 0.455176i | \(0.150424\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.99410 | −0.132451 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.69787 | −0.251567 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 29.3887 | 1.29502 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.30648 | −0.0574589 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −12.1789 | −0.534593 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 28.2066 | 1.23575 | 0.617877 | − | 0.786274i | \(-0.287993\pi\) | ||||
0.617877 | + | 0.786274i | \(0.287993\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.17407 | 0.313700 | 0.156850 | − | 0.987622i | \(-0.449866\pi\) | ||||
0.156850 | + | 0.987622i | \(0.449866\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −9.31666 | −0.406612 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9.55691 | 0.416305 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.6829 | 0.768821 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.71211 | −0.0742993 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.0378083 | −0.00163766 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −51.8647 | −2.24231 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 34.1962 | 1.47568 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.07954 | −0.390360 | −0.195180 | − | 0.980767i | \(-0.562529\pi\) | ||||
−0.195180 | + | 0.980767i | \(0.562529\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.95385 | −0.126762 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 29.8072 | 1.27680 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 31.3830 | 1.34184 | 0.670919 | − | 0.741530i | \(-0.265900\pi\) | ||||
0.670919 | + | 0.741530i | \(0.265900\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.32695 | −0.0566328 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.15168 | 0.304672 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.6124 | 0.578860 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.82345 | 0.162296 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 19.5763 | 0.829474 | 0.414737 | − | 0.909941i | \(-0.363874\pi\) | ||||
0.414737 | + | 0.909941i | \(0.363874\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.82955 | −0.0773818 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.63373 | −0.406736 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −41.3845 | −1.74415 | −0.872074 | − | 0.489373i | \(-0.837226\pi\) | ||||
−0.872074 | + | 0.489373i | \(0.837226\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 28.3560 | 1.19295 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −6.83882 | −0.287204 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18.1712 | 0.761774 | 0.380887 | − | 0.924621i | \(-0.375619\pi\) | ||||
0.380887 | + | 0.924621i | \(0.375619\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.45424 | −0.353799 | −0.176900 | − | 0.984229i | \(-0.556607\pi\) | ||||
−0.176900 | + | 0.984229i | \(0.556607\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.63918 | −0.360907 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 38.3606 | 1.59975 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.9679 | 0.623121 | 0.311561 | − | 0.950226i | \(-0.399148\pi\) | ||||
0.311561 | + | 0.950226i | \(0.399148\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.230736 | −0.00958906 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11.3950 | −0.472742 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.95351 | −0.329401 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.99219 | 0.0823670 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −15.1400 | −0.624894 | −0.312447 | − | 0.949935i | \(-0.601149\pi\) | ||||
−0.312447 | + | 0.949935i | \(0.601149\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.57000 | −0.0646906 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −10.2391 | −0.421178 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −21.5490 | −0.884912 | −0.442456 | − | 0.896790i | \(-0.645893\pi\) | ||||
−0.442456 | + | 0.896790i | \(0.645893\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −20.6391 | −0.846121 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 15.3319 | 0.627491 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 33.7469 | 1.37886 | 0.689430 | − | 0.724352i | \(-0.257861\pi\) | ||||
0.689430 | + | 0.724352i | \(0.257861\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.5524 | −0.634398 | −0.317199 | − | 0.948359i | \(-0.602742\pi\) | ||||
−0.317199 | + | 0.948359i | \(0.602742\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.96659 | 0.242978 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.31877 | −0.134927 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −39.5930 | −1.60703 | −0.803514 | − | 0.595285i | \(-0.797039\pi\) | ||||
−0.803514 | + | 0.595285i | \(0.797039\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 10.8441 | 0.439424 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.30648 | −0.0528545 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.6653 | 0.430767 | 0.215383 | − | 0.976530i | \(-0.430900\pi\) | ||||
0.215383 | + | 0.976530i | \(0.430900\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.194377 | −0.00783803 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.94294 | −0.198995 | −0.0994975 | − | 0.995038i | \(-0.531724\pi\) | ||||
−0.0994975 | + | 0.995038i | \(0.531724\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 26.9675 | 1.08392 | 0.541958 | − | 0.840406i | \(-0.317683\pi\) | ||||
0.541958 | + | 0.840406i | \(0.317683\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 35.5732 | 1.42750 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.23084 | 0.0493127 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −18.9002 | −0.756008 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.58262 | 0.0632036 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.62500 | 0.184411 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −38.6565 | −1.53889 | −0.769446 | − | 0.638712i | \(-0.779468\pi\) | ||||
−0.769446 | + | 0.638712i | \(0.779468\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −14.4210 | −0.573184 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 22.1918 | 0.880655 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.00000 | 0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.185855 | 0.00735231 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.02450 | 0.237953 | 0.118977 | − | 0.992897i | \(-0.462039\pi\) | ||||
0.118977 | + | 0.992897i | \(0.462039\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20.6890 | −0.815896 | −0.407948 | − | 0.913005i | \(-0.633756\pi\) | ||||
−0.407948 | + | 0.913005i | \(0.633756\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −9.40594 | −0.370359 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 26.7240 | 1.05063 | 0.525315 | − | 0.850908i | \(-0.323948\pi\) | ||||
0.525315 | + | 0.850908i | \(0.323948\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.85219 | 0.111958 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.38058 | −0.0933024 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 24.5007 | 0.958788 | 0.479394 | − | 0.877600i | \(-0.340857\pi\) | ||||
0.479394 | + | 0.877600i | \(0.340857\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −30.3764 | −1.18690 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.79730 | 0.0701193 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −17.9495 | −0.699214 | −0.349607 | − | 0.936896i | \(-0.613685\pi\) | ||||
−0.349607 | + | 0.936896i | \(0.613685\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 42.8531 | 1.66679 | 0.833397 | − | 0.552675i | \(-0.186393\pi\) | ||||
0.833397 | + | 0.552675i | \(0.186393\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −9.63373 | −0.374143 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.39057 | 0.131481 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −44.6497 | −1.72884 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −37.8669 | −1.46402 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.21055 | 0.0853372 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.9187 | 0.806358 | 0.403179 | − | 0.915121i | \(-0.367905\pi\) | ||||
0.403179 | + | 0.915121i | \(0.367905\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 33.5426 | 1.29105 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 37.5378 | 1.44270 | 0.721348 | − | 0.692573i | \(-0.243523\pi\) | ||||
0.721348 | + | 0.692573i | \(0.243523\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.03876 | −0.231746 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −19.8323 | −0.759974 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −21.7111 | −0.830753 | −0.415376 | − | 0.909650i | \(-0.636350\pi\) | ||||
−0.415376 | + | 0.909650i | \(0.636350\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.86866 | −0.377062 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14.5211 | 0.554013 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7.95351 | −0.303005 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.4383 | 0.511218 | 0.255609 | − | 0.966780i | \(-0.417724\pi\) | ||||
0.255609 | + | 0.966780i | \(0.417724\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.600281 | −0.0228028 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 35.9811 | 1.36484 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.235126 | −0.00890604 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −10.4139 | −0.393889 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −37.1966 | −1.40489 | −0.702447 | − | 0.711736i | \(-0.747909\pi\) | ||||
−0.702447 | + | 0.711736i | \(0.747909\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.759790 | −0.0286560 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.71676 | −0.252968 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.62869 | 0.174080 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.4426 | 0.392179 | 0.196089 | − | 0.980586i | \(-0.437176\pi\) | ||||
0.196089 | + | 0.980586i | \(0.437176\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.17128 | −0.306447 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.80187 | 0.367083 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.31877 | −0.124115 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −18.0823 | −0.675296 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 33.4983 | 1.24928 | 0.624638 | − | 0.780914i | \(-0.285247\pi\) | ||||
0.624638 | + | 0.780914i | \(0.285247\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.85531 | −0.329789 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −8.40517 | −0.312592 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −42.1010 | −1.56359 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24.7916 | 0.919469 | 0.459735 | − | 0.888056i | \(-0.347945\pi\) | ||||
0.459735 | + | 0.888056i | \(0.347945\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 30.0242 | 1.11201 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −11.3778 | −0.420824 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.51313 | 0.166696 | 0.0833481 | − | 0.996520i | \(-0.473439\pi\) | ||||
0.0833481 | + | 0.996520i | \(0.473439\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.14111 | 0.189633 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9.93967 | −0.366132 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.2604 | 0.708505 | 0.354252 | − | 0.935150i | \(-0.384735\pi\) | ||||
0.354252 | + | 0.935150i | \(0.384735\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.58262 | 0.0581389 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11.1762 | 0.410016 | 0.205008 | − | 0.978760i | \(-0.434278\pi\) | ||||
0.205008 | + | 0.978760i | \(0.434278\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −47.3455 | −1.73461 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.84017 | 0.250269 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 15.6277 | 0.571023 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.11214 | 0.150054 | 0.0750270 | − | 0.997181i | \(-0.476096\pi\) | ||||
0.0750270 | + | 0.997181i | \(0.476096\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −44.2028 | −1.61084 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −28.1903 | −1.02595 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 45.8571 | 1.66670 | 0.833352 | − | 0.552742i | \(-0.186419\pi\) | ||||
0.833352 | + | 0.552742i | \(0.186419\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −9.88066 | −0.358645 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.0542 | 0.763213 | 0.381606 | − | 0.924325i | \(-0.375371\pi\) | ||||
0.381606 | + | 0.924325i | \(0.375371\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.98139 | −0.325148 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 12.3893 | 0.447935 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.85219 | 0.102986 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.97553 | 0.215483 | 0.107742 | − | 0.994179i | \(-0.465638\pi\) | ||||
0.107742 | + | 0.994179i | \(0.465638\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −25.3099 | −0.911516 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 23.3308 | 0.839152 | 0.419576 | − | 0.907720i | \(-0.362179\pi\) | ||||
0.419576 | + | 0.907720i | \(0.362179\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.24237 | 0.331996 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.15207 | −0.0413302 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.0386263 | 0.00138393 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.309613 | −0.0110788 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −39.0417 | −1.39524 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −44.1241 | −1.57486 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16.1562 | −0.575905 | −0.287953 | − | 0.957645i | \(-0.592975\pi\) | ||||
−0.287953 | + | 0.957645i | \(0.592975\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 16.2786 | 0.579535 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.54415 | −0.303795 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.21055 | 0.0784988 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −40.8899 | −1.45022 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 16.5884 | 0.587590 | 0.293795 | − | 0.955869i | \(-0.405082\pi\) | ||||
0.293795 | + | 0.955869i | \(0.405082\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.12488 | −0.287438 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.738852 | −0.0261061 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.99410 | −0.105659 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −21.1681 | −0.746079 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −41.5177 | −1.46149 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −13.0829 | −0.459969 | −0.229984 | − | 0.973194i | \(-0.573868\pi\) | ||||
−0.229984 | + | 0.973194i | \(0.573868\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.99860 | −0.280869 | −0.140434 | − | 0.990090i | \(-0.544850\pi\) | ||||
−0.140434 | + | 0.990090i | \(0.544850\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 11.0090 | 0.386103 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 51.4878 | 1.80354 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.86913 | 0.0653927 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.600281 | −0.0209755 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21.3754 | 0.746008 | 0.373004 | − | 0.927830i | \(-0.378328\pi\) | ||||
0.373004 | + | 0.927830i | \(0.378328\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −25.1332 | −0.876088 | −0.438044 | − | 0.898954i | \(-0.644329\pi\) | ||||
−0.438044 | + | 0.898954i | \(0.644329\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −9.31666 | −0.324364 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 51.5180 | 1.79145 | 0.895727 | − | 0.444604i | \(-0.146655\pi\) | ||||
0.895727 | + | 0.444604i | \(0.146655\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −52.9584 | −1.83932 | −0.919661 | − | 0.392713i | \(-0.871536\pi\) | ||||
−0.919661 | + | 0.392713i | \(0.871536\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12.6051 | 0.437267 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.21891 | 0.215472 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −13.9730 | −0.483555 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.57077 | 0.296249 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15.6430 | 0.540056 | 0.270028 | − | 0.962852i | \(-0.412967\pi\) | ||||
0.270028 | + | 0.962852i | \(0.412967\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20.0032 | 0.689766 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 47.9153 | 1.65029 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.31877 | −0.114169 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.00000 | 0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 26.7523 | 0.918136 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.74355 | 0.162607 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −11.4578 | −0.392308 | −0.196154 | − | 0.980573i | \(-0.562845\pi\) | ||||
−0.196154 | + | 0.980573i | \(0.562845\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.03529 | −0.0696056 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 27.2015 | 0.929187 | 0.464594 | − | 0.885524i | \(-0.346200\pi\) | ||||
0.464594 | + | 0.885524i | \(0.346200\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.794861 | 0.0271203 | 0.0135602 | − | 0.999908i | \(-0.495684\pi\) | ||||
0.0135602 | + | 0.999908i | \(0.495684\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.0585689 | 0.00199602 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −40.1721 | −1.36747 | −0.683737 | − | 0.729729i | \(-0.739646\pi\) | ||||
−0.683737 | + | 0.729729i | \(0.739646\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −26.0918 | −0.887146 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −33.5765 | −1.14032 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13.6124 | 0.461770 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.93967 | −0.336793 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.62495 | 0.122686 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.36599 | −0.113791 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.07543 | −0.0363147 | −0.0181573 | − | 0.999835i | \(-0.505780\pi\) | ||||
−0.0181573 | + | 0.999835i | \(0.505780\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 11.5838 | 0.390710 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.83898 | 0.196720 | 0.0983600 | − | 0.995151i | \(-0.468640\pi\) | ||||
0.0983600 | + | 0.995151i | \(0.468640\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23.8634 | 0.803066 | 0.401533 | − | 0.915845i | \(-0.368478\pi\) | ||||
0.401533 | + | 0.915845i | \(0.368478\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 14.6634 | 0.492905 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7.83140 | 0.262953 | 0.131476 | − | 0.991319i | \(-0.458028\pi\) | ||||
0.131476 | + | 0.991319i | \(0.458028\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.68676 | −0.224267 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.83882 | −0.229109 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.33475 | 0.0446656 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 73.2613 | 2.44886 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9.88066 | −0.329906 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −10.7576 | −0.358786 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −49.4622 | −1.64782 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.83417 | 0.0943151 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6.32828 | −0.210359 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 34.0608 | 1.13097 | 0.565485 | − | 0.824758i | \(-0.308689\pi\) | ||||
0.565485 | + | 0.824758i | \(0.308689\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.77851 | −0.0921574 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.58092 | 0.118641 | 0.0593205 | − | 0.998239i | \(-0.481107\pi\) | ||||
0.0593205 | + | 0.998239i | \(0.481107\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.3950 | −0.377118 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 11.3647 | 0.375704 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9.15291 | 0.302256 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17.7970 | 0.587070 | 0.293535 | − | 0.955948i | \(-0.405168\pi\) | ||||
0.293535 | + | 0.955948i | \(0.405168\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 23.9958 | 0.790690 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.309613 | −0.0101910 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.47278 | 0.147064 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.31567 | 0.174590 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −41.8452 | −1.37290 | −0.686448 | − | 0.727179i | \(-0.740831\pi\) | ||||
−0.686448 | + | 0.727179i | \(0.740831\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.02163 | −0.0334827 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −23.9146 | −0.782929 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −20.6391 | −0.674971 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −45.8519 | −1.49792 | −0.748959 | − | 0.662617i | \(-0.769446\pi\) | ||||
−0.748959 | + | 0.662617i | \(0.769446\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −54.2854 | −1.77154 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 54.3692 | 1.77238 | 0.886192 | − | 0.463318i | \(-0.153341\pi\) | ||||
0.886192 | + | 0.463318i | \(0.153341\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.241153 | −0.00785303 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −18.5095 | −0.602113 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −6.36608 | −0.206870 | −0.103435 | − | 0.994636i | \(-0.532983\pi\) | ||||
−0.103435 | + | 0.994636i | \(0.532983\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.99410 | −0.0971926 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 22.3178 | 0.723706 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 40.7296 | 1.31936 | 0.659681 | − | 0.751545i | \(-0.270691\pi\) | ||||
0.659681 | + | 0.751545i | \(0.270691\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −18.5084 | −0.598918 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 10.8441 | 0.350539 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.97359 | 0.0960223 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.6384 | −0.923819 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −9.38100 | −0.302298 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.494325 | −0.0159129 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −46.0953 | −1.48232 | −0.741162 | − | 0.671326i | \(-0.765725\pi\) | ||||
−0.741162 | + | 0.671326i | \(0.765725\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9.84215 | 0.316175 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6.02712 | −0.193419 | −0.0967097 | − | 0.995313i | \(-0.530832\pi\) | ||||
−0.0967097 | + | 0.995313i | \(0.530832\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.8417 | −0.347569 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −9.31666 | −0.298372 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −24.6234 | −0.787771 | −0.393885 | − | 0.919160i | \(-0.628869\pi\) | ||||
−0.393885 | + | 0.919160i | \(0.628869\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.23084 | 0.0393380 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.39135 | 0.172133 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 37.3295 | 1.19063 | 0.595313 | − | 0.803494i | \(-0.297028\pi\) | ||||
0.595313 | + | 0.803494i | \(0.297028\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −21.9360 | −0.698938 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.02387 | 0.0644206 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −11.6695 | −0.371067 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 37.2932 | 1.18466 | 0.592329 | − | 0.805696i | \(-0.298209\pi\) | ||||
0.592329 | + | 0.805696i | \(0.298209\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 17.4820 | 0.554775 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 32.8467 | 1.04131 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.93327 | 0.219579 | 0.109789 | − | 0.993955i | \(-0.464982\pi\) | ||||
0.109789 | + | 0.993955i | \(0.464982\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.14777 | 0.131230 |
(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 | 8008.2.a.x.1.4 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8008.2.a.x.1.4 | ✓ | 12 | 1.1 | even | 1 | trivial |