Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3808,2,Mod(1,3808)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3808, 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("3808.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3808 = 2^{5} \cdot 7 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3808.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: | \(30.4070330897\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.4022000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{6} - 2x^{5} - 7x^{4} + 10x^{3} + 14x^{2} - 8x - 4 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-0.350492\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3808.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.692013 | 0.399534 | 0.199767 | − | 0.979843i | \(-0.435982\pi\) | ||||
0.199767 | + | 0.979843i | \(0.435982\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.18514 | 0.977225 | 0.488613 | − | 0.872501i | \(-0.337503\pi\) | ||||
0.488613 | + | 0.872501i | \(0.337503\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.52112 | −0.840373 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.76273 | −1.43602 | −0.718009 | − | 0.696034i | \(-0.754946\pi\) | ||||
−0.718009 | + | 0.696034i | \(0.754946\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.00528 | 0.833514 | 0.416757 | − | 0.909018i | \(-0.363167\pi\) | ||||
0.416757 | + | 0.909018i | \(0.363167\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.51215 | 0.390435 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.29587 | −0.756125 | −0.378062 | − | 0.925780i | \(-0.623410\pi\) | ||||
−0.378062 | + | 0.925780i | \(0.623410\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.692013 | −0.151010 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.05647 | −0.220289 | −0.110145 | − | 0.993916i | \(-0.535131\pi\) | ||||
−0.110145 | + | 0.993916i | \(0.535131\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.225153 | −0.0450306 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.82068 | −0.735291 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.24782 | 0.603105 | 0.301553 | − | 0.953450i | \(-0.402495\pi\) | ||||
0.301553 | + | 0.953450i | \(0.402495\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.23052 | 0.221008 | 0.110504 | − | 0.993876i | \(-0.464753\pi\) | ||||
0.110504 | + | 0.993876i | \(0.464753\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.29587 | −0.573738 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.18514 | −0.369356 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.17626 | 0.193377 | 0.0966884 | − | 0.995315i | \(-0.469175\pi\) | ||||
0.0966884 | + | 0.995315i | \(0.469175\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.07969 | 0.333017 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.21534 | −0.189805 | −0.0949024 | − | 0.995487i | \(-0.530254\pi\) | ||||
−0.0949024 | + | 0.995487i | \(0.530254\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.149665 | −0.0228238 | −0.0114119 | − | 0.999935i | \(-0.503633\pi\) | ||||
−0.0114119 | + | 0.999935i | \(0.503633\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.50900 | −0.821234 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.529996 | 0.0773078 | 0.0386539 | − | 0.999253i | \(-0.487693\pi\) | ||||
0.0386539 | + | 0.999253i | \(0.487693\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.692013 | 0.0969012 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.32395 | −0.868662 | −0.434331 | − | 0.900753i | \(-0.643015\pi\) | ||||
−0.434331 | + | 0.900753i | \(0.643015\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −10.4072 | −1.40331 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.28079 | −0.302097 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.93372 | −0.381938 | −0.190969 | − | 0.981596i | \(-0.561163\pi\) | ||||
−0.190969 | + | 0.981596i | \(0.561163\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.4131 | −1.58933 | −0.794666 | − | 0.607048i | \(-0.792354\pi\) | ||||
−0.794666 | + | 0.607048i | \(0.792354\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.52112 | 0.317631 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.56696 | 0.814531 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.61983 | −0.930910 | −0.465455 | − | 0.885072i | \(-0.654109\pi\) | ||||
−0.465455 | + | 0.885072i | \(0.654109\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.731091 | −0.0880130 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.23146 | −0.502181 | −0.251091 | − | 0.967964i | \(-0.580789\pi\) | ||||
−0.251091 | + | 0.967964i | \(0.580789\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.412507 | 0.0482803 | 0.0241402 | − | 0.999709i | \(-0.492315\pi\) | ||||
0.0241402 | + | 0.999709i | \(0.492315\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.155809 | −0.0179912 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.76273 | 0.542764 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.5585 | −1.63796 | −0.818979 | − | 0.573823i | \(-0.805460\pi\) | ||||
−0.818979 | + | 0.573823i | \(0.805460\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.91939 | 0.546599 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.652935 | 0.0716689 | 0.0358344 | − | 0.999358i | \(-0.488591\pi\) | ||||
0.0358344 | + | 0.999358i | \(0.488591\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.18514 | 0.237012 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.24753 | 0.240961 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13.9425 | −1.47790 | −0.738952 | − | 0.673758i | \(-0.764679\pi\) | ||||
−0.738952 | + | 0.673758i | \(0.764679\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.00528 | −0.315039 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.851538 | 0.0883004 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7.20195 | −0.738904 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.93914 | 0.907632 | 0.453816 | − | 0.891095i | \(-0.350062\pi\) | ||||
0.453816 | + | 0.891095i | \(0.350062\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 12.0074 | 1.20679 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.45105 | −0.641903 | −0.320952 | − | 0.947096i | \(-0.604003\pi\) | ||||
−0.320952 | + | 0.947096i | \(0.604003\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.25097 | −0.320327 | −0.160164 | − | 0.987090i | \(-0.551202\pi\) | ||||
−0.160164 | + | 0.987090i | \(0.551202\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.51215 | −0.147570 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.27557 | −0.510009 | −0.255005 | − | 0.966940i | \(-0.582077\pi\) | ||||
−0.255005 | + | 0.966940i | \(0.582077\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.49962 | −0.239420 | −0.119710 | − | 0.992809i | \(-0.538196\pi\) | ||||
−0.119710 | + | 0.992809i | \(0.538196\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.813990 | 0.0772606 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.18186 | −0.487468 | −0.243734 | − | 0.969842i | \(-0.578372\pi\) | ||||
−0.243734 | + | 0.969842i | \(0.578372\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.30854 | −0.215272 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7.57666 | −0.700462 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.00000 | −0.0916698 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.6836 | 1.06215 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.841033 | −0.0758334 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.4177 | −1.02123 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.8709 | 1.58578 | 0.792892 | − | 0.609362i | \(-0.208574\pi\) | ||||
0.792892 | + | 0.609362i | \(0.208574\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.103570 | −0.00911887 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −17.9932 | −1.57207 | −0.786035 | − | 0.618181i | \(-0.787870\pi\) | ||||
−0.786035 | + | 0.618181i | \(0.787870\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.29587 | 0.285788 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −8.34874 | −0.718545 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.23571 | 0.276445 | 0.138222 | − | 0.990401i | \(-0.455861\pi\) | ||||
0.138222 | + | 0.990401i | \(0.455861\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.44222 | −0.376784 | −0.188392 | − | 0.982094i | \(-0.560328\pi\) | ||||
−0.188392 | + | 0.982094i | \(0.560328\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.366764 | 0.0308871 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −14.3133 | −1.19694 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.09695 | 0.589370 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.692013 | 0.0570763 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.81102 | 0.394134 | 0.197067 | − | 0.980390i | \(-0.436858\pi\) | ||||
0.197067 | + | 0.980390i | \(0.436858\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.6543 | −0.867032 | −0.433516 | − | 0.901146i | \(-0.642727\pi\) | ||||
−0.433516 | + | 0.901146i | \(0.642727\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.52112 | −0.203820 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.68887 | 0.215975 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.61144 | −0.128607 | −0.0643035 | − | 0.997930i | \(-0.520483\pi\) | ||||
−0.0643035 | + | 0.997930i | \(0.520483\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.37626 | −0.347060 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.05647 | 0.0832615 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 19.0236 | 1.49004 | 0.745022 | − | 0.667040i | \(-0.232439\pi\) | ||||
0.745022 | + | 0.667040i | \(0.232439\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −7.20195 | −0.560671 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −15.8539 | −1.22681 | −0.613404 | − | 0.789769i | \(-0.710200\pi\) | ||||
−0.613404 | + | 0.789769i | \(0.710200\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.96832 | −0.305255 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.30928 | 0.635427 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.39955 | −0.486549 | −0.243275 | − | 0.969957i | \(-0.578222\pi\) | ||||
−0.243275 | + | 0.969957i | \(0.578222\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.225153 | 0.0170200 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.03017 | −0.152597 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 19.7775 | 1.47824 | 0.739121 | − | 0.673572i | \(-0.235241\pi\) | ||||
0.739121 | + | 0.673572i | \(0.235241\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.7792 | 1.69316 | 0.846581 | − | 0.532260i | \(-0.178657\pi\) | ||||
0.846581 | + | 0.532260i | \(0.178657\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.59001 | −0.634991 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.57031 | 0.188973 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.76273 | −0.348285 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.82068 | 0.277914 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.40889 | −0.101944 | −0.0509719 | − | 0.998700i | \(-0.516232\pi\) | ||||
−0.0509719 | + | 0.998700i | \(0.516232\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.65742 | 0.263267 | 0.131633 | − | 0.991298i | \(-0.457978\pi\) | ||||
0.131633 | + | 0.991298i | \(0.457978\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.54442 | 0.325433 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 22.6113 | 1.61099 | 0.805495 | − | 0.592602i | \(-0.201899\pi\) | ||||
0.805495 | + | 0.592602i | \(0.201899\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.3510 | −0.946428 | −0.473214 | − | 0.880948i | \(-0.656906\pi\) | ||||
−0.473214 | + | 0.880948i | \(0.656906\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.27302 | −0.371930 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.24782 | −0.227952 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.65570 | −0.185482 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.66349 | 0.185125 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 15.6973 | 1.08581 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.5748 | 0.796840 | 0.398420 | − | 0.917203i | \(-0.369559\pi\) | ||||
0.398420 | + | 0.917203i | \(0.369559\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.92822 | −0.200638 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.327040 | −0.0223040 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.23052 | −0.0835334 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.285460 | 0.0192896 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.00528 | 0.202157 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.2790 | −0.889230 | −0.444615 | − | 0.895722i | \(-0.646659\pi\) | ||||
−0.444615 | + | 0.895722i | \(0.646659\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.567637 | 0.0378425 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 23.5760 | 1.56480 | 0.782398 | − | 0.622778i | \(-0.213996\pi\) | ||||
0.782398 | + | 0.622778i | \(0.213996\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.1700 | −1.13463 | −0.567314 | − | 0.823501i | \(-0.692017\pi\) | ||||
−0.567314 | + | 0.823501i | \(0.692017\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.29587 | 0.216852 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 21.5395 | 1.41110 | 0.705551 | − | 0.708659i | \(-0.250700\pi\) | ||||
0.705551 | + | 0.708659i | \(0.250700\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.15812 | 0.0755472 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −10.0747 | −0.654420 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.9134 | −0.899985 | −0.449992 | − | 0.893032i | \(-0.648573\pi\) | ||||
−0.449992 | + | 0.893032i | \(0.648573\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.28389 | 0.469197 | 0.234598 | − | 0.972092i | \(-0.424622\pi\) | ||||
0.234598 | + | 0.972092i | \(0.424622\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.8663 | 0.953676 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.18514 | 0.139604 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.90500 | −0.630240 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.451839 | 0.0286341 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.83826 | −0.305388 | −0.152694 | − | 0.988273i | \(-0.548795\pi\) | ||||
−0.152694 | + | 0.988273i | \(0.548795\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.03168 | 0.316339 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.51215 | 0.0946943 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.24023 | 0.264498 | 0.132249 | − | 0.991217i | \(-0.457780\pi\) | ||||
0.132249 | + | 0.991217i | \(0.457780\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.17626 | −0.0730895 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.18814 | −0.506833 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.93053 | 0.242367 | 0.121183 | − | 0.992630i | \(-0.461331\pi\) | ||||
0.121183 | + | 0.992630i | \(0.461331\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −13.8187 | −0.848878 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9.64840 | −0.590473 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 30.6455 | 1.86849 | 0.934245 | − | 0.356633i | \(-0.116075\pi\) | ||||
0.934245 | + | 0.356633i | \(0.116075\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.342060 | −0.0207787 | −0.0103893 | − | 0.999946i | \(-0.503307\pi\) | ||||
−0.0103893 | + | 0.999946i | \(0.503307\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.07969 | −0.125869 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.07234 | 0.0646647 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.5416 | 1.05398 | 0.526988 | − | 0.849873i | \(-0.323321\pi\) | ||||
0.526988 | + | 0.849873i | \(0.323321\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.10229 | −0.185730 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −29.5940 | −1.76543 | −0.882715 | − | 0.469909i | \(-0.844287\pi\) | ||||
−0.882715 | + | 0.469909i | \(0.844287\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −19.9864 | −1.18807 | −0.594035 | − | 0.804439i | \(-0.702466\pi\) | ||||
−0.594035 | + | 0.804439i | \(0.702466\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.98384 | −0.295217 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.21534 | 0.0717394 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.18600 | 0.362630 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.83826 | 0.165813 | 0.0829065 | − | 0.996557i | \(-0.473580\pi\) | ||||
0.0829065 | + | 0.996557i | \(0.473580\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.41060 | −0.373239 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 18.1969 | 1.05589 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.17499 | −0.183614 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.149665 | 0.00862657 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.46421 | −0.256462 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −27.1243 | −1.55313 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.9778 | 0.626536 | 0.313268 | − | 0.949665i | \(-0.398576\pi\) | ||||
0.313268 | + | 0.949665i | \(0.398576\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.24971 | −0.127982 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.8668 | 1.12655 | 0.563273 | − | 0.826271i | \(-0.309542\pi\) | ||||
0.563273 | + | 0.826271i | \(0.309542\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.9055 | −0.955553 | −0.477776 | − | 0.878481i | \(-0.658557\pi\) | ||||
−0.477776 | + | 0.878481i | \(0.658557\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.50900 | 0.310397 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.80503 | 0.382209 | 0.191104 | − | 0.981570i | \(-0.438793\pi\) | ||||
0.191104 | + | 0.981570i | \(0.438793\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −15.4685 | −0.866070 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.65077 | −0.203766 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.29587 | −0.183387 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.676647 | −0.0375336 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.72977 | −0.0956564 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.529996 | −0.0292196 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23.6993 | 1.30263 | 0.651315 | − | 0.758808i | \(-0.274218\pi\) | ||||
0.651315 | + | 0.758808i | \(0.274218\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.96550 | −0.162509 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −16.6504 | −0.909709 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.09300 | 0.0595395 | 0.0297697 | − | 0.999557i | \(-0.490523\pi\) | ||||
0.0297697 | + | 0.999557i | \(0.490523\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.58591 | −0.194760 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.86065 | −0.317372 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.59754 | −0.0860086 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −21.6284 | −1.16107 | −0.580537 | − | 0.814234i | \(-0.697157\pi\) | ||||
−0.580537 | + | 0.814234i | \(0.697157\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.8211 | 0.900412 | 0.450206 | − | 0.892925i | \(-0.351350\pi\) | ||||
0.450206 | + | 0.892925i | \(0.351350\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −11.4822 | −0.612875 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.2360 | 0.598030 | 0.299015 | − | 0.954248i | \(-0.403342\pi\) | ||||
0.299015 | + | 0.954248i | \(0.403342\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.24633 | −0.490744 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.692013 | −0.0366252 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −16.5430 | −0.873106 | −0.436553 | − | 0.899679i | \(-0.643801\pi\) | ||||
−0.436553 | + | 0.899679i | \(0.643801\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.13723 | −0.428275 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.08521 | 0.424363 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.901387 | 0.0471808 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −23.9945 | −1.25250 | −0.626252 | − | 0.779621i | \(-0.715412\pi\) | ||||
−0.626252 | + | 0.779621i | \(0.715412\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.06402 | 0.159507 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.32395 | 0.328323 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.52152 | −0.285893 | −0.142947 | − | 0.989730i | \(-0.545658\pi\) | ||||
−0.142947 | + | 0.989730i | \(0.545658\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −7.90120 | −0.408016 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.76060 | 0.502696 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.6513 | −0.752585 | −0.376293 | − | 0.926501i | \(-0.622801\pi\) | ||||
−0.376293 | + | 0.926501i | \(0.622801\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.3669 | 0.633574 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.08107 | 0.310728 | 0.155364 | − | 0.987857i | \(-0.450345\pi\) | ||||
0.155364 | + | 0.987857i | \(0.450345\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10.4072 | 0.530402 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.377324 | 0.0191805 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −11.7879 | −0.597671 | −0.298835 | − | 0.954305i | \(-0.596598\pi\) | ||||
−0.298835 | + | 0.954305i | \(0.596598\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.05647 | −0.0534280 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −12.4515 | −0.628095 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −31.8124 | −1.60065 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.8898 | −1.14881 | −0.574404 | − | 0.818572i | \(-0.694766\pi\) | ||||
−0.574404 | + | 0.818572i | \(0.694766\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.28079 | 0.114182 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −36.9705 | −1.84622 | −0.923109 | − | 0.384539i | \(-0.874360\pi\) | ||||
−0.923109 | + | 0.384539i | \(0.874360\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.69806 | 0.184214 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 10.7496 | 0.534150 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.60223 | −0.277692 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.15953 | −0.354016 | −0.177008 | − | 0.984209i | \(-0.556642\pi\) | ||||
−0.177008 | + | 0.984209i | \(0.556642\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.23915 | 0.110449 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.93372 | 0.144359 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.42676 | 0.0700367 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.07407 | −0.150538 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −29.6690 | −1.44943 | −0.724713 | − | 0.689051i | \(-0.758028\pi\) | ||||
−0.724713 | + | 0.689051i | \(0.758028\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.4657 | 1.19239 | 0.596193 | − | 0.802841i | \(-0.296679\pi\) | ||||
0.596193 | + | 0.802841i | \(0.296679\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.33618 | −0.0649674 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.225153 | −0.0109215 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.4131 | 0.600711 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −9.90500 | −0.478218 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.50038 | −0.120439 | −0.0602195 | − | 0.998185i | \(-0.519180\pi\) | ||||
−0.0602195 | + | 0.998185i | \(0.519180\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17.8990 | 0.860169 | 0.430084 | − | 0.902789i | \(-0.358484\pi\) | ||||
0.430084 | + | 0.902789i | \(0.358484\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.91118 | 0.235473 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.48199 | 0.166566 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.78957 | −0.467231 | −0.233615 | − | 0.972329i | \(-0.575056\pi\) | ||||
−0.233615 | + | 0.972329i | \(0.575056\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.52112 | −0.120053 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.7723 | 0.796877 | 0.398438 | − | 0.917195i | \(-0.369552\pi\) | ||||
0.398438 | + | 0.917195i | \(0.369552\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −30.4664 | −1.44425 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.32929 | 0.157470 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.46455 | −0.446660 | −0.223330 | − | 0.974743i | \(-0.571693\pi\) | ||||
−0.223330 | + | 0.974743i | \(0.571693\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.78835 | 0.272563 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7.37289 | −0.346409 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.56696 | −0.307864 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 25.7452 | 1.20431 | 0.602154 | − | 0.798380i | \(-0.294309\pi\) | ||||
0.602154 | + | 0.798380i | \(0.294309\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.82068 | −0.178334 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15.2232 | −0.709017 | −0.354508 | − | 0.935053i | \(-0.615352\pi\) | ||||
−0.354508 | + | 0.935053i | \(0.615352\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −25.1295 | −1.16787 | −0.583935 | − | 0.811801i | \(-0.698488\pi\) | ||||
−0.583935 | + | 0.811801i | \(0.698488\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.86073 | 0.0862894 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 22.0858 | 1.02201 | 0.511005 | − | 0.859578i | \(-0.329273\pi\) | ||||
0.511005 | + | 0.859578i | \(0.329273\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.61983 | 0.351851 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.11514 | −0.0513828 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.712816 | 0.0327753 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.742075 | 0.0340487 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 15.9434 | 0.730000 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −11.3333 | −0.517830 | −0.258915 | − | 0.965900i | \(-0.583365\pi\) | ||||
−0.258915 | + | 0.965900i | \(0.583365\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.53500 | 0.161182 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.731091 | 0.0332658 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 19.5333 | 0.886961 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.65208 | 0.346749 | 0.173374 | − | 0.984856i | \(-0.444533\pi\) | ||||
0.173374 | + | 0.984856i | \(0.444533\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 13.1646 | 0.595323 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.72345 | −0.303425 | −0.151713 | − | 0.988425i | \(-0.548479\pi\) | ||||
−0.151713 | + | 0.988425i | \(0.548479\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.24782 | 0.146275 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 26.2379 | 1.17931 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.23146 | 0.189807 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 31.7247 | 1.42019 | 0.710096 | − | 0.704105i | \(-0.248652\pi\) | ||||
0.710096 | + | 0.704105i | \(0.248652\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10.9711 | −0.490151 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 14.6228 | 0.651997 | 0.325998 | − | 0.945370i | \(-0.394300\pi\) | ||||
0.325998 | + | 0.945370i | \(0.394300\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −14.0965 | −0.627284 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.74613 | −0.121960 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15.0973 | 0.669178 | 0.334589 | − | 0.942364i | \(-0.391403\pi\) | ||||
0.334589 | + | 0.942364i | \(0.391403\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.412507 | −0.0182483 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 12.5925 | 0.555972 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.10382 | −0.313032 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.52423 | −0.111015 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.42857 | −0.194393 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 24.6836 | 1.08141 | 0.540703 | − | 0.841213i | \(-0.318158\pi\) | ||||
0.540703 | + | 0.841213i | \(0.318158\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.24305 | −0.0543547 | −0.0271774 | − | 0.999631i | \(-0.508652\pi\) | ||||
−0.0271774 | + | 0.999631i | \(0.508652\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.155809 | 0.00680005 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.23052 | 0.0536024 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.8839 | −0.951473 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.39625 | 0.320970 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.65244 | −0.158205 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.5279 | −0.498394 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 13.6863 | 0.590608 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.76273 | −0.205145 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.7406 | −0.934703 | −0.467352 | − | 0.884072i | \(-0.654792\pi\) | ||||
−0.467352 | + | 0.884072i | \(0.654792\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 15.7635 | 0.676476 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.46202 | −0.233967 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 30.2901 | 1.29511 | 0.647556 | − | 0.762018i | \(-0.275791\pi\) | ||||
0.647556 | + | 0.762018i | \(0.275791\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 31.2948 | 1.33563 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.7044 | −0.456023 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.5585 | 0.619090 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.77868 | 0.0755010 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.56186 | −0.278035 | −0.139018 | − | 0.990290i | \(-0.544394\pi\) | ||||
−0.139018 | + | 0.990290i | \(0.544394\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.449786 | −0.0190239 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.29587 | −0.139152 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 24.1250 | 1.01675 | 0.508373 | − | 0.861137i | \(-0.330247\pi\) | ||||
0.508373 | + | 0.861137i | \(0.330247\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −11.3231 | −0.476366 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.91939 | −0.206595 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −20.3512 | −0.853166 | −0.426583 | − | 0.904448i | \(-0.640283\pi\) | ||||
−0.426583 | + | 0.904448i | \(0.640283\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 29.3914 | 1.22999 | 0.614997 | − | 0.788530i | \(-0.289157\pi\) | ||||
0.614997 | + | 0.788530i | \(0.289157\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.974972 | −0.0407300 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.237867 | 0.00991976 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13.7482 | 0.572344 | 0.286172 | − | 0.958178i | \(-0.407617\pi\) | ||||
0.286172 | + | 0.958178i | \(0.407617\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.53098 | 0.105184 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.652935 | −0.0270883 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 30.1193 | 1.24741 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −16.5561 | −0.684509 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.94284 | 0.121464 | 0.0607320 | − | 0.998154i | \(-0.480657\pi\) | ||||
0.0607320 | + | 0.998154i | \(0.480657\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.05565 | −0.167110 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 15.6473 | 0.643645 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.89968 | 0.365466 | 0.182733 | − | 0.983163i | \(-0.441506\pi\) | ||||
0.182733 | + | 0.983163i | \(0.441506\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.18514 | −0.0895821 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −9.23907 | −0.378130 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −31.6963 | −1.29508 | −0.647538 | − | 0.762033i | \(-0.724201\pi\) | ||||
−0.647538 | + | 0.762033i | \(0.724201\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.02587 | −0.286591 | −0.143296 | − | 0.989680i | \(-0.545770\pi\) | ||||
−0.143296 | + | 0.989680i | \(0.545770\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 19.2105 | 0.782311 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 25.5303 | 1.03796 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 34.4722 | 1.39918 | 0.699591 | − | 0.714543i | \(-0.253365\pi\) | ||||
0.699591 | + | 0.714543i | \(0.253365\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.24753 | −0.0910747 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.59278 | 0.0644371 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.02437 | −0.0413741 | −0.0206870 | − | 0.999786i | \(-0.506585\pi\) | ||||
−0.0206870 | + | 0.999786i | \(0.506585\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.83778 | −0.0741063 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.9782 | 0.643259 | 0.321629 | − | 0.946866i | \(-0.395770\pi\) | ||||
0.321629 | + | 0.946866i | \(0.395770\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.157524 | −0.00633143 | −0.00316572 | − | 0.999995i | \(-0.501008\pi\) | ||||
−0.00316572 | + | 0.999995i | \(0.501008\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.03644 | 0.161977 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 13.9425 | 0.558595 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.8235 | −0.952942 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 10.8628 | 0.433817 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.17626 | 0.0469008 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.0474 | 1.03693 | 0.518465 | − | 0.855099i | \(-0.326504\pi\) | ||||
0.518465 | + | 0.855099i | \(0.326504\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8.00989 | 0.318365 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 39.0504 | 1.54967 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.00528 | 0.119073 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 10.6680 | 0.422020 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −34.9914 | −1.38208 | −0.691039 | − | 0.722818i | \(-0.742847\pi\) | ||||
−0.691039 | + | 0.722818i | \(0.742847\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.8670 | 0.783478 | 0.391739 | − | 0.920076i | \(-0.371874\pi\) | ||||
0.391739 | + | 0.920076i | \(0.371874\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.226316 | −0.00891119 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 25.5462 | 1.00433 | 0.502163 | − | 0.864773i | \(-0.332538\pi\) | ||||
0.502163 | + | 0.864773i | \(0.332538\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.9725 | 0.548469 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.851538 | −0.0333744 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −20.5504 | −0.804200 | −0.402100 | − | 0.915596i | \(-0.631720\pi\) | ||||
−0.402100 | + | 0.915596i | \(0.631720\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −39.3176 | −1.53627 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.03998 | −0.0405735 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14.4156 | −0.561551 | −0.280776 | − | 0.959773i | \(-0.590592\pi\) | ||||
−0.280776 | + | 0.959773i | \(0.590592\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.9184 | −0.580260 | −0.290130 | − | 0.956987i | \(-0.593699\pi\) | ||||
−0.290130 | + | 0.956987i | \(0.593699\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.07969 | 0.0807685 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 7.20195 | 0.279280 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.43123 | −0.132858 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9.18926 | −0.355277 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 59.1201 | 2.28231 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.899084 | 0.0346571 | 0.0173286 | − | 0.999850i | \(-0.494484\pi\) | ||||
0.0173286 | + | 0.999850i | \(0.494484\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.860239 | 0.0331106 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −19.7181 | −0.757827 | −0.378914 | − | 0.925432i | \(-0.623702\pi\) | ||||
−0.378914 | + | 0.925432i | \(0.623702\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.93914 | −0.343053 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 16.3149 | 0.625189 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.09474 | 0.194945 | 0.0974724 | − | 0.995238i | \(-0.468924\pi\) | ||||
0.0974724 | + | 0.995238i | \(0.468924\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.07048 | 0.270149 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −11.8819 | −0.453322 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −19.0052 | −0.724042 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.77065 | 0.105400 | 0.0527002 | − | 0.998610i | \(-0.483217\pi\) | ||||
0.0527002 | + | 0.998610i | \(0.483217\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −12.0074 | −0.456124 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −9.70687 | −0.368203 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.21534 | −0.0460344 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 14.9056 | 0.563783 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 42.4680 | 1.60399 | 0.801997 | − | 0.597328i | \(-0.203771\pi\) | ||||
0.801997 | + | 0.597328i | \(0.203771\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.87682 | −0.146217 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.801431 | 0.0301836 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.45105 | 0.242617 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −46.2542 | −1.73711 | −0.868556 | − | 0.495591i | \(-0.834952\pi\) | ||||
−0.868556 | + | 0.495591i | \(0.834952\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 36.7037 | 1.37650 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.30001 | −0.0486858 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −31.2766 | −1.16968 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −9.62827 | −0.359574 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 29.5694 | 1.10275 | 0.551376 | − | 0.834257i | \(-0.314103\pi\) | ||||
0.551376 | + | 0.834257i | \(0.314103\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.25097 | 0.121072 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.04055 | 0.187460 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.731257 | −0.0271582 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.58624 | 0.244270 | 0.122135 | − | 0.992513i | \(-0.461026\pi\) | ||||
0.122135 | + | 0.992513i | \(0.461026\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −4.47048 | −0.165573 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.149665 | −0.00553558 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17.3643 | −0.641364 | −0.320682 | − | 0.947187i | \(-0.603912\pi\) | ||||
−0.320682 | + | 0.947187i | \(0.603912\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.51215 | 0.0557764 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 36.2912 | 1.33680 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 26.6329 | 0.979707 | 0.489853 | − | 0.871805i | \(-0.337050\pi\) | ||||
0.489853 | + | 0.871805i | \(0.337050\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.85439 | −0.251802 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 38.7890 | 1.42303 | 0.711515 | − | 0.702671i | \(-0.248009\pi\) | ||||
0.711515 | + | 0.702671i | \(0.248009\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.5128 | 0.385158 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.64613 | −0.0602286 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.27557 | 0.192765 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.97854 | 0.145179 | 0.0725894 | − | 0.997362i | \(-0.476874\pi\) | ||||
0.0725894 | + | 0.997362i | \(0.476874\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.34814 | −0.122013 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −23.2811 | −0.847286 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.41672 | 0.196874 | 0.0984369 | − | 0.995143i | \(-0.468616\pi\) | ||||
0.0984369 | + | 0.995143i | \(0.468616\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.48199 | 0.126388 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.41577 | −0.268821 | −0.134411 | − | 0.990926i | \(-0.542914\pi\) | ||||
−0.134411 | + | 0.990926i | \(0.542914\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.49962 | 0.0904922 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.50900 | −0.199178 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.81664 | −0.318350 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.6536 | −0.528423 | −0.264211 | − | 0.964465i | \(-0.585112\pi\) | ||||
−0.264211 | + | 0.964465i | \(0.585112\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.93429 | 0.105676 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −31.6813 | −1.13950 | −0.569748 | − | 0.821819i | \(-0.692959\pi\) | ||||
−0.569748 | + | 0.821819i | \(0.692959\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.277056 | −0.00995214 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.813990 | −0.0292017 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.00561 | 0.143516 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20.1533 | 0.721141 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −12.4089 | −0.443458 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.52123 | −0.125678 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 40.5020 | 1.44374 | 0.721870 | − | 0.692028i | \(-0.243283\pi\) | ||||
0.721870 | + | 0.692028i | \(0.243283\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.71998 | 0.0968338 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.18186 | 0.184246 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −37.3047 | −1.32473 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −9.56275 | −0.339156 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 21.5399 | 0.762981 | 0.381491 | − | 0.924373i | \(-0.375411\pi\) | ||||
0.381491 | + | 0.924373i | \(0.375411\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.529996 | 0.0187499 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 35.1507 | 1.24199 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.96466 | −0.0693314 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.30854 | 0.0813653 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 21.2071 | 0.746525 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −47.9994 | −1.68757 | −0.843784 | − | 0.536683i | \(-0.819677\pi\) | ||||
−0.843784 | + | 0.536683i | \(0.819677\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.5842 | 0.477007 | 0.238503 | − | 0.971142i | \(-0.423343\pi\) | ||||
0.238503 | + | 0.971142i | \(0.423343\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.236710 | −0.00830179 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 41.5693 | 1.45611 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.493278 | 0.0172576 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 7.57666 | 0.264750 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −45.6149 | −1.59197 | −0.795986 | − | 0.605315i | \(-0.793047\pi\) | ||||
−0.795986 | + | 0.605315i | \(0.793047\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.84854 | −0.308441 | −0.154220 | − | 0.988036i | \(-0.549287\pi\) | ||||
−0.154220 | + | 0.988036i | \(0.549287\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.742075 | 0.0258357 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −14.2215 | −0.494531 | −0.247265 | − | 0.968948i | \(-0.579532\pi\) | ||||
−0.247265 | + | 0.968948i | \(0.579532\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.10407 | −0.107809 | −0.0539043 | − | 0.998546i | \(-0.517167\pi\) | ||||
−0.0539043 | + | 0.998546i | \(0.517167\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12.1390 | 0.421099 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.00000 | 0.0346479 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −34.6429 | −1.19887 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.70144 | −0.162506 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −45.6207 | −1.57500 | −0.787501 | − | 0.616313i | \(-0.788626\pi\) | ||||
−0.787501 | + | 0.616313i | \(0.788626\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.4517 | −0.636264 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −20.4794 | −0.705349 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −8.67133 | −0.298303 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −11.6836 | −0.401453 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −13.8309 | −0.474674 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.24269 | −0.0425988 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 34.9002 | 1.19496 | 0.597481 | − | 0.801883i | \(-0.296168\pi\) | ||||
0.597481 | + | 0.801883i | \(0.296168\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 18.1570 | 0.620955 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.60518 | −0.0548319 | −0.0274160 | − | 0.999624i | \(-0.508728\pi\) | ||||
−0.0274160 | + | 0.999624i | \(0.508728\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 48.0128 | 1.63818 | 0.819088 | − | 0.573667i | \(-0.194480\pi\) | ||||
0.819088 | + | 0.573667i | \(0.194480\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.841033 | 0.0286623 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 21.0701 | 0.717236 | 0.358618 | − | 0.933484i | \(-0.383248\pi\) | ||||
0.358618 | + | 0.933484i | \(0.383248\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13.9839 | −0.475468 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.692013 | 0.0235020 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 69.3382 | 2.35214 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −22.8997 | −0.775926 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −22.5366 | −0.762749 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 11.4177 | 0.385989 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8.61011 | −0.290743 | −0.145371 | − | 0.989377i | \(-0.546438\pi\) | ||||
−0.145371 | + | 0.989377i | \(0.546438\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.96411 | 0.0662479 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 11.1694 | 0.376305 | 0.188153 | − | 0.982140i | \(-0.439750\pi\) | ||||
0.188153 | + | 0.982140i | \(0.439750\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33.6407 | 1.13210 | 0.566051 | − | 0.824371i | \(-0.308471\pi\) | ||||
0.566051 | + | 0.824371i | \(0.308471\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.43621 | −0.149122 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −51.2232 | −1.71991 | −0.859953 | − | 0.510374i | \(-0.829507\pi\) | ||||
−0.859953 | + | 0.510374i | \(0.829507\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −17.8709 | −0.599370 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −23.4297 | −0.784926 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.74680 | −0.0584543 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 43.2167 | 1.44458 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.19713 | −0.0733601 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.99652 | 0.133291 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.32395 | −0.210681 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.103570 | 0.00344661 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 49.7757 | 1.65460 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.43221 | −0.213578 | −0.106789 | − | 0.994282i | \(-0.534057\pi\) | ||||
−0.106789 | + | 0.994282i | \(0.534057\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 16.2639 | 0.539438 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 48.8018 | 1.61688 | 0.808438 | − | 0.588581i | \(-0.200313\pi\) | ||||
0.808438 | + | 0.588581i | \(0.200313\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.10975 | −0.102918 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −18.7704 | −0.620530 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 17.9932 | 0.594187 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 38.2201 | 1.26076 | 0.630382 | − | 0.776285i | \(-0.282898\pi\) | ||||
0.630382 | + | 0.776285i | \(0.282898\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.59677 | 0.250322 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −12.7167 | −0.418575 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.264840 | −0.00870787 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8.19607 | 0.269194 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 22.9110 | 0.751686 | 0.375843 | − | 0.926683i | \(-0.377353\pi\) | ||||
0.375843 | + | 0.926683i | \(0.377353\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.29587 | −0.108018 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 13.7481 | 0.450093 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −10.4072 | −0.340353 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33.7022 | 1.10100 | 0.550501 | − | 0.834835i | \(-0.314437\pi\) | ||||
0.550501 | + | 0.834835i | \(0.314437\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −11.6988 | −0.381776 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 18.0639 | 0.588865 | 0.294433 | − | 0.955672i | \(-0.404869\pi\) | ||||
0.294433 | + | 0.955672i | \(0.404869\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.28397 | 0.0418119 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 8.34874 | 0.271585 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −46.2560 | −1.50312 | −0.751559 | − | 0.659666i | \(-0.770698\pi\) | ||||
−0.751559 | + | 0.659666i | \(0.770698\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.23970 | 0.0402423 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.70917 | 0.152705 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −19.9327 | −0.645683 | −0.322842 | − | 0.946453i | \(-0.604638\pi\) | ||||
−0.322842 | + | 0.946453i | \(0.604638\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.07863 | −0.0996221 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −10.7044 | −0.346024 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.23571 | −0.104486 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.4858 | −0.951155 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 13.3003 | 0.428598 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.99198 | 0.257271 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.0746 | 0.323978 | 0.161989 | − | 0.986793i | \(-0.448209\pi\) | ||||
0.161989 | + | 0.986793i | \(0.448209\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.28079 | −0.0732694 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −25.4973 | −0.818248 | −0.409124 | − | 0.912479i | \(-0.634166\pi\) | ||||
−0.409124 | + | 0.912479i | \(0.634166\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.44222 | 0.142411 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.468248 | −0.0149959 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −33.9875 | −1.08736 | −0.543678 | − | 0.839294i | \(-0.682969\pi\) | ||||
−0.543678 | + | 0.839294i | \(0.682969\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 66.4045 | 2.12230 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.30183 | 0.201202 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −33.4135 | −1.06572 | −0.532862 | − | 0.846202i | \(-0.678884\pi\) | ||||
−0.532862 | + | 0.846202i | \(0.678884\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 49.4090 | 1.57430 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.366764 | −0.0116742 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.158117 | 0.00502783 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.9427 | 0.951160 | 0.475580 | − | 0.879672i | \(-0.342238\pi\) | ||||
0.475580 | + | 0.879672i | \(0.342238\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 16.4002 | 0.520445 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −29.1739 | −0.924873 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.35532 | 0.169605 | 0.0848023 | − | 0.996398i | \(-0.472974\pi\) | ||||
0.0848023 | + | 0.996398i | \(0.472974\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.49414 | −0.142188 |
(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 | 3808.2.a.j.1.4 | ✓ | 6 | |
4.3 | odd | 2 | 3808.2.a.n.1.3 | yes | 6 | ||
8.3 | odd | 2 | 7616.2.a.bw.1.4 | 6 | |||
8.5 | even | 2 | 7616.2.a.ca.1.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3808.2.a.j.1.4 | ✓ | 6 | 1.1 | even | 1 | trivial | |
3808.2.a.n.1.3 | yes | 6 | 4.3 | odd | 2 | ||
7616.2.a.bw.1.4 | 6 | 8.3 | odd | 2 | |||
7616.2.a.ca.1.3 | 6 | 8.5 | even | 2 |