Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7938,2,Mod(1,7938)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7938, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("7938.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7938 = 2 \cdot 3^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7938.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: | \(63.3852491245\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 1134) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7938.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.24264 | −1.27920 | −0.639602 | − | 0.768706i | \(-0.720901\pi\) | ||||
−0.639602 | + | 0.768706i | \(0.720901\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.24264 | −1.73140 | −0.865699 | − | 0.500566i | \(-0.833125\pi\) | ||||
−0.865699 | + | 0.500566i | \(0.833125\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.24264 | −1.43216 | −0.716080 | − | 0.698018i | \(-0.754065\pi\) | ||||
−0.716080 | + | 0.698018i | \(0.754065\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.24264 | 0.904534 | ||||||||
\(23\) | −7.24264 | −1.51019 | −0.755097 | − | 0.655613i | \(-0.772410\pi\) | ||||
−0.755097 | + | 0.655613i | \(0.772410\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.00000 | −1.00000 | ||||||||
\(26\) | 6.24264 | 1.22428 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.24264 | 0.787839 | 0.393919 | − | 0.919145i | \(-0.371119\pi\) | ||||
0.393919 | + | 0.919145i | \(0.371119\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.757359 | −0.136026 | −0.0680129 | − | 0.997684i | \(-0.521666\pi\) | ||||
−0.0680129 | + | 0.997684i | \(0.521666\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.00000 | −0.657596 | −0.328798 | − | 0.944400i | \(-0.606644\pi\) | ||||
−0.328798 | + | 0.944400i | \(0.606644\pi\) | |||||||
\(38\) | 6.24264 | 1.01269 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.48528 | −0.856657 | −0.428329 | − | 0.903623i | \(-0.640897\pi\) | ||||
−0.428329 | + | 0.903623i | \(0.640897\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.48528 | −0.988996 | −0.494498 | − | 0.869179i | \(-0.664648\pi\) | ||||
−0.494498 | + | 0.869179i | \(0.664648\pi\) | |||||||
\(44\) | −4.24264 | −0.639602 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7.24264 | 1.06787 | ||||||||
\(47\) | 13.2426 | 1.93164 | 0.965819 | − | 0.259218i | \(-0.0834648\pi\) | ||||
0.965819 | + | 0.259218i | \(0.0834648\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 5.00000 | 0.707107 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −6.24264 | −0.865699 | ||||||||
\(53\) | −4.24264 | −0.582772 | −0.291386 | − | 0.956606i | \(-0.594116\pi\) | ||||
−0.291386 | + | 0.956606i | \(0.594116\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.24264 | −0.557086 | ||||||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.24264 | −0.799288 | −0.399644 | − | 0.916670i | \(-0.630866\pi\) | ||||
−0.399644 | + | 0.916670i | \(0.630866\pi\) | |||||||
\(62\) | 0.757359 | 0.0961847 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.24264 | −1.00700 | −0.503499 | − | 0.863996i | \(-0.667954\pi\) | ||||
−0.503499 | + | 0.863996i | \(0.667954\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.24264 | 0.859543 | 0.429772 | − | 0.902938i | \(-0.358594\pi\) | ||||
0.429772 | + | 0.902938i | \(0.358594\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.00000 | 0.819288 | 0.409644 | − | 0.912245i | \(-0.365653\pi\) | ||||
0.409644 | + | 0.912245i | \(0.365653\pi\) | |||||||
\(74\) | 4.00000 | 0.464991 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.24264 | −0.716080 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.24264 | 1.03988 | 0.519939 | − | 0.854203i | \(-0.325955\pi\) | ||||
0.519939 | + | 0.854203i | \(0.325955\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 5.48528 | 0.605748 | ||||||||
\(83\) | 7.75736 | 0.851481 | 0.425740 | − | 0.904845i | \(-0.360014\pi\) | ||||
0.425740 | + | 0.904845i | \(0.360014\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 6.48528 | 0.699326 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.24264 | 0.452267 | ||||||||
\(89\) | −5.48528 | −0.581439 | −0.290719 | − | 0.956808i | \(-0.593895\pi\) | ||||
−0.290719 | + | 0.956808i | \(0.593895\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −7.24264 | −0.755097 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −13.2426 | −1.36587 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.4853 | 1.26769 | 0.633844 | − | 0.773461i | \(-0.281476\pi\) | ||||
0.633844 | + | 0.773461i | \(0.281476\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −5.00000 | −0.500000 | ||||||||
\(101\) | 7.75736 | 0.771886 | 0.385943 | − | 0.922523i | \(-0.373876\pi\) | ||||
0.385943 | + | 0.922523i | \(0.373876\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.757359 | −0.0746248 | −0.0373124 | − | 0.999304i | \(-0.511880\pi\) | ||||
−0.0373124 | + | 0.999304i | \(0.511880\pi\) | |||||||
\(104\) | 6.24264 | 0.612141 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.24264 | 0.412082 | ||||||||
\(107\) | 2.48528 | 0.240261 | 0.120131 | − | 0.992758i | \(-0.461669\pi\) | ||||
0.120131 | + | 0.992758i | \(0.461669\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.24264 | −0.214806 | −0.107403 | − | 0.994216i | \(-0.534254\pi\) | ||||
−0.107403 | + | 0.994216i | \(0.534254\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 20.4853 | 1.92709 | 0.963547 | − | 0.267541i | \(-0.0862110\pi\) | ||||
0.963547 | + | 0.267541i | \(0.0862110\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 4.24264 | 0.393919 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.00000 | 0.636364 | ||||||||
\(122\) | 6.24264 | 0.565182 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.757359 | −0.0680129 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.75736 | 0.599619 | 0.299809 | − | 0.953999i | \(-0.403077\pi\) | ||||
0.299809 | + | 0.953999i | \(0.403077\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.75736 | −0.677764 | −0.338882 | − | 0.940829i | \(-0.610049\pi\) | ||||
−0.338882 | + | 0.940829i | \(0.610049\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 8.24264 | 0.712056 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 19.9706 | 1.70620 | 0.853100 | − | 0.521747i | \(-0.174720\pi\) | ||||
0.853100 | + | 0.521747i | \(0.174720\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.72792 | 0.401017 | 0.200509 | − | 0.979692i | \(-0.435741\pi\) | ||||
0.200509 | + | 0.979692i | \(0.435741\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −7.24264 | −0.607789 | ||||||||
\(143\) | 26.4853 | 2.21481 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −7.00000 | −0.579324 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.00000 | −0.328798 | ||||||||
\(149\) | −16.2426 | −1.33065 | −0.665324 | − | 0.746554i | \(-0.731707\pi\) | ||||
−0.665324 | + | 0.746554i | \(0.731707\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.75736 | −0.224391 | −0.112195 | − | 0.993686i | \(-0.535788\pi\) | ||||
−0.112195 | + | 0.993686i | \(0.535788\pi\) | |||||||
\(152\) | 6.24264 | 0.506345 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.0000 | −1.11732 | −0.558661 | − | 0.829396i | \(-0.688685\pi\) | ||||
−0.558661 | + | 0.829396i | \(0.688685\pi\) | |||||||
\(158\) | −9.24264 | −0.735305 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.7574 | −0.920907 | −0.460454 | − | 0.887684i | \(-0.652313\pi\) | ||||
−0.460454 | + | 0.887684i | \(0.652313\pi\) | |||||||
\(164\) | −5.48528 | −0.428329 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −7.75736 | −0.602088 | ||||||||
\(167\) | 24.2132 | 1.87367 | 0.936837 | − | 0.349766i | \(-0.113739\pi\) | ||||
0.936837 | + | 0.349766i | \(0.113739\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 25.9706 | 1.99774 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6.48528 | −0.494498 | ||||||||
\(173\) | −10.9706 | −0.834076 | −0.417038 | − | 0.908889i | \(-0.636932\pi\) | ||||
−0.417038 | + | 0.908889i | \(0.636932\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.24264 | −0.319801 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 5.48528 | 0.411139 | ||||||||
\(179\) | 16.2426 | 1.21403 | 0.607016 | − | 0.794690i | \(-0.292366\pi\) | ||||
0.607016 | + | 0.794690i | \(0.292366\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.2426 | 1.50462 | 0.752312 | − | 0.658807i | \(-0.228939\pi\) | ||||
0.752312 | + | 0.658807i | \(0.228939\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 7.24264 | 0.533935 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 13.2426 | 0.965819 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.48528 | −0.613973 | −0.306987 | − | 0.951714i | \(-0.599321\pi\) | ||||
−0.306987 | + | 0.951714i | \(0.599321\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.51472 | −0.324977 | −0.162488 | − | 0.986710i | \(-0.551952\pi\) | ||||
−0.162488 | + | 0.986710i | \(0.551952\pi\) | |||||||
\(194\) | −12.4853 | −0.896391 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −16.9706 | −1.20910 | −0.604551 | − | 0.796566i | \(-0.706648\pi\) | ||||
−0.604551 | + | 0.796566i | \(0.706648\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.7574 | 1.04612 | 0.523061 | − | 0.852295i | \(-0.324790\pi\) | ||||
0.523061 | + | 0.852295i | \(0.324790\pi\) | |||||||
\(200\) | 5.00000 | 0.353553 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −7.75736 | −0.545806 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0.757359 | 0.0527677 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −6.24264 | −0.432849 | ||||||||
\(209\) | 26.4853 | 1.83203 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.48528 | −0.446465 | −0.223233 | − | 0.974765i | \(-0.571661\pi\) | ||||
−0.223233 | + | 0.974765i | \(0.571661\pi\) | |||||||
\(212\) | −4.24264 | −0.291386 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.48528 | −0.169890 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 2.24264 | 0.151891 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.7279 | −0.785360 | −0.392680 | − | 0.919675i | \(-0.628452\pi\) | ||||
−0.392680 | + | 0.919675i | \(0.628452\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −20.4853 | −1.36266 | ||||||||
\(227\) | 26.4853 | 1.75789 | 0.878945 | − | 0.476923i | \(-0.158248\pi\) | ||||
0.878945 | + | 0.476923i | \(0.158248\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −24.9706 | −1.65010 | −0.825051 | − | 0.565059i | \(-0.808853\pi\) | ||||
−0.825051 | + | 0.565059i | \(0.808853\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.24264 | −0.278543 | ||||||||
\(233\) | −20.4853 | −1.34204 | −0.671018 | − | 0.741441i | \(-0.734143\pi\) | ||||
−0.671018 | + | 0.741441i | \(0.734143\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.72792 | −0.241139 | −0.120570 | − | 0.992705i | \(-0.538472\pi\) | ||||
−0.120570 | + | 0.992705i | \(0.538472\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.51472 | −0.548481 | −0.274241 | − | 0.961661i | \(-0.588426\pi\) | ||||
−0.274241 | + | 0.961661i | \(0.588426\pi\) | |||||||
\(242\) | −7.00000 | −0.449977 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −6.24264 | −0.399644 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 38.9706 | 2.47964 | ||||||||
\(248\) | 0.757359 | 0.0480924 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.7279 | 1.18210 | 0.591048 | − | 0.806636i | \(-0.298714\pi\) | ||||
0.591048 | + | 0.806636i | \(0.298714\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 30.7279 | 1.93185 | ||||||||
\(254\) | −6.75736 | −0.423994 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 5.48528 | 0.342162 | 0.171081 | − | 0.985257i | \(-0.445274\pi\) | ||||
0.171081 | + | 0.985257i | \(0.445274\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 7.75736 | 0.479251 | ||||||||
\(263\) | −22.9706 | −1.41643 | −0.708213 | − | 0.705999i | \(-0.750498\pi\) | ||||
−0.708213 | + | 0.705999i | \(0.750498\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −8.24264 | −0.503499 | ||||||||
\(269\) | −10.9706 | −0.668887 | −0.334444 | − | 0.942416i | \(-0.608548\pi\) | ||||
−0.334444 | + | 0.942416i | \(0.608548\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.4853 | 0.758427 | 0.379213 | − | 0.925309i | \(-0.376195\pi\) | ||||
0.379213 | + | 0.925309i | \(0.376195\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −19.9706 | −1.20647 | ||||||||
\(275\) | 21.2132 | 1.27920 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −19.2132 | −1.15441 | −0.577205 | − | 0.816599i | \(-0.695857\pi\) | ||||
−0.577205 | + | 0.816599i | \(0.695857\pi\) | |||||||
\(278\) | −4.72792 | −0.283562 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −22.4558 | −1.33960 | −0.669802 | − | 0.742540i | \(-0.733621\pi\) | ||||
−0.669802 | + | 0.742540i | \(0.733621\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −24.9706 | −1.48435 | −0.742173 | − | 0.670208i | \(-0.766205\pi\) | ||||
−0.742173 | + | 0.670208i | \(0.766205\pi\) | |||||||
\(284\) | 7.24264 | 0.429772 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −26.4853 | −1.56611 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −17.0000 | −1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 7.00000 | 0.409644 | ||||||||
\(293\) | −10.9706 | −0.640907 | −0.320454 | − | 0.947264i | \(-0.603835\pi\) | ||||
−0.320454 | + | 0.947264i | \(0.603835\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 4.00000 | 0.232495 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 16.2426 | 0.940911 | ||||||||
\(299\) | 45.2132 | 2.61475 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 2.75736 | 0.158668 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −6.24264 | −0.358040 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 28.0000 | 1.59804 | 0.799022 | − | 0.601302i | \(-0.205351\pi\) | ||||
0.799022 | + | 0.601302i | \(0.205351\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.9706 | −0.622084 | −0.311042 | − | 0.950396i | \(-0.600678\pi\) | ||||
−0.311042 | + | 0.950396i | \(0.600678\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.9706 | 1.01576 | 0.507878 | − | 0.861429i | \(-0.330430\pi\) | ||||
0.507878 | + | 0.861429i | \(0.330430\pi\) | |||||||
\(314\) | 14.0000 | 0.790066 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9.24264 | 0.519939 | ||||||||
\(317\) | 16.9706 | 0.953162 | 0.476581 | − | 0.879131i | \(-0.341876\pi\) | ||||
0.476581 | + | 0.879131i | \(0.341876\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −18.0000 | −1.00781 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 31.2132 | 1.73140 | ||||||||
\(326\) | 11.7574 | 0.651180 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 5.48528 | 0.302874 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.4853 | −1.01604 | −0.508021 | − | 0.861344i | \(-0.669623\pi\) | ||||
−0.508021 | + | 0.861344i | \(0.669623\pi\) | |||||||
\(332\) | 7.75736 | 0.425740 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −24.2132 | −1.32489 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.48528 | 0.244329 | 0.122164 | − | 0.992510i | \(-0.461016\pi\) | ||||
0.122164 | + | 0.992510i | \(0.461016\pi\) | |||||||
\(338\) | −25.9706 | −1.41261 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.21320 | 0.174005 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 6.48528 | 0.349663 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 10.9706 | 0.589781 | ||||||||
\(347\) | 6.72792 | 0.361174 | 0.180587 | − | 0.983559i | \(-0.442200\pi\) | ||||
0.180587 | + | 0.983559i | \(0.442200\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −24.9706 | −1.33664 | −0.668322 | − | 0.743872i | \(-0.732987\pi\) | ||||
−0.668322 | + | 0.743872i | \(0.732987\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.24264 | 0.226134 | ||||||||
\(353\) | 21.0000 | 1.11772 | 0.558859 | − | 0.829263i | \(-0.311239\pi\) | ||||
0.558859 | + | 0.829263i | \(0.311239\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −5.48528 | −0.290719 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −16.2426 | −0.858450 | ||||||||
\(359\) | −10.7574 | −0.567752 | −0.283876 | − | 0.958861i | \(-0.591620\pi\) | ||||
−0.283876 | + | 0.958861i | \(0.591620\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 19.9706 | 1.05108 | ||||||||
\(362\) | −20.2426 | −1.06393 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.7279 | −0.612193 | −0.306096 | − | 0.952001i | \(-0.599023\pi\) | ||||
−0.306096 | + | 0.952001i | \(0.599023\pi\) | |||||||
\(368\) | −7.24264 | −0.377549 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.21320 | −0.373486 | −0.186743 | − | 0.982409i | \(-0.559793\pi\) | ||||
−0.186743 | + | 0.982409i | \(0.559793\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −13.2426 | −0.682937 | ||||||||
\(377\) | −26.4853 | −1.36406 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.27208 | 0.0653423 | 0.0326711 | − | 0.999466i | \(-0.489599\pi\) | ||||
0.0326711 | + | 0.999466i | \(0.489599\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 8.48528 | 0.434145 | ||||||||
\(383\) | −24.2132 | −1.23724 | −0.618618 | − | 0.785692i | \(-0.712307\pi\) | ||||
−0.618618 | + | 0.785692i | \(0.712307\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4.51472 | 0.229793 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 12.4853 | 0.633844 | ||||||||
\(389\) | −10.2426 | −0.519322 | −0.259661 | − | 0.965700i | \(-0.583611\pi\) | ||||
−0.259661 | + | 0.965700i | \(0.583611\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 16.9706 | 0.854965 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.2426 | 1.01595 | 0.507975 | − | 0.861372i | \(-0.330394\pi\) | ||||
0.507975 | + | 0.861372i | \(0.330394\pi\) | |||||||
\(398\) | −14.7574 | −0.739720 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −5.00000 | −0.250000 | ||||||||
\(401\) | −29.4853 | −1.47242 | −0.736212 | − | 0.676751i | \(-0.763388\pi\) | ||||
−0.736212 | + | 0.676751i | \(0.763388\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.72792 | 0.235515 | ||||||||
\(404\) | 7.75736 | 0.385943 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16.9706 | 0.841200 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −35.0000 | −1.73064 | −0.865319 | − | 0.501221i | \(-0.832884\pi\) | ||||
−0.865319 | + | 0.501221i | \(0.832884\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −0.757359 | −0.0373124 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 6.24264 | 0.306071 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −26.4853 | −1.29544 | ||||||||
\(419\) | −7.75736 | −0.378972 | −0.189486 | − | 0.981883i | \(-0.560682\pi\) | ||||
−0.189486 | + | 0.981883i | \(0.560682\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.2426 | −0.694144 | −0.347072 | − | 0.937839i | \(-0.612824\pi\) | ||||
−0.347072 | + | 0.937839i | \(0.612824\pi\) | |||||||
\(422\) | 6.48528 | 0.315699 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4.24264 | 0.206041 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 2.48528 | 0.120131 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 37.2426 | 1.79391 | 0.896957 | − | 0.442117i | \(-0.145772\pi\) | ||||
0.896957 | + | 0.442117i | \(0.145772\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.97056 | −0.190813 | −0.0954065 | − | 0.995438i | \(-0.530415\pi\) | ||||
−0.0954065 | + | 0.995438i | \(0.530415\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.24264 | −0.107403 | ||||||||
\(437\) | 45.2132 | 2.16284 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11.7279 | −0.559743 | −0.279872 | − | 0.960037i | \(-0.590292\pi\) | ||||
−0.279872 | + | 0.960037i | \(0.590292\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.51472 | −0.452058 | −0.226029 | − | 0.974121i | \(-0.572574\pi\) | ||||
−0.226029 | + | 0.974121i | \(0.572574\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 11.7279 | 0.555333 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.97056 | 0.234575 | 0.117288 | − | 0.993098i | \(-0.462580\pi\) | ||||
0.117288 | + | 0.993098i | \(0.462580\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 23.2721 | 1.09584 | ||||||||
\(452\) | 20.4853 | 0.963547 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −26.4853 | −1.24302 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.5147 | 0.538636 | 0.269318 | − | 0.963051i | \(-0.413202\pi\) | ||||
0.269318 | + | 0.963051i | \(0.413202\pi\) | |||||||
\(458\) | 24.9706 | 1.16680 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 34.2426 | 1.59484 | 0.797419 | − | 0.603425i | \(-0.206198\pi\) | ||||
0.797419 | + | 0.603425i | \(0.206198\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.75736 | −0.406989 | −0.203495 | − | 0.979076i | \(-0.565230\pi\) | ||||
−0.203495 | + | 0.979076i | \(0.565230\pi\) | |||||||
\(464\) | 4.24264 | 0.196960 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 20.4853 | 0.948962 | ||||||||
\(467\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 27.5147 | 1.26513 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 31.2132 | 1.43216 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3.72792 | 0.170511 | ||||||||
\(479\) | −13.2426 | −0.605072 | −0.302536 | − | 0.953138i | \(-0.597833\pi\) | ||||
−0.302536 | + | 0.953138i | \(0.597833\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 24.9706 | 1.13856 | ||||||||
\(482\) | 8.51472 | 0.387835 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7.00000 | 0.318182 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.75736 | −0.124948 | −0.0624739 | − | 0.998047i | \(-0.519899\pi\) | ||||
−0.0624739 | + | 0.998047i | \(0.519899\pi\) | |||||||
\(488\) | 6.24264 | 0.282591 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.72792 | −0.303627 | −0.151813 | − | 0.988409i | \(-0.548511\pi\) | ||||
−0.151813 | + | 0.988409i | \(0.548511\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −38.9706 | −1.75337 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.757359 | −0.0340064 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.7279 | −0.480248 | −0.240124 | − | 0.970742i | \(-0.577188\pi\) | ||||
−0.240124 | + | 0.970742i | \(0.577188\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −18.7279 | −0.835868 | ||||||||
\(503\) | −24.2132 | −1.07961 | −0.539807 | − | 0.841789i | \(-0.681503\pi\) | ||||
−0.539807 | + | 0.841789i | \(0.681503\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −30.7279 | −1.36602 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6.75736 | 0.299809 | ||||||||
\(509\) | 7.75736 | 0.343839 | 0.171919 | − | 0.985111i | \(-0.445003\pi\) | ||||
0.171919 | + | 0.985111i | \(0.445003\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −5.48528 | −0.241945 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −56.1838 | −2.47096 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.4558 | 0.720944 | 0.360472 | − | 0.932770i | \(-0.382616\pi\) | ||||
0.360472 | + | 0.932770i | \(0.382616\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.2426 | 0.885149 | 0.442574 | − | 0.896732i | \(-0.354065\pi\) | ||||
0.442574 | + | 0.896732i | \(0.354065\pi\) | |||||||
\(524\) | −7.75736 | −0.338882 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 22.9706 | 1.00156 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 29.4558 | 1.28069 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 34.2426 | 1.48321 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 8.24264 | 0.356028 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 10.9706 | 0.472975 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.9706 | −0.643635 | −0.321817 | − | 0.946802i | \(-0.604294\pi\) | ||||
−0.321817 | + | 0.946802i | \(0.604294\pi\) | |||||||
\(542\) | −12.4853 | −0.536289 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.48528 | −0.277291 | −0.138645 | − | 0.990342i | \(-0.544275\pi\) | ||||
−0.138645 | + | 0.990342i | \(0.544275\pi\) | |||||||
\(548\) | 19.9706 | 0.853100 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −21.2132 | −0.904534 | ||||||||
\(551\) | −26.4853 | −1.12831 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 19.2132 | 0.816291 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.72792 | 0.200509 | ||||||||
\(557\) | 40.9706 | 1.73598 | 0.867989 | − | 0.496583i | \(-0.165412\pi\) | ||||
0.867989 | + | 0.496583i | \(0.165412\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 40.4853 | 1.71234 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 22.4558 | 0.947243 | ||||||||
\(563\) | 18.7279 | 0.789288 | 0.394644 | − | 0.918834i | \(-0.370868\pi\) | ||||
0.394644 | + | 0.918834i | \(0.370868\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 24.9706 | 1.04959 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −7.24264 | −0.303894 | ||||||||
\(569\) | −24.9411 | −1.04559 | −0.522793 | − | 0.852460i | \(-0.675110\pi\) | ||||
−0.522793 | + | 0.852460i | \(0.675110\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.9706 | −0.877591 | −0.438795 | − | 0.898587i | \(-0.644595\pi\) | ||||
−0.438795 | + | 0.898587i | \(0.644595\pi\) | |||||||
\(572\) | 26.4853 | 1.10741 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 36.2132 | 1.51019 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −35.9411 | −1.49625 | −0.748124 | − | 0.663559i | \(-0.769045\pi\) | ||||
−0.748124 | + | 0.663559i | \(0.769045\pi\) | |||||||
\(578\) | 17.0000 | 0.707107 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 18.0000 | 0.745484 | ||||||||
\(584\) | −7.00000 | −0.289662 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 10.9706 | 0.453190 | ||||||||
\(587\) | −3.21320 | −0.132623 | −0.0663115 | − | 0.997799i | \(-0.521123\pi\) | ||||
−0.0663115 | + | 0.997799i | \(0.521123\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.72792 | 0.194811 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.00000 | −0.164399 | ||||||||
\(593\) | −5.48528 | −0.225254 | −0.112627 | − | 0.993637i | \(-0.535926\pi\) | ||||
−0.112627 | + | 0.993637i | \(0.535926\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −16.2426 | −0.665324 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −45.2132 | −1.84891 | ||||||||
\(599\) | −22.9706 | −0.938552 | −0.469276 | − | 0.883052i | \(-0.655485\pi\) | ||||
−0.469276 | + | 0.883052i | \(0.655485\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.9706 | 0.733035 | 0.366517 | − | 0.930411i | \(-0.380550\pi\) | ||||
0.366517 | + | 0.930411i | \(0.380550\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2.75736 | −0.112195 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 38.9706 | 1.58177 | 0.790883 | − | 0.611967i | \(-0.209622\pi\) | ||||
0.790883 | + | 0.611967i | \(0.209622\pi\) | |||||||
\(608\) | 6.24264 | 0.253173 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −82.6690 | −3.34443 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −37.9411 | −1.53243 | −0.766214 | − | 0.642586i | \(-0.777862\pi\) | ||||
−0.766214 | + | 0.642586i | \(0.777862\pi\) | |||||||
\(614\) | −28.0000 | −1.12999 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 28.4558 | 1.14559 | 0.572795 | − | 0.819699i | \(-0.305859\pi\) | ||||
0.572795 | + | 0.819699i | \(0.305859\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.51472 | 0.0608817 | 0.0304408 | − | 0.999537i | \(-0.490309\pi\) | ||||
0.0304408 | + | 0.999537i | \(0.490309\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 10.9706 | 0.439879 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 1.00000 | ||||||||
\(626\) | −17.9706 | −0.718248 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −14.0000 | −0.558661 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24.4853 | −0.974744 | −0.487372 | − | 0.873195i | \(-0.662044\pi\) | ||||
−0.487372 | + | 0.873195i | \(0.662044\pi\) | |||||||
\(632\) | −9.24264 | −0.367653 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −16.9706 | −0.673987 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 18.0000 | 0.712627 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.45584 | 0.175995 | 0.0879976 | − | 0.996121i | \(-0.471953\pi\) | ||||
0.0879976 | + | 0.996121i | \(0.471953\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 46.7279 | 1.84277 | 0.921385 | − | 0.388652i | \(-0.127059\pi\) | ||||
0.921385 | + | 0.388652i | \(0.127059\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.27208 | 0.0893246 | 0.0446623 | − | 0.999002i | \(-0.485779\pi\) | ||||
0.0446623 | + | 0.999002i | \(0.485779\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −31.2132 | −1.22428 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −11.7574 | −0.460454 | ||||||||
\(653\) | −24.0000 | −0.939193 | −0.469596 | − | 0.882881i | \(-0.655601\pi\) | ||||
−0.469596 | + | 0.882881i | \(0.655601\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −5.48528 | −0.214164 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 39.2132 | 1.52753 | 0.763765 | − | 0.645495i | \(-0.223349\pi\) | ||||
0.763765 | + | 0.645495i | \(0.223349\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 42.1838 | 1.64076 | 0.820379 | − | 0.571820i | \(-0.193762\pi\) | ||||
0.820379 | + | 0.571820i | \(0.193762\pi\) | |||||||
\(662\) | 18.4853 | 0.718451 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −7.75736 | −0.301044 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −30.7279 | −1.18979 | ||||||||
\(668\) | 24.2132 | 0.936837 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 26.4853 | 1.02245 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −27.4853 | −1.05948 | −0.529740 | − | 0.848160i | \(-0.677710\pi\) | ||||
−0.529740 | + | 0.848160i | \(0.677710\pi\) | |||||||
\(674\) | −4.48528 | −0.172767 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 25.9706 | 0.998868 | ||||||||
\(677\) | 34.2426 | 1.31605 | 0.658026 | − | 0.752995i | \(-0.271392\pi\) | ||||
0.658026 | + | 0.752995i | \(0.271392\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3.21320 | −0.123040 | ||||||||
\(683\) | −41.6985 | −1.59555 | −0.797774 | − | 0.602956i | \(-0.793989\pi\) | ||||
−0.797774 | + | 0.602956i | \(0.793989\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −6.48528 | −0.247249 | ||||||||
\(689\) | 26.4853 | 1.00901 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.24264 | −0.237481 | −0.118741 | − | 0.992925i | \(-0.537886\pi\) | ||||
−0.118741 | + | 0.992925i | \(0.537886\pi\) | |||||||
\(692\) | −10.9706 | −0.417038 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6.72792 | −0.255388 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 24.9706 | 0.945150 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −13.7574 | −0.519608 | −0.259804 | − | 0.965661i | \(-0.583658\pi\) | ||||
−0.259804 | + | 0.965661i | \(0.583658\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 24.9706 | 0.941783 | ||||||||
\(704\) | −4.24264 | −0.159901 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −21.0000 | −0.790345 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 25.6985 | 0.965127 | 0.482563 | − | 0.875861i | \(-0.339706\pi\) | ||||
0.482563 | + | 0.875861i | \(0.339706\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 5.48528 | 0.205570 | ||||||||
\(713\) | 5.48528 | 0.205425 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 16.2426 | 0.607016 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 10.7574 | 0.401461 | ||||||||
\(719\) | −2.27208 | −0.0847342 | −0.0423671 | − | 0.999102i | \(-0.513490\pi\) | ||||
−0.0423671 | + | 0.999102i | \(0.513490\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −19.9706 | −0.743227 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 20.2426 | 0.752312 | ||||||||
\(725\) | −21.2132 | −0.787839 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25.7279 | 0.954196 | 0.477098 | − | 0.878850i | \(-0.341689\pi\) | ||||
0.477098 | + | 0.878850i | \(0.341689\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 38.9706 | 1.43941 | 0.719705 | − | 0.694280i | \(-0.244277\pi\) | ||||
0.719705 | + | 0.694280i | \(0.244277\pi\) | |||||||
\(734\) | 11.7279 | 0.432886 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.24264 | 0.266967 | ||||||||
\(737\) | 34.9706 | 1.28816 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10.4853 | 0.385707 | 0.192854 | − | 0.981228i | \(-0.438226\pi\) | ||||
0.192854 | + | 0.981228i | \(0.438226\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −34.7574 | −1.27512 | −0.637562 | − | 0.770399i | \(-0.720057\pi\) | ||||
−0.637562 | + | 0.770399i | \(0.720057\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 7.21320 | 0.264094 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.2426 | −0.629193 | −0.314596 | − | 0.949226i | \(-0.601869\pi\) | ||||
−0.314596 | + | 0.949226i | \(0.601869\pi\) | |||||||
\(752\) | 13.2426 | 0.482909 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 26.4853 | 0.964537 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12.9706 | 0.471423 | 0.235712 | − | 0.971823i | \(-0.424258\pi\) | ||||
0.235712 | + | 0.971823i | \(0.424258\pi\) | |||||||
\(758\) | −1.27208 | −0.0462040 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.0000 | 0.761249 | 0.380625 | − | 0.924730i | \(-0.375709\pi\) | ||||
0.380625 | + | 0.924730i | \(0.375709\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −8.48528 | −0.306987 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 24.2132 | 0.874859 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12.4853 | 0.450231 | 0.225115 | − | 0.974332i | \(-0.427724\pi\) | ||||
0.225115 | + | 0.974332i | \(0.427724\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −4.51472 | −0.162488 | ||||||||
\(773\) | −45.2132 | −1.62621 | −0.813103 | − | 0.582120i | \(-0.802223\pi\) | ||||
−0.813103 | + | 0.582120i | \(0.802223\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.78680 | 0.136026 | ||||||||
\(776\) | −12.4853 | −0.448195 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 10.2426 | 0.367216 | ||||||||
\(779\) | 34.2426 | 1.22687 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −30.7279 | −1.09953 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 31.2132 | 1.11263 | 0.556315 | − | 0.830971i | \(-0.312215\pi\) | ||||
0.556315 | + | 0.830971i | \(0.312215\pi\) | |||||||
\(788\) | −16.9706 | −0.604551 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 38.9706 | 1.38389 | ||||||||
\(794\) | −20.2426 | −0.718384 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 14.7574 | 0.523061 | ||||||||
\(797\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 5.00000 | 0.176777 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 29.4853 | 1.04116 | ||||||||
\(803\) | −29.6985 | −1.04804 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −4.72792 | −0.166534 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −7.75736 | −0.272903 | ||||||||
\(809\) | 9.00000 | 0.316423 | 0.158212 | − | 0.987405i | \(-0.449427\pi\) | ||||
0.158212 | + | 0.987405i | \(0.449427\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23.4558 | 0.823646 | 0.411823 | − | 0.911264i | \(-0.364892\pi\) | ||||
0.411823 | + | 0.911264i | \(0.364892\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −16.9706 | −0.594818 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 40.4853 | 1.41640 | ||||||||
\(818\) | 35.0000 | 1.22375 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 32.1838 | 1.12322 | 0.561611 | − | 0.827402i | \(-0.310182\pi\) | ||||
0.561611 | + | 0.827402i | \(0.310182\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 40.6985 | 1.41866 | 0.709330 | − | 0.704877i | \(-0.248998\pi\) | ||||
0.709330 | + | 0.704877i | \(0.248998\pi\) | |||||||
\(824\) | 0.757359 | 0.0263839 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −16.9706 | −0.590124 | −0.295062 | − | 0.955478i | \(-0.595340\pi\) | ||||
−0.295062 | + | 0.955478i | \(0.595340\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 49.9411 | 1.73453 | 0.867263 | − | 0.497849i | \(-0.165877\pi\) | ||||
0.867263 | + | 0.497849i | \(0.165877\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −6.24264 | −0.216425 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 26.4853 | 0.916013 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 7.75736 | 0.267974 | ||||||||
\(839\) | 15.5147 | 0.535628 | 0.267814 | − | 0.963471i | \(-0.413699\pi\) | ||||
0.267814 | + | 0.963471i | \(0.413699\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.0000 | −0.379310 | ||||||||
\(842\) | 14.2426 | 0.490834 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −6.48528 | −0.223233 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −4.24264 | −0.145693 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 28.9706 | 0.993098 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −28.1838 | −0.964994 | −0.482497 | − | 0.875898i | \(-0.660270\pi\) | ||||
−0.482497 | + | 0.875898i | \(0.660270\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.48528 | −0.0849452 | ||||||||
\(857\) | −5.48528 | −0.187374 | −0.0936868 | − | 0.995602i | \(-0.529865\pi\) | ||||
−0.0936868 | + | 0.995602i | \(0.529865\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −43.6985 | −1.49097 | −0.745487 | − | 0.666521i | \(-0.767783\pi\) | ||||
−0.745487 | + | 0.666521i | \(0.767783\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −37.2426 | −1.26849 | ||||||||
\(863\) | 0.213203 | 0.00725753 | 0.00362876 | − | 0.999993i | \(-0.498845\pi\) | ||||
0.00362876 | + | 0.999993i | \(0.498845\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 3.97056 | 0.134925 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −39.2132 | −1.33022 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 51.4558 | 1.74351 | ||||||||
\(872\) | 2.24264 | 0.0759454 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −45.2132 | −1.52936 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 25.6985 | 0.867776 | 0.433888 | − | 0.900967i | \(-0.357141\pi\) | ||||
0.433888 | + | 0.900967i | \(0.357141\pi\) | |||||||
\(878\) | 11.7279 | 0.395798 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −36.5147 | −1.23021 | −0.615106 | − | 0.788444i | \(-0.710887\pi\) | ||||
−0.615106 | + | 0.788444i | \(0.710887\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 49.6985 | 1.67249 | 0.836244 | − | 0.548358i | \(-0.184747\pi\) | ||||
0.836244 | + | 0.548358i | \(0.184747\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 9.51472 | 0.319653 | ||||||||
\(887\) | 39.7279 | 1.33393 | 0.666967 | − | 0.745088i | \(-0.267592\pi\) | ||||
0.666967 | + | 0.745088i | \(0.267592\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −11.7279 | −0.392680 | ||||||||
\(893\) | −82.6690 | −2.76641 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −4.97056 | −0.165870 | ||||||||
\(899\) | −3.21320 | −0.107166 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −23.2721 | −0.774875 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −20.4853 | −0.681330 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −37.9411 | −1.25981 | −0.629907 | − | 0.776670i | \(-0.716907\pi\) | ||||
−0.629907 | + | 0.776670i | \(0.716907\pi\) | |||||||
\(908\) | 26.4853 | 0.878945 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.2721 | 0.472855 | 0.236428 | − | 0.971649i | \(-0.424023\pi\) | ||||
0.236428 | + | 0.971649i | \(0.424023\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −32.9117 | −1.08922 | ||||||||
\(914\) | −11.5147 | −0.380873 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −24.9706 | −0.825051 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 33.4558 | 1.10361 | 0.551803 | − | 0.833974i | \(-0.313940\pi\) | ||||
0.551803 | + | 0.833974i | \(0.313940\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −34.2426 | −1.12772 | ||||||||
\(923\) | −45.2132 | −1.48821 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 20.0000 | 0.657596 | ||||||||
\(926\) | 8.75736 | 0.287785 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.24264 | −0.139272 | ||||||||
\(929\) | −10.0294 | −0.329055 | −0.164528 | − | 0.986372i | \(-0.552610\pi\) | ||||
−0.164528 | + | 0.986372i | \(0.552610\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −20.4853 | −0.671018 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −30.4558 | −0.994949 | −0.497475 | − | 0.867479i | \(-0.665739\pi\) | ||||
−0.497475 | + | 0.867479i | \(0.665739\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −40.6690 | −1.32577 | −0.662887 | − | 0.748720i | \(-0.730669\pi\) | ||||
−0.662887 | + | 0.748720i | \(0.730669\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 39.7279 | 1.29372 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −27.5147 | −0.894581 | ||||||||
\(947\) | 21.5147 | 0.699134 | 0.349567 | − | 0.936911i | \(-0.386329\pi\) | ||||
0.349567 | + | 0.936911i | \(0.386329\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −43.6985 | −1.41851 | ||||||||
\(950\) | −31.2132 | −1.01269 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.51472 | 0.211032 | 0.105516 | − | 0.994418i | \(-0.466351\pi\) | ||||
0.105516 | + | 0.994418i | \(0.466351\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −3.72792 | −0.120570 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 13.2426 | 0.427850 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.4264 | −0.981497 | ||||||||
\(962\) | −24.9706 | −0.805083 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −8.51472 | −0.274241 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.69848 | −0.215409 | −0.107704 | − | 0.994183i | \(-0.534350\pi\) | ||||
−0.107704 | + | 0.994183i | \(0.534350\pi\) | |||||||
\(968\) | −7.00000 | −0.224989 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −26.4853 | −0.849953 | −0.424977 | − | 0.905204i | \(-0.639718\pi\) | ||||
−0.424977 | + | 0.905204i | \(0.639718\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 2.75736 | 0.0883515 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.24264 | −0.199822 | ||||||||
\(977\) | 13.9706 | 0.446958 | 0.223479 | − | 0.974709i | \(-0.428259\pi\) | ||||
0.223479 | + | 0.974709i | \(0.428259\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 23.2721 | 0.743779 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 6.72792 | 0.214697 | ||||||||
\(983\) | −15.5147 | −0.494843 | −0.247421 | − | 0.968908i | \(-0.579583\pi\) | ||||
−0.247421 | + | 0.968908i | \(0.579583\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 38.9706 | 1.23982 | ||||||||
\(989\) | 46.9706 | 1.49358 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 50.2132 | 1.59507 | 0.797537 | − | 0.603269i | \(-0.206136\pi\) | ||||
0.797537 | + | 0.603269i | \(0.206136\pi\) | |||||||
\(992\) | 0.757359 | 0.0240462 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14.0000 | −0.443384 | −0.221692 | − | 0.975117i | \(-0.571158\pi\) | ||||
−0.221692 | + | 0.975117i | \(0.571158\pi\) | |||||||
\(998\) | 10.7279 | 0.339586 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 7938.2.a.bj.1.1 | 2 | ||
3.2 | odd | 2 | 7938.2.a.bp.1.2 | 2 | |||
7.3 | odd | 6 | 1134.2.g.j.163.1 | yes | 4 | ||
7.5 | odd | 6 | 1134.2.g.j.487.1 | yes | 4 | ||
7.6 | odd | 2 | 7938.2.a.bk.1.1 | 2 | |||
21.5 | even | 6 | 1134.2.g.i.487.1 | yes | 4 | ||
21.17 | even | 6 | 1134.2.g.i.163.1 | ✓ | 4 | ||
21.20 | even | 2 | 7938.2.a.bq.1.2 | 2 | |||
63.5 | even | 6 | 1134.2.e.s.865.2 | 4 | |||
63.31 | odd | 6 | 1134.2.h.s.541.1 | 4 | |||
63.38 | even | 6 | 1134.2.e.s.919.2 | 4 | |||
63.40 | odd | 6 | 1134.2.e.r.865.2 | 4 | |||
63.47 | even | 6 | 1134.2.h.r.109.2 | 4 | |||
63.52 | odd | 6 | 1134.2.e.r.919.2 | 4 | |||
63.59 | even | 6 | 1134.2.h.r.541.1 | 4 | |||
63.61 | odd | 6 | 1134.2.h.s.109.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1134.2.e.r.865.2 | 4 | 63.40 | odd | 6 | |||
1134.2.e.r.919.2 | 4 | 63.52 | odd | 6 | |||
1134.2.e.s.865.2 | 4 | 63.5 | even | 6 | |||
1134.2.e.s.919.2 | 4 | 63.38 | even | 6 | |||
1134.2.g.i.163.1 | ✓ | 4 | 21.17 | even | 6 | ||
1134.2.g.i.487.1 | yes | 4 | 21.5 | even | 6 | ||
1134.2.g.j.163.1 | yes | 4 | 7.3 | odd | 6 | ||
1134.2.g.j.487.1 | yes | 4 | 7.5 | odd | 6 | ||
1134.2.h.r.109.2 | 4 | 63.47 | even | 6 | |||
1134.2.h.r.541.1 | 4 | 63.59 | even | 6 | |||
1134.2.h.s.109.2 | 4 | 63.61 | odd | 6 | |||
1134.2.h.s.541.1 | 4 | 63.31 | odd | 6 | |||
7938.2.a.bj.1.1 | 2 | 1.1 | even | 1 | trivial | ||
7938.2.a.bk.1.1 | 2 | 7.6 | odd | 2 | |||
7938.2.a.bp.1.2 | 2 | 3.2 | odd | 2 | |||
7938.2.a.bq.1.2 | 2 | 21.20 | even | 2 |